Convex optimization for des planning and operation in radial distribution systems with high penetration of photovoltaic resources

In this paper, distributed energy storage (DES) devices, like batteries and ultra-capacitors, are used to alleviate detrimental impacts of high penetration photovoltaic (PV) resources on distribution systems. The impacts are studied at mainly two time resolutions - one minute and one hour. To determine accurately the size of the required DES for the purpose of mitigating the impacts of large-scale distributed PV, sizing procedures based on OpenDSS are proposed. After determining the total size of the required DES, optimization techniques can be used to choose the optimal locations for the DES along the feeder, which is a continuous optimization problem taking into account equality constraints of the AC power flow. The continuity of the problem and the radial network structure make it possible to apply a convex optimization technique called second order cone programming (SOCP) relaxation to obtain the globally optimal solution and avoid the problem of NP-hardness. The exactness of the introduced SOCP relaxation is sensitive to the chosen objective function and additional quadratic equalities. The necessary and sufficient condition of exactness for the SOCP relaxation of the DES optimal allocation and operation in radial distribution systems is studied. The proposed methods are applied to an actual feeder in the southwestern US with high penetration of PV using actual measured data. The simulation results demonstrate the efficacy of the proposed approaches.