求解最优潮流问题的内点半定规划法

基于内点半定规划(semi-definite programming,SDP),提出一种求解最优潮流(optimal power flow,OPF)的新方法--SDP-OPF法。该方法将非凸OPF问题等价转换为半定规划问题,然后应用原始-对偶内点法求解。根据OPF半定规划模型的特点,采用基于半定规划的稀疏技术,使存储效率和计算性能得以大幅度提高。以4节点的简单电力系统为例,展示模型等价转换的过程及如何获取原OPF问题的解。IEEE-300节点等6个标准系统的仿真计算表明：所提算法具有超线性收敛性,其计算结果与内点非线性规划的结果一致,且能保证解的全局最优性,可在多项式时间内完成,是一种应用前景广阔的方法。     

基于半定规划的{0,1}-经济调度

基于内点半定规划,提出一种直接求解{0,1}-经济调度问题({0,1}-ED)的新方法.通过引入辅助变量,该方法将原整数变量约束转化为凸二次约束,进而将{0,1}-ED问题转化为半定规划问题,并用内点法进行求解.对于大系统整数变量的微小偏差,应用简单的启发式技术调整.ED-420等9个测试系统的仿真结果表明,所提方法能够有效地处理{0,1}-经济调度,对于大多数问题都可以得到较精确的结果,计算时间具有多项式复杂性.     

A semidefinite programming method with graph partitioning technique for optimal power flow problems

A new semidefinite programming (SDP) method with graph partitioning technique to solve optimal power flow (OPF) problems is presented in this paper. The non-convex OPF problem is converted into its convex SDP model at first, and then according to the characters of power system network, the matrix variable of SDP is re-arranged using the chordal extension of its aggregate sparsity pattern by the graph partitioning technique. A new SDP-OPF model is reformulated with the re-arranged matrix variable, and can be solved by the interior point method (IPM) for SDP. This method can reduce the consumption of computer memory and improve the computing performance significantly. Extensive numerical simulations on seven test systems with sizes up to 542 buses have shown that this new method of SDP-OPF can guarantee the global optimal solutions within the polynomial time same as the original SDP-OPF, but less CPU times and memory.     

Global optimization for the OPF problem via two‐degree SDP method

This letter proposes a two‐degree semidefinite programming (SDP) method for achieving the global optimum of the optimal power flow (OPF) problem. The method extends the variables to four degrees, and formulates an SDP problem with a two‐degree extended matrix. It satisfies the rank‐1 condition. Experimental results show that this method is more reliable for reaching the OPF's global optimum than existing SDP methods. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

基于内点半定规划法的含UPFC的最优潮流

传统最优潮流(OPF)问题是一个非凸优化问题,统一潮流控制器(UPFC)的引入进一步增加了OPF问题的非凸程度,因此传统内点法无法有效保证所得解的全局最优性。基于此,将对初值选取不敏感、具有全局收敛能力的内点半定规划(SDP)算法推广至计及UPFC的电力系统OPF问题中,将UPFC变量添加至系统状态变量中,并对增广变量进行优化重组,利用直角坐标的二次形态将含UPFC的OPF问题映射到SDP空间。对IEEE 30、57、118、300节点系统和一个实际系统进行算例测试,结果表明所提算法有效保证了所得解的全局最优性,对增广变量的优化重组有效提高了算法的计算效率和数值稳定性。     

Cost/benefits analysis of an optimal power flow: the PG&Eexperience

This paper documents the results of a study to analyze the potential costs and benefits that may be realized from the future on-line use of an optimal power flow (OPF) application in PG&E's new energy management system (EMS). This application minimizes production cost while eliminating thermal overloads using active power controls. The methodology of the study was to simulate as closely as possible the operation of the PG&E power system under the currently used method based on a modified economic dispatch algorithm and the optimal dispatch provided by the OPF. The modified economic dispatch method is based on an economic dispatch with some manual redispatching to eliminate thermal overloads consistent with existing operating procedures. The results of the study showed that the use of this OPF application resulted in a substantial increase of the MW transfer capability of a constrained transmission corridor in the PG&E system. This increase can potentially result in substantial annual savings due to reduced operating costs. Furthermore, the study showed that this application can minimize load shedding, if the other control options have been exhausted, to eliminate thermal overloads, can produce realistic solutions for infeasible problems and could conceivably validate/improve current operating procedures under a wide range of operating conditions     

Numerical experiments with an optimal power flow algorithm based onparametric techniques

This paper presents the results of numerical experiments with a new optimal power flow (OPF) algorithm based on a parametric technique. The approach consists of relaxing the original OPF problem by incorporating parametric terms to the objective function, the equality and inequality constraints. Such relaxation assures that any arbitrary initial solution, feasible or unfeasible, be the optimal solution of the OPF problem. As the scalar parameter changes, a family of OPF problems is created, whose necessary conditions are solved by Newton's method. An efficient strategy is proposed for updating the parameter and the optimal set of active inequality constraints of each intermediate problem. Two applications of the methodology are reported: the economic dispatch problem and the minimum transmission loss problem. These problems were solved for an 810-bus and a 2256-bus equivalent network of the South/Southeast interconnected Brazilian power system. The results show that the parametric approach is robust and efficient when applied to large-scale OPF problems     

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。     

A new approach to generation scheduling in interconnected power systems using predictor-corrector proximal multiplier method

The purpose of this paper is to elaborate a new generation scheduling algorithm in the interconnected power systems. Typically, the generation scheduling problem as a mixed integer non-linear programming can be effectively solved by the generalized Benders decomposition technique which decouples an original problem into the master problem and subproblems to tremendously allow fast and accurate solutions of large-scale problems. In order to formulate efficient inter-temporal optimal power flow (OPF) subproblems, we will explore a regional decomposition framework based on predictor-corrector proximal multiplier method. In fact, this scheme can find the most economic generation schedules under the power transactions for a multi-utility system without the exchange of each utility’s own private information and major disruption to existing economic dispatch or OPF adopted by individual utilities.     

一种基于扩展线性规划的在线最优潮流方法

提出了一种基于对偶松弛法的扩展凸规划和序列线性规划相结合的在线最优潮流方法。通过分析核心约束交换逻辑的物理内涵,使优化过程清晰可理解;通过一个独立的探测和处理不可行解的预过程,使核心优化计算摆脱了不可行问题;通过引入控制效能指标,使低效控制解的数目减少,增强了结果的可操作性;通过扩展凸规划方法,使各种可分目标得到有效处理,部分实现了目标函数和算法自身的分离。该方法可灵活应用于在线安全校正控制及在线优化调度。在几个测试系统及一个省级实际电网上进行了数值试验,结果表明该方法是快速可靠的。     

基于半定规划法的含分布式潮流控制器最优潮流

分布式潮流控制器能够灵活地提升现有线路的输电能力,从而降低系统运行成本,但该设备的引入会增加电力系统最优潮流问题的复杂度与非凸程度。针对分布式潮流控制器的结构及原理进行了分析,提出一种简化的稳态功率模型,并考虑到装置运行时各串联单元自身容量限制,给出实际电网中分布式潮流控制器线路的潮流可行域。基于此,采用对初值选取不敏感的半定规划法建立含分布式潮流控制器的系统最优潮流模型,并选用原对偶内点法进行求解。算例测试结果表明,所提方法能有效解决含分布式潮流控制器的系统潮流优化问题。     

基于非线性内点方法的含有串联柔性输电系统装置的阻塞调度

提出了一种基于非线性内点方法的含有串联FACTS装置的阻塞调度方法。针对调节线路有功潮流问题选取了串联FACTS装置的控制参数和模型，并把FACTS对系统的调节作用表述成附加功率的形式。不引入FACTS的控制目标方程，而是在包含FACTS控制参数的变量空间内进行寻优，可以考虑FACTS的多种调节方式。该方法具有较好的鲁棒性和收敛性，易于利用原有的潮流优化算法和程序。     

基于自适应步长ADMM的直流配电网分布式最优潮流

直流配电网的发展前景广阔,其最优潮流(OPF)问题关系到电网经济运行,具有重要的工程意义。针对放射状直流配电网,以二阶锥规划(SOCP)凸松弛理论为基础,建立了考虑电压、电流、功率约束的SOCP-OPF凸规划模型,并提出一种基于交替方向乘子法(ADMM)的分布式最优潮流计算方法,以解决传统集中式优化方式面临的诸多难题。相比已有研究,该方法在各节点配置计算单元,无需全局协调或分层分区,利用相邻主体间少量的信息传递即可通过并行计算得出全局最优解;优化模型中考虑了配电线路传输电流限制,约束条件更全面;计算方法中设计了自适应步长调整机制,计算效率较高。IEEE 33节点和IEEE 123节点的算例分析验证了所提算法的准确性和良好的收敛性。     

发电市场预调度计划模型及算法的研究

结合中国发电市场的实际情况,根据最优潮流原理,以整个预调度周期内的市场购电费用（MPC）最小为目标,建立了预调度计划模型,并根据预调度计划的特点,将模型目标简化为各时段的市场清算电价（MCP0最小,同时设计了三段式预调度算法：用静态规划法求解整个顶调度计划周期内的优化问题,用优先级求解机组组合问题,用改进的Powell法求解最优潮流问题。算例结果表明,预调度模型和算法下的市场清算电价能跟踪系统负荷变化,且该模型算法具有复杂度低、结果最佳性较好的特点。     

A decentralized solution to the DC-OPF of interconnected power systems

This paper presents a new method for the decentralized solution of the DC optimal power flow (OPF) problem in large interconnected power systems. The method decomposes the overall OPF problem of a multiarea system into independent OPF subproblems, one for each area. The solutions of the OPF subproblems of the different areas are coordinated through a pricing mechanism until they converge to the global OPF solution. The prices used for the coordination of the subproblem solutions are the prices of electricity exchanges between adjacent areas. Test results from the application of the method to the three-area RTS-96 and the Balkan power system are reported.     

基于TCSC的优化阻塞模型设计与应用研究

针对柔性交流输电装置控制线路潮流的特点,在传统OFF的基础上,将调整网络参数与经济调度方法相结合,研究了计及TCSC的优化阻塞调度模型。求解过程中,把TCSC对系统的调节作用表述成节点附加功率的形式,并将TCSC控制参数纳入变量空间内寻优。IEEE5系统的仿真结果验证了该方法的有效性。     

大规模系统月度机组组合和安全校核算法

采用时序优化方式解决月度机组组合和电网安全校核问题,针对电力市场和节能调度模式,建立了优化数学模型。利用拉格朗日松弛算法进行月度720时段机组组合优化,利用非线性内点最优潮流算法进行电网安全校核。以IEEE RTS标准算例和中国华东电网为例进行大规模优化性能分析,结果表明该算法是解决大规模电力系统月度发电计划和电网安全校核的有效方法。     

含规模化储能系统的最优潮流模型与求解方法

大规模储能系统的应用可提高电网运行的经济性,其优化调度的难点是如何处理能量约束。提出了一种含储能系统经济调度的滚动优化思路,在建立储能系统细化模型的基础上,构造了考虑规模化储能系统的多时段最优潮流模型,并对剩余能量约束进行了松弛与自适应调整。通过等效变换与Lagrange松弛,推导出其对偶问题进行求解。该对偶问题是一个凸的半正定规划,且在一定条件下对偶间隙为零,有效提高了解的全局最优性。对储能系统单点接入和多点接入的算例进行了测试,并与内点法计算的结果进行了比较,验证了所提模型和算法的有效性。     

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.     

基于参数线性规划的电-气综合能源系统最优能量流算法

电-气综合能源系统(integrated electricity-gas system,IEGS)的最优能量流(optimal energy flow,OEF)计算是其优化规划与运行分析的基础。针对现有电-气综合能源系统最优能量流求解方法存在的数据交互频繁、收敛性差以及难以保证隐私性等问题,提出了一种基于参数线性规划的电-气综合能源系统最优能量流计算方法。首先,建立计及有功网损的电力网络最优直流潮流模型,以及基于二阶锥松弛的天然气网络最优潮流模型。其次,基于参数线性规划理论,建立了电-气耦合功率与电力网络潮流最优解的关联函数。然后,将该关联函数传递至天然气系统中进行联合优化,并返回电-气耦合功率信息至电力系统中求解,分别得到最优能量流的天然气流与电力潮流结果。仿真分析表明所提方法能够通过单次信息交互准确求解最优能量流,同时交互信息量较小且不包含隐私信息,适用于最优能量流的分解式计算。