The impact of different corona models on FD algorithms for the solution of multiconductor transmission lines equations

Abstract

In this study, the implementation of different corona discharge models in a transient program for overhead multiconductor lines based on the implicit Crank‐Nicolson Finite Difference Time Domain method is presented. Among different corona models available in the literature, two empirical models (Gary's and Suliciu's models) and a physics‐based model (Malik's model) are discussed, which are broadly used in EMT programs, and their predictions under fast‐front lightning surges and slow‐front switching impulses are assessed. The authors critically review the dynamic capacitance approach in terms of numerical accuracy, when dealing with slowly varying voltages, and applicability, regarding dispersive models assuming a non‐instantaneous charge‐voltage relation. The alternative voltage‐controlled generator approach is proposed, which is successfully included in the implicit Crank‐Nicolson scheme. One of the objectives of this study is to show how different corona models may predict overvoltages with huge discrepancies, depending on the transient waveform and the propagation distance, despite the similarity of the q‐v hysteresis curves. More evident discrepancies between models under fast‐front voltage waves are reported, rather than for switching impulses. The consistency of these results in terms of the models' features and q‐v curves is analysed, highlighting the necessity for new engineering tools for corona simulation of general predictive capability.

The Corona Phenomenon in Overhead Lines: Critical Overview of Most Common and Reliable Available Models

“…The introduction of a harsh discontinuity of the p.u.l. dynamic capacitance (i.e., an abrupt change in the propagation velocity of traveling waves) requires careful implementation in FDTD approaches in order to avoid numerical instability [51].…”

“…Including the delayed dependence of the charge over the voltage in C dyn would be in contrast with the assumptions underlying the transmission line theory, leading to erroneous results. Alternative approaches with distributed voltage-controlled current generators may be also employed [51].…”

Tower Models for Power Systems Transients: A Review

“…IEC [2] and ANSI/IEEE [3,4] standards establish, on a solid theoretical and practical ground, definitions, principles, and rules, providing application guidelines and computational examples. Power systems insulation is exposed not only to normal stresses associated with steady-state conditions (e.g., due to corona effect [5,6]), but also to external and internal overvoltages. External overvoltages occur under lightning discharges, while internal overvoltages are caused by faults and switching operations.…”

Design of an Internal Down-Lead System for a 400 kV Composite Tower and Investigation of Lightning Performance

“…For the capacitance of the downlead, the value directly depends on the magnitude and the change rate of the applied voltage. According to the previous work [127,128], the capacitance is dq/dV, and the Q − V curve gives the regulation of the capacitance development. Neglecting the effect of the thickness of the hollow crossarm, the value of C is a piecewise function.…”

“…When the increased voltage is above the corona threshold voltage to emanate the streamer from the conductor, the capacitance of the downlead will be correspondingly increased. According to Grey model [128], the capacitance is expressed as (4.9). Where coefficient η is given by 1.121 + 6.8a for negative polarity.…”