A Reduced Subgradient Algorithm for Solving Combined Economic Emission Dispatch Problem with Valve Point Effect in Power Grid

This paper deals with dynamic combined economic emission dispatch problem of an electric power system consisting of thermal, hydro and photovoltaic (PV) power plants. Mathematical models of these plants as well as the model of dynamic combined economic-environmental nonlinear optimization problem are given. The proposed optimization model was implemented in publicly available GAMS software, and the result is the optimal load distribution among the plants during a one-day optimization period. The software is applied to the power system without PV power plants and with a number of new PV plants added to the existing hydrothermal system. The results quantify the positive effects of PV power plants on both fuel cost and greenhouse gas reduction and recommendations are given related to the application of PV generation in modern systems. Software efficiency in solving both dynamic economic dispatch (DED) and dynamic combined economic emission dispatch (DCEED) problems is discussed, and the conclusions are drawn about its application possibilities.

The objective of the economic dispatch problems of electrical power generation is to schedule the committed generating units output so as to meet the required load demand while satisfying the system equality and inequality constraints. This paper solves the combined economic emission dispatch problem by using various price penalty factor approaches and Lagrange's method. The price penalty factor for the combined economic emission dispatch (CEED) problem is the ratio of fuel cost to emission value. Most of the existing papers use Max-Max Price penalty factor for the CEED problem. This paper analyses and compares the impact of four different penalty factors over the optimization solution and convergence of the calculation procedure for the CEED problem. The considered penalty factors are Min-Max, Max-Max, Min-Min and Max-Min price penalty factors. The CEED problem is solved for the IEEE 30 bus system and an Indian utility system with six generating units using various price penalty factors. The simulated results show that Min-Max price penalty factor gives the best optimization solution in comparison to other price penalty factors for the CEED problem.

In this research, a quantum computing idea based bat algorithm (QBA) is proposed to solve many-objective combined economic emission dispatch (CEED) problem. Here, CEED is represented using cubic criterion function to reduce the nonlinearities of the system. Along with economic load dispatch, emissions of SO2, NOx, and CO2 are considered as separate three objectives, thus making it a four-objective (many-objective) optimization problem. A unit-wise price penalty factor is considered here to convert all the objectives into a single objective in order to compare the final results with other previously used methods like Lagrangian relaxation (LR), particle swarm optimization, and simulated annealing. QBA is applied in six-unit power generation system for four different loads. The obtained results show QBA successfully solve many-objective CEED problem with greater superiority than other methods found in the literature in terms of quality results, robustness, and computational performance. In the end of this paper, a detailed future research direction is provided based on the simulation results and its analysis. The outcome of this research demonstrates that the inclusion of quantum computing idea in metaheuristic technique provides a useful and reliable tool for solving such many-objective optimization problem.

Power generation system largely depends on fossil fuels to generate electricity. Due to various reasons, the reserves of fossil fuels are declining and will become too expensive in near future. At the same time, generation of power from fossil fuels causes hazardous gases and particulates to emit, which pollutes the air and causes significant and long term damages on the environment. For this reason, extensive research works have been conducted for last few decades from different perspectives to reduce both the fuel cost as well as the emission of hazardous gases in power generation system. This power generation problem is commonly referred to as the combined economic emission dispatch (CEED) problem. This paper provides a comprehensive review on the uses of different optimization techniques to solve CEED problem. Authors have found advanced nature-inspired methods as the most suitable and successful, and have concluded combinational hybrid methods as the most prospective methods to solve CEED problem.

In this paper, a new variant of harmony search algorithm called self-adaptive differential harmony search (SADHS) algorithm is proposed to solve the combined economic emission dispatch (CEED) problems. The proposed algorithm is tested on 6- and 40 unit test systems to show the effectiveness. The simulation results obtained by the proposed algorithm are compared with the results of differential harmony search (DHS) algorithm. The results obtained by the proposed algorithm are found to be better than DHS algorithm in terms of quality of solution, speed of convergence and CPU time.

The objective of the economic dispatch problem of electrical power generation is to schedule the committed generating unit's output so as to meet the required load demand while satisfying the system equality and inequality constraints. This paper solves the combined economic emission dispatch problem by Min-Max and Max-Max price penalty factor approaches using Lagrange's method. The price penalty factor for the combined economic emission dispatch (CEED) is the ratio of fuel cost to emission value. The literature papers reported that most of them use Max-Max Price penalty factor for the CEED problem. This paper analyses Min-Max and Max-Max price penalty factors for CEED problem. This problem is solved for a five generator system by considering the valve point effect for both fuel cost and emission function. The total fuel cost by considering valve point effect of the combined economic emission dispatch problem is less when using Min-Max price penalty factor approach in comparison to Max-Max price penalty factor.

A power system operation at minimum cost is no longer the only measure for electrical power dispatch. Combined Economic Emission Dispatch (CEED) problem is attained by considering both the economy and emission objectives with necessary constraints. The stability of the power system is also considered as an important factor in the performance of the power system. Several optimization techniques are slow for such complex optimization tasks and are not suitable for on-line use. This paper presents an effective optimization algorithm, for solving security constrained combined economic emission dispatch problem. Also, the power system stability plays an important role in power system. Power system stability criteria are also considered in this paper for better performance of the entire power system. In this paper, an efficient optimization technique called Modified Artificial Bee Colony Optimization is used to solve the CEED problem. The performance of the proposed approach is compared with the other optimization techniques. The experimental result shows that the proposed system results in better solution for CEED problem with the maintenance of system stability.

Microgrid is a novel small-scale system of the centralized electricity for a small-scale community such as villages and commercial area. Microgrid consists of micro-sources like distribution generator, solar and wind units. A microgrid is consummate specific purposes like reliability, cost reduction, emission reduction, efficiency improvement, use of renewable sources and continuous energy source. In the microgrid, the Energy Management System is having a problem of Economic Load Dispatch (ELD) and Combined Economic Emission Dispatch (CEED) and it is optimized by meta-heuristic techniques. The key objective of this paper is to solve the Combined Economic Emission Dispatch (CEED) problem to obtain optimal system cost. The CEED is the procedure to scheduling the generating units within their bounds together with minimizing the fuel cost and emission values. The newly introduced Interior Search Algorithm (ISA) is applied for the solution of ELD and CEED problem. The minimization of total cost and total emission is obtained for four different scenarios like all sources included all sources without solar energy, all sources without wind energy and all sources without solar and wind energy. In both scenarios, the result shows the comparison of ISA with the Reduced Gradient Method (RGM), Ant Colony Optimization (ACO) technique and Cuckoo Search Algorithm (CSA) for the two different cases which are ELD without emission and CEED with emission. The results are calculated for different Power Demand of 24 h. The results obtained to ISA give comparatively better cost reduction as compared with RGM, ACO and CSA which shows the effectiveness of the given algorithm.

Multiobjective multi-verse optimization algorithm to solve combined economic, heat and power emission dispatch problems

Economic load dispatch is one of the vital purposes in electrical power system operation, management and planning. Economic dispatch problem is one of the most important problems in electric power system operation. In large scale system, the problem is more complex and difficult to find out optimal solution because it is nonlinear function and it contains number of local optimal. Combined economic emission dispatch (CEED) problem is to schedule the committed generating units outputs to meet the required load demand at minimum operating cost with minimum emission simultaneously. The main aim of economic load dispatch is to reduce the total production cost of the generating system and at the same time the necessary equality and inequality constraints should also be fulfilled. This leads to the development of CEED techniques. There are various techniques proposed by several researchers to solve CEED problem based on optimization techniques. But still some problems such as slower convergence and higher computational complexity exist in using the optimization techniques such as GA for solving CEED problem. This paper proposes an efficient and reliable technique for combined fuel cost economic optimization and emission dispatch using the Modified Ant Colony Optimization algorithm (MACO) to produce better optimal solution. The simulation results reveal the significant performance of the proposed MACO approach.

In past two decades solution to the Dynamic Economic Load Dispatch (DELD) problem considering emission and transmission losses along with Valve Point Loading (VPL) effect has been investigated by researchers using several meta-heuristic techniques. Numerical techniques such as lambda iteration method, dynamic programming etc. have been unable to solve the ELD problem with VPL effect. This paper presents a systematic performance evaluation of meta-heuristic techniques named as Particle Swarm Optimization and the Genetic Algorithm for combined economic emission dispatch problem considering Valve Point Loading (VPL) to meet 24 hr. load profile on IEEE 9 bus test case with 3 generator units.

The geographically spatial and controlled distribution of fossil fuel resources, catastrophic global warming, and depletion of fossil fuel resources have forced us to integrate zero- or low-emissions energy resources, such as wind and solar, in the generation mix. These renewable energy resources are unexhausted, available around the globe, and free of cost. The advancement in wind and solar technologies has caused an appreciable decrease in installed the and global levelized costs of electricity via these sources. Therefore, the penetration of renewable energy resources in the generation mix can provide a promising solution to the above-mentioned problems. The aim of simultaneously reducing fuel consumption in terms of “Fuel Cost” and “Emission” in thermal power plants is called a combined economic emission dispatch problem. It is a combinatorial and multi-objective optimization problem. The solution of this problem is to allocate the load demand and losses on the committed units in such way that the overall costs of the generation and emission of thermal units are reduced, while the legal bounds (constraints) are met. It is a highly non-linear and complex optimization problem. The valve-point loading effect makes this problem non-convex. The addition of renewable energy resources (RERs) adds more complexities to this problem because they are intermittent. In this work, chaotic salp swarm algorithms (CISSA) are used to solve the combined economic emission dispatch problem. Chaos is used as an alternative to randomization for the tuning of the control variable to improve the trait of obtaining global extrema. Different test cases having different combinations of thermal, solar, and wind units are solved using the proposed algorithm. The results show the superiority of this study in comparison to the existent research results in terms of the cost of generation and emissions.

Mathematical optimization provides the best possible results to a problem. The latest trend in optimization, called hybrid optimization methods, combines two or more optimization techniques, deterministic and non-deterministic, with the aim of overcoming the limitation of one technique by the advantage(s) of the other technique(s). A hybrid particle swarm bat algorithm optimization technique that uses the frequency tuning technique of bat algorithm at the velocity updating stage in particle swarm optimization (PSO) was developed for avoiding premature convergence limitation of PSO using the potential of BA to escape being trapped at local optimum. Implementation of the developed optimization method for solving the combined economic emission dispatch problem of 28 Bus 7 Generators Nigeria power network showed that H-PS-BA optimization method performed better than PSO by 0.07%. Cite this article as: T. Muhammed Adekilekun, A. Gafari Abiola, O. Muniru Olajide, S. Mufutau Adewolu and B. Isaac Adekunle, "Hybrid optimization technique for solving combined economic emission dispatch problem of power systems," Turk J Electr Power Energy Syst, 2022; 2(2), 158-167.

To overcome the challenges of conventional power systems, such as increasing power demand, requirements of stability and reliability, and increasing integration of renewable energy sources, the concept of microgrids was introduced and is currently one of the most important solutions for solving the mentioned problems. Generally, microgrids have two operating modes, namely grid-connected and islanded modes. Based on the literature and its unique characteristics, the islanded mode is more challenging than the other one. In this paper, a new self-adaptive comprehensive differential evolution (SACDE) algorithm is proposed for solving economic load dispatch (ELD) and combined economic emission dispatch (CEED) problems, achieving optimal power consumption in isolated microgrids. Initially, SACDE is employed for solving the ELD problem as a single-objective function, meaning that the operational cost is just considered as the objective function, and thereby, the resources are scheduled accordingly. Then, a multi-objective platform based on SACDE is also proposed to solve the CEED problem. It means two objective functions, including operational cost and emission, are simultaneously optimized. For evaluating the performance of the proposed method, three different scenarios under various cases are considered. According to the results, when SACDE is employed to solve the single objective function (cost minimization) problem, it has better performance than other methods. In terms of the bi-objective scheme (cost and emission minimization), SACDE is significantly superior to the price penalty factor technique which is frequently used in previous studies.

This article presents a new optimization approach called the Wild Horse Optimizer (WHO). It is designed to be user-friendly, effective, and to converge rapidly when addressing economic dispatch (ED). Given that ED is a nonlinear and complex optimization problem, the primary goal of the WHO is to minimize overall generation costs while adhering to the system's equality and inequality constraints. The Combined Economic Emission Dispatch (CEED) problem is also considered, which considers the environmental impacts stemming from the emissions of gaseous pollutants produced by fossil-fueled power plants. To demonstrate the capabilities of the WHO, various networks with 3, 6, 10, 13, 15, and 40 stations have been tested and applied to resolve multiple ED scenarios, including factors such as valve point effects, losses, and prohibited operating zones. The simulation results indicate that the WHO's approach is significantly more effective than the methods found in current academic literature. This analysis highlights the strengths of the WHO's strategies compared to alternatives, suggesting they may offer better solutions to the challenges identified in previous studies.