Optimal Economic Dispatch Research Articles

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

Retraction Note: Enhanced multi-objective crisscross optimization for dynamic economic emission dispatch considering demand response and wind power uncertainty

Retraction Note: Enhanced multi-objective crisscross optimization for dynamic economic emission dispatch considering demand response and wind power uncertainty

Economic optimal dispatch of active distribution network with CCHP multi-microgrid based on analytical target cascading

When multiple CCHP microgrids are integrated into an active distribution network (ADN), the microgrids and the distribution network serve as distinct stakeholders, making the economic optimal dispatch of the system more complex. This paper proposes a distributed dispatch model of ADN with CCHP multi-microgrid, and refines the objective functions of each region. The analytical target cascading approach (ATC) is employed to model the power transaction as virtual sources/loads, and solve the optimal dispatch in parallel. Case studies demonstrate the proposed distributed model is capable of achieving economic optimization for both stakeholders.

Research on Multi-Microgrid Electricity–Carbon Collaborative Sharing and Benefit Allocation Based on Emergy Value and Carbon Trading

In response to climate change, the proportion of renewable energy penetration is increasing daily. However, there is a lack of flexible energy transfer mechanisms. The optimization effect of low-carbon economic dispatch in a single park is limited. In the context of the sharing economy, this study proposes a research method for multi-park electricity sharing and benefit allocation based on carbon credit trading. Firstly, a framework for multi-park system operation is constructed, and an energy hub model is established for the electrical, cooling, and heating interconnections with various energy conversions. Secondly, a park carbon emission reduction trading model is established based on the carbon credit mechanism, further forming an optimal economic and environmental dispatch strategy for multi-park electricity sharing. Matlab+Gurobi is used for solving. Then, based on asymmetric Nash bargaining, the comprehensive contribution rate of each park is calculated by considering their energy contribution and carbon emission reduction contribution, thereby achieving a fair distribution of cooperation benefits among multiple parks. The results show that the proposed method can effectively reduce the overall operational cost of multiple parks and decrease carbon emissions, and the benefit allocation strategy used is fair and reasonable, effectively motivating the construction of new energy in parks and encouraging active participation in cooperative operations by all parks.

Distributed predefined-time optimal economic dispatch for microgrids

With the massive popularization of distributed generators, optimal economic dispatch has been a key optimization problem to maintain stable and efficient work of the whole system. In this paper, a new smooth reconstruction penalty function with continuous and piecewise linear differential is designed to deal with generation power constraints, which promotes to obtain a better suboptimal solution compared with the existing smooth penalty methods. A distributed predefined-time optimal economic dispatch strategy is presented by utilizing a time-based function. By employing the proposed strategy, the minimization of the generation cost with transmission loss under the power balance constraint and generation minimum/maximum constraints can be realized within a predefined settling time. The performance of the proposed optimization strategy is evaluated by simulations and hardware-in-the-loop experiments in terms of validity verification, robustness to load change and topology reconfiguration, plug-and-play functionality, and comparison with the existing results to illustrate the advantages of fast convergence and near optimal results.

Synergizing renewable energy sources in building-integrated hybrid energy systems via niche-ant colony optimization

The rapid advancement of Building-Integrated Hybrid Energy Systems (BIHES), characterized by renewable energy sources with variable generation patterns, presents significant challenges for effective integration and utilization. This paper introduces an optimal economic dispatch strategy for commercial BIHES using a Niche-Ant Colony Optimization (NACO) Algorithm. BIHES integrates renewable sources such as 200 kW photovoltaic panels, 150 kW wind turbines, and 500 kWh energy storage systems within commercial buildings. A detailed mathematical model for economic dispatch leverages a multi-load demand of 1.2 MW and flexible adjustment capabilities. The model aims to maximize on-site renewable energy use while balancing grid interaction. The NACO Algorithm, tested through comprehensive simulations, demonstrated significant improvements, resulting in a 12.96 % reduction in environmental costs, an 18.4 % reduction in the Levelized Cost of Energy (LCOE), and a 14.25 % reduction in total operational costs compared to traditional methods. Additionally, the system achieved annual CO2 savings of 25,000 tons, increased renewable energy absorption by 22 %, reduced grid dependency by 30 %, and decreased energy purchase costs by 20 %. Energy storage optimization also extended the storage system's lifecycle by 15 %. These results highlight the enhanced synergy and complementarity of multiple energy sources within BIHES, showcasing its potential for substantial economic and environmental benefits.

Decision-focused learning under decision dependent uncertainty for power systems with price-responsive demand

Contemporary power systems are experiencing a growing integration of flexible resources on the consumer side. Different from flexible demand that submits specific bids to energy markets, price-responsive demand (PRD) adjusts its power consumption without notice, simply based on the resulting electricity prices as well as internal priorities and limitations. In this paper, we demonstrate how a high penetration of PRD (the behavior of which is invisible to the operator during the day-ahead unit commitment stage) results in systematic inefficiency costs and formulate the so-termed decision-focused learning problem of learning to provide a demand forecast which, once fed as an input to the operator’s economic dispatch optimization problem, results in an efficient dispatch. Interestingly, the prescribed demand forecast affects the resulting prices, which in turn affect the actual demand realization, giving rise to a decision-dependent uncertainty. Motivated by the problem’s hard-to-evaluate objective function, we solve it using Bayesian optimization. The empirical evaluations demonstrate significant savings in the effective real-time system cost, compared to the current practice of using the default demand forecast. Moreover, the method is shown to achieve a system cost that is fairly close to the one achieved by a system that fully integrates PRD into the day-ahead process; but without requiring any change in the operator’s existing dispatch algorithm while avoiding all efforts necessary for the integration of flexible demand, which is a widely pursued field of ongoing research.

An advanced kernel search optimization for dynamic economic emission dispatch with new energy sources

Integrating renewable energy sources, such as wind and photovoltaic power generation, into the power grid is crucial for sustainable power system development and mitigating pollutant emissions. However, these sources’ inherent uncertainty and randomness pose significant challenges to grid operations. Metaheuristic algorithms offer efficient solutions to optimization problems in this context and are widely employed in practice. Kernel Search Optimization (KSO) has emerged as a prominent metaheuristic algorithm due to its parameter-free nature and applicability to power dispatch problems. Nevertheless, KSO’s limited local search capabilities necessitate enhancements for improved performance. This paper introduces an enhanced variant of KSO, termed Upgraded Kernel Search Optimization (UKSO), which incorporates differential evolution techniques, including mutation, crossover, and selection mechanisms, to bolster KSO’s search capabilities and overall performance. The efficacy and feasibility of UKSO are evaluated through comprehensive testing using the CEC2017 benchmark. Comparative analysis demonstrates that UKSO outperforms other algorithms by achieving more optimal solutions. To address power dispatch challenges in the context of renewable energy sources, a Two-Time Energy Dispatch (TTED) model is proposed, leveraging a weighted summation approach to minimize total fuel costs and pollution emissions simultaneously. The application of the Prophet model, based on Bayesian fitting, facilitates accurate prediction of wind and photovoltaic power outputs. Through experimentation across small (8 and 14 units) and large (58 units) systems, the feasibility of UKSO and TTED is validated. In complex scenarios, UKSO demonstrates a 0.69% to 3.64% reduction in pollution emissions and a 0.99% to 1.23% decrease in economic costs compared to KSO under varying weight configurations. Furthermore, UKSO achieves a renewable energy generation utilization rate exceeding 90%, emphasizing its ability to iterate efficiently through complex problems and its efficacy in addressing renewable power dispatch challenges. These results highlight the practical significance of UKSO in optimizing power systems and provide valuable insights for future research and applications in this domain.

Hybrid technique for optimizing charging-discharging behaviour of EVs and demand response for cost-effective PV microgrid system

At present, the unstable availability of renewable energy and the unpredictability of its usage have a negative impact on the reliable functioning of a microgrid. Furthermore, the presence of electric vehicles (EVs) as a variable load can significantly disrupt the secure management of the micro grid. This manuscript proposes a hybrid technique for charging-discharging behavior of EVs and demand side response for photovoltaic (PV) microgrid (MG) system. The proposed hybrid system is joint execution of both the seahorse optimization algorithm (SHO) and multi domain attention-depend conditional generative adversarial network (MDACGAN) technique. Commonly it is named as SHO - MDACGAN technique. The main objective of the proposed technique is to minimizing the operating cost of the microgrid, Maximizing the use rate of photovoltaic energy and minimizing power fluctuation between the main grid and the micro grid. The proposed microgrid economic system that incorporates transferable load (TL), electric vehicles, and other distributed generations (DG) such as photovoltaic and energy storage units (ES). To deal with the unpredictability of renewable energy supplies in MG, the proposed SHO and MDACGAN techniques are applied to solve the economic dispatch optimization model that considers the uncertainty of MG. By then, the performance of the proposed technique is executed in the MATLAB platform and contrasted with various existing techniques. In every technique, the proposed strategy yields superior outcomes like Heap Based Optimizer (HBO), Salp Swarm Algorithm (SSA) and Particle swarm optimization (PSO). From the result, it concludes that the proposed technique shows low cost of 1.2$and higher SoC of 0.78 % compared with other existing methods.

Optimal economic environmental power dispatch by using artificial bee colony algorithm

<span>Today, most power plants worldwide use fossil fuels such as natural gas, coal, and oil as the primary resource for energy reproduction primarily. The new term for economic environmental power dispatch (EEPD) problems is on the minimum total cost of the generator and fossil fuel emissions to address atmosphere pollution. Thus, the significant objective functions are identified to minimize the cost of generation, most minor emission pollutants, and lowest system losses individually. As an alternative, an Artificial Bee Colony (ABC) swarming algorithm is applied to solve the EEPD problem separately in the power systems on both standard IEEE 26 bus system and IEEE 57 bus system using a MATLAB programming environment. The performance of the introduced algorithm is measured based on simple mathematical analysis such as a simple deviation and its percentage from the obtained results. From the mathematical measurement, the ABC algorithm showed an improvement on each identified single objective function as compared with the gradient approach of using the Newton Raphson method in a short computational time.</span>

Carbon Neutrality Computational Cost Optimization for Economic Dispatch With Carbon Capture Power Plants in Smart Grid

To achieve carbon neutrality, reducing carbon emissions is crucial in dispatching problems in smart grid. Though renewable energy such as wind power has low carbon emissions, it suffers from random generation, which makes the thermal power necessary for a stable supply power system. To reduce carbon emissions, the thermal power plants are transformed into carbon capture power plants, which brings new challenges to economic dispatch algorithms. Besides, there are usually many constraints to keep the security operation of power systems, which incurs a large problem scale and high computational cost. Most existing methods either do not consider reducing carbon emissions, or suffer from high computational costs. In this paper, a framework for the carbon capture plants with wind power to reduce both running costs and carbon emissions is designed to support carbon neutrality. To reduce computational cost, initial-training and fine-tuning are used. A deep neural network is employed to describe the relationship between users' load and the constraints, which provides guides for finding the active constraints. Therefore, the problem scale can be significantly decreased, making the optimal dispatching strategy obtained quickly. The experimental results on real-world data show that the proposed framework can obtain the optimal strategy efficiently.

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

Bi-Level Inverse Robust Optimization Dispatch of Wind Power and Pumped Storage Hydropower Complementary Systems

This paper presents a bi-level inverse robust economic dispatch optimization model consisting of wind turbines and pumped storage hydropower (PSH). The inner level model aims to minimize the total generation cost, while the outer level introduces the optimal inverse robust index (OIRI) for wind power output based on the ideal perturbation constraints of the objective function. The OIRI represents the maximum distance by which decision variables in the non-dominated frontier can be perturbed. Compared to traditional methods for quantifying the worst-case sensitivity region using polygons and ellipses, the OIRI can more accurately quantify parameter uncertainty. We integrate the grid multi-objective bacterial colony chemotaxis algorithm and the bisection method to solve the proposed model. The former is adopted to solve the inner level problem, while the latter is used to calculate the OIRI. The proposed approach establishes the relationship between the maximum forecast deviation and the minimum generation cost associated with each non-dominated solution in the optimal load allocation. To demonstrate its economic viability and effectiveness, we simulate the proposed approach using real power system operation data and conduct a comparative analysis.

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.

Combined emission economic dispatch using quantum-inspired particle swarm optimization and its variants

The ever-increasing electricity demand, its dependency on fossil fuels, and the consequent environmental degradation are major concerns of this era. The worldwide domination of fossil fuels in bulk electricity generation is rapidly increasing the emissions of CO2 and other environmentally dangerous gases that are contributing to climate change. The economic and emission dispatch are two important problems in thermal power generation whose combination produces a complex highly constrained nonlinear optimization problem known as combined economic and emission dispatch. The optimization of combined economic and emission dispatch aims to allocate the generation of committed units to minimize fuel cost and emissions, simultaneously while honoring all equality and inequality constraints. Therefore, in this article, we investigate a solution of the combined economic and emission dispatch problem using quantum particle swarm optimization and its two modified versions, that is, enhanced quantum particle swarm optimization and quantum particle swarm optimization integrated with weighted mean personal best and adaptive local attractor. The enhanced quantum particle swarm optimization algorithm achieves particles’ diversification at early stages and shows good performance in local search at later stages. The quantum particle swarm optimization integrated with weighted mean personal best and adaptive local attractor boosts search performance of quantum particle swarm optimization and attains better global optimality. The suggested methods are employed to achieve solution for the combined economic and emission dispatch in four distinct systems, encompassing two scenarios with 6 units each, one with a 10-unit configuration, and another with an 11-unit setup. A comparative analysis with methodologies documented in existing literature reveals that the proposed approach outperforms others, demonstrating superior computational performance and robust efficiency.

Multistrategy Fusion Particle Swarm for Dynamic Economic Dispatch Optimization of Renewable Energy Sources

This paper presents a multistrategy fusion particle swarm optimization model for dynamic economic dispatching of renewable energy in distribution networks. The objective is to minimize active network losses and system voltage deviation while considering the integration of distributed energy sources and static reactive power compensators. The algorithm incorporates specific strategies, including a particle position change strategy based on the midpipeline convergence approach, a strategy for generating exploding particles near the optimal particles, and a particle velocity update strategy relying on the global optimal particle position. The inertia weights and particle position update methods of the simplified particle swarm optimization algorithm are also utilized. Simulation experiments are conducted on an IEEE 33 bus radial distribution system, demonstrating the effective optimization of system losses while ensuring system voltage stability. This research contributes to the scientific understanding of renewable energy integration in distribution networks and its economic dispatching.

Optimization of economic dispatch using updated differential evolution algorithm

Optimization of economic dispatch using updated differential evolution algorithm

Optimal economic dispatch of a virtual power plant based on gated recurrent unit proximal policy optimization

The intermittent renewable energy in a virtual power plant (VPP) brings generation uncertainties, which prevents the VPP from providing a reliable and user-friendly power supply. To address this issue, this paper proposes a gated recurrent unit proximal policy optimization (GRUPPO)-based optimal VPP economic dispatch method. First, electrical generation, storage, and consumption are established to form a VPP framework by considering the accessibility of VPP state information. The optimal VPP economic dispatch can then be expressed as a partially observable Markov decision process (POMDP) problem. A novel deep reinforcement learning method called GRUPPO is further developed based on VPP time series characteristics. Finally, case studies are conducted over a 24-h period based on the actual historical data. The test results illustrate that the proposed economic dispatch can achieve a maximum operation cost reduction of 6.5% and effectively smooth the supply–demand uncertainties.

Research on bi‐layer low carbon scheduling strategy for source‐load collaborative optimization based on node carbon emission intensity

AbstractTo accurately calculate the carbon emission of integrated energy system (IES), and fully explore the potential for load side on carbon emission reduction, this paper proposes a method of guiding load to participate in demand response based on node carbon emission intensity, and constructs a bi‐layer low‐carbon scheduling model for source‐load collaborative optimization. First, the carbon flow calculation model of IES in the total process is established, such as source, network, load, and storage. It can depict the carbon emission characteristics of energy conversion equipment and energy storage devices. The principle of proportional sharing is used to track carbon emission flows, the changes in carbon emission intensity at each node is perceived from a spatiotemporal perspective. Second, carbon flow analysis is incorporated into the load demand response mechanism, and a carbon emission model for load aggregator (LA) after demand response is established based on the node carbon emission intensity. Third, a bi‐layer low‐carbon scheduling model is constructed, which considers the source‐load collaborative optimization. The upper layer is the optimal economic dispatch of IES operators, while the lower layer is the optimal economic dispatch of LAs. Finally, the effectiveness of the proposed method is verified using the system as an example, such as improved 14‐node power grid, 6‐node heating network, and 6‐node nature gas network.

Economic Dispatch Optimization Strategies and Problem Formulation: A Comprehensive Review

Economic Dispatch Problems (EDP) refer to the process of determining the power output of generation units such that the electricity demand of the system is satisfied at a minimum cost while technical and operational constraints of the system are satisfied. This procedure is vital in the efficient energy management of electricity networks since it can ensure the reliable and efficient operation of power systems. As power systems transition from conventional to modern ones, new components and constraints are introduced to power systems, making the EDP increasingly complex. This highlights the importance of developing advanced optimization techniques that can efficiently handle these new complexities to ensure optimal operation and cost-effectiveness of power systems. This review paper provides a comprehensive exploration of the EDP, encompassing its mathematical formulation and the examination of commonly used problem formulation techniques, including single and multi-objective optimization methods. It also explores the progression of paradigms in economic dispatch, tracing the journey from traditional methods to contemporary strategies in power system management. The paper categorizes the commonly utilized techniques for solving EDP into four groups: conventional mathematical approaches, uncertainty modelling methods, artificial intelligence-driven techniques, and hybrid algorithms. It identifies critical research gaps, a predominant focus on single-case studies that limit the generalizability of findings, and the challenge of comparing research due to arbitrary system choices and formulation variations. The present paper calls for the implementation of standardized evaluation criteria and the inclusion of a diverse range of case studies to enhance the practicality of optimization techniques in the field.