含VSC-HVDC的交直流系统内点法最优潮流计算

电压源换流器(voltage source converter,VSC)在稳态模型和工作原理上与传统高压直流输电(high voltage directcurrent,HVDC)的换流器有本质区别,因此传统的交直流系统最优潮流计算方法不适用于含基于电压源换流器高压直流输电(VSC based HVDC,VSC-HVDC)的交直流系统。讨论一种适用于原对偶内点法(primal-dual interior-pointmethod,PDIPM)和预测校正内点法(predictor-corrector PDIPM,PCPDIPM)解最优潮流的VSC-HVDC稳态模型。基于该稳态模型,将VSC-HVDC直流网络与交流系统结合起来,对交直流系统进行联立求解,并对多组算例进行仿真和分析,算例结果表明原对偶内点法在解决含VSC-HVDC的最优潮流问题的能力上,保持了传统内点法最优潮流的高效性,而在同样的条件下,预测–校正内点法迭代次数大大少于原对偶内点法。     

基于自动微分技术的VSC-HVDC内点法最优潮流

根据电压源换流器–高压直流输电(voltage sourceconverter-high voltage direct current,VSC-HVDC)的稳态潮流模型,结合自动微分(automatic differentiation,AD)技术,提出一种基于原对偶内点法的交直流系统最优潮流算法。该算法利用高效的基于操作符重载的AD工具生成雅可比(Jacobian)矩阵和海森(Hessian)矩阵,减少了微分表达式推导和代码编写的工作量,提高了程序的开发效率。多个算例的仿真结果表明,该算法保持了传统原对偶内点法在解决含VSC-HVDC的交直流最优潮流问题上的高效性,且对VSC的不同控制方式组合均具有良好的适应性。     

动态最优潮流的预测/校正解耦内点法

从动态最优潮流中动静态变量的弱耦合关系出发,深入分析了原对偶内点法的解耦思想及其产生的根本原因,然后将该解耦策略推广应用于预测/校正环节的线性方程求解,提出动态最优潮流的预测/校正解耦内点法.该算法利用预测/校正原对偶内点法的优势,提高了动态最优潮流的迭代计算效率.同时,针对线性修正方程组常数项的特点,进一步提出了一种分组解耦同步迭代策略,使动态变量和各时段静态变量在预测/校正环节中实现同步解耦计算,从而进一步提高了动态最优潮流的解耦计算效率.通过典型算例的仿真分析与对比,验证了该算法的有效性.     

潮流约束和机组爬坡速度的调度问题求解

采用原对偶内点算法对动态安全经济调度问题进行求解。IEEE30节点算例测试，对有无支路潮流约束进行了比较分析，表明本文模型的有效性和内点算法的灵活性。     

原对偶内点算法对电力系统无功的优化分析

针对电力系统中无功优化的问题,从非线性规划的角度进行分析,提出了一种原对偶内点算法.考虑无功问题的定位复杂且非线性,利用原对偶内点算法进行位置判断及潮流分析.通过实际案例进行验证,结果显示原对偶内点算法的无功定位精准度、计算时间均优于已有遗传算法.     

原-对偶内点法最优潮流在电力系统中的应用

结合电力系统的特性，提出了一种基于稀疏技术的原－对偶内点法求解最优潮流问题，它在处理等式约束和变量型不等式约束时，能够同时处理函数型不等式约束，并且没有新的注入元注入系统。提出了一种新的迭代步长和中心方向的修改策略，同经典的牛顿法最优潮流比较表明，不需要预估有效约束集和进行试验迭代，易于编程实现。     

一种恢复最优潮流可行性的实用方法

最优潮流无解时,以往只能凭借经验和反复调试才能恢复其可行性.文中提出了一种最优潮流的扩展模型来恢复最优潮流的可行性.在等式约束和不等式约束中加入松弛变量,并在目标函数中加入相应的惩罚项,采用改进的原对偶内点法来求解.算例仿真的结果表明:当原问题可行时,该模型可以收敛到原问题的最优解;当前约束或者控制变量越界导致原问题无解时,可以自动到更大的可行域内寻优,快速得到近似解,并且可以明确指出导致原问题无解的关键约束,从计算结果中可以方便地得到调整的措施,即调整有功、无功补偿量或者安全约束指标.改进的算法在各种情况下都有很好的收敛性.与其他模型和方法的比较说明了该模型和算法的优越性.该方法可以在多个方面得到实际应用.     

基于自动微分技术的含UPFC电力系统最优潮流

根据UPFC的稳态潮流模型,提出了基于原对偶内点法与自动微分(AD)技术相结合的含UPFC最优潮流算法。采用自动微分技术实现了雅可比矩阵和海森矩阵的自动生成,减少了微分表达式的推导,从而提高了开发效率。算例仿真结果表明,该算法对含UPFC的OPF模型具有良好的适用性和收敛性。     

一种求解多目标最优潮流的模糊优化算法

将模糊集理论和非线性原－对偶路径跟踪内点法应用于求解具有可伸缩约束的多目标最优潮流问题,选择合适的加速因子以改善算法的收敛性,并与单目标非线性最优潮流问题的计算结果进行了比较。对几个试验系统的计算表明,该算法具有稳定收敛性能,优化结果精确,灵活方便,处理变量不等工约束和函数不等式约束的能力很强,适合于求解大规模电力系统的多目标优化问题。     

多目标最优潮流问题的模糊建模及内点解法

针对多目标最优潮流问题,用模糊集理论将多目标函数和部分可伸缩的约束条件模糊化借助于最大,最小算子把多目标模糊最优潮流问题转化为标准的单目标非线性规划问题,并采用原－对偶路径跟踪内点进行求解,从而使最优潮流问题在更加符合实际情况的模型上实现优化,且其迭代收敛性得到了明显提高。     

Optimal Spinning Reserve Allocation with Full AC Network Constraints Via a Nonlinear Interior Point Method

An effective optimal spinning reserve allocation (OSRA) method is proposed in this paper using Optimal Power Flow (OPF). It enables optimal allocation of spinning reserve and load curtailment incorporating full AC network constraints and dynamic restriction on generation such as ramp-rate constraints. A Primal-Dual Interior Point (PDIP) method, which can efficiently handle both equality constraints and inequality constraints, is employed to solve the formulated dynamic OPF problem. In this model, spinning reserve and load curtailment constraints impose an interdependency between the generation output of units which usually are separable in conventional Newton OPF. A decomposition algorithm is therefore derived to handle the interdependency so that the constraint matrix of generation and that of network can be handled separately by slightly changing the entries of Hessian matrix. Therefore, the proposed method is not only still able to utilize the elegant super sparsity technique of Newton method, but also eliminates its ineffective binding active set determination procedure. Furthermore, the influences of spinning reserve on spot price (SP) are also discussed. A shift effect is observed.     

基于非线性互补问题函数的半光滑牛顿最优潮流算法

提出了一种新的基于非线性互补问题(NCP)函数的半光滑牛顿方法，以用于求解最优潮流(OPF)问题。通过引入NCP函数，将OPF模型KKT条件的互补松弛约束转化为等式约束，并采用非光滑牛顿法求解。算法的突出优势在于能够有效地处理OPF模型中的不等式约束，从而完全避免了OPF计算中起作用的不等式约束的识别问题。同时，文中利用电力系统的弱耦合特性，构造了牛顿分解算法。IEEE多个算例的数值试验表明：提出的算法具有很好的收敛特性和计算效果，有很好的实际应用前景。     

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     

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.     

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     

考虑发电报价和N-1安全约束的ATC建模与仿真

基于最优潮流(OPF)算法,建立电力市场条件下可用输电能力(ATC)计算模型.构造发电区域总有功出力最大、用电区域总负荷最大、区域间输电经济效益最大等3个目标函数,全面分析比较电网间可用输电能力.该模型考虑了输电线路故障对输电能力的影响,引入线路N-1故障的潮流方程及相应的不等式约束条件,使电力系统在故障时有负荷裕度,保证输电安全.最后采用LINGO软件对IEEE 30节点电网进行仿真计算,验证了该模型的合理性和可靠性,表明该模型为电力系统安全经济运行提供了有效分析方法.     

Optimal power flow solutions under variable load conditions

This work presents a methodology to calculate a sequence of optimal power flow (OPF) solutions under variable load conditions. The aim is to obtain a set of optimal operating points in the neighborhood of the bounds of the region defined by the load flow equations and a set of operational limits. For this, an algorithm based on the continuation method and on a primal-dual interior point optimization method is proposed. Such an algorithm consists of two main steps: the predictor step, which uses a linear approximation of the Karush-Kuhn-Tucker (KKT) conditions to estimate a new operating point for an increment in the system load; and the corrector step, which calculates the optimum corresponding to the new load level via a nonlinear primal-dual interior point method. Indices for critical buses and inequality constraints are a byproduct of the methodology. In addition, sensitivity analysis is performed to calculate the amount of reactive compensation which allows for a pre-specified increase in the system load. Results for realistic test systems are presented     

含暂态能量裕度约束最优潮流问题的线性规划解法

提出了计及暂态稳定约束最优潮流问题的线性规划模型。利用暂态能量裕度的解析灵敏度分析方法表达暂态稳定裕度增量与控制变量增量之间的线性关系,以此显式描述暂态稳定性约束,并加入到常规线性化最优潮流的不等式约束中。并采用单纯形法求解。对WSCC3机9节点系统的优化计算结果表明,该模型能较好地保证系统的暂态稳定性,有效地解决系统运行的经济性和安全性的结合问题。     

具有变量范围约束的潮流算法在OPF中的应用

提出一类新的电力系统最优潮流(OPF)算法.运用函数变换法模拟变量不等式约束,建立具有变量范围约束的潮流方程,并将目标函数与其上限值构成优化目标方程,与变量范围约束潮流方程一起组成扩展的变量范围约束潮流方程.该方程为非线性不定方程组.逐次收缩目标函数上限值,运用广义逆矩阵和牛顿-拉夫逊法求解,将OPF问题转化为一系列求解非线性不定方程组的一维优化逼近过程.介绍了以最小发电费用为目标的潮流优化问题和以最小有功网损为目标的无功优化问题的新算法,通过实例验证了算法的实用性.     

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