Energy Management for a User Interactive Smart Community: A Stackelberg Game Approach

This paper studies a three party energy management problem in a user interactive smart community that consists of a large number of residential units (RUs) with distributed energy resources (DERs), a shared facility controller (SFC) and the main grid. A Stackelberg game is formulated to benefit both the SFC and RUs, in terms of incurred cost and achieved utility respectively, from their energy trading with each other and the grid. The properties of the game are studied and it is shown that there exists a unique Stackelberg equilibrium (SE). A novel algorithm is proposed that can be implemented in a distributed fashion by both RUs and the SFC to reach the SE. The convergence of the algorithm is also proven, and shown to always reach the SE. Numerical examples are used to assess the properties and effectiveness of the proposed scheme.Comment: 6 pages, 4 figure

A Game Theoretical Approach to Modeling Energy Consumption with Consumer Preference

Abstract-We propose a new game theoretical equilibrium model to analyze residential users' electricity consumption behavior in smart grid where energy usage and price data are exchanged between users and utilities via advanced communication. Consideration is given to users' possible preference on convenience over cost-saving under the real-time pricing in smart grid, and each user is assumed to have a preferred time window for using a particular appliance. As a result, each user (player) in the proposed energy consumption game wishes to maximize a payoff or utility consisting of two parts: the negative of electricity cost and the convenience of using appliances during their preferred time windows. Extensive numerical tests suggest that users with less flexibility on their preferred usage times have larger impact on the system performance at equilibrium. This provide insights for utilities to design their pricing based demand response schemes

A Stackelberg game-theoretic approach to optimal real-time pricing for the smart grid

This paper proposes a Stackelberg game approach to maximize the profit of the electricity retailer (utility company) and minimize the payment bills of its customers. The electricity retailer determines the retail price through the proposed smart energy pricing scheme to optimally adjust the real-time pricing with the aim to maximize its profit. The price information is sent to the customers through a smart meter. According to the announced price, the customers can automatically manage the energy use of appliances in the households by the proposed optimal electricity consumption scheduling system with the aim to minimize their electricity bills. We model the interactions between the retailer and its electricity customers as a 1-leader, N-follower Stackelberg game. At the leader’s side, i.e., for the retailer, we adopt genetic algorithms to maximize its profit while at the followers’ side, i.e., for customers, we develop an analytical solution to the linear programming problem to minimize their bills. Simulation results show that the proposed approach is beneficial for both the customers and the retailer

Optimization models and algorithms for demand response in smart grid.

For demand response in smart grid, a utility company wants to minimize total electricity cost and end users want to maximize their own utility. The latter is considered to consist of two parts in this research: electricity cost and convenience/comfort. We first develop a system optimal (SO) model and a user equilibrium (UE) model for the utility company and end users, respectively and compare the difference of the two. We consider users\u27 possible preference on convenience over cost-saving under the real-time pricing in smart grid, and each user is assumed to have a preferred time window for using a particular appliance. As a result, each user in the proposed energy consumption game wishes to maximize a payoff or utility consisting of two parts: the negative of electricity cost and the convenience of using appliances during their preferred time windows. Numerical results show that users with less flexibility on their preferred usage times have larger impact on the system performance at equilibrium. Second, we found that instead of minimizing total cost, if utility company is regulated to maximize the social welfare, the user equilibrium model can achieve identical optimal solution as the system optimal model. We then design a demand response pricing frame work to accomplish this goal under alternative secondary objectives. We also investigate the non-uniqueness of the user equilibrium solution and prove that there exist alternative user equilibrium solutions. In this case, robust pricing is considered using multi-level optimization for the user equilibrium. Third, we study empirical data from a demand response pilot program in Kentucky in an attempt to understand consumer behavior under demand response and to characterize the thermo dynamics when set point for heat, ventilation and air conditioning (HVAC) is adjusted for demand response. Although sample size is limited, it helps to reveal the great variability in consumers\u27 response to demand response event. Using the real data collected, we consider to minimize the peak demand for a system consisting of smart thermostats, advanced hot water heaters and battery systems for storage. We propose a mixed integer program model as well as a heuristic algorithm for an optimal consumption schedule so that the system peak during a designated period is minimized. Therefore, we propose a consumption scheduling model to optimally control these loads and storage in maximizing efficiency without impacting thermal comfort. The model allows pre-cooling and pre-heating of homes to be performed for variable loads in low-demand times. We propose several future works. First, we introduce the concept of elastic demand to our SO model and UE model. The system problem maximizes net benefit to the energy consumers and the user problem is the usual one of finding equilibrium with elastic demand. The Karush-Kuhn-Tucker (KKT) conditions can be applied to solve the elastic demand problems. We also propose to develop algorithms for multi-level pricing models and further collect and analyze more field data in order to better understand energy users\u27 consumption behavior

Game Theoretic Model Predictive Control for Autonomous Driving

This study presents two closely-related solutions to autonomous vehicle control problems in highway driving scenario using game theory and model predictive control. We first develop a game theoretic four-stage model predictive controller (GT4SMPC). The controller is responsible for both longitudinal and lateral movements of Subject Vehicle (SV) . It includes a Stackelberg game as a high level controller and a model predictive controller (MPC) as a low level one. Specifically, GT4SMPC constantly establishes and solves games corresponding to multiple gaps in front of multiple-candidate vehicles (GCV) when SV is interacting with them by signaling a lane change intention through turning light or by a small lateral movement. SV’s payoff is the negative of the MPC’s cost function , which ensures strong connection between the game and that the solution of the game is more likely to be achieved by a hybrid MPC (HMPC). GCV’s payoff is a linear combination of the speed payoff, headway payoff and acceleration payoff. . We use decreasing acceleration model to generate our prediction of TV’s future motion, which is utilized in both defining TV’s payoffs over the prediction horizon in the game and as the reference of the MPC. Solving the games gives the optimal gap and the target vehicle (TV). In the low level , the lane change process are divided into four stages: traveling in the current lane, leaving current lane, crossing lane marking, traveling in the target lane. The division identifies the time that SV should initiate actual lateral movement for the lateral controller and specifies the constraints HMPC should deal at each step of the MPC prediction horizon. Then the four-stage HMPC controls SV’s actual longitudinal motion and execute the lane change at the right moment. Simulations showed the GT4SMPC is able to intelligently drive SV into the selected gap and accomplish both discretionary land change (DLC) and mandatory lane change (MLC) in a dynamic situation. Human-in-the-loop driving simulation indicated that GT4SMPC can decently control the SV to complete lane changes with the presence of human drivers. Second, we propose a differential game theoretic model predictive controller (DGTMPC) to address the drawbacks of GT4SMPC. In GT4SMPC, the games are defined as table game, which indicates each players only have limited amount of choices for a specific game and such choice remain fixed during the prediction horizon. In addition, we assume a known model for traffic vehicles but in reality drivers’ preference is partly unknown. In order to allow the TV to make multiple decisions within the prediction horizon and to measure TV’s driving style on-line, we propose a differential game theoretic model predictive controller (DGTMPC). The high level of the hierarchical DGTMPC is the two-player differential lane-change Stackelberg game. We assume each player uses a MPC to control its motion and the optimal solution of leaders’ MPC depends on the solution of the follower. Therefore, we convert this differential game problem into a bi-level optimization problem and solves the problem with the branch and bound algorithm. Besides the game, we propose an inverse model predictive control algorithm (IMPC) to estimate the MPC weights of other drivers on-line based on surrounding vehicle’s real-time behavior, assuming they are controlled by MPC as well. The estimation results contribute to a more appropriate solution to the game against driver of specific type. The solution of the algorithm indicates the future motion of the TV, which can be used as the reference for the low level controller. The low level HMPC controls both the longitudinal motion of SV and his real-time lane decision. Simulations showed that the DGTMPC can well identify the weights traffic vehicles’ MPC cost function and behave intelligently during the interaction. Comparison with level-k controller indicates DGTMPC’s Superior performance

Game Theoretic Model Predictive Control for Autonomous Driving

This study presents two closely-related solutions to autonomous vehicle control problems in highway driving scenario using game theory and model predictive control. We first develop a game theoretic four-stage model predictive controller (GT4SMPC). The controller is responsible for both longitudinal and lateral movements of Subject Vehicle (SV) . It includes a Stackelberg game as a high level controller and a model predictive controller (MPC) as a low level one. Specifically, GT4SMPC constantly establishes and solves games corresponding to multiple gaps in front of multiple-candidate vehicles (GCV) when SV is interacting with them by signaling a lane change intention through turning light or by a small lateral movement. SV’s payoff is the negative of the MPC’s cost function , which ensures strong connection between the game and that the solution of the game is more likely to be achieved by a hybrid MPC (HMPC). GCV’s payoff is a linear combination of the speed payoff, headway payoff and acceleration payoff. . We use decreasing acceleration model to generate our prediction of TV’s future motion, which is utilized in both defining TV’s payoffs over the prediction horizon in the game and as the reference of the MPC. Solving the games gives the optimal gap and the target vehicle (TV). In the low level , the lane change process are divided into four stages: traveling in the current lane, leaving current lane, crossing lane marking, traveling in the target lane. The division identifies the time that SV should initiate actual lateral movement for the lateral controller and specifies the constraints HMPC should deal at each step of the MPC prediction horizon. Then the four-stage HMPC controls SV’s actual longitudinal motion and execute the lane change at the right moment. Simulations showed the GT4SMPC is able to intelligently drive SV into the selected gap and accomplish both discretionary land change (DLC) and mandatory lane change (MLC) in a dynamic situation. Human-in-the-loop driving simulation indicated that GT4SMPC can decently control the SV to complete lane changes with the presence of human drivers. Second, we propose a differential game theoretic model predictive controller (DGTMPC) to address the drawbacks of GT4SMPC. In GT4SMPC, the games are defined as table game, which indicates each players only have limited amount of choices for a specific game and such choice remain fixed during the prediction horizon. In addition, we assume a known model for traffic vehicles but in reality drivers’ preference is partly unknown. In order to allow the TV to make multiple decisions within the prediction horizon and to measure TV’s driving style on-line, we propose a differential game theoretic model predictive controller (DGTMPC). The high level of the hierarchical DGTMPC is the two-player differential lane-change Stackelberg game. We assume each player uses a MPC to control its motion and the optimal solution of leaders’ MPC depends on the solution of the follower. Therefore, we convert this differential game problem into a bi-level optimization problem and solves the problem with the branch and bound algorithm. Besides the game, we propose an inverse model predictive control algorithm (IMPC) to estimate the MPC weights of other drivers on-line based on surrounding vehicle’s real-time behavior, assuming they are controlled by MPC as well. The estimation results contribute to a more appropriate solution to the game against driver of specific type. The solution of the algorithm indicates the future motion of the TV, which can be used as the reference for the low level controller. The low level HMPC controls both the longitudinal motion of SV and his real-time lane decision. Simulations showed that the DGTMPC can well identify the weights traffic vehicles’ MPC cost function and behave intelligently during the interaction. Comparison with level-k controller indicates DGTMPC’s Superior performance

Efficient double auction mechanisms in the energy grid with connected and islanded microgrids

Doctor of PhilosophyDepartment of Electrical and Computer EngineeringSanjoy DasThe future energy grid is expected to operate in a decentralized fashion as a network of autonomous microgrids that are coordinated by a Distribution System Operator (DSO), which should allocate energy to them in an efficient manner. Each microgrid operating in either islanded or grid-connected mode may be considered to manage its own resources. This can take place through auctions with individual units of the microgrid as the agents. This research proposes efficient auction mechanisms for the energy grid, with is-landed and connected microgrids. The microgrid level auction is carried out by means of an intermediate agent called an aggregator. The individual consumer and producer units are modeled as selfish agents. With the microgrid in islanded mode, two aggregator-level auction classes are analyzed: (i) price-heterogeneous, and (ii) price homogeneous. Under the price heterogeneity paradigm, this research extends earlier work on the well-known, single-sided Kelly mechanism to double auctions. As in Kelly auctions, the proposed algorithm implements the bidding without using any agent level private infor-mation (i.e. generation capacity and utility functions). The proposed auction is shown to be an efficient mechanism that maximizes the social welfare, i.e. the sum of the utilities of all the agents. Furthermore, the research considers the situation where a subset of agents act as a coalition to redistribute the allocated energy and price using any other specific fairness criterion. The price homogeneous double auction algorithm proposed in this research ad-dresses the problem of price-anticipation, where each agent tries to influence the equilibri-um price of energy by placing strategic bids. As a result of this behavior, the auction’s efficiency is lowered. This research proposes a novel approach that is implemented by the aggregator, called virtual bidding, where the efficiency can be asymptotically maximized, even in the presence of price anticipatory bidders. Next, an auction mechanism for the energy grid, with multiple connected mi-crogrids is considered. A globally efficient bi-level auction algorithm is proposed. At the upper-level, the algorithm takes into account physical grid constraints in allocating energy to the microgrids. It is implemented by the DSO as a linear objective quadratic constraint problem that allows price heterogeneity across the aggregators. In parallel, each aggrega-tor implements its own lower-level price homogeneous auction with virtual bidding. The research concludes with a preliminary study on extending the DSO level auc-tion to multi-period day-ahead scheduling. It takes into account storage units and conven-tional generators that are present in the grid by formulating the auction as a mixed inte-ger linear programming problem