Artificial bee colony optimization for multi-area economic dispatch

This paper presents artificial bee colony optimization for solving multi-area economic dispatch (MAED) problem with tie line constraints considering transmission losses, multiple fuels, valve-point loading and prohibited operating zones. Artificial bee colony optimization is a swarm-based algorithm inspired by the food foraging behavior of honey bees. The effectiveness of the proposed algorithm has been verified on three different test systems, both small and large, involving varying degree of complexity. Compared with differential evolution, evolutionary programming and real coded genetic algorithm, considering the quality of the solution obtained, the proposed algorithm seems to be a promising alternative approach for solving the MAED problems in practical power system.     

Review on application and comparison of metaheuristic techniques to multi-area economic dispatch problem

This paper presents both application and comparison of the metaheuristic techniques to multi-area economic dispatch (MAED) problem with tie line constraints considering transmission losses, multiple fuels, valve-point loading and prohibited operating zones. The metaheuristic techniques such as differential evolution, evolutionary programming, genetic algorithm and simulated annealing are applied to solve MAED problem. These metaheuristic techniques for MAED problem are evaluated on three different test systems, both small and large, involving varying degree of complexity and the results are compared against each other     

Experimental studies on impedance basedfault location for long transmission lines

Current Transformer (CT) modeling, by which CT’s characteristics can be studied has a significant importance in CT selection and design. In spite of numerous studies about closed-core CT model, only a few works have been conducted on air-gapped ones with the following problems: models of which required data is easily-accessible, have poor simulations of magnetization process; on the contrary, models which have satisfactory simulations, are hard to be established because of the hard-to-get required data. Therefore, based on Preisach Theory, a novel air-gapped CT model is deduced from the closed core CT model. The proposed model is accurate and can be established easily. The saturation and remanence properties of closed-core CT and air-gapped CT are simulated and compared.     

Multi-area power systems economic dispatch using nonlinear convex network flow programming

This paper presents a new nonlinear convex network flow programming (NLCNFP) model and algorithm for solving the security-constrained multi-area economic dispatch (MAED) problem. The tie-line security and transfer constraints in each area are considered in the MAED model. A simple analysis of a buying and selling contract in a multi-area environment is also made. The NLCNFP model of security-constrained multi-area economic dispatch was set up and solved by using a combined method of quadratic programming (QP) and network flow programming (NFP). The concept of maximum basis in the network flow graph was introduced to change the constrained model into an unconstrained QP model, which was easily solved by the reduced gradient method. The proposed approach is tested on a system of four interconnected areas with satisfactory results.     

A decomposition approach to nonlinear multi-area generationscheduling with tie-line constraints using expert systems

The authors propose a rigorous method to treat multiarea generation scheduling with tie line limits. An expert system was used for obtaining the initial solution. As the generation scheduling problem involves unit commitment and economic dispatch, the method adopts an iterative procedure to deal with these two phases. The hourly load demand and the area power generation will cause the tie flows to change. To maintain the operation security in every area, the spinning reserve should comply with the area power generation rather than its load demand. After economic dispatch, it is necessary to adjust the unit commitment in each area for preserving the spinning reserve requirements. Heuristics were used to modify the generation unit combinations. The objective is to find an economic generation schedule for a multiarea system. The interchange transactions among areas represent the transportation problem, embedded within the nonlinear optimization process. The equivalent system concept is adopted, and the transmission losses are included in this study. A four-area system with each area consisting of 26 units was used to test the efficiency of the proposed algorithm     

Evolutionary programming based economic dispatch of generators with prohibited operating zones

This paper presents a new approach using evolutionary programming for solving the economic dispatch (ED) problem of generators when some/all of the units have prohibited operating zones. In this method, additional constraints such as spinning reserve requirements and ramp-rate limits are also considered besides taking into account network losses. The proposed method is implemented for solving a few example dispatch problems. The results obtained by this new approach are compared with those obtained using traditional methods. The study results have shown that the approach developed is feasible and efficient.     

Reserve constrained multi-area economic dispatch employing differential evolution with time-varying mutation

For a power pool that involves several generation areas interconnected by tie-lines, the objective of economic dispatch (ED) is to determine the most economical generation dispatch strategy that could supply the area load demands without violating the tie-line capacity constraints. The objective of multi-area economic dispatch (MAED) is to determine the generation levels and the interchange power between areas which would minimize total fuel cost while satisfying power balance constraint, upper/lower generation limits, ramp rate limits, transmission constraints and other practical constraints. In reserve constrained MAED (RCMAED) problem inter-area reserve sharing can help in reducing the operational cost while ensuring that spinning reserve requirements in each area are satisfied. The tie-line limits too play a pivotal role in optimizing the cost of operation. The cost curves of modern generating units are discontinuous and non-convex which necessitates the use of powerful heuristic search based methods that are capable of locating global solutions effectively, with ease. This paper explores and compares the performance of various differential evolution (DE) strategies enhanced with time-varying mutation to solve the reserve constrained MAED (RCMAED) problem.The performance is tested on (i) two-area, four generating unit system, (ii) four area, 16-unit system and (iii) two-area, 40-unit system. The results are found to be superior compared to some recently published results.     

Neural networks approach for solving economic dispatch problem withtransmission capacity constraints

This study presents a new approach using Hopfield neural networks for solving the economic dispatch (ED) problem with transmission capacity constraints. The proposed method is based on an improved Hopfield neural network which was presented by Gee et al. (1994). The authors discussed a new mapping technique for quadratic 0-1 programming problems with linear equality and inequality constraints. The special methodology improved the performance of Hopfield neural networks for solving combinatorial optimization problems. The authors have now modified Gee and Prager's (GP) method in order to solve ED with transmission capacity constraints. Constraints are handled using a combination of the GP model and the model of Abe et al. (1992). The proposed method (PHN) has achieved efficient and accurate solutions for two-area power systems with 3, 4, 40 and 120 units. The PHN results are very close to those obtained using the quadratic programming method     

Evolutionary programming techniques for different kinds of economic dispatch problems

This paper is aimed at exploring the performance of the different evolutionary programming (EP) techniques for all kinds of economic dispatch (ED) problems. The three EP techniques considered here differ in the kind of mutation they use: Gaussian, Cauchy and combined Gaussian–Cauchy mutation. The kinds of problems tested are: ED of generators with prohibited operating zones (POZ), ED of generators with piecewise quadratic cost functions (PQCF), combined economic–environmental dispatch (CEED) and multi-area economic dispatch (MAED). The three EP techniques have been developed in Matlab 6.5 and numerical examples typical to each kind of ED have been tested. The simulation results are compared and discussed to show the relative performances of the different EP techniques.     

Real-time economic dispatch with line flow and emission constraintsusing quadratic programming

The presence of multiple constraints due to network line flow limits and emission allowances in the economic dispatch of modern power systems makes the conventional Lambda-Delta iterative approach no longer effective. This paper proposes a practical strategy based on quadratic programming (QP) techniques to solve the real-time economic dispatch problem. It formulates the problem with a quadratic objective function based on the unit's cost curves in quadratic or piecewise-quadratic forms. The operation constraints are modeled as linear equality/inequality equations, resulting in a typical QP problem. Goal programming techniques are also incorporated in the formulation which guarantees the best available solution even under infeasible conditions. In addition, the proposed strategy formulates the problem in the second phase dispatch in real-time by including a set of emergency control variables to provide effective control strategies for properly relieving constraint violations if they exist. The effectiveness of the proposed strategy is demonstrated by an example power dispatch problem     

电力系统输电运行弹性空间建模与效益评估

电力负荷增长和新能源接入给电网安全、经济运行带来了新的挑战。为提高电网运行安全裕度,在更大空间内实现资源优化配置,需要在现有设备基础上,挖掘电网的电能输送潜力。为此,提出输电环节运行弹性空间的概念,以挖掘输电线路与联络线的运行弹性空间。文中提出两种提高输电运行弹性空间的方式及其建模方法:①基于转移分布因子,建立线路故障短时增容弹性模型;②基于互联外网静态等值模型,建立考虑外网运行约束的联络线调整弹性模型。在此基础上,提出考虑输电运行弹性空间的N-1安全经济调度优化模型。最后,通过IEEE 30节点与IEEE 9节点互联系统评估了输电运行弹性空间的效益。仿真表明,考虑输电运行弹性空间的调度方法相较于常规调度方法可有效提高风电消纳,降低电网运行成本。     

Dynamic optical economic dispatch under system availability constraints

In this paper we have developed a dynamic optimal economic dispatch policy based on a stochastic availability model of large-scale power systems and a piece-wise constant incremental fuel cost model. Using these models the optimal economic dispatch under given system availability constraint is formulated as a dynamic nonlinear optimization problem. The random variations of demands, available generation capacities and available tie line capacities are considered as constraints in the problem. In order to solve the optimization problem an efficient algorithm based on the rule of merit-order loading has been developed. The algorithm allows large dimensionality of the system and randomness of the system parameters. The algorithm can also be easily implemented on a dispatch computer. In order to illustrate the effect of the proposed method on system generation economy and availability, an example is presented giving detailed numerical results which are very encouraging. As far as the authors know, such an economic dispatch problem which maintains the system availability index at the highest possible level (under the given system environment) has never been considered in the literature before.     

Multi-area economic dispatch with reserve sharing using dynamically controlled particle swarm optimization

A dynamically controlled PSO (DCPSO) is proposed to solve Multi-area Economic Dispatch (MAED) problem with reserve sharing. The objective of MAED problem is to determine the optimal value of power generation and interchange of power through tie-lines interconnecting the areas in such a way that the total fuel cost of thermal generating units of all areas is minimized while satisfying operational and spinning reserve constraints. The control equation of the proposed PSO is augmented by introducing improved cognitive and social components of the particle’s velocity. The parameters of the governing equation are dynamically controlled using exponential functions. The overall methodology effectively regulates the velocities of particles during their whole course of flight in such a way that results in substantial improvement of the performance of PSO. The effectiveness of the proposed method has been investigated on multi-area 4 generators, 40 generators and 140 generators test systems with multiple constraints such as reserve sharing and tie-line power. The application results show that the proposed DCPSO method is very promising for large-dimensional MAED problems.     

Security constrained economic load dispatch using improved particle swarm optimization suitable for utility system

The objective of this paper is to evolve simple and effective methods for the economic load dispatch (ELD) problem with security constraints in thermal units, which are capable of obtaining economic scheduling for utility system. In the proposed improved particle swarm optimization (IPSO) method, a new velocity strategy equation is formulated suitable for a large scale system and the features of constriction factor approach (CFA) are also incorporated into the proposed approach. The CFA generates higher quality solutions than the conventional PSO approach. The proposed approach takes security constraints such as line flow constraints and bus voltage limits into account. In this paper, two different systems IEEE-14 bus and 66-bus Indian utility system have been considered for investigations and the results clearly show that the proposed IPSO method is very competent in solving ELD problem in comparison with other existing methods.     

A simple two stage optimization algorithm for constrained powereconomic dispatch

A simple two stage optimization algorithm is proposed and investigated for fast computation of constrained power economic dispatch control problems. The method is a simple demonstration of the hierarchical aggregation-disaggregation (HAD) concept. The algorithm first solves an aggregated problem to obtain an initial solution. This aggregated problem turns out to be classical economic dispatch formulation, and it can be solved in 1% of overall computation time. In the second stage, a linear programming method finds optimal solution which satisfies power balance constraints, generation and transmission inequality constraints and security constraints. Implementation of the algorithm for IEEE systems and EPRI Scenario systems shows that the two stage method obtains an average speedup ratio of 10.64 as compared to the classical LP-based method     

基于启发式线性规划的大规模安全约束调度快速求解方法

提升大规模安全约束经济调度优化模型的求解性能是开展大电网跨省区电力电量全局优化平衡的前提与基础。首先分析问题的物理特性,通过并行计算求解不考虑机组爬坡约束的分时段约束松弛模型。基于对松弛解的分析获得可用于指导安全约束经济调度模型改进的有用信息,以约束剔除和约束增加的方式提出了基于启发式线性规划的大规模安全约束经济调度快速求解方法。将所提算法运用于新英格兰10机扩展系统和中国实际电网,验证了所提算法的正确性和有效性。     

Application of linear programming redispatch technique to dynamicgeneration allocation

Consideration is given to dispatch problems that involve the allocation of system generation optimally among generating units while tracking a load curve and observing the power rate limits of the units, system spinning reserve requirements, and other security constraints. Two methods are used in the solution of the problem. The first method is a quadratic programming technique combined with a linear programming redispatch technique. The latter utilizes a linear programming formulation of the dynamic dispatch problem about the base case static economic dispatch solution. The second method is based on the Dantzig-Wolfe decomposition technique. Tests and computer results of four systems of different combinations of units and intervals are given to show the advantages of the techniques proposed     

A particle swarm optimization for economic dispatch with nonsmooth cost functions

This work presents a new approach to economic dispatch (ED) problems with nonsmooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have nonsmooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. A modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. A constraint treatment mechanism is devised in such a way that the dynamic process inherent in the conventional PSO is preserved. Moreover, a dynamic search-space reduction strategy is devised to accelerate the optimization process. To show its efficiency and effectiveness, the proposed MPSO is applied to test ED problems, one with smooth cost functions and others with nonsmooth cost functions considering valve-point effects and multi-fuel problems. The results of the MPSO are compared with the results of conventional numerical methods, Tabu search method, evolutionary programming approaches, genetic algorithm, and modified Hopfield neural network approaches.     

机会约束随机动态经济调度的凸松弛迭代求解法

大规模风电并网给电力系统运行带来了重大技术挑战,其出力的随机性和波动性增加了线路传输能力和备用调节能力不足的风险,传统的确定性经济调度方法已不完全适用。首先提出了一种基于混合高斯分布的机会约束随机动态经济调度模型,该模型将最小备用约束和线路传输容量约束建模为机会约束,并引入调频机组的仿射控制策略以实时平衡风功率的波动。然后提出了一种机会约束规划的松弛迭代求解方法,将随机调度模型转化为二次规划模型以实现快速有效求解。利用中国西南某省25个风电场的现场数据以及IEEE 118节点系统进行算例分析,验证了混合高斯分布对风电预测误差的拟合精度,以及所提方法的可行性。     

Network loss minimization with voltage security using differential evolution

This paper presents a differential evolution (DE) based optimal power flow (OPF) for reactive power dispatch in power system planning studies. DE is a simple population-based search algorithm for global optimization and has a minimum number of control parameters. The problem is formulated as a mixed integer non-linear optimization problem taking into account both continuous and discrete control variables. The proposed method determines control variable settings such as generator voltages (continuous), tap positions (discrete) and the number of shunt reactive compensation devices to be switched (discrete) for real power loss minimization in the transmission system using DE algorithm. Most of the evolutionary algorithm applications to optimization problems apply penalty function approach to handle the inequality constraints, involving penalty coefficients. The correct combination of these coefficients can be determined only by a trial and error basis. In the proposed approach, the inequality constraints are handled by penalty parameterless scheme. Voltage security margin was evaluated using continuation power flow (CPF), to ensure the feasibility of the optimal control variable setting. The suitability of the method was tested on IEEE 14 and IEEE RTS 24-bus systems and results compared with sequential quadratic programming (SQP) method. The DE provides near global solutions comparable to that obtained using SQP.