A linear programming-based framework of interval power flow analysis for distribution systems

The interval power flow (IPF) method is widely employed to address the uncertainties of renewable energy sources (RESs) in power systems. However, limited research exists on the application of mathematical optimization-based approaches to compute IPF results. Furthermore, a comprehensive framework for analyzing the derived IPF results and formulating appropriate countermeasures is still lacking. Therefore, this paper proposes a novel linear programming-based framework of IPF analysis for distribution systems, designed to enhance IPF calculation efficiency and keep system state variables within recommended limits utilizing controllable equipment. First, a linearized IPF model is proposed to improve calculation efficiency. The over-limit of system state variables is analysed based on the IPF results. Then, A countermeasure strategy utilizing controllable equipment is proposed to maintain system security under potential extreme scenarios. The output intervals of the controllable equipment are determined as scheduling references ensuring secure operation under the uncertainties. The numerical results demonstrate that the linearized formulation computes the IPF results 6.57 times faster than the non-linear method, with insignificant calculation errors (below 0.06 % for magnitudes and 0.02° for angles). The countermeasure method can successfully keep state variables within predefined ranges and provide system operators with effective scheduling reference intervals of controllable equipment under uncertainties.