微粒群算法及其在电力系统中的应用研究
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摘要
随着电力系统规模的同益扩大和电力市场改革的实施,保证电力系统安全、经济、稳定、可靠地运行越来越重要,同时,需要考虑的安全和经济因素也日趋复杂,因而针对电力系统规划、运行中的不同目标,选择不同的控制变量和约束条件,就构成了不同类型的优化问题,因此需借助优化理论加以解决。微粒群优化算法是一种新兴的智能优化算法,其概念简单,实现容易,自从Kennedy和Eberhart于1995年提出以来,在短短几年之内便获得了很大的发展,并在一些领域获得了成功应用。微粒群优化算法具有较强的全局搜索能力,但同时也有易陷入局部极值的缺点。本文主要研究了微粒群优化算法及其在电力系统中的应用研究,主要研究内容如下:
◆微粒群算法微粒轨迹收敛性分析
提出标准微粒群优化算法微粒运动轨迹收敛的充分条件。基于标准微粒群优化算法迭代矩阵的谱半径,对微粒运动轨迹的收敛性进行了分析,给出并证明了收敛的充分条件。提出一种简便的等高线图判别法,该方法能通过参数的位置判断微粒轨迹是否收敛并衡量收敛速度。对标准微粒群优化算法的进行动态行为分析,实例表明提出的微粒轨迹收敛充分条件是正确的。
◆微粒群算法改进研究
对微粒群优化算法进行深入研究,提出三种改进的微粒群算法:
构造出一种基于梯度法的微粒群优化算法。结合微粒群寻优过程中的梯度信息,对算法迭代过程进行了分析,对惯性权重作了适当的调整,提高了收敛速度;在算法收敛出现停滞时,对全局最优值沿负梯度方向变异,改变种群搜索方向,以防止算法陷入局部极值。并采用本文提出的标准微粒群优化算法微粒轨迹收敛充分条件对该算法微粒轨迹的收敛性进行分析,得出其收敛的充分条件。仿真结果表明,梯度微粒群优化算法具有优良的搜索性能。
针对微粒群优化算法的优缺点,对部分较优微粒进行退火操作,提出一种精英退火微粒群算法。在退火操作中,结合Logistic方程的特点设计了一种新的错位调整方式,对当前已知最优区域重点搜索。该算法能增强算法探索和开发的能力,避免计算量过度增加。典型测试函数结果显示,该方法有效提高了算法的收敛性能。
标准微粒群优化算法受限,仅适用于连续问题的求解。本文在标准微粒群优化算法的基础上,增加了离散化过程,提出了一种离散化微粒群算法。首先提出一种设定区间离散化方法;然后提出一种基于贪婪法的离散化方法,给出贪婪度函数,并提出简单贪婪、概率贪婪两种离散化方法。对贪婪法离散化的过程进行详细分析,探究离散化过程的各种性质。算例表明提出的离散化方法是有效可行的:参数选取合适的概率贪婪法能有效地克服微粒群算法易于陷入局部极值的缺点,具有优良的收敛性能。
◆微粒群算法在电力系统中的应用研究
机组优化组合问题是一个典型的混合组合优化问题。综合分析机组组合问题的各种约束,对机组出力上下限进行了调整,提出并证明了机组功率平衡、备用可行的判据,进而推出了机组组合的可行性判据。将梯度微粒群优化算法应用于机组组合问题的求解。将机组启停状态变量和机组输出功率连续变量融合为一个变量,提出了伪输出功率编码,降低了计算的时间复杂度;对机组分类动态调整,对多时段有效地直接优化;对各种约束进行数学处理、修复处理,提高了种群质量。采用机组组合可行判据判断微粒是否可行,并对不可行微粒进行可行化调整。优化结果显示该方法是一种有效可行的方法。
综合考虑各级负载的供电恢复与最少开关操作数,建立了舰船电力系统故障恢复模型。将本文提出的微粒群离散化方法融入精英退火微粒群算法,应用于舰船电力系统网络故障恢复问题的求解。将负载的失电、正常线路供电、备用线路供电分别映射为0,1,2三个离散位置,采用惩罚函数法处理约束。算例表明,该方法能获得更好的故障恢复方案,并具有优良的收敛性能。
With the development of the power system and power market reformation, it is more and more important to assure the safety, economy, stabilization, and reliability of the power system. With the emergence of new nature and requests, there are different kinds of optimization problems in field of power system. It is, therefore, necessary to develop practical algorithm according to the characteristic of modern power system. Particle swarm optimization algorithm is a sort of rising intelligent algorithm. Its concept is simple and it is easy to be implemented. After being presented by Kennedy and Eberhart in 1995, it has achieved great development in several years and has been successfully applied to some fields. Particle swarm optimization algorithm has a strong ability to achieve the most optimistic result. Meanwhile it has a disadvantage so far as its local minimum is concerned. In this dissertation, particle swarm optimization algorithm and its application research on power system are mainly discussed. The major innovations in this article are as follows:
Research on particle swarm optimization particle trajectories
The sufficient condition for the convergence of standard particle swarm optimization algorithm's particle trajectories, which is studied based on the spectral radius of algorithm's iteration matrix, is proposed and proved. And a kind of convenient contour map discriminance is put forward. This discriminance can be used to judge if the algorithm is convergent, measure the convergence rate. Dynamic movement analyzes and examples validate the sufficient condition for the convergence of particle trajectories.
Research on modification of particle swarm optimization
The particle swarm optimization is studied deeply and three kinds of modified PSO are put forward:
A kind of gradient particle swarm optimization is presented. This method can enhance the convergence rate by tuning the inertia weight based on analyzing the gradient information in iteration process. When the optimum information of the swarm is stagnant, the global best is mutated in its minus gradient direction to change the searching direction of the swarm and reduce the possibility of trapping in local optimum. Particle trajectories of this algorithm are studied based on the sufficient condition for the convergence of particle trajectories in standard particle swarm optimization algorithm. Simulation results verify the correctness and efficiency of this method.
A sort of elitist annealing particle swarm optimization algorithm is proposed. Part of the particle swarm is annealed in this algorithm. A new kind of annealing method based on the character of the Logistic function is designed. Then the currently best space is searched more detailedly. This algorithm can enhance the exploration and exploitation ability of the algorithm; at the same time the computation time is well controlled. Typical function optimization problem results show that this method possesses good convergent performance with faster convergent rate.
The standard particle swarm optimization algorithm is limited in the continuous problem. A discretization process is added and a universal particle swarm optimization algorithm is put forward. First, a kind of section-set discrete method is proposed; then, a kind of greed discrete method (including Simple greed method and probability greed method) is presented. And the influence of the parameter on the discretization process is analyzed. Simulation tests indicate that proposed discrete method is efficient. And the probability greed method with appropriate parameter, which can solve the problem of local minimum of the particle swarm optimization algorithm effectively, possesses strong convergence capability.
Application research on power system of particle swarm optimization
Unit commitment problem is a typical mixed combinatorial optimization problem. Various constraints are considered and analyzed. First the capacity constraints of units are modified. Then a necessary and sufficient condition is developed to determine whether the system demand constraints and the spinning reserve requirements can be satisfied by adjusting generation levels. At last the feasibility criterion of the commitment states is proposed. The gradient particle swarm optimization algorithm is applied to the unit commitment problem. A new kind of coding, pseudo active power coding, in which the up/down variable and the active power variable are fused into one variable, is proposed. Then the time complexity of computing is reduced effectively. The units are classified according to their states in every period. And the states of the units are adjusted dynamically in different periods. Then the unit commitment is optimized in all periods directly. Mathematical methods and repair methods are used to deal with the constraints. Then the quality of the swarm is improved. The results of numerical simulation demonstrate that this algorithm is efficient and practical.
A kind of integrated fault restoration model of the shipboard power system is put forward, in which the service restoration of all loads and the number of switches are considered. The elitist annealing particle swarm optimization algorithm fused with the proposed discrete method is applied to the fault reconfiguration of the shipboard power system. The lost, normal, and spare power supply states of the load are coded into 0, 1, and 2. The constraints are processed by the penalty function method. Shipboard power system fault restoration tests show that better service restoration can be provided by this method, which possesses strong convergence capability.
◆微粒群算法微粒轨迹收敛性分析
提出标准微粒群优化算法微粒运动轨迹收敛的充分条件。基于标准微粒群优化算法迭代矩阵的谱半径,对微粒运动轨迹的收敛性进行了分析,给出并证明了收敛的充分条件。提出一种简便的等高线图判别法,该方法能通过参数的位置判断微粒轨迹是否收敛并衡量收敛速度。对标准微粒群优化算法的进行动态行为分析,实例表明提出的微粒轨迹收敛充分条件是正确的。
◆微粒群算法改进研究
对微粒群优化算法进行深入研究,提出三种改进的微粒群算法:
构造出一种基于梯度法的微粒群优化算法。结合微粒群寻优过程中的梯度信息,对算法迭代过程进行了分析,对惯性权重作了适当的调整,提高了收敛速度;在算法收敛出现停滞时,对全局最优值沿负梯度方向变异,改变种群搜索方向,以防止算法陷入局部极值。并采用本文提出的标准微粒群优化算法微粒轨迹收敛充分条件对该算法微粒轨迹的收敛性进行分析,得出其收敛的充分条件。仿真结果表明,梯度微粒群优化算法具有优良的搜索性能。
针对微粒群优化算法的优缺点,对部分较优微粒进行退火操作,提出一种精英退火微粒群算法。在退火操作中,结合Logistic方程的特点设计了一种新的错位调整方式,对当前已知最优区域重点搜索。该算法能增强算法探索和开发的能力,避免计算量过度增加。典型测试函数结果显示,该方法有效提高了算法的收敛性能。
标准微粒群优化算法受限,仅适用于连续问题的求解。本文在标准微粒群优化算法的基础上,增加了离散化过程,提出了一种离散化微粒群算法。首先提出一种设定区间离散化方法;然后提出一种基于贪婪法的离散化方法,给出贪婪度函数,并提出简单贪婪、概率贪婪两种离散化方法。对贪婪法离散化的过程进行详细分析,探究离散化过程的各种性质。算例表明提出的离散化方法是有效可行的:参数选取合适的概率贪婪法能有效地克服微粒群算法易于陷入局部极值的缺点,具有优良的收敛性能。
◆微粒群算法在电力系统中的应用研究
机组优化组合问题是一个典型的混合组合优化问题。综合分析机组组合问题的各种约束,对机组出力上下限进行了调整,提出并证明了机组功率平衡、备用可行的判据,进而推出了机组组合的可行性判据。将梯度微粒群优化算法应用于机组组合问题的求解。将机组启停状态变量和机组输出功率连续变量融合为一个变量,提出了伪输出功率编码,降低了计算的时间复杂度;对机组分类动态调整,对多时段有效地直接优化;对各种约束进行数学处理、修复处理,提高了种群质量。采用机组组合可行判据判断微粒是否可行,并对不可行微粒进行可行化调整。优化结果显示该方法是一种有效可行的方法。
综合考虑各级负载的供电恢复与最少开关操作数,建立了舰船电力系统故障恢复模型。将本文提出的微粒群离散化方法融入精英退火微粒群算法,应用于舰船电力系统网络故障恢复问题的求解。将负载的失电、正常线路供电、备用线路供电分别映射为0,1,2三个离散位置,采用惩罚函数法处理约束。算例表明,该方法能获得更好的故障恢复方案,并具有优良的收敛性能。
With the development of the power system and power market reformation, it is more and more important to assure the safety, economy, stabilization, and reliability of the power system. With the emergence of new nature and requests, there are different kinds of optimization problems in field of power system. It is, therefore, necessary to develop practical algorithm according to the characteristic of modern power system. Particle swarm optimization algorithm is a sort of rising intelligent algorithm. Its concept is simple and it is easy to be implemented. After being presented by Kennedy and Eberhart in 1995, it has achieved great development in several years and has been successfully applied to some fields. Particle swarm optimization algorithm has a strong ability to achieve the most optimistic result. Meanwhile it has a disadvantage so far as its local minimum is concerned. In this dissertation, particle swarm optimization algorithm and its application research on power system are mainly discussed. The major innovations in this article are as follows:
Research on particle swarm optimization particle trajectories
The sufficient condition for the convergence of standard particle swarm optimization algorithm's particle trajectories, which is studied based on the spectral radius of algorithm's iteration matrix, is proposed and proved. And a kind of convenient contour map discriminance is put forward. This discriminance can be used to judge if the algorithm is convergent, measure the convergence rate. Dynamic movement analyzes and examples validate the sufficient condition for the convergence of particle trajectories.
Research on modification of particle swarm optimization
The particle swarm optimization is studied deeply and three kinds of modified PSO are put forward:
A kind of gradient particle swarm optimization is presented. This method can enhance the convergence rate by tuning the inertia weight based on analyzing the gradient information in iteration process. When the optimum information of the swarm is stagnant, the global best is mutated in its minus gradient direction to change the searching direction of the swarm and reduce the possibility of trapping in local optimum. Particle trajectories of this algorithm are studied based on the sufficient condition for the convergence of particle trajectories in standard particle swarm optimization algorithm. Simulation results verify the correctness and efficiency of this method.
A sort of elitist annealing particle swarm optimization algorithm is proposed. Part of the particle swarm is annealed in this algorithm. A new kind of annealing method based on the character of the Logistic function is designed. Then the currently best space is searched more detailedly. This algorithm can enhance the exploration and exploitation ability of the algorithm; at the same time the computation time is well controlled. Typical function optimization problem results show that this method possesses good convergent performance with faster convergent rate.
The standard particle swarm optimization algorithm is limited in the continuous problem. A discretization process is added and a universal particle swarm optimization algorithm is put forward. First, a kind of section-set discrete method is proposed; then, a kind of greed discrete method (including Simple greed method and probability greed method) is presented. And the influence of the parameter on the discretization process is analyzed. Simulation tests indicate that proposed discrete method is efficient. And the probability greed method with appropriate parameter, which can solve the problem of local minimum of the particle swarm optimization algorithm effectively, possesses strong convergence capability.
Application research on power system of particle swarm optimization
Unit commitment problem is a typical mixed combinatorial optimization problem. Various constraints are considered and analyzed. First the capacity constraints of units are modified. Then a necessary and sufficient condition is developed to determine whether the system demand constraints and the spinning reserve requirements can be satisfied by adjusting generation levels. At last the feasibility criterion of the commitment states is proposed. The gradient particle swarm optimization algorithm is applied to the unit commitment problem. A new kind of coding, pseudo active power coding, in which the up/down variable and the active power variable are fused into one variable, is proposed. Then the time complexity of computing is reduced effectively. The units are classified according to their states in every period. And the states of the units are adjusted dynamically in different periods. Then the unit commitment is optimized in all periods directly. Mathematical methods and repair methods are used to deal with the constraints. Then the quality of the swarm is improved. The results of numerical simulation demonstrate that this algorithm is efficient and practical.
A kind of integrated fault restoration model of the shipboard power system is put forward, in which the service restoration of all loads and the number of switches are considered. The elitist annealing particle swarm optimization algorithm fused with the proposed discrete method is applied to the fault reconfiguration of the shipboard power system. The lost, normal, and spare power supply states of the load are coded into 0, 1, and 2. The constraints are processed by the penalty function method. Shipboard power system fault restoration tests show that better service restoration can be provided by this method, which possesses strong convergence capability.
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