Modified neo-fuzzy neuron-based approach for economic and environmental optimal power dispatch

At the central energy management center in a power system, the real time controls continuously track the load changes and endeavor to match the total power demand with total generation in such a manner that the operating cost is minimized while all the operating constraints are satisfied. However, due to the strict government regulations on environmental protection, operation at minimum cost is no longer the only criterion for dispatching electrical power. The idea behind the environmentally constrained economic dispatch formulation is to estimate the optimal generation schedule of generating units in such a manner that fuel cost and harmful emission levels are both simultaneously minimized for a given load demand. Conventional optimization techniques become very time consuming and computationally extensive for such complex optimization tasks. These methods are hence not suitable for on-line use. Neural networks and fuzzy systems can be trained to generate accurate relations among variables in complex non-linear dynamical environment, as both are model-free estimators. The existing synergy between these two fields has been exploited in this paper for solving the economic and environmental dispatch problem on-line. A multi-output modified neo-fuzzy neuron (NFN), capable of real time training is proposed for economic and environmental power generation allocation.This model is found to achieve accurate results and the training is observed to be faster than other popular neural networks. The proposed method has been tested on medium-sized sample power systems with three and six generating units and found to be suitable for on-line combined environmental economic dispatch (CEED).     

Recurrent neural network for combined economic and emission dispatch

Recently, the combined economic and emission dispatch (CEED) problem, which aims to simultaneously decrease fuel cost and reduce environmental emissions of power systems, has been a widespread concern. To improve the utilization efficiency of primary energy, combined heat and power (CHP) units are likely to play an important role in the future. The goal of this study is to propose an approach to solve the CEED problems in a CHP system which consists of eight power generators (PGs), two CHP units and one heat only unit. Owing to the existence of power loss in power transmission line and the non-convex feasible region of CHP units, the proposed problem is a nonlinear, multi-constraints, non-convex multi-objectives (MO) optimization problem. To deal with it, a recurrent neural network (RNN) combined with a novel technique is developed. It means that the feasible region is separated into two convex regions by using two binary variables to search for different regions. In the frame of the neurodynamic optimization, existence and convergence of the dynamic model are analyzed. It shows that the convergence solution obtained by RNN is the optimal solution of CEED problem. Numerical simulation results show that the proposed algorithm can generate solutions efficiently.     

An approach to on-line power dispatch with ambient air pollution constraints

An on-line optimal environmental/economic dispatch methodology for electric power generation is developed in this paper. Aside from the conventional economic dispatch, constraints on air quality (such as those specified by the U.S. Environmental Protection Agency) are added to the minimum fuel cost problem. Using the integrated Gaussian puff model based on the statistical turbulent theory, rapid dynamic features of pollutant dispersion and its forecast surrounding the plants are emphasized. By applying a convex programming algorithm repeatedly, a set of marginal environmental imposts for the power plants at different times are obtained. Such imposts are incorporated with the fuel cost in the ordinary short-term economic dispatching program to indirectly account for the environmental impact of power generation on the quality of the ambient air. The approach is specifically taken to have little modification for existing economic dispatch programs and be implemented for real power networks. The proposed approach has been simulated in a power system with three plants and three monitoring points.     

Performance comparison of enhanced PSO and DE variants for dynamic energy/reserve scheduling in multi-zone electricity market

During the last decade, energy regulatory policies all over the globe have been influenced by the introduction of competition. In a multi-area deregulated power market, competitive bidding and allocation of energy and reserve is crucial for maintaining performance and reliability. The increased penetration of intermittent renewable generation requires for sufficient allocation of reserve services to maintain security and reliability. As a result the market operators and generating companies are opting for market models for joint energy and reserve dispatch with a cost minimization/profit maximization goal. The joint dispatch (JD) problem is more complex than the traditional economic dispatch (ED) due to the additional constraints like the reserve limits, transmission limits, area power balance, energy-reserve coupling constraints and separate sectional price offer curves for both, energy and reserve.The present work proposes a model for the joint static/dynamic dispatch of energy and reserve in deregulated market for multi-area operation using enhanced versions of particle swarm optimization (PSO) and differential evolution (DE). A parameter automation strategy is employed in the classical PSO and DE algorithms (i) to enhance their search capability; (ii) to avoid premature convergence; and (iii) to maintain a balance between global and local search. The performance of enhanced PSO and DE variants is compared for single/multi-area power systems for static/dynamic operation, taking both linear and non-smooth cost functions. The proposed approach is validated on two test systems for different demands, reserve requirements, tie-line capacities and generator outages.     

Water cycle algorithm-based economic dispatcher for sequential and simultaneous objectives including practical constraints

The article presents an efficient methodology based-on water cycle algorithm (WCA) to solve single and multiple objectives of economic load dispatch (ELD) aiming to generate the optimal value of the active generated power for each unit. Three objectives are adopted for optimisation either sequentially or concurrently; they are: (i) fuel cost considering valve-ripple effect, (ii) emission rate, and (iii) total network loss. The generating unit prohibited zones along with ramp rate limits and generating unit power limits specify the inequality constraints of the problem while maintaining system power balance. Usually, optimisation of simultaneous multiple objectives produces set of non-dominated Pareto-front solutions. To help the decision maker, the best compromise solution is carefully picked among optimal Pareto-front points. The proposed WCA-based methodology is demonstrated on three test cases with various complexities and under number of objective scenarios. Numerical results and further subsequent comparisons to other challenging optimisers indicate the viability and confirm the strength of the proposed WCA-based ELD method.     

The application of one rank cuckoo search algorithm for solving economic load dispatch problems

In this paper, a one rank cuckoo search algorithm (ORCSA) is proposed for solving economic load dispatch (ELD) problems. The main objective of the ELD problem is to minimize total cost of thermal generators while satisfying power balance constraint, prohibited operating zones, ramp rate constraints and operating limits of generators. Moreover, the generating units considered in this paper have different characteristics such as quadratic fuel cost function, nonconvex fuel cost function and multiple fuel options. The proposed ORCSA method has been developed by performing two modifications on the original cuckoo search algorithm (CSA) to improve optimal solution quality and computational time. The first modification is to merge new solution generated from both Lévy flights and replacement a fraction of egg together and to evaluate and rank the solutions at once only. A bound by best solution mechanism has been used in the second modification for properly handling the inequality constraints. The proposed ORCSA method has been tested on different systems with different characteristics of thermal units and constraints. The results obtained by ORCSA have been compared to those from other methods available in the literature and the result comparison has indicated that the ORCSA method can obtain better solution quality than many other methods. Therefore, the proposed ORCSA can be a very effective and efficient method for solving ELD problems.     

Modified shuffled frog leaping algorithm with genetic algorithm crossover for solving economic load dispatch problem with valve-point effect

This paper addresses a hybrid solution methodology involving modified shuffled frog leaping algorithm (MSFLA) with genetic algorithm (GA) crossover for the economic load dispatch problem of generating units considering the valve-point effects. The MSFLA uses a more dynamic and less stochastic approach to problem solving than classical non-traditional algorithms, such as genetic algorithm, and evolutionary programming. The potentiality of MSFLA includes its simple structure, ease of use, convergence property, quality of solution, and robustness. In order to overcome the defects of shuffled frog leaping algorithm (SFLA), such as slow searching speed in the late evolution and getting trapped easily into local iteration, MSFLA with GA cross-over is put forward in this paper. MSFLA with GA cross-over produces better possibilities of getting the best result in much less global as well as local iteration as one has strong local search capability while the other is good at global search. This paper proposes a new approach for solving economic load dispatch problems with valve-point effect where the cost function of the generating units exhibits non-convex characteristics, as the valve-point effects are modeled and imposed as rectified sinusoid components. The combined methodology and its variants are validated for the following four test systems: IEEE standard 30 bus test system, a practical Eastern Indian power grid system of 203 buses, 264 lines, and 23 generators, and 13 and 40 thermal units systems whose incremental fuel cost function take into account the valve-point loading effects. The results are quite promising and effective compared with several benchmark methods.     

Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect

The growing costs of fuel and operation of power generating units warrant improvement of optimization methodologies for economic dispatch (ED) problems. The practical ED problems have non-convex objective functions with equality and inequality constraints that make it much harder to find the global optimum using any mathematical algorithms. Modern optimization algorithms are often meta-heuristic, and they are very promising in solving nonlinear programming problems. This paper presents a novel approach to determining the feasible optimal solution of the ED problems using the recently developed Firefly Algorithm (FA). Many nonlinear characteristics of power generators, and their operational constraints, such as generation limitations, prohibited operating zones, ramp rate limits, transmission loss, and nonlinear cost functions, were all contemplated for practical operation. To demonstrate the efficiency and applicability of the proposed method, we study four ED test systems having non-convex solution spaces and compared with some of the most recently published ED solution methods. The results of this study show that the proposed FA is able to find more economical loads than those determined by other methods. This algorithm is considered to be a promising alternative algorithm for solving the ED problems in practical power systems.     

电动汽车参与经济调度的多目标模型

电动汽车通过V2G技术可以作为电网负荷侧的备用容量,由此提出了一个多目标优化模型,将电动汽车车主成本和经济调度成本作为其目标函数,并让电动汽车通过有序充放电来作为经济调度时的备用容量.在满足各种约束条件下,采用多目标遗传算法(NSGA-Ⅱ)对模型进行求解.电动汽车的负荷特性、负荷波动、真实风能输出和机组停运状态均采用蒙特卡洛算法得到,并以一小时为时间间隔来进行仿真.由模型的求解结果可知,通过选择合适的pareto解集中的值,可以节省车主成本和经济调度的成本,并且可以实现对负荷削峰填谷的功能.     

Stochastic unit commitment problem

The electric power industry is undergoing restructuring and deregulation. We need to incorporate the uncertainty of electric power demand or power generators into the unit commitment problem. The unit commitment problem is to determine the schedule of power generating units and the generating level of each unit. The objective is to minimize the operational cost which is given by the sum of the fuel cost and the start‐up cost. In this paper we propose a new algorithm for the stochastic unit commitment problem which is based on column generation approach. The algorithm continues adding schedules from the dual solution of the restricted linear master program until the algorithm cannot generate new schedules. The schedule generation problem is solved by the calculation of dynamic programming on the scenario tree.     

Environmental economic dispatch in multi-area power system employing improved differential evolution with fuzzy selection

In a deregulated multi-area electrical power system the objective is to determine the most economical generation dispatch strategy that could satisfy the area load demands, the tie-line limits and other operating constraints. Usually, economic dispatch (ED) deals only with the cost minimization, but minimization of emission content has also become an equally important concern due to the mandatory requirement of pollution reduction for environmental protection. Environmental economic dispatch (EED) is a complex multi-objective optimization (MOO) problem with conflicting goals. Normally a fuzzy ranking is employed to rank the large number of Pareto solutions obtained after solving a MOO problem. But in this paper the preference of the decision maker (DM) is used to guide the search and to select the population for the next generation. An improved differential evolution (DE) method is proposed where the selection operation is modified to reduce the complexity of multi-attribute decision making with the help of a fuzzy framework. Solutions are assigned a fuzzy rank on the basis of their level of satisfaction for different objectives before the population selection and then the fuzzy rank is used to select and pass on better solutions to the next generation. A well distributed Pareto-front is obtained which presents a large number of alternate trade-off solutions for the power system operator. A momentum operation is also included to prevent stagnation and to create Pareto diversity. Studies are carried out on three test cases and results obtained are found to be better than some previous literature.     

Solving Multi-Area Environmental/Economic Dispatch by Pareto-Based Chemical-Reaction Optimization Algorithm

In this study, we present a Pareto-based chemical-reaction optimization (PCRO) algorithm for solving the multi-area environmental/economic dispatch optimization problems. Two objectives are minimized simultaneously, i.e., total fuel cost and emission. In the proposed algorithm, each solution is represented by a chemical molecule. A novel encoding mechanism for solving the multi-area environmental/economic dispatch optimization problems is designed to dynamically enhance the performance of the proposed algorithm. Then, an ensemble of effective neighborhood approaches is developed, and a self-adaptive neighborhood structure selection mechanism is also embedded in PCRO to increase the search ability while maintaining population diversity. In addition, a grid-based crowding distance strategy is introduced, which can obviously enable the algorithm to easily converge near the Pareto front. Furthermore, a kinetic-energy-based search procedure is developed to enhance the global search ability. Finally, the proposed algorithm is tested on sets of the instances that are generated based on realistic production. Through the analysis of experimental results, the highly effective performance of the proposed PCRO algorithm is favorably compared with several algorithms, with regards to both solution quality and diversity.      

A Solution to the Combined Economic and Emission Dispatch Using Hybrid PSOGSA Algorithm

This article presents a new hybrid algorithm based on particle swarm optimization (PSO) and the gravitational search algorithm (GSA) for solving the combined economic and emission dispatch (CEED) problem in power systems. Performance of this approach for the CEED problem is studied and evaluated on three test systems with 3, 6, and 40 generating units, with various cost curve nature and different constraints. The results obtained are compared to those reported in the recent literature. Those results show that the proposed algorithm provides an effective and robust high-quality solution of the CEED problem.     

Particle swarm optimization with crazy particles for nonconvex economic dispatch

The paper presents an effective evolutionary method for economic power dispatch. The idea is to allocate power demand to the on-line power generators in such a manner that the cost of operation is minimized. Conventional methods assume quadratic or piecewise quadratic cost curves of power generators but modern generating units have non-linearities which make this assumption inaccurate. Evolutionary optimization methods such as genetic algorithms (GA) and particle swarm optimization (PSO) are free from convexity assumptions and succeed in achieving near global solutions due to their excellent parallel search capability. But these methods usually tend to converge prematurely to a local minimum solution, particularly when the search space is irregular. To tackle this problem “crazy particles” are introduced and their velocities are randomized to maintain momentum in the search and avoid saturation. The performance of the PSO with crazy particles has been tested on two model test systems, compared with GA and classical PSO and found to be superior.     

Solution to non-convex economic dispatch problem with valve point effects by incremental artificial bee colony with local search

In literature, economic power dispatch problems are generally categorized as convex and non-convex optimization problems. In this study, incremental artificial bee colony (IABC) and incremental artificial bee colony with local search (IABC-LS) have been used for the solution of the economic dispatch problem with valve point effect. In these kind of problems, fuel cost curve increases as sinusoidal oscillations. In the solution of the problem B loss matrix has been used for the calculation of the line losses. Total fuel cost has been minimized under electrical constraints. IABC and IABC-LS methods have been applied to four different test systems one with 6 buses 3 generators, the other with 14 buses 5 generators (IEEE), the third one with 30 buses 6 generators (IEEE) and the last one is 40-generator system. The obtained best values have been compared with different methods in literature and the results of them have been discussed.     

Dynamic economic load dispatch using hybrid swarm intelligence based harmony search algorithm

This paper presents the hybrid harmony search algorithm with swarm intelligence (HHS) to solve the dynamic economic load dispatch problem. Harmony Search (HS) is a recently developed derivative-free, meta-heuristic optimization algorithm, which draws inspiration from the musical process of searching for a perfect state of harmony. This work is an attempt to hybridize the HS algorithm with the powerful population based algorithm PSO for a better convergence of the proposed algorithm. The main aim of dynamic economic load dispatch problem is to find out the optimal generation schedule of the generators corresponding to the most economical operating point of the system over the considered timing horizon. The proposed algorithm also takes care of different constraints like power balance, ramp rate limits and generation limits by using penalty function method. Simulations were performed over various standard test systems with 5 units, 10 units and 30 units and a comparative study is carried out with other recently reported results. The findings affirmed the robustness and proficiency of the proposed methodology over other existing techniques.     

Congestion management by determining optimal location of series FACTS devices using hybrid bacterial foraging and Nelder–Mead algorithm

In this paper, the Thyristor-Controlled Series-Compensated (TCSC) devices are located for congestion management in the power system by considering the non-smooth fuel cost function and penalty cost of emission. For this purpose, it is considered that the objective function of the proposed optimal power flow (OPF) problem is minimizing fuel and emission penalty cost of generators. A hybrid method that is the combination of the bacterial foraging (BF) algorithm with Nelder–Mead (NM) method (BF-NM) is employed to solve the OPF problems. The optimal location of the TCSC devices are then determined for congestion management. The size of the TCSC is obtained by using of the BF-NM algorithm to minimize the cost of generation, cost of emission, and cost of TCSC. The simulation results on IEEE 30-bus, modified IEEE 30-bus and IEEE 118-bus test system confirm the efficiency of the proposed method for finding the optimal location of the TCSC with non-smooth non-convex cost function and emission for congestion management in the power system. In addition, the results clearly show that a better solution can be achieved by using the proposed OPF problem in comparison with other intelligence methods.     

A primary unit commitment approach with a modification process

This paper introduces an approach to one of the most important problems in electrical power system called the Unit Commitment (UC). The proposed method PUC-MP which stands for the primary unit commitment-modification process, addresses this problem firstly by using a simple and new priority for operating the generating units in each hour, and then, using a modification process which enhances the solution quality with lower cost. The PUC-MP takes advantage of both deterministic and stochastic algorithms in its structure to solve the discrete-variable part of the UC problem for choosing a suitable combination of units in each hour, and also, continuous-variable part of it which is dispatching the operating units’ output power to the power network load economically. The latter part which is called economic dispatch (ED) has been solved using an intelligent algorithm which in turn has been customized by two new ideas to increase its efficiency. Simulation results show that this new approach even without using its modification process can be considered as an effective approach which surpasses some other popular and recently reported methods in producing near-optimal and robust solutions.     

An improved artificial bee colony optimization algorithm based on orthogonal learning for optimal power flow problem

The increasing fuel price has led to high operational cost and therefore, advanced optimal dispatch schemes need to be developed to reduce the operational cost while maintaining the stability of grid. This study applies an improved heuristic approach, the improved Artificial Bee Colony (IABC) to optimal power flow (OPF) problem in electric power grids. Although original ABC has provided robust solutions for a range of problems, such as the university timetabling, training neural networks and optimal distributed generation allocation, its poor exploitation often causes solutions to be trapped in local minima. Therefore, in order to adjust the exploitation and exploration of ABC, the IABC based on the orthogonal learning is proposed. Orthogonal learning is a strategy to predict the best combination of two solution vectors based on limited trials instead of exhaustive trials, and to conduct deep search in the solution space. To assess the proposed method, two fuel cost objective functions with high non-linearity and non-convexity are selected for the OPF problem. The proposed IABC is verified by IEEE-30 and 118 bus test systems. In all case studies, the IABC has shown to consistently achieve a lower cost with smaller deviation over multiple runs than other modern heuristic optimization techniques. For example, the quadratic fuel cost with valve effect found by IABC for 30 bus system is 919.567 $/hour, saving 4.2% of original cost, with 0.666 standard deviation. Therefore, IABC can efficiently generate high quality solutions to nonlinear, nonconvex and mixed integer problems.     

Load-frequency control service in a deregulated environment

In a deregulated environment, independent generators and utility generators may or may not participate in the load-frequency control of the system. For the purpose of evaluating the performance of such a system, a flexible method has been developed and implemented. The method assumes that load frequency control is performed by an ISO based on parameters defined by the participating generating units. The participating units comprise utility generators and independent power producers. The utilities define the units, which will be under load-frequency control, while the independent power producers may or may not participate in the load frequency control. For all the units, which participate in the load-frequency control, the generator owner defines (a) generation limits, (b) rate of change and (c) economic participation factor. This information is transmitted to the ISO. This scheme allows the utilities to economically dispatch their own system, while at the same time permit the ISO to control the interconnected system operation.