Determination of available transfer capability using multi-objective contingency constrained optimal power flow with post-contingency corrective rescheduling

In a new competitive electricity market, accurate information should be shared to provide nondiscriminatory access to all participants. Key information to determine how much power can be shipped through the network is dubbed available transfer capability (ATC). This paper presents a methodology for the calculation of ATC, which is performed through a fuzzy logic approach to parallelizing contingency constrained optimal power flow (CCOPF). This algorithm may be used by utilities to optimize economy interchange for severe contingencies analyzed without disclosing details of their operating cost to competitors. In fact, the main objective of fuzzy multi-objective CCOPF is to determine the minimization of both the base-case (pre-contingency) operating cost and the post-contingency correction times as conflicting but fuzzy goals. Also, Benders decomposition is adopted to partition the fuzzy formulation with contingency constraints, which allows for post-contingency corrective rescheduling, motivated by the improvement of the computational efficiency using parallel processing. The IEEE-30 bus system is employed to test the proposed algorithm and the results are comprehensively demonstrated by a distinct comparison between the conventional optimal power flow and the CCOPF with respect to the same array of transactions, base-case, and generation/line outages.     

静态安全约束下基于Benders分解算法的可用传输容量计算

在电力市场环境下，可用传输容量(ATC)是反映输电线路可用于交易的剩余容量的重要指标。文中以最优潮流为基础，采用Benders分解方法将考虑静态安全约束的ATC计算问题分解为一个基态主问题和一系列与各预想事故有关的子问题。主问题用来处理基态潮流和相应约束以及由子问题所返回的Benders割(cut)约束，而各子问题用来处理各预想事故和形成相应的静态安全约束。文章给出了相应的数学模型，并提出了两种改进的求解策略。4节点和IEEE30节点系统的计算结果表明了该方法和求解策略的有效性。     

Contingency constrained optimal reactive power flow procedures forvoltage control in planning and operation

The paper presents a preventive secure contingency constrained approach to power system voltage profile optimization suitable both for VAr planning and for short term reactive scheduling. The solution of the problems is based upon the implementation of two optimal reactive power flow (ORPF) programs: the first relevant to determining a workable state (security aspect); and the second relevant to attaining the optimal and secure point (global target). The first ORPF is solved by recursively employing a linear programming algorithm, whilst the second is based on the Han-Powell algorithm. In the paper, emphasis is given to the introduction of the contingency constraints in the ORPF models. The N-1 security constraints are explicitly introduced in the programs in order to obtain an operating point preventive-secure with respect to a selected contingency set. The performances of the procedures are shown by presenting the numerical results obtained from their applications to a small test network and to the large ENEL transmission system     

Chaotic artificial bee colony algorithm based solution of security and transient stability constrained optimal power flow

Due to the increase rapidly of electricity demand and the deregulation of electricity markets, the energy networks are usually run close to their maximum capacity to transmit the needed power. Furthermore, the operators have to run the system to ensure its security and transient stability constraints under credible contingencies. Security and transient stability constrained optimal power flow (STSCOPF) problem can be illustrated as an extended OPF problem with additional line loading and rotor angle inequality constraints. This paper presents a new approach for STSCOPF solution by a chaotic artificial bee colony (CABC) algorithm based on chaos theory. The proposed algorithm is tested on IEEE 30-bus test system and New England 39-bus test system. The obtained results are compared to those obtained from previous studies in literature and the comparative results are given to show validity and effectiveness of proposed method.     

基于SCUC的可入网混合电动汽车优化调度方法

在可入网混合电动汽车(PHEV)有望规模化应用的背景下,以传统的计及安全约束的机组最优组合(SCUC)问题为基础,发展了能够容纳PHEV的电力系统优化调度数学模型。所发展的模型以保证系统安全运行为前提,兼顾了PHEV车主的经济效益与发电的碳排放成本。利用PHEV作为可移动电量储存单元的特性,将模型解耦为机组最优组合与计及交流潮流约束的充/放电计划优化2个子模型。应用混合整数规划方法和牛顿—拉夫逊潮流算法迭代求解优化问题,可以同时获取日前机组调度计划和各时段的PHEV最优接纳容量及充/放电计划等结果。最后,以6节点和IEEE 118节点2个系统为例,验证了所构建模型的正确性和有效性。     

Optimal supply curve bidding using Benders decomposition in competitive electricity markets

This paper describes a new approach for optimal supply curve bidding (OSCB) using Benders decomposition in competitive electricity markets. The inclusion of physical unit constraints and transmission security constraints will assure a subsequent feasible solution for the problem. We decompose the problem into a base-case OSCB (without unit and network constraints) and subproblems for checking the feasibility of unit and network constraints. For a given base-case OSCB schedule, line flow violations are minimized by adjusting units’ generation and phase shifters. In case transmission violations cannot be removed, additional linear constraints are introduced in the master problem in the form of price signals for rescheduling OSCB. An IEEE 24-bus system is used to demonstrate the effectiveness of the proposed approach.     

Dynamic security constrained optimal power flow/VAr planning

Traditionally security constrained optimal power flow and VAr planning methods consider static security observing voltage profile and flow constraints under normal and post contingency conditions. Ideally, these formulations should be extended to consider dynamic security. This paper reports on a BC Hydro/CEPEL joint effort establishing a dynamic security constrained OPF/VAr planning tool which considers simultaneously static constraints as well as voltage stability constraints. This paper covers the details of formulation and implementation of the tool together with the test results on a large scale North American utility system and a reduced Brazilian system     

求解非光滑燃料费用函数的基于进化规划的机组最优潮流

提出求解具有非光滑燃料费用函数的存在爬坡率限制的最优潮流方法。针对两次、阶梯形、联合循环机组的非光滑燃料费用函数,介绍一个基于进化规划的算法。在该算法中,为避免早熟,交叉操作随后代的数目非线性变化。介绍了所提出的进化算法应用于有线路约束的IEEE30节点系统和印度62节点系统的情况。以MVA为单位的线路潮流直接采用牛顿-拉夫逊法计算。算例证明所提出的进化算法简单,对求解具有非光滑燃料费用函数的存在很多约束的最优潮流问题有效。     

基于非线性内点法的安全约束最优潮流:（二）算法实现

提出一种考虑多预想事故的安全约束最优潮流内点算法实施方案.讨论了预想事故集中,起作用预想事故的监视与强制策略及不可行预想事故的辨识.根据简约KKT(Karush-Kuhn-Tucker)系统的带边列分块对角特殊结构,推导了内点安全约束最优潮流的一种分解协调实施算法.为保证预想事故扫描对安全约束最优潮流的支撑,提出了一种能量管理系统中安全约束最优潮流和静态安全分析模块间的衔接和交互方案.算法在IEEE 14节点等4个系统上,对全部非解列型开断事故进行了大量的计算,结果表明,算法有效、可靠.安全约束最优潮流解与经典最优潮流解在安全性和经济性上的比较则显示了将静态安全约束引入经典最优潮流的必要性.     

考虑二重预想事故的在线电压稳定预防控制

提出了一种基于原对偶内点算法的安全约束最优潮流的数学模型,以控制代价最小化为目标,不仅考虑了正常状态下的安全约束,还同时考虑到了预想事故后的安全约束以及电压稳定裕度的约束。在线电压稳定评估系统中,同时考虑单重预想事故及其引发的继发性二重预想事故,分别进行筛选和排序,综合形成预想事故集。根据预想事故集,基于上述模型依次对其中每一预想事故进行预防控制,构建在线电压稳定预防控制模块,当系统处于不安全状态时,能够及时提供合理的预防控制策略,保证系统安全运行。以IEEE 118节点测试系统为算例,验证了所提出模型的正确性。     

基于可行空间并行的安全约束最优潮流

为了提高电网控制决策的实时性,文中将计及预想故障安全约束的经济性优化问题分解为以发电成本最小为目标的基态最优潮流主问题和预想故障安全校核子问题,并提出一种基于可调空间切片并行的分解协调算法进行求解,以避免交替迭代。首先,按不同比例对可调空间进行切片形成多个切片方案,并基于并行计算平台采用原始-对偶内点法对各切片方案进行基态最优潮流主问题求解;然后,对各优化后方式进行预想故障并行安全校核;接着从通过安全校核的切片方案中挑选出发电成本最小的方案;最后,以贵州省某市电网为算例分析验证了所提方法的有效性。     

Network loss minimization with voltage security using differential evolution

This paper presents a differential evolution (DE) based optimal power flow (OPF) for reactive power dispatch in power system planning studies. DE is a simple population-based search algorithm for global optimization and has a minimum number of control parameters. The problem is formulated as a mixed integer non-linear optimization problem taking into account both continuous and discrete control variables. The proposed method determines control variable settings such as generator voltages (continuous), tap positions (discrete) and the number of shunt reactive compensation devices to be switched (discrete) for real power loss minimization in the transmission system using DE algorithm. Most of the evolutionary algorithm applications to optimization problems apply penalty function approach to handle the inequality constraints, involving penalty coefficients. The correct combination of these coefficients can be determined only by a trial and error basis. In the proposed approach, the inequality constraints are handled by penalty parameterless scheme. Voltage security margin was evaluated using continuation power flow (CPF), to ensure the feasibility of the optimal control variable setting. The suitability of the method was tested on IEEE 14 and IEEE RTS 24-bus systems and results compared with sequential quadratic programming (SQP) method. The DE provides near global solutions comparable to that obtained using SQP.     

基于安全域的电力系统有功及无功优化

提出了一种同时计及电力系统有功及无功的新型优化潮流模型与算法。在构建优化潮流(OPF)的数学模型时借助了3种电力系统安全域的概念与方法,它们分别是:满足系统潮流约束(母线电压约束、支路热稳定极限以及发电机出力限制)的“静态安全域”、“静态电压稳定域”以及针对既定的网络结构和既定的网络结构变化过程的保证系统暂态稳定性的“动态安全域”。在此基础上,利用电力系统的有功功率与支路角之间、无功功率与节点电压幅值之间的仿射关系,建立了通过二次规划来求解优化潮流(OPF)的算法。文中最后在新英格兰10机39节点系统中演示了所提出算法的有效性。     

基于支路耗散功率转归分量的最优潮流模型与算法

针对最优潮流模型中线路安全稳定约束表达式的复杂性,运用支路耗散功率的转归分量方法给出了一种以电源出力为变量的近似线性表达式,构建了一种最优潮流模型。对模型中线性度不同的约束,采用逐次线性化和逐段线性化相结合的方法处理。在求解过程中直接考虑线路安全稳定约束,避免了牛顿法被动校验和变更约束带来的模型和求解的低效性。仿真结果表明,文中的模型和算法改进了最优潮流的收敛性和求解速度。     

基于启发式线性规划的大规模安全约束调度快速求解方法

提升大规模安全约束经济调度优化模型的求解性能是开展大电网跨省区电力电量全局优化平衡的前提与基础。首先分析问题的物理特性,通过并行计算求解不考虑机组爬坡约束的分时段约束松弛模型。基于对松弛解的分析获得可用于指导安全约束经济调度模型改进的有用信息,以约束剔除和约束增加的方式提出了基于启发式线性规划的大规模安全约束经济调度快速求解方法。将所提算法运用于新英格兰10机扩展系统和中国实际电网,验证了所提算法的正确性和有效性。     

A solution to security constrained non-convex economic dispatch problem by modified subgradient algorithm based on feasible values

A security constrained power dispatch problem with non-convex total cost rate function for a lossy electric power system is formulated. Then, an iterative solution method proposed by us and based on modified subgradient algorithm operating on feasible values (F-MSG) is used to solve it.Since all equality and inequality constraints in our nonlinear optimization model are functions of bus voltage magnitudes and phase angles, off-nominal tap settings and susceptance values of svar systems, they are taken as independent variables. Load flow equations are added to the model as equality constraints. The unit generation constraints, transmission line capacity constraints, bus voltage magnitude constraints, off-nominal tap setting constraints and svar system susceptance value constraints are added into the optimization problem as inequality constraints. Since F-MSG algorithm requires that all inequality constraints should be expressed in equality constraint form, all inequality constraints are converted into equality constraints by the method, which does not add any extra independent variable into the model and reducing the solution time because of it, before application of it to the optimization model.The proposed technique is tested on IEEE 30-bus and IEEE 57 bus test systems. The minimum total cost rates and the solution times obtained from F-MSG algorithm and from the other techniques are compared, and the outperformance of the F-MSG algorithm with respect to the other methods in each test system is demonstrated.     

变负荷条件下追踪电力系统安全最优运行轨迹的参数化方法

提出一种追踪线性约束下凸可分规划问题最优解轨迹的参数化方法。该参数优化算法可在对偶松弛凸可分规划算法的主循环之外,通过少量参数化扩展得到。参数分析表明最优解轨迹的性态是一条分段线性曲线,解轨迹上的破点和不可行现象存在密切关系。将这种方法应用到电力系统有功最优潮流问题中,得到一种统一经济调度和安全约束调度的参数化安全约束调度(security constrained economic dispatch,SCED)新算法,它可快速追踪变负荷条件下系统安全最优运行轨迹。算法在IEEE14-300节点测试系统及2个省级实际系统上通过测试,数值试验和几何分析表明了该方法的计算特性和物理内涵,同时清楚地显示了目前调度模式中存在的问题和改进方向。     

电力系统最优主动解列断面搜索模型及算法

解列是电力系统在故障时结构完整性得不到保证的情况下分裂为2个或多个孤立稳定运行子系统的过程或操作。及时恰当的主动解列操作将能有效地避免因保护连锁动作使得电力系统被动解列而崩溃所造成的巨额经济损失。结合图论中的相关概念和输电网最优解列的物理过程,建立电力系统最优主动解列断面选择问题的完整数学模型,并基于含连通图约束的背包问题(connected graph constrained knapsackproblem,CGKP)及其求解算法提出"搜索调整"的2阶段求解方法。为降低问题的复杂性,将完整数学模型分解成图的最优平衡分割问题和基于优化潮流的调节问题,并分2个阶段分别求解。其中,图的最优平衡分割问题又被分解成多个CGKP,利用基于含CGKP的图分割方法进行求解。所提出的主动解列策略具有较强理论基础,计算复杂度低,算例的计算结果证明了该模型及算法的正确性和有效性。     

Power systems operation using particle swarm optimization technique

This paper presents a proposed technique for solving different optimization problems using particle swarm optimization (PSO) technique as a modern optimization technique. The security constrained optimal active power dispatch is solved by a proposed optimal effective localized area (OELA) in large-scale power system at different operating conditions. However, the boundaries of this area can be increased or decreased depending on the amount and type of the operation problems as well as the control action requirements to remove these problems. Hence, minimum control variables are adjusted in a small-localized area to steer the system to secure and reliable operation condition. The optimal operation of ready reserve is introduced using an efficient proposed procedure considering the security constraints of the transmission lines power flows. Different emergency condition problems are solved using the OELA applied to different standard test systems.     

计及风险控制策略的电力系统可用输电容量决策

针对风电装机容量较高的电力系统,在可用输电容量计算时需要合理计及风电机组出力不确定性可能导致的各种风险,文中在可用输电容量决策中引入了风险控制策略,在保证由于风电出力不确定性所引起的系统潮流越限风险不超过给定允许水平的同时,将由于风电机组实际出力不足而导致购电成本超过给定限值的风险控制在一定范围内。首先,将计及风险控制的可用输电容量决策描述为机会约束规划问题;然后,利用半不变量的Gram-Charlier级数展开理论计算相应可用输电容量决策方案下系统的安全风险和经济风险;最后,采用多目标差异进化算法求解所发展的优化模型,并以IEEE 118节点系统为例验证了所提出模型和方法的可行性与有效性。