Composite System Reliability Evaluation Research Articles

An efficient cross-entropy method addressing high-dimensional dependencies for composite systems reliability evaluation

Cross-entropy (CE) based importance sampling (IS) accelerates the reliability evaluation of power system greatly, but is mainly focused on the CEIS of independent random variables (RVs) or low-dimensional correlated RVs (CRVs). To extend the CE method to high-dimensional CRVs while avoiding the “curse of dimensionality” in optimizing a high-dimensional IS probability density function (IS-PDF), an efficient CE method termed as CE-DRDM, is developed from a dimension-reduced dependence model (DRDM). First, based on the DRDM’s original hierarchical disaggregate structure (HDS), the CE-DRDM which conducts the CEIS for a single aggregate RV rather than the high-dimensional CRVs is proposed. Second, to solve the issue that the performance of CE-DRDM may degrade in the case of high penetration of renewable energy, the CE-DRDM is enhanced by improving the DRDM’s HDS, and then a novel CE optimization method is proposed, through which the analytical updating formulas of IS-PDF parameters can be derived. Thirdly, the CE-DRDM is further enhanced by using a sparse density estimator, based on which the number of IS-PDF parameters needed to be optimized in the CE optimization reduces greatly, and consequently the optimization accuracy improves accordingly. Finally, the validity of CE-DRDM is verified by several numerical cases with high-dimensional dependencies.

Cross-entropy based importance sampling for composite systems reliability evaluation with consideration of multivariate dependence

Multivariate kernel density estimation (KDE) is powerful for dependence modeling, but producing a non-sparse probability density estimation model. To address this issue, a sparse density estimation technique termed as generalized cross-entropy (GCE) density estimator, is proposed to estimate the joint probability density function (PDF) of correlated random variables (RVs). Moreover, to effectively accelerate the composite systems reliability evaluation, a unified cross-entropy based importance sampling (CEIS) method accommodating both GCE and KDE density estimators is presented, and a creative CE optimization approach is also developed based on the composition sampling algorithm, through which the analytical updating rules of IS-PDF parameters can be derived even though GCE and KDE estimators do not belong to the exponential distribution family (EF). Compared to the KDE estimator, the GCE estimator encounters much less dimensionality difficulty in CE optimization due to the model sparsity merit, and consequently achieves more accurate IS-PDF parameters and better CEIS efficiency. The superiority of GCE estimator over KDE estimator in correlation modeling and CEIS is verified by several numerical tests.

Cluster-based stratified sampling for fast reliability evaluation of composite power systems based on sequential Monte Carlo simulation

An essential aspect in the operation and expansion of the electricity infrastructure is to ensure a reliable power supply, despite uncertainty (mainly caused by random failures, variability of renewable sources, and load growth). Reliability evaluation of composite power systems is a valuable tool for identifying possible deficiencies in operation. Power systems operation is becoming more variable and stochastic. Consequently, there is an urgent need to update the tools used to analyze their reliability. This article presents a novel method based on cluster-based stratified sampling (CBSS) and sequential Monte Carlo simulations (SMCS) to improve the reliability evaluation of composite power systems. Here, clustering algorithms are applied to reduce the number of observations required by traditional SMCS. The proposed approach is applied to RTS-79, RTS-96, and RTS-GMLC electrical networks to verify its accuracy and speed. The results obtained demonstrate that CBSS increase calculation speed in highly reliable networks, while preserving information on the probability distribution of the reliability indices.

Reliability evaluation of composite generation and transmission systems via binary logistic regression and parallel processing

In power system planning studies that involve the search for optimal investments with low risks for the power grid, probabilistic reliability assessments provide very useful tools and indices. A challenge faced in the application of these tools is related to the computational effort demanded by the evaluation process, especially when the combined effects of failure of generation and transmission equipment are considered. In this context, the present work proposes a new method for efficient estimation of the main composite reliability indices by combining Binary Logistic Regression (BLR) technique, a machine learning tool used for binary data classification, with the non-Sequential Monte Carlo simulation (NS-MCS) method. In addition, a computational parallelization strategy is incorporated to the proposed method to improve even more the efficiency of the composite reliability assessment. The performance of the proposed approach is analyzed by evaluating composite reliability indices for the IEEE-RTS considering two different generation and load scenarios, in addition to a real large-scale power system. The results obtained are compared with those using the NS-MCS method in its conventional version.

Reliability evaluation of a composite power system in the presence of renewable generations

Power system reliability evaluation plays a vital role in the planning and operation studies by reflecting the system safety level. In this paper, a combination of a non-sequential Monte Carlo simulation (MCS)-based model and an improved Estimation of Distribution Algorithm (EDA) is exploited for evaluating the reliability of the composite power systems considering variability and uncertainty of wind farms (WFs) and Photovoltaic (PV) units. Variability of these resources is defined as the random fluctuation of wind speed and solar irradiation caused by changes in the atmosphere, while their uncertainty results from output power forecast errors. In the proposed model, the states of traditional generating units, transmission lines, WFs, and PV units are constructed using non-sequential MCS. These states can be achieved based on the component failure probability for dispatchable traditional generators and transmission lines along with the Probability Distribution Functions (PDFs) of renewable generations. To enhance the computational efficiency of the MCS in the sampling step, the improved EDA upgraded with the Population-Based Incremental Learning (PBIL) algorithm is employed. The proposed mathematical model for reliability evaluation of composite power system is applied to the IEEE RTS 24-bus system, and numerical studies are performed under several case studies. The simulation results confirm the proficiency of the proposed method to improve the computational efficiency, while the high accuracy of reliability evaluation of the composite power system is attained.

A convolutional neural network-based approach to composite power system reliability evaluation

This paper proposes a machine learning-based approach in conjunction with Monte Carlo simulation (MCS) to improve the computation efficiency of composite power system reliability evaluation. Traditional composite system reliability evaluation approaches are computationally demanding and may become inapplicable to large integrated power grids due to the requirements of repetitively solving optimal power flow (OPF) for a large number of system states. Machine learning-based approaches have been used to avoid solving OPF in composite system reliability evaluation except in the training stage. However, current approaches have been derived to classify system states into success and failure states (i.e., up or down). In other words, they can be used to evaluate power system probability and frequency reliability indices, but they cannot be used to evaluate power and energy reliability indices unless OPF is solved for each failure state to determine minimum load curtailments. In this paper, a convolutional neural network (CNN)-based regression approach is proposed to determine the minimum amount of load curtailments of sampled states without solving OPF, except in the training stage. Minimum load curtailments are then used to evaluate power and energy indices (e.g., expected demand not supplied) as well as to evaluate the probability and frequency indices. The proposed approach is applied on several systems including the IEEE Reliability Test Systems (The IEEE RTS and IEEE RTS-96) and Saskatchewan Power Corporation in Canada. Results show that the proposed approach is computationally efficient (fast and accurate) in calculating the most common composite system reliability indices. The developed source code of the proposed method is available to the community for future research and development.

Modeling multivariate dependence by nonparametric pair-copula construction in composite system reliability evaluation

The correlated variation of bus loads, wind powers, etc., has a significant impact on the power system operation risk. The construction of the accurate dependence model becomes vital in the field of power system reliability evaluation. Most currently used methods in estimating the multivariate joint probability density function (PDF) may encounter obstacles such as modeling accuracy and the curse of dimensionality, especially in the high-dimensional case. To address such problems, a nonparametric pair-copula construction (NPCC), which decomposes the joint PDF into a product of marginal PDFs and a set of bivariate copula (also called pair-copula) densities based on graph theoretic algorithm, is used in this paper to achieve an accurate modeling of the multivariate correlation. To construct a unified framework of nonparametric estimation, the marginal PDFs and the bivariate copula densities are both estimated in a data-driven mode. Moreover, a PDF transformation method is also proposed in estimating the bivariate copula densities, aiming to avoid the problem that the distribution range of the transformed variables in the pair-copula densities exceeds its feasible domain. The performance of the proposed NPCC is verified by a modified version of IEEE-RTS79 with complex correlation among bus loads and wind powers.

Dimension Reduction Based Non-Parametric Disaggregation for Dependence Modeling in Composite System Reliability Evaluation

The correlated variation of bus loads and wind powers has posed a challenge to power system security. How to construct an accurate dependence model becomes vital for power system reliability evaluation. Most currently used methods in estimating the multivariate probability density function (PDF) not only ignore the aggregation constraint but also encounter the curse of dimensionality. In this paper, a new non-parametric disaggregation (ND) technique is presented to disaggregate an aggregate variable (e.g. system load) into non-aggregate variables (e.g. bus loads) while meeting the aggregation constraint. An innovative hierarchical dimension reduction technique is proposed and integrated into the ND model to transform a high-dimensional conditional PDF estimation into some low-dimensional estimations, which effectively resolves the difficulty associated with high dimensionality. The above two techniques are incorporated into an effective three-stage conditional sampling method to form the proposed dimension reduction based ND model (DRND) for high-dimensional dependence modeling in composite system reliability evaluation. The validity of the proposed DRND is verified by three test systems, i.e. MRTS79, MRTS96, and the latest RTS-GMLC.

Composite System Reliability Evaluation With Essential Reliability Services Assessment of Wind Power Integrated Power Systems

With the increasing penetration of renewable resources and the retirements of conventional coal-fired generation units, power systems are undergoing significant transformation with the instantaneous renewable generation penetration sometimes approaching over 50 percent of the demand. This transformation makes the need for comprehensive reliability assessment critical to properly account for the composite system adequacy and the sufficiency of essential reliability services (ERSs). This paper introduces a probabilistic approach to evaluate the reliability of wind power integrated power systems considering ERSs including frequency and voltage support, in conjunction with resource adequacy. To consider stochasticity in system operating conditions, the proposed approach utilizes sequential Monte-Carlo Simulation (SMCS) as the probabilistic analysis methodology and formulates probabilistic reliability metrics representing the composite system adequacy and the ERSs. The proposed approach and metrics are demonstrated on a synthetic test system. Simulation results illustrate the efficacy of the proposed approach and its importance in analyzing the impact of increasing wind power penetration as well as wind turbine generators (WTGs) providing ERSs on system reliability.

Data‐driven efficient reliability evaluation of power systems with wind penetration: an integrated GANs and CE method

The conventional Monte Carlo simulation may not be efficient enough for reliability evaluation of composite power systems. The cross-entropy (CE) algorithm is a promising state-of-the-art fast sampling method, while it has not been well developed in this field due to the implicit probability distributions of penetrated renewable energies. Specifically, the CE sampling requires the distributions of interest to be explicit and parametric, while some preconceived probabilistic distribution functions (PDFs) such as the Weibull distribution of wind speed make the results to deviate from the reality sometimes. In this study, a data-driven efficient approach for reliability evaluation of power systems with wind penetration is proposed utilising generative adversarial networks (GANs) and CE sampling. The distributions of wind speeds in multiple wind farms are estimated by GANs considering their spatial correlation without any prior knowledge. With the trained generative network mapping from the explicit Gaussian noise to the raw wind speed data, the CE sampling is successfully enabled to efficiently sample the system states with implicit PDFs, which are associated with wind speeds and component failures. A real wind speed dataset and the RTS testing system are utilised to verify the proposed integrated method, including the accuracy of distribution estimation and reliability evaluation result, as well as the speed-up efficiency of sampling.

Probabilistic Operational Reliability of Composite Power Systems Considering Multiple Meteorological Factors

External weather conditions have significant effects on the operation of composite power systems. Stochastic renewable generations, random loads, dynamic thermal ratings, and failure probabilities of outdoor power devices are all influenced by diverse meteorological factors. To integrate the probabilistic impacts of multiple meteorological factors and their resulting uncertainties, a new nested sampling framework for probabilistic operational reliability evaluation of composite power systems is proposed. As one critical step of the framework, a general modeling method to fit the probability distribution of each meteorological factor at each time point by historical weather records is presented in details, and several specific distributions are introduced for the first time to refine the accuracy of probabilistic weather representation. In subsequent tests, the actual failure records and corresponding meteorological data are used to validate the performance of the proposed framework. Several existing methods, considering but not fully considering meteorological effects, are adopted for comparisons to verify the effectiveness of the proposed method in the test case. As one benefit of the proposed framework, uncertainty importance measures of all involved random variables are available and discussed as well.

Enhanced Cross Entropy Method for Composite Power System Reliability Evaluation

Cross entropy method (CEM) can effectively accelerate the reliability evaluation of power system. It is mainly utilized to conduct importance sampling (IS) on discrete component state variables and independent or fully correlated continuous variables. To carry out IS on continuous variables with complicated correlation, this paper proposes an enhanced CEM (ECEM) that addresses the following two problems: the first one is the probabilistic modeling of the joint probability density function (PDF) for the correlated continuous variables, and the second one is the IS on the modeled joint PDF. For the first one, a Gaussian mixture model (GMM) is utilized to estimate the original joint PDF of correlated continuous variables. For the second one, the parameters of the GMM based joint PDF are optimized directly by a direct-updating-rule based method (DURM) to obtain the optimal IS-PDF. Furthermore, as an alternative to DURM, a Nataf transformation based method (NTM) is also presented to distort the parameters of the GMM-based joint PDF indirectly. Compared with NTM, which is suitable for normal copula correlation, DURM has a much wider application scope without any restriction on the correlation type. Finally, an improved unbiased estimator for the reliability index is presented to further accelerate ECEM. Test studies on RTS79 and MRTS with wind farm verify the effectiveness of ECEM.

The reliability and operation test system of power grid with large-scale renewable integration

This paper proposes a reliability and operational test system named XJTU-ROTS2017, characterized by large-scale renewable power integration and long-distance transmission. The test system has 38 nodes, 63 lines, 15 transformers and 20 generators in three areas, with peak load 10,421 MW and total installed capacity 16050 MW. Electricity primarily transmits from a resource-rich area to a load area, carrying wind/solar power generation. The determination of component parameters and grid topology is based on design manuals and typical practices. The test system can be conveniently applied to reliability evaluation and operation optimization of composite power systems integrating coal/hydro/solar/wind resources. Finally, the extended applications to AC/DC hybrid power systems and interconnected power systems are discussed.

A Hybrid Monte Carlo Simulation and Multi Label Classification Method for Composite System Reliability Evaluation

This paper presents a new approach for reliability evaluation of composite power systems by combining Monte Carlo simulation and multi label k-nearest neighbor (MLKNN) algorithm. MLKNN is a classification technique in which target vector of each instance is assigned into multiple classes. In this paper, MLKNN is used to classify states (failure or success at system or bus level) of a complete power system without requiring optimal power flow (OPF) analysis, except in the training phase. As a result, the computational burden to perform OPF is reduced dramatically. For illustration, the proposed method is applied to the IEEE 30 BUS Test System and IEEE Reliability Test System. The obtained results from various case studies demonstrate that MLKNN based reliability evaluation provides promising results in both classification accuracy and computation time in evaluating the composite power system reliability.

MPLP-Based Fast Power System Reliability Evaluation Using Transmission Line Status Dictionary

Composite power system reliability evaluation is computationally time-consuming because the optimal power flow (OPF) with the least load curtailment is calculated for a large number of samples. Most current studies of probabilistic simulation methods focus on sampling techniques to improve the sampling efficiency and decrease the calculations of the OPF. This paper proposes a fast reliability evaluation method that accelerates the calculation of the OPF using multi-parametric linear programming (MPLP). In this paper, the sampled transmission line statuses are considered by the transmission line status dictionary (TLSD). We match the line status of each sample with the scenarios in the TLSD. For matching samples, the generation status and the sampled load are treated as MPLP parameters of the DC-OPF evaluation model. A dynamic learning algorithm is applied to solve the MPLP problem. Case studies are conducted on both IEEE Reliability Test Systems and a provincial power system in China. The results show that the proposed method improves the evaluation efficiency by 23–30 times compared with the normal DC-OPF-based model.

Analytical model for fast reliability evaluation of composite generation and transmission system based on sequential Monte Carlo simulation

This paper proposes an analytical reliability evaluation (RE) model for composite generation and transmission system (CGTS) based on the sequential Monte Carlo simulation (MCS) method. The main idea is to partition the chronological system state sequence produced by sequential MCS into a set of mutually exclusive events based on the law of total probability. An analytical model is developed by extracting the component reliability parameters (CRPs) from system reliability index calculation formula of each mutually exclusive event. Once the proposed model is established, system reliability indices with variable CRPs can be obtained directly, rather than repeatedly performing the time-consuming sequential MCS process. In addition, sensitivity coefficients of system reliability indices with respect to CRPs can be obtained using the developed analytical model. A 4-unit generation system, the CGTS of IEEE-RTS system and a 91-bus power system are used for case study to validate the correctness and effectiveness of the proposed analytical RE model.

Contingency selection and ranking for composite power system reliability evaluation

In this paper, a probabilistic performance index (PI) has been developed to perform contingency selection and ranking. The results show that considering up to the second level contingency is satisfactory for both accuracy and computation time requirements. The results obtained constitute an essential basis for the analysis of power systems in terms of adequacy assessment and reliability evaluation. To substantiate the study results, comparison with other similar studies was performed.

Probabilistic Performance Index based Contingency Screening for Composite Power System Reliability Evaluation

Composite power system reliability involves assessing the adequacy of generation and transmission system to meet the demand at major system load points. Contingency selection was being the most tedious step in reliability evaluation of large electric systems. Contingency in power system might be a possible event in future which was not predicted with certainty in earlier research. Therefore, uncertainty may be inevitable in power system operation. Deterministic indices may not guarantee the randomness in reliability assessment. In order to account for volatility in contingencies, a new performance index proposed in the current research. Proposed method assimilates the uncertainty in computational procedure. Reliability test systems like Roy Billinton Test System-6 bus system and IEEE-24 bus reliability test systems were used to test the effectiveness of a proposed method.

Reliability Evaluation of Composite Power Systems Considering Wind Farms Based on Cross Entropy and Dynamic Orthogonal List

With large-scale wind farms integrated into power systems, the computational requirements for reliability evaluation of composite power systems are increasing. This paper introduces a new concept of dynamic orthogonal list, which is a form of multiple failure retrievals to avoid repeatedly calling the optimal power flow (OPF) program in the stage of state evaluation. An existing algorithm of cross-entropy (CE) method was developed to deal with the rare events in sampling. The major contribution of CE is to achieve convergence faster and reduce the number of samples, thus shortening the consuming time in the stage of sampling. This paper proposes a fast reliability evaluation process which combines the CE method with dynamic orthogonal list (CE-DOL), comprehensively improving the computational efficiency of Monte Carlo simulation (MCS). The proposed method is tested on a modified IEEE-RTS 79 system. In addition, for comparison purposes, the efficiencies of MCS, CE, and CE-DOL are estimated in the cases of different system adequacies. It is shown that, in range of certain reliability level, the proposed method is much more efficient compared with the CE method. Finally, the applicability of different methods is analyzed under different system reliability levels.

A Systematic Review of Reliability Studies on Composite Power Systems: A Coherent Taxonomy Motivations, Open Challenges, Recommendations, and New Research Directions

Power systems has been subjected to significant upgrades in terms of structure and capacity. Reliability evaluation of composite power systems has surfaced as an essential step in operation and planning stages of the modern power system. It is an effective tool to investigate the ability of power systems to supply customers with reliable power service. The purpose of this review is to enhance the knowledge of reliability studies conducted on composite power systems by providing a critical and systematic review. This work investigates peer-reviewed articles published between 2007 and 2017 in three reliable databases. The findings reveal that the reliability of composite power systems has received considerable attention over the last few years. Secondly, investigation studies demonstrated a crucial role in verifying the impact of adopting new technologies. Third, studies on this topic have been intensively conducted in Asia, which highlights the promising sectors in these regions. However, researchers have generally focused on developing several aspects (e.g., evaluation speed and wind power integration) at the expense of others (e.g., realistic studies and other renewable energy resources). The lack of practical applications is evident in the surveyed publications. These findings imply a potential incoordination between the needs of the real applications and researchers’ tendencies. Future reliability evaluation scholars are advised to consider the findings of this systematic review including concentrating on insufficiently covered topics and enhance the coordination among the efforts devoted in this area.