基于新型进化算法和微机集群的电力系统并行无功优化研究
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摘要
电力系统无功电压自动控制的发展大致可以分为四个阶段,即设备级就地分散控制阶段、厂站级就地协调控制阶段、区域级协调控制阶段和全局协调控制阶段。其中尤以基于无功优化、集安全性和经济性于一体的全局协调优化控制为最高追求目标,其条件随着SCADA数据准确率和EMS实用化水平的不断提高正日渐成熟,相应的需求也日益迫切。因此,无功优化问题是目前电力系统领域中的研究热点之一,研究内容主要包括两个方面,即考虑更多实际需求的详细建模和快速准确的求解。本文着重研究无功优化问题的求解方法。
在数学上,无功优化是一种同时具有连续变量和离散变量、具有非线性的目标函数、非线性的等式和不等式约束的复杂优化问题,具有非凸性和多极值性,其快速准确求解相当困难。目前主要有基于导数的数学规划方法和智能优化算法等两类求解方法,前者以内点法为最新发展,后者以进化算法为典型代表。两者各有优缺点,前者计算速度快,但理论上容易陷入局部极小点,在处理离散控制变量和不可行问题方面存在困难;后者能以较大概率找到全局最优解,便于处理离散控制变量和不可行问题,但容易陷入早熟,计算速度慢。
为解决基于进化算法的无功优化的早熟和计算速度慢的缺点,前人做了大量工作。归纳起来,主要有三个努力方向:(1)利用进化算法与其它智能优化算法或内点法的互补性来构造混合算法;(2)运用与无功优化相关的电力系统计算和运行方面的经验和知识来简化计算模型、减小问题规模;(3)运用并行计算来加速计算。本文的研究也大致按照这三个方向展开:
第2章从全局搜索能力较强的进化规划(EP)入手,首先比较了四种EP方案用于求解无功优化问题时的性能;然后研究了所谓的自适应快速EP方案用于求解无功优化问题时的有效性;最后根据比较分析中总结出来的规律,对两种EP方案进行了成功的改进。研究总体表明,EP用于求解无功优化问题时速度太慢。
第3章将差异进化算法(DE)首次用于求解无功优化问题,研究了其寻优机理和参数设置的问题,并通过与其它进化算法和粒子群算法的比较分析了它的性能。结果表明,对求解无功优化问题而言,DE总体上是一种比较优秀的新型进化算法,值得进一步研究和应用。但同时也发现,DE需要相对较大的群体规模才能避免早熟收敛。当系统规模较大时,这将导致计算时间很长,在单机计算的条件下难以满足在线无功优化的需要。
第4章研究运用并行计算技术来加快DE用于求解无功优化问题时的计算速度,并以微机集群为平台加以实现。算例分析表明,并行化的确可以大大提高DE求解无功优化问题的速度,采用并行DE和适当规模的集群可以较好地实现电力系统的在线无功优化。但同时也发现,并行计算的加速效果随集群规模的扩大而迅速饱和,有必要通过算法本身的改进来降低所需的群体规模,从而进一步加快计算或使用更小规模的集群以降低成本。
第5章首先分析了DE和EP的互补性,然后利用这种互补性设计了名为DEEP的混合算法。它以DE为主体,并通过EP的随机变异操作引入新的遗传信息以缓解早熟压力。算例分析表明DEEP具有如下优点:(1)可以有效克服DE需要相对较大的群体规模才能避免早熟的缺点,从而可以大大节省计算时间。主从并行化时,DEEP还可将繁衍操作分散到从进程进行而不致使优化结果明显变差,从而可以进一步节省计算时间。(2)是一种通用的算法,且性能对参数不敏感,唯一的参数设为固定值即可。(3)由于采用了合理的主辅群体机制,对辅助群体不做适应度评估,故新增的计算时间几乎可以忽略不计,十分适于求解无功优化这种适应度评估非常耗时的优化问题。
第6章运用协同进化技术提供的系统框架,将分解协调技术引入了DE,并利用电力系统无功电压之间的关系具有局部性的特点将电网分成若干个尽可能独立的区域以减少协调工作量,由此构造了一种协同DE与电网分区相结合的无功优化方法CCDE-PSD;针对其特点,还设计了一种三层主从并行结构来实现其并行化。算例分析表明,CCDE-PSD及其并行化的方案设计都是合理有效的。无论从解的质量还是计算时间来看,CCDE-PSD都明显优于普通DE,可以在使用更小的群体规模和更少的进化代数的情况下获得更好的解。
第7章总结全文,并展望了值得进一步开展的工作。
The development of automatic reactive power and voltage control in power systems can be roughly divided into four phases, namely the apparatus level local dispersed control, the power plant and substation level local coordinated control, the regional coordinated control and the global coordinated control. And the highest objective is the reactive power optimization (RPO) based global coordinated optimal control that addresses both the security and the economic issues. Its precondition is maturating with the improvement of the data accuracy of SCADA and the practicability of EMS, and the demand for it is becoming more and more urgent. Therefore, RPO is one of the hotspots in the power engineering research field. The contents of research mainly consist of two aspects: the detailed modelization considering more practical requirements and the fast as well as accurate solution. This thesis concentrates on studying the solution methods of RPO.
Mathematically, RPO is a non-convex and multimodal complex optimization problem involving nonlinear objective function, nonlinear equality and inequality constraints and both continuous and discrete variables. It is quite difficult to be solved quickly and accurately. Currently, mainly two classes of methods are used to solve RPO, namely the gradient-based mathematical programming methods and the intelligent optimization methods. The new development of the former class is the interior point methods (IPM) and the typical representatives of the latter class are evolutionary algorithms (EAs). Each class of methods have its own advantages and disadvantages: the former is fast, but is theoretically easy to converge to local minima and has difficulties in handling discrete variables and infeasibility problems; the latter can find global solutions in high probability and is good at handling discrete variables and infeasibility problems, but is slow and suffers from the problem of premature convergence.
In order to overcome the disadvantages of EA-based RPO, many researches have been conducted, from which three directions can be summarized: (1) constructing hybrid algorithms using the complementary features between EAs and other intelligent optimization methods or IPMs; (2) simplifying the model and reducing the problem size using RPO-related experiences and knowledge in the field of power system calculation and operation; (3) accelerating the computation using parallel computing technologies. The work of this thesis roughly follows these three directions.
Chapter 2 starts from evolutionary programming (EP) that has good global search ability. The performances of four EP schemes on solving RPO problems are first compared. The effectiveness of the so called adaptive fast EP on solving RPO problems is then studied. Finally, according to the principles summarized from the comparison study, successful improvements on two of the four EP schemes are made. As a whole, the researches in this chapter show that EP is generally too slow for solving RPO problems.
Chapter 3 applies differential evolution (DE) to solve RPO problems for the first time. The mechanism and parameter setting of DE are first analyzed. Performance of DE on RPO problems is then studied with comparison to other EAs and the particle swarm optimization algorithm. The study shows that generally, DE is an excellent new EA for solving RPO problems, it is worthy of further studies and applications. However, it is also found that DE requires relatively large population size to avoid premature convergence. When the target power system is large, this will make the computational time too long to be acceptable for online RPO.
Chapter 4 manages to improve the speed of DE for solving RPO problems by using parallel computing technologies, and parallel computing is implemented on a PC-cluster. Case study shows that parallelization does significantly improve the speed of DE for solving RPO problems; it is possible to realize online RPO with clusters of moderate size. However, it is also found that the efficiency of parallelization saturates quickly with the increase of the cluster size. Therefore, it is necessary to improve the algorithm itself to reduce the required population size and hence to further accelerate the computation or enable the use of clusters of smaller sizes for economic consideration.
Chapter 5 first analyzes the complementary feature of DE and EP. This feature is then utilized to design a hybrid algorithm named DEEP. DEEP maintains the main body of DE, while uses the EP-style random mutation to introduce new genetic information to mitigate the pressure of premature convergence. Case studies show that DEEP has three advantages. First, it can effectively overcome the disadvantage of DE that requires relatively large population size to avoid premature convergence, which can greatly save the computational time. When extended to master-slave parallel computing, the reproduction step of DEEP can also be carried out dispersedly by slave processes without significant deterioration of solution quality, which can further save computational time. Second, DEEP is a universal algorithm. Its performance is not parametrically sensitive. Its only parameter can just be set to a fixed value. Third, due to the adoption of a novel scheme of primary population plus auxiliary population, and fitness evaluation is not arranged for the auxiliary populations, the additional time consumption of DEEP is negligible. So it is very suitable to use DEEP to solve optimization problems like RPO that consume most of the computational time on fitness evaluation.
Chapter 6 utilizes the architecture provided by cooperative co-evolution to introduce the decomposition and coordination technique into DE. The local property of the relationship between reactive power and voltage is also utilized to decompose a power system into several sub-systems that are as independent as possible to reduce the work of coordination. Based on these techniques, a method combining cooperative co-evolutionary DE and power system decomposition (CCDE-PSD) is proposed for solving RPO problems. According to the characteristic of the CCDE-PSD, a three-leveled master slave parallel computing topology is also designed to improve the computational speed. Case study shows that the design of both the CCDE-PSD and its parallelization scheme are effective. The CCDE-PSD is superior to basic DE with respect to both solution quality and computational speed. It can reach better solutions with smaller population size and fewer generations.
Chapter 7 concludes the thesis and points out some directions for future research.
在数学上,无功优化是一种同时具有连续变量和离散变量、具有非线性的目标函数、非线性的等式和不等式约束的复杂优化问题,具有非凸性和多极值性,其快速准确求解相当困难。目前主要有基于导数的数学规划方法和智能优化算法等两类求解方法,前者以内点法为最新发展,后者以进化算法为典型代表。两者各有优缺点,前者计算速度快,但理论上容易陷入局部极小点,在处理离散控制变量和不可行问题方面存在困难;后者能以较大概率找到全局最优解,便于处理离散控制变量和不可行问题,但容易陷入早熟,计算速度慢。
为解决基于进化算法的无功优化的早熟和计算速度慢的缺点,前人做了大量工作。归纳起来,主要有三个努力方向:(1)利用进化算法与其它智能优化算法或内点法的互补性来构造混合算法;(2)运用与无功优化相关的电力系统计算和运行方面的经验和知识来简化计算模型、减小问题规模;(3)运用并行计算来加速计算。本文的研究也大致按照这三个方向展开:
第2章从全局搜索能力较强的进化规划(EP)入手,首先比较了四种EP方案用于求解无功优化问题时的性能;然后研究了所谓的自适应快速EP方案用于求解无功优化问题时的有效性;最后根据比较分析中总结出来的规律,对两种EP方案进行了成功的改进。研究总体表明,EP用于求解无功优化问题时速度太慢。
第3章将差异进化算法(DE)首次用于求解无功优化问题,研究了其寻优机理和参数设置的问题,并通过与其它进化算法和粒子群算法的比较分析了它的性能。结果表明,对求解无功优化问题而言,DE总体上是一种比较优秀的新型进化算法,值得进一步研究和应用。但同时也发现,DE需要相对较大的群体规模才能避免早熟收敛。当系统规模较大时,这将导致计算时间很长,在单机计算的条件下难以满足在线无功优化的需要。
第4章研究运用并行计算技术来加快DE用于求解无功优化问题时的计算速度,并以微机集群为平台加以实现。算例分析表明,并行化的确可以大大提高DE求解无功优化问题的速度,采用并行DE和适当规模的集群可以较好地实现电力系统的在线无功优化。但同时也发现,并行计算的加速效果随集群规模的扩大而迅速饱和,有必要通过算法本身的改进来降低所需的群体规模,从而进一步加快计算或使用更小规模的集群以降低成本。
第5章首先分析了DE和EP的互补性,然后利用这种互补性设计了名为DEEP的混合算法。它以DE为主体,并通过EP的随机变异操作引入新的遗传信息以缓解早熟压力。算例分析表明DEEP具有如下优点:(1)可以有效克服DE需要相对较大的群体规模才能避免早熟的缺点,从而可以大大节省计算时间。主从并行化时,DEEP还可将繁衍操作分散到从进程进行而不致使优化结果明显变差,从而可以进一步节省计算时间。(2)是一种通用的算法,且性能对参数不敏感,唯一的参数设为固定值即可。(3)由于采用了合理的主辅群体机制,对辅助群体不做适应度评估,故新增的计算时间几乎可以忽略不计,十分适于求解无功优化这种适应度评估非常耗时的优化问题。
第6章运用协同进化技术提供的系统框架,将分解协调技术引入了DE,并利用电力系统无功电压之间的关系具有局部性的特点将电网分成若干个尽可能独立的区域以减少协调工作量,由此构造了一种协同DE与电网分区相结合的无功优化方法CCDE-PSD;针对其特点,还设计了一种三层主从并行结构来实现其并行化。算例分析表明,CCDE-PSD及其并行化的方案设计都是合理有效的。无论从解的质量还是计算时间来看,CCDE-PSD都明显优于普通DE,可以在使用更小的群体规模和更少的进化代数的情况下获得更好的解。
第7章总结全文,并展望了值得进一步开展的工作。
The development of automatic reactive power and voltage control in power systems can be roughly divided into four phases, namely the apparatus level local dispersed control, the power plant and substation level local coordinated control, the regional coordinated control and the global coordinated control. And the highest objective is the reactive power optimization (RPO) based global coordinated optimal control that addresses both the security and the economic issues. Its precondition is maturating with the improvement of the data accuracy of SCADA and the practicability of EMS, and the demand for it is becoming more and more urgent. Therefore, RPO is one of the hotspots in the power engineering research field. The contents of research mainly consist of two aspects: the detailed modelization considering more practical requirements and the fast as well as accurate solution. This thesis concentrates on studying the solution methods of RPO.
Mathematically, RPO is a non-convex and multimodal complex optimization problem involving nonlinear objective function, nonlinear equality and inequality constraints and both continuous and discrete variables. It is quite difficult to be solved quickly and accurately. Currently, mainly two classes of methods are used to solve RPO, namely the gradient-based mathematical programming methods and the intelligent optimization methods. The new development of the former class is the interior point methods (IPM) and the typical representatives of the latter class are evolutionary algorithms (EAs). Each class of methods have its own advantages and disadvantages: the former is fast, but is theoretically easy to converge to local minima and has difficulties in handling discrete variables and infeasibility problems; the latter can find global solutions in high probability and is good at handling discrete variables and infeasibility problems, but is slow and suffers from the problem of premature convergence.
In order to overcome the disadvantages of EA-based RPO, many researches have been conducted, from which three directions can be summarized: (1) constructing hybrid algorithms using the complementary features between EAs and other intelligent optimization methods or IPMs; (2) simplifying the model and reducing the problem size using RPO-related experiences and knowledge in the field of power system calculation and operation; (3) accelerating the computation using parallel computing technologies. The work of this thesis roughly follows these three directions.
Chapter 2 starts from evolutionary programming (EP) that has good global search ability. The performances of four EP schemes on solving RPO problems are first compared. The effectiveness of the so called adaptive fast EP on solving RPO problems is then studied. Finally, according to the principles summarized from the comparison study, successful improvements on two of the four EP schemes are made. As a whole, the researches in this chapter show that EP is generally too slow for solving RPO problems.
Chapter 3 applies differential evolution (DE) to solve RPO problems for the first time. The mechanism and parameter setting of DE are first analyzed. Performance of DE on RPO problems is then studied with comparison to other EAs and the particle swarm optimization algorithm. The study shows that generally, DE is an excellent new EA for solving RPO problems, it is worthy of further studies and applications. However, it is also found that DE requires relatively large population size to avoid premature convergence. When the target power system is large, this will make the computational time too long to be acceptable for online RPO.
Chapter 4 manages to improve the speed of DE for solving RPO problems by using parallel computing technologies, and parallel computing is implemented on a PC-cluster. Case study shows that parallelization does significantly improve the speed of DE for solving RPO problems; it is possible to realize online RPO with clusters of moderate size. However, it is also found that the efficiency of parallelization saturates quickly with the increase of the cluster size. Therefore, it is necessary to improve the algorithm itself to reduce the required population size and hence to further accelerate the computation or enable the use of clusters of smaller sizes for economic consideration.
Chapter 5 first analyzes the complementary feature of DE and EP. This feature is then utilized to design a hybrid algorithm named DEEP. DEEP maintains the main body of DE, while uses the EP-style random mutation to introduce new genetic information to mitigate the pressure of premature convergence. Case studies show that DEEP has three advantages. First, it can effectively overcome the disadvantage of DE that requires relatively large population size to avoid premature convergence, which can greatly save the computational time. When extended to master-slave parallel computing, the reproduction step of DEEP can also be carried out dispersedly by slave processes without significant deterioration of solution quality, which can further save computational time. Second, DEEP is a universal algorithm. Its performance is not parametrically sensitive. Its only parameter can just be set to a fixed value. Third, due to the adoption of a novel scheme of primary population plus auxiliary population, and fitness evaluation is not arranged for the auxiliary populations, the additional time consumption of DEEP is negligible. So it is very suitable to use DEEP to solve optimization problems like RPO that consume most of the computational time on fitness evaluation.
Chapter 6 utilizes the architecture provided by cooperative co-evolution to introduce the decomposition and coordination technique into DE. The local property of the relationship between reactive power and voltage is also utilized to decompose a power system into several sub-systems that are as independent as possible to reduce the work of coordination. Based on these techniques, a method combining cooperative co-evolutionary DE and power system decomposition (CCDE-PSD) is proposed for solving RPO problems. According to the characteristic of the CCDE-PSD, a three-leveled master slave parallel computing topology is also designed to improve the computational speed. Case study shows that the design of both the CCDE-PSD and its parallelization scheme are effective. The CCDE-PSD is superior to basic DE with respect to both solution quality and computational speed. It can reach better solutions with smaller population size and fewer generations.
Chapter 7 concludes the thesis and points out some directions for future research.
引文
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