An iterative linear DistFLow for dynamic optimization in distributed generation planning studies

This paper implements an iterative linear DistFlow for the modelling of radial distribution grids. The method is intended for dynamic optimizations under gird constraints, and in the presence of distributed generation including storage units with time coupled constraints. It is demonstrated that traditional piecewise linearization for the losses estimation in conventional linear DistFlow can lead to significant errors. This is due in particular to the setting of static upper bounds for the active and reactive branch flows in the linearization process, which may differ greatly from the actual power. The proposed iterative approach addresses this shortcoming with successive runs of linear DistFlow and updates for the flows upper bounds, dynamically along the simulated horizon. The method is compared to conventional linear DistFlow as well as other relaxed formulations such as Second Order Conic Programming and Quadratic Programming. All the methods are discriminated with regard to a reference AC power flow, in terms of error for the voltages and losses profiles on different test systems. The proposed iterative procedure displays the lowest error for the line losses with five to forty times more accuracy than conventional linearized formulations. It also outperforms the Second Order Conic relaxation in terms of scalability with one month dynamic simulation (at 1 h time step) run in 7 min with 30 distributed units on a 69-bus system. The approach is further validated with typical uses cases for the operation, the sizing, and the siting of distributed assets consisting of solar generators and storage units. Especially, the procedure is coupled with a genetic algorithm in order to test different system configurations on a 90-bus system. The solutions are discriminated in terms of number of assets, installed capacities, connection bus(es), installation costs, system losses and system self-sufficiency.