Reactive power dispatch considering voltage stability with seeker optimization algorithm

Optimal reactive power dispatch (ORPD) has a growing impact on secure and economical operation of power systems. This issue is well known as a non-linear, multi-modal and multi-objective optimization problem where global optimization techniques are required in order to avoid local minima. In the last decades, computation intelligence-based techniques such as genetic algorithms (GAs), differential evolution (DE) algorithms and particle swarm optimization (PSO) algorithms, etc., have often been used for this aim. In this work, a seeker optimization algorithm (SOA) based method is proposed for ORPD considering static voltage stability and voltage deviation. The SOA is based on the concept of simulating the act of human searching where search direction is based on the empirical gradient by evaluating the response to the position changes and step length is based on uncertainty reasoning by using a simple Fuzzy rule. The algorithm's performance is studied with comparisons of two versions of GAs, three versions of DE algorithms and four versions of PSO algorithms on the IEEE 57 and 118-bus power systems. The simulation results show that the proposed approach performed better than the other listed algorithms and can be efficiently used for the ORPD problem.     

Backtracking search optimization based economic environmental power dispatch problems

This paper presents the solution for a nonlinear constrained multi objective of the economic and emission load dispatch (EELD) problem of thermal generators of power systems by means of the backtracking search optimization technique. Emission substance like NO_X, power demand equality constraint and operating limit constraint are considered here. The aim of backtracking search optimization (BSA) is to find a global solution under the influence of two new crossover and mutation operations. BSA has capability to deal with multimodal problems due to its powerful exploration and exploitation capability. BSA is out of excessive sensitivity to control parameters as it has single control parameter. The performance of BSA is compared with existing newly developed optimization techniques in terms quality of solution obtained, computational efficiency and robustness for multi objective problems.     

基于随机模拟粒子群算法的含风电场电力系统经济调度

由于风电具有随机性,目前尚无法较准确预测其出力,因此含有风电的电力系统经济调度不再是-个常规意义下的确定性问题.利用传统的方法也难获得既经济又有较高可靠性的解.本文建立了基于机会约束规划的含风电场的电力系统经济调度数学模型,以概率的形式描述相关约束条件,考虑了机组的爬坡约束、出力限制,线路潮流限制、备用约束及负荷平衡等约束条件,利用基于随机模拟的粒子群算法求解该问题.通过IEEE30节点系统的算例验证,表明该模型与算法的有效性.     

Optimal reactive power dispatch using quasi-oppositional teaching learning based optimization

This paper presents a newly developed teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal reactive power dispatch (ORPD) problem by minimizing real power loss, voltage deviation and voltage stability index. To accelerate the convergence speed and to improve solution quality quasi-opposition based learning (QOBL) concept is incorporated in original TLBO algorithm. The proposed TLBO and quasi-oppositional TLBO (QOTLBO) approaches are implemented on standard IEEE 30-bus and IEEE 118-bus test systems. Results demonstrate superiority in terms of solution quality of the proposed QOTLBO approach over original TLBO and other optimization techniques and confirm its potential to solve the ORPD problem.     

基于改进粒子群算法的电力系统经济负荷分配

提出了一种应用随机优化理论求解电力系统经济负荷分配的新方法,该方法以电力市场全天购电费用最小为目标函数,将高斯算子和交叉算子引入基本粒子群算法中。针对基本粒子群算法（PSO）的局限性,通过引入新的算子,克服了PSO算法前期精度低、后期收敛速度慢、易于陷入局部最优等缺点,在速度和精度上满足了计算要求。算例结果表明,所提出的方法能有效解决电力市场电力系统经济负荷分配问题。     

Solving economic load dispatch problems in power systems using chaotic and Gaussian particle swarm optimization approaches

The objective of the Economic Dispatch Problems (EDPs) of electric power generation is to schedule the committed generating units outputs so as to meet the required load demand at minimum operating cost while satisfying all units and system equality and inequality constraints. Recently, global optimization approaches inspired by swarm intelligence and evolutionary computation approaches have proven to be a potential alternative for the optimization of difficult EDPs. Particle swarm optimization (PSO) is a population-based stochastic algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Inspired by the swarm intelligence and probabilities theories, this work presents the use of combining of PSO, Gaussian probability distribution functions and/or chaotic sequences. In this context, this paper proposes improved PSO approaches for solving EDPs that takes into account nonlinear generator features such as ramp-rate limits and prohibited operating zones in the power system operation. The PSO and its variants are validated for two test systems consisting of 15 and 20 thermal generation units. The proposed combined method outperforms other modern metaheuristic optimization techniques reported in the recent literature in solving for the two constrained EDPs case studies.     

Solution of optimal reactive power dispatch of power systems using hybrid particle swarm optimization and imperialist competitive algorithms

Management of reactive power resources is essential for secure and stable operation of power systems in the standpoint of voltage stability. In power systems, the purpose of optimal reactive power dispatch (ORPD) problem is to identify optimal values of control variables to minimize the objective function considering the constraints. The most popular objective functions in ORPD problem are the total transmission line loss and total voltage deviation (TVD). This paper proposes a hybrid approach based on imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) to find the solution of optimal reactive power dispatch (ORPD) of power systems. The proposed hybrid method is implemented on standard IEEE 57-bus and IEEE 118-bus test systems. The obtained results show that the proposed hybrid approach is more effective and has higher capability in finding better solutions in comparison to ICA and PSO methods.     

考虑多风能预测场景的虚拟电厂日内滚动柔性优化调度方法

随着分布式可再生能源接入电网的比例日益提高,其出力间歇性和随机性给电力系统的安全稳定和经济运行带来了一系列的负面影响,虚拟电厂为分布式可再生能源可靠并网提供了新的途径。针对虚拟电厂中风电机组出力的不确定性及预测误差,考虑了由多个风能预测服务商基于不同预测方法提供多个风电出力预测场景,以期望运行成本最小为目标,制定虚拟电厂每个场景对应的最优调度计划。为应对风力状况的随机波动,虚拟电厂当前时段考虑下一时段所有风电出力场景下的计划调整成本。并以期望运行总成本最小为目标,构建基于多风能预测结果的虚拟电厂柔性优化调度模型,并设计了日内虚拟电厂出力计划的滚动调度策略。通过数值仿真,对比分析了不同预测场景下虚拟电厂的运行成本,验证了所提模型的可行性和有效性。     

基于分区电价的跨区电力调度双层优化模型

为充分利用跨区调度资源,提出一种基于分区电价的跨区电力调度双层优化模型。采用等效发电成本曲线对区域内部的煤电机组出力进行建模,采用一种基于整数规划的机会约束方法对风电和光伏出力进行建模。建立与分级调度模式相适应的双层优化模型,作为上级调度机构的上层模型以区域间送受电量为决策变量,以区域间送受电量价值最大化为目标,下层模型实现区域内部的经济调度。根据卡罗需-库恩-塔克(KKT)条件将双层模型转化为单层模型进行求解。算例结果验证了所提模型的有效性。所提模型在送电区域和受电区域之间维持一定的电价差异,通过传输较少的电量缓解受电区域的电力供需矛盾。     

基于鲸鱼优化算法的无功优化调度

针对目前电力系统中的无功优化问题尚缺乏一种能兼顾求解的高效性与全局搜索最优性的方法,本文将一种新的启发式算法--鲸鱼优化算法(WOA)运用到电网无功优化调度中,以系统有功功率损耗最低为目标函数,通过引入惩罚函数建立无功优化模型,对IEEE-14节点系统与IEEE-30节点系统进行仿真,并利用单因素方差分析法(One-way ANOVA)将所得结果与之前的粒子群优化算法(PSO)及引入加速度系数的时变粒子群优化(PSO-TVAC)进行比较,研究表明WOA算法在迭代次数、搜索能力及收敛问题上的潜力,并证明了在解决电力系统无功优化问题上的鲁棒性和有效性,同时也为解决非线性约束问题提供了新途径。     

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 semidefinite programming method with graph partitioning technique for optimal power flow problems

A new semidefinite programming (SDP) method with graph partitioning technique to solve optimal power flow (OPF) problems is presented in this paper. The non-convex OPF problem is converted into its convex SDP model at first, and then according to the characters of power system network, the matrix variable of SDP is re-arranged using the chordal extension of its aggregate sparsity pattern by the graph partitioning technique. A new SDP-OPF model is reformulated with the re-arranged matrix variable, and can be solved by the interior point method (IPM) for SDP. This method can reduce the consumption of computer memory and improve the computing performance significantly. Extensive numerical simulations on seven test systems with sizes up to 542 buses have shown that this new method of SDP-OPF can guarantee the global optimal solutions within the polynomial time same as the original SDP-OPF, but less CPU times and memory.     

A hybrid multi-agent based particle swarm optimization algorithm for economic power dispatch

This paper presents a new multi-agent based hybrid particle swarm optimization technique (HMAPSO) applied to the economic power dispatch. The earlier PSO suffers from tuning of variables, randomness and uniqueness of solution. The algorithm integrates the deterministic search, the Multi-agent system (MAS), the particle swarm optimization (PSO) algorithm and the bee decision-making process. Thus making use of deterministic search, multi-agent and bee PSO, the HMAPSO realizes the purpose of optimization. The economic power dispatch problem is a non-linear constrained optimization problem. Classical optimization techniques like direct search and gradient methods fails to give the global optimum solution. Other Evolutionary algorithms provide only a good enough solution. To show the capability, the proposed algorithm is applied to two cases 13 and 40 generators, respectively. The results show that this algorithm is more accurate and robust in finding the global optimum than its counterparts.     

电力系统经济负荷分配的量子粒子群算法

本文首次将量子粒子群算法用于电力系统经济负荷分配中。该算法是以粒子群中粒子的收敛特性为基础,依据量子物理理论提出的,改变了传统粒子群算法的搜索策略,可使粒子在整个可行解空间中搜索寻求全局最优解。同时该算法的进化方程中不需要速度向量,而且进化方程的形式更简单,参数较少且容易控制。对两个算例进行仿真测试,证实该算法可有效解决经济负荷分配问题;性能对比显示,该算法求得的解优于已有的改进粒子群算法及其它优化算法所求得的解。本文为量子粒子群算法用于经济负荷分配的实用化研究奠定了必要的理论基础。     

基于粒子群优化算法的AGC机组调配研究

电力市场下AGC机组的调配问题是辅助服务领域中的一个重要研究内容。提出了一种基于粒子群优化算法的AGC机组调配方案。该方法基于AGC机组调配的数学模型,考虑了机组调节容量,调节速率等约束条件。介绍了算法的基本原理,并分析了参数的不同取值对算法收敛性的影响。实际系统的算例表明,利用粒子群优化算法,不仅可以克服整数规划法可能得不到最优解的缺点,而且与遗传算法比较具有收敛性好,收敛速度快的优点,从而为AGC机组的调配问题提供了一种新的有效算法。     

Optimal reactive power dispatch based on harmony search algorithm

This paper presents a harmony search algorithm for optimal reactive power dispatch (ORPD) problem. Optimal reactive power dispatch is a mixed integer, nonlinear optimization problem which includes both continuous and discrete control variables. The proposed algorithm is used to find the settings of control variables such as generator voltages, tap positions of tap changing transformers and the amount of reactive compensation devices to optimize a certain object. The objects are power transmission loss, voltage stability and voltage profile which are optimized separately. In the presented method, the inequality constraints are handled by penalty coefficients. The study is implemented on IEEE 30 and 57-bus systems and the results are compared with other evolutionary programs such as simple genetic algorithm (SGA) and particle swarm optimization (PSO) which have been used in the last decade and also other algorithms that have been developed in the recent years.     

基于IGDT的网架重构过程中风电场出力调度

风电具有启动功率小、启动速度快等特点,在停电系统恢复过程中利用风电为其提供功率支持,可以加快系统负荷的恢复。由于风电出力的不确定性,需要对风电场出力进行调度,减小风电场出力的波动范围,在保证已恢复系统安全的前提下提高风电的利用效率。为此,文中提出了一种基于信息间隙决策理论(IGDT)的风电场出力调度方法。首先建立不考虑风电出力不确定性时的风电场出力参考值确定性模型,然后基于IGDT方法将确定性优化模型转变为考虑风电不确定性的风电场出力调度优化模型,再利用人工蜂群算法对优化模型进行求解,最后以IEEE 39节点系统和江苏实际系统为例验证了文中方法的有效性。     

随机风电接入的电力系统动态经济调度多场景协同优化

针对随机风电接入的电力系统动态经济调度问题,采用场景法应对随机风电接入带来的不确定性,并以发电总成本最小为优化目标,结合多学科协同优化算法的核心思想建立基于多场景解耦的电力系统动态经济调度协同优化模型。引入动态松弛算法求解模型的系统级优化问题,有效克服传统多学科协同优化算法的不足;采用网格计算工具并行求解由多场景构建的子学科优化问题,大幅提高求解规模和计算效率。含风电的IEEE 39节点系统仿真结果表明,所提模型是可行有效的,并且优化效果要优于基于GAMS-BARON求解器的传统场景法。     

Balancing risk and cost in fuzzy economic dispatch including wind power penetration based on particle swarm optimization

Utilization of renewable energy resources such as wind energy for electric power generation has assumed great significance in recent years. Wind power is a source of clean energy and is able to spur the reductions of both consumption of depleting fuel reserves and emissions of pollutants. However, since the availability of wind power is highly dependent on the weather conditions, the penetration of wind power into traditional utility grids may incur certain security implications. Therefore, in economic power dispatch including wind power penetration, a reasonable tradeoff between system risk and operational cost is desired. In this paper, a bi-objective economic dispatch problem considering wind penetration is formulated, which treats operational costs and security impacts as conflicting objectives. Different fuzzy membership functions are used to reflect the dispatcher’s attitude toward the wind power penetration. A modified multi-objective particle swarm optimization (MOPSO) algorithm is adopted to develop a power dispatch scheme which is able to achieve compromise between economic and security requirements. Numerical simulations including sensitivity analysis are reported based on a typical IEEE test power system to show the validity and applicability of the proposed approach.     

基于参数规划的含储能和风电电力系统低碳经济调度

为了实现“双碳”目标以及适应新能源快速发展的形势,基于参数规划及工程博弈论提出了一种含储能和风电电力系统的多目标低碳经济调度方法。以系统发电成本、碳排放量、储能寿命折损为目标构建多目标优化模型,采用系数约束法将模型转化为参数线性规划模型,求解参数规划模型可获得Pareto前沿的精确解析表达式,从而进一步构建工程博弈问题,精炼得到对多目标具有公平性的唯一Pareto最优解,为决策者提供参考。算例分析结果表明,所提调度方法能够充分兼顾各目标的优化程度,保证电力系统调度的环保性与经济性,可有效应用于新能源电力系统的低碳经济调度。