基于模糊评价的配电网络多目标优化研究
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摘要
配电网络是连接输电网络和用户侧的中间环节，直接为广大用户提供电能，具有电压等级低、损耗大、自动化程度低等特点。配电网络的运行工况是否合理，不仅关系到用户侧电能质量的优劣，而且直接影响到网络运行的安全性和经济性。配电网络的优化运行主要包括电压/无功优化和重构。电压/无功优化是以变压器分接头和并联补偿电容器为控制变量，通过合理调整无功潮流的分布，减少无功功率传输造成的压降和网损。配电网络重构以分段开关和联络开关为控制手段，通过合理调整网络结构，重新分配各馈线的负荷。由于控制变量均为离散变量，因此配网电压/无功优化和重构问题均可表示为含有约束条件的非线性组合优化问题，并具有多目标、多极值点、目标函数和约束条件为非线性方程组、目标函数难以由控制变量显式表达等特点。
本文引入了模糊评价、智能搜索和多目标优化等理论和方法，针对配电网络的优化运行进行深入研究，具有重要的理论意义和实际意义。取得的创新性成果和主要研究工作如下：
1．基于模糊评价的中低压配电网络电压调整
在我国中低压配电网络中广泛使用的电压/无功调节手段是无载调压变压器和固定补偿电容器，其调整频率只能达到每年几次的水平，传统的静态和动态电压/无功优化方法并不适用。
计及调节频率的限制和电压/无功优化问题的多目标性，提出了一种基于模糊评价的中低压配电网络电压多目标优化模型和算法。该模型以提高节点电压质量和降低网络损耗为目标，以变压器分接头和并联补偿电容器为控制变量。约束条件包括潮流方程等。优化中同时考虑最大、最小两种运行方式，以计及较长时间段内工况变化对节点电压的影响。即认为，如果各节点电压在极端工况条件下满足要求，则该周期内所有时段的节点电压均能保证合格。采用模糊评价将模型转化为单目标优化，运用主动禁忌搜索算法求解。首先构造模糊隶属度函数对各目标的满意度进行评价，将各目标函数值折算为该目标的满意度，使得不同量纲、不同工况的各个目标之间可以相互比较。然后在模糊评价的基础上，用加权求和法将多目标优化问题转换为单目标优化问题。最后对转化后的单目标优化问题采用主动禁忌搜索算法求解。由于引入了反馈机制，主动禁忌搜索算法能够根据优化的过程对主要参数进行自适应性的调整，显著提高了算法的优化效率和适应性。对实际系统的优化结果表明，电压多目标优化模型能够同时考虑节点电压和网络损耗目标，有效计及较长时间段内负荷变化对节点电压的影响。求解方法可以合理评价不同量纲的目标函数，并有效求得最优解。优化后，各工况下的节点电压合格率显著提高，网络损耗也均有一定程度的降低。
2．计及DG影响的配网多目标电压/无功优化
随着高效小容量发电技术的成熟和社会对环境保护问题的日益关注，分布在负荷附近的分布式发电(DG)设备越来越多地接入配电网络。配电网络将由单一电源、辐射形结构转变为遍布电源和负荷的复杂网络，传统的规划、运行等面临重大变化。DG的功率注入对配电网络的电压分布和功率损耗都将造成影响，启停和出力的变化则可能引起节点电压的波动。
针对DG接入后配电网络运行优化问题的特点，提出了一种计及DG的配电网络多目标电压/无功优化模型和算法。该模型以提高电压质量、降低网络损耗和抑制电压波动等为目标，以变压器分接头和并联补偿电容器等为控制手段，适应DG接入造成的影响。采用基于模糊评价的主动禁忌搜索算法求解多目标优化模型。为便于反映“电压合格”和“电压偏差最小”两者重要性的差别，分别构造“电压合格”和“电压偏差”两个不同参数的隶属度函数分别对节点电压进行评价。根据各目标两两之间的相对重要性构建判断矩阵，采用判断矩阵法确定各目标的权重值。在目标函数增多的情况下，利用该方法可以保证权重系数的合理性和一致性，提高了优化求解方法的适应性。算例系统的优化结果表明，该方法能够充分考虑DG接入对配电网络电压/无功优化可能造成的影响，求解过程中可以兼顾各个目标，在保证电压合格的基础上，有效提高电压质量、降低网络损耗、抑制电压波动。
3．配网重构及综合优化
配电网络重构属于带约束的非线性组合优化问题，传统的数学优化方法和启发式方法均难以保证获得全局最优解。智能优化算法具有逃离局部最优解陷阱、搜索得到全局最优解的能力。对网络中分段开关和联络开关的状态进行编码，是利用智能优化算法求解重构问题的关键步骤，编码方案的优劣对优化效率和计算结果有直接的影响。提出了基于环路分析的配网重构问题的十进制编码方案，即在网络拓扑结构分析的基础上，对每个联络开关对应环路中的全部开关依次编号，从而形成编码。该方案具有简便易行、物理意义明晰、编码效率高等优点。采用主动禁忌搜索算法求解配网重构问题，不同方法的优化计算和结果比较表明，该方法可以以更少的目标函数计算次数得到最优解，具有更高的搜索效率。
在研究配网重构问题的基础上，提出了一种配电网络综合优化模型，综合应用电压/无功调节设备和分段、联络开关两类不同性质的控制手段，实现降低网损、提高电压质量和均衡负荷等优化目标。利用判断矩阵法确定各目标的权重系数，采用基于模糊评价的主动禁忌搜索算法求解综合优化模型。仿真算例表明，该方法可以利用电压/无功调节手段和分段、联络开关两类控制手段，并兼顾多个优化目标，显著提高节点电压质量、降低网络损耗和均衡负荷。
4．配电网络优化运行分析软件
根据配电系统运行的实际需要，开发了实用化的配电网络运行优化软件包。该软件包具有历史数据分析、数据维护、潮流计算、电压/无功优化、配网重构和配电网络综合优化等功能，可用于配电网络的优化运行分析。开发过程中，利用标准模板库提供的基本算法和数据结构，可以实现效率高、可读性好的高质量代码。采用面向对象的编程思想构建软件的体系结构，根据数据结构和对应的函数对软件功能进行划分和封装，可以提高代码的可复用度，降低系统维护的难度。以智能优化算法类和潮流计算类为例，对核心计算部分的体系结构进行了详细的介绍。
Distribution networks connect transmission networks and loads to supply electricity to the customers directly. The characteristics of distribution networks are low voltage grades, great power losses and inferior automatic levels. Operating conditions of a distribution network influence not only the energy quality of customers but also the security and economy of the distribution network itself. Optimal operation of distribution networks includes volt/var optimization and reconfiguration. The volt/var optimization regulates reactive power flow by adjusting tap-changers and switching shunt capacitors to reduce the voltage drop and the active power losses. The reconfiguration alters the topological structures of distribution networks and redistributes loads by changing the open/close states of the sectionalizing and tie switchers. The regulating means of volt/var optimization and reconfiguration, such as tap-changers, shunt capacitors, sectionalizing and tie switchers, are all discrete variables. Therefore, the optimal operation of distribution networks is modeled as a restricted nonlinear combinational optimization. The characteristics of the model include multi-objective, local-optima, nonlinear objective functions and equation restrictions. Furthermore, the objective can hardly be expressed as an explicit function of control variables.
Introducing the theory and methods of fuzzy evaluation, intelligent optimization and multi-objective optimization, the distribution networks optimal operation is researched systematically. The main contributions of the dissertation are shown as follows.
1. Fuzzy-evaluation based voltage regulation in middle-low voltage networks
The volt/var regulating means in middle-low voltage distribution networks are non-load tap-changers and fixed shunt capacitors, and the regulating frequencies are limited to several times a year. Therefore, traditional static and dynamic volt/var optimization models are not applicable any longer.
Considering the regulating frequency restrictions and multi-objective in the volt/var problem, a fuzzy evaluation based multi-objective optimization model and a solution method are proposed for voltage regulation in distribution networks. The model aims to improve voltage profiles and reduce active power losses by adjusting tap-changers and switching shunt capacitors. The maximum and minimum load conditions are both considered in optimization process to represent the load variations in a long period, that is, if the voltage profiles in peak and valley load conditions are eligible, those during this period are believed to be acceptable. The fuzzy evaluated multi-objective model is transformed to a single objective optimization problem, which is solved by reactive tabu search (RTS) algorithm. The solving process is shown as the following. Firstly, membership functions are constructed to evaluate the objectives, so that the satisfactions of different objectives in various operating conditions can be compared. Secondly, the multi-objective optimization is transformed to a single objective optimization by weighted-sum approach. Finally, the single objective optimization problem is solved by RTS. The feedback procedure adjusts the principal parameters in RTS according to the optimization process. The efficiency and applicability of RTS are improved significantly. The simulation on a practical distribution system shows that, the proposed model optimizes the two objectives with the load variations in a long period considered. The solving method evaluates the objectives with different units fairly and obtains the optimal solutions effectively. The regulation results, significantly improved voltage profiles and reduced active power losses, show the efficiency of the proposed method.
2. Volt/var multi-objective optimization with distributed generators With the development of small-capacity generation techniques and concern on environmental protection, increasing number of distributed generators (DGs) are connected to distribution networks. This trend will change the current structure, planning and operation of distribution networks. Power injection from DGs influences voltage profiles and active power losses. The output variation and start-stop process of DGs may cause voltage variation.
Considering the characteristics of optimal operation in distribution networks with DG connected, a multi-objective volt/var optimization model and a solving method are proposed. The model aims to improve voltage profiles, reduce active power losses and limit the voltage variation by adjusting tap-changers and shunt capacitors, accommodating the influences of DG. The fuzzy-evaluation based RTS is employed to search for the solutions. To distinguish the different importance of voltage eligibility and voltage deviation minimization, two membership functions are constructed to evaluate the voltage profiles respectively. The weights of objectives are determined by the fuzzy judgment matrix, which is constructed according to the relative importance of every two objectives. The fuzzy judgment matrix approach ensures the coherence of the weights and improves the adaptability of the proposed method. The solving process improves the voltage profiles, reduces active power losses and limits the voltage variations without violating voltage restrictions. The simulation results show that the proposed model improves all the objectives with DG influences considered.
3. Distribution networks reconfiguration and comprehensive optimization
To solve the reconfiguration problem in the intelligent optimization methods, an important step is to code the status of the sectionalizing and tie switchers. The quality of coding affects the solving efficiency and optimization results directly. A topological analysis based decimal coding scheme is presented, that is, to close each tie switch and number all the switches on the looped branch. The scheme is easy to be realized and the codes have a high efficiency in representing the structures. The RTS is employed to solve the reconfiguration model. The simulation results, getting the global best solution with fewer objective-calculation times compared with the other approaches, demonstrates the efficiency of the proposed method.
A comprehensive optimal regulation model for distribution networks is presented, which utilizes the volt/var regulating means, sectionalizing and tie switchers to reduce active power losses, improve voltage profiles and balance loads. Fuzzy judgment matrix approach decides the weights of different objectives. The model is solved by RTS based on fuzzy-evaluation. The proposed method optimizes the objectives using various regulating means comprehensively.
4. Software development for distribution networks optimal operation According to the practical demand of distribution network operation, a software
package for optimal operating analysis is developed. The software package has several modules, including historical data analysis, data maintenance, power flow calculation, volt/var optimization, reconfiguration and comprehensive optimal regulation. The standard template library provides various algorithms and data structures, which are utilized to program high quality code with good readability. The software package is constructed by object-oriented programming (OOP), which divides and encapsulates the classes according to the data structure and the corresponding functions. OOP improves the reusability of the codes and alleviates the cost of maintenance. The structure of core parts, power flow calculation and intelligent optimization, are introduced in detail.
本文引入了模糊评价、智能搜索和多目标优化等理论和方法，针对配电网络的优化运行进行深入研究，具有重要的理论意义和实际意义。取得的创新性成果和主要研究工作如下：
1．基于模糊评价的中低压配电网络电压调整
在我国中低压配电网络中广泛使用的电压/无功调节手段是无载调压变压器和固定补偿电容器，其调整频率只能达到每年几次的水平，传统的静态和动态电压/无功优化方法并不适用。
计及调节频率的限制和电压/无功优化问题的多目标性，提出了一种基于模糊评价的中低压配电网络电压多目标优化模型和算法。该模型以提高节点电压质量和降低网络损耗为目标，以变压器分接头和并联补偿电容器为控制变量。约束条件包括潮流方程等。优化中同时考虑最大、最小两种运行方式，以计及较长时间段内工况变化对节点电压的影响。即认为，如果各节点电压在极端工况条件下满足要求，则该周期内所有时段的节点电压均能保证合格。采用模糊评价将模型转化为单目标优化，运用主动禁忌搜索算法求解。首先构造模糊隶属度函数对各目标的满意度进行评价，将各目标函数值折算为该目标的满意度，使得不同量纲、不同工况的各个目标之间可以相互比较。然后在模糊评价的基础上，用加权求和法将多目标优化问题转换为单目标优化问题。最后对转化后的单目标优化问题采用主动禁忌搜索算法求解。由于引入了反馈机制，主动禁忌搜索算法能够根据优化的过程对主要参数进行自适应性的调整，显著提高了算法的优化效率和适应性。对实际系统的优化结果表明，电压多目标优化模型能够同时考虑节点电压和网络损耗目标，有效计及较长时间段内负荷变化对节点电压的影响。求解方法可以合理评价不同量纲的目标函数，并有效求得最优解。优化后，各工况下的节点电压合格率显著提高，网络损耗也均有一定程度的降低。
2．计及DG影响的配网多目标电压/无功优化
随着高效小容量发电技术的成熟和社会对环境保护问题的日益关注，分布在负荷附近的分布式发电(DG)设备越来越多地接入配电网络。配电网络将由单一电源、辐射形结构转变为遍布电源和负荷的复杂网络，传统的规划、运行等面临重大变化。DG的功率注入对配电网络的电压分布和功率损耗都将造成影响，启停和出力的变化则可能引起节点电压的波动。
针对DG接入后配电网络运行优化问题的特点，提出了一种计及DG的配电网络多目标电压/无功优化模型和算法。该模型以提高电压质量、降低网络损耗和抑制电压波动等为目标，以变压器分接头和并联补偿电容器等为控制手段，适应DG接入造成的影响。采用基于模糊评价的主动禁忌搜索算法求解多目标优化模型。为便于反映“电压合格”和“电压偏差最小”两者重要性的差别，分别构造“电压合格”和“电压偏差”两个不同参数的隶属度函数分别对节点电压进行评价。根据各目标两两之间的相对重要性构建判断矩阵，采用判断矩阵法确定各目标的权重值。在目标函数增多的情况下，利用该方法可以保证权重系数的合理性和一致性，提高了优化求解方法的适应性。算例系统的优化结果表明，该方法能够充分考虑DG接入对配电网络电压/无功优化可能造成的影响，求解过程中可以兼顾各个目标，在保证电压合格的基础上，有效提高电压质量、降低网络损耗、抑制电压波动。
3．配网重构及综合优化
配电网络重构属于带约束的非线性组合优化问题，传统的数学优化方法和启发式方法均难以保证获得全局最优解。智能优化算法具有逃离局部最优解陷阱、搜索得到全局最优解的能力。对网络中分段开关和联络开关的状态进行编码，是利用智能优化算法求解重构问题的关键步骤，编码方案的优劣对优化效率和计算结果有直接的影响。提出了基于环路分析的配网重构问题的十进制编码方案，即在网络拓扑结构分析的基础上，对每个联络开关对应环路中的全部开关依次编号，从而形成编码。该方案具有简便易行、物理意义明晰、编码效率高等优点。采用主动禁忌搜索算法求解配网重构问题，不同方法的优化计算和结果比较表明，该方法可以以更少的目标函数计算次数得到最优解，具有更高的搜索效率。
在研究配网重构问题的基础上，提出了一种配电网络综合优化模型，综合应用电压/无功调节设备和分段、联络开关两类不同性质的控制手段，实现降低网损、提高电压质量和均衡负荷等优化目标。利用判断矩阵法确定各目标的权重系数，采用基于模糊评价的主动禁忌搜索算法求解综合优化模型。仿真算例表明，该方法可以利用电压/无功调节手段和分段、联络开关两类控制手段，并兼顾多个优化目标，显著提高节点电压质量、降低网络损耗和均衡负荷。
4．配电网络优化运行分析软件
根据配电系统运行的实际需要，开发了实用化的配电网络运行优化软件包。该软件包具有历史数据分析、数据维护、潮流计算、电压/无功优化、配网重构和配电网络综合优化等功能，可用于配电网络的优化运行分析。开发过程中，利用标准模板库提供的基本算法和数据结构，可以实现效率高、可读性好的高质量代码。采用面向对象的编程思想构建软件的体系结构，根据数据结构和对应的函数对软件功能进行划分和封装，可以提高代码的可复用度，降低系统维护的难度。以智能优化算法类和潮流计算类为例，对核心计算部分的体系结构进行了详细的介绍。
Distribution networks connect transmission networks and loads to supply electricity to the customers directly. The characteristics of distribution networks are low voltage grades, great power losses and inferior automatic levels. Operating conditions of a distribution network influence not only the energy quality of customers but also the security and economy of the distribution network itself. Optimal operation of distribution networks includes volt/var optimization and reconfiguration. The volt/var optimization regulates reactive power flow by adjusting tap-changers and switching shunt capacitors to reduce the voltage drop and the active power losses. The reconfiguration alters the topological structures of distribution networks and redistributes loads by changing the open/close states of the sectionalizing and tie switchers. The regulating means of volt/var optimization and reconfiguration, such as tap-changers, shunt capacitors, sectionalizing and tie switchers, are all discrete variables. Therefore, the optimal operation of distribution networks is modeled as a restricted nonlinear combinational optimization. The characteristics of the model include multi-objective, local-optima, nonlinear objective functions and equation restrictions. Furthermore, the objective can hardly be expressed as an explicit function of control variables.
Introducing the theory and methods of fuzzy evaluation, intelligent optimization and multi-objective optimization, the distribution networks optimal operation is researched systematically. The main contributions of the dissertation are shown as follows.
1. Fuzzy-evaluation based voltage regulation in middle-low voltage networks
The volt/var regulating means in middle-low voltage distribution networks are non-load tap-changers and fixed shunt capacitors, and the regulating frequencies are limited to several times a year. Therefore, traditional static and dynamic volt/var optimization models are not applicable any longer.
Considering the regulating frequency restrictions and multi-objective in the volt/var problem, a fuzzy evaluation based multi-objective optimization model and a solution method are proposed for voltage regulation in distribution networks. The model aims to improve voltage profiles and reduce active power losses by adjusting tap-changers and switching shunt capacitors. The maximum and minimum load conditions are both considered in optimization process to represent the load variations in a long period, that is, if the voltage profiles in peak and valley load conditions are eligible, those during this period are believed to be acceptable. The fuzzy evaluated multi-objective model is transformed to a single objective optimization problem, which is solved by reactive tabu search (RTS) algorithm. The solving process is shown as the following. Firstly, membership functions are constructed to evaluate the objectives, so that the satisfactions of different objectives in various operating conditions can be compared. Secondly, the multi-objective optimization is transformed to a single objective optimization by weighted-sum approach. Finally, the single objective optimization problem is solved by RTS. The feedback procedure adjusts the principal parameters in RTS according to the optimization process. The efficiency and applicability of RTS are improved significantly. The simulation on a practical distribution system shows that, the proposed model optimizes the two objectives with the load variations in a long period considered. The solving method evaluates the objectives with different units fairly and obtains the optimal solutions effectively. The regulation results, significantly improved voltage profiles and reduced active power losses, show the efficiency of the proposed method.
2. Volt/var multi-objective optimization with distributed generators With the development of small-capacity generation techniques and concern on environmental protection, increasing number of distributed generators (DGs) are connected to distribution networks. This trend will change the current structure, planning and operation of distribution networks. Power injection from DGs influences voltage profiles and active power losses. The output variation and start-stop process of DGs may cause voltage variation.
Considering the characteristics of optimal operation in distribution networks with DG connected, a multi-objective volt/var optimization model and a solving method are proposed. The model aims to improve voltage profiles, reduce active power losses and limit the voltage variation by adjusting tap-changers and shunt capacitors, accommodating the influences of DG. The fuzzy-evaluation based RTS is employed to search for the solutions. To distinguish the different importance of voltage eligibility and voltage deviation minimization, two membership functions are constructed to evaluate the voltage profiles respectively. The weights of objectives are determined by the fuzzy judgment matrix, which is constructed according to the relative importance of every two objectives. The fuzzy judgment matrix approach ensures the coherence of the weights and improves the adaptability of the proposed method. The solving process improves the voltage profiles, reduces active power losses and limits the voltage variations without violating voltage restrictions. The simulation results show that the proposed model improves all the objectives with DG influences considered.
3. Distribution networks reconfiguration and comprehensive optimization
To solve the reconfiguration problem in the intelligent optimization methods, an important step is to code the status of the sectionalizing and tie switchers. The quality of coding affects the solving efficiency and optimization results directly. A topological analysis based decimal coding scheme is presented, that is, to close each tie switch and number all the switches on the looped branch. The scheme is easy to be realized and the codes have a high efficiency in representing the structures. The RTS is employed to solve the reconfiguration model. The simulation results, getting the global best solution with fewer objective-calculation times compared with the other approaches, demonstrates the efficiency of the proposed method.
A comprehensive optimal regulation model for distribution networks is presented, which utilizes the volt/var regulating means, sectionalizing and tie switchers to reduce active power losses, improve voltage profiles and balance loads. Fuzzy judgment matrix approach decides the weights of different objectives. The model is solved by RTS based on fuzzy-evaluation. The proposed method optimizes the objectives using various regulating means comprehensively.
4. Software development for distribution networks optimal operation According to the practical demand of distribution network operation, a software
package for optimal operating analysis is developed. The software package has several modules, including historical data analysis, data maintenance, power flow calculation, volt/var optimization, reconfiguration and comprehensive optimal regulation. The standard template library provides various algorithms and data structures, which are utilized to program high quality code with good readability. The software package is constructed by object-oriented programming (OOP), which divides and encapsulates the classes according to the data structure and the corresponding functions. OOP improves the reusability of the codes and alleviates the cost of maintenance. The structure of core parts, power flow calculation and intelligent optimization, are introduced in detail.
引文
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