An optimization model for distribution system reinforcement integrated uncertainties of photovoltaic systems

In this paper, a two-stage model for the optimal planning of distribution systems considering uncertainties of photovoltaic systems is presented. The uncertainties in intermittent power of photovoltaic are taken as input variables by a probability distribution function. The proposed model determines the optimal sizing and timeframe of the equipments (feeders and transformer substations) in distribution systems. Therefore, the optimal displacement, sizing and installation period of PV are also specified. The objective function is minimizing the life-cycle costs of the planning project. The technical constraints are used to guarantee the operability of the distribution system including alternating current power flow, feeders upgrading section, substations upgrading capacity, limited of nodal voltage and PV capacity. The binary variables are also employed in the model in order to represent the cost function of the equipment as well as the investment and upgrade decisions. The algorithm is programmed in GAMS environment. The feasibility and effectiveness of the proposed model are verified in a 15-bus test system.