A Reinforcement Learning Approach Based on Group Relative Policy Optimization for Economic Dispatch in Smart Grids

The increased complexity of modern energy network raises the necessity of flexible and reliable methods for smart grid operation. To this end, this article is centered on the economic dispatch problem (EDP) in smart grids, which aims at scheduling generators to meet the total demand at the minimized cost. This article proposes a fully distributed algorithm to address the EDP over directed networks and takes into account communication delays and noisy gradient observations. In particular, the rescaling gradient technique is introduced in the algorithm design and the implementation of the distributed algorithm only resorts to row-stochastic weight matrices, which allows each generator to locally allocate the weights on the messages received from its in-neighbors. It is proved that the optimal dispatch can be achieved under the assumptions that the nonidentical constant communication delays inflicting on each link are uniformly bounded and the noises embroiled in gradient observation of every generator are bounded variance zero mean. Simulations are provided to validate and testify the effectiveness of the presented algorithm.

Economical dispatch of power is a significant real time optimization problem in the operation of power system, which allocates the loads on the committed generating units to reduce the generation cost, while meeting all the inequality and equality constraints. Traditionally, economic load dispatch problems have been formulated as convex optimization problem and various classical methods such as gradient methods, base-point participation factor method, etc. have been used for solving them. The traditional formulation is a quadratic input-output curve or piece wise linear cost curve, which are continuous and convex, however, real generating units have valve loading effects, which make the cost curve discontinuous and non-convex and hence the economic dispatch problem is no longer simple to handle. Thus, the classical methods cannot be employed for non-convex problems. The non-convex, non-linear and discontinuous economic dispatch (ED) problem can be better solved by metaheuristic approaches. Such approaches often require tuning of their respective evolutionary parameters. Although, solution to such type of problem have already been solved by different metaheuristic optimization techniques in previous studies as well, however, the algorithm employed in this paper to solve Power Economic Load Dispatch (PELD) problem is adaptive real coded quantum-inspired evolutionary algorithm, which does not require tuning of evolutionary parameters and performs better than some of the existing techniques on standard 6-bus 3 machine system and IEEE 14 bus 5 unit system.

This paper is dedicated to solving the economic dispatch problem in smart grids, which aims at minimizing the total generation cost while satisfying the power supply-demand balance and generation capacity constraints. A distributed algorithm is proposed to solve the economic dispatch problem over directed communication topologies that are time-varying unbalanced. Its features are that the proposed algorithm is push-based, and the model of line losses is integrated into the problem of our interest to reduce the power losses. Resorting to geometric graph theory and convex analysis, it is proved that the incremental costs achieve consensus at a convergence rate O(1 / √t ) with t being the number of iterations. Furthermore, robustness of the proposed algorithm is investigated solving the EDP when the communication information undergoes arbitrary large but bounded constant delays and the local gradients involve observation noises with zero-mean and bounded variance. Finally, three case studies implemented on an islanded microgrid, the IEEE 30-bus system and the IEEE 118-bus system are tested to demonstrate the effectiveness of the proposed algorithm.

Solving non-convex economic load dispatch problem via artificial cooperative search algorithm

In this paper, a distributed optimization algorithm based on state-based potential game (SPG) is proposed for the real-time economic dispatch (RTED) problem in smart grids. Under the DC power flow approximation, we formulate the RTED with coupled operational constraints as a centralized optimization problem (C-RTED). By treating each node in the grid as an agent, we convert the C-RTED into an SPG by augmenting its objective function in the designed game with a local augmented Lagrange-like function, leading to a distributed algorithm for solving the C-RTED problem. We reveal that the stationary-state Nash equilibrium of the SPG exactly identifies the global optimum of the constrained C-RTED problem. The proposed algorithm is capable of handling both equality and inequality constraints in complicated forms, and can be further simplified to entail lower communication burden. Simulations on the IEEE 9-, 39-, and 118-bus systems confirm that the algorithm can quickly converge to the global optimum even under unreliable communication and plug-and-play operations.

This paper considers the optimal economic dispatch of power generators in a smart electric grid for allocating power between generators to meet load requirements at a minimum total cost. We present a decentralized algorithm where, each generator independently adjusts its power output using only a measurement of the frequency deviation of the grid and minimal information exchange with its neighbors. Existing algorithms assume that frequency deviation is proportional to the load imbalance. In practice this is seldom exactly correct. We assume here that the only thing known about this relationship is that it is an unknown, odd, strictly increasing function. We provide a proof of convergence and simulations verifying the efficacy of the algorithm.

This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices. This method integrates features including photovoltaic (PV) systems, energy storage coupling, varied energy roles,... | Find, read and cite all the research you need on Tech Science Press

Economic dispatch (ED) is one of the optimization problems in power system operation and planning. The practical ED problems have non-smooth cost functions with equality and inequality constraints. It becomes more complicated problem when valve point effects of generator are considered and results multiple local minima. This makes the ED problems are difficult to find global optimum solution when using any mathematical approach due to non-convex cost function. The Classical particle swarm optimization (PSO) has ability to reach near global optimum solution by tuning some parameters but always stuck at local minima. In this paper, an iteration particle swarm optimization (IPSO) is proposed to solve ED problems with valve point effects. The proposed algorithm is introduced a new parameter in the original velocity equation of PSO in order to enrich searching behaviour, solution quality and avoid being trapped at local minima. The proposed IPSO algorithm has been implemented on two test power systems (consisting 3 and 13 generating units) to validate its effectiveness. The simulation results confirmed that IPSO algorithm has better convergence characteristic and more robust compared to PSO and some published results.

Event-triggered scheme for finite-time distributed economic dispatch in smart grids

The Economic Dispatch (ED) is one of the most important optimization problems in power systems the ultimate goal of the ED is to minimize the cost of operations in a power generation. In this paper, the Woodpecker Mating Algorithm (WMA) is used to solve the ED problem considering the nonlinear properties of generators such as valve point effects (VPE), prohibited operating zones (POZ), ramp rate limits, multiple fuel options, and transmission loss. The WMA algorithm is a novel metaheuristic algorithm inspired by the mating behavior of woodpeckers and sound intensity (a physical quantity). The WMA is implemented on six test systems of different operational dimensions and characteristics to show its capacity for solving the ED problem. The results are compared with the latest and most efficient methods introduced in the literature. Proving the efficiency of the WMA to solve the ED problem, simulation results are promising and offer the optimal fuel cost of production.

SummaryThis paper studies distributed resource allocation problem for agents with input dead‐zone, which is not considered in the existing work. At first, the primal problem is transformed to an auxiliary problem by using the exact penalty method to deal with local inequality constraints. It is assumed that the explicit expressions of cost functions and local inequality constraints are unknown to agents but the values of the cost and constraint functions can be obtained. Under such a setup, the extremum seeking control is used to estimate the gradient information. Thus, to obtain the optimal allocation, a novel distributed algorithm is designed by the virtue of the extremum seeking control and a dynamic compensating mechanism which is used to handle the effects of the input dead‐zone. Due to a two time‐scale structure of the designed distributed algorithm, the semi‐globally practically asymptotical convergence of all agents' decisions to the optimal allocation is obtained by the singular perturbation technique. Finally, numerical examples of economic dispatch in smart grids are given to verify the effectiveness of our proposed method.

The objective of the economic dispatch problem of electrical power generation is to schedule the committed generating unit's output so as to meet the required load demand while satisfying the system equality and inequality constraints. This paper solves the combined economic emission dispatch problem by Min-Max and Max-Max price penalty factor approaches using Lagrange's method. The price penalty factor for the combined economic emission dispatch (CEED) is the ratio of fuel cost to emission value. The literature papers reported that most of them use Max-Max Price penalty factor for the CEED problem. This paper analyses Min-Max and Max-Max price penalty factors for CEED problem. This problem is solved for a five generator system by considering the valve point effect for both fuel cost and emission function. The total fuel cost by considering valve point effect of the combined economic emission dispatch problem is less when using Min-Max price penalty factor approach in comparison to Max-Max price penalty factor.

Solving non-convex economic dispatch problem with valve point effects using modified group search optimizer method

Power grid operations rely on the trustworthy operation of critical control center functionalities, including the so-called Economic Dispatch (ED) problem. The ED problem is a large-scale optimization problem that is periodically solved by the system operator to ensure the balance of supply and load while maintaining reliability constraints. In this paper, we propose a semantics-based attack generation and implementation approach to study the security of the ED problem.1 Firstly, we generate optimal attack vectors to transmission line ratings to induce maximum congestion in the critical lines, resulting in the violation of capacity limits. We formulate a bilevel optimization problem in which the attacker chooses manipulations of line capacity ratings to maximinimize the percentage line capacity violations under linear power flows. We reformulate the bilevel problem as a mixed integer linear program that can be solved efficiently. Secondly, we describe how the optimal attack vectors can be implemented in commercial energy management systems (EMSs). The attack explores the dynamic memory space of the EMS, and replaces the true line capacity ratings stored in data regions with the optimal attack vectors. In contrast to the well-known false data injection attacks to control systems that require compromising distributed sensors, our approach directly implements attacks to the control center server. Our experimental results on benchmark power systems and five widely utilized EMSs show the practical feasibility of our attack generation and implementation approach.

This article proposes a novel optimization technique “Mutation based Statistically tracked GWO (MSGWO)” for solving, smart grid economic load dispatch problem which includes the uncertainties associated with the wind power generation, solar power generation and Plug-in electric vehicles (PEVs). Such a model incorporating renewable energy resources (RERs) faces an innovative challenge with the inclusion of PEVs, which might act as sources, loads and energy storages. One of the foremost concerns with such a complex model is to control the charging and/or discharging of these vehicles as per the hourly load demand of the system to such an extent that it can operate with minimum possible stress on the system with reduced overall optimum cost and emission. The extraordinary strength of the proposed optimization technique, which is tested on IEEE 300 bus system, is demonstrated in the results which are superior to those obtained from other optimization techniques: GA, PSO, GWO, Modified GWO and EO.