Probabilistic Security Assessment Research Articles

A machine-learning based probabilistic perspective on dynamic security assessment

Probabilistic security assessment and real-time dynamic security assessments (DSA) are promising to better handle the risks of system operations. The current methodologies of security assessments may require many time-domain simulations for some stability phenomena that are unpractical in real-time. Supervised machine learning is promising to predict DSA as their predictions are immediately available. Classifiers are offline trained on operating conditions and then used in real-time to identify operating conditions that are insecure. However, the predictions of classifiers can be sometimes wrong and hazardous if an alarm is missed for instance.A probabilistic output of the classifier is explored in more detail and proposed for probabilistic security assessment. An ensemble classifier is trained and calibrated offline by using Platt’ scaling to provide accurate probability estimates of the output. Imbalances in the training database and a cost-skewness addressing strategy are proposed for considering that missed alarms are significantly worse than false alarms. Subsequently, risk-minimised predictions can be made in real-time operation by applying cost-sensitive learning. Through case studies on a real data-set of the French transmission grid and on the IEEE 6 bus system using static security metrics, it is showcased how the proposed approach reduces inaccurate predictions and risks. The sensitivity on the likelihood of contingency is studied as well as on expected outage costs. Finally, the scalability to several contingencies and operating conditions are showcased.

Theory and Method of Power System Integrated Security Region Irrelevant to Operation States: An Introduction

Abstract How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem. The computational burden of probabilistic security assessment is even more unimaginable. In order to solve such problems, a security region (SR) methodology is proposed, which is a brand-new methodology developed on the basis of the classical point-wise method. Tianjin University has been studying the SR methodology since the 1980s, and has achieved a series of original breakthroughs that are described in this paper. The integrated SR introduced in this paper is mainly defined in the power injection space, and includes SRs to ensure steady-state security, transient stability, static voltage stability, and small-disturbance stability. These SRs are uniquely determined for a given network topology (as well as location and clearing process for transient faults) and given system component parameters, and are irrelevant to operation states. This paper presents 11 facts and related remarks to introduce the basic concepts, composition, dynamics nature, and topological and geometric characteristics of SRs. It also provides a practical mathematical description of SR boundaries and fast calculation methods to determine them in a concise and systematic way. Thus, this article provides support for the systematic understanding, future research, and applications of SRs. The most critical finding on the topological and geometric characteristics of SRs is that, within the scope of engineering concern, the practical boundaries of SRs in the power injection space can be approximated by one or a few hyperplanes. Based on this finding, the calculation time for power system probabilistic security assessment (i.e., risk analysis) and power system optimization with security constraints can be decreased by orders of magnitude.

Framework for trajectory‐based probabilistic security assessment of power systems

Transmission system operators prepare against threats to system security through preventive actions and the planning of corrective actions. Required actions are determined by performing security analyses according to some reliability management approach and criterion. Probabilistic approaches have been proposed as an alternative to the deterministic N − 1 approach, by using a probabilistically filtered contingency list. This study begins by formally defining system trajectories, as a means of connecting the initiating contingency to the system response, corrective control, and restoration activities. A system trajectory considers the realisation of exogenous variables, as well as a sequence of contingencies and the subsequent system response and control behaviours. Using this definition, it is argued that the system trajectory should be modelled until service and component outages are resolved, rather than only modelling its reaction to the initiating contingency. The authors then propose some simplifying assumptions to achieve a scalable approach to probabilistic real-time security assessment. To support this argument, contingency-based and trajectory-based probabilistic security assessments are compared in terms of their residual risk (the risk associated with future system trajectories that are not modelled). This comparison shows that security assessments based on trajectories allow for previously implicit assumptions on modelling accuracy to be made explicit.

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.

Transient stability probability of a power system incorporating a wind farm

An analytical approach for probabilistic evaluation of transient stability of a power system incorporating a wind farm is presented in this study. Based on the fact that the boundary of practical dynamic security region (PDSR) of a power system with double fed induction generators (DFIG) can be approximated by one or few hyper-planes in nodal power injection space, transient stability criterion for given configurations of pre-fault, fault-on and post-fault of a power system is to be expressed by certain expressions of linear combination of nodal injection vector and the transient stability probability (TSP) is further obtained with a much more simplified expression than the complex integral. Furthermore, considering uncertainties of nodal injection power including wind power and load, TSP is calculated analytically by Cornish-Fisher expansion, which can provide reliable evaluation results with high accuracy and much less computing time compared with Monte Carlo simulation. TSP and its visualization can further help operators and planners be aware of the degree of stability or instability and find critical components to monitor and reinforce. Test results on the New England 10-generators and 39-buses power system show the method’s effectiveness and significance for probabilistic security assessment.

Probabilistic energy security analysis for development of the energy system

ABSTRACTThe aim of the article is to present the method of probabilistic energy security assessment and evaluate energy security of the development scenarios of the central heat system for strategic planning. The method of energy security assessment is introduced, including a model of formation of disturbances from threats and a model of development of a disrupted energy system as well as the algorithm of calculation of the energy security coefficient. The article also presents a few scenarios (on various disturbances) for the development of the Kaunas city district heating system: one generation technology in a monopoly scenario, and limited monopoly where the capacity is limited to 60% and 40% for one generation technology. Sensitivity analysis identified the most important parameter of the energy system: energy generation monopoly factor.

An importance sampling technique for probabilistic security assessment in power systems with large amounts of wind power

Larger amounts of variable renewable energy sources bring about larger amounts of uncertainty in the form of forecast errors. When taking operational and planning decisions under uncertainty, a trade-off between risk and costs must be made. Today's deterministic operational tools, such as N-1-based methods, cannot directly account for the underlying risk due to uncertainties. Instead, several definitions of operating risks, which are probabilistic indicators, have been proposed in the literature. Estimating these risks require estimating very low probabilities of violations of operating constraints. Crude Monte-Carlo simulations are very computationally demanding for estimating very low probabilities. In this paper, an importance sampling technique from mathematical finance is adapted to estimate very low operating risks in power systems given probabilistic forecasts for the wind power and the load. Case studies in the IEEE 39 and 118 bus systems show a decrease in computational demand of two to three orders of magnitude.

A probabilistic security assessment approach to power systems with integrated wind resources

Renewable energy sources, such as wind and photovoltaic solar, have added additional uncertainty to power systems. These sources, further to the conventional sources of uncertainty due to stochastic nature of both the load and the availability of generation resources and transmission assets, make clear the limitations of the conventional deterministic power flow in power system analysis and security assessment applications. In order to manage uncertainties, probabilistic approaches can provide a valuable contribution.In this paper, we propose a new scheme for probabilistic security assessment. The model can deal with various types of probability distributions modeling power injections and can explicitly represent the effects on system security of correlation among nodal power injections (such as wind power) and of contingencies due to branch and generating unit outages. In addition, the steady-state behavior of the frequency regulation is explicitly included in the model. A new approach to deal with current limits is also proposed.Extensive testing on both the modified IEEE-14 bus test system and the Sicilian power system indicates good performance of the proposed approach in comparison with the result obtained by the computationally more demanding Monte Carlo approach.

Probabilistic steady-state and dynamic security assessment of power transmission system

Two-level system model based probabilistic steady-state and dynamic security assessment model is introduced in this paper. Uncertainties of nodal power injection caused by wind power and load demand, steady-state and dynamic security constraints and transitions between system configurations in terms of failure rate and repair rate are considered in the model. Time to insecurity is used as security index. The probability distribution of time to insecurity can be obtained by solving a linear vector differential equation. The coefficients of the differential equation are expressed in terms of configuration transition rates and security transition probabilities. The model is implemented in complex system successfully for the first time by using the following effective measures: firstly, calculating configuration transition rates effectively based on component state transition rate matrix and system configuration array; secondly, calculating the probability of random nodal power injection belonging to security region effectively according to practical parts of critical boundaries of security region represented by hyper-planes; thirdly, locating non-zero elements of coefficient matrix and then implementing sparse storage of coefficient matrix effectively; finally, calculating security region off-line for on-line use. Results of probabilistic security assessment can be used to conduct operators to analyze system security effectively and take preventive control. Test results on New England 10-generators and 39-buses power system verify the reasonableness and effectiveness of the method.

Power system probabilistic security assessment using Bayes classifier

This paper presents a method for power system security assessment based on the Bayes classifier. This method can be applied to calculate probabilistic security indices as well as on-line security assessment. In general, the determination of security breach is a cumbersome and time-consuming process due to dynamic and steady-state effects. These effects can be incorporated by considering transient stability, satisfaction of system load without violation of constraints, and voltage stability studies. The variation of the system load, as well as contingencies, may cause system transition to a different operating state. It is impractical if not impossible to evaluate all these situations, such as contingencies resulting from load variation. The straightforward Monte Carlo simulation, one of the possible methods in power system reliability analysis, requires the evaluation of a system operating state for each sampled state and is computation-intensive. In the proposed method, first the joint probability density of feature vectors has been obtained by using some training data. Once this joint distribution is obtained, the Bayes classifier provides the assessment of system security without complicated contingency analyses and can reduce the computational burden. Security status of a given feature vector can be determined by a posteriori probability rule called Bayes rule, which can be implemented in on-line security assessment or power system reliability studies.

A Probability Method for Bulk Power System Security Assessment, II - Development of Probability Models for Normally-Operating Components

The paper continues the discussion of a probability method for the "on-line" assessment of the near-term future security of an operating bulk power system begun in Reference [1]. The present paper presents the development of probability models for normally- operating components needed for implementation of the probabilistic security assessment method.