Integration of voltage dependent power injections of distributed generators into the power flow by using a damped Newton method

Voltage dependent active and reactive power injections are used to improve the grid integration of distributed generators, such as photovoltaic systems. In state-of-the-art literature these power injections are considered during power flow calculations via an external loop, which requires to perform multiple (up to ten or more) power flow calculations in order to obtain one static operation point. In this paper it is shown how to integrate voltage dependent power injections into the nonlinear grid equations in order to solve for a static working point by means of performing one Newton power flow calculation. That makes the external loop unnecessary and save computational time. Furthermore, it is shown for a two-bus system that the integration of voltage dependent power injections into the nonlinear grid equations can exhibit ill-conditioned power mismatch functions. Therefore, a damped Newton method is used in order to avoid numerical oscillations. Simulations of the IEEE 118-bus test system and a real German 234-bus test system show that the damped method converges faster and is computationally more efficient than the external approach currently used in literature and state-of-the-art simulation tools in power systems. In addition, the implemented power flow algorithm is validated in the laboratory for a two-bus system and a numerical example of a low-voltage feeder is given.