An Evolutionary Framework for Bi-objective Dynamic Economic and Environmental Dispatch Problems

The dynamic economic dispatch (DED) problem is an extension of the conventional static load dispatch problem in the context of electrical power generation. In this paper, issues related to the implementation of the several soft computing techniques are highlighted for a successful application to solve dynamic economic dispatch (DED) problem, which is a constrained optimization problem in power systems. First of all, a survey covering the basics of the techniques is presented and then implementation of the techniques in the DED problem is discussed. The soft computing techniques, namely multi-layered perceptron neural network (MLP NN), genetic algorithm (GA), Imperialist Competitive Algorithm(ICA), particle swarm (PSO) and are applied to solve the DED problem. The Evolutionary Algorithms are tested on power system consisting 3 generating units and the results are compared together. Suggestion is presented to improve techniques.

Single period economic dispatch cannot handle the intertemporal constraints in multi-period environment. To cope with this issue, the extension of economic dispatch over multiple time intervals (i.e., dynamic economic dispatch) has been introduced that considers the intertemporal constraints between different time intervals. Another issue is determining the most economical generation dispatch that could supply the area demand without violating the tie-line capacity, which cannot be solved by conventional economic dispatch problems. However, this study shows that the most economic schedule of power generation cannot satisfy echo-system expectation; therefore, making a compromise between fuel cost and environmental issues, a hot-button subject in industrialized nations, seems to be crucial. To reach the goals a bi-objective multi-area dynamic economic dispatch approach, which can handle intertemporal and multi-area constraints concurrently, is proposed to assist power system operators more and more. Finally, a hybrid algorithm, namely gray wolf optimizer-particle swarm optimization is introduced to solve the proposed problem and also a set of benchmark problems. By implementing the proposed approach on two small (10-unit, three areas) and large (40-unit, four areas) scale test systems, about 3.1% and 3.3% improvement in generation cost is obtained, respectively compare to the best reported results in the literature.

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.

This article introduces a relatively current method named grasshopper optimization algorithm (GOA) for explaining power system based dynamic economic load dispatch (DELD) problem. However, like other optimization approaches, GOA suffers from premature convergence and a slow convergence rate. Thus, to boost the convergence mobility of GOA, oppositional based learning (OBL) is merged with the GOA approach. Moreover, another improvization, namely, chaotic concept, is also integrated with the GOA to improve its solution quality. The suggested oppositional based chaotic grasshopper optimization algorithm (OCGOA) method is applied to handle the DELD problem in the most efficient manner. Among the renewable energies, intermittent wind energy (WE) is the most sustainable one and remains technically and economically advantageous for electrical energy generation. The thermal and wind based power systems are hybridized, so that power generation is distributed among the operating units in an equivalent manner such that overall cost and loss part are optimized until all practical constraints are fulfilled. The production cost of the unpredictable wind generation power is further incorporated in the operational cost by employing a probability density function (PDF) formula. The precision and performance of the suggested GOA and OCGOA approaches are validated on 6-unit and 10-unit DELD systems for conventional and wind based energy systems. The efficacy and performance of the suggested OCGOA is judged by comparing it with conventional GOA and other presently developed meta-heuristic optimization techniques found in the literature.

This paper introduces a hybrid mutualism based pathfinder algorithm (mPFA) for solving the bid-based dynamic economic load dispatch (BBDED) problem by taking into consideration of various bidding strategies in a deregulated environment. In a deregulated environment BBDED problem is evolved to achieve different goals, such as resource scheduling, maximize social profits, and simultaneously to intend power system security. The IEEE-30 bus test system is considered, which contains 6-power generators and 2-consumers who are supposed to bid in two separate trading periods under various bidding strategies in a day-ahead electricity market. The market co-ordinator known as independent system operator (ISO) matches different bids received from supply and demand side participants and tries to maximize the social profit. In this work, a novel hybrid meta-heuristic algorithm, namely mPFA is proposed, which combines the Pathfinder algorithm (PFA) and the mutualism phase of the Symbiotic Organisms Search (SOS) algorithm. The proposed mPFA scheme avoids the slow and premature convergence of original PFA by exploration with PFA and exploitation with the mutualism phase of SOS. The proposed hybrid scheme was compared to different meta-heuristic algorithms, including Pathfinder algorithm (PFA), Differential Evolution (DE) algorithm, particle swarm optimizer (PSO), and Salp Swarm Algorithm (SSA). The simulation results show that mPFA has the capability and adequacy to solve BBDED.

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.

This paper presents the application of Competitive Swarm Optimizer (CSO) for solving bid-based dynamic economic dispatch (BBDED) problem considering transmission line loss under various bidding strategy. In a competitive electricity market, the bid-based dynamic economic dispatch is evolved to achieve resource scheduling and to maximize social profits. The IEEE-30 bus test system with 6-generator, two trading period and two customers under different bidding strategies in the day-ahead electricity market is considered. The Independent System Operator (ISO) maximizes the social profit by matching the bids received from the supply and demand side. The simulation results of CSO are compared with the Differential Evolution (DE) algorithm, Salp Swarm Algorithm (SSA) and particle swarm optimizer (PSO). The simulation results demonstrate the potential and effectiveness of CSO to solve BBDED.

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.

The krill herd (KH) approach is proposed in this article for tackling the dynamic economic dispatch (DED) problem with the integration of wind power generation, including constraints such as valve-point loadings and prohibited operating zones (PoZs). The purpose of resolving the DED problem is to determine the optimum feasible combination of power outputs for all allocated generating units within a given period while simultaneously meeting dynamic operational constraints and power demand. Due to the addition of valve points and PoZs to the cost characteristics of the generating unit, the DED issue becomes a highly non-linear and non-convex optimization issue. When transmission losses are taken into account, the DED problem becomes significantly more complex to solve. KH is a swarm-inspired algorithm based on krill individual herding behavior. KH employs two global and two local tactics, and these work in parallel, making KH a powerful algorithm. The effectiveness of the KH method is investigated and validated through extensive testing on various test systems, including 5-, 6-, 10-, 16-, and 30-unit test systems. Extensive studies are conducted to evaluate the efficacy of the proposed KH algorithm; the present research work compares the convergence properties of the suggested approach with those of the other recently published methods. In addition to reduced generation costs compared to other results published in recent literature, the numerical findings of the KH approach reveal that it has strong convergence qualities.

The simplicity and robustness of the artificial bee colony (ABC) algorithm has attracted the attention of optimisation researchers. Although ABC has fewer tuned parameters, making it an easy-to-use tool, it has shown better performance than other prominent optimisation algorithms such as differential evolution (DE), evolutionary algorithms (EA) and particle swarm optimisation (PSO) algorithms at solving optimisation problems. Despite these advantages, researchers have found that the standard ABC actually suffers from slow convergence speed on unimodal functions and is often trapped in local minima of multimodal functions. Most problematically, it does not balance the exploitation and exploration stages, leading to various inefficiencies in terms of capability. This paper presents a new ABC variant referred to as JA-ABC4b, which has been formulated to balance exploitation and exploration in order to boost optimisation performance. JA-ABC4b has been experimentally tested on 27 benchmark functions and economic environmental dispatch (EED) problems. The results have revealed a robust performance of JA-ABC4b in comparison to other existing ABC variants and other optimisation algorithms.

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.

Differential Evolution (DE), a vector population based stochastic optimization method has been introduced to the public in 1995. During the last 25 years research on and with DE has reached an impressive state, yet there are still many open questions, In this paper ,An improved differential evolution (IDE) algorithm was presented for power system Dynamic economic dispatch(IDED), Dynamic economic dispatch (DED), an extension of the economic dispatch problem, is a method of scheduling the online generators with a predicted load demand over acertain period of time taking into account the various constraints imposed on the system operation. The results indicate that IDE algorithm outperforms GA ,PSO and DE algorithms in solving DED problems.

Energy management system (EMS) in microgrids (MGs) encompasses both dynamic economic dispatch (DED) and dynamic emission dispatch problems, known as dynamic economic emission dispatch (DEED). In this paper, this system is implemented for an MG with different distributed generations. The aim of 24-hour-cycle scheduling is to determine the generation level of diesel generators (DGs), participation rate of responsive loads and their incentives, charging/discharging status of the battery, and the amount of exchanged energy with the main grid. The scheduling task is performed with the objectives of minimizing operation costs and emissions and maximizing the benefit of MG operator (MGO) resulting from the demand response (DR). Due to their interactive operation, the customers’ behavioral model and the relevant cost functions have a significant impact on the optimal operation. In this paper, the cost function of customers is developed in the incentive-based DR program (DRP) with the aim of receiving a more realistic incentive and then it is combined with DEED. Finally, the zero energy balance (ZEB) interaction between the MG and the main grid is proposed as a solution. Regarding the multi-objective and nonlinear optimization problem, the proposed method, with the help of whale optimization algorithm (WOA), is implemented on a small-scale MG in MATLAB software, where electrical loads are also taken into account. Simulation results highlight the fact that the integration of DR into DEED along with import/export ZEB between the MG and the main grid leads to optimal operation and reduced power imported from the main grid, and helps maintain the load/generation balance.

This paper introduces a solution to Dynamic Economic Dispatch (DED) problem using a hybrid optimization methodology bacterial foraging and PSO-DE (BPSO-DE) by integrating Bacterial foraging optimization Algorithm (BFOA), Particle Swarm Optimization (PSO) and Differential Evolution (DE). In the proposed method BFOA performs local search and global search for entire search space is accomplished through PSO-DE operators in this way they move to reach the global optimization. The BFOA also takes care of the constraints such as ramp-rate limits, valve-point loading effects, system load demand, prohibited operating zones, power losses and spinning reserve capacity. A ten unit test system is considered to show the effectiveness of the proposed method over other existing methods.

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.