粒子群算法改进及其在电力系统的应用
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摘要
电力系统是一个复杂大系统，在规模日益扩大与社会对电能供应的“安全、可靠、经济、优质、低碳”等多项质量指标不断提出更高要求的背景下，为确保电力系统运行控制目标的实现，需要面对各种复杂优化问题。其复杂性主要体现在目标与约束复杂、多极值、高维、多目标以及存在诸多不确定因素等，这些均给建模方法与算法创新带来重大挑战，如何构建合适的优化模型及创造实用高效算法是解决问题的关键。现代群智能优化算法具有对目标函数零要求、实施简单及并行搜索等优点，在复杂优化领域得到越来越多的应用而倍受青睐。本研究旨在：从群智能的本质特征出发，分析粒子群算法学习模式的构造及关键要素，力图认识PSO易于“早熟”的根本原因；提出创新的粒子群学习模式，并基于新模式设计高效PSO改进算法；应用随机分析理论与差分方法研究粒子群动态轨迹及其稳定域，进一步揭示PSO的工作机理，为算法的改进提供理论基础；将改进算法与电力系统具体问题相结合并求解，提出更有效的实用方案。
群智能与仿生学原理、随机分析理论与差分方法、拟阵理论、优化理论与算法设计理论是研究上述问题的有力工具。本文采用理论研究与实证分析相结合的方法，主要研究内容及成果包括：
1.应用群智能理论研究PSO易于“早熟”的主要原因，指出原有学习模式本质的“被动性”机制是其重要原因之一。提出一种新的带主动探索意识的学习模式，将新的学习模式与Logistic混沌遍历实现技术相结合，发展出一种新的改进粒子群算法（AEPSO），通过实验测试分析验证了算法的有效性。
2.基于拟阵理论，提出一种适合于拟阵特性的一般组合优化问题的新型离散粒子群算法：基于拟阵理论，将PSO的进化策略引入到贪心算法(Greedy algorithm)的寻优搜索过程中，运用粒子群的群智能特性改善贪心算法的全局搜索性能，提出一种具有较强全局搜索能力的新型离散粒子群算法，简记为MDPSO。采用背包等组合优化问题对改进算法进行实验测试分析，验证了算法的可行性和有效性。
3.基于文化在组织团体中的核心价值思想，利用“信念空间”中的文化信息构造个性化动态适应参数，培育种群的多样性。提出一种改进的多目标粒子群算法(CBCMPSO),采用多目标算法测评指标体系与测试函数对改进算法的品质和性能进行了实验测试分析,表明新算法的多项质量指标均较优。
4.应用随机分析理论与差分方法推导出一种新的粒子群动态分析模型(γ GPSO模型)；证明了算法依赖于参数设置的一、二阶稳定域边界表达式，绘制出稳定区域、谱半径的等高线图与均值轨迹图，为PSO的改进及参数设置提供理论基础与直观工具。
5.给出改进算法在电力系统的应用实例，进一步验证了算法的可行性和有效性：1) AEPSO经济调度算法的设计与仿真测试；2) MDPSO需求侧资源优化算法的设计与仿真测试。
Electric power system is a complex system, increasing the size and social to the powersupply of "safe, reliable, affordable, high quality, low-carbon" and many other qualityindicators under the background of ever-higher demands, to ensure the implementation ofpower system operation control of the target, face a variety of complex optimization problems.Its complexity is mainly reflected in the objectives and constraints of complex, more extreme,high-dimensional, multi-objective, and there exist many uncertain factors, these aresignificant challenges on modeling and algorithm for innovation, how to build a suitableoptimization models and creating practical and efficient algorithm is the key to solving theproblem. Modern intelligent optimization algorithm with zero on the objective functionrequirements, implementing simple and advantages of parallel search, in the field of complexoptimization are a growing number of applications received significant attention. Thisresearch aimed at: from group intelligent of nature features starting, analysis particle swarmalgorithm learning mode of constructed and the key elements, tried to awareness PSO easy to" premature " of fundamental causes; made innovation of particle swarm learning mode, andbased on new mode design efficient PSO improved algorithm; application random analysistheory and difference method research particle swarm dynamic trajectory and stability domain,further reveals PSO of work mechanism, for algorithm of improved provides theoryFoundation; will improved algorithm and power system specific problem phase combinationand solution, More effective and practical programmes.
Swarm intelligence and Bionics principle, stochastic analysis theory and finite differencemethods, matroid theory, optimization theory and algorithms design theory is a powerful toolto study this problem. This article uses a combination of theoretical study and empiricalanalysis method, the main research content and outcomes include:
1. Swarm intelligence theory application research on the main reason of PSO is easy to"premature", pointed out that the original learning model nature of "passive" mechanism isone of the important reasons. Come up with a new sense of exploration with active learningmodel and Logistic chaos through new learning mode for combining technology, developed anew and improved Particle Swarm Optimization (AEPSO), and by experimental test analysisto verify the validity of the algorithm.
2. Based on matroid theory, proposed a matroid property of General-suitable forcombinatorial optimization problems of a combined population of evolutionary learning mode:Modular evolutionary learning mode based on vector (m1,m2,m-m1-m2). In turn proposed an improved discrete Particle Swarm Optimization (MDPSO), using Backpack to experimentaltests improved algorithms in combinatorial optimization problems such as analysis, feasibilityand effectiveness of the verification algorithm.
3. Based on the culture in the Organization's core values,"belief space" constructingpersonalized dynamic adaptation of cultural information in parameters, fostering speciesdiversity. Come up with an improved multi-objective Particle Swarm Optimization(CBCMPSO), using multi-objective evaluation index system and algorithm testing function toimprove the quality and performance of the algorithm of the test and analysis of experiments,indicating a new algorithm for multiple quality indicators are better.
4. Derivation of out stochastic analysis theory and finite difference methods for dynamicanalysis model of a new particle swarm (γ-GPSO model) or proved algorithm depends on theparameter settings for one or two-stage stability region expression draws out of the stable area,contour map of the spectral radius and mean, a map providing a theoretical basis for improvedPSO and its parameter settings and intuitive tools. Derivation of out stochastic analysis theoryand finite difference methods for dynamic analysis model of a new particle swarm (γ-GPSOmodel) or proved algorithm depends on the parameter settings for one or two-stage stabilityregion expression draws out of the stable area, contour map of the spectral radius and mean, amap providing a theoretical basis for improved PSO and its parameter settings and intuitivetools.
5. Gives examples of improved algorithm in power system applications, furthervalidation of the feasibility and effectiveness of the algorithm:1) design and simulation ofAEPSO economic dispatching algorithm testing;2) MDPSO design of demand-side resourceoptimization algorithm and simulation testing.
群智能与仿生学原理、随机分析理论与差分方法、拟阵理论、优化理论与算法设计理论是研究上述问题的有力工具。本文采用理论研究与实证分析相结合的方法，主要研究内容及成果包括：
1.应用群智能理论研究PSO易于“早熟”的主要原因，指出原有学习模式本质的“被动性”机制是其重要原因之一。提出一种新的带主动探索意识的学习模式，将新的学习模式与Logistic混沌遍历实现技术相结合，发展出一种新的改进粒子群算法（AEPSO），通过实验测试分析验证了算法的有效性。
2.基于拟阵理论，提出一种适合于拟阵特性的一般组合优化问题的新型离散粒子群算法：基于拟阵理论，将PSO的进化策略引入到贪心算法(Greedy algorithm)的寻优搜索过程中，运用粒子群的群智能特性改善贪心算法的全局搜索性能，提出一种具有较强全局搜索能力的新型离散粒子群算法，简记为MDPSO。采用背包等组合优化问题对改进算法进行实验测试分析，验证了算法的可行性和有效性。
3.基于文化在组织团体中的核心价值思想，利用“信念空间”中的文化信息构造个性化动态适应参数，培育种群的多样性。提出一种改进的多目标粒子群算法(CBCMPSO),采用多目标算法测评指标体系与测试函数对改进算法的品质和性能进行了实验测试分析,表明新算法的多项质量指标均较优。
4.应用随机分析理论与差分方法推导出一种新的粒子群动态分析模型(γ GPSO模型)；证明了算法依赖于参数设置的一、二阶稳定域边界表达式，绘制出稳定区域、谱半径的等高线图与均值轨迹图，为PSO的改进及参数设置提供理论基础与直观工具。
5.给出改进算法在电力系统的应用实例，进一步验证了算法的可行性和有效性：1) AEPSO经济调度算法的设计与仿真测试；2) MDPSO需求侧资源优化算法的设计与仿真测试。
Electric power system is a complex system, increasing the size and social to the powersupply of "safe, reliable, affordable, high quality, low-carbon" and many other qualityindicators under the background of ever-higher demands, to ensure the implementation ofpower system operation control of the target, face a variety of complex optimization problems.Its complexity is mainly reflected in the objectives and constraints of complex, more extreme,high-dimensional, multi-objective, and there exist many uncertain factors, these aresignificant challenges on modeling and algorithm for innovation, how to build a suitableoptimization models and creating practical and efficient algorithm is the key to solving theproblem. Modern intelligent optimization algorithm with zero on the objective functionrequirements, implementing simple and advantages of parallel search, in the field of complexoptimization are a growing number of applications received significant attention. Thisresearch aimed at: from group intelligent of nature features starting, analysis particle swarmalgorithm learning mode of constructed and the key elements, tried to awareness PSO easy to" premature " of fundamental causes; made innovation of particle swarm learning mode, andbased on new mode design efficient PSO improved algorithm; application random analysistheory and difference method research particle swarm dynamic trajectory and stability domain,further reveals PSO of work mechanism, for algorithm of improved provides theoryFoundation; will improved algorithm and power system specific problem phase combinationand solution, More effective and practical programmes.
Swarm intelligence and Bionics principle, stochastic analysis theory and finite differencemethods, matroid theory, optimization theory and algorithms design theory is a powerful toolto study this problem. This article uses a combination of theoretical study and empiricalanalysis method, the main research content and outcomes include:
1. Swarm intelligence theory application research on the main reason of PSO is easy to"premature", pointed out that the original learning model nature of "passive" mechanism isone of the important reasons. Come up with a new sense of exploration with active learningmodel and Logistic chaos through new learning mode for combining technology, developed anew and improved Particle Swarm Optimization (AEPSO), and by experimental test analysisto verify the validity of the algorithm.
2. Based on matroid theory, proposed a matroid property of General-suitable forcombinatorial optimization problems of a combined population of evolutionary learning mode:Modular evolutionary learning mode based on vector (m1,m2,m-m1-m2). In turn proposed an improved discrete Particle Swarm Optimization (MDPSO), using Backpack to experimentaltests improved algorithms in combinatorial optimization problems such as analysis, feasibilityand effectiveness of the verification algorithm.
3. Based on the culture in the Organization's core values,"belief space" constructingpersonalized dynamic adaptation of cultural information in parameters, fostering speciesdiversity. Come up with an improved multi-objective Particle Swarm Optimization(CBCMPSO), using multi-objective evaluation index system and algorithm testing function toimprove the quality and performance of the algorithm of the test and analysis of experiments,indicating a new algorithm for multiple quality indicators are better.
4. Derivation of out stochastic analysis theory and finite difference methods for dynamicanalysis model of a new particle swarm (γ-GPSO model) or proved algorithm depends on theparameter settings for one or two-stage stability region expression draws out of the stable area,contour map of the spectral radius and mean, a map providing a theoretical basis for improvedPSO and its parameter settings and intuitive tools. Derivation of out stochastic analysis theoryand finite difference methods for dynamic analysis model of a new particle swarm (γ-GPSOmodel) or proved algorithm depends on the parameter settings for one or two-stage stabilityregion expression draws out of the stable area, contour map of the spectral radius and mean, amap providing a theoretical basis for improved PSO and its parameter settings and intuitivetools.
5. Gives examples of improved algorithm in power system applications, furthervalidation of the feasibility and effectiveness of the algorithm:1) design and simulation ofAEPSO economic dispatching algorithm testing;2) MDPSO design of demand-side resourceoptimization algorithm and simulation testing.
引文
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