Artificial Bee Colony Algorithm for An Optimal Solution for Combined Economic and Emission Dispatch Problem

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.

Economical dispatch of power is a significant real time optimization problem in the operation of power system, which allocates the loads on the committed generating units to reduce the generation cost, while meeting all the inequality and equality constraints. Traditionally, economic load dispatch problems have been formulated as convex optimization problem and various classical methods such as gradient methods, base-point participation factor method, etc. have been used for solving them. The traditional formulation is a quadratic input-output curve or piece wise linear cost curve, which are continuous and convex, however, real generating units have valve loading effects, which make the cost curve discontinuous and non-convex and hence the economic dispatch problem is no longer simple to handle. Thus, the classical methods cannot be employed for non-convex problems. The non-convex, non-linear and discontinuous economic dispatch (ED) problem can be better solved by metaheuristic approaches. Such approaches often require tuning of their respective evolutionary parameters. Although, solution to such type of problem have already been solved by different metaheuristic optimization techniques in previous studies as well, however, the algorithm employed in this paper to solve Power Economic Load Dispatch (PELD) problem is adaptive real coded quantum-inspired evolutionary algorithm, which does not require tuning of evolutionary parameters and performs better than some of the existing techniques on standard 6-bus 3 machine system and IEEE 14 bus 5 unit system.

In the current scenario Economic Dispatch problem has taken a suitable twist as the public has become increasingly concerned with environmental matters. The dispatch of systems to minimise pollutants, as well as to achieve minimum cost are the two main constraints to be dealt with. In this paper, Global optimization techniques such as Honey Bee’s and Simulated Annealing techniques are employed together (HB-SA) to solve the Combined static Economic and Emission dispatch (CEED) problems in power system. This paper clearly is justified with the results, separately obtained for the above two techniques and is also provided with the results on applying both the algorithms separately. With practical consideration, Economic Dispatch will have non-smooth cost functions with equality and inequality constraints that make the problem, a large-scale highly constrained non linear optimization problem. As to demonstrate the effectiveness of the proposed method, it is subjected to the CEED problems considering (or) handling valve point loading effects. Comparison with other optimization techniques showed the superiority of the proposed HB-SA approach and confirmed its potential for solving nonlinear CEED problems.

Solving non-convex economic load dispatch problem via artificial cooperative search algorithm

Optimizing multiple objectives is a common challenge in complex decision-making scenarios, where improving one objective often comes at the expense of another. In power system generation, two critical objectives must be simultaneously minimized: the total generation cost and the total emissions released. This study introduces a multi-objective optimization method developed to address these dual objectives. The proposed approach aims to identify the optimal solution to the economic dispatch problem, balancing the trade-off between minimizing generation costs and reducing environmental impact by lowering total emissions. Heuristic optimization is used to solve this multi-objective combined economic and emission dispatch (MOCEED) problems through the implementation of Multi-Objective Evolutionary Programming (MOEP). In this study, the Weighted Sum Method (WSM) is combined with the Evolutionary Programming (EP) technique to minimize both objectives. The developed approach is validated on the IEEE 30-Bus RTS, which consists of six generators. The effectiveness of the developed technique is evaluated and compared the results against scenarios without optimization. Simulations are performed using MATLAB software, and the results demonstrate that the proposed Multi-Objective Evolutionary Programming (MOEP) successfully identifies the optimal generator outputs, achieving significant reductions in both total generation cost and emissions. These results highlight the method's capability to provide superior solutions for multi-objective economic dispatch problems.

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.

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.

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

A self adaptive hybrid enhanced artificial bee colony algorithm for continuous optimization problems

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.

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.

Ant lion optimizer (ALO) is a newly developed population-based search algorithm inspired by hunting mechanism of antlions and based on five steps of hunting the ants, i.e., the random walk of ants, building traps, entrapment of ants in traps, catching preys and re-building traps. This paper presents the application of ALO algorithm for the solution of non-convex and dynamic economic load dispatch problem of electric power system. The performance of ALO algorithm is tested for economic load dispatch problem of four IEEE benchmarks of small-scale power systems, and the results are verified by a comparative study with lambda iteration method, particle swarm optimization algorithm, genetic algorithm, artificial bee colony, evolutionary programming and Grey Wolf optimizer (GWO). Comparative results show that the performance of ant lion optimizer algorithm is better than recently developed GWO algorithm and other well-known heuristics and meta-heuristics search algorithms.

Moth flame optimization algorithm is novel nature inspired heuristic paradigm inspired by navigation method of moths in nature and based on the concept that the moth eventually converges toward the light. This paper presents the application of MFO algorithm for the solution of non-convex and dynamic economic load dispatch problem of electric power system. The performance of MFO algorithm is tested for non-convex, convex and dynamic economic load dispatch problem of seven IEEE benchmarks and the results are verified by a comparative study with lambda iteration method, particle swarm optimization algorithm, genetic algorithm (GA), artificial bee colony, evolutionary programming (EP) and grey wolf optimizer (GWO). Also, in the proposed research, the impact of renewable energy sources (i.e. wind and solar) has been taken into consideration along with conventional thermal power generating units. Also, critical analysis has been made for percentage cost saving with due consideration of solar and wind power units and it has been experimentally observed that the addition of renewable energy sources to conventional thermal power system results in significant cost saving. Comparative results show that the performance of Moth Flame Optimizer Algorithm is better than recently developed GWO algorithm and other well known heuristics and meta-heuristics search algorithms.

This paper proposes an efficient chaotic differential harmony search (CDHS) algorithm to solve the dynamic economic and emission dispatch (DEED) problem with security constraints. The main objective of DEED problem is to determine the optimal power generation schedule for the online generating units over a time horizon at the same time satisfying the environmental and security constraints along with other generator constraints. The DEED problem is formulated as a nonlinear constrained multi-objective optimization problem. The fuel cost and emission are considered as two competing objectives. It is converted into a single objective function by introducing a price penalty factor. The price penalty factor blends the emission with the fuel cost. In the proposed algorithm, chaotic variables are introduced instead of random number generator in the differential mutation operator of differential harmony search (DHS) algorithm to accelerate the DHS algorithm to reach the global optimal solution quickly. The effectiveness of the proposed CDHS algorithm is demonstrated on IEEE-30 bus system with valve point effects, ramp rate limits, prohibited operating zones, and security constraints for a period of 24 hours. The simulation results obtained by the proposed CDHS algorithm are compared with DHS algorithm. The optimal solution obtained by the proposed algorithm is better than DHS algorithm in terms of solution quality, speed of convergence and computational time.

The Economic Load Dispatch (ELD) is considered to minimize the only fuel cost in power system planning and operation. Due to environmental issues, the emission amount released by thermal power generation should be considered in minimizing the total cost generation as well. This make the power dispatch problem become multi-objective problem that called Economic and Emission Load Dispatch (EELD). This paper investigates the performances of Artificial Bee colony (ABC) algorithm for determining optimal solution for EELD problem. In this paper, the EELD problem is formulated as a single objective problem by taking minimization of total cost and emission level as separated objective. The cost characteristic of thermal generator considered the effect of opening and closing of the valve for practical application. The ABC algorithm has been tested on standard test systems which is 10-generating unit test system in order to validate the effectiveness of proposed ABC algorithm. The results obtained have been compared with reported result by other methods in literature. From the result, it found that ABC algorithm is better than other methods for minimizing fuel cost of thermal power generation and obtained comparative results in reducing the emission level.