Dynamic 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.

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.

Multi-Objective Stochastic Paint Optimizer for Solving Dynamic Economic Emission Dispatch with Transmission Loss Prediction Using Random Forest Machine Learning Model

Dynamic economic emission dispatch problems are complex optimization tasks in power systems that aim to simultaneously minimize both fuel costs and pollutant emissions while satisfying various system constraints. Traditional methods often involve solving intricate nonlinear load flow equations or employing approximate loss formulas to account for transmission losses. These methods can be computationally expensive and may not accurately represent the actual transmission losses, affecting the overall optimization results. To address these limitations, this study proposes a novel approach that integrates transmission loss prediction into the dynamic economic emission dispatch (DEED) problem. A Random Forest machine learning model was offline-trained to predict transmission losses accurately, eliminating the need for repeated calculations during each iteration of the optimization process. This significantly reduced the computational burden of the algorithm and improved its efficiency. The proposed method utilizes a powerful multi-objective stochastic paint optimizer to solve the highly constrained and complex dynamic economic emission dispatch problem integrated with random forest-based loss prediction. A fuzzy membership-based approach was employed to determine the best compromise Pareto-optimal solution. The proposed algorithm integrated with loss prediction was validated on widely used five and ten-unit power systems with B-loss coefficients. The results obtained using the proposed algorithm were compared with seventeen algorithms available in the literature, demonstrating that the multi-objective stochastic paint optimizer (MOSPO) outperforms most existing algorithms. Notably, for the Institute of Electrical and Electronics Engineers (IEEE) thirty bus system, the proposed algorithm achieves yearly fuel cost savings of USD 37,339.5 and USD 3423.7 compared to the existing group search optimizer algorithm with multiple producers (GSOMP) and multi-objective multi-verse optimization (MOMVO) algorithms.

Optimizing dynamic economic dispatch through an enhanced Cheetah-inspired algorithm for integrated renewable energy and demand-side management

This study presents the Enhanced Cheetah Optimizer Algorithm (ECOA) designed to tackle the intricate real-world challenges of dynamic economic dispatch (DED). These complexities encompass demand-side management (DSM), integration of non-conventional energy sources, and the utilization of pumped-storage hydroelectric units. Acknowledging the variability of solar and wind energy sources and the existence of a pumped-storage hydroelectric system, this study integrates a solar-wind-thermal energy system. The DSM program not only enhances power grid security but also lowers operational costs. The research addresses the DED problem with and without DSM implementation to analyze its impact. Demonstrating effectiveness on two test systems, the suggested method's efficacy is showcased. The recommended method's simulation results have been compared to those obtained using Cheetah Optimizer Algorithm (COA) and Grey Wolf Optimizer. The optimization results indicate that, for both the 10-unit and 20-unit systems, the proposed ECOA algorithm achieves savings of 0.24% and 0.43%, respectively, in operation costs when Dynamic Economic Dispatch is conducted with Demand-Side Management (DSM). This underscores the advantageous capability of DSM in minimizing costs and enhancing the economic efficiency of the power systems. Our ECOA has greater adaptability and reliability, making it a promising solution for addressing multi-objective energy management difficulties within microgrids, particularly when demand response mechanisms are incorporated. Furthermore, the suggested ECOA has the ability to elucidate the multi-objective dynamic optimal power flow problem in IEEE standard test systems, particularly when electric vehicles and renewable energy sources are integrated.

Integrating renewable energy sources and electric vehicles in dynamic economic emission dispatch: an oppositional-based equilibrium optimizer approach

ABSTRACT This article proposes a solution to the Dynamic Economic Emission Dispatch (DEED) problem, which incorporates wind, solar and plug-in electric vehicles (PEVs) into the optimization challenge. The new model, called Wind-Solar-Plug in Electric Vehicle (WSPEV) DEED, utilizes an optimization technique called the Oppositional-based Equilibrium Optimizer (OEO) method with the Weibull and Beta distributions to model wind and solar resources. The charging and discharging patterns of PEVs are also considered in the model. The proposed approach is evaluated through several scenarios involving Renewable Energy Sources (RESs) and PEVs, and the simulation results demonstrate the effectiveness of the proposed model in achieving a sustainable and cost-effective power system. The WSPEV DEED model provides a valuable solution to the DEED problem, which is crucial for successfully integrating RESs and PEVs into the power system for a sustainable future.

Distributed Multiagent Reinforcement Learning With Action Networks for Dynamic Economic Dispatch.

A new class of distributed multiagent reinforcement learning (MARL) algorithm suitable for problems with coupling constraints is proposed in this article to address the dynamic economic dispatch problem (DEDP) in smart grids. Specifically, the assumption made commonly in most existing results on the DEDP that the cost functions are known and/or convex is removed in this article. A distributed projection optimization algorithm is designed for the generation units to find the feasible power outputs satisfying the coupling constraints. By using a quadratic function to approximate the state-action value function of each generation unit, the approximate optimal solution of the original DEDP can be obtained by solving a convex optimization problem. Then, each action network utilizes a neural network (NN) to learn the relationship between the total power demand and the optimal power output of each generation unit, such that the algorithm obtains the generalization ability to predict the optimal power output distribution on an unseen total power demand. Furthermore, an improved experience replay mechanism is introduced into the action networks to improve the stability of the training process. Finally, the effectiveness and robustness of the proposed MARL algorithm are verified by simulation.

Krill herd technique for dynamic economic dispatch problems with the integration of wind power generation

The krill herd (KH) approach is proposed in this article for tackling the dynamic economic dispatch (DED) problem with the integration of wind power generation, including constraints such as valve-point loadings and prohibited operating zones (PoZs). The purpose of resolving the DED problem is to determine the optimum feasible combination of power outputs for all allocated generating units within a given period while simultaneously meeting dynamic operational constraints and power demand. Due to the addition of valve points and PoZs to the cost characteristics of the generating unit, the DED issue becomes a highly non-linear and non-convex optimization issue. When transmission losses are taken into account, the DED problem becomes significantly more complex to solve. KH is a swarm-inspired algorithm based on krill individual herding behavior. KH employs two global and two local tactics, and these work in parallel, making KH a powerful algorithm. The effectiveness of the KH method is investigated and validated through extensive testing on various test systems, including 5-, 6-, 10-, 16-, and 30-unit test systems. Extensive studies are conducted to evaluate the efficacy of the proposed KH algorithm; the present research work compares the convergence properties of the suggested approach with those of the other recently published methods. In addition to reduced generation costs compared to other results published in recent literature, the numerical findings of the KH approach reveal that it has strong convergence qualities.

A variegated GWO algorithm implementation in emerging power systems optimization problems

This paper proposes a novel hybrid algorithm which is mathematically modelled by amalgamating the superior features of recently developed Grey Wolf Optimizer (GWO), Sine Cosine Algorithm (SCA), and Crow Search Algorithm (CSA). Researchers have already implemented the aforementioned three algorithms and obtained superior quality results for solving diverse optimization problems. The novel hybrid Variegated GWO Algorithm (VGWO) developed in this proposed research work is initially realized and validated for solving IEEE CEC-C06 2019 benchmark functions. Thereafter, the proposed VGWO is utilized as an optimization tool to solve three emerging and complex power system optimization problems which includes energy management of microgrid systems operated in both islanded and grid-connected mode, dynamic economic emission dispatch and reactive power planning (RPP) problem. A comparative analysis of the proposed VGWO approach with other established metaheuristics is undertaken for each optimization problem. Numerical results show that the novel hybrid VGWO algorithm outperformed an ample number of optimization techniques in providing better quality solutions. The proposed hybrid algorithm yielded a 36.93% reduction in active power loss and 36.80% reduction in operating cost with respect to base case condition for RPP problem. Likewise while solving microgrid energy management problems 9–30% savings was realized in the generation cost compared to the ones mentioned in literature. The capability of handling many complex constraints within a minimum amount of computational time to provide consistently best solutions prioritize the proposed hybrid algorithm among its kinds. Statistical analysis validates the authenticity and viability of the proposed algorithm.

Decentralized Coordination of DERs for Dynamic Economic Emission Dispatch

This paper focuses on the dynamic economic emission dispatch (DEED) problem, to coordinate the distributed energy resources (DERs) in a power system and achieve economical and environmental operation. Distributed energy storages (ESs) are introduced into problem formulation in which charging/discharging efficiency is taken into account. By relaxing the nonconvexity induced by the charging/discharging model of ESs and network losses, we convert the non-convex DEED problem into its convex equivalency. Then, through a Lagrangian duality reformulation, an equivalent unconstrained consensus optimization model is established—a novel consensus-based decentralized algorithm, where the incremental cost is chosen as the consensus variable. At each iteration, only one primal variable requires sub-optimization, and it is completely locally updated. This is different from the well-known alternating direction method of multiplier (ADMM)-based algorithms where more than one subproblem needs to be solved at each iteration. The results of the comparative experiments also reflect the algorithm’s advantage in terms of computational efficiency. The simulation results validate the effectiveness of the proposed algorithm, achieving a balance between emissions and economic considerations.

Multicounty fuel constraint‐based dynamic economic dispatch problem using horse herd optimization

AbstractDue to the diminution of fossil fuels, the profitable usage of fuel for the generation of power is reducing. It is an extremely vital concern for power generation companies. The fossil fuel‐based power plant must operate within its fuel limits and contractual restrictions. Therefore, economic optimization is required to optimize the fuel cost for generation under fuel constraints. To address this issue, in this work, a horse herd optimization algorithm (HOA) is developed to solve multicounty fuel‐constrained dynamic economic dispatch with demand‐side management incorporating wind turbine generators, solar photovoltaic plants, and pumped hydro storage plants. The efficiency of the suggested HOA algorithm has been revealed on a selected test system. The HOA technique shows better convergence as compared with the other methods. Moreover, the computation time requirement of the HOA technique is also lower than that of other compared methods. From numerical results, it is observed that the consumption of fuel is sufficiently high if constraints are incorporated into the problem. Simulation results are matched up to those obtained from hierarchical particle swarm optimization with time‐varying acceleration coefficients, fast convergence evolutionary programming, and differential evolution. After comparison, it is observed that the recommended HOA offers a better‐quality solution.

Dynamic Economic Dispatch Problem in Hybrid Wind Based Power Systems Using Quasi Oppositional Based Chaotic Honey Badger Algorithm

This article proposes a dynamic economic load dispatch (DELD) including wind power involvement process, which is capable to produce least possible generation cost of electrical systems by integrating large-scale wind power penetration. The primary component of hybridized power system comprises of conventional thermal generators and wind generators. To expedite the convergence flexibility and escape the clarifications from the confined optimal purpose, quasi-oppositional based learning (Q-OBL) is combined with HBA, which results in quasi oppositional chaotic honey badger algorithm (QOHBA). Moreover, chaotic strategy is integrated with QOHBA to boost the convergence speed as well as enhance the performance of the basic honey badger algorithm (HBA). The proposed QOCHBA is suggested to explain wind-based shared DELD problem to reduce thermal-wind generation energy cost. The superiority and expediency of the prospective technique is proved through its operation in two benchmark investigation systems. We use probability density functions (PDF) for wind energy (WE) forecasting to assessment dynamic working reserve necessities, based on the readjust of uncertainty in the prediction. To establish the efficacy of the recommended QOCHBA method in explaining non-linear, non-convex, and constrained DELD problem, the suggested structures are implemented on benchmark of 10-unit in addition to 15-unit test methods.

Price formation in short-term electricity market scheduling

Price formation is important for monitoring/development of an electricity market since the short/long-run efficiencies depend on the prices representing the economic signals. However, existing approaches cannot capture the contribution of suppliers’ bidding behavior to short-term price formation. As a result, regulators cannot evaluate these contributions. This can result in market monitoring failure/inefficient regulatory decisions that entail short-run market distortion or compromised investment respectively. This paper proposes a novel approach enabling regulators to retrace these contributions for every single non-zero shadow price formed in a dynamic security-constrained economic dispatch (SCED) problem. The decomposition of dual variables in a linear representation of SCED is adopted to evaluate the marginal contribution of the offered prices. The proposed theory yields explicit functions mapping the SCED shadow prices (i.e., locational marginal prices, and marginal values of (i) binding generation capacity limits, (ii) binding transmission capacity limits, and (iii) binding ramping limits) to the offered prices. Counterintuitively, the results show that increasing the offered prices will not necessarily leads to an increase in the shadow prices, especially the locational marginal prices. In addition, it is shown that the offered prices can pose long-run implications by contributing to the shadow prices associated with the marginal value of transmission/generation capacity.

Differential evolution algorithm with improved crossover operation for combined heat and power economic dynamic dispatch problem with wind power

Abstract This paper proposes a differential evolution algorithm with improved crossover operation (ICRDE) to deal with combined heat and power dynamic economic dispatch (CHPDED) problems with wind power. First, the improved crossover operation is used to maintain the population diversity by using original individuals, first mutated individuals, and second mutated individuals. Second, the scaling factor and weighted factor are incorporated into the mutation operation to improve the convergence efficiency of the algorithm. Third, adaptive control parameters are introduced to balance local exploitation and global exploration. Moreover, after being updated by the mutation and crossover operation of ICRDE at each generation, the solutions of ICRDE will be further amended using a constraint handling method, which improves the chance of acquiring feasible solutions. Experimental results demonstrate that ICRDE has strong global optimization ability and surpasses the compared algorithms for the CEC2017 benchmark functions, the combined heat and power economic dispatch problems, and the CHPDED problem with and without wind power.

Economic emission dispatch considering electric vehicles and wind power using enhanced multi-objective exchange market algorithm

Due to the environmental concerns and the high penetration of wind power (WP) and electric vehicles (EVs), reducing the generation costs and emissions, coordinating EV charging in the distribution networks, and addressing the WP uncertainty, are among the most challenging issues in power system control and operation. Hence, the multi-objective dynamic economic emission dispatch problem (MDEEDP) integrated with EVs and wind farms has become one of the hottest topics in this research area. In this paper, the MDEEDP in the presence of EVs, the random behavior of EV drivers, and WP uncertainty is solved using a new multi-objective evolutionary algorithm called the enhanced multi-objective exchange market algorithm. In the proposed algorithm, the novel point-to-point distance technique is introduced to find the Pareto front solutions set (PFSS) with a uniform and diverse distribution. Also, smart strategy management for charging and discharging EVs is proposed to smooth the load curve. The effectiveness of the proposed method and performance of the proposed smart strategy are investigated on two single-objective and multi-objective test systems, including EVs and wind farms, considering uncertainty and system constraints such as ramp rate limits. The simulation results show that the PFSS of the MDEEDP is well extracted by the proposed method while maintaining its uniformity and diversity. The presence of EVs and the application of the proposed smart strategy lead to a reduction of 2,926,497 ($) in the operation costs for test system 1, and, 38,694,698.28 ($) and 7,832,876.64 (kg), respectively in the operation costs and emissions for test system 2, assuming the same load curve throughout the year. In addition, the load factor in test systems 1, and 2 is improved by 11 and 19 percent, respectively.

A nondominated sorting genetic algorithm III with three crossover strategies for the combined heat and power dynamic economic emission dispatch with or without prohibited operating zones

This paper presents a nondominated sorting genetic algorithm III with three crossover strategies (NSGA-III-TCS) for the combined heat and power dynamic economic emission dispatch (CHPDEED) problems with or without prohibited operating zones. The first strategy updates the individuals of the first nondomination rank by a modified improvisation of the harmony search algorithm, which accelerates the information exchanges of the elite individuals. The second strategy regulates the individuals of the last nondomination rank according to a modified single-point crossover of the genetic algorithm, which strengthens the convergence of the population. The third strategy adjusts the remaining individuals in terms of a modified DE/rand-to-best/1 mutation of the differential evolution algorithm, and it guides these individuals to move towards the ones which have at least one minimum objective function value, which is beneficial for expanding the distribution range of the population. NSGA-III-TCS obtains the largest average hypervolumes and shows a desirable convergence for six CHPDEED problems. NSGA-III-TCS achieves relatively high coverage rates in most cases, indicating the dominance of the Pareto sets of NSGA-III-TCS over those of the other algorithms. Also, it has relatively low average spacings for all problems, suggesting the good evenness of the Pareto sets.

An approach to attain a balanced trade-off solution for dynamic economic emission dispatch problem on a microgrid system

An approach to attain a balanced trade-off solution for dynamic economic emission dispatch problem on a microgrid system

A modified Particle Swarm Optimization algorithm with enhanced search quality and population using Hummingbird Flight patterns

This study proposes a modified Particle Swarm Optimization (PSO) algorithm based on Hummingbird Flight (HBF) patterns to enhance the search quality and population diversity. The HBF has five concepts: (1) Smaller steps toward position updating are more likely than larger ones, (2) Position changes are made step by step throughout the flight, (3) Flight energy is conserved during the nectar-searching process, (4) Hummingbirds do not fly in large groups in confined spaces, and (5) Simultaneous position changes in all directions are not realistic. A comprehensive study on two CEC-2010 and CEC-2013 benchmark suites is conducted to verify the effectiveness of the proposed PSO-HBF algorithm. The proposed algorithm is also evaluated and compared to other well-known PSO algorithms using shifted and rotated CEC 2005 and CEC 2014 benchmark functions. Four cases in economic dispatch, the 10-unit reserve constraint, and the 30-unit dynamic economic dispatch (DED) are further examined. The last two cases investigate how the proposed PSO-HBF deals with large-scale practical problems. The results demonstrated that the PSO-HBF algorithm is superior to seven other modified algorithms, improving eight and ten functions on the 2010 and 2013 benchmarks, respectively. Furthermore, achieving the third rank among the nineteen improved PSO algorithms based on the 2005 functions confirms the effectiveness of the proposed algorithm. Moreover, in two cases of the DED problem, the results of PSO-HBF show significant improvement over previously published papers. The PSO-HBF algorithm’s source code can be accessed publicly at http://www.optim-app.com/projects/psohbf.

Optimization of Non-Convex Economic Dispatch Problem Using Hybrid Approach Based on Bacterial Foraging and Genetic Algorithm

Fulfillment of consumer demand is a foremost challenge for all electrical power utilities. An electrical power system consists of several generating units and each of these units owns a distinct operating set of operating parameters. A fundamental challenges lies in a fact that there may not be a correlation between operating costs of these machines and their generated output. Major reason for lack of the correlation includes the ramp-rate limits, transmission losses and manipulation due to valve-points in the generation units cost function, and thus, it becomes a non-linear optimization problem. In view of this fact, it creates a rigorous need to devise a robust solution to cater for such a non-linear optimization scenario. In this paper, bacterial foraging and genetic algorithms based hybrid technique is used to effectively tackle the economic dispatch problem. The presented technique incorporates two modifications in the original bacterial foraging algorithm including differential evolution inspired bacterial movement and genetic algorithm based bacterial reproduction. Where inspired bacterial movement involves modification in the directional movement for each bacterium in such a manner that every bacterium tries to improve its direction and position based on differential evolution. The proposed technique is applied to non-convex dynamic economic dispatch (DED) problem in order to obtain optimal solution within feasible functional limits while satisfying the load demand at the same time. The obtained results demonstrate that the proposed hybrid approach outperform the other techniques in term of optimal solution and significant reduction of computational time in the given scenarios.

Sine-Cosine Algorithm for the Dynamic Economic Dispatch Problem With the Valve-Point Loading Effect

Dynamic economic dispatch (DED) deals with the allocation of predicted load demand over a certain period of time among the thermal generating units at minimum fuel cost. The objective function of DED becomes highly complex and nonlinear after considering various operating constraints like valve point loading, ramp rate limit, transmission loss, and generation limits. In this study, the sine-cosine algorithm has been presented to solve the DED problem with various constraints. The randomly placed swarm finds an optimum solution according to their fitness values and keeps the path towards the best solution attained by each swarm. The swarm avoid local optima in the exploration stage and move towards the solution exploitation stage using sine and cosine functions. The proposed technique has been tested in several test systems. The results obtained by the proposed technique have been compared with those obtained by other published methods employing the same test systems. The results validate the superiority and the effectiveness of the proposed technique over other well-known techniques.

An initialization-free distributed algorithm for dynamic economic dispatch problems in microgrid: Modeling, optimization and analysis

In this paper, a distributed optimization algorithm is designed for a hybrid microgrid network to minimize the total generation cost in a dynamic economic dispatch problem (DEDP). The hybrid microgrid model is constructed with different types of traditional power resources, renewable energy and energy storage batteries, which are subject to the supply–demand balance, capacity, and ramp-rate constraints of the generation facilities. Meantime, from the perspective of environment protection, the pollutant emissions from traditional generators are considered to reduce its impact on environment. Firstly, we transform the multi-objective optimization problem to a single objective optimization problem through the weight-sum method. Then, compared to the most existing centralized algorithms, we propose a fully distributed algorithm that does not depend on the initialization process to solve the dynamic dispatch problem. Moreover, we assume that the optimization objective functions are convex functions rather than a strictly standard quadratic function, and the convergence of the proposed algorithm is analyzed through convex analysis and a Lyapunov function method. Finally, some experiments with quadratic or non-quadratic cost functions and comparison examples are simulated, the experimental results verify that the optimal solution satisfies the constraints of the supply–demand constraints and capacity inequalities in each time slot.