Elliptic Fields


What is Q-Lab ?

The symbol "Q" stands for electric charge. Q-Lab (or qLab) represents a collection of methods and tools for evaluation of electric charge including its creation, propagation and accumulation.

Q-Lab extends the Virtual High Voltage Lab (VHVLab) [5.1] that was focused on prediction of discharge inception and breakdowns for devices in the medium voltage range. The main component of VHVLab is evaluation of the inception voltage at critical field spots in the gas insulation. Once the inception spots are identified VHVLab uses heuristic rules for the assessment of breakdown and the withstand voltages.

Q-Lab makes the next step of discharge evaluation and assumes that the charge created during the discharge will be accumulated on surfaces of solid dielectrics. This surface charge leads within nanoseconds to the stage of saturation, which significantly changes the field distribution and the further development of the discharge.

A few characteristics of the inception and saturation models are presented below. More details are included in the referenced papers and in the user documentation of the qLab.

VHVLab: Discharge Inception in Gases. Background Field Stage

Inception and breakdown in weakly homogeneous fields are well correlated with the field strength on the surface of electrodes and insulators. Therefore, the surface field strength calculated by Elfi2D or Elfi3D could be directly used to judge about the dielectric performance of high and ultra-high voltage devices [5.2]. Typically, a stress limit corresponding to the surface roughness or particle size is specified for different components of the device to ensure a small probability of inception.

In case of strongly inhomogeneous fields, which are typical in the medium voltage range, designers cannot rely on the value of the surface stress only. A useful characteristic provides the streamer inception voltage Uinc specifying the voltage level at which an inception may occur. The evaluation of Uinc is based on a numerical computation of a streamer integral representing the number of electrons that are needed to create a self-propagating streamer head. This integral is evaluated along a field line started from critical surface spots selected by the user. The computation of Uinc requires the knowledge of effective ionization coefficients and the streamer constants. For air and SF6 VHVLab makes use of values obtained in scope of a research project performed at ETH Zurich [5.3]. These coefficients have been proven in many engineering computations performed in the last 20 years [5.4], [5.5].

VHVLab does not include numerical computation of discharge propagation, leader transition or breakdown. A reliable numerical procedure for assessment of these phenomena in engineering environment is still an open research topic. Currently, VHVLab uses heuristic models like streamer distance rule or the surface-capacitance-based leader inception for estimation of withstand voltage in air [5.6], [5.7].

The original VHVLab-tool is limited to the analysis of the background field without any surface charges. This type of analysis is still available in the new Q-Lab-tool where it is integrated as the "background field stage". It provides foundation for evaluation of next stages as shown below.

Q-Lab: Saturation Stage

Q-Lab assumes that the source of electric charge is a partial discharge (like streamers) propagating from critical inception spots to the surface of solid dielectrics where the charge is accumulated, see example in Fig. 5.1. The accumulated surface charge has a significant impact on the electric field, which may lead to a saturation stage. For a saturated surface additional charge carriers are prevented from being deposed on this surface.

A comprehensive investigation of the charging process dynamics performed recently by NTNU Trondheim [5.8] - [5.10] has shown that a saturation in air occurs almost immediately after the streamer discharges reached the dielectric surface (within a nanoseconds range). This indicates that the saturation stage can be achieved during the standard LI-tests (lasting more than a few microseconds). Q-Lab does not attempt to simulate the dynamics of the discharge and the charge accumulation processes. Instead, Q-Lab offers a static computation that utilizes the saturation boundary condition implemented by Elfi2d and Elfi3d [2.2], [1.9], [3.4].

Fig. 5.1. Fast camera images of partial discharges (streamers) in a rod-barrier-grounded-plane arrangement during an LI test: a) streamers starting from the rod arriving at the barrier, b) streamers above and below the barrier due to inceptions on both sides of the barrier, c) streamers bypassing the barrier after saturation stage is achieved (longer exposure of the camera), d) rod-barrier-grounded-plane geometry. Source: NTNU Trondheim.

Q-Lab makes an assessment where the saturation boundary condition should be applied. An important role play the user defined "seed points", which indicate where the streamer discharges of the specified polarity arrive at dielectric surfaces. Based on the seed points and the background field computation (without any surface charge) Q-Lab makes an initial estimation of the surface patches affected by the charge accumulation where the saturation boundary condition is applied. The size of these patches is iteratively corrected as soon as the polarity of the computed charge density differs from the polarity of the seed point. A detailed description of this procedure is presented in [5.11].

After the saturation charge location and values have been computed a new equilibrium representing so called "saturation stage" is defined. In this stage the user can go back to the inception analysis, which may indicate that some of the old inception points are no longer critical but new critical points may appear at different locations. Q-Lab enables evaluation of the new inception points, in the same way as described above for the background field stage, but now under taking into account the accumulated saturation charge. In case of new discharges the user may define additional seed points and recalculate the saturation charge until all locations where it is accumulated are found and corrected according to the seed point polarity.

For example, in Fig. 5.1a the initial seed point is defined on the upper surface of the barrier. The saturation charge accumulated only on this surface may initiate a new inception below the barrier as shown in Fig. 5.1b. A new discharge will depose a charge of the opposite polarity on the lower barrier surface. A recalculation of the saturation stage with both seed points on each barrier side will enable evaluation of both negative and positive charge layers, which can be useful to judge whether a puncture of the barrier is possible.

Q-Lab: Restrike Stage

The accumulated charge remains on the affected surface provided that no breakdown occured in the saturation stage. The remaining charge may become critical after the potentials of electrodes have changed during the test. For the LI-test the potential of the active electrode will be close to zero after a few hundred microseconds. This may trigger a "restrike" between the electrode and the accumulated charge. Such a restrike can be predicted by the Q-Lab's inception analysis performed for the "restrike stage". In this stage the potential of all electrodes is multiplied by zero and the saturation charge is assumed as the only excitation in the restrike model.

Another kind of the restrike stage is defined for the AC tests. The saturation charge accumulated in the first AC-half-period will enhance the field strength during the following half period (after a few milliseconds). This kind of restrike stage is critical since it lowers down the inception voltage Uinc comparing with the original inception conditions in the background field stage. A similar effect may also occur during the LI-test after changing the polarity of the test voltage. Q-Lab computes the AC-restrike by multiplying the potential of all electrodes by "-1" and applying the surface charge previously obtained in the saturation stage for the originally defined potentials.


[5.1] A. Blaszczyk, T. Christen, P. Kaufmann, Ch. Winkelmann, P. Homayonifar, A. Pedersen: ‘Virtual High Voltage Lab. Computer-based dielectric testing’, ABB Review 2021/2.

[5.2] N. De Kock, M. Mendik, Z. Andjelic and A. Blaszczyk, Application of 3D boundary element method in the design of EHV GIS components. IEEE Mag. on Electrical Insulation, Vol.14, No. 3, pp. 1722, May/June 1998.

[5.3] K. Petcharaks: Applicability of the Streamer Breakdown Criterion to Inhomogeneous Gas Gaps, Ph. D. Thesis No. 11192, ETH Zurich, 1995.

[5.4] A. Blaszczyk, H. Böhme, A. Pedersen A., M. Piemontesi, Simulation based spark-over prediction in the medium voltage range, International Symposium on High Voltage Engineering (ISH), Bangalore 2001.

[5.5] P. Simka, E-M. Borrelli, A. Blaszczyk, Air breakdown at sharp edges, IEEE 2nd International Conference on Dielectrics (ICD), Budapest 2018.

[5.6] A. Kuechler, Hochspannungstechnik, Springer VDI, 2nd edition Heidelberg 2005.

[5.7] A. Pedersen, T. Christen, A. Blaszczyk, H. Böhme, Streamer inception and propagation models for designing air insulated power devices, IEEE Conf. Electr. Insul. Dielectr. Phenomena (CEIDP), 2009.

[5.8] H. K. Meyer, Dielectric barriers under lightning impulse stress, PhD. Diss., No. 106, NTNU Trondheim 2019.

[5.9] H.K. Meyer, A. Blaszczyk, M. Schueller, F. Mauseth, A. Pedersen, "Surface charging of dielectric barriers in short rod-plane air gaps. Experiments and simulations", IEEE Conf. on High Voltage Engineering and Application, ICHVE 2018, Greece.

[5.10] H.K. Meyer, F. Mauseth, R. Marskar, A. Pedersen, A. Blaszczyk, ‘Streamer and surface charge dynamics in non-uniform air gaps with a dielectric barrier’, IEEE Trans. on Dielectrics and Electrical Insulation, Vol. 26, No. 4, August 2019.

[5.11] A. Blaszczyk, E. Morelli, P. Homayonifar, “Surface Charging Models for Prediction of Withstand Voltage in Medium Voltage Range”, IEEE Trans. on Magnetics, Vol. 57, June 2021.
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