A Multi-step Piecewise Linear Approximation Based Solution for Load Pick-up Problem in Electrical Distribution System

TL;DR

This paper introduces a multi-step piecewise linear approximation method to improve the accuracy and efficiency of solving the load pick-up problem in electrical distribution systems, addressing nonlinearity and reducing computation time.

Contribution

It proposes a dynamic multi-step PWL approximation approach that reduces errors and computational time in solving the LPP problem in EDS, enhancing practical applicability.

Findings

Significantly reduces modeling and solving time for LPP.

Improves accuracy of PWL approximation in network power flow constraints.

Effective in real-world 13-bus and 1066-bus EDS case studies.

Abstract

The load pick-up (LPP) problem searches the optimal configuration of the electrical distribution system (EDS), aiming to minimize the power loss or provide maximum power to the load ends. The piecewise linearization (PWL) approximation method can be used to tackle the nonlinearity and nonconvexity in network power flow (PF) constraints, and transform the LPP model into a mixed-integer linear programming model (LPP-MILP model).However, for the PWL approximation based PF constraints, big linear approximation errors will affect the accuracy and feasibility of the LPP-MILP model's solving results. And the long modeling and solving time of the direct solution procedure of the LPP-MILP model may affect the applicability of the LPP optimization scheme. This paper proposes a multi-step PWL approximation based solution for the LPP problem in the EDS. In the proposed multi-step solution procedure, the variable upper bounds in the PWL approximation functions are dynamically renewed to reduce the approximation errors effectively. And the multi-step solution procedure can significantly decrease the modeling and solving time of the LPP-MILP model, which ensure the applicability of the LPP optimization scheme. For the two main application schemes for the LPP problem (i.e. network optimization reconfiguration and service restoration), the effectiveness of the proposed method is demonstrated via case studies using a real 13-bus EDS and a real 1066-bus EDS.