Assessing the Plurality of Actors and Policy...

Research ArticleAssessing the Plurality of Actors and Policy InteractionsAgent-Based Modelling of Renewable Energy Market Integration

Marc Deissenroth Martin Klein Kristina Nienhaus and Matthias Reeg

German Aerospace Center Institute of Engineering Thermodynamics Department of Systems Analysis and Technology AssessmentPfaffenwaldring 38-40 70569 Stuttgart Germany

Correspondence should be addressed to Marc Deissenroth marcdeissenrothdlrde

Received 2 June 2017 Revised 1 September 2017 Accepted 31 October 2017 Published 10 December 2017

Academic Editor Liz Varga

Copyright copy 2017 Marc Deissenroth et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The ongoing deployment of renewable energy sources (RES) calls for an enhanced integration of RES into energy marketsaccompanied by a new set of regulations In Germany for instance the feed-in tariff legislation for renewables has been successivelyreplaced by first optional and then obligatory marketing of RES on competitive wholesale marketsThis paper introduces an agent-basedmodel that allows studying the impact of changing energy policy instruments on the economic performance of RES operatorsandmarketersThemodel structure its components and linkages are presented in detail an additional case study demonstrates thecapability of our sociotechnical modelWe find that changes in the political framework cannot bemapped directly to RES operatorsas behaviour of intermediary market actors has to be considered as well Characteristics and strategies of intermediaries are thus animportant factor for successful RES marketing and further deployment It is shown that the model is able to assess the emergenceand stability of market niches

1 Introduction

Electricity and heat production are the main sources ofworldwide CO2eq emissions and hence one of the maindrivers of anthropogenic climate change [1] In order toensure a successful transition of these sectors to carbon-freeor low-carbon a further expansion of the usage of renewableenergy sources (RES) is needed [2] To initiate the neces-sary investments and changes in technical organizationaland financial regimes various policy approaches are beingdiscussed and implemented In 2016 most countries in theworld had RES targets or support policies in place [3]

As one of the earliest examples the German governmenthas adopted targets for the installation of renewables by2025 the share of renewable energy in the electricity sectorshall be expanded to 40ndash45 and to 55ndash60 by the year2035 [4] The most important policy instrument to achievethese targets is the Renewable Energy Sources Act (GermanldquoErneuerbare Energien Gesetzrdquo) (EEG) which was enactedin 2000 [5] Its longevity and structural stability make ita fruitful case study to investigate energy policy in the

field In its original state it mainly operated as a feed-intariff (FiT) law which guaranteed a fixed remuneration forrenewable energy sources for electricity (RES-E) It has beeneffective in fostering the deployment of RES-E [6] Severalamendments and revisions have been undertaken such as in2012 when theGerman government introduced for exampleamonthly adjustment of feed-in tariffs for solar panels and anoptional variable market premium to support the marketingfrom RES-E at the power exchange [7 8] (see ldquoThe MarketPremiumrdquo in the appendix)

The main intention of the EEG is to have a regulatoryimpact on the market conditions and the technoeconomicregime as well as on the involved market actors who playa key role in the energy systemrsquos transition as they providethe necessary investments in RES-E technologies Howeverthe invoked investment dynamics were not stable underall circumstances With the fall of system prices and theaccompanying relative sluggish adjustments of incentives thedeployment of solar plants in Germanywent up from roughly20GW in 2008 to 75 GWa in the years 2010ndash2012 Thedeployment went back to 19 GW in 2014 [9] which created

HindawiComplexityVolume 2017 Article ID 7494313 24 pageshttpsdoiorg10115520177494313

2 Complexity

considerable market distortions and unstable investmentbehaviour

The deployment and integration of RES can only bereliably regulated as long as policy instruments do considerthe interdependencies and interactions with and of theinvolved actors aswell as the resultingmarket interplay on theinvestment dynamics The motivation for the developmentof the agent-based model AMIRIS is therefore to studythe adequacy of policy measures which affect the entitiesthat comprise the electricity system the aim is to examinethe impact of policy on the involved market actors on themicrolevel (eg income situation of renewable power plantoperators) as well as their effects on the macrolevel (egpower exchange prices and market structure) [10]

The remainder of the paper is structured as followsIn Section 2 we will elaborate on the complexity of theenergy system transition and our motivation to choose anagent-based model (ABM) approach to address our researchquestions Section 3 will give a brief overview of the AMIRISmodel For further detail the technically interested readercan refer to Section 4 which describes the agents and theirbehaviours in detail To exemplify themodelrsquos capabilities andquestions to be addressed Section 5 presents a case studyon the marketing of RES-E at the power exchange and howan amendment of the policy regime affects market actors indifferent ways Here we will show how the heterogeneity ofagents for example different portfolios affects the incomeand behaviour of the represented renewable electricity mar-keters and power plant operators Section 6 discusses the casestudy and gives an overview of the lessons learned from theuse of the ABM approach Section 7 concludes with lessonslearned from both the case study and themodelling approachin general

2 Modelling the Complexity ofEnergy Transitions

21 Challenges of Modelling the Impact of Energy PolicyMeasures on the Behaviour of Actors The pathway of thedevelopment of the global energy system namely the antic-ipated shift of supply from centralized fossil-fuelled powerplants towards a decarbonised and RES dominated regimeis uncertain many possible energy futures are conceivable[12] Part of the uncertainty of which energy future willmaterialize results from the unexplored behaviour of themarket actors who implement new technologies as theirrelationships and intentions remain understudied Bale etal [13] state that ldquoEnergy systems can be understood ascomplex adaptive systems in that they have interrelatedheterogeneous elements (agents and objects) In additionthere is no autonomous control over the whole system andin that sense self-organized emergent behaviour arises thatcannot be predicted by understanding each of the componentelements separatelyrdquo As such the result of markets at themacrolevel of the system is based on a variety of individualactions on the microlevel [14]

In Germany individual options of choices and the num-ber of actors in the system have increased substantially sincethe liberalization of electricity markets and the introduction

of the EEG and its several amendments [17] They decideunder the influence of cognitive biases [18 19] and inherentuncertainty and are therefore only bounded rational [20]Policies are directed towards those actors to induce a desiredcollective behaviour and are uncertain in their effect as well

Electricity is different to most other commodities forat least two reasons it is not storable at low costs and thedemand side is only marginally elastic Hence it is necessaryto balance supply and demand on short notice at all timesin order to ensure system stability This situation got morechallenging with the large-scale integration of RES-E intothe system Due to inherent output forecast limitations andtheir nondispatchability RES-E can always be subjected tohigh balance energy cost due to day-ahead forecast errorsand cannot hedge risks on future markets [21ndash24] As suchadditional intermediary market actors which specialize inforecasting and dispatching variable renewable energy (VRE)emerged These intermediary market actors increased theorder of complexity in the market

Additionally complicating is the fact that diverse elec-tricity markets like spot and futures control energy as wellas CO2 certificates markets interacting with and influencingeach other [25] As a result the heterogeneous power plantand marketing actors can react very differently to energypolicy adjustments and the development of the electricitysystem as a whole can follow diverse pathways [26] This isa tremendous challenge from a modelling perspective

22 Overview of Agent-Based Models in Energy SystemModelling Given the challenges mentioned above we havechosen an agent-based modelling (ABM) approach whichaddresses these questions by placing the actors their interre-lationships and their influencing environment in the centreof the modelling exercise [14] The origin of the ABMapproach is found in the field of artificial intelligence andcellular automata research and has been used for analysingcomplex and interrelated systems in such various researchdomains as ecology social sciences and software engineering[27]TheABM approach enables themodeller to describe thecomplex relationships of the systems entities by identifyinga set of attributes behavioural rules adaptations of thosebehavioural rules in response to the behaviour of others andthe environment and an environment itself [28]The analysisis executed step by step and allows for developing these rela-tionships on an evolutionary path in an artificial laboratory-like environment [29 30] Agent-based models are thereforeparticularly suitable for the simulation of multiply linkedand complex systems with autonomous actors The systemrsquosbehaviour is not centrally determined but evolves bottom-upfrom the actions taken by the individual agents to a complexsystem with emergent structures

The ABM approach has been successfully applied in theenergy sciences Recent publications have investigated therole of certain technologies like the market diffusion of PV[31 32] and biomass power plants [33] or the value of storagetechnologies [34] Others have put their focus on certainaspects of the demand side of the energy system as this aspectis associated with a need for a more ldquohumanrdquo modelling andpreference depiction their works focus on demand response

Complexity 3

Technoeconomic regimeTechnology and cost environment which determines the material scope of decision-making of actors

Coordination mechanisms coordinate the decisions of actors via for example market or bureaucraticstructures

Regulatory framework regulates coordination and constrainsor expands the scope of decision-making of actors orinfluences the technoeconomic regime via policy instruments

Actors adapt toenvironment andcoordinate for example via markets

Figure 1 A sketch of the system that is represented by the AMIRIS model

[35ndash37] adoption of dynamic tariffs [38] price elasticities[39] and smart meter diffusion [40] among others Anotherbranch focuses on energy trading on the balancing mar-ket [41] the merit order effect [42] emission trading andinvestment decisions [43] and forecasting [44 45] For acomprehensive review of energy market applications thereader might want to refer to [25 46] and to [47] for a specialfocus on newly emerging market structures

23 Conceptual Approach of the AMIRIS Model Figure 1depicts the modelrsquos scope of analysis it shows componentsand interrelations between actors regulatory frameworkstechnologies and markets which are addressed by the sim-ulation The technoeconomic layer represents technologiesand corresponding costs that are available to the actors ofthe energy system It is characterized by technical parameterslike efficiencies and durability values and cost parametersIn this sense the technoeconomic layer determines what istechnically feasible Actors sketched as dots in the technoeco-nomic layer coordinate themselves for example via marketslike the spot market and balancing energymarketsTheymayset up contracts to invest in technologies and sell or buyenergy

The technoeconomic layer is influenced in several ways bythe overlying regulatory framework layer which may changethe apparent costs of technologies by for example increaseof research and development in certain technologies deploy-ment incentives like feed-in tariffs or the financial promotionof RES-E direct marketing The term direct marketing hererefers to selling RES-E at market places for electricity via themarket premium model under the EEG (see ldquoThe MarketPremiumrdquo in the appendix) Furthermore this layer may aswell enhance or reduce actors action space by regulatingmarkets or by setting up rules that prohibit certain decisionsand behaviours of actors

Solid arrows represent possible vectors of analysiswhile dashed arrows are not explicitly incorporated inthe model More influences may appear in such a systemthat are not subject to the actual implementation like

for example feedback from actors to the regulatory levelor impacts from actors onto the technoeconomic layeritself

With the ambition to model the agents and the impactof policy framework adoptions in the process of market inte-gration of RES-E knowledge about the relevant actors andtheir expectations motivations and strategies is requiredTo depict the qualitative differences among market actorssystematic actors analysis has been carried out The actorscharacteristics of RES-E power plant operators and directmarketers have been developed on the basis of documentanalysis and expert interviews [10 48] These two agentstypes are modelled in detail compared to other (system)relevant actors of the power system (see Sections 3 and4) The assumptions were then tested and reassessed insemistructured expert interviews with representatives fromthe most important actor groups as well as in the context ofan actor workshop An exemplified version of the typecast ofactors into agents is given in the case study in Section 5 Thecurrent state of the model will be presented in the followingtwo sections

3 AMIRIS Model Overview

31 Agent Topology Themodel comprises two different typesof agents (a) agents with scope of decision-making and (b)agents without scope of decision-making Type (a) agentsare able to adapt to changed circumstances and may decidewhich action to perform Contrary to this type (b) agentshave strictly defined tasks to perform during simulation fromwhich they cannot deviate The model covers the followingtype (a) and type (b) agents

(i) Wind solar and biomass power plant operator agentsas well as the thermal power plant operators generateelectricity with their plants (type (a))

(ii) Direct marketer agents trade electricity from RES onthe power exchangemarket and control powermarket(type (a))

4 Complexity

Regu

lato

ry fr

amew

ork

Minutereservemarket

Energyexchange

Storageoperator

(Load)

Money owVirtual power owRegulatory inuence

Supplier

Windplant owners

Photovoltaicplant owners

Bioenergyplant owners

Conventionalpower plantowners

Directmarketers

System operator

Input dataFeed-in renewables balance energy price marginal costs conventional power plants load

Figure 2 The AMIRIS model

(iii) Optionally a storage operator agent can be associatedwith a direct marketer that in turn can improve theoperation and coordination of plants in her portfolio(type (a))

(iv) The day-ahead power exchange market agent deter-mines the wholesale power market price via a meritorder model (its implementation is discussed inSection 432) (type (b))

(v) The negative minute reserve market allows offeringcontrol power provision (type (b))

(vi) The grid operator agent manages the generated elec-tricity from wind solar and biomass which is nottraded by direct marketers It is sold mandatorily onthe day-ahead power exchange market (type (b))

(vii) The total load of the German power system serves asa static demand sink (type (b))

(viii) The regulatory framework agent holds informationabout the total installed power in the system theremuneration schemes and undertakes calculationsaccording to the EEG (type (b))

The agents interact in a changing environment influencedby the energy policy framework of the Renewable EnergySources Act (EEG) and its corresponding RES-E supportscheme as well as the Energy Industry Act [49] and gridregulations Figure 2 gives a schematic overview of themodel interconnections Boxes represent agents in themodel

multilayered boxes indicate that these agent types havemultiple instances during the course of simulation Solid linesrepresent money and power flows which are differentiatedby open and closed arrows respectively Regulatory influenceis depicted with dashed lines Wind PV and biomass powerplant operators (PPOs) can sell electricity either to the directmarketer or to the grid operator

As the focus of the AMIRIS model is to investigate theeffects of the market integration process of renewable energysources on the involved actors the cost and revenue structureof marketers that trade electricity from RES-E PPOs areimplemented in detail and will be discussed in Section 421PPOs can sign contract with direct marketers and switchcontracts at the beginning of each year if a better offer isreceived (see also Section 422)

32 Process Overview and Scheduling The model has a one-hour time resolution and is usually run over the course of8ndash20 calculative years Computation time on a conventionaldesktop computer is in the order of minutes Internal timeis set by the regulatory framework class The following stepsare calculated each time frame which equals one calculativehour

(i) Generated electricity and its virtual distribution todirect marketers or to grid operator are determined

(ii) The residual load the merit order and correspondingwholesale power market price are calculated

Complexity 5

Table 1 External input parameters for the AMIRISmodel 119897 indicates the type of the primary product as follows 119897 = 1 uranium 119897 = 2 lignite119897 = 3 coal and 119897 = 4 gas Index 119894 defines the power plant type with 119894 = 1 nuclear 119894 = 2 lignite 119894 = 3 coal 119894 = 4 combined cycle gas turbine(CCGT) 119894 = 5 open cycle gas turbine (OCGT) 119894 = 6 offshore wind 119894 = 7 onshore wind 119894 = 8 photovoltaics and 119894 = 9 biomass

Parameter Description Unit119862119897prim(119905) Time series of costs of the primary products used for the calculation of the stock market prices [euroMWh]119862carb(119905) Time series of cost for carbon dioxide emission certificates [euro119905CO2]119862119894var(119905) Time series of variable costs of conventional power plant of type 119894 = 1ndash5 [euroMWh]120578119894min(119905) Time series of minimal efficiency of conventional power plant of type 119894 = 1ndash5 []120578119894max(119905) Time series of maximal efficiency of conventional power plant of type 119894 = 1ndash5 []119908119894(119905) Normalized generation potential time series for 119894 = 6 7 8 []120572119894 Availability factor to regard shut-down periods (1205721 = 08 1205722 = 08 1205723 = 07 1205724 = 07 and 1205725 = 10) -PRbal(119881) Histogram of 2011 prices for balancing energy [euroMWh]119888mark Costs for marketing [euro]119888IT Costs for IT [euroa]119888tradevar Costs of charges for trading at the exchange market [euroMWh]119888tradefix Costs for permission of trading at the exchange market [euroa]119888liab Costs for the liability of equity to be able to trade at the exchange market payed once [euro]119888persspec(119881) Specific costs for personnel depending on traded volume [euroMWh]119888fcst(P) Costs for forecast of electricity generation volume dependent on installed capacity [euroMW]119872(119905) Time series of management premium according to the EEG [euroMWh]119877(119905) Time series of remuneration for renewable energy power plants according to the German Renewable Energy Act [euroMWh]119875119894inst(119905) Time series of installed power of corresponding technology 119894 [MW]119863(119905) Time series of demand for Germany [MWh]119866119894(119905) Power generation in 119905 from technology 119894 [MWh]

(iii) The grid operator calculates the marginal capacityprice for the control power provision of the negativeminute reserve market by a regression model

(iv) With an appropriate portfolio marketers can offerfirm capacity at the control power market

(v) Revenues and costs are assigned to the marketers andthe power plant operators

(vi) Marketers forecast the electricity production of theirportfolio and estimate the market price at 119905 + 24 hand decide on curtailment of contractedRES-E powerplants

33 Modelling Framework AMIRIS uses the free and opensource agent-based modelling and simulation developmentframework Repast Simphony which facilitates model designexecution and data export and serves as an initial contextbuilder for our model Repast Simphony has been con-jointly developed by the University of Chicago and ArgonneNational Laboratory [50] It is available directly from the web(httprepastsourceforgenet (last accessed 23092015))and licensed under ldquonewBSDrdquo (ldquoNewBSDrdquo is a BSD 3-ClauseLicense see httpsopensourceorglicensesBSD-3-Clause(last accessed 23092015)) The model is implemented inthe Java programming language (httpwwworaclecomtechnetworkjavaindexhtml (last accessed 23092015))

4 Agents and Input Data

41 Input Data At initialization of the program several datafiles are read according to the scenario under investigation

The files contain time series and lists as shown in Table 1 thatcan be categorized as input for (a) the electricity generationfrom renewable and conventional power plants (b) the calcu-lation of marginal costs of conventional power plants (c) thedirect marketersrsquo typecast and (d) the regulatory frameworkThe total installed power in the system 119875inst(119905) for all typesof technologies is based on a study for the Federal Ministryof Environment Nature Conservation Building and NuclearSafety covering long term scenarios of renewable energyplant deployments in Germany [51] For conventional powerplants the installed power is multiplied by an availabilityfactor to take shut-down periods into account In order torepresent the electricity generation of fluctuating renewablepower plants normalized generation potential time series119908(119905) for wind and solar are used These generation timeseries are derived by the EnDat module of the energy systemmodel REMix [52 53] EnDat uses a historic weather timeseries containing wind speeds and solar radiation of the year2006 that is processed with characteristic system curves forwind and photovoltaic power plants in Germany [52] In themodel the shape of the demand curve 119863(119905) is representedby the total German electricity demand of 2011 [16] Thescale can be varied according to the underlying scenariostudy Marginal costs are determined regarding fuel specificcosts and additional variable costs as well as costs for carbondioxide emission certificates Fuel specific costs are calculatedby primary product costs and efficiencies for correspon-dent technologies The calculationsrsquo underlying scenarios arefound in [51] and details on the applied values are given in[10]

6 Complexity

Costs 119888 for various marketing services for compensationsare represented in Table 1 and used for a typecast of the coststructure of actors The use of the various cost parameters isdescribed further in Section 421

The input for the regulatory framework is given bya time series 119872(119905) containing the management premiumand its decrease over time [54] (compare also ldquoRevenuerdquoin Section 421) The Renewable Energy Sources Act [4]and its remuneration schemes for different technologies arerepresented by time series 119877(119905)42 Agents with Scope of Decision-Making

421 The Direct Marketing Agents In the process of sim-ulation the direct marketer agents have the possibility ofbasing their decisions on the current market conditions Themarketerrsquos business is to profitably sell renewable electricityat the power exchange market Success or failure of theirbusinesses is evaluated by the profits 119901(119905) which is thedifference between revenues 119894(119905) and costs 119888(119905)

119901 (119905) = 119894 (119905) minus 119888 (119905) (1)

The typecast parameters shown in Table 2 allow a repre-sentation of the real market actors heterogeneity Differenttypes of marketers with diverse revenue and cost structures(compare Section 5) are implemented in the model Theforecast quality of a marketer described by 120590 and 120583 iscrucial for a successful business By reducing forecast errorsbalancing energy procurement costs can be minimised

Revenue Revenues can be generated by the support schemeas well as on two markets the power exchange marketand the control energy market with revenues 119894XM and 119894CErespectively In reality the control energy market consistsof the primary secondary and minute reserve marketsOn these pay-as-bid markets participants can offer controlpower to the system operator for grid stability require-ments The balancing energy market determines the cost (orincomes) for a trader or supplier that deviates from their day-ahead schedule within its corresponding balancing regionBalancing market prices are determined by control energydemand requirements of the system operator Hence it israther an accounting system than a market

Additional regulated revenues are derived from payoutsof the management premium 119872(119905) for direct marketingWithin the implementation of the market premium schemein the year 2012 the management premium has been intro-duced as additional entity for compensating for the costsassociated with direct marketing duties compared to theFiT scheme (see ldquoThe Market Premiumrdquo in the appendix)The more efficiently direct marketers fulfill their marketingservices for RES-E power plant operators (PPO) the higherthe decision scope for either increasing their own profits orthe bonus payments to their associated PPOs (see also ldquoBonusPaymentsrdquo below)

Whereas the power exchange market represents themarketerrsquos primary source of revenue participation in thecontrol energy market is optional The model allows forthe participation in the negative minute reserve market

Table 2 Variables describing properties of direct marketers Varia-tions of variable values are used to define the type of marketer andto reflect heterogeneity of actors

Variable Unit Description

120590price

Uncertainty of priceforecast of direct marketerdepending on the tradedvolume 119881 with values 01502 or 025

120590power

Uncertainty of powerforecast of direct marketerwith values 015 02 or 025

120583power

Estimated value of powerforecast of direct marketerwith values 005 01 or 015

P [MW]

Power generation portfolioof marketer that isP = sum120591rc P120591rc oftechnologies 120591 in

remuneration classes rcC [euro] Initial capital of marketer

(due to opportunity costs with the day-ahead spot marketbiddings and the required curtailed operation mode positivereserve provision is financially not attractive for RES-E plantoperators and is therefore not modelled) The marginalcapacity price at which bids of the direct marketing agentsare accepted is determined by the grid operator agent everyfourth simulated time step by a multiple linear regressionmodel (compare Section 431)

The direct marketing agents can follow two biddingstrategies to maximize profits

(i) ldquoLow-Risk-Strategyrdquo with this strategy marketersoffer a capacity price on the pay-as-bid market corre-sponding to the median of the preceding monthrsquos 1804 h-price-blocks This way acceptance of a bid is verylikely but only at a relative low capacity price ΠCE

(ii) ldquoHigh-Risk-Strategyrdquo with this strategy marketersoffer a capacity price on the pay-as-bid market corre-sponding to the median of the preceding monthrsquos 1804 h-price-blocks plus the standard deviation of thesepricesThis way acceptance of a bid is less likely but incase of acceptance a relatively high capacity priceΠCEis ensured

Further revenue 119894bal(119905) can originate in case the own localimbalance can reduce the imbalances of the correspondingbalancing grid region

Costs Both fixed and variable costs are considered in thetotal cost determination For yearly fixed costs 119888fix IT andtrading permission are regarded Further upon starting thedirect marketing business the marketer has to provide aliable equity The different positions of variable costs dependprimarily on the amount of electricity traded by the directmarketer Trading fees are to be paid for each traded MWh

Complexity 7

100 200 300 400 5000Installed power (MW)

0

10

20

30

40

50Sp

ec p

erso

nnel

cost

(euroM

Wh)

(a)

00

01

02

03

04

05

06

07

2000 3000 4000 50001000Installed power (MW)

Spec

per

sonn

el co

st (euro

MW

h)(b)

Figure 3 Specific personnel costs 119888persvar per installed capacity of the marketers in the model Data from [11]

whereas costs for balancing energy depend on the deviationbetween the forecast and actual VRE generation

The balancing energy price is determined at each timestep by the grid operator by uniform random selection outof a price histogram based on balancing energy prices ofthe year 2011 in Germany The balancing price as well asthe balancing volume may take negative and positive valuesthus balancing costs can contribute to the marketersrsquo revenuefor 119888bal(119905) lt 0 and 119894bal(119905) = minus119888bal(119905) (see also (A1) in theappendix)

Payments for balancing energy and expenses for the staffand IT are the largest cost positions for direct marketers[11]The specific personnel costs reveal substantial economiesof scale and range from several euroMWh for portfoliossmaller than 50MW to only eurocentsMWh for +500MWof contracted VRE capacities (compare Figure 3) Addi-tionally expenses for the power output forecast 119888fcst affectthe profit calculation As direct marketers mainly managea generation portfolio and do not own the correspondingplants a competition for acquisition of generation plantsfollows To bind customers and to be financially attractive topotential new customers marketers make bonus paymentsfor the contracted power plant operators another cost factordescribed in the following section

Bonus Payments At the start of the simulation the bonusis defined to be half of the management premium of thecorresponding year that is 119888bonus(119905 = 0) = (12)119872(119905 = 0) Inorder to guarantee the direct marketer flexibility and controlover costs bonus payments can be adopted at the end of eachsimulated year Within each adoption process the specificoperating results120573(ORspec) are evaluated Further the ratio ofcapital to operating results may additionally adjust the bonuspayouts by 1205731015840(ORcapital) in case of negative operating results

Table 3 Definition of bonus parameters 120573 and 1205731015840 depending onoperating results (OR) that is ORcapital = CORORspec [euroMWh] 120573 ORcapital 1205731015840ge10 11 0 00[06 10[ 105 ]0-1] 05[04 06[ 100 ]1-2] 07[02 04[ 095 ]2-3] 08lt02 090 ]3-4] 0875

]4-5] 095

The values for the bonus adjustments are given in Table 3The bonus does not merely increase the profit margins of themarketers instead they will invest their surpluses to increasethe bonus payouts for the PPOs if the specific operationalresults are larger than 05 euroMWhThis definition ensuresa competition between the marketers seeking to attract newPPOs In the model bonus costs are thus calculated by

119888bonus (119905)=

119888bonus (119905 minus 1) sdot 120573 (ORspec) sdot 1205731015840 (ORcapital) for OR lt 0119888bonus (119905 minus 1) sdot 120573 (ORspec) for OR ge 0

(2)

Curtailment The AMIRIS model allows for a market-drivencurtailment of RES-E according to the incentives of theimplemented policy instrument In case of potentially highrenewable electricity generation and low demand the mar-keter may decide to switch off plants of her portfolio toavoid payments due to negative wholesale electricity prices

8 Complexity

(compare Section 432) The marketerrsquos decision is based ona price forecast given by

Πfcst (119905) = Πperf (119905 + 24) sdot (1 + 120590price sdot 119892) (3)

with the random error variable 119892 drawn from a normaldistribution times the perfect foresight price Πperf (119905 + 24)Plant specific opportunity costs for curtailment determinewhether RES-E generation is being curtailed The estimationof these costs depends on the variable market premium 119865(119905)and the management premium 119872(119905) according to

1003816100381610038161003816Πfcst (119905)1003816100381610038161003816 ge 119865 (119905) + 119872 (119905) for Πfcst (119905) lt 0 (4)

In case the sumof both premiums is lower than or equal to theabsolute value of the forecast wholesale power market priceΠfcst(119905) the direct marketer will advise the correspondingPPOs to shut-down generation

422 The RES-E Power Plant Operator Agents The potentialgeneration of electricity from renewables is given by the plantoperatorrsquos installed capacityPrc120591 multiplied by a normalizedweather time series 119908119894(119905)

119866rc120591 (119905) = P120591rc (119905) sdot 119908119894 (119905) (5)

with 119894 = 120591 in this casePlant operator agents are distinguished primarily by the

generation technology 120591 in operation that is plants usingwind solar radiation or biomass as well as by the corre-sponding remuneration class rc the technology is assignedto (see also Section 434) The height of the remunerationclass rc is calculated from empirical data about historicaldevelopments of FiTs and so-called ldquovalues to be appliedrdquo(replacing the FiT in the direct marketing regime) [55]Each RES-E technology is subdivided in four representativeremuneration classes since the remuneration for a specificplant depends on the year of installation the resource sitethe type and size of the technology and the energy carrierin use (the resource site is taken into account for windpower plants the type and size of technology is relevantfor PV and biomass plants and the energy carrier in usefor biomass plants only) Table 4 lists all characterizingparameters for the renewable power plant agents Theirrevenue is based on the remuneration of the fed-in electricityas well as on the bonus payments 119894bonus they receive fromthe direct marketers The value of 119894bonus corresponds to thecosts of the marketer 119888bonus PPOs opting for direct marketingreceive new bonus offers at the beginning of each year fromdifferent direct marketing agents (see also ldquoBonus Paymentsrdquoin Section 421) To capture transaction costs when switchingthe partnering agent the difference between the old and newbonus offer must at least exceed a certain threshold 119909minThisthreshold increases with the height of the remuneration classrc as the relative attractiveness of additional bonus paymentscorrelates directly with the height of remuneration an agentis already receiving (see also Section 5)

43 Agents without Scope of Decision-Making Figure 2 showsall agents in the AMIRIS model Direct marketers and power

Table 4 Variables that characterize the type of renewable powerplant agents


120591 - RES-E technology of thepower plant operator

rc - Remuneration class thisagent is assigned to

P120591rc(119905) [MW]Installed capacity of this

technology in thecorresponding

remuneration class

119909min [euroMWh]

Threshold which needs tobe exceeded by a newbonus offer in order to

switch contracts with directmarketers

plant operators are implemented with heterogeneous charac-teristicsThey have several options for decision-making Nev-ertheless other agents without scope of decision-making areinevitable to complete the electricity systems representationHence they hold important information for the hole systemsfunctionality They perform model endogenous calculationsthat are not subject to their own pursuit of strategic goals likerevenue maximization

431 Grid Operator Agent According to the Ordinance ona Nationwide Equalisation Scheme (German ldquoAusgleich-smechanismusverordnungrdquo) [56] the grid operator is re-sponsible for the settlement of the support schemes in placeand the payouts of FiTs andmarket premiums to the PPOs ordirectmarketers respectively He calculates ex post the heightof the market premium for each remuneration class rc Forthis he receives the past months market values MV120591 of theVREs from the wholesale power market agent

The agent also determines the balance energy price byuniform random selection of PRbal Additionally the gridoperator conducts the auctions for the negative minutereserve market The marginal capacity price MCPCE isdetermined by a multiple linear regression model with theindependent variables of the wholesale power market price1199091 the load 1199092 and the onshore wind feed-in 1199093

MCPCE (119905) = minus1205721 sdot sum119905+4119905=ℎ 1199091ℎ4 minus 1205722 sdot sum119905+4119905=ℎ 1199092ℎ4 + 1205723sdot sum119905+4119905=ℎ 1199093ℎ4 + 120573

(6)

with 1205721 = 05304 1205722 = 00029 1205723 = 00005 and 120573 = 1541The estimation of the regression parameters 120572 has been

derived from the negative minute reserve prices of the year2011 [10]

432Wholesale PowerMarket Agent The agent representingthe power exchangemarket defines thewholesale power priceevery time step and disburses the market revenue to the cor-responding agents according to the uniform market clearing

Complexity 9

Table 5 Associated residual loads RL and wholesale power prices according to analysis of market situations with low (0ndash20 euroMWh) andnegative (lt0 euroMWh) prices in Germany 2011 [15 16]

Power price [euroMWh] 20 10 5 0 minus5 minus10 minus30 minus50 minus75 minus100RL intervals [GW] 296 271 266 261 257 207 157 117 87 67

minus10

0

10

20

30

40

50

60

10 20 30 40 50 60 700Time (month)

Pric

e (euro

MW

h)

Figure 4 Average monthly wholesale power market prices gener-ated by the model (the underlying data input is given in the casestudy Section 5) The line represents a linear fit to the data

price MCPXM For the calculation of the MCPXM a meritorder model is implemented The merit order calculation isbased on the residual load and the marginal costs of theconventional power plants MCPPconv Marginal costs of eachpower block 119902 of 200MW are set by (see also Table 1)

(i) fixed and variable costs of primary products 119862prim(119905)(including fuel transportation or shipping)

(ii) certificate costs of carbon dioxide emissions 119862carb(119905)(iii) efficiencies 120578(119905) of the power plants(iv) other variable costs 119862var(119905) (ie for insurance etc)

Once these costs are determined they are ordered from thelowest to the highest value The MCPXM is set by the last200MW power bloc 119902 needed to satisfy the residual load

MCPXM (119905) = min(MCPPconv | 119899sum119894=1

119902119894 le RL) (7)

Simulated average monthly clearing prices are shown inFigure 4 for the years 2014 to 2019 Over the course of thesimulation the price-spread increases due to rising CO2-certificate and fossil fuel prices but the average price decreasesdue to the increased VRE feed-in with marginal costs ofapproximately 0 euroMWh The general structure of the pricecurve reoccurs annually because only one representativeweather year and load profile are used

Conventional must-run (must-run capacities are dueto power plants that offer complementary goods on othermarkets (like ancillary services or heat) and therefore need tobe present in the wholesale market at all times irrespectiveof very low or negative wholesale market prices) capacity

is included via the definition of so-called ldquoresidual loadintervalsrdquo The residual load intervals have been derivedfrom the analysis of market conditions in which wholesalemarket prices have dropped below 20 euroMWh (reference year2011 [10]) If the lower-bound of an interval boundary isexceeded in a specific hour the regular MCPXM calculationmechanism described above is replaced by the associatedprice of the corresponding residual load interval Table 5 givesthe residual load reference values and its associated wholesalepower prices of the year 2011 in Germany Over the courseof the simulation the interval boundaries decrease from yearto year according to the development of the retirement ofconventional base-load capacities in [51]

The calibration of the power exchange model is con-ducted by markups and markdowns of the conventionalpower plant agents which are added to or subtracted fromthe MCPPconv values The validation of the merit order modelcan be found in [10]

433 Demand Side Agent The modelrsquos demand side isrepresented by a time series comprising total load values foreach simulation stepThe annual total energy consumption isscaled according to scenario A values from [51]

434 Regulatory Framework Agent The regulatory frame-work agent holds all the energy policy information necessaryfor simulating the market integration process of RES-EThe law differentiates the remuneration for PPOs dependenton the general type of the RES-E technology installed thepotential full-load-hours at the installation site for windonshore plants the size of the plant for PV plants andthe chosen technology of biomass plants as well as on thecorresponding biomass substrate in use [4] In additionas remunerations decrease over the years (since 2012 thedecrease of remunerations for wind onshore and PV plantsis carried out on a quarterly or even monthly basis) acomplicated payout structure has evolved in reality since2000 As a consequence by the year 2017 there are over 5000different remuneration categories within the EEG supportscheme and about 15 Mio RES-E power plants in place [55]

A mapping of plants to actors in every detail wouldrequire knowledge about each owner plant type and remu-neration for each plant Besides the fact that such informationis if at all not easy to accessmapping of all PPOs individuallywould lead to a multiagent system (MAS) with over a millionagents to be parametrized

Therefore four different remuneration classes are definedfor each year and each renewable technology type 120591 Thismore homogeneous assignment allows for a transparenthandling of the remuneration schemes in the model Eachclass contains information about the remuneration the tech-nology and the corresponding installed power

10 Complexity

Table 6 Table representing the direct marketersrsquo initial portfolios

Direct marketer BM [MW] PV [MW] Wind [MW]Big utility 522 1697 14145Municipal utility 904 3394 8492Small municipal utility 395 3394 1619Green electricity provider 930 1697 3237Startup 2602 23759 6873

The regulatory framework agent saves and updates thisinformation at the beginning of each year and remits therelevant data to the grid operator agent who is in chargefor the payouts of the support instrument in place (see alsoSection 431) Further the agent calculates the referencemarket values MV120591ref on a monthly basis and governs theheight of the management premium (compare ldquoThe MarketPremiumrdquo in the appendix)

5 Case Study

51 Model Setup and Agent Parametrization In this sectiona case study shall demonstrate the modelrsquos basic workingmode and give an example for possible fields of analysesThe case study examines the effects of a change in theregulatory framework taking into account the interplay ofthe power plant owners and their possibility of changing theircontracted direct marketers

The regulatory framework refers to the market premiumunder the German Renewable Energy Sources Act (EEG) inits version of 2012 [7] when the market premium scheme hasbeen introduced Two variations of the correspondent man-agement premium are analysed In ldquoScenario 1rdquo the level ofthe management premium 119872(119905) for variable (VRE) and dis-patchable renewables is set to 37 euroMWh and 1125 euroMWhrespectively in accordance with the initial values of the EEG2012 In ldquoScenario 2rdquo 119872(119905) for VRE is reduced by 50to 185 euroMWh for dispatchable renewables no changes areassumedThis decrease of themanagement premium forVREreflects the decision of policymakers in 2012 when figuringout that the original height of 119872(119905) has led to considerablewindfall profits for wind PPOs

On the basis of an actor analysis [10 48] (compareSection 421) five different types of direct marketers wereaggregated for this case study (1) big utility representing bigand medium power supply companies (2) municipal utility(3) small municipal utility (4) green electricity provider and(5) startup The technology specific size of the portfolios islinearly growing each month according to the underlyingtime series of installed power of each technology Thesenumbers are based on empirical data on the number of plantoperators receiving FiTs or market premiums published bythe grid operators in Germany [55] In the simulation yearlychanges in portfolio sizes and composition might take placedue to the marketersrsquo competition for PPOs The simulationperiod for the case study is set to 2014 to 2019

The initial technology specific composition of the portfo-lios for the starting year 2014 is displayed in Table 6 A moredetailed resolution disclosing corresponding remuneration

classes can be found in Table 9 Other important differentia-tion factors are the direct marketersrsquo specific forecast capabil-ities as well as their capital resources (compare Section 421and the appendix) Their initial parametrization is given inTable 7

In Section 421 we describe how the bonus payments ofmarketers are changing throughout the simulationThe PPOscan cancel their contract at the end of each simulation yearand enter into a new contract with another direct marketeroffering higher bonus payments if the corresponding thresh-old value of 119909min is exceeded (compare Section 422) Thethreshold 119909min depicts transaction costs and is parametrizedaccording to the power plantsrsquo remuneration classes It isassumed that contracts for plants in lower remunerationclasses have lower thresholds as they gain proportionallyhigher revenues (compare Section 422) Values have beenderived by taking the height of the starting bonus roundingit to an integer and dividing it by four The corresponding119909min values per remuneration class are displayed in Table 8

52 Results

Scenario 1 In this scenario the height of the managementpremium is set according to the EEG2012Overall good oper-ating results are achieved by all marketers in this case exceptfor the smallmunicipal utility (see Figure 5(a))Thismarketershows a nonprofitable operation for 5 of the 6 simulatedyears and operates with constantly decreasing bonus payoutsThe big municipal utility and the green electricity providerstart with the highest operating results of about 12 euroMWHand 18 euroMWh respectively Their average results showa decrease in the following years and a convergence to05 euroMWh Both marketers increase their bonus payoutsaccordingly reaching a maximum of up to 25 euroMWh inthe last year of simulation The operating results of startupsand big utilities exhibit a slow but steady growth for thefirst-mentioned marketer and a nearly constant income onaverage for the big utilities Both fluctuate around a profit of05 euroMWhanddecrease or increase their bonus payouts overthe years according to their operational results

The specific balance energy cost (compare Figure 5(c))of the small municipal utility is between double and triplethe costs of its competitors This cost factor does not changesignificantly over time and therefore poses a constant burdenfor the marketer

The switch of power plant owners to other marketersoffering a higher bonus payment starts after year two ofthe simulation At this moment the gap between lowestand highest bonus offered is large enough to encourageplant owners with a small threshold to switch the marketingpartner The small municipal utility is the first to loseclients to the green electricity provider as the differenceof the bonus payouts is the largest between these two seeFigure 5(b) In the following years a part of the clients ofall other marketers switch to the green electricity provideras well except for clients from the big municipal utilityOver the course of the simulation the big utilities portfoliois reduced by about 5GW the one of the small municipalutility is reduced by about 27GW and the startup loses

Complexity 11

Table 7 Table representing the direct marketersrsquo initial forecast uncertainties and capital resources

Direct marketer 120590price 120590power 120583power MeuroBig utility 015 015 005 100Municipal utility 015 015 005 50Small municipal utility 025 025 015 20Green electricity provider 02 015 005 20Startup 015 02 01 20

Table 8 Table representing the power plant ownersrsquo changing thresholds 119909min

Remuneration class WAB [euroMWh] PV [euroMWh] BM [euroMWh]1 05 05 052 10 10 203 15 15 154 20 20 10

Table 9 Installed capacity per remuneration class as assigned to the marketers at the beginning of simulation

Direct marketer BM [MW] PV [MW] Wind [MW]Big utility

RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195

Municipal utilityRC 1 719 1761 1030RC 2 45 1134 3339RC 3 125 59 3725RC 4 15 440 398

Small municipal utilityRC 1 240 1761 206RC 2 15 1134 668RC 3 125 59 745RC 4 15 440 -

Green electricity providerRC 1 479 881 412RC 2 30 567 1336RC 3 375 29 1490RC 4 46 220 -

StartupRC 1 599 12329 824RC 2 37 7940 2671RC 3 1750 412 2980RC 4 216 3077 398

about 2GW The sum of them is added to the portfolio ofthe green electricity provider doubling its portfolio size seeFigure 7(a)

Scenario 2 In the scenario with a 50 reduced managementpremium for VRE the simulation shows a different devel-opment of the marketers business success as can be seen inFigure 6 The ldquobig municipal utilityrdquo and green electricityprovider start with positive operating results the other

marketersrsquo results are negative Whereas the green electricityprovider can assure his income throughout the simulationand increases his bonus payouts the ldquobig municipal utilityrdquoearns about 05 euroMWh until year four hardly changing thebonus In this year the gap between own bonus payoutsand the highest payouts of the green electricity provider islarge enough to lose wind and biomass power plants Theloss of biomass plants especially reduces the high profitableincome from the reserve market and accordingly the bonus

12 Complexity

Big utilityMunicipal utilitySmall municipal utility

Green electricity providerStartup

minus15

minus10

minus05

00

05

10

15

20Operational result

1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35

40Specic balance energy costs



1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25

301e7 Income control energy



(euro)

1 2 3 4 5 60(Year)

(d)

Figure 5 Specific operational results bonus payouts balance energy costs and income from the control energy market for all 5 marketersin the first scenario

is reduced in the following years with negative results of aboutminus08 euroMWhThe startup has an operational result of just below zero

depletes all its available capital until the fourth year and

reduces its bonus payout to 0 euroMWh Already after thesecond year the bonus difference to the green electricityprovider is too large losing a part of its biomass power plantsto this competitor Accordingly the income of the reserve

Complexity 13

minus4

minus3

minus2

minus1

0

1

2

3Specic operational result

(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7

8 1e7 Income control energy

(euro)

1 2 3 4 5 60(Year)



(d)

Figure 6 Specific operational results bonus payouts balance energy costs and income from the control energy market for all 5 marketersin the second scenario with reduced management premium

market decreases while the cost for balance energy increasesThe specific operational result drops to about minus1 euroMWh inyear threeThe capital of the startup is used up and bonus pay-ments are stopped Biomass wind and photovoltaic power

plant operators switch to the green electricity provider thatoffers the highest bonus payouts The new portfolio impliesa reduction of balance energy costs leading to a positiveoperational result in year four Yet the capital stock remains

14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM

Big municipal utility

Green electricity provider Green electricity provider

Small municipal utility



Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Evolution of the marketersrsquo portfolios for Scenario 1 (a) and Scenario 2 (b)

negative and bonus payouts are still ceased A large fractionof the remaining biomass plants leave the startup resultingin increased balance energy costs and negative operationalresults of up to minus2 euroMWh in the following years

With an operational result of about minus06 euroMWh overthe years the big utility gradually reduces its bonus payoutwithout hardly any effect on its resultsThe only slow decreaseof bonus is due to the operational result to capital ratiocompare Table 3 and Figure 8 The small municipal utilityloses money for every MWh produced On average thismarketer is losing every year 06 euroMWh more than in theprevious year After the fourth year it stops bonus payoutsand most of its portfoliorsquos wind and biomass plants switchto another marketer At the end of simulation it is thegreen electricity provider that increases its portfolio by about45 GW from the big utility 35 GW from ldquobig municipalutilityrdquo 3 GW from small municipal utility and 17GW fromthe startup Figure 7(b)

6 Discussion

61 Discussion of Case Study Results The case study revealsvaluable insights concerning the income and portfoliodynamics of different RES-E marketer actor classes Scenario1 shows that incumbent marketers such as big utilities thatfocus on a largewind power portfolio-share can benefit due toeconomies of scale from lower specific operational costs andbetter forecast qualities On absolute levels their economicsuccess is among the best (see Figures 8 and 9) Howeverwe also identify a mediating disutility of scale As describedearlier marketers can profit by trading electricity on differentelectricity markets namely the wholesale power market andthe negative minute reserve market Yet only the electricityof biomass plants has been allowed to participate in thecontrol power market in the model (since 2017 also windpower plant operators are allowed to bid firm capacity onthe control power market if certain prequalifying conditionsare fulfilled in a pilot phase) Trading electricity of thesecontrollable plants implies less balancing costs and improvesoverall operational results The access to this dispatchable

resource is limited and unevenly distributed among themarketersrsquo portfolios However the actors analysis revealedthat upcoming small marketers often have better access tobiomass PPOs through personal connections to local farmersand thus comparatively more biomass contracted in theirportfolio Having access to this dispatchable energy sourcecan mitigate the disadvantages of small portfolio sizes Incombination with an adequate forecast quality this can leadto financially successful marketing of RES-E as the results ofthe green electricity provider depict allowing a niche of newmarket entrants to survive next to incumbent marketers

Additionally the model allows the investigation of howthe market structure changes if marketers are enabled tocompete for new PPOs to complement their portfolio Thebonus payout follows a simple adjustment rule the higher theoperational result is the higher the bonus marketers pay totheir contracted PPOs This leads to a convergence towardsa common specific operational result for all marketers inScenario 1 (except for the small municipal utility) and ensuresa strong competition concerning the bonus payout andthe attraction of new PPOs In this scenario the bonusadjustments and the contract switches of PPOs to othermarketers are onlymoderately dynamic Comparatively smallgaps between bonus heights arise and plant capacities of onlyabout 10GW in total switch marketers Except for the smallmunicipal utility the system stabilizes to a state in which foursuccessful marketers coexist

Slight changes in the regulatory framework (a reduc-tion of the management premium for VRE) lead to com-pletely changed income and portfolio dynamics compareFigures 10 and 11 In Scenario 2 only one marketer managesto trade the electricity profitably and to increase bonusheights All other marketers have to decrease their bonuspayouts and thus a large difference in payouts exists betweenthe marketers even in an early stage of simulation Startupsfor example struggle in the first four years with their oper-ational result just below zero During this time they reducethe bonus height to be profitable In year four the startupmanages to have a positive result but at the same time itsbonus payouts ceased and a large difference in bonus height to

16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)

1e7 Operational result total

minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035

040 Specic business costs

Big utilityMunicipal utilitySmall municipal utilityGreen electricity providerStartup

1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5

6 Total business costs

(Meuro)


1 2 3 4 5 60(Year)

Figure 8 Scenario 1 results The balance reflects all income and expenses at the market including payments for balance energy excludingthe business costs Business costs are considered in the operational result

Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10

12 1e9 Income wholesale market

(euro)

1 2 3 4 5 60(Year)

1e9 Income market premium

00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)

1e9 Payments to BM PPOs

00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)

1e9 Payments to PV PPOs

00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20

25 1e9 Payments to wind PPOs

(euro)

1 2 3 4 5 60(Year)


Green electricityproviderStartup



Figure 9 Scenario 1 results Income and expenses of the marketers

18 Complexity

00

01

02

03

04

05Specic business costs

minus2

minus1

0

1

2

3

4

5 1e7 Total operational result

minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 10 Scenario 2 resultsThe balance reflects all income and expenses at themarket including payments for balance energy and excludingthe business costs Business costs are considered in the operational result

Complexity 19

00

02

04

06

08

10

12 1e9 Payments to PV PPOs

00

05

10

15

20

25

30

35

40 1e9 Payments to BM PPOs

1e9 Income wholesale market

00

05

10

15

20

25

30

35

40 1e9 Income market premium

0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1e9 Payments to wind PPOs

00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity

the other marketers has emerged Even with a well balancedportfolio with a relatively large share of biomass plants theycannot offer bonus payouts and lose the biomass plants tocompetitors With the remaining variable renewables in theirportfolio and forecasts of minor quality it is impossible forthe startup to trade profitably

Clearly the observed effect of a changed managementpremium depends on the initial parametrization of thestudied marketers as well as on the behaviour of the powerplant owners It is therefore important that an rigorous andprofound actors analysis is performed to gain parametervalues from empirical actors data A relative comparisonbetween two scenario variants as presented here should beuncritical however The question of parameter choice isdiscussed in the upcoming subsection

62 Model Outlook Overcoming Current Weaknesses Inagent-based modelling the complexity of the modelled sys-tems inevitably hampers the reporting of results as well as thepolicy advice However for some years now attempts havebeen made to establish standards for the model description[57] model calibration and validation [58] and the settingup of simulation experiments [59]

In this line of reasoning some of the used parameterassumptions should be systematically elaborated in furtherstudies Only an automated sensitivity analysis of a broad setof parameters would offer the required confidence intervalsfor a comprehensive quantitative evaluation For examplethe setting of a starting bonus for all marketers is not veryrealistic Starting conditions should be adapted to the actorsaccording to their capabilities in order to avoid skewedresults in the beginning of the simulation The thresholdparameter 119909119909min and the capital of the marketers can onlybe based on educated guesses so far Individual decisions andconfidentiality limit the information flow in these cases

Likewise the decision-making of actors has to be studiedand implemented with sufficient accuracy The presentedbonus adjustment rules are grounded on the assumptionthat marketers aim for an operational result of 05 euroMWh(stated as ldquotypical marginrdquo in power trading in general in theinterviews) and adapt the bonus payouts according to thebudgetary surplus An alternative approach would assign dif-ferent goals for the operational results to different marketersHowever it would be hard to estimate the marketers aim forthe operational results individually as those numbers wouldbe handled confidentially in real-world examples in mostcases An even more sophisticated approach would optimizethe marketerrsquos profit in dependence on the choice of bonusheight

Improvements of the presented bonus adjustment ruleswould certainly address the current myopic decision rules asthey are only based on operational results and the capital ofthe last year Additional learning from previous years wouldimprove the adoption of decision thresholds

In general the adaptability of AMIRISrsquo agentsmdashhowthey change behaviours during the simulationmdashneeds to beenhanced In this context an important development goal isthemodel endogenous expansion of installed RES-E capacityThis would allow for an estimation of the possible height of

incentives to reach certain deployment goals and to studypotential barriers for RES-E investments Developments forthis are currently carried out

Further model enhancements consider the use of flexibil-ity options the analysis of the demand side and the mod-elling of additional support mechanisms This way furtherrelevant dimensions in the future energy systemrsquos complexityare represented

Besides the use as a standalone model AMIRIS maycomplement studies done with traditional energy systemoptimization models in order to enhance insights for theelectricity system transformation from a market-based per-spective (for a recent example see eg [60]) This way theso-called ldquoefficiency gaprdquo between optimal and real marketoutcomes could be analysed Additionally conclusions mightbe drawn from such complementary studies about why deci-sions of heterogeneous actors on the microlevel might notnecessarily result in a cost-optimal system configuration atthe macrolevel and likewise on necessary policy instrumentsdesign to achieve a cost-optimal system configuration

63 Lessons Learned Using an Agent-Based Model ApproachIn a recent study Macal presented a classification ofagent-based modelling approaches namely individualautonomous interactive and adaptive ABMs in increasingorder of sophistication [61] In adaptive ABMs agentschange behaviours during the simulation In comparisonan interactive agent-based model offers individuality of theagents with a diverse set of characteristics endogenous andautonomous behaviours and direct interactions betweenagents and the environment [61] AMIRIS falls under theinteractive category The agents are modelled with particularscopes in decision-making for example the marketersrsquodecisions regarding the adjustment of bonuses The agentsrsquointeractions such as the one between marketer and plantoperator or between marketer and market determine theirsuccess on the microlevel of actors Nevertheless agents donot change behaviours during simulation

For the purpose of themodel however this adaptability isnot necessary in order to study complex system interrelationsWith the case study we present evidence for the existence ofeconomic niches that arise for smaller upcoming marketersand which can prevent a market concentration towards thebiggest marketers with best forecast qualities and lowest spe-cific operational incomes We thus show that specific agentattributes like portfolio composition and size are decisive forthe evolutionary economic success of marketers This showsthat sophisticated behavioural modelling is not always neces-sary in an ABM to make claims about emergent phenomenain systems and the complexity of agent interactions Likewiseit would be hard to gain these insights about portfolio effectsfrom other simulation methods but ABM

The modelled market modules have been validated withclassical ldquohistory friendlyrdquo methods (compare [10]) Resultsof AMIRIS depend on the interplay between several imple-mented modules generating a macrooutcome that remainshard to validate due to missing empirical data about marketstructure developments Therefore model results are to beinterpreted as possible and plausible tendencies of the system

Complexity 21

developmentmdashan interpretation that is suitable for mostmodels with explorative character including ABMs

AMIRIS allows importing changes in the regulatoryframework as input parameters for explorative scenariosconsidering that no normative system targets are to beachieved by individual actors Specific policy interventionscan be dynamically traced in the model According tothe classification of intervention modelling carried out byChappin [62] this level should be aimed for when assessinginterventions in a model context In this way our approachallows examining the impact of policy instruments consider-ing the complex interplay between the regulatory frameworkthe actors and the technoeconomic regime (see also Figure 1)

7 Conclusion

The agent-based model AMIRIS has been developed inorder to analyse the impact of policy instruments regulatingrenewable energy market integration The model depicts theelectricity system as a complex sociotechnical system andfocuses on the interdependencies between the regulatoryframework actors andmarketsThemodel contributes to thescientific literature in several ways

AMIRIS offers configurations of scenarios under differentexternal input parameters like RES-E policy support mech-anisms While there are other energy related ABMs thatexplore the impact of policy instruments on energy markets(see eg [42 43]) the focus on RES-E in a high temporalresolution and the typecast of actor groups is unique in thefield of energy systems analysis to our best knowledge

Different agent specifications enable defining the degreeof uncertainty and bounded rationality of the actors andmodelling heterogeneous system entities Marketers espe-cially can be defined in detail by specifying for example theirportfolios and cost structures and their capitalization andforecast uncertaintiesThe specification of agents is crucial forthe right interpretation of simulation results so actor analyseshave been conducted prior to model implementation andsimulations The gained insights from such analyses are usedto map agent decision rules and to characterize the actorsand to configure corresponding parameters in AMIRIS Itis shown that many market dynamics can be unraveled ifheterogeneous agent attributes are taken into consideration

The case study demonstrated how only minor policychanges can have a considerable effect on the agent popu-lation This indicates how well-prepared and parametrized atransition of regulatory framework conditions has to be inorder to further ensure the functioning of the system andthe survival of particular actor classes In Scenario 2 forexample the economic survival of the startup and furthermarketers might have been possible in case the regulatoryframework would have been changed by more circumspectplanning We thus show that the intermediary market actorshave to be considered in case amendments of RES-E policyinstruments are planned as new interdependencies betweenplant operators and marketers arise

Niches play a vital role in innovation formation insociotechnical systems and are a fundamental driver ofsystem transition [63] With AMIRIS the emergence and

stability of energy market niches can be depicted withoutprior knowledge about their prospect of success Theireconomic success would be hard to identify and trace inother more traditional modes of simulation The model isthus also business relevant if the results are viewed from anactors perspective For instance the case study revealed thatcompetition and related changes of actorsrsquo portfoliosmay leadto bankruptcy of otherwise successful marketers

To sum up the paper demonstrates that agent-basedmodels are suitable in multiple dimensions to study thedynamics of electricity systems under transition which aredriven by a diverse set of heterogeneous actors While thereis still many open development goals (see Section 62) we donot regard any of these issues raised as a fundamental concernimpossible to overcome

Studying the energy system transition demands methodsthat are able to capture the systemrsquos complexity and dynamicsAn important property of ABM approaches is their abilityto flexibly use models in the model enabling the researcherto represent the system in multiple layers We conclude thatagent-based modelling approaches like AMIRIS have theability to enhance the knowledge that is required to ensure asuccessful energy system transition while preventing systembreakages

Appendix

The revenue calculation is described in detail in the followingsection Revenue can be generated at the wholesale (XM)and control energy market (CE) balancing energy (bal) canadd to the revenue if circumstances are favourable The totalrevenue is given by

119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)

The sold volume119881XM(119905) traded at the power exchangemarketis refunded with the management premium 119872(119905) and allowsearnings of

119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)

with the wholesale power market price ΠXM(119905) Likewiserevenues from the control energy market equate to

119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)

The revenue frombalancing energy equals negative balancingcosts of the marketer that is

119894bal (119905) = minus119888bal (119905) (A4)

The fix costs are calculated as

119888fix = 119888IT + 119888tradefix (A5)

Variable costs equate to

119888var (119905) = 119888XMtrading (119905) + 119888persvar (119905) + 119888bal (119905)+ 119888fcst (119905) + 119888bonus (119905) (A6)

22 Complexity

Trading costs are based on the fees at the exchangemarket forevery traded MWh with

119888XMtrading (119905) = 119888tradevar sdot 119881 (119905) (A7)

In case balancing energy is required the correspondingvolume 119881bal(119905) must be procured for a price PRbal and costsare defined as

119888bal (119905) = PRbal sdot 119881bal (119905) (A8)

According to the actors analysis the prices PRfcst per MWtypically decrease with larger portfolio sizes so

119888fcst (119905) = 119888fcst (P) sdot P (119905) (A9)

The size of119881bal(119905) is the difference between the real actual119881(119905)and the forecast 119881fcst(119905) electricity feed-in at time 119905

119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)

where the latter has been forecast by the marketer 24ℎ beforeand is determined by

119881fcst (119905 + 24 h) = 119881 (119905 + 24 h)sdot (1 + 120583power + 120590power sdot 119892) (A11)

with 119892 representing a random variable from a normaldistribution 119881(119905 + 24 h) denotes the actual feed-in volume24 h ahead The revenue of the RES operator agents is basedon the remuneration and the bonus payments from the directmarketer that is

119894 (119905) = 119881el sdot (Πrc (119905) + 119894bonus (119905)) (A12)

The Market Premium The aim of the market premiumunder the EEG is to integrate renewable energy sourcesinto the energy market system by fostering direct marketingProducers receive a financial compensation for the differencebetween energy-source-specific values to be applied (replac-ing the fixed feed-in tariff) as a calculation basis and themar-ket value This is the average energy-source-specific monthlyvalue of the hourly contracts on the spotmarket for electricity(Part 3 Division 1 and Annex 1 EEG 2017) Compensating foroccurring costs fromdirectmarketing the values to be appliedare higher than the replaced feed-in tariffs The difference isset to 2 euroMWh for dispatchable renewables and 4 euroMWhfor intermittent renewables (Section 53 EEG 2017) UnderEEG 2012 such a difference has been separately disclosed as amanagement premium (Section 33g EEG 2012)

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

The authors are grateful to Wolfram Krewitt who originallyconceived the development of an agent-based simulation

model for the analysis of the market integration of renew-ables They would also like to show their gratitude to UlrichFrey Benjamin Fuchs EvaHauserWolfgangHauserThomasKast Uwe Klann Uwe Leprich Tobias Naegler Nils RoloffChristoph Schimeczek Yvonne Scholz Bernd Schmidt San-dra Wassermann Rudolf Weeber and Wolfgang Weimer-Jehle for their expert advice and contributions to the develop-ment of AMIRIS They are thankful to all colleagues of theirdepartment for numerous fruitful discussions on AMIRISrsquosdevelopment and application For the recent and ongoingfunding they are much obliged to the German Ministry forthe Environment theGermanMinistry for EconomicAffairsthe German Ministry for Research and internal funding bythe DLR within several research projects (Grant nos BMUFKZ 0325015 BMU FKZ 0325182 BMWi FKZ 03ET4020ABMWi FKZ 03SIN108 BMWi FKZ 03ET4032B BMWi FKZ03ET4025B and BMBF FKZ 03SFK4D1)

References

[1] IPCC Mitigation of Climate Change Contribution of WorkingGroup III to the Fifth Assessment Report of the IntergovernmentalPanel on Climate Change Summary for Policymakers Cam-bridge University Press Cambridge UK 2014

[2] IEA ldquoWorld Energy Outlook 2015rdquo Digestive Endoscopy 2015httpdxdoiorg101787weo-2015-en

[3] REN21 Renewables 2016 Global Status Report REN21 Sec-retariat Paris 2016 httpwwwren21netGSR-2016-Report-Full-report-EN

[4] J Scheffler ldquoGesetz fur den Vorrang Erneuerbarer Energienndash EEGrdquo in Die gesetzliche Basis und Forderinstrumente derEnergiewende essentials pp 5ndash31 Springer Fachmedien Wies-baden Wiesbaden 2014


[6] U Busgen and W Durrschmidt ldquoThe expansion of electricitygeneration from renewable energies inGermanyrdquoEnergy Policyvol 37 no 7 pp 2536ndash2545 2009 httpdxdoiorg101016jenpol200810048

[7] EEG ldquoGesetz fur den Vorrang Erneuerbarer Energien (Erneu-erbare-Energien-Gesetz)rdquo 2012 httpswwwerneuerbare-en-ergiendeEERedaktionDEGesetze-Verordnungeneeg 2012bfhtml

[8] M Klobasa M Ragwitz F Sensfuszlig et al ldquoNutzenwirkung derMarktpramierdquo Working Paper Sustainability and InnovationNo S 12013 Fraunhofer Institut fur System- und Innovations-forschung ISI

[9] Federal Ministry for Economic Affairs ldquoEnergy RenewableEnergy Sources in Figuresrdquo National and International Devel-opment 2014

[10] R Matthias K Nienhaus N Roloff et al ldquoWeiterentwick-lung eines agentenbasierten Simulationsmodells (AMIRIS) zurUntersuchung des Akteursverhaltens bei der Marktintegrationvon Strom aus erneuerbaren Energien unter verschiedenenFordermechanismenrdquoDeutsches Zentrum fur Luft- undRaum-fahrt eV (DLR) 2013 httpelibdlrde82808

[11] R Schemm and B Daniel ldquoMake oder Buyrdquo ErneuerbareEnergien vol 10 no 2014 pp 40ndash43 2014

Complexity 23

[12] AGrunwald ldquoEnergy futuresDiversity and the need for assess-mentrdquo Futures vol 43 no 8 pp 820ndash830 2011 httpdxdoiorg101016jfutures201105024

[13] C S Bale L Varga and T J Foxon ldquoEnergy and complexityNew ways forwardrdquo Applied Energy vol 138 pp 150ndash159 2015

[14] L Tesfatsion ldquoChapter 16 Agent-Based Computational Eco-nomics A Constructive Approach to EconomicTheoryrdquoHand-book of Computational Economics vol 2 pp 831ndash880 2006

[15] EEX ldquoEEX Spot-price data from the year 2011rdquo httpswwweexcomdemarktdatenstromspotmarkt

[16] ENTSO-E ldquoENTSO-E load and consumption datardquo httpswwwentsoeeudb-queryconsumptionmonthly-consump-tion-of-a-specific-country-for-a-specific-range-of-time

[17] L Matthias and L Annette ldquoThe 2014 German RenewableEnergy Sources Act revision - from feed-in tariffs to direct mar-keting to competitive biddingrdquo Journal of Energy and NaturalResources Law vol 33 no 2 pp 131ndash146 2015 httpdxdoiorg1010800264681120151022439

[18] D Kahneman Thinking Fast and Slow Penguin Books Lon-don UK 2011

[19] A Tversky and D Kahneman ldquoJudgent Under UncertaintyHeuristics and Biasesrdquo Science vol 185 pp 1124ndash1131 1974

[20] W Brian Arthur ldquoInductive Reasoning and Bounded Rational-ityrdquoThe American Economic Review vol 84 no 2 pp 406ndash4111994 httpwwwjstororgstable2117868

[21] M G De Giorgi A Ficarella andM Tarantino ldquoError analysisof short term wind power prediction modelsrdquo Applied Energyvol 88 no 4 pp 1298ndash1311 2011

[22] M LangeAnalysis for theUncertainty ofWind Power Prediction[PhD thesis] Carl von Ossietzky University of OldenburgGermany 2003

[23] S Rentzing ldquoIm Schatten der Photovoltaikrdquo Neue Energie vol10 pp 48ndash51 2011

[24] O Tietjen Analyses of Risk Factors in Conventional andRenewable Energy Dominated Electricity Markets [PhD thesis]Masterarbeit an der Freien Universiterlin (FU) und PotsdamInstitute for Climate Impact Research (PIK) 2014

[25] A Weidlich Engineering Interrelated Electricity Markets - Anagentbased computational Approach [PhD thesis] Disseration- Universitat Karlsruhe TH - Faculty of Economics 2008

[26] G Gallo ldquoElectricity market games How agent-based mod-eling can help under high penetrations of variable genera-tionrdquo The Electricity Journal vol 29 no 2 pp 39ndash46 2016httpdxdoiorg101016jtej201602001

[27] B Wooldrige An Introduction to Multi-Agent Systems JohnWiley and Sons Chichester UK 2002

[28] C M MacAl and M J North ldquoTutorial on agent-basedmodelling and simulationrdquo Journal of Simulation vol 4 no 3pp 151ndash162 2010 httpdxdoiorg101057jos20103

[29] J M Epstein and R L Axtell Growing artificial societiesSocial science from the bottom up Massachusetts Institute ofTechnology Cambridge USA 1996

[30] J H Holland and J H Miller ldquoArtificial adaptive agents ineconomic theoryrdquo The American Economic Review vol 81 pp365ndash370 1991

[31] V Rai and S A Robinson ldquoAgent-based modeling ofenergy technology adoption Empirical integration ofsocial behavioral economic and environmental factorsrdquoEnvironmental Modelling and Software vol 70 pp 163ndash177 2015 httpwwwsciencedirectcomsciencearticlepiiS1364815215001231via3Dihub

[32] J Palmer G Sorda and R Madlener ldquoModeling the diffusionof residential photovoltaic systems in Italy An agent-basedsimulationrdquo Technological Forecasting amp Social Change vol 99pp 106ndash131 2015

[33] G Sorda Y Sunak and R Madlener ldquoAn agent-based spatialsimulation to evaluate the promotion of electricity from agri-cultural biogas plants in Germanyrdquo Ecological Economics vol89 pp 43ndash60 2013

[34] F Genoese andM Genoese ldquoAssessing the value of storage in afuture energy system with a high share of renewable electricitygenerationrdquo Energy Systems vol 5 no 1 pp 19ndash44 2014

[35] S YousefiM PMoghaddam andV JMajd ldquoOptimal real timepricing in an agent-based retail market using a comprehensivedemand response modelrdquo Energy vol 36 no 9 pp 5716ndash57272011

[36] M Zheng C J Meinrenken and K S Lackner ldquoAgent-basedmodel for electricity consumption and storage to evaluateeconomic viability of tariff arbitrage for residential sectordemand responserdquo Applied Energy vol 126 pp 297ndash306 2014

[37] Z Zhou F Zhao and J Wang ldquoAgent-based electricity marketsimulation with demand response from commercial buildingsrdquoIEEETransactions on Smart Grid vol 2 no 4 pp 580ndash588 2011

[38] A Kowalska-Pyzalska K Maciejowska K Suszczynski KSznajd-Weron and R Weron ldquoTurning green Agent-basedmodeling of the adoption of dynamic electricity tariffsrdquo EnergyPolicy vol 72 pp 164ndash174 2014

[39] P R Thimmapuram and J Kim ldquoConsumersrsquo price elasticity ofdemand modeling with economic effects on electricity marketsusing an agent-based modelrdquo IEEE Transactions on Smart Gridvol 4 no 1 pp 390ndash397 2013

[40] T Zhang and W J Nuttall ldquoEvaluating Governmentrsquos Policieson Promoting Smart Metering Diffusion in Retail ElectricityMarkets via Agent-Based Simulationrdquo Journal of ProductInnovation Management vol 28 no 2 pp 169ndash186 2011

[41] R A C van der Veen A Abbasy and R A Hakvoort ldquoAgent-based analysis of the impact of the imbalance pricing mech-anism on market behavior in electricity balancing marketsrdquoEnergy Economics vol 34 no 4 pp 874ndash881 2012

[42] F Sensfuszlig M Ragwitz and M Genoese ldquoThe merit-ordereffect A detailed analysis of the price effect of renewableelectricity generation on spot market prices in GermanyrdquoEnergy Policy vol 36 no 8 pp 3076ndash3084 2008

[43] J C Richstein E J L Chappin and L J de Vries ldquoCross-border electricitymarket effects due to price caps in an emissiontrading system An agent-based approachrdquo Energy Policy vol71 pp 139ndash158 2014

[44] G Li and J Shi ldquoAgent-based modeling for trading wind powerwith uncertainty in the day-ahead wholesale electricity marketsof single-sided auctionsrdquo Applied Energy vol 99 pp 13ndash222012

[45] L A Wehinger G Hug-Glanzmann M D Galus andG Andersson ldquoModeling electricity wholesale markets withmodel predictive and profit maximizing agentsrdquo IEEE Transac-tions on Power Systems vol 28 no 2 pp 868ndash876 2013

[46] F Sensuszlig M Genoese M Ragwitz and D Most ldquoAgent-basedSimulation of Electricity Markets -A Literature Reviewrdquo EnergyStudies Review vol 15 no 2 2007

[47] P Ringler D Keles and W Fichtner ldquoAgent-based modellingand simulation of smart electricity grids and markets - Aliterature reviewrdquo Renewable amp Sustainable Energy Reviews vol57 pp 205ndash215 2016

24 Complexity

[48] SWassermannM Reeg and K Nienhaus ldquoCurrent challengesofGermanyrsquos energy transition project and competing strategiesof challengers and incumbents The case of direct marketing ofelectricity from renewable energy sourcesrdquo Energy Policy vol76 pp 66ndash75 2015

[49] ENWG ldquoGesetz uber die Elektrizitats- und GasversorgungrdquoBundesanzeiger des Bundesministerium fr Justiz 2005 httpswwwgesetze-im-internetdeenwg 2005

[50] M J North N T Collier J Ozik et al ldquoComplex adaptivesystems modeling with Repast Simphonyrdquo Complex AdaptiveSystems Modeling vol 1 no 1 p 3 2013

[51] N Joachim T Pregger T Naegler et al ldquoLong-term scenariosand strategies for the deployment of renewable energies inGermany in view of European and global developmentsrdquo DLRPortal 2012 httpelibdlrde76044

[52] Y Scholz Renewable energy based electricity supply at low costsdevelopment of the REMix model and application for Europe[PhD thesis] Universitat Stuttgart Germany 2012

[53] D Stetter Enhancement of the REMix energy system modelGlobal renewable energy potentials optimized power plant sitingand scenario validation [PhD thesis] Universitat StuttgartGermany 2014

[54] MaPrV Verordnung uber die Hohe derManagementpramie furStrom aus Windenergie und solarer Strahlungsenergie 2012httpswwwclearingstelle-eegdemaprv

[55] Ubertragungsnetzbetreiber httpswwwnetztransparenzdeEEGVerguetungs-und-Umlagekategorien

[56] AusglMechV ldquoVerordnung zur Weiterentwcklung des bun-desweiten Ausgleichmechanismusrdquo Bundesanzeiger des Bun-desministerium fur Justiz 2010

[57] V Grimm U Berger D L DeAngelis J G Polhill J Giske andS F Railsback ldquoThe ODD protocol A review and first updaterdquoEcological Modelling vol 221 no 23 pp 2760ndash2768 2010

[58] P Windrum G Fagiolo and A Moneta ldquoEmpirical Validationof Agent-Based Models Alternatives and Prospectsrdquo Journal ofArtificial Societies and Social Simulation vol 10 no 2 2007httpjassssocsurreyacuk1028html

[59] I Lorscheid B-O Heine and M Meyer ldquoOpening the ldquoblackboxrdquo of simulations increased transparency and effective com-munication through the systematic design of experimentsrdquoComputational and Mathematical Organization Theory vol 18no 1 pp 22ndash62 2012 httpsdoiorg101007s10588-011-9097-3

[60] O Weiss D Bogdanov K Salovaara and S HonkapuroldquoMarket designs for a 100 renewable energy system Caseisolated power system of Israelrdquo Energy vol 119 pp 266ndash2772017

[61] C M Macal ldquoEverything you need to know about agent-basedmodelling and simulationrdquo Journal of Simulation vol 10 no 2pp 144ndash156 2016

[62] E J L Chappin Simulating Energy Transitions [PhD thesis]TU Delft 2011 httpresolvertudelftnluuid

[63] FWGeels ldquoTechnological transitions as evolutionary reconfig-uration processes A multi-level perspective and a case-studyrdquoResearch Policy vol 31 no 8-9 pp 1257ndash1274 2002

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Journal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Complexity

considerable market distortions and unstable investmentbehaviour

The deployment and integration of RES can only bereliably regulated as long as policy instruments do considerthe interdependencies and interactions with and of theinvolved actors aswell as the resultingmarket interplay on theinvestment dynamics The motivation for the developmentof the agent-based model AMIRIS is therefore to studythe adequacy of policy measures which affect the entitiesthat comprise the electricity system the aim is to examinethe impact of policy on the involved market actors on themicrolevel (eg income situation of renewable power plantoperators) as well as their effects on the macrolevel (egpower exchange prices and market structure) [10]

The remainder of the paper is structured as followsIn Section 2 we will elaborate on the complexity of theenergy system transition and our motivation to choose anagent-based model (ABM) approach to address our researchquestions Section 3 will give a brief overview of the AMIRISmodel For further detail the technically interested readercan refer to Section 4 which describes the agents and theirbehaviours in detail To exemplify themodelrsquos capabilities andquestions to be addressed Section 5 presents a case studyon the marketing of RES-E at the power exchange and howan amendment of the policy regime affects market actors indifferent ways Here we will show how the heterogeneity ofagents for example different portfolios affects the incomeand behaviour of the represented renewable electricity mar-keters and power plant operators Section 6 discusses the casestudy and gives an overview of the lessons learned from theuse of the ABM approach Section 7 concludes with lessonslearned from both the case study and themodelling approachin general

2 Modelling the Complexity ofEnergy Transitions

21 Challenges of Modelling the Impact of Energy PolicyMeasures on the Behaviour of Actors The pathway of thedevelopment of the global energy system namely the antic-ipated shift of supply from centralized fossil-fuelled powerplants towards a decarbonised and RES dominated regimeis uncertain many possible energy futures are conceivable[12] Part of the uncertainty of which energy future willmaterialize results from the unexplored behaviour of themarket actors who implement new technologies as theirrelationships and intentions remain understudied Bale etal [13] state that ldquoEnergy systems can be understood ascomplex adaptive systems in that they have interrelatedheterogeneous elements (agents and objects) In additionthere is no autonomous control over the whole system andin that sense self-organized emergent behaviour arises thatcannot be predicted by understanding each of the componentelements separatelyrdquo As such the result of markets at themacrolevel of the system is based on a variety of individualactions on the microlevel [14]

In Germany individual options of choices and the num-ber of actors in the system have increased substantially sincethe liberalization of electricity markets and the introduction

of the EEG and its several amendments [17] They decideunder the influence of cognitive biases [18 19] and inherentuncertainty and are therefore only bounded rational [20]Policies are directed towards those actors to induce a desiredcollective behaviour and are uncertain in their effect as well

Electricity is different to most other commodities forat least two reasons it is not storable at low costs and thedemand side is only marginally elastic Hence it is necessaryto balance supply and demand on short notice at all timesin order to ensure system stability This situation got morechallenging with the large-scale integration of RES-E intothe system Due to inherent output forecast limitations andtheir nondispatchability RES-E can always be subjected tohigh balance energy cost due to day-ahead forecast errorsand cannot hedge risks on future markets [21ndash24] As suchadditional intermediary market actors which specialize inforecasting and dispatching variable renewable energy (VRE)emerged These intermediary market actors increased theorder of complexity in the market

Additionally complicating is the fact that diverse elec-tricity markets like spot and futures control energy as wellas CO2 certificates markets interacting with and influencingeach other [25] As a result the heterogeneous power plantand marketing actors can react very differently to energypolicy adjustments and the development of the electricitysystem as a whole can follow diverse pathways [26] This isa tremendous challenge from a modelling perspective

22 Overview of Agent-Based Models in Energy SystemModelling Given the challenges mentioned above we havechosen an agent-based modelling (ABM) approach whichaddresses these questions by placing the actors their interre-lationships and their influencing environment in the centreof the modelling exercise [14] The origin of the ABMapproach is found in the field of artificial intelligence andcellular automata research and has been used for analysingcomplex and interrelated systems in such various researchdomains as ecology social sciences and software engineering[27]TheABM approach enables themodeller to describe thecomplex relationships of the systems entities by identifyinga set of attributes behavioural rules adaptations of thosebehavioural rules in response to the behaviour of others andthe environment and an environment itself [28]The analysisis executed step by step and allows for developing these rela-tionships on an evolutionary path in an artificial laboratory-like environment [29 30] Agent-based models are thereforeparticularly suitable for the simulation of multiply linkedand complex systems with autonomous actors The systemrsquosbehaviour is not centrally determined but evolves bottom-upfrom the actions taken by the individual agents to a complexsystem with emergent structures

The ABM approach has been successfully applied in theenergy sciences Recent publications have investigated therole of certain technologies like the market diffusion of PV[31 32] and biomass power plants [33] or the value of storagetechnologies [34] Others have put their focus on certainaspects of the demand side of the energy system as this aspectis associated with a need for a more ldquohumanrdquo modelling andpreference depiction their works focus on demand response

Complexity 3
















4 Complexity

Regu

lato

ry fr

amew

ork

Minutereservemarket

Energyexchange

Storageoperator

(Load)


Supplier

Windplant owners




Directmarketers

System operator















Complexity 5











6 Complexity




119901 (119905) = 119894 (119905) minus 119888 (119905) (1)







120590price


120590power


120583power


P [MW]









Complexity 7


0

10

20

30

40

50Sp

ec p

erso

nnel

cost

(euroM

Wh)

(a)

00

01

02

03

04

05

06

07


Spec

per

sonn

el co

st (euro

MW

h)(b)







]4-5] 095


119888bonus (119905)=


(2)


8 Complexity







119866rc120591 (119905) = P120591rc (119905) sdot 119908119894 (119905) (5)










remuneration class

119909min [euroMWh]







(6)




Complexity 9



minus10

0

10

20

30

40

50

60

10 20 30 40 50 60 700Time (month)

Pric

e (euro

MW

h)







119902119894 le RL) (7)









10 Complexity




5 Case Study







52 Results




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 3
















4 Complexity

Regu

lato

ry fr

amew

ork

Minutereservemarket

Energyexchange

Storageoperator

(Load)


Supplier

Windplant owners




Directmarketers

System operator















Complexity 5











6 Complexity




119901 (119905) = 119894 (119905) minus 119888 (119905) (1)







120590price


120590power


120583power


P [MW]









Complexity 7


0

10

20

30

40

50Sp

ec p

erso

nnel

cost

(euroM

Wh)

(a)

00

01

02

03

04

05

06

07


Spec

per

sonn

el co

st (euro

MW

h)(b)







]4-5] 095


119888bonus (119905)=


(2)


8 Complexity







119866rc120591 (119905) = P120591rc (119905) sdot 119908119894 (119905) (5)










remuneration class

119909min [euroMWh]







(6)




Complexity 9



minus10

0

10

20

30

40

50

60

10 20 30 40 50 60 700Time (month)

Pric

e (euro

MW

h)







119902119894 le RL) (7)









10 Complexity




5 Case Study







52 Results




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




4 Complexity

Regu

lato

ry fr

amew

ork

Minutereservemarket

Energyexchange

Storageoperator

(Load)


Supplier

Windplant owners




Directmarketers

System operator















Complexity 5











6 Complexity




119901 (119905) = 119894 (119905) minus 119888 (119905) (1)







120590price


120590power


120583power


P [MW]









Complexity 7


0

10

20

30

40

50Sp

ec p

erso

nnel

cost

(euroM

Wh)

(a)

00

01

02

03

04

05

06

07


Spec

per

sonn

el co

st (euro

MW

h)(b)







]4-5] 095


119888bonus (119905)=


(2)


8 Complexity







119866rc120591 (119905) = P120591rc (119905) sdot 119908119894 (119905) (5)










remuneration class

119909min [euroMWh]







(6)




Complexity 9



minus10

0

10

20

30

40

50

60

10 20 30 40 50 60 700Time (month)

Pric

e (euro

MW

h)







119902119894 le RL) (7)









10 Complexity




5 Case Study







52 Results




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 5











6 Complexity




119901 (119905) = 119894 (119905) minus 119888 (119905) (1)







120590price


120590power


120583power


P [MW]









Complexity 7


0

10

20

30

40

50Sp

ec p

erso

nnel

cost

(euroM

Wh)

(a)

00

01

02

03

04

05

06

07


Spec

per

sonn

el co

st (euro

MW

h)(b)







]4-5] 095


119888bonus (119905)=


(2)


8 Complexity







119866rc120591 (119905) = P120591rc (119905) sdot 119908119894 (119905) (5)










remuneration class

119909min [euroMWh]







(6)




Complexity 9



minus10

0

10

20

30

40

50

60

10 20 30 40 50 60 700Time (month)

Pric

e (euro

MW

h)







119902119894 le RL) (7)









10 Complexity




5 Case Study







52 Results




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




6 Complexity




119901 (119905) = 119894 (119905) minus 119888 (119905) (1)







120590price


120590power


120583power


P [MW]









Complexity 7


0

10

20

30

40

50Sp

ec p

erso

nnel

cost

(euroM

Wh)

(a)

00

01

02

03

04

05

06

07


Spec

per

sonn

el co

st (euro

MW

h)(b)







]4-5] 095


119888bonus (119905)=


(2)


8 Complexity







119866rc120591 (119905) = P120591rc (119905) sdot 119908119894 (119905) (5)










remuneration class

119909min [euroMWh]







(6)




Complexity 9



minus10

0

10

20

30

40

50

60

10 20 30 40 50 60 700Time (month)

Pric

e (euro

MW

h)







119902119894 le RL) (7)









10 Complexity




5 Case Study







52 Results




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 7


0

10

20

30

40

50Sp

ec p

erso

nnel

cost

(euroM

Wh)

(a)

00

01

02

03

04

05

06

07


Spec

per

sonn

el co

st (euro

MW

h)(b)







]4-5] 095


119888bonus (119905)=


(2)


8 Complexity







119866rc120591 (119905) = P120591rc (119905) sdot 119908119894 (119905) (5)










remuneration class

119909min [euroMWh]







(6)




Complexity 9



minus10

0

10

20

30

40

50

60

10 20 30 40 50 60 700Time (month)

Pric

e (euro

MW

h)







119902119894 le RL) (7)









10 Complexity




5 Case Study







52 Results




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




8 Complexity







119866rc120591 (119905) = P120591rc (119905) sdot 119908119894 (119905) (5)










remuneration class

119909min [euroMWh]







(6)




Complexity 9



minus10

0

10

20

30

40

50

60

10 20 30 40 50 60 700Time (month)

Pric

e (euro

MW

h)







119902119894 le RL) (7)









10 Complexity




5 Case Study







52 Results




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 9



minus10

0

10

20

30

40

50

60

10 20 30 40 50 60 700Time (month)

Pric

e (euro

MW

h)







119902119894 le RL) (7)









10 Complexity




5 Case Study







52 Results




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

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40000

50000

Insta

lled

(MW

)

0

10000

20000

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40000

50000

Insta

lled

(MW

)

0

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50000

Insta

lled

(MW

)

0

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40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




10 Complexity




5 Case Study







52 Results




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 11







RC 1 360 881 1648RC 2 22 567 5342RC 3 125 29 5960RC 4 15 220 1195








12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

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50000

Insta

lled

(MW

)

0

10000

20000

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40000

50000

Insta

lled

(MW

)

0

10000

20000

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40000

50000

Insta

lled

(MW

)

0

10000

20000

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50000

Insta

lled

(MW

)

0

10000

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50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




12 Complexity



minus15

minus10

minus05

00

05

10

15


1 2 3 4 5 60(Year)

(euroM

Wh)

(a)



08

10

12

14

16

18

20

22

24

26Bonus payout

1 2 3 4 5 60(Year)

(euroM

Wh)

(b)

00

05

10

15

20

25

30

35




1 2 3 4 5 60(Year)

(euroM

Wh)

(c)

00

05

10

15

20

25




(euro)

1 2 3 4 5 60(Year)

(d)





Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 13

minus4

minus3

minus2

minus1

0

1

2


(euroM

Wh)

1 2 3 4 5 60(Year)



(a)

00

02

04

06

08

10

12

14

16Bonus payout

(euroM

Wh)

1 2 3 4 5 60(Year)



(b)

0

1

2

3

4

5


(euroM

Wh)

1 2 3 4 5 60(Year)



(c)

0

1

2

3

4

5

6

7


(euro)

1 2 3 4 5 60(Year)



(d)




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




14 Complexity

Big utility

WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM WindPV

BM

WindPV

BM






Big utility

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

Figure 7 Continued

Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 15

WindPV

BM WindPV

BM

Startup

(a)

Startup

(b)

0

10000

20000

30000

40000

50000In

stalle

d (M

W)

0

10000

20000

30000

40000

50000

Insta

lled

(MW

)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)




6 Discussion





16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




16 Complexity

0

20

40

60

80

100

120

140

160Capital

(Meuro)

1 2 3 4 5 60(Year)

0

5000

10000

15000

20000

25000

30000

(GW

h)

Total traded volume

1 2 3 4 5 60(Year)


minus05

00

05

10

15

20

(euro)

1 2 3 4 5 60(Year)

minus5

0

5

10

15

20

25

(Meuro)

Balance

1 2 3 4 5 60(Year)

000

005

010

015

020

025

030

035



1 2 3 4 5 60(Year)

(euroM

Wh)

0

1

2

3

4

5


(Meuro)


1 2 3 4 5 60(Year)


Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 17


00

05

10

15

20

25

30

(euro)

1 2 3 4 5 60(Year)

minus02

00

02

04

06

08

10


(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

30

35

(euro)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

1 2 3 4 5 60(Year)


00

02

04

06

08

10

12

(euro)

1 2 3 4 5 60(Year)

00

05

10

15

20


(euro)

1 2 3 4 5 60(Year)






18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




18 Complexity

00

01

02

03

04


minus2

minus1

0

1

2

3

4


minus50

0

50

100

150

200Capital

minus20

minus10

0

10

20

30

40

50

60 Balance

0

2

4

6

8

10


0

10000

20000

30000

40000

50000

60000

(GW

h)

Total traded volume



(Meuro)

(Meuro)

(Meuro)

(euroM

Wh)

(euro)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 19

00

02

04

06

08

10


00

05

10

15

20

25

30

35



00

05

10

15

20

25

30

35


0

1

2

3

4

5

6

7


minus05

00

05

10

15

25

20

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)

1 2 3 4 5 60(Year)


00

05

10

15

20

25

(euro)

(euro)

(euro)

(euro) (euro)

(euro)

1 2 3 4 5 60(Year)






20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




20 Complexity














Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 21



7 Conclusion









Appendix


119894 (119905) = 119894XM (119905) + 119894CE (119905) + 119894bal (119905) (A1)


119894XM (119905) = 119881XM (119905) sdot (ΠXM (119905) + 119872 (119905)) (A2)


119894CE (119905) = 119881CE (119905) sdot ΠCE (119905) (A3)


119894bal (119905) = minus119888bal (119905) (A4)


119888fix = 119888IT + 119888tradefix (A5)



22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




22 Complexity








119881bal (119905) = 119881 (119905) minus 119881fcst (119905) (A10)








Acknowledgments



References












Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 23





































24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




24 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Assessing the Plurality of Actors and Policy...

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