Warm-start piecewise linear approximation-based solution for load pick-up problem in electrical distribution system

Abstract

As the core sub-problem of both network reconfiguration and service restoration of the electrical distribution system (EDS), the load pick-up (LPP) problem in EDS searches the optimal configuration of the EDS, aiming to minimise the power loss or provide as much power as possible to load ends. The piecewise linearisation (PWL) approximation method can be used to tackle the network power flow constraints’ non-linearity in the LPP problem model, and transform the LPP model into a mixed-integer linear programming model (LPP-MILP model). The errors in the PWL approximation of the network power flow constraints may affect the feasibility of the solving results of the LPP-MILP model. The single method to reduce the PWL approximation errors by increasing the number of discretisations in PWL function is not stable. Moreover, the solution efficiency of the LPP-MILP model is sacrificed severely. In this study, a warm-start PWL approximation-based solution for the LPP problem is proposed. The variable upper bounds in the PWL approximation functions are renewed dynamically in the warm-start solution procedure to reduce the PWL approximation errors with higher computational efficiency. Modified IEEE 33-bus radial distribution test system and a real and large distribution system, 1066-bus system, are used to test and verify the effectiveness and robustness of the proposed methodology.

Keywords

• linear programming
• load flow
• integer programming
• piecewise linear techniques
• approximation theory
• distributed power generation
• power loss
• piecewise linearisation approximation method
• network power flow constraints
• lpp problem model
• lpp model
• mixed-integer linear programming model
• lpp-milp model
• pwl approximation errors
• pwl function
• pwl approximation-based solution
• pwl approximation functions
• radial distribution test system
• warm-start piecewise linear approximation-based solution
• load pick-up problem
• electrical distribution system
• core sub-problem
• network reconfiguration
• service restoration
• eds