Emission Dispatch Problem Research Articles

A comparative analysis between price‐penalty factor method and fractional programming method for combined economic emission dispatch problem using novel hybrid CSA‐JAYA algorithm

A comparative analysis between price‐penalty factor method and fractional programming method for combined economic emission dispatch problem using novel hybrid CSA‐JAYA algorithm

Dynamic economic emission dispatch using whale optimization algorithm for multi-objective function

Introduction. Dynamic Economic Emission Dispatch is the extended version of the traditional economic emission dispatch problem in which ramp rate is taken into account for the limit of generators in a power network. Purpose. Dynamic Economic Emission Dispatch considered the treats of economy and emissions as competitive targets for optimal dispatch problems, and to reach a solution it requires some conflict resolution. Novelty. The decision-making method to solve the Dynamic Economic Emission Dispatch problem has a goal for each objective function, for this purpose, the multi-objective problem is transformed into single goal optimization by using the weighted sum method and then control/solve by Whale Optimization Algorithm. Methodology. This paper presents a newly developed metaheuristic technique based on Whale Optimization Algorithm to solve the Dynamic Economic Emission Dispatch problem. The main inspiration for this optimization technique is the fact that metaheuristic algorithms are becoming popular day by day because of their simplicity, no gradient information requirement, easily bypass local optima, and can be used for a variety of other problems. This algorithm includes all possible factors that will yield the minimum cost and emissions of a Dynamic Economic Emission Dispatch problem for the efficient operation of generators in a power network. The proposed approach performs well to perform in diverse problem and converge the solution to near best optimal solution. Results. The proposed strategy is validated by simulating on MATLAB® for 5 IEEE standard test system. Numerical results show the capabilities of the proposed algorithm to establish an optimal solution of the Dynamic Economic Emission Dispatch problem in a several runs. The proposed algorithm shows good performance over the recently proposed algorithms such as Multi-Objective Neural Network trained with Differential Evolution, Particle swarm optimization, evolutionary programming, simulated annealing, Pattern search, multi-objective differential evolution, and multi-objective hybrid differential evolution with simulated annealing technique.

Hybrid Flower Pollination Algorithm with Sequential Quadratic Programming Technique for Solving Dynamic Combined Economic Emission Dispatch Problem

This paper presents the solution of highly complex, non-linear, multi-objective Dynamic Combined Economic Emission Dispatch (DCEED) problem. DCEED is a power system optimization problem with conflicting objectives of fuel cost and emission. DCEED includes constraints like valve point loading effect, Transmission Losses and Ramp Rate limits. Solution of DCEED problem is given by a novel Hybridized Flower Pollination Algorithm (FPA) with Sequential Quadratic Programming (SQP). FPA is a nature inspired population based meta-heuristic optimization technique that models its search on the flower pollination process. The non-convex nature of generation because of numerous operational, physical and dynamic constraints, makes search space highly multi model and complex. This makes DCEED a challenging as well as an attractive problem for research. The effectiveness of FPA-SQP is tested and validated by applying it on IEEE Standard 5-unit and 10-unit non-convex test system in MATLAB environment for the time interval of 24 hours. The results achieved by this algorithm show significant reduction in cost and emission as compared to other available techniques in the literature.

Economic and Emission Dispatch Problems Using a New Hybrid Algorithm

Environmental legislation, with its increasing pressure on the energy sector to control greenhouse gases, is a driving force to reduce CO2 emissions, forced the power system operators to consider the emission problem as a consequential matter beside the economic problems, so the economic power dispatch problem has become a multi-objective optimization problem. This paper sets up an new hybrid algorithm combined in two algorithm, the harmony search algorithm and ant colony optimization (HSA-ACO), to solve the optimization with combined economic emission dispatch. This problem has been formulated as a multi-objective problem by considering both economy and emission simultaneously. The feasibility of the proposed approach was tested on 3-unit and 6-unit systems. The simulation results show that the proposed algorithm gives comparatively better operational fuel cost and emission in less computational time compared to other optimization techniques.

A review of optimization methods for economic and emission dispatch considering PV and wind energy

The power generation system has fossil fuels as their major electricity generation source. This source is not reliable and environmentally friendly so, the alternative source such as renewable energy (RE) is getting much attention in the development of a power generation system. To achieve optimal power output for the power system there is a necessity to solve the economic and emission dispatch (EED) problem considering the operational system constraints. Numerous types of research on optimization of fossil fuel cost and emission roles have been focused to solve the concerned power dispatch issue. This paper represents a comprehensive study on combined economic and emission dispatch (CEED) problem with respect to conventional and unconventional energy sources. To optimize the power dispatch problem, the existing algorithm consisting of optimization methods and objective functions in integrated renewable energy sources (RES) system is tested and reviewed. This paper presented various optimization methods applied to different test systems to minimize emission and cost for power dispatch with PV and wind. Future trends and necessary steps next in the field of power dispatch are also been deliberated.

Solving combined economic emission dispatch problem in wind integrated power systems

<p>A meta-heuristic based optimization method for solving combined economic emission dispatch (CEED) problem for the power system with thermal and wind energy generating units is proposed in this paper. Wind energy is environmentally friendly and abundantly available, but the intermittency and variability of wind power affects the system operation. Therefore, the system operator (SO) must aware of wind forecast uncertainty and dispatch the wind power accordingly. Here, the CEED problem is solved by including the nonlinear characteristics of thermal generators, and the stochastic behavior of wind generators. The stochastic nature of wind generators is handled by using probability distribution analysis. The purpose of this CEED problem is to optimize fuel cost and emission levels simultaneously. The proposed problem is changed into a single objective optimization problem by using weighted sum approach. The proposed problem is solved by using particle swarm optimization (PSO) algorithm. The feasibility of proposed methodology is demonstrated on six generator power system, and the obtained results using the PSO approach are compared with results obtained from genetic algorithm (GA) and enhanced genetic algorithms (EGA).</p>

An improved Manta ray foraging optimizer for cost-effective emission dispatch problems

Recently, Manta ray foraging optimization (MRFO) has been developed and applied for solving few engineering optimization problems. In this paper, an elegant approach based on MRFO integrated with Gradient-Based Optimizer (GBO), named MRFO–GBO, is proposed to efficiently solve the economic emission dispatch (EED) problems. The proposed MRFO–GBO aims to reduce the probability of original MRFO to get trapped into local optima as well as accelerate the solution process. The goal of solving optimal Economic Emission Dispatch (EED) is to economically provide all required electrical loads as well as minimizing the emission with satisfying the operating equality and inequality constraints. Single and multi-objective EED problems are solved using the proposed MRFO–GBO and classical MRFO. In multi-objective EED, fuzzy set theory is adapted to determine the best compromise solution among Pareto optimal solutions. The proposed algorithm is firstly validated through well-known CEC’17 test functions, and then applied for solving several scenarios of EED problems for three electrical systems with 3-generators, 5-generators, and 6-generators. The validation is achieved through different load levels of the tested systems to prove the robustness of the proposed algorithm. The results obtained by the proposed MRFO–GBO are compared with those obtained by recently published optimization techniques as well as the original MRFO and GBO. The results illustrate the ability of the proposed MRFO–GBO in effectively solving the single and multi-objective EED problems in terms of precision, robustness, and convergence characteristics.

Solving dynamic economic and emission dispatch in power system integrated electric vehicle and wind turbine using multi-objective virus colony search algorithm

Climate change and development of today’s power grids have led to unprecedented changes in the old power grid in terms of fossil fuel consumption level and environmental pollution. So, the ancillary power plants and services have found a good position in power systems. In this paper, renewable energy generators such as wind energy units and plug-in electric vehicles (PEVs) are being integrated in the multi-objective dynamic economic emission dispatch (DEED) problem during a day, which minimizes wind-thermal electrical energy cost and emissions obtained by fossil-fueled power generators at the same time. To obtain a real-world problem, consider several practical and nonlinear constraints such as valve-point effect, ramp-up/ramp-down, prohibited zones, and power generation boundaries. Since the proposed multi-objective problem consists of different variables and constrains, the classical mathematic methods cannot guarantee finding the best solution. Therefore, this paper suggested a new multi-objective virus colony search (MOVCS) based on non-dominated sorting theory and fuzzy decision making for finding the best solution among Pareto fronts. Also, PEVs are remarkable and stochastic power demands and, unlike conventional demands, four dissimilar charging scenarios are considered. The efficiency of the proposed method and model is investigated on some test systems with the presence of wind units and electric vehicles during the day and night. The results are evaluated based on appropriate performance criteria. The results obtained from the proposed algorithm are compared with other algorithms, which indicates the efficiency, accuracy, and speed of this algorithm in solving the proposed problem.

Solution of Combined Economic Emission Dispatch Problem Using Improved and Chaotic Population-Based Polar Bear Optimization Algorithm

This paper proposes a novel improved polar bear optimization (IPBO) algorithm and employs it along with polar bear optimization (PBO) and chaotic population-based variants of polar bear optimization algorithm to solve combined economic emission dispatch (CEED) problem. PBO is a meta-heuristic technique inspired by the hunting mechanisms of polar bears in harsh arctic regions based only on their sense of sight. Polar bears in nature exhibits hunting of prey not only on their sight but also on their keen sense of smell. Hence, a novel improved variant of PBO which enhances its operation by equipping it with tracking capabilities utilizing polar bears sense of smell has been proposed in this study. The validity of novel IPBO is tested through 5 benchmark functions and 140 units Korean ED problem. Furthermore, the impact of different population initialization methods is also observed on the capabilities of conventional PBO. The proposed chaotic population based PBO, improved PBO (IPBO) and PBO are employed to solve IEEE 3 unit and 6-unit CEED problem. CEED is a multi-objective power system optimization problem with conflicting objectives of cost and emission. The simulations performed undertake each objective individually as well as collectively. The results achieved by each technique are analyzed statistically through Wilcoxon rank sum test (WRST), probability density function and cumulative density function. Both the statistical and numerical analysis of results showcase the strength of each solution technique as well as their ability to improve cost and emissions in the solution of CEED problem.

Developing Chaotic Artificial Ecosystem-Based Optimization Algorithm for Combined Economic Emission Dispatch

In this paper, Chaotic Artificial Ecosystem-based Optimization Algorithm (CAEO) is proposed and utilized to determine the optimal solution which achieves the economical operation of the electrical power system and reducing the environmental pollution produced by the conventional power generation. Here, the Combined Economic Emission Dispatch (CEED) problem is represented using a max/max Price Penalty Factor (PPF) to confine the system's nonlinearity. PPF is considered to transform a four-objective problem into a single-objective optimization problem. The proposed modification of AEO raises the effectiveness of the populations to achieve the best fitness solution by well-known 10 chaotic functions and this is valuable in both cases of the single and multi-objective functions. The CAEO algorithm is used for minimizing the economic load dispatch and the three bad gas emissions which are sulfur dioxide (SO2), nitrous oxide (NOx), and carbon dioxide (CO2). To evaluate the proposed CAEO, it is utilized for four different levels of demand in a 6-unit power generation (30-bus test system) and 11-unit power generation (69-bus test system) with a different value of load demand (1000, 1500, 2000, and 2500MW). Statistical analysis is executed to estimate the reliability and stability of the proposed CAEO method. The results obtained by CAEO algorithm are compared with other methods and conventional AEO to prove that the modification is to boost the search strength of conventional AEO. The results display that the CAEO algorithm is superior to the conventional AEO and the others in achieving the best solution to the problem of CEED in terms of efficient results, strength, and computational capability all over study cases. In the second scenario of the bi-objective problem, the Pareto theory is integrated with a CAEO to get a series of Non-Dominated (ND) solutions, and then using the fuzzy approach to determine BCS.

Novel Emission Dispatch for Adding Electric Vehicles and Renewable Energy Sources With Short-Term Frequency Stability

This research proposes a novel emission dispatch formulation which solves for the optimal amount of electric vehicles (EVs) and renewable energy sources (RES) that minimizes emission while ensuring short-term frequency stability of the power system. Unlike emission dispatch of previous research, which often neglected the added risks associated with more RES, the proposed formulation is characterized by the addition of (a) short-term frequency stability constraint and (b) EVs and RES capacity defined as part of the optimization variables. These two characteristics are utilized to solve for a risk-inclusive solution to the emission dispatch problem which gives a more realistic prospect to reducing emissions. Three test areas, loosely based on OECD countries, illustrate the effect of the proposed formulation where several insights about emission reductions are revealed.

Multi-objective Optimization of Combined Economic Emission Dispatch Problem in Solar PV Energy Using Hybrid Bat-Crow Search Algorithm

The current paper deals with multi-objective fuel cost optimization of a conventional power plant (CPP) and emission minimization in CPPs and Solar PV Power Plants (SPVPPs) using hybrid Bat-Crow search algorithm. To resolve this complicated, non-convex, and excessively nonlinear problem, a variety of meta-heuristic optimization algorithms are developed and effectively employed. To handle the evolutionary multi-objective algorithms’ inadequacies like early convergences, slowly meeting Pareto-optimal front, and narrow trapping, generally applying a combination of different algorithms is unusual. This paper presents the hybrid evolutionary multi-objective optimization process, which is based on combining the Crow search optimization with the Bat algorithm for dealing with the combined economic emission dispatch (CEED) through SPVPP. A hybrid technique combined with the proposed constriction handling method can balance out exploitation and exploration tasks. Different IEEE standard bus systems were tested with the proposed hybrid method using the quadratic cost function and monitoring the transmission losses. The result of proposed algorithm is compared with Bat, PSO and Crow Search Algorithm. The proposed method can be effective with the simulation results.

Constrained Multiobjective Equilibrium Optimizer Algorithm for Solving Combined Economic Emission Dispatch Problem

This research implements a recent evolutionary‐based algorithm of equilibrium optimizer to resolve the constrained combined economic emission dispatch problem. This problem has two objective functions that represent the minimizing of generation costs and minimizing the emission of environmental pollution caused by generators. The proposed algorithm integrates the dominant criteria for multiobjective functions that allow the decision‐maker to detect all the Pareto boundaries of constrained combined economic emission dispatch problem. In order to save the effort for the decision‐maker to select the best compromise alternative, a cluster study was carried out to minimize the size of the Pareto boundary to an acceptable size, representing all the characteristics of the main Pareto frontier. On the other hand, in order to deal with the infringement of constraints, a repair algorithm was used to preserve the viability of the particles. The proposed algorithm is applied to solve the standard 30‐bus IEEE system with 6 generators to validate its robustness and efficiency to produce a well‐distributed Pareto frontier for constrained combined economic emission dispatch problem. Compared with other studies, good results in solving constrained combined economic emission dispatch problem are obtained and a reasonable reduced Pareto set is found.

An agile and intelligent dynamic economic emission dispatcher based on multi-objective proximal policy optimization

The recent development in power systems claims the improvement of the efficiency to solve dynamic economic emission dispatch (DEED) problem. However, the popular pure optimization framework based on evolutionary algorithms only starts the compute-intensive optimization process after receiving the power demand, which causes significant delays To address this limitation, this research defines a novel dynamic economic emission dispatcher (DEEDer) problem and the dispatcher learning framework. It is different from previous research and the most current algorithms in the advantage of transferring the on-line compute-intensive optimization task to off-line. To solve the dispatcher, we model the dispatching process as a conditional deterministic Markov Decision Process (MDP) and propose the multi-objective proximal policy optimization (MOPPO). The Benchmark Test Set with 10,000 different dispatching tasks for 5-unit and 10-unit system is released to evaluate the generalization of the dispatcher. The experiment results indicate that the neural network dispatcher trained with MOPPO is hundreds to thousands of times faster than the state-of-the-art pure optimization algorithms. Meanwhile, the dispatcher not only has comparable performance as the state-of-the-art multi-objective optimization algorithms in standard dispatching task but also shows generalization on generating Pareto optimal solutions given any possible dispatching task. Following the DEEDer framework, the proposed method makes it possible to dispatch power in a more agile way as the timely response to the changing of power demand while still controlling economic and emission.

A quantum class topper optimization algorithm to solve combined emission economic dispatch problem

A combined emission and economic dispatch problem is referred as a complex multi-objective problem related to power system. In this article, an hybridized version of class topper optimization known as quantum class topper optimization is proposed to solve this problem. In quantum class topper optimization, quantum mechanism is used to enhance the searching ability of the proposed algorithm. The exploration, exploitation and convergence behavior of quantum class topper optimization is validated using benchmark functions. Later, four test cases on combined emission and economic dispatch are used to test the effectiveness of quantum class topper optimization. These four tests prove that the proposed optimization algorithm is effective to solve this real time optimization problem.

Multi-objective learning backtracking search algorithm for economic emission dispatch problem

The backtracking search algorithm (BSA) as a novel intelligent optimizer belongs to population-based evolutionary algorithms. In this paper, a multi-objective learning backtracking search algorithm (MOLBSA) is proposed to solve the environmental/economic dispatch (EED) problem. In this algorithm, we design two novel learning strategies: a leader-choosing strategy, which takes a sparse solution from an external archive as leader; a leader-guiding strategy, which updates individuals with the guidance of leader. These two learning strategies have outstanding performance in improving the uniformity and diversity of obtained Pareto front. The extreme solutions, compromise solution and three metrics obtained by MOLBSA are further compared with those of well-known multi-objective optimization algorithms in IEEE 30-bus 6-unit test system and 10-unit test system. Simulation results demonstrate the capability of MOLBSA in generating well-distributed and high-quality approximation of true Pareto front for the EED problem.

Performance Assessment of a set of Multi-Objective Optimization Algorithms for Solution of Economic Emission Dispatch Problem

This paper addresses the realistic economic emission dispatch (EED) problem by considering the operating fuel cost and environmental emission as two conflicting objectives, and power balance and generator limits as two constraints. A novel dynamic multi-objective optimization algorithm, namely the multi-objective differential evolution with recursive distributed constraint handling (RDC-MODE) has been proposed and successfully employed to address this challenging EED problem. It has been thoroughly investigated in two different test cases at three different load demands. The efficiency of the RDC-MODE is also compared with two other multi-objective evolutionary algorithms (MOEAs), namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swam optimization (MOPSO). Performance evaluation is carried out by comparing the Pareto fronts, computational time and three non-parametric performance metrics. The statistical analysis is also performed, to demonstrate the ascendancy of the proposed RDC-MODE algorithm. Investigation of the performance metrics revealed that the proposed RDC-MODE approach was capable of providing good Pareto solutions while retaining sufficient diversity. It renders a wide opportunity to make a trade-off between operating cost and emission under different challenging constraints.

Assessment of Dynamic Economic and Emission Dispatch Problem using WOA in Networked Grids with Photovoltaic Power Injection

Since decades, the main aim for the researchers is to get reliable and inexpensive electricity out of available resources. Till now, different economic dispatch methods have been developed to meet the challenges of continuous and sustainable electricity production at optimized cost. Due to the increase of public awareness on environmental protection, the utilities have forced to use renewable energy sources to modify the operation strategies to reduce the pollution and atmospheric emissions produced due to power plants. This paper represents the allocation of dynamic economic emission dispatch (DEED) problem involving thermal and photovoltaic (PV) generation system as hybrid dynamic economic emission dispatch (HDEED) to meet the minimization of both the cost of fuel and emission simultaneously. Whale optimization algorithm (WOA) is used to minimize the total cost of operation and emission levels while dispatching power to committed generation units considering all operational constraints. To show the efficiency, the proposed technique is applied to solve the dynamic economic emission dispatch problem on 5- and 10-unit test systems. The technique is also used to solve the HDEED problem on IEEE 30-bus 6-unit and IEEE 57-bus 7-unit test system with and without renewable generation. The results obtained after injection of photovoltaic power into existing power systems show the effectiveness of the proposed techniques to reduce the cost of operation and emission levels.

An Elitist Multi-Objective Particle Swarm Optimization Algorithm for Sustainable Dynamic Economic Emission Dispatch Integrating Wind Farms

In recent years, wind energy has been widely used as an alternative energy source as it is a clean energy with a low running cost. However, the high penetration of wind power (WP) in power networks has created major challenges due to their intermittency. In this study, an elitist multi-objective evolutionary algorithm called non-dominated sorting particle swarm optimization (NSPSO) is proposed to solve the dynamic economic emission dispatch (DEED) problem with WP. The proposed optimization technique referred to as NSPSO uses the non-dominated sorting principle to rank the non-dominated solutions. A crowding distance calculation is added at the end of all iterations of the algorithm. In this study, WP is represented by a chance-constraint which describes the probability that the power balance cannot be met. The uncertainty of WP is described by the Weibull distribution function. In this study, the chance constraint DEED problem is converted into a deterministic problem. Then, the NSPSO is applied to simultaneously minimize the total generation cost and emission of harmful gases. To proof the performance of the proposed method, the ten-unit and forty-unit systems—including wind farms—are used. Simulation results obtained by the NSPSO method are compared with other optimization techniques that were presented recently in the literature. Moreover, the impact of the penetration ratio of WP is investigated.

Solution to the Economic Emission Dispatch Problem Using Numerical Polynomial Homotopy Continuation

The economic emission dispatch (EED) is a highly constrained nonlinear multiobjective optimization problem with a convex (or nonconvex) solution space. These characteristics and constraints make the EED a difficult problem to solve. Several approaches for a solution have been proposed, such as deterministic techniques, stochastic techniques, or a combination of both. This work presents the use of an algebraic (deterministic) technique, the numerical polynomial homotopy continuation (NPHC) method, to solve the EED problem. A comparison with the sequential quadratic programming (SQP) algorithm and the nondominated sorting genetic algorithm II (NSGA-II) is also presented. Results show that the NPHC algorithm finds all the roots (solutions) of the problem starting from any initial point and assures an accurate solution with a good convergence time. In addition, the NPHC algorithm provides a more accurate solution than the SQP algorithm and the NSGA-II.