An Improved Harmonic Load Flow Formulation

Abstract

The paper contributes an improved harmonic load flow formulation with fewer convergence problems but the same accurate results as traditional formulations. The proposed formulation approaches the harmonic load flow problem as a single nonlinear equation system where the harmonic bus voltage influence on nonlinear load behavior is considered and harmonic bus voltages at linear buses are not included as unknowns. This formulation allows any sort of nonlinear load to be considered and uses the Newton-Raphson method with true Jacobian matrix to reduce the inherent increase in the number of iterations caused by the presence of highly distorted bus voltages. The numerical results obtained when solving a three-bus network operating under highly distorted bus voltages using traditional harmonic load flow formulations and the improved formulation are comparatively discussed.     

Influence of phasor adjustment of harmonic sources on the allowable penetration level of distributed generation

Harmonic distortion caused by increasing size of inverter-based distributed generation (DG) can give rise to power quality problems in distribution power networks. Therefore, it is very important to determine allowable DG penetration level by considering the harmonic related problems. In this study, an optimization methodology is proposed for maximizing the penetration level of DG while minimizing harmonic distortions considering different load profiles. The methodology is based on updating the voltage magnitude and angle at point of common coupling depending on the size of DG to be utilized in the harmonic power flow modeling. The harmonic parameters are determined by using decoupled harmonic power flow method, in which the harmonic source modeling with harmonic current spectrum angle adjustment is embedded, while the nonlinear loads and inverter-based DGs are connected to the distribution power network. The allowable penetration level of DGs is determined based on power quality constraints including total harmonic voltage distortion, individual harmonic voltage distortion, and RMS bus voltage limits in the optimization framework. Fuzzy-c means clustering method is also applied to decrease the computational effort of the optimization process in the long-term load profile. The effectiveness of the proposed method is illustrated on the IEEE 33-bus radial distribution network for different scenarios.     

计及谐波功率修正的独立微电网三相潮流计算

以整流装置带负载为代表的非线性负荷是引起微电网谐波的主要因素之一,而微电网中的非线性负荷比例越来越高,在潮流计算过程中必须考虑谐波潮流与基波潮流的相互影响。提出一种计及谐波功率修正的独立微电网潮流计算方法,该方法立足于独立微电网的运行控制特点和三相非正弦条件下的电流物理分量功率理论,将微电网系统模型及整流装置谐波源耦合矩阵建模作为分析基础;通过对分布式电源节点以及整流装置接口的处理,先求解交流基波的三相潮流,再计算各节点三相谐波电压和注入谐波电流,并以谐波功率对基波功率的修正偏差作为潮流计算的收敛条件。算例分析表明,采用上述独立微电网潮流计算及功率修正方法得出的潮流结果与时域仿真结果之间具有较好的对应关系,验证了所提方法的有效性。     

An enhanced RCGA for a rapid and reliable load flow solution of electrical power systems

The paper presents a reliable and fast load flow solution by using a real-coded genetic algorithm (RCGA), bus reduction technique and sparsity technique. The proposed load flow solution firstly used reduction technique to eliminate the load buses. Then, the power flow problem is solved for the generator buses only using real-coded GA to calculate the phase angles. Thus, the load flow problem becomes a single objective function, where the voltage magnitudes are specified resulted in reduced computation time for the solution. Once the phase angle has been calculated, the system is restored by calculating the voltages of the load buses in terms of the calculated voltages of the generator buses. A sparsity technique is used to reduce the computation time further as well as the storage requirements. The proposed load flow solution also can efficiently solve the load flow problems for ill-conditioned power systems whereas the conventional RCGA alone fails to solve these systems. The proposed method was demonstrated on 14-bus IEEE, 30-bus IEEE and 300-bus IEEE, and a practical system 362-busbar Iraqi National Grid. The proposed solution has reliable convergence, a highly accurate solution and much less computing time for on-line applications. The method can conveniently be applied for on-line analysis and planning studies of large power systems.     

A fast and efficient load flow technique for unbalanced distribution system

This paper presents a fast and efficient load flow technique for unbalanced distribution system. The proposed load flow technique is derived by promulgating the concept of conventional backward forward sweep (BFS) technique of power flow study for distribution system. The proposed technique employs a novel load-impedance matrix (LIM) to calculate the bus voltages in a single step unlike the conventional BFS approach which involves two separate steps (backward sweep and forward sweep) to perform the same and this improvement is claimed as the novelty of this work. This distinctive feature makes the proposed algorithm faster in operation. Nodal voltages, at any iteration, may be calculated, directly, from the values obtained in the previous iteration by utilizing LIM. A simple concept of set theory is adopted here to construct the LIM. Special treatments are also included in this method to analyze weakly meshed systems. The proposed technique is flexible enough to accommodate any sort of changes in the existing network topology through LIM. It is tested on different three-phase balanced and unbalanced radial distribution systems as well as weakly meshed networks for load flow study. A separate case study is also presented to check the validity of the proposed load flow technique for various transformer connections. The obtained results demonstrate the effectiveness of the proposed technique. Furthermore, performance comparison reveals that the proposed algorithm is, computationally, faster and robust than the conventional power flow techniques reported in the recent state-of-the-art literatures.     

Voltage control settings to increase wind power based on probabilistic load flow

In this paper, network constrained setting of voltage control variables based on probabilistic load flow techniques is presented. The method determines constraint violations for a whole planning period together with the probability of each violation and leads to the satisfaction of these constraints with a minimum number of control corrective actions in a desired order. The method is applied to define fixed positions of tap-changers and reactive compensation capacitors for voltage control of a realistic study case network with increased wind power penetration. Results show that the proposed method can be effectively applied within the available control means for the limitation of voltages within desired limits at all load buses for various degrees of wind power penetration.     

Optimal reactive power control of DGs for voltage regulation of MV distribution systems using sensitivity analysis method and PSO algorithm

This paper addresses the problem of reactive power control of distributed generation (DG) units in the medium voltage (MV) distribution systems to maintain the system voltages within the predefined limits. An efficient approach for the load flow calculation is used here which is based on the topological structure of the network. It has been formulated for the radial distribution systems. A direct voltage sensitivity analysis method is developed in this paper which is also based on the topological structure of the network and independent of the network operating points. Thus, the sensitivity matrix is calculated once with the load flow program and it is used in all the system working conditions. The problem of DGs reactive power control is formulated as an optimization problem which uses the sensitivity analysis for linearizing the system around its operating points. The objective of the optimization problem is to return the system voltages inside the permitted range by using the reactive power of DGs in an optimal way. The optimal solutions are obtained by implementing particle swarm optimization (PSO) algorithm. Then, the results are verified by running a load flow considering new values of DGs reactive power. The procedure is repeated as long as a voltage violation is observed. Simulation results reveal that the proposed algorithm is capable of keeping the system voltages within the permitted limits.     

多谐波源系统的非迭代式谐波潮流分析

为研究多谐波源系统的电能质量问题,提出一种快速的非迭代式谐波潮流分析算法。该算法将基频下的谐波源视为恒功率负荷,根据基频结果计算谐波源的运行参数及模型。联立求解系统的谐波导纳方程和谐波源模型方程,无需迭代即可得到系统中所有节点的各次谐波电压。该算法可考虑谐波源的各次谐波电压和谐波电流之间的相互耦合,也可考虑系统中多个谐波源之间的相互抵消作用。算法以AC/DC整流装置类谐波源为例阐述,可拓展应用于含其他非线性电力电子装置类谐波源的系统中。以存在多个分散式谐波源的实际系统为例,Matlab编程实现算法并与PSCAD时域仿真对比,结果表明:算法准确度高、计算速度快。     

Harmonic modelling of PV systems for probabilistic harmonic load flow studies

Probabilistic harmonic load flow (HLF) is currently enjoying renewed popularity. This is not surprising since in the near future, thousands of photovoltaic (PV) systems will be integrated into distribution systems. However, as yet, there is no model capable of explaining PV harmonic current behaviour in probabilistic HLF studies. To fill this gap, the harmonic modelling of PV systems proposed in this paper has three key points. First, it provides an effective model of the relationship between PV harmonic current emission and background harmonic voltages. Second, it statistically characterises PV harmonic currents (relative magnitude and phase angle) at different fundamental‐frequency current output intervals using historical time‐series data. In this statistical characterisation, the first fifth moments of each PV harmonic current are used to accurately approximate the raw probability density function (PDF) by means of the Legendre series. Finally, the third key point of this harmonic modelling is a method capable of determining the distribution functions of PV harmonic currents (absolute magnitude and phase angle), based on the statistical characterisation and a fundamental‐frequency probabilistic PV model. The numerical results obtained confirm the effectiveness of this PV model. Copyright © 2014 John Wiley & Sons, Ltd.     

电网中非线性负荷谐波功率方向的确定

电力系统中有谐波存在时,应该了解谐波功率的方向,并按谐波功率的方向确定谐波源的位置。作者从最简单的非线性电路出发,通过比较常规电路的计算结果和频域分析结果,总结了非线性负荷形成谐波功率的特点,提出了确定谐波功率方向的方法,论述了非线性用户的电能计量问题,为进一步完善电能计量工作提供了依据。     

基于不同次数谐波下品质因数一致性的孤岛检测方法

针对基于谐波电压或阻抗的孤岛检测方法所存在的盲区较大且阈值难以设定的问题,提出一种基于不同次数谐波下品质因数一致性的孤岛检测判据,并结合q轴谐波电流扰动法作为新型孤岛检测方案。推导了微网发生孤岛后负载品质因数的计算公式。由于负载固有的品质因数与谐波次数无关,发生孤岛后不同次数谐波下的品质因数是一致的,而并网时计算的品质因数没有确定的物理含义,不同次数谐波下其值差异大,利用这一特性判别是否发生孤岛。理论分析了所提方法的可行检测区,结果表明其能实现孤岛的小盲区快速检测,且满足计算要求所需要的谐波扰动很小,对电能质量影响小。相比于谐波电压或阻抗检测法,所提方法对主网参数的适应性更强,阈值设定简单。在多种负载和线路参数场景下进行了仿真分析,结果验证了所提方法的正确性和有效性。     

监测点优化配置下考虑谐波约束的多节点分布式光伏最大配置方案研究

随着中国分布式光伏渗透率不断提高,其对配电网谐波的影响也越发严重。通过研究系统中谐波监测点的最佳配置,并以对谐波监测点处谐波影响最小为目标提出了多节点的分布式光伏配置方法,从而降低分布式光伏对配电网谐波影响。首先根据单节点接入分布式光伏发电(Distributed Photovoltaic Generation,DG)达到极限时全网其余各节点是否可观测到该节点产生的谐波,定义了谐波监测范围,进而利用敏感因子法以监测点数量少和监测范围全覆盖为目标,计算了谐波监测点的最佳配置方案。此后,以监测点谐波含量最少及系统光伏最大消纳为目标,使用粒子群算法计算得到了分布式光伏配置方案。通过上海某配电系统算例,验证了方案的有效性。     

树状网络潮流计算的新算法

介绍了一种适合树状网络潮流计算的新算法-交替迭代算法。该算法以电压和线路损耗功率交替迭代进行。文中对算法进行了收敛性分析,并证明：当树状网络存在稳态运行解时,给出的交替迭代算法是收敛的。以IEEE 33节点、RBTS68节点等系统为例,证实了该算法具有计算速度快、迭代次数少、收敛精度高、易于编程的特点。     

含双馈风机的配电网模糊谐波潮流计算

针对配电网中存在着大量的不确定因素对接有双馈风机的配电网节点进行基波和谐波模糊建模.并考虑节点内部存在的关系:在节点基波建模中,考虑并联补偿器和功率因数的关系可以提高理论收敛程度;在节点谐波建模中,考虑风机负荷、无源负荷和非线性负荷的关系可以极大简化模糊谐波建模的复杂程度.最后把双馈风机接入典型33节点辐射型配电网进行...     

电力系统潮流计算的符号分析方法研究

提出了一种运用符号分析的方法进行电力系统潮流计算的新思路,根据电网络的拓扑求解方法和图论理论,将复杂网络的拓扑分析方法引入电力系统,实现潮流计算的符号化.该算法直接将电力网络元件的参数进行符号表达,通过求解网络的k-树有效地生成电力网络节点电压方程中各节点电压的符号表达式,进而获得潮流解;并通过采用广义树法系统地生成复杂网络的树组,解决生成网络全部k-树时计算量和存储量随网络顶点数目的增加而过快增长的难点,有效地提高了算法的计算速度.与传统的潮流计算方法相比,该方法不存在计算的收敛性问题及其多解现象,算例分析验证了该算法的正确性.     

Fast approximate power-flow solution for contingency evaluation

A fast approximate power-flow solution technique suitable for contingency analysis is described. In the method discussed, voltages are represented by rectangular coordinates and only voltage-controlled busbars are retained in the iterative process which estimates the correction vector to be added to the assumed value of the busbar-voltage vector. Power mismatches are obtained only at two stages instead of computing the same at every iteration. The original network is restored on obtaining convergence, and the voltages of the load busbars are calculated. The principle of current injection in the opposite direction to simulate a line outage without altering the network is applied to the reduced network to calculate the power mismatches even when the outage is between two load busbars or between a load busbar and a generator busbar. This feature permits the same base-case Jacobian and its inverse to be used, eliminating the need for the repetitive computation of the Jacobian and its inverse for different contingency studies. Hence the method is very fast, is acceptably accurate and offers an efficient alternative to existing methods of contingency analysis.     

解耦-补偿牛顿型三相潮流

首次将三相潮流计算中三相约束条件转化为单相正序约束条件，不仅简化了分析，而且 为直接采用单相潮流算法铺平了道路。将性能良好的牛顿-拉夫逊法、P-Q分解法与电力 网元件的三相解耦或三相解耦-补偿模型结合，形成了性能优良的解耦-补偿牛顿型三相潮 流算法——即解耦-补偿牛顿-拉夫逊法和解耦-补偿P-Q分解法。提出的三相潮流算法 不仅适合于不对称三相电力系统正常运行方式的分析，而且也适合于不对称三相电力系统非 正常运行方式，如稳态单相断线或开路的分析。算例表明，两种方法具有良好的收敛特性和 快速的计算速度，且非常适于并行计算。     

三相桥式整流电路中谐波电流的计算新方法

提出了一种实用的新方法来计算三相桥式整流器所产生的谐波电流。本方法考虑了交流侧电抗及电网中存在的谐波电压,导出了交直流两侧谐波电流的计算公式。计算与实测结果表明,本方法准确实用。     

考虑光伏发电及负荷概率性的储能容量优化

高渗透率光伏系统的接入增加了负荷的波动性,对配电网的稳定运行带来一定影响,需要配置合理的储能装置以保障配电网的稳定运行。在考虑光伏发电及负荷概率性的基础上,提出了一种储能容量优化的新方法：将负荷与机组发电的差作为对储能功率的需求,先分别求得一天中不同采样点负荷与机组发电的概率性序列,再利用卷差运算求得储能功率的概率性序列,最后根据统计学原理确定储能的最大充放电功率及最优容量。所提方法为光伏系统接入配电网的储能容量规划工作提供了新的思路。     

Three-phase harmonic distortion state estimation algorithm based on evolutionary strategies

This paper presents a new methodology to estimate unbalanced harmonic distortions in a power system, based on measurements of a limited number of given sites. The algorithm utilizes evolutionary strategies (ES), a development branch of evolutionary algorithms. The problem solving algorithm herein proposed makes use of data from various power quality meters, which can either be synchronized by high technology GPS devices or by using information from a fundamental frequency load flow, what makes the overall power quality monitoring system much less costly. The ES based harmonic estimation model is applied to a 14 bus network to compare its performance to a conventional Monte Carlo approach. It is also applied to a 50 bus subtransmission network in order to compare the three-phase and single-phase approaches as well as the robustness of the proposed method.