电力系统分布式无功电压优化控制研究
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摘要
电力系统无功电压运行优化是实现电力系统最优资源配置,提高系统的安全性和经济效益的重要手段。本文详细探讨了全网无功电压优化的算法、实用化和实现方案。针对目前无功电压优化算法存在的不足,根据电力系统分布、分散的特点,提出了基于电网分区的分布式并行无功优化算法,并对其进行了多目标、软约束的模糊化处理和离散控制变量的罚函数处理,利用直接非线性原—对偶内点法寻优求解。将该算法与多Agent技术相结合,提出了基于多Agent技术的分布式无功电压优化系统的设计方案。具体的研究内容包括:
1.基于电网分区的分布式并行无功优化算法
本文首先分析了无功电压优化的研究现状,总结了以往优化算法的优缺点,得到了当前系统运行对优化算法的要求,即优化算法应适应电力系统分布、分散的特点,适应电力市场发展的需要,能够快速收敛,数据通信量少,便于实现。针对以上要求,提出了基于电网分区的分布式并行无功优化算法。对于单目标无功电压优化,根据实际电网分区情况,采用分解协调法复制各分区的边界节点,建立分解协调模型,采用增广拉格朗日法将求分解协调模型的极小值问题转化为求增广拉格朗日函数的鞍点问题,然后采用辅助问题原理分解变量和增广拉格朗日函数,从而将全网无功电压优化问题分解为多个分区的分布式并行优化问题。对于多目标的无功优化问题,首先用分解协调法,将全网的多目标无功优化问题转化为求解各个分区的多目标无功优化问题,然后用上述单目标优化算法分解每一个单目标优化问题,再将各个目标综合,得到多个分区的多目标分布并行优化问题。辅助问题原理建立了一个用于分布式并行优化的计算框架,各分区可根据具体情况自主选择优化算法。该算法将原问题分解为多个并行求解的子问题,缩小了问题的规模,降低了问题的复杂程度。仿真结果表明,对于粗粒度、大型电力系统的优化计算,相对于其它算法,本算法具有收敛速度快、数据通信量少等特点。
2.对于各分区的多目标无功电压优化问题,采用梯形模糊隶属度函数,将每一个目标模糊化,求解多个目标函数最小隶属度的最大化问题,从而将多目标优化问题转化为单目标问题。然后采用直接非线性原—对偶内点法进行优化计算,计算速度快,准确率高。本文详细推导了采用模糊集理论和内点法求解分区
Voltage and reactive power optimization is an important means for power resources configuration and improvement of system security and economic profit. This dissertation discusses the voltage and reactive power optimization algorithm, and its practicability and application scheme. To overcome the shortcomings of existing algorithms, the distributed parallel reactive power optimization algorithm based on sub-area division of the power systems is proposed according to the distributed and decentralized characteristics of the power system. Here, multi-objective function and soft constraints are modeled using fuzzy sets, and the multi-objective reactive power optimization problem is solved by the direct nonlinear primal-dual interior point algorithm. Combined above methods with the multi-agent technology, a multi-agent system based distributed voltage and reactive power system is proposed. The research includes following contents:1. Distributed parallel reactive power optimization algorithm based on sub-area division of the power systems. The merits and shortcomings of the existing optimization algorithms are summarized. According to these summarizations, optimization algorithm is required to be adaptive to the distributed and decentralized characteristics of power systems, thus leads to a fast convergence property, minimum data transfer and easy application. So the sub-area division based distributed and parallel reactive power optimization is proposed for the above requirements. For the single objective optimization, the decomposition and coordination method is adopted to build the decomposition and coordination model according to the existing sub-area division conditions of power networks. Then using the Augmented Lagrange method, the minimization problem of decomposition and coordination model can be changed to the saddle point problem of augmented Lagrangian function. Finally, the so called auxiliary problem principle (APP) is selected to decompose variables as well as the functions. This transforms the voltage and reactive optimization problem of the whole
networks to some sub-problems in some sub-areas. As for the multi-objective reactive power optimization, the decomposition and coordination method is conducted to change the original problem into some related multi-objective optimization sub-problems in some sub-areas. Then the above single objective method is used to deal with each sub-object. The multi-area multi-objective distributed parallel optimization can be concluded due to the integration of the sub-objects. The auxiliary problem principle establishes a frame for distributed and parallel optimization, and each sub-area has its self-determination to choose the optimization algorithm for its own area. This algorithm decomposes the primal problem into several sub-problems solving parallel which reduces the size and complexity of the optimization problem. Simulation results show that this algorithm is effective with faster convergence property and less data transfer than other algorithms.2. Trapezoid fuzzy membership functions are used to process every object. Then the multi-objective voltage and reactive power optimization problem of each sub-area, is reformulated as a single objective problem, which is to maximize minimal membership of the object functions. Using the direct nonlinear primal-dual interior point algorithm, the single objective problem can be solved The way of solving the multi-objective reactive power optimization of a sub-area with fuzzy sets theory and interior point algorithm is deduced in detail here.3. The practical application research of the distributed parallel reactive power optimization algorithm based on sub-area division of the power systems is studied in this dissertation.(1) As the local reference bus is defined in each sub-area in the algorithm, multi-reference buses are brought out in the whole power system. In order to make the optimization results accord with the need of global optimization, it is necessary to coordinate the multi-reference buses of sub-areas and make only one real reference bus in the whole power system. A—variable idea is introduced to solve this problem. Here, every bus voltage phase is a A—variable which can be expressed by the local phase plus the local reference phase. The new iteration formulae of auxiliary problem
principle are deduced with new kernel function constructed in the light of this idea.(2) The soft constraints of optimization problem are handled with fuzzy sets in the dissertation. Firstly all the constraints variables are classified. Secondly soft constraints are modeled with trapezoid fuzzy membership functions. Then slack variables are introduced to transform the inequality constraints into equation ones. Thirdly the non-negative restrictions with respect to the slack variables are eliminated by the logarithm barrier functions. Last the new optimization model is solved by direct nonlinear primal-dual interior point algorithm. As for the discrete control variables, a fictitious cost function created by quadratic penalty function is appended to the original objective function. In order to handle the discrete variables effectively and prevent them from converging at some local optimal solution, the discrete control variables are treated as continuous ones in early iterations in the optimization process. When the binding inequality constraints are essentially determined and the changes of the discrete variables in two consecutive iterations are less than a given tolerance in late iterations, a quadratic penalty function should be introduced to drive the discrete variables toward their neighborhood centers.4. The distributed and parallel reactive power optimization algorithm based on sub-area division of the power systems is firstly combined with the multi-agent technology according to its characteristics. The multi-agent system based distributed voltage and reactive power system is proposed in this dissertation. On one hand, The distributed and parallel characteristic of the algorithm is suitable for multi-agent system, On the other hand, the multi-agent technology can coordinate the decentralized logical or physical systems to solve a problem in parallel. The multi-agent system provides a flexible intelligent platform for application of the algorithm. The multi-agent system proposed in this dissertation is of hierachical and distributed structure. The functions and operation mechanism are introduced. The two-level scheme is put forward for power system secondary voltage contingency control. Several key problems in practical applications are also discussed. Some instructive work about the multi-agent system based distributed voltage and reactive
1.基于电网分区的分布式并行无功优化算法
本文首先分析了无功电压优化的研究现状,总结了以往优化算法的优缺点,得到了当前系统运行对优化算法的要求,即优化算法应适应电力系统分布、分散的特点,适应电力市场发展的需要,能够快速收敛,数据通信量少,便于实现。针对以上要求,提出了基于电网分区的分布式并行无功优化算法。对于单目标无功电压优化,根据实际电网分区情况,采用分解协调法复制各分区的边界节点,建立分解协调模型,采用增广拉格朗日法将求分解协调模型的极小值问题转化为求增广拉格朗日函数的鞍点问题,然后采用辅助问题原理分解变量和增广拉格朗日函数,从而将全网无功电压优化问题分解为多个分区的分布式并行优化问题。对于多目标的无功优化问题,首先用分解协调法,将全网的多目标无功优化问题转化为求解各个分区的多目标无功优化问题,然后用上述单目标优化算法分解每一个单目标优化问题,再将各个目标综合,得到多个分区的多目标分布并行优化问题。辅助问题原理建立了一个用于分布式并行优化的计算框架,各分区可根据具体情况自主选择优化算法。该算法将原问题分解为多个并行求解的子问题,缩小了问题的规模,降低了问题的复杂程度。仿真结果表明,对于粗粒度、大型电力系统的优化计算,相对于其它算法,本算法具有收敛速度快、数据通信量少等特点。
2.对于各分区的多目标无功电压优化问题,采用梯形模糊隶属度函数,将每一个目标模糊化,求解多个目标函数最小隶属度的最大化问题,从而将多目标优化问题转化为单目标问题。然后采用直接非线性原—对偶内点法进行优化计算,计算速度快,准确率高。本文详细推导了采用模糊集理论和内点法求解分区
Voltage and reactive power optimization is an important means for power resources configuration and improvement of system security and economic profit. This dissertation discusses the voltage and reactive power optimization algorithm, and its practicability and application scheme. To overcome the shortcomings of existing algorithms, the distributed parallel reactive power optimization algorithm based on sub-area division of the power systems is proposed according to the distributed and decentralized characteristics of the power system. Here, multi-objective function and soft constraints are modeled using fuzzy sets, and the multi-objective reactive power optimization problem is solved by the direct nonlinear primal-dual interior point algorithm. Combined above methods with the multi-agent technology, a multi-agent system based distributed voltage and reactive power system is proposed. The research includes following contents:1. Distributed parallel reactive power optimization algorithm based on sub-area division of the power systems. The merits and shortcomings of the existing optimization algorithms are summarized. According to these summarizations, optimization algorithm is required to be adaptive to the distributed and decentralized characteristics of power systems, thus leads to a fast convergence property, minimum data transfer and easy application. So the sub-area division based distributed and parallel reactive power optimization is proposed for the above requirements. For the single objective optimization, the decomposition and coordination method is adopted to build the decomposition and coordination model according to the existing sub-area division conditions of power networks. Then using the Augmented Lagrange method, the minimization problem of decomposition and coordination model can be changed to the saddle point problem of augmented Lagrangian function. Finally, the so called auxiliary problem principle (APP) is selected to decompose variables as well as the functions. This transforms the voltage and reactive optimization problem of the whole
networks to some sub-problems in some sub-areas. As for the multi-objective reactive power optimization, the decomposition and coordination method is conducted to change the original problem into some related multi-objective optimization sub-problems in some sub-areas. Then the above single objective method is used to deal with each sub-object. The multi-area multi-objective distributed parallel optimization can be concluded due to the integration of the sub-objects. The auxiliary problem principle establishes a frame for distributed and parallel optimization, and each sub-area has its self-determination to choose the optimization algorithm for its own area. This algorithm decomposes the primal problem into several sub-problems solving parallel which reduces the size and complexity of the optimization problem. Simulation results show that this algorithm is effective with faster convergence property and less data transfer than other algorithms.2. Trapezoid fuzzy membership functions are used to process every object. Then the multi-objective voltage and reactive power optimization problem of each sub-area, is reformulated as a single objective problem, which is to maximize minimal membership of the object functions. Using the direct nonlinear primal-dual interior point algorithm, the single objective problem can be solved The way of solving the multi-objective reactive power optimization of a sub-area with fuzzy sets theory and interior point algorithm is deduced in detail here.3. The practical application research of the distributed parallel reactive power optimization algorithm based on sub-area division of the power systems is studied in this dissertation.(1) As the local reference bus is defined in each sub-area in the algorithm, multi-reference buses are brought out in the whole power system. In order to make the optimization results accord with the need of global optimization, it is necessary to coordinate the multi-reference buses of sub-areas and make only one real reference bus in the whole power system. A—variable idea is introduced to solve this problem. Here, every bus voltage phase is a A—variable which can be expressed by the local phase plus the local reference phase. The new iteration formulae of auxiliary problem
principle are deduced with new kernel function constructed in the light of this idea.(2) The soft constraints of optimization problem are handled with fuzzy sets in the dissertation. Firstly all the constraints variables are classified. Secondly soft constraints are modeled with trapezoid fuzzy membership functions. Then slack variables are introduced to transform the inequality constraints into equation ones. Thirdly the non-negative restrictions with respect to the slack variables are eliminated by the logarithm barrier functions. Last the new optimization model is solved by direct nonlinear primal-dual interior point algorithm. As for the discrete control variables, a fictitious cost function created by quadratic penalty function is appended to the original objective function. In order to handle the discrete variables effectively and prevent them from converging at some local optimal solution, the discrete control variables are treated as continuous ones in early iterations in the optimization process. When the binding inequality constraints are essentially determined and the changes of the discrete variables in two consecutive iterations are less than a given tolerance in late iterations, a quadratic penalty function should be introduced to drive the discrete variables toward their neighborhood centers.4. The distributed and parallel reactive power optimization algorithm based on sub-area division of the power systems is firstly combined with the multi-agent technology according to its characteristics. The multi-agent system based distributed voltage and reactive power system is proposed in this dissertation. On one hand, The distributed and parallel characteristic of the algorithm is suitable for multi-agent system, On the other hand, the multi-agent technology can coordinate the decentralized logical or physical systems to solve a problem in parallel. The multi-agent system provides a flexible intelligent platform for application of the algorithm. The multi-agent system proposed in this dissertation is of hierachical and distributed structure. The functions and operation mechanism are introduced. The two-level scheme is put forward for power system secondary voltage contingency control. Several key problems in practical applications are also discussed. Some instructive work about the multi-agent system based distributed voltage and reactive
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