An improved bacterial foraging algorithm for combined static/dynamic environmental economic dispatch

Economic dispatch is carried out at the energy control center to find out the optimal output of thermal generating units such that power balance criterion is met, unit operating limits are satisfied and the fuel cost is minimized. With growing environmental awareness and strict government regulations throughout the world, it has become essential to optimize not only the total fuel cost but also the harmful emissions, both, under static as well as dynamic conditions. The static environment economic dispatch finds the optimal output of generating units for a fixed load demand at a given time, while the dynamic environmental economic dispatch schedules the output of online generators with changing power demands over a certain time period (normally one day) so as to minimize these two conflicting objectives, simultaneously. In this paper, the price penalty factor approach is employed for simultaneous minimization of cost and emission. The generator ramp rate constraints, non-convex and discontinuous nature of cost function and the large number of generators in practical power plants, make this problem very difficult to solve. Here, a fuzzy ranking approach is employed to identify the solution which offers the best compromise between cost and emission objectives.     

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.     

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.     

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.     

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.     

电站多台机组经济运行算法研究

研究电厂多台机组经济运行的调度算法,开发 了电厂经济运行计算平台并将其加载在网控培训仿真机教员台上．首次将等微增率算法、浮 点数编码遗传算法和变尺度混沌优化算法等3种调度算法集中到一个计算平台上．给出了3种 调度算法的计算结果．采用3种调度方案的计算平台投入运行后将给电厂带来可观的经济效 益．     

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.     

动态粒子群算法在经济负荷分配中的应用

将一种惯性权重动态调整的粒子群算法用于求解复杂的不连续、非凸、非线性电力系统的经济负荷分配(ED)问题,使其在满足各机组负荷和运行约束的条件下总的发电费用最小.算法惯性权重随不同粒子距全局最优点的距离不同而动态调整,从而提高了基本粒子群算法的收敛速度,避免其容易陷入局部极值.将算法应用到经济负荷分配问题的Matlab仿真结果表明,所提出的方法不仅提高了解的寻优能力和收敛速度,而且随着问题规模的增大,其优化结果要好于其它方法.     

Optimal generation scheduling based on AHP/ANP

This paper proposes an application of the analytic hierarchy process (AHP) and analytic network process (ANP) for enhancing the selection of generating power units for appropriate price allocation in a competitive power environment. The scheme addresses adequate ranking, prioritizing, and scheduling of units before optimizing the pricing of generation units to meet a given demand. In the deregulated environment, the classical optimization techniques will be insufficient for the above-mentioned purpose. Hence, by incorporating the interaction of factors such as load demand, generating cost curve, bid/sale price, unit up/down cost, and the relative importance of different generation units, the scheme can be implemented to address the technical and nontechnical constraints in unit commitment problems. This information is easily augmented with the optimization scheme for an effective optimal decision. The scheme proposed is tested using the IEEE 39-bus test system.     

基于人工蜂群优化法的多区域电力系统经济调度

针对多区域电力系统经济调度问题,在满足联络线传输限制、多种燃料特征、阀点效应和禁止运转区的约束条件下,综合考虑多区域电力负载成本最小的要求,建立数学计算模型,利用人工蜂群优化法快速地寻找全局最优解。通过两个不同规模、不同程度复杂性的仿真测试系统进行计算,结果验证了所提算法的可行性。考虑获得解的质量,将人工蜂群优化算法与DE、EP、RCGA算法进行对比分析,结果表明所提算法在实际电力系统中解决多区域经济分配问题具有有效性和优越性。     

Large scale economic dispatch of power systems using oppositional invasive weed optimization

This paper presents an evolutionary hybrid algorithm of invasive weed optimization (IWO) merged with oppositional based learning to solve the large scale economic load dispatch (ELD) problems. The oppositional invasive weed optimization (OIWO) is based on the colonizing behavior of weed plants and empowered by quasi opposite numbers. The proposed OIWO methodology has been developed to minimize the total generation cost by satisfying several constraints such as generation limits, load demand, valve point loading effect, multi-fuel options and transmission losses. The proposed algorithm is tested and validated using five different test systems. The most important merit of the proposed methodology is high accuracy and good convergence characteristics and robustness to solve ELD problems. The simulation results of the proposed OIWO algorithm show its applicability and superiority when compared with the results of other tested algorithms such as oppositional real coded chemical reaction, shuffled differential evolution, biogeography based optimization, improved coordinated aggregation based PSO, quantum-inspired particle swarm optimization, hybrid quantum mechanics inspired particle swarm optimization, modified shuffled frog leaping algorithm with genetic algorithm, simulated annealing based optimization and estimation of distribution and differential evolution algorithm.     

Recursive estimation of incremental cost curves

The economic scheduling of power generation among fossil fuel plants has historically been based on incremental cost curves which relate the rate of change of cost with respect to change in power delivered to the transmission system. These curves are based on steady-state measurements and are up-dated periodically, normally weekly or monthly, to reflect changes in operating conditions.

Since the load of a power system is constantly changing, one or more of the generation units must be in a dynamic state at any given time. Also, changes in such quantities as ambient temperature and feedwater temperature affect the overall system efficiency. Thus the incremental cost given by a cost curve is at best only an approximation of the actual incremental cost. In this work, a superior estimation technique is used to model this economic metric. It features on-line, real-time capabilities which allow the algorithm to adaptively follow structural changes in the generating system. The practical problems of divergence and parameter initialization are also treated. The experimental results presented demonstrate that the developed real-time method is accurate and will fit in a mini-computer controller.     

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.     

Mine blast algorithm for environmental economic load dispatch with valve loading effect

Neural Computing and Applications - Economic load dispatch (ELD) is the process of allocating the required load between the available generation units such that the cost of operation is minimized....     

考虑新能源接入的电力多目标优化调度

发展新能源技术是减少化石能源依赖以及解决污染排放问题的有效途径,但是规模化的新能源并网也会影响电网的安全稳定运行。为研究以风电、电动汽车为代表的新能源并网对电力调度的影响,建立综合考虑电网运行成本、污染排放、日负荷方差等因素的多目标动态环境经济安全调度模型,并采用基于分解的多目标进化算法（MOEA/D-M2M）进行复杂约束条件下的调度分析。对含风电和电动汽车并网的10机系统进行仿真研究,验证了所提调度模型及方法的合理性及有效性。     

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.     

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.     

A Chance Constrained Optimal Reserve Scheduling Approach for Economic Dispatch Considering Wind Penetration

The volatile wind power generation brings a full spectrum of problems to power system operation and management, ranging from transient system frequency fluctuation to steady state supply and demand balancing issue. In this paper, a novel wind integrated power system day-ahead economic dispatch model, with the consideration of generation and reserve cost is modelled and investigated. The proposed problem is first formulated as a chance constrained stochastic nonlinear programming (CCSNLP), and then transformed into a deterministic nonlinear programming (NLP). To tackle this NLP problem, a three-stage framework consists of particle swarm optimization (PSO), sequential quadratic programming (SQP) and Monte Carlo simulation (MCS) is proposed. The PSO is employed to heuristically search the line power flow limits, which are used by the SQP as constraints to solve the NLP problem. Then the solution from SQP is verified on benchmark system by using MCS. Finally, the verified results are feedback to the PSO as fitness value to update the particles. Simulation study on IEEE 30-bus system with wind power penetration is carried out, and the results demonstrate that the proposed dispatch model could be effectively solved by the proposed three-stage approach.      

An economic dispatch algorithm of combined cycle units

This paper presents a method to solve the economic dispatch (ED) problem for thermal unit systems involving combined cycle (CC) units. The ED problem finds the optimal generation of each unit in order to minimize the total generation cost while satisfying the total demand and generating-capacity constraints. A CC unit presents multiple configurations or states, each state having its own unique cost curve. Therefore, in performing ED, we need to be able to shift between these cost curves. Moreover, the cost curve is not convex for some of these states. Hence, ED becomes a non-convex optimization problem, which is difficult to solve by conventional methods. In this paper we present a new technique, developed to find the global solution, that is based on the calculation of the infimal convolution. The paper includes the results for a case test and we compare our solution with other techniques.     

An expert system for unit commitment and power demand prediction using fuzzy logic and neural networks

Abstract: The paper discusses the implementation of a fuzzy logic and artificial neural networks approach to providing a structural framework for the representation, manipulation and utilisation of data and information concerning prediction of power demand and generation commitments. An algorithm has been implemented and trained to predict the power demand at each load point on an hourly basis. The neural network is then implemented to supply the brute force necessary to accommodate the large amount of sensory data to provide the initial evaluation of the generation units to be committed. Results of the fuzzy model show a reasonable correspondence with the actual power demand. A standard deviation error for an hourly based prediction is limited to 4.4. Further refinement of the fuzzy model may produce further improvements.
Implementation of artificial neural networks for scheduling an hourly unit commitment based on load demands is also discussed The backpropagation technique based on the I/O mapping method has been chosen for structuring the neural network. Geographically related load points and generating units are clustered into groups. Grouping has significantly reduced the number of inputs and outputs to the neural network and, hence, reduced the system complexity. As a result, both training requirements and running real time interaction are significantly improved. The expert system would replace and utilise the requirement for skilled dispatchers in scheduling the generators. It is anticipated that this facility is more accurate, dynamic, adaptive and more efficient than a skilled dispatcher. The overall cost of power generation is expected to be less if the new facility is used. Initial results have reflected a satisfactory correlation between predicted and actual results, with a standard deviation error of 1.71% and 1.96% in the base load units of HTPS and ATPS respectively.