Probabilistic spinning reserve adequacy evaluation for generating systems using an Markov chain Monte Carlo‐integrated cross‐entropy method

Abstract

Spinning reserve plays an important role in balancing generation and demand mismatch within a short time interval. Probabilistic spinning reserve adequacy evaluation (PSRAE) is useful to aid operators in monitoring the adequacy of system upward spinning reserve exposed to unforeseen disturbances and making risk-adverse decisions for unit dispatching. As a short time period, for example, 30 s-15 min, is usually considered in PSRAE, the generating system in question is commonly of high reliability, which renders naive non-sequential Monte Carlo methods inefficient. In this study, the high reliability phenomenon of generating systems is explained through a toy case study, thereafter, aiming to develop an efficient method for PSRAE, a simulation method based on the cross-entropy which has been widely applied in many areas to improve naive Monte Carlo methods for tackling rare-event simulation issues, integrated with Markov chain Monte Carlo is proposed. The indices of loss of load probability and expected demand not supplied are used to quantify the spinning reserve inadequacy risk. Through case studies conducted on the RTS-79, usefulness of the PSRAE is discussed and the proposed method is proven to be superior to the classical cross-entropy method and thus could be taken as a candidate tool for the PSRAE to practical systems.

Reliability assessment of distribution networks through graph theory, topology similarity and statistical analysis

“…For example, the process of VD 1 calculation through deep first searching is demonstrated in Fig. 3, which is formulated as VD 1 = 2.5 × 0.7 + 2.5 + 2 × 0.8 + 1.8 × 0.9 + 2.5 + 1.5 × 1 = 11.97 (6) Similarly, the equation of VD 2 is as VD 2 = 2 × 0.8 + 1.5 × 1 = 3.1…”

“…Current researches in reliability largely focus on the computational efficiency. Some approaches have been addressed to improve the computational efficiency in power system applications [5][6][7]. Besides, reliability is considered as an optimisation objective in the study of network expansion [8] and network topology optimisation [9].…”

Risk assessment of stochastic spinning reserve of a wind‐integrated multi‐state generating system based on a cross‐entropy method

“…around 0.001 occ./h [18]) of the underlying Markov process used for characterising the stochastic short‐term behaviour of the prevailing healthy system, and thus are extremely difficult to sample if a Monte Carlo method is resorted to for outputting kinds of statistical index estimations for a large system in question [19]. In response, advantageous Monte Carlo methods dedicated for circumventing such scarcity have been developed in several monographs [20–24]. Unfortunately, none of these variance reduction methods takes into account generation unit multi‐state behaviour for spinning reserve studies of a wind power penetrated generating system.…”

“…In this paper, as an extension to the author's previous work [23, 24], an accelerated non‐sequential Monte Carlo method via a cross‐entropy (CE)‐based importance sampling technique is proposed, intentionally for a real‐time PSRAE of a wind‐integrated multi‐state generating system. The main contribution is to establish an efficient simulation tool for addressing the concern about the full picture of imminent spinning reserve inadequacy risk induced by rare unit forced outages together with forecast errors of wind power and load demand on the basis of minute looking‐ahead time scale.…”

Accelerated distribution systems reliability evaluation by multilevel Monte Carlo simulation: implementation of two discretisation schemes

“…Several methods have been proposed to improve the computational efficiency of crude MCS in power system applications [7][8][9][10]. However, there is a lack of research to improve the computational efficiency of MCS applications in distribution system reliability evaluation by employing advanced MCS methods.…”