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Discrete convolution (DC) is a generally accepted approach for the probabilistic analysis such as reliability assessment and probabilistic load flow. However, it has a strong precondition that the stochastic variables being convolved must be independent, which may not be fully satisfied in all cases. Using copula functions, this letter derives the formulation of DC for dependent variables. The performance of the proposed dependent discrete convolution (DDC) is illustrated using reliability assessment involving wind power. The result shows that the DDC inherits the efficient and reliable performance of DC, indicating a promising potential for practical applications. [ABSTRACT FROM PUBLISHER]

Summary: Hybrid PV‐wind distribution system planning is challenging due to the uncertainties of the system components. Therefore, this paper presents a novel optimization procedure based on scenario aggregation (SA) approach for the planning of such a distribution system. The proposed procedure uses random distributions, which are built for each time step, to model the system uncertainties. System uncertainties include solar irradiance, wind velocity, system load, and energy market price. The objective function of the optimization problem measures the annual cost of the proposed system. Results of the suggested SA optimization procedure are then compared with results of two‐stage stochastic programming (SP) to verify the effectiveness of the proposed method. A case study for a grid‐connected hybrid PV‐wind distribution system in North Texas is presented to illustrate the proposed method. One‐year system components' data are collected to create the stochastic distributions needed to represent system uncertainties. The results of the SP give optimal system configuration that minimizes the system annual cost and meets reliability and load requirements of the proposed system. These results are compared with those obtained using the simpler SA approach. The case study shows that the proposed SA method gives close results compared with two‐stage SP when the uncertainty of the system is reasonable. [ABSTRACT FROM AUTHOR]

• A multi-timescale behavior-driven DR modeling framework is proposed. • We jointly use analytical and data-driven approaches to model DR uncertainties. • The uncertainties in the load recovery process are considered. • A capacity value evaluation algorithm considering DR operation is developed. Demand response (DR) is regarded as an effective tool to mitigate the operational uncertainties and enhance the reliability of power supply in smart grids. However, with the time-varying attribute, to what extent DR could be committed is a major concern for utilities. This paper proposes a new approach to assess the capacity value (CV) of DR with a methodological framework developed for the uncertainty modeling of DR. The novelty of this framework is its inclusion of both physical and human-related analyses in DR programs, which allows the characterization of DR variability to be accurate for the CV estimation. To achieve this, the demand-side activities in DR are disaggregated into several modules as load usage, contract selection and actual performance. Based on their intrinsic properties, different parametric models are proposed to represent the impact of each technical/social factor on the availability of DR. The parameters of these models are determined using learning-based algorithms to adapt to various behavior patterns of consumers. The outputs of the framework will serve as the quantifiers of DR capability and are integrated into reliability-based CV evaluation. The results of case studies verify the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A Linear PMU placement approach is proposed. • The topological observability of the network has been considered. • The model is developed to include single contingencies both on the lines and PMUs. • The measurement redundancy among the set of solutions is maximized. Abstract A novel linear approach for Phasor Measurement Units (PMUs) placement is proposed in this paper to ensure the topological observability taking into consideration the impacts caused by the adjacent zero-injection buses (ZIBs). The observability analysis in the paper is performed utilizing merely the main topological observability rules. Furthermore, the model is developed to include all possible single contingencies both on the lines and PMUs even where adjacent ZIBs are highly interconnected. To this end, the common approach for handling contingencies is enhanced. Moreover, the presented framework incorporates a subsidiary objective, i.e. maximizing the measurement redundancy among the set of solutions with the minimum number of PMUs beside the main objective, i.e. minimizing the number of the required PMUs. In this regard, a unified Integer Linear Programming (ILP) is used to solve the proposed optimisation problem. It is worth noting that the suggested approach is applied to different test systems like IEEE 14-bus, 30-bus, 39-bus, 57-bus as well as 118-bus system to validate the effectiveness and efficiency of the proposed framework and the obtained results are compared to those reported by the prior researches. [ABSTRACT FROM AUTHOR]

This paper considers the problem of approximating the failure frequency of large-scale composite $\boldsymbol{k}$ -terminal reliability systems. In such systems, the nodes ($\boldsymbol{k}$ of which are terminals) are connected through components, which are subject to random failure and repair processes. At any time, a system failure occurs if the surviving system fails to connect all the $\boldsymbol{k}$ terminals together. We assume that each component's up times and down times follow statistically independent stationary random processes, and these processes are statistically independent across the components. In this setting, the exact computation of failure frequency is known to be computationally intractable (NP-hard). In this paper, we present an algorithm to approximate the failure frequency for any given multiplicative error factor that runs in polynomial time in the number of (minimal) cutsets. Moreover, for the special case of all-terminal reliability systems, i.e., where all the nodes are terminals, we propose an algorithm for approximating the failure frequency within an arbitrary multiplicative error that runs in polynomial time in the number of nodes (which can be much smaller than the number of cutsets). Our simulation results confirm that the proposed method is much faster and more accurate than the standard Monte Carlo simulation technique for approximating the failure frequency. [ABSTRACT FROM AUTHOR]

This paper presents a distributionally robust planning model to determine the optimal allocation of wind farms in a multi-area power system, so that the expected energy not served (EENS) is minimized under uncertain wind power and generator forced outages. Unlike conventional stochastic programming approaches that rely on detailed information of the exact probability distribution, the proposed method attempts to minimize the expectation term over a collection of distributions characterized by accessible statistical measures, so it is more practical in cases where the detailed distribution data is unavailable. This planning model is formulated as a two-stage problem, where the wind power capacity allocation decisions are determined in the first stage, before the observation of uncertainty outcomes, and operation decisions are made in the second stage under specific uncertainty realizations. In this paper, the second-stage decisions are approximated by linear decision rule functions, so that the distributionally robust model can be reformulated into a tractable second-order cone programming problem. Case studies based on a five-area system are conducted to demonstrate the effectiveness of the proposed method [ABSTRACT FROM PUBLISHER]

This paper investigates the impacts of transient instability on power system reliability. Traditionally, composite system reliability evaluation has been performed based on steady-state estimation of load curtailments; system dynamics have often been ignored, mostly due to computational complexity. In this paper, three probabilistic transient stability indices are proposed to assess system robustness against dynamic contingencies and to account for system instability in computing reliability indices. A direct method is utilized for transient stability assessment based on computing the energy margin of the system under fault events (energy margins measure the ability of a system to withstand contingencies). Energy margins along with the probability of occurrences of the events are used to update the probabilistic transient stability indices. The dependencies of reliability and stability indices on the fault clearing time are also evaluated. This method is applied on the reduced Western Electricity Coordinating Council and the New England 39 bus test systems. The results indicate the importance of considering the effect of stability in reliability evaluation. [ABSTRACT FROM PUBLISHER]

This paper proposes a distributionally robust optimization model for solving unit commitment (UC) problems considering volatile wind power generation. The uncertainty of wind power is captured by an ambiguity set that defines a family of wind power distributions, and the expected total cost under the worst-case distribution is minimized. Compared with stochastic programming, this method may have less dependence on the data of exact probability distributions. It should also outperform the conventional robust optimization methods because some distribution information can be incorporated into the ambiguity sets to generate less conservative results. In this paper, the UC model is formulated based on the typical two-stage framework, where the UC decisions are determined in a here-and-now manner, and the economic dispatch decisions are assumed to be wait-and-see, made after the observation of wind power outcomes. For computational tractability, the wait-and-see decisions are addressed by linear decision rule approximation, assuming that the economic dispatch decisions affinely depend on uncertain parameters as well as auxiliary random variables introduced to describe distributional characteristics of wind power generation. It is shown in case studies that this decision rule model tends to provide a tight approximation to the original two-stage problem, and the performance of UC solutions may be greatly improved by incorporating information on wind power distributions into the robust 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]

Abstract: This paper proposes a methodology for studying the effects of fire on the electrical distribution network of a city. The study leverages the Model of Urban Fire Spread (MUFS) software application to simulate an urban fire along with its subsequent suppression, and performs extensive simulations of different fire spread scenarios on a synthetic city named Micropolis. The damage caused to the electrical infrastructure for a given fire spread scenario is quantified using a parameter called the Load Loss Damage Index (LLDI). Since most distribution networks contain Normally Open switches for reliability purposes, this paper uses a simple graph theoretic approach for rerouting power across isolated sections of the network which are damaged by fire. Our approach attempts to minimize the voltage drops at the most downstream customer points by rerouting power along paths of minimum impedance. Important conclusions drawn from the analysis of the LLDI values generated from extensive simulation runs are presented. [Copyright &y& Elsevier]

The growing penetration of variable renewable sources and the competitive power system environment make the application of probabilistic reliability techniques all the more important. Although probabilistic methods have been widely used in resource adequacy assessment, using probabilistic methodologies for reliability evaluation including system dynamic security need to be investigated. This paper proposes a probabilistic methodology for integrated reliability evaluation considering resource adequacy and dynamic security assessment in a unified framework. Sequential Monte Carlo simulation (SMCS) is chosen because of its ability to consider time-varying sequential characteristics. By using an optimization model, which minimizes load curtailment for adequacy assessment, and representing stability preserving protection systems in security assessment, the proposed approach gives quantitative integrated reliability evaluation results. In addition, two acceleration methods are introduced to improve computational efficiency. The proposed approach is demonstrated on a synthetic test system and the results illustrate the efficacy of an integrated reliability evaluation approach. [ABSTRACT FROM AUTHOR]

Highlights • Capacity credit (CC) of demand response (DR) under the smart-grid is assessed. • Proposed a hybrid probabilistic-possibilistic framework for DR modeling. • Both exogenous and endogenous uncertainties associated with DR are considered. • A reliability-based algorithm combining operation optimization is developed. • The impacts of various factors on DR CC are analyzed through numerical studies. Abstract As a featured smart-grid technology, demand response (DR) provides utility companies with unprecedented flexibility to improve the reliability of electricity service in future power systems. However, due to the uncertainties arising from the demand side, the extent to which DR can be utilized for capacity support poses a major question to the utilities. To address this issue, this paper proposes a new methodological framework to assess the potential reliability value of DR in smart grids. The framework is established on the concept of capacity credit (CC), and it accommodates different types of uncertainties (i.e., probabilistic and possibilistic) accrued from physical and anthropogenic factors in DR programs. The capability of DR during operation is considered as a synthesized result of multiple facets, i.e., users' load characteristics, participation levels, and load recoveries, and different models are developed to represent each component. To characterize the stochastic nature of demand responsiveness, the fuzzy theory is introduced, and possibilistic models are proposed to describe the human-related uncertainties under incomplete information. In addition, considering that in reality, DR operation could affect the comfort of customers, the dynamics of demand-side participation have also been incorporated in our study, in which two utility-based indices are defined to quantify the effect of such interdependency. Using a probabilistic propagation technique, the different types of uncertainties involved can be normalized and systematically addressed under the same framework. Then, the relevant models can be applied to the CC evaluation procedures, wherein two dispatching schemes (i.e., reliability-driven and coordinated management) are considered to study the effect of DR operation on its CC. The proposed methodology is tested on a modified RTS system, and the obtained results confirm its effectiveness. [ABSTRACT FROM AUTHOR]

• The role of grid-connected parking lots (GPL) on the power reliability is studied. • GPLs are viewed as virtual energy storage units and statistically modeled. • The evaluation is conducted from a physical-social system perspective. • Fuzzy logic approach is used to model individuals' participation of Vehicle-to-Grid. • The influential factors for the capacity value of GPLs are analyzed. This paper presents a study to investigate the potential role of public plug-in electric vehicle grid-connected parking lot (GPL) in improving the sustainability of power supply as virtual energy storage in the urban grid. For this, a comprehensive evaluation framework is proposed which introduces an extension of the generation-oriented concept of capacity value to GPL, with the aim of assessing their contribution to adequacy of supply for different settings. In order to capture the volatility in the available energy from GPL, a compound parametric model is developed from the perspective of physical-social system. Comparing with peer studies, our proposed approach has prominent advantages: (a) it accounts the effects from both technical and human factors associated with the GPL operations; (b) it considers the uncertainty of vehicle users' preference for using GPL and its potential dynamics with the externalities. Hence, it can provide a more comprehensive and realistic representation of the operating characteristics of the GPL. A general framework based on the sequential Monte-Carlo simulation method is developed to derive the corresponding capacity value indices. The effectiveness of the proposed method is validated through implementation on both a standard test case and a real distribution system in China. The obtained results suggest that the capacity value of GPLs could vary significantly, dependent on both the operational characteristics of facilities and the charging pattern of electric vehicles. Additionally, the uncertainties in drivers' behaviors can have a noticeable impact on the reliability benefits of GPL program. [ABSTRACT FROM AUTHOR]