Improving distribution system reliability calculation efficiency using multilevel Monte Carlo method

Abstract

Power distribution system reliability is generally evaluated by sequential Monte Carlo simulation (MCS). To obtain a high accuracy, we found that sequential MCS technique needs long execution time. In this paper, we show that reliability indices could be evaluated using a novel sequential multilevel Monte Carlo technique that improves the computational efficiency of MCS. The key idea behind the multilevel Monte Carlo method is to use computationally cheaper low-accuracy solutions of coarse grids as control variates for high-accuracy solutions of fine grids. Therefore, the proposed method can construct multilevel estimators of reliability indices with lower variance. Reliability indices are modelled based on stochastic differential equations and exponential probability distributions. The Milstein path discretisation is used to approximate the numerical solution of stochastic differential equations. Case studies are performed on a small distribution system. Numerical results are presented to demonstrate the computational cost-effectiveness of the proposed method in comparison with the sequential MCS.

A system reliability estimation method by the fourth moment saddle point approximation and copula functions

“…, , , and represents mean value, standard deviation, the third and the fourth central moment of the random variable Y. Then, according to the relation in Equations (11) and (12), the first four moments of the standardized variable Ys are respectively 0, 1, and − 3, in which = ∕ 3 and = ∕ 4 are the skewness and kurtosis of variable Y. The CGF of Ys is established as follows…”

“…Hence, several methods to solve this numerical problem have been presented. A lot of studies for system reliability have pay more attention to the application of simulation-based approaches, 10,11 bounding techniques, 12,13 the probabilistic network evaluation technique, 14 and variations of response surface methods (RSMs) 15,16 have also been employed.…”

Research and application of efficient risk analysis method for electric power grid multiple faults under widespread wildfire disasters

“…Zhao 5 proposed a fast sampling method based on Monte Carlo sampling for grid risk assessment and system implementation; Wang 6 reported a study of risk assessment using Monte Carlo simulation for the safe operation of a large power grid; Chen 7 conducted intensive studies of risk assessment of power grid operation modes based on Monte Carlo simulation; Zhu 8 carried out a reliability evaluation of Sichuan Power Network using Monte Carlo simulation technique; Shi et al 9 proposed a power grid risk analysis method based on assuming the fault obeys normal distribution; He et al 10 evaluated the risk in urban network planning based on fuzzy theory, and the probability of the risk factors are assessed by questionnaire; Cheng et al 11 put forward a power system reliability evaluation method based on the assumption that component's fault is normal distribution; Li et al 12 raised a transmission line overload risk assessment method, and the transmission line overload fault is assumed to be normal distribution; Deng et al 13 proposed a risk assessment of power system in wind power uncertain environment, and the wind power output is assumed to be normal distribution; Wang et al 14 and He et al 15 assumed that probability distribution of transmission lines or transformer faults is approximately Weibull distribution; and it is very common that the transmission lines tripping probability or failure rate of a given unit in power system is assumed to be a fixed value in several studies. [16][17][18][19][20][21][22][23] These methods have good computational efficiency for risk assessment of a large power grid. But, they set the failure probability of grid components at a fixed value or an assumed distribution without analyzing the contribution of each component to the grid risk.…”

Accelerating System Adequacy Assessment using the Multilevel Monte Carlo Approach

“…The MLMC approach has recently been used in a reliability context to speed up the estimation of the average mission time of large systems in [6]. In [7], electrical distribution system risk metrics were estimated using MLMC, using a multi-scale approach to simulate component failures and repairs.…”