Non-sequential Monte Carlo Simulation Research Articles

Optimal power flow in hybrid AC-DC systems considering N-k security constraints in the preventive-corrective control stage

The optimal power flow methods for AC-DC systems containing VSC-HVDC generally only consider the economy during normal operation, overlooking the distribution of line transmission power in fault conditions. As a result, lines that continue to operate after a fault may experience overloading or operate at full capacity. Thus, a method for optimal power flow calculation is proposed that incorporates N-k security constraints in the preventive-corrective control stage for secure and economic operation of hybrid AC-DC systems. This method ensures that the line transmission power in the system meets the limits in the normal, short-term fault, and long-term fault states. In addition to the optimal power flow in the normal state, the method incorporates the system's imbalance as an indicator to evaluate system resilience. It combines this indicator with the economic, network loss, and performance metrics of the system, forming a two-stage bi-level multi-objective optimization model. Furthermore, to address the curse of dimensionality in anticipating system fault sets, a method for generating the anticipated fault set using non-sequential Monte Carlo simulation is proposed, along with a fault scenario search approach based on robust thinking to identify the most severe faults. Finally, the traditional IEEE 30-bus system was improved, and simulation verification was conducted using examples of an AC/DC system with a three-terminal DC network and a wind-solar-storage hybrid AC/DC system with a three-terminal DC network. The simulation results indicate that the proposed optimal power flow method considering the preventive-corrective control stage with N-k security constraints can effectively enhance system resilience. Furthermore, it improves the economic efficiency while ensuring the secure operation of the system.

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.

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.

Reliability Assessment of Power Systems in High-Load Areas with High Proportion of Gas-Fired Units Considering Natural Gas Loss

The “dual-carbon” policy underscores the crucial importance of a secure and stable natural gas supply to ensure the reliable operation of power systems. In high-load areas with a high proportion of gas-fired units and no alternative energy supply, urgent attention needs to be paid to the impact of natural gas loss on power system reliability. Given this background, a method to evaluate power system reliability that considers natural gas supply fluctuations is proposed. In this method, a reliability model of the natural gas supply chain based on the minimal cut set theory is constructed and the influence of policy regulations and economic market factors on system components is quantified. Then, a reliability-evaluation model for a power system that considers gas loss is constructed, and a non-sequential Monte Carlo simulation is used to solve it. Afterward, a reliability-evaluation method considering the power system reserve capacity is proposed. Finally, case studies on a natural gas system with a 14-node power system of a certain area are performed to verify the effectiveness of the proposed method, and the simulation results demonstrate that the reliability of the energy supply directly affects the reliability of the power system.

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.

Model-and-data hybrid driven method for power system Operational reliability evaluation with high penetration of renewable energy

With the rising penetration of renewable energy, the fluctuation of operating conditions such as wind speed and light intensity affects the reliability of the power system. It leads to the repeated reliability evaluation of the power systems and increases the computational complexity. Based on the non-sequential Monte Carlo simulation (NMCS) and back propagation neural network (BPNN), a new model-and-data hybrid driven method for power system reliability evaluation is proposed. Firstly, NMCS is used to calculate the system reliability indices under different operating conditions to obtain the input data for neural network training. Then, the proposed Multiple BPNN (M-BPNN) is used to establish the highly nonlinear mapping relationship between operating conditions and system reliability indices, which can significantly reduce the calculation time of power system operational reliability evaluation with high penetration of renewable energy. The IEEE-RTS 79 system is used to verify the effectiveness and efficiency of the proposed method, and sensitivity analysis is performed.

Incorporating gas pipeline leakage failure modes in risk evaluation of electricity-gas integrated energy systems

In order to incorporate the gas leakage failure in the EGIES risk evaluation, a multi-state Markov state transition model considering gas pipeline leakage is creatively developed, and the analytical formulas to calculate the involved transition rate parameters in this model are derived. The concept of virtual gas load is presented to reflect the impacts of gas pipeline leakage on the operation of natural gas network, and then the EGIES network analysis model considering the virtual load nodes is presented. A bi-level sampling method based on the mixed sequential and non-sequential Monte Carlo simulation is proposed to simulate the chronological and non-chronological aspects of EGIES simultaneously. The load curtailment based EGIES risk indices, including the gas leakage risk indices, are also designed. An EGIES with a modified RBTS and a 7-node gas system is used to demonstrate the application of the proposed method. The results indicate that pipeline leakage failures have significant impacts on the reliability of EGIES. Ignoring pipeline leakage failures in the risk evaluation of EGIES will result in an overly underestimation of system risk.

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.

Demand Management for Resilience Enhancement of Integrated Energy Distribution System against Natural Disasters

For energy sustainability, the integrated energy distribution system (IEDS) is an efficient and clean energy system, which is based on the coordinated operation of a power distribution network, a gas distribution network and a district heating system. In this paper, considering the damage of natural disasters to IEDS, a demand management strategy is proposed to improve resilience of IEDS and ensure stable operation, which is divided into three stages. In the first stage, the electricity, natural gas and thermal energy are co-optimized in the simulating fault state to develop the importance ranking of transmission lines and gas pipelines. In the second stage, the natural disasters are classified as surface natural disasters and geological natural disasters. According to the types of natural disasters, the demand management strategy includes semi-emergency demand management scheme and full-emergency demand management scheme in the electrical resilience mode and the integrated resilience mode, respectively. In the third stage, the non-sequential Monte-Carlo simulation and scenario reduction algorithm are applied to describe potential natural disaster scenarios. According to the importance ranking of transmission lines and gas pipelines, a demand management strategy is formulated. Finally, the proposed strategy is applied on an IEEE 33-bus power system and a 19-node natural gas system. Its effectiveness is verified by numerical case studies.

Well-Being Analysis Applied to the Study of Composite Systems Flexibility Considering Wind Energy Sources

This paper presents a methodology to evaluate, via well-being analysis, the flexibility of composite electrical systems, considering wind energy sources. By adding wind farms to different system bars, it is possible to assess which configuration provides the best adequacy and safety level for the system. The evaluation is based on probabilistic indices of Loss of Load Expectation (LOLE) and Expected Marginal State (EMS). Such indices are obtained by well-being analysis, combining deterministic criteria with probabilistic methods. Non-Sequential Monte Carlo Simulation is used to consider the probabilistic and intermittent characteristics of wind sources. The methodology is applied to the IEEE-RTS test system.

A Novel Framework for the Operational Reliability Evaluation of Integrated Electric Power–Gas Networks

This paper proposes a new framework for the operational reliability evaluation of integrated electric power-gas networks (IEPGNs). First, a novel approach for modeling the failure modes of natural gas pipelines is presented. This approach utilizes the concept of virtual nodes and employs a gas release rate model to consider the pinhole, hole, and rupture failure modes of pipelines. Thereafter, a four-state Markov model for natural gas-fired generators (NGFGs) with dual-fuel capabilities is proposed. The area risk method is extended to include the proposed reliability models, and the partial reliability indices of the area risk method are evaluated using a non-sequential Monte Carlo simulation (NSMCS). A nonlinear optimization model is also proposed to calculate electric and gas load curtailments for each system state in NSMCS. This model is linearized to obtain a mixed-integer linear programming (MILP) model for reducing the computational burden. The computational performance of NSMCS is further improved by adopting cross entropy (CE)-based importance sampling (IS). Finally, the efficacy of the proposed framework is demonstrated on three test systems. Case studies validate the importance of considering the proposed reliability models of IEPGNs for operational reliability evaluation. The impacts of operational strategies on the operational reliability indices are also demonstrated.

Reliability Evaluation of Cyber-Physical Power Systems Considering Random Failures in Measurement and Remote Control

In integrated cyber-physical power systems (CPPS), the malfunctions of cyber system deeply affect the dispatcher’s remedial action scheme, and thus have a significant impact on the reliability of the physical power system. The random failures of electrical devices in physical power system and the random outages of measurement and remote control in cyber system are both considered for the CPPS reliability evaluation in this paper. Firstly, the component outage models in physical, access, backbone and application layers are presented. Then, a linearized DC state estimation (SE) model is introduced and the SE errors incurred by measurement failures, i.e. bad and lost measurements, are interpreted. Moreover, the impact of SE errors and remote control failures on the corrective action scheme of the control center during the fault recovery process is simulated by a novel modification of the classical optimal load shedding (OLS) model. Finally, to verify the effectiveness and validity of the proposed CPPS reliability evaluation method, the communication network topologies of the cyber system for the RBTS and IEEE-RTS96 are designed, and then the reliability evaluation based on the presented component outage models and the novel modified OLS model are conducted by the non-sequential Monte Carlo simulation (NMCS).

Generation maintenance scheduling with renewable sources based on production and reliability costs

This work proposes an efficient method for solving the generation maintenance scheduling (GMS) problem, defined through an interactive process carried out between the independent system operator (ISO) and generation companies (GENCOs). In this problem, starting from a schedule previously informed by GENCOs, it is desired to minimize the expected costs of production and system load shedding for the period of analysis from the ISO point of view. The Evolution Strategy metaheuristic is used to solve the resulting optimization problem. The non-sequential Monte Carlo simulation and Cross-Entropy methods are combined to efficiently assess the maintenance schedules searched during the solving process. Uncertainties related to the behavior of load, unavailability of generation equipment, and variability of renewable energy sources are taken into account in the modeling and solution of the GMS problem. The performance of the proposed method is tested with the IEEE-RTS modified with the inclusion of renewable sources.

Reliability Assessment of Converter- Dominated Power Systems Using Variance-Based Global Sensitivity Analysis

With the proliferation of renewable energy and power electronic converters in power systems, the reliability issue has raised more research attention than ever before. This paper proposes a comprehensive framework to assess the reliability of a power system considering the effect from various power converter uncertainties. For the converter stage, we formulate a reliability model for each power converter based on several semiconductor devices, for which ambient uncertainties and converter topologies are considered. For the system stage, we estimate system reliability indicators through a non-sequential Monte Carlo simulation and calculate their variances. Afterward, we leverage machine learning regression algorithms between two stages to establish a nonlinear reliability relation. Moreover, a variance-based sensitivity analysis (SA) is conducted to rank and identify the most influential converter uncertainties with respect to the variance of system EENS. Based on the SA conclusions, system operators can take proactive actions to mitigate the potential risk of the system.

Reliability Analysis of Power Systems Integrated With High-Penetration of Power Converters

With the growing penetration of power electronic converters in power systems, the issue of reliability becomes more critical than ever before. This paper proposes a hierarchical reliability framework to evaluate the electric power system reliability from the power electronic converter level to the overall system level. On the converter level, the reliability model of a power electronic converter is developed based on the power electronic devices it is composed of, for which various hourly based input profiles and converter topologies are considered. On the system level, reliability metrics such as expected energy not served (EENS) and loss of load expectation (LOLE) are estimated through a non-sequential Monte Carlo simulation. Machine learning regression models, such as support vector regression (SVR), and random forests (RF) are implemented to bridge the nonlinear reliability relationship between two levels. The proposed framework is demonstrated through the modified IEEE Reliability Test System (RTS) 24-bus network. Numerical results show power converter reliability should be considered as an important factor when evaluating overall system reliability performance.

Body Mass Index in Human Gait for Building Risk Assessment Using Graph Theory.

This article presents a comprehensive study of human physiology to determine the impact of body mass index (BMI) on human gait. The approach followed in this study consists of a mathematical model based on the centre of mass of the human body, the inertia of a person in motion and the human gait speed. Moreover, the study includes the representation of a building using graph theory and emulates the presence of a person inside the building when an emergency takes place. The optimal evacuation route is obtained using the breadth-first search (BFS) algorithm, and the evacuation time prediction is calculated using a Gaussian process model. Then, the risk of the building is quantified by using a non-sequential Monte Carlo simulation. The results open up a new horizon for developing a more realistic model for the assessment of civil safety.

Resilience Assessment of Distribution Systems Integrated With Distributed Energy Resources

The resilience of electric systems is receiving growing attention due to their increased vulnerability to infrastructure damages and widespread outages from frequent extreme climactic conditions attributed to global warming effects. Resilience evaluation methods should recognize the uncertainties and correlations in the performance variations of different types of energy resources, load characteristics, extreme events and their impacts on the grid elements. However, there is a lack of established methods and resilience metrics that are widely accepted. In this context, this paper presents the development of probabilistic extreme event model, impact assessment model, and optimal restoration model for active distribution systems, and integrates the models using a non-sequential Monte Carlo Simulation framework. The inter-dependencies of time-varying demand, renewable energy output, and energy storage characteristics are incorporated in the framework. A set of metrics is proposed to quantify the resilience of the system against extreme events and their outage impacts at the load points. The metrics and their probability distribution thus obtained can be utilized in probabilistic value-based investment planning to select appropriate measures to enhance the system resilience. Selected case studies are conducted on the IEEE 69-bus test system to show the efficacy of the proposed framework.

Reliability Evaluation of Smart Distribution Grids with Renewable Energy Sources and Demand Side Management

Technical advances and reduced technology costs have led to a significant increase in the use of renewable energy-based distributed generators (DGs) in the existing distribution grids. Modern distribution grid operation is also related to the efforts and incentives to influence changes in customers’ behavior and load use, known as demand side management (DSM). The effective implementation of renewable energy source (RES)-based DGs and DSM, particularly in microgrid operating modes, may benefit customers and distribution networks. This changes in the reliability performance of distribution networks owing to the integration of wind and photovoltaic DGs are evaluated in this study along with the implementation of load shifting and peak clipping DSM schemes for residential, commercial, and industrial load sectors. A reliability evaluation is based on energy not supplied and unavailability (hours per year), calculated by considering the seasonal changes in wind speed and solar irradiation, which are represented by their corresponding Weibull distribution functions. Load variations are incorporated using a normal distribution function. The reliability performances of different RES-based DGs and DSM schemes are evaluated using the non-sequential Monte Carlo simulation approach for modeling the random occurrence of faults in the system resulting in customer interruptions with the corresponding repair times required to restore the supply.

Data-driven Operation Risk Assessment of Wind-integrated Power Systems via Mixture Models and Importance Sampling

The increasing penetration of highly intermittent wind generation could seriously jeopardize the operation reliability of power systems and increase the risk of electricity outages. To this end, this paper proposes a novel data-driven method for operation risk assessment of wind-integrated power systems. Firstly, a new approach is presented to model the uncertainty of wind power in lead time. The proposed approach employs k-means clustering and mixture models (MMs) to construct time-dependent probability distributions of wind power. The proposed approach can also capture the complicated statistical features of wind power such as multimodality. Then, a non-sequential Monte Carlo simulation (NSMCS) technique is adopted to evaluate the operation risk indices. To improve the computation performance of NSMCS, a cross-entropy based importance sampling (CE-IS) technique is applied. The CE-IS technique is modified to include the proposed model of wind power. The method is validated on a modified IEEE 24-bus reliability test system (RTS) and a modified IEEE 3-area RTS while employing the historical data of wind generation. The simulation results verify the importance of accurate modeling of short-term uncertainty of wind power for operation risk assessment. Further case studies have been performed to analyze the impact of transmission systems on operation risk indices. The computational performance of the framework is also examined.