Scalable algorithm for the dynamic reconfiguration of the distribution network using the Lagrange relaxation approach

- MILP problem is formulated using the “path-switch-to-switch” approach.
- Lagrange relaxation approach is used to decompose the original problem.
- Single- and multi-objective formulations are proposed.

This paper proposes a new methodology for the dynamic reconfiguration of the distribution network (DRDN) which is based on the Lagrange relaxation approach. The aim of DRDN is to determine the optimal topologies (configurations) of the distribution network over the specified time interval. The objective is to minimize the active power losses, subject to the following constraints: branch power flow capacities, allowed ranges of bus voltages, radial network configuration, and limited number of switching (open/close) operations for all switching devices. The paper first introduces the “path-switch-to-switch” approach for the modelling of distribution networks, which is used to formulate DRDN as the mixed integer linear programming (MILP) problem. Then, the specified MILP problem is solved using the Lagrange relaxation approach in two-step procedure. In the first step, the associated Lagrange dual problem is solved, which is created by relaxing the switching operation constraints. The Lagrange dual problem is decoupled and much easier to solve than the original problem. In the second step, the solution of the Lagrange dual problem is used to perform the heuristic search, providing the suboptimal, though feasible solution of the original problem. Finally, the presented DRDN model is extended to multi-objective formulation, which also includes the impact of the network reliability and the switching costs to the DRDN process. The robustness and scalability of the developed algorithm (for application in large-scale distribution networks) are demonstrated with two test examples: 15-bus test benchmark and 1021-bus real-world test system.