Economic Dispatch Problem Research Articles

Data-driven stochastic dynamic economic dispatch for combined heat and power systems using particle swarm optimization

In modern power systems, the uncertain behavior of renewable energy sources (RESs) may result in deviations from the optimal operating dispatches for the various power sources. The electric power generation from Combined Heat and Power (CHP) units is characterized by high efficiency with less pollution. To use CHP units more efficiently, the dynamic economic dispatch problem is applied to obtain the optimal power and heat sources’ outputs to satisfy heat and power demands while meeting the different operational constraints. In this paper, data-driven stochastic optimization is used to model these uncertainties utilizing the Generative Adversarial Networks in scenario generation that are accurate and do not require fitting models or modeling probability distributions. Then, the Fast Forward Selection technique is used to decrease the number of scenarios to improve system tractability. The results obtained indicate that the variability in electrical load, photovoltaic (PV), and wind turbine (WT) output significantly impacts the overall operational costs of the power system. Therefore, it is essential to incorporate the uncertainties associated with electrical load, PV, and WT when aiming for accurate results in economic dispatch. the study found that the overall operation cost of the dynamic economic dispatch of the electrical system for 24 hours after integrating RES achieved a daily savings of 2.5 % in the first scenario. Furthermore, the findings demonstrate that RESs positively contribute to reducing the total operational costs of the power system. The economic dispatch of CHP systems is influenced by the integration of RESs and the uncertainties associated with electrical parameters.

Economic Load Dispatch Problem Analysis Based on Modified Moth Flame Optimizer (MMFO) Considering Emission and Wind Power

In electrical power system engineering, the economic load dispatch (ELD) problem is a critical issue for fuel cost minimization. This ELD problem is often characterized by non-convexity and subject to multiple constraints. These constraints include valve-point loading effects (VPLEs), generator limits, emissions, and wind power integration. In this study, both emission constraints and wind power are incorporated into the ELD problem formulation, with the influence of wind power quantified using the incomplete gamma function (IGF). This study proposes a novel metaheuristic algorithm, the modified moth flame optimization (MMFO), which improves the traditional moth flame optimization (MFO) algorithm through an innovative flame selection process and adaptive adjustment of the spiral length. MMFO is a population-based technique that leverages the intelligent behavior of flames to effectively search for the global optimum, making it particularly suited for solving the ELD problem. To demonstrate the efficacy of MMFO in addressing the ELD problem, the algorithm is applied to four well-known test systems. Results show that MMFO outperforms other methods in terms of solution quality, speed, minimum fuel cost, and convergence rate. Furthermore, statistical analysis validates the reliability, robustness, and consistency of the proposed optimizer, as evidenced by the consistently low fitness values across iterations.

An integrated binary metaheuristic approach in dynamic unit commitment and economic emission dispatch for hybrid energy systems

The current generation portfolio is obligated to incorporate zero-emissions energy sources, predominantly wind and solar, due to the depletion of fossil fuels and the alarming rate of global warming. In the current scenario, power engineers must devise a compromised solution that not only advocates for the adoption of renewable energy sources (RES) but also efficiently schedules all conventional power generation units to balance the increasing load demand while simultaneously minimizing fuel costs and harmful emissions that are currently addressed by Unit Commitment (UC) and Combined Economic Emission Dispatch (CEED) problem solutions. However, the integration of renewable energy resources (RES) further complicates the UC-CEED problem due to their intermittent nature. Recently, metaheuristic algorithms are acquiring momentum in resolving constrained UC-CEED problems due to their improved global solution ability, adaptability, and derivative-free construction. In this research, a computationally efficient binary hybrid version of crow search algorithm and improvised grey wolf optimization is proposed, namely Crow Search Improved Binary Grey Wolf Optimization Algorithm (CS-BIGWO) by inclusion of nonlinear control parameter, weight-based position updating, and mutation approach. Statistical results on standard mathematical functions prove the supremacy of the proposed algorithm over conventional algorithms. Further, a novel optimization strategy is devised by integrating enhanced lambda iteration with the CS-BIGWO algorithm (CS-BIGWO-λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}) to solve a day-ahead UC-CEED problem of the hybrid energy system incorporating cost functions of RES. For the model, a day-ahead forecast of wind power and solar photovoltaic power is obtained by using the Levy-Flight Chaotic Whale Optimization Algorithm optimized Extreme Learning Machines(LCWOA-ELM). The proposed algorithm is tested for the UC-CEED solution of an IEEE-39 bus system with two distinct cases: (1) without RES integration and (2) with RES integration. Several independent trial runs are executed, and the performance of the algorithms is assessed based on optimal UC schedules, fuel cost, emission quantization, convergence curve, and computational time. For case 1, the proposed algorithm resulted in a percentage reduction of 0.1021% in fuel cost and 0.7995% in emission. In contrast, for test case 2, it resulted in a percentage reduction of 0.12896% in fuel cost and 0.772% in emission with the proposed algorithm. The results validate the dominance of the proposed methodology over existing methods in terms of lower fuel costs and emissions.

Multi-Objetive Dispatching in Multi-Area Power Systems Using the Fuzzy Satisficing Method

The traditional mathematical models for solving the economic dispatch problem at the generation level primarily focus on minimizing overall operational costs while ensuring demand is met across various periods. However, contemporary power systems integrate a diverse mix of generators from both conventional and renewable energy sources, contributing to economically efficient energy production and playing a pivotal role in reducing greenhouse gas emissions. As the complexity of power systems increases, the scope of economic dispatch must expand to address demand across multiple regions, incorporating a range of objective functions that optimize energy resource utilization, reduce costs, and achieve superior economic and technical outcomes. This paper, therefore, proposes an advanced optimization model designed to determine the hourly power output of various generation units distributed across multiple areas within the power system. The model satisfies the dual objective functions and adheres to stringent technical constraints, effectively framing the problem as a nonlinear programming challenge. Furthermore, an in-depth analysis of the resulting and exchanged energy quantities demonstrates that the model guarantees the hourly demand. Significantly, the system’s efficiency can be further enhanced by increasing the capacity of the interconnection links between areas, thereby generating additional savings that can be reinvested into expanding the links’ capacity. Moreover, the multi-objective model excels not only in meeting the proposed objective functions but also in optimizing energy exchange across the system. This optimization is applicable to various types of energy, including thermal and renewable sources, even those characterized by uncertainty in their primary resources. The model’s ability to effectively manage such uncertainties underscores its robustness, instilling confidence in its applicability and reliability across diverse energy scenarios. This adaptability makes the model a significant contribution to the field, offering a sophisticated tool for optimizing multi-area power systems in a way that balances economic, technical, and environmental considerations.

An Improved Non-dominated Sorting Genetic Algorithm for the Optimal Economic Emission Dispatch Problem with Wind Power Sources

An Improved Non-dominated Sorting Genetic Algorithm for the Optimal Economic Emission Dispatch Problem with Wind Power Sources

Optimal solution of multiobjective stable environmental economic power dispatch problem considering probabilistic wind and solar PV generation

The Environmental Economic Power Dispatch (EEPD) problem, a widely studied bi-objective nonlinear optimization challenge in power systems, traditionally focuses on the economic dispatch of thermal generators without considering network security constraints. However, environmental sustainability necessitates reducing emissions and increasing the penetration of renewable energy sources (RES) into the electrical grid. The integration of high levels of RES, such as wind and solar PV, introduces stability issues due to their uncertain and intermittent nature. This paper addresses these concerns by formulating and solving the Stable Environmental Economic Power Dispatch (SEEPD) problem, which includes fixed zonal reserve capacity from conventional thermal generators and uncertain reserves from RES. Uncertainties in RES and load demand are modeled using random variable generation techniques, applying Gaussian, Weibull, and log-normal probability density functions (PDFs) for load demand, wind velocity, and solar irradiance, respectively. The stochastic SEEPD problem extends to multiple periods by replicating the single-period problem for each interval in the planning horizon, linking periods through intertemporal ramping costs, physical ramp rate, and fixed zonal reserve constraints on dispatch variables. Multi-Objective Evolutionary Algorithms (MOEAs) have gained importance for solving complex nonlinear problems involving multi-objective functions. This paper applies the latest MOEAs to tackle the proposed SEEPD problem, incorporating stochastic wind and solar PV power sources. Network security constraints, such as transmission line capacities and bus voltage limits, are considered along with constraints on generator capabilities and intertemporal spinning reserves, ramp-up and ramp-down constraints for thermal generators. A bidirectional coevolutionary-based multi-objective evolutionary algorithm is employed, integrating an advanced constraint-handling technique to ensure compliance with system constraints. The simulation results show that the proposed formulation achieves a better trade-off between various conflicting objective functions compared to other state-of-the-art MOEAs.

A multi-objective robust dispatch strategy for renewable energy microgrids considering multiple uncertainties

The demand for low-carbon transformations and the uncertainty of renewable energy sources and loads present significant challenges for the optimal dispatch of microgrid. This study proposed a multi-objective robust dispatch strategy to reduce the risks associated with the uncertainty of renewable energy source output and loads while promoting low-carbon and economical microgrid operation. The economic emission dispatch problem for a microgrid was formulated as a multi-objective robust dual-layer optimization model. Consequently, a high-dimensional adjustable linear polyhedral uncertainty set was proposed to describe the uncertainty of renewable energy sources and loads. This study transformed the original model into an easy-to-solve single-layer second-order cone programming optimal power flow optimization model by employing second-order cone relaxation and duality transformation. Thereafter, a synthetic membership function was proposed to determine the optimal compromise solution. To determine the charging and discharging statuses of the battery storage system and the electricity traded between the microgrid and the external power grid, a battery storage system control strategy based on time-of-use electricity prices and real-time power flow calculations was proposed. Simulations conducted on a modified IEEE-30 bus system demonstrated that the proposed strategy effectively reduced the economic costs and carbon emissions of the microgrid by 8.23 % and 2.43 %, respectively.

Research on distributed optimal scheduling method based on consensus

Abstract With access to large-scale distributed power sources, the physical structure of the power grid system tends to be distributed. The application of traditional centralized optimal scheduling methods will lead to a surge in communication overhead and computational complexity, which will affect the performance and efficiency of the solution. In this paper, the minimum operating cost of the system is taken as the goal, and the distributed direct current optimal power flow (DC-OPF) optimization calculation of the photovoltaic-storage power generation system is considered to approximately solve the economic dispatch problem. The DC optimal power flow model with energy storage charging penalty is constructed. Then, the distributed optimization method based on the consensus alternating direction multiplier method (ADMM) is adopted. By decoupling the objective function and constraints of the whole system problem, the fully distributed DC-OPF calculation is realized by introducing the global consensus variable to deal with the boundary buses. Finally, the improved IEEE 30-bus example is used to test the method, and the simulation results verify the convergence and accuracy of the method.

Solving power system economic emission dispatch problem under complex constraints via dimension differential learn butterfly optimization algorithm with FDC-based

The economic emission dispatch (EED) aims to minimize the fuel and pollutant emission costs of generator units under various complex constraints. Optimizing the EED problem is of crucial importance for alleviating the current energy and environmental pressures. In this work, nearly all known complex constraints in the EED problem, including the valve-point effect, transmission line power loss, prohibited operating zones, and ramp-rate limits, are taken into account, and an enhanced version of butterfly optimization algorithm (FDCDLBOA) is proposed to solve it. First, a new adaptive fragrance is employed to optimize the instability caused by target differences and improve the convergence performance. Second, the proposed dimension differential learning strategy evolves the position of individuals with the help of superior dimensional information in the population, and this extensive learning exchange can balance global and local search, maintain diversity, and get rid of local optima. Third, the Fitness-Distance-Constraint (FDC) guide selection method is employed for the first time to handle the complex constraints of EED problems, enhancing the ability of individuals to bypass the infeasible search areas. After evaluating the proposed FDCDLBOA on CEC 2022 test suite, it is applied to solve 8 EED cases, encompassing small-, medium- and large-scale systems. Notably, the 280-generator case is the first large-scale test to exceed 200 generators. Compared with 9 representative algorithms, FDCDLBOA performs outstandingly in terms of robustness, improvement index (IF), mean constraint violation (MV), feasibility rate (FR) and Quade multiple comparison, among which IF, MV, FR, and Quade are all employed for evaluating the EED problem for the first time. The presented results confirm that the proposed method effectively enhances the robustness of high-quality solutions and the ability to handle complex constraints, demonstrating strong competitiveness and potential in solving the EED problem.

Physics-informed convolutional neural network for microgrid economic dispatch

The variability of renewable energy generation and the unpredictability of electricity demand create a need for real-time economic dispatch (ED) of assets in microgrids. However, solving numerical optimization problems in real-time can be incredibly challenging. This study proposes using a convolutional neural network (CNN) based on deep learning to address these challenges. Compared to traditional methods, CNN is more efficient, delivers more dependable results, and has a shorter response time when dealing with uncertainties. While CNN has shown promising results, it does not extract explainable knowledge from the data. To address this limitation, a physics-inspired CNN model is developed by incorporating constraints of the ED problem into the CNN training to ensure that the model follows physical laws while fitting the data. The proposed method can significantly accelerate real-time economic dispatch of microgrids without compromising the accuracy of numerical optimization techniques. The effectiveness of the proposed data-driven approach for optimal allocation of microgrid resources in real-time is verified through a comprehensive comparison with conventional numerical optimization approaches.

Economic Load Dispatch Problem Solution Based on Linear Variational Inequalities-dynamic Neural Network

Economic Load Dispatch Problem Solution Based on Linear Variational Inequalities-dynamic Neural Network

An innovative bio-inspired Aquila technique for efficient solution of combined power and heat economic dispatch problem

In the field of power systems, the optimization challenge of combined heat and power units economic dispatch (CHPUED) holds immense importance. This study presents an improved Aquila optimization technique (IAQT) that effectively tackles the CHPUED. The primary objective of the enhanced IAQT model is to minimize the overall cost of power generation in CHP systems while satisfying demand and operational constraints. However, to achieve more accurate cost estimations and avoid suboptimal solutions, it is crucial to consider transmission losses in the optimization model. By incorporating transmission losses, the IAQT algorithm can allocate power generation resources more effectively, leading to improved system efficiency and reduced operational costs. The proposed IAQT algorithm addresses the limitations of the standard AQT and introduces novel features to enhance its search capabilities. One key limitation of the standard AQT is its heavy reliance on the best solution found during optimization. To overcome this drawback, the enhanced IAQT model eliminates the dependency on the best solution and enables a more thorough exploration of the search space. Moreover, the algorithm incorporates specific limitations and constraints for each dimension of the newly generated solutions, ensuring their feasibility and validity. The standard AQT and proposed IAQT are tested on CEC 20 benchmark functions. Moreover, the proposed approach is extensively evaluated through experimentation and testing on various scenarios, including 7–48-unit and large 96-unit systems with/without losses. Furthermore, the overall costs for the 7 unit-system are considered including the reserve constraint. The results exhibit the remarkable performance and efficiency of the enhanced IAQT model, outperforming the standard version and several previously reported results. This validation underscores the significant contribution of the study in addressing the CHPUED and highlights its potential for real-world applications.

Security-constrained economic dispatch of power systems with line outage using firefly algorithm

The Security-constrained Economic Dispatch (SCED) problem is the problem of finding the optimal generation dispatch for a power system that minimizes the operating cost while ensuring the security of the system. The security of the system is defined as the ability of the system to withstand disturbances without violating any operational constraints. Line outage is a common disturbance that can affect the security of a power system. The Firefly Algorithm, inspired by the flashing behavior of fireflies in nature, is a metaheuristic optimization technique known for its effectiveness in solving complex and dynamic optimization problems. In this study, the FA is adapted to the SCED problem with a specific focus on enhancing grid resilience during line outage scenarios. The proposed method aims to simultaneously optimize the economic cost of power generation and the system's ability to withstand line outages. To demonstrate the effectiveness of the proposed approach, extensive simulations are conducted on standard IEEE test systems with varying degrees of complexity and network sizes. The results showcase the superior performance of the SCEDL-Firefly Algorithm compared to traditional optimization methods, as it provides a resilient dispatch solution that can effectively adapt to unexpected line outages while maintaining economic efficiency. Overall, this research contributes to the advancement of secure economic dispatch techniques and power system resilience by leveraging the Firefly Algorithm's capabilities. The findings offer valuable insights for power system operators and planners seeking to enhance grid reliability in the presence of line outages, ultimately promoting a more sustainable and resilient energy infrastructure.

Optimal Scheduling of Renewable Sources Based Micro Grid With PV and Battery Storage Using Crayfish Optimization Algorithm

ABSTRACTEnvironmental concerns and energy security are pressing issues of the 21st century, with a heavy reliance on fossil fuels causing significant environmental pollution and resource depletion. To mitigate these problems, it is crucial to explore and implement alternative clean energy sources. This manuscript proposes a novel crayfish optimization algorithm (COA) for optimal scheduling in a hybrid power system that incorporates various renewable energy sources, like battery energy storage systems (BESS), fuel cells (FC), wind turbines (WT), micro turbines (MT) and photovoltaic (PV) panels. The importance of the work lies in its ability to optimize the entire operating costs of a grid‐connected microgrid while improving the accuracy and efficiency of energy management. The COA method addresses economic dispatch problems and manages energy within the grid‐connected microgrid, accounting for high levels of uncertainty. The proposed approach, tested using MATLAB Simulink, achieved a cost value of 252, outperforming existing methods such as GTO, PSO, SSA, and ALO. This illustrates the potential of the proposed technique to provide more cost‐effective and efficient energy management solutions in hybrid power systems.

Application on power system economic dispatch of marine predator algorithm improved by asymmetric information exchange

The solution to the economic dispatch (ED) problem for power systems allows the power sector to reduce operating costs. However, the ED problem is a complex nonlinear and nonconvex optimization problem whose solution requires powerful algorithms. We propose a new version of the Marine Predator Algorithm (MPA), called IMPA, for solving complex ED problems. The algorithm introduces an asymmetric information exchange (AIE) mechanism, which not only accelerates to escape of local optima but also enriches the diversity of search. In this work, 12 benchmark functions were used to test the performance of the proposed algorithm IMPA. Then, the IMPA was used to solve the ED engineering problem of power system containing of 6, 13, 40, and complex 140 units. The minimum and average costs searched by IMPA are 1657962.7265$/h and 1657962.7265$/h, and they are much lower than the results of the MPA and NMPA, which means that our proposed improved IMPA improves the performance of MPA for solving the economic dispatch problem of large-scale power systems. The results show that the solutions obtained by IMPA are more competitive than those of MPA and NMPA, which provides an additional solution for cost reduction of the power system.

Optimal aggregation and disaggregation for coordinated operation of virtual power plant with distribution network operator

Virtual power plants (VPPs) offer an effective approach for managing distributed energy resources (DERs), including microturbines, distributed generators, demand response aggregators, and energy storage systems. This technology significantly enhances the economic efficiency and flexibility of distribution network systems. This study aims to facilitate a flexible power exchange between the distribution network system and the upper-level grid by aggregating the power flexibility of heterogeneous DERs via a VPP. Additionally, it introduces a methodology for optimal aggregation and disaggregation within a coordinated operation framework between the VPP and distribution network operator (DNO). On one hand, the VPP can determine its day-ahead feasible region and real-time flexible regulation power based on operational constraints of DERs and representative data provided by the DNO, circumventing the need for detailed network information. On the other hand, day-ahead and real-time correction procedures for the DER cost functions are proposed, effectively neutralizing the impact of network operational constraints on these cost functions. Consequently, precise cost functions for both the active power and the flexible regulation power aggregated by the VPP are derived. Employing this aggregated cost function enables the determination of a cost-minimized optimal scheduling solution in real-time by solving a fundamental economic dispatch problem, significantly alleviating computational demands. Finally, case studies demonstrate that the proposed method achieves an error in aggregated power of only 0.77%, compared to the precise computation method that requires comprehensive system information. The proposed optimal VPP disaggregation scheme exhibits power discrepancies of 0.63% and cost discrepancies of 0.91% relative to the precise method. Additionally, when implementing the most cost-effective demand response plan based on the proposed cost function, the average costs for aggregators are reduced by 19.7%.

Distributed predefined-time economic dispatch based on event-triggered strategy for microgrids under directed graphs

The proliferation of new energy solutions and the enhanced accessibility of distributed power sources have significantly increased the complexity and variability of microgrid structures. Due to inherent limitations in its operational mode, the traditional centralized optimization method falls short in effectively addressing the economic dispatch problem in contemporary microgrids. In this paper, a distributed optimization method is devised to address the economic dispatch problem of microgrids under directed graphs by leveraging the consensus algorithm of multi-agent systems. We define the incremental cost of each microgrid unit as the consensus variable, achieving convergence through a pioneering combination of event-triggered strategy and predefined-time control theory. This approach not only optimizes resource use but also ensures timely and efficient solution convergence, addressing critical gaps in existing methodologies. This approach enables control over the upper bound of convergence time for optimal solutions by directly adjusting time parameters in the controller under the directed graph. Consequently, it achieves coordinated control of the power output in microgrids within a predefined time while reducing the communication resources between nodes with event-triggered mechanism. The effectiveness of the proposed algorithm is verified through simulation and analysis.

Multi-objective Approach for Dynamic Economic Emission Dispatch Problem Considering Power System Reliability and Transmission Loss Prediction Using Cascaded Forward Neural Network

This study addresses the significant problem of Dynamic Economic Emission Dispatch (DEED), a critical consideration in power systems from both economic and environmental protection viewpoints. Reliability stands as another vital facet, impacting maintenance and operation perspectives. The integration of Artificial Neural Network (ANN)-based transmission loss prediction into the DEED model is also essential to address specific limitations and enhance the overall performance of the dispatch process. Traditionally, the DEED model relies on a single B-loss coefficient to estimate transmission losses. While this approach simplifies calculations, it fails to account for the significant variations in demand that occur throughout the dispatch period and it leads to inaccuracies in loss prediction, especially in dynamic environments. Using a single coefficient, the model cannot adequately capture the complex, non-linear relationships between power generation, load, and transmission losses under different operating conditions. To overcome this limitation, this study introduces an ANN-based loss prediction method integrated into the DEED model and uses trained ANN to replace the process of finding B-loss coefficients during each dispatch period. This paper also introduces a strategy leveraging the multi-objective northern goshawk optimizer algorithm, characterized by a non-dominated sorting and crowding distance mechanism, to enhance DEED considerations incorporating reliability (DEEDR). This novel algorithm improves the solution space effectively, maintains high population diversity and enables an even distribution of individuals sharing the same rank in the objective space. The fundamental objective of this study is to balance fuel cost, emission, and system reliability in power system operations. Compared with a few existing multi-objective optimization algorithms, this study demonstrates superior performance in generating a series of non-dominated solutions. The experimental results highlight its competitive and potential as an efficient tool in the DEED and DEEDR problems, promising a synergistic coordination of economy, environmental protection, and system reliability benefits in power system management.

Proportional‐integral‐differential‐inspired acceleration in distributed optimal control strategy for direct current microgrids

AbstractA PID‐inspired accelerated distributed optimal control algorithm is proposed for the economic dispatch problem of a multi‐bus DC microgrid, which contains both conventional generators (CGs) and renewable generators (RGs). Firstly, a constrained optimization problem with the aim of minimizing the power generation cost of the DC microgrid is established. To solve the optimization problem, an accelerated distributed optimal control algorithm in the discrete‐time domain is proposed. The convergence speed of the proposed algorithm is significantly improved compared to the existing distributed optimization algorithms without acceleration terms. More importantly, the communication cost is greatly reduced. The proposed algorithm is in a fully distributed manner, which means each controller only relies on the limited information from neighbouring controllers to achieve optimal cooperative control and bus voltage regulation across multiple buses. Finally, the effectiveness of the proposed algorithm is validated through numerical simulations.

A new model of electrical cyber–physical systems considering stochastic communication link failures

This article establishes a model for electrical cyber–physical systems (ECPS), integrating the power grid, power information network and control network. The power grid is modelled based on DC power flow. The power information network enables the exchange of information between the power grid and control network. Stochastic communication link failure is a common problem in real control networks. To address this issue, this article models the control network as a Bernoulli network. The incorporation of an asynchronous gossip algorithm with price penalty factors enables the model to analyse multi-target combined economic emission dispatch problems (CEED) involving line losses in an imperfect control network. The effectiveness and validity of the model are illustrated through simulations.