Short-term hydrothermal scheduling through evolutionary programming technique

An efficient short-term hydrothermal scheduling algorithm based on the evolutionary programming (EP) technique is proposed. In the algorithm, the thermal generating units in the system are represented by an equivalent unit. The power balance constraints, total water discharge constraint, reservoir volume constraints and the constraints on the operation limits of the equivalent thermal and hydro units are fully taken into account. The effectiveness of the proposed algorithm is demonstrated through an example system and the results are compared with those obtained by the classical gradient search and simulated annealing (SA) approaches. Numerical results show that the proposed EP approach provides a cheaper schedule even than the SA approach and hence, has more powerful ability to achieve the global optimum solution than the SA approach.     

An improved PSO technique for short-term optimal hydrothermal scheduling

This paper presents a new approach to the solution of optimal power generation to short-term hydrothermal scheduling problem, using improved particle swarm optimization (IPSO) technique. The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydraulic network, water transport delay and scheduling time linkage that make the problem of finding global optimum difficult using standard optimization methods. In this paper an improved PSO technique is suggested that deals with an inequality constraint treatment mechanism called as dynamic search-space squeezing strategy to accelerate the optimization process and simultaneously, the inherent basics of conventional PSO algorithm is preserved. To show its efficiency and robustness, the proposed IPSO is applied on a multi-reservoir cascaded hydro-electric system having prohibited operating zones and a thermal unit with valve point loading. Numerical results are compared with those obtained by dynamic programming (DP), nonlinear programming (NLP), evolutionary programming (EP) and differential evolution (DE) approaches. The simulation results reveal that the proposed IPSO appears to be the best in terms of convergence speed, solution time and minimum cost when compared with established methods like EP and DE.     

处理梯级水电站复杂约束的短期水火电系统环境经济优化调度

首先建立采用迭代费用惩罚系数的单目标水火电系统环境经济优化调度模型;其次为解决梯级水电站由于时间耦合性和空间相关性而带来的同时处理发电流量约束、库容约束和动态水量平衡约束的难题,给出约束条件的启发式处理方法,使得在满足上述复杂约束的同时,更利于最优解的搜寻。对总装机容量为2 975 MW的水火电系统(包含一个含4水电机组的梯级水电站和3个火电机组)进行仿真计算,结果不仅表明了该启发式约束条件处理方法的可行性和有效性,而且对比进化算法和差分进化算法所得结果,每天的燃料费用分别降低了4 303.96$和1 311.96$,污染气体排放量分别减少8 231.37 lb和1 522.37 lb。     

Efficient real coded genetic algorithm to solve the non-convex hydrothermal scheduling problem

A simple and efficient optimisation procedure based on real coded genetic algorithm is proposed for the solution of short-term hydrothermal scheduling problem with continuous and non-smooth/non-convex cost function. The constraints like load-generation balance, unit generation limits, reservoir flow balance, reservoir physical limitations and reservoir coupling are also considered. The effectiveness of the proposed algorithm is demonstrated on a multichain-cascaded hydrothermal system that uses non-linear hydro generation function, includes water travel times between the linked reservoirs, and considers the valve point loading effect in thermal units. The proposed algorithm is equipped with an effective constraint-handling technique, which eliminates the need for penalty parameters. A simple strategy based on allowing infeasible solutions to remain in the population is used to maintain diversity. The same problem is also solved using binary coded genetic algorithm. The features of both algorithms are same except the crossover and mutation operators. In real coded genetic algorithm, simulated binary crossover and polynomial mutation are used against the single point crossover and bit-flipping mutation in binary coded genetic algorithm. The comparison of the two genetic algorithms reveals that real coded genetic algorithm is more efficient in terms of thermal cost minimisation for a short-term hydrothermal scheduling problem with continuous search space.     

Fast Convergence Evolutionary Programming for Multi-area Economic Dispatch

This paper develops and suggests fast convergence evolutionary programming (FCEP) for solving multi-area economic dispatch problem with tie-line constraints, transmission losses, multiple fuels, valve point effect, and disallowed operating region. Evolutionary programming (EP), a class of evolutionary algorithm, is based on the basic genetic operation of human chromosomes. EP has the ability to seek out the global or close to the global optima. FCEP has been developed to boost convergence speed and solution quality. The efficacy of the developed technique has been tested on three different types of test systems. Test results have been compared with those acquired from improved fast evolutionary programming, EP and other stated evolutionary techniques. It has been observed from the comparison that the developed FCEP has the ability to offer superior solution.     

求解非光滑燃料费用函数的基于进化规划的机组最优潮流

提出求解具有非光滑燃料费用函数的存在爬坡率限制的最优潮流方法。针对两次、阶梯形、联合循环机组的非光滑燃料费用函数,介绍一个基于进化规划的算法。在该算法中,为避免早熟,交叉操作随后代的数目非线性变化。介绍了所提出的进化算法应用于有线路约束的IEEE30节点系统和印度62节点系统的情况。以MVA为单位的线路潮流直接采用牛顿-拉夫逊法计算。算例证明所提出的进化算法简单,对求解具有非光滑燃料费用函数的存在很多约束的最优潮流问题有效。     

Artificial immune system for dynamic economic dispatch

Dynamic economic dispatch determines the optimal scheduling of online generator outputs with predicted load demands over a certain period of time taking into consideration the ramp rate limits of the generators. This paper proposes artificial immune system based on the clonal selection principle for solving dynamic economic dispatch problem. This approach implements adaptive cloning, hyper-mutation, aging operator and tournament selection. Numerical results of a ten-unit system with nonsmooth fuel cost function have been presented to validate the performance of the proposed algorithm. The results obtained from the proposed algorithm are compared with those obtained from particle swarm optimization and evolutionary programming. From numerical results, it is found that the proposed artificial immune system based approach is able to provide better solution than particle swarm optimization and evolutionary programming in terms of minimum cost and computation time.     

Optimal Spinning Reserve for a Wind-Thermal Power System Using EIPSO

This paper presents an evolutionary iteration particle swarm optimization (EIPSO) algorithm to solve the nonlinear optimal scheduling problem. A new index called iteration best is incorporated into particle swarm optimization (PSO) to improve the solution quality. The new PSO, named iteration PSO (IPSO), is embedded into evolutionary programming (EP) to further improve the computational efficiency. The EIPSO is then applied to solve the optimal spinning reserve for a wind-thermal power system (OSRWT). Results are used to evaluate the effects of wind generation on the spinning reserve selection of a power system. The OSRWT program considers the outage cost as well as the total operation cost of thermal units to evaluate the level of spinning reserve. The up spinning reserve (USR) and down spinning reserve (DSR) are also introduced into the OSRWT problem. The optimal scheduling of spinning reserve was reached while minimizing the sum of total operation cost and outage cost. Two practical power systems are used as numerical examples to test the new algorithm. The feasibility of the new algorithm is demonstrated by the numerical example, and EIPSO solution quality and computational efficiency are compared to those of other algorithms.     

Differential evolution technique-based short-term economic generation scheduling of hydrothermal systems

This paper presents differential evolution (DE)-based optimization technique for solving short-term economic generation scheduling of hydrothermal systems. A multi-reservoir cascaded hydrothermal system with non-linear relationship between water discharge rate, power generation and net head is considered here. The water transport delay between the connected reservoirs is also taken into account. Several equality and non-equality constraints on thermal units as well as hydro units and the effect of valve-point loading are also included in the problem formulation. The effectiveness of the proposed method is demonstrated on two test systems comprising of hydro and thermal units. Convergence characteristic of the proposed technique has been found to be quite satisfactory. The results obtained by the proposed technique are compared with other evolutionary methods. It is seen that the proposed technique is capable of producing encouraging solutions.     

A genetic algorithm solution approach to the hydrothermal coordination problem

In this paper, a genetic algorithm solution to the hydrothermal coordination problem is presented. The generation scheduling of the hydro production system is formulated as a mixed-integer, nonlinear optimization problem and solved with an enhanced genetic algorithm featuring a set of problem-specific genetic operators. The thermal subproblem is solved by means of a priority list method, incorporating the majority of thermal unit constraints. The results of the application of the proposed solution approach to the operation scheduling of the Greek Power System, comprising 13 hydroplants and 28 thermal units, demonstrate the effectiveness of the proposed algorithm.     

Optimal control strategy of a DC micro grid

Microgrids include distributed energy resources, controllable loads, and storage devices, and they can be classified into AC and DC types, depending on the characteristics of the supply voltage. In this paper, an optimal control strategy for a DC microgrid is proposed, and the strategy is aimed at minimizing the daily total energy costs. The DC micro grid can include non-dispatchable generation units (such as photovoltaic power generation) and dispatchable generation units, energy storage systems (batteries), and controllable/not controllable loads. The control strategy is based on a two-step procedure, i.e., (1) the implementation of one day-ahead scheduling and (2) a very short-time predictive control. The day-ahead scheduling is formulated using integer linear programming methodology and is aimed at achieving the optimal scheduling of controllable loads. The very short-time predictive control is based on the solution of a non-linear, multi-period, optimization problem and is aimed at achieving the real-time optimal charging/discharging profile of storage powers and the real-time optimal profile of powers of dispatchable generators thereby minimizing the cost of total daily energy. For both procedures, optimization models were formulated and solved, including technical constraints that guaranteed an adequate lifetime of the storage system. Case studies relative to a DC microgrid obtained by a modification of the actual structure of the electrical power plant of an Italian industrial facility were investigated in order to show the feasibility and the effectiveness of the proposed approach.     

Contingency constrained economic load dispatch using improved particle swarm optimization for security enhancement

This paper presents a contingency constrained economic load dispatch (CCELD) using proposed improved particle swarm optimization (IPSO), conventional particle swarm optimization (PSO), evolutionary programming (EP) techniques such as classical EP (CEP), fast-EP (FEP) and mean of classical and fast EP (MFEP) to alleviate line overloading. Power system security enhancement deals with the task of taking remedial action against possible network overloads in the system following the occurrences of contingencies. Line overload can be removed by means of generation redispatching. In the proposed improved PSO, a new velocity strategy equation with scaling factor is proposed and the constriction factor approach (CFA) utilizes the eigen value analysis and controls the system behaviour. The CCELD problem is a twin objective function viz. minimization of fuel cost and minimization of severity index. This proposed IPSO-based CCELD approach generates higher quality solution in terms of optimal cost, minimum CPU time and minimum severity index than the other methods. Simulation results on IEEE-118 bus and IEEE-30 bus test systems are presented and compared with the results of other approaches.     

基于连续线性规划的梯级水电站优化调度

梯级水电站优化调度是一个多时段、多变量和多约束条件的大规模优化问题,其求解过程非常复杂。文章尝试采用连续线性规划的优化方法来解决梯级水电站长期优化调度问题。通过采用泰勒级数一阶描述形式,对优化调度目标函数和约束条件中的非线性约束进行线性化处理,建立了基于连续线性规划算法的优化调度数学模型,提出了用连续线性规划技术求解梯级水电站优化调度问题的算法,并采用迭代步长的动态比例缩减因子保证算法能快速准确地收敛到优化问题的最优解。利用Matlab7.0编制连续线性规划梯级水电站优化调度程序,一个两级梯级水电站群的仿真分析结果表明,该算法可用于求解梯级水电站优化调度问题,并可快速得到非线性问题的最优解。     

基于模糊机会约束规划的水火电力系统多目标随机调度模型

针对水火电力系统运行调度中所包含的不同种类的不确定量,提出了一种基于模糊随机机会约束规划的短期水火电力系统多目标优化调度模型。将调度周期开始的水库蓄水量作为一个三角模糊量,以描述初始蓄水预测可能存在的误差。针对某些随机变量可能由于历史数据不足而存在误差的问题,用模糊随机变量替代这些随机变量,描述水火电力系统运行中的不确定性。在考虑整个系统发电煤耗最小化和污染物排放最小化的目标同时,考虑了龙头电站周期末蓄水量最大的优化目标,并引入了火电机组煤耗量与梯级水电站蓄水量目标的协调函数。按照模糊机会约束和随机机会约束的确定性等价形式,将短期水火电调度不确定模型转化为确定性模型。以一个8级梯级水电站和6台火电机组组成的水火电力系统为实例进行计算,验证了所提出的水火电力系统随机调度模型的正确性。     

群居蜘蛛优化算法在水电站优化调度中的应用及其效能分析

针对水电站优化调度高维、非线性、多约束以及模型不易求解的特点,本文提出将群居蜘蛛优化算法应用于水电站优化调度。算法依据群居蜘蛛的协同机制全局寻优,能够避免早熟收敛和陷于局部最优值,获得最优的水库调度决策。结合具体实例并与动态规划、遗传算法的效能进行比较,结果表明该方法不仅寻优效果好,而且稳健性强,参数少、搜索效率高,是一种有效的水电站优化调度模型的求解方法,可在实际中推广应用。     

文化算法及其在梯级水电站长期优化调度中的应用

针对梯级水电站长期优化调度难处理的多变量、高维数问题,根据文化算法(CA)原理,利用进化规划模式在群体空间产生群体,设计接受函数选择优秀群体的经验并提炼为信念空间的环境知识和标准知识,通过施加小扰动信号方式解决信念空间可能出现的局部收敛问题,再设计影响函数指导群体空间群体进化;首次把该算法应用于梯级水电站长期优化调度问...     

Nonconvex economic dispatch by integrated artificial intelligence

This paper presents a new algorithm by integrating evolutionary programming (EP), tabu search (TS) and quadratic programming (QP) methods to solve the nonconvex economic dispatch problem (NED). A hybrid EP and TS were used for quality control, and Fletcher's quadratic programming technique for solving. EP and TS determines the segment of a cost curve used, which is piecewise quadratic natured. Operation constraints are modeled as linear equality or inequality equations, resulting in a typical QP problem. Fletcher's QP was chosen to enhance the performance. The fitness function is constructed from priorities without penalty terms. Numerical results show that the proposed method is more effective than other previously developed evolutionary computation algorithms     

Teaching learning based optimization for short-term hydrothermal scheduling problem considering valve point effect and prohibited discharge constraint

This article presents a novel teaching learning based optimization (TLBO) to solve short-term hydrothermal scheduling (HTS) problem considering nonlinearities like valve point loading effects of the thermal unit and prohibited discharge zone of water reservoir of the hydro plants. TLBO is a recently developed evolutionary algorithm based on two basic concept of education namely teaching phase and learning phase. In first phase, learners improve their knowledge or ability through the teaching methodology of teacher and in second part learners increase their knowledge by interactions among themselves. The algorithm does not require any algorithm-specific parameters which makes the algorithm robust. Numerical results for two sample test systems are presented to demonstrate the capabilities of the proposed TLBO approach to generate optimal solutions of HTS problem. To test the effectiveness, three different cases namely, quadratic cost without prohibited discharge zones; quadratic cost with prohibited discharge zones and valve point loading with prohibited discharge zones are considered. The comparison with other well established techniques demonstrates the superiority of the proposed algorithm.     

Non-linear optimization with constraints: A cook-book approach

Based on the stationary co-content theorem in non-linear circuit theory and the penalty function approach in non-linear programming theory, a canonical circuit for simulating general non-linear programming problems with equality and/or inequality constraints has been developed. the task of solving a non-linear optimization problem with constraints reduces to that of finding the solution of the associated canonical circuit using a circuit simulation program, such as SPICE. A catalogue of canonical circuits is given for each class of non-linear programming problem. Using this catalogue, an engineer can solve non-linear optimization problems by a cook-book approach without learning any theory on non-linear programming. Several examples are given which demonstrate how SPICE can be used, without modification, for solving linear programming problems, quadratic programming problems, and polynomial programming problems.     

Scheduling hydro power systems with restricted operating zones anddischarge ramping constraints

An optimization-based algorithm is presented for scheduling hydro power systems with restricted operating zones and discharge ramping constraints. Hydro watershed scheduling problems are difficult to solve because many constraints, continuous and discrete, including hydraulic coupling of cascaded reservoirs have to be considered. Restricted or forbidden operating zones as well as minimum generation limits of hydro units result in discontinuous preferred operating regions, and hinder direct applications of efficient continuous optimization methods such as network flow algorithms. Discharge ramping constraints due to navigational, environmental and recreational requirements in a hydro system add another dimension of difficulty since they couple generation or water discharge across time horizon. Integrated consideration of the above constraints is very challenging. The key idea of this paper is to use additional sets of multipliers to relax discontinuous operating region and discharge ramping constraints on individual hydro units so that a two-level optimization structure is formed. The low level consists of a continuous discharge scheduling subproblem determining the generation levels of all units in the entire watershed, and a number of pure integer scheduling subproblems determining the hydro operating states, one for each unit. The discharge subproblem is solved by a network flow algorithm, and the integer scheduling problems are solved by dynamic programming with a small number of states and well-structured transitions