## 1 Introduction  
As global attention to environmental protection and sustainable development increases, traditional fossil fuel-based power generation is gradually being replaced by renewable energy sources [1]. The uncertainty introduced by renewable energy generation significantly impacts the security and stability of power systems [2, 3]. Load supply capability (LSC) is a crucial aspect of evaluating the security and stability of a power system, as adequate LSC is fundamental to its safe and stable operation [4]. In this view, it is necessary to study how to quantify the influence of renewable energy generation on LSC, which can provide a reference for the planning of renewable energy installations and the real-time dispatch of renewable energy generation. Many studies have been conducted on the evaluation of the LSC. However, the terms used in these studies are not consistent [5]. In order to avoid confusion, a review of the existing works is provided herein. First of all, the term \"load capability\", first introduced in 2000, is defined as the maximum percentage load increase given an arbitrary load growth pattern before encountering electrical or operational constraint violations [6]. In subsequent studies, the concept is also referred to as \"available load supply capability (ALSC)\" [4; 7; 8]. More specifically, reference [4] applied the Latin hypercube sampling-Monte Carlo simulation (LHS-MCS) method for a probabilistic evaluation of ALSC. Reference [7] studied the impact of power flow entropy on probabilistic ALSC. Reference [8] combined renewable energy power forecasting with probabilistic ALSC evaluation, achieving probabilistic forecasting of ALSC. Secondly, the term \"total supply capability (TSC)\", also called as \"power supply capability (PSC)\" [9; 10], was proposed in 2011 by [PERSON] et al. [11]. It is defined as the maximum load that a distribution system can provide under the N-1 security criterion. The two main differences between TSC and load capability are that load capability focuses on operational constraints, whereas TSC focuses on N-1 security constraints, and TSC does not specify a load growth pattern. [PERSON] et al. subsequently conducted a series of studies to supplement and refine the TSC family indices. For instance, reference [5] improved the ASC index within the TSC family, and reference [10] examined the TSC evaluation primarily considering user reliability requirements constraints. The third term is \"loadability\", which lacks a unified definition and carries different meanings in various studies. For example, reference [12] defined loadability as a knee or turning point of the power flow solution curve, which can be obtained through a robust two-stage algorithmic framework proposed in the study. In reference [13], loadability refers to the system's capability to accommodate added load, and it is derived through an optimization procedure. In reference [14], loadability is defined as an index calculated based on network parameters and system states. In summary, despite the different terms used, studies on LSC consistently aim to determine the maximum load the power system can support. The studies vary by considering different decision variables and constraints tailored to specific scenarios and applications. As for solving algorithms, the optimization problem defined by load capability (also referred to as ALSC) is relatively simple and can be solved using the repeated power flow (RPF) method [4; 8]. On the other hand, the problems involving TSC or loadability without a specified load growth pattern are more complex and often solved using the optimal power flow (OPF) method [14]. The continuation power flow (CPF) method is frequently used to address loadability problems that account for static voltage stability constraints [15]. In this paper, ALSC and RPF are chosen because we focus more on operational constraints and computational convenience. All the above works have made a significant contribution to the evaluation of the LSC.