Online Voltage Stability Assessment Research Articles

Online assessment of short-term voltage stability based on hybrid model and data-driven approach

With the continuously increasing integration of renewable energy sources into power grids, the dynamic response of a power system is becoming more complex. For example, the interaction between the dynamic loads and low-voltage ride-through of renewable energy generators makes the voltage response more rapid and unpredictable. Ensuring the accuracy and speed of traditional voltage stability assessment methods is difficult. This study developed a novel hybrid model and data-driven voltage stability assessment approach. First, the equivalent parameters of a power system were calculated based on the measured data, and the parameters were constantly modified based on the response data. To further improve the accuracy of the approach, a data-driven method was introduced to correct the assessment results using a Thevenin equivalent-based assessment. The difference between the Thevenin and system impedances, which better reflects the system stability, was included in the data-driven input data. Finally, by combining the clear physical mechanism of the model-driven method and high accuracy of the data-driven method, the final the assessment process was a serial combination of the model- and data-driven methods. The effectiveness of the method was verified using an IEEE New England 10-generator 39-bus test system and a 100-bus actual system in China. The results showed that the method developed was more accurate and had higher robustness under data loss and noise conditions than other methods.

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.

A Data-Driven and Data-Based Framework for Online Voltage Stability Assessment Using Partial Mutual Information and Iterated Random Forest

Due to the rapid development of phasor measurement units (PMUs) and the wide area of interconnection of modern power systems, the security of power systems is confronted with severe challenges. A novel framework based on data for static voltage stability margin (VSM) assessment of power systems is presented. The proposed framework can select the key operation variables as input features for the assessment based on partial mutual information (PMI). Before the feature selection procedure is completed by PMI, a feature preprocessing approach is applied to remove redundant and irrelevant features to improve computational efficiency. Using the selected key variables, a voltage stability assessment (VSA) model based on iterated random forest (IRF) can rapidly provide the relative VSM results. The proposed framework is examined on the IEEE 30-bus system and a practical 1648-bus system, and a desirable assessment performance is demonstrated. In addition, the robustness and computational speed of the proposed framework are also verified. Some impact factors for power system operation are studied in a robustness examination, such as topology change, variation of peak/minimum load, and variation of generator/load power distribution.

A Novel Thévenin Equivalent Model Considering the Correlation of Source-Grid-Load in Power Systems

The coupled single-port circuit has been proposed for online voltage stability assessment based on wide-area measurements and grid equations. This circuit can explicitly reflect the influence of grid and load on voltage stability. However, it does not consider the impact of power generation. A novel Thevenin equivalent (TE) circuit considering the influence of source-grid-load on voltage stability is proposed in this paper. First, the impact of source-grid-load on the voltage of an individual load bus is divided into three parts according to the node-voltage equation. They are then decomposed into two components, respectively associated with the TE voltage and the TE impedance according to the TE circuit’s characteristics. Finally, an online identification method for the parameters of the proposed TE circuit based on wide-area measurements is developed. Compared with the coupled single-port circuit, the proposed method has the advantage of being able to consider the influence of power generation on voltage stability and being consistent in form with traditional TE circuit without requiring approximation. Case studies on the IEEE 118-bus system illustrate the accuracy and effectiveness of the proposed method.

Online assessment of voltage stability using Newton‐Corrector algorithm

Online assessment of voltage stability using Newton‐Corrector algorithm

Reconstruction Residuals Based Long-term Voltage Stability Assessment Using Autoencoders

Real-time voltage stability assessment (VSA) has long been an extensively research topic. In recent years, rapidly mounting deep learning methods have pushed online VSA to a new height that large amounts of learning algorithms are applied for VSA from the perspective of measurement data. Deep learning methods generally require a large dataset which contains measurements in both secure and insecure states, or even unstable state. However, in practice, the data of insecure or unstable state is very rare, as the power system should be guaranteed to operate far away from voltage collapse. Under this circumstance, this paper proposes an autoencoder based method which merely needs data of secure state to evaluate voltage stability of a power system. The principle of this method is that an autoencoder purely trained by secure data is expected to only create precise reconstruction for secure data, while it fails to rebuild data of insecure states. Thus, the residual of reconstruction is effective in indicating VSA. Besides, to develop a more accurate and robust algorithm, long short-term memory (LSTM) networks combined with fully-connected (FC) layers are used to build the autoencoder, and a moving strategy is introduced to bias the features of testing data toward the secure feature domain. Numerous experiments and comparison with traditional machine learning algorithms demonstrate the effectiveness and high accuracy of the proposed method.

Construction of decision tree based on C4.5 algorithm for online voltage stability assessment

This paper constructs decision tree (DT) using C4.5 algorithm for online voltage stability assessment. The entire process includes three steps: sample acquisition, attribute selection and DT construction. First, P-V curves analysis is performed to generate samples for DT. Participation factor analysis and relief algorithm are then used to select attributes for DT. C4.5 algorithm is finally applied to construct DT. The case study on a practical power system demonstrates that DT can extract operating guidelines from offline voltage stability analysis results, and helps system operators assess voltage stability status in real-time.

Machine Learning Techniques Applied to On-Line Voltage Stability Assessment: A Review

Electric power systems have become larger, more complex and found to be operating close to their stability limits with small security margin. In such situation, fast and accurate assessment of voltage stability is necessary in order to prevent large-scale blackouts. Due to its ability to learn off-line and produce accurate results on-line, machine learning (ML) techniques i.e., artificial neural networks, decision trees, support vector machines, fuzzy logic and adaptive neuro-fuzzy inference system are widely applied for on-line voltage stability assessment. This paper focuses on providing a clear review of the latest ML techniques employed in on-line voltage stability assessment. For each technique, a brief description is first presented and then a detailed review of the finding published research papers discussed the application of this technique in on-line voltage stability assessment is presented. Based on the conducted review, some discussions and limitations of ML techniques are finally presented.

ON-LINE VOLTAGE STABILITY EVALUATION USING NEURO-FUZZY INFERENCE SYSTEM AND MOTH-FLAME OPTIMIZATION ALGORITHM

Purpose. In recent years, the problem of voltage instability has received special attention from many utilities and researchers. The present paper deals with the on-line evaluation of voltage stability in power system using Adaptive Neuro-Fuzzy Inference System (ANFIS). The developed ANFIS model takes the voltage magnitudes and their phases obtained from the weak buses in the system as input variables. The weak buses identification is formulated as an optimization problem considering the operating cost, the real power losses and the voltage stability index. The recently developed Moth-Flame Optimization (MFO) algorithm was adapted to solve this optimization problem. The validation of the proposed on-line voltage stability assessment approach was carried out on IEEE 30-bus and IEEE 118-bus test systems. The obtained results show that the proposed approach can achieve a higher accuracy compared to the Multi-Layer Perceptron (MLP) and Radial Basis Function (RBF) neural networks.

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.

Enhanced-Online-Random-Forest Model for Static Voltage Stability Assessment Using Wide Area Measurements

Application of data mining based methods in online voltage stability assessment has attracted vast attentions in recent years. To account for significant system changes, most of the data mining based methods reconstruct an entire model based on the updated training database. Instead of entirely rebuilding a model in offline mode, this paper presents a novel online learning framework for monitoring the voltage stability of a transmission grid using wide area measurements. A new enhanced online random forest model based on the drift detection and online bagging techniques is proposed. It enables to online update the trees involving tree growth and/or tree replacement. The trees in the forest are then combined via a weighted majority voting, which makes the decision model better adapted to system changes. The framework was first demonstrated on the IEEE 57-bus system, and then applied to a practical power system, the Taiwan power (Taipower) system composed of 1821 buses. In addition to accuracy-based measures, robustness and speed of the proposed framework were also validated. Extensive studies demonstrate that the proposed framework is able to provide reliable and accurate online voltage stability assessment.

Robust Thevenin Equivalent Parameter Estimation for Voltage Stability Assessment

This letter presents a robust approach to accurate estimation of Thevenin equivalent (TE) parameters using phasor measurement unit (PMU) data for online voltage stability assessment. The TE parameter estimation is formulated as a worst-case robust least squares problem to take PMU uncertainties into account. A second-order cone programming technique is then utilized to solve the problem. Case studies on several IEEE standard networks and a practical power system, along with comparative results, illustrate the effectiveness and robustness of the presented approach.

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.

Online Voltage Stability Assessment for Load Areas Based on the Holomorphic Embedding Method

This paper proposes an online steady-state voltage stability assessment scheme to evaluate the proximity to voltage collapse at each bus of a load area. Using a non-iterative holomorphic embedding method (HEM) with a proposed physical germ solution, an accurate loading limit at each load bus can be calculated based on online state estimation on the entire load area and a measurement-based equivalent for the external system. The HEM employs a power series to calculate an accurate P – V curve at each load bus and accordingly evaluates the voltage stability margin considering load variations in the next period. An adaptive two-stage Pade approximant method is proposed to improve the convergence of the power series for accurate determination of the nose point on the P – V curve with moderate computational burden. The proposed method is first illustrated in detail on a four-bus test system and then demonstrated on a load area of the Northeast Power Coordinating Council 48-geneartor 140-bus power system.

Power System Voltage Stability Assessment Using a Hybrid Approach Combining Dragonfly Optimization Algorithm and Support Vector Regression

In this paper, an efficient approach based on the combination of dragonfly optimization (DFO) algorithm and support vector regression (SVR) has been proposed for online voltage stability assessment. As the performance of the SVR model extremely depends on careful selection of its parameters, the DFO algorithm involves SVR parameters setting, which significantly ameliorates their performance. In the proposed approach, the voltage magnitudes of the phasor measurement unit (PMU) buses are adopted as the input data for the hybrid DFO–SVR model, while the minimum values of voltage stability index (VSI) are taken as the output vector. Using the data provided by PMUs as the input variables makes the proposed model capable of assessing the voltage stability in a real-time manner, which helps the operators to adopt the required measures to avert large blackouts. The predictive ability of the proposed hybrid model was investigated and compared with the adaptive neuro-fuzzy inference system (ANFIS) through the IEEE 30-bus and the Algerian 59-bus systems. According to the obtained results, the proposed DFO–SVR model can successfully predict the VSI. Moreover, it provides a better performance than the ANFIS model.

The Amalgamation of SVR and ANFIS Models with Synchronized Phasor Measurements for On-Line Voltage Stability Assessment

This paper presents the application of support vector regression (SVR) and adaptive neuro-fuzzy inference system (ANFIS) models that are amalgamated with synchronized phasor measurements for on-line voltage stability assessment. As the performance of SVR model extremely depends on the good selection of its parameters, the recently developed ant lion optimizer (ALO) is adapted to seek for the SVR’s optimal parameters. In particular, the input vector of ALO-SVR and ANFIS soft computing models is provided in the form of voltage magnitudes provided by the phasor measurement units (PMUs). In order to investigate the effectiveness of ALO-SVR and ANFIS models towards performing the on-line voltage stability assessment, in-depth analyses on the results have been carried out on the IEEE 30-bus and IEEE 118-bus test systems considering different topologies and operating conditions. Two statistical performance criteria of root mean square error (RMSE) and correlation coefficient (R) were considered as metrics to further assess both of the modeling performances in contrast with the power flow equations. The results have demonstrated that the ALO-SVR model is able to predict the voltage stability margin with greater accuracy compared to the ANFIS model.

On-line Assessment of Voltage Stability using Synchrophasor Technology

Series of blackouts encountered in recent years in power system have been occurred because either of voltage or angle instability or both together was not detected within time and progressive voltage or angle instability further degraded the system condition, because of increase in loading. This paper presents the real-time assessment methodology of voltage stability using Phasor Measurement Unit (PMU) with observability of load buses only in power network. PMUs are placed at strategically obtained location such that minimum number of PMU’s can make all load buses observable. Data obtained by PMU’s are used for voltage stability assessment with the help of successive change in the angle of bus voltage with respect to incremental load, which is used as on-line voltage stability predictor (VSP). The real-time voltage phasors obtained by PMU’s are used as real time voltage stability indicator. The case study has been carried out on IEEE-14 bus system and IEEE-30 bus systems to demonstrate the results.

Extreme Learning Machine Approach for Real Time Voltage Stability Monitoring in a Smart Grid System using Synchronized Phasor Measurements

Online voltage stability monitoring using real-time measurements is one of the most important tasks in a smart grid system to maintain the grid stability. Loading margin is a good indicator for assessing the voltage stability level. This paper presents an Extreme Learning Machine (ELM) approach for estimation of voltage stability level under credible contingencies using real-time measurements from Phasor Measurement Units (PMUs). PMUs enable a much higher data sampling rate and provide synchronized measurements of real-time phasors of voltages and currents. Depth First (DF) algorithm is used for optimally placing the PMUs. To make the ELM approach applicable for a large scale power system problem, Mutual information (MI)-based feature selection is proposed to achieve the dimensionality reduction. MI-based feature selection reduces the number of network input features which reduces the network training time and improves the generalization capability. Voltage magnitudes and phase angles received from PMUs are fed as inputs to the ELM model. IEEE 30-bus test system is considered for demonstrating the effectiveness of the proposed methodology for estimating the voltage stability level under various loading conditions considering single line contingencies. Simulation results validate the suitability of the technique for fast and accurate online voltage stability assessment using PMU data.

Extended synchrophasor-based online voltage stability assessment using synchronous generator-derived indices

Summary This paper proposes and investigates the online application of generator-derived real-time voltage stability assessment indices in large interconnected power systems. The indices are based on synchrophasor measurements from synchronous generators and are used in the prediction of the system's margin to voltage collapse in real-time. Comparative analyses are carried out between the newly proposed indices, an existing effective generator reactive power reserve index, and two line-based indices. Results obtained from testing the proposed indices on the New England 39-bus test system show that the proposed indices are simple to implement, more responsive to system dynamics and provide a more accurate estimation of the system's margin to voltage collapse compared with the existing indices. Furthermore, the suitability of the proposed indices for small disturbance voltage instability and large disturbance voltage instability conditions were demonstrated. In addition, the proposed indices are subsequently deployed on a programmable logic controller for real-time closed-loop testing with the real-time digital simulator. Copyright © 2016 John Wiley & Sons, Ltd.

Wide-Area Voltage Monitoring and Optimization

As the power demand becomes higher all over the world, transmission lines are often carrying electric power near their limits, which can cause power systems to be operated under serious stress. Voltage collapse is one of the more critical problems that impacts power system operational security and many of the recent major blackouts were caused, at least partially, by voltage collapse. Therefore, a fast and accurate voltage stability monitor is necessary for the modern system, together with a fast calculation of possible remedial actions. The development and application of wide-area measurement systems established the foundation of online assessment of voltage stability in large-scale power systems. In this paper, a voltage stability (QV) index based on phasor measurements is used to identify the weak buses and a new parallel optimization method that increases this voltage stability margin is introduced. Results on the IEEE standard systems show the accuracy and efficiency of the methods.