Optimization of field grading for a 1000 KV wide-band voltage divider Joni Klüss a, * , Jari H € allstr € om b , Alf-Peter Elg c a Aalto University, Department of Electrical Engineering and Automation, P.O. Box 13000, FI-00076 Aalto, Finland b Centre for Metrology and Accreditation (MIKES), P.O. Box 9, 02151 Espoo, Finland c SP Technical Research Institute of Sweden, P. O. Box 857, SE-50115 Borås, Sweden article info Article history: Received 9 June 2014 Received in revised form 16 September 2014 Accepted 17 November 2014 Available online 2 December 2014 Keywords: HVDC transmission Electromagnetic fields Finite element methods Voltage dividers Voltage measurement abstract An HVDC reference voltage divider has been designed for high accuracy and wide-band measurements up to 1000 kV. To maintain wide-band characteristics, field distribution must be optimized in order to minimize the response time of the divider. To compensate the stray capacitance, a capacitive path that surrounds the resistive reference divider is added to function as a shield. Optimal capacitance values producing a matched distribution are obtained using 3D FEM simulations. Factors affecting the perfor- mance of the divider are assessed by simulating multiple scenarios representing different practical considerations in real-life applications. © 2014 Elsevier B.V. All rights reserved. Introduction Increasing transmission voltages in high voltage d.c. (HVDC) have accentuated the need for traceable calibrations of d.c. line voltage at levels above several 100 kV. The reference system for calibration of class 0.2 measurement requires preferably an order of magnitude lower uncertainty for the reference (IEC 61869), thereby setting the requirement for d.c. measurement uncertainty to 0.02%. A good response to voltages with signal components up to several kilohertz is also required to enable measurement of superimposed ripple voltages and to prevent damage during possible flashovers. Precision HVDC dividers are traditionally based on a resistive design, whereas high voltage a.c. (HVAC) dividers from 50 Hz and above typically rely on a capacitive or a transformer design. Owing to the high resistance inherent in d.c. dividers, increasing the fre- quency from d.c. to even very low frequency (VLF) a.c. will usually lead to problems related to stray capacitances. The stray capaci- tance to ground together with the high resistance of the divider forms a low pass filter. The cut-off frequency of this filter often affects the response of the divider, sometimes even in the VLF range. The experience from lightning impulse voltage (LI) reference divider designs can be applied also to wide-band d.c. dividers. One approach in resistive LI divider designs is based on non-linear high voltage resistance distribution [1,2], and another on field grading using additional electrodes [3e5]. The latter approach was chosen for the divider described in this paper. Field grading has been used to extend the frequency range also on some earlier designs of reference d.c. dividers [6,7], but not on 1000 kV level [8]. Voltage divider design The system consists of two concentric parallel dividers (Fig. 1) [9]. A capacitive shield divider surrounds the resistive reference divider. The wide-band capacitive divider, made of dry polypropylene ca- pacitors, has parallel bleeding resistors to ensure a stable d.c. behavior. The estimated bandwidth of the shield divider extends to tens of kilohertz. Care has been taken to minimize the inductance of the low voltage part of the shield divider, which was designed to have a high capacitance. The shield divider is composed of three parallel branches surrounding the reference divider. The response of the reference divider will closely follow the wide-band response of * Corresponding author. E-mail addresses: joni.kluss@aalto.fi (J. Klüss), jari.hallstrom@mikes.fi (J. H€ allstr€ om), alf.elg@sp.se (A.-P. Elg). Contents lists available at ScienceDirect Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat http://dx.doi.org/10.1016/j.elstat.2014.11.005 0304-3886/© 2014 Elsevier B.V. All rights reserved. Journal of Electrostatics 73 (2015) 140e150