Intelligent 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.

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.

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.

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

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.

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.

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

We present a consensus-based approach to the optimal economic dispatch of power generators in a smart microgrid. Under the proposed approach, generators independently make adjustments to their power frequency primary controller set points using three pieces of information: (a) their own marginal cost of generation, (b) the measured frequency deviation, and (c) marginal generation cost of a subset of other generators obtained using local message exchanges. We show that in the absence of power losses, these independent adjustments can be designed in such a way that frequency deviations are reduced to zero, and additionally, the overall cost of generation is minimized; that a slight modification to enforce harp power constraints on power generation achieves the same as long as the global optimum is within those bounds. When power losses are taken into account, our algorithm still reduces the frequency deviations to zero; however, in this case, the total cost of generation is only approximately minimized, though the resulting suboptimality can be shown to be negligible for typical levels of power losses. The proposed approach can be thought of as a gradient search of a carefully chosen objective function, whose minimization only requires the frequency deviation and message exchanges between neighboring generators. We prove that the algorithm uniformly converges to the global optimum and illustrate its performance using numerical simulations.

The state-of-the-art MW-frequency control is performed by two hierarchical mechanisms: economic dispatch (ED) and automatic generation control (AGC). The ED is solved every 5 min identifying the most economic generation dispatch and reserve schedule. AGC is a feedback control system that regulates area control error by sending signals to regulation reserve every 2-6 s. In system with high renewable penetration and associated high net-load variability, the conventional ED-AGC hierarchical model may result in degraded MW-frequency performance and increasing operational cost. In this paper, an AGC dynamic constrained ED model is proposed to provide a more reliable and economical regulation reserve schedule in handling high net load variability. The continuous AGC dynamics is transformed into discrete state-space model, and the fast AGC dynamics are eliminated to reduce the system order. The discretized reduced-order AGC dynamics are incorporated into the ED to optimize the regulation schedule. The proposed model can be applied in a look-ahead mode with very short-term load forecast or in a look-back mode to provide a “perfect dispatch” benchmark based on historical net load data. The 5-bus and 118-bus systems are tested to demonstrate the effectiveness of the proposed model.

Multi-objective dynamic economic emission dispatch of electric power generation integrated with game theory based demand response programs

Decentralized algorithms to solve the economic dispatch problem (EDP) in smart grids have been a significant focus within engineering research due to their advantages in scalability, robustness, and flexibility. Its purpose is to optimize the generation power of each generator to jointly achieve the minimal total generation cost on the premise of satisfying the total demand and generation capacity. Recently, the emergence of data security and the requirement for complex computing have led to a resurgence of activity in this area. To address EDP while considering the issues of private security and computation efficiency, we propose a novel privacy-protected decentralized random sleep algorithm over an unbalanced directed network. On the one hand, the proposed algorithm can effectively protect sensitive information by adding conditional noises in the state exchange. On the other hand, it can also promote computation efficiency over an unbalanced directed network by incorporating the random sleep strategy into the decentralized inexact gradient method with the gradient rescaling technique. It is proved that the proposed algorithm is able to achieve the optimal solution of the EDP. Furthermore, we also provide theoretical proof to guarantee the convergence and privacy properties of the proposed algorithm. Finally, two simulation examples of EDP in smart grids are provided to demonstrate the effectiveness of the proposed algorithm.

Designing an efficient distributed economic dispatch (DED) strategy for the smart grid (SG) in the presence of multiple generators plays a paramount role in obtaining various benefits of a new generation power system, such as easy implementation, low maintenance cost, high energy efficiency, and strong robustness against uncertainties. It has drawn a lot of interest from a wide variety of scientific disciplines, including power engineering, control theory, and applied mathematics. We present a state-of-the-art review of some theoretical advances toward DED in the SG, with a focus on the literature published since 2015. We systematically review the recent results on this topic and subsequently categorize them into distributed discrete- and continuous-time economic dispatches of the SG in the presence of multiple generators. After reviewing the literature, we briefly present some future research directions in DED for the SG, including the distributed security economic dispatch of the SG, distributed fast economic dispatch in the SG with practical constraints, efficient initialization-free DED in the SG, DED in the SG in the presence of smart energy storage batteries and flexible loads, and DED in the SG with artificial intelligence technologies.

<p>Power grid is an interconnected system of supplying electricity from the supplier to the consumer, consisting of electricity generating plant, high voltage transmission lines- to carry electricity from the generating plant to the load center, and distribution lines- to carry electricity from load centers to individual consumers. A lot of research is being pursued to develop technologies for improving the next generation of power grid called the Smart Power Grid. The Smart Power Grid will have sophisticated communication infrastructure to improve the efficiency of electricity generation using renewable energy sources like the sun, water, etc and also to inform consumers of their electricity usage pattern. Also, the electricity market is now divided into three sections- generation, transmission and distribution. Private companies are competing with each other to provide electricity at the most competitive market price. We have developed two algorithms to help generating companies achieve their goal of meeting the hourly electricity need of the consumers and to do so at a minimum total cost.</p>

A survey on applications of Alternating Direction Method of Multipliers in smart power grids