A Linear Model for AC Power Flow Analysis in Distribution Networks

The standard power flow (PF) equations are nonlinear, and their integration in the optimal PF (OPF) problem leads to a nonconvex hard-to-solve model. To attack the issue, this paper presents a linear PF model wherein real and imaginary parts of nodal voltages are variables. In the model, loads are interpreted via ZIP model including constant impedance, constant current, and constant power components. To preserve linearity of the model, the complex power is represented via a quadratic function of the hosting node voltage. The function coefficients are derived via curve fitting approaches. Since the model is linear, its solution does not need repetition and can be effectively integrated in the OPF problem. The price for the simplification is the inaccuracy induced by curve fitting approaches. The performance of the model is tested on different benchmark systems with 12, 28, 33, 70, 481, 1921, and 3681 nodes.