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Reliability evaluation of bulk power systems (BPSs) has inherent computational complexity due to the numerous system states and the time‐consuming system state analysis, including power flow calculation, load curtailment, recognition of split power systems and network reconfiguration. In this study, a novel uniform‐design based method is proposed to improve the computational efficiency of power system reliability evaluation. The main idea is that the uniform‐design technique is used to generate the system states in reliability evaluation, which makes the sampled states more uniform and representative in the overall state space compared to the enumerated system states in an analytical method or the random‐generated system states in Monte Carlo simulation. As a result, the sample size and the computational time can be significantly reduced. In addition, the confidence intervals of the reliability indices, such as LOLP, FLOL and EENS, are given. And the estimation errors of reliability indices are discussed. The proposed method is tested on several BPSs, including the IEEE‐RTS79, IEEE‐RTS96 and a real BPS in China. All the case studies indicate that the proposed technique can significantly improve the computational efficiency of BPS reliability evaluation. [ABSTRACT FROM AUTHOR]

Highlights • Smart grid technologies are explored as resilience enhancement measures for enabling the self-adaptive ability of power systems. • The concept of weather condition-based demand response program pricing mechanism is proposed. • Network topology optimization is first applied to realize the potential of transmission network in surviving the natural hazard by enhancing the system resilience. • A sequential Monte Carlo Simulation based evaluation methodology is developed by incorporating smart grid technologies which are used as resiliency resources. Abstract Natural hazards are great threats to the safe and reliable operation of electric power systems. Some high-impact low-probability (HILP) events usually cause severe load losses to the power grid. Therefore, the enhancement of power system resilience appears to be particularly important. Nowadays, novel smart grid technologies provide more flexible ways for the power system operation. However, these technologies are not comprehensively incorporated in the resilience assessment framework to quantify their contribution for resilience enhancement. In this paper, fragility models for transmission lines and towers and sequential wind data are applied to simulate the operational states of power system under windstorm events. Then, a demand side management (DSM) program termed weather condition based real time pricing (WCRTP) framework is proposed to regulate the customer's electricity consumption behavior according to the extreme weather conditions. A network topology optimization (NTO) operation strategy is applied to mitigate the transmission congestion and realize the potential of transmission capacity by optimizing the network topology. The sequential Monte Carlo Simulation (MCS) method based resilience enhancement evaluation framework is developed to incorporate WCRTP and NTO. Numerical case studies are performed on modified RTS-79 systems. Both methods are proved to be effective self-adaptive measures for power systems in both customer behavior regulation aspect and transmission strategy aspect to boost the system resilience, which could eventually help power system operators to deal with the natural hazards in a more flexible, resourceful, and reliable manner. [ABSTRACT FROM AUTHOR]

Linear power flow models are widely used in power systems to simplify the nonlinear power flow equations. The DC power flow model is one of the representatives. There are many other linear power flow models that improve the DC power flow model with the inclusion of $\boldsymbol{Q}$ and $\boldsymbol{v}$. However, existing linear models are derived based on empirical mathematical approximation without a general methodology guidance. In this paper, we found that the fundamental difference among different linear power flow models lies in the formulation of “independent variables.” Based on this finding, a general formulation of linear power flow models is proposed. The linearization error is theoretically analyzed. In particular, the case when $\boldsymbol{ \theta }$ and $\boldsymbol{v^{\scriptscriptstyle k}}$ are regarded as independent variables is thoroughly investigated. Method for finding the linear power flow with the minimum error is presented. The formulation of the independent variables associated with the minimum linearization error is determined by the distribution of state variables $\boldsymbol{v}$ and $\boldsymbol{\theta }$. It is shown that the linearization error when $\boldsymbol{v^{\scriptscriptstyle 2}}$ is regarded as an independent variable is normally smaller than that for $\boldsymbol{v}$ because of the special properties of the distribution of $\boldsymbol{v}$ in power grids. [ABSTRACT FROM AUTHOR]

Power system reliability evaluation (PSRE) typically involves with finding the system (or bus) reliability index from known component reliability parameters. In this paper, we consider the case of using the system (or bus) reliability index to obtain the unknown component reliability parameter (UCRP). This problem is called the inverse PSRE problem. Analytical model of the inverse PSRE problem is constructed and formulated as the nonlinear algebraic equations. In particular, analytical models for the composite generation and transmission system and the generating system are developed based on the state enumeration method. Solution method using the interval analysis is developed by transforming the nonlinear algebraic equations into the interval nonlinear equations with UCRPs represented by the interval numbers. A modified Krawczyk-operator algorithm based on interval bisection elimination scheme is developed to overcome the difficulty of selecting the appropriate initial interval in the problem-solving process. The RBTS, IEEE-RTS, and a 91-bus system are used for the case study to verify the effectiveness of the proposed model and the solution method. In addition, an application to power system planning is investigated to examine how the component reliability parameters can be modified quantitatively to achieve the desired system reliability improvement. [ABSTRACT FROM AUTHOR]

Exhausting fossil fuels and increasing environmental pollutions call for the wider deployment of plug-in hybrid electric vehicles (PHEVs), which enable the interactions of transportation and electric sectors. The extra loads for charging massive PHEVs could compromise the power system reliability and impose considerable stress on the power system. Transmission line congestions and generation capacity inadequacy could be caused under this circumstance. However, there is little literature which comprehensively studies the impact of large-scale PHEVs on the bulk power system reliability when smart grid technologies are incorporated including smart charging and flexible transmission topology control technologies. This work studies the impacts of different charging strategies and transmission network operation strategies on the bulk power system reliability with high PHEVs integration. An evolution strategy particle swarm optimization (ESPSO) algorithm is applied to optimize the charging load of PHEVs and shave the peak load. A network topology optimization (NTO) operation strategy is employed to lessen the transmission congestions and reduce the load curtailment. Based on the sequential Monte Carlo simulation method, these technologies are integrated into the reliability evaluation process. Numerical studies and sensitivity analysis are conducted on modified IEEE RTS-79 systems. The results verify the effectiveness of the technologies to realize the potential of existing power system infrastructures so as to relieve the stress caused by the PHEVs load, increase the available penetration of PHEVs and promote the bulk power system reliability which is meaningful for power system planning and risk management. [ABSTRACT FROM AUTHOR]

In this paper, a reliability evaluation model and a bilevel unreliability allocation model for the ±500-kV HVdc transmission system with the double-circuit lines on the same tower (DCLST) are proposed. The reliability evaluation indices associated with this DCLST HVdc system are also defined. The reliability model is based on the characteristics of common starting point and terminal point structure and double-circuit HVdc coordination operation. And it is developed by integrating HVdc subsystem reliability models together. A multistate Markov model for the dc line (DCL) subsystem is built by considering the common-cause outage of four DCLs on the same tower. The reliability evaluation model of the ac filter (ACF) subsystem is constructed by considering the derated capacity operation state caused by ACF failures. On the other hand, a bilevel unreliability allocation model is constructed based on the proportion-allocation criterion. The allocation model is embedded into the reliability evaluation model so that all reliability indices can be allocated to each component after only one reliability evaluation calculation. As a result, the impact of each component on the system reliability and weak components of the system can be explicitly and unambiguously identified. An actual ±500-kV HVdc transmission project with the DCLST is used for case study to validate the effectiveness of the proposed models and indices. [ABSTRACT FROM PUBLISHER]

In this paper, an optimal reliability allocation (ORA) model of ±800 kV ultra-high voltage direct current (HVDC) transmission system is proposed. The model intends to provide the means to determine the availability requirements of components in the bidding process of ±800 kV ultra HVDC transmission projects. In this model, the component availability is optimized based on the prespecified system reliability. The objective function is composed of the component investment cost and the operation and maintenance cost. The ORA is formulated as a constrained nonlinear programming problem, and the genetic algorithm (GA) is used to find its solution. An improved dagger sampling (IDS) method is proposed to evaluate the reliability of ultra HVDC systems, and a bisection method is used to generate the initial population of the GA. An actual ultra HVDC project is used to conduct the case study. Results show that the proposed ORA model can minimize the component investment, operation, and maintenance costs, while achieving optimal allocation of the system reliability index to obtain the availability of components. In addition, the impact of the component spare on the ORA result is investigated. Performance comparison on the sampling efficiency of the IDS method and the direct Monte Carlo sampling method is also presented. [ABSTRACT FROM AUTHOR]

Wind profile, wake effect, and wind turbine outage create considerable impact on the energy production of a wind farm. This paper proposes a Markovian wind farm generation model that incorporates these factors. This model considers the wind farm as a generating unit with multiple generation states. The probability, frequency of occurrence, and transition rate of each state can be obtained using the collected wind profile data and wind turbine reliability parameters. The power output of each state is calculated using Jensen wake model and enumerated wind farm layouts. The proposed model is verified by a sequential Monte Carlo simulation approach using a test wind farm and recorded wind profile data from four different sites in North Dakota, USA. A state merging technique is developed to enable the application of the proposed model to adequacy assessment. The Roy Billiton Test System with a test wind farm is used to demonstrate the application of the proposed model and the procedure to adequacy assessment. Moreover, this paper investigates the influence of wake effect, peak load, seasonal wind pattern, wind turbine reliability parameters, and wind turbine type on system adequacy. [ABSTRACT FROM AUTHOR]

Wind speed probability distributions estimated at relevant wind installation sites are widely used in electric power systems to evaluate appropriate wind energy indices in system performance and cost evaluation. An accurate estimation of wind speed probability distribution is essential to the increase of computational accuracy of these indices. To achieve this goal, a new analytical approach designated as the mixture kernel density model is developed. This model can produce highly accurate estimation of wind speed probability distributions. The mixture kernel density function consists of a selected number of kernel densities with weight coefficients. An analytic relation between the weight coefficients and the asymptotic integrated mean squared error is derived and used in the Lagrangian multiplier method to obtain the optimal weight coefficients that minimize the asymptotic integrated mean squared error. As a result, the requirement of choosing an optimal bandwidth in the conventional kernel density models is eliminated. The goodness-of-fit of the proposed mixture kernel density model and six conventional models is assessed on collected wind speed samples using the Chi-square and the Kolmogorov–Smirnov tests. Applicability of the proposed model is demonstrated using six types of wind turbine generators and three major wind energy assessment indices on eight actual wind sites. The results show that the mixture kernel density model is more accurate than other models for wind speed probability distribution estimation. Moreover, the most preferable wind turbine generator and the wind site containing the richest wind resources can be identified using the proposed model. [ABSTRACT FROM AUTHOR]

Many utilities in developing countries are investing in installation and renewing of Electrical Distribution System (EDS) components, such as overhead lines, cables and switching devices, to improve the EDS reliability and meet the rapid increase of load demand. In the beginning stage of investment, it is very difficult to evaluate the EDS reliability by using traditional methods due to EDS topology not being fully determined. This paper presents a comprehensive model for forecasting EDS reliability, which is built separately into two parts, i.e. the models for EDS failures and planned outages. Firstly, a three-layer Artificial Neural Network (ANN) model is proposed to forecast the EDS reliability considering EDS failures. Each neuron in the ANN input layer represents a key influencing factor of EDS failures, which are recognized by Gray Relational Analysis (GRA) method. The proposed ANN is trained using historical reliability data of an EDS. In addition, a planned outage reliability model is also built according to the magnitude of investment and type of planned outage. The priorities of improvement measures can also be obtained using the GRA to improve the EDS reliability. Case studies of practical EDSs illustrate the efficiency and applicability of the proposed techniques. [ABSTRACT FROM AUTHOR]

Integration of large-scale wind power is very challenging for cost-effective and secure operations of power systems. The development of bundled wind–thermal generation and transmission system is viewed as a promising means to cope with the challenges. This paper presents a method to optimize the planning of bundled wind–thermal generation and transmission system. A comprehensive optimization planning model is formulated by taking the unit generation cost as the objective function and using the compensating capacity of thermal generating units and the rated capacity of converter station as the constraints. The proposed model takes into account the fuel cost of thermal generating units, the capital costs and maintenance costs of wind turbine generators, thermal generating units, converter stations, transmission lines, and the losses of the system. The simulated annealing algorithm is used as the solver of the model. Case studies are conducted to demonstrate the effectiveness of this proposed method. [ABSTRACT FROM AUTHOR]

Energy production of a wind farm is greatly affected by the wake-effect. In wind farm planning, it is essential to optimize the layout of wind turbine generators (WTGs) to alleviate the impact of wake-effect. This paper presents a new wind farm layout optimization model with an objective function to maximizing equivalent power of the wind farm. The proposed model incorporates the discrete joint probability distribution and characteristics of the wind, wind energy model, and the wake-effect. A particle swarm optimization algorithm is used to solve the optimization problem. In the optimization process, geometric analysis is conducted to determine the upstream WTGs and to calculate the horizontal and deviating distances among WTGs along the wind direction. An effective look-up table is constructed to directly determine the upstream/downstream WTGs. Then the optimal layout of a wind farm can be obtained. The proposed technique is applied to the wind farm layout optimization and the modified Roy Billinton Test System and IEEE Reliability Test System for reliability analysis of a generating system containing a wind farm. Simulation results demonstrate the validity and flexibility of the proposed technique in the layout optimization of WTGs in a wind farm. [ABSTRACT FROM AUTHOR]

Integration of large-scale wind power creates challenges for power system operations. One of the effective ways of dealing with these challenges is to build thermal power plants to form bundled wind–thermal generation system (BWTGS), i.e., using thermal power to alleviate the fluctuation of wind power. This paper presents a method for optimal capacity and type planning of BWTGS with the given wind farms. Branch-descending technique (BDT) is used to generate candidate schemes of thermal generating units by analyzing the rules of total cost changing with the reduction of the number of thermal generating units. The optimal scheme of BWTGS can be obtained by simulating a long-term operation process of BWTGS and comparing the total costs of all schemes. Techniques to accelerate computation, such as combining redundant states in dynamic programming (DP) algorithm and the saving-branch-cost technique in BDT, are developed to reduce the computational complexity. The major advantage of the proposed method is that it can be used to obtain not only the optimal capacity of thermal generating units, but also the optimal type and number of thermal generating units. Case studies are conducted to demonstrate the effectiveness of this proposed method. [ABSTRACT FROM AUTHOR]

Double 12-pulse ultra HVDC transmission systems of \pm 800 kV and \pm 660 kV have larger transmission capacities, more complicated configurations, more complex operation modes, and more components, in comparison to \pm 500 kV or less HVDC transmission systems. Hence, the reliability evaluation of the ultra HVDC transmission system is more complicated than that of the HVDC system. To thoroughly describe different operating modes, this paper presents two new reliability measures for ultra HVDC transmission systems, that is, partial monopole forced outage times and partial bipole-forced outage times. Reliability evaluation models for individual subsystems, including converter transformers (CT), ac filters, converter valve groups, and smoothing reactors have been built considering operation modes and configuration characteristics. In particular, the reliability model of the CT subsystem was built by considering the type and the number of standby CTs, and that of the ac filter subsystem was built by considering the capacity state table of filters. A reliability evaluation model for ultra HVDC transmission systems was proposed by combining reliability logic relationships among subsystems and using the state enumeration method. Case studies of practical ultra HVDC transmission systems illustrate the correctness of indices and the proposed models. In addition, sensitivity analysis and standby analysis of major components were also conducted. [ABSTRACT FROM PUBLISHER]

Power outages in urban area carry heavy social and economic costs. Although social cost, especially public sentiment, is concerned by engineers and managers, it has been only qualitatively investigated without a rigorous model in the state‐of‐the‐art research and practice of service restoration (SR) for a long time. To fill this gap, this paper investigates a hybrid model which takes public sentiment into consideration by quantifying public sentiment triggered by power outage. Furthermore, conventional SR method focused on the optimization model with ideal conditions, which leaves a large room for improvement in complex environment. To improve the robustness of the model, the authors propose a reinforcement learning framework to analyze emergency management process without prior rules. At each time step, the optimal decision can be made automatically by a learned model. The numerical simulations with modified IEEE 33‐bus and IEEE 123‐bus systems demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Conventional transmission congestion evaluations are normally based on deterministic approaches. One of the major disadvantages associated with the deterministic approach is that it is unable to fully reflect the impacts of the random component failures. The deterministic approach can only answer whether a congestion occurs or not, but is unable to quantify the severity of the congestion. This paper presents a systematic congestion evaluation technique using a series of reliability indices including congestion probability, congestion frequency, expected congestion capacity, and energy. These indices can be used to characterize the severity of the congestion at both the transmission component and entire system levels. The proposed approach includes a probabilistic congestion evaluation model and a network solution algorithm taking into account the random failures of power system components, such as generating units, transmission lines, and transformers. The entire evaluation approach is based on the non-sequential Monte Carlo technique. The paper also presents study results on the change of congestion severity of transmission line and overall system using the proposed indices and the effect of some of the parameters on the system congestion. Case studies on the IEEE-RTS indicate that the proposed method is effective and feasible. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Topology has a significant effect on the reliability performance of an electrical collector system (ECS) of wind farms. Novel indices for the reliability of wind farm ECS are presented based on topological features of wind farm ECS in this paper. The concept of the section for a wind farm ECS is defined. The probability table of multistate capacity (PTMC) for a wind turbine generator (WTG) and the Probability Table of the Number of WTG in Up-state (PTNU) for a section can be created. Based on the PTMC and PTNU, PTMC of a wind farm can be established using the state enumeration algorithm and the matrix operations. Therefore, the reliability evaluation model considering effects of wind speed and component failures can be built. The proposed model not only considers the multi-failures of ECS components including failures of cable feeder, WTG, and wind turbine transformer (WTT) but also states of switching devices in failure, disconnection, and switching processes. Four wind farm ECS topologies, i.e., radial topology, single-sided ring topology, double-sided ring topology, and star topology, are implemented. Case studies on the reliability evaluation of wind farm ECS are used to verify the feasibility and validity of the proposed technique. [ABSTRACT FROM AUTHOR]

Wind turbine power converter system (WTPCS) is a crucial device in a wind energy conversion system. This paper presents the new failure rate models and a reliability evaluation technique for the (WTPCS) considering effects of wind speeds, which can be named by the multistate probability analysis method. The case studies on the WTPCS of a 2 MW wind turbine with a permanent magnet synchronous generator are conducted using wind speed data at Lauwersoog and Valkenburg wind sites in Holland. The results indicate that reliability of the WTPCS is affected significantly by variations of wind speed and the rated wind speed of wind turbine. The effectiveness of the proposed method is demonstrated by examples. [ABSTRACT FROM AUTHOR]

Due to the lack of feeder corridors, the Chinese utility companies frequently choose the technique of putting multiple overhead feeders on a same tower (MFST) to meet the load demand in a heavy load area. In many situations, the distance among the feeders of MFST in an electrical distribution network (EDN) is usually too small to meet the requirements of safety regulation for repairing and maintenance. Therefore, when a fault occurs on a feeder of MFST, the other feeders have to be in a triggered passive outage (TPO) state to assist the repairing of the failed feeder. This paper presents a reliability evaluation algorithm for EDNs containing MFST using the section technique. The definition of TPO and the equivalent TPO rate and TPO duration are also proposed. Based on the TPO parameters and the section technique, the reliability evaluation algorithm containing the MFST can be obtained. Case studies on the modified RBTS-BUS6 and the EDNs of three districts in Dongguan city, China, show that the MFST has a significant impact on the EDN reliability and should be considered in the reliability evaluation. The results also show the effectiveness and applicability of the proposed approach. [ABSTRACT FROM PUBLISHER]

Abstract: The electrical energy production and reliability benefits of a wind energy conversion system (WECS) at a specific site depend on many factors, including the statistical characteristics of the site wind speed and the design characteristics of the wind turbine generator (WTG) itself, particularly the cut-in, rated and cut-out wind speed parameters. In general, the higher the degree of the wind site matching with a WECS is, the more are the energy and reliability benefits. An electrical energy production and reliability benefit index designated as the Equivalent Capacity Ratio (ECR) is introduced in this paper. This index can be used to indicate the electrical energy production, the annual equivalent utilization time and the credit of a WECS, and quantify the degree of wind site matching with a WECS. The equivalent capacity of a WECS is modeled as the expected value of the power output random variable with the probability density function of the site wind speed. The analytical formulation of the ECR is based on a mathematical derivation with high accuracy. Twelve WTG types and two test systems are used to demonstrate the effectiveness of the proposed model. The results show that the ECR provides a useful index for a WTG to evaluate the energy production and the relative reliability performance in a power system, and can be used to assist in the determination of the optimal WTG type for a specific wind site. [Copyright &y& Elsevier]

The economic and reliability benefits of adding a wind energy conversion system (WECS) to a power system are highly dependent on the wind turbine generator (WTG) installation design, i.e., the type and number of WTG. This paper presents an approach to determine the optimum installation design at each wind site considering the WTG parameters, the total cost of WECS and the power system reliability performance. The model is formulated as a combinatorial constrained optimization problem with a nonlinear, nondifferentiable objective function, which consists of the capital, maintenance and operating costs, and the costumer interruption costs. A number of constraints, including the total installed capacity at a specific wind site and the capital cost, are considered in the model. The model is solved using a genetic algorithm with adaptive crossover and mutation probabilities based on the standard deviation of chromosome fitness in a generation population. The proposed model and algorithm are tested on two power systems. The results show that the proposed approach can be used to obtain the maximum economic and reliability benefits associated with a WECS installation and is a powerful search technique for determining the optimum number and type of WTG considering reliability performance and costs. [ABSTRACT FROM PUBLISHER]

Abstract: Power system component failures can generally be classified into two categories: repairable random failures and aging failures. An essential step in power system reliability evaluation is the calculation of component unavailability. The paper presents a new model for calculating the unavailability due to aging failures using the normal distribution. It is based on the strictly mathematical derivation and can be used more easily with high accuracy compared to the traditional model. An example of seven generating units and two test systems of the RBTS and the IEEE-RTS were used to demonstrate effectiveness of the proposed model and its applications in power system reliability evaluation. [Copyright &y& Elsevier]

Abstract: Weak part analysis of a system is a key element in a system reliability quantification process. It enables the weakest areas of a system to be recognized and assists in directing remedial measures for improving the system reliability. This paper presents a novel approach to identifying the weak parts using the unreliability tracing (UT) technique and introduces the proportional sharing principle (PSP). The model for tracing the unreliability of a complex network is presented based on reliability evaluation methods using minimal cut sets (MCSs) and the PSP. The system UT sharing factors (UTSFs) are derived to easily identify the major unreliability contributions (MUCs) in a system. The method is illustrated using three cases and the UT, UTSF and the reliability impact analysis of different components are discussed. The results show that the developed technique can be applied to complex networks for UT tracing and recognizing the MUC. [Copyright &y& Elsevier]

Abstract: Wind power is a very useful renewable energy source that is attracting consideration around the world due to its non-exhaustive nature and its environmental and social benefits. The correlation between multiple wind sites has a significant impact on the reliability of power systems containing wind energy conversion systems (WECS). Conventional methods cannot be directly applied to evaluate the reliability of WECS in the absence of comprehensive modeling techniques that recognize the correlation of the wind speeds at different wind farm locations. This paper proposes a model for power system reliability assessment that can consider the wind speed correlation and preserve the statistical characteristics of wind speeds, such as the mean and deviation of the wind speed time series (WSTS). A time-shifting technique is used to produce a new WSTS for a given correlation between two wind sites. The optimal shifted time at the two sites is determined using a linear interpolation technique. The probability distributions of the generated power and the system reliability indices with different degrees of correlation between the two sites are compared using two reliability test systems, i.e. the RBTS and the IEEE-RTS. The results show that the proposed method is useful in evaluating the reliability of WECS with correlation between two wind sites. [Copyright &y& Elsevier]

Abstract: This paper proposes an analytical model and algorithm for tracing power flow (TPF). The concept, construction approach and properties of extended incidence matrix (EIM) are developed. By using results of an AC or DC power flow solution from any off-line program or state estimation, the extended incidence matrix, generation and load power vectors, and distribution factor matrix are derived so that the analytical model of power transfers between generators and loads can be built. The major advantage of the proposed method is that the matrix theory is used to directly build the TPF model and no proportional sharing assumption on the flow distribution is needed. The method was tested using a 4-bus system, and the IEEE 30-bus and IEEE 14-bus power systems. The case studies indicate that the developed technique can be applied to any power system with or without loop flows. [Copyright &y& Elsevier]

• The proposed multi-state model prevents the underestimation of reliability level caused by two-state failure model. • The proposed model can accurately evaluate the reliability index, which better reflects the multiple operation states. • Different TES strategies will lead to different operation decisions and reliability results of CSP plants. • The SF size and the TES capacity are positively correlated with the system reliability level. But the system reliability index tends to be stable when the SF size and the TES capacity are large. This paper proposes a multi-state reliability evaluation model for the concentrated solar power (CSP) plant considering partial function failure. Firstly, the component functions and components' consequences of random failure of CSP plants are analyzed. Core components affecting the output of CSP plants are selected. The CSP plant is divided into three subsystems: the heat collection, the heat exchange, and the power generation subsystems, according to the component function. Each subsystem is equivalent to a two-state component. Thus, an 8-state Markov model of CSP plant is established. The CSP plant can be operated in a partial function failure state as thermal energy storage (TES) or generation, depending on the functions of solar-heat and heat-electricity conversion. On this basis, the 8-state model can be simplified to a 4-state model by combining the partial function failure states of the same effect. Finally, the 4-state model is applied to the sequential Monte Carlo simulation for the reliability evaluation of power systems containing CSP plants. Two TES strategies are considered in the simulation: One is based on solar field (SF) average output, another is designed to satisfy the load preferentially. The proposed model is tested on the modified RBTS/IEEE RTS systems to verify the effectiveness. [ABSTRACT FROM AUTHOR]

The increasing penetration of renewable energy, such as wind power, has brought great challenges to the power system operation due to its uncertainty. Flexibility, which measures the ability of power system to deal with the uncertainties, is critical for power system to adapt to the new era of renewable energy. The rising electrical demand of the water distribution system (WDS) creates opportunities for power system to leverage the flexibility provided by WDS. This paper investigates the water-energy relationship between these two systems and makes full use of the water pumps and tanks in the WDS to enhance the power system flexibility. Current WDS designs did not consider well the role WDS plays in the power system. This hinders the WDS from being fully used by power system to provide flexibility. An optimization model is proposed to determine the optimal tank size of WDS, which may provide the maximum available flexibility of power system. The effect of tank size on water quality is also investigated to ensure that the supplied water quality is not compromised. Moreover, a Benders-based heuristic algorithm is proposed to find the optimization solution more efficiently and to protect the data of each energy system. Results of case study highlight the merit of the proposed optimization design and the advantage of using WDS to provide flexibility for power system. [ABSTRACT FROM AUTHOR]

Power electronic devices are important in the modern power system. Control functions and operational characteristics of power electronic devices bring higher nonlinearity and heavier calculation burden to power system analysis, especially in optimization problems. In this article, a general steady-state model of power electronic devices in the AC-DC hybrid grid is proposed, which considers the high voltage direct current (HVDC) connections and the flexible AC transmission systems (FACTS). Power electronic devices are equivalently represented by impedance, transformers, and controlled sources. The linearized steady-state model is derived and then the specific formulation with minimized error is presented. The effectiveness of the proposed method is verified by optimal power flow (OPF) calculation in the IEEE and Polish test systems. [ABSTRACT FROM AUTHOR]

This paper intends to address the dynamic repair scheduling of electric power transmission systems based on look-ahead strategy approximation. The objective is to minimize system functionality loss during the restoration stage after disruptive events. A series of decisions regarding which damaged component to be repaired has to be made successively considering currently available information of repair time and its uncertainty in the future. To achieve this goal, the dynamic repair scheduling problem is represented as a stochastic Markovian decision process (MDP). To overcome the computational complexity of MDP derived from exponentially growing state space, the cost-to-go function is approximated by a look-ahead strategy based on repair importance ordering. Stage-dependent coefficients are used to balance the approximated functionality loss at different decision stages. The tradeoff between the efficiency and optimality can be achieved by adjusting the look-ahead depth and the updating policy of look-ahead strategy. The IEEE-14 and 118-bus systems were used for performance evaluation of the proposed method and comparison with various approaches. The results show that it can produce decisions close to the best-known solutions within small amount of time. [ABSTRACT FROM AUTHOR]

Contingency screening is vital for maintaining the transmission system reliability. Bilevel programming is a powerful tool for the accurate identification of critical events. To accelerate the contingency screening with bilevel programming, this study proposes a root-event-based dynamic space pruning algorithm. A root event is an event in which all the failed components have contributions to the event impact. Considering the fact that numerous N − k events describe the same critical scenario, the proposed space pruning principles partition the N − k event space into the subspace of root events and the complement subspace. To accelerate the screening of subspace of root events, bilevel programming is constructed to identify new critical events having high risk and causing more severe load shedding than the root event. Besides, relaxed bilevel programming is proposed to accelerate the screening of the complement subspace. The relaxed scheme replaces the constraints of power flow by constraints of transmission capacity, and enables the identification of most of the critical events in the complement subspace with a low computational cost. Case studies on the IEEE RTS and a provincial grid in China indicate that the proposed algorithm significantly accelerates the screening process without missing critical events. [ABSTRACT FROM AUTHOR]

Contingency screening is vital for maintaining the transmission system reliability. Bilevel programming is a powerful tool for the accurate identification of critical events. To accelerate the contingency screening with bilevel programming, this study proposes a root‐event‐based dynamic space pruning algorithm. A root event is an event in which all the failed components have contributions to the event impact. Considering the fact that numerous N − k events describe the same critical scenario, the proposed space pruning principles partition the N − k event space into the subspace of root events and the complement subspace. To accelerate the screening of subspace of root events, bilevel programming is constructed to identify new critical events having high risk and causing more severe load shedding than the root event. Besides, relaxed bilevel programming is proposed to accelerate the screening of the complement subspace. The relaxed scheme replaces the constraints of power flow by constraints of transmission capacity, and enables the identification of most of the critical events in the complement subspace with a low computational cost. Case studies on the IEEE RTS and a provincial grid in China indicate that the proposed algorithm significantly accelerates the screening process without missing critical events. [ABSTRACT FROM AUTHOR]

Highlights • An analytical model is proposed to obtain system reliability indices in a direct way. • The proposed model can obtain system reliability indices with high accuracy. • The model builds a visual relation of reliability indices and reliability parameters. • The model facilitates sensitivity analysis to identify the weak link of the system. Abstract 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. [ABSTRACT FROM AUTHOR]

The increase in wind power penetration leads to the risk of energy supply interruption in integrated electricity‐heat energy systems (IHES). This paper presents an analytical‐based approach for the efficient operational reliability evaluation of the IHES. The wind power distribution characteristic model considering correlation is constructed based on Hidden Markov Model (HMM). To reduce computational complexity, a critical system state identification (CSSI) method is proposed that characterises both random device failures and wind power uncertainty. Under each critical system state, the analytical function relationship between the reliability index and the uncertainty factors is established based on the virtual stochastic response surface (VSRS) method. The analytical function can directly calculate the reliability index when the wind power output varies, avoiding a large number of repeated calculations of the optimal load‐shedding model of the system and reducing the time required for reliability assessment. This allows the operator to evaluate the operational reliability of the integrated energy system in real‐time. The numerical simulation of the test system combining the IEEE 33‐node distribution system and the existing 28‐node heating system proves the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Conventionally, the 2-parameter Weibull model, Arrhenius-Weibull model, has been used vastly for transformer aging-dependent unavailability modeling. However, this model only uses the lifetime feature to describe the transformer's degradation process and to calibrate the Weibull parameters, which harms the accuracy of aging-dependent unavailability forecasting. In response, this paper develops a 3-calibratable-parameter Weibull model for evaluating the transformer aging-dependent unavailability. In the proposed model, both the individualized aging threshold and lifetime are taken into the calibration of the Weibull parameters to accurately characterize the heterogeneity in transformer populations. First, a degree of polymerization (DP) analysis and Monte Carlo Simulation (MCS) based approach is proposed for estimating the transformers’ uncertain aging thresholds and lifetimes. Then, the Maximum Likelihood Estimate and Particle Swarm Optimization are jointly adopted to model the relationship among the calibratable Weibull parameters, aging threshold, and lifetime. Finally, the analytical formula of aging-dependent unavailability is derived from the established 3-calibratable-parameter Weibull model using an integral-discretization method. A real utility application example in China's Chongqing power system has been presented to validate and demonstrate the practicality and usefulness of this method. [ABSTRACT FROM AUTHOR]

The continuous-time model is widely used to design load frequency control (LFC) schemes for power systems with delays and demand response (DR). In practice, however, the LFC system works in a sampled-data manner. The plant operates continuously while the control updates every few seconds. This paper focuses on the sampled-data LFC system with DR and the delay. Based on the linear quadratic regulator (LQR) theory, an optimal control scheme is designed to regulate the DR and generation units in a sampled-data manner. The LQR controller can be applied to the LFC system with constant and time-varying delays, regardless of DR. An observer is also designed to make the state-feedback control law feasible. The observer is efficient in that its gain is delay independent. Case studies on the one-area and multi-area LFC systems are conducted to verify the effectiveness of the proposed LFC controller. Simulation results also demonstrate the excellent stability and performance of the proposed LQR controller in the sampled-data LFC-DR system. [ABSTRACT FROM AUTHOR]

This paper proposes a novel repair rule set (RRS) for scheduling the power system infrastructure repair after the occurrence of extreme events. RRS is made up of multiple repair rules, each of them can be applied in arbitrary post-disaster failure scenarios to rank the repair actions by priority. A learning-to-rank technique called AdaRank is used to train the repair rules by combining the weak learners derived from the dynamic repair scheduling model. Then, RRS is constructed by iteratively clustering the training cases and retraining the repair rule for each cluster. Increasing the number of repair rules within RRS allows it to differentiate various types of failure scenarios, thereby improving its performance. Further combined with multi-label K nearest neighbor (ML-KNN) technique, RRS is able to schedule the repair without the full knowledge of real-time failure information, such as the estimated repair time. The results of case studies on IEEE-118 test systems show that the proposed method has a desirable performance compared to the exact mathematical optimization model. Moreover, it reduces the requirement for failure information while significantly improving the computational efficiency. [ABSTRACT FROM AUTHOR]

• A novel sparse density estimator named GCE is presented for dependence modeling. • A CE method using GCE is developed to get the IS-PDF of correlated RVs (CRVs) • Composite system reliability evaluation is greatly accelerated using IS-PDF of CRVs. 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. [ABSTRACT FROM AUTHOR]

• The cross-entropy (CE) method addressing high-dimensional dependencies is explored. • A CE method termed as CE-DRDM is developed from dimension reduced dependence model. • An improved hierarchical disaggregate structure is proposed to enhance CE-DRDM. • A novel CE optimization is used to derive the analytic formula of IS-PDF parameter. • A novel sparse density estimator is used to reduce the number of IS-PDF parameter. 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. [ABSTRACT FROM AUTHOR]

The icing on transmission lines threatens the power system security while the heat caused by power transmission losses can prevent icing growth. This paper proposes a preventive scheduling model for mitigating the glaze icing by optimizing the distribution of power losses on ice-coated transmission lines. An analytical glaze icing growth model is established based on the heat balance theory, which builds a direct relationship between icing growth and power transmission losses. Accordingly, the analytical glaze icing model is embedded into the proposed scheduling model to quantify the impact of power system schedules on transmission line icing and reduce the glaze icing of transmission lines. The scheduling model co-optimizes active power dispatch, demand response, and reactive power optimization for promoting the de-icing effect. To overcome the computational difficulties, the analytical glaze icing growth model is further linearized, and the Lagrangian relaxation method is adopted for identifying a practical solution. Case studies are conducted on different icing scenarios in the IEEE RTS-79 test system to verify the validity of the proposed model. Results show that the proposed preventing scheduling model can avoid the icing on transmission lines for mild ice disasters, while efficiently restraining the icing growth on transmission lines when they cannot be completely de-iced in severe storms. [ABSTRACT FROM AUTHOR]

The integration of the variable renewable energies makes the operation conditions of the power system ever-changeable. Consequently, the power system operational reliability evaluation is increasingly important. This paper introduces the concept of decision-dependent uncertainty (DDU) in the operational reliability evaluation. Unlike the exogenous uncertainties, DDU reveals that the decisions of the system operation could significantly affect the resolution of the uncertainties which influence the reliability metrics. In this paper, the proposed DDU modeling method links the device reliability indices, i.e., the forced outage rate, and the operational-decision variables. The impacts of DDU on operational reliability are analyzed based on a reliability-constrained stochastic unit commitment (UC) model. An adaptive reliability improvement UC (ARIUC) algorithm is proposed to efficiently solve the problem. Case studies underline the necessity of considering DDU in power system operational reliability evaluations. [ABSTRACT FROM AUTHOR]

The cross-entropy (CE) method can accelerate power system reliability evaluation effectively. An importance sampling (IS) based iterative parameter updating algorithm is usually used in CE optimization. However, the efficiency in capturing the concerned samples for parameter updating may be unsatisfactory, especially for a system with intrinsic nature of rare failure events. Besides, the stopping criterion of this iterative algorithm is usually determined subjectively, incurring insufficient or excessive parameter updating and a resultant higher computational burden of the entire simulation. To address the above two problems, a CE method based on subset simulation and minimum computational burden criterion is proposed. In CE optimization, the subset simulation combined with M-H sampling is adopted as an alternative to IS to effectively improve the efficiency of capturing desired samples for parameter updating at each iteration. Moreover, a novel quantitative stopping criterion is presented in such a way that the computational burden for the entire simulation is estimated and compared after each parameter updating iteration, and the optimal parameters corresponding to the minimum computational burden can be determined. The computational performance of the proposed method is validated by comparing the proposed approach with existing methods under several numerical tests including a realistic power system. [ABSTRACT FROM AUTHOR]

In this paper, a coupled interaction matrix is proposed to describe the interactions between line outages and the load shed at buses. The coupled interaction matrix is effectively estimated by the Expectation Maximization algorithm. A highly probabilistic coupled interaction model is further proposed to efficiently generate cascades with both line outages and the load shed based on the coupled interaction matrix and the distribution of initial outages. To mitigate cascading failures, critical links are identified based on the coupled interaction matrix by calculating a comprehensive severity index that considers the consequences of both line outages and the load shed. Simulation results on the IEEE 300-bus system verify the effectiveness of the proposed approach. The cascades generated from the coupled interaction model match the statistics of the original cascades very well. The identified critical links based on the comprehensive severity index enable a proper tradeoff between reducing line outages and reducing the load shed, leading to a better mitigation effect than only considering either line outages or the load shed. [ABSTRACT FROM AUTHOR]

• The scheduling demand for adequacy and flexibility are accurately captured. • Enhance the adaptability to non-hyperspherical data distribution of clustering. • Reduce the relative error of total cost in system expansion planning. • The proposed method is effective in LP/MILP models and GEP/GTEP problems. • Investigate the influence of new energy and model parameters on selection methods. Due to the computational burden of the system expansion planning (SEP) models, it is a common approach to select representative days by clustering to make the SEP models tractable. However, the performance of the selection of representative days is unsatisfactory, as the conventional methods fail to properly capture the demand for adequacy and flexibility in system scheduling and to effectively cluster the feature vectors that are commonly high-dimensional and highly non-hyperspherical distributed. This paper proposes a spectral clustering based demand-oriented (SCDOR) representative days selection method, which extracts the daily net load duration curve (NLDC) and net load ramp duration curve (NLRDC) as a feature vector to accurately capture demand for the adequacy and flexibility. Additionally, the feature vectors are regarded as connected vertices in a graph, and the representative days are obtained through the graph partition by spectral clustering that is adaptable to different data distribution. The superior performance of SCDOR is demonstrated through the case studies with different levels of modeling complexity on the Texas power system and IEEE RTS-79 system. [ABSTRACT FROM AUTHOR]

• A model of hardening planning is proposed to minimize the long-term system risk. • A function of system risk regarding unavailability of given components is derived. • The model avoids repeated MCS-based risk evaluation so that improves the efficiency. • The model can obtain better solution and have higher computation efficiency. Hardening components is an effective way to decrease the load loss risk caused by component outages in power systems. The system hardening against the long-term risk usually faces the computation burden problem brought up by the risk evaluation. This paper proposes a deterministic hardening planning model to minimize the long-term system risk of load curtailment, which eases the computational cost concern. To accomplish this task, a set of system events with load loss and corresponding load curtailments are obtained by an improved Monte Carlo simulation. An analytical function of system risk index with respect to the unavailability of components is derived and can calculate the risk index rapidly. Then, the deterministic model is constructed by applying the analytical function into the stochastic problem of system hardening planning. The greedy algorithm is developed to solve the model. The proposed model and method improve the computation efficiency by avoiding the repeated time-consuming risk evaluations. Case studies are conducted on the RBTS, RTS79, and a modified RTS96 system. Performances of the proposed model and method are compared with that of the conventional reliability optimization method (CROM). Results demonstrate that the model obtains better solution than the existing study on hardening planning for long-term risk, and has higher computation efficiency than CROM. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

A tie-line security region provides all possible tie-line power injections with which constraints in a regional network will not be violated. With the high penetration of renewables, a sharp increase or decrease of renewable power requires a good depiction of the tie-line security region considering time coupling. However, the tie-line power security region with time coupling is a high-dimension polytope, which leads to a considerable computational burden. This paper presents a fast algorithm to approximate the original high-dimension tie-line security region considering time coupling. A few lower-dimension polytopes associated with combinations of different periods are calculated for the approximation. An evaluation method with clear physical explanations is established to measure the accuracy of the approximation. The method converts the evaluation to two linear programming problems based on the mathematical relationship between optimal points and polytope vertices. Under a Monte Carlo framework, the statistical analysis is employed to measure the accuracy using five presented indices. The performance of the proposed methods is verified by the case studies on the IEEE 118-bus test system and a 661-bus utility system. [ABSTRACT FROM AUTHOR]

Linear power flow models are widely used in power system analysis because it brings huge computational benefits, especially for power system optimization problems. The improvement of the linearization accuracy is greatly beneficial to the power system operation considering the large amount of power scheduled based on linear power flow models. We find that the linearization error substantially changes with different selections of the variable space. In this paper, we formulate a model to find the linear power flow model with the minimized linearization error based on the optimal selection of the variable space. The expression of the variable space is generalized as a polynomial function. A simplified model of power losses is proposed. The difference between the selection of the variable space and the common hot-start approaches is illustrated. The effectiveness of the proposed linear power flow model is verified by power flow calculation and optimal power flow (OPF) calculation in the IEEE and Polish test systems. [ABSTRACT FROM AUTHOR]

The integrated flexibility of distributed multi-energy systems (DMES) has been recognized as a valuable balancing resource to the centralized energy system, which can be characterized by an integrated flexible region (IFR) of multiple energy inputs. Notably, the IFR is only captured for one single period in previous studies, whereas the time coupling in consecutive periods has a significant impact on the integrated flexibility. This paper proposes a modified IFR-based approach to characterize and measure the integrated flexibility of DMES considering the temporal coupling constraints. First, operation constraints of the DMES are formulated, followed by a vertex search method to obtain the IFR, i. e, a polytope that visualizes those operation constraints. Then, an approximation approach is proposed to decompose the original IFR into a series of lower-dimension IFRs, each of which corresponds to a specific period. The influence of states of adjacent periods is directly reflected by the position change of the vertices. The decoupled IFRs can be incorporated conveniently into the multi-period economic dispatch of the centralized energy system. Moreover, the Volume of the IFRs (VFR) is introduced as an index to quantify the flexibility of the DMES. The performance of the proposed methods is verified by the case studies. • An integrated feasible region considering time coupling constraints is explored. • A vertex search-based method characterizes the integrated flexible region. • The time coupling constraint affects the integrated feasible region. • An index is proposed to measure the flexibility of multi-energy systems. • Integrated flexibility facilitates the accommodation of renewable energy. [ABSTRACT FROM AUTHOR]

• A stochastic economic dispatch model in power systems with data centers is proposed. • The load of data centers is regulated to promote renewable integration. • Uncertainties of both renewables and DCs are considered. • Benders decomposition and a new type of group based multi-cut approach is applied to solve the problem. • The benefits of applying data centers in renewable integration is analyzed. The management of the demand side in the power system, such as data centers (DCs), can improve the stability of the grid and bring economic benefits in planning and operation. Considering the increasing applications of big data and net-based technologies, the computational jobs in different region can be shifted as flexible load. In this paper, a new type of decomposition method is proposed to solve the model of the stochastic economic dispatch (ED) incorporating DCs, which considers the uncertainties of job arriving rates in DCs and wind generation in power systems. The original ED formulations are decomposed with Benders decomposition to improve computational performance, and a new type of group based multi-cut Benders decomposition is applied to improve the convergence. Case studies on a joint 18-bus system illustrate the benefits of spacial coordination between DCs and power system. The comparison between single-cut and multi-cut approach proved the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Introduce the risk masking effect for contingency analysis of transmission system. • Propose a screening model for top incremental risk events. • Perform case studies to illustrate the advantage of screening with incremental risk. Screening of severe contingency event is vital in transmission system operation and planning. This study investigates the reliability issue of load loss with static analysis of contingency events of the transmission system. As not all high-risk events provide a more critical impact than its sub-events, the risk index is not always efficient for contingency screening. In this context, this paper proposes a contingency screening model with incremental risk for transmission system. Firstly, the significance of both the risk and the incremental risk of contingency events is analyzed. We show that the use of incremental risk can avoid the "risk masking effect", which is defined as the situation that high-risk events with weak reference value may mask the events with valuable information about more critical cases. Secondly, the optimization objective of contingency screening is set to maximize the incremental risk of contingency event. The purpose is to directly identify the events that describe a more critical impact than its sub-events and to improve the screening efficiency over that by the risk assessment. Finally, a recursive screening algorithm is designed to identify the set of N − k events with high incremental risk. Case studies on the IEEE-RTS and a provincial grid in China were carried out to show that the events with incremental risk only account for a small proportion of the total high-risk events. Thus, identification of N − k events with more critical impact than sub-events is achieved for system risk analysis in that enumeration of all the high-risk events is not required. [ABSTRACT FROM AUTHOR]