求解最优潮流KKT系统的一类新模型及算法设计

电力工业的市场化改革对最优潮流(optim al pow er flow,OPF)的计算精度和速度提出了更高的要求.本文针对OPF模型中存在大量的无功界约束的特性,把一般非线性不等式约束和界约束分开处理,通过引入一个对角矩阵和非线性互补函数,建立了与OPF问题的K arush-Kuhn-Tucker(KKT)系统等价的约束非光滑方程新模型.进一步,基于新建立的模型,提出了一类具有理论上收敛性保证的投影半光滑N ew ton型算法.相对于传统的解OPF的KKT系统和非线性互补函数方法,新方法一方面保持了非线性互补函数法无需识别有效集的优点,同时又减少了问题的维数,且投影计算保持了无功界约束的可行性.IEEE多个算例的数值试验显示本文所提出的模型和算法具有较好的计算效果.     

智能电网互补能源供用电实时定价算法研究

在智能电网背景下,针对化石能源短缺、峰时供电压力大的现状,提出了由光伏和化石燃料互补供电的方式,并建立了社会福利最大化用户侧微电网实时定价模型。该模型中,电力供应商通过制定实时电价来协调用户对两种类型能源所发电能的使用量,并设计了实时定价算法来求解模型。仿真结果表明,相比仅靠化石能源供电的大电网,互补供电方式能有效降低化石能源峰时供电量和价格,提升社会福利,这为以后智能电网的有效管理提供了参考。     

Optimal power flow using an Improved Colliding Bodies Optimization algorithm

This paper proposes Improved Colliding Bodies Optimization (ICBO) algorithm to solve efficiently the optimal power flow (OPF) problem. Several objectives, constraints and formulations at normal and preventive operating conditions are used to model the OPF problem. Applications are carried out on three IEEE standard test systems through 16 case studies to assess the efficiency and the robustness of the developed ICBO algorithm. A proposed performance evaluation procedure is proposed to measure the strength and robustness of the proposed ICBO against numerous optimization algorithms. Moreover, a new comparison approach is developed to compare the ICBO with the standard CBO and other well-known algorithms. The obtained results demonstrate the potential of the developed algorithm to solve efficiently different OPF problems compared to the reported optimization algorithms in the literature.     

改进混沌PSO算法的电力系统最优潮流计算

电力工业的市场化改革对最优潮流（Optimal Power Flow,OPF）的计算精度和速度提出了更高的要求。在分析最优潮流理论及其算法的基础上,对比一些经典解算法,引入粒子群优化算法（PSO）来计算发电厂成本耗费问题。考虑到传统PSO算法处理OPF约束条件时,对随机粒子个体的质量和速度的选取不能保证,且收敛速度慢,并容易陷入局部最优解,提出改进的混沌粒子群算法,即利用混沌运动特性来改进粒子群算法。利用该算法与其他算法对IEEE5节点算例进行分析比较,结果表明改进的混沌微粒群优化算法可较好处理最优潮流约束条件,有效提高了PSO算法的全局收敛能力和计算精度。在处理最优潮流问题上具有一定的有效性和优越性。     

Particle swarm optimization with an aging leader and challengers algorithm for the solution of optimal power flow problem

Solution of optimal power flow (OPF) problem aims to optimize a selected objective function such as fuel cost, active power loss, total voltage deviation (TVD) etc. via optimal adjustment of the power system control variables while at the same time satisfying various equality and inequality constraints. In the present work, a particle swarm optimization with an aging leader and challengers (ALC-PSO) is applied for the solution of the OPF problem of power systems. The proposed approach is examined and tested on modified IEEE 30-bus and IEEE 118-bus test power system with different objectives that reflect minimization of fuel cost or active power loss or TVD. The simulation results demonstrate the effectiveness of the proposed approach compared with other evolutionary optimization techniques surfaced in recent state-of-the-art literature. Statistical analysis, presented in this paper, indicates the robustness of the proposed ALC-PSO algorithm.     

最优潮流问题的解耦半光滑牛顿型算法

提出一种求解最优潮流（OPF）问题的新算法--解耦半光滑牛顿型算法.该算法是对作者的投影半光滑Newton算法的改进和提高,它除了保持原算法不必识别不等式约束、对界约束的特殊处理以减少讨论问题的维数等优点外,其显著的特点是结合了电力系统固有的弱耦合性质,构造了求解OPF问题的一类解耦半光滑牛顿算法.解耦算法可达到加快计算速度、提高计算效率的目的.IEEE多个算例的数值实验以及与其他方法的比较均显示了新算法具有良好的计算效果.     

Optimal wind turbines placement within a distribution market environment

This paper proposes a hybrid optimization method for optimal allocation of wind turbines (WTs) that combines genetic algorithm (GA) and market-based optimal power flow (OPF). The method jointly maximizes net present value (NPV) related to WTs investment made by WTs’ developers and social welfare (SW) considering different combinations of wind generation and load demand over a year. The GA is used to choose the optimal size while the market-based OPF to determine the optimal number of WTs at each candidate bus. The stochastic nature of both load demand and wind power generation is modeled by hourly time series analysis. The effectiveness of the method is demonstrated with an 84-bus 11.4 kV radial distribution system.     

Multiobjective optimal power flow using interior search algorithm: A case study on a real-time electrical network

Optimal power flow (OPF) is a vital concern in an electrical network. In consequence of the intricacy of the power systems, the conventional formulations are not adequate for current situation. Hence, in this study, the multiobjective OPF (MOOPF) problem has been modeled to diminish the production cost, environmental emission, and losses and to enhance the voltage stability and voltage profile simultaneously. This study proposes the application of interior search algorithm (ISA) for resolving MOOPF problem. The simulations have been carried out on three various test systems such as IEEE 30-bus system, IEEE 57-bus system, and Tamil Nadu Generation and Distribution Corporation Limited, as a real part of 62 bus Indian utility system (IUS) to infer the efficacy of ISA in solving the OPF problems. The simulation results have been compared with other techniques. The comparison shows that ISA is used in resolving MOOPF problems.     

A modified MOEA/D approach to the solution of multi-objective optimal power flow problem

This study presents a modified multi-objective evolutionary algorithm based decomposition (MOEA/D) approach to solve the optimal power flow (OPF) problem with multiple and competing objectives. The multi-objective OPF considers the total fuel cost, the emissions, the power losses and the voltage magnitude deviations as the objective functions. In the proposed MOEA/D, a modified Tchebycheff decomposition method is introduced as the decomposition approach in order to obtain uniformly distributed Pareto-Optimal solutions on each objective space. In addition, an efficiency mixed constraint handling mechanism is introduced to enhance the feasibility of the final Pareto solutions obtained. The mechanism employs both repair strategy and penalty function to handle the various complex constraints of the MOOPF problem. Furthermore, a fuzzy membership approach to select the best compromise solution from the obtained Pareto-Optimal solutions is also integrated. The standard IEEE 30-bus test system with seven different cases is considered to verify the performance of the proposed approach. The obtained results are compared with those in the literatures and the comparisons confirm the effectiveness and the performance of the proposed algorithm.     

面向微博的情感影响最大化模型

社交网络中影响最大化问题是寻找具有最大影响范围的节点。影响最大化的大部分求解算法仅仅依赖社交网络图。基于微博的转发关系树和微博内容的情感倾向性,以及用户的社交网络图,提出了一个能够刻画用户情感影响的情感影响最大化模型——情感影响分配模型(sentiment influence distribution,SID),证明了SID模型下的情感影响最大化问题是一个NP难问题,给出了一个具有精度保证的贪心算法。在真实的微博数据上的实验结果表明,SID模型能够有效地找出情感影响最大化的节点集,同时具有很高的扩展性。     

Graphical models for optimal power flow

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithm for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. Numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.     

Enhanced goal attainment method for solving multi-objective security-constrained optimal power flow considering dynamic thermal rating of lines

Security-constrained optimal power flow (SCOPF) is an important problem in power system operation. Dynamic thermal rating (DTR), as an effective method to increase transmission capacity of power systems, has been recently considered in some optimal power flow (OPF) and SCOPF models. Additionally, in today power systems, OPF problem involves various objectives leading to multi-objective OPF models. In this paper, a new multi-objective SCOPF model considering DTR of transmission lines is presented. In addition, a new multi-objective solution method is proposed to solve the multi-objective SCOPF problem. The proposed method is an enhanced version of goal attainment technique in which the search capability of this technique to cover borders of the Pareto frontier is enhanced. The proposed multi-objective DTR-included SCOPF model as well as the proposed multi-objective solution method are tested on the IEEE 118-bus test system and the obtained results are compared with the results of other alternatives.     

Market power and welfare effects in DC power flow electricity models with thermal line losses

A nodal electric power network with Cournot–Nash interaction among power generators is formulated as a mixed complementarity problem. The model incorporates a direct current (DC) power flow approximation with thermal line losses to model real-time flows. We include constant wheeling rate and variable congestion charges for transmission of electricity. Market power and welfare effects are measured in an aggregated Indiana electric grid model. We find that imposing DC power flow constraints in a model results in significant changes in social welfare estimates. Line losses are also an important factor affecting market power and welfare of market participants in the case study.     

Optimal placement of UPFC in power systems using immune algorithm

This paper presents the application of immune algorithm (IA) to find optimal location of unified power flow controller (UPFC) to achieve optimal power flow (OPF) and congestion management. Objective function in the OPF, that is to be minimized, is the overall cost functions, which includes the total active and reactive production cost function of the generators and installation cost of UPFCs. The OPF constraints are generators, transmission lines and UPFCs limits. In power system, it may not always be possible to dispatch all of the contracted power transactions due to congestion of the transmission corridors. We propose IA method to minimize the objective function under all equality and inequality constraints. Simulations are performed on 4-bus, IEEE 14-bus and IEEE 30-bus test systems for optimal location of UPFC and the results obtained are encouraging and will be useful in electrical restructuring.     

Application of Hyper-Spherical Search algorithm for optimal energy resources dispatch in residential microgrids

This paper presents a residential hybrid thermal/electrical grid-connected home energy system (HES), including a fuel-cell with combined heat and power and a battery-based energy storage system. The minimum operation cost of this integrated energy system is achieved by proper scheduling of different energy resources, found by applying a new powerful optimization algorithm, the Hyper-Spherical Search (HSS) algorithm, to the system's scheduling problem. This is the first time that HSS is used to face the energy resource dispatch problem. The HSS has been only tested in mathematical problems in the previous study. The optimization procedure generates an efficient look-up table in which the powers generated by different energy resources are determined for all time intervals. The effect of different electricity tariffs for purchasing electricity from the main grid on the operation costs of the system is investigated. Moreover, a battery is properly dispatched in the energy system to decrease the operation costs. A real load demand is used in the simulation. The results of HSS are compared with the harmony search algorithm and the colonial competitive algorithm to show the power and effectiveness of HSS to find the optimal dispatch strategy of energy resources for the first time. This is the first time that HSS is compared with CCA. The results of this paper are expected to contribute to home energy systems and real projects.     

基于有重叠社区划分的社会网络影响最大化方法研究

社会网络中影响最大化问题是指在特定传播模型下,对于给定的值,寻找具有最大影响范围的节点集,这是一个组合优化问题,Kempe等人已经证明该问题是NP-hard问题,其研究在理论和现实应用中都具有重大意义。文中提出一种新的影响最大化算法——有重叠社区划分的影响最大化算法(K-clique Heuristic算法),该算法的思路是在现实社会网络中跨越多个社交圈子的节点的传播领域越广,其交叉性更强、传播范围更广、影响力更大。所提算法与已有典型算法有相近的运行结果,且有更好的现实应用性和可解释性,为这项具有挑战性的研究提供了新的思路和方法。     

一种基于RAN架构无线接入网系统容量最大化的功率分配算法

针对新型RAN架构无线接入网中功率分配问题进行研究, 建立系统容量最大化的最优化数学模型, 提出了一种基于RAN架构无线接入网的系统容量最大化的功率分配算法, 并且应用人工鱼群算法求解了算法中目标函数的全局最优解, 即一组使系统容量最大化的发射功率。仿真结果表明, 与现有的分布式网络架构中非合作的功率控制博弈算法相比, 新算法可以显著提高系统容量, 即证明了该算法的有效性。     

多机电力系统PSS参数优化新方法

机械回路谐振引起了励磁系统频率特性曲线出现“波峰”和“波谷”, 造成现有方法不易准确测量或计算励磁系统相位滞后角. 为此, 本文提出一种新的多机系统PSS参数优化方法. 首先, 重新定义基于多机模型的励磁系统相位滞后角, 并推导出相应的计算公式, 基于新定义的计算方法不再受机械回路谐振的影响, 可以得出更合理的计算结果.然后, 在PSS增益整定时, 将问题描述转化为多机系统部分输出量反馈的优化模型, 通过求解Levine-Athans方程组得到最佳PSS增益. 最后将所提方法应用于一个8机电力系统, 与传统方法比较后, 表明电力系统阻尼特性得到进一步改善.     

Exchange market algorithm based optimum reactive power dispatch

In this paper, an exchange market algorithm (EMA) approach is applied to solve highly non-linear power system optimal reactive power dispatch (ORPD) problems. ORPD is most vital optimization problems in power system study and are usually devised as optimal power flow (OPF) problem. The problem is formulated as nonlinear, non-convex constrained optimization problem with the presence of both continuous and discrete control variables. The EMA searches for optimal solution via two main phases; namely, balanced market and oscillation market. Each of the phases comprises of both exploration and exploitation, which makes the algorithm unique. This uniqueness of EMA is exploited in this paper to solve various vital objectives associated with ORPD problems. Programs are developed in MATLAB and tested on standard IEEE 30 and IEEE 118 bus systems. The results obtained using EMA are compared with other contemporary methods in the literature. Simulation results demonstrate the superiority of EMA in terms of its computational efficiency and robustness. Consumed function evaluation for each case study is mentioned in the convergence plot itself for better clarity. Parametric study is also performed on different case studies to obtain the suitable values of tuneable parameters.     

Congestion management by determining optimal location of series FACTS devices using hybrid bacterial foraging and Nelder–Mead algorithm

In this paper, the Thyristor-Controlled Series-Compensated (TCSC) devices are located for congestion management in the power system by considering the non-smooth fuel cost function and penalty cost of emission. For this purpose, it is considered that the objective function of the proposed optimal power flow (OPF) problem is minimizing fuel and emission penalty cost of generators. A hybrid method that is the combination of the bacterial foraging (BF) algorithm with Nelder–Mead (NM) method (BF-NM) is employed to solve the OPF problems. The optimal location of the TCSC devices are then determined for congestion management. The size of the TCSC is obtained by using of the BF-NM algorithm to minimize the cost of generation, cost of emission, and cost of TCSC. The simulation results on IEEE 30-bus, modified IEEE 30-bus and IEEE 118-bus test system confirm the efficiency of the proposed method for finding the optimal location of the TCSC with non-smooth non-convex cost function and emission for congestion management in the power system. In addition, the results clearly show that a better solution can be achieved by using the proposed OPF problem in comparison with other intelligence methods.