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

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.

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.

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.

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.

The Economic Dispatch Problem (EDP) plays a critical role in power system operations by trying to allocate power generation across multiple units at minimal cost while satisfying complex operational constraints. Traditional optimization techniques struggle with the non-convexities introduced by factors such as valve-point effects, prohibited operating zones, and spinning reserve requirements. While metaheuristics methods have shown promise, they often suffer from convergence issues and constraint-handling limitations. In this study, we introduce a novel application of Group Relative Policy Optimization (GRPO), a reinforcement learning framework that extends Proximal Policy Optimization by integrating group-based learning and relative performance assessments. The proposed GRPO approach incorporates smart initialization, adaptive exploration, and elite-guided updates tailored to the EDP’s structure. Our method consistently produces high-quality, feasible solutions with faster convergence compared to state-of-the-art metaheuristics and learning-based methods. For instance, in the case of the 15-unit system, GRPO achieved the best cost of USD 32,421.67/h with full constraint satisfaction in just 4.24 s, surpassing many previous solutions. The algorithm also demonstrates excellent scalability, generalizability, and stability across larger-scale systems without requiring parameter retuning. These results highlight GRPO’s potential as a robust and efficient tool for real-time energy scheduling in smart grid environments.

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.

Integrating renewable energy into power grids is seen in increase in recent years since these energy sources are sustainable and clean. However, the integration brings about considerable technical challenges associated with fluctuations and uncertainties of the energy availability whilst maintaining the stability of smart grids. The prediction of renewable energy generation is key to achieve optimal power dispatch in renewable-intensive smart grids. However, uncertain interruption and prediction errors will make an optimal decision more challenging. Model predictive control (MPC) is an effective way to overcome the discrepancies between the prediction and the real-world system through a closed-loop correction over iteration process. This study develops an improved MPC scheme used with a hybrid energy storage system for optimal power dispatch in a smart grid. This hybrid renewable energy system consists of a wind farm, a hydrogen/oxygen storage system and several fuel cells (FCs). In this study, particle swarm optimization (PSO) with a back propagation (BP) artificial neural network is developed to predict the wind energy availability by using measured data. Then, a genetic algorithm (GA) is combined with a state space model (SSM) to achieve the MPC control. A dataset of 24-hour ahead predictive generation is calibrated from the measured data and is defined for optimal power flow between the grid, the wind farm and the storage subsystem so as to balance the supply and load. The optimization target is to achieve a minimal energy exchange between the power grid and the hybrid renewable energy storage system. Based on actual measured data, the test results have shown that the proposed methodology can maximize the local usage of wind power whilst minimizing the power exchange with the grid. An optimal power dispatch strategy is proved to be effective to meet the demand and efficiency with dynamic control of the FCs. The usage of the intermittent wind power is increased from 45% to 90% in the four test studies. Therefore, this work can minimize the impact of fluctuating renewable energy on the power grid and enhance uptakes of FC-based energy systems. This is particularly economic and relevant to the remote and under-developed regions where their power networks are weak and vulnerable.

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

Hybrid distributed finite-time neurodynamic optimization of electric vehicle charging schemes management in microgrid considering time-varying factors

As the proportion of flexible load resources in smart grids continues to rise, resulting in increasingly complex grid structures, significant changes in grid characteristics, and increased risks to grid operation and control, it will be difficult to intelligently regulate the grid solely by relying on traditional resource regulation methods, and the dispatchable space for traditional resources will become smaller and smaller. To this end, this paper conducts an exploratory investigation on the modeling techniques for flexible loads participation in smart grid dispatching. First, a classification of the flexible loads involved in grid regulation is made. Secondly, according to the flexible load classification, the modeling techniques of different classes of flexible loads are reviewed and studied; then, the flexible load dispatching modes for different operating states and different control tasks, and under different control methods are discussed deeply. Moreover, the technological economics and feasibility of these different flexible load dispatching modes are compared. Finally, an outlook and conclusion are made.

This paper focuses on the design of an initialization-free distributed finite-time algorithm for the economic dispatch problem in smart grid, where the generation units only communicate with its neighbors to minimize the total cost cooperatively. Firstly, the optimal solution of the economic dispatch problem is analyzed in accordance with the saddle-point dynamics. Then, an initialization-free finite-time algorithm is presented to guarantee the active power generation and the incremental cost converge to the optimal solution in a distributed manner. At last, some numerical simulations are preformed to validate the proposed method.

This paper gives an overview of the Particle Swarm Optimization technique with the aim of investigating its applicability to minimizing losses in a power distribution system. The suitability of this method is investigated by emphasizing the impact of its intrinsic parameters on the results. The investigation employs particle swarm optimization on a test system by controlling the generator voltages, transformer taps and the reactive power in the capacitor banks for each load bus. In total it contains 33 control variables: 5 generators (not including the terminal bus), 4 transformers and 24 capacitor banks. A theoretical approach of the PSO is given in the beginning, followed by the simulation results and analyses.

Non-Lipschitz Growth Functions as a Natural Way of Modelling Finite Time Behaviour in Auto-immune Dynamics

Power generation and transmission infrastructure is vulnerable to the interaction of various Distributed Generations (DG), which leads to the imbalance of power system operation, frequent voltage drops or spikes, and even power outages. This phenomenon not only wastes energy, but also affects grid security. The main reason is a delayed feedback of circuit failure and load changes, and the optimization of energy management system and path is an effective way to solve the above problems. In this paper, a method of multi-objective optimization based on ANFIS algorithm is proposed which can help to improve the demand response, energy storage and management of smart power grid, reduce the volatility of DGs, reducing electricity costs and improving energy efficiency. Firstly, based on the ANFIS algorithm, the distributed power generation control mode, inverter control, real-time electricity price calculation method, energy transfer and storage scheme are improved, and the optimization path of the energy management system is defined. Secondly, the advantages of ANFIS algorithm in response speed and running stability are verified by comparing with other algorithms. Finally, a distributed energy microgrid is constructed for simulation verification. The results show that :(1) ANFIS optimization algorithm has good adaptability in smart grid, and has advantages in large amount of data processing and information transmission; (2) The verification model based on ANFIS has strong elasticity and efficient response speed. The research results will help solve various problems in the smart grid, including establishing a clear energy management system path, maintaining the stable operation of the power system, providing users with more reasonable power plans and the lowest cost of electricity.

In this article, we present a finite time stopping criterion for consensus algorithms in networks with dynamic communication topology. Recent results provide asymptotic convergence to the consensus algorithm. However, the asymptotic convergence of these algorithms pose a challenge in the practical settings where the response from agents is required in finite time. To this end, we propose a Maximum-Minimum protocol which propagates the global maximum and minimum values of agent states (while running consensus algorithm) in the network. We establish that global maximum and minimum values are strictly monotonic even for a dynamic topology and can be utilized to distributively ascertain the closeness to convergence in finite time. We show that each node can have access to the global maximum and minimum by running the proposed Maximum-Minimum protocol and use it as a finite time stopping criterion for the otherwise asymptotic consensus algorithm. The practical utility of the algorithm is illustrated through experiments where each agent is instantiated by a NodeJS socket.io server.