Interval analysis based coordinated dispatch of battery energy storage systems and flexible loads for distribution systems considering extreme operating scenarios

Interval optimization (IO)-based dispatch methods are widely used to address the uncertainty of renewable energy sources (RESs) in distribution systems. However, existing studies rarely embed interval power flow (IPF) information into IO-based dispatch models to mitigate state-variable limit violations. This work proposes an interval analysis based coordinated dispatch approach for battery energy storage systems and flexible loads that explicitly incorporates IPF-derived extreme operating scenarios. A linearized power flow formulation solved via successive linear programming is developed to compute IPF efficiently. Potential statutory violations of state variables are analyzed based on the IPF results to obtain the corresponding extreme operating scenarios. A coordinated dispatch strategy considering these extreme scenarios is formulated as a mixed-integer linear programming (MILP) problem that defines the operating intervals of flexible resources to ensure system security under the uncertainties. The simulation results show that the proposed dispatch framework eliminates security-limit violations while achieving the lowest mean operation cost with the tightest 95 % confidence interval among all comparison methods. Compared with a nonlinear method, the proposed MILP dispatch method exhibits below 1 % errors and 2000 times faster speeds. These results indicate the proposed framework has superior economic performance, high accuracy, and significant computational efficiency.