Voltage Collapse Point Research Articles

Improving voltage collapse point under transmission line outage by optimal placement and sizing of SVC using genetic algorithm

In many power systems, voltage instability can increase the risk of voltage collapse and, as a result, turn the power system toward a blackout. Therefore, increasing the voltage collapse point is required. A transmission line outage is an emergency condition in power systems that can lead to voltage instability and voltage collapse. Thus, it is expected to employ shunt-connected flexible AC transmission systems (FACTS) such as the static var compensator (SVC) to increase the voltage collapse point when lines outage. This paper presents the genetic algorithm (GA) application to optimal placement and sizing of an SVC for increasing voltage collapse points following lines outage. The continuation power flow (CPF) technique has been used to determine the maximum loading point (MLP) corresponding to the point of voltage collapse. Also, to reduce the number of scenarios when line outages occur, a list in ascending order is established based on the line outage priority (LOP). The IEEE 14-bus test system is chosen to carry out simulations, and an SVC will be installed in the system based on the GA results. Simulation results confirm the effectiveness of an SVC for improving voltage stability as well as increasing voltage profile.

Improvement of voltage stability and loadability of power system employing the placement of unified power flow controller using artificial neural network

<span lang="EN-US">This paper proposes a voltage stability and loadability improvement model of power systems by incorporating the optimal placement of flexible alternating current transmission systems (FACTS) using an artificial neural network (ANN) called OPFANN. The key aspect of this model is to identify the weakest lines which having the most probability of voltage collapse utilized for placing FACTS devices. As installing a new power system network with rapidly increasing power demand cannot be possible, the operator usually operates the power system close to the stability limit. In this regard, continuous monitoring and improvement of system voltage stability and loadability of the existing system are vital issues for energy management systems nowadays. However, the proposed OPFANN introduces a more straightforward and faster scheme for voltage stability monitoring systems using ANN. Intelligent and reliable data samples have been designed to train the ANN based on two-line voltage stability indices (LVSI) techniques. Compared with other works, OPFANN effectively improves voltage stability and loadability at the load point by installing the unified power flow controller (UPFC) FACTS devices to the weakest lines. OPFANN can provide information on voltage collapse points using ANN and reduce the further computational cost of LVSI. Finally, OPFANN ensures faster and more secure operation of the power system.</span>

Contingency ranking method for voltage security assessment based on critical eigenvalue trajectory

In voltage security assessment it is of great importance to determine the most critical contingencies of the system. However, most of the contingency ranking methods fail to capture the nonlinear behavior of the system, which is more pronounced in the proximity of the system to the voltage collapse point. This paper proposes a contingency ranking method that considers the trajectory of the critical eigenvalue of the jacobian matrix of the power flow equations when the load grows as an indicator of the closeness of the power system to the voltage collapse point. The proposed critical eigenvalue trajectory (CET)-based method utilizes a linear extrapolation of the eigenvalue trajectory. Therefore, for each analyzed contingency, two equilibrium points are obtained and associated with their respective critical eigenvalue, which leads to a linear extrapolation of each critical eigenvalue trajectory. The contingency ranking method is applied on the IEEE 57-bus test system. The results analysis show a good accuracy of the method, specially for the most critical cases. Besides the performance analysis, CET-based method presents good results when compared to the results of two other ranking methods, implemented according to the literature and tested on the same test system.

Reactive Power Compensation Strategy of the Electric Vehicle Connected to the Distribution Network in the Limit State Considering Voltage Constraint

To solve the voltage stability problem of electric vehicles connected to the distribution network in the limit state, a reactive power compensation strategy based on the holomorphic embedding method and electrical distance is proposed. Firstly, the load model of the electric vehicle charging station is constructed, and the limit of the charging power of the electric vehicle connected to a certain bus is obtained. Then, the power flow embedding equation of the power system is constructed by the holomorphic embedding method, and the analytical expression of the voltage rational function is introduced based on the Padé approximation algorithm. The voltage collapse point is solved by the distribution of zeros and poles of the rational function. Then, a method of reactive power and voltage control partition based on electrical distance is proposed. According to the principle of weak regional coupling and strong interval coupling, the power system is divided into several regions by spectral clustering and a k-means clustering algorithm. The order of the voltage stability margin value s is obtained by connecting the limit charging power to each bus of the power system. In this paper, the reactive power compensation strategy proposes to add reactive power compensation devices to the buses with the weakest voltage stability margin in different zones. Finally, compared with other reactive power compensation strategies 1 and 2, the reactive power compensation strategy provided in this paper is increased by 1.626121813 and 1.160494345 times, respectively. The superiority of this method is verified by simulation.

A New Approach for Long-Term Stability Estimation Based on Voltage Profile Assessment for a Power Grid

Load flow solutions refer to the steady-state stability of power systems and have a crucial role in the design and planning of slow-changing elements; e.g., in online tab changing actions, automatic generation control, over-excitation limiters and the power recovery characteristics of a load. Therefore, the purpose of this work was to show the connectivity between load flow analysis and long-term voltage stability using a generator model by introducing a novel voltage stability assessment based on the multi-machine dynamic model along with the load flow study for a power grid. The Euclidean distance (ED) was used to introduce a new voltage stability index based on the voltage phasor profile for real-time monitoring purposes. The effects of reactive power compensation, in addition to load-generation patterns and network topology changes in the system behavior, could be seen clearly on the voltage profiles of the buses. Thus, the increased values for the EDs of the buses’ voltage amplitudes—from 0 to around 1.5 (p.u.)—implied that the system was approaching the voltage collapse point, corresponding to the Jacobian matrix singularity of the load flow equation. Moreover, the weakest load bus with respect to any system change was also identified. Indeed, the criticality of any network interruption was in direct proportion to this voltage stability index. The proposed method was validated using the IEEE 118-bus test system.

Coordinated voltage control for improved power system voltage stability by incorporating the reactive power reserve from wind farms

The absorption and output characteristics of reactive power of the doubly-fed induction generator (DFIG) greatly influence the voltage stability of PCC (Point of Common Coupling) where the wind farms are integrated into the bulk power grid. This study proposes a reactive power compensation strategy for coordinated voltage control (CVC) of PCC with large-scale wind farms to achieve the expected voltage quality of the power grid through a minimum amount of control actions in emergencies. To this end, the mechanism of reactive power and voltage control inside DFIG is first analyzed. Then, the concept of reactive power reserve (RPR) sensitivity concerning control actions is introduced and an index of voltage stability margin is proposed to evaluate and analyze the distance between the current operating point and the voltage collapse point by analyzing the relationship between reactive power reserve and voltage stability margin. In the event of an emergency, critical reactive power reserves are obtained to reduce the dimension and complexity of the control problem. The sensitivity of reactive power reserve and the control are formulated into a convex quadratic programming problem to optimize the control strategies for voltage stability. The proposed technology has been validated on the IEEE 39-bus system.

Effect of Uniformly Distributed Parameter Line Models on the Evaluation of PV Curves and of the Maximum Loading Condition

PV curves are generally obtained by considering lumped models of transmission lines. This approximated model can yield an inaccurate estimation of the maximum loading condition of the system. This letter shows that accuracy can be improved by considering line models with uniformly distributed parameters. Analytical evaluations of the PV curve and of the voltage collapse point of a two-bus system are obtained by applying the Ossanna's theorem. Then the impact of different line models on large-scale systems is evaluated through a continuation power flow analysis of a real-world model of the Sicilian transmission system including the Sicily-Malta 120 km cable connection.

A novel method for online voltage stability assessment based on PMU measurements and Thevenin equivalent

From the power systems security point of view, determining the voltage stability margin is essential for the operation of systems. An inaccurate determination of the maximum loading factor or voltage collapse point in a power system may cause voltage instability and blackout of the system. So, applying a proper method with high accuracy and high speed is vital in analysing voltage stability in power systems. This article presents a novel method based on Thevenin equivalent of power systems to accurately determine load-ability margin using phasor measurement units (PMUs) data. The proposed method is based on the fact that at the voltage collapse point, the characteristic curves of ‘the reactive power at the receiving end’ and ‘the reactive power of the load’ in the weakest bus are tangential to each other. Furthermore, online application of the proposed method requires accurate estimation of the ‘ZIP load model’ and ‘Thevenin equivalent’ of the system. The proposed method is designed to determine the load-ability margin, ZIP load model and Thevenin equivalent of the power system, simultaneously. This characteristic of the method makes it possible to be applied for online voltage stability assessments. To demonstrate the effectiveness of the proposed method, the simulation results for IEEE 14-bus, 39-bus New England and IEEE 300-bus are presented and analysed.

Voltage stability assessment using TCSC and SVC based FACTS controllers

The Most causes of Voltage instability is the sources of reactive power .In order to protect the total system from voltage instability the reactive loads can be reduced or extra reactive power can be added to reach the Voltage collapse point .The Flexible AC transmission devices(FACTS) have made it flexible and possible to prevent Voltage instability by Fast and Flexible control method . Voltage collapse point is predicted with TCSC and SVC devices and is compared with each other. The Voltage stability Indicator is derived to identify the voltage collapse point. it is concluded that voltage stability index provides a simple means to predict vulnerability of a bus in a Multibus system for voltage collapse.

Effect of ambient temperature variations on estimation of proximity of the voltage collapse point

Due to deforestation, greenhouse gases and increasing air conditioner systems, the temperatures are changing drastically and the effects are prominent in summer and winter seasons. These ambient temperature variations are affecting the transmission system parameters and also the voltages at various buses. Changes in the transmission line parameters have non-negligible impact on system performance and present Energy Management applications are not considering these temperature variations in the power system state estimation. In this paper, impact of temperature variations on the power system Voltage Stability assessment is considered. Voltage stability assessment methods make use of the load flow results. Load flow results without considering the temperature variations are inaccurate in the real-time and leading to the erroneous results in the voltage stability assessment. In view of this, studies have been carried out on IEEE 30-bus, 118-bus and 300-bus systems, incorporating the seasonal temperature variations on various types of conductors, and also demonstrated the impact with conventional and ZIP type load models. In this paper, four voltage stability indices NLVSI, L m n , FVSI and VCPI(power) are used for identifying the proximity of voltage collapse point, critical line, critical bus voltage, critical bus angle, total system active power loss, total system reactive power loss etc.

Relaxed decoupled direct calculation of voltage collapse points and its application in static voltage stability region boundary formation

Static voltage stability is critical for the operation of power grids. With the penetration of renewable energies, region-based method become a choice to present the stability of a power grid. Static voltage stability region is hence a useful and intuitive tool to determine the safety margin of a power grid. The formation of static voltage stability region is however time consuming. To overcome such issue, this work proposes a relaxed decoupled direct calculation (RDDC) method to find voltage collapse points (VCPs). The direct calculation of VCPs is a Newton-Raphson type method and faces the sensitivity issue of the initial values. Boundary tracking method provides a framework to utilize the information from neighbor VCPs and hence is integrated with the proposed RDDC method. The results show that the RDDC method is able to calculating VCPs as precise as continuation power flow with less computational time. When RDDC is integrated with boundary tracking, results show that the static voltage stability region boundary can be generated with high precision, and computational performance improvement can be observed for all the test systems from nine buses to ten thousand of buses. This demonstrates the applicability and scalability of the proposed method to power systems with different scales.

Multi-objective economic operation of modern power system considering weather variability using adaptive cuckoo search algorithm

Currently, most of the power systems are being integrated with flexible AC transmission system devices and renewable energy sources for operating with enhanced security margins and balancing the increasing demand cost-effectively. On the other side, the trend of increasing global warming and extremely changing weather conditions is continuing across the world. Under this scenario, it is essential to realize their effect on various power system components and its economic operation. In this paper, the parameters namely resistance of the transmission line/transformer, load and solar photovoltaic generation are modeled considering ambient temperature effect. Later, economic schedule under changing weather conditions is proposed for attaining multi-objectives simultaneously like total operating cost of conventional energy, real power loss, average voltage collapse point indicator index and average voltage deviation index. Also, the dispatchable problems in the transmission system and various practical operating constraints are handled via optimally setting the parameters of optimal unified power flow controller. The optimization problem is solved using adaptive cuckoo search algorithm (ACSA), in which a dynamically increasing switching parameter in a power of three is adopted for adjusting the random walk between local optima and global optima. The superiority of the proposed ACSA in solving the multiobjective, nonlinear complex optimization problem over basic CSA and particle swarm optimization, chicken swarm optimization and flower pollination algorithm is presented by illustrating various case studies on standard IEEE 14, 30 and 118–bus test systems.

Unsupervised feature learning for online voltage stability evaluation and monitoring based on variational autoencoder

With the increase of uncertain elements in power systems and extensive deployment of online monitoring devices, it is necessary to search a more real-time and robust voltage stability assessment method. This study, using PMU monitoring data, explores a novel data-driven approach for long-term voltage stability assessment based on variational autoencoder (VAE). Our method is capable of extracting the most representative features by an unsupervised data mining method in a probabilistic learning way. Different from most of familiar feature extraction methods, it regularizes latent features in an expected stochastic distribution. Furthermore, a statistical indicator by sampling latent features after variance reduction is proposed to assess long-term voltage stability. Our approach is tested in various simulated power systems with different load increment models. Other cases show the accuracy and speed of our approach for estimating voltage collapse point. These testing cases successfully demonstrate the accuracy and effectiveness of our approach.

Voltage collapse point evaluation considering the load dependence in a power system stability problem

<span lang="EN-US">Voltage Stability has emerged in recent decades as one of the most common phenomena, occurrence in Electrical Power Systems. Prior researches focused on the development of algorithm indices to solve the stability problem and in the determination of factors with most influence in voltage collapse to solve the stability problem. This paper evaluates the influence that the load dependence has with the voltage on the phenomenon of the voltage stability and especially on the characteristics the collapse point or instability point. Load modeling used is detailed and comparisons of the results obtained are made with those described in the bibliography and those obtained with commercial software. The results of the load margin are also compared when a constant load or a voltage-dependent load is considered as well as the values obtained at the maximum load point and the point of voltage instability.</span>

An Asymptotic Numerical Continuation Power Flow to Cope with Non-Smooth Issue

Continuation power flow (CPF) calculation is very important for analyzing voltage stability of power system. CPF calculation needs to deal with non-smooth constraints such as the generator buses reactive power limits. It is still a technical challenge to determine the step size while dealing with above non-smooth constraints in CPF calculation. In this paper, an asymptotic numerical method (ANM) based on Fischer‐Burmeister (FB) function, is proposed to calculate CPF. We first used complementarity constraints to cope with non-smooth issues and introduced the FB function to formulate the complementarity constraints. Meanwhile, we introduced new variables for substitution to meet the quadratic function requirements of ANM. Compared with the conventional predictor-corrector method combining with heuristic PV-PQ (PV and PQ are used to describe bus types. PV means that the active power and voltage of the bus are known. PQ means that the active and reactive power of bus are known.) bus type switching, ANM can effectively solve the PV-PQ bus type switching problem in CPF calculation. Furthermore, to assure high efficiency, ANM can rapidly approach the voltage collapse point by self-adaptive step size adjustment and constant Jacobian matrix used for power series expansion. However, conventional CPF needs proper step set in advance and calculates Jacobian matrix for each iteration. Numerical tests on a nine-bus network and a 182-bus network validate that the proposed method is more robust than existing methods.

Propinquity of voltage collapse prediction for power system using indices

Continuous assessment of voltage stability is vivacious in safeguarding the electrical power system (EPS) operation. The final outcome of voltage instability is proximity to voltage collapse. The critical operating conditions of the transmission lines may possibly lead to voltage collapse with certain disturbances in electrical power supply. Quite a lot of Voltage Stability Indices (VSIs) have been technologically advanced in to estimate the proximity to voltage collapse. A few VSIs are computationally efficient, while the rest are said not to accomplish as expected under all circumstances. The study recommends a voltage stability index such as Composite Severity Index (CSI) and New Voltage Stability Index (NVSI) which are vigorous based on its theoretical nitty-gritties. The recommended index has been meritoriously tested on IEEE 30 bus and IEEE 118 bus test system under various operating conditions in order to weigh its efficacy. Also, it is shown that CSI and NVSI index could be used for estimating the distance to Voltage Collapse Point (VCP). The validation is done with Lmn, LQP and FVSI indices. The results designate its possibilities for the assessment of voltage stability.

Improvement of Power System Loading Margin with Reducing Network Investment Cost Using SVC

Under emergency conditions to reduce the harms from environmental deterioration, one of the recently focused developments in the power industry is to make the existing transmission networks sufficiently utilize their capability in power transfer. From the detailed analysis and many studies, voltage instability was found to be the main factor responsible for several blackout events. As an index to indicate the level of static voltage stability of a transmission system, the Loading Margin (LM) or Voltage Stability Margin (VSM), represents the maximum power that can be transferred between generators and loads before voltage collapse point achieved is generally measured in system planning. In this paper, under each contingency with high Risk Index (RI) value, the Modal Analysis (MA) technique is used to determine which buses need Static VAR Compensator (SVC) installation, and with maximum LM and minimum SVC installation cost composed into the multi-objective function. The optimal LM enhancement problem is formulated as a multi-objective optimization problem (MOP) and solved by using the fitness sharing multi-objective particle swarm optimization (MOPSO) algorithm for a Pareto front set. The proposed method may be tested on the IEEE 24-bus reliability test system (RTS) and IEEE 14-bus system.

Online voltage stability and load margin assessment using wide area measurements

A power system is continuously exposed to changes in load and operating conditions. This results in voltage variation which may lead to instability at times. Therefore, it is required to assess the voltage stability continuously for which a stability index is used. This paper uses phasor measurement data from selected buses to estimate the states of the system. Thevenin equivalent of the system is calculated and a voltage stability index obtained using ratio of change in load power to change in voltage magnitude. The index provides how close the system is towards instability, following load variation and/or change in topology. When the proposed index is equal to 1, the system reaches voltage collapse point. For any lower value of the index, the system is in stable region and when it approaches 1, it is vulnerable to collapse. Load margin assessment is performed when the system is voltage stressed and obtained for selected stressed buses using a least square technique. Load margins of buses around the stressed buses are also calculated which is useful in situational awareness of a system. Several case studies are performed on 39 bus New England test system and 233 bus North Eastern Indian grid by varying load and topology of the system. Different types of loads are also considered in the testing. The methods for stability index calculation and load margin assessment are found to be accurate. Comparative performance of the proposed technique with available method is also presented.

Modified affine arithmetic based continuation power flow analysis for voltage stability assessment under uncertainty

Continuation power flow (CPF) analysis has been used in the literature to determine the voltage collapse point from active power versus voltage curves (PV curves) for steady-state voltage stability assessment. Affine arithmetic-based (AA) CPF analysis to determine PV curve bounds under uncertainty in power generation was introduced in the literature to overcome the problem of large computational time with Monte Carlo (MC) simulations, by getting a faster solution with a reasonably good accuracy. However, AA operations lead to more noise terms and hence overestimation of bounds. In the present work, a modified AA (modAA)-based CPF analysis is proposed to determine PV curve bounds by considering uncertainties associated with active and reactive power injections at all buses in the system. The proposed method reduces the overestimation caused by the AA operations and gives more accurate solution bounds. The proposed modAA-based CPF analysis is tested on 5-bus test case, IEEE 57, European 1354 and Polish 2383-bus systems. The simulation results with the proposed method are compared with MC simulations and AA-based CPF analysis to show the efficacy of the proposed method.

An Optimal Thévenin Equivalent Estimation Method and its Application to the Voltage Stability Analysis of a Wind Hub

A simplified voltage stability analysis method is to use a static Thevenin equivalent to represent the electrical connection to a load center. Assuming fixed values of the Thevenin voltage and reactance, a power-voltage ( $PV$ ) curve analysis can be performed to find the voltage collapse point and stability margin. This paper proposes a method to compute the static Thevenin equivalent voltage and reactance of a power system using measured data. The method is validated with simulated PMU data and with 24-hour SCADA data at a wind hub on a medium voltage transmission system in the US western system. For the wind hub, the Thevenin equivalent parameters are used to compute the maximum power transfer capability of the wind hub as constrained by voltage stability. Then the method is extended to online application by using short data windows and forgetting factors.