Probabilistic Transient Stability Research Articles

A High Computationally Efficient Parallel Partial Gaussian Process for Large-Scale Power System Probabilistic Transient Stability Assessment

A High Computationally Efficient Parallel Partial Gaussian Process for Large-Scale Power System Probabilistic Transient Stability Assessment

Advanced Probabilistic Transient Stability Assessment for Operational Planning: A Physics-Informed Graphical Learning Approach

Advanced Probabilistic Transient Stability Assessment for Operational Planning: A Physics-Informed Graphical Learning Approach

Classification Study of New Power System Stability Considering Stochastic Disturbance Factors

Power system instability causes many local or large-scale power outage accidents. To maintain sustainable development, a new power system construction aimed at maximizing new energy consumption is being put on the agenda. However, with a large increase in stochastic disturbance factors (SDFs), the system gradually shows strong stochasticity, and the stability presents greater complexity. It is necessary to analyze the impact on the system based on different processing methods of SDFs to maintain system stability. This paper delves into the impact of SDFs on system stability by analyzing and summarizing both stochastic variables and processes. Initially, the SDFs in the power system are meticulously analyzed and categorized. When the SDFs are treated as stochastic variables, the probabilistic stability is classified and evaluated based on a probability analysis method, which includes the probabilistic small-disturbance stability, the probabilistic transient stability, and the probabilistic voltage stability. When the SDFs are treated as stochastic processes, the stochastic stability is classified and evaluated by using a stochastic analysis method, including the stochastic small-disturbance stability, the stochastic transient stability, and the stochastic voltage stability. Finally, the research perspectives on SDFs and system stability are discussed and prospected.

Debiased Uncertainty Quantification Approach for Probabilistic Transient Stability Assessment

System instability does not occur often in practice and thus the historical data for training a machine learning method has to address the imbalanced and multi-modal probabilistic distribution in the probabilistic transient stability assessment (PTSA). This letter proposes a transient stability index (TSI) density-based weighting scheme and feature-TSI similarity regularization to address that, yielding debiased uncertainty quantification for PTSA in the presence of uncertain wind generations and loads. Numerical results on the IEEE 39-bus and Illinois 200-bus power systems demonstrate the significantly improved performance of the proposed method over other state-of-the-art machine learning approaches in PTSA.

Physics-Informed Sparse Gaussian Process for Probabilistic Stability Analysis of Large-Scale Power System With Dynamic PVs and Loads

This paper proposes a physics-informed sparse Gaussian process (SGP) for probabilistic stability assessment of large-scale power systems in the presence of uncertain dynamic PVs and loads. The differential and algebraic equations considering uncertainties from dynamic PVs and loads are reformulated to a nonlinear mapping relationship that allows the application of SGP. Thanks to the nonparametric characteristic of Gaussian process, the proposed framework does not require distributions of uncertain inputs and this distinguishes it from existing approaches. As the original Gaussian process is not scalable to large-scale systems with high dimensional uncertain inputs, this paper develops the SGP with a stochastic variational inference technique. It leads to approximately two orders of complex reduction. A data pre-processing step is also introduced to tackle the coexistence of stable and unstable cases by sample clustering and constructing separate SGPs. The probabilistic transient stability index is analyzed to assess system stability under different uncertain dynamics loads and PVs. Comparisons are performed with the sampling-based, the polynomial chaos expansion-based, and traditional Gaussian process-based methods on the modified IEEE 118-bus and Texas 2000-bus systems under various scenarios, including different levels of uncertainties and the existence of nonlinear correlations among dynamic PVs. The impacts of data quality and quantity issues are also investigated. It is shown that the proposed SGP achieves significantly improved computational efficiency while maintaining high accuracy with a limited number of data.

A risk-based machine learning approach for probabilistic transient stability enhancement incorporating wind generation

ABSTRACT Power systems are becoming more complex than ever and are consequently operating close to their limit of stability. Considering its significance in power system security, it is important to propose a novel approach for enhancing the transient stability, considering uncertainties. Current deterministic industry practices of transient stability assessment ignore the probabilistic nature of variables. Moreover, the time-domain simulation approach for transient stability evaluation can be very computationally intensive, especially for a large-scale system. The impact of wind penetration on transient stability is critical to investigate, as it does not possess the inherent inertia of synchronous generators. Thus, this paper proposes a risk-based, machine learning decision-making approach, for probabilistic transient stability enhancement, by replacing circuit breakers, including the impact of wind generation. The IEEE 14-bus test system was used to test and validate the effectiveness of the proposed approach. DIgSILENT PowerFactory and MATLAB were utilised for transient stability simulations (for obtaining training data for machine learning), and applying machine learning algorithms, respectively.

Prediction of probabilistic transient stability using support vector regression

ABSTRACT The increasing uncertainty in power systems has brought various challenges, including transient stability assessment. The conventional approaches, such as, time-domain simulation approach and direct method (based on Lyapunov function and transient energy function), to estimate the transient stability are not appropriate for online application, as they suffer from various drawbacks of large computation time (time-domain simulation) and delivering approximate results (direct method). The field of machine learning and soft computing provides a good alternative to the conventional approaches, for transient stability evaluation. Thus, this paper aims to discuss the application of support vector machine (SVM) for predicting the probabilistic transient stability. DIgSILENT PowerFactory was utilised for conducting time-domain simulations (to obtain the training data), and MATLAB was used for support vector regression (SVR) training. For the SVR model, fault type, fault location, fault clearing time, and system load were chosen as the predictors and the transient stability index (TSI) was used as the response. Various regression metrics were computed, for the IEEE 14-bus system, to validate the effectiveness of the proposed approach. The results obtained verify the efficiency of the proposed approach and provide a great potential to be applied for online dynamic security assessment (DSA).

Improved Multi-point estimation method based probabilistic transient stability assessment for power system with wind power

With the increasing penetration of wind power, probabilistic transient stability assessment becomes critical to deal with the uncertainties and correlations of wind power, thus improving the reliability of power system. This paper proposes an improved multi-point estimation based probabilistic transient stability assessment method. Extreme learning machine (ELM) is introduced to describe the uncertainty of practical wind power output. Gauss-Hermite integral based multi-point estimation method is proposed to calculate transient stability criterion derived through practical dynamic security region (PDSR). Optimal number of the sampling points is determined based on PDSR hyperplanes and an improved particle swarm optimization algorithm (IPSO). Test results on the New England 10-generators 39-buses system and a practical provincial power system in China show that the calculation accuracy of the proposed method is higher than that of other commonly-used point-estimation methods without much loss of computational efficiency under different wind power penetration and correlation levels.

Prediction of Probabilistic Transient Stability Using Support Vector Machine

Transient stability assessment is an integral part of dynamic security assessment of power systems. Traditional methods of transient stability assessment, such as time domain simulation approach and direct methods, are appropriate for offline studies and thus, cannot be applied for online transient stability prediction, which is a major requirement in modern power systems. This motivated the requirement to apply an artificial intelligence-based approach. In this regard, supervised machine learning is beneficial for predicting transient stability status, in the presence of uncertainties. Therefore, this paper examines the application of a binary support vector machine-based supervised machine learning, for predicting the transient stability status of a power system, considering uncertainties of various factors, such as load, faulted line, fault type, fault location and fault clearing time. The support vector machine is trained using a Gaussian Radial Basis function kernel and its hyperparameters are optimized using Bayesian optimization. Results obtained for the IEEE 14-bus test system demonstrated that the proposed method offers a fast technique for probabilistic transient stability status prediction, with an excellent accuracy. DIgSILENT PowerFactory and MATLAB was utilized for transient stability time-domain simulations (for obtaining training data for support vector machine) and for applying support vector machine, respectively.

Application of supervised machine learning for prediction of probabilistic transient stability

ABSTRACT Evaluation of transient stability is integral to dynamic security assessment of power systems. It deals with the assessment of the ability of the system to remain in equilibrium for large disturbances, such as faults. Deterministic approaches for transient stability assessment are becoming unsuitable, considering the rising uncertainties. Moreover, due to its intensive computation effort, the conventional time-domain approach for transient stability assessment is not appropriate for online application, thereby motivating the requirement to apply a soft computing technique. Thus, this paper investigates artificial neural network-based supervised machine learning, for predicting the transient stability of a power system, considering uncertainties of load, faulted line, fault type, fault location, and fault clearing time. The training of the neural network was accomplished using suitable system features as inputs, and probabilistic transient stability status indicator as the output. Results obtained for the IEEE 14-bus test system demonstrated that the proposed method offers a fast technique for probabilistic transient stability prediction with a superior accuracy, and thereby, signifying a strong possibility for neural network application in dynamic security assessment. DIgSILENT PowerFactory and MATLAB was utilised for transient stability time-domain simulations (for obtaining training data for the neural network), and for applying supervised machine learning, respectively.

Impact of renewable generation on probabilistic dynamic security assessment of a power transmission system

ABSTRACT Dynamic security assessment (DSA) is a vital part of power system planning and operation. Although various phenomena, such as line thermal loading, voltage stability, and frequency stability, are of interest in DSA, this paper particularly focuses on transient rotor angle stability of conventional synchronous generators in a transmission system. Integration of large wind and photovoltaic (PV) farms to the bulk power systems has brought various challenges to the conventional rotor angle transient stability of synchronous generators. It is, therefore, of immense importance to examine and comprehend the impact of various renewable generations and their penetration levels on the probabilistic transient stability. This paper uses time-domain simulation approach to analyse these impacts in terms of probability of system instability, based on the transient stability index (TSI). Various case studies are conducted on the IEEE 39-bus test system, considering the probabilistic nature of parameters (faulted line/bus, fault type, fault location, and fault duration). The results obtained indicate that hybrid renewable energy integration is the best choice for achieving the highest probabilistic dynamic security, considering (N-1) and (N-2) line and (N-1) bus faults.

Design and Implementation of Probabilistic Transient Stability Approach to Assess the High Penetration of Renewable Energy in Korea

Recently, because of the many environmental problems worldwide, Korea is moving to increase its renewable energy output due to the Renewable 3020 Policy. Renewable energy output can change depending on environmental factors. It is for this reason that institutions should consider the instability of renewables when linked to the electric system. This paper describes the methodology of renewable energy capacity calculation based on probabilistic transient stability assessment. Probabilistic transient stability assessment consists of four algorithms: first, to create probabilistic scenarios based on the effective capacity history of renewable energy; second, to evaluate probabilistic transient stability based on transient stability index, interpolation-based transient stability index estimation, reduction-based transient stability index calculation, etc.; third, to implement multiple scenarios to calculate renewable energy capacity using probabilistic evaluation index; and finally, to create a probabilistic transient stability assessment simulator based on Python. This paper calculated renewable energy capacity based on large-scale power system to validate consistency of the proposed paper.

A Preventive Dispatching Method for High Wind Power-Integrated Electrical Systems Considering Probabilistic Transient Stability Constraints

This paper proposes a probabilistic transient stability-constrained preventive dispatching method for power systems under a high inclusion of wind power. First, a set of instability mode (IM)-categorized probabilistic transient stability constraints (PTSCs) are constructed, which facilitate the development of a dispatching plan against various fault scenarios. Next, to avoid massive transient stability simulations in each dispatching operation, a machine learning-based model is trained to predict the critical clearing time (CCT) and IM for all preconceived fault scenarios. Based on the predictions, the system operation plan is assessed with respect to the PTSCs. Then, the sensitivity of the probabilistic level of the CCT is calculated to the active power generated from the critical generators for each IM category. Accordingly, the implicit PTSCs are converted into explicit dispatching constraints, and the dispatch is rescheduled to ensure the probabilistic stability requirements of the system are met at an economical operating cost. The proposed approach is validated on two modified IEEE test systems, reporting high computational efficiency and high-quality solutions.

Probabilistic Stacked Denoising Autoencoder for Power System Transient Stability Prediction With Wind Farms

To address the uncertainties of renewable energy and loads in transient stability assessment with credible contingencies, this letter proposes a stacked denoising autoencoder (SDAE)-based probabilistic prediction method. The correlations among wind farms have been effectively considered through the variable transformation via the Cholesky decomposition. SDAE allows learning the mapping relationship between operational features and the transient stability margin. The possible operation scenarios are sampled under different confidence levels to generate appropriate inputs for SDAE to assess the probabilistic transient stability distribution. Results on the modified IEEE 39-bus system show that our proposed method can achieve a similar level of accuracy as the benchmark and improved Monte Carlo simulations-based methods while having much higher computational efficiency.

Probabilistic framework for transient stability contingency ranking of power grids with active distribution networks: application in post disturbance security assessment

The conventional distribution network is becoming an active grid due to widespread integration of distributed energy resources (DERs). This integration raises great concerns about security of the power system considering the growing interactions between the transmission and active distribution systems. One way to ensure stability of the integrated power system is prediction of critical contingencies which can jeopardize the power system security. Therefore, this paper aims to investigate transient stability contingency ranking in power grids considering the uncertainties raised by DERs of active distribution networks. To this end, probabilistic transient stability prediction framework is provided, in which the probability density function of transient stability condition is calculated based on the normalized stability indicators. The normalized stability indicators are based on the rotor angle and rotor speed. The normalized stability indicators are only utilized in the case of using fault data for prediction. Based on the proposed scheme, the instability of generators is anticipated through the proposed probabilistic transient stability prediction framework. Also, the effects of the probable topology changes on the line overload and also the voltage profile are investigated. Finally, the performance of the proposed method is validated and compared with the time domain simulation under various operating conditions.

Probabilistic transient stability assessment of power system considering wind power uncertainties and correlations

This paper proposes a simple yet effective method for power system probabilistic transient stability assessment considering the wind farm uncertainties and correlations. Specifically, the inverse Nataf transformation based three-point estimation method and the Cornish-Fisher expansion have been integrated together to deal with the uncertainties and the correlations among different wind farms. Then, by resorting to the extended dynamic security region approach, the transient stability criterion is derived as a linear combination of nodal injection vector under a given fault condition. New indices for the identification of critical lines have also been developed. Extensive simulation results carried out on four different systems, including the practical GZ power system in China show that the computational efficiency of the proposed method is much higher than the Monte Carlo-based method and other methods almost without the loss of accuracy. The effectiveness of the proposed method under different penetrations of wind power with different degree of correlations is also validated. It is shown that correlation among wind farms has a larger impact on the transient stability results with a higher penetration level of renewable energy.

Calculating probability density function of critical clearing time: Novel Formulation, implementation and application in probabilistic transient stability assessment

Due to increasing of uncertainty in nowaday power systems, probabilistic security assessment has become one of the challenging issues in power systems. This paper, proposes a new real-time approach for calculating probabilistic critical clearing time (CCT) which is applicable to probabilistic transient stability assessment. The proposed method aims to provide a low computational burden and high-accuracy to calculate the probabilistic density function (PDF) of CCT in two stages. In the first stage, proposed method presents a novel sensitivity based approach, which calculates CCT in the first step of the simulation. Determination of CCT by taking structure preserving into account, guarantees the accuracy of the proposed method. In the second stage, by applying Quasi Monte Carlo (QMC) simulation, the PDF of CCT is obtained. Several different parameters that affect uncertainty of CCT such as load and generation and also fault location are considered in order to obtain the PDF of CCT. Several case studies have been conducted on IEEE 9 bus and 68 bus test systems to show the efficiency of the proposed method. Simulation results indicate that the proposed method has notable accuracy along with substantial speed in performing the required calculations.

Integrated Evaluation of Reliability and Stability of Power Systems

This paper investigates the impacts of transient instability on power system reliability. Traditionally, composite system reliability evaluation has been performed based on steady-state estimation of load curtailments; system dynamics have often been ignored, mostly due to computational complexity. In this paper, three probabilistic transient stability indices are proposed to assess system robustness against dynamic contingencies and to account for system instability in computing reliability indices. A direct method is utilized for transient stability assessment based on computing the energy margin of the system under fault events (energy margins measure the ability of a system to withstand contingencies). Energy margins along with the probability of occurrences of the events are used to update the probabilistic transient stability indices. The dependencies of reliability and stability indices on the fault clearing time are also evaluated. This method is applied on the reduced Western Electricity Coordinating Council and the New England 39 bus test systems. The results indicate the importance of considering the effect of stability in reliability evaluation.

Probabilistic Transient Stability Constrained Optimal Power Flow for Power Systems With Multiple Correlated Uncertain Wind Generations

This paper proposes a novel probabilistic transient stability constrained optimal power flow (P-TSCOPF) model to simultaneously consider uncertainties and transient stability for power system preventive control. While detailed wind generator model with rotor flux magnitude and angle control strategy is used to describe the dynamic behaviors of wind generators, uncertain factors with correlations, such as probabilistic load injections, stochastic fault clearing time, and multiple correlated wind generations, are also included to form a representative P-TSCOPF model. A new GSO-PE approach, consisting of an improved group search optimization (GSO) and $2m + 1$ point estimated (PE) method with Cholesky decomposition, is then designed to effectively solve this challenging P-TSCOPF problem. The proposed P-TSCOPF model and GSO-PE solution approach have been thoroughly tested on a modified New England 39-bus system with correlated uncertain wind generations. Comparative results with Monte Carlo (MC) simulations have confirmed the validity of the P-TSCOPF model and demonstrated the effectiveness of GSO-PE method.

A Bayes Inference Method for Probabilistic Transient Stability Assessment of Power Systems

A Bayesian inference approach is proposed for power systems transient stability assessment. Such assessment is crucial for modern power systems, which must often operate close to their stability limits, and are facing increasing levels of uncertainty. In particular, the estimation of the transient instability probability of a system is discussed in the paper, with some hints to interval estimation. First, the theoretical foundations of probabilistic stability assessment are reviewed according to already established models, which allow an analytical formulation of the instability probability in terms of the basic random variables affecting stability, such as the fault clearing time and the critical clearing time. Then, the novelty of the paper is illustrated, consisting in the above estimation, motivated by the observation that the parameters of the basic random variables (e.g. the expected values of the clearing times), being unknown in practice, have to be estimated. A large series of numerical simulations show that the proposed estimation method constitutes a very efficient method. Moreover, other numerous simulations have been performed for the purpose of a robustness analysis, showing that the methodology efficiency appears to hold also when departing from the assumptions made on prior parameter distributions and also on basic model distributions