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This study proposes a decentralised robust fuzzy control strategy for islanded operation of an AC microgrid with voltage source inverters. The objective is to design a robust controller for regulating the load voltage and sharing power among distributed generators (DGs) in the presence of uncertainties in the system and non-linear loads. The AC microgrid consists of parallel DGs connected to a main AC bus. A Takagi-Sugeno fuzzy approach is developed in this article to achieve stability and desired performance in dealing with non-linearities in the islanded microgrid and H∞ criterion is used to obtain a robust control strategy in presence of uncertainties raised by unmodelled and high frequency dynamics. Therefore, a non-convex condition in H∞ optimisation problem is converted to a convex linear matrix inequality (LMI) condition and is solved by MATLAB LMI toolbox. In order to develop a decentralized system, P-f and Q-V droop controllers are used to specify set-points for local inverter controllers in each DG. The effectiveness of the proposed control strategy in presence of constant power load and DG accidental outage is validated by the simulation of a microgrid test system in MATLAB SimPowerSystems toolbox. Comparison with cascaded proportional integral controller shows advantages of robust T-S controller. [ABSTRACT FROM AUTHOR]

The authors consider the problem of multi-player evolutionary game with two strategies and an arbitrary number of players. A randomised probabilistic access model is considered where the users randomly select the strategies. The strategies are a selection between two radio access technologies to receive service from. For a fair resource allocation between a number of users, the payoff function of each player is considered to be inversely proportional to the number of players choosing a strategy. It is valid for the radio access technology selection problem where resources are divided fairly between the users. The necessary and sufficient conditions for the existence and uniqueness of a mixed Nash equilibrium point of the game is provided. In addition, it is proved that the mixed Nash equilibrium point of the game is globally asymptotically stable and also evolutionarily stable strategy. [ABSTRACT FROM AUTHOR]

This study proposes a decentralised robust fuzzy control strategy for islanded operation of an AC microgrid with voltage source inverters. The objective is to design a robust controller for regulating the load voltage and sharing power among distributed generators (DGs) in the presence of uncertainties in the system and non‐linear loads. The AC microgrid consists of parallel DGs connected to a main AC bus. A Takagi‐Sugeno fuzzy approach is developed in this article to achieve stability and desired performance in dealing with non‐linearities in the islanded microgrid and H∞ criterion is used to obtain a robust control strategy in presence of uncertainties raised by unmodelled and high frequency dynamics. Therefore, a non‐convex condition in H∞ optimisation problem is converted to a convex linear matrix inequality (LMI) condition and is solved by MATLAB LMI toolbox. In order to develop a decentralized system, P–f and Q–V droop controllers are used to specify set‐points for local inverter controllers in each DG. The effectiveness of the proposed control strategy in presence of constant power load and DG accidental outage is validated by the simulation of a microgrid test system in MATLAB SimPowerSystems toolbox. Comparison with cascaded proportional integral controller shows advantages of robust T‐S controller. [ABSTRACT FROM AUTHOR]

The authors consider the problem of multi‐player evolutionary game with two strategies and an arbitrary number of players. A randomised probabilistic access model is considered where the users randomly select the strategies. The strategies are a selection between two radio access technologies to receive service from. For a fair resource allocation between a number of users, the payoff function of each player is considered to be inversely proportional to the number of players choosing a strategy. It is valid for the radio access technology selection problem where resources are divided fairly between the users. The necessary and sufficient conditions for the existence and uniqueness of a mixed Nash equilibrium point of the game is provided. In addition, it is proved that the mixed Nash equilibrium point of the game is globally asymptotically stable and also evolutionarily stable strategy. [ABSTRACT FROM AUTHOR]

This study addresses a robust counterpart of the deterministic mean field control in a multi‐agent system. A decentralised mean field algorithm is proposed to solve a min–max control problem for a large population of heterogeneous agents. In the proposed leader following scheme, the leader tracks a reference signal which is unknown to the followers and each follower tracks a convex combination of the population state average and the leader's state. The leader plays a robust min–max game against disturbance and the followers play a mean field εN ‐Nash game against each other and at the same time, each follower plays a robust min–max game against the disturbance. For all the players, finite horizon quadratic cost is considered. In the proposed decentralised algorithm, followers do not need the knowledge about each of leader's and other followers' states and they only use an estimate of the population state average. In this way, propose a policy iteration method which guarantees the convergence to the saddle point mean field εN ‐Nash solution. The proposed method is applied to a large population of agents and compared with centralised algorithm to demonstrate the results. [ABSTRACT FROM AUTHOR]

In this paper, an agent matching method for bilateral contracts in a multi-agent market is proposed. Each agent has a hierarchical representation of its trading commodity attributes by a tree structure of fuzzy attributes. Using this structure, the similarity between the trees of each pair of buyer and seller is computed using a new ordered fuzzy similarity algorithm. Then, using the concept of Stackelberg equilibrium in a leader–follower game, matchmaking is performed among the sellers and buyers. The fuzzy similarities of each agent with others in its personal viewpoint have been used as its payoffs in a bimatrix game. Through a case study for bilateral contracts of energy, the capabilities of the proposed agent-based system are illustrated. [ABSTRACT FROM AUTHOR]

In a competitive electricity market, suppliers seek the optimal bidding strategy, maximising their individual profit. Due to the uncertainties, unknown parameters and dynamics of electricity market, the optimal bidding strategies cannot be attained through straightforward optimisation methods. In this study, the supply function equilibrium model is considered together with uniform price market clearing mechanism. The interaction among suppliers is modelled as an incomplete information game problem and multi-agent reinforcement learning (MARL) is utilised to find the optimal bidding strategy of the suppliers in a non-cooperative game. The proposed framework is an extension, from single agent Markov decision process to Markov game process, which is suitable for studying multi-agent decision making problems in stochastic environments. In this study, a Markov game model of the electricity market is proposed and a new state-action and Markov model of electricity market is proposed to built up the MARL environment. In addition, a learning-based non-cooperative MARL method is utilised for learning the optimal bidding strategies of the suppliers in a day-ahead electricity market. The proposed method is successfully applied to IEEE-30-bus power system. To examine the statistical significance of the results, the T-test method is applied to compare the competitive behaviour of the players in both multi- and single-agent frameworks. [ABSTRACT FROM AUTHOR]

In a competitive electricity market, suppliers seek the optimal bidding strategy, maximising their individual profit. Due to the uncertainties, unknown parameters and dynamics of electricity market, the optimal bidding strategies cannot be attained through straightforward optimisation methods. In this study, the supply function equilibrium model is considered together with uniform price market clearing mechanism. The interaction among suppliers is modelled as an incomplete information game problem and multi‐agent reinforcement learning (MARL) is utilised to find the optimal bidding strategy of the suppliers in a non‐cooperative game. The proposed framework is an extension, from single agent Markov decision process to Markov game process, which is suitable for studying multi‐agent decision making problems in stochastic environments. In this study, a Markov game model of the electricity market is proposed and a new state‐action and Markov model of electricity market is proposed to built up the MARL environment. In addition, a learning‐based non‐cooperative MARL method is utilised for learning the optimal bidding strategies of the suppliers in a day‐ahead electricity market. The proposed method is successfully applied to IEEE‐30‐bus power system. To examine the statistical significance of the results, the T‐test method is applied to compare the competitive behaviour of the players in both multi‐ and single‐agent frameworks. [ABSTRACT FROM AUTHOR]