Optimal Power Flow Subject to Security Constraints Solved With a Particle Swarm Optimizer

This paper presents a novel approach to solve an optimal power flow problem with embedded security constraints (OPF-SC), represented by a mixture of continuous and discrete control variables, where the major aim is to minimize the total operating cost, taking into account both operating security constraints and system capacity requirements. The particle swarm optimization (PSO) algorithm with reconstruction operators (PSO-RO) has been used as the optimization tool. Such operators guarantee searching the optimal solution within the feasible space, reducing the computation time and improving the quality of the solution. Results on systems from the specialized literature are adopted to validate the proposed approach.     

基于改进平衡优化器的电力系统最优潮流计算

针对原始平衡优化器(equilibrium optimizer,EO)难以较好平衡算法搜索能力和利用能力的不足,提出一种基于自适应生成概率的改进平衡优化器(modified equilibrium optimizer,MEO)来求解电力系统的最优潮流计算问题。以系统网损、电压偏移和发电成本为目标,将改进平衡优化器用于IEEE118节点系统的潮流计算问题。通过与原始平衡优化器和粒子群算法(particle swarm optimization,PSO)进行对比,改进平衡优化器在3个目标上均取得了较好的求解结果,验证了改进算法的优越性。     

计及经济性和光伏消纳率的微电网多目标优化策略研究

县域微电网的发展规模不断壮大,存在着微网运营支出成本与分布式可再生能源消纳率无法同时兼优的问题,基于此建立以日运营支出成本最小和光伏消纳率最大的双目标函数,计及功率平衡、功率范围等约束,建立了微电网优化运行模型。引入多目标粒子群算法对双目标问题进行折衷求解,最后以某一工业园区的总用电负荷和光伏预测数据为例,与标准粒子群算法单一目标下的优化结果进行对比分析,验证了所提模型和算法的有效性。     

An Improved Particle Swarm Optimization for the Combined Heat and Power Dynamic Economic Dispatch Problem

—This study presents a novel improved particle swarm optimization algorithm to solve the combined heat and power dynamic economic dispatch problem. This problem is formulated as a challenging non-convex and non-linear optimization problem considering practical characteristics, such as valve-point effects, transmission losses, ramp-rate limits, mutual dependency of power and heat, spinning reserve requirements, and transmission security constraints. The proposed method combines classical particle swarm optimization with a chaotic mechanism, time-variant acceleration coefficients, and a self-adaptive mutation scheme to prevent premature convergence and improve solution quality. Moreover, multiple efficient constraint handling strategies are employed to deal with complex constraints. The effectiveness of the proposed improved particle swarm optimization for solving the combined heat and power dynamic economic dispatch problem is validated on three different test systems, and the results are compared with those of other variants of particle swarm optimization as well as other methods reported in the literature. The numerical results demonstrate the superiority of improved particle swarm optimization in solving the combined heat and power dynamic economic dispatch problem while strictly satisfying all the constraints.     

Power systems operation using particle swarm optimization technique

This paper presents a proposed technique for solving different optimization problems using particle swarm optimization (PSO) technique as a modern optimization technique. The security constrained optimal active power dispatch is solved by a proposed optimal effective localized area (OELA) in large-scale power system at different operating conditions. However, the boundaries of this area can be increased or decreased depending on the amount and type of the operation problems as well as the control action requirements to remove these problems. Hence, minimum control variables are adjusted in a small-localized area to steer the system to secure and reliable operation condition. The optimal operation of ready reserve is introduced using an efficient proposed procedure considering the security constraints of the transmission lines power flows. Different emergency condition problems are solved using the OELA applied to different standard test systems.     

基于节点不平衡功率的粒子群潮流转移控制算法

通过将潮流转移的校正控制转化为非线性规划问题,提出了基于节点不平衡功率的潮流转移控制算法。首先将常规优化问题中的功率平衡等式转化为节点不平衡功率,作为优化目标处理,避免了常规人工智能优化算法中必须先满足潮流等式后再优化求解的弊端,提高了计算速度;然后应用信息充分交流的粒子群优化方法求解该模型。为了克服粒子群算法的早熟,采用混沌序列初始化粒子位置,发生早熟停滞时进行混沌寻优,以增强搜索多样性。该方法可同时计及实施过程中的各种约束。系统负荷较重时,常规方法无法使用,但文中所述算法依然有效。利用新英格兰39节点系统验证了该方法的有效性。     

考虑N-1安全网络约束的输电网结构优化

输电网结构优化是控制输电阻塞的手段之一。且当负荷处于较低水平、系统裕度较高时,也可以通过结构优化提高设备的利用率。为了在开断部分线路的同时保证系统安全性,建立考虑N-1安全网络约束的输电网结构优化模型。通过对可开断线路潮流方程进行线性化,将原有模型转化成混合整数线性规划形式。为了应对负荷的短期波动及风电出力不确定性对电网结构优化结果的影响,采用吸引子传播(AP)聚类算法构建不同的运行场景。以修改的IEEE-RTS 24节点系统为例对所提模型进行验证和分析,结果表明,在满足一定的安全约束条件下,断开某些输电网线路可以减轻输电阻塞、降低系统的运行成本、提高线路的负载率水平。     

面向可靠性提升的关联规则驱动下配电网投资规划优选模型与方法

随着清洁能源的接入、供需交互的加深,当前计及完备潮流方程与网络安全约束的投资规划优化模型在面对大量改造措施决策时,存在计算繁琐、收敛性差的问题。提出了一种基于改造措施与可靠性指标关联规则取代潮流与网络安全约束的配电网投资规划优选模型与方法,该模型中配电网可靠性指标与改造措施间的关联关系通过选择合适的机器学习算法实现。分析了可靠性与改造措施的关联规则,分别以可靠性提升最大和投资费用最少为目标建立基于关联规则驱动的配电网投资规划优选模型,考虑各类改造措施对配电网可靠性指标的提升效益,实现配电网投资规划方案优选。通过实例验证了所提投资规划优选优化模型和求解方法的快速性、可行性与有效性。     

基于粒子群优化算法的输变电设备检修优化

传统的检修优化模型中,设备的检修状态变量采用0、1二元变量表示,无法用粒子群优化算法(PSO)求解。提出了一种新的输变电设备检修优化模型。该模型用整数表示检修状态变量,使得检修约束得以简化,有利于PSO的求解。仿真结果表明,与遗传算法(GA)相比,在该模型下PSO收敛速度更快,获得更优的解。     

Multi-area Environmental Economic Dispatch with Reserve Constraints Using Enhanced Particle Swarm Optimization

In this paper, the multi-area environmental economic dispatch (MAEED) problem with reserve constraints is solved by proposing an enhanced particle swarm optimization (EPSO) method. The objective of MAEED problem is to determine the optimal generating schedule of thermal units and inter-area power transactions in such a way that total fuel cost and emission are simultaneously optimized while satisfying tie-line, reserve, and other operational constraints. The spinning reserve requirements for reserve-sharing provisions are investigated by considering contingency and pooling spinning reserves. The control equation of the particle swarm optimization (PSO) is modified by improving the cognitive component of the particle's velocity using a new concept of a preceding experience. In addition, the operators of PSO are dynamically controlled to maintain a better balance between cognitive and social behavior of the swarm. The effectiveness of the proposed EPSO has been investigated on four areas, 16 generators and four areas, 40 generators test systems. The application results show that EPSO is very promising to solve the MAEED problem.     

考虑安全性和经济性的连锁故障预防控制策略

为阻止源头性故障引发连锁故障的安全问题,文章提出一种考虑安全性和经济性的连锁故障预防控制策略.首先,根据继电保护的动作特性给出一种判别连锁故障的数学形式.其次,以电网安全裕度和发电运行成本分别评价系统的安全性和经济性,以支路脆弱性评估方法选取初始故障,构建了针对不同初始故障作用下的连锁故障预防控制模型.该模型是一种双层...     

A solution to security constrained non-convex economic dispatch problem by modified subgradient algorithm based on feasible values

A security constrained power dispatch problem with non-convex total cost rate function for a lossy electric power system is formulated. Then, an iterative solution method proposed by us and based on modified subgradient algorithm operating on feasible values (F-MSG) is used to solve it.Since all equality and inequality constraints in our nonlinear optimization model are functions of bus voltage magnitudes and phase angles, off-nominal tap settings and susceptance values of svar systems, they are taken as independent variables. Load flow equations are added to the model as equality constraints. The unit generation constraints, transmission line capacity constraints, bus voltage magnitude constraints, off-nominal tap setting constraints and svar system susceptance value constraints are added into the optimization problem as inequality constraints. Since F-MSG algorithm requires that all inequality constraints should be expressed in equality constraint form, all inequality constraints are converted into equality constraints by the method, which does not add any extra independent variable into the model and reducing the solution time because of it, before application of it to the optimization model.The proposed technique is tested on IEEE 30-bus and IEEE 57 bus test systems. The minimum total cost rates and the solution times obtained from F-MSG algorithm and from the other techniques are compared, and the outperformance of the F-MSG algorithm with respect to the other methods in each test system is demonstrated.     

基于改进粒子群优化算法的电力市场下的无功优化

在厂网分开、竞价上网的市场模式下综合考虑电力系统安全约束，建立了以有功网损和无功费用最小为目标函数并包含各种运行约束条件的电力系统无功优化数学模型。应用改进粒子群优化算法求解该无功优化模型，并结合动态调整罚函数法将无功优化问题转化成无约束求极值问题，从而有效地提高了改进粒子群优化算法的全局收敛能力和计算精度，使电网公司取得了最大经济效益。以IEEE30节点系统为例进行了仿真计算，结果表明了本文采用的无功优化模型和算法的正确性、适用性和较好的经济性。     

电力市场初期两部制无功定价方法

提出了一种电力市场初期的两部制无功定价方法,以有功电能成本和无功电量成本最优为目标函数,以潮流方程为等式约束,以运行及安全约束为不等式约束。建议的内点非线性规划法原理简单、计算量小。所提两部制无功电价模型的核心想法为:一方面,提出电力市场下无功源以运行成本参与竞争,以解决现有的一部制电价对无功的运行成本补偿不足的问题;另一方面,提出一种新的无功容量电价分解方案,以解决现有的一部制电价对无功投资成本回收不明确的问题。电量电价加容量电价形成了建议的两部制无功电价。IEEE-30节点系统算例验证了建议的无功优化算法和无功价格模型的有效性和实用性。     

Expected security cost‐based FACTS device allocation using hybrid PSO

This paper presents FACTS device allocation for market‐based power systems. The purpose of the FACTS installation is to provide benefit for all entities. Therefore, we use a concept of minimizing expected security cost (ESC), implying to maximize social welfare, to minimize operating reserve, and to minimize load interruption in annual basis. The FACTS device investment cost is also taken into account. The ESC considers operating cost under normal state and contingencies along with their associated probabilities to occur. Annual basis bid data is used to compute ESC as well as the cost data for load interruption and reserve procurement. This paper also considers control actions among multiple FACTS device to achieve minimum ESC. To solve the overall problem, particle swarm optimization is utilized to obtain optimal FACTS device allocation as main problem while sequential quadratic programing is used to solve optimal power flow as suboptimization problem. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Modified particle swarm optimization for nonconvex economic dispatch problems

This paper presents modified particle swarm optimization to solve economic dispatch problems with non-smooth/non-convex cost functions. Particle swarm optimization performs well for small dimensional and less complicated problems but fails to locate global minima for complex multi-minima functions. This paper proposes Gaussian random variables in velocity term which improves search efficiency and guarantees a high probability of obtaining the global optimum without considerably worsening the speed of convergence and the simplicity of the structure of particle swarm optimization. The efficacy of the proposed method has been demonstrated on four test problems and four different non-convex economic dispatch problems with valve-point effects, prohibited operating zones with transmission losses, multiple fuels with valve point effects and the large-scale Korean power system with valve-point effects and prohibited operating zones. The results of the proposed approach are compared with those obtained by other evolutionary methods reported in the literature. It is found that the proposed modified particle swarm optimization based approach is able to provide better solution.     

计及价格弹性负荷及风电的随机安全约束经济调度

基于机会约束规划,提出一种计及价格弹性负荷响应及风电不确定性的随机安全约束经济调度模型。模型考虑了输电断面潮流机会约束,并通过设置安全概率水平,控制输电断面潮流越限的概率。利用潮流灵敏度分析方法将分支潮流约束、输电断面潮流约束线性化,进而将输电断面潮流机会约束转化为常规约束,最终将所建随机优化模型转化为确定性二次规划模型,验证了所提模型及方法的有效性。     

Multi-objective optimization of hydrothermal energy system considering economic and environmental aspects

Along with continuous global warming, the environmental problems, besides the economic objective, are expected to play more and more important role in the operation of hydrothermal power system. In this paper, the short-term multi-objective economic environmental hydrothermal scheduling (MEEHS) model is developed to analyze the operating approach of MEEHS problem, which simultaneously optimize energy cost as well as the pollutant emission effects. Meanwhile, transmission line losses among generation units, valve-point loading effects of thermal units and water transport delay between hydraulic connected reservoirs are taken into consideration in the problem formulation. In order to solve MEEHS problem, a new multi-objective cultural algorithm based on particle swarm optimization (MOCA-PSO) is presented in way of combining the cultural algorithm framework with particle swarm optimization (PSO) to carry though the evolution of population space. Furthermore, an effective constrain handling method is proposed to handle the operational constraints of MEEHS problem. The proposed method is applied to a hydrothermal power system consisting of four hydro plants and three thermal units for the case studies. Compared with several previous methods, the simulation solutions of MOCA-PSO with smaller fuel cost and lower emission effects proves that it can be an alternative method to deal with MEEHS problems. The obtained results demonstrate that the change of optimization objective leads to the shift of optimal operation schedules. Finally, the scheduling results of MEEHS problem offer enough choices to the decision makers. Thus, the operation with better performance of environment is achieved by more energy system cost.     

一种新的水火电力系统优化潮流模型

提出了一种新的水火电力系统的优化潮流模型,该模型以最小化燃料费用和污染排放量为目标。模型中的约束条件考虑了网损和系统稳定性2个方面,其中网损用发电量和发电量转移分配系数表示,系统的暂态稳定性和静态电压稳定性分别用动态安全域和静态电压稳定域的方式表示。该文还就目标函数中考虑燃料费用和污染排放比例关系进行了研究。优化模型的雅克比矩阵由网损和各节点发电量之间的灵敏度因子以及动态安全域和静态电压安全域的系数构成。该模型的求解使用牛顿-拉夫逊迭代法实现,并采用一种新的初值设定方法以提高计算的收敛特性。通过2个标准系统算例验证了该模型的有效性。     

An Improved Particle Swarm Optimization for Nonconvex Economic Dispatch Problems

This paper presents an efficient approach for solving economic dispatch (ED) problems with nonconvex cost functions using an improved particle swarm optimization (IPSO). Although the particle swarm optimization (PSO) approaches have several advantages suitable to heavily constrained nonconvex optimization problems, they still can have the drawbacks such as local optimal trapping due to premature convergence (i.e., exploration problem), insufficient capability to find nearby extreme points (i.e., exploitation problem), and lack of efficient mechanism to treat the constraints (i.e., constraint handling problem). This paper proposes an improved PSO framework employing chaotic sequences combined with the conventional linearly decreasing inertia weights and adopting a crossover operation scheme to increase both exploration and exploitation capability of the PSO. In addition, an effective constraint handling framework is employed for considering equality and inequality constraints. The proposed IPSO is applied to three different nonconvex ED problems with valve-point effects, prohibited operating zones with ramp rate limits as well as transmission network losses, and multi-fuels with valve-point effects. Additionally, it is applied to the large-scale power system of Korea. Also, the results are compared with those of the state-of-the-art methods.