## 1 Introduction  
Renewable energy, such as solar energy and wind energy, is clean and sustainable, and can relieve human dependence on fossil fuels. Therefore, it is necessary to study how renewable energy impacts the power system operation. As power grids continue expanding, uncertainties from load growth and massive integration of renewable energy have increased the randomness in power systems [1], which can deteriorate the security of the power system [2]. Therefore, against the background of large-scale integration of new energy generation into the grid, the security of the power system encounters serious challenges. The available load supply capability (ALSC) of the power system is an important indicator to measure the security of the power system. The power system must maintain sufficient ALSC to meet power demand, support socio-economic development, and overcome challenges such as extreme weather conditions. Consequently, it is critical to calculate accurately the available load supply capability (ALSC) of the power system, since an adequate load supply capability works as the foundation for guaranteeing the security of the power system, and accurate evaluation of ALSC can provide quantitative references for the load supply capability of the power system, and hence assist system operators develop grid operation plans. The definition of ALSC is the maximum load growing percentage without violating any electrical constraint. ALSC evaluation can quantify the flexibility about the load growth and security margin of the power system. This information is important and can be helpful for reactive power compensation device placement, network reconfiguration, network planning, etc. [3]. There are some studies with regard to the calculation methods of the supply capability of power system. References [4; 5] use the continuation power flow (CPF) to calculate the available transfer capability of power systems. References [6; 7] evaluate the transfer capability by optimal power flow (OPF). CPF has a fast computing speed but lacks flexibility, and it is difficult to handle constraints and control strategies. OPF can consider the effects of various uncertainties of renewable energy but suffers from high computational complexity [8]. Therefore, in order to remain a good balance between the accuracy and feasibility for the ALSC of renewable-energy-based power systems, this paper adopts the repeated power flow (RPF) method [9; 10], which is has the advantages of simple calculation procedure and high flexibility. RPF calculation is based on the multiple normal power flow calculations. In normal power flow calculation, only one slack bus is set up, and all power imbalance of the network is handled by this slack bus. When the power imbalance of the system is small, the power flow calculation model with a single slack bus will not affect the calculation results. However, when the power imbalance becomes large, it is not suitable to use the power flow calculation model with a single slack bus to calculate the power flow. Due to the limitation of the maximum output of generators, it is difficult for a single slack bus to bear all the power imbalance of the system. The continuously increasing load in RPF calculation process will bring a significant power imbalance. Therefore, a single slack bus is not suitable for the RPF calculation. The power flow calculation model considering multiple slack buses can make up for the above deficiencies [11; 12]. It sets up multiple slack buses to share the power imbalance of the power system together, which can make the results of the power flow calculation fit the practical situation better. But according to the best knowledge of the authors, in existing studies on the RPF method for solving ALSC problem, some studies do not consider multi-slack buses [3]. In the studies that consider multi-slack buses, power imbalance allocation is only conducted once to share the power imbalance caused by load increment and the allocation principle is the ratio of the current power of the generators [13].