Method For Voltage Stability Assessment Research Articles

Continuation Load Flow Considering Discontinuous Behaviors of Distribution Grids

The reduction in bus voltage magnitudes as the load demand grows may lead to sudden disconnection of loads and/or distributed generation units, in distribution grids, caused by undervoltage protection schemes. As proposed in this paper, this discontinuous behavior of distribution grids can be modeled as a sudden load variation in traditional static voltage stability assessment methods, such as the continuation power flow (CPFLOW). A discussion on the impacts of these discontinuities on the equilibrium diagram of the system is presented in this paper, as well as a set of numerical simulations showing that the traditional CPFLOW algorithm presents convergence problems caused by the discontinuities under analysis. From this perspective, this paper proposes an algorithm based on novel predictor/corrector and identification schemes, which are capable of successively calculating the discontinuities that exist in the equilibrium loci of the system under analysis, as well as the maximum loadability point and the type of bifurcation. A simplified modeling approach that eliminates the need for a complex (and computationally expensive), detailed description of distribution grids is also elaborated and incorporated into the proposed algorithm. The simulated examples show that the proposed algorithm adequately handles the problem, yelding more accurate results than the traditional CPFLOW algorithm.

A model and data hybrid-driven short-term voltage stability real-time monitoring method

This paper proposes a model and data hybrid-driven short-term voltage stability assessment method. First, a double-generator-one-load (DGOL) simplified model for short-term voltage stability analysis is introduced, and the mechanism of the occurrence of short-term voltage instability is analysed based on a DGOL model. Then, a model and data hybrid-driven online application algorithm is proposed, which includes a pre-fault analysis module and a real-time monitoring module. At last, a two-dimensional index is proposed to evaluate the short-term voltage stability margin. Simulation work is first conducted based on the DGOL system to illustrate the advantage of the proposed simplified model, and on the EPRI 36-bus system to demonstrate the effectiveness of online application algorithm.

Measurement-Based Voltage Stability Assessment Considering Generator VAR Limits

This paper proposes a measurement-based voltage stability assessment method considering VAR limits of generators. Traditional measurement-based methods for monitoring a load bus or a load area often simplify the external system as a simple constant electromotive force (e.m.f.) behind a Thevenin impedance, which may give inaccurate voltage stability margin when some external generator reaches its VAR limit. In this paper, a novel method is proposed to consider the VAR limits of generators by deriving a relationship between the variations of their e.m.f. and the load, which can be identified and tracked in real time. Thus, a more accurate voltage stability margin is derived by an analytical expression under variations of both generator terminal voltages and loads. The proposed method is compared with a typical Thevenin method and demonstrated on a two-area system and the IEEE 39-bus power system.

Online dynamic voltage stability assessment method of AC/DC power systems

The reactive power absorption of conventional line commutated converter–high-voltage direct current transmission systems challenges on the voltage stability of AC/DC power systems. Many online dynamic voltage stability assessment approaches have been put forward to AC power systems, but the impact of DC transmissions is seldom taken into account for AC/DC power systems. In this study, an online dynamic voltage stability assessment method of AC/DC power systems is proposed. The proposed method models the converter as an equivalent AC voltage source in series with the internal impedance by utilising the control mode model of DC transmission systems and the measured data of the converter bus. The equivalent AC voltage source can identify the dynamic of DC transmissions. Then the AC/DC power system can be modelled by the equivalent AC power system. Based on the nodal equivalent method, the proposed method establishes a voltage stability index of the equivalent AC power systems for the dynamic voltage stability assessment of AC/DC power systems. The simulation demonstrated the effectiveness of the proposed method.

Dynamic Thévenin equivalent and reduced network models for PMU-based power system voltage stability analysis

Abstract Measurement-based real-time voltage stability assessment methods typically use a Thevenin Equivalent (TE) model. The TE is computed under the assumption that all generators and loads seen from an individual load-bus are constant during the time-window when measurements are obtained. This assumption does not hold in actual power systems. In fact, load changes at other load-buses result in variations on the voltage of a single-port equivalent model of the power system as seen from a load-bus. To consider these variations, this paper uses an interpolation method to develop a dynamic TE model from synchrophasor measurements, which is suitable for measurement-based real-time voltage stability assessment. In addition, a reduced network model is proposed to separate and quantify the impact of other loads and generators on the voltage stability of an interested load-bus in networks without full observability. The proposed method has been assessed through various simulation scenarios, and illustrated using actual field measurements.

A Fast Sensitivity-Based Preventive Control Selection Method for Online Voltage Stability Assessment

Modern power system suffers voltage instability more frequently due to the increasing load. Sensitivity analysis based preventive control is widely recognized as an effective method for preventing voltage instability. However, the well-known load margin based sensitivity methods are not suitable for real-time application since they must solve the left eigenvector of zero eigenvalue of the Jacobi matrix at the critical point and require the system-wide information. Therefore, this paper proposes a fast sensitivity-based method for selecting the most effective preventive controls. The sensitivity analysis uses a local voltage stability index, i.e., load impedance modulus margin, which is derived from the local measurements (nodal voltage and current), and the sensitivity ranking can be obtained more accurately and faster than traditional methods based on load margin. Such computational advantages make it suitable for online application. The effectiveness of the proposed method is successfully validated by both small and large-scale power systems.

Voltage stability assessment using multi-objective biogeography-based subset selection

We propose a method for voltage stability assessment of power systems using a support vector machine (SVM). We input the information from measurement signals to the SVM. The objectives of this paper are twofold: (1) to select the minimum number of features for training an SVM using multi-objective optimization (MOO); (2) to find the minimum misclassification rate for the SVM. To address these objectives, the training data size is decreased in two stages. First, a mutual information (MI) criterion is used to remove the less significant measurements from the data set. Second, the most relevant features are selected using multi-objective biogeography-based optimization (MOBBO). The minimization objectives are the measurement data size and the misclassification rate of the SVM. The BBO-based MO methods are vector evaluated BBO (VEBBO), nondominated sorting BBO (NSBBO), niched Pareto BBO (NPBBO), and strength Pareto BBO (SPBBO). These four MOO methods are compared using Pareto front normalized hypervolume, relative coverage, and statistical analysis. The methods are applied to a 39-bus benchmark system and a 66-bus real power grid. The results verify that the reduced measurement data using MOO lead to efficient and accurate SVMs. For the real power grid, the trained SVM accurately predicts the voltage stability of the system by using only 8% of the measurement data. The misclassification rates of the SVMs are as low as 2% for the real power grid. Normalized hypervolume, relative coverage, and statistical tests indicate that NSBBO performs better than the other methods.

A Distributed Transmission-Distribution-Coupled Static Voltage Stability Assessment Method Considering Distributed Generation

The recent rapid development of distributed generation (DG) necessitates the consideration of transmission–distribution interactions in voltage stability assessment (VSA), and how to perform a transmission–distribution-coupled static VSA (TDVSA) has become a pressing problem. To resolve this urgent issue, this paper first theoretically analyzes the impacts of the voltage-maintaining capacity and low-voltage tripping of DG units on the static voltage stability of an integrated transmission–distribution system and then proposes a distributed TDVSA method that fully considers these impacts when assessing the voltage stability of the integrated system. As the core of the method, a distributed continuation power flow algorithm is designed that includes a distribution-equivalencing-based predictor, a distributed transmission–distribution corrector, and a step-length regulator and requires only a limited amount of data to be exchanged between the transmission system operator (TSO) and the distribution system operator (DSO). Numerical simulations show that even in the case of low DG penetration, a cascading low-voltage tripping event can significantly degrade an integrated system's voltage stability, and only the proposed distributed TDVSA method can produce an accurate assessment. In addition, the number of iterations between the TSO and DSO is shown to be limited, indicating the potential of applying the proposed method to future grids.

GECM-Based Voltage Stability Assessment Using Wide-Area Synchrophasors

Voltage instability is a crucial issue in the secure operation of power grids. Several methods for voltage stability assessment were presented. Some of them are highly computationally intensive, while others are reported not to work properly under all circumstances. This paper proposes a new methodology based on the generator equivalent circuit model (GECM) and the phasor measurement unit (PMU) technology for online voltage stability monitoring of a power grid. First, the proposed methodology utilizes synchronized phasor (synchrophasor) measurements to determine the impedance parameters of a transmission grid by means of the recursive least squares (RLS) algorithm. Furthermore, it incorporates the dynamic models of generators to handle the cases with generator reactive power limit violations. After that, an enhanced voltage stability index with GECMs incorporated is developed for reliable and accurate voltage stability assessment. The proposed methodology was first demonstrated on several standard IEEE power systems, and then applied to a practical power system, the Taiwan power (Taipower) system. The test results demonstrate the flexibility and effectiveness of the proposed methodology.

Numerical polynomial homotopy continuation method to locate all the power flow solutions

The manuscript addresses the problem of finding all solutions of power flow equations or other similar non-linear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly the direct methods for transient stability analysis and voltage stability assessment. Here, the authors introduce a novel form of homotopy continuation method called the numerical polynomial homotopy continuation method that is mathematically guaranteed to find all the solutions without ever encountering a bifurcation. Since finding real solutions is much more challenging, first the authors embed the real form of power flow equation in complex space, and then track the generally unphysical solutions with complex values of real and imaginary parts of the voltages. The solutions converge to physical real form in the end of the homotopy. The so-called gamma-trick mathematically rigorously ensures that all the paths are well-behaved along the paths, so unlike other continuation approaches, no special handling of bifurcations is necessary. The method is embarrassingly parallelisable. The authors demonstrate the technique performance by solving several test cases up to the 14 buses. Finally, they discuss possible strategies for scaling the method to large size systems, and propose several applications for security assessments.

Voltage Stability Assessment Using Equivalent Nodal Analysis

This paper presents a simple method for voltage stability assessment by reducing the bus impedance matrix of a network into its two-bus equivalent model at a referred bus. Closed-form equations of the equivalent model could then be derived to facilitate an equivalent nodal analysis at the referred bus to determine its voltage stability limit. The method was also shown to have parallels with the well-accepted modal analysis of the Jacobian matrix. These include defining geometric indices to identify critical buses and participation factors to quantify contribution of network elements to their criticality. The method however does not require post power flow solution processing of the Jacobian matrix; such computational advantage may make it suitable for online applications. The IEEE 300-bus system was tested with the method which was shown to be valid and computationally robust and efficient.

Utilization of Events Measured by WAMS-BIOZE-Detector for System Voltage Stability Evaluation

Abstract: The paper summarizes results of research work focused on development of the voltage stability assessment method and its software implementation. Developed voltage stability detection algorithm is based on local synchronous phasor measurement. The Thevenin equivalence based assessment method, the identification algorithm as well as the developed WAMS-BIOZE-Detektor software are presented. The proposed voltage stability indices have different sensitivity to events in power systems. Sensitivity of the indices was tested by using records of various disturbances and failures in a HV grid. Test results validate applicability of the indices in practice. Finally, the index with the highest applicability for online detection is recommended.

Hybrid voltage stability assessment (VSA) for N − 1 contingency

With the growing deployment of phasor measurement units (PMUs), measurement-based voltage stability assessment (VSA) that estimates the system Thevenin equivalent has been widely discussed in recent years. This approach attracts favorable attentions mainly for its simplicity and great potential in real-time applications, as opposed to the continuation power flow (CPF) method which is model-based VSA. However, the existing measurement-based VSA deals with the normal case, but not any contingency case because there is no measurement data for a contingency case which is hypothetical. With this motivation, a hybrid VSA method is proposed based on both model-based and measurement-based techniques. First, an enhanced model-based sensitivity analysis estimating the post-contingency status is proposed, and then it is combined with the measurement-based Thevenin equivalent approach. The proposed sensitivity analysis has the feature of simplicity, which is aligned with the measurement-based Thevenin equivalent. Test results with the IEEE 14, 39, and 118-bus systems show that the proposed sensitivity is highly accurate in estimating N−1 contingency system variables and the proposed hybrid VSA method for N−1 contingency captures the insecure contingencies successfully. The proposed method greatly broadens the practical application of PMUs for VSA under N−1 contingency.

Analysis of Continuous Power Flow Method, Model Analysis, Linear Regression and ANN for Voltage Stability Assessment for Different Loading Conditions

This Paper presents voltage stability assessment through P-V curve and bus voltage sensitivity factor. Active power margin is used to measure the distance to instability. Analyses by using computational methods are used to obtain P-V curve of power system. Continuation power flow starting with initial operating point and increasing load to the maximum loading point and to reduce the size of the jacobian matrix modal analysis is adopted. A data statistics analysis tool is used to run linear regression. In this paper the linear regression method with ANN is compared with conventional methods and voltage stability is improved within less iterations.

A New Method for Static Voltage Stability Assessment based on The Local Loadability Boundary

Abstract This paper proposes a new method for assessing static voltage stability based on the local loadability boundary or P- Q curve in two dimensional power parameter space. The proposed method includes three main steps. The first step is to determine the critical buses and the second step is building the local loadability boundary or the saddle node bifurcation set for those critical buses. The final step is assessing the static voltage stability through the distance from current operating point to the boundary. The critical buses are defined through the right eigenvector by direct method. The boundary obtained by the proposed method that is combining a variation of standard direct method and Thevenin equivalent model of electric power system is a quadratic curve. And finally the distance is computed through the Euclid norm of normal vector of the boundary at the closest saddle node bifurcation point. The advantage of the proposed method is that it keeps the advantages of both efficient methods, the accuracy of the direct method and simple of Thevenin Equivalent based method. Thus, the proposed method holds some promise in terms of performing the real time voltage stability assessment of power system. Test results of New England 39 bus system are presented to show the effectiveness of the proposed method.

An innovative technique to evaluate network equivalent for voltage stability assessment in a widespread sub-grid system

The equivalent two-bus network models currently available are obtained by lumping all the series impedances and shunt admittances of transmission lines within a series equivalent impedance, to assess voltage stability of multi-bus power system. This paper reports the development of an equivalent pi-network model using a new methodology considering series and shunt parts of line loss separately obtained from the operational parameters of optimal power flow solution of the original multi-bus power network, which can be applied to assess the overall voltage stability status of the system accurately by developing the concept of a generalized global voltage stability margin (GVSM). Simulation results for a typical longitudinal power supply (LPS) system and a robust practical (Indian Eastern Grid) system establish that the pi-equivalent model obtained by the proposed method is highly promising for assessing voltage stability of any power system at any operating point in global scenario in a better way as compared to available series equivalent model. Continuation power flow (CPF) method has also been adopted here to verify the potential of the proposed method for voltage stability assessment. In the proposed equivalent network the generators have been modeled more accurately considering optimal operating criteria.

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

Abstract 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.

Contingency screening and ranking method for voltage stability assessment

The paper presents a method capable of selecting contingencies that lead to voltage insecurities. The contingencies are ordered according to their effect on the system operating state. Insecurities are measured by the apparent power margin between the busbar injected power at the operating point under analysis and an estimate of the maximum injection, as well as by the region of operation in the SV curve. The influence index translates the margin reduction after the disturbance. The method allows nodal as well as affected area analysis. The N/NE Brazilian system is used in an illustrative numerical example. Computational time is no burden for real-time operational analysis.

Determination of power system coherent bus groups by novel sensitivity-based method for voltage stability assessment

This paper presents a method that is used to determine the coherent bus groups of a system with similar reactive reserve basins. The differences between this proposed method and another widely accepted voltage stability analysis method are highlighted in this paper and results obtained from the proposed method are discussed. This method is highlighted as being more efficient and requiring comparatively less VQ curve computations. Definitions are proposed for the categorization of buses by the cause of their loading limitation. Results obtained from the test systems support the method's validity and the validity of the bus categories proposed. By determining the reactive reserve margin, it is possible to determine which generators will have an impact on the maximum permissible loading of a bus and which will not. This information is particularly useful for performing voltage stability analysis.

Determination of Power System Coherent Bus Groups by Novel Sensitivity-Based Method for Voltage Stability Assessment

This paper presents a method that is used to determine the coherent bus groups of a system with similar reactive reserve basins. The differences between this proposed method and another widely accepted voltage stability analysis method are highlighted, and results obtained from the proposed method are discussed. This method is more efficient and requires comparatively less VQ curve computations. Definitions are proposed for the categorization of buses by the cause of their loading limitation. Results obtained from the test systems support the method's validity and the validity of the bus categories proposed. By determining the reactive reserve margin, it is possible to determine which generators will have an impact on the maximum permissible loading of a bus and which will not. This information is particularly useful for performing voltage stability analysis.