Analysis of small-signal stability of power systems with photovoltaic generators

This paper presents a theoretical analysis of the small-signal stability of a power system in which a synchronous generator and a photovoltaic (PV) generator supply power to an infinite bus. The problem considered here is to investigate the existence of the equilibrium points of the system and their stability. In terms of this problem, by focusing on the condition to be satisfied by the equilibrium points and appropriately using the intermediate value theorem, we derive a sufficient condition on the magnitude of the PV current for the existence of the equilibrium points. The condition is given as inequalities with respect to the system parameters. These inequalities show that, if the power system from which the PV generator is removed has equilibrium points, then equilibrium points exist also in the original system as long as the PV current is small. Moreover, we analyze the stability of the equilibrium points and show that the equilibrium points found under our existence condition are asymptotically stable. These results imply that, when the PV current is below a certain level, the existence of the asymptotically stable equilibrium points is preserved even though the PV generator is introduced.