多故障暂态稳定约束最优潮流的轨迹灵敏度法

将暂态稳定约束最优潮流(transient stability constrained optimal power flow,TSC-OPF)计算过程分解为潮流、暂态稳定及轨迹灵敏度、降阶二次规划最优潮流3个子问题的交替求解。在迭代过程中,根据潮流和暂态稳定计算得到状态变量和代数变量时变轨迹;由此判断系统的稳定性,并计算失稳时刻状态变量和初始时刻代数变量对发电机有功和无功功率的轨迹灵敏度;据此将暂态稳定约束最优潮流问题转化以发电机有功和无功功率增量为独立变量的降阶二次规划最优潮流问题;求解这个二次规划模型得到发电机有功和无功功率增量。通过这种交替求解,最终能寻找到满足暂态稳定约束的最优潮流解。以此为基础,提出了不受故障类型和模式影响的多故障处理方法。新英格兰10机39节点和UK 20机100节点系统的计算结果表明,所提方法在计算精度和速度方面具有一定优势。     

基于轨迹灵敏度的暂态稳定约束最优潮流计算

为将暂态稳定约束最优潮流问题转化为最优潮流和暂态稳定两个子问题,根据暂态稳定计算结果求出发电机转角及转速相对于机械输入功率的轨迹灵敏度。基于轨迹灵敏度,计算出在最领先发电机和最落后发电机之间转移的有功功率,据此修改其在最优潮流模型中的有功功率上下限,从而实现两个子问题的交替求解。并且推导出准确的轨迹灵敏度及初值计算公式,利用上述公式,得更小的转移功率值,从而使功率转移后系统的优化程度更高。同时在惯性中心坐标下采用最大转角判据找出最领先机和最落后机,并以3机9节点和10机39节点系统为例,验证了该方法的可行性。     

含暂态能量裕度约束多故障最优潮流计算

借助暂态能量裕度对发电机有功和无功出力的解析灵敏度，将暂态能量裕度约束直接加入最优潮流模型中，建立含暂态能量裕度约束多故障最优潮流逐次线性规划模型，采用单纯形法求解，取得了较好的效果。此外，还提出了根据大步长单故障最优潮流近似计算获得的暂态能量裕度进行故障扫描方法，并寻找到同一失稳模式下影响系统稳定的关键故障，验证了满足关键故障稳定性要求的最优潮流解可以同时满足同失稳模式下的其它故障的稳定约束。新英格兰10机39节点系统的最优潮流及暂态稳定计算验证了所提方法的有效性。所有优化结果均用一个在电力系统中广泛使用的暂态稳定仿真程序进行了验证。     

Coordinated preventive control of transient stability with multi-contingency in power systems using trajectory sensitivities

In this paper, the challenging multi-contingency transient stability constrained optimal power flow problem is partitioned into two sub-problems, namely optimal power flow (OPF) and transient stability control, solved in turn with conventional well trusted power system analysis tools instead of tackling it directly using a complicated integrated approach. Preventive multi-contingency transient stability control is carried out with generation rescheduling based on trajectory sensitivities using results obtained from a conventional transient stability simulation. A new iterative approach is proposed to optimally redistribute the generation from the critical machines to noncritical machines with the help of conventional OPF. Results on the New England 10-machine 39-bus systems demonstrate that the proposed method is capable of handling multiple contingencies and complex power system models effectively with solution quantity and time comparable with conventional integrated approaches.     

一种计及暂态稳定约束最优潮流的快速方法

给出了一种求解暂态稳定约束下最优潮流(OTS)的快速方法。在该方法中,首先将势能边界面法与最小二乘法相结合,建立系统暂态稳定裕度与系统运行参数变化之间非线性关系的函数表达式;然后基于该函数表达式形成暂态稳定约束条件引入到常规最优潮流(OPF)模型中,从而形成OTS问题的数学模型。该文建立的OTS分析方法不仅使得OTS的求解规模与常规OPF相同,而且计算量亦与常规OPF基本一样。对新英格兰10机39节点典型系统的算例仿真表明了该OTS分析方法的有效性。     

基于生成对抗网络的暂态稳定预防控制

针对电力系统暂态稳定预防控制在线计算的复杂性,提出一种基于生成对抗网络的暂态稳定预防控制方法。通过将暂态稳定预防控制建模为样本空间映射问题,该方法利用数据驱动方法训练生成模型,建立从暂态失稳运行空间到暂态稳定运行空间的映射。模型通过调整电网中发电机的有功出力,提高电网的暂态稳定裕度,使电网运行点满足暂态稳定校核的要求。与传统优化建模方法相比,所提方法通过神经网络的前馈推断求解控制策略,无需迭代求解,极大地提高了求解效率。基于新英格兰39节点系统的测试结果验证了所提方法的可行性和有效性。     

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.     

基于简化预测—校正内点法的拟直流最优潮流

在大规模电力系统最优潮流的在线计算应用中,传统直流最优潮流算法虽然有着很高的计算效率,但是由于其完全忽略了电压和无功功率的影响,计算结果精度偏低。文中通过引入无功功率来修正有功功率平衡方程,提出了基于拟直流模型的最优潮流算法。为进一步提高计算效率,提出了一种简化预测—校正内点算法,该算法通过对最优潮流模型中不等式约束进行简化处理,形成只含上限约束的广义不等式约束,大大简化了程序的编写。通过对IEEE 30,118,300节点系统以及Polish 2 736,3 120节点系统的仿真测试,验证了算法的可行性和有效性。     

Unified Analysis of Single Machine Equivalent and Trajectory Sensitivity to Formulate a Novel Transient Stability-constrained Optimal Power Flow Approach

Abstract—This article proposes a new transient stability constraint that permits quantifying the degree of instability of a power system from the active power dispatched by generators. Based on this constraint, which is derived from both single machine equivalent and trajectory sensitivity methods, a new transient stability-constrained optimal power flow is formulated in the Euclidian space to preventively control the transient stability in realistic power systems. The validity and the effectiveness of the proposed method are numerically demonstrated in the WSCC 3-machine, 9-bus and Mexican 46-machine, 190-bus systems.     

Artificial bee colony algorithm for solving multi-objective optimal power flow problem

This paper presents a new and efficient method for solving optimal power flow (OPF) problem in electric power systems. In the proposed approach, artificial bee colony (ABC) algorithm is employed as the main optimizer for optimal adjustments of the power system control variables of the OPF problem. The control variables involve both continuous and discrete variables. Different objective functions such as convex and non-convex fuel costs, total active power loss, voltage profile improvement, voltage stability enhancement and total emission cost are chosen for this highly constrained nonlinear non-convex optimization problem. The validity and effectiveness of the proposed method is tested with the IEEE 9-bus system, IEEE 30-bus system and IEEE 57-bus system, and the test results are compared with the results found by other heuristic methods reported in the literature recently. The simulation results obtained show that the proposed ABC algorithm provides accurate solutions for any type of the objective functions.     

Optimal power flow solution of two-terminal HVDC systems using genetic algorithm

The usage extensively of high voltage direct current (HVDC) transmission links in recent years makes it necessary further work in this area. Therefore, two-terminal HVDC transmission link is one of most important elements in electrical power systems. HVDC link representation is mostly ignored and simplified for optimal power flow (OPF) studies in power systems. OPF problem of purely alternating current (AC) power systems is defined as minimization of the fuel cost to subjected equality and inequality constraints. Hence, OPF software of purely AC power systems is extended by taking into consideration power transfer control characteristics of HVDC links. In this paper, OPF problem of integrated AC–DC power systems is first solved by genetic algorithm that is a heuristic algorithm based on evolutionary. The proposed method is tested on two test systems which are the modified 5-node test system and the modified WSCC 9-bus test system. In order to show effectiveness and efficiency of the proposed method, the obtained results are compared to that reported in the literature.     

基于线性化最优潮流的电网可用输电能力计算

可用输电能力(ATC)是评价互联电网运行安全稳定裕度的重要测度指标。针对交流最优潮流(OPF)模型计算ATC时在收敛性方面的不足,提出一种计及电压和网损的线性潮流方程,在此基础上构造用于ATC计算的OPF计算模型,并通过先估计网损、再求解优化问题的2步求解策略得到ATC的计算结果。IEEE 39节点系统的算例分析验证了所提方法的正确性和有效性。     

Optimal power flow using differential evolution algorithm

This paper presents an evolutionary-based approach to solve the optimal power flow (OPF) problem. The proposed approach employs differential evolution (DE) algorithm for optimal settings of OPF control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objective functions that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. In addition, non-smooth piecewise quadratic cost function has been considered. The simulation results of the proposed approach are compared to those reported in the literature. The results demonstrate the potential of the proposed approach and show its effectiveness and robustness to solve the OPF problem for the systems considered.     

A two stage model for rotor angle transient stability constrained optimal power flow

Transient stability constrained optimal power flow (TSCOPF) is a nonlinear optimization problem with both algebraic and differential equations. This paper utilizes the Imperialist Competitive Algorithm (ICA) as an evolutionary optimization algorithm and Artificial Neural Network (ANN) to develop a robust and efficient two stages scheme to solve TSCOPF problem. In the first stage an Artificial Neural Network is constructed to predict the rotor-angle transient stability margin, and is then incorporated in the TSC-OPF as the transient stability estimator. To solve the proposed TSC-OPF problem the ICA is used as the optimizer. The performance of the proposed method is verified over the WSCC three-machine, nine-bus system under different loading conditions and fault scenarios.     

Single and Multi-objective Optimal Power Flow Using Grey Wolf Optimizer and Differential Evolution Algorithms

This article applies the grey wolf optimizer and differential evolution (DE) algorithms to solve the optimal power flow (OPF) problem. Both algorithms are used to optimize single objective functions sequentially under the system constraints. Then, the DE algorithm is utilized to solve multi-objective OPF problems. The indicator of the static line stability index is incorporated into the OPF problem. The fuzzy-based Pareto front method is tested to find the best compromise point of multi-objective functions. The proposed algorithms are used to determine the optimal values of the continuous and discrete control variables. These algorithms are applied to the standard IEEE 30-bus and 118-bus systems with different scenarios. The simulation results are investigated and analyzed. The achieved results show the effectiveness of the proposed algorithms in comparison with the other recent heuristic algorithms in the literature.     

An improved teaching–learning-based optimization algorithm using Lévy mutation strategy for non-smooth optimal power flow

One of the major tools for power system operators is optimal power flow (OPF) which is an important tool in both planning and operating stages, designed to optimize a certain objective over power network variables under certain constraints. This article investigates the possibility of using recently emerged evolutionary-based approach as a solution for the OPF problems which is based on a new teaching–learning-based optimization (TLBO) algorithm using Lévy mutation strategy for optimal settings of OPF problem control variables. The performance of this approach is studied and evaluated on the standard IEEE 30-bus and IEEE 57-bus test systems with different objective functions and is compared to methods reported in the literature. At the end, the results which are extracted from implemented simulations confirm Lévy mutation TLBO (LTLBO) as an effective solution for the OPF problem.     

Distributed multi-step Q(λ) learning for Optimal Power Flow of large-scale power grids

This paper presents a novel distributed multi-step Q(λ) learning algorithm (DQ(λ)L) based on multi-agent system for solving large-scale multi-objective OPF problem. It does not require any manipulation to the conventional mathematical Optimal Power Flow (OPF) model. Large-scale power system is first partitioned to subsystems and each subsystem is managed by an agent. Each agent adopts the standard multi-step Q(λ) learning algorithm to pursue its own objectives independently and approaches to the global optimal through cooperation and coordination among agents. The proposed DQ(λ)L has been thoroughly studied and tested on the IEEE 9-bus and 118-bus systems. Case studies demonstrated that DQ(λ)L is a feasible and effective for solving multi-objective OPF problem in large-scale complex power grid.     

Reactive power market development considering power system security

In the new open access environment, in pursuit of profit, power producers tend to operate closer to the security boundaries and consequently, the voltage instability, which is caused by insufficient reactive power support, threats system security and reliability. This paper presents a day-ahead reactive power market based on uniform auction price scheme considering voltage security. First, expected payment function (EPF), identified earlier in the literature to construct a bidding framework for synchronous generators, is modified. Then, the modified EPF is used as the objective function of optimal power flow problem to clear reactive power market. Finally, the OPF, including overload, voltage drop and voltage stability margin in its constraints, is solved by binary coded genetic algorithm. The validity of the proposed reactive power market is studied based on the IEEE 24-bus reliability test system.     

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。