Abstract Power system reliability evaluation measures the system’s ability to properly and continually supply the demand under uncertain conditions. The large penetration of wind power generation, which is an intermittent energy source, introduces some major challenges for maintaining the system reliability level. In order to deal with uncertainties, nonsequential or sequential Monte Carlo simulation (MCS) may be used for probabilistic reliability evaluation. Power systems are composed by components that may be accurately modeled by independent random variables and also by time-varying energy sources and loads, which are represented by time series. These time series can be statistically correlated, both spatially and temporally, and disregarding the dependencies that may exist between them may produce an incorrect reliability evaluation. This chapter presents a model for representing statistically dependent time-varying variables (wind, solar, river inflows, load, etc.) in nonsequential MCS-based reliability evaluation. The results show that the model can correctly represent the effects of statistical dependence, what is normally achieved by sequential simulation, but requiring as little computational effort as the nonsequential simulation. This facility gains importance nowadays with the large penetration of wind generation that is being observed all over the world, both onshore and offshore.
Introduction
Power systems reliability evaluation measures the system’s ability to fulfil its function of properly attending the customer demand under uncertainty conditions. In order to deal with uncertainties, the probabilistic reliability evaluation can be performed by two distinct representations of the system. In the state space rep- resentation, the system states are randomly sampled by nonsequential Monte Carlo simulation (MCS). In the chronological representation, the states are sequentially sampled to simulate system operation by sequential MCS.
Sequential MCS tends to produce more accurate results in the presence of time- varying elements, such as load curves and wind generation, because the time series are explicitly represented and therefore the correlation and statistical dependency between them are preserved [1–3]. However, sequential MCS has a high computational cost and can become prohibitive for practical large systems.
On the other hand, nonsequential MCS has a much lower computational cost but the representation of time-varying elements is not straightforward. Some hybrid simulation models have been proposed [4, 5] in order to obtain the accuracy of sequential MCS with a computational cost similar to nonsequential MCS, but still requiring extra computation time.
Nonsequential MCS-based models do not consider the statistical dependence between time series because the system states are obtained by sampling the state space based on the hypothesis that the events are independent. However, disregarding some dependencies, which may exist between wind generations located at different sites and/or time-varying loads, for example, may produce incorrect reliability indices. The dependence representation has been applied to systems with at most two wind series [6] or without consideration of time-varying load [7]. A model applicable to several time series has been initially presented in [8] and further evolved in [9]. Although efficient and precise, the model efficiency is sensitive to the number of time-varying elements considered.
Therefore, this chapter presents a flexible and an efficient model for representation of any number of statistically dependent time-varying elements (wind, solar, river inflows, load, etc.) in nonsequential MCS-based reliability evaluation. The model can correctly represent the effects of statistical dependence and correlation on the reliability indices, what is normally achieved by sequential simu- lation, but requiring as little computational effort as the nonsequential simulation.
The organization of the chapter is as follows: Sect. 2 presents the conventional approach for reliability evaluation using nonsequential MCS; Sect. 3 introduces the influence of correlated time-varying elements; Sect. 4 proposes a model for representation of time-varying elements in nonsequential MCS; Sect. 5 presents the results obtained with the proposed model and Sect. 6 contains the main conclusions.