Linear method for steady-state analysis of radial distribution systems

Linear methods for steady-state analysis of distribution systems are getting more and more important due to the spreading of distributed energy resources, such as distributed generation, storage systems, active demand. This paper proposes a new linear method based on a Jacobian approach for radial distribution network with lateral derivations and distributed energy resources. The set of the linear equations modeling the distribution system is firstly presented and, then, solved in a closed form. It includes the full π-model for lines, ZIP model for uncontrolled loads, both P-Q and P-V control for distributed energy resources. The adoption of a peculiar set of modeling variables and the radial topology of the network allows to obtain high accuracy and low computational times. The effectiveness of the method is tested on both a 24-nodes and a 237-nodes network. The method is firstly applied to sensitivity analysis and compared with other linearized methods in terms of accuracy and computational efficiency; then, it is applied to the power flow analysis and compared with the classical non linear load flow.