Economic Dispatch In Smart Grids Research Articles

An edge‐based event‐triggered delayed distributed algorithm for economic dispatch in smart grids

AbstractThis paper presents an edge‐based event‐triggered delay distributed algorithm for solving the economic dispatch problem (EDP) in smart grids. The objective of the EDP is to minimize the total generation cost by allocating power to individual generators, each with its local generation constraint. To save the overhead of communication resources between agents, an edge‐based event‐triggered mechanism is suggested. By setting distinct triggering thresholds for each communication edge, the agent may efficiently regulate the communication frequency among all neighbors. However, in practice, owing to the instability of the network, the agent may receive information regarding its neighbors, leading to communication lags for every communication link. The virtual agent technique and double‐stochastic matrix augmentation technique provide an equivalent delay‐free EDP. It is demonstrated that the proposed algorithm can asymptotically converge to the global optimal solution as long as the communication delay is arbitrary, time‐varying, and random, but bounded. Objective and clear evidence is provided through a case study in smart grids to verify the algorithm's feasibility.

Distributed optimization of multi-integrator agent systems with mixed neighbor interactions

In this paper, we consider a constrained distributed optimization problem for multi-integrator agent systems with mixed neighbor interactions, where the neighbors of the agents can be classified as cooperative or noncooperative by introducing a cooperation-competition network into the modeling of the communication graph. The agent’s goal is to optimize the total objective function of the cooperators. Since agents can only communicate with their neighbors, they are unable to obtain complete information about cooperators. The distributed optimization algorithm is proposed to classify cooperative subnetworks by introducing additional auxiliary variables, and the outputs of all agents exponentially converge to the optimal solution of the optimization problem under the condition of satisfying the global equality constraint of the subnetwork. The Lyapunov stability theory is used to analyze the algorithm’s convergence. Simulation results show the effectiveness of the proposed algorithm in two examples of economic dispatch in smart grids and optimal area coverage in multi-sensor networks.

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

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.

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

This paper considers the finite-time distributed economic dispatch problem in smart grids: the power generated by individual generators are designed to satisfy a certain demand while minimizing the total generation cost in a distributed manner, which guarantees the convergence in finite time. The proposed method facilitates the solution of real time power dispatch problems. First, a class of distributed economic dispatch algorithm is proposed to achieve the optimal solution in finite-time with and without capacity limitations. Second, in order to reduce the information exchange requirements, a distributed, asynchronous event-triggered communication scheme is established which is free of Zeno with guaranteed finite-time convergence. Furthermore, both proposed algorithms are robust to the time-varying communication networks. Simulation results illustrate the effectiveness and scalability of the distributed algorithms.

Convergence analysis of a distributed gradient algorithm for economic dispatch in smart grids

The increasingly complex modern energy network arouses the need of flexible and dependable approaches to solve the economic dispatch problem (EDP) in the smart grids. Toward this end, this paper develops a fresh distributed algorithm with constant step-size, which aims to schedule the power generation among generators by complying with individual generation capacity limits to satisfy the total load demand at the minimized cost. The convergence of the proposed algorithm is analyzed through utilizing the Lyapunov method and the spectral decomposition technique. When the selected constant step-size is smaller than a specifically provided upper bound, the theoretical analysis demonstrates that the proposed algorithm can linearly achieve the optimal solution of the EDP under the smooth and strongly convex assumption on generation cost functions. In particular, the linear convergence rate of the proposed algorithm is tunable, and a relationship among the linear convergence rate, generation cost functions, network topology, weight matrix and constant step-size is established. The availability of the proposed algorithm is verified through simulation experiments.

Push-Based Distributed Economic Dispatch in Smart Grids Over Time-Varying Unbalanced Directed Graphs

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.

DisEHPPC: Enabling Heterogeneous Privacy-Preserving Consensus-Based Scheme for Economic Dispatch in Smart Grids.

These days, the increasing incremental cost consensus-based algorithms are designed to tackle the economic dispatch (ED) problem in smart grids (SGs). However, one principal obstruction lies in privacy disclosure for generators and consumers in electricity activities between supply and demand sides, which may bring great losses to them. Hence, it is extraordinarily essential to design effective privacy-preserving approaches for ED problems. In this article, we propose a two-phase distributed and effective heterogeneous privacy-preserving consensus-based (DisEHPPC) ED scheme, where a demand response (DR)-based framework is constructed, including a DR server, data manager, and a set of local controllers. The first phase is that Kullback-Leibler (KL) privacy is guaranteed for the privacy of consumers' demand by the differential privacy method. The second phase is that (ε,δ) -privacy is, respectively, achieved for the generation energy of generators and the sensitivity of electricity consumption to electricity price by designing the privacy-preserving incremental cost consensus-based (PPICC) algorithm. Meanwhile, the proposed PPICC algorithm tackles the formulated ED problem. Subsequently, we further carry out the detailed theoretical analysis on its convergence, optimality of final solution, and privacy degree. It is found that the optimal solution for the ED problem and the privacy preservation of both supply and demand sides can be guaranteed simultaneously. By evaluation of a numerical experiment, the correctness and effectiveness of the DisEHPPC scheme are confirmed.

Achieving Acceleration for Distributed Economic Dispatch in Smart Grids Over Directed Networks

In this paper, the economic dispatch problem (EDP) in smart grids is investigated over a directed network, which concentrates on allocating the generation power among the generators to satisfy the load demands with minimal total generation cost while complying with all constraints of local generation capacity. Each generator possesses its own local generation cost, and the total generation cost is the sum of all local generation costs. To deal with EDP, most of the existing methods, such as strategy based on push-sum, surmount the unbalancedness induced by the directed network via employing column-stochastic weights, which might be infeasible in distributed implementation. In contrast, in order to be suitable for the directed network with row-stochastic weights, we develop a novel directed distributed Lagrangian momentum algorithm, named as D-DLM, which integrates distributed gradient tracking method with two types of momentum terms and utilizes non-uniform step-sizes with respect to the updates of Lagrangian multipliers. If the largest step-size and the maximum momentum coefficient are positive and sufficiently small, D-DLM can linearly allocate the optimal dispatch on condition that the generation costs are smooth and strongly convex. Finally, a variety of studies on EDP in smart grids are simulated.

Distributed Robust Algorithm for Economic Dispatch in Smart Grids Over General Unbalanced Directed Networks

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.

A Finite-Time Distributed Optimization Algorithm for Economic Dispatch in Smart Grids

The economic dispatch problem (EDP) is one of the fundamental and important problems in power systems. The objective of EDP is to determine the output generation of generators to minimize the total generation cost under various constraints. In this article, a finite-time consensus-based distributed optimization algorithm is proposed to solve EDP. It is only required that each device in the communication network has access to its own local generation cost function, designed virtual local demand and its neighbors' local optimization variables. The proposed finite-time algorithm can solve EDP, if the gain parameters in the algorithm satisfy some conditions under undirected and connected time-varying graphs. Moreover, the bounded or linear increasing assumption on the gradient and subgradient of objecive functions is relaxed in this algorithm. Examples under several cases are provided to verify the effectiveness of the proposed distributed optimization algorithm.

A Gossip-Based Distributed Algorithm for Economic Dispatch in Smart Grids With Random Communication Link Failures

Motivated by the fact that gossip algorithms are asynchronous and suitable for the sensor networks with random link failures, a gossip-based distributed algorithm for the economic dispatch problem in smart grids is addressed in this paper. Random communication link failure phenomena is very common in a realistic communication network. By modeling a network as a Bernoulli network, the proposed algorithm can solve the economic dispatch problem in the imperfect communication network. Mean square consensus and almost sure consensus are adopted to analyze the convergence of the algorithm. Using matrix theory and perturbation theory, we prove that the algorithm can achieve mean square consensus and almost sure consensus . Therefore, the proposed algorithm converges to the optimal solution of the economic dispatch problem with probability 1. The convergence speed of the algorithm is discussed and simulation results show that the convergence rate is governed by the second largest eigenvalue of the system matrix. Case studies are designed to illustrate the effectiveness and plug-and-play capability of the algorithm.

Sequence‐based differential evolution for solving economic dispatch considering virtual power plant

The economic dispatch (ED) of distributed energy resources (DERs) is an important and challenging problem in smart grid operation. Different frameworks are proposed for solving this issue, among which the virtual power plant (VPP) is considered as a promising means for ED in smart grids with DERs. This study presents a novel optimisation algorithm entitled sequence-based differential evolution (SDE) for solving generation dispatch among several DERs with VPPs. In the proposed method, a novel and efficient initialisation technique, namely sequence-based deterministic initialisation, is used to generate high-quality initial population. Besides, a self-adaptation mechanism is utilised to eliminate the difficulty of tuning the problem-specific control parameters of the algorithm. Subsequently, the SDE is applied for solving the ED model to obtain the optimal power generation share of the VPP. Case studies compare the solutions obtained by the proposed method with several state-of-the-art algorithms in the existing literature. It is validated the proposed method is advantageous for ED with VPPs in better solution accuracy, less computational burden, and faster convergence.

Distributed Extremum Seeking for Optimal Resource Allocation and Its Application to Economic Dispatch in Smart Grids.

This paper proposes a first-order extremum-seeking algorithm to solve the resource allocation problem, where the specific expression form and gradient information of the local cost functions are not required. Agents take advantage of measurements of local cost functions to minimize the sum of their cost functions while satisfying the resource constraint, where agents exchange the estimated decisions with their neighbors under an undirected and connected graph. Making use of the Lyapunov stability theory and the average analysis method, the convergence of the proposed algorithm to the neighborhood of the optimal solution is presented. In addition, it is obtained that the designed algorithm is semiglobally practically asymptotically stable. Then, the first-order algorithm is extended to the second-order algorithm with low-pass filters, which achieves better convergence performance than the first-order algorithm. Finally, the effectiveness of the proposed algorithm is illustrated by numerical examples and its application to economic dispatch in smart grids.

Distributed Real-Time Economic Dispatch in Smart Grids: A State-Based Potential Game Approach

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.

A Decentralized Approach for Frequency Control and Economic Dispatch in Smart Grids

This paper proposes a decentralized approach for frequency control and economic dispatch in smart grids with distributed energy resources and responsive demands. The approach is implemented based on a distributed multi-agent system, in which each agent works in a collaborative manner via local computation and peer to peer communication. The approach is comprised of two strategies. A consensus-based strategy is implemented at the supply side to regulate system frequency economically. Self-adaptive updating rules are proposed for the key parameters to improve the accuracy and robustness of the consensus-based strategy. A threshold-based strategy is implemented at the demand side to provide ancillary services for frequency regulation. Simulation results are presented to demonstrate the effectiveness and robustness of the approach.

Distributed Event-Triggered Scheme for Economic Dispatch in Smart Grids

To reduce information exchange requirements in smart grids, an event-triggered communication-based distributed optimization is proposed for economic dispatch. In this work, the $\theta$ -logarithmic barrier-based method is employed to reformulate the economic dispatch problem, and the consensus-based approach is considered for developing fully distributed technology-enabled algorithms. Specifically, a novel distributed algorithm utilizes the minimum connected dominating set (CDS), which efficiently allocates the task of balancing supply and demand for the entire power network at the beginning of economic dispatch. Further, an event-triggered communication-based method for the incremental cost of each generator is able to reach a consensus, coinciding with the global optimality of the objective function. In addition, a fast gradient-based distributed optimization method is also designed to accelerate the convergence rate of the event-triggered distributed optimization. Simulations based on the IEEE 57-bus test system demonstrate the effectiveness and good performance of proposed algorithms.

Smart Grid Economic Dispatch

This paper describes a smart grid economic dispatch (SGED) approach without considering the network equality security constraints. The economic dispatch (ED) problem is one of the fundamental problems in the power system. The objective of ED is to reduce the total power generation cost. The SGED is performed for a test system that comprises three generators and one battery storage device (a 5 MW hydrogen storage unit), considering the consumer power demand. The economic dispatch will be performed for the whole day. The economic dispatch is performed according to the ascending power production cost.

A robust distributed system incremental cost estimation algorithm for smart grid economic dispatch with communications information losses

With an increasing number of controllable distributed energy resources deployed and integrated into the power system, how to economically manage these distributed resources will become a challenge for the future smart grid. To solve the issue, consensus based distributed economic dispatch algorithms have been introduced in the literature as computationally scalable approaches. However, in real-world applications with imperfect communications networks, the performance of consensus-based economic dispatch algorithms degrades when information losses occur. In this paper, a robust distributed system incremental cost estimation (RICE) algorithm is introduced to solve the Economic Dispatch Problem (EDP) in a smart grid environment in a distributed way considering communications information losses. Unlike the existing consensus-based algorithms to solve EDP, RICE algorithm has two updating layers running in parallel in each distributed controller: one layer uses the gossip updating rule to estimate the system׳s average power mismatch, while the other layer uses the consensus updating rule to update the system Incremental Cost (IC) estimation. In this approach, the vulnerability of consensus-based algorithms to communications information losses is eliminated. The convergence and optimality of the algorithm are guaranteed as long as the undirected communications topology among local controllers is connected. Several case studies are presented to illustrate the performance of the proposed algorithm, and show the robustness under different information loss scenarios with different communications topologies.

Distributed Dynamic Programming-Based Approach for Economic Dispatch in Smart Grids

In this paper, the discrete economic dispatch problem is formulated as a knapsack problem. An effective distributed strategy based on distributed dynamic programming algorithm is proposed to optimally allocate the total power demand among different generation units considering the generation limits and ramping rate limits. The proposed distributed strategy is implemented based on a multiagent system framework which only requires local computation and communication among neighboring agents. Thus, it enables the sharing of computational and communication burden among distributed agents. In addition, the proposed strategy can be implemented with asynchronous communication, which may lead to simpler implementation and faster convergence speed. Simulation results with a four-generator system and the IEEE 162-bus system are presented to demonstrate the effectiveness of the proposed distributed strategy.

Decentralized Economic Dispatch in Smart Grids by Self-Organizing Dynamic Agents

In this paper, we propose a decentralized and self-organizing solution framework aimed at addressing economic dispatch (ED) analysis in a distributed scenario. In particular we will demonstrate that, under some hypotheses, the solution of the ED analysis can be obtained by computing proper weighted averages of the variable of interests. To compute these global quantities we propose the deployment of a network of cooperative dynamic agents solving distributed average consensus problems. Thanks to this decentralized/nonhierarchical paradigm, all the basic operations needed to solve the economic dispatch problem could be easily processed by the agents. Simulation results obtained on the 118 and 300 bus IEEE test networks are presented and discussed in order to prove the effectiveness of the proposed framework.