  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.
