# Power System Reliability Evaluation Based on Chronological Booth-Balieriaux Method
## 1 Introduction  
Power system reliability is considered one of the most important factors in the operation and planning of a power system. Because of the unexpected failures of generators, system operators must secure additional capacity to ensure the system runs reliably [1; 2]. On the other hand, the indiscriminate expansion of generators can lead to high social costs. Therefore, it is necessary to establish reliability standards and quantitatively express reliability to develop appropriate generation expansion planning [3]. Therefore, several indices have been suggested. The deterministic reliability indices are represented by a system margin based on the supply capacity according to the demand, and the probabilistic reliability indices express the risk of loss of load probabilistically. Although the relative influence of each generator on reliability is difficult to explain using the deterministic indices, probabilistic indices can quantify risk more effectively because they consider generator failures [4]. As power systems have become more variable and complex, probabilistic reliability indices that could effectively quantify risk have become popular in many electricity markets, and these probabilistic indices are currently adopted in stipulating reliability standards [5; 6; 7; 8; 9]. Probabilistic reliability indices are obtainable via reliability evaluations. Reliability evaluation methods include stochastic methods, which are simulation-based, and deterministic methods conducted via mathematical processes, such as convolution. The deterministic method evaluates reliability by estimating system availability distribution based on the probability of generator failure (forced outage rate, FOR) [10; 11; 12]. On the other hand, thestochastic method estimates reliability through sampling approaches, such as a Monte Carlo simulation, which is a representative stochastic algorithm [13]. Deterministic methods show consistent results, but they are computationally expensive. In contrast, although stochastic methods have poor reproducibility, they are simple to implement and can quickly evaluate reliability [14]. For practical reliability evaluations, it is essential to consider the realistic aspects of a power system, including preventative maintenance and generator failure. Considering that the maintenance schedule affects daily (or hourly) system availability, reliability must be assessed individually according to availability [15; 16]. On the other hand, this procedure results in a substantial computational load, making it challenging for a deterministic reliability evaluation incorporating maintenance in large-scale system cases. [PERSON] and [PERSON] proposed a deconvolution method to reduce the time required for each reliability evaluation [17]. Instead of performing several evaluations, some studies attempted to account for the impact of maintenance within a single process. For example, WASP-IV adjusts the generation capacity to accommodate the decrease in availability caused by maintenance [18]. [PERSON] [19] and [PERSON] and [PERSON] [20] modified the FOR depending on the maintenance period by assuming maintenance as a probabilistic factor. Nevertheless, previous approaches might be unsuitable in some instances. Consequently, several studies have used stochastic methods to study maintenance [21; 22; 23]. In recent years, the complexity of power systems has increased significantly because of the integration of renewable generation resources. Recent studies have also analyzed the effects of renewable resources on the reliability of the system [24; 25]. On the other hand, most research is biased toward the stochastic method, which is relatively tractable for studying chronological patterns compared to the deterministic method [26; 27; 28; 29; 30; 31]. Nevertheless, a study of the deterministic method, which can serve as a benchmark for validating or converging results should be used because the stochastic method may be inconsistent and potentially inaccurate.