Simplified hybrid PD model in voids

Simplified Hybrid PD Model in Voids G. Ala, R. Candela, P. Romano, F. Viola Abstract – In this paper a novel approach to model partial discharges (PD) activity taking place inside a spherical void in epoxy resin system has been traced. The approach is based on a time varying conductance of the inner void, subjected to multistress conditions: voltage, temperature and pressure. A simple lumped circuit macro-model simulates the global effects of PD activity: the different parameters influencing the discharge phenomenon in the void are taking into account by using a physical approach resulting in a time varying conductance inside the circuit. The evaluated PD activity has been compared with experimental and simulated one for the accessible and inaccessible part of the system. A discussion on the observed changes in PD activity has been reported. Φ Index Terms-- Partial discharge (PD), void, PD model, electrical insulation, Weibull function, probability function. I. INTRODUCTION T HE necessity of higher and higher voltage levels in power systems has driven to a stronger demand of insulating materials with high electrical performances at affordable costs. Synthetic polymers, which meet these requirements, unfortunately are affected by some aging problems also due to internal partial discharges (PD) phenomena. These discharges take place in consequence of unavoidable local defects produced by the industrial manufacturing process, i.e. the inclusion of small air void in the polymer, and promote local erosion of the material surrounding the void, that may cause electric breakdown of the component in time. The difficulty of performing reliable life predictions, in presence of such degradation phenomena, together with the need for non-destructive analysis, has promoted a wide band studies [1]. The evaluation of the charge in picocoulombs, involved in the discharge process, offers a non-destructive detection but gives a little information on type of PD. Subsequent phasecharge-rate patterns can be successfully used to distinguish different PD activity [2], [3]. The modelization of partial discharge phenomena has been raised several times by many authors. Many models, based on the circuital approach (Whitehead model of the three capacitors) and the Maxwellian approach (Pedersen mostly), have been developed. In both cases, the choice of electrical parameters (voltage, capacitance value, etc.) and physical parameters (ionization, surface conductivity, work function, temperature, etc.) influencing the pulse repetition and the stochastic properties of PD, was fundamental [4]-[8]. G. Ala, R. Candela, P. Romano and F. Viola are with Università degli Studi di Palermo, Dipartimento di Ingegneria Elettrica, Elettronica e delle Telecomunicazioni, viale delle Scienze 90128 Palermo, Italia (e-mail: guido.ala@unipa.it; roberto.candela@unipa.it, pietro.romano@unipa.it, fabio.viola@unipa.it). Φ 978-1-4244-9303-6/11/$26.00 ©2011 IEEE 451 By using the experience gained in the implementation of previous PD’s model, the new simplified model is able to obtain values of the induced charge and PD patterns very similar to those experimentally observed [9]. II. SIMPLIFIED CIRCUITAL MODEL 
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A. Whitehead’s equivalent circuit model In Fig.1 a combination of the basic IEC 60270 [11] test circuit and the Whitehead [4] equivalent circuit model is shown. Sketch of the dielectric specimen is reported in Fig.2 where C2 is the capacitance of the void; C1 and C3 are the column capacitance of the dielectric before and after the void (sketched with a darker insulation); C4 is the remaining capacitance of the dielectric (lighter insulation). The time-varying conductance G(t) models the PD phenomenon. C1 Filter Z C2 Ck iPD U0 50Hz - - - - + + + + - Electric field + + insulation Fig. 2. Sketch of the dielectric specimen. The inner part contains the spherical void. The darker insulation characterizes C1 and C3 capacitance, the lighter the remaining bulk capacitance C4. - - - - - - R d r1 + + + + + + Fig. 3. Sketch of the spherical void in generic discharge condition. R is the spherical void radius, d is the equatorial area of the void not directly exposed to discharge activity, r1 identifies the polar area of the void directly exposed to discharge activity. A spherical cavity has been embedded in an epoxy specimen. The air gap thickness has been set to 2 mm, and the material simulated is a bisphenolic epoxy resin ($"), widely employed in electrical industry for embedding purpose in electrical machine construction. Without considering t
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;>- R50 Fig. 1. Simulation model of the Whitehead’s equivalent void circuit. Four capacitance are used to simulate the dielectric-void specimen. Effect of the discharge is modeled with a time varying conductance G(t). A 50 Hz voltage generator feeds the circuit, filter impedance and detection impedance are reporter together with a coupling capacitance according to IEC 60270 basic PD test circuits. Ck is a coupling capacitor and R50 is a detection impedance. A 50 Hz generator feeds the circuit together with the filter impedance. 452 B. Void model By considering a spherical void of radius R, in the middle of a solid dielectric material between a couple of plane electrodes, it is known that the electric field distribution inside and outside the void can be evaluated solving the Laplace equation: (3) ∇2V = 0 where V is the scalar potential function. Equation (3) can be rewritten by spherical coordinates in a two-dimensional form: 1 ∂  2 ∂V  1 1 ∂  ∂V   sin θ =0 r + 2 2 r ∂r  ∂r  r sin θ ∂θ  ∂θ  (4) Inside the cavity the solution is: 3ε Vi = − E0 r cosθ ε 0 + 2ε The surface de-trapping rate is:  t  −  τ tr  N s = N e e (5) where ε0 and ε are the absolute permittivity of the gas inside the void and of the surrounding dielectric respectively, and E0 is the electric field in absence of the void. The field inside the void, due to the external voltage, along the main diametral axis (θ = 0) is: 3ε ∂V Ei = − E0 = f (T )E0 = ∂r ε 0 + 2ε (6) As can be noted in (6), the temperature acts on the electric field through a function of the solid dielectric permittivity ε(T), and so through the f (T) parameter. By combining (5) with (6) the following equation holds: Vi = 3ε V0 = f (T )V0 ε 0 + 2ε (7) where Vi is the voltage at capacitance C2, and V0 is the voltage at C4. In Fig. 3 the areas involved and not in the PD activity are shown. During the ionization phenomenon the major conductance is given by the plasma channel, as the plasma channel expires the remaining conductance is given by the surface conductivity GS of the resin, which can be set to 10-18 S at 20°C [9]. C. Probabilistic approach The global electric field inside the cavity has to take into account the charge deposited on the polar area [9]: q E = f (T )E0 + 2 πr1 ε 0 (8) In the polar areas the concentrated charge q is not a constant quantity, it may change because of the transferred charge ∆q, due to the previous discharge: ∆q = −∫ G(t )Ei (t )d ⋅ dt (9) ∆t where ∆t is the period of the discharge. The number of trapped electrons in the polar area is: Ne = q(t ) e where e is the elementary charge. Only a part of the Ne electrons released on the void surface promotes the discharge, some of them diffuse into energetically deeper traps and/or into depth of the insulating material from where they are no more extractable. To consider this loss from a phenomenological point of view, the surviving electrons, useful to trigger the discharge, could be modeled roughly by an exponential decay term exp(-t/τtr) with a time constant τtr representing an effective lifetime of the electrons in an extractable trap. In addition, these electrons are supposed to be thermally de-trapped and then emitted from the surface on the basis of the Φtr function value, which is Φ tr = Φ − eE 4πε 0 (12) where v0 is the fundamental photon frequency of the resin, Kb is the Boltzmann constant (8.617385ּ◌10-5 eVK-1), T is the absolute temperature. A natural radiation phenomenon generates also electrons useful for the triggering: ρ N r = Cr Φ r   πR 3 (1 − µ −0.5 )  p 0 (13) E  B   Ei ≥ Einc = p  1 + n   p cr  ( p 2 R )  (14) where CrΦr = 2ּ◌106 kg-1 s-1, (ρ/p)0 = 10-5 kg m-3Pa-1 is the pressure reduced gas density and µ is the ratio between the applied voltage and the streamer inception voltage derived from: where (E/p)cr = 24.2 VPa-1 m-1, B = 8.6 (Pa m)0.5, n = 0.5. The transferred charge ∆q can be assumed equal to: (15) ∆q = ε 0πr12 E − Er ( where (11) where Φ is the de-trapping work function of the material expressed in eV. 453 ) Er = 0.2(E / p )cr is the residual electric field. The total rate production of electrons ready to trigger a discharge becomes: (16) Nt = N s + N r In order to consider the statistical aspect of PD, the following probability function has been defined:  N dt  −   P(dt ) = ∑ pi 1 − e  α  i =1  m t i βi    (17) where m is the number of elementary Weibull functions fitting experimental data and αi and βi their parameters. This probability function has been chosen because it has better capability to reproduce the observed different statistical aspects of PD phenomena (internal, corona, surface discharges) also at different temperatures. D. (10)  Φtr   − KbT  v0e Weibull’s inception circuital scheme 
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0.01 0.005 0 -0.005 -0.01 0 ∑ - 0.005 0.01 0.02 0.015 Time [s] Fig. 7. Voltage on R50 resistance, different picks are present. ∫ Krec 1 0.02 0.015 0.01 Time [s] Fig. 6. Voltage on the capacitance void. At a different voltage levels the discharge starts, since the availability of free electrons does not coincide with the exceeding of the inception voltage. The sinusoidal voltage generator is set to 25 kV.

+ GS + x 10 ∑ -3 9 G(t) 8 Fig. 5. Time-variable conductance model. On the right the evaluation loop of the conductance is drawn with a thicker line. The PD current is enforced by a controlled current generator.

VR50 [V] Vi(t0)>Vinc ∫ yes >= V 4 t VR50 [V] Vi t0 Vi [V] 1 yes x 10 7 6 5 4 III. VALIDATION OF THE MODEL 3 
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3000 [11] Discharge [pC] 2000 [12] 1000 0 [13] -1000 -2000 -3000 0 [14] 0.02 0.01 0.015 Time [s]
Fig. 9. Phase-discharge distribution, the sinusoidal voltage waveform is only reporter in order to aid the phase evaluation. For a time interval of 0.8s a mean value of discharges can be estimated equal to 650 pC. 0.005
Dielectric Barrier Discharge (DBD)”, 40th Annual Meeting of the IEEE Industry Applications Society (IAS2005), Hong Kong, 2005, pp. 2315-2319. IEC Standard 60270 “High-Voltage Test Techniques - Partial Discharge Measurements”, 2000. P. Romano, “Influence on PD paramethers due to voltage conducted disturbance”, IEEE Trans. Dielectrics and Electrical Insulation, vol. 11, No. 1, Feb. 2004, pp. 161-165. P. Y. Chia, A. C. Liew, “Novel approach to partial discharge signal modeling in dielectric insulation void using extension of lumped capacitance model”, International Conference on Power System Technology, (PowerCon 2000), Perth, WA, Australia, Dic 2000, pp. 1207-1212. H. A. Illias, G. Chen, P. L. Lewin, “Modeling of partial discharges from a spherical cavity within a dielectric material under variable frequency electric fields”, IEEE Conference on Electrical Insulation and Dielectric Phenomena, 26-29 October 2008, Quebec City, Quebec, Canada. pp. 447-450. VI. BIOGRAPHIES IV. CONCLUSION A novel approach for modeling the PD activity in a spherical void embedded in a epoxy dielectric has been proposed. A simple lumped circuit macro-model simulates the global effects of PD activity: the different parameters influencing the discharge phenomenon in the void are taking into account by using a physical approach resulting in a time varying conductance inside the circuit. Different aspects have been considered in order to validate the proposed model. In the final full paper the characterization in presence of harmonic content and different gap void will be presented. V. REFERENCES [1] L. Simoni "A general phenomenological life model for insulating materials under combined stresses", IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 6, Apr 1999, pp.250 – 258. [2] R.Candela, G.Mirelli, R.Schifani, "PD Recognition by Means of Statistical and Fractal Parameters and Neural Network", IEEE Transactions on Dielectric and Electrical Insulation, Vol. 7, 2000, pp. 87-94. [3] A. Abate, G. Ala, R. Candela, P. Romano: “DWT-based method for partial discharge pattern recognition”. Communications to SIMAI, Vol. 2, 2007 DOI: 10.1685/CSC06133 pp.1-5. [4] Whitehead S., Dielectric Breakdown of Solids (Clarendon Press, Oxford) 1953. [5] A. Pedersen, “Partial Discharges in Voids in Solid Dielectrics. An Alternative Approach”, 1987 Annual Report - Conference on Electrical Insulation and Dielectric Phenomena, IEEE publication 87 CH2462-0, pp. 58-64. [6] R. J. Van Brunt, “Physics and Chemestry of partial discharge and corona”, IEEE Trans. Dielectrics and Electrical Insulation,, vol. 1, No. 5, Oct. 1994, pp. 761-1783. [7] L. Niemeyer, "A generalized approach to partial discharge modeling", IEEE Trans. EI, Vol. 2, pp. 510-527, 1995. [8] L. Testa, S. Serra, G. C. Montanari “Advanced modeling of electron avalanche process in polymeric dielectric voids: Simulations and experimental validation” Journal of Applied Physics 108, 034110 2010, pp.1-10. [9] R. Schifani, R. Candela, P. Romano, “On PD mechanisms at high temperature in voids included in an epoxy resin”, IEEE Trans. Dielectrics and Electrical Insulation, vol. 8, No.4, pp. 589-597, Aug. 2001. [10] S. Bhosle, G. Zissis, J.J. Damelincourt, A. Capdevila, K. Gupta, F.P. Dawson, V.F. Tarasenko, “Electrical modeling of an homogeneous 455 Guido Ala was born in 1964. He received the Laurea degree (Master degree) in Electrotechnical Engineering (cum laude and with honours) and the Ph.D. degree in Electrotechnical Engineering (Electrical Sciences) from the University of Palermo, Italy, in 1989 and in 1994, respectively. After various industrial experiences he joined the Department of Electrical, Electronic and Telecommunication Engineering of the University of Palermo where he was appointed as an university researcher from 1996 to 2004. Since 2005 he is an associate professor at the same Department. He teaches Fundamental of Circuit Theory, Principles of Electrical Engineering, Electromagnetic Compatibility, also for Ph.D. students, and is the director of the Faculty master degree course in Electrical Engineering. His main research interests are in the fields of electromagnetic numerical methods, electromagnetic transient analysis, lightning, electromagnetic compatibility. He has been tutor of students working with MIUR projects fellowships. Roberto Candela received the Laurea degree in electrical engineering and the Ph.D. degree from the Università degli Studi di Palermo, Palermo, Italy, in 1996 and 2001, respectively. He is currently researcher with the Dipartimento di Ingegneria Elettrica, Elettronica, e delle Telecomunicazioni, Università degli Studi di Palermo. He is the holder of the course of “Electrotechnics” at the Engineering Faculty of Palermo. His research activity is mainly in the field of insulating systems diagnosis, partial discharge measurements, multifactor stress effects and electric field simulations. Pietro Romano was born in Palermo, Italy on 15 May 1967. He received the MSc. and Ph.D. degrees in Electrical Engineering from the University of Palermo, Italy, in 1993 and 1998, respectively. He is now a researcher at the Department of Electrical Engineering and teaches Basic Electrical Engineering and Electrotechnics. His research activity is mainly in the field of insulating systems diagnosis, partial discharge measurements, multifactor stress effects and electric field simulations. Fabio Viola received the Laurea degree in electrical engineering and the Ph.D. degree from the Università degli Studi di Palermo, Palermo, Italy, in 2002 and 2006, respectively. He is currently researcher with the Dipartimento di Ingegneria Elettrica, Elettronica, e delle Telecomunicazioni, Università degli Studi di Palermo. He is the holder of the course of “Electrotechnics” at the Engineering Faculty of Palermo. His research interests are in the field of electromagnetic compatibility, where he works on developing and employing numerical methods for the study of linear and nonlinear aspects of electromagnetic compatibility.