Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2013 Article ID 872624 7 pageshttpdxdoiorg1011552013872624
Research ArticleOptimization and Coordination of HAFDV PINN Control byImproved PSO
Bin Huang Nengling Tai and Wentao Huang
School of Electronic Information and Electrical Engineering Shanghai Jiao Tong University Shanghai 200240 China
Correspondence should be addressed to Bin Huang hbsjtugmailcom
Received 8 June 2012 Accepted 25 January 2013
Academic Editor Pierluigi Siano
Copyright copy 2013 Bin Huang et al This 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
The new hybrid active filter (HAF) is composed of the larger-capacity passive filter banks and the smaller-capacity active filter It isdifficult to tune the parameters of a PI controller using the DC capacitor voltage control In this paper the improved particle swarmoptimization (improved PSO) algorithm is proposed to solve the coordinated design problem and the neural network weights asthe particle swarm optimization are adopted to optimize the system parameters Comparing with the conventional PI controllerthe results of PINN controller prove the effectiveness of designed method on both the transient and steady-state performance ofthe hybrid active filter DC bus voltage (HAFDV) controllers
1 Introduction
Microgrid an entity of various distributed energy resources(DERs) with different characteristics and mutual comple-mentation can operate in phase withmacrogrid and improveenergy utilization efficiency and electricity supply reliabilityDue to the applications of nonlinear elements the harmonicinterference on the micronetwork is growing In order toensure the safety of the macrogrid we use the hybrid activefilter to remove the harmonics of the micronetwork
Hybrid active filter which has dynamic better compen-sation characteristics and a greater compensation capacity isused to suppress harmonics and reactive power compensa-tion of the macrogrid Reference [1] studied the capacitanceand voltage of the active filter it is not suitable for alarger-capacity macrogrid References [2ndash4] designed the PIcontroller of the DC bus voltage without optimizing the con-trollers Therefore improved PSO optimizes the parametersof HPF controller using PI neural network instead of theconventional PI The time-domain results demonstrate theeffectiveness of the proposed design method of the HAF DCbus voltage controllers
2 Problem Formulations
In this section the mathematical model of HPF is presentedin detail and then the HAFDV controllers will be consideredas an example to verify the effects of this method
21 Modeling of HAF The structure of the proposed hybridactive power filter (HAPF) is shown in Figure 1 It is com-posed of a smaller-scale three-phase voltage source inverter(VSI) employing pulse-width modulation (PWM) with alarge capacitor at the DC side and an output filter to eliminatethe high-frequency ripples at the output side A couplingtransformer connects VSI in series with a group of passivepower filters And all of them are connected in shunt withMicrogrid
22 Formulations of the HAF DC Bus Voltage ControllersThe main objective of the control scheme is to force all theharmonics of load current to flow into passive filter [5ndash8] Ahysteresis current controller is used to switch the bridge armof the active filter [9ndash11]
2 Journal of Control Science and Engineering
AC
Active filterOutput filter
Coupling transformer
PF
119885119904
+
minus
Microgrid119868119904
119880dc
Figure 1 Configuration of the hybrid active power filter
The control scheme is indicated in Figure 2 It builds thereference currents for the HAF based on the instantaneousactive and reactive power theory The synchronous referenceframe (SRF) theory is used to extract the fundamentalcomponent of the source current by transformation of thesupply currents (119894
119906119894119907119894119908) into the reference frameThe system
under study is a three-wire system where the zero sequencemay be neglectedThe following are basic equations for thesetransformations
[119894119901
119894119902
] = radic2
3[sin120596119905 minus cos120596119905
minus cos120596119905 minus sin120596119905]
times[[[
[
1 minus1
2minus1
2
0radic3
2minusradic3
2
]]]
]
[
[
119894119906
119894119907
119894119908
]
]
(1)
where the two-phase sinusoidal signals sin120596119905 and cos120596119905 areresulted from the phase-locked loop (PLL) circuit
The lowpass filter is used to extract the DC componentsrealized by moving average to 80Hz The extracted DCcomponents are transformed back into a-b-c coordinates toobtain the fundamental components (119894
119906119891119894119907119891119894119908119891) of source
currents as shown in
[119894119901119895
119894119902119895
] = [sin120596119905 minus cos120596119905
minus cos120596119905 minus sin120596119905] [
119894119901
119894119902
]
[
[
119894119906119891
119894119907119891
119894119908119891
]
]
= radic2
3
[[[[[[[
[
1 0
minus1
2
radic3
2
minus1
2minusradic3
2
]]]]]]]
]
[119894119901119895
119894119902119895
]
(2)
So each current harmonic component (119894119906ℎ119894119907ℎ119894119908ℎ) is given
by
[
[
119894119906ℎ
119894119907ℎ
119894119908ℎ
]
]
= [
[
119894119906
119894119907
119894119908
]
]
minus [
[
119894119906119891
119894119907119891
119894119908119891
]
]
(3)
The source current is controlled to follow this referencecurrent by switching the voltage source inverter with ahysteresis current controller
23 The Objective Function Conventional PI controller isused to maintain the DC bus voltage of the HAF by compen-sating the voltage losses [12ndash14] Conventional PI controllerparameters are often obtained by several experiments It isdifficult to adjust all the parameters This paper designs PIneural network controller combined with improved PSOThe interlayer and output layer linking weights of PI neuralnetwork (PINN) are used as the optical parameters of PSO
According to the formulae (1)ndash(3) A-phase fundamentalcurrent increment values are obtained bys
Δ119894119886= radic
2
3sin120596119905 sdot Δ119894pf (4)
where Δ119894pf is the increment of the grid active currentcomponent
So the exchange active power with HAF and supplysystem is calculated as
119875119891
= radic3119864119886sdot Δ119894119886
int
Δ119905
0
119875119891119889119905 =
119862dc [(119880dc + Δ119880119862dc
)2
minus 119880dc2
]
2
+ int
Δ119905
0
119870119894ca119889119905
(5)
where119864119886is A-phase line voltageRMS119862dc is a capacitor value
119880dc is the ideal steady-state value of the HAF DC voltageΔ119880119862dc
is the increment of capacitor voltage during Δ119905 119870 isa constant with switching characteristics of capacitor and the119894ca is RMS in A-phase of 119894
119888
According to the formulae (4)-(5) with neglecting theitem (Δ119880
119862dc)2 and linearization near the operating point after
Laplace transform the PI regulator 119866pi(119904) controlled object119866119907(119904) and voltage detection 119866
119891(119904) are given by
119866pi (119904) =
119870119901(119879119894+ 1)
119879119894119904
119866119907(119904) =
119870119894119864119886
119862dc119880dc119904
119866119891(119904) =
119870119891
119879119891119904 + 1
(6)
where 119870119875is a proportional coefficient 119879
119894is an integral
constantFigure 3 shows the system transfer function it is
expressed as
119866 (119904) =
119866pi (119904) 119866119907 (119904)
1 + 119866pi (119904) 119866119907 (119904) 119866119891 (119904) (7)
The disadvantage of conventional PI controller lies inthe difficulty to resolve the trade-off among smoothness
Journal of Control Science and Engineering 3
LPF
Three
TwoThree
Two
transform inversetransform
PI
PLL
119894119906
119894119907
119894119908
119894119886
119894119887
D-q D-q
119894119889
119894119902
119906119907
119894119901119891
119894119902119891
+
+
minus
minusΔ
119889
119902119889
119902
119894119901119895
119894119902119895
119894119906119891
119894119907119891
119894119908119891
minus
minus
minus +
+
+119894119906ℎ
119894119907ℎ
119894119908ℎ
sin 120596119905 and cos 120596119905generators
minus1
lowast
119880dc
119880dc119880dc
Figure 2 The control scheme of HAF
PINN
Δ119880
minus119866119901119894(119904) 119866119907(119904)
119866119891(119904)
119880lowastdc119880dc
Figure 3 System transfer function
Controlled object
119879PINN
119870PINN
119903
119910
119910
1199061 1199091
1199062 1199092
11987111
11987112
11987121
11987122
119907119906998400998400 119909998400998400
11990619984001199091
998400
11990629984001199092
998400
1198711998400
1198712998400
Figure 4 The structure of PINN
fastness and accuracyThemajor parameters of the HAF DCbus voltage controller require experiments and high skills insystem debugging process and will be fixed eventually
A PINN controller shown in the dotted line in Figure 3is adopted as the DC bus voltage controller instead of theconventional PI controller so the system transfer function ismodified into
119866 (119904) =
PINN (119878)119870119894119864119886119879119891119904 + PINN (119878)119870
119894119864119886
119862dc119880dc1198791198911199042 + 119862dc119880dc + PINN (119878)119870
119894119864119886119870119891
(8)
Initial improved PSO and PINN parameters
Generate position and velocity and calculate adaptive value
Start
Evaluate the fitness and calculate the new adaptive value
Update position and velocity
Yes
Get the PINN structure
No
PINN-BP learning and predicting
Find the local optimum position 119875119894119889 andglobe optimum position 119892119894119889
Achieving condition
Figure 5 The flow chart of improved PSO
The improved PSO algorithm is applied to the optimiza-tion of PINN parameters An objective optimization problemcan be defined as follows
119883PINN = NN(119870PINN 119879PINN)119883PINN are neural networkvectors representing the decision variables 119891
119899(119883PINN) is
4 Journal of Control Science and Engineering
G G
M M
G
GM M
G G
M M
G G
M M
M M M M M M M M
Gen Gen GenG
Gen Gen Gen Gen Gen
Motor Motor Motor Motor Motor Motor MotorMotor
MotorMotorMotorMotorMotorMotorMotorMotor
Transformer Transformer
11 kV 11 kV 11 kV 11 kVMV1 MV2 MV3 MV4
400 V LV1 400 V LV2 400 V LV3 400 V LV4
400 V ESB1
Emergency gen
Figure 6 Microgrid system single line figure
15
1
05
0
minus05
minus1
minus150 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level
6
5
4
3
2
1
0
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level
Figure 7 The current and spectrum of one phase at the 11 kV level
the objective function 119892119895(119870PINN) and ℎ
119896(119879PINN) represent
the constraints
3 Improved PSO
Particle swarm optimization inspired by the social behaviorof a bird flock was originally designed by Kennedy andEberhart in 1995 The original idea is to simulate the birdsrsquofood-hunting for the global optimal point One particlepresents a bird and it can calculate the adaptive value of itscurrent position and every particle records the optimal valuesearched by itself [15 16]
The particles have their memory and each particle keepstracking of its local best position (119901id) and its correspondingfitness The particle with the greatest fitness is called theglobal best position (119892id) of the swarm The basic PSO
algorithm has many defects such as falling into local opti-mum and being impacted by the fact that it is insensitiveto environment variables precocious and so on The paperadopted improved PSO which has multigroup particles tosearch different parts of the solution space When 119901id and119892id are obtained a particle updates its velocity and positionbased on (9) In the end the algorithm will check the resultsuntil the best solution is found or termination conditions aresatisfied
119907119896+1
id = 120582 times 119907119896
id + 1205731times random () times (119901
119896
id minus 119909119896
id)
+ 1205732times random () times (119892
119896
id minus 119909119896
id)
119909119896+1
id = 119909119896
id + 119907119896+1
id
(9)
where 1205731 1205732
ge 0 120582 is the inertia weight factor 1205731and 120573
2
are acceleration constants random() is a random number
Journal of Control Science and Engineering 5
1
08
06
04
02
020 40 60 80 100 120 140 160 180 200
Simple (119899)
119910(119905)
PINN
Figure 8 Improved PSO optimizes PINN
700600500400300200100
0
119890(119905)
0 5 10 15 20 25 30 35 40 45 50Step (119899)
Figure 9 Convergence curve of adaptive value
between 0 and 1 119907id and 119909id are the velocity and the currentposition of particle at iteration id
The improved PSO algorithmoptimizes PINNcontrollerswhich is defined as proportional integral function of neu-rons PINN is a dynamic multilayer feed forward neural net-work The parameters of PINN (119870PINN119879PINN) are optimizedby improved PSO
Neural network of PINN applies 2 times 2 times 1 structureshown in Figure 4 The input layer of the PINN has twoneurons of proportion The two neurons (119870PINN119879PINN) inthemiddle layer are proportional and integral elements of theinput signal and the weights from input layer to the middlelayer are remained of constant value (minus1 +1) In order tominimize the objective function value the mean square error(MSE) function has been employed in (10) The improvedPSO adjusts the network weights by the back-propagation(BP) algorithm [17] The flow chart of the improved PSO isshown in Figure 5 Consider the following
119869 =1
119898
119899
sum
ℎ=1
[119903 (119896) minus 119910 (119896)]2
(10)
The improved PSO shows many advantages Firstly itinitializes the improved PSO and PINN parameters whichcontain the initial particles their positions and velocities Foreach particle it evaluates the fitness function [18] Secondly itgenerates position and velocity and calculates adaptive valueconsidering the steady error and setting time It calculatesthe value of every particle in all subgroups Besides it cantrain PINN structure with current positions of the particlesby BP learning and predicting In addition improved PSO
Table 1 Harmonic of microgrid system
Harmonic order A percentage of content ()5 1224717 08434311 58320313 45484223 21118625 21000735 13269937 13059947 11776349 114342All 849
can find the local optimum position 119901id and globe optimumposition 119892id through selecting the particles with minimal 119869Furthermore it evaluates and calculates the fitness and thenew adaptive value by using (9) What is more is that it canupdate the velocity and the position of each particle Thenew position is kept if the current position is dominated bypositioning the 119901id otherwise the current position replacesit in space neither of them is randomly selected Finally itcan judge the termination criterion the procedure goes to thethird step until it is satisfied
4 Results
The proposed island Microgrid system is shown in Figure 6and the primary parameters of system are as follows Thesystem comprises four 11 kV medium-voltage buses with two4000 kW generator engines and two 3000 kWmotors drivenby 12-pulse inverters linking each other through the circuitbreakers and four 400V low-voltage buses with some motorsand loads connected by the circuit breaker In addition a1500 kW of emergency engine is installed on the low-voltageside of power supply in case of emergency
The harmonic parameters of the proposed island Micro-grid system are summarized in Table 1 while the total THD
119894
is 849 it exceeds the national standard of China Figure 7shows the current and spectrum of one phase at the 11 kVlevel For the security of the grid HAF is used between thebus and inverter
6 Journal of Control Science and Engineering
12
1
08
06
04
02
0
minus020 005 01 015 02 025 03 035
Time (s)
119880dc
(pu)
(a) DC bus voltage control with PINN
25
2
15
1
05
00 005 01 015 02 025
Time (s)
119880dc
(pu)
(b) DC bus voltage control with conventional PI
Figure 10 Compare PINN with conventional PI
150
100
50
0
minus50
minus100
minus1500 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level with HAF
10
9876543210
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level with HAF
Figure 11 The current and spectrum of one phase at the 11 kV level with HAF
Table 2 Parameters of PF
The PF of HAF 119871ohm 119862120583F 119876
11th 19185 1371 4013th 11301 1667 40
Theperformance of theHAFdepends on theDCbus volt-age control optimization shown in Figure 1 The simulationparameters are total power 119875all = 32MW a single motorpower factor cos120593 = 909 119862
119880cd= 3000 120583F out filter 119871out =
05mH 119862out = 500 120583F and 119880dc = 6000V The parameters ofimproved PSO are set to be max119881id = 20 min119881id = minus20 thepopulation size is 100 the iteration times are 50 the inertiaweight factor is 08 the acceleration constants 120573
1and 120573
2both
are 3 random() is a random number between 0 and 1 and thesample and saturation of BP are 200 and 2 respectively So theoptimum weights of PINN which are trained by improved
PSO are 830376 and 000283987 The parameters of PF aresummarized in Table 2
The step response of 119880lowastdc(PU) jumps from 07 to 10 andthe 119880dc tracks the given value with PINN by improved PSOoptimization as shown in Figure 8 Training PINN to 26 stepsthe error 119890(119905) of algorithm is 14169119890
minus005 shown in Figure 9The optimization result for the DC bus voltage control ofPINN is effective
The HAF with DC bus voltage control by PINN isinstalled in the island microgrid system It can be seen fromFigure 10 that PINN has advantages over the conventionalPI and that the filtering functions are well performed bythe DC bus voltage controller under the different operatingconditions The maximum overshoot of the traditional PI isclose to 19 compared with 19 the maximum overshoot of119880dc with PINN is lowered to about 095 when 119880
lowast
dc is 07 TheDC bus voltage with PINN is stable at 013 s which is thelower than conventional PI and the response is quicker andsmoother than the conventional PI
Journal of Control Science and Engineering 7
Table 3 Harmonic of microgrid system with HAF
Harmonic order A percentage of content ()5 03007797 011124111 0049815213 0019656523 00076863325 00046405535 027077737 0279686All 096
By using the HAF with DC bus voltage PINN control thetotal THD
119894of the island Microgrid system is reduced from
849 to 096 Figure 11 presents the results of the smoothcurrent and reduced harmonic All the harmonics are thatlower than the national standards are summarized in Table 3
5 Conclusions
Due to the harmonic interference of nonlinear loads theHAF is used to protect the security of the island Microgridsystem An optimizationmethod based on improved PSO fordesign ofHAFDVcontrol is developed by usingPINN insteadof conventional PI The coordinated design problem of DCbus voltage control is formulated as a nonlinear constrainedobjective optimization problem where improved PSO isemployed to search for the optimal solutions Comparingcontrollers of PINN and conventional PI simulation resultsshow that HAFDV control with PINN has more effectivecontrol results better stability and lower overshoot of DCvoltage and more rapid response than conventional PI
References
[1] Z Ke L An X Xiang-yang and Z Wei ldquoDC side capacitorrsquosdesign and voltage control in high-capacity active power filterrdquoPower Electronics vol 4 no 41 2007
[2] GMing zhen R Zhen T Zhuo yao and L Q zhan ldquoOptimiza-tion design for capacity on passive active hybrid power filtersrdquoJournal of the China Railway Society vol 5 no 21 pp 43ndash461999
[3] L Shiguo ldquoOptimal design of DC voltage close loop control foran active power filterrdquo inProceedings of International ConferenceonPower Electronics andDrive Systems vol 2 pp 565ndash570 1995
[4] Z Dong L Zheng-yu and C Guo-zhu ldquoCapacitor voltagecontrol of shunt active power filterrdquo Power Electronics vol 10no 41 2007
[5] H Akagi and T Hatada ldquoVoltage balancing control for a three-level diode-clamped converter in a medium-voltage trans-formerless hybrid active filterrdquo IEEE Transactions on PowerElectronics vol 24 no 3 pp 571ndash579 2009
[6] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid active filter for reactive and harmonics compensationin a distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 3 pp 670ndash677 2009
[7] H Akagi and R Kondo ldquoA transformerless hybrid active filterusing a three-level Pulsewidth Modulation (PWM) converterfor amedium-voltagemotor driverdquo IEEE Transactions on PowerElectronics vol 25 no 6 pp 1365ndash1374 2010
[8] A Luo W Zhu R Fan and K Zhou ldquoStudy on a novelhybrid active power filter applied to a high-voltage gridrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 2344ndash23522009
[9] P T Cheng S Bhattacharya and D M Divan ldquoControlof square-wave inverters in high-power hybrid active filtersystemsrdquo IEEE Transactions on Industry Applications vol 34no 3 pp 458ndash472 1998
[10] R Inzunza and H Akagi ldquoA 66-kV transformerless shunthybrid active filter for installation on a power distributionsystemrdquo in Proceedings of the 35th Annual Power ElectronicsSpecialists Conference (PESCrsquo04) pp 4630ndash4636 June 2004
[11] A Luo Z Shuai W Zhu Z J Shen and C Tu ldquoDesign andapplication of a hybrid active power filter with injection circuitrdquoIET Power Electronics vol 3 no 1 pp 54ndash64 2010
[12] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid power filter to enhance power quality in a medium-voltage distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 8 pp 2885ndash2893 2009
[13] J Dixon DC Link ldquoFuzzy control for an active power filtersensing the line current onlyrdquo in Proceedings of the AnnualPower Electronics Specialists Conference (PESC rsquo97) vol 2 pp1109ndash1114 1997
[14] N Hatti K Hasegawa andH Akagi ldquoA 66-kV transformerlessmotor drive using a five-level diode-clamped PWM inverter forenergy savings of pumps and blowersrdquo IEEE Transactions onPower Electronics vol 24 no 3 pp 796ndash803 2009
[15] I M Supratid ldquoA multi-subpopulation particle swarm opti-mization a hybrid intelligent computing for function opti-mizationrdquo in Proceedings of the 3rd International Conference onNatural Computation (ICNC rsquo07) vol 5 pp 679ndash684 August2007
[16] C Fan and Y Wan ldquoAn adaptive simple particle swarmoptimization algorithmrdquo in Proceedinhs of the Chinese Controland Decision Conference (CCDC rsquo08) pp 3067ndash3072 July 2008
[17] N Dongxiao G Zhihong and X Mian ldquoResearch on neuralnetworks based on culture particle swarm optimization and itsapplication in power load forecastingrdquo in Proceedings of the 3rdInternational Conference on Natural Computation (ICNC rsquo07)pp 270ndash274 August 2007
[18] L Rui G Yirong X Yujuan and L Ming ldquoA novel multi-swarm particle swarm optimization algorithm applied in activecontour modelrdquo in Proceedings of the WRI Global Congress onIntelligent Systems (GCIS rsquo09) pp 139ndash143 May 2009
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International Journal of
2 Journal of Control Science and Engineering
AC
Active filterOutput filter
Coupling transformer
PF
119885119904
+
minus
Microgrid119868119904
119880dc
Figure 1 Configuration of the hybrid active power filter
The control scheme is indicated in Figure 2 It builds thereference currents for the HAF based on the instantaneousactive and reactive power theory The synchronous referenceframe (SRF) theory is used to extract the fundamentalcomponent of the source current by transformation of thesupply currents (119894
119906119894119907119894119908) into the reference frameThe system
under study is a three-wire system where the zero sequencemay be neglectedThe following are basic equations for thesetransformations
[119894119901
119894119902
] = radic2
3[sin120596119905 minus cos120596119905
minus cos120596119905 minus sin120596119905]
times[[[
[
1 minus1
2minus1
2
0radic3
2minusradic3
2
]]]
]
[
[
119894119906
119894119907
119894119908
]
]
(1)
where the two-phase sinusoidal signals sin120596119905 and cos120596119905 areresulted from the phase-locked loop (PLL) circuit
The lowpass filter is used to extract the DC componentsrealized by moving average to 80Hz The extracted DCcomponents are transformed back into a-b-c coordinates toobtain the fundamental components (119894
119906119891119894119907119891119894119908119891) of source
currents as shown in
[119894119901119895
119894119902119895
] = [sin120596119905 minus cos120596119905
minus cos120596119905 minus sin120596119905] [
119894119901
119894119902
]
[
[
119894119906119891
119894119907119891
119894119908119891
]
]
= radic2
3
[[[[[[[
[
1 0
minus1
2
radic3
2
minus1
2minusradic3
2
]]]]]]]
]
[119894119901119895
119894119902119895
]
(2)
So each current harmonic component (119894119906ℎ119894119907ℎ119894119908ℎ) is given
by
[
[
119894119906ℎ
119894119907ℎ
119894119908ℎ
]
]
= [
[
119894119906
119894119907
119894119908
]
]
minus [
[
119894119906119891
119894119907119891
119894119908119891
]
]
(3)
The source current is controlled to follow this referencecurrent by switching the voltage source inverter with ahysteresis current controller
23 The Objective Function Conventional PI controller isused to maintain the DC bus voltage of the HAF by compen-sating the voltage losses [12ndash14] Conventional PI controllerparameters are often obtained by several experiments It isdifficult to adjust all the parameters This paper designs PIneural network controller combined with improved PSOThe interlayer and output layer linking weights of PI neuralnetwork (PINN) are used as the optical parameters of PSO
According to the formulae (1)ndash(3) A-phase fundamentalcurrent increment values are obtained bys
Δ119894119886= radic
2
3sin120596119905 sdot Δ119894pf (4)
where Δ119894pf is the increment of the grid active currentcomponent
So the exchange active power with HAF and supplysystem is calculated as
119875119891
= radic3119864119886sdot Δ119894119886
int
Δ119905
0
119875119891119889119905 =
119862dc [(119880dc + Δ119880119862dc
)2
minus 119880dc2
]
2
+ int
Δ119905
0
119870119894ca119889119905
(5)
where119864119886is A-phase line voltageRMS119862dc is a capacitor value
119880dc is the ideal steady-state value of the HAF DC voltageΔ119880119862dc
is the increment of capacitor voltage during Δ119905 119870 isa constant with switching characteristics of capacitor and the119894ca is RMS in A-phase of 119894
119888
According to the formulae (4)-(5) with neglecting theitem (Δ119880
119862dc)2 and linearization near the operating point after
Laplace transform the PI regulator 119866pi(119904) controlled object119866119907(119904) and voltage detection 119866
119891(119904) are given by
119866pi (119904) =
119870119901(119879119894+ 1)
119879119894119904
119866119907(119904) =
119870119894119864119886
119862dc119880dc119904
119866119891(119904) =
119870119891
119879119891119904 + 1
(6)
where 119870119875is a proportional coefficient 119879
119894is an integral
constantFigure 3 shows the system transfer function it is
expressed as
119866 (119904) =
119866pi (119904) 119866119907 (119904)
1 + 119866pi (119904) 119866119907 (119904) 119866119891 (119904) (7)
The disadvantage of conventional PI controller lies inthe difficulty to resolve the trade-off among smoothness
Journal of Control Science and Engineering 3
LPF
Three
TwoThree
Two
transform inversetransform
PI
PLL
119894119906
119894119907
119894119908
119894119886
119894119887
D-q D-q
119894119889
119894119902
119906119907
119894119901119891
119894119902119891
+
+
minus
minusΔ
119889
119902119889
119902
119894119901119895
119894119902119895
119894119906119891
119894119907119891
119894119908119891
minus
minus
minus +
+
+119894119906ℎ
119894119907ℎ
119894119908ℎ
sin 120596119905 and cos 120596119905generators
minus1
lowast
119880dc
119880dc119880dc
Figure 2 The control scheme of HAF
PINN
Δ119880
minus119866119901119894(119904) 119866119907(119904)
119866119891(119904)
119880lowastdc119880dc
Figure 3 System transfer function
Controlled object
119879PINN
119870PINN
119903
119910
119910
1199061 1199091
1199062 1199092
11987111
11987112
11987121
11987122
119907119906998400998400 119909998400998400
11990619984001199091
998400
11990629984001199092
998400
1198711998400
1198712998400
Figure 4 The structure of PINN
fastness and accuracyThemajor parameters of the HAF DCbus voltage controller require experiments and high skills insystem debugging process and will be fixed eventually
A PINN controller shown in the dotted line in Figure 3is adopted as the DC bus voltage controller instead of theconventional PI controller so the system transfer function ismodified into
119866 (119904) =
PINN (119878)119870119894119864119886119879119891119904 + PINN (119878)119870
119894119864119886
119862dc119880dc1198791198911199042 + 119862dc119880dc + PINN (119878)119870
119894119864119886119870119891
(8)
Initial improved PSO and PINN parameters
Generate position and velocity and calculate adaptive value
Start
Evaluate the fitness and calculate the new adaptive value
Update position and velocity
Yes
Get the PINN structure
No
PINN-BP learning and predicting
Find the local optimum position 119875119894119889 andglobe optimum position 119892119894119889
Achieving condition
Figure 5 The flow chart of improved PSO
The improved PSO algorithm is applied to the optimiza-tion of PINN parameters An objective optimization problemcan be defined as follows
119883PINN = NN(119870PINN 119879PINN)119883PINN are neural networkvectors representing the decision variables 119891
119899(119883PINN) is
4 Journal of Control Science and Engineering
G G
M M
G
GM M
G G
M M
G G
M M
M M M M M M M M
Gen Gen GenG
Gen Gen Gen Gen Gen
Motor Motor Motor Motor Motor Motor MotorMotor
MotorMotorMotorMotorMotorMotorMotorMotor
Transformer Transformer
11 kV 11 kV 11 kV 11 kVMV1 MV2 MV3 MV4
400 V LV1 400 V LV2 400 V LV3 400 V LV4
400 V ESB1
Emergency gen
Figure 6 Microgrid system single line figure
15
1
05
0
minus05
minus1
minus150 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level
6
5
4
3
2
1
0
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level
Figure 7 The current and spectrum of one phase at the 11 kV level
the objective function 119892119895(119870PINN) and ℎ
119896(119879PINN) represent
the constraints
3 Improved PSO
Particle swarm optimization inspired by the social behaviorof a bird flock was originally designed by Kennedy andEberhart in 1995 The original idea is to simulate the birdsrsquofood-hunting for the global optimal point One particlepresents a bird and it can calculate the adaptive value of itscurrent position and every particle records the optimal valuesearched by itself [15 16]
The particles have their memory and each particle keepstracking of its local best position (119901id) and its correspondingfitness The particle with the greatest fitness is called theglobal best position (119892id) of the swarm The basic PSO
algorithm has many defects such as falling into local opti-mum and being impacted by the fact that it is insensitiveto environment variables precocious and so on The paperadopted improved PSO which has multigroup particles tosearch different parts of the solution space When 119901id and119892id are obtained a particle updates its velocity and positionbased on (9) In the end the algorithm will check the resultsuntil the best solution is found or termination conditions aresatisfied
119907119896+1
id = 120582 times 119907119896
id + 1205731times random () times (119901
119896
id minus 119909119896
id)
+ 1205732times random () times (119892
119896
id minus 119909119896
id)
119909119896+1
id = 119909119896
id + 119907119896+1
id
(9)
where 1205731 1205732
ge 0 120582 is the inertia weight factor 1205731and 120573
2
are acceleration constants random() is a random number
Journal of Control Science and Engineering 5
1
08
06
04
02
020 40 60 80 100 120 140 160 180 200
Simple (119899)
119910(119905)
PINN
Figure 8 Improved PSO optimizes PINN
700600500400300200100
0
119890(119905)
0 5 10 15 20 25 30 35 40 45 50Step (119899)
Figure 9 Convergence curve of adaptive value
between 0 and 1 119907id and 119909id are the velocity and the currentposition of particle at iteration id
The improved PSO algorithmoptimizes PINNcontrollerswhich is defined as proportional integral function of neu-rons PINN is a dynamic multilayer feed forward neural net-work The parameters of PINN (119870PINN119879PINN) are optimizedby improved PSO
Neural network of PINN applies 2 times 2 times 1 structureshown in Figure 4 The input layer of the PINN has twoneurons of proportion The two neurons (119870PINN119879PINN) inthemiddle layer are proportional and integral elements of theinput signal and the weights from input layer to the middlelayer are remained of constant value (minus1 +1) In order tominimize the objective function value the mean square error(MSE) function has been employed in (10) The improvedPSO adjusts the network weights by the back-propagation(BP) algorithm [17] The flow chart of the improved PSO isshown in Figure 5 Consider the following
119869 =1
119898
119899
sum
ℎ=1
[119903 (119896) minus 119910 (119896)]2
(10)
The improved PSO shows many advantages Firstly itinitializes the improved PSO and PINN parameters whichcontain the initial particles their positions and velocities Foreach particle it evaluates the fitness function [18] Secondly itgenerates position and velocity and calculates adaptive valueconsidering the steady error and setting time It calculatesthe value of every particle in all subgroups Besides it cantrain PINN structure with current positions of the particlesby BP learning and predicting In addition improved PSO
Table 1 Harmonic of microgrid system
Harmonic order A percentage of content ()5 1224717 08434311 58320313 45484223 21118625 21000735 13269937 13059947 11776349 114342All 849
can find the local optimum position 119901id and globe optimumposition 119892id through selecting the particles with minimal 119869Furthermore it evaluates and calculates the fitness and thenew adaptive value by using (9) What is more is that it canupdate the velocity and the position of each particle Thenew position is kept if the current position is dominated bypositioning the 119901id otherwise the current position replacesit in space neither of them is randomly selected Finally itcan judge the termination criterion the procedure goes to thethird step until it is satisfied
4 Results
The proposed island Microgrid system is shown in Figure 6and the primary parameters of system are as follows Thesystem comprises four 11 kV medium-voltage buses with two4000 kW generator engines and two 3000 kWmotors drivenby 12-pulse inverters linking each other through the circuitbreakers and four 400V low-voltage buses with some motorsand loads connected by the circuit breaker In addition a1500 kW of emergency engine is installed on the low-voltageside of power supply in case of emergency
The harmonic parameters of the proposed island Micro-grid system are summarized in Table 1 while the total THD
119894
is 849 it exceeds the national standard of China Figure 7shows the current and spectrum of one phase at the 11 kVlevel For the security of the grid HAF is used between thebus and inverter
6 Journal of Control Science and Engineering
12
1
08
06
04
02
0
minus020 005 01 015 02 025 03 035
Time (s)
119880dc
(pu)
(a) DC bus voltage control with PINN
25
2
15
1
05
00 005 01 015 02 025
Time (s)
119880dc
(pu)
(b) DC bus voltage control with conventional PI
Figure 10 Compare PINN with conventional PI
150
100
50
0
minus50
minus100
minus1500 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level with HAF
10
9876543210
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level with HAF
Figure 11 The current and spectrum of one phase at the 11 kV level with HAF
Table 2 Parameters of PF
The PF of HAF 119871ohm 119862120583F 119876
11th 19185 1371 4013th 11301 1667 40
Theperformance of theHAFdepends on theDCbus volt-age control optimization shown in Figure 1 The simulationparameters are total power 119875all = 32MW a single motorpower factor cos120593 = 909 119862
119880cd= 3000 120583F out filter 119871out =
05mH 119862out = 500 120583F and 119880dc = 6000V The parameters ofimproved PSO are set to be max119881id = 20 min119881id = minus20 thepopulation size is 100 the iteration times are 50 the inertiaweight factor is 08 the acceleration constants 120573
1and 120573
2both
are 3 random() is a random number between 0 and 1 and thesample and saturation of BP are 200 and 2 respectively So theoptimum weights of PINN which are trained by improved
PSO are 830376 and 000283987 The parameters of PF aresummarized in Table 2
The step response of 119880lowastdc(PU) jumps from 07 to 10 andthe 119880dc tracks the given value with PINN by improved PSOoptimization as shown in Figure 8 Training PINN to 26 stepsthe error 119890(119905) of algorithm is 14169119890
minus005 shown in Figure 9The optimization result for the DC bus voltage control ofPINN is effective
The HAF with DC bus voltage control by PINN isinstalled in the island microgrid system It can be seen fromFigure 10 that PINN has advantages over the conventionalPI and that the filtering functions are well performed bythe DC bus voltage controller under the different operatingconditions The maximum overshoot of the traditional PI isclose to 19 compared with 19 the maximum overshoot of119880dc with PINN is lowered to about 095 when 119880
lowast
dc is 07 TheDC bus voltage with PINN is stable at 013 s which is thelower than conventional PI and the response is quicker andsmoother than the conventional PI
Journal of Control Science and Engineering 7
Table 3 Harmonic of microgrid system with HAF
Harmonic order A percentage of content ()5 03007797 011124111 0049815213 0019656523 00076863325 00046405535 027077737 0279686All 096
By using the HAF with DC bus voltage PINN control thetotal THD
119894of the island Microgrid system is reduced from
849 to 096 Figure 11 presents the results of the smoothcurrent and reduced harmonic All the harmonics are thatlower than the national standards are summarized in Table 3
5 Conclusions
Due to the harmonic interference of nonlinear loads theHAF is used to protect the security of the island Microgridsystem An optimizationmethod based on improved PSO fordesign ofHAFDVcontrol is developed by usingPINN insteadof conventional PI The coordinated design problem of DCbus voltage control is formulated as a nonlinear constrainedobjective optimization problem where improved PSO isemployed to search for the optimal solutions Comparingcontrollers of PINN and conventional PI simulation resultsshow that HAFDV control with PINN has more effectivecontrol results better stability and lower overshoot of DCvoltage and more rapid response than conventional PI
References
[1] Z Ke L An X Xiang-yang and Z Wei ldquoDC side capacitorrsquosdesign and voltage control in high-capacity active power filterrdquoPower Electronics vol 4 no 41 2007
[2] GMing zhen R Zhen T Zhuo yao and L Q zhan ldquoOptimiza-tion design for capacity on passive active hybrid power filtersrdquoJournal of the China Railway Society vol 5 no 21 pp 43ndash461999
[3] L Shiguo ldquoOptimal design of DC voltage close loop control foran active power filterrdquo inProceedings of International ConferenceonPower Electronics andDrive Systems vol 2 pp 565ndash570 1995
[4] Z Dong L Zheng-yu and C Guo-zhu ldquoCapacitor voltagecontrol of shunt active power filterrdquo Power Electronics vol 10no 41 2007
[5] H Akagi and T Hatada ldquoVoltage balancing control for a three-level diode-clamped converter in a medium-voltage trans-formerless hybrid active filterrdquo IEEE Transactions on PowerElectronics vol 24 no 3 pp 571ndash579 2009
[6] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid active filter for reactive and harmonics compensationin a distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 3 pp 670ndash677 2009
[7] H Akagi and R Kondo ldquoA transformerless hybrid active filterusing a three-level Pulsewidth Modulation (PWM) converterfor amedium-voltagemotor driverdquo IEEE Transactions on PowerElectronics vol 25 no 6 pp 1365ndash1374 2010
[8] A Luo W Zhu R Fan and K Zhou ldquoStudy on a novelhybrid active power filter applied to a high-voltage gridrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 2344ndash23522009
[9] P T Cheng S Bhattacharya and D M Divan ldquoControlof square-wave inverters in high-power hybrid active filtersystemsrdquo IEEE Transactions on Industry Applications vol 34no 3 pp 458ndash472 1998
[10] R Inzunza and H Akagi ldquoA 66-kV transformerless shunthybrid active filter for installation on a power distributionsystemrdquo in Proceedings of the 35th Annual Power ElectronicsSpecialists Conference (PESCrsquo04) pp 4630ndash4636 June 2004
[11] A Luo Z Shuai W Zhu Z J Shen and C Tu ldquoDesign andapplication of a hybrid active power filter with injection circuitrdquoIET Power Electronics vol 3 no 1 pp 54ndash64 2010
[12] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid power filter to enhance power quality in a medium-voltage distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 8 pp 2885ndash2893 2009
[13] J Dixon DC Link ldquoFuzzy control for an active power filtersensing the line current onlyrdquo in Proceedings of the AnnualPower Electronics Specialists Conference (PESC rsquo97) vol 2 pp1109ndash1114 1997
[14] N Hatti K Hasegawa andH Akagi ldquoA 66-kV transformerlessmotor drive using a five-level diode-clamped PWM inverter forenergy savings of pumps and blowersrdquo IEEE Transactions onPower Electronics vol 24 no 3 pp 796ndash803 2009
[15] I M Supratid ldquoA multi-subpopulation particle swarm opti-mization a hybrid intelligent computing for function opti-mizationrdquo in Proceedings of the 3rd International Conference onNatural Computation (ICNC rsquo07) vol 5 pp 679ndash684 August2007
[16] C Fan and Y Wan ldquoAn adaptive simple particle swarmoptimization algorithmrdquo in Proceedinhs of the Chinese Controland Decision Conference (CCDC rsquo08) pp 3067ndash3072 July 2008
[17] N Dongxiao G Zhihong and X Mian ldquoResearch on neuralnetworks based on culture particle swarm optimization and itsapplication in power load forecastingrdquo in Proceedings of the 3rdInternational Conference on Natural Computation (ICNC rsquo07)pp 270ndash274 August 2007
[18] L Rui G Yirong X Yujuan and L Ming ldquoA novel multi-swarm particle swarm optimization algorithm applied in activecontour modelrdquo in Proceedings of the WRI Global Congress onIntelligent Systems (GCIS rsquo09) pp 139ndash143 May 2009
International Journal of
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Active and Passive Electronic Components
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RotatingMachinery
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Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Journal of Control Science and Engineering 3
LPF
Three
TwoThree
Two
transform inversetransform
PI
PLL
119894119906
119894119907
119894119908
119894119886
119894119887
D-q D-q
119894119889
119894119902
119906119907
119894119901119891
119894119902119891
+
+
minus
minusΔ
119889
119902119889
119902
119894119901119895
119894119902119895
119894119906119891
119894119907119891
119894119908119891
minus
minus
minus +
+
+119894119906ℎ
119894119907ℎ
119894119908ℎ
sin 120596119905 and cos 120596119905generators
minus1
lowast
119880dc
119880dc119880dc
Figure 2 The control scheme of HAF
PINN
Δ119880
minus119866119901119894(119904) 119866119907(119904)
119866119891(119904)
119880lowastdc119880dc
Figure 3 System transfer function
Controlled object
119879PINN
119870PINN
119903
119910
119910
1199061 1199091
1199062 1199092
11987111
11987112
11987121
11987122
119907119906998400998400 119909998400998400
11990619984001199091
998400
11990629984001199092
998400
1198711998400
1198712998400
Figure 4 The structure of PINN
fastness and accuracyThemajor parameters of the HAF DCbus voltage controller require experiments and high skills insystem debugging process and will be fixed eventually
A PINN controller shown in the dotted line in Figure 3is adopted as the DC bus voltage controller instead of theconventional PI controller so the system transfer function ismodified into
119866 (119904) =
PINN (119878)119870119894119864119886119879119891119904 + PINN (119878)119870
119894119864119886
119862dc119880dc1198791198911199042 + 119862dc119880dc + PINN (119878)119870
119894119864119886119870119891
(8)
Initial improved PSO and PINN parameters
Generate position and velocity and calculate adaptive value
Start
Evaluate the fitness and calculate the new adaptive value
Update position and velocity
Yes
Get the PINN structure
No
PINN-BP learning and predicting
Find the local optimum position 119875119894119889 andglobe optimum position 119892119894119889
Achieving condition
Figure 5 The flow chart of improved PSO
The improved PSO algorithm is applied to the optimiza-tion of PINN parameters An objective optimization problemcan be defined as follows
119883PINN = NN(119870PINN 119879PINN)119883PINN are neural networkvectors representing the decision variables 119891
119899(119883PINN) is
4 Journal of Control Science and Engineering
G G
M M
G
GM M
G G
M M
G G
M M
M M M M M M M M
Gen Gen GenG
Gen Gen Gen Gen Gen
Motor Motor Motor Motor Motor Motor MotorMotor
MotorMotorMotorMotorMotorMotorMotorMotor
Transformer Transformer
11 kV 11 kV 11 kV 11 kVMV1 MV2 MV3 MV4
400 V LV1 400 V LV2 400 V LV3 400 V LV4
400 V ESB1
Emergency gen
Figure 6 Microgrid system single line figure
15
1
05
0
minus05
minus1
minus150 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level
6
5
4
3
2
1
0
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level
Figure 7 The current and spectrum of one phase at the 11 kV level
the objective function 119892119895(119870PINN) and ℎ
119896(119879PINN) represent
the constraints
3 Improved PSO
Particle swarm optimization inspired by the social behaviorof a bird flock was originally designed by Kennedy andEberhart in 1995 The original idea is to simulate the birdsrsquofood-hunting for the global optimal point One particlepresents a bird and it can calculate the adaptive value of itscurrent position and every particle records the optimal valuesearched by itself [15 16]
The particles have their memory and each particle keepstracking of its local best position (119901id) and its correspondingfitness The particle with the greatest fitness is called theglobal best position (119892id) of the swarm The basic PSO
algorithm has many defects such as falling into local opti-mum and being impacted by the fact that it is insensitiveto environment variables precocious and so on The paperadopted improved PSO which has multigroup particles tosearch different parts of the solution space When 119901id and119892id are obtained a particle updates its velocity and positionbased on (9) In the end the algorithm will check the resultsuntil the best solution is found or termination conditions aresatisfied
119907119896+1
id = 120582 times 119907119896
id + 1205731times random () times (119901
119896
id minus 119909119896
id)
+ 1205732times random () times (119892
119896
id minus 119909119896
id)
119909119896+1
id = 119909119896
id + 119907119896+1
id
(9)
where 1205731 1205732
ge 0 120582 is the inertia weight factor 1205731and 120573
2
are acceleration constants random() is a random number
Journal of Control Science and Engineering 5
1
08
06
04
02
020 40 60 80 100 120 140 160 180 200
Simple (119899)
119910(119905)
PINN
Figure 8 Improved PSO optimizes PINN
700600500400300200100
0
119890(119905)
0 5 10 15 20 25 30 35 40 45 50Step (119899)
Figure 9 Convergence curve of adaptive value
between 0 and 1 119907id and 119909id are the velocity and the currentposition of particle at iteration id
The improved PSO algorithmoptimizes PINNcontrollerswhich is defined as proportional integral function of neu-rons PINN is a dynamic multilayer feed forward neural net-work The parameters of PINN (119870PINN119879PINN) are optimizedby improved PSO
Neural network of PINN applies 2 times 2 times 1 structureshown in Figure 4 The input layer of the PINN has twoneurons of proportion The two neurons (119870PINN119879PINN) inthemiddle layer are proportional and integral elements of theinput signal and the weights from input layer to the middlelayer are remained of constant value (minus1 +1) In order tominimize the objective function value the mean square error(MSE) function has been employed in (10) The improvedPSO adjusts the network weights by the back-propagation(BP) algorithm [17] The flow chart of the improved PSO isshown in Figure 5 Consider the following
119869 =1
119898
119899
sum
ℎ=1
[119903 (119896) minus 119910 (119896)]2
(10)
The improved PSO shows many advantages Firstly itinitializes the improved PSO and PINN parameters whichcontain the initial particles their positions and velocities Foreach particle it evaluates the fitness function [18] Secondly itgenerates position and velocity and calculates adaptive valueconsidering the steady error and setting time It calculatesthe value of every particle in all subgroups Besides it cantrain PINN structure with current positions of the particlesby BP learning and predicting In addition improved PSO
Table 1 Harmonic of microgrid system
Harmonic order A percentage of content ()5 1224717 08434311 58320313 45484223 21118625 21000735 13269937 13059947 11776349 114342All 849
can find the local optimum position 119901id and globe optimumposition 119892id through selecting the particles with minimal 119869Furthermore it evaluates and calculates the fitness and thenew adaptive value by using (9) What is more is that it canupdate the velocity and the position of each particle Thenew position is kept if the current position is dominated bypositioning the 119901id otherwise the current position replacesit in space neither of them is randomly selected Finally itcan judge the termination criterion the procedure goes to thethird step until it is satisfied
4 Results
The proposed island Microgrid system is shown in Figure 6and the primary parameters of system are as follows Thesystem comprises four 11 kV medium-voltage buses with two4000 kW generator engines and two 3000 kWmotors drivenby 12-pulse inverters linking each other through the circuitbreakers and four 400V low-voltage buses with some motorsand loads connected by the circuit breaker In addition a1500 kW of emergency engine is installed on the low-voltageside of power supply in case of emergency
The harmonic parameters of the proposed island Micro-grid system are summarized in Table 1 while the total THD
119894
is 849 it exceeds the national standard of China Figure 7shows the current and spectrum of one phase at the 11 kVlevel For the security of the grid HAF is used between thebus and inverter
6 Journal of Control Science and Engineering
12
1
08
06
04
02
0
minus020 005 01 015 02 025 03 035
Time (s)
119880dc
(pu)
(a) DC bus voltage control with PINN
25
2
15
1
05
00 005 01 015 02 025
Time (s)
119880dc
(pu)
(b) DC bus voltage control with conventional PI
Figure 10 Compare PINN with conventional PI
150
100
50
0
minus50
minus100
minus1500 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level with HAF
10
9876543210
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level with HAF
Figure 11 The current and spectrum of one phase at the 11 kV level with HAF
Table 2 Parameters of PF
The PF of HAF 119871ohm 119862120583F 119876
11th 19185 1371 4013th 11301 1667 40
Theperformance of theHAFdepends on theDCbus volt-age control optimization shown in Figure 1 The simulationparameters are total power 119875all = 32MW a single motorpower factor cos120593 = 909 119862
119880cd= 3000 120583F out filter 119871out =
05mH 119862out = 500 120583F and 119880dc = 6000V The parameters ofimproved PSO are set to be max119881id = 20 min119881id = minus20 thepopulation size is 100 the iteration times are 50 the inertiaweight factor is 08 the acceleration constants 120573
1and 120573
2both
are 3 random() is a random number between 0 and 1 and thesample and saturation of BP are 200 and 2 respectively So theoptimum weights of PINN which are trained by improved
PSO are 830376 and 000283987 The parameters of PF aresummarized in Table 2
The step response of 119880lowastdc(PU) jumps from 07 to 10 andthe 119880dc tracks the given value with PINN by improved PSOoptimization as shown in Figure 8 Training PINN to 26 stepsthe error 119890(119905) of algorithm is 14169119890
minus005 shown in Figure 9The optimization result for the DC bus voltage control ofPINN is effective
The HAF with DC bus voltage control by PINN isinstalled in the island microgrid system It can be seen fromFigure 10 that PINN has advantages over the conventionalPI and that the filtering functions are well performed bythe DC bus voltage controller under the different operatingconditions The maximum overshoot of the traditional PI isclose to 19 compared with 19 the maximum overshoot of119880dc with PINN is lowered to about 095 when 119880
lowast
dc is 07 TheDC bus voltage with PINN is stable at 013 s which is thelower than conventional PI and the response is quicker andsmoother than the conventional PI
Journal of Control Science and Engineering 7
Table 3 Harmonic of microgrid system with HAF
Harmonic order A percentage of content ()5 03007797 011124111 0049815213 0019656523 00076863325 00046405535 027077737 0279686All 096
By using the HAF with DC bus voltage PINN control thetotal THD
119894of the island Microgrid system is reduced from
849 to 096 Figure 11 presents the results of the smoothcurrent and reduced harmonic All the harmonics are thatlower than the national standards are summarized in Table 3
5 Conclusions
Due to the harmonic interference of nonlinear loads theHAF is used to protect the security of the island Microgridsystem An optimizationmethod based on improved PSO fordesign ofHAFDVcontrol is developed by usingPINN insteadof conventional PI The coordinated design problem of DCbus voltage control is formulated as a nonlinear constrainedobjective optimization problem where improved PSO isemployed to search for the optimal solutions Comparingcontrollers of PINN and conventional PI simulation resultsshow that HAFDV control with PINN has more effectivecontrol results better stability and lower overshoot of DCvoltage and more rapid response than conventional PI
References
[1] Z Ke L An X Xiang-yang and Z Wei ldquoDC side capacitorrsquosdesign and voltage control in high-capacity active power filterrdquoPower Electronics vol 4 no 41 2007
[2] GMing zhen R Zhen T Zhuo yao and L Q zhan ldquoOptimiza-tion design for capacity on passive active hybrid power filtersrdquoJournal of the China Railway Society vol 5 no 21 pp 43ndash461999
[3] L Shiguo ldquoOptimal design of DC voltage close loop control foran active power filterrdquo inProceedings of International ConferenceonPower Electronics andDrive Systems vol 2 pp 565ndash570 1995
[4] Z Dong L Zheng-yu and C Guo-zhu ldquoCapacitor voltagecontrol of shunt active power filterrdquo Power Electronics vol 10no 41 2007
[5] H Akagi and T Hatada ldquoVoltage balancing control for a three-level diode-clamped converter in a medium-voltage trans-formerless hybrid active filterrdquo IEEE Transactions on PowerElectronics vol 24 no 3 pp 571ndash579 2009
[6] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid active filter for reactive and harmonics compensationin a distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 3 pp 670ndash677 2009
[7] H Akagi and R Kondo ldquoA transformerless hybrid active filterusing a three-level Pulsewidth Modulation (PWM) converterfor amedium-voltagemotor driverdquo IEEE Transactions on PowerElectronics vol 25 no 6 pp 1365ndash1374 2010
[8] A Luo W Zhu R Fan and K Zhou ldquoStudy on a novelhybrid active power filter applied to a high-voltage gridrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 2344ndash23522009
[9] P T Cheng S Bhattacharya and D M Divan ldquoControlof square-wave inverters in high-power hybrid active filtersystemsrdquo IEEE Transactions on Industry Applications vol 34no 3 pp 458ndash472 1998
[10] R Inzunza and H Akagi ldquoA 66-kV transformerless shunthybrid active filter for installation on a power distributionsystemrdquo in Proceedings of the 35th Annual Power ElectronicsSpecialists Conference (PESCrsquo04) pp 4630ndash4636 June 2004
[11] A Luo Z Shuai W Zhu Z J Shen and C Tu ldquoDesign andapplication of a hybrid active power filter with injection circuitrdquoIET Power Electronics vol 3 no 1 pp 54ndash64 2010
[12] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid power filter to enhance power quality in a medium-voltage distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 8 pp 2885ndash2893 2009
[13] J Dixon DC Link ldquoFuzzy control for an active power filtersensing the line current onlyrdquo in Proceedings of the AnnualPower Electronics Specialists Conference (PESC rsquo97) vol 2 pp1109ndash1114 1997
[14] N Hatti K Hasegawa andH Akagi ldquoA 66-kV transformerlessmotor drive using a five-level diode-clamped PWM inverter forenergy savings of pumps and blowersrdquo IEEE Transactions onPower Electronics vol 24 no 3 pp 796ndash803 2009
[15] I M Supratid ldquoA multi-subpopulation particle swarm opti-mization a hybrid intelligent computing for function opti-mizationrdquo in Proceedings of the 3rd International Conference onNatural Computation (ICNC rsquo07) vol 5 pp 679ndash684 August2007
[16] C Fan and Y Wan ldquoAn adaptive simple particle swarmoptimization algorithmrdquo in Proceedinhs of the Chinese Controland Decision Conference (CCDC rsquo08) pp 3067ndash3072 July 2008
[17] N Dongxiao G Zhihong and X Mian ldquoResearch on neuralnetworks based on culture particle swarm optimization and itsapplication in power load forecastingrdquo in Proceedings of the 3rdInternational Conference on Natural Computation (ICNC rsquo07)pp 270ndash274 August 2007
[18] L Rui G Yirong X Yujuan and L Ming ldquoA novel multi-swarm particle swarm optimization algorithm applied in activecontour modelrdquo in Proceedings of the WRI Global Congress onIntelligent Systems (GCIS rsquo09) pp 139ndash143 May 2009
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
4 Journal of Control Science and Engineering
G G
M M
G
GM M
G G
M M
G G
M M
M M M M M M M M
Gen Gen GenG
Gen Gen Gen Gen Gen
Motor Motor Motor Motor Motor Motor MotorMotor
MotorMotorMotorMotorMotorMotorMotorMotor
Transformer Transformer
11 kV 11 kV 11 kV 11 kVMV1 MV2 MV3 MV4
400 V LV1 400 V LV2 400 V LV3 400 V LV4
400 V ESB1
Emergency gen
Figure 6 Microgrid system single line figure
15
1
05
0
minus05
minus1
minus150 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level
6
5
4
3
2
1
0
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level
Figure 7 The current and spectrum of one phase at the 11 kV level
the objective function 119892119895(119870PINN) and ℎ
119896(119879PINN) represent
the constraints
3 Improved PSO
Particle swarm optimization inspired by the social behaviorof a bird flock was originally designed by Kennedy andEberhart in 1995 The original idea is to simulate the birdsrsquofood-hunting for the global optimal point One particlepresents a bird and it can calculate the adaptive value of itscurrent position and every particle records the optimal valuesearched by itself [15 16]
The particles have their memory and each particle keepstracking of its local best position (119901id) and its correspondingfitness The particle with the greatest fitness is called theglobal best position (119892id) of the swarm The basic PSO
algorithm has many defects such as falling into local opti-mum and being impacted by the fact that it is insensitiveto environment variables precocious and so on The paperadopted improved PSO which has multigroup particles tosearch different parts of the solution space When 119901id and119892id are obtained a particle updates its velocity and positionbased on (9) In the end the algorithm will check the resultsuntil the best solution is found or termination conditions aresatisfied
119907119896+1
id = 120582 times 119907119896
id + 1205731times random () times (119901
119896
id minus 119909119896
id)
+ 1205732times random () times (119892
119896
id minus 119909119896
id)
119909119896+1
id = 119909119896
id + 119907119896+1
id
(9)
where 1205731 1205732
ge 0 120582 is the inertia weight factor 1205731and 120573
2
are acceleration constants random() is a random number
Journal of Control Science and Engineering 5
1
08
06
04
02
020 40 60 80 100 120 140 160 180 200
Simple (119899)
119910(119905)
PINN
Figure 8 Improved PSO optimizes PINN
700600500400300200100
0
119890(119905)
0 5 10 15 20 25 30 35 40 45 50Step (119899)
Figure 9 Convergence curve of adaptive value
between 0 and 1 119907id and 119909id are the velocity and the currentposition of particle at iteration id
The improved PSO algorithmoptimizes PINNcontrollerswhich is defined as proportional integral function of neu-rons PINN is a dynamic multilayer feed forward neural net-work The parameters of PINN (119870PINN119879PINN) are optimizedby improved PSO
Neural network of PINN applies 2 times 2 times 1 structureshown in Figure 4 The input layer of the PINN has twoneurons of proportion The two neurons (119870PINN119879PINN) inthemiddle layer are proportional and integral elements of theinput signal and the weights from input layer to the middlelayer are remained of constant value (minus1 +1) In order tominimize the objective function value the mean square error(MSE) function has been employed in (10) The improvedPSO adjusts the network weights by the back-propagation(BP) algorithm [17] The flow chart of the improved PSO isshown in Figure 5 Consider the following
119869 =1
119898
119899
sum
ℎ=1
[119903 (119896) minus 119910 (119896)]2
(10)
The improved PSO shows many advantages Firstly itinitializes the improved PSO and PINN parameters whichcontain the initial particles their positions and velocities Foreach particle it evaluates the fitness function [18] Secondly itgenerates position and velocity and calculates adaptive valueconsidering the steady error and setting time It calculatesthe value of every particle in all subgroups Besides it cantrain PINN structure with current positions of the particlesby BP learning and predicting In addition improved PSO
Table 1 Harmonic of microgrid system
Harmonic order A percentage of content ()5 1224717 08434311 58320313 45484223 21118625 21000735 13269937 13059947 11776349 114342All 849
can find the local optimum position 119901id and globe optimumposition 119892id through selecting the particles with minimal 119869Furthermore it evaluates and calculates the fitness and thenew adaptive value by using (9) What is more is that it canupdate the velocity and the position of each particle Thenew position is kept if the current position is dominated bypositioning the 119901id otherwise the current position replacesit in space neither of them is randomly selected Finally itcan judge the termination criterion the procedure goes to thethird step until it is satisfied
4 Results
The proposed island Microgrid system is shown in Figure 6and the primary parameters of system are as follows Thesystem comprises four 11 kV medium-voltage buses with two4000 kW generator engines and two 3000 kWmotors drivenby 12-pulse inverters linking each other through the circuitbreakers and four 400V low-voltage buses with some motorsand loads connected by the circuit breaker In addition a1500 kW of emergency engine is installed on the low-voltageside of power supply in case of emergency
The harmonic parameters of the proposed island Micro-grid system are summarized in Table 1 while the total THD
119894
is 849 it exceeds the national standard of China Figure 7shows the current and spectrum of one phase at the 11 kVlevel For the security of the grid HAF is used between thebus and inverter
6 Journal of Control Science and Engineering
12
1
08
06
04
02
0
minus020 005 01 015 02 025 03 035
Time (s)
119880dc
(pu)
(a) DC bus voltage control with PINN
25
2
15
1
05
00 005 01 015 02 025
Time (s)
119880dc
(pu)
(b) DC bus voltage control with conventional PI
Figure 10 Compare PINN with conventional PI
150
100
50
0
minus50
minus100
minus1500 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level with HAF
10
9876543210
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level with HAF
Figure 11 The current and spectrum of one phase at the 11 kV level with HAF
Table 2 Parameters of PF
The PF of HAF 119871ohm 119862120583F 119876
11th 19185 1371 4013th 11301 1667 40
Theperformance of theHAFdepends on theDCbus volt-age control optimization shown in Figure 1 The simulationparameters are total power 119875all = 32MW a single motorpower factor cos120593 = 909 119862
119880cd= 3000 120583F out filter 119871out =
05mH 119862out = 500 120583F and 119880dc = 6000V The parameters ofimproved PSO are set to be max119881id = 20 min119881id = minus20 thepopulation size is 100 the iteration times are 50 the inertiaweight factor is 08 the acceleration constants 120573
1and 120573
2both
are 3 random() is a random number between 0 and 1 and thesample and saturation of BP are 200 and 2 respectively So theoptimum weights of PINN which are trained by improved
PSO are 830376 and 000283987 The parameters of PF aresummarized in Table 2
The step response of 119880lowastdc(PU) jumps from 07 to 10 andthe 119880dc tracks the given value with PINN by improved PSOoptimization as shown in Figure 8 Training PINN to 26 stepsthe error 119890(119905) of algorithm is 14169119890
minus005 shown in Figure 9The optimization result for the DC bus voltage control ofPINN is effective
The HAF with DC bus voltage control by PINN isinstalled in the island microgrid system It can be seen fromFigure 10 that PINN has advantages over the conventionalPI and that the filtering functions are well performed bythe DC bus voltage controller under the different operatingconditions The maximum overshoot of the traditional PI isclose to 19 compared with 19 the maximum overshoot of119880dc with PINN is lowered to about 095 when 119880
lowast
dc is 07 TheDC bus voltage with PINN is stable at 013 s which is thelower than conventional PI and the response is quicker andsmoother than the conventional PI
Journal of Control Science and Engineering 7
Table 3 Harmonic of microgrid system with HAF
Harmonic order A percentage of content ()5 03007797 011124111 0049815213 0019656523 00076863325 00046405535 027077737 0279686All 096
By using the HAF with DC bus voltage PINN control thetotal THD
119894of the island Microgrid system is reduced from
849 to 096 Figure 11 presents the results of the smoothcurrent and reduced harmonic All the harmonics are thatlower than the national standards are summarized in Table 3
5 Conclusions
Due to the harmonic interference of nonlinear loads theHAF is used to protect the security of the island Microgridsystem An optimizationmethod based on improved PSO fordesign ofHAFDVcontrol is developed by usingPINN insteadof conventional PI The coordinated design problem of DCbus voltage control is formulated as a nonlinear constrainedobjective optimization problem where improved PSO isemployed to search for the optimal solutions Comparingcontrollers of PINN and conventional PI simulation resultsshow that HAFDV control with PINN has more effectivecontrol results better stability and lower overshoot of DCvoltage and more rapid response than conventional PI
References
[1] Z Ke L An X Xiang-yang and Z Wei ldquoDC side capacitorrsquosdesign and voltage control in high-capacity active power filterrdquoPower Electronics vol 4 no 41 2007
[2] GMing zhen R Zhen T Zhuo yao and L Q zhan ldquoOptimiza-tion design for capacity on passive active hybrid power filtersrdquoJournal of the China Railway Society vol 5 no 21 pp 43ndash461999
[3] L Shiguo ldquoOptimal design of DC voltage close loop control foran active power filterrdquo inProceedings of International ConferenceonPower Electronics andDrive Systems vol 2 pp 565ndash570 1995
[4] Z Dong L Zheng-yu and C Guo-zhu ldquoCapacitor voltagecontrol of shunt active power filterrdquo Power Electronics vol 10no 41 2007
[5] H Akagi and T Hatada ldquoVoltage balancing control for a three-level diode-clamped converter in a medium-voltage trans-formerless hybrid active filterrdquo IEEE Transactions on PowerElectronics vol 24 no 3 pp 571ndash579 2009
[6] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid active filter for reactive and harmonics compensationin a distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 3 pp 670ndash677 2009
[7] H Akagi and R Kondo ldquoA transformerless hybrid active filterusing a three-level Pulsewidth Modulation (PWM) converterfor amedium-voltagemotor driverdquo IEEE Transactions on PowerElectronics vol 25 no 6 pp 1365ndash1374 2010
[8] A Luo W Zhu R Fan and K Zhou ldquoStudy on a novelhybrid active power filter applied to a high-voltage gridrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 2344ndash23522009
[9] P T Cheng S Bhattacharya and D M Divan ldquoControlof square-wave inverters in high-power hybrid active filtersystemsrdquo IEEE Transactions on Industry Applications vol 34no 3 pp 458ndash472 1998
[10] R Inzunza and H Akagi ldquoA 66-kV transformerless shunthybrid active filter for installation on a power distributionsystemrdquo in Proceedings of the 35th Annual Power ElectronicsSpecialists Conference (PESCrsquo04) pp 4630ndash4636 June 2004
[11] A Luo Z Shuai W Zhu Z J Shen and C Tu ldquoDesign andapplication of a hybrid active power filter with injection circuitrdquoIET Power Electronics vol 3 no 1 pp 54ndash64 2010
[12] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid power filter to enhance power quality in a medium-voltage distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 8 pp 2885ndash2893 2009
[13] J Dixon DC Link ldquoFuzzy control for an active power filtersensing the line current onlyrdquo in Proceedings of the AnnualPower Electronics Specialists Conference (PESC rsquo97) vol 2 pp1109ndash1114 1997
[14] N Hatti K Hasegawa andH Akagi ldquoA 66-kV transformerlessmotor drive using a five-level diode-clamped PWM inverter forenergy savings of pumps and blowersrdquo IEEE Transactions onPower Electronics vol 24 no 3 pp 796ndash803 2009
[15] I M Supratid ldquoA multi-subpopulation particle swarm opti-mization a hybrid intelligent computing for function opti-mizationrdquo in Proceedings of the 3rd International Conference onNatural Computation (ICNC rsquo07) vol 5 pp 679ndash684 August2007
[16] C Fan and Y Wan ldquoAn adaptive simple particle swarmoptimization algorithmrdquo in Proceedinhs of the Chinese Controland Decision Conference (CCDC rsquo08) pp 3067ndash3072 July 2008
[17] N Dongxiao G Zhihong and X Mian ldquoResearch on neuralnetworks based on culture particle swarm optimization and itsapplication in power load forecastingrdquo in Proceedings of the 3rdInternational Conference on Natural Computation (ICNC rsquo07)pp 270ndash274 August 2007
[18] L Rui G Yirong X Yujuan and L Ming ldquoA novel multi-swarm particle swarm optimization algorithm applied in activecontour modelrdquo in Proceedings of the WRI Global Congress onIntelligent Systems (GCIS rsquo09) pp 139ndash143 May 2009
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Journal of Control Science and Engineering 5
1
08
06
04
02
020 40 60 80 100 120 140 160 180 200
Simple (119899)
119910(119905)
PINN
Figure 8 Improved PSO optimizes PINN
700600500400300200100
0
119890(119905)
0 5 10 15 20 25 30 35 40 45 50Step (119899)
Figure 9 Convergence curve of adaptive value
between 0 and 1 119907id and 119909id are the velocity and the currentposition of particle at iteration id
The improved PSO algorithmoptimizes PINNcontrollerswhich is defined as proportional integral function of neu-rons PINN is a dynamic multilayer feed forward neural net-work The parameters of PINN (119870PINN119879PINN) are optimizedby improved PSO
Neural network of PINN applies 2 times 2 times 1 structureshown in Figure 4 The input layer of the PINN has twoneurons of proportion The two neurons (119870PINN119879PINN) inthemiddle layer are proportional and integral elements of theinput signal and the weights from input layer to the middlelayer are remained of constant value (minus1 +1) In order tominimize the objective function value the mean square error(MSE) function has been employed in (10) The improvedPSO adjusts the network weights by the back-propagation(BP) algorithm [17] The flow chart of the improved PSO isshown in Figure 5 Consider the following
119869 =1
119898
119899
sum
ℎ=1
[119903 (119896) minus 119910 (119896)]2
(10)
The improved PSO shows many advantages Firstly itinitializes the improved PSO and PINN parameters whichcontain the initial particles their positions and velocities Foreach particle it evaluates the fitness function [18] Secondly itgenerates position and velocity and calculates adaptive valueconsidering the steady error and setting time It calculatesthe value of every particle in all subgroups Besides it cantrain PINN structure with current positions of the particlesby BP learning and predicting In addition improved PSO
Table 1 Harmonic of microgrid system
Harmonic order A percentage of content ()5 1224717 08434311 58320313 45484223 21118625 21000735 13269937 13059947 11776349 114342All 849
can find the local optimum position 119901id and globe optimumposition 119892id through selecting the particles with minimal 119869Furthermore it evaluates and calculates the fitness and thenew adaptive value by using (9) What is more is that it canupdate the velocity and the position of each particle Thenew position is kept if the current position is dominated bypositioning the 119901id otherwise the current position replacesit in space neither of them is randomly selected Finally itcan judge the termination criterion the procedure goes to thethird step until it is satisfied
4 Results
The proposed island Microgrid system is shown in Figure 6and the primary parameters of system are as follows Thesystem comprises four 11 kV medium-voltage buses with two4000 kW generator engines and two 3000 kWmotors drivenby 12-pulse inverters linking each other through the circuitbreakers and four 400V low-voltage buses with some motorsand loads connected by the circuit breaker In addition a1500 kW of emergency engine is installed on the low-voltageside of power supply in case of emergency
The harmonic parameters of the proposed island Micro-grid system are summarized in Table 1 while the total THD
119894
is 849 it exceeds the national standard of China Figure 7shows the current and spectrum of one phase at the 11 kVlevel For the security of the grid HAF is used between thebus and inverter
6 Journal of Control Science and Engineering
12
1
08
06
04
02
0
minus020 005 01 015 02 025 03 035
Time (s)
119880dc
(pu)
(a) DC bus voltage control with PINN
25
2
15
1
05
00 005 01 015 02 025
Time (s)
119880dc
(pu)
(b) DC bus voltage control with conventional PI
Figure 10 Compare PINN with conventional PI
150
100
50
0
minus50
minus100
minus1500 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level with HAF
10
9876543210
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level with HAF
Figure 11 The current and spectrum of one phase at the 11 kV level with HAF
Table 2 Parameters of PF
The PF of HAF 119871ohm 119862120583F 119876
11th 19185 1371 4013th 11301 1667 40
Theperformance of theHAFdepends on theDCbus volt-age control optimization shown in Figure 1 The simulationparameters are total power 119875all = 32MW a single motorpower factor cos120593 = 909 119862
119880cd= 3000 120583F out filter 119871out =
05mH 119862out = 500 120583F and 119880dc = 6000V The parameters ofimproved PSO are set to be max119881id = 20 min119881id = minus20 thepopulation size is 100 the iteration times are 50 the inertiaweight factor is 08 the acceleration constants 120573
1and 120573
2both
are 3 random() is a random number between 0 and 1 and thesample and saturation of BP are 200 and 2 respectively So theoptimum weights of PINN which are trained by improved
PSO are 830376 and 000283987 The parameters of PF aresummarized in Table 2
The step response of 119880lowastdc(PU) jumps from 07 to 10 andthe 119880dc tracks the given value with PINN by improved PSOoptimization as shown in Figure 8 Training PINN to 26 stepsthe error 119890(119905) of algorithm is 14169119890
minus005 shown in Figure 9The optimization result for the DC bus voltage control ofPINN is effective
The HAF with DC bus voltage control by PINN isinstalled in the island microgrid system It can be seen fromFigure 10 that PINN has advantages over the conventionalPI and that the filtering functions are well performed bythe DC bus voltage controller under the different operatingconditions The maximum overshoot of the traditional PI isclose to 19 compared with 19 the maximum overshoot of119880dc with PINN is lowered to about 095 when 119880
lowast
dc is 07 TheDC bus voltage with PINN is stable at 013 s which is thelower than conventional PI and the response is quicker andsmoother than the conventional PI
Journal of Control Science and Engineering 7
Table 3 Harmonic of microgrid system with HAF
Harmonic order A percentage of content ()5 03007797 011124111 0049815213 0019656523 00076863325 00046405535 027077737 0279686All 096
By using the HAF with DC bus voltage PINN control thetotal THD
119894of the island Microgrid system is reduced from
849 to 096 Figure 11 presents the results of the smoothcurrent and reduced harmonic All the harmonics are thatlower than the national standards are summarized in Table 3
5 Conclusions
Due to the harmonic interference of nonlinear loads theHAF is used to protect the security of the island Microgridsystem An optimizationmethod based on improved PSO fordesign ofHAFDVcontrol is developed by usingPINN insteadof conventional PI The coordinated design problem of DCbus voltage control is formulated as a nonlinear constrainedobjective optimization problem where improved PSO isemployed to search for the optimal solutions Comparingcontrollers of PINN and conventional PI simulation resultsshow that HAFDV control with PINN has more effectivecontrol results better stability and lower overshoot of DCvoltage and more rapid response than conventional PI
References
[1] Z Ke L An X Xiang-yang and Z Wei ldquoDC side capacitorrsquosdesign and voltage control in high-capacity active power filterrdquoPower Electronics vol 4 no 41 2007
[2] GMing zhen R Zhen T Zhuo yao and L Q zhan ldquoOptimiza-tion design for capacity on passive active hybrid power filtersrdquoJournal of the China Railway Society vol 5 no 21 pp 43ndash461999
[3] L Shiguo ldquoOptimal design of DC voltage close loop control foran active power filterrdquo inProceedings of International ConferenceonPower Electronics andDrive Systems vol 2 pp 565ndash570 1995
[4] Z Dong L Zheng-yu and C Guo-zhu ldquoCapacitor voltagecontrol of shunt active power filterrdquo Power Electronics vol 10no 41 2007
[5] H Akagi and T Hatada ldquoVoltage balancing control for a three-level diode-clamped converter in a medium-voltage trans-formerless hybrid active filterrdquo IEEE Transactions on PowerElectronics vol 24 no 3 pp 571ndash579 2009
[6] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid active filter for reactive and harmonics compensationin a distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 3 pp 670ndash677 2009
[7] H Akagi and R Kondo ldquoA transformerless hybrid active filterusing a three-level Pulsewidth Modulation (PWM) converterfor amedium-voltagemotor driverdquo IEEE Transactions on PowerElectronics vol 25 no 6 pp 1365ndash1374 2010
[8] A Luo W Zhu R Fan and K Zhou ldquoStudy on a novelhybrid active power filter applied to a high-voltage gridrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 2344ndash23522009
[9] P T Cheng S Bhattacharya and D M Divan ldquoControlof square-wave inverters in high-power hybrid active filtersystemsrdquo IEEE Transactions on Industry Applications vol 34no 3 pp 458ndash472 1998
[10] R Inzunza and H Akagi ldquoA 66-kV transformerless shunthybrid active filter for installation on a power distributionsystemrdquo in Proceedings of the 35th Annual Power ElectronicsSpecialists Conference (PESCrsquo04) pp 4630ndash4636 June 2004
[11] A Luo Z Shuai W Zhu Z J Shen and C Tu ldquoDesign andapplication of a hybrid active power filter with injection circuitrdquoIET Power Electronics vol 3 no 1 pp 54ndash64 2010
[12] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid power filter to enhance power quality in a medium-voltage distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 8 pp 2885ndash2893 2009
[13] J Dixon DC Link ldquoFuzzy control for an active power filtersensing the line current onlyrdquo in Proceedings of the AnnualPower Electronics Specialists Conference (PESC rsquo97) vol 2 pp1109ndash1114 1997
[14] N Hatti K Hasegawa andH Akagi ldquoA 66-kV transformerlessmotor drive using a five-level diode-clamped PWM inverter forenergy savings of pumps and blowersrdquo IEEE Transactions onPower Electronics vol 24 no 3 pp 796ndash803 2009
[15] I M Supratid ldquoA multi-subpopulation particle swarm opti-mization a hybrid intelligent computing for function opti-mizationrdquo in Proceedings of the 3rd International Conference onNatural Computation (ICNC rsquo07) vol 5 pp 679ndash684 August2007
[16] C Fan and Y Wan ldquoAn adaptive simple particle swarmoptimization algorithmrdquo in Proceedinhs of the Chinese Controland Decision Conference (CCDC rsquo08) pp 3067ndash3072 July 2008
[17] N Dongxiao G Zhihong and X Mian ldquoResearch on neuralnetworks based on culture particle swarm optimization and itsapplication in power load forecastingrdquo in Proceedings of the 3rdInternational Conference on Natural Computation (ICNC rsquo07)pp 270ndash274 August 2007
[18] L Rui G Yirong X Yujuan and L Ming ldquoA novel multi-swarm particle swarm optimization algorithm applied in activecontour modelrdquo in Proceedings of the WRI Global Congress onIntelligent Systems (GCIS rsquo09) pp 139ndash143 May 2009
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 Journal of Control Science and Engineering
12
1
08
06
04
02
0
minus020 005 01 015 02 025 03 035
Time (s)
119880dc
(pu)
(a) DC bus voltage control with PINN
25
2
15
1
05
00 005 01 015 02 025
Time (s)
119880dc
(pu)
(b) DC bus voltage control with conventional PI
Figure 10 Compare PINN with conventional PI
150
100
50
0
minus50
minus100
minus1500 01 02 03 04 05 06 07 08 09 1
Curr
ent (
)
Time (s)
(a) The current of one phase at the 11 kV level with HAF
10
9876543210
Curr
ent s
pect
rum
()
0 5 10 15 20 25 30 35 40 45 50Harmonic order
(b) The spectrum of one phase at the 11 kV level with HAF
Figure 11 The current and spectrum of one phase at the 11 kV level with HAF
Table 2 Parameters of PF
The PF of HAF 119871ohm 119862120583F 119876
11th 19185 1371 4013th 11301 1667 40
Theperformance of theHAFdepends on theDCbus volt-age control optimization shown in Figure 1 The simulationparameters are total power 119875all = 32MW a single motorpower factor cos120593 = 909 119862
119880cd= 3000 120583F out filter 119871out =
05mH 119862out = 500 120583F and 119880dc = 6000V The parameters ofimproved PSO are set to be max119881id = 20 min119881id = minus20 thepopulation size is 100 the iteration times are 50 the inertiaweight factor is 08 the acceleration constants 120573
1and 120573
2both
are 3 random() is a random number between 0 and 1 and thesample and saturation of BP are 200 and 2 respectively So theoptimum weights of PINN which are trained by improved
PSO are 830376 and 000283987 The parameters of PF aresummarized in Table 2
The step response of 119880lowastdc(PU) jumps from 07 to 10 andthe 119880dc tracks the given value with PINN by improved PSOoptimization as shown in Figure 8 Training PINN to 26 stepsthe error 119890(119905) of algorithm is 14169119890
minus005 shown in Figure 9The optimization result for the DC bus voltage control ofPINN is effective
The HAF with DC bus voltage control by PINN isinstalled in the island microgrid system It can be seen fromFigure 10 that PINN has advantages over the conventionalPI and that the filtering functions are well performed bythe DC bus voltage controller under the different operatingconditions The maximum overshoot of the traditional PI isclose to 19 compared with 19 the maximum overshoot of119880dc with PINN is lowered to about 095 when 119880
lowast
dc is 07 TheDC bus voltage with PINN is stable at 013 s which is thelower than conventional PI and the response is quicker andsmoother than the conventional PI
Journal of Control Science and Engineering 7
Table 3 Harmonic of microgrid system with HAF
Harmonic order A percentage of content ()5 03007797 011124111 0049815213 0019656523 00076863325 00046405535 027077737 0279686All 096
By using the HAF with DC bus voltage PINN control thetotal THD
119894of the island Microgrid system is reduced from
849 to 096 Figure 11 presents the results of the smoothcurrent and reduced harmonic All the harmonics are thatlower than the national standards are summarized in Table 3
5 Conclusions
Due to the harmonic interference of nonlinear loads theHAF is used to protect the security of the island Microgridsystem An optimizationmethod based on improved PSO fordesign ofHAFDVcontrol is developed by usingPINN insteadof conventional PI The coordinated design problem of DCbus voltage control is formulated as a nonlinear constrainedobjective optimization problem where improved PSO isemployed to search for the optimal solutions Comparingcontrollers of PINN and conventional PI simulation resultsshow that HAFDV control with PINN has more effectivecontrol results better stability and lower overshoot of DCvoltage and more rapid response than conventional PI
References
[1] Z Ke L An X Xiang-yang and Z Wei ldquoDC side capacitorrsquosdesign and voltage control in high-capacity active power filterrdquoPower Electronics vol 4 no 41 2007
[2] GMing zhen R Zhen T Zhuo yao and L Q zhan ldquoOptimiza-tion design for capacity on passive active hybrid power filtersrdquoJournal of the China Railway Society vol 5 no 21 pp 43ndash461999
[3] L Shiguo ldquoOptimal design of DC voltage close loop control foran active power filterrdquo inProceedings of International ConferenceonPower Electronics andDrive Systems vol 2 pp 565ndash570 1995
[4] Z Dong L Zheng-yu and C Guo-zhu ldquoCapacitor voltagecontrol of shunt active power filterrdquo Power Electronics vol 10no 41 2007
[5] H Akagi and T Hatada ldquoVoltage balancing control for a three-level diode-clamped converter in a medium-voltage trans-formerless hybrid active filterrdquo IEEE Transactions on PowerElectronics vol 24 no 3 pp 571ndash579 2009
[6] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid active filter for reactive and harmonics compensationin a distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 3 pp 670ndash677 2009
[7] H Akagi and R Kondo ldquoA transformerless hybrid active filterusing a three-level Pulsewidth Modulation (PWM) converterfor amedium-voltagemotor driverdquo IEEE Transactions on PowerElectronics vol 25 no 6 pp 1365ndash1374 2010
[8] A Luo W Zhu R Fan and K Zhou ldquoStudy on a novelhybrid active power filter applied to a high-voltage gridrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 2344ndash23522009
[9] P T Cheng S Bhattacharya and D M Divan ldquoControlof square-wave inverters in high-power hybrid active filtersystemsrdquo IEEE Transactions on Industry Applications vol 34no 3 pp 458ndash472 1998
[10] R Inzunza and H Akagi ldquoA 66-kV transformerless shunthybrid active filter for installation on a power distributionsystemrdquo in Proceedings of the 35th Annual Power ElectronicsSpecialists Conference (PESCrsquo04) pp 4630ndash4636 June 2004
[11] A Luo Z Shuai W Zhu Z J Shen and C Tu ldquoDesign andapplication of a hybrid active power filter with injection circuitrdquoIET Power Electronics vol 3 no 1 pp 54ndash64 2010
[12] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid power filter to enhance power quality in a medium-voltage distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 8 pp 2885ndash2893 2009
[13] J Dixon DC Link ldquoFuzzy control for an active power filtersensing the line current onlyrdquo in Proceedings of the AnnualPower Electronics Specialists Conference (PESC rsquo97) vol 2 pp1109ndash1114 1997
[14] N Hatti K Hasegawa andH Akagi ldquoA 66-kV transformerlessmotor drive using a five-level diode-clamped PWM inverter forenergy savings of pumps and blowersrdquo IEEE Transactions onPower Electronics vol 24 no 3 pp 796ndash803 2009
[15] I M Supratid ldquoA multi-subpopulation particle swarm opti-mization a hybrid intelligent computing for function opti-mizationrdquo in Proceedings of the 3rd International Conference onNatural Computation (ICNC rsquo07) vol 5 pp 679ndash684 August2007
[16] C Fan and Y Wan ldquoAn adaptive simple particle swarmoptimization algorithmrdquo in Proceedinhs of the Chinese Controland Decision Conference (CCDC rsquo08) pp 3067ndash3072 July 2008
[17] N Dongxiao G Zhihong and X Mian ldquoResearch on neuralnetworks based on culture particle swarm optimization and itsapplication in power load forecastingrdquo in Proceedings of the 3rdInternational Conference on Natural Computation (ICNC rsquo07)pp 270ndash274 August 2007
[18] L Rui G Yirong X Yujuan and L Ming ldquoA novel multi-swarm particle swarm optimization algorithm applied in activecontour modelrdquo in Proceedings of the WRI Global Congress onIntelligent Systems (GCIS rsquo09) pp 139ndash143 May 2009
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Journal of Control Science and Engineering 7
Table 3 Harmonic of microgrid system with HAF
Harmonic order A percentage of content ()5 03007797 011124111 0049815213 0019656523 00076863325 00046405535 027077737 0279686All 096
By using the HAF with DC bus voltage PINN control thetotal THD
119894of the island Microgrid system is reduced from
849 to 096 Figure 11 presents the results of the smoothcurrent and reduced harmonic All the harmonics are thatlower than the national standards are summarized in Table 3
5 Conclusions
Due to the harmonic interference of nonlinear loads theHAF is used to protect the security of the island Microgridsystem An optimizationmethod based on improved PSO fordesign ofHAFDVcontrol is developed by usingPINN insteadof conventional PI The coordinated design problem of DCbus voltage control is formulated as a nonlinear constrainedobjective optimization problem where improved PSO isemployed to search for the optimal solutions Comparingcontrollers of PINN and conventional PI simulation resultsshow that HAFDV control with PINN has more effectivecontrol results better stability and lower overshoot of DCvoltage and more rapid response than conventional PI
References
[1] Z Ke L An X Xiang-yang and Z Wei ldquoDC side capacitorrsquosdesign and voltage control in high-capacity active power filterrdquoPower Electronics vol 4 no 41 2007
[2] GMing zhen R Zhen T Zhuo yao and L Q zhan ldquoOptimiza-tion design for capacity on passive active hybrid power filtersrdquoJournal of the China Railway Society vol 5 no 21 pp 43ndash461999
[3] L Shiguo ldquoOptimal design of DC voltage close loop control foran active power filterrdquo inProceedings of International ConferenceonPower Electronics andDrive Systems vol 2 pp 565ndash570 1995
[4] Z Dong L Zheng-yu and C Guo-zhu ldquoCapacitor voltagecontrol of shunt active power filterrdquo Power Electronics vol 10no 41 2007
[5] H Akagi and T Hatada ldquoVoltage balancing control for a three-level diode-clamped converter in a medium-voltage trans-formerless hybrid active filterrdquo IEEE Transactions on PowerElectronics vol 24 no 3 pp 571ndash579 2009
[6] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid active filter for reactive and harmonics compensationin a distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 3 pp 670ndash677 2009
[7] H Akagi and R Kondo ldquoA transformerless hybrid active filterusing a three-level Pulsewidth Modulation (PWM) converterfor amedium-voltagemotor driverdquo IEEE Transactions on PowerElectronics vol 25 no 6 pp 1365ndash1374 2010
[8] A Luo W Zhu R Fan and K Zhou ldquoStudy on a novelhybrid active power filter applied to a high-voltage gridrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 2344ndash23522009
[9] P T Cheng S Bhattacharya and D M Divan ldquoControlof square-wave inverters in high-power hybrid active filtersystemsrdquo IEEE Transactions on Industry Applications vol 34no 3 pp 458ndash472 1998
[10] R Inzunza and H Akagi ldquoA 66-kV transformerless shunthybrid active filter for installation on a power distributionsystemrdquo in Proceedings of the 35th Annual Power ElectronicsSpecialists Conference (PESCrsquo04) pp 4630ndash4636 June 2004
[11] A Luo Z Shuai W Zhu Z J Shen and C Tu ldquoDesign andapplication of a hybrid active power filter with injection circuitrdquoIET Power Electronics vol 3 no 1 pp 54ndash64 2010
[12] V F Corasaniti M B Barbieri P L Arnera and M I VallaldquoHybrid power filter to enhance power quality in a medium-voltage distribution networkrdquo IEEE Transactions on IndustrialElectronics vol 56 no 8 pp 2885ndash2893 2009
[13] J Dixon DC Link ldquoFuzzy control for an active power filtersensing the line current onlyrdquo in Proceedings of the AnnualPower Electronics Specialists Conference (PESC rsquo97) vol 2 pp1109ndash1114 1997
[14] N Hatti K Hasegawa andH Akagi ldquoA 66-kV transformerlessmotor drive using a five-level diode-clamped PWM inverter forenergy savings of pumps and blowersrdquo IEEE Transactions onPower Electronics vol 24 no 3 pp 796ndash803 2009
[15] I M Supratid ldquoA multi-subpopulation particle swarm opti-mization a hybrid intelligent computing for function opti-mizationrdquo in Proceedings of the 3rd International Conference onNatural Computation (ICNC rsquo07) vol 5 pp 679ndash684 August2007
[16] C Fan and Y Wan ldquoAn adaptive simple particle swarmoptimization algorithmrdquo in Proceedinhs of the Chinese Controland Decision Conference (CCDC rsquo08) pp 3067ndash3072 July 2008
[17] N Dongxiao G Zhihong and X Mian ldquoResearch on neuralnetworks based on culture particle swarm optimization and itsapplication in power load forecastingrdquo in Proceedings of the 3rdInternational Conference on Natural Computation (ICNC rsquo07)pp 270ndash274 August 2007
[18] L Rui G Yirong X Yujuan and L Ming ldquoA novel multi-swarm particle swarm optimization algorithm applied in activecontour modelrdquo in Proceedings of the WRI Global Congress onIntelligent Systems (GCIS rsquo09) pp 139ndash143 May 2009
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Top Related