488 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1,JANUARY 2005 An Integro-Differential Equation Technique for the Computation of Radiated EMI Due to Corona on HV Power Transmission Lines S. K. Nayak and M. Joy Thomas Abstract—This paper presents a novel technique for the compu- tation of radiated electromagnetic interference (EMI) levels due to corona on high-voltage (HV) transmission lines. The EMI levels computed using the present technique for various HV transmission lines from around the world matches well with the experimentally measured values, thus validating the present technique. Using the technique developed, the influence of transmission line length, dis- tance of observation point from the line, conductor diameter as well as the transmission line configuration on the radiated EM field has been studied. It is seen that for observation points which are close to the transmission line corridor, the total radiated electric field remains almost constant for line lengths above 1500 m. For obser- vation points which are far away, a longer length of the line needs to be considered for computation of the total electric field. In the study, it is seen that the transmission line conductor height and line configuration have marginal influence on the radiated electric field. Index Terms—Corona, electromagnetic interference (EMI), high-voltage transmission lines, radio interference (RI), radio noise (RN). I. INTRODUCTION E LECTROMAGNETIC interference (EMI) from high-voltage (HV) transmission lines is caused by corona which is generated due to the electrical breakdown of the air surrounding the conductors at high voltage. When the conductor surface electric field exceeds the corona onset electric field, a partial breakdown occurs in the surrounding air near the conductor surface and is called the corona discharge [1]. The streamer generated during corona discharge transports electric charges into the surrounding air during a discharge cycle. These moving charges cause currents to be induced on the transmission line conductors. Since the charge is moved by a time varying electric field, it is equivalent to a current pulse and this current pulse is the source of the time varying EMI field. For estimating this radiated EMI field or radio noise (RN) or radio interference (RI) as they are popularly known among electrical power engineers, various empirical relationships [2]–[4] are available. However, one has to give arbitrary corrections to match the predicted noise levels with the measured levels. In the present work, an expression based on Maxwell’s equa- tion has been made use of for the computation of radiated EMI Manuscript received December 4, 2003. Paper no. TPWRD-00351-2003. The authors are with the Department of High Voltage Engineering, Indian Institute of Science, Bangalore 560012, India (e-mail: sisir@hve.iisc.ernet.in; thoma@hve.iisc.ernet.in). Digital Object Identifier 10.1109/TPWRD.2004.838644 Fig. 1. Time-domain representation of the corona current pulses. field from a coronating HV line. The computational results using the present method are in good agreement with the measured re- sults reported in the literature [2], [5]. II. MATHEMATICAL FORMULATION OF THE RADIATED EM FIELD A. Electrical Characteristics of Corona Current Pulses The time varying corona current pulses generated during a discharge cycle are double exponential in nature and can be rep- resented by the following equation [6] (1) where , , and are constants and is in nanoseconds. The time-domain representations of the positive and negative corona pulses, used for the computation are shown in Fig. 1 along with the values of , , and [7]. B. Spatial Distribution of the Coronating Points on Transmission Lines Each corona discharge point radiates electric field and thus the total electric field at the observation point is due to the sum of the electric fields radiated from each corona discharge point. Since the corona phenomenon is distributed along the transmis- sion line, the length of the line certainly influences the mag- nitude of the total radiated EMI field at any observation point 0885-8977/$20.00 © 2005 IEEE