376 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 28, NO. 1, JANUARY 2013 Parametric Study on Unit Step Responses of Impulse Voltage Measuring Systems Based on FDTD Simulations Hiroki Oka, Yoshihiro Baba, Member, IEEE, Masaru Ishii, Fellow, IEEE, Naoto Nagaoka, Member, IEEE, and Akihiro Ametani, Life Fellow, IEEE Abstract—Unit step responses (USRs) of a USR-measuring system recommended by the International Electrotechnical Commission have been computed using the finite-difference time-domain (FDTD) method for various conditions of grounding and shield ring. The USR measuring system subject to analysis has a resistor divider of height 3.3 m and resistance 9 k . It follows from FDTD-computed results that USR parameters are not much influenced by either the laboratory-floor conductivity or its relative permittivity if is higher than or equal to 10 mS/m, and they are close to the USR parameters for . When is lower than about 0.1 mS/m, USR parameters are more influenced by and . Variations in the partial response time , the experimental response time , the settling time , and the overshoot , due to the differences of and , are 8 ns, 14 ns, 150 ns, and 50%, respectively. Even if the width of a horizontal metal sheet is extended from 2 to 3 m, these variations are not much reduced. The extension of the width of a vertical metal sheet from 1 to 2 m does not influence the USR parameters much, either. The installing height of a shield ring influences the USR parameters: with decreasing , and decrease while and increase. Note that the FDTD-computed USR for 0.1 S/m and 10 agrees well with the corresponding measured USR. Index Terms—Finite-difference time-domain (FDTD) method, impulse voltage, resistor divider, unit step response (USR). I. INTRODUCTION T HE International Electrotechnical Commission (IEC) 60060-2 Standard [1] states that an impulse high-voltage (HV) measuring system is supposed to be calibrated by com- parison with the corresponding reference measuring system. The unit step response (USR) measurement of an impulse HV measuring system is considered one of the fundamental methods for evaluating the response characteristics of the divider. Although a USR measurement is not required by the Manuscript received March 17, 2012; revised August 01, 2012; accepted September 01, 2012. Date of publication October 16, 2012; date of current ver- sion December 19, 2012. This work was supported by the Ministry of Educa- tion, Culture, Sports, Science and Technology (MEXT) of Japan under Grant 21760220. Paper no. TPWRD-00277-2012. H. Oka, Y. Baba, N. Nagaoka, and A. Ametani are with the Department of Electrical Engineering, Doshisha University, Kyoto 610-0321, Japan (e-mail: dtk0152@mail4.doshisha.ac.jp; ybaba/nnagaoka/aametani@mail.doshisha.ac. jp). M. Ishii is with the Institute of Industrial Science, the University of Tokyo, Tokyo 153-8505, Japan (e-mail: ishii@iis.u-tokyo.ac.jp). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2012.2217399 IEC standard to be carried out, it has been frequently employed in research and development of an impulse HV measuring system since a USR measurement could be made without the corresponding reference system. The stability of the USR of an impulse HV measuring system is of great importance [2]. It has been reported in [3] that partial response times and settling times, measured at eight different laboratories in Japan for the same megavolt (MV)-class impulse voltage measuring system, have about 30% variations. This in- dicates that reproducible measurements of the USR of a MV class impulse voltage measuring system at different sites are quite difficult. Recently, USRs of impulse HV measuring systems have been analyzed using electromagnetic computation methods [4]–[8]. For example, differences in USR parameters between values, computed using the numerical electromagnetics code (NEC-2) [9] based on the method of moments [10], and corresponding measured values are about 20%–30% [6], which could be re- garded as relatively good accuracy. Note that in this USR sim- ulation with NEC-2, a horizontal metal sheet, on which an im- pulse HV measuring system would be placed, was represented by an infinitely extending, perfectly conducting plane, and a ver- tical metal sheet was represented by a thin-wire coarse grid. Therefore, NEC-2 did not allow them to study influences of horizontal and vertical metal sheets and of a laboratory floor on USR. The reason for relatively large variations (20%–30%) [3] in partial response times and settling times measured for the same MV class impulse voltage measuring system might be due to differences of widths of horizontal and vertical metal sheets and differences of conductivity and/or permittivity of laboratory floors. In this paper, the USR of an MV class impulse voltage measuring system, whose configuration is recommended by IEC, is analyzed using electromagnetic modeling software, programmed by ourselves on the basis of the finite-difference time-domain (FDTD) method [11] for solving Maxwell’s equations. Influences on USR of physical sizes of horizontal and vertical metal sheets, constitutive constants of a laboratory floor, and suspended height of a shield ring and its diameter are intensively studied. The structure of this paper is as follows. In Section II, a model of an impulse HV measuring system, to be analyzed using the FDTD method, is shown. In Section III, the FDTD-computed USR is compared with the corresponding measured one. In Section IV, influences on USR of the conduc- tivity and relative permittivity of a laboratory floor, widths of 0885-8977/$31.00 © 2012 IEEE