Power Economic Dispatch Research Articles

A New Bat Optimization Algorithm to Solve EPD Problem Solving with Transmission Loss

The economic power dispatch (EPD) is an integral part of the power system, and the major roles and purpose of its use are for achieving a reliable and efficient operation out of power system generation networks, and this operation should be obtained by minimizing the generator fuel cost. Getting optimal solutions to EPD problem requires efficient optimization algorithms. Novel Bat Algorithm (NBA) is one of the most recent methods and it has already proven its efficiency and reliability for solving the EPD problem. This paper proposes Novel Bat Algorithm (NBA) in order to solve the EPD problem based on the large scale power system. The NBA has proved its efficiency and it gave a perfect performance for small-scale systems compared with the original Bat algorithm (BA), because of considering the Doppler Effect and assumed that bat can move between various habitats. The study of the EPD for large-scale power systems is more important than study it for small ones, because all power systems in countries are considered large networks. This is why all modern studies focus on the study of EPD for large systems. To test the performance of NBA during small and large scale power system, we have applied it to many systems, including 3-thermal units, 6-thermal units, 31-Iraqi thermal units and IEEE 40-thermal units respectively, with transmission losses and generator limits, and we have made a comparison of the obtained results of NBA with other optimization methods. The Iraqi thermal units have been utilized as a new data.

A Two-Stage Mathematical Programming Approach for the Solution of Combined Heat and Power Economic Dispatch

The optimal generation scheduling of combined heat and power units aims to minimize total cost of generation units satisfying power and heat demands.The combined heat and power economic dispatch problem should be solved considering a series of electrical and operational constraints, which will be more complicated considering valve-point effects of power-only units and nonconvex feasible operating regions of cogeneration units. In such a case, the problem has nonconvex and nondifferential characteristic. In this article, a two-stage model is proposed to handle the nonconvexity and nondifferentiability of valve-point effects in cost functions of power-only units. The proposed model obtains a convex feasible operating region in the first stage using a linear approximation model. In addition, an equivalent formulation is proposed in the second stage to handle the nondifferentiable term of valve-point effects using the obtained convex feasible operating regions. The proposed model is implemented on two case studies to evaluate performance of the proposed model.

Economic Power and Heat Dispatch in Cogeneration Energy Systems Using Manta Ray Foraging Optimizer

Economic Power and Heat Dispatch (EPHD) in Cogeneration Energy Systems (CES) is considered as one of non linear hard optimization problems. It is optimally scheduling the of heat and power generation units. It aims at minimizing the total fuel cost (TFC) of cogeneration units considering their operational limits. In this paper, a Manta Ray Foraging Optimization Algorithm (MRFOA), which is a recent meta-heuristic optimization technique, is developed to solve the EPHD problem in CES with additional non-convex valve point effects. The simplicity and effectiveness motivate the attempt of employing the MRFOA to minimize the TFC for power units only, cogeneration units and heat units only. The equality constraints by supplying the total loading of power and heat is are maintained. In addition, the inequality operational bounds of power only and heat only units are satisfied while the dynamic operational bounds of cogeneration units are not jeopardized. Three test systems are analyzed to estimate the MRFOA performance for solving the EPHD problem in CES, which involve 5 units, 7 units, and 48 units. It is worth noticing that the optimal solutions demonstrate MRFOA capability, feasibility and efficiency of better solutions obtained in terms of TFC compared with other optimization methods and the ability of implementation of MRFOA on EPHD issue in CES..

Combined Heat and Power Economic Emission Dispatch Using Hybrid NSGA II-MOPSO Algorithm Incorporating an Effective Constraint Handling Mechanism

This research work proposes a synergistic hybrid metaheuristic algorithm a merger of Nondominated Sorting Genetic Algorithm II and Multiobjective Particle Swarm Optimization algorithm for solving the highly complicated combined heat and power economic emission dispatch problem to operate the power system economically and to reduce the impact of environmental pollution. During the iteration, based on ranking, the population is divided into two halves. The exploration is carried out by Nondominated Sorting Genetic Algorithm II using the upper half of the population. The modification of Multiobjective Particle Swarm Optimization to effectively exploit the lower half of the population is done by increasing the personal learning coefficient, decreasing the global learning coefficient and by using an adaptive mutation operator. To satisfy the linear, nonlinear constraints, and to ensure the populations always lie in the Feasible Operating Region of the cogeneration plant, an effective constraint handling mechanism is developed. The proposed hybrid algorithm with an effective constraint handling mechanism enhances the searching capability by effective information interchange. The algorithm is applied to standard test functions and test systems while considering the valve point effects of the thermal plants, transmission power losses, bounds of the units and feasible operating region of the cogeneration units. The hybrid algorithm can obtain a well spread and diverse Pareto optimal solution and also can converge to the actual Pareto optimal front faster than some of the existing algorithms. The statistical analysis reveals that the proposed hybrid algorithm is a viable alternative to solve this complicated and vital problem.

Optimal Combined Heat and Power Economic Dispatch Using Stochastic Fractal Search Algorithm

Combined heat and power (CHP) generation is a valuable scheme for concurrent generation of electrical and thermal energies. The interdependency of power and heat productions in CHP units introduces complications and non-convexities in their modeling and optimization. This paper uses the stochastic fractal search (SFS) optimization technique to treat the highly non-linear CHP economic dispatch (CHPED) problem, where the objective is to minimize the total operation cost of both power and heat from generation units while fulfilling several operation interdependent limits and constraints. The CHPED problem has bounded feasible operation regions and many local minima. The SFS, which is a recent metaheuristic global optimization solver, outranks many current reputable solvers. Handling constraints of the CHPED is achieved by employing external penalty parameters, which penalize infeasible solution during the iterative process. To confirm the strength of this algorithm, it has been tested on two different test systems that are regularly used. The obtained outcomes are compared with former outcomes achieved by many different methods reported in literature of CHPED. The results of this work affirm that the SFS algorithm can achieve improved near-global solution and compare favorably with other commonly used global optimization techniques in terms of the quality of solution, handling of constraints and computation time.

Solution of Economic and Environmental Power Dispatch Problem of an Electrical Power System using BFGS-AL Algorithm

Abstract This paper presents a deterministic optimization strategy to solve the economic-environmental power dispatch (EEPD) problem of an electrical power system, using a Broyden Fletcher Goldfarb Shanno based on the augmented Lagrangian (BFGS-AL) algorithm. This problem is a nonlinear constrained multi-objective optimization. The objectives of this optimization are minimized the total fuel cost and emission amount for thermal generators while satisfying electric power systems equality and inequality constraints. The proposed approach is applied on the standard IEEE 30 bus test system, where the power transmission losses are taken into account. Simulation results proved that the proposed approach gives better-quality solution in terms of accuracy and convergence to the best compromise solution compared to other deterministic and meta-heuristic optimization techniques.

Performance Analysis of APSO and Firefly Algorithm for Short Term Optimal Scheduling of Multi-Generation Hybrid Energy System

This paper presents a modified and novel form of the conventional short-term hydrothermal scheduling problem by incorporating the effects of adding the photovoltaic energy source to the conventional grid. A photovoltaic energy source is intermittent in nature, therefore, to determine the optimal power contribution of the photovoltaic source towards the economic dispatch problem, a detailed strategy is presented in this paper. The proposed design method includes the forecasting of the photovoltaic system’s parameters using the Auto-Regressive Integrated Moving Average (ARIMA) model. The analytical model is developed based on the fractional integral polynomials for studying the characteristics of the single photovoltaic module. The optimization of power allocation in the system consisting of conventional and non-conventional energy sources is highly non-linear and classical deterministic methods can not be guaranteed to determine the optimal solution for economic power dispatch. The global optima of such non-linear and non-convex problems can be determined using swarm-based intelligence techniques. This paper presents accelerated particle swarm optimization and the firefly algorithm to determine a solution for short-term non-linear scheduling problems. The multiple test cases have been presented to demonstrate the effectiveness of the proposed solution over classical methods. The overall generation cost of the selected hybrid system is reduced using the proposed methods while meeting the generation constraints of each energy source. Moreover, due to the stochastic nature of the meta-heuristic techniques, a comprehensive statistical comparison, based on the independent T-test results, is also presented to highlight the algorithm which performs better for selected scheduling problems. It has been demonstrated that accelerated particle swarm optimization gives lower mean generation cost of the system whereas the execution time of the firefly algorithm is better compared to its counterpart.

CHP Economic Dispatch Considering Prohibited Zones to Sustainable Energy Using Self-Regulating Particle Swarm Optimization Algorithm

Economic dispatch is the optimal scheduling for generating units with technical constraints. Combined heat and power economic dispatch (CHPED) refers to minimization of the total energy cost for generating electricity and heat supply to load demand. This planning model integrates heat and power energy to balance energy supply and demand, mitigate climate change and improve energy efficiency of sustainable cities and green buildings. In this paper for the first time, self-regulating particle swarm optimization (SRPSO) algorithm is utilized for solving the CHPED problem by considering valve point effects and prohibited zones on fuel cost function of pure generation units and electrical power losses in transmission systems. The main advantage of SRPSO algorithm to PSO algorithm is the inertia weight flexibility with respect to search conditions. In this algorithm, unlike PSO algorithm that inertia weight reduces in each iteration, this value increases or reduces proportional to particles’ positions, which will lead particles to achieve optimal value with higher speed. The capability and effectiveness of the proposed algorithm are evaluated on a large-scale energy system using MATLAB environment. The results obtained by SRPSO algorithm are outperformed by other optimization methods from the economic, sustainable energy and time consumption point of view.

Complex power economic dispatch with improved loss coefficients

Standard economic dispatch (ED) of power generating units traditionally considers only real power generation and real power losses. Real power losses are often treated using the approximate B-loss coefficients, which are pre-calculated for a power system using load flow solution for certain base-case loading conditions. These coefficients do not assure accuracy for large deviations from the base-case loading conditions, as they are derived with few assumptions that assure an adequate accuracy for small deviations from the base-case conditions. Reactive power loss is unlike the real part as it does not have straightforward closed-form expressions for ED involving reactive power concerns. Inspired by old Kron’s loss formula derivations, this paper presents new original closed-form expressions for active and reactive power loss formulas, which are derived mainly to improve the deficiencies of the traditional ED formulations that use less accurate real power loss expressions and ignore reactive power demands and losses. The obtained coefficients are tested on four different-size test systems, and the results are compared with those obtained from solutions of both the load flow and B-coefficients for wide deviations from the base-case operating conditions. Then, the paper presents the mathematical model of the combined active-reactive complex power ED (CPED) including complex power losses using the new derived improved complex power loss coefficients that guarantee more accurate real power losses while considering reactive power concerns. The proposed CPED scheme using the new coefficients is then tested on the four test systems and compared for five costing methods of reactive power. Results and comparisons presented in this paper will show that the active and reactive power loss formulas can achieve more realistic results and accuracy for different system sizes and operating conditions, in addition to showing that reactive power consideration can significantly change outcomes of the standard ED.

Application of the stochastic fractal search algorithm and compromise programming to combined heat and power economic–emission dispatch

Combined heat and power (CHP) generation is a competent configuration for simultaneous production of thermal and electric energy. The interdependency of heat and power outputs of CHP units presents complications and non-convexities in modelling and optimization. The nonlinear constrained economic dispatch optimization problem becomes more complex when one considers the pollution produced by generating units, transmission losses and valve-point effects of thermal units. This article uses the stochastic fractal search algorithm to solve the bi-objective combined heat and power economic dispatch (CHPED) problem. The CHPED problem has bounded feasible operating regions and many local minima. The compromise programming method is used to transform the two objective functions into an aggregated objective function. The results are compared with previous results obtained by many different methods reported in the literature. The results reveal that the proposed algorithm achieves a better near-global solution and compares favourably with other commonly used global optimization techniques.

Scheduling of combined heat and generation outputs in power systems using a new hybrid multi-objective optimization algorithm

In this paper, a hybrid optimization algorithm, consisted of weighted vertices-based optimizer (WVO) and particle swarm optimization (PSO) algorithm, is proposed to solve three economic frameworks for scheduling of power sources in order to meet the required power demand in power systems. These frameworks are economic power dispatch, economic emission power dispatch and combined heat and economic power dispatch problems. The basic idea of weighted vertices optimizer (WVO) is given from the bisection root-finding method in mathematics. It uses swarm intelligence and evolutionary strategy to efficiently find the optimum solution. However, the original WVO algorithm has some flaws in complex problems with a high number of variables and constraints. Therefore, this paper presents hybrid WVO–PSO algorithm which solved the mentioned flaws and also improved its speed and accuracy. In this algorithm, varying speed is defined for each vertex by using PSO which helps better exploration through the search space. To evaluate the performance of WVO–PSO, it is applied to some of well-known and complex emission/economic dispatch (EED), combined heat and power economic dispatch (CHPED) and combined heat and power emission/economic dispatch (CHPEED) problems and then the driven results are compared with other recent methods which demonstrates better performance of the proposed method in solving non-convex and constrained EED, CHPED and CHPEED problem in terms of minimizing costs and emissions.

Improved Hybrid Biogeography-Based Algorithm for Combined Heat and Power Economic Dispatch with Feasible Operating Region and Energy Saving Potential

A hybrid algorithm, biogeography based optimization with simulated annealing (SABBO), is proposed in this paper by integrating the SA strategy into a basic BBO algorithm to solve combined heat and power unit economic dispatch (CHPED) problem. In this modified algorithm, a simulated annealing operator is used to randomly perturb the best individual retains after migration and mutation operating in the basic BBO. Elitism solution is further optimized to enhance the algorithm convergence capacity, and to prevent the algorithm from getting trapped into local optimum. Several benchmark functions are then taken to test the proposed method's optimal capacity, and the results show that SABBO could significantly outperform the basic BBO algorithm and mostly as the best solution listed BBO algorithms with different versions. Then, various systems are taken to tested SABBO algorithm, compared with the basic BBO and algorithms from references. Test results indicate that the SABBO is better than others to solve CHPED problems including large-scale ones. Further, the energy saving potential is calculated based on the whole plant's feasible operating region to work as guidance for economic operation.

Reactive Power Management through Dispatch Analysis using Evolutionary Algorithms

Sufficient reactive power requires to maintain system terminal voltages. Reactive power is an important ancillary service requires to be provided locally. Reactive power management involves two main important parts economical reactive power procurement and economical reactive power dispatch which also satisfy technical constraints. Main centering of this work is to dispatch reactive power by considering it as important optimization problem of power system. ORPD is solved as single objective function and multi objective function. Two main objective functions (1) Minimization of real power loss and (2) Diminution of L-index are considered and problem is tested for different IEEE bus systems and results were compared for SPEA and NSGA-II techniques.

Heat Transfer Search Algorithm for Combined Heat and Power Economic Dispatch

This paper suggests heat transfer search (HTS) algorithm for solving complicated combined heat and power economic dispatch (CHPED) problem. The valve point effect, prohibited operating zones of conventional thermal generators and transmission loss are taken into consideration. The main objective of the CHPED problem is to minimize the total fuel cost for producing electricity and heat supplying to a load demand. HTS is a novel meta-heuristic optimization algorithm that is based on the law of thermodynamics and heat transfer. The efficiency of the suggested HTS algorithm has been confirmed on four test systems. Test results of the suggested HTS algorithm have been compared with those achieved by other evolutionary algorithms. It has been observed from the comparison that the suggested HTS algorithm has the ability to offer superior solution.

Solving the multi-objective economic emission dispatch problems using Fast Non-Dominated Sorting TVAC-PSO combined with EMA

In this study, the Fast Non-Dominated Time-Varying Acceleration Coefficient-Particle Swarm Optimization (TVAC-PSO) combined with Exchange Market Algorithm (EMA) is proposed to solve the economic emission dispatch problems consisting of Combined Heat and Power Economic Emission Dispatch (CHPEED) and Dynamic Economic Emission Dispatch (DEED) multi-objective optimization problems considering operational constraints. A two-stage approach has been used to select the Best Compromise Solutions (BCSs), as the best solution which minimizes the operational cost and emission, simultaneously. For this purpose, at the first stage, applying Fuzzy Clustering Mean (FCM), the obtained Pareto Optimal Front (POF) is divided into several separated clusters. Then, using the Technique for Order of Performance by Similarity to Ideal Solution (TOPSIS), a single BCS is selected among each cluster. At first, the superiority of the proposed algorithm is evaluated on a number of benchmark functions, as well as the 48-unit CHPED test case. Then, to demonstrate the ability of the proposed algorithm in solving the multi-objective problem by finding the POF, the presented method has been applied to three case studies, and the results are compared with other algorithms in this field. Furthermore, a new test case is presented to confirm the proposed algorithm’s performance. The results verify the proposed method’s superiority over other available techniques in the literature. One of the most important novelty of this study is solving a multi-objective DEED problem considering the Ramp Rate Limits (RRLs), Valve Point Loading Effect (VPLE), power transmission loss impact, Spinning Reserve Requirements (SRRs), Prohibited Operating Zones (POZs) and Multiple Fuel Units (MFUs) simultaneously, for the first time.

Wind Energy Uncertainties in Multi-objective Environmental/Economic Dispatch Based on Multi-objective Evolutionary Algorithm

This paper a Multi-objective Honey Bee Mating Optimization (MOHBMO) is proposed for Environmental/ Economic Power Dispatch (EED) problem. This paper proposes a new environmental/economic load dispatch model that considers cost and emission function coefficients with uncertainties and the constraints of ramp rate. Due to the environmental concerns that arise from the emissions produced via fossil-fueled electric power plants, the classical economic dispatch, which operates electric power systems so as to minimize only the total fuel cost, can no longer be considered alone. Actually, EED problem is the scheduling of generators which fulfill the load demand of the power plants using fossil fuel and also making combined production, in order for them to perform with minimum cost and emission. Therefore, by EED, emissions can be reduced by dispatch of power generation to minimize emissions. Which is affect on power generated, system loads, fuel cost and emission coefficients in real-world situations. The MOHBMO technique has been carried out on the IEEE 30- and 118-bus test system. This technique is compared with other techniques which reveals the superiority of the proposed approach and confirms its potential for solving other power systems problems.

Many-Objective Optimal Power Dispatch Strategy Incorporating Temporal and Spatial Distribution Control of Multiple Air Pollutants

Traditional economic/environment dispatch usually aims to reduce emission, but neglects air pollutant dispersion and lacks target-oriented control. This paper proposes a many-objective optimal power dispatch (MaOOPD) strategy incorporating temporal and spatial distribution (TSD) control of multiple air pollutants. Ground level concentration, i.e., the TSD, of air pollutant is estimated by a novel air pollutant dispersion model specifically constructed for thermal power plants. A MaOOPD model is developed to cut generation cost, reduce CO2 emission, and control the TSD of PM2.5, SO2, and NO2 simultaneously. To determine a compromise solution, a decision-making method which exploits atmospheric environmental capacity margin is employed, so that actual needs of atmospheric environmental protection are captured. Case studies indicate that not only can the strategy reduce air pollution effectively, but also it can achieve a dynamic tradeoff among the objectives as weather conditions and background pollution vary, leading to an authentic economic environmental power dispatch.

Electric Forecasting using Nature Inspired Optimization Techniques

Now a day, there exists huge competition among power industries in terms of fulfilling various customers’ electrical needs. Reliable and quality power supply is no doubt a basic need for all power consumers. Moreover, planning & operation engineers also targets for proper unit commitment, economic power dispatch, etc., and highly depend upon good power system planning. Therefore, Electric Forecasting (EF) is a major criterion for power engineers. In this manuscript, Artificial Neural Network (ANN), being a well established tool for modeling non-linear and black box systems, is used to forecast hydro generation power plant, energy met and peak demand of India. Furthermore, in this competitive world, ANN model is further optimized using genetic algorithm (GA) and particle swarm optimization (PSO) to explore accurate forecasting model with minimal amount of error. These optimization methods explore highly diversified search area, resulting in more accurate forecasting results in comparison to ANN when trained with standard back propagation training algorithm.

An Improved Harmony Search Algorithm for solved the Combined Heat and Power Economic Dispatch

An Improved Harmony Search Algorithm for solved the Combined Heat and Power Economic Dispatch

Consensus‐based distributed approach to lossy economic power dispatch of distributed energy resources

Consensus‐based distributed approach to lossy economic power dispatch of distributed energy resources