Sequential Monte Carlo Simulation Research Articles

MCS-ML based line vulnerability for infrastructural resilience assessment with multi-wind speed cyclonic zones

The resilience of critical infrastructure is paramount for power systems prone to cyclonic activities characterized by varying wind speeds. This study conducts a thorough examination of the impact of cyclone lasting for a week on transmission lines for each passing day. Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) is applied to extract hourly wind speed data for the cyclone. Sequential Monte Carlo Simulation (SMCS) is used to model the day-wise hourly transmission line fragility and determination of line vulnerabilities across high, medium, and low wind speed zones. Fragility curves are developed to depict the correlation between wind speeds and line failure probabilities in each zone. The line outage scenarios are generated based on the critical wind speeds and collapse wind speeds for each zone. Line Vulnerability Index (LVI) is proposed to determine the vulnerability and the resilience status of the transmission lines. Machine Learning (ML) based models, FFNN (Feed Forward Neural Network) and RFC (Random Forest Classifier), are proposed for assessment of infrastructure resilience by vulnerability ranking of the lines. Hourly wind speed and hourly line failure probability are the inputs to train the ML models and, LVI and ranking are predicted for the IEEE 30-bus system.

Enhancing reliability assessment in distributed generation networks: Incorporating dynamic correlation of wind-solar power output uncertainty

Amidst escalating environmental concerns and energy scarcity, the integration of distributed generation (DG) within distribution networks (DN) has emerged as a pivotal developmental trend. The uncertainty inherent in renewable energy output often disrupts DG networks. Notably, the dynamic correlation between key renewable sources, such as wind and solar energy, significantly influences the reliability analysis of these networks.To comprehensively assess the impact of wind-solar power output uncertainty and its dynamic correlation on DN reliability, this study leverages copula theory to express the dynamic correlation coefficient between wind and solar power. This coefficient is formulated as the dynamic correlation of wind-solar power through copula dynamic correlation coefficient. Employing an auto-regressive moving average (ARMA) model with constraints solved using maximum likelihood kernel (MLK), we construct the wind-solar joint output (WSJO) model. Subsequently, utilizing sequential Monte Carlo simulation (MCS) with the WSJO model, we analyze DN reliability. In case of DN failure, the WSJO model generates random samples of the wind-solar joint output sequence. Subsequent power restoration to governed islands enables the calculation of DN reliability indices. The WSJO model constructed in this study accounts for wind resource output uncertainty and dynamic correlation, aligning more closely with actual distributed generation output and enhancing the accuracy of reliability assessment. Finally, we simulate the improved IEEE-RBTS-BUS6-F4 system to underscore the crucial role of considering wind-solar energy's dynamic correlation in DN reliability assessment.

A methodology to correlate river inflows in state sampling Monte Carlo simulation

This paper proposes a methodology to sample inflow states of run-of-the-river hydropower plants that are spatially correlated, preserving the statistical dependence among them, in Non-Sequential Monte Carlo Simulation (MCS). The technique used to correlate the inflows of hydro plants in the Brazilian synthetic series generation model, which is based on the correlation matrix and Cholesky Decomposition, is adapted to be used in the sampling stage. Nataf transformation is used for addressing non-normality of the inflow data. The solution method is such that no assumption about the data probability distribution is necessary. Although the methodology is applied to inflows in this paper, it can be applied to any other quantity, such as winds. A case study is proposed to evaluate the correlation of the sampled inflows and the impact on the reliability indices. Besides, it is investigated the effect when inflows states are clustered to reduce the number of states in the system for better computational efficiency. Case study shows that the reliability indices obtained with the proposed methodology are within the confidence interval of the indices calculated by the Sequential MCS with an execution time as fast as the Non-Sequential one, while the non-consideration of correlation causes very significant errors. Simulation with 50 clusters produces equally good results with a reduction of 75 % of the execution time. Sensitivity analysis showed that halving the number of clusters maintains the accuracy of the results, while 10 clusters results in overestimating system reliability. Different degrees of correlation have been simulated, showing that the higher the correlation among the hydro plants, the less reliable the system becomes.

Sym4state.jl: An efficient computation package for magnetic materials

Exploring magnetic configurations of magnets often involves utilizing the four-state method to obtain the magnetic interaction matrix, and Monte Carlo method to simulate spin textures and phase transition processes. However, computing the interaction matrix between magnetic atoms using the four-state method requires plenty of individual calculations. Despite manual simplifying the number of individual calculations based on material's symmetry is possible, there remains a necessity for an automated approach to streamline the process for high-throughput screening of magnetic materials. Meanwhile, the traditional sequential Monte Carlo simulation encounters challenges of low efficiency and long time consuming in dealing with large systems. Furthermore, the prior parallelism in the Heisenberg model was limited to parallel computation of the system's energy or run several replicas in parallel. Hence, in our pursuit of comprehensive parallelization for the Heisenberg model, we have introduced a novel adaptation of the checkerboard algorithm, enabling a fully parallelizable simulation of the Heisenberg model. To address these problems, we have developed Sym4state.jl, a program specifically designed to simplify the computation of magnetic interaction matrix and simulate spin textures under various environmental conditions. This program, available as a Julia package, can be freely accessed at https://github.com/A-LOST-WAPITI/Sym4state.jl. Program summaryProgram title: Sym4state.jlCPC Library link to program files:https://doi.org/10.17632/s6dkmgrjfw.1Developer's repository link:https://github.com/A-LOST-WAPITI/Sym4state.jlLicensing provisions: MITProgramming language: JuliaNature of problem: Employing the four-state method to calculate magnetic interaction matrix for magnetic materials can be simplified based on material symmetry, however, there is a lack of automated approach to streamline the simplification. Additionally, the commonly used Metropolis method for simulating magnetic texture can only make parallel computation of the system's energy or run several replicas in parallel, which could hardly boost the performance when simulating the large-scale magnetic textures.Solution method: We simplify the four-state method calculations by utilizing the principles of energy invariance under symmetry operations and time reversal operations. To enhance the efficiency of the Metropolis algorithm, we have designed a strategy to divide the entire 2D lattice into multiple domains. We then execute the Metropolis algorithm in parallel for each individual domain, thereby improving the overall computational efficiency.Additional comments including restrictions and unusual features: While the methods aimed at simplifying the four-state method and parallelizing the Metropolis algorithm are applicable to both 2D and 3D systems, the current program is specifically designed for the calculation and simulation of magnetism in 2D materials. As a result, compatibility with 3D systems has not yet been implemented.

Flow-Network-Based Method for the Reliability Analysis of Decentralized Power System Topologies With a Sequential Monte-Carlo Simulation

Flow-Network-Based Method for the Reliability Analysis of Decentralized Power System Topologies With a Sequential Monte-Carlo Simulation

Application of Bayesian networks based on Sequential Monte Carlo simulation and physical model in fault diagnosis of horizontal three-phase separator system

In offshore production platforms, horizontal three-phase separator is common process equipment. Its main function is to complete the dehydration and degassing of crude oil. Separator system is more complex, and its failure may cause significant economic losses and disastrous consequences. Therefore, it is critical to accurately and quickly identify where and why faults occur in the separator system. In this study, separator fault diagnosis model based on Bayesian networks is developed. Moreover, Sequential Monte Carlo simulation and physical model are introduced to overcome field problems such as missing separator failure data and the inability of experts to provide accurate empirical knowledge. Using this model, 13 faults in a separator in an offshore crude oil processing system are successfully diagnosed. Meanwhile, the proposed model is compared with deep neural network, convolutional neural network, and deep residual network, with accuracy rates of 100%, 91.34%, 87.99%, and 94.62%, respectively. Then, the diagnostic accuracy of each model for different faults is also compared in this paper under various signal-to-noise ratios. The results show that the method proposed in this paper has better noise immunity compared to the other three models. Therefore, the accuracy and robustness of the proposed model is further demonstrated. Finally, to analyze the fault-tolerance of the proposed model, 2–3 error evidence is randomly entered. The results show that the proposed model has better fault tolerance compared to data-driven Bayesian networks.

Reliability Assessment for Integrated Seaport Energy System Considering Multiple Thermal Inertia

With the rapid development of global trade, a large number of goods and resources are imported and exported via seaports. Multiple thermal loads and renewable energy merge into seaports, making the energy supply and demand structure increasingly complex. The traditional seaport becomes an integrated seaport energy system (ISES). Due to the complicated energy interaction of cooling, heating, electricity, and gas subsystems, the ISES urgently require reliable and secure operation. Hence, this paper proposes a new reliability assessment method for the ISES that considers thermal inertia. Firstly, the operational structure of the ISES is established considering multi-energy coupling relationships. Then, a two-stage optimal load curtailment model is constructed with multiple thermal inertias. In addition, the reliability assessment method for the ISES is proposed based on the sequential Monte Carlo simulation method. Simulations are presented to verify the effectiveness of the proposed method.

Composite reliability evaluation of Integrated Nepal Power System

Abstract the worth of reliability has been increasing with the advancement of technology. Based on the involvement of the various functional zones, the assessment of the reliability of the power system is divided into 3 Hierarchy levels (HL). The composite reliability (HL II) involves the availability of generation systems and transmission systems in evaluating the reliability of power systems. In this paper, the composite reliability of the Integrated Nepal Power System (INPS) is assessed using sequential Monte Carlo Simulation (MCS). Based on the trip data of the various Hydro Electric Power Plant (HEPP) units of Nepal and of transmission line, the artificial UP and DOWN sequence of the composite system is simulated. The power output of the Hydro-Electric Power Plant (HEPP) is varied based on the variation of seasonal flow. The system state is compared with the hourly load data of various load centers of INPS to determine the reliability indices like LOLP, LOLE, and EENS. As the eastern part of INPS doesn’t have a generating unit, it is found to have lower reliability. The reliability of INPS can be improved by improving the reliability of load centers that have a lower value of reliability indices.

Reliability modeling of wave energy converters based on pelamis technology

Wave generators, as renewable sources, are increasingly applied for power generation in developed electric networks. With the development of wave generator technologies, large-scale devices such as oscillating water columns, pelamis, wave-dragon, oyster, buoy, sea wave slot cone converter, and tapchan have been invented to extract electrical power from wave energies. The output of wave generators relies on the height and period of waves, and because of the wide variation in these quantities, the produced power from them changes widely. Therefore, in electric networks incorporating large wave generators, reliability is influenced and should be analyzed. In this paper, for the first time, the reliability modeling of pelamis, as a kind of commercial-scale wave generator, is executed. In the proposed multi-state reliability model of pelamis, failures of composed components and changes in the production of power are addressed. To obtain the optimal number of power states in the model, the XB factor is computed. Then, to reduce the number of power states in the model, the fuzzy c-means clustering methodology is applied. The obtained model is used to examine the adequacy assessment of an electric network containing a pelamis farm. Numerical results show that wave converters can improve the reliability performance of electric systems. However, wave period and height affect the reliability indices of the power system. The effectiveness of the proposed method is validated by comparing the outcomes obtained by the analytical and Sequential Monte Carlo Simulation methods.

Reliability Evaluation Method of Multi-Voltage Levels Distribution System Considering the Influence of Sense-Control Terminal Faults

With the existing reliability evaluation methods, it is difficult to realize the overall evaluation of multi-voltage levels distribution systems, and sense-control terminal faults are not considered in the process of reliability evaluation. Therefore, a reliability evaluation method for multi-voltage levels distribution networks considering the influence of the fault of the sensing and control terminal is proposed. Firstly, based on the component reliability model, system state selection method, and reliability index, a reliability evaluation method for distribution networks considering sense-control terminal faults has been proposed. Secondly, the features of a multi-voltage levels distribution network are analyzed. The sequential Monte Carlo simulation method and the failure mode effects analysis method are combined, and a collaborative evaluation method for power supply reliability of multi-voltage levels distribution systems is proposed. Eventually, the effectiveness of the proposed method is proved by an example comparison, and the impact of the terminal fault on the reliability of distribution network is analyzed. The reliability evaluation results can provide technical support for the planning of the distribution network.

Quantifying the resilience of ICT-enabled grid services in cyber-physical energy system

Information and Communication Technology (ICT) is vital for the operation of modern power systems, giving rise to Cyber-Physical Energy Systems (CPESs). ICT enables the grid services (GSs) needed for monitoring and controlling the physical parameters of the power system, especially for remedying the impact of disturbances. But the ICT integration makes the overall system more complex, leading to new and unforeseen disturbances. This motivates the need for a resilient system design capable of absorbing and recovering from such disturbances. The current state of the art lacks a comprehensive resilience assessment of ICT-enabled GSs in CPESs. To address this, a novel method and metrics to assess the resilience of GSs in CPESs are presented in this paper. An operational state model of a GS, with three states, i.e., normal, limited and failed, is used to capture its performance, which is essential for quantifying its resilience. Sequential Monte Carlo simulations are performed with the model to capture the behaviour of ICT components to compute the operational state trajectory of the GSs. Metrics are then derived to quantify the resilience and its constituting phases. The method is demonstrated using two ICT system designs for the CIGRE MV benchmark grid, considering the state estimation as an exemplary GS. The simulation results show that the proposed method can capture the differences between ICT system designs with regard to resilience metrics. The contribution can, therefore, be used to analyse, compare and potentially improve the resilience of ICT system designs for CPES.

Copula based model for representation of hybrid power plants in non-sequential Monte Carlo reliability evaluation

This article aims to propose models that allow the representation of the correlation between intermittent renewable generation in reliability evaluation based on non-sequential Monte Carlo Simulation (MCS). The models make use of the theory of Copulas, specifically the theory of Archimedean Copulas. To represent hybrid power plants with different types of energy sources (wind and solar, for example), it is used the theory of Hierarchical Archimedean Copulas. The models are validated by calculating generation reliability indices by three different approaches that are then compared: sequential MCS (that uses the chronological simulation), classical non-sequential MCS (that assumes independency between random variables) and the non-sequential MCS incorporating the Copula based models. The results show that the use of Copulas is able to represent accurately the correlation and complementarity between the sources, without the computational burden of the chronological simulation.

Active learning-based structural reliability evaluation Kriging model and sequential importance sampling

The efficient analysis of structural system reliability with multiple failure modes and small failure probabilities presents significant challenges for active Kriging methods. This paper proposes a novel method, PAK-SEIS, which combines the Parallel Active learning Kriging model and the Sequential Importance Sampling method to overcome these challenges. The proposed method includes a new sequential importance sampling method that integrates the sequential Monte Carlo simulation (MCS) and kernel density estimation to construct the optimal importance density. Additionally, the proposed parallel learning strategy allows for the selection of multiple new training samples, reducing performance function calls and refining iterations of Kriging models. The PAK-SEIS method gradually approximates the optimal importance density by updating multiple new training samples and failure modes in parallel at each iteration based on a small number of candidate samples. Candidate samples generated in the final sequence can cover all limit state surfaces, and all Kriging models are accurately constructed. The PAK-SEIS method can effectively address system reliability problems with small failure probability, multiple failure regions, and implicit functions. Two examples demonstrate the efficiency and accuracy of the proposed PAK-SEIS method.

Tolerable random interruption duration based reliability estimation of stand alone hybrid renewable energy system by network reduction and sequential Monte Carlo simulation

AbstractThis paper presents a novel tolerable random interruption duration (TRID) concept for estimation of reliability indices of stand‐alone hybrid renewable energy system (SAHRES) during down time. This concept utilizes the ignorance of interruption duration if it is tolerable in event of failure. It uses a framework using network reduction technique and sequential Monte Carlo simulation (SMCS) suitable for present research whereas the solution in such cases is not feasible with analytical method. Thus reliability indices such as mean up time, mean down time, failure frequency, system failure rate, interruption duration and system unavailability are estimated using SMCS. Modelling aspects are considered for load, capacity, renewable energy system and TRID due to network outage. The impact of considering random tolerable interruption duration has been demonstrated on the reliability indices and case study is presented to show the effect of change of TRID on reliability indices. A sample SAHRES has been considered for the study.

Modeling demand flexibility impact on the long-term adequacy of generation systems

This paper proposes a novel probabilistic model for quantifying the impact of demand flexibility (DF) on the long-term generation system adequacy via Sequential Monte Carlo Simulation (SMCS) method. Unlike load shedding, DF can be considered an important instrument to postpone bulk consumption from periods with limited reserves to periods with more generating capacity available, avoiding load shedding and increasing the integration of variable renewable generation, such as wind power. DF has been widely studied in terms of its contribution to the system’s social welfare, resulting in numerous innovative approaches ranging from the flexibility modeling of individual electric loads to the definition of aggregation strategies for optimally deploying this lever in competitive markets. To add to the current state-of-the-art, a new model is proposed to quantify DF impact on the traditional reliability indices, such as the Loss of Load Expectation (LOLE) and the Expected Energy Not Supplied (EENS), enabling a new perspective for the DF value. Given the diverse mechanisms associated with DF of different consumer types, the model considers the uncertainties associated with the demand flexibility available in each hour of the year and with the rebound effect, i.e., the subsequent change of consumption patterns following a DF mobilization event. Case studies based on a configuration of the IEEE-RTS 79 test system with wind power demonstrate that the DF can substantially improve the reliability indices of the static and operational reserve while decreasing the curtailment of variable generation cause by unit scheduling priorities or by short-term generation/demand imbalances.

Scalable and portable computational framework enabling online probabilistic remaining useful life (RUL) estimation

This work demonstrates a framework that enables online prognostics in adhesive joints by estimating the real-time probabilistic remaining useful life (RUL) using ANNs based hybrid physics models and vectorized sequential Monte Carlo (SMC) simulations. The framework is developed by integrating the physics-based damage degradation model and uncertainty quantification (UQ) techniques to estimate both probabilistic fatigue failure life and RUL. The fatigue damage growth (FDG) simulator, a hybrid surrogate model that simulates real-time fatigue degradation in adhesive joints, is used. In the initial set of results, the generalized framework is validated by estimating the probabilistic fatigue failure life using two UQ methods: Markov Chain Monte Carlo (MCMC) and SMC method. The computational results are successfully compared against experimental data. The conventional MCMC sampling methods are inherently serial, which limits the exploitation of the computational speed-up provided by the FDG simulator and hinders the real-time life predictions. The SMC method quantifies the uncertainties by parallelizing the sampling process, significantly reducing computational time and enabling real-time prediction. Next, the generalized framework is used to estimate probabilistic RUL from the fatigue crack propagation data. The parallel SMC method showed very good speedup compared to the MCMC method. To further enhance the computational speed-up with SMC method, vectorized FDG simulations are introduced into the framework and good scalability is achieved. Finally, the portability of the framework is demonstrated by deploying it on the portable Raspberry Pi cluster.

Reliability Evaluation for Integrated Electricity-Gas Systems Considering Hydrogen

Regarded as the cleanest and a versatile energy carrier, green hydrogen generated with renewable energy is receiving increased attention in the transition to a carbon-neutral society. On the other hand, the integration of hydrogen tightens the coupling between power systems and natural gas systems, which highlights the importance of reliability evaluation of the integrated electricity-gas systems (IEGSs) with hydrogen. This paper proposes a reliability evaluation model for the IEGSs considering the effects of hydrogen. The power to hydrogen and methane process is proposed to convert the surplus renewable energy to hydrogen and methane, which are then mixed into natural gas systems. A novel optimal energy shedding model is proposed to explicitly account for the impact of hydrogen on the energy flow. To consider the temporal feature of renewable energy, a sequential Monte Carlo simulation approach is applied to evaluate the reliability of the IEGSs. The numerical simulations are performed on the integrated IEEE 24-bus and 20-node energy systems and the integrated IEEE 72-bus and 40-node energy systems to verify the effectiveness of the proposed model.

Reliability evaluation of high permeability renewable energy distribution network considering energy storage charge and discharge strategy

Energy storage is an important device of the new distribution system with dual characteristics of energy producing and consuming. It can be used to perform multiple services to the system, such as levelling the peak and filling the valley, smoothing intermittent generation output, renewable generation accommodation, frequency response, load following, voltage stability, etc. Energy storage’s role in enhancing the quality and reliability of power supply in the new distribution system has greatly attracted attentions. Considering the multiple functions and flexible operations of energy storage and their impact on system reliability, this paper proposes a new multi-state modelling and reliability analysis method for the new distribution network considering energy storage charge–discharge strategy. Firstly, the probability distribution of intermittent distributed generation is analysed and their multi-state models are established. Then, the typical energy storage charge–discharge operating strategies are simulated, from which their state of charge distributions are obtained and multi-state model is constructed. Finally, the reliability analysis method of active distribution network using sequential Monte Carlo simulation is established. Simulations are performed on IEEE RBTS test system, and results verify the correctness and the validity of the proposed method.

A Comparative Study Between Bayesian Network and Hybrid Statistical Predictive Models for Proactive Power System Network Resilience Enhancement Operational Planning

Enhancing the operational resilience of the distribution system network (DSN) proactively in a hurricane-prone region requires a pre-hurricane event DSN optimization model, built on accurate hurricane-induced DSN line fault prediction scenarios. In the past, the resilience evaluation methods such as statistical sequential and non-sequential Monte Carlo simulation (MCS) contingency-based technique, and Machine learning-based Bayesian Networks (BN) technique, have been proposed to strengthen the operational resilience of the DSN proactively against the forecasted oncoming hurricane events. However, a comparative study is largely unexplored to evaluate which of these two methods is best for proactive operational planning decision-making against the forecasted oncoming hurricane event. In this paper, the Bayesian network (BN) and combined statistical DSN’s Fragility-curve(FC)-Monte Carlo simulation (MCS)-Scenario reduction (SCENRED) predictive algorithms were developed. The DSN line fault prediction scenarios simulated leveraging the predicted oncoming hurricane Ewiniar data were utilized to perform pre-hurricane DSN optimization to proactively decrease the DSN expected load loss. The pre-event system optimization problems were formulated in a mixed integer linear programming (MILP) approach and solved using a CPLEX solver in general algebraic modelling system (GAMS) on a redesigned 48-bus DSN. The simulated initial expected load loss of 39% of 35 MWh was decreased to 35.34%, and then to 30.71% with the use of combined statistical DSN’s FC-MCS-SCENRED, and the BN-DSN predictive models. These results were validated using the Electrical transient analyzer program (ETAP).This study confirmed that the BN-DSN predictive model is a better operational planning tool compared to combined statistical DSN’s line FC-MCS-SCENRED predictive model.

Reliability assessment of cyber-physical power systems considering the impact of predicted cyber vulnerabilities

This paper presents a reliability assessment technique for cyber-physical power systems (CPPSs) that incorporates cybersecurity issues by considering non-normal random variables with non-linear dependencies. Our model uses bidirectional encoder representations from transformers (BERTs) to predict the severity of cyber vulnerabilities by analyzing their textual description. This practical model allows the engineer to manually enter text that describes threats to predict the probability of cyber vulnerability. We use a Bayesian attack graph to simulate the attack paths and a Markov model to demonstrate the consequences of cyber attacks on the CPPS. Furthermore, a hybrid approximate-analytical approach is employed to assess the overall reliability of the CPPS when considering the load and wind generation uncertainties, given their non-linear dependencies. The proposed method is implemented on the modified IEEE Reliability Test System. The results demonstrate that the reliability indices for a simultaneous cyber attack on corporate networks and wind farm control centers are more significant than those obtained for other attack scenarios. The proposed prediction method is highly accurate, and the predicted vulnerability scores align with those provided by the National Vulnerability Database. The results are compared with sequential Monte Carlo simulation, subset simulation, and cross-entropy-based importance sampling methods. The comparison shows that the proposed method outperforms other methods in terms of convergence speed and accuracy.