Dynamic Economic Dispatch Problem Research Articles

An Improved Equilibrium Optimizer with a Decreasing Equilibrium Pool

Big Data is impacting and changing the way we live, and its core lies in the use of machine learning to extract valuable information from huge amounts of data. Optimization problems are a common problem in many steps of machine learning. In the face of complex optimization problems, evolutionary computation has shown advantages over traditional methods. Therefore, many researchers are working on improving the performance of algorithms for solving various optimization problems in machine learning. The equilibrium optimizer (EO) is a member of evolutionary computation and is inspired by the mass balance model in environmental engineering. Using particles and their concentrations as search agents, it simulates the process of finding equilibrium states for optimization. In this paper, we propose an improved equilibrium optimizer (IEO) based on a decreasing equilibrium pool. IEO provides more sources of information for particle updates and maintains a higher population diversity. It can discard some exploration in later stages to enhance exploitation, thus achieving a better search balance. The performance of IEO is verified using 29 benchmark functions from IEEE CEC2017, a dynamic economic dispatch problem, a spacecraft trajectory optimization problem, and an artificial neural network model training problem. In addition, the changes in population diversity and computational complexity brought by the proposed method are analyzed.

Multiobjective multi verse optimization algorithm to solve dynamic economic emission dispatch problem with transmission loss prediction by an artificial neural network

To overcome the drawback of using only one B-loss coefficient for a widely varying demand pattern that occurs during the entire period of a dynamic economic emission dispatch model, this research work presents a new approach to integrating artificial neural network-based loss prediction into the dynamic economic emission dispatch model. The trained neural network will predict the transmission loss only once during each interval of the dispatch period. The novelty of the work lies in employing a trained neural network to replace the existing procedure of solving complex power flow equations or B-loss coefficients during every iteration. A potent multiobjective multiverse optimization algorithm along with an effective constraint handling mechanism is employed to solve the highly complicated dynamic economic emission dispatch model. A fuzzy membership-based approach is adopted to help the decision-maker select one optimal solution from the Pareto Optimal solutions during each hour of the dispatch period. The proposed algorithm is tested on four systems of varying complexity including a large-scale IEEE 118 bus power system with fifty-four thermal generators. The results obtained are compared with 16 state-of-the-art algorithms to prove the competitive behavior of the algorithm. For an IEEE 30 bus system, the proposed algorithm results in a saving of 92.92$ in fuel cost and a reduction of emission levels by 0.0375 tons per day. The total time taken by the algorithm is faster than the well-known non dominated sorted genetic algorithm II and multiobjective particle swarm optimization algorithm by 30 times and 7.6 times respectively.

Investigation on New Metaheuristic Algorithms for Solving Dynamic Combined Economic Environmental Dispatch Problems

In this paper, the dynamic combined economic environmental dispatch problems (DCEED) with variable real transmission losses are tackled using four metaheuristics techniques. Due to the consideration of the valve-point loading effects (VPE), DCEED have become a non-smooth and more complex optimization problem. The seagull optimization algorithm (SOA), crow search algorithm (CSA), tunicate swarm algorithm (TSA), and firefly algorithm (FFA), as both nature and biologic phenomena-based algorithms, are investigated to solve DCEED problems. Our proposed algorithms, SOA, TSA, and FFA, were evaluated and applied on the IEEE five-unit test system, and the effectiveness of the proposed CSA approach was applied on two-unit, five-unit, and ten-unit systems by considering VPE. We defined CSA for different objective functions, such as cost of production, emission, and CEED, by considering VPE. The obtained results reveal the efficiency and robustness of the CSA compared to SOA, TSA, FFA, and to other optimization algorithms reported recently in the literature. In addition, Matlab simulation results show the advantages of the proposed approaches for solving DCEED problems.

AEFA Based Optimal Dynamic Economic Load Dispatch Problem Considering Penetration of Renewable Energy Systems

In power system, maintaining the load generation balance is critical. This paper proposes an artificial electric field algorithm (AEFA) for dynamic economic load dispatch (DELD) in a power system with security constraints, taking into account renewable energy sources (RES).. The RES penetration and total savings are examined considering variation of underestimation and overestimation costs associated with RES. Further, the impact of increased RES penetration on thermal fuel and overall costs has been studied. The AEFA algorithm performs better than PSO and DE, in terms of performance. The result reveals that when RES penetration rises savings as well as net cost of RES rises. Numerically, at 65% penetration of RES, a savings of 28.19% is achieved in the generator fuel cost and the RES penetration leads to a reduction in the thermal unit’s fuel cost.

Metaheuristic Technique based on Realistic Mimicking of Grey Wolf’s Hunting Process for Solving Dynamic Economic Dispatch Problem with Electric Vehicles

This paper proposes a realistic variant of grey wolf optimizer with the dynamic behavior of prey position and hence called as Realistic Grey Wolf Optimizer (RGWO). The proposed method is employed to solve 23 benchmark problems and a well-known complex power system problem of dynamic economic dispatch of power by generating units taking into consideration of electric vehicles with valve point effect, ramp-rate, transmission losses for a time interval of 24 hours. The prey position is modeled dynamic i.e., it is considered to be moving and is not static as considered in an earlier version of GWO with the help of probability distribution function. The probability distribution function which is considered here is Levy Flight, Cauchy, Gamma, Gaussian, and Weibull. Thereafter, the statistical testing is done with the help of the Wilcoxon Rank test and Wilcoxon Signed Rank test to investigate the significance of the different variants of RGWO. The experimental results and statistical testing show that the modification proposed in RGWO significantly improves the performance of GWO and hence the algorithm is utilized to find dynamic economic dispatch along with electric vehicles considering different constraints effectively.

Multi-objective Dynamic Environmental Economic Dispatch Problem Considering Plug in Electric Vehicles by Using the Improved Exchange Market Algorithm

Global Warming and progression of modern power networks have profoundly changed traditional power grids in terms of fossil fuel consumption and emission of toxic gases. Therefore, auxiliary power plants and ancillary services have been introduced as an effective alternative, to overcome these new challenges in power systems. In this work, the dynamic environmental economic dispatch (DEED) problem, is investigated by considering the plug-in electric vehicles (PEVs), minimizing the fuel cost and greenhouse gas emissions from fossil fuel units. In the mentioned problem, to make it more practical, various operational constraints, including valve-point loading effect (VPLE), ramp rate limits (RRLs) and generation capacity limits are considered. This paper proposes a new multi-objective exchange market algorithm (EMA) based on the non-dominated sorting theory to find the Pareto front. In addition, the impacts of PEVs, as an uncertainty source, on the mentioned problem are analysed in four different charging scenarios. The efficiency of the proposed method has been detailed on three experimental systems and the obtained results are compared with other algorithms in this field. The results show that the maximum percentage reduction in costs for test cases 1 to 3, are about 2.13, 2.69, and 39.48, respectively, and bout 45.96, 48.20 and 44.07, for emission, respectively. The comparative analysis verify the proposed method efficiency, and accuracy in solving the suggested problem.

Hybrid Dragonfly and Pattern Search Algorithm Applied to Dynamic Economic Dispatch Problem

Background: In this paper, a novel hybridisation of the dragonfly algorithm (DFA) with the pattern search (PS) algorithm is applied to the dynamic economic dispatch (DED) problem. The DED problem is non-convex, non-linear, and non-smooth and considering practical constraints such as the loading effect of the valve point and ramp rate limits. The conventional DFA is stuck in the local optima and converges prematurely. Introduction: The characteristics of the optimality of the electric power system are dependent on reliability and high economy. Economic dispatch (ED) significantly contributes in deriving the optimal solutions for the operation of a power system. ED aims to generate electric power at the optimum cost among all generating units in order to satisfy the load demand considering all practical and operational constraints. Practical constraints, such as the effect of steam valves, the dynamic behaviour of ramp rate limits, losses due to transmission of power, and prohibited operating zones, convert the linear and convex problem to a non-convex and non-linear problem. Method: Planning and scheduling of output electric power from committed generating units to fulfill the load demand for a scheduled period are termed as DED. The practical generators of thermal power experience the effect of steam valve, real-time ramp rate limit, and technical constraints. DED satisfies all practical, technical, and operational constraints. The DFA was a newly proposed method taking the inspiration of the behaviour of dragonflies for hunting and migrating towards food. The random movement of dragonfly clusters depicts their static characteristics for exploring in the local search space for exploitation competencies, whereas the dynamic behaviour of swarms is used for exploring the global search space by moving in a single direction for a long distance. Result: The efficiency of the proposed method is validated for six well-known benchmark functions. The hybrid technique is compared with the conventional DFA. The proposed hybrid technique combining of the DFA and PS algorithm is also applied for four different test systems with diverse generating units. The proposed technique shows better efficiency for the optimum cost as compared to other recently applied techniques. Conclusion: To overcome difficulties, a PS method is hybridised with the original DFA. The application of the proposed technique improves the capability of search and convergence property The validation of the proposed method by applying to the DED problem shows its effectiveness for generation scheduling and estimating.

A bottlenose dolphin optimizer: An application to solve dynamic emission economic dispatch problem in the microgrid

In this article, a new optimization technique is proposed. The proposed technique is a nature-inspired population-based meta-heuristic optimization technique which is inspired from bottlenose dolphins. Therefore, it is named as bottlenose dolphin optimizer. The proposed method replicates the mud ring feeding strategy used by them. In this study, mud ring feeding technique is mathematically modeled and is examined with two case studies for the superiority in comparison to other existing optimization techniques. The first case study includes benchmark functions which are used to examine the exploration, exploitation, local minima and convergence characteristics of the proposed technique. In second case study, a real-time optimization problem related to power systems i.e. a dynamic emission economic dispatch problem is considered. The two case studies show that the proposed technique exhibits a better exploration and exploitation capabilities as compared to some of the existing well known optimization algorithms.

A novel hybrid soft computing optimization framework for dynamic economic dispatch problem of complex non-convex contiguous constrained machines.

The reformations of the electrical power sector have resulted in very dynamic and competitive market that has changed many elements of the power industry. Excessive demand of energy, depleting the fossil fuel reserves of planet and releasing the toxic air pollutant, has been causing harm to earth habitats. In this new situation, insufficiency of energy supplies, rising power generating costs, high capital cost of renewable energy equipment, environmental concerns of wind power turbines, and ever-increasing demand for electrical energy need efficient economic dispatch. The objective function in practical economic dispatch (ED) problem is nonlinear and non-convex, with restricted equality and inequality constraints, and traditional optimization methods are incapable of resolving such non-convex problems. Over the recent decade, meta-heuristic optimization approaches have acquired enormous reputation for obtaining a solution strategy for such types of ED issues. In this paper, a novel soft computing optimization technique is proposed for solving the dynamic economic dispatch problem (DEDP) of complex non-convex machines with several constraints. Our premeditated framework employs the genetic algorithm (GA) as an initial optimizer and sequential quadratic programming (SQP) for the fine tuning of the pre-optimized run of GA. The simulation analysis of GA-SQP performs well by acquiring less computational cost and finite time of execution, while providing optimal generation of powers according to the targeted power demand and load, whereas subject to valve point loading effect (VPLE) and multiple fueling option (MFO) constraints. The adequacy of the presented strategy concerning accuracy, convergence as well as reliability is verified by employing it on ten benchmark case studies, including non-convex IEEE bus system at the same time also considering VPLE of thermal power plants. The potency of designed optimization seems more robust with fast convergence rate while evaluating the hard bounded DEDP. Our suggested hybrid method GA-SQP converges to achieve the best optimal solution in a confined environment in a limited number of simulations. The simulation results demonstrate applicability and adequacy of the given hybrid schemes over conventional methods.

Solution to dynamic economic dispatch with prohibited operating zones via MILP.

Dynamic economic dispatch (DED) problem considering prohibited operating zones (POZ), ramp rate constraints, transmission losses and spinning reserve constraints is a complicated non-linear problem which is difficult to solve efficiently. In this paper, a mixed integer linear programming (MILP) method is proposed to solve such a DED problem. Firstly, a novel MILP formulation for DED problem without considering the transmission losses, denoted by MILP-1, is presented by using perspective cut reformulation technique. When the transmission losses are considered, the quadratic terms in the transmission losses are replaced by their first order Taylor expansions, and then an MILP formulation for DED considering the transmission losses, denoted by MILP-2, is obtained. Based on MILP-1 and MILP-2, an MILP-iteration algorithm is proposed to solve the complicated DED problem. The effectiveness of the MILP formulation and MILP iteration algorithm are assessed by several cases and the simulation results show that both of them can solve to competitive solutions in a short time.

A multi-strategy firefly algorithm based on rough data reasoning for power economic dispatch.

Dynamic economic dispatch (DED) is a multi constraint and nonlinear complex problem, which is embodied in the dynamic decision-making coupled with each other in time and space. It is generally transformed into a high-dimensional multi constraint optimization problem. In this paper, a multi Strategy firefly algorithm (MSRFA) is proposed to solve the DED problem. MSRFA puts forward three strategies through the idea of opposite learning strategy and rough data reasoning to optimize the initialization and iteration process of the algorithm, improve the convergence speed of the algorithm in medium and high dimensions, and improve the escape ability when the algorithm falls into local optimization; The performance of MSRFA is tested in the simulation experiment of DED problem. The experimental results show that MSRFA can search the optimal power generation cost and minimum load error in the experiment, which reflects MSRFA superior stability and ability to jump out of local optimization. Therefore, MSRFA is an efficient way to solve the DED problem.

Artificial Intelligence Based Demand Side Management Approach to Solve Non-Linear Dynamic Economic Emission Dispatch Problem

Artificial Intelligence Based Demand Side Management Approach to Solve Non-Linear Dynamic Economic Emission Dispatch Problem

Multiobjective Multi Verse Optimization Algorithm to Solve Dynamic Economic Emission Dispatch Problem with Transmission Loss Prediction by an Artificial Neural Network

Multiobjective Multi Verse Optimization Algorithm to Solve Dynamic Economic Emission Dispatch Problem with Transmission Loss Prediction by an Artificial Neural Network

Implementation of β-chaotic mapping to improved elephant herding optimisation to dynamic economic dispatch problem

Implementation of β-chaotic mapping to improved elephant herding optimisation to dynamic economic dispatch problem

Implementation of β-chaotic mapping to improved elephant herding optimisation to dynamic economic dispatch problem

Implementation of β-chaotic mapping to improved elephant herding optimisation to dynamic economic dispatch problem

The Extension of Auxiliary Problem Principle for Solving Dynamic Economic Dispatch Problem in Power Systems

In this paper, we study the convex optimization problem with linear constraint, and the objective function is composed of m separable convex functions. Considering the special case where the objective function is composed of two separable convex functions, the auxiliary problem principle (APP) is an effective parallel distributed algorithm for solving the special case. Inspired by the principle of APP, a natural idea to solve separable convex optimization problem with m ≥ 3 is to extend the method of APP, resulting in the APP‐like algorithm. The convergence of the APP‐like algorithm is not clear yet. In this paper, we give a sufficient condition for the convergence of the APP‐like algorithm. Specifically, the APP algorithm is a special case of the APP‐like algorithm when m = 2. However, simulation results show that the convergence efficiency of the APP‐like algorithm is affected by the selection of penalty parameter. Therefore, we propose an improved APP‐like algorithm in this paper. Simulation results show that the improved APP‐like algorithm is robust to the selection of penalty parameter and that the convergence efficiency of the improved APP‐like algorithm is better when compared with the APP‐like algorithm.

Dynamic Economic Dispatch of Power System Network Having Thermal Units and Electric Vehicles using IGWO

Dynamic economic dispatch (DED) is a complex power system problem. The problem becomes more complex with inclusion of  electric vehicles. In the presented paper,  Improved Grey Wolf Optimizer (IGWO) is proposed to solve this complex problem. IGWO is having a better balance between exploitation and exploration for the complex problem such as  Dynamic Economic Dispatch (DED) taking into account of valve- point effect, transmission losses and ramp-rate limits with and without electric vehicles (EVs). The efficiency of the algorithm is demonstrated on solving different DED problems for 5 generator and 15 generator test systems with and without losses along with different charging profile distribution of electric vehicles.  The results showcased by IGWO is compared with the other algorithm. The results obtained by IGWO algorithm  using repair method adopted in solving dynamic economic dispatch problem is giving competitive results as compared to the results given by other algorithm present in literature.

Virtual-Action-Based Coordinated Reinforcement Learning for Distributed Economic Dispatch

A unified distributed reinforcement learning (RL) solution is offered for both static and dynamic economic dispatch problems (EDPs). Each agent is assigned with a fixed, discrete, virtual action set, and a projection method generates the feasible, actual actions to satisfy the constraints. A distributed algorithm, based on singularly perturbed system, solves the projection problem. A distributed form of Hysteretic Q-learning achieves coordination among agents. Therein, the Q-values are developed based on the virtual actions, while the rewards are produced by the projected actual actions. The proposed algorithm deals with continuous action space and power loads without using function approximations. Theoretical analysis and comparative simulation studies verify algorithm's convergence and optimality.

An enhanced exploratory whale optimization algorithm for dynamic economic dispatch

Dynamic economic dispatch (DED) considering valve-point effects and transmission losses is a complex constrained optimization problem with non-smooth, non-linear and non-convex characteristics which has always been a significant challenge. To tackle the DED problem, an enhanced exploratory whale optimization algorithm (EEWOA) and a constraint handling technique considering the unit efficiency are proposed. Firstly, an adaptive enhanced exploratory prey mechanism is created to enhance population diversity of whale swarm, and the EEWOA method is developed. Secondly, a constraint handling technology is designed to improve the variable repairing ability, including coarse-tuning by heuristics and fine-tuning by forced repair technique. The proposed EEWOA is compared with several state-of-the-art optimization algorithms in terms of efficiency and effectiveness on 13 classical benchmarks, and three DED with different scales. According to the simulation results, EEWOA shows outstanding advantages on the benchmarks and the DED cases.

A novel oppositional learning-based chaotic sine cosine algorithm for the dynamic thermal–wind economic dispatch problem

Wind power generation is efficiently utilized with traditional thermal power generation in the dynamic economic emission dispatch (DEED) problem to achieve the demand power of scheduled periods with minimum generation cost and emission of pollutants. This study uses a novel oppositional learning-based chaotic sine cosine algorithm (SCA) (OL-CSCA) to solve a new model of wind energy-based DEED, called dynamic thermal–wind economic emission dispatch (DTWEED). The concepts of oppositional learning and chaos are introduced into the SCA to strengthen its optimization performance. The effectiveness of the proposed model is tested by solving four cases (generation cost, spinning reserve based generation cost, emission and combined cost–emission) using OL-CSCA. The novelty of DTWEED is shown by comparing the results of different cases with the traditional DEED model. Comparison of the results of OL-CSCA for different cases of DEED and DTWEED with the results of SCA and other algorithms demonstrated its robustness and proficiency.