Generalized Nash Game Research Articles

Regional Operation of Electricity-Hythane Integrated Energy System Considering Coupled Energy and Carbon Trading

The deepening implementation of the energy and carbon market imposes trading requirements on multiple regional integrated energy system participants, including power generation plants, industrial users, and carbon capture, utilization, and storage (CCUS) facilities. Their diverse roles in different markets strengthen the interconnections among these subsystems. On the other hand, the operation of CCUS, containing carbon capture (CS), power-to-hydrogen (P2H), and power-to-gas (P2G), results in the coupling of regional carbon reduction costs with the operation of electricity and hythane networks. In this paper, we propose a regional economic dispatching model of an integrated energy system. The markets are organized in a centralized form, and their clearing conditions are considered. CCUS is designed to inject hydrogen or natural gas into hythane networks, operating more flexibly. A generalized Nash game is applied to analyze the multiple trading equilibria of different entities. Simulations are carried out to derive a different market equilibrium regarding network scales, seasonal load shifts, and the ownership of CCUS. Simulation results in a 39-bus/20-node coupled network indicate that the regional average carbon prices fluctuate from ¥1078.82 to ¥1519.03, and the organization of independent CCUS is more preferred under the proposed market structure.

A peer‐to‐peer joint energy and reserve market considering renewable generation uncertainty: A generalized Nash equilibrium approach

AbstractPeer‐to‐peer (P2P) energy trading enhances distribution network resilience by reducing energy demand from central power plants and enabling distributed energy resources to support critical loads after extreme events. However, adequate reserves from main grids are still required to ensure real‐time energy balance in distribution networks due to the uncertainty in renewable generation. This paper introduces a novel two‐stage joint energy and reserve market for prosumers, wherein local flexible resources are fully utilized to manage renewable generation uncertainty. In contrast to cooperative optimization methods, the interactions between prosumers are modelled as a generalized Nash game (GNG), considering that prosumers are self‐interested and should follow distribution network constraints. Then, linear decision rules are employed to ensure a feasible market equilibrium and develop a privacy‐preserving algorithm to guide prosumers toward the market equilibrium with a proven convergence. Finally, the numerical study on a modified IEEE 33‐power system demonstrates that the designed market effectively manages renewable generation uncertainty, and that the algorithm converges to the market equilibrium.

Decentralized frequency regulation service provision for virtual power plants: A best response potential game approach

The high-renewable-penetrated power system frequently requires frequency regulation services. By aggregating heterogeneous demand-side flexible resources, the virtual power plants (VPP) are able to quickly respond to the frequency regulation signal, enabling them promising frequency regulation service providers. However, due to the difference in ownership, it is unlikely that the self-interested demand-side resources are willing to follow the VPP-oriented dispatch results. To bridge this gap, this paper proposes a decentralized game-based mechanism for the frequency regulation service provision inside the VPP. Firstly, the supply function-based bidding models of aggregated demand-side resources, namely, demand-side flexible resources and renewable distributed generations, are established. Then, a non-cooperative generalized Nash game for frequency regulation service provision is formulated. The existence, uniqueness, and competitive efficiency loss of the game are analyzed by designing an equivalent best response potential game of the original game. Additionally, a decentralized look-ahead real-time market clearing mechanism for frequency regulation service provision inside the VPP is proposed based on dual decomposition algorithm. Finally, the effectiveness and computation efficiency of the proposed method are validated in the case studies. Meanwhile, it is shown that the competition efficiency loss can be effectively reduced from around 80% to 6% when increasing the demand-side resource population from 20 to 2000 as well as balancing the demand-side resource composition.

Emission reduction estimation by coupling peer-to-peer energy sharing with carbon emission markets considering temporal and spatial factors

This paper presents an energy-sharing market coupled with carbon emission trading to quantify peer-to-peer energy-sharing markets’ economic and environmental influences. We establish a bi-level peer-to-peer energy sharing market considering the interaction between energy prosumers and the system operator. An interaction algorithm and generalized Nash game are thus applied in this work. With the simulation results, we find that the daily disutility of provincial systems is reduced by about 7 ¥ when time-of-use electricity rates are applied. This pricing strategy can encourage prosumers to participate in energy-sharing transactions. The subsidies of electricity rates, carbon prices, and renewable energy investments can improve the social welfare of the whole system. Considering the development of power generation technology and emission reduction targets, the change of optimization parameters in the next 30 years is analyzed in the example. It can be concluded that the total CO2 emission in 2050 will be reduced to almost half of that in 2020 in the energy-sharing markets. The subsidy of renewable energy generation and stricter CO2 emission constraints may accelerate the reduction of carbon emissions.

Distributed energy trading on networked energy hubs under network constraints

A distributed energy trading scheme with non-discriminatory pricing for a cluster of networked energy hubs (NEHs) is proposed. First, each energy hub (EH) is treated as a self-interested agent. The hybrid AC/DC microgrid (MG)-embedded EH model is proposed to optimize the operating costs under corresponding local energy balance constraints. The supply limits of the input energy systems, e.g., electrical feeders and natural gas pipelines, are represented as the global coupling constraints among NEHs. Then, to obtain the optimal operation and trading strategies, the distributed energy trading is formulated as a generalized Nash game (GNG). To ensure the solubility of the GNG problem, the existence and uniqueness of the generalized Nash equilibrium (GNE) are proved. Furthermore, to transform the complexity of the solution, the multivariable GNG problem is reformulated as a N+1 Nash game (NG) without coupling constraints, the equivalence between NG and the solution set of variational inequality (VI) problem is established. Then, an efficient distributed projection-based algorithm is proposed to compute a Nash equilibrium (NE) for the NG problem. Finally, a potential game-based centralized solution method is also implemented as a baseline, and the comparison of simulation results demonstrates the effectiveness of our proposed algorithm.

An Energy Sharing Mechanism Considering Network Constraints and Market Power Limitation

As the number of prosumers with distributed energy resources (DERs) grows, the conventional centralized operation scheme may suffer from conflicting interests, privacy concerns, and incentive inadequacy. In this paper, we propose an energy sharing mechanism to address the above challenges. It takes into account network constraints and fairness among prosumers. In the proposed energy sharing market, all prosumers play a generalized Nash game. The market equilibrium is proved to have nice features in a large market or when it is a variational equilibrium. To deal with the possible market failure, inefficiency, or instability in general cases, we introduce a price regulation policy to avoid market power exploitation. The improved energy sharing mechanism with price regulation can guarantee existence and uniqueness of a socially near-optimal market equilibrium. Some advantageous properties are proved, such as prosumer's individual rationality, a sharing price structure similar to the locational marginal price, and the tendency towards social optimum with an increasing number of prosumers. For implementation, a practical bidding algorithm is developed with convergence condition. Experimental results validate the theoretical outcomes and show the practicability of our model and method.

A novel price-driven energy sharing mechanism for charging station operators

To address the deviations of energy schedules and increase benefits, charging station operators (CSOs) hope to trade energy in a low-cost and efficient way. Energy sharing has been noticed as a way to improve social welfare. When energy has commodity attributes, designing a better sharing mechanism from energy scarcity to stimulate prosumer flexibility and achieve optimal social welfare needs to be studied. In this paper, a novel price-driven energy sharing mechanism is designed for prosumers. A prosumer surplus model including energy utility is established to extend the prosumer flexibility. Value identity based on the “shared electricity price” enables prosumers to agree on a price voluntarily. It is proven that the new mechanism has the same unique optimal solution as the social planner's problem. Unlike the existing sharing mechanisms based on the generalized Nash game, the new mechanism can achieve optimal social welfare in a market with finite prosumers. On this basis, a local energy sharing model of CSOs is established, where the network constraints of the local system and time-varying utility are considered in the sharing process. The simulations show that the new mechanism can efficiently use the prosumers' generation and load flexibility to achieve better social welfare.

Solving PEV Charging Strategies with an Asynchronous Distributed Generalized Nash Game Algorithm in Energy Management System

As plug-in electric vehicles (PEVs) become more and more popular, there is a growing interest in the management of their charging power. Many models exist nowadays to manage the charging of plug-in electric vehicles, and it is important that these models are implemented in a better way. This paper investigates a price-driven charging management model in which all plug-in electric vehicles are informed of the charging strategies of neighboring plug-in electric vehicles and adjust their own strategies to minimize the cost, while an aggregator determines the unit price based on overall electricity consumption to coordinate the charging strategies of the plug-in electric vehicles. In this article, we used an asynchronous distributed generalized Nash game algorithm to investigate a charging management model for plug-in electric vehicles in a smart charging station (SCS). In a charging management model, we need to consider constraints on the charge and discharge rates of plug-in electric vehicles, the battery capacity, the amount of charge per plug-in electric vehicle, and the maximum electrical load that the whole system can allow. Meeting the constraints of plug-in electric vehicles and smart charging stations, the model coordinates the charging strategy of each plug-in electric vehicle to ultimately reduce the cost of smart charging stations, which is the cost that the smart charging station should pay to the higher-level power supply facility. To the best of our knowledge, this algorithm used in this paper has not been used to solve this model, and it has better performance than the generalized Nash equilibria (GNE) seeking algorithm originally used for this model, which is called a fast alternating direction multiplier method (Fast-ADMM). In the simulation results, the asynchronous algorithm we used showed a correlation error of 0.0076 at the 713th iteration, compared to 0.0087 for the synchronous algorithm used for comparison, and the cost of the smart charging station was reduced to USD 4800.951 after coordination using the asynchronous algorithm, which was also satisfactory. We used an asynchronous algorithm to better implement a plug-in electric vehicle charging management model; this also demonstrates the potential advantages of using an asynchronous algorithm for solving the charging management model for plug-in electric vehicles.

Using inverse optimization to learn cost functions in generalized Nash games

As demonstrated by Ratliff et al. (2014), inverse optimization can be used to recover the objective function parameters of players in multi-player Nash games. These games involve the optimization problems of multiple players in which the players can affect each other in their objective functions. In generalized Nash equilibrium problems (GNEPs), a player’s set of feasible actions is also impacted by the actions taken by other players in the game. We extend the framework of Ratliff et al. (2014) to find inverse optimization solutions for a specific class of GNEPs known as jointly convex GNEPs. The resulting formulation is then applied to a simulated multi-player transportation problem on a road network. We see that our model recovers parameterizations that produce the same flow patterns as the original parameterizations and that this holds true across multiple networks, different assumptions regarding players’ perceived costs, and the majority of restrictive capacity settings and the associated numbers of players. Code for the project can be found at: https://github.com/sallen7/IO_GNEP.

Non-Convex Generalized Nash Games for Energy Efficient Power Allocation and Beamforming in mmWave Networks

Network management is a fundamental ingredient for efficient operation of wireless networks. With increasing bandwidth, number of antennas and number of users, the amount of information required for network management increases significantly. Therefore, distributed network management is a key to efficient operation of future networks. This paper focuses on the problem of distributed joint beamforming control and power allocation in ad-hoc mmWave networks. Over the shared spectrum, a number of multi-input-multi-output links attempt to minimize their supply power by simultaneously finding the locally optimal power allocation and beamformers in a self-organized manner. Our design considers a family of non-convex quality-of-service constraint and utility functions characterized by monotonicity in the strategies of the various users. We propose a two-stage, decentralized optimization scheme, where the adaptation of power levels and beamformer coefficients are iteratively performed by each link. We first prove that given a set of receive beamformers, the power allocation stage converges to an optimal generalized Nash equilibrium of the generalized power allocation game. Then we prove that iterative minimum-mean-square-error adaptation of the receive beamformer results in an overall converging scheme. Several transmit beamforming schemes requiring different levels of information exchange are also compared in the proposed allocation framework. Our simulation results show that allowing each link to optimize its transmit filters using the direct channel results in a near optimum performance with very low computational complexity, even though the problem is highly non-convex.

Generalized Nash equilibrium analysis of transmission and distribution coordination in coexistence of centralized and local markets

The increasing scale of distributed energy resources connected to distribution networks can not only solve the operational problems in the distribution system, but it can also supply the transmission system with flexibility and ancillary services. Thus, the design of a market framework to suit this situation is required. This paper builds a generalized Nash game model with shared constraints for the joint day-ahead market where the centralized market coexists with the local market. In this model, the transmission system operator clears the centralized market assuming that resources of distribution systems are fixed, the distribution system operator clears the local market assuming that resources of the transmission system are fixed, and the clearing of the two markets are conducted simultaneously. Subsequently, the generalized Nash game model can be reformulated to a variational inequality problem that can be solved by the Goldstein–Levitin–Polyak projection method, and more than one generalized Nash equilibrium solution is obtained by the parametrized variational inequality approach. Finally, case studies on two systems, which consist of a 30-bus transmission system and 33-bus distribution system, and a practical 343-bus transmission system and 110-bus distribution system, respectively, are used to verify the effectiveness of the proposed method.

Electric vehicle charging schedule considering shared charging pile based on Generalized Nash Game

Electric vehicle (EV) will not only effectively promote the popularization of charging facilities, but also reduce the dependence on fuel vehicles. However, large-scale charging behaviours of EVs will bring new challenges to match between charging facilities and EVs. Due to the limited capacity of the centralized charging stations, it is difficult to meet the charging demands of EVs in certain areas, especially during the peak load periods. To solve the insufficiency of charging capacity caused by the mismatch between charging stations and EV charging loads, this paper proposes a hierarchical scheduling model of EVs considering shared charging piles. The upper scheduling model determines the charging time of EVs based on the charging demands. The lower scheduling model coordinates charging stations and shared charging piles to determine the charging locations of EVs. The sharing scheme of private charging piles is determined by sharing capacity model based on the generalized Nash game. The quantum particle swarm algorithm with the dynamic feedback mechanism is adopted for a better convergence of the solving process of the hierarchical scheduling model. The simulation results on IEEE 33-node system are conducted to validate the effectiveness of the proposed model and solution algorithm, which show the extensive potential applications in EV scheduling.

The replicator dynamics of generalized Nash games

Generalized Nash Games are a powerful modelling tool, first introduced in the 1950's. They have seen some important developments in the past two decades. Separately, Evolutionary Games were introduced in the 1960's and seek to describe how natural selection can drive phenotypic changes in interacting populations. In this paper, we show how the dynamics of these two independently formulated models can be linked under a common framework and how this framework can be used to expand Evolutionary Games. At the center of this unified model is the Replicator Equation and the relationship we establish between it and the lesser known Projected Dynamical System.

Non-cooperative game pricing strategy for maximizing social welfare in electrified transportation networks

This paper proposes a non-cooperative game pricing strategy framework by the approach of profit-sharing and user equilibrium principles, - to maximize the social welfare of the electrified transportation system stakeholders consisting of electricity wholesalers, fast charging stations, and electric vehicle users. Electricity wholesalers propose profit-sharing contracts to sell electricity to each fast charging station. Fast charging stations compete with each other to develop the optimal retail price while considering their electricity selling revenue and the traveling cost of electric vehicle users for the purpose of maximal social welfare. Non-cooperative game competition between fast charging stations is formulated as a generalized Nash game. Wardrop user equilibrium principle is applied for path selection for electric vehicle users. A Newton-type fixed-point algorithm is developed to solve the generalized Nash equilibrium point. Meanwhile, the nonlinear program is solved by the commercial solver KNITRO. A case study demonstrates the effectiveness of the proposed pricing strategy in maximizing the total profits of the fast charging station retailers, wholesalers, and electric vehicle users.

Douglas–Rachford splitting algorithm for solving state-dependent maximal monotone inclusions

In this paper, we provide a new application of the Douglas–Rachford splitting method for finding a zero of the sum of two maximal monotone operators where one of them depends implicitly on the state variable. Our proposed algorithms are much simpler with better rate of convergence than existing results and can be implemented under general conditions. Applications to generalized Nash games and quasivariational inequalities are provided. Numerical experiments are also given to illustrate the convergence rate of the proposed algorithms.

Distributed Generalized Nash Equilibrium Seeking for Energy Sharing Games in Prosumers

With the proliferation of distributed generators and energy storage systems, traditional passive consumers in power systems have been gradually evolving into the so-called “prosumers,” i.e., proactive consumers, which can both produce and consume power. To encourage energy exchange among prosumers, energy sharing is increasingly adopted, which is usually formulated as a generalized Nash game (GNG). In this paper, a distributed approach is proposed to seek the Generalized Nash equilibrium (GNE) of the energy sharing game. To this end, we first prove the strong monotonicity of the game. Then, the GNG is converted into an equivalent optimization problem. An algorithm based on Nesterov's methods is thereby devised to solve the equivalent problem and consequently find the GNE in a distributed manner. The convergence of the proposed algorithm is proved rigorously based on the nonexpansive operator theory. The performance of the algorithm is validated by experiments with three prosumers, and the scalability is tested by simulations using 1888 prosumers.

Genericity Analysis of Multi-Leader-Disjoint-Followers Game

Multi-leader-follower games are models which combine bilevel programming with generalized Nash games. Due to their many applications, they have attracted more and more attention in the last few yea...

Approaching Prosumer Social Optimum via Energy Sharing With Proof of Convergence

With the advent of prosumers, the traditional centralized operation may become impracticable due to computational burden, privacy concerns, and conflicting interests. In this article, an energy sharing mechanism is proposed to accommodate prosumers' strategic decision-making on their self-production and demand in the presence of capacity constraints. Under this setting, prosumers play a generalized Nash game. We prove main properties of the game: an equilibrium exists and is partially unique; no prosumer is worse off by energy sharing and the price-of-anarchy is 1-O(1/I) where I is the number of prosumers. In particular, the PoA tends to 1 with a growing number of prosumers, meaning that the resulting total cost under the proposed energy sharing approaches social optimum. We prove that the corresponding prosumers' strategies converge to the social optimal solution as well. Finally we propose a bidding process and prove that it converges to the energy sharing equilibrium under mild conditions. Illustrative examples are provided to validate the results.

A distributed normalized Nash equilibrium seeking algorithm for power allocation among micro-grids

In this paper, a power allocation problem based on the Cournot game and generalized Nash game is proposed. After integrating dynamic average consensus algorithm and distributed projection neural network through singular perturbation systems, a normalized Nash equilibrium seeking algorithm is presented to solve the proposed power allocation problem in a distributed way. Combine Lyapunov stability with the singular perturbation analysis, the convergence of the proposed algorithm is analyzed. A simulation on IEEE 118-bus confirms that the proposed distributed algorithm can adjust the power allocation according to different situations, while keeping the optimal solution within the feasible set.

Energy Trading and Generalized Nash Equilibrium in Combined Heat and Power Market

The increasingly wide application of technologies such as combined heat and power (CHP) systems and micro energy management systems has enhanced the coupling of various types of energy. In this paper, a generalized Nash game model is built in this paper to simulate the multi-round auction in combined heat and power market (CHPM). In this model, the consumer demand curves are deduced from the partial derivatives of their payoff functions, and the thermal comfort of the consumers is considered in their payoff functions. The integrated energy suppliers (IES) compete with each other in the CHPM. The generalized Nash game model is applied to describe their rational economic behavior. First, the existence and uniqueness of the generalized Nash equilibrium is proven in detail. Subsequently, a distributed algorithm based on the augmented Lagrangian approach is designed to solve this generalized Nash game model. Through the distributed algorithm, the participants can protect their privacy without revealing their generation parameters or energy consumption schedule to other participants. Finally, by simulating the multi-round auction, it was found that the proposed method has faster convergence than standard Lagrangian approaches.