Distributed extremum‐seeking based resource allocation algorithm with input dead‐zone

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.

ABSTRACTThis paper studies a distributed constraint optimization problem for a multi‐agent system with unknown cost functions and asymmetric input dead‐zone. First, the constraint optimization problem is transformed into an unconstrained optimization problem by using the exact penalty method. As only measurements of the cost functions and local inequality constraints are available, a distributed extremum‐seeking algorithm is presented based on an event‐triggered communication scheme to reduce communication frequency. Moreover, to address the impact of input dead‐zones, a dynamic compensation scheme is introduced into the designed algorithm. Due to the dual time‐scale structure of the designed distributed algorithm, singular perturbation techniques are used to achieve semiglobally practically asymptotical convergence of the decision variables of all agents to the optimal solution. Finally, simulations verify the effectiveness of the proposed 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.

Event-triggered scheme for finite-time distributed 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.

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.

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.

In this article, we study nondifferentiable resource allocation problems (RAPs). In our problem, the decisions of agents are subject to coupling inequality constraints, local inequality constraints, and local convex set constraints. In contrast to existing RAPs, the cost functions are nonsmooth and the inequality constraints are nonsmooth and nonlinear in our problem. Based on differential inclusions and projection methods, we exploit a fully distributed subgradient-based resource allocation algorithm to optimally allocate the network resources. With the help of the set-valued LaSalle invariance principle, we prove the global convergence of the algorithm to the optimal resource allocation of our problem. Finally, our method is applied to the economic dispatch problems of smart grids. With our method, the generations of generating units converge to the optimal power generation.

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

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.

Various distributed optimization methods have been developed for solving problems which have simple local constraint sets and whose objective function is the sum of local cost functions of distributed agents in a network. Motivated by emerging applications in smart grid and distributed sparse regression, this paper studies distributed optimization methods for solving general problems which have a coupled global cost function and have inequality constraints. We consider a network scenario where each agent has no global knowledge and can access only its local mapping and constraint functions. To solve this problem in a distributed manner, we propose a consensus-based distributed primal-dual perturbation (PDP) algorithm. In the algorithm, agents employ the average consensus technique to estimate the global cost and constraint functions via exchanging messages with neighbors, and meanwhile use a local primal-dual perturbed subgradient method to approach a global optimum. The proposed PDP method not only can handle smooth inequality constraints but also non-smooth constraints such as some sparsity promoting constraints arising in sparse optimization. We prove that the proposed PDP algorithm converges to an optimal primal-dual solution of the original problem, under standard problem and network assumptions. Numerical results illustrating the performance of the proposed algorithm for a distributed demand response control problem in smart grid are also presented.

In this article, a distributed resource allocation problem for second‐order multi‐agent systems over undirected switching topologies is investigated. For the distributed resource allocation problem, most of the existing algorithms depend on the gradient of cost function with specific expression, which may be unknown to agents. To deal with unknown cost functions, the extremum seeking control is introduced in the designed distributed resource allocation algorithm to estimate the gradient of the cost function only by the value of the cost. Besides, an estimator is proposed to estimate the optimal Lagrange multiplier associated with the equality constraint. The communication graph is supposed to be switched among a set of undirected subgraphs, which may be connected or unconnected. For undirected and connected switching graphs, the average dwell‐time constraint is used to describe the switching frequency. For the undirected graphs, containing connected and unconnected ones, both the average dwell‐time and the time‐ratio constraints are used to model the switching signal. For the two cases, the semi‐globally practically asymptotical stability of the designed algorithm is established. The obtained results are verified by an example.

This paper investigates finite-time resource allocation problems (RAPs) for uncertain nonlinear fractional-order multi-agent systems (FOMASs), considering global equality and local inequality constraints. Each agent is described by high-order dynamics with multiple-input multiple-output and only knows its local objective function. Due to the characteristics of dynamic systems, the outputs of agents are inconsistent with their inputs, making it challenging to satisfy the inequality constraints when solving RAPs. To address this complex optimization control problem, a novel hierarchical algorithm is proposed, consisting of a distributed estimator and a local controller. Specifically, the distributed estimator is established by adopting the ϵ-exact penalty function and the gradient descent method. This estimator enables the system states to reach the optimal solution of RAPs within a finite time. Furthermore, the local controller is presented based on the fractional-order tracking differentiator and adaptive neural control approach. Under this controller, the system states are slaved to track the optimal signals generated by the estimator within a finite time. In both the estimator and controller algorithms, the finite-time stability is uniformly guaranteed with the help of Lyapunov functions. Finally, the effectiveness of our algorithm is demonstrated through three simulation examples.

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 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.