Abstract
We compute an optimal day-ahead dispatch plan for distribution networks with stochastic resources and batteries, while accounting for grid and battery losses. We formulate and solve a scenario-based AC Optimal Power Flow (OPF), which is by construction non-convex. We explain why the existing relaxation methods do not apply and we propose a novel iterative scheme, corrected DistFlow (CoDistFlow), to solve the scenario-based AC OPF problem in radial networks. It uses a modified branch flow model for radial networks with angle relaxation that accounts for line shunt capacitances. At each step, it solves a convex problem based on a modified DistFlow OPF with correction terms for line losses and node voltages. Then, it updates the correction terms using the results of a full load flow. We prove that under a mild condition, a fixed point of CoDistFlow provides an exact solution to the full AC power flow equations. We propose treating battery losses similarly to grid losses by using a single-port electrical equivalent instead of battery efficiencies. We evaluate the performance of the proposed scheme in a simple and real electrical networks. We conclude that grid and battery losses affect the feasibility of the day-ahead dispatch plan and show how CoDistFlow can handle them correctly.
Highlights
The monotonously increasing deployment of distributed energy resources, if adopted passively, can lead to raising the costs of the investment and operation of power distribution systems, which may affect the widespread adoption of this technology [1]
We proposed CoDistFlow to solve the nonconvex scenario-based AC Optimal Power Flow (OPF) with intermittent renewable resources and battery storage, where current relaxation practices do not apply
CoDistFlow handles the non-convexity of the scenario-based AC Optimal Power Flow (AC OPF) by iterating until convergence over an improved DistFlow approximation with correction terms for line losses and nodal voltages computed via load flows based on the battery power values obtained by the previous iteration
Summary
The monotonously increasing deployment of distributed energy resources, if adopted passively, can lead to raising the costs of the investment and operation of power distribution systems, which may affect the widespread adoption of this technology [1]. Computing a dispatch plan for a distribution network with stochastic resources and storage devices while accounting for operational constraints and system losses involves an AC Optimal Power Flow (AC OPF) This problem involves the non-linear power flow equations, it is, as well known, nonconvex and hard to solve. There are methods that apply approximations by modifying the physical description of the power flow equations, e.g., the DC load flow [8], [9] for transmission networks and, most importantly, the DistFlow approximation [10] that has been historically applied to radial distribution networks In this category, there exist methods which linearize the AC power flow equations around an operating point, e.g., the load-zero point, as applied in [11], [12]. In [17], it is shown that under specific conditions the dual gap is zero solving the dual problem leads to the global optimal solution
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