In this work, we review papers that employ game theoretic tools to study the operation and design of modern electric grids. We consider four topics in this context: energy trading, energy balancing, grid planning, and system reliability, and we demonstrate the advantages of using game-theoretic approaches for analyzing complex interactions among independent players. The results and conclusions provide insights regarding many aspects of design and operation, such as efficient methodologies for expansion planning, cyber-security, and frequency stability, or fair-benefit allocation among players. A central conclusion is that modeling the system from the perspective of one entity with unlimited information and control span is often impractical, so correct modeling of the selfish behavior of independent players may be critical for the development of future power systems. Another conclusion is that correct usage of incentives by appropriate regulation or sophisticated pricing mechanisms may improve the social welfare, and, in several cases, the results obtained are as good as those obtained by central planning. Using an extensive content analysis, we point to several trends in the current research and attempt to identify the research directions that are currently at the focus of the community.

Although the deployment and integration of isolated microgrids is gaining widespread support, regulation of microgrid frequency under high penetration levels of renewable sources is still being researched. Among the numerous studies on frequency stability, one key approach is based on integrating an additional loop with virtual inertia control, designed to mimic the behavior of traditional synchronous machines. In this survey, recent works related to virtual inertia control methods in islanded microgrids are reviewed. Based on a contextual analysis of recent papers from the last decade, we attempt to better understand why certain control methods are suitable for different scenarios, the currently open theoretical and numerical challenges, and which control strategies will predominate in the following years. Some of the reviewed methods are the coefficient diagram method, H-infinity-based methods, reinforcement-learning-based methods, practical-swarm-based methods, fuzzy-logic-based methods, and model-predictive controllers.

We consider energy storage systems having nonlinear efficiency functions, which are becoming increasingly important as shown in several recent works, and propose an optimal solution based on Pontryagin's minimum principle. A central challenge in such problems is the hard limits on the state variable, which restrict the use of the minimum principle. To address this challenge, we propose to include the capacity constraints in the objective function with a proper weighting constant. We show that this approach allows formulation of the problem based on the classical minimum principle, and eventually leads to an efficient optimal control strategy. The proposed solution is compared to a dynamic programming algorithm. Numeric experiments reveal that for lossless storage devices dynamic programming is beneficial, since it enables fast and accurate solutions when a low number of samples is used. However, for lossy storage devices the situation is the opposite, and the minimum principle provides faster and more accurate solutions, since its computational complexity is almost unaffected by changes in the system parameters.

We propose an optimal control method for storage systems that are affected by the power grid's ramp constraints. Such problems are becoming increasingly important in recent years due to the integration of renewable energy sources, which often leads to duck curve effects. The main idea of the proposed method is to limit the number of computations in the forward recursion stage by applying an ongoing trimming process, which reduces the number of discrete energy values being scanned. As a result, the practical range of values is significantly reduced, which leads to a lower computational burden. To verify our results, the proposed method is compared to a classic solution method from the literature, showing a significant improvement in overall execution time and memory requirements when considering a typical test case.

In this brief, we propose a suboptimal control update for lossless storage systems that operates based on the instantaneous value of the load power and generalizes previously suggested solutions for energy management problems. The proposed control update performs under uncertain conditions and does not require statistical information about the load profile. We leverage tools from Pontryagin’s minimum principle and stochastic dynamic programming methods to derive the control strategy and then investigate its stability properties using the Lyapunov analysis. However, the analysis of this control paradigm presents significant challenges, among which the key difficulty arises due to the presence of nonlinear feedback terms. To address this challenge, we first introduce a coordinate transformation, which transforms the original problem into an equivalent stabilization problem, and then verify its stability properties using the Lyapunov function theory and LaSalle’s invariance principle. We show that the proposed control policy works for both continuous-time and stochastic load profiles, and it keeps the stored energy within the capacity bounds by following the optimal path.