Theoretical Investigation On The Long-term Evolutionarily Stable Equilibrium Of Multi-population Strategic Games In Electricity Market

In recent years,with the large-scale access of various distributed renewables to the power grid and the conceptions of Energy Interconnection and “Internet+” Smart Energy successively proposed,the smart grids(SGs)have developed rapidly.The electricity market(EM)in the context of SG is also gradually opening up and meanwhile,the stakeholders in it are becoming more diverse and the competition between them becomes more and more complicated.At this point,the EM not only contains traditional power grid enterprises(PGEs),generation corporations(GENCOs)and electricity consumers(ECS),but also contains a large number of new power supply entity(NPSE)operators,who are mainly electric selling entities such as emerging electricity sales service providers and load aggregators.Simultaneously,a large number of distributed generation(DG),energy storage,controllable loads and electric vehicles(EVs)appear in SG,and the operators of them also have the chance to participate in EM competition.Such traditional decision-making agents and emerging stakeholders both affect the development of the EM to some extent,making the dynamic interactive decision-making behaviors in it very complicated.However,faced with increasingly complex multi-agent optimization decision-making issues in the open and competitive EM,the traditional optimization theory system based on single-agent decision-making has been unable to solve such complex decision problems.In contrast,game theory gradually becomes a powerful mathematical tool to address these difficult problems.As a new branch of game theory,evolutionary game theory(EGT),which is founded based on assumptions of bounded rationality and limited information,can well reveal the evolution rules of group behavior and accurately predict the swarm behavior of individuals through dynamic interactive decision-making processes of imitation,learning and communication among individuals,such that it has developed rapidly in fields of economy,management,social sciences,and engineering,etc.Compared with classical game theory,which focuses on static equilibrium and comparative static equilibrium,EGT emphasizes the dynamics of equilibrium and is implemented based on the limited rationality of participants.Moreover,the strategic equilibrium between players in EGT is often the result of continuous learning,imitation and dynamic adjustment,rather than the result of one-time selection,thus it is closer to the actual game situation.Currently,the EGT-related research work in EM is extremely rare.To this end,based on the core concepts of evolutionarily stable strategy(ESS),replicator dynamics(RD),evolutionarily stable equilibrium(ESE)and asymptotically stable internal equilibrium point(ASEP)in EGT,and the Lyapunov stability theory,this paper conducts in-depth theoretical analysis and dynamic simulation on the ESE characteristics of long-term dynamic interactive behavioral decision-making in multi-population multi-strategy evolutionary games under normal circumstances,and then applies them to implement theoretical investigation on the long-term ESE characteristics of multi-population strategic games in open and competitive EM.These evolutionary game models are established based on the dynamic interactive decision-making of incomplete rational stakeholders.In this dissertation,the major investigations on the long-term ESE characteristics of evolutionary games in the open and competitive EM are implemented from three aspects: typical scenarios of two-population and three-population asymmetric evolutionary games in the EM,long-term bidding evolutionary game of supply-side power generation market(PGM),and evolutionary games in power demand-side response management(DRM).Details are presented as follows:First,this dissertation conducts an in-depth theoretical investigation on the models and long-term ESE analysis methods of general multi-population multi-strategy evolutionary games,thus proposing an effective multi-population multi-strategy evolutionary game theoretical analysis and dynamic simulation research method system.In this method system,the long-term ESE characteristics of general multi-population multi-strategy evolutionary games are summarized and the relative net payoff(RNP)parameters are completely defined for them from the application perspective.The research shows that the long-term ESE state(i.e.,ESS)achieved in various evolutionary game models is determined only by the RNP parameters defined for them.Therefore,appropriate adjustment of these RNP parameters can effectively guide the entire evolutionary game system to evolve toward a desired long-term ESE state.In the research method system,this dissertation also elaborates the modeling ideas of general N-population two-strategy asymmetric evolutionary game(AEG)and three-population N-strategy AEG,and provides the calculation method for them during convergent iteration.This research method system lays a solid theoretical foundation for the application research of EGT in subsequent chapters.Moreover,the models,methods and conclusions obtained in this research method system all have certain universality and effectiveness,which can be used to investigate the long-term dynamic interactive behavioral decision-making issues in multi-population multi-strategy evolutionary games involving non-complete rational stakeholders in related fields.Second,based on the above-proposed research method system,this dissertation,based on the core concepts of RD,ESS and ESE in EGT,proposes a theoretical research method that is suitable for analyzing the long-term equilibrium stability of typical scenarios in the open and competitive EM.Concretely,this dissertation investigates a typical two-population AEG scenario where two types of generator populations participate in long-term bidding in the generation-side market,as well as a typical three-population AEG scenario where PGE,NPSE and ECS participate in the long-term electricity-price and electricity amount competition in the demand-side EM.The theoretical investigation reveals that these typical multi-population AEG scenarios contain different numbers of long-term ESE states that are all strict Nash equilibrium(NE)states.In addition,effective supervision implemented by the government to above generation-side and demand-side EMs will affect the payoff matrix of the typical multi-population AEG scenarios and change the ASEP distribution of the entire EMs,thus finally guiding the EMs to evolve toward an expected long-term ESE state,which is a strictly refined NE state.In such desired state,all generator populations in the generation-side EM tend to quote a high electricity price during the bidding process.In addition,PGEs and NPSEs in the demand-side EM will cooperate to provide a time-of-use electricity price that allows them to benefit more and meanwhile,ECS will choose PGEs’ time-of-use electricity price for power consumption to maximize their own interests.The above expected long-term ESE state will help the electricity price of the open EMs to be flat and stable with small fluctuations,promote power grids to complete peak shaving and load leveling,increase the profits of all parties,and at the same time significantly increase the resource allocation rate of the open EMs,and finally effectively promote its long-term healthy and stable operation.Third,based on the above investigation on the long-term ESE characteristics of typical scenarios in the open and competitive EM environment,this dissertation further proposes a theoretical research method that is suitable for analyzing the long-term bidding ESE characteristics of an evolutionary game involving two GENCO populations with three bidding strategies in the supply-side homogeneous and heterogeneous power generation markets.Among these,aiming at the homogeneous PGM,the qualitative research based on theoretical analysis and dynamic simulation reveals that the final bidding ESE of this homogeneous market is only determined by 6 defined RNP parameters,resulting in a total of 64 bidding game scenarios in the market.Moreover,the market contains a total of 288 long-term bidding evolution states in these scenarios,including 82 long-term bidding ESE states,85 evolutionarily unstable bidding equilibrium states and 121 evolutionarily critical bidding equilibrium states.Aiming at the heterogeneous market,first,the qualitative research shows that in the case of no government supervision,such heterogeneous PGM will spontaneously form a total of 9 evolutionarily stable bidding strategies and in the case of government supervision,it will only achieve a long-term bidding ESE state under three bidding strategies,i.e.,simultaneously quote at a high price,or a middle price,or a low price.Such long-term bidding state is only determined by this market’s defined RNP parameters.Further,the quantitative research on this heterogeneous PGM under two specific clearing mechanisms shows that under the clearing mechanism of Pay As Bid(PAB),all types of GENCO populations are more likely to choose the high/middle bidding strategy and the electricity-price fluctuation is higher.Therefore,the government needs to formulate some reasonable on-grid bidding rules to actively guide various GENCO populations to offer a lower quotation to prevent the market electricity-price from being raised and monopolizing.In contrast,under the Market Clearing Price(MCP)mechanism,the competition among GENCO populations is much tougher,and GNECO populations are more willing to simultaneously adopt a low-price quotation strategy when participating in market bidding with the aim of being given them a market clearing opportunity and maximizing their economic profits.Therefore,when the total power generation demand of this heterogeneous PGM is the same and the total power generation capacity of all GENCO populations is not fully satisfied,the Market Clearing Price-based clearing mechanism is easier than the clearing mechanism of Pay As Bid in terms of guiding all GENCO populations to participate in the market bidding with a low-price quotation strategy.Moreover,the market prices fluctuate more gently in Market Clearing Price-based clearing mechanism,which is more conducive to the long-term healthy and stable operation of the power supply-side market.Fourth,based on the above theoretical investigation on the typical multi-population AEG scenarios in the open EM,this dissertation finally proposes a theoretical research method that is suitable for analyzing the long-term ESE characteristics of user populations participating in smart power consumption,dispatching and distribution(SPCDD)in power DRM in the open EM environment.During the study,an N-population AEG(nPAEG)model is developed for the non-complete rational user populations participating in power DRM in the open EM.The advantage of this nPAEG model is that it makes full use of EGT to reveal the evolution rules of user population behavior and accurately predict the population behavior of the individual users from another new perspective based on bounded rationality and limited information conditions.Therefore,this model is closer to the actual dynamic interactive decision-making situation when user populations participate in SPCDD.The case study indicates that appropriate and attractive incentive pricing from utility companies such as PGE and NPSE plays a crucial role in guiding and facilitating different user populations to actively participate in SPCDD in the dynamic interactive decision-making process of multiple user populations.At this time,driven by profitability,convergence and continuous dynamic interaction,all user populations will achieve a long-term ESE at a significant proportion(i.e.,the user engagement)under the strategy of choosing to participate in SPCDD.This is of great significance for the improvement of safe and stable operation level and peak shaving and load leveling profits of the power grid,as well as the healthy development of the SG.In contrast,other factors such as the initial value of the user engagement,the form of the comfort utility function and its key parameter settings,the number of user populations and the size of the population may affect the final evolution of the user engagement and related profit of each user population to a certain extent,but the promotion effect they play is weaker than the electricity price incentive and can be neglected.Lastly,this dissertation summarizes all the research work presented above.In addition,this dissertation prospects the next research directions of the main research work.Moreover,the dissertation prospects the application of evolutionary games on complex networks in complex smart dispatching and control strategies research for cyber-physical-social systems(CPSS)integrated SGs in the context of open EM.Here,the Robot of Smart Energy Control(RoboEC)is taken as an SG example in the prospect section,which claims that EGT can be used to accurately reveal the conformity and learning behavior characteristics of RoboECs in the dynamic interactive decision-making process.We believe that a dynamic evolutionary game model with characteristics of conformity and learning behaviors can be established for the RoboEC in the future.Such model can effectively reduce the computational difficulty of RoboEC’s collaboration and autonomy,so that the virtual parallel artificial system can spontaneously evolve into a better dispatching strategy space,and multiple optimal equilibrium boundary points can emerge.Through the summarizations and prospects,this dissertation claims that EGT needs to be cross-integrated with some disciplines such as complex system theory,cybernetics and population dynamics theory in the future.Such cross-integration research work is promising and predictably,it will have broad application prospects in the long-term dynamic interactive behavioral decision-making issues involving different stakeholders with incomplete rationality and limited information characteristics in SG in the context of open and competitive EM.