Modified quadrature method for accurate voltage measurement in optical voltage transducer H. Monsef and T. Ghomian Abstract: There are fewer problems encountered with optical voltage transducers in comparison with their inductive and capacitive counterparts. As a result they are considered as proper candidates for replacing conventional inductive and capacitive transformers. Lighter weight, smaller size, larger dynamic range, wider bandwidth, insensitivity to electromagnetic interference, stability over temperature change, absence of iron core saturation, low maintenance and replacement cost, are some of the advantages of optical voltage transducers over inductive and capacitive transformers. A modified quadrature method is introduced to measure the voltage with the minimum number of sensors. Another advantage of this method is the possibility of improving the accuracy of the measurement by using a correction factor. The correction factor is determined by considering the level of accuracy, environmental conditions and the number of sensors. Simulation results show the validity and effectiveness of this method over a wide range of variation. 1 Introduction High voltage levels of transmission networks and the need for accurate measurement devices have caused optical voltage transducers to become important through their high accuracy, low weight and small size. The problems in manufacturing, maintenance and accuracy of inductive and capacitive voltage transformers have pushed research work towards designing simpler and more accurate transformers. Although capacitive and inductive transformers are used for the purpose of measurement and protection in the networks, they cause problems such as core saturation and improper transient responses which decrease the accuracy of measurement and efficiency of the protection schemes. As a result the need for research work toward newer measurement techniques is inevitable. Advance in optical science has made the construction of more accurate transformers possible. The insensitivity of optical signals to electromagnetic noise, the economic superiority of isolation with optical fibres, the wide bandwidth and proper frequency response of optical signals, and the compatibility of optical output signals with digital electronic devices, have caused a preference for optical techniques over electromagnetic ones [1–6] . In this paper a type of optical transducer with few electric field sensors is studied. The sensors measure one field component ideally at one point. By using all-dielectric field sensors one can overcome the problems associated with regions of extremely high electric field intensity. The integrated optic Pockels cell (IOPC) is useful in such designs and it provides for all the advantages of optical voltage transducers [7]. A new algorithm called the modified quadrature method is introduced for numerical calculation of the field integral. By using this algorithm the effect of stray fields caused by conductors or external voltage sources and other environ- mental influences is minimised. A changeable correction factor, which increases the accuracy of the measurements in the presence of environ- mental conditions, is also introduced. The method gives the number of sensors for reaching a desired accuracy. Numerical simulation using shows the effectiveness of the modified quadrature method for the design of optical voltage transducers. 2 Theory The voltage between two points a and b is calculated by the following integral: V ba ¼ Z Gab ~ E  ~ dl ð1Þ where G ab is any arbitrary path from point a to point b. Considering G ab along the x-axis of the cartesian co- ordinate system with a at the origin, (1) can be written as the following linear integral: V b ¼ Z b 0 E x ðxÞdx ð2Þ where E x ðxÞ is the electric field component along the x-axis. By measuring the electric field at several points in the space between the two electrodes the integral can be approxi- mated as a finite weighted sum V b ¼ Z b 0 E x ðxÞdx  X N i¼1 a i E x ðx i Þ ð3Þ where a i is the weight, x i is the abscissa, N is the number of sensors and E x ðx i Þ is the amount of x-component of the electric field at point x i . E-mail: hmonsef@matn.com The authors are with the ECE Dept., Faculty of Engineering, University of Tehran Centre of Excellence on Applied Electromagnetic Systems r The Institution of Engineering and Technology 2006 IEE Proceedings online no. 20050189 doi:10.1049/ip-gtd:20050189 Paper first received 21st May and in final revised form 25th July 2005 524 IEE Proc.-Gener. Transm. Distrib., Vol. 153, No. 5, September 2006