基于混合整数二阶锥规划的主动配电网最优潮流研究

最优潮流是一个非线性优化问题,其具有复杂繁琐、维数高、约束多以及变量多的特性。将其应用于主动配电网也是当下研究热点。文章建立了使主动配电网有功损耗最小的最优潮流模型;考虑配电网可控单元和开关状态,采用改进后的辐射状约束与潮流约束进行变换,合理松弛后变为二阶锥约束,建立混合整数二阶锥规划模型。采用Yalmip工具包进行建模,调用Gurobi商用算法包对其进行求解计算;通过算例对采用粒子群算法与采用混合整数二阶锥规划方法的计算结果进行对比分析,结果证明混合整数二阶锥方法更适用于主动配电网,验证了该方法的高效性和稳定性。     

基于蚁群算法的环网方向保护配合最小断点集计算

利用复杂环网方向保护最优配合中最小断点集（MBPS）的启发性知识，将MBPS的计算问题等价为0-1整数规划问题。基于蚁群优化算法基本原理，构造了适用于MBPS问题的启发信息计算公式，改进了更新信息素浓度的计算方法，提出了计算MBPS的新方法。相对于其他计算MBPS的算法，所述算法所需迭代次数较少，通过一次计算即可同时获得多组最优解。     

基于内点割平面法的混合整数最优潮流算法

提出了一种采用内点割平面法求解混合整数最优潮流(OPF)的算法。该算法循环执行3个步骤：①求解OPF的可行解并将其线性化；②从线性内点法的最优解中判断基变量；③根据基变量产生混合整数割平面。与单纯形割平面法相比，内点割平面法不仅简单易实现，计算效率高，而且随着问题规模的增加，更能发挥其多项式时间特性的优点。文中还对退化问题的处理以及稀疏技巧的应用进行了深入的讨论。通过对IEEE典型系统的数值仿真计算显示出所提算法对于大型电力系统最优潮流问题的精确求解是非常有效的。     

改进PSO算法解决电力系统机组优化组合问题

机组组合优化问题是一个大规模、离散、非线性的混合整数规划问题,所以求解比较困难,不容易找到理论上的最优解。在基本粒子群算法的基础上,使用一种空间收缩策略,加快了算法的收敛速度。同时为了避免算法出现“早熟”现象,让粒子不仅根据自身和同伴中的最好个体进行调整自己的飞行速度,并且向其他个体学习。通过该算法进行仿真计算,证明了该算法的有效性。     

基于原-对偶内点法和混合整数规划法的机组组合问题研究

电力系统机组组合能带来显著的经济效益,随着电力市场的不断发展,在电力系统优化运行中变得尤为重要。然而电力系统机组组组合问题是一个大规模、非凸、非线性混合整数优化问题,至今仍然没有找到一种理想的优化算法。因此针对其特点,采用了原-对偶内点法和混合整数规划法相结合的算法,首先利用混合整数规划法形成伴随规划来处理离散变量,再通过内点法求解伴随规划子问题和负荷经济分配,充分发挥了两种算法在求解机组组合问题上的优势。文中对标准10机组24时段系统算例进行了仿真测试并与之前的各种优化算法进行了对比,结果表明了本文算法模型解决机组组合问题的有效性和优越性。     

基于改进模拟植物生长算法的输电网络扩展规划

输电网络规划是一个复杂的组合优化问题,若以选择线路回数为变量抽象出模型,则输电网扩展问题可以归结为一类整数规划问题.对模拟植物生长算法进行改进,形成了适于解整数规划问题的改进模拟植物生长算法,并将此算法应用到电力系统输电网络扩展规划中.为了加快算法收敛,采用了Kruskal算法来获取初始点,提出了一种快速判别网络连通的算法.最后,实例计算结果表明了该方法的可行性.     

基于改进遗传模拟退火算法的无功优化

针对目前电力系统无功优化算法所存在的问题，提出了一种将遗传算法与模拟退火算法及牛顿下山法相结合的混合求解算法。首先根据个体适应度值进行自适应交叉和变异操作并采用模拟退火进行个体更新，以便增加群的多样性，避免陷入局部最优；然后采用牛顿下山法加快模拟退火部分的求解过程，并采用十进制整数编码和保存最优个体法来提高计算速度和精度。以IEEE 30-bus系统和一某实际电力系统为例对所提出算法的性能和求解精度进行了测试，结果表明改进的混合遗传算法比传统的遗传算法在计算速度和全局收敛方面有了很大提高。     

求解无功优化的非线性同伦内点法

在无功优化计算中，由于严格的节点电压限制，网络拓扑的变化或无功电源的不足等多种原因可能会导致原问题不存在最优解。采用常规的优化方法或内点方法还不能有交地检测出这种不可行问题。该文基于非线性同伦内点法提出了检测无功优化不可行问题的新算法，该算法不仅能在原问题有解的情况下求出近似的最优解，而且能通过同伦变量的值快速并准确地判别出原问题是否出现了不可行情况，并以IEEE30节点系统为试验系统，对采用非线性同伦内点法的优化计算结果的正确性与检测优化计算中出现的不可行问题的有效性进行了验证。     

模拟退火算法在输电网络扩展规划中的应用

输电网络扩展规划是一个非线性组合优化问题,文中用模拟退火算法有效地解决了该问题.首先用直流潮流模型建立该问题的非线性整数规划模型,然后用模拟退火算法求解该模型的最优解,并对具体实施步骤作了多处优化改进.最后,通过分别对Garver 6节点和IEEE 24节点两个算例的测试,并与Lingo软件得出的计算结果做比较,表明改进的模拟退火算法能更快搜索到较优可行解.     

交流潮流约束机组组合的交替方向乘子法

求交流潮流约束机组组合(AC power flow constrained unitcommitment,ACUC)问题的最优解具有复杂性,不仅需要考虑问题中的多个整数变量,问题本身也具有NP-hard特点。该文提出了ACUC问题的一种新求解方法,采用交替方向乘子法(alternatingdirectionmethodofmultipliers,ADMM)分解和协调ACUC数学模型。通过对0/1整数变量的复制,并令其中一个复制变量可连续变化,原问题可转换为一个具有可分结构的混合整数非线性规划(mixedinteger nonlinear programming,MINLP)问题,应用ADMM方法可将该问题的求解转化为两个子问题的交替求解。通过对IEEE39节点和118节点系统的验证计算,以结果说明了所举方法能有效地处理整数变量,在ACUC问题中具有可行性。在与其他算法的对比中,也体现出ADMM算法的目标费用更低、计算时间更短的特点。     

Mean field theory for optimal power flow

We present a method based on mean field theory to cope with the mixed nonlinear integer programming, especially with optimal power flow problems involving both continuous and discrete variables, in a more exact manner. That is, we first formulate OPF as a mixed integer programming, and then derive its mean field equations as well as the annealing algorithm, by taking advantage of the characteristics of the original problems. Numerical simulations have verified effectiveness of this approach for small power systems     

Multi-area generation scheduling algorithm with regionally distributed optimal power flow using alternating direction method

This paper calls attention to the core issue as to the multi-area generation scheduling algorithm in interconnected electric power systems. This algorithm consists in deciding upon on/off states of generating units and their power outputs to meet the demands of customers under the consideration of operational technical constraints and transmission networks while keeping the generation cost to a minimum. In treating the mixed integer nonlinear programming (MINLP) problem, the generalized Benders decomposition (GBD) is applied to simply decouple a primal problem into a unit commitment (UC) master problem and inter-temporal optimal power flow (OPF) sub-problems. Most prominent in this work is that the alternating direction method (ADM) is introduced to accomplish the regional decomposition that allows efficient distributed solutions of OPF. Especially, the proposed distributed scheme whose effectiveness is clearly illustrated on a numerical example can find the most economic dispatch schedule incorporated with power transactions on a short-term basis where utilities are less inclined to pool knowledge about their systems or to telemeter measured system and cost data to the common system operator and nevertheless the gains from trade such as economy interchange are vital as well.     

An interior point nonlinear programming for optimal power flowproblems with a novel data structure

This paper presents a new interior point nonlinear programming algorithm for optimal power flow problems (OPF) based on the perturbed KKT conditions of the primal problem. Through the concept of the centering direction, the authors extend this algorithm to classical power flow (PF) and approximate OPF problems. For the latter, CPU time can be reduced substantially. To efficiently handle functional inequality constraints, a reduced correction equation is derived, the size of which depends on that of equality constraints. A novel data structure is proposed which has been realized by rearranging the correction equation. Compared with the conventional data structure of Newton OPF, the number of fill-ins of the proposed scheme is roughly halved and CPU time is reduced by about 15% for large scale systems. The proposed algorithm includes four kinds of objective functions and two different data structures. Extensive numerical simulations on test systems that range in size from 14 to 1047 buses, have shown that the proposed method is very promising for large scale application due to its robustness and fast execution time     

求解离散无功优化问题的精确连续化方法

提出了一种求解离散无功优化问题的新算法。该方法对离散变量进行二进制编码,从而将离散变量转化为若干0-1变量的线性组合,并将二进制变量约束转化为等价的互补约束,再利用非线性互补函数将互补约束转化为等价的非光滑方程,对其进行光滑化处理后,将原问题转化成可微的非线性规划问题,并采用非线性原对偶内点算法求解。此外,还对离散变量编码的原理以及应用原对偶内点法中遇到的求导难点进行了介绍,并通过几个不同规模试验系统的计算分析,验证该方法能有效处理离散变量,而且具有良好的收敛性和精确性。     

Impact of Fault Level Constraints on the Economic Operation of Power Systems

The aim of this paper is to prove that fault levels may have a significant impact on the economic operation of modern power systems. First, we present a simple method for the incorporation of fault level constraints (FLCs) in the optimal power flow (OPF), the main optimization tool for the economic operation of power systems. The constraints imposed by fault levels are converted to simple nonlinear (inequality) constraints, described by variables of the conventional OPF. Most common OPF-solving engines already have the computational capacity to handle numerous nonlinear constraints, such as the ones described by the power balance equations on buses. Therefore, once FLCs are converted to nonlinear constraints described by OPF variables, they can be directly introduced to any optimization process performing the OPF. We applied this enhanced OPF on a simple 12-bus network. The results verified the significant impact fault levels have on the optimum operating point of the power system     

On a nonlinear multiple-centrality-corrections interior-pointmethod for optimal power flow

Large scale nonlinear optimal power flow (OPF) problems have been efficiently solved by extensions from linear programming to nonlinear programming of the primal-dual logarithmic barrier interior-point method and its predictor-corrector variant. Motivated by the impressive performance of the nonlinear predictor-corrector extension, in this paper we extend from linear programming to nonlinear OPF the efficient multiple centrality corrections (MCC) technique that was developed by Gondzio. The numerical performance of the proposed MCC algorithm is evaluated on a set of power networks ranging in size from 118 buses to 2098 buses. Extensive computational results demonstrate that the MCC technique is fast and robust, and outperforms the successful predictor-corrector technique     

A Robust Approach to Optimal Power Flow With Discrete Variables

Optimal power flow (OPF) belongs to the nonlinear optimization problem with discrete variables. The interior point cutting plane method (IPCPM), which possesses the advantages of both the interior point method and the cutting plane method, becomes a very promising approach to the large-scale OPF. It employs a successive linearization process and iteratively solves the mixed integer linear programming problem. However, case studies have shown that: if the problem has multiple solutions, the optimal solutions will converge to the interior of the optimal face, and the cutting planes cannot be generated due to the failure to identify the optimal base. This paper presents a new general optimal base identification method for solving the problem. The new approach significantly improves the robustness and efficiency of IPCPM. Simulation results on IEEE test systems indicate that the algorithm proposed can not only properly deal with various types of optimal solutions but also greatly enlarge the application area of IPCPM.      

含UPFC的电力系统最优潮流计算

由于UPFC能够控制母线电压和线路潮流,包含UPFC的电力系统最优潮流模型中须引入附加的等式约束和不等式的约束,增加了优化计算的复杂性,本文应用直接非线性原一对偶路径跟踪内点算法进行求解,并给出了3个试验系统的优化计算结果,验证该方法的有效性。     

一种带动态修正加速策略的最优潮流内点算法

采用了一种新的动态修正迭代步长的加速收敛策略,提高了原一对偶内点算法解算电力系统最优潮流问题的收敛性能.对IEEE14、30、118节点测试系统进行了数值试验,并与牛顿法和不引入该修正策略进行了比较.表明了本算法良好的数值稳定性、较强的处理不等式约束的能力,优化结果精确,充分显示了内点算法应用于大规模电力系统优化问题的实用性.