Simple and efficient method for steady-state voltage stability assessment of radial distribution systems

A new static voltage stability index of a radial distribution system is proposed to faithfully evaluate the severity of the loading situation, thereby predicting for voltage instability at definite load value. The proposed index includes different parameters which affect the steady-state voltage stability of distribution systems, therefore it gives accurate results. The maximum value of 1 of that index denotes the point where the system reaches the point of collapse whereas a minimum value of 0 shows the state of no load. The performance of the new index was tested on two radial distribution systems consisting of 33 and 85 buses. Comparison between the results of the new index and those of previous indices showed that the new index yielded reliable results in predicting voltage stability condition of the system. The new index overcomes the problem which faces many previous indices especially as the load approaches the critical point. Analysis of the two-bus equivalents of the test systems under different scenarios is also presented. A new P–Q plane of stability is introduced based on the equation of the proposed index. The active, reactive and apparent power margins are then directly determined from the voltage stability boundary.     

基于广域量测信息的负荷裕度灵敏度计算新方法

提出一种基于广域量测信息的电力系统负荷裕度灵敏度(LMS)分析方法。根据电力系统的广域量测信息,在线计算电力系统中各负荷节点的负荷裕度;依据所得的负荷裕度,提出一种基于广域量测信息的节点负荷裕度对有功、无功及机端电压的灵敏度分析方法;针对所提的LMS方法,进一步提出了改善系统电压稳定性的相关控制策略;最后将所提方法应用到New England 39节点系统和IEEE 118节点系统中,仿真结果验证了所提方法的正确性和有效性。     

Thevenin’s equivalent based P–Q–V voltage stability region visualization and enhancement with FACTS and HVDC

Voltage source converter based Flexible Alternating Current Transmission System (FACTS) devices are considered to be key technology to alleviate voltage instability. This paper examines the enhancements in feasible operating P–Q–V space with FACTS and HVDC. Thevenin’s equivalent at the load bus is applied to draw P–Q–V curve (shows the boundary of the maximum real, reactive power and the minimum voltage magnitude) and area of voltage stability region (AVSR) in a three-dimensional diagram. A visualization framework for voltage stability region in MATLAB environment is implemented to study the impact of FACTS (SVC, STATCOM, and TCSC) and HVDC. The best possible location of shunt controllers is obtained using AVSR and index ‘L’. The line stability indices are calculated and compared to verify the weakest line for installation of series controllers. The inclusive study has been performed on IEEE-14 and IEEE-30 bus systems. The results show the enhancement in area of voltage stability region in all cases with maximum in case of HVDC.     

Energy requirement for distributed energy resources with battery energy storage for voltage support in three-phase distribution lines

Integration of distributed energy resources (DER) into distribution systems is a new concept for improving system capacity and stability, feeder voltage, and supply quality and reliability. This paper has addressed voltage support in distribution systems by energy injection from a battery storage distributed energy system. An operation strategy for an inverter interface battery energy storage DER has been developed for maximum improvement in feeder voltage with minimum energy injection from the DER. A control strategy has been proposed for inverter based battery storage DER to regulate network voltage effectively, through operating the DER to generate real (P) and reactive (Q) power with Q priority. The implementation of the inverter interface DER with battery energy storage will save fuel cost of DER but be of much higher capital cost than using a rotary generator. The proposed technique has been evaluated by simulation on a three-phase distribution system with time varying loads. Test results indicate that DER operating with Q priority offers the best solution for maximum voltage improvement. The results also confirm that DER injecting P and Q at the ratio of maximum voltage sensitivity of line presents better solution for power loss reduction than the solution offered by the DER operating with Q priority.     

Optimal capacitor placement for enhancing voltage stability in distribution systems using analytical algorithm and Fuzzy-Real Coded GA

Two algorithms for optimal capacitor placement, with a view to enhance voltage stability are introduced. In the analytical algorithm the nodes, whose voltage stability index values are lower than a threshold value, are ranked in ascending order as the candidate nodes for compensation. The additional reactive power compensation to be provided at a node is obtained by solving linearized VSI formula. The maximum compensation at each node is limited to the initial reactive power delivered by the respective node prior to compensation for avoiding over-dimensioning of the capacitor banks. However, capacitor placement based on voltage stability index has proven less than satisfactory and not always indicated the appropriate placement.As an alternative a fuzzy expert system is used for extracting suitability of capacitor location from power loss reduction index and improving the voltage profile within voltage constraints. A combination of fuzzy expert system for capacitor placement and real coded GA for capacitor sizing, with a view to enhance voltage stability is proposed for optimal capacitor placement. The result is enhancement of the overall system stability index and potential achievement of maximum net money savings due to power and energy loss reduction vs. expenditure in capacitors.The overall accuracy and reliability of the proposed Fuzzy-Real Coded GA algorithm has been validated and tested on 33-node radial distribution system. Comparison of obtained results with those in recent publications showed that the Fuzzy-Real Coded GA algorithm is capable of producing high-quality solutions with good performance of convergence, and demonstrated viability.     

基于局部电压稳定指标的电压/无功分区调节方法

提出一种局部电压稳定指标和动态经济压差法相结合的电压/无功分区调节新方法.首先利用局部电压稳定指标对系统负荷节点的电压稳定度进行排序;接着针对排完序的负荷节点划分电压/无功调节区,推导并采用局部电压稳定指标灵敏度计算调节区内各负荷节点间电压相互影响程度,根据节点间电压相互影响程度辨识区域内的电压/无功调节关键节点和非关键节点;然后借助动态经济压差法计算电压/无功调节关键节点无功补偿量;最后将所提方法应用于IEEE-14系统中,算例仿真结果验证了文中所提方法的可行性和有效性     

Power system voltage stability and security assessment

The purpose of this investigation is to review the recent research progress in voltage stability and security assessment of power systems. This paper presents the fundamental concepts of voltage stability, gives a short recall of the classical voltage theory and different criteria currently available for predicting voltage collapse problems in power systems, which have been associated with multiple power flow solutions, bifurcation, dynamics of tap changers, stochastic loads, singular values, etc. The various methods for studying voltage collapse are compared. The application of expert system techniques to assist in the decision-making process of the reactive power/voltage control problem of power systems and future research directions towards voltage stability and security assessment will also be proposed in this paper.     

Steady-state analysis of the effect of reactive generation limits in voltage stability

Voltage collapse phenomena are highly affected by reactive power generation limits. Saturation of the reactive power generation limits of a unit may result in a deterioration of the voltage stability. However, in some cases when the power network is operating close to the voltage collapse point, the reactive power generation saturation of a unit can change the system voltages immediately from stable to unstable; thus, a dynamic voltage collapse leading to blackout may follow. This paper presents a steady-state analysis of the immediate instability caused by reactive power generation saturation phenomena. For this purpose, the paper proposes a novel index that evaluates “when” and “why” a reactive power generation saturation will only result in a deterioration of the system voltage stability or, on the contrary, it will make the system voltages immediately unstable.     

改善接入地区电压稳定性的风电场无功控制策略

针对大规模风电场接入电网带来的电压无功问题,提出一种改善接入地区电压稳定性的变速恒频风电场无功控制策略,在系统发生扰动时,以接入点为电压控制点,扰动前的稳态电压为控制目标,动态调节风电场输出无功功率,维持接入点电压水平。实际应用时,该策略利用系统部分雅可比矩阵推导风电场的电压无功灵敏度信息,并根据风电场的无功输出能力计算风电场无功调整量,同时通过设置控制死区和延时,避免了风电机组的频繁调控。仿真算例表明,采用所提策略能够充分发挥变速恒频电机风电场的快速无功调节能力,有效抑制风速扰动、负荷变化等因素引起的电压波动,维持接入地区电网的电压稳定性。     

Optimal coordinated voltage emergency control against voltage collapse

This paper presents a novel model for optimal coordinated voltage emergency control (OCVEC). It takes account of the dynamics of loads and discrete/continuous nature of controls with coordination of dissimilar controls at different geographical locations in order to keep the desired voltage profiles against voltage collapse during an emergency. An integration index of the bus voltage deviation is adopted as the voltage stability performance index. The sensitivities of this performance index with respect to controls are derived using the optimal control theory. Since the sensitivities can be evaluated using the fast quasi-steady-state time domain simulation results, the intractable OCVEC model can be transformed into a tractable problem of quadratic programming. The effectiveness of the proposed model and its solution strategy is validated by case studies on the New England 39-bus and Nordic 32 power systems.     

Capability curve based enhanced reactive power control strategy for stability enhancement and network voltage management

Reactive power has become a vital resource in modern electricity networks due to increased penetration of distributed generation. This paper examines the extended reactive power capability of DFIGs to improve network stability and capability to manage network voltage profile during transient faults and dynamic operating conditions. A coordinated reactive power controller is designed by considering the reactive power capabilities of the rotor-side converter (RSC) and the grid-side converter (GSC) of the DFIG in order to maximise the reactive power support from DFIGs. The study has illustrated that, a significant reactive power contribution can be obtained from partially loaded DFIG wind farms for stability enhancement by using the proposed capability curve based reactive power controller; hence DFIG wind farms can function as vital dynamic reactive power resources for power utilities without commissioning additional dynamic reactive power devices. Several network adaptive droop control schemes are also proposed for network voltage management and their performance has been investigated during variable wind conditions. Furthermore, the influence of reactive power capability on network adaptive droop control strategies has been investigated and it has also been shown that enhanced reactive power capability of DFIGs can substantially improve the voltage control performance.     

基于GMR技术确定电压弱节点的特征根灵敏度指标

一般性的多机系统表达(GMR)技术能够简单快速地形成系统的状态矩阵,从而方便地计算系统的特征根及特征根灵敏度。基于GMR技术,分别给出了两种确定系统电压弱节点(或无功补偿点)的特征根灵敏度指标,即特征根的无功灵敏度指标和导纳灵敏度指标。根据该灵敏度指标可以有效地选择系统的电压薄弱点,进行节点电压控制。并在五节点的系统上进行了计算分析,结果表明在该特征根灵敏度指标所确定的电压弱节点进行无功补偿可以得到最佳的补偿效果。     

计及风电场静态电压稳定性的VMP系统无功电压控制策略研究

随着规模化、集群化风电基地的初步建成,风电作为一种清洁高效的能源得到了快速的发展,但短时间内大规模风电场集中接入电网,给电网的功率平衡带来扰动,造成了电网电压的不稳定。针对风电场并网后的电压控制问题,研究了大规模风电场并网的静态电压稳定机理。并在现有调压手段的基础上,通过适时调整风电机组无功出力,升压站变压器抽头以及调无功补偿装置,进一步提出了基于分层管理的无功功率/电压控制策略,并将该策略嵌入到风电场电压/无功自动管理平台(VMP)。通过新疆某地区风电场现场试验发现,该控制策略能够改善低电压穿越期间无功表现,提高风电场无功电压的稳定性,同时避免了功率振荡的产生。该研究结果可以为风电场无功电压协调控制的理论研究和工程实际提供参考依据。     

Voltage stability enhancement using VSC-OPF including wind farms based on Genetic algorithm

This paper describes the impact of wind generation to enhance the voltage stability of power system in optimal power flow problem. In this work, the Voltage Stability Constrained Optimal Power Flow (VSCOPF) algorithm is used, which combines the economical aspects and the voltage stability control of power system networks. A voltage stability index called L-index has been utilized to identify the most sensitive node prone to voltage collapse. Here Improved Genetic Algorithm (IGA) with mixed form of representation has been used for multi-objective formulation. Real power setting and voltage magnitudes are represented as floating point numbers and transformer tap settings and capacitors as integers. For effecting genetic processing, crossover and mutation operator, which can be directly deal with floating point number and integers, are used. The IGA has been implemented on IEEE 30 bus system to study the impact of wind farm on voltage stability. The obtained simulation shows the effectiveness of Improved Genetic algorithm on voltage stability of the power systems.     

电力系统静态电压稳定性在线监控(一)--一种可在线应用的计及负荷静态特性的电压稳定指标

基于局部量测数据和负荷静态特性．提出了一种可在线应用的节点静态电压稳定指标。首先介绍了ZIP负荷模型,然后用戴维南等值电路简化系统,将线路电流表达式整理成实部和虚部．消去负荷有功后代入ZIP负荷模型中的无功表达式得二次方程式．用根判别式得到以无功表示的电压稳定指标VSIQ;同理得以有功表示的电压稳定指标VSIP;取两者中的较小值作为节点电压稳定指标VSI。比较各节点VSI,最小值对应的节点即为系统最薄弱节点。以IEEE14节点和IEEE30节点系统为例,仿真系统在不同负荷特性下VSI的变化曲线。结果显示：恒定功率分量所占比例越大则节点VSI越小,电压稳定性越差;恒定功率比重相等情况下,恒定电流分量比重越大．节点电压稳定性越差．     

A new intelligent algorithm for online voltage stability assessment and monitoring

This paper presents a new approach for assessing power system voltage stability based on artificial feed forward neural network (FFNN). The approach uses real and reactive power, as well as voltage vectors for generators and load buses to train the neural net (NN). The input properties of the NN are generated from offline training data with various simulated loading conditions using a conventional voltage stability algorithm based on the L-index. The performance of the trained NN is investigated on two systems under various voltage stability assessment conditions. Main advantage is that the proposed approach is fast, robust, accurate and can be used online for predicting the L-indices of all the power system buses simultaneously. The method can also be effectively used to determining local and global stability margin for further improvement measures.     

电力系统实时等值及电压稳定性分析

根据实时测量的负荷节点的电压、电流相量,将整个系统等值为一简单的两节点系统,在此基础上进行电压稳定性分析,提出了一种根据定义的节点电压稳定性指标能快速估计节点电压稳定性的方法,并将其扩展到计及负荷静态特性的情况.文章分析了发电机无功功率极限对电压稳定性的影响.通过中国电力科学研究院EPRI-36节点系统算例,验证了该分析方法是一种简单、快速、有效的方法,且可应用于电力系统电压稳定性的实时监控.     

Voltage stability boundary and margin enhancement with FACTS and HVDC

Voltage stability is a major concern of today’s power system, especially under heavily loaded conditions because of reactive power limits. FACTs devices are very effective solution to prevent voltage instability and voltage collapse due to fast and very flexible control. In this paper, the impacts of SVC, STATCOM, TCSC and HVDC on voltage stability boundary (VSB) in P–Q plane have been studied. The bus impedance matrix and load flow results are used to find the voltage stability boundary. The Z_bus is modified to take into account the effect of FACTS on VSB. The variable susceptance model for SVC and variable series impedance power flow model for TCSC are used in Newton Raphson’s method. The STATCOM is modelled as variable voltage source connected in series with an equivalent impedance of the shunt connected transformer. Similarly HVDC is also modelled as two STATCOMs connected at each end of the line one as rectifier and another as inverter. Some important bus and line stability indices are evaluated to determine the most effective location for SVC/STATCOM and TCSC/HVDC respectively in order to achieve the maximum enhancement of voltage stability margin. The study has been carried out on IEEE-14 bus and IEEE-30 bus test systems using MATLAB programming. A comprehensive study is done to compare the effectiveness of FACTS devices and HVDC on voltage stability margins.     

Optimal placement and sizing of distributed generators based on a novel MPSI index

The Objective: This paper presents a method to identify the optimal location and size of DGs based on the power stability index and particle swarm optimization (PSO) algorithm.Materials and methods: First, a novel maximum power stability index (MPSI) is derived from the well-established theorem of maximum power transfer. The MPSI is utilized as an objective function to determine the optimal DG locations. Next, a PSO-based model with randomized load is developed to optimize DG sizing in view of the system’s real power losses.Results and Conclusion: Lastly, a IEEE 30-bus test system is employed in the simulation. The performance of proposed MPSI index are comparable with other voltage stability indices. The DG optimization model considering voltage stability and loss minimization provides better results compared to that obtained using only loss minimization approach.     

Robustness evaluation of static voltage stability in power systems

Several upper and/or lower bounds to nodal voltage variations are derived in this paper, by exploiting what we call the Hermitian power equations of power systems. Bound inequalities are established for nodal voltage variations in terms of singular values of structural characteristics of power systems, which are running at steady‐state equilibria and subject to nodal active/reactive power injection increments and structural perturbations. The results can be employed for robustness and sensitiveness evaluation of static voltage stability without load flow computations. Examples are provided to illustrate the results. Copyright © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.