A direct Newton–Raphson economic emission dispatch

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

An improved Manta ray foraging optimizer for cost-effective 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.

With the increasing concern over environment protection, Economic Emission Dispatch (EED) problem has received much attention. It is essentially a Multi-objective Optimization Problem, which minimizes both fuel cost and emission pollution simultaneously, as well as meets some system limits. This study transforms EED problem to a single-objective problem with weighted sum method, and then use Newton method to solve the equality constraint iteratively and introduce a common penalty function to deal with the inequality constraint. Moreover, this study tries to propose a new meta-heuristic algorithm inspired by kernel tricks to solve EED problem with no hyper parameters to be tuned. The new algorithm can map a non-linear objective function into a linear one with higher-dimension. Thus the optimization process could be transformed into a linear process, which is more likely to get the optimum solution. When applied in the 3 real-world EED cases with valve point, the new algorithm achieved a better performance compared with other algorithms in the literature.

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.

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.

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.

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.

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.

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.

Increasing environmental concerns have led to a push for renewable energy sources to be extensively used to reduce emissions. In this paper, we investigate a hybrid dynamic economic emission dispatch (HDEED) problem involving thermal, wind, and photovoltaic (PV) generation systems. Our formulation considers the stochastic nature of both wind and PV generated power, and differences because of mismatches between the actual and allocated wind and PV power. A hybrid backtracking search algorithm with sequential quadratic programming was used to minimize the total operational costs and emissions, while dispatching power to the committed generation units subject to all operational constraints. To verify the efficacy, we applied the proposed technique to solve the dynamic economic emission dispatch problem on five and ten unit test systems. The proposed technique was also used to solve the HDEED problem on IEEE 30 bus, 6-unit and IEEE 57 bus, 7-unit test systems, with and without renewable generation. The results of our numerical simulations show the efficiency of the proposed technique with respect to reducing operational costs and emissions. Moreover, our results show that by incorporating renewable energy into existing power systems, we can reduce operational costs and emissions.

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.

Multi-objective economic emission dispatch based on an extended crisscross search optimization algorithm

Due to growing concerns over environmental protection, economic and environmentally responsible power dispatching has become a hot topic in the field of power system control. Multi-objective optimization minimizes fuel costs and pollution emissions without violating operational constraints. To solve this problem, the MOP is decomposed into individual objects via the weighted sum method, and Newton’s method is used to tackle equality constraints iteratively. To this end, a hybrid algorithm (HKSOPSO-CP) based on kernel search optimization (KSO) and particle swarm optimization (PSO) with Cauchy perturbation is proposed in this paper. An experiment with 23 CEC benchmark functions shows that HKSOPSO-CP offers better performance compared with various popular algorithms proposed in recent years. When employed to solve the IEEE standard economic emission dispatch (EED) problems with 6, 10, 40, and 110 units, the proposed HKSOPSO-CP algorithm produces results indicating a better trade-off between the objectives relating to fuel costs and emissions compared to other algorithms that have recently been reported on in the literature.

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.