Distributed decision-making in a shared power network: a game-theoretic framework for integrated electricity and gas systems.

Generalized Nash equilibrium problems (GNEPs) allow, in contrast to standard Nash equilibrium problems, a dependence of the strategy space of one player from the decisions of the other players. In this paper, we consider jointly convex GNEPs which form an important subclass of the general GNEPs. Based on a regularized Nikaido-Isoda function, we present two (nonsmooth) reformulations of this class of GNEPs, one reformulation being a constrained optimization problem and the other one being an unconstrained optimization problem. While most approaches in the literature compute only a so-called normalized Nash equilibrium, which is a subset of all solutions, our two approaches have the property that their minima characterize the set of all solutions of a GNEP. We also investigate the smoothness properties of our two optimization problems and show that both problems are continuous under a Slater-type condition and, in fact, piecewise continuously differentiable under the constant rank constraint qualification. Finally, we present some numerical results based on our unconstrained optimization reformulation.

Over current relay coordination in a meshed distribution system with multiple distributed renewable energy sources (RES) is a very challenging for the protection engineers. The exiting over current relays in the distribution system is set for some predefined network topology and fault currents. Connection of RES results change in network topology and causes additional fault current contribution from these power sources in the distribution systems. The contribution of fault currents from incoming RESs under changed network topology results in mal-operation of over current relays. Modifications of the existing over current relay settings for each new incoming RES is not practically feasible in field. Fault current limiters (FCL) have the capability to block the fault current under fault duration and offers very low resistance to the normal load currents in the distribution systems. This feature of FCL is utilized in this article to restore the over current relay coordination in the distribution system under RES penetration. These FCL devices will eliminate the impact of fault currents on the exiting over current relay coordination in the distribution systems. So, this is a non-adaptive type of over current relay coordination protection scheme, in which the settings of over current relay are not changes as per the injection of RES. The proposed non-adaptive over current relay coordination approaches is implemented in 33 KV distribution side of for IEEE 30 bus system.

The generalized Nash equilibrium problem is an extension of the standard Nash equilibrium problem where both the utility function and the strategy space of each player depend on the strategies chosen by all other players. Recently, the generalized Nash equilibrium problem has emerged as an effective and powerful tool for modeling a wide class of problems arising in many fields and yet solution algorithms are extremely scarce. In this paper, using a regularized Nikaido-Isoda function, we reformulate the generalized Nash equilibrium problem as a mathematical program with complementarity constraints (MPCC). We then propose a suitable method for this MPCC and under some conditions, we establish the convergence of the proposed method by showing that any accumulation point of the generated sequence is a M-stationary point of the MPCC. Numerical results on some generalized Nash equilibrium problems are reported to illustrate the behavior of our approach.

We consider generalized Nash equilibrium problems (GNEPs) with non-convex strategy spaces and non-convex cost functions. This general class of games includes the important case of games with mixed-integer variables for which only a few results are known in the literature. We present a new approach to characterize equilibria via a convexification technique using the Nikaido–Isoda function. To any given instance of the GNEP, we construct a set of convexified instances and show that a feasible strategy profile is an equilibrium for the original instance if and only if it is an equilibrium for any convexified instance and the convexified cost functions coincide with the initial ones. We develop this convexification approach along three dimensions: We first show that for quasi-linear models, where a convexified instance exists in which for fixed strategies of the opponent players, the cost function of every player is linear and the respective strategy space is polyhedral, the convexification reduces the GNEP to a standard (non-linear) optimization problem. Secondly, we derive two complete characterizations of those GNEPs for which the convexification leads to a jointly constrained or a jointly convex GNEP, respectively. These characterizations require new concepts related to the interplay of the convex hull operator applied to restricted subsets of feasible strategies and may be interesting on their own. Note that this characterization is also computationally relevant as jointly convex GNEPs have been extensively studied in the literature. Finally, we demonstrate the applicability of our results by presenting a numerical study regarding the computation of equilibria for three classes of GNEPs related to integral network flows and discrete market equilibria.

We consider a class of finite-dimensional variational inequalities where both the operator and the constraint set can depend on a parameter. Under suitable assumptions, we provide new estimates for the Lipschitz constant of the solution, which considerably improve previous ones. We then consider the problem of computing the mean value of the solution with respect to the parameter and, to this end, adapt an algorithm devised to approximate a Lipschitz function whose analytic expression is unknown, but can be evaluated in arbitrarily chosen sample points. Finally, we apply our results to a class of Nash equilibrium problems, and generalized Nash equilibrium problems on networks.

We consider the problem of robust downlink power control in orthogonal frequency-division multiple access (OFDMA)-based heterogeneous wireless networks (HetNets) composed of macrocells and underlaying small cells. A non-cooperative setting is assumed where the macro base stations (MBSs) and small cell base stations (SBSs) compete with each other to maximize their own capacities considering imperfect channel state information. A robust Stackelberg game (RSG) is formulated to model this hierarchical competition where the MBSs and SBSs act as the leaders and the followers, respectively. The formulated RSG can be expressed as an equilibrium program with equilibrium constraints (EPEC). A comprehensive study of this RSG is provided considering various power constraints (e.g., total and spectral mask), various interference constraints (e.g., individual and global), and different uncertainty models (e.g., column-wise and ellipsoidal). We show how the different constraints and uncertainty models change the property of the game (e.g., Nash equilibrium problem (NEP) or generalized Nash equilibrium problem (GNEP)) and accordingly impact the choice of analysis method (e.g., game theory or variational inequality (VI)), solution (e.g., closed-form or numerical), and the design of algorithms and their distributive properties (e.g., totally distributed, semi-distributed, and centralized). A robust Stackelberg equilibrium (RSE) is considered to be the solution and its existence and uniqueness are investigated. Also, algorithms are proposed to arrive at the RSE. Numerical results show the effectiveness of robust solutions in an imperfect information environment.

The slurry column reactor has the most promising prospect in FT synthesis. In this paper, the gas distributor developed for slurry column rector was analyzed to find an improved gas distributor with small energy consumption, good distribution performance and the good characteristics of preventing backflow. A novel gas distributor which is employed in the slurry column reactor was proposed and multiphase flow patterns were numerically studied. The single phase flow patterns of the new slurry column gas distributor were simulated and the smaller preventing-backflow ball was found out. When connect the upper and lower two openings to form one opening, there is lower pressure drop in the gas distributor, unevenness also reduced accordingly. The overall gas holdup was consistent with the experimental data. The performance of the preventing-backflow ball was also studied in this paper. Some design requirements were put forward in order to stroke the liquid flow back.

Emission of greenhouse gases and depletion of fossil fuel reserves are two key drivers, which are forcing the mankind to generate the future energy demand from the renewable energy resources. These resources are generally distributed in nature and are directly integrated at distribution levels. Increasing penetration of the distributed energy resources in distribution power networks creates additional operational and control issues. These are mostly regulatory, economical load dispatching, power quality and protection issues.Generally power distribution systems are protected with the help of dedicated over current based protection schemes. But increasing share of distributed energy resources penetration in electric utilities poses a serious threat to the existing protection coordination schemes of the distribution systems. Distributed energy resources connected distribution networks become interconnected in nature and protection coordination schemes, which are designed for unidirectional flow of fault currents become ineffective/non-functional.Therefore, new protection coordination schemes are required for providing the adequate protection coordination for distributed energy resources connected electric power networks. In the available literature, the protection coordination schemes for radial distribution systems and developments in the area of protection coordination are discussed in detail. A thorough review for all these protection coordination schemes for distribution systems with and without distributed energy resources is done in this review article. It includes the analytical and artificial intelligence based techniques application for coordination of protective relays in the distribution systems. The limitations and research gaps in the area of protection coordination schemes are also presented in this review article.The aim of this research paper is to bring all the available research in the area of relay coordination on one platform, so that it will help the emerging researcher to identify the future scope of relay coordination application for distributed energy resources connected distribution systems.

This paper studies the market interactions between MicroGrids (MGs) and Aggregators (AGs) from a noncooperative perspective. Specifically, we study a Generalized Nash Equilibrium Problem (GNEP), where players are the MGs and AGs, and aim at maximizing their respective benefits. MGs' actions are the generated energy as well as the traded energy with other MGs, whereas AGs actions are the load scheduling of their subscribed users. The variational solutions of the GNEP are characterized and a distributed algorithm for its computation is proposed. By numerical simulations, it is shown that the variational solutions of the GNEP perform close to the solution of the network utility maximization problem.

To deliver high performance and reliability to the mobile users in accessing mobile cloud services, the major interest is currently given to the integration of centralized cloud computing and distributed edge computing infrastructures. In such a heterogeneous network ecosystem, multiple cloudlets from different service providers coexist. However, to meet the stringent latency requirements of computation-intensive and mission-critical applications, overloaded cloudlets can offload some of the incoming job requests to their relatively under-loaded neighboring cloudlets. In this paper, we propose a novel economic and non-cooperative game-theoretic model for load balancing among competitive cloudlets. This model aims to maximize the utilities of all the competing cloudlets while meeting the end-to-end latency of the users. We characterize the problem as a generalized Nash equilibrium problem and investigate the existence and uniqueness of a pure-strategy Nash equilibrium. We design a variational inequality based algorithm to compute the pure-strategy Nash equilibrium. We show that all the competing cloudlets are able to maximize their utilities by employing our proposed Nash equilibrium computation offload strategy in both under- and overloaded conditions. We also show through numerical evaluations that our load balancing model outperforms some of the existing game-theoretic load balancing frameworks, especially in a highly overloaded condition.

In this paper, we study the calmness of a generalized Nash equilibrium problem (GNEP) with non-differentiable data. The approach consists in obtaining some error bound property for the KKT system associated with the generalized Nash equilibrium problem, and returning to the primal problem thanks to the Slater constraint qualification.

We propose a new solution concept for generalized Nash equilibrium problems. This concept leads, under suitable assumptions, to unique solutions, which are generalized Nash equilibria and the result of a mathematical procedure modeling the process of finding a compromise. We first compute the favorite strategy for each player, if he could dictate the game, and use the best response on the others’ favorite strategies as starting point. Then, we perform a tracing procedure, where we solve parametrized generalized Nash equilibrium problems, in which the players reduce the weight on the best possible and increase the weight on the current strategies of the others. Finally, we define the limiting points of this tracing procedure as solutions. Under our assumptions, the new concept selects one reasonable out of typically infinitely many generalized Nash equilibria.

This paper develops an algorithm for solving the generalized Nash equilibrium problem (GNEP) in non-cooperative games. The problem involves a set of players, each with a cost function that depends on their own decision as well as the decisions of other players. The goal is to find a decision vector that minimizes the cost for each player. Unlike most of the existing algorithms for GNEP, which require full information exchange among all players, this paper considers a more realistic scenario where players can only communicate with a subset of players through a connectivity graph. The proposed algorithm enables each player to estimate the decisions of other players and update their own and others’ estimates through local communication with their neighbors. By introducing a network Lagrangian function and applying the Douglas-Rachford splitting method (DR), the GNEP is reformulated as a zero-finding problem. It is shown that the DR method can find the generalized Nash equilibrium (GNE) of the original problem under some mild conditions.

The envisioned smart grid aims at improving the interaction between the supply- and the demand-side of the electricity network, creating unprecedented possibilities for optimizing the energy usage at different levels of the grid. In this paper, we propose a distributed demand-side management (DSM) method intended for smart grid users with load prediction capabilities, who possibly employ dispatchable energy generation and storage devices. These users participate in the day-ahead market and are interested in deriving the bidding, production, and storage strategies that jointly minimize their expected monetary expense. The resulting day-ahead grid optimization is formulated as a generalized Nash equilibrium problem (GNEP), which includes global constraints that couple the users' strategies. Building on the theory of variational inequalities, we study the main properties of the GNEP and devise a distributed, iterative algorithm converging to the variational solutions of the GNEP. Additionally, users can exploit the reduced uncertainty about their energy consumption and renewable generation at the time of dispatch. We thus present a complementary DSM procedure that allows them to perform some unilateral adjustments on their generation and storage strategies so as to reduce the impact of their real-time deviations with respect to the amount of energy negotiated in the day-ahead. Finally, numerical results in realistic scenarios are reported to corroborate the proposed DSM technique.

Non-additive network pricing with non-cooperative mobility service providers