A new approach of point estimate method for probabilistic load flow

This paper analyses the power system load flow using new point estimate method considering uncertainties, which may happen in the power system. These uncertainties may arise from different sources, such as load demands or generation unit outages. A novel probabilistic load flow based on new point estimate method has been proposed in this paper. The proposed method surpasses the previous point estimate methods when generalizing the approach to multiple random variables with various probabilistic distributions. Addressing the results of Monte Carlo simulation method as reference, the new point estimate method is applied to IEEE 14-bus test system and the advantages of this new method have been presented. The results reveal that the proposed point estimate method has less computational burden and time comparing than Monte Carlo simulation method while the accuracy remains at a high level.     

概率最优潮流的点估计算法

针对电力市场运营中存在的不确定因素,该文提出一种基于三点估计的概率最优潮流算法。这种算法采用随机变量的高阶矩构造估计点,通过随机变量与目标函数之间的确定性关系对目标函数进行点估计,得到目标函数的统计特征值。文中所提出的算法能方便地将概率问题转化为确定性问题处理,因此可利用电力系统中已有的计算资源,提高计算效率。IEEE-30和118节点系统算例表明,和蒙特卡罗仿真及两点估计法相比,基于三点估计法的概率最优潮流分析计算量小,结果准确,得到的概率信息能更全面地反映电力市场的运行状况。     

A two-point estimate method for uncertainty modeling in multi-objective optimal reactive power dispatch problem

Due to nonlinear and discrete variables and constraints, optimal reactive power dispatch (ORPD) is a complex optimization problem in power systems. In this paper, the purpose is to solve multi objective ORPD (MO-ORPD) problem considering bus voltage limits, the limits of branches power flow, generators voltages, transformers tap changers and the amount of compensation on weak buses. The objectives of this paper are real power losses and voltage deviations from their corresponding nominal values, which are conflicting objectives. Because of the stochastic behavior of loads, the MO-ORPD problem requires a probabilistic approach. Hence, in this paper, a two-point estimate method (TPEM) is proposed to model the load uncertainty in MO-ORPD problem. Moreover, the proposed method is compared with some other methods such as deterministic approaches and Monte Carlo simulations (MCS). The obtained results approve the efficiency of the proposed methodology. The proposed models are implemented and solved using GAMS optimization package and verified using IEEE 14-bus and IEEE 30-bus standard test systems.     

Correlated probabilistic load flow using a point estimate method with Nataf transformation

Wind speed as well as the power output of wind turbine generators (WTGs) have high correlations and may not be normally distributed. In this paper, the method of Zhao’s point estimate method (PEM) combined with Nataf transformation was applied into correlated probabilistic load flow (PLF) calculation. This method can deal with correlated input random variables (RVs) with normal or non-normal probability distributions. Instead of joint probability density functions (PDFs) of multivariate RVs, this method only requires data of the marginal distribution function of each input RV and their correlation coefficients. The effectiveness of the proposed method is demonstrated by the numerical tests on IEEE 14-bus and the IEEE 118-bus systems. Besides, relative average errors compared with correlated Monte Carlo Simulation (CMCS) are analyzed.     

Maximum loadability of power systems using hybrid particle swarm optimization

The problem of voltage stability is one of the main concerns in the operation of power systems. There are different approaches to estimate the voltage stability of the system. One of these approaches is to find the margin from the current operating point to the maximum loading point of the system. Finding this maximum loading point can be formulated as an optimization problem. This paper utilizes the newly developed evolutionary particle swarm optimization in solving this optimization problem. Details of the implementation of the proposed method to two test systems (Ward-Hale 6-bus) and (IEEE 14-bus) are presented. The results are compared to those obtained by the widely used continuation power flow technique. Good agreement has been obtained proving the validity and applicability of the proposed method.     

Optimal power flow with emission and non-smooth cost functions using backtracking search optimization algorithm

Economic operation of electric energy generating systems is one of the prevailing problems in energy systems. In this paper, a new method called the Backtracking Search Optimization Algorithm (BSA) is proposed for solving the optimal power flow problem. This method is tested for 16 different cases on the IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus test systems. In addition to the traditional generating fuel cost, multi-fuels options, valve-point effect and other complexities have been considered. Furthermore, different objectives such as voltage profile improvement, voltage stability enhancement and emission reduction are considered. The obtained results are compared with those obtained using some well-known optimization algorithms. This comparison highlights the effectiveness of the BSA method for solving different OPF problems with complicated and non-smooth objective functions.     

Probabilistic Load Flow Evaluation With Hybrid Latin Hypercube Sampling and Cholesky Decomposition

Monte Carlo simulation method combined with simple random sampling (SRS) suffers from long computation time and heavy computer storage requirement when used in probabilistic load flow (PLF) evaluation and other power system probabilistic analyses. This paper proposes the use of an efficient sampling method, Latin hypercube sampling (LHS) combined with Cholesky decomposition method (LHS-CD), into Monte Carlo simulation for solving the PLF problems. The LHS-CD sampling method is investigated using IEEE 14-bus and 118-bus systems. The method is compared with SRS and LHS only with random permutation (LHS-RP). LHS-CD is found to be robust and flexible and has the potential to be applied in many power system probabilistic problems.     

考虑光伏出力相关性的配电网概率潮流

分布式光伏发电出力随机性强,且同一区域内的光伏出力相关性显著。考虑光伏接入的配电网概率潮流研究,关键在于相关非正态的光伏输入随机变量的处理。采用Nataf变换进行相关非正态输入随机变量的抽样,并与点估计方法相结合,提出了考虑光伏出力相关性的配电网概率潮流计算方法。与传统处理相关问题的正交变换相比,Nataf变换能够反映相关系数在不同变量空间中的变化,因此,在处理相关非正态随机变量方面,Nataf变换比正交变换法更为精确。通过对含有分布式光伏发电的IEEE 33节点算例系统的计算,验证了Nataf变换的优越性。进一步,分析了不同光照强度相关系数、负荷功率波动大小以及估计点个数对概率潮流计算结果精度的灵敏度。     

Ant Colony System-Based Algorithm for Constrained Load Flow Problem

This paper presents the ant colony system (ACS) method for network-constrained optimization problems. The developed ACS algorithm formulates the constrained load flow (CLF) problem as a combinatorial optimization problem. It is a distributed algorithm composed of a set of cooperating artificial agents, called ants, that cooperate among them to find an optimum solution of the CLF problem. A pheromone matrix that plays the role of global memory provides the cooperation between ants. The study consists of mapping the solution space, expressed by an objective function of the CLF on the space of control variables [ant system (AS)-graph], that ants walk. The ACS algorithm is applied to the IEEE 14-bus system and the IEEE 136-bus system. The results are compared with those given by the probabilistic CLF and the reinforcement learning (RL) methods, demonstrating the superiority and flexibility of the ACS algorithm. Moreover, the ACS algorithm is applied to the reactive power control problem for the IEEE 14-bus system in order to minimize real power losses subject to operating constraints over the whole planning period.     

基于改进多点估计与最大熵的概率谐波潮流算法

随着可再生能源发电的大规模接入,电力系统中的谐波呈现出更加明显的随机性、波动性等不确定性特征。为研究电力系统的不确定性谐波水平,提出了一种基于改进多点估计与最大熵分布的概率谐波潮流算法。首先,基于离散近似理论,确定独立标准正态分布随机变量的多重采样点和权重;然后,根据随机变量空间变换,获得功率、谐波电流等任意分布随机变量的权重与采样点,并据此计算谐波电压等输出随机变量的统计特征,进而基于最大熵分布求取输出变量的概率分布。相比传统点估计结合级数展开算法,所提算法通过改进的多点估计,提升了计算效率与准确度;通过引入最大熵分布,保证了概率密度函数拟合效果。利用改进的IEEE 33节点系统验证了不同分析场景下所提方法的性能以及相比传统算法的优势,并依据该方法分析了谐波潮流计算中输入随机变量相关性对系统谐波水平的影响。     

Differential search algorithm for solving multi-objective optimal power flow problem

In this paper, a simple and efficient nature inspired search method based on differential search algorithm (DSA) has been presented and used for optimal power flow (OPF) problem in power systems. By using the proposed DSA method, the power system parameters such as real power generations, bus voltages, load tap changer ratios and shunt capacitance values are optimized for the certain objective functions. Different types of single-objective and multi-objective functions on IEEE 9-bus, IEEE 30-bus and IEEE 57-bus power systems are used to test and verify the efficiency of the proposed DSA method. By comparing with several optimization methods, the results obtained by using the proposed DSA method are presented in detail. The results achieved in this work illustrate that the DSA method can successfully be used to solve the non-linear and non-convex problems related to power systems.     

基于阿基米德Copula和拉丁超立方采样的概率最优潮流计算

提出一种考虑随机变量相关性的概率最优潮流算法。选用广义lambda分布拟合最优潮流模型中的随机变量,建立逆累积分布函数;基于Clayton、Gumbel、Frank、Joe生成元,构筑4种部分嵌套式阿基米德Copula模型对随机变量的相关性结构建模;选取Kendall秩相关系数描述随机变量的相关性,采用相关系数匹配法求取Copula模型的参数;基于生成元的拉普拉斯逆变换,将阿基米德Copula与拉丁超立方采样相结合,生成相关的随机样本用于概率最优潮流计算。对某地区10个风电场风速样本的建模和分析,验证了广义lambda分布和部分嵌套式阿基米德Copula模型的有效性。基于IEEE 118节点系统对2种拉丁超立方采样法进行了对比。     

含大型风电场的电力系统多时段动态优化潮流

大型风电场的并网对电力系统的优化运行提出了新的挑战。该文对含风电场的电力系统优化潮流问题进行了研究，建立了多时段动态优化潮流模型，为了考虑风速随机变化的特点，提出了分时段策略，将风机在每个时段输出功率的期望值用于优化潮流的计算。文中对现有含风电场的潮流计算方法进行了分析，推导了异步风力发电机的无功－电压特性方程，在此基础上提出了含风电场的潮流计算新方法，并将其应用于提出的动态优化潮流模型中。算例表明该方法是有效的，具有一定的实用性。     

Probabilistic power flow with non-conforming electric loads

A comprehensive model for probabilistic power flow is proposed for the purpose of estimating the statistics of bus voltage magnitudes and circuit currents, given the statistics of the loads. The proposed method is based on the quadratized power flow model and a non-conforming electric load model. The statistics of the electric load are accurately represented with the statistics of a few independent random variables and the statistics of bus voltage magnitudes and circuit current flows are computed from the linearized model of bus voltage and circuit current flow with respect to these independent load random variables. The method is validated via Monte Carlo simulations in which the problem is fully solved for each random sample, thus incorporating non-linearities resulting from the AC power flow equations. Both the linearization solution and the Monte Carlo approach are based on the Single Phase Quadratic Power Flow (SPQPF) model of the power system. The proposed method has been implemented and applied to the IEEE 24-bus Reliability Test System (RTS). The results are presented in the paper.     

Post-Outage Reactive Power Flow Calculations by Genetic Algorithms: Constrained Optimization Approach

This paper presents genetic algorithm-based post-outage voltage and reactive power calculations for transmission line and transformer outages. Deficiencies of the traditional sensitivity-based (linear) methods are overcome by formulation of a line outage as nonlinear constrained optimization problem for a bounded network. The proposed optimization problem is later solved for bounded network variables by genetic algorithms. The accuracy of the method is tested on IEEE 14-bus and IEEE 57-bus test systems. Simulation results are compared both with the results of a full power flow study and with the results of the papers presented in the literature. The results have shown that the proposed method improves the accuracy of post-outage voltage and reactive power values with less computational effort.     

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.     

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.     

Nataf变换三点估计分布式发电网络的概率潮流分析

为提高三相不平衡发电系统概率潮流分析算法效率,在考虑发电机负载需求和注入功率不确定性基础上,提出一种使用概率分析和径向功率流的分析方法。首先,基于Nataf变换对三点估计算法进行改进,从而使算法能够处理不完整的多变量信息,并利用随机变量相关性提高输出变量估计的准确度。其次,对分布式发电网络模型进行研究,并结合Nataf变换三点估计算法实现了潮流分析;最后,通过在改进IEEE 57总线测试系统上,与蒙特卡洛模拟法进行对比验证,表明所提算法在51总线处的电压幅值累计分布函数,以及输出随机变量准确度指标上均要优于三点估计算法,说明了所提算法的有效性。     

基于拟蒙特卡洛的半不变量法概率潮流计算

随着风电并网容量的增加,概率潮流计算方法在计及风电出力不确定性的同时,还需考虑邻近风电场由于风速相关性导致的风电出力相关性问题。针对风电出力波动范围较大且存在相关性的特点,提出一种可考虑输入变量相关性的基于拟蒙特卡洛的半不变量法概率潮流计算方法。该方法利用基于Nataf变换的拟蒙特卡洛法产生具有相关性的风电出力样本,在各样本点处进行半不变量法概率潮流计算,基于各风电出力样本下的状态变量正态分布特性,依全概率公式整合所得正态分布得到最终的概率潮流结果。基于IEEE 30节点系统的算例分析表明,所提方法在较小采样规模下具有很高的计算精度,能够较精确地得到系统状态变量的概率分布。     

适用于超大规模电网的在线概率潮流算法

针对半不变量概率潮流算法受电网规模影响较大的特点,对传统概率潮流算法进行了优化改进。在随机变量较少的情况下,通过求取部分灵敏度矩阵的方法减少计算量。随机变量较多时,采用网络等值与分解的方法减小待计算电网规模,有效提升了半不变量概率潮流算法的计算速度。通过标准节点系统与多个大型电网模型的仿真分析验证了所提算法的准确性与实用性。