Probabilistic Load Flow for Distribution Networks with Photovoltaic Generators Part 1: Theoretical Concepts and Models

Connections of distributed generation (DG) systems to distribution systems are increasing in number, though they may often be associated with the need of costly grid reinforcements or new control issues to maintain optimal operating conditions. Appropriate analysis tools are required to check distribution networks operating conditions in the evolving scenario. Load flow (LF) calculations are typically needed to assess the allowed DG penetration level for a given network in order to ensure that voltage and current limits are not exceeded. The present paper deals with the solution of the LF problem in distribution networks with photovoltaic (PV) DG. Suitable models for the active power produced by PV DG units and the power absorbed by the loads are to be used for representing the uncertainty for solar energy availability and loads variation. The proposed models have been incorporated in a radial distribution probabilistic load flow (PLF) program that has been developed by using Monte Carlo techniques. In this paper the theoretical concepts and the software implementation are described. The developed program allows probabilistic predictions of power flows at the various sections of distribution feeders and voltage profiles at all nodes of a network. In the second part of the paper the application to a practical case study is presented to show the results of the proposed method.