3810 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 26, NO. 12, DECEMBER 2011 Letters Impedance Identification Procedure of Three-Phase Balanced Voltage Source Inverters Based on Transient Response Measurements Virgilio Valdivia, Student Member, IEEE, Antonio L´ azaro, Member, IEEE, Andr´ es Barrado, Member, IEEE, Pablo Zumel, Member, IEEE, Cristina Fern´ andez, Member, IEEE, and Marina Sanz, Member, IEEE Abstract—Impedance-based models are commonly used to per- form system-level stability analysis of distributed power systems. In this paper, a new impedance identification procedure for three- phase balanced voltage source inverters voltage source inverters (VSIs) is proposed. This procedure is based on the transient re- sponse of the inverter to simple passive load step tests. Trans- fer function models are obtained from the transient response by means of a well-established and easy to use identification algo- rithm. The performance of the proposal is validated through both simulation and experimental results obtained on VSIs for aircraft applications. Index Terms—Impedance measurement, stability, system iden- tification, three phase voltage source inverter. I. INTRODUCTION N OWADAYS, ac power-electronics-based distributed power systems are being used in an increasing amount of new applications, e.g., more-electric-aircraft and new naval ships power systems [1]–[4]. In addition to linear passive loads, these systems comprise nonlinear active loads, such as power converters. Due to the interaction between load and source sub- systems, the system-level behavior is complex, so that the in- teraction can lead to degradation in the ac bus power quality and even to instabilities. Consequently, system-level dynamic modeling to analyze these interactions is regarded as a powerful tool [3]–[5]. System-level stability analysis is commonly carried out using small-signal impedance-based models, by applying the Nyquist criteria to the ratio between the output impedance of the source subsystems and the input impedance of the load subsystems. This methodology has been extensively applied to analyze dc Manuscript received October 1, 2010; revised February 7, 2011; accepted March 24, 2011. Date of current version December 6, 2011. This work was sup- ported by the Spanish Ministry of Science and Innovation through the research project SAUCE (DPI: 2009-12501) and by the private contract with the Eu- ropean Aeronautic Defense and Space Company–Construcciones Aeron´ auticas S. A. under the research project HVDC (Code: 04-AEC0527-000050/2005) fi- nanced by The European Regional Development Fund via the Aerospace Sector Plan of the Community of Madrid. This paper was presented in part at the IEEE Control and Modeling for Power Electronics Conference COMPEL, Boulder, USA, June 28-30 2010. Recommended for publication by Associate Editor R. Burgos. The authors are with the Power Electronics Systems Group, Electronics Tech- nology Department, Carlos III University of Madrid, Legan´ es 28911, Spain (e-mail: vvaldivi@ing.uc3m.es; alazaro@ing.uc3m.es; barrado@ing.uc3m.es; pzumel@ing.uc3m.es; cfernand@ing.uc3m.es; cmsanz@ing.uc3m.es). Digital Object Identifier 10.1109/TPEL.2011.2141687 distributed systems [6], [7]. In the case of three-phase ac sys- tems, the generalized Nyquist criteria can be applied to the impedance ratio expressed in the synchronous reference frame d-q [4], [8], [9] in which three-phase balanced ac signals become dc quantities at steady state. The stability analysis of three-phase ac systems using the d-q frame input-output impedances is dis- cussed in [3], [10], [11]. Furthermore, this impedance represen- tation has been applied to the design of EMI filters for PWM rectifiers [12], [13]. However, such distributed systems are commonly made up of subsystems from commercial manufacturers. For confidentiality reasons, the designer of the power distribution system usually has no detailed data available about the subsystem impedance characteristics. Hence, impedance measurement techniques are required. Impedance measurement methods for dc subsystems have been widely reported in the literature [6], [7], [14], [15] but relatively few works deal with impedance measurements of three-phase ac subsystems [9], [16]. The aim of this paper is to present a new identification procedure of the impedance of three-phase balanced voltage source inverters (VSIs) with ca- pacitive output, defined in the d-q frame. The main advantage of the proposed method is its simplicity, as it is based on the iden- tification of transfer function models from the VSI transient response to simple passive load steps. The coefficients of the transfer function models are identified using a well-established and easy to use parametric identification algorithm. Both sim- ulation results and first experimental results are presented to illustrate and validate the proposal. This paper is organized as follows: 1) Section II presents the proposed experimental tests to ob- tain the transient response of the converter, from which the impedance is identified. The main experimental issues to be considered are also discussed briefly here. 2) The impedance identification procedure from the mea- sured transient response is explained in Section III. 3) Simulation and experimental results are presented and dis- cussed in Sections IV and V, respectively. The methodol- ogy is illustrated as well as practical considerations and limitations of the procedure are discussed, with regards to both the experimental and the identification processes. II. IDENTIFICATION EXPERIMENTS The small-signal output impedance of a three-phase VSI un- der balanced conditions can be modeled in the d-q frame by 0885-8993/$26.00 © 2011 IEEE