Ac Impedance Measurement Techniques Y.L. Familiant, K.A. Corzine, J. Huang, and M. Belkhayat † University of Missouri - Rolla † Newport News Shipbuilding 1870 Miner Circle 4101 Washington Avenue Rolla, MO 65401 Newport News, VA 23607 Abstract - Naval ship as well as aerospace power systems are incorporating a greater degree of power electronic switching sources and loads. Although these power electronics based components provide exceptional performance, they are prone to instability due to their high efficiency and constant power characteristics which lead to negative impedance. When designing these systems, integrators must consider the impedance versus frequency at a system interface (which designates source and load). Stability criterions have been developed in terms of source and load impedance for both dc and ac systems and it is often helpful to have techniques for impedance measurement. For dc systems, the measurement techniques have been well established. This paper suggests several methods for measuring ac impedance including utilization of power converters, induction machines and chopper circuits. Simulation results on an example ac system demonstrate the effectiveness of the proposed methods. I. INTRODUCTION Power electronic based systems are prone to negative impedance instability due to the constant-power nature of the individual components [1-5]. Previous research has shown that the instabilities can be avoided in some systems by modification of the power electronic controls [2]. Other research has defined admittance space criteria based on a dc interface which can be used to design system components [3]. Recent research has shown that stability criteria for ac systems can be developed based on the q-d impedances of the source and load (defined at a particular system interface) [4]. Along these lines, a method of ac impedance measurement was proposed which is based on series injection of perturbation voltages [5]. This paper suggests additional ac impedance measurement techniques which are based on shunt current injection. In particular, two types of power converters are proposed for current injection as well as a wound rotor induction machine. II. CONSTANT-POWER LOAD SYSTEM A. System Description Figure 1 shows the example system used to illustrate impedance measurement concepts. For simplicity, a fixed- frequency ac power source with input inductors is used to represent a utility grid or a synchronous generator. The source is connected to a full-bridge IGBT rectifier through an input R-L-C filter; the purpose of which is to eliminate PWM frequency switching harmonics from voltages at the source terminals. Constant power load performance is achieved by keeping the dc bus voltage dc v constant across the constant resistance load r . The rectifier control also maintains unity power factor at the source terminals (a-b-c). Table I contains a list of parameters and operating conditions used in the example system. Table I. Example system parameters. Ω = 01 . 0 s r mH 4 . 0 = s l Ω = 01 . 0 r r Ω = 9 . 18 f r mH 1 = f l F 81 . 2 μ = f c Ω = 6 . 67 load r F 3300 μ = dc c V 500 * = dc v V 133 = s v Hz 60 = e f ~ ~ ~ Current injection v as i as i al i bs i cl i cs i bl v bs v cs i bi i ai i ci r s l s r fl l f r load c dc v dc v dc v a , v , v b c PWM control r fc a b c ar br cr n c f T a ,T ,T b c T a T b T c T b T c n T a Figure 1. Example active rectifier system. v a 0-7803-8987-5/05/$20.00 ©2005 IEEE. 1850