Economic Dispatch Problem Research Articles

Multi-Objective Dynamic Economic and Emission Generation Scheduling of Coordinated Power System Considering Renewable Energy Sources and Pumped Storage Hydro Plants via Fuzzy Surrogate-Assisted Coronavirus Herd Immunity Optimization

Globally, the power generation from renewable energy sources (RES) has received considerable attention to reduce pollutant emissions and the total operating costs of power generation. In this context, this study aims to extend the multi-objective dynamic economic and emission dispatch (MODEED) problem by incorporating RES and pumped storage hydro plants. The complex constrained MODEED problem is solved by a fuzzy surrogate-assisted coronavirus herd immunity optimization (FSACHIO) algorithm in which a self-adaptive speed factor and Lévy flight mechanism are utilized to ensure populace diversity, prevent premature convergence and achieve an ideal stability among the exploration and exploitation of the algorithm. Surrogate worth tradeoff methodology is used to discover a solution that provides the optimal balance between the objectives such as operating expenses and emission pollutants. The performance of FSACHIO algorithm is validated on a small-scale and a large-scale test systems, involving 10-unit, and 40-unit test systems, and compared with that of the coronavirus herd immunity optimization, red fox optimizer, Remora optimization algorithm, and other erstwhile approaches. Besides, a fuzzy constraint handling method based on a dominance relationship is integrated to fulfill the restrictions of the MODEED problem. The simulation results reveal that: (i) the operating costs and emissions are reduced by 173785.54 $/day and 2992.1848 lb/day in the small-scale test system and by 6383.9903 $/day and 216631.4877 lb/day in the large-scale test system, respectively for the MODEED problem with the presence of RES and pumped storage hydro plants; (ii) the suggested approach may offer a well-distributed Pareto-optimal frontier and superior tradeoffs among the operating expenses and pollution objectives in comparison to the other approaches.

Fully Distributed Economic Dispatch with Random Wind Power Using Parallel and Finite-Step Consensus-Based ADMM

In this paper, a fully distributed strategy for the economic dispatch problem (EDP) in the smart grid is proposed. The economic dispatch model considers both traditional thermal generators and wind turbines (WTs), integrating generation costs, carbon trading expenses, and the expected costs associated with the unpredictability of wind power. The EDP is transformed into an equivalent optimization problem with only an equality constraint and thus can be solved by an alternating-direction method of multipliers (ADMM). Then, to tackle this problem in a distributed manner, the outer-layer framework of the proposed strategy adopts a parallel ADMM, where different variables can be calculated simultaneously. And the inner-layer framework adopts a finite-step consensus algorithm. Convergence to the optimal solution is achieved within a finite number of communication iterations, which depends on the scale of the communication network. In addition, leveraging local and neighbor information, a distributed algorithm is designed to compute the eigenvalues of the Laplacian matrix essential for the finite-step algorithm. Finally, several numerical examples are presented to verify the correctness and effectiveness of the proposed strategy.

Modified Opposition-Based Particle Swarm Optimization for Combined Economic and Emission Dispatch Problem

Modification of the particle swarm optimization (PSO) method is proposed with an opposition-based learning strategy to find the optimal solution to electrical power dispatch problems. The objective of the proposed algorithm is to address the combined economic and emissions dispatch problem (CEED) of thermal power plants. This problem includes constraints such as the valve point effect, prohibited zones of operation, and ramp rate limits. In order to assess its performance, the proposed algorithm is first evaluated using a set of benchmark functions. Later, three thermal generating systems having 6, 10, and 40 units respectively are regarded as the test systems to validate the proposed method. The proposed method is tested, and a comparison of the results are made with popular optimization techniques reported in the literature such as PDE, MODE, NSGA II, and MOSSA. Promising results have been obtained with opposition-based PSO in comparison with their current equivalents. A comparison was made between the fuel cost, emissions, and CPU time of the proposed method with the two other PSO variants: inertia factor PSO (IFPSO) and constriction factor PSO (CFPSO). The results showed a decline in the overall cost by approximately 3.73% and a decrease in CPU time by as much as 2.6 s. Furthermore, the obtained predictions consistently exhibit a high level of accuracy, typically approaching 100%.

Comparison of the PSO Algorithm and JAYA Algorithm for Economic Load Dispatch

The electrical power industry has undergone the significant changes, leading to a competitive market and the need for optimal economic dispatch solutions. As energy resources becoming scarce, prices rise, environmental concerns intensify, and electricity consumption increases, classical optimization techniques struggle to handle these complex issues. This project compares particle swarm optimization (PSO) and JAYA optimization method for economic load dispatch (ELD) problems in the electrical power industry. PSO has gained recognition as an effective solution for ELD problems in the last decade. The aim of this study is to show that Jaya optimization is the best optimization methodology for ELD problems. By comparing the performance, convergence speed, and accuracy of PSO and JAYA optimization, this paper aims to provide insights into the superiority of JAYA optimization. Key Words: Economic Load dispatch, Optimization method, PSO algorithm, JAYA algorithm, Incremental fuel cost

Minimization of fuel cost for generator systems with valve point effect using modified PSO

The goal of this research is to lay the groundwork for understanding the particle swarm optimization technique. The applicability of this technique is proven by solving a variety of Constraint and unconstraint optimization problems. During the operation of the power system, economic load dispatch is a vital optimization activity for allocating generation between the committed units to divide the power while meeting various system constraints economically. In this work, the modified PSO method's application to the electrical power system's economic load dispatch problem on 3-generator, 5-generator and 13-generator systems are also investigated. In this research work Exterior penalty method is applied to convert constraint optimization problem into unconstraint optimization problem

Golden jackal optimization for economic load dispatch problems with complex constraints

This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.

Resilient distributed optimization for cyber–physical systems under adversarial environments: An event-based method

This work presents a resilient distributed optimization algorithm based on the event-triggering mechanism for cyber–physical systems (CPSs) to optimize an average of convex cost functions corresponding to multiple agents under adversarial environments. Two attack scenarios, including the f-total (each agent is affected by at most f malicious agents in the whole network) and the f-local (each agent is affected by at most f malicious agents in its in-neighbor set) attacks are considered. Subsequently, the convergence conditions under these two attack scenarios are provided, respectively, both of which guarantee that the state values of benign agents converge to a bounded error range. The optimality conditions are also presented by theoretical analysis, which guarantee that the state values of benign agents converge to a safety interval constructed by local optimal values under certain graph conditions, despite the misbehavior of malicious agents. In addition, four numerical examples are presented to show the effectiveness and superiority of the event-triggering resilient distributed optimization (RDO-E) algorithm. Compared to existing resilient algorithms, the proposed method achieves resilient distributed optimization with higher accuracy and less demanding communication overheads. Finally, by applying the proposed method to the multi-microgrid system, a resilient economic dispatch problem (REDP) is successfully solved, which validates the practical viability of the RDO-E algorithm.

Optimal renewable-integrated economic load dispatch for a large-scale power system using One-to-One Optimization Algorithm

This study presents the application of a new meta-heuristic algorithm called One-to-One optimization algorithm (OOBO) for solving the renewable-integrated economic load dispatch problem (RI-ELD) with consideration of both wind and solar power plants. The whole study focuses on minimizing the overall expenses of fuel (OEF) for all thermal electric power plants (TEPPs). The considered power system consists of twenty TEPPs with different working limits. OOBO is applied to solve the given problem in three cases of load demand level, including 2500, 2600, and 2700 MW. The results achieved by OOBO in the three cases are compared with other meta-heuristic algorithms called Coati optimization algorithm (COA) in the four aspects, such as Best OEF (Bst.OEF), Average OEF (Aver.OEF), Maximum OEF (Max.OEF). OOBO not only outperforms COA in all comparison aspects but also provides faster convergence speed to the optimal values of OEF at all three cases of load demand. Moreover, OOBO shows its surprising stability over COA regardless of the increase of load demand in Case 2 and Case 3. By observing these results, OOBO deserved the highly effective search tool for solving the large-scale and highly complex RI-ELD problem.

Distributed Optimization of Islanded Microgrids Integrating Multi-Type VSG Frequency Regulation and Integrated Economic Dispatch

The question of how to simultaneously perform frequency regulation and integrated economic scheduling for microgrids with low-inertia islanding operation under communication constraints is a difficult problem that needs to be solved for many current applications. To this end, this paper establishes a microgrid scheduling control model containing a virtual synchronous generator (VSG) with multiple types of power sources and proposes a distributed optimization algorithm that integrates frequency regulation and comprehensive economic scheduling to simultaneously realize frequency regulation and economic scheduling in a microgrid. Firstly, a distributed economic dispatch problem is proposed based on a comprehensive consideration of the costs and benefits of various types of power VSGs, as well as the overall inertia and standby capacity requirements of the microgrid, which minimizes the integrated costs incurred by the participation of each type of VSG in the frequency regulation and improves the stable operation of the microgrid in terms of frequency under perturbation. Then, the optimal scheduling problem is solved by reconstructing the optimization problem based on considering the dynamic characteristics of microgrid inverters and using event-triggered communication to sense and compensate for the supply-demand imbalance online. The proposed method can avoid inter-layer coordination across time scales, improve the inertia, frequency regulation capability, and economy of the system, and enhance its robustness to short-term communication failures. Finally, simulation results are used to verify the effectiveness of the method.

Quantification of Uncertainty Cost Functions for Controllable Solar Power Modeling

Navigating the secheduling of generation resources of energy in power systems marked by a significant presence of renewable generation involves intricate optimization challenges. The conventional tools for resolving such challenges include programming techniques and heuristic approaches, both contingent upon a precisely articulated target function for optimization. Traditional optimization tools rely on precisely defined target functions, but the evolving landscape of power systems introduces complexity, especially with unpredictable behaviors of renewable sources. The research specifically quantifies penalty costs associated with photovoltaic (PV) generators, employing probabilistic methods for a robust mathematical analysis. The developed analytical model enhances adaptability in economic dispatch problems, considering uncertainty in decision-making. Validation using Monte Carlo simulation emphasizes uncertainty in PV generation and highlights the advantages of the proposed analytic model. The quadratic form of the model aligns coherently with simulation outcomes, contributing significantly to understanding uncertainty quantification in solar power modeling. The research aims to refine controllable solar power models, establish robust uncertainty cost functions, and improve the accuracy of economic dispatch strategies. Ultimately, this work promotes the seamless integration of solar energy into diverse and dynamic energy grids.

Efficient economic operation based on load dispatch of power systems using a leader white shark optimization algorithm

This article proposes the use of a leader white shark optimizer (LWSO) with the aim of improving the exploitation of the conventional white shark optimizer (WSO) and solving the economic operation-based load dispatch (ELD) problem. The ELD problem is a crucial aspect of power system operation, involving the allocation of power generation resources to meet the demand while minimizing operational costs. The proposed approach aims to enhance the performance and efficiency of the WSO by introducing a leadership mechanism within the optimization process, which aids in more effectively navigating the complex ELD solution space. The LWSO achieves increased exploitation by utilizing a leader-based mutation selection throughout each generation of white sharks. The efficacy of the proposed algorithm is tested on 13 engineer benchmarks non-convex optimization problems from CEC 2020 and compared with recent metaheuristic algorithms such as dung beetle optimizer (DBO), conventional WSO, fox optimizer (FOX), and moth-flame optimization (MFO) algorithms. The LWSO is also used to address the ELD problem in different case studies (6 units, 10 units, 11 units, and 40 units), with 20 separate runs using the proposed LWSO and other competitive algorithms being statistically assessed to demonstrate its effectiveness. The results show that the LWSO outperforms other metaheuristic algorithms, achieving the best solution for the benchmarks and the minimum fuel cost for the ELD problem. Additionally, statistical tests are conducted to validate the competitiveness of the LWSO algorithm.

Research on Dynamic Economic Dispatch Optimization Problem Based on Improved Grey Wolf Algorithm

The dynamic economic dispatch (DED) problem is a typical complex constrained optimization problem with non-smooth, nonlinear, and nonconvex characteristics, especially considering practical situations such as valve point effects and transmission losses, and its objective is to minimize the total fuel costs and total carbon emissions of generating units during the dispatch cycle while satisfying a series of equality and inequality constraints. For the challenging DED problem, a model of a dynamic economic dispatch problem considering fuel costs is first established, and then an improved grey wolf optimization algorithm (IGWO) is proposed, in which the exploitation and exploration capability of the original grey wolf optimization algorithm (GWO) is enhanced by initializing the population with a chaotic algorithm and introducing a nonlinear convergence factor to improve weights. Furthermore, a simple and effective constraint-handling method is proposed for the infeasible solutions. The performance of the IGWO is tested with eight benchmark functions selected and compared with other commonly used algorithms. Finally, the IGWO is utilized for three different scales of DED cases, and compared with existing methods in the literature. The results show that the proposed IGWO has a faster convergence rate and better global optimization capabilities, and effectively reduces the fuel costs of the units, thus proving the effectiveness of IGWO.

Optimizing the resource allocation in cyber physical energy systems based on cloud storage and IoT infrastructure

Given the prohibited operating zones, losses, and valve point effects in power systems, energy optimization analysis in such systems includes numerous non-convex and non-smooth parameters, such as economic dispatch problems. In addition, in this paper, to include all possible scenarios in economic dispatch problems, multi-fuel generators, and transmission losses are considered. However, these features make economic dispatch problems more complex from a non-convexity standpoint. In order to solve economic dispatch problems as an important consideration in power systems, this paper presents a modified robust, and effective optimization algorithm. Here, some modifications are carried out to tackle such a sophisticated problem and find the best solution, considering multiple fuels, valve point effect, large-scale systems, prohibited operating zones, and transmission losses. Moreover, a few complicated power systems including 6, 13, and 40 generators which are fed by one type of fuel, 10 generators with multiple fuels, and two large-scale cases comprised of 80 and 120 generators are analyzed by the proposed optimization algorithm. The effectiveness of the proposed method, in terms of accuracy, robustness, and convergence speed is evaluated, as well. Furthermore, this paper explores the integration of cloud storage and internet of things (IoT) to augment the adaptability of monitoring capabilities of the proposed method in handling non-convex energy resource management and allocation problems across various generator quantities and constraints. The results show the capability of the proposed algorithm for solving non-convex energy resource management and allocation problems irrespective of the number of generators and constraints. Based on the obtained results, the proposed method provides good results for both small and large systems. The proposed method, for example, always yields the best results for the system of 6 power plants with and without losses, which are $15,276.894 and $15,443.7967. Moreover, the improvements made in the proposed method have allowed the economic dispatch problem regarding multi-fuel power plants to be solved not only with optimal results ($623.83) but also in less than 35 iterations. Lastly, the difference between the best-obtained results ($121,412) and the worst-obtained results ($121,316.1992) for the system of 40 power plants is only about $4 which is quite acceptable.

Ekonomik yük dağıtım problemi için elektrik baliği optimizasyonu

The Economic Load Dispatch (ELD) problem is an essential aspect of power system planning and operational scheduling. Different techniques and algorithms have been recommended to solve it, aiming to minimize the cost of power generation with satisfying the load requirements. In this paper, a new algorithm called Electric Fish Optimization (EFO) is used to solve the ELD problem by considering the line losses, ramp rate limits, maximum and minimum capacities of the generators and prohibited operating zones (POZ). The algorithm has been utilized in test systems consisting of 6 and 15 units and its outcomes have been compared to those from previous research studies. The proposed algorithm has been shown to achieve minimum cost, indicating its superiority and effectiveness in addressing power system planning challenges. It is evident that the presented algorithm offers a valuable solution for optimizing ELD problems.

An application of Gorilla troops optimizer in solving the problem of economic load dispatch considering valve point loading effect

Economic load dispatch (ELD) is one of the fundamental and important optimization problems in an electrical power system. The goal of the ELD problem is to minimize the overall cost of fuel used by generators while satisfying the different constraints like power balance limitations, operational capacity limits, ramp-rate limits, and prohibited operating zones and valve point loading effect (VPLE). The paper introduces a novel optimization technique, termed Gorilla Troop Optimization (GTO), inspired by the mimic’s behavior of gorilla troops, for solving the Economic Load Dispatch (ELD) Problem. The ELD Problem is assessed both with and without the valve-point effect, considering best, average, and worst fuel costs in dollars per hour ($/hr). The proposed GTO is applied to four different case studies to find the best global solution. The effectiveness of the GTO is evaluated using four distinct IEEE unit systems, including the IEEE 3-unit, 6-unit, 10-unit, and 40-unit test systems. From the simulation results, it has been realized that GTO show superior results as compared to other algorithms in terms of the total fuel cost minimization, convergence speed, and computation time to achieve the global optimal solution in all the case studies.

Optimization and Statistical Analysis for an Independent Microgrid Operation through an Innovative Fusion of Demand Response Programs

Microgrid operations face increased difficulty due to the unpredictability of renewable energy sources, such as solar and wind. To address this challenge, energy storage devices are widely employed. Another method to enhance the safety and dependability of microgrids is the Demand Response Program (DRP), which lowers peak demand and shifts it to off-peak times.
 In an effort to reduce overall operating expenses, this paper employs several DRPs to solve the Unit Commitment Economic Dispatch (UCED) problem for a self-sufficient microgrid. To enhance both the operation and financial effectiveness of the microgrid, a novel combination of DRPs is presented in this article. Ultimately, users will benefit from this combination.
 The modeling of DRPs is based on consumer benefit and price elasticity models. The UCED issue is formulated and solved in GAMS using mixed-integer nonlinear programming (MINLP). The study demonstrates the proposed strategy on an 11-Bus Microgrid. According to optimization findings, operational expenses are reduced by 17.43%, 18.8%, 19.81%, and 14.3% with 0% load shedding when TOU-RTP-CPP-DLC DRPs are implemented.
 In the DLC-DRP scenario, only consumers benefit. When compared to DLC-DRP alone, the suggested RTP+DLC-DRP combination decreases operational expenses by 15.93% and increases consumer advantages. Thus, both the microgrid operator and its users benefit from the proposed strategy.

Jellyfish search algorithm for economic load dispatch under the considerations of prohibited operation zones, load demand variations, and renewable energy sources

<span lang="EN-US">This paper suggests a modified version of the former economic load dispatch (MELD) problem with the integration of wind power plant (WPP) and solar power plants (SPP) into thermal units (TUs). The target of the whole study is to cut the total producing electricity cost (TPEC) as much as possible. Three meta-heuristic algorithms, including particle swarm optimization (PSO), jellyfish search (JS) and salp swarm algorithm (SSA), are applied to solve the MELD. The real performance of these optimization tools is tested on the first system with six thermal units considering prohibited zones, and the second system with the combination of the first system and one solar, and two WPPs. In addition, the variation of load demand in 24 hours per day is also taken into account in the second system. JS is proved to be the most effective method for dealing with MELD. Furthermore, JS can also reach lower or the same TPEC as other previous algorithms. Hence, JS is a recommended to be a strong computing method for dealing with the MELD problem. </span>

A Robust Distributed Algorithm for Solving the Economic Dispatch Problem with the Penetration of Renewables and Battery Systems

In the field of energy networks, for their effective functioning, it is necessary to distribute the required load between all online generating units in a proper way to cover the demand. The load schedule is obtained by solving the so-called Economic Dispatch Problem (EDP). The EDP can be solved in many ways, resulting in a power distribution plan between online generating units in the network so that the resulting price per unit of energy is minimal. This article focuses on designing a distributed gradient algorithm for solving EDP, supplemented by models of renewable sources, Battery Energy Storage System (BESS), variable fuel prices, and consideration of multiple uncertainties at once. Specifically, these are: time-variable transport delays, noisy gradient calculation, line losses, and drop-off packet representations. The algorithm can thus be denoted as robust, which can work even in unfavorable conditions commonly found in real applications. The capabilities of the presented algorithm will be demonstrated and evaluated on six examples.

Solving large-scale combined heat and power economic dispatch problems by using deep reinforcement learning based crisscross optimization algorithm

The extensive interconnection in bulk power systems brings great challenges in the economic dispatch problems, especially the large-scale combined heat and power economic dispatch (CHPED), which is quite intractable due to complex thermal and electrical couplings in cogeneration units. Most meta-heuristic algorithms cannot work well while considering non-convexity, discontinuity, and non-differentiability. Particularly, when it comes to the high dimensional and large-scale CHPED problems, these algorithms are either easy to trap in the local optimum or quite time-consuming. To address these issues, a novel deep reinforcement learning (DRL) based crisscross optimization (CSO) algorithm is proposed for the first time, which can (1) improve the searching ability of CSO, (2) enhance the overall searching efficiency, and (3) perform extraordinarily well for the large-scale CHPED problems. Firstly, to further improve the global search ability, DRL is employed to reduce dimensionality and narrow the search space of the initial population of the CSO algorithm. Then, DRL is updated by the deep deterministic policy gradient (DDPG) strategy, which can facilitate an instantaneous decision in accelerating CSO. Thereafter, by adopting each decision provided by DRL, a great difference may occur in the same scenario to speed up the crossover procedure and guide the upcoming search round. On this basis, the enhanced CSO algorithm could quickly carry out crossovers with search space contraction and dimensionality reduction. Finally, experiments on four test systems have substantiated the effectiveness of the proposed algorithm, especially the superiority over other state-of-the-art techniques in solving large-scale CHPED problems.

Enhancing time series aggregation for power system optimization models: Incorporating network and ramping constraints

In this paper, we extend a recently developed Basis-Oriented time series aggregation approach for aggregating input-data in power system optimization models which has proven to be exact in simple economic dispatch problems. We extend this methodology to include network and ramping constraints, for the latter, to handle temporal linking, we developed a heuristic that, in its current version, relies on the dual solution to find a partition of the input data, which is then aggregated. Our numerical results, for a 3-bus system, show that with network constraints only, we reduced the number of hours needed for an exact approximation by a factor of 1747, and a factor of 12 with network and ramping constraints. Moreover, our findings suggest that in the presence of temporal linking, aggregations of variable length must be employed to obtain an exact result (i.e., the same objective function value in the aggregated model) while maintaining the computational tractability. Our findings also imply that better performing aggregations do not necessarily correspond to commonly used lengths like days or weeks; additionally, we also prove that this input-data partition, based on the dual information, is always possible for these models independent of their size.