Research ArticleIdentification of Generating Units That Abuse Market Power inElectricity Spot Market Based on AdaBoost-DT Algorithm

Qian Sun Yuting Xie Xiuzhen Hu En Lu Yi Wang and Ning Wang

Guangdong Power Exchange Center Guangzhou 510000 China

Correspondence should be addressed to Xiuzhen Hu huxiuzhen126com

Received 3 March 2021 Revised 5 April 2021 Accepted 29 April 2021 Published 13 May 2021

Academic Editor Yan Gao

Copyright copy 2021 Qian Sun et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

-e identification of generating units that abuse market power is an essential part of risk prevention in a spot market especially inthe early stage of the construction of the spot market In this study a model for identifying generating units that abuse marketpower is designed based on the AdaBoost-DTalgorithm It is targeted at the imbalance between samples of generating units thatabuse market power and normal generating units in the spot market First the four main methods by which market power isabused by generating units in the spot market are described collusion economic withholding physical withholding and extremequotation Second the specific characteristics of the four methods are analyzed and the identification indexes for generating unitsthat abuse market power are established -ereafter a sample set of generating units that abuse market power using differentmethods is constructed Furthermore a training set is formed with samples of normal generating units to construct a model basedon the AdaBoost-DTalgorithm for identifying generating units that abuse market power Finally the spot market data of a certainregion are used for an example analysis -e results show that the accuracy of model identification is 97 which validatesthe method

1 Introduction

Since the promulgation of Zhongfa [2015] No 9 and itsrelevant supporting documents Chinarsquos electricity markethas begun to undergo a new round of reform-is concept isproposed to discover prices in the spot market and establishan electricity market with all available trading varieties andperfect functions [1] In July 2020 Chinarsquos National De-velopment and Reform Commission and National EnergyAdministration jointly issued the Notice on Strengtheningthe Work Related to the Power Spot Market Pilot Contin-uous Trial Settlement to further promote the development ofthe spot market -e trading rules of the spot market underthe new scenario are still preliminary Furthermore duringmarket trading generating units abuse market power byexploiting the drawbacks in the market rules to obtain highprofits -is severely impairs the capability for price dis-covery in the spot market [2]-erefore the establishment ofa set of identification methods for units that abuse marketpower in the spot market and thereby maintain the safe

stable and reliable operation of the electricity market ishighly significant

Based on the abuse of market power by generating unitsXue et al [3] review the problem of market power abuse interms of researchmethods and control Yan et al [4] design amechanism to prevent the abuse of market power by gen-erating units while Chen et al [5] summarize the funda-mental concept of market power common market powermonitoring indexes and market power mitigation methodsMoreover the study introduces the implementation status ofthree typical electricity markets the United States theUnited Kingdom and Northern Europe -ese studiespresented the definition of market power methods to abusemarket power and methods to mitigate market powerHowever these works do not identify the abuse of marketpower by generating units Li et al [6] propose variousevaluationmethods to comprehensively assess market powerin electricity markets from different perspectives Liu et al[7] consider five types of market indicators (market supplyand demand market structure bidding strategy supplier

HindawiMathematical Problems in EngineeringVolume 2021 Article ID 5559185 13 pageshttpsdoiorg10115520215559185

position and trading results) and propose a system forevaluating the abuse of market power by generating unitsZhao et al [8] propose a process for implementing thecomprehensive evaluation index system of the electricitymarket based on the multilevel fuzzy comprehensive eval-uation method In these studies evaluation indexes based onthe characteristics of data on generating units are con-structed as well as the comprehensive evaluation method toidentify market power abuse However the comprehensiveevaluation method is not applicable to large volumes ofpower transaction data that display high dimensionality Wuet al [9] focus on a simplified version of the convex hullpricing model analyze the potential market manipulationbehavior and manipulation ability of market participants inthe simplified model and propose an index to quantifymarket power Dai et al [10] build a multi-leader-followerStackelberg game based on real-time pricing model thestrategic interaction behavior between multiple electricityretailers and users while simultaneously considering thepower load uncertainty of users and the price competitionamong electricity retailers which can reduce the real-timeelectricity price Dai et al [11] propose a dynamic pricingscheme based on Stackelberg game for an electric vehiclecharging station with a photovoltaic system -ese re-searchers have analyzed market power and real-time elec-tricity price but they have not identified the abuse of marketpower Sun et al [12] construct a method for identifyingmarket power abuse in cartel-type generating units based onthe ranked multivariate Logit model Liu et al [13] proposethe identification of the abuse of market power in theelectricity market based on the cloud model and fuzzy Petrinet using the pattern recognition approach Xu et al [14]propose an intelligent identification method that is appli-cable to computer analysis to identify violations by powergeneration enterprises It is based on an improved supportvector machine and provides a reference for the creditevaluation of electricity market entities -ese studiesidentify the market power abuse behavior of generatingunits through intelligent identification algorithms How-ever the distribution of generating units that abuse marketpower and normal generating units in the electricity marketis unbalanced-erefore the accuracy of these algorithms inidentifying data with unbalanced positive and negativesamples has not been considered By considering thecharacteristics of the spot market (high data dimensionalitylarge data volume and unbalanced positive and negativesamples) this study adopts the AdaBoost algorithm whichhas significant advantages in handling the unbalancedsample problem

-e AdaBoost algorithm is a classical integrated learningmethod that has been used in various fields for recognitionproblems In electric power field Li et al [15] propose acomposite perturbation classification strategy for powerquality based on the conditional mutual information averageoptimal feature selection method and AdaBoost dynamicintegrated classifier Chen et al [16] address the short-comings of small current ground fault routing with un-balanced sample data dimensional catastrophe and highempirical risk -ey propose a new method for small current

ground fault line selection based on sample data processingand the AdaBoost method -ese studies validate the ad-vantages of the AdaBoost algorithm in solving the sampledata imbalance problem However the speed of recognitionneeds to be improved Yao et al [17] propose the AdaBoost-decision tree (AdaBoost-DT) identification method thatintegrates multiple features to identify partial discharges of agas-insulated composite apparatus Zhang et al [18] con-struct a new composite DT algorithm -ey design andimplement a DT-based remote sensing image classificationsystem-e AdaBoost evolving DTalgorithm is proposed byZhao et al [19] -eir experimental results show that theAdaBoost evolving DT can achieve a high recognition ac-curacy in a short period of time -us the advantage of theAdaBoost algorithm in solving the unbalanced sample dataproblem is combined with the advantages of the DT (iesmall computational volume high recognition accuracy andhigh recognition speed) -is is suitable for scenarios wherefew generating units abuse market power in the spot marketand the market data volume is large

-is study develops a method based on the AdaBoost-DT for identifying generating units that abuse market powerin the spot market First the overall framework for iden-tifying generating units that abuse market power in the spotmarket is designed Second the different means of marketpower abuse by generating units in the spot market areanalyzed Furthermore the identification indexes for marketpower abuse by generating units are constructed to form thesample and training sets of generating units that abusemarket power -ereafter an AdaBoost-DT model foridentifying generating units that abuse market power isdeveloped Finally the method is applied to the spot marketin a region and compared with other methods to verify itseffectiveness

2 General Rationale for Identifying GeneratingUnits That Abuse Market Power

Amethod is designed based on the AdaBoost-DT techniqueto identify generating units that abuse market power in thespot market by combining multiple means -e generalrationale is as follows

First the methods by which generating units abusemarket power are classified into collusion physical with-holding economic withholding and extreme quotationAdditionally indicators for identifying each of these fourmeans are developed

Second the data on the generating units in the spotmarket are used to calculate the identification indexes andconstruct the characteristics of generating units that abusemarket power -ereby a sample of generating units thatabuse market power in different ways is formed Togetherwith the normal generating unit samples a sample set isformed

-ereafter an equal sample weight is assigned to eachgenerating unit sample in the sample set and the DTmodelis trained According to the classification error rate of the DTmodel the weight of the samples in the sample set is ad-justed while the weight of the misclassified samples is

2 Mathematical Problems in Engineering

increased and the weight of the correctly classified samplesis reduced -e new DTmodel is trained such that the newmodel pays more attention to the misclassified samplesIteration is continued until the misclassified samples aresufficiently few or the iteration terminates when it attains theset value -e weighted voting method is used to combine allthe DT models to form the final AdaBoost-DT model foridentifying generating units that abuse market power

Finally a model for identifying generating units thatabuse market power is used to determine such units in themarket -ereafter the identification results are evaluated

3 Modalities and Indicators of Market PowerAbuse by Generating Units

31 Main Methods by Which Generating Units Abuse MarketPower Market power in the electricity market refers to thecapability of market members to manipulate the electricityprice in the market and maintain it at an abnormal level for acertain period of time with the aim of making a profit -ereare several methods by which generating units can abusemarket power [20]

311 Collusion Collusion refers to the scenario whereingenerating units participating in the market conclude anldquoalliancerdquo through negotiations and contract signing andsubsequently apply the negotiated quotation strategy toquote high prices to obtain excessive profits Alternativelycertain generating units quote high prices to increase themarket clearing price so that other generating units in theldquoalliancerdquo can obtain excessive profits and take turns to ldquobethe bankerrdquo [21] When a generating unit has a large marketshare the long-term gains that can be obtained throughcollusion among generating units are relatively substantialand collusion among generating units is more likely tooccur Additionally the quotation and its variations bycolluding generating units tend to have certain similarities

312 Withholding Generating unit capacity withholdingrefers to the scenario wherein a unit does not participate inthe market with its available capacity (which should betraded in the market by the unit) because of certain de-liberate actions of the unit including physical and economicwithholding

(1) Physical Withholding Physical withholding refers to theintentional underreporting of available generating capacityby the generating unit -is is mainly in the form of falseclaims that the generating unit is faulty and cannot generateelectricity or that the equipment is undergoing or requiresoverhauling -e intention is to reduce its own generatingcapacity and thereby its supply to the market Generatingunits frequently misreport physical withholding as failure ofthe unit to evade market regulation and thereby abusemarket power -erefore if the target generating unit usesphysical withholding its profits are determined by analyzingthe influence of the unavailability of the unit on the marketclearing price [15]

(2) Economic Withholding Economic withholding refers tothe unreasonably high price (significantly higher than thecost of power generation) quoted by a generating unit for apart of its capacity that results in nongeneration by that partWhile participating in the market the quoted price of aneconomically withheld generating unit is frequently close tothe maximum market price [22] or significantly higher thanits power generation cost and historical quoted price -isresults in an increase in the clearing price and consequentlya high profit -erefore it is possible to determine whether agenerating unit has abused its market power through eco-nomic withholding by comparing its historical price quo-tations with its winning bids

313 Extreme Quotation Extreme quotation refers to thefollowing acts (1) frequently quoting a price that exceedsthat of similar generating units and their own historicallyquoted prices at the time of market quotation and (2) fre-quently quoting at excessively low prices to ensure that thegenerating units win the bids -e main characteristic ofgenerating units with extreme quotations is that these ensuea high number of quotations with extremely high or lowprices at the time of quotation It is possible to determinewhether generating units have abused market powerthrough extreme quotations by comparing their quotedprice levels in the market with winning bids

32 Indicators of Market Power Abuse by Generating UnitsTo better identify generating units that abuse market powerin the spot market identification indexes are constructedconsidering three aspects market structure market be-havior and market performance -is is based on thecharacteristics of generating units that abuse market powerin different ways and considering the principles of sys-tematicity scientificity and operability

Market structure characteristics mainly reflect themarket share and position of the generating units whilemarket behavior characteristics mainly reflect the behaviorof the generating units participating in the market includingthe reporting scenario and quotation strategy Marketperformance characteristics mainly reflect the performanceof the generating units participating in the market includingthe winning scenario of the generating units -e specificdefinitions and formulas of the identifying indicators ofmarket power abuse by the generating units are as follows

321 Market Structure Category

(1) Market Share [23] Market share is defined as the pro-portion of a generating unitrsquos generating capacity to the totalgenerating capacity of all the generating units in the marketIt is calculated using the following formula

si qi

1113936Nj1 qj

(1)

where si is the market share of the i-th generating unit in themarket N is the total number of generating units in the

Mathematical Problems in Engineering 3

market and qi is the generating capacity of the i-th gen-erating unit in the market considering the maximum de-clared capacity of generating unit irsquos current offer -egenerating unitrsquos market share characteristics are used toreflect whether it has market power Moreover when itsmarket share is excessively large it is the key generating unitin the spot market and has a decisive influence on theclearing price in the market(2) Key Supplier Index [23] -e key supplier index is thenumber of generating units that must be utilized to satisfythe market demand -at is the market is undersuppliedwhen the key supplier does not contribute It is calculated asfollows

OPSi 1113936

Nj1 q

bidj minus q

bidi

D (2)

where OPSi denotes the critical supplier index for generatingunit i qbidi denotes the declared capacity of generating unit iqbidj denotes the declared capacity of generating unit j Ddenotes the entire market demand for power at time t andOPSilt 1 is the key supplier for that time period when thegenerating unit hasmarket power-is generating unitmay bea key generator for the entire system or for a particular region

322 Market Behavior Category

(1) Weighted Average Quotation [24] -e average quotedprice of a generating unit is defined as the sum of the productof the declared tariff and declared capacity of each segmentof the effective quoted segment of the unit in the spotmarket divided by the declared capacity It is calculated asfollows

Pi 1113936

Yh1 pih times qih

1113936Yh1 qih

(3)

where Pi is the average quoted price of generating unit i pihrepresents the declared price of the h-th segment of thegenerating unit qih represents the declared capacity of the h-th segment of the generating unit and Y represents the totalnumber of declared segments in the generating unitrsquosquotation curve -e weighted average quotation of thegenerating unit reflects the quotation of the generating unitIf the weighted average quotation is higher the generatingunit is suspected of quoting a higher price

(2) Relative Level of Quotations -e relative level of quotedprices reflects the overall level of the generating unitrsquos quotedprice in the market It is calculated by the following formula

_Pi Pi minus 1113936

Nj1 PjN

1113936Nj1 PjN

times 100 (4)

where _Pi is the relative level of quotations for generating unit iand Pi is the average quoted price of the unit at present -ecloser the quoted price is to the average quoted price of all thegenerating units in the market the closer it is to zero If thequoted price is significantly different from zero it implies that

it is significantly different from the average quoted price of allthe generating units in the market and that the degree ofabnormal quoting by the generating unit is high(3) Capacity Pricing Index [25] A generating unitrsquos capacitypricing index is the sum of its declared electricity price andthe product of the declared capacity multiplier -is indexcan reflect the declared high price of the generating unit It iscalculated according to the following formula

CPIi 1113944

Y

h1pih lowast qih lowast 1001113872 1113873

3 (5)

where CPIi is the capacity pricing index of generating unit i-is index can reflect the relationship between the quantityand price of the generating unit(4) High Quotation Rate [25] High quotation rate is definedas the number of times a generating unitrsquos offer attains thehigh quotation level in a cycle as a fraction of the number ofoffers by the generating unit in that cycle It is calculated bythe following formula

Ri NUMhi

NUMi

(6)

where Ri is the high quotation rate of generating unit iNUMhi is the number of times that an offer by generatingunit i attains the high quotation level and NUMi is the totalnumber of offers by generating unit i If the high quotationrate of a generating unit is high it indicates that it displaysabnormal offer behavior with the aim of increasing themarket clearing price and gaining excess profit

(5) Similarity in High Quotation Rates -e high quotationrate for a generating unit is calculated as shown in (6) -eformula for calculating the similarity in high quotation ratebetween generating units i and j over S cycles is

HBij 1113944S

s1

Ri minus Rj1113872 11138732

1113969

(7)

where HBij is the similarity in the generating unitsrsquo highquotation rate Ri and Rj are the high quotation rates forgenerating units i and j respectively in the s-th cycle -elower the HBij is the higher the likelihood of simultaneoushigh quotations by i and j-e likelihood of collusion betweengenerating units with similar offers can be reflected to acertain extent by the similarity in their high quotation ratesover a number of cycles If HBij is close to zero it is necessaryto conduct focused monitoring of these two generating units

(6) Generating Unit Failure Rate Generating unit failure rateis defined as the fraction of time that a generating unit is outof service or being overhauled It is calculated by the fol-lowing formula

Fi Tfail

Talltimes 100 (8)

where Fi denotes the failure rate of the generating unit Tfaildenotes the total time of failure or overhaul of the generating

4 Mathematical Problems in Engineering

unit within a period of time and Tall denotes the period oftime

(7) Correlation Coefficient of the Quotation Curve -ecorrelation coefficient of the quotation curve of generatingunit i reflects the correlation between this curve and thequotation curve of generating unit j -e formula is asfollows

Rij Cov Pi Pj1113872 1113873

Var Pi1113858 1113859Var Pj1113960 1113961

1113969 (9)

where Rij denotes the correlation coefficient of the quotationcurve of generating units i and j Cov(Pi Pj) is the covarianceof the quotation series Pi and Pj Var[Pi] is the variance of Piand Var[Pj] is the variance of Pj -e correlation coefficientof the quotation curves can reflect the degree of correlationbetween the quotations of the generating units the larger itis the higher the similarity between the quotations of thegenerating units is and the higher the possibility of collusionis between these -e generating units with a high corre-lation coefficient of quotation curve are those with the risk ofldquocollusionrdquo

323 Market Performance Category

(1) Rate of Increase in Clearing Prices -e clearing priceescalation rate for a specified generating unit is the actualmarket clearing price minus the simulated clearing price in afully competitive market divided by the simulated clearingprice in a fully competitive market -e simulated clearingprice is obtained by modifying the declaration behavior ofthe generating units that abuse market power and thenrecalculating the clearing -e formula is as follows

Pilowast

Pclear

minus Piclearlowast

Piclearlowast times 100 (10)

where Pilowast denotes the rate of increase in the generating

unitrsquos clearing price Pclear denotes the actual market clearingprice and Pclearlowast

i denotes the simulated clearing price in afully competitive market both after modifying the offer ofgenerating unit i -e higher the clearing price escalationrate the higher the risk of market power abuse by thegenerating unit(2) Rate of Winning Bids [24] -e rate of winning bids isdefined as the proportion of the generating unitrsquos totalwinning bid to its declared total power It is calculated by thefollowing formula

WRi qwini

qbiti

(11)

where WRi qwini and qbidi are the winning bid rate total bidwinning electricity and total declared electricity respec-tively of generating unit i(3) Out-of-Merit Capacity Index [23] -e out-of-merit ca-pacity index is defined as the ratio of the out-of-merit

capacity of the generating unit as a fraction of the unitrsquosactual declared capacity to the market unsuccessful bid (thesum of the available capacity of all the generating units thatparticipated in the bidding system and failed to win the bid)as a fraction of the market declared capacity in a certaintrading period It is calculated using the following formula

OCIi qoci qbidi

QocQbid times 100 (12)

where OCIi is the out-of-merit capacity index of generatingunit i qoci is the power of generating unit i with unsuccessfulbids qbidi is the declared capacity of generating unit i Qoc isthe power with unsuccessful bids in the market and Qbid isthe total declared capacity in the market

As is evident from the definition of the out-of-meritcapacity index its magnitude is primarily related to the ratioof out-of-merit capacity to available capacity of the gener-ating unit and the ratio of the remaining system capacity toavailable market capacity In an ideal electricity market theratio of each generating unitrsquos out-of-merit capacity to itsavailable capacity should be relatively close to the ratio of theremaining capacity of the system to the available marketcapacity -us the ideal out-of-merit capacity index shouldbe 100 If the out-of-merit capacity index of a generating unitis less than 100 for a specified time period it indicates thatthe unitrsquos offer for that time period is normal Otherwise itindicates that the unitrsquos offer for that time period is higherthan that of the majority of the units in the system and thatthe unit may have engaged in collusive bidding behavior

Depending on the different means by which the gen-erating unit abuses market power (each of which has dif-ferent characteristics) the specific problems are analyzed ona case-by-case basis as shown in Table 1

4 Model Based on AdaBoost-DT Algorithm forIdentifying Generating Units That AbuseMarket Power

41 Sample and Sample Set of Generating Units at AbuseMarket Power Based on the different methods by whichgenerating units abuse market power and the indicators usedto identify these the sample of generating units that abusemarket power and the sample set used for model training areconstructed in the spot market CONTEXT

First an indicator set for generating units that abusemarket power is constructed Using spot market data andindicators for identifying market power abuse the indicatorset of generating units that abuse market power is constructedfor different methods of abusing market power as shown in

Xi xmij | j 1 2 J m 1 2 M1113966 1113967 (13)

where Xi denotes the set of indicators of the i-th generatingunit that abuses market power xm

ij denotes the m-th indi-cator of the j-th risk of generating unit i J denotes the totalnumber of methods of market power abuse and M denotesthe number of indicators

Mathematical Problems in Engineering 5

-ereafter a sample of generating units that abusemarket power and a sample set are constructed Based on theset of indicators obtained from (13)ndash(15) a sample ofgenerating units that abuse market power and a sample set ofgenerating units that abuse market power are created (asshown in (16))

yi

j 1113944M

m1x

mij middot ωm

j minus clowastj ge 0

0 1113944M

m1x

mij middot ωm

j minus clowastj le 0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

Ti yi Xi1 Xi2 XiJ1113966 1113967 (15)

T T1 T2 Tn Tn+1 TN1113864 1113865 (16)

where yi denotes the label of generating unit i It takes valuesin the range 0 1 2 3 4 representing normal collusivephysically withheld economically withheld and extremequotation generating units respectively

ωmj denotes the weight of the m-th indicator of the j-th

method of market power abuse clowastj is the threshold of the j-thgenerating unit that abuses market power All the generatingunits beyond this threshold are identified as generating unitsthat abuse market power as determined by experts Ti de-notes the i-th generating unit sample It includes the labels yiof different methods of abusing market power and the in-dicator Xij of generating units that abuse market power Tdenotes the set of samples used for model training Itconsists of the samples of generating units that abuse market

power (T1 T2 Tn) and a sample of a normal generatingunit (Tn+1 TN)

42 AdaBoost-DT Recognition Model -e fundamentalconcept underlying the AdaBoost algorithm [26] is as fol-lows (1) vary the classifier weights based on the misclassifiedsamples by continuously iterating until a sufficiently smallerror rate is attained and (2) combine the different classifiersof each iteration by a strategy to form the final strongclassifier (as shown in Figure 1) by first training weakclassifier 1 using the original training set and then read-justing the weights of the samples in the training set which isthen used to train weak classifier 2 Iterations continue untila sufficiently marginal error rate is achieved Finally theweighted voting method is used to combine the weakclassifiers -e AdaBoost algorithm has good generalizationcapability and practicality [27] Different weights areassigned to different samples through cyclic training toachieve accurate classification by increasing the focus ondifficult samples

Using DTas a weak classifier samples of generating unitswith different labels in the training set are used as inputs tothe AdaBoost algorithm for training -ereafter the un-known generating unit samples are identified -e specificsteps of the algorithm are as follows

Step 1 Initialize the weight distribution of the training dataBased on the obtained training set each generating unit

sample in the training set is assigned an identical weight inthe first iteration as shown in (17) -e weights of thegenerating unit samples are updated in each iteration

Table 1 Methods and indicators for identifying abuse of market power by generating units

Methods of abusingmarket power Indicator Quantitative characteristics of indicator

Collusion

Market share Large market shareKey supplier index Key supplier index lt1

Quotation curve correlation coefficient Large quotation curve correlation coefficientSimilarity in high quotation rates Similarity in the high quote ratio close to zero

Winning rate High winning rateClearing price escalation rate High clearing price escalation rate

Physical withholding

Market share Large market shareKey supplier index Key supplier index lt1

Failure rate High failure rateOut-of-merit capacity index Large out-of-merit capacity index

Bid winning rate Low bid winning rateClearing price escalation rate High clearing price escalation rate

Economic withholding

Market share Large market shareKey supplier index Key supplier index lt1High quotation rate Large high quotation rate

Out-of-merit capacity index Large out-of-merit capacityBid winning rate Low bid winning rate

Clearing price escalation rate High clearing price escalation rate

Extreme quotation

Market share Large market shareKey supplier index Key supplier index lt1

Weighted average quotation Excessively high or low weighted average quotationRelative level of quotations Relative level of quotations significantly different from zeroCapacity pricing index Excessively high or low capacity pricing index

Clearing price escalation rate High clearing price escalation rate

6 Mathematical Problems in Engineering

D(1) ω11ω12 ω1N1113864 1113865 (17)

where ω1i (1N) is the weight of the first generating unitsample i in the first iteration (i 1 2 N)

Step 2 Iterative training of weak classifiers

(1) Denote the number of iterations by k (k 1 2 K)Set the weight coefficient of each generating unitsample at the k-th iteration as D(k) ωk1 ωk2 ωkN to obtain the k-th weak classifier Gk(xi)

(2) Calculate the weighted classification error rate ek forthe weak classifier Gk(xi) on the training set Herethe weighted classification error rate represents thesum of the weights of all the generating unit samplesthat have been misclassified by the current classifier

ek P Gk xi( 1113857neyi( 1113857 1113944m

i1ωkiI Gk xi( 1113857neyi( 1113857 (18)

(3) Calculate the weight coefficient of the weak classifierGk(xi) It is combined with the weighted error rate ekto calculate the weight coefficient of the weak clas-sifier using (19) -e weighting coefficient indicatesthe importance of the weak classifier Gk(xi) in thefinal classifier -e smaller the error rate the largerthe weight coefficient [28] -e weight coefficient ofthe k-th weak classifier Gk(xi) is

αk 12log

1 minus ek

ek

(19)

(4) Update the weight distribution of the trainingdataset

D(k + 1) ωk+11ωk+12 ωk+1N1113966 1113967 (20)

where ωk+1i denotes the weight of the i-th generatingunit sample in the (K+ 1)-st iteration It is calculatedas follows

ωk+1i ωki

Zk

exp minus αkyiGk xi( 1113857( 1113857 (21)

where Zk is the normalization factor such thatD(k+ 1) is a probability distribution It is calculatedas

Zk 1113944m

i1ωki exp minus αkyiGk xi( 1113857( 1113857 (22)

From the above-stated equation the weight ofcorrectly classified generating unit samples is re-duced according to the k-th iteration of classificationwhereas the weight of misclassified generating unitsamples increases Misclassified generating unitsamples play a larger role in the next iteration [29]-is enables each generating unit sample to belearned completely through this process

(5) Repeat (1)ndash(4) in Step 2 to obtain a series of weakclassifiers and their corresponding weights

Step 3 Linear combination of weak classifiers using weightparameters

f(x) 1113944K

k1αkGk(x) (23)

-e continuous function f(x) is transformed into adiscrete function using the sign() function -us the finalidentification model is

Originaltraining set

(n units)

Training set 1after adjustingsample weight

Training set 2after adjustingsample weight

Training set nafter adjustingsample weight

Weak classifier 1

helliphellip

Weak classifier 2 Weak classifier 3 Weak classifier n + 1helliphellip

Train Train Train TrainVary the samplesweights based onthe misclassified

samples

Strong classifier

Weighted voting method

Vary the samplesweights based onthe misclassified

samples

Figure 1 AdaBoost algorithm flow

Mathematical Problems in Engineering 7

G(x) sign(f(x)) sign 1113944K

k1αkGk(x)⎛⎝ ⎞⎠ (24)

Use identification models to identify generating unitsthat abuse market power in the spot market

5 Analysis of Calculation Examples

-e data on the spot market of a region in 2005 (containinginformation on 170 generating units) are used to validate themethod proposed in this study for identifying the anomalousgenerating units in the spot market -e method is based onAdaBoost and DT techniques -e distribution of positiveand negative samples is shown in Figure 2 Among the 170generating units the number of units abusing market poweraccounts for a quarter including 14 collusive units 7physical holding units 9 economic holding units and 10extreme quotation units

51 Samples of Generating Units at Abuse Market PowerConsidering the indicators for identifying generating unitsthat abuse market power and the actual scenario of the spotmarket in a certain region and based on the relevant data ofgenerating units in the market the sample of generatingunits abusing market power and the sample set are con-structed A few samples of the generating units that abusemarket power are presented in Tables 2ndash5

52 Indicators forModel Evaluation In this study accuracyrecall and F-Measure are used to evaluate the model foridentifying generating units that abuse market power Ac-curacy represents the fraction of genuine positive samplesout of all the samples identified as positive recall is thefraction of all the positive samples that are identified aspositive and F-Measure is a composite index of accuracyand recall -e formulas for the three evaluation indexes areas follows

pre TP

TP + FP

rec TP

TP + FN

Fminus pre times rec times 2pre + rec

(25)

where pre denotes the accuracy of the recognitionmodel thehigher the accuracy the better the model being evaluatedrec denotes the recall of the recognition model the higherthe recall the better the model being evaluated F-denotesthe F-measure of the recognition model the closer it is toone the better is the model TP denotes a positive samplethat is correctly recognized FP denotes a negative samplethat is recognized as a positive sample and FN denotes apositive sample that is recognized as a negative sample

6 Results of Model Identification

Of the sample set of generating units that abuse marketpower obtained above 70 is used as the training set to trainthe recognition model -e remaining (30) is used as thevalidation set to verify the accuracy of the model recogni-tion -e accuracy of the classification is low when thenumber of iterations of the AdaBoost algorithm is relativelymarginal However when this number is excessively large itcauses overfitting-e validation accuracy increases with thenumber of iterations -e result is shown in Figure 2Meanwhile the time utilized for the iteration increases withthe number of iterations

Figure 3 shows that the accuracy of classification in-creases with the number of iterations However it is es-sentially stable when the number of iterations is higher than30 -us the number of iterations of the classifier can be setas 30 For the different methods by which generating unitscan abuse market power the results of the model evaluationindexes for the AdaBoost-DT identification model areshown in Figure 4

Collusive generating unitPhysically withheld generating unitEconomically withheld generating unitExtreme quotation generating unitNormal generating unit

14 79

10

130

Figure 2 Distribution of positive and negative samples

8 Mathematical Problems in Engineering

To validate the model this study compares the results ofidentification using DT SVM [14 30] and AdaBoost-SVMas shown in Figure 5

To better illustrate the relationship between the accu-racies of AdaBoost-DT and AdaBoost- SVM recognitionwith the number of iterations the assessment of the

Table 5 Samples of extreme quotation generating units

Generatingunit

Marketshare

Key supplierindex

Weighted averagequotation

Relative level ofquotations

Capacity pricingindex

Clearing price escalationrate ()

7 00960 09725 800 04652 5934839 5338 00555 09912 26889 -05075 870 268

Table 2 Samples of collusive generating units

Generatingunit

Marketshare

Key supplierindex

Quotation curve correlationcoefficient

Similarity in highquotation rates

Bid winning rate()

Clearing price escalationrate ()

1 00789 09816 05504 05281 7147 13172 00680 09880 05489 05245 5283 1250

Table 3 Samples of physically withheld generating units

Generatingunit

Marketshare

Key supplierindex

Failure rate()

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

3 00906 09733 523 19715 0 6304 00525 09913 676 121575 3833 427

Table 4 Samples of economically withheld generating units

Generatingunit

Marketshare

Key supplierindex

High quotationrate

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

5 00806 09756 05 1971477 0 5706 00625 09893 04 1084313 45 347

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

Figure 3 Relationship between recognition accuracy and number of iterations

Mathematical Problems in Engineering 9

0 1 2 3 4090

092

094

096

098

100

Type of generating units

PreRecF-

Figure 4 Results of the evaluation indicators of the AdaBoost-DT model

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(a)

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(b)

0 1 2 3 4

086

088

090

092

094

096

098

100

Type of generating units

PreRecF-

(c)

Figure 5 Results of the evaluation indicators

10 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

increased and the weight of the correctly classified samplesis reduced -e new DTmodel is trained such that the newmodel pays more attention to the misclassified samplesIteration is continued until the misclassified samples aresufficiently few or the iteration terminates when it attains theset value -e weighted voting method is used to combine allthe DT models to form the final AdaBoost-DT model foridentifying generating units that abuse market power

Finally a model for identifying generating units thatabuse market power is used to determine such units in themarket -ereafter the identification results are evaluated

3 Modalities and Indicators of Market PowerAbuse by Generating Units

31 Main Methods by Which Generating Units Abuse MarketPower Market power in the electricity market refers to thecapability of market members to manipulate the electricityprice in the market and maintain it at an abnormal level for acertain period of time with the aim of making a profit -ereare several methods by which generating units can abusemarket power [20]

311 Collusion Collusion refers to the scenario whereingenerating units participating in the market conclude anldquoalliancerdquo through negotiations and contract signing andsubsequently apply the negotiated quotation strategy toquote high prices to obtain excessive profits Alternativelycertain generating units quote high prices to increase themarket clearing price so that other generating units in theldquoalliancerdquo can obtain excessive profits and take turns to ldquobethe bankerrdquo [21] When a generating unit has a large marketshare the long-term gains that can be obtained throughcollusion among generating units are relatively substantialand collusion among generating units is more likely tooccur Additionally the quotation and its variations bycolluding generating units tend to have certain similarities

312 Withholding Generating unit capacity withholdingrefers to the scenario wherein a unit does not participate inthe market with its available capacity (which should betraded in the market by the unit) because of certain de-liberate actions of the unit including physical and economicwithholding

(1) Physical Withholding Physical withholding refers to theintentional underreporting of available generating capacityby the generating unit -is is mainly in the form of falseclaims that the generating unit is faulty and cannot generateelectricity or that the equipment is undergoing or requiresoverhauling -e intention is to reduce its own generatingcapacity and thereby its supply to the market Generatingunits frequently misreport physical withholding as failure ofthe unit to evade market regulation and thereby abusemarket power -erefore if the target generating unit usesphysical withholding its profits are determined by analyzingthe influence of the unavailability of the unit on the marketclearing price [15]

(2) Economic Withholding Economic withholding refers tothe unreasonably high price (significantly higher than thecost of power generation) quoted by a generating unit for apart of its capacity that results in nongeneration by that partWhile participating in the market the quoted price of aneconomically withheld generating unit is frequently close tothe maximum market price [22] or significantly higher thanits power generation cost and historical quoted price -isresults in an increase in the clearing price and consequentlya high profit -erefore it is possible to determine whether agenerating unit has abused its market power through eco-nomic withholding by comparing its historical price quo-tations with its winning bids

313 Extreme Quotation Extreme quotation refers to thefollowing acts (1) frequently quoting a price that exceedsthat of similar generating units and their own historicallyquoted prices at the time of market quotation and (2) fre-quently quoting at excessively low prices to ensure that thegenerating units win the bids -e main characteristic ofgenerating units with extreme quotations is that these ensuea high number of quotations with extremely high or lowprices at the time of quotation It is possible to determinewhether generating units have abused market powerthrough extreme quotations by comparing their quotedprice levels in the market with winning bids

32 Indicators of Market Power Abuse by Generating UnitsTo better identify generating units that abuse market powerin the spot market identification indexes are constructedconsidering three aspects market structure market be-havior and market performance -is is based on thecharacteristics of generating units that abuse market powerin different ways and considering the principles of sys-tematicity scientificity and operability

Market structure characteristics mainly reflect themarket share and position of the generating units whilemarket behavior characteristics mainly reflect the behaviorof the generating units participating in the market includingthe reporting scenario and quotation strategy Marketperformance characteristics mainly reflect the performanceof the generating units participating in the market includingthe winning scenario of the generating units -e specificdefinitions and formulas of the identifying indicators ofmarket power abuse by the generating units are as follows

321 Market Structure Category

(1) Market Share [23] Market share is defined as the pro-portion of a generating unitrsquos generating capacity to the totalgenerating capacity of all the generating units in the marketIt is calculated using the following formula

si qi

1113936Nj1 qj

(1)

where si is the market share of the i-th generating unit in themarket N is the total number of generating units in the

Mathematical Problems in Engineering 3

market and qi is the generating capacity of the i-th gen-erating unit in the market considering the maximum de-clared capacity of generating unit irsquos current offer -egenerating unitrsquos market share characteristics are used toreflect whether it has market power Moreover when itsmarket share is excessively large it is the key generating unitin the spot market and has a decisive influence on theclearing price in the market(2) Key Supplier Index [23] -e key supplier index is thenumber of generating units that must be utilized to satisfythe market demand -at is the market is undersuppliedwhen the key supplier does not contribute It is calculated asfollows

OPSi 1113936

Nj1 q

bidj minus q

bidi

D (2)

where OPSi denotes the critical supplier index for generatingunit i qbidi denotes the declared capacity of generating unit iqbidj denotes the declared capacity of generating unit j Ddenotes the entire market demand for power at time t andOPSilt 1 is the key supplier for that time period when thegenerating unit hasmarket power-is generating unitmay bea key generator for the entire system or for a particular region

322 Market Behavior Category

(1) Weighted Average Quotation [24] -e average quotedprice of a generating unit is defined as the sum of the productof the declared tariff and declared capacity of each segmentof the effective quoted segment of the unit in the spotmarket divided by the declared capacity It is calculated asfollows

Pi 1113936

Yh1 pih times qih

1113936Yh1 qih

(3)

where Pi is the average quoted price of generating unit i pihrepresents the declared price of the h-th segment of thegenerating unit qih represents the declared capacity of the h-th segment of the generating unit and Y represents the totalnumber of declared segments in the generating unitrsquosquotation curve -e weighted average quotation of thegenerating unit reflects the quotation of the generating unitIf the weighted average quotation is higher the generatingunit is suspected of quoting a higher price

(2) Relative Level of Quotations -e relative level of quotedprices reflects the overall level of the generating unitrsquos quotedprice in the market It is calculated by the following formula

_Pi Pi minus 1113936

Nj1 PjN

1113936Nj1 PjN

times 100 (4)

where _Pi is the relative level of quotations for generating unit iand Pi is the average quoted price of the unit at present -ecloser the quoted price is to the average quoted price of all thegenerating units in the market the closer it is to zero If thequoted price is significantly different from zero it implies that

it is significantly different from the average quoted price of allthe generating units in the market and that the degree ofabnormal quoting by the generating unit is high(3) Capacity Pricing Index [25] A generating unitrsquos capacitypricing index is the sum of its declared electricity price andthe product of the declared capacity multiplier -is indexcan reflect the declared high price of the generating unit It iscalculated according to the following formula

CPIi 1113944

Y

h1pih lowast qih lowast 1001113872 1113873

3 (5)

where CPIi is the capacity pricing index of generating unit i-is index can reflect the relationship between the quantityand price of the generating unit(4) High Quotation Rate [25] High quotation rate is definedas the number of times a generating unitrsquos offer attains thehigh quotation level in a cycle as a fraction of the number ofoffers by the generating unit in that cycle It is calculated bythe following formula

Ri NUMhi

NUMi

(6)

where Ri is the high quotation rate of generating unit iNUMhi is the number of times that an offer by generatingunit i attains the high quotation level and NUMi is the totalnumber of offers by generating unit i If the high quotationrate of a generating unit is high it indicates that it displaysabnormal offer behavior with the aim of increasing themarket clearing price and gaining excess profit

(5) Similarity in High Quotation Rates -e high quotationrate for a generating unit is calculated as shown in (6) -eformula for calculating the similarity in high quotation ratebetween generating units i and j over S cycles is

HBij 1113944S

s1

Ri minus Rj1113872 11138732

1113969

(7)

where HBij is the similarity in the generating unitsrsquo highquotation rate Ri and Rj are the high quotation rates forgenerating units i and j respectively in the s-th cycle -elower the HBij is the higher the likelihood of simultaneoushigh quotations by i and j-e likelihood of collusion betweengenerating units with similar offers can be reflected to acertain extent by the similarity in their high quotation ratesover a number of cycles If HBij is close to zero it is necessaryto conduct focused monitoring of these two generating units

(6) Generating Unit Failure Rate Generating unit failure rateis defined as the fraction of time that a generating unit is outof service or being overhauled It is calculated by the fol-lowing formula

Fi Tfail

Talltimes 100 (8)

where Fi denotes the failure rate of the generating unit Tfaildenotes the total time of failure or overhaul of the generating

4 Mathematical Problems in Engineering

unit within a period of time and Tall denotes the period oftime

(7) Correlation Coefficient of the Quotation Curve -ecorrelation coefficient of the quotation curve of generatingunit i reflects the correlation between this curve and thequotation curve of generating unit j -e formula is asfollows

Rij Cov Pi Pj1113872 1113873

Var Pi1113858 1113859Var Pj1113960 1113961

1113969 (9)

where Rij denotes the correlation coefficient of the quotationcurve of generating units i and j Cov(Pi Pj) is the covarianceof the quotation series Pi and Pj Var[Pi] is the variance of Piand Var[Pj] is the variance of Pj -e correlation coefficientof the quotation curves can reflect the degree of correlationbetween the quotations of the generating units the larger itis the higher the similarity between the quotations of thegenerating units is and the higher the possibility of collusionis between these -e generating units with a high corre-lation coefficient of quotation curve are those with the risk ofldquocollusionrdquo

323 Market Performance Category

(1) Rate of Increase in Clearing Prices -e clearing priceescalation rate for a specified generating unit is the actualmarket clearing price minus the simulated clearing price in afully competitive market divided by the simulated clearingprice in a fully competitive market -e simulated clearingprice is obtained by modifying the declaration behavior ofthe generating units that abuse market power and thenrecalculating the clearing -e formula is as follows

Pilowast

Pclear

minus Piclearlowast

Piclearlowast times 100 (10)

where Pilowast denotes the rate of increase in the generating

unitrsquos clearing price Pclear denotes the actual market clearingprice and Pclearlowast

i denotes the simulated clearing price in afully competitive market both after modifying the offer ofgenerating unit i -e higher the clearing price escalationrate the higher the risk of market power abuse by thegenerating unit(2) Rate of Winning Bids [24] -e rate of winning bids isdefined as the proportion of the generating unitrsquos totalwinning bid to its declared total power It is calculated by thefollowing formula

WRi qwini

qbiti

(11)

where WRi qwini and qbidi are the winning bid rate total bidwinning electricity and total declared electricity respec-tively of generating unit i(3) Out-of-Merit Capacity Index [23] -e out-of-merit ca-pacity index is defined as the ratio of the out-of-merit

capacity of the generating unit as a fraction of the unitrsquosactual declared capacity to the market unsuccessful bid (thesum of the available capacity of all the generating units thatparticipated in the bidding system and failed to win the bid)as a fraction of the market declared capacity in a certaintrading period It is calculated using the following formula

OCIi qoci qbidi

QocQbid times 100 (12)

where OCIi is the out-of-merit capacity index of generatingunit i qoci is the power of generating unit i with unsuccessfulbids qbidi is the declared capacity of generating unit i Qoc isthe power with unsuccessful bids in the market and Qbid isthe total declared capacity in the market

As is evident from the definition of the out-of-meritcapacity index its magnitude is primarily related to the ratioof out-of-merit capacity to available capacity of the gener-ating unit and the ratio of the remaining system capacity toavailable market capacity In an ideal electricity market theratio of each generating unitrsquos out-of-merit capacity to itsavailable capacity should be relatively close to the ratio of theremaining capacity of the system to the available marketcapacity -us the ideal out-of-merit capacity index shouldbe 100 If the out-of-merit capacity index of a generating unitis less than 100 for a specified time period it indicates thatthe unitrsquos offer for that time period is normal Otherwise itindicates that the unitrsquos offer for that time period is higherthan that of the majority of the units in the system and thatthe unit may have engaged in collusive bidding behavior

Depending on the different means by which the gen-erating unit abuses market power (each of which has dif-ferent characteristics) the specific problems are analyzed ona case-by-case basis as shown in Table 1

4 Model Based on AdaBoost-DT Algorithm forIdentifying Generating Units That AbuseMarket Power

41 Sample and Sample Set of Generating Units at AbuseMarket Power Based on the different methods by whichgenerating units abuse market power and the indicators usedto identify these the sample of generating units that abusemarket power and the sample set used for model training areconstructed in the spot market CONTEXT

First an indicator set for generating units that abusemarket power is constructed Using spot market data andindicators for identifying market power abuse the indicatorset of generating units that abuse market power is constructedfor different methods of abusing market power as shown in

Xi xmij | j 1 2 J m 1 2 M1113966 1113967 (13)

where Xi denotes the set of indicators of the i-th generatingunit that abuses market power xm

ij denotes the m-th indi-cator of the j-th risk of generating unit i J denotes the totalnumber of methods of market power abuse and M denotesthe number of indicators

Mathematical Problems in Engineering 5

-ereafter a sample of generating units that abusemarket power and a sample set are constructed Based on theset of indicators obtained from (13)ndash(15) a sample ofgenerating units that abuse market power and a sample set ofgenerating units that abuse market power are created (asshown in (16))

yi

j 1113944M

m1x

mij middot ωm

j minus clowastj ge 0

0 1113944M

m1x

mij middot ωm

j minus clowastj le 0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

Ti yi Xi1 Xi2 XiJ1113966 1113967 (15)

T T1 T2 Tn Tn+1 TN1113864 1113865 (16)

where yi denotes the label of generating unit i It takes valuesin the range 0 1 2 3 4 representing normal collusivephysically withheld economically withheld and extremequotation generating units respectively

ωmj denotes the weight of the m-th indicator of the j-th

method of market power abuse clowastj is the threshold of the j-thgenerating unit that abuses market power All the generatingunits beyond this threshold are identified as generating unitsthat abuse market power as determined by experts Ti de-notes the i-th generating unit sample It includes the labels yiof different methods of abusing market power and the in-dicator Xij of generating units that abuse market power Tdenotes the set of samples used for model training Itconsists of the samples of generating units that abuse market

power (T1 T2 Tn) and a sample of a normal generatingunit (Tn+1 TN)

42 AdaBoost-DT Recognition Model -e fundamentalconcept underlying the AdaBoost algorithm [26] is as fol-lows (1) vary the classifier weights based on the misclassifiedsamples by continuously iterating until a sufficiently smallerror rate is attained and (2) combine the different classifiersof each iteration by a strategy to form the final strongclassifier (as shown in Figure 1) by first training weakclassifier 1 using the original training set and then read-justing the weights of the samples in the training set which isthen used to train weak classifier 2 Iterations continue untila sufficiently marginal error rate is achieved Finally theweighted voting method is used to combine the weakclassifiers -e AdaBoost algorithm has good generalizationcapability and practicality [27] Different weights areassigned to different samples through cyclic training toachieve accurate classification by increasing the focus ondifficult samples

Using DTas a weak classifier samples of generating unitswith different labels in the training set are used as inputs tothe AdaBoost algorithm for training -ereafter the un-known generating unit samples are identified -e specificsteps of the algorithm are as follows

Step 1 Initialize the weight distribution of the training dataBased on the obtained training set each generating unit

sample in the training set is assigned an identical weight inthe first iteration as shown in (17) -e weights of thegenerating unit samples are updated in each iteration

Table 1 Methods and indicators for identifying abuse of market power by generating units

Methods of abusingmarket power Indicator Quantitative characteristics of indicator

Collusion

Market share Large market shareKey supplier index Key supplier index lt1

Quotation curve correlation coefficient Large quotation curve correlation coefficientSimilarity in high quotation rates Similarity in the high quote ratio close to zero

Winning rate High winning rateClearing price escalation rate High clearing price escalation rate

Physical withholding

Market share Large market shareKey supplier index Key supplier index lt1

Failure rate High failure rateOut-of-merit capacity index Large out-of-merit capacity index

Bid winning rate Low bid winning rateClearing price escalation rate High clearing price escalation rate

Economic withholding

Market share Large market shareKey supplier index Key supplier index lt1High quotation rate Large high quotation rate

Out-of-merit capacity index Large out-of-merit capacityBid winning rate Low bid winning rate

Clearing price escalation rate High clearing price escalation rate

Extreme quotation

Market share Large market shareKey supplier index Key supplier index lt1

Weighted average quotation Excessively high or low weighted average quotationRelative level of quotations Relative level of quotations significantly different from zeroCapacity pricing index Excessively high or low capacity pricing index

Clearing price escalation rate High clearing price escalation rate

6 Mathematical Problems in Engineering

D(1) ω11ω12 ω1N1113864 1113865 (17)

where ω1i (1N) is the weight of the first generating unitsample i in the first iteration (i 1 2 N)

Step 2 Iterative training of weak classifiers

(1) Denote the number of iterations by k (k 1 2 K)Set the weight coefficient of each generating unitsample at the k-th iteration as D(k) ωk1 ωk2 ωkN to obtain the k-th weak classifier Gk(xi)

(2) Calculate the weighted classification error rate ek forthe weak classifier Gk(xi) on the training set Herethe weighted classification error rate represents thesum of the weights of all the generating unit samplesthat have been misclassified by the current classifier

ek P Gk xi( 1113857neyi( 1113857 1113944m

i1ωkiI Gk xi( 1113857neyi( 1113857 (18)

(3) Calculate the weight coefficient of the weak classifierGk(xi) It is combined with the weighted error rate ekto calculate the weight coefficient of the weak clas-sifier using (19) -e weighting coefficient indicatesthe importance of the weak classifier Gk(xi) in thefinal classifier -e smaller the error rate the largerthe weight coefficient [28] -e weight coefficient ofthe k-th weak classifier Gk(xi) is

αk 12log

1 minus ek

ek

(19)

(4) Update the weight distribution of the trainingdataset

D(k + 1) ωk+11ωk+12 ωk+1N1113966 1113967 (20)

where ωk+1i denotes the weight of the i-th generatingunit sample in the (K+ 1)-st iteration It is calculatedas follows

ωk+1i ωki

Zk

exp minus αkyiGk xi( 1113857( 1113857 (21)

where Zk is the normalization factor such thatD(k+ 1) is a probability distribution It is calculatedas

Zk 1113944m

i1ωki exp minus αkyiGk xi( 1113857( 1113857 (22)

From the above-stated equation the weight ofcorrectly classified generating unit samples is re-duced according to the k-th iteration of classificationwhereas the weight of misclassified generating unitsamples increases Misclassified generating unitsamples play a larger role in the next iteration [29]-is enables each generating unit sample to belearned completely through this process

(5) Repeat (1)ndash(4) in Step 2 to obtain a series of weakclassifiers and their corresponding weights

Step 3 Linear combination of weak classifiers using weightparameters

f(x) 1113944K

k1αkGk(x) (23)

-e continuous function f(x) is transformed into adiscrete function using the sign() function -us the finalidentification model is

Originaltraining set

(n units)

Training set 1after adjustingsample weight

Training set 2after adjustingsample weight

Training set nafter adjustingsample weight

Weak classifier 1

helliphellip

Weak classifier 2 Weak classifier 3 Weak classifier n + 1helliphellip

Train Train Train TrainVary the samplesweights based onthe misclassified

samples

Strong classifier

Weighted voting method

Vary the samplesweights based onthe misclassified

samples

Figure 1 AdaBoost algorithm flow

Mathematical Problems in Engineering 7

G(x) sign(f(x)) sign 1113944K

k1αkGk(x)⎛⎝ ⎞⎠ (24)

Use identification models to identify generating unitsthat abuse market power in the spot market

5 Analysis of Calculation Examples

-e data on the spot market of a region in 2005 (containinginformation on 170 generating units) are used to validate themethod proposed in this study for identifying the anomalousgenerating units in the spot market -e method is based onAdaBoost and DT techniques -e distribution of positiveand negative samples is shown in Figure 2 Among the 170generating units the number of units abusing market poweraccounts for a quarter including 14 collusive units 7physical holding units 9 economic holding units and 10extreme quotation units

51 Samples of Generating Units at Abuse Market PowerConsidering the indicators for identifying generating unitsthat abuse market power and the actual scenario of the spotmarket in a certain region and based on the relevant data ofgenerating units in the market the sample of generatingunits abusing market power and the sample set are con-structed A few samples of the generating units that abusemarket power are presented in Tables 2ndash5

52 Indicators forModel Evaluation In this study accuracyrecall and F-Measure are used to evaluate the model foridentifying generating units that abuse market power Ac-curacy represents the fraction of genuine positive samplesout of all the samples identified as positive recall is thefraction of all the positive samples that are identified aspositive and F-Measure is a composite index of accuracyand recall -e formulas for the three evaluation indexes areas follows

pre TP

TP + FP

rec TP

TP + FN

Fminus pre times rec times 2pre + rec

(25)

where pre denotes the accuracy of the recognitionmodel thehigher the accuracy the better the model being evaluatedrec denotes the recall of the recognition model the higherthe recall the better the model being evaluated F-denotesthe F-measure of the recognition model the closer it is toone the better is the model TP denotes a positive samplethat is correctly recognized FP denotes a negative samplethat is recognized as a positive sample and FN denotes apositive sample that is recognized as a negative sample

6 Results of Model Identification

Of the sample set of generating units that abuse marketpower obtained above 70 is used as the training set to trainthe recognition model -e remaining (30) is used as thevalidation set to verify the accuracy of the model recogni-tion -e accuracy of the classification is low when thenumber of iterations of the AdaBoost algorithm is relativelymarginal However when this number is excessively large itcauses overfitting-e validation accuracy increases with thenumber of iterations -e result is shown in Figure 2Meanwhile the time utilized for the iteration increases withthe number of iterations

Figure 3 shows that the accuracy of classification in-creases with the number of iterations However it is es-sentially stable when the number of iterations is higher than30 -us the number of iterations of the classifier can be setas 30 For the different methods by which generating unitscan abuse market power the results of the model evaluationindexes for the AdaBoost-DT identification model areshown in Figure 4

Collusive generating unitPhysically withheld generating unitEconomically withheld generating unitExtreme quotation generating unitNormal generating unit

14 79

10

130

Figure 2 Distribution of positive and negative samples

8 Mathematical Problems in Engineering

To validate the model this study compares the results ofidentification using DT SVM [14 30] and AdaBoost-SVMas shown in Figure 5

To better illustrate the relationship between the accu-racies of AdaBoost-DT and AdaBoost- SVM recognitionwith the number of iterations the assessment of the

Table 5 Samples of extreme quotation generating units

Generatingunit

Marketshare

Key supplierindex

Weighted averagequotation

Relative level ofquotations

Capacity pricingindex

Clearing price escalationrate ()

7 00960 09725 800 04652 5934839 5338 00555 09912 26889 -05075 870 268

Table 2 Samples of collusive generating units

Generatingunit

Marketshare

Key supplierindex

Quotation curve correlationcoefficient

Similarity in highquotation rates

Bid winning rate()

Clearing price escalationrate ()

1 00789 09816 05504 05281 7147 13172 00680 09880 05489 05245 5283 1250

Table 3 Samples of physically withheld generating units

Generatingunit

Marketshare

Key supplierindex

Failure rate()

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

3 00906 09733 523 19715 0 6304 00525 09913 676 121575 3833 427

Table 4 Samples of economically withheld generating units

Generatingunit

Marketshare

Key supplierindex

High quotationrate

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

5 00806 09756 05 1971477 0 5706 00625 09893 04 1084313 45 347

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

Figure 3 Relationship between recognition accuracy and number of iterations

Mathematical Problems in Engineering 9

0 1 2 3 4090

092

094

096

098

100

Type of generating units

PreRecF-

Figure 4 Results of the evaluation indicators of the AdaBoost-DT model

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(a)

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(b)

0 1 2 3 4

086

088

090

092

094

096

098

100

Type of generating units

PreRecF-

(c)

Figure 5 Results of the evaluation indicators

10 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

market and qi is the generating capacity of the i-th gen-erating unit in the market considering the maximum de-clared capacity of generating unit irsquos current offer -egenerating unitrsquos market share characteristics are used toreflect whether it has market power Moreover when itsmarket share is excessively large it is the key generating unitin the spot market and has a decisive influence on theclearing price in the market(2) Key Supplier Index [23] -e key supplier index is thenumber of generating units that must be utilized to satisfythe market demand -at is the market is undersuppliedwhen the key supplier does not contribute It is calculated asfollows

OPSi 1113936

Nj1 q

bidj minus q

bidi

D (2)

where OPSi denotes the critical supplier index for generatingunit i qbidi denotes the declared capacity of generating unit iqbidj denotes the declared capacity of generating unit j Ddenotes the entire market demand for power at time t andOPSilt 1 is the key supplier for that time period when thegenerating unit hasmarket power-is generating unitmay bea key generator for the entire system or for a particular region

322 Market Behavior Category

(1) Weighted Average Quotation [24] -e average quotedprice of a generating unit is defined as the sum of the productof the declared tariff and declared capacity of each segmentof the effective quoted segment of the unit in the spotmarket divided by the declared capacity It is calculated asfollows

Pi 1113936

Yh1 pih times qih

1113936Yh1 qih

(3)

where Pi is the average quoted price of generating unit i pihrepresents the declared price of the h-th segment of thegenerating unit qih represents the declared capacity of the h-th segment of the generating unit and Y represents the totalnumber of declared segments in the generating unitrsquosquotation curve -e weighted average quotation of thegenerating unit reflects the quotation of the generating unitIf the weighted average quotation is higher the generatingunit is suspected of quoting a higher price

(2) Relative Level of Quotations -e relative level of quotedprices reflects the overall level of the generating unitrsquos quotedprice in the market It is calculated by the following formula

_Pi Pi minus 1113936

Nj1 PjN

1113936Nj1 PjN

times 100 (4)

where _Pi is the relative level of quotations for generating unit iand Pi is the average quoted price of the unit at present -ecloser the quoted price is to the average quoted price of all thegenerating units in the market the closer it is to zero If thequoted price is significantly different from zero it implies that

it is significantly different from the average quoted price of allthe generating units in the market and that the degree ofabnormal quoting by the generating unit is high(3) Capacity Pricing Index [25] A generating unitrsquos capacitypricing index is the sum of its declared electricity price andthe product of the declared capacity multiplier -is indexcan reflect the declared high price of the generating unit It iscalculated according to the following formula

CPIi 1113944

Y

h1pih lowast qih lowast 1001113872 1113873

3 (5)

where CPIi is the capacity pricing index of generating unit i-is index can reflect the relationship between the quantityand price of the generating unit(4) High Quotation Rate [25] High quotation rate is definedas the number of times a generating unitrsquos offer attains thehigh quotation level in a cycle as a fraction of the number ofoffers by the generating unit in that cycle It is calculated bythe following formula

Ri NUMhi

NUMi

(6)

where Ri is the high quotation rate of generating unit iNUMhi is the number of times that an offer by generatingunit i attains the high quotation level and NUMi is the totalnumber of offers by generating unit i If the high quotationrate of a generating unit is high it indicates that it displaysabnormal offer behavior with the aim of increasing themarket clearing price and gaining excess profit

(5) Similarity in High Quotation Rates -e high quotationrate for a generating unit is calculated as shown in (6) -eformula for calculating the similarity in high quotation ratebetween generating units i and j over S cycles is

HBij 1113944S

s1

Ri minus Rj1113872 11138732

1113969

(7)

where HBij is the similarity in the generating unitsrsquo highquotation rate Ri and Rj are the high quotation rates forgenerating units i and j respectively in the s-th cycle -elower the HBij is the higher the likelihood of simultaneoushigh quotations by i and j-e likelihood of collusion betweengenerating units with similar offers can be reflected to acertain extent by the similarity in their high quotation ratesover a number of cycles If HBij is close to zero it is necessaryto conduct focused monitoring of these two generating units

(6) Generating Unit Failure Rate Generating unit failure rateis defined as the fraction of time that a generating unit is outof service or being overhauled It is calculated by the fol-lowing formula

Fi Tfail

Talltimes 100 (8)

where Fi denotes the failure rate of the generating unit Tfaildenotes the total time of failure or overhaul of the generating

4 Mathematical Problems in Engineering

unit within a period of time and Tall denotes the period oftime

(7) Correlation Coefficient of the Quotation Curve -ecorrelation coefficient of the quotation curve of generatingunit i reflects the correlation between this curve and thequotation curve of generating unit j -e formula is asfollows

Rij Cov Pi Pj1113872 1113873

Var Pi1113858 1113859Var Pj1113960 1113961

1113969 (9)

where Rij denotes the correlation coefficient of the quotationcurve of generating units i and j Cov(Pi Pj) is the covarianceof the quotation series Pi and Pj Var[Pi] is the variance of Piand Var[Pj] is the variance of Pj -e correlation coefficientof the quotation curves can reflect the degree of correlationbetween the quotations of the generating units the larger itis the higher the similarity between the quotations of thegenerating units is and the higher the possibility of collusionis between these -e generating units with a high corre-lation coefficient of quotation curve are those with the risk ofldquocollusionrdquo

323 Market Performance Category

(1) Rate of Increase in Clearing Prices -e clearing priceescalation rate for a specified generating unit is the actualmarket clearing price minus the simulated clearing price in afully competitive market divided by the simulated clearingprice in a fully competitive market -e simulated clearingprice is obtained by modifying the declaration behavior ofthe generating units that abuse market power and thenrecalculating the clearing -e formula is as follows

Pilowast

Pclear

minus Piclearlowast

Piclearlowast times 100 (10)

where Pilowast denotes the rate of increase in the generating

unitrsquos clearing price Pclear denotes the actual market clearingprice and Pclearlowast

i denotes the simulated clearing price in afully competitive market both after modifying the offer ofgenerating unit i -e higher the clearing price escalationrate the higher the risk of market power abuse by thegenerating unit(2) Rate of Winning Bids [24] -e rate of winning bids isdefined as the proportion of the generating unitrsquos totalwinning bid to its declared total power It is calculated by thefollowing formula

WRi qwini

qbiti

(11)

where WRi qwini and qbidi are the winning bid rate total bidwinning electricity and total declared electricity respec-tively of generating unit i(3) Out-of-Merit Capacity Index [23] -e out-of-merit ca-pacity index is defined as the ratio of the out-of-merit

capacity of the generating unit as a fraction of the unitrsquosactual declared capacity to the market unsuccessful bid (thesum of the available capacity of all the generating units thatparticipated in the bidding system and failed to win the bid)as a fraction of the market declared capacity in a certaintrading period It is calculated using the following formula

OCIi qoci qbidi

QocQbid times 100 (12)

where OCIi is the out-of-merit capacity index of generatingunit i qoci is the power of generating unit i with unsuccessfulbids qbidi is the declared capacity of generating unit i Qoc isthe power with unsuccessful bids in the market and Qbid isthe total declared capacity in the market

As is evident from the definition of the out-of-meritcapacity index its magnitude is primarily related to the ratioof out-of-merit capacity to available capacity of the gener-ating unit and the ratio of the remaining system capacity toavailable market capacity In an ideal electricity market theratio of each generating unitrsquos out-of-merit capacity to itsavailable capacity should be relatively close to the ratio of theremaining capacity of the system to the available marketcapacity -us the ideal out-of-merit capacity index shouldbe 100 If the out-of-merit capacity index of a generating unitis less than 100 for a specified time period it indicates thatthe unitrsquos offer for that time period is normal Otherwise itindicates that the unitrsquos offer for that time period is higherthan that of the majority of the units in the system and thatthe unit may have engaged in collusive bidding behavior

Depending on the different means by which the gen-erating unit abuses market power (each of which has dif-ferent characteristics) the specific problems are analyzed ona case-by-case basis as shown in Table 1

4 Model Based on AdaBoost-DT Algorithm forIdentifying Generating Units That AbuseMarket Power

41 Sample and Sample Set of Generating Units at AbuseMarket Power Based on the different methods by whichgenerating units abuse market power and the indicators usedto identify these the sample of generating units that abusemarket power and the sample set used for model training areconstructed in the spot market CONTEXT

First an indicator set for generating units that abusemarket power is constructed Using spot market data andindicators for identifying market power abuse the indicatorset of generating units that abuse market power is constructedfor different methods of abusing market power as shown in

Xi xmij | j 1 2 J m 1 2 M1113966 1113967 (13)

where Xi denotes the set of indicators of the i-th generatingunit that abuses market power xm

ij denotes the m-th indi-cator of the j-th risk of generating unit i J denotes the totalnumber of methods of market power abuse and M denotesthe number of indicators

Mathematical Problems in Engineering 5

-ereafter a sample of generating units that abusemarket power and a sample set are constructed Based on theset of indicators obtained from (13)ndash(15) a sample ofgenerating units that abuse market power and a sample set ofgenerating units that abuse market power are created (asshown in (16))

yi

j 1113944M

m1x

mij middot ωm

j minus clowastj ge 0

0 1113944M

m1x

mij middot ωm

j minus clowastj le 0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

Ti yi Xi1 Xi2 XiJ1113966 1113967 (15)

T T1 T2 Tn Tn+1 TN1113864 1113865 (16)

where yi denotes the label of generating unit i It takes valuesin the range 0 1 2 3 4 representing normal collusivephysically withheld economically withheld and extremequotation generating units respectively

ωmj denotes the weight of the m-th indicator of the j-th

method of market power abuse clowastj is the threshold of the j-thgenerating unit that abuses market power All the generatingunits beyond this threshold are identified as generating unitsthat abuse market power as determined by experts Ti de-notes the i-th generating unit sample It includes the labels yiof different methods of abusing market power and the in-dicator Xij of generating units that abuse market power Tdenotes the set of samples used for model training Itconsists of the samples of generating units that abuse market

power (T1 T2 Tn) and a sample of a normal generatingunit (Tn+1 TN)

42 AdaBoost-DT Recognition Model -e fundamentalconcept underlying the AdaBoost algorithm [26] is as fol-lows (1) vary the classifier weights based on the misclassifiedsamples by continuously iterating until a sufficiently smallerror rate is attained and (2) combine the different classifiersof each iteration by a strategy to form the final strongclassifier (as shown in Figure 1) by first training weakclassifier 1 using the original training set and then read-justing the weights of the samples in the training set which isthen used to train weak classifier 2 Iterations continue untila sufficiently marginal error rate is achieved Finally theweighted voting method is used to combine the weakclassifiers -e AdaBoost algorithm has good generalizationcapability and practicality [27] Different weights areassigned to different samples through cyclic training toachieve accurate classification by increasing the focus ondifficult samples

Using DTas a weak classifier samples of generating unitswith different labels in the training set are used as inputs tothe AdaBoost algorithm for training -ereafter the un-known generating unit samples are identified -e specificsteps of the algorithm are as follows

Step 1 Initialize the weight distribution of the training dataBased on the obtained training set each generating unit

sample in the training set is assigned an identical weight inthe first iteration as shown in (17) -e weights of thegenerating unit samples are updated in each iteration

Table 1 Methods and indicators for identifying abuse of market power by generating units

Methods of abusingmarket power Indicator Quantitative characteristics of indicator

Collusion

Market share Large market shareKey supplier index Key supplier index lt1

Quotation curve correlation coefficient Large quotation curve correlation coefficientSimilarity in high quotation rates Similarity in the high quote ratio close to zero

Winning rate High winning rateClearing price escalation rate High clearing price escalation rate

Physical withholding

Market share Large market shareKey supplier index Key supplier index lt1

Failure rate High failure rateOut-of-merit capacity index Large out-of-merit capacity index

Bid winning rate Low bid winning rateClearing price escalation rate High clearing price escalation rate

Economic withholding

Market share Large market shareKey supplier index Key supplier index lt1High quotation rate Large high quotation rate

Out-of-merit capacity index Large out-of-merit capacityBid winning rate Low bid winning rate

Clearing price escalation rate High clearing price escalation rate

Extreme quotation

Market share Large market shareKey supplier index Key supplier index lt1

Weighted average quotation Excessively high or low weighted average quotationRelative level of quotations Relative level of quotations significantly different from zeroCapacity pricing index Excessively high or low capacity pricing index

Clearing price escalation rate High clearing price escalation rate

6 Mathematical Problems in Engineering

D(1) ω11ω12 ω1N1113864 1113865 (17)

where ω1i (1N) is the weight of the first generating unitsample i in the first iteration (i 1 2 N)

Step 2 Iterative training of weak classifiers

(1) Denote the number of iterations by k (k 1 2 K)Set the weight coefficient of each generating unitsample at the k-th iteration as D(k) ωk1 ωk2 ωkN to obtain the k-th weak classifier Gk(xi)

(2) Calculate the weighted classification error rate ek forthe weak classifier Gk(xi) on the training set Herethe weighted classification error rate represents thesum of the weights of all the generating unit samplesthat have been misclassified by the current classifier

ek P Gk xi( 1113857neyi( 1113857 1113944m

i1ωkiI Gk xi( 1113857neyi( 1113857 (18)

(3) Calculate the weight coefficient of the weak classifierGk(xi) It is combined with the weighted error rate ekto calculate the weight coefficient of the weak clas-sifier using (19) -e weighting coefficient indicatesthe importance of the weak classifier Gk(xi) in thefinal classifier -e smaller the error rate the largerthe weight coefficient [28] -e weight coefficient ofthe k-th weak classifier Gk(xi) is

αk 12log

1 minus ek

ek

(19)

(4) Update the weight distribution of the trainingdataset

D(k + 1) ωk+11ωk+12 ωk+1N1113966 1113967 (20)

where ωk+1i denotes the weight of the i-th generatingunit sample in the (K+ 1)-st iteration It is calculatedas follows

ωk+1i ωki

Zk

exp minus αkyiGk xi( 1113857( 1113857 (21)

where Zk is the normalization factor such thatD(k+ 1) is a probability distribution It is calculatedas

Zk 1113944m

i1ωki exp minus αkyiGk xi( 1113857( 1113857 (22)

From the above-stated equation the weight ofcorrectly classified generating unit samples is re-duced according to the k-th iteration of classificationwhereas the weight of misclassified generating unitsamples increases Misclassified generating unitsamples play a larger role in the next iteration [29]-is enables each generating unit sample to belearned completely through this process

(5) Repeat (1)ndash(4) in Step 2 to obtain a series of weakclassifiers and their corresponding weights

Step 3 Linear combination of weak classifiers using weightparameters

f(x) 1113944K

k1αkGk(x) (23)

-e continuous function f(x) is transformed into adiscrete function using the sign() function -us the finalidentification model is

Originaltraining set

(n units)

Training set 1after adjustingsample weight

Training set 2after adjustingsample weight

Training set nafter adjustingsample weight

Weak classifier 1

helliphellip

Weak classifier 2 Weak classifier 3 Weak classifier n + 1helliphellip

Train Train Train TrainVary the samplesweights based onthe misclassified

samples

Strong classifier

Weighted voting method

Vary the samplesweights based onthe misclassified

samples

Figure 1 AdaBoost algorithm flow

Mathematical Problems in Engineering 7

G(x) sign(f(x)) sign 1113944K

k1αkGk(x)⎛⎝ ⎞⎠ (24)

Use identification models to identify generating unitsthat abuse market power in the spot market

5 Analysis of Calculation Examples

-e data on the spot market of a region in 2005 (containinginformation on 170 generating units) are used to validate themethod proposed in this study for identifying the anomalousgenerating units in the spot market -e method is based onAdaBoost and DT techniques -e distribution of positiveand negative samples is shown in Figure 2 Among the 170generating units the number of units abusing market poweraccounts for a quarter including 14 collusive units 7physical holding units 9 economic holding units and 10extreme quotation units

51 Samples of Generating Units at Abuse Market PowerConsidering the indicators for identifying generating unitsthat abuse market power and the actual scenario of the spotmarket in a certain region and based on the relevant data ofgenerating units in the market the sample of generatingunits abusing market power and the sample set are con-structed A few samples of the generating units that abusemarket power are presented in Tables 2ndash5

52 Indicators forModel Evaluation In this study accuracyrecall and F-Measure are used to evaluate the model foridentifying generating units that abuse market power Ac-curacy represents the fraction of genuine positive samplesout of all the samples identified as positive recall is thefraction of all the positive samples that are identified aspositive and F-Measure is a composite index of accuracyand recall -e formulas for the three evaluation indexes areas follows

pre TP

TP + FP

rec TP

TP + FN

Fminus pre times rec times 2pre + rec

(25)

where pre denotes the accuracy of the recognitionmodel thehigher the accuracy the better the model being evaluatedrec denotes the recall of the recognition model the higherthe recall the better the model being evaluated F-denotesthe F-measure of the recognition model the closer it is toone the better is the model TP denotes a positive samplethat is correctly recognized FP denotes a negative samplethat is recognized as a positive sample and FN denotes apositive sample that is recognized as a negative sample

6 Results of Model Identification

Of the sample set of generating units that abuse marketpower obtained above 70 is used as the training set to trainthe recognition model -e remaining (30) is used as thevalidation set to verify the accuracy of the model recogni-tion -e accuracy of the classification is low when thenumber of iterations of the AdaBoost algorithm is relativelymarginal However when this number is excessively large itcauses overfitting-e validation accuracy increases with thenumber of iterations -e result is shown in Figure 2Meanwhile the time utilized for the iteration increases withthe number of iterations

Figure 3 shows that the accuracy of classification in-creases with the number of iterations However it is es-sentially stable when the number of iterations is higher than30 -us the number of iterations of the classifier can be setas 30 For the different methods by which generating unitscan abuse market power the results of the model evaluationindexes for the AdaBoost-DT identification model areshown in Figure 4

Collusive generating unitPhysically withheld generating unitEconomically withheld generating unitExtreme quotation generating unitNormal generating unit

14 79

10

130

Figure 2 Distribution of positive and negative samples

8 Mathematical Problems in Engineering

To validate the model this study compares the results ofidentification using DT SVM [14 30] and AdaBoost-SVMas shown in Figure 5

To better illustrate the relationship between the accu-racies of AdaBoost-DT and AdaBoost- SVM recognitionwith the number of iterations the assessment of the

Table 5 Samples of extreme quotation generating units

Generatingunit

Marketshare

Key supplierindex

Weighted averagequotation

Relative level ofquotations

Capacity pricingindex

Clearing price escalationrate ()

7 00960 09725 800 04652 5934839 5338 00555 09912 26889 -05075 870 268

Table 2 Samples of collusive generating units

Generatingunit

Marketshare

Key supplierindex

Quotation curve correlationcoefficient

Similarity in highquotation rates

Bid winning rate()

Clearing price escalationrate ()

1 00789 09816 05504 05281 7147 13172 00680 09880 05489 05245 5283 1250

Table 3 Samples of physically withheld generating units

Generatingunit

Marketshare

Key supplierindex

Failure rate()

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

3 00906 09733 523 19715 0 6304 00525 09913 676 121575 3833 427

Table 4 Samples of economically withheld generating units

Generatingunit

Marketshare

Key supplierindex

High quotationrate

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

5 00806 09756 05 1971477 0 5706 00625 09893 04 1084313 45 347

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

Figure 3 Relationship between recognition accuracy and number of iterations

Mathematical Problems in Engineering 9

0 1 2 3 4090

092

094

096

098

100

Type of generating units

PreRecF-

Figure 4 Results of the evaluation indicators of the AdaBoost-DT model

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(a)

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(b)

0 1 2 3 4

086

088

090

092

094

096

098

100

Type of generating units

PreRecF-

(c)

Figure 5 Results of the evaluation indicators

10 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

unit within a period of time and Tall denotes the period oftime

(7) Correlation Coefficient of the Quotation Curve -ecorrelation coefficient of the quotation curve of generatingunit i reflects the correlation between this curve and thequotation curve of generating unit j -e formula is asfollows

Rij Cov Pi Pj1113872 1113873

Var Pi1113858 1113859Var Pj1113960 1113961

1113969 (9)

where Rij denotes the correlation coefficient of the quotationcurve of generating units i and j Cov(Pi Pj) is the covarianceof the quotation series Pi and Pj Var[Pi] is the variance of Piand Var[Pj] is the variance of Pj -e correlation coefficientof the quotation curves can reflect the degree of correlationbetween the quotations of the generating units the larger itis the higher the similarity between the quotations of thegenerating units is and the higher the possibility of collusionis between these -e generating units with a high corre-lation coefficient of quotation curve are those with the risk ofldquocollusionrdquo

323 Market Performance Category

(1) Rate of Increase in Clearing Prices -e clearing priceescalation rate for a specified generating unit is the actualmarket clearing price minus the simulated clearing price in afully competitive market divided by the simulated clearingprice in a fully competitive market -e simulated clearingprice is obtained by modifying the declaration behavior ofthe generating units that abuse market power and thenrecalculating the clearing -e formula is as follows

Pilowast

Pclear

minus Piclearlowast

Piclearlowast times 100 (10)

where Pilowast denotes the rate of increase in the generating

unitrsquos clearing price Pclear denotes the actual market clearingprice and Pclearlowast

i denotes the simulated clearing price in afully competitive market both after modifying the offer ofgenerating unit i -e higher the clearing price escalationrate the higher the risk of market power abuse by thegenerating unit(2) Rate of Winning Bids [24] -e rate of winning bids isdefined as the proportion of the generating unitrsquos totalwinning bid to its declared total power It is calculated by thefollowing formula

WRi qwini

qbiti

(11)

where WRi qwini and qbidi are the winning bid rate total bidwinning electricity and total declared electricity respec-tively of generating unit i(3) Out-of-Merit Capacity Index [23] -e out-of-merit ca-pacity index is defined as the ratio of the out-of-merit

capacity of the generating unit as a fraction of the unitrsquosactual declared capacity to the market unsuccessful bid (thesum of the available capacity of all the generating units thatparticipated in the bidding system and failed to win the bid)as a fraction of the market declared capacity in a certaintrading period It is calculated using the following formula

OCIi qoci qbidi

QocQbid times 100 (12)

where OCIi is the out-of-merit capacity index of generatingunit i qoci is the power of generating unit i with unsuccessfulbids qbidi is the declared capacity of generating unit i Qoc isthe power with unsuccessful bids in the market and Qbid isthe total declared capacity in the market

As is evident from the definition of the out-of-meritcapacity index its magnitude is primarily related to the ratioof out-of-merit capacity to available capacity of the gener-ating unit and the ratio of the remaining system capacity toavailable market capacity In an ideal electricity market theratio of each generating unitrsquos out-of-merit capacity to itsavailable capacity should be relatively close to the ratio of theremaining capacity of the system to the available marketcapacity -us the ideal out-of-merit capacity index shouldbe 100 If the out-of-merit capacity index of a generating unitis less than 100 for a specified time period it indicates thatthe unitrsquos offer for that time period is normal Otherwise itindicates that the unitrsquos offer for that time period is higherthan that of the majority of the units in the system and thatthe unit may have engaged in collusive bidding behavior

Depending on the different means by which the gen-erating unit abuses market power (each of which has dif-ferent characteristics) the specific problems are analyzed ona case-by-case basis as shown in Table 1

4 Model Based on AdaBoost-DT Algorithm forIdentifying Generating Units That AbuseMarket Power

41 Sample and Sample Set of Generating Units at AbuseMarket Power Based on the different methods by whichgenerating units abuse market power and the indicators usedto identify these the sample of generating units that abusemarket power and the sample set used for model training areconstructed in the spot market CONTEXT

First an indicator set for generating units that abusemarket power is constructed Using spot market data andindicators for identifying market power abuse the indicatorset of generating units that abuse market power is constructedfor different methods of abusing market power as shown in

Xi xmij | j 1 2 J m 1 2 M1113966 1113967 (13)

where Xi denotes the set of indicators of the i-th generatingunit that abuses market power xm

ij denotes the m-th indi-cator of the j-th risk of generating unit i J denotes the totalnumber of methods of market power abuse and M denotesthe number of indicators

Mathematical Problems in Engineering 5

-ereafter a sample of generating units that abusemarket power and a sample set are constructed Based on theset of indicators obtained from (13)ndash(15) a sample ofgenerating units that abuse market power and a sample set ofgenerating units that abuse market power are created (asshown in (16))

yi

j 1113944M

m1x

mij middot ωm

j minus clowastj ge 0

0 1113944M

m1x

mij middot ωm

j minus clowastj le 0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

Ti yi Xi1 Xi2 XiJ1113966 1113967 (15)

T T1 T2 Tn Tn+1 TN1113864 1113865 (16)

where yi denotes the label of generating unit i It takes valuesin the range 0 1 2 3 4 representing normal collusivephysically withheld economically withheld and extremequotation generating units respectively

ωmj denotes the weight of the m-th indicator of the j-th

method of market power abuse clowastj is the threshold of the j-thgenerating unit that abuses market power All the generatingunits beyond this threshold are identified as generating unitsthat abuse market power as determined by experts Ti de-notes the i-th generating unit sample It includes the labels yiof different methods of abusing market power and the in-dicator Xij of generating units that abuse market power Tdenotes the set of samples used for model training Itconsists of the samples of generating units that abuse market

power (T1 T2 Tn) and a sample of a normal generatingunit (Tn+1 TN)

42 AdaBoost-DT Recognition Model -e fundamentalconcept underlying the AdaBoost algorithm [26] is as fol-lows (1) vary the classifier weights based on the misclassifiedsamples by continuously iterating until a sufficiently smallerror rate is attained and (2) combine the different classifiersof each iteration by a strategy to form the final strongclassifier (as shown in Figure 1) by first training weakclassifier 1 using the original training set and then read-justing the weights of the samples in the training set which isthen used to train weak classifier 2 Iterations continue untila sufficiently marginal error rate is achieved Finally theweighted voting method is used to combine the weakclassifiers -e AdaBoost algorithm has good generalizationcapability and practicality [27] Different weights areassigned to different samples through cyclic training toachieve accurate classification by increasing the focus ondifficult samples

Using DTas a weak classifier samples of generating unitswith different labels in the training set are used as inputs tothe AdaBoost algorithm for training -ereafter the un-known generating unit samples are identified -e specificsteps of the algorithm are as follows

Step 1 Initialize the weight distribution of the training dataBased on the obtained training set each generating unit

sample in the training set is assigned an identical weight inthe first iteration as shown in (17) -e weights of thegenerating unit samples are updated in each iteration

Table 1 Methods and indicators for identifying abuse of market power by generating units

Methods of abusingmarket power Indicator Quantitative characteristics of indicator

Collusion

Market share Large market shareKey supplier index Key supplier index lt1

Quotation curve correlation coefficient Large quotation curve correlation coefficientSimilarity in high quotation rates Similarity in the high quote ratio close to zero

Winning rate High winning rateClearing price escalation rate High clearing price escalation rate

Physical withholding

Market share Large market shareKey supplier index Key supplier index lt1

Failure rate High failure rateOut-of-merit capacity index Large out-of-merit capacity index

Bid winning rate Low bid winning rateClearing price escalation rate High clearing price escalation rate

Economic withholding

Market share Large market shareKey supplier index Key supplier index lt1High quotation rate Large high quotation rate

Out-of-merit capacity index Large out-of-merit capacityBid winning rate Low bid winning rate

Clearing price escalation rate High clearing price escalation rate

Extreme quotation

Market share Large market shareKey supplier index Key supplier index lt1

Weighted average quotation Excessively high or low weighted average quotationRelative level of quotations Relative level of quotations significantly different from zeroCapacity pricing index Excessively high or low capacity pricing index

Clearing price escalation rate High clearing price escalation rate

6 Mathematical Problems in Engineering

D(1) ω11ω12 ω1N1113864 1113865 (17)

where ω1i (1N) is the weight of the first generating unitsample i in the first iteration (i 1 2 N)

Step 2 Iterative training of weak classifiers

(1) Denote the number of iterations by k (k 1 2 K)Set the weight coefficient of each generating unitsample at the k-th iteration as D(k) ωk1 ωk2 ωkN to obtain the k-th weak classifier Gk(xi)

(2) Calculate the weighted classification error rate ek forthe weak classifier Gk(xi) on the training set Herethe weighted classification error rate represents thesum of the weights of all the generating unit samplesthat have been misclassified by the current classifier

ek P Gk xi( 1113857neyi( 1113857 1113944m

i1ωkiI Gk xi( 1113857neyi( 1113857 (18)

(3) Calculate the weight coefficient of the weak classifierGk(xi) It is combined with the weighted error rate ekto calculate the weight coefficient of the weak clas-sifier using (19) -e weighting coefficient indicatesthe importance of the weak classifier Gk(xi) in thefinal classifier -e smaller the error rate the largerthe weight coefficient [28] -e weight coefficient ofthe k-th weak classifier Gk(xi) is

αk 12log

1 minus ek

ek

(19)

(4) Update the weight distribution of the trainingdataset

D(k + 1) ωk+11ωk+12 ωk+1N1113966 1113967 (20)

where ωk+1i denotes the weight of the i-th generatingunit sample in the (K+ 1)-st iteration It is calculatedas follows

ωk+1i ωki

Zk

exp minus αkyiGk xi( 1113857( 1113857 (21)

where Zk is the normalization factor such thatD(k+ 1) is a probability distribution It is calculatedas

Zk 1113944m

i1ωki exp minus αkyiGk xi( 1113857( 1113857 (22)

From the above-stated equation the weight ofcorrectly classified generating unit samples is re-duced according to the k-th iteration of classificationwhereas the weight of misclassified generating unitsamples increases Misclassified generating unitsamples play a larger role in the next iteration [29]-is enables each generating unit sample to belearned completely through this process

(5) Repeat (1)ndash(4) in Step 2 to obtain a series of weakclassifiers and their corresponding weights

Step 3 Linear combination of weak classifiers using weightparameters

f(x) 1113944K

k1αkGk(x) (23)

-e continuous function f(x) is transformed into adiscrete function using the sign() function -us the finalidentification model is

Originaltraining set

(n units)

Training set 1after adjustingsample weight

Training set 2after adjustingsample weight

Training set nafter adjustingsample weight

Weak classifier 1

helliphellip

Weak classifier 2 Weak classifier 3 Weak classifier n + 1helliphellip

Train Train Train TrainVary the samplesweights based onthe misclassified

samples

Strong classifier

Weighted voting method

Vary the samplesweights based onthe misclassified

samples

Figure 1 AdaBoost algorithm flow

Mathematical Problems in Engineering 7

G(x) sign(f(x)) sign 1113944K

k1αkGk(x)⎛⎝ ⎞⎠ (24)

Use identification models to identify generating unitsthat abuse market power in the spot market

5 Analysis of Calculation Examples

-e data on the spot market of a region in 2005 (containinginformation on 170 generating units) are used to validate themethod proposed in this study for identifying the anomalousgenerating units in the spot market -e method is based onAdaBoost and DT techniques -e distribution of positiveand negative samples is shown in Figure 2 Among the 170generating units the number of units abusing market poweraccounts for a quarter including 14 collusive units 7physical holding units 9 economic holding units and 10extreme quotation units

51 Samples of Generating Units at Abuse Market PowerConsidering the indicators for identifying generating unitsthat abuse market power and the actual scenario of the spotmarket in a certain region and based on the relevant data ofgenerating units in the market the sample of generatingunits abusing market power and the sample set are con-structed A few samples of the generating units that abusemarket power are presented in Tables 2ndash5

52 Indicators forModel Evaluation In this study accuracyrecall and F-Measure are used to evaluate the model foridentifying generating units that abuse market power Ac-curacy represents the fraction of genuine positive samplesout of all the samples identified as positive recall is thefraction of all the positive samples that are identified aspositive and F-Measure is a composite index of accuracyand recall -e formulas for the three evaluation indexes areas follows

pre TP

TP + FP

rec TP

TP + FN

Fminus pre times rec times 2pre + rec

(25)

where pre denotes the accuracy of the recognitionmodel thehigher the accuracy the better the model being evaluatedrec denotes the recall of the recognition model the higherthe recall the better the model being evaluated F-denotesthe F-measure of the recognition model the closer it is toone the better is the model TP denotes a positive samplethat is correctly recognized FP denotes a negative samplethat is recognized as a positive sample and FN denotes apositive sample that is recognized as a negative sample

6 Results of Model Identification

Of the sample set of generating units that abuse marketpower obtained above 70 is used as the training set to trainthe recognition model -e remaining (30) is used as thevalidation set to verify the accuracy of the model recogni-tion -e accuracy of the classification is low when thenumber of iterations of the AdaBoost algorithm is relativelymarginal However when this number is excessively large itcauses overfitting-e validation accuracy increases with thenumber of iterations -e result is shown in Figure 2Meanwhile the time utilized for the iteration increases withthe number of iterations

Figure 3 shows that the accuracy of classification in-creases with the number of iterations However it is es-sentially stable when the number of iterations is higher than30 -us the number of iterations of the classifier can be setas 30 For the different methods by which generating unitscan abuse market power the results of the model evaluationindexes for the AdaBoost-DT identification model areshown in Figure 4

Collusive generating unitPhysically withheld generating unitEconomically withheld generating unitExtreme quotation generating unitNormal generating unit

14 79

10

130

Figure 2 Distribution of positive and negative samples

8 Mathematical Problems in Engineering

To validate the model this study compares the results ofidentification using DT SVM [14 30] and AdaBoost-SVMas shown in Figure 5

To better illustrate the relationship between the accu-racies of AdaBoost-DT and AdaBoost- SVM recognitionwith the number of iterations the assessment of the

Table 5 Samples of extreme quotation generating units

Generatingunit

Marketshare

Key supplierindex

Weighted averagequotation

Relative level ofquotations

Capacity pricingindex

Clearing price escalationrate ()

7 00960 09725 800 04652 5934839 5338 00555 09912 26889 -05075 870 268

Table 2 Samples of collusive generating units

Generatingunit

Marketshare

Key supplierindex

Quotation curve correlationcoefficient

Similarity in highquotation rates

Bid winning rate()

Clearing price escalationrate ()

1 00789 09816 05504 05281 7147 13172 00680 09880 05489 05245 5283 1250

Table 3 Samples of physically withheld generating units

Generatingunit

Marketshare

Key supplierindex

Failure rate()

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

3 00906 09733 523 19715 0 6304 00525 09913 676 121575 3833 427

Table 4 Samples of economically withheld generating units

Generatingunit

Marketshare

Key supplierindex

High quotationrate

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

5 00806 09756 05 1971477 0 5706 00625 09893 04 1084313 45 347

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

Figure 3 Relationship between recognition accuracy and number of iterations

Mathematical Problems in Engineering 9

0 1 2 3 4090

092

094

096

098

100

Type of generating units

PreRecF-

Figure 4 Results of the evaluation indicators of the AdaBoost-DT model

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(a)

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(b)

0 1 2 3 4

086

088

090

092

094

096

098

100

Type of generating units

PreRecF-

(c)

Figure 5 Results of the evaluation indicators

10 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

-ereafter a sample of generating units that abusemarket power and a sample set are constructed Based on theset of indicators obtained from (13)ndash(15) a sample ofgenerating units that abuse market power and a sample set ofgenerating units that abuse market power are created (asshown in (16))

yi

j 1113944M

m1x

mij middot ωm

j minus clowastj ge 0

0 1113944M

m1x

mij middot ωm

j minus clowastj le 0

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(14)

Ti yi Xi1 Xi2 XiJ1113966 1113967 (15)

T T1 T2 Tn Tn+1 TN1113864 1113865 (16)

where yi denotes the label of generating unit i It takes valuesin the range 0 1 2 3 4 representing normal collusivephysically withheld economically withheld and extremequotation generating units respectively

ωmj denotes the weight of the m-th indicator of the j-th

method of market power abuse clowastj is the threshold of the j-thgenerating unit that abuses market power All the generatingunits beyond this threshold are identified as generating unitsthat abuse market power as determined by experts Ti de-notes the i-th generating unit sample It includes the labels yiof different methods of abusing market power and the in-dicator Xij of generating units that abuse market power Tdenotes the set of samples used for model training Itconsists of the samples of generating units that abuse market

power (T1 T2 Tn) and a sample of a normal generatingunit (Tn+1 TN)

42 AdaBoost-DT Recognition Model -e fundamentalconcept underlying the AdaBoost algorithm [26] is as fol-lows (1) vary the classifier weights based on the misclassifiedsamples by continuously iterating until a sufficiently smallerror rate is attained and (2) combine the different classifiersof each iteration by a strategy to form the final strongclassifier (as shown in Figure 1) by first training weakclassifier 1 using the original training set and then read-justing the weights of the samples in the training set which isthen used to train weak classifier 2 Iterations continue untila sufficiently marginal error rate is achieved Finally theweighted voting method is used to combine the weakclassifiers -e AdaBoost algorithm has good generalizationcapability and practicality [27] Different weights areassigned to different samples through cyclic training toachieve accurate classification by increasing the focus ondifficult samples

Using DTas a weak classifier samples of generating unitswith different labels in the training set are used as inputs tothe AdaBoost algorithm for training -ereafter the un-known generating unit samples are identified -e specificsteps of the algorithm are as follows

Step 1 Initialize the weight distribution of the training dataBased on the obtained training set each generating unit

sample in the training set is assigned an identical weight inthe first iteration as shown in (17) -e weights of thegenerating unit samples are updated in each iteration

Table 1 Methods and indicators for identifying abuse of market power by generating units

Methods of abusingmarket power Indicator Quantitative characteristics of indicator

Collusion

Market share Large market shareKey supplier index Key supplier index lt1

Quotation curve correlation coefficient Large quotation curve correlation coefficientSimilarity in high quotation rates Similarity in the high quote ratio close to zero

Winning rate High winning rateClearing price escalation rate High clearing price escalation rate

Physical withholding

Market share Large market shareKey supplier index Key supplier index lt1

Failure rate High failure rateOut-of-merit capacity index Large out-of-merit capacity index

Bid winning rate Low bid winning rateClearing price escalation rate High clearing price escalation rate

Economic withholding

Market share Large market shareKey supplier index Key supplier index lt1High quotation rate Large high quotation rate

Out-of-merit capacity index Large out-of-merit capacityBid winning rate Low bid winning rate

Clearing price escalation rate High clearing price escalation rate

Extreme quotation

Market share Large market shareKey supplier index Key supplier index lt1

Weighted average quotation Excessively high or low weighted average quotationRelative level of quotations Relative level of quotations significantly different from zeroCapacity pricing index Excessively high or low capacity pricing index

Clearing price escalation rate High clearing price escalation rate

6 Mathematical Problems in Engineering

D(1) ω11ω12 ω1N1113864 1113865 (17)

where ω1i (1N) is the weight of the first generating unitsample i in the first iteration (i 1 2 N)

Step 2 Iterative training of weak classifiers

(1) Denote the number of iterations by k (k 1 2 K)Set the weight coefficient of each generating unitsample at the k-th iteration as D(k) ωk1 ωk2 ωkN to obtain the k-th weak classifier Gk(xi)

(2) Calculate the weighted classification error rate ek forthe weak classifier Gk(xi) on the training set Herethe weighted classification error rate represents thesum of the weights of all the generating unit samplesthat have been misclassified by the current classifier

ek P Gk xi( 1113857neyi( 1113857 1113944m

i1ωkiI Gk xi( 1113857neyi( 1113857 (18)

(3) Calculate the weight coefficient of the weak classifierGk(xi) It is combined with the weighted error rate ekto calculate the weight coefficient of the weak clas-sifier using (19) -e weighting coefficient indicatesthe importance of the weak classifier Gk(xi) in thefinal classifier -e smaller the error rate the largerthe weight coefficient [28] -e weight coefficient ofthe k-th weak classifier Gk(xi) is

αk 12log

1 minus ek

ek

(19)

(4) Update the weight distribution of the trainingdataset

D(k + 1) ωk+11ωk+12 ωk+1N1113966 1113967 (20)

where ωk+1i denotes the weight of the i-th generatingunit sample in the (K+ 1)-st iteration It is calculatedas follows

ωk+1i ωki

Zk

exp minus αkyiGk xi( 1113857( 1113857 (21)

where Zk is the normalization factor such thatD(k+ 1) is a probability distribution It is calculatedas

Zk 1113944m

i1ωki exp minus αkyiGk xi( 1113857( 1113857 (22)

From the above-stated equation the weight ofcorrectly classified generating unit samples is re-duced according to the k-th iteration of classificationwhereas the weight of misclassified generating unitsamples increases Misclassified generating unitsamples play a larger role in the next iteration [29]-is enables each generating unit sample to belearned completely through this process

(5) Repeat (1)ndash(4) in Step 2 to obtain a series of weakclassifiers and their corresponding weights

Step 3 Linear combination of weak classifiers using weightparameters

f(x) 1113944K

k1αkGk(x) (23)

-e continuous function f(x) is transformed into adiscrete function using the sign() function -us the finalidentification model is

Originaltraining set

(n units)

Training set 1after adjustingsample weight

Training set 2after adjustingsample weight

Training set nafter adjustingsample weight

Weak classifier 1

helliphellip

Weak classifier 2 Weak classifier 3 Weak classifier n + 1helliphellip

Train Train Train TrainVary the samplesweights based onthe misclassified

samples

Strong classifier

Weighted voting method

Vary the samplesweights based onthe misclassified

samples

Figure 1 AdaBoost algorithm flow

Mathematical Problems in Engineering 7

G(x) sign(f(x)) sign 1113944K

k1αkGk(x)⎛⎝ ⎞⎠ (24)

Use identification models to identify generating unitsthat abuse market power in the spot market

5 Analysis of Calculation Examples

-e data on the spot market of a region in 2005 (containinginformation on 170 generating units) are used to validate themethod proposed in this study for identifying the anomalousgenerating units in the spot market -e method is based onAdaBoost and DT techniques -e distribution of positiveand negative samples is shown in Figure 2 Among the 170generating units the number of units abusing market poweraccounts for a quarter including 14 collusive units 7physical holding units 9 economic holding units and 10extreme quotation units

51 Samples of Generating Units at Abuse Market PowerConsidering the indicators for identifying generating unitsthat abuse market power and the actual scenario of the spotmarket in a certain region and based on the relevant data ofgenerating units in the market the sample of generatingunits abusing market power and the sample set are con-structed A few samples of the generating units that abusemarket power are presented in Tables 2ndash5

52 Indicators forModel Evaluation In this study accuracyrecall and F-Measure are used to evaluate the model foridentifying generating units that abuse market power Ac-curacy represents the fraction of genuine positive samplesout of all the samples identified as positive recall is thefraction of all the positive samples that are identified aspositive and F-Measure is a composite index of accuracyand recall -e formulas for the three evaluation indexes areas follows

pre TP

TP + FP

rec TP

TP + FN

Fminus pre times rec times 2pre + rec

(25)

where pre denotes the accuracy of the recognitionmodel thehigher the accuracy the better the model being evaluatedrec denotes the recall of the recognition model the higherthe recall the better the model being evaluated F-denotesthe F-measure of the recognition model the closer it is toone the better is the model TP denotes a positive samplethat is correctly recognized FP denotes a negative samplethat is recognized as a positive sample and FN denotes apositive sample that is recognized as a negative sample

6 Results of Model Identification

Of the sample set of generating units that abuse marketpower obtained above 70 is used as the training set to trainthe recognition model -e remaining (30) is used as thevalidation set to verify the accuracy of the model recogni-tion -e accuracy of the classification is low when thenumber of iterations of the AdaBoost algorithm is relativelymarginal However when this number is excessively large itcauses overfitting-e validation accuracy increases with thenumber of iterations -e result is shown in Figure 2Meanwhile the time utilized for the iteration increases withthe number of iterations

Figure 3 shows that the accuracy of classification in-creases with the number of iterations However it is es-sentially stable when the number of iterations is higher than30 -us the number of iterations of the classifier can be setas 30 For the different methods by which generating unitscan abuse market power the results of the model evaluationindexes for the AdaBoost-DT identification model areshown in Figure 4

Collusive generating unitPhysically withheld generating unitEconomically withheld generating unitExtreme quotation generating unitNormal generating unit

14 79

10

130

Figure 2 Distribution of positive and negative samples

8 Mathematical Problems in Engineering

To validate the model this study compares the results ofidentification using DT SVM [14 30] and AdaBoost-SVMas shown in Figure 5

To better illustrate the relationship between the accu-racies of AdaBoost-DT and AdaBoost- SVM recognitionwith the number of iterations the assessment of the

Table 5 Samples of extreme quotation generating units

Generatingunit

Marketshare

Key supplierindex

Weighted averagequotation

Relative level ofquotations

Capacity pricingindex

Clearing price escalationrate ()

7 00960 09725 800 04652 5934839 5338 00555 09912 26889 -05075 870 268

Table 2 Samples of collusive generating units

Generatingunit

Marketshare

Key supplierindex

Quotation curve correlationcoefficient

Similarity in highquotation rates

Bid winning rate()

Clearing price escalationrate ()

1 00789 09816 05504 05281 7147 13172 00680 09880 05489 05245 5283 1250

Table 3 Samples of physically withheld generating units

Generatingunit

Marketshare

Key supplierindex

Failure rate()

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

3 00906 09733 523 19715 0 6304 00525 09913 676 121575 3833 427

Table 4 Samples of economically withheld generating units

Generatingunit

Marketshare

Key supplierindex

High quotationrate

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

5 00806 09756 05 1971477 0 5706 00625 09893 04 1084313 45 347

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

Figure 3 Relationship between recognition accuracy and number of iterations

Mathematical Problems in Engineering 9

0 1 2 3 4090

092

094

096

098

100

Type of generating units

PreRecF-

Figure 4 Results of the evaluation indicators of the AdaBoost-DT model

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(a)

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(b)

0 1 2 3 4

086

088

090

092

094

096

098

100

Type of generating units

PreRecF-

(c)

Figure 5 Results of the evaluation indicators

10 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

D(1) ω11ω12 ω1N1113864 1113865 (17)

where ω1i (1N) is the weight of the first generating unitsample i in the first iteration (i 1 2 N)

Step 2 Iterative training of weak classifiers

(1) Denote the number of iterations by k (k 1 2 K)Set the weight coefficient of each generating unitsample at the k-th iteration as D(k) ωk1 ωk2 ωkN to obtain the k-th weak classifier Gk(xi)

(2) Calculate the weighted classification error rate ek forthe weak classifier Gk(xi) on the training set Herethe weighted classification error rate represents thesum of the weights of all the generating unit samplesthat have been misclassified by the current classifier

ek P Gk xi( 1113857neyi( 1113857 1113944m

i1ωkiI Gk xi( 1113857neyi( 1113857 (18)

(3) Calculate the weight coefficient of the weak classifierGk(xi) It is combined with the weighted error rate ekto calculate the weight coefficient of the weak clas-sifier using (19) -e weighting coefficient indicatesthe importance of the weak classifier Gk(xi) in thefinal classifier -e smaller the error rate the largerthe weight coefficient [28] -e weight coefficient ofthe k-th weak classifier Gk(xi) is

αk 12log

1 minus ek

ek

(19)

(4) Update the weight distribution of the trainingdataset

D(k + 1) ωk+11ωk+12 ωk+1N1113966 1113967 (20)

where ωk+1i denotes the weight of the i-th generatingunit sample in the (K+ 1)-st iteration It is calculatedas follows

ωk+1i ωki

Zk

exp minus αkyiGk xi( 1113857( 1113857 (21)

where Zk is the normalization factor such thatD(k+ 1) is a probability distribution It is calculatedas

Zk 1113944m

i1ωki exp minus αkyiGk xi( 1113857( 1113857 (22)

From the above-stated equation the weight ofcorrectly classified generating unit samples is re-duced according to the k-th iteration of classificationwhereas the weight of misclassified generating unitsamples increases Misclassified generating unitsamples play a larger role in the next iteration [29]-is enables each generating unit sample to belearned completely through this process

(5) Repeat (1)ndash(4) in Step 2 to obtain a series of weakclassifiers and their corresponding weights

Step 3 Linear combination of weak classifiers using weightparameters

f(x) 1113944K

k1αkGk(x) (23)

-e continuous function f(x) is transformed into adiscrete function using the sign() function -us the finalidentification model is

Originaltraining set

(n units)

Training set 1after adjustingsample weight

Training set 2after adjustingsample weight

Training set nafter adjustingsample weight

Weak classifier 1

helliphellip

Weak classifier 2 Weak classifier 3 Weak classifier n + 1helliphellip

Train Train Train TrainVary the samplesweights based onthe misclassified

samples

Strong classifier

Weighted voting method

Vary the samplesweights based onthe misclassified

samples

Figure 1 AdaBoost algorithm flow

Mathematical Problems in Engineering 7

G(x) sign(f(x)) sign 1113944K

k1αkGk(x)⎛⎝ ⎞⎠ (24)

Use identification models to identify generating unitsthat abuse market power in the spot market

5 Analysis of Calculation Examples

-e data on the spot market of a region in 2005 (containinginformation on 170 generating units) are used to validate themethod proposed in this study for identifying the anomalousgenerating units in the spot market -e method is based onAdaBoost and DT techniques -e distribution of positiveand negative samples is shown in Figure 2 Among the 170generating units the number of units abusing market poweraccounts for a quarter including 14 collusive units 7physical holding units 9 economic holding units and 10extreme quotation units

51 Samples of Generating Units at Abuse Market PowerConsidering the indicators for identifying generating unitsthat abuse market power and the actual scenario of the spotmarket in a certain region and based on the relevant data ofgenerating units in the market the sample of generatingunits abusing market power and the sample set are con-structed A few samples of the generating units that abusemarket power are presented in Tables 2ndash5

52 Indicators forModel Evaluation In this study accuracyrecall and F-Measure are used to evaluate the model foridentifying generating units that abuse market power Ac-curacy represents the fraction of genuine positive samplesout of all the samples identified as positive recall is thefraction of all the positive samples that are identified aspositive and F-Measure is a composite index of accuracyand recall -e formulas for the three evaluation indexes areas follows

pre TP

TP + FP

rec TP

TP + FN

Fminus pre times rec times 2pre + rec

(25)

where pre denotes the accuracy of the recognitionmodel thehigher the accuracy the better the model being evaluatedrec denotes the recall of the recognition model the higherthe recall the better the model being evaluated F-denotesthe F-measure of the recognition model the closer it is toone the better is the model TP denotes a positive samplethat is correctly recognized FP denotes a negative samplethat is recognized as a positive sample and FN denotes apositive sample that is recognized as a negative sample

6 Results of Model Identification

Of the sample set of generating units that abuse marketpower obtained above 70 is used as the training set to trainthe recognition model -e remaining (30) is used as thevalidation set to verify the accuracy of the model recogni-tion -e accuracy of the classification is low when thenumber of iterations of the AdaBoost algorithm is relativelymarginal However when this number is excessively large itcauses overfitting-e validation accuracy increases with thenumber of iterations -e result is shown in Figure 2Meanwhile the time utilized for the iteration increases withthe number of iterations

Figure 3 shows that the accuracy of classification in-creases with the number of iterations However it is es-sentially stable when the number of iterations is higher than30 -us the number of iterations of the classifier can be setas 30 For the different methods by which generating unitscan abuse market power the results of the model evaluationindexes for the AdaBoost-DT identification model areshown in Figure 4

Collusive generating unitPhysically withheld generating unitEconomically withheld generating unitExtreme quotation generating unitNormal generating unit

14 79

10

130

Figure 2 Distribution of positive and negative samples

8 Mathematical Problems in Engineering

To validate the model this study compares the results ofidentification using DT SVM [14 30] and AdaBoost-SVMas shown in Figure 5

To better illustrate the relationship between the accu-racies of AdaBoost-DT and AdaBoost- SVM recognitionwith the number of iterations the assessment of the

Table 5 Samples of extreme quotation generating units

Generatingunit

Marketshare

Key supplierindex

Weighted averagequotation

Relative level ofquotations

Capacity pricingindex

Clearing price escalationrate ()

7 00960 09725 800 04652 5934839 5338 00555 09912 26889 -05075 870 268

Table 2 Samples of collusive generating units

Generatingunit

Marketshare

Key supplierindex

Quotation curve correlationcoefficient

Similarity in highquotation rates

Bid winning rate()

Clearing price escalationrate ()

1 00789 09816 05504 05281 7147 13172 00680 09880 05489 05245 5283 1250

Table 3 Samples of physically withheld generating units

Generatingunit

Marketshare

Key supplierindex

Failure rate()

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

3 00906 09733 523 19715 0 6304 00525 09913 676 121575 3833 427

Table 4 Samples of economically withheld generating units

Generatingunit

Marketshare

Key supplierindex

High quotationrate

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

5 00806 09756 05 1971477 0 5706 00625 09893 04 1084313 45 347

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

Figure 3 Relationship between recognition accuracy and number of iterations

Mathematical Problems in Engineering 9

0 1 2 3 4090

092

094

096

098

100

Type of generating units

PreRecF-

Figure 4 Results of the evaluation indicators of the AdaBoost-DT model

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(a)

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(b)

0 1 2 3 4

086

088

090

092

094

096

098

100

Type of generating units

PreRecF-

(c)

Figure 5 Results of the evaluation indicators

10 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

G(x) sign(f(x)) sign 1113944K

k1αkGk(x)⎛⎝ ⎞⎠ (24)

Use identification models to identify generating unitsthat abuse market power in the spot market

5 Analysis of Calculation Examples

-e data on the spot market of a region in 2005 (containinginformation on 170 generating units) are used to validate themethod proposed in this study for identifying the anomalousgenerating units in the spot market -e method is based onAdaBoost and DT techniques -e distribution of positiveand negative samples is shown in Figure 2 Among the 170generating units the number of units abusing market poweraccounts for a quarter including 14 collusive units 7physical holding units 9 economic holding units and 10extreme quotation units

51 Samples of Generating Units at Abuse Market PowerConsidering the indicators for identifying generating unitsthat abuse market power and the actual scenario of the spotmarket in a certain region and based on the relevant data ofgenerating units in the market the sample of generatingunits abusing market power and the sample set are con-structed A few samples of the generating units that abusemarket power are presented in Tables 2ndash5

52 Indicators forModel Evaluation In this study accuracyrecall and F-Measure are used to evaluate the model foridentifying generating units that abuse market power Ac-curacy represents the fraction of genuine positive samplesout of all the samples identified as positive recall is thefraction of all the positive samples that are identified aspositive and F-Measure is a composite index of accuracyand recall -e formulas for the three evaluation indexes areas follows

pre TP

TP + FP

rec TP

TP + FN

Fminus pre times rec times 2pre + rec

(25)

where pre denotes the accuracy of the recognitionmodel thehigher the accuracy the better the model being evaluatedrec denotes the recall of the recognition model the higherthe recall the better the model being evaluated F-denotesthe F-measure of the recognition model the closer it is toone the better is the model TP denotes a positive samplethat is correctly recognized FP denotes a negative samplethat is recognized as a positive sample and FN denotes apositive sample that is recognized as a negative sample

6 Results of Model Identification

Of the sample set of generating units that abuse marketpower obtained above 70 is used as the training set to trainthe recognition model -e remaining (30) is used as thevalidation set to verify the accuracy of the model recogni-tion -e accuracy of the classification is low when thenumber of iterations of the AdaBoost algorithm is relativelymarginal However when this number is excessively large itcauses overfitting-e validation accuracy increases with thenumber of iterations -e result is shown in Figure 2Meanwhile the time utilized for the iteration increases withthe number of iterations

Figure 3 shows that the accuracy of classification in-creases with the number of iterations However it is es-sentially stable when the number of iterations is higher than30 -us the number of iterations of the classifier can be setas 30 For the different methods by which generating unitscan abuse market power the results of the model evaluationindexes for the AdaBoost-DT identification model areshown in Figure 4

Collusive generating unitPhysically withheld generating unitEconomically withheld generating unitExtreme quotation generating unitNormal generating unit

14 79

10

130

Figure 2 Distribution of positive and negative samples

8 Mathematical Problems in Engineering

To validate the model this study compares the results ofidentification using DT SVM [14 30] and AdaBoost-SVMas shown in Figure 5

To better illustrate the relationship between the accu-racies of AdaBoost-DT and AdaBoost- SVM recognitionwith the number of iterations the assessment of the

Table 5 Samples of extreme quotation generating units

Generatingunit

Marketshare

Key supplierindex

Weighted averagequotation

Relative level ofquotations

Capacity pricingindex

Clearing price escalationrate ()

7 00960 09725 800 04652 5934839 5338 00555 09912 26889 -05075 870 268

Table 2 Samples of collusive generating units

Generatingunit

Marketshare

Key supplierindex

Quotation curve correlationcoefficient

Similarity in highquotation rates

Bid winning rate()

Clearing price escalationrate ()

1 00789 09816 05504 05281 7147 13172 00680 09880 05489 05245 5283 1250

Table 3 Samples of physically withheld generating units

Generatingunit

Marketshare

Key supplierindex

Failure rate()

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

3 00906 09733 523 19715 0 6304 00525 09913 676 121575 3833 427

Table 4 Samples of economically withheld generating units

Generatingunit

Marketshare

Key supplierindex

High quotationrate

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

5 00806 09756 05 1971477 0 5706 00625 09893 04 1084313 45 347

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

Figure 3 Relationship between recognition accuracy and number of iterations

Mathematical Problems in Engineering 9

0 1 2 3 4090

092

094

096

098

100

Type of generating units

PreRecF-

Figure 4 Results of the evaluation indicators of the AdaBoost-DT model

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(a)

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(b)

0 1 2 3 4

086

088

090

092

094

096

098

100

Type of generating units

PreRecF-

(c)

Figure 5 Results of the evaluation indicators

10 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

To validate the model this study compares the results ofidentification using DT SVM [14 30] and AdaBoost-SVMas shown in Figure 5

To better illustrate the relationship between the accu-racies of AdaBoost-DT and AdaBoost- SVM recognitionwith the number of iterations the assessment of the

Table 5 Samples of extreme quotation generating units

Generatingunit

Marketshare

Key supplierindex

Weighted averagequotation

Relative level ofquotations

Capacity pricingindex

Clearing price escalationrate ()

7 00960 09725 800 04652 5934839 5338 00555 09912 26889 -05075 870 268

Table 2 Samples of collusive generating units

Generatingunit

Marketshare

Key supplierindex

Quotation curve correlationcoefficient

Similarity in highquotation rates

Bid winning rate()

Clearing price escalationrate ()

1 00789 09816 05504 05281 7147 13172 00680 09880 05489 05245 5283 1250

Table 3 Samples of physically withheld generating units

Generatingunit

Marketshare

Key supplierindex

Failure rate()

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

3 00906 09733 523 19715 0 6304 00525 09913 676 121575 3833 427

Table 4 Samples of economically withheld generating units

Generatingunit

Marketshare

Key supplierindex

High quotationrate

Out-of-merit capacityindex

Bid winning rate()

Clearing price escalationrate ()

5 00806 09756 05 1971477 0 5706 00625 09893 04 1084313 45 347

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

Figure 3 Relationship between recognition accuracy and number of iterations

Mathematical Problems in Engineering 9

0 1 2 3 4090

092

094

096

098

100

Type of generating units

PreRecF-

Figure 4 Results of the evaluation indicators of the AdaBoost-DT model

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(a)

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(b)

0 1 2 3 4

086

088

090

092

094

096

098

100

Type of generating units

PreRecF-

(c)

Figure 5 Results of the evaluation indicators

10 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

0 1 2 3 4090

092

094

096

098

100

Type of generating units

PreRecF-

Figure 4 Results of the evaluation indicators of the AdaBoost-DT model

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(a)

0 1 2 3 4

08

10

Type of generating units

PreRecF-

(b)

0 1 2 3 4

086

088

090

092

094

096

098

100

Type of generating units

PreRecF-

(c)

Figure 5 Results of the evaluation indicators

10 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

recognition results is simplified here -e accuracy of rec-ognition is the mean of the accuracies of the five sets (0 1 23 and 4) Figure 6 shows a comparison of the two modelsbased on the relationship between the recognition accuracyand the number of iterations while Figure 7 shows acomparison based on the relationship between the iterationtime and the number of iterations

Figure 6 shows that the accuracy of identification byAdaBoost-SVM is higher when the number of iterations isless than 10 Furthermore the accuracy of identification byAdaBoost-DT is significantly higher than that for AdaBoost-SVM when the number of iterations is larger than 10Meanwhile it is apparent from Figure 7 that AdaBoost-DTiterates faster In Figures 4 and 5 the pre rec and F-resultsfor each of the five generating units derived from the

different models are averaged to obtain the results of theevaluation indexes of the different models -e specificresults are shown in Table 6

-e experiment results demonstrate that the recognitioneffect of the SVM model is marginally higher than that of theDT model when the AdaBoost algorithm is not used forintegration learning When it is used for integration learningthe recognition accuracy of the AdaBoost-DT model im-proves from 076 to 097 relative to the single DTmodel andthe recognition effect significantly improves Compared withthe single SVM model the recognition accuracy of theAdaBoost-SVM model improves from 082 to 093 -erecognition effect is also improved Furthermore the rec-ognition accuracy of the AdaBoost-DTmodel is higher thanthat of AdaBoost-SVM which indicates the effectiveness ofthe former for identifying groups that abuse market power

7 Conclusion

-is study analyzes the four methods market power abuse bygenerating units based on the actual scenario in the spotmarket constructs identification indexes of market powerabuse by generating units based on three dimensions(market structure behavior and performance) and de-velops an AdaBoost-DT identification model by con-structing samples of generating units that abuse marketpower and sample sets for model training according to thedata characteristics of generating units of the spot market-e conclusions are as follows

(1) -is study makes use of the advantage of the Ada-Boost-DT algorithm in unbalanced sample identifi-cation -e AdaBoost-DT algorithm displays a highidentification accuracy of generating units fromunbalanced positive and negative samples in the spotmarket Additionally it is fast and robust that is itcan rapidly and effectively identify the generatingunits that abuse market power

(2) -is study compares the AdaBoost-DT algorithmwith the DTalgorithm as well as the AdaBoost-SVMalgorithm and the SVM algorithm-e identificationaccuracies of the DT and SVM algorithms are not ashigh as those of the AdaBoost-DT and AdaBoost-SVM algorithms Notably when the number of it-erations is small the AdaBoost-SVM algorithm has ahigher accuracy but with an increase in the numberof iterations the AdaBoost-DT algorithm shows abetter performance

(3) With the increase of iterations of the AdaBoost al-gorithm the recognition accuracy of abusing marketpower units becomes increasingly higher but the

0 10 20 30 40 50

082

084

086

088

090

092

094

096

098

100

Acc

urac

y

Number of iterations

AdaBoost-DTAdaBoost-SVM

Figure 6 Recognition accuracy vs number of iterations forAdaBoost-DT and AdaBoost-SVM

AdaBoost-DTAdaBoost-SVM

0 10 20 30 40 50

0

100

200

300

400

Tim

e (m

s)

Number of iterations

Figure 7 Iteration time vs number of iterations for AdaBoost-DTand AdaBoost-SVM

Table 6 Comparison of identification results of different classifiers

Pre Rec F-DT 082 081 0815SVM 086 084 085AdaBoost-DT 097 095 096AdaBoost-SVM 093 092 093

Mathematical Problems in Engineering 11

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

recognition time also lengthens -erefore consid-ering the recognition accuracy and recognition timean appropriate number of iterations is selected

Data Availability

-e data used to support the findings of this study weresupplied by Guangdong Power Exchange Center underlicense and so cannot be made freely available Requests foraccess to these data should be made to Yuting Xie(597862406qqcom)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was supported by the Science and TechnologyProject Assistance of China Southern Power Grid Corpo-ration (Project No GDKJXM20200211)

References

[1] CPC Central Committee and State Council Some Opinions onFurther Deepening Power System Reform (ZF [2015] No 9)CPC Central Committee and State Council Beijing China2018

[2] Z Wu C Kang Q Xia et al ldquoBidding strategy of powersuppliers based on game theoryrdquo Power System Automationvol 26 no 9 pp 7ndash11 2002

[3] Y Xue T Li X Yin et al ldquoResearch framework of generalizedcongestion and market powerrdquo Power System Automationvol 34 no 21 pp 1ndash10 2010

[4] M Yan Z Gong Y Yang et al ldquoDesign of market operationmonitoring mechanism under Yunnan electric power spotmarket environmentrdquo China Southern Power Grid Technol-ogy vol 12 no 12 pp 16ndash22 2018

[5] Q Chen J Yang Y Huang et al ldquoOverview of market powermonitoring and mitigation mechanism in foreign powermarketsrdquo China Southern Power Grid Technology vol 12no 12 pp 9ndash15 2018

[6] C Li Q Xia and Z Hu ldquoEvaluation method of power plantmarket power based on effective competitionrdquo Power GridTechnology vol 30 no 10 pp 75ndash80 2006

[7] D Liu R Li X Chen et al ldquoPower market supervision indexand market evaluation systemrdquo Power System Automationvol 2004 no 9 pp 16ndash21 2004

[8] Z Zhao S Yuan Q Nie et al ldquoContinuous reinforcementalgorithm and robust economic dispatching-based spotelectricity market modeling considering strategic behaviors ofwind power producers and other participantsrdquo Journal ofElectrical and Computer Engineering vol 2019 Article ID9406072 16 pages 2019

[9] C Wu and J Sun ldquoAnalysis method of potential marketpower in electricity market under convex hull pricing moderdquoPower System Automation vol 45 no 6 pp 101ndash108 2021

[10] Y Dai Y Gao Y Gao H Gao H Zhu and L Li ldquoA real-timepricing scheme considering load uncertainty and pricecompetition in smart grid marketrdquo Journal of Industrial ampManagement Optimization vol 16 no 2 pp 777ndash793 2020

[11] Y Dai Y Qi Li Lu et al ldquoA dynamic pricing scheme forelectric vehicle in photovoltaic charging station based onStackelberg game considering user satisfactionrdquo Computers ampIndustrial Engineering vol 154 no 10 Article ID 1071172021

[12] B Sun R Deng J Xie et al ldquoIdentification of cartel type unitcollusion bidding based on ordered multivariate logit modelrdquoPower System Automation vol 45 no 6 pp 109ndash115 2021

[13] D Liu Q Zhang X Li et al ldquoIdentification of potentialhazardous behaviors in power market based on cloud modeland fuzzy Petri netrdquo Power System Automation vol 43 no 2pp 25ndash37 2019

[14] H Xu Z Cheng H Zhang et al ldquoIdentification of marketpower abuse violations by power generation enterprises basedon improved support vector machinerdquo Journal of North ChinaElectric Power University (Natural Tural Science Editionvol 47 no 04 pp 86ndash95 2020

[15] C Li K Liu X Xiao et al ldquoPower quality composite dis-turbance classification based on conditional mutual infor-mation feature selection method and AdaBoost algorithmrdquoHigh Voltage Technology vol 45 no 2 pp 579ndash585 2019

[16] K Chen W Xiaoguang J Chen et al ldquoSmall currentgrounding fault line selection based on sample data pro-cessing and AdaBoostrdquo Chinese Journal of Electrical Engi-neering vol 34 no 34 pp 6228ndash6237 2014

[17] L Yao W Zheng Y Qian et al ldquoPartial discharge com-prehensive feature decision tree recognition method based onAdaBoostrdquo Power System Protection and Control vol 39no 21 pp 104ndash114 2011

[18] X Zhang Z Liang J Zhang et al ldquoApplication of Adatreealgorithm in remote sensing image classificationrdquo Journal ofWuhan University (Information Science Edition) vol 38no 12 pp 1460ndash1464 2013

[19] M Zhao E Chen and R Song ldquoAdaBoost evolutionarydecision tree algorithm based on Ensemble LearningrdquoComputer Applications and Software vol 2007 no 3 pp 1ndash212007

[20] J Lin Y Ni and F Wu ldquoReview of market power in powermarketrdquo Power Grid Technology vol 2002 no 11 pp 70ndash762002

[21] Q Yan C Qin M Nie et al ldquoForecasting the electricitydemand and market shares in retail electricity market basedon system dynamics and Markov chainrdquo MathematicalProblems in Engineering vol 2018 Article ID 467185011 pages 2018

[22] H Zhou F Zhang and Z Han ldquoResearch on economicpersistence in power marketrdquo Power System Automationvol 2005 no 8 pp 16ndash20 2005

[23] L Liu H Gao Y Wang et al ldquoRobust optimizationmodel forphotovoltaic power producerrsquos bidding decision-making inelectricity marketrdquo Mathematical Problems in Engineeringvol 2020 Article ID 6109648 8 pages 2020

[24] J Xie C Lu S Lu et al ldquoRisk assessment of power marketbased on ordinal relation entropy weight methodrdquo ChinaPower vol 1 no 12 2021

[25] J Chen H Zhou Z Han et al ldquoApplication of volume priceindex to power supplier quotation analysisrdquo Journal ofZhejiang University (Engineering Edition) vol 2005 no 6pp 915ndash920 2005

[26] S Wu and H Nagahashi ldquoParameterized AdaBoost intro-ducing a parameter to speed up the training of real AdaBoostrdquoIEEE Signal Processing Letters vol 21 no 6 pp 687ndash6912014

12 Mathematical Problems in Engineering

[27] P-B Zhang and Z-X Yang ldquoA novel AdaBoost frameworkwith robust threshold and structural optimizationrdquo IEEETransactions on Cybernetics vol 48 no 1 pp 64ndash76 2018

[28] W Hu J Gao Y Wang O Wu and S Maybank ldquoOnlineadaboost-based parameterized methods for dynamic dis-tributed network intrusion detectionrdquo IEEE Transactions onCybernetics vol 44 no 1 pp 66ndash82 2014

[29] F Xiao Y Wang L He H Wang W Li and Z Liu ldquoMotionestimation from surface electromyogram using adaboost re-gression and average feature valuesrdquo IEEE Access vol 7pp 13121ndash13134 2019

[30] Y Dai and P Zhao ldquoA hybrid load forecasting model basedon support vector machine with intelligent methods forfeature selection and parameter optimizationrdquo Applied En-ergy vol 279 no 1 Article ID 115332 2020

Mathematical Problems in Engineering 13