Determination of Partial Discharge Time Lag in Void using Physical Model Approach

Transcription

1 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 22, o. 1; February Determination of Partial Discharge Time Lag in Void using Physical Model Approach H. A. Illias, M. A. Tunio, H. Mokhlis UM High Voltage Laboratory Department of Electrical Engineering Faculty of Engineering, University of Malaya 563 Kuala Lumpur, Malaysia G. Chen Tony Davies High Voltage Laboratory University of Southampton Southampton, SO17 1BJ United Kingdom and A. H. A. Bakar UM Power Energy Dedicated Advanced Centre (UMPEDAC) Level 4, Wisma R&D, University of Malaya 5999 Kuala Lumpur, Malaysia ABSTRACT Repetition of partial discharge (PD) activities within a dielectric insulation of high voltage equipment may lead to dielectric breakdown, eventually resulting in failure of the whole equipment. Thus, PD measurement is essential in high voltage insulation system. Modeling of PD activity may increase an understanding of PD phenomenon. One of the parameters which can be determined from PD modeling is the statistical time lag. In this work, a physical model of PD using finite element analysis (FEA) method has been developed to determine the relationship of statistical time lag with different applied stresses; these include different applied voltage, frequency and temperature. The statistical time lag as a function of different applied stresses was determined through comparison between measurement and simulation results. The proposed experimental-modeling approach may increase an understanding on the physical explanation about the statistical time lag. Index Terms - Insulation, finite element methods, partial discharges. 1 ITRODUCTIO DIELECTRIC breakdowns in high voltage equipment are normally preceded by repetition of partial discharges (PD). Therefore, in order to avoid dielectric breakdown, it is essential to perform PD measurement on high voltage insulation system. PD measurement is widely used as a tool for insulation diagnosis and performance assessment of insulation system. The behavior of PD events is influenced by many factors, which determine the ageing and deterioration level of dielectric insulation [1, 2]. The conditions of the applied stress factors include the amplitude, frequency and waveform of the applied voltage and material temperature [3, 4]. The defect and type of the material factors include the location, size, shape, humidity and pressure of the defect and also the type of Manuscript received on 2 February 214, in final form 1 July 214, accepted 15 July 214. the gas within the defect [5-7]. One of the parameters related to PD, which varies depending on these factors is the statistical time lag. umerous studies have been undertaken to investigate the statistical time lag of PD events. Measurement of PD within a cylindrical void in polycarbonate was undertaken to study the statistical time lag of PD events at different frequency of the applied voltage [8, 9]. At lower applied frequencies, the statistical time lag was longer due to the period of the applied voltage is longer. Thus, the time lag is dependent on the frequency of the applied voltage. From PD measurement within a spherical void in an epoxy resin, the number of PD was found to be lower when the applied voltage decreases [1]. This is due to the surface charge decay being more significant at lower applied frequency, reducing the electron generation rate, resulting in a longer statistical time lag and lower number of PDs per cycle. This result is opposite to PD measurement in a cylindrical void but both works relate PD activity to the statistical time lag. DOI 1.119/TDEI

2 464 H. A. Illias et al.: Determination of Partial Discharge Time Lag in Void using Physical Model Approach In most of the previous works reported, the statistical time lag is determined through applying an impulse voltage of magnitude higher than the inception voltage across a test sample. The time between the voltage application and a PD occurrence is measured as the statistical time lag. Although this method manages to estimate the statistical time lag successfully, it is only limited to impulse voltage application. Therefore, in this work, an experimental-modeling approach is proposed in determination of PD statistical time lag. A PD model using finite element analysis (FEA) method has been developed to determine the relationship of statistical time lag with different applied stresses. The measurement results were reproduced by the simulation results to obtain the statistical time lag as a function of different applied stresses. The simulation of PD used in this work is based on the previous model that has been reported in [11]. The occurrence of a PD event is modeled using a probability function, which depends on the electron generation rate, surface charge decay rate and charge distribution along the void surface [11-14]. From the proposed approach in this work, an understanding on the physical explanation about the statistical time lag on the occurrence of PD may be attained. 2 STATISTICAL TIME LAG Statistical time lag, τ stat is the time difference between the time when the inception field is exceeded and the occurrence of a PD. τ stat is a result of unavailability of a free electron to initiate a PD after the inception field is exceeded, resulting in a time delay of a PD occurrence. This time delay varies with different conditions of the applied stress and also the defect conditions. Variation in τ stat influences the cycle to cycle behavior of PD events and statistical behavior of PD patterns, such as the number of PDs per cycle, total PD charge magnitude per cycle and the maximum and minimum charge magnitudes. The unavailability of a free electron to initiate a PD may be due to a very low electron generation rate, a high PD surface charge decay rate or high electron attachment rate within a defect in a dielectric material. 3 PD MEASUREMET SETUP The PD measurement setup that has been used in this work is based on the OMICRO mtronix PD detector [1, 11, 15]. The test object, as shown in Figure 1, comprises of a spherical void located in the middle of a cylindrical epoxy resin, which is connected to two cylindrical electrodes on the top and bottom surfaces of the epoxy resin. The top electrode was connected to an applied voltage and the bottom electrode was kept grounded. The test object was immersed in mineral oil. The void in the epoxy resin was prepared by injecting an air bubble into the epoxy resin before it turned into solid. Then, the cured resin with the bubble was cut into a smaller piece and placed at the middle of a larger amount of uncured epoxy resin. After that, the uncured epoxy and the smaller piece with an air bubble was cured for 24 h at ambient temperature, followed by post cured for 4 h at 9 o C and finally cooled down to ambient temperature for 2 h. Spherical void Epoxy resin Test sample To applied voltage 2r void To ground 38 mm Figure 1. Test object. Table 1. Dimensions of the test samples that were prepared. Epoxy resin thickness, h mat (mm) Void radius, r void (mm) Applied voltage amplitude, V app (kv) Applied frequency, f (Hz) Table 1 shows the dimensions of the test samples that were created and the applied voltage amplitude used for each PD experiment. Test samples 1, 2 and 3 were used for PD experiment of variable applied voltage amplitude, V app, material temperature, T mat and applied voltage frequency, f respectively. The measurement was taken for 5 applied voltage cycles. 4 PD MODEL The PD model was developed using finite element analysis (FEA) method. The geometry of the PD model was developed based on the test object geometry shown in Figure 1. Referring to Figure 2, the PD model comprises of a cylindrical dielectric material (permittivity, ε r of 4.4), a spherical void in the middle of the material (ε r of 1) and top and bottom void surfaces (ε r of 4.4). The thickness of the void surface was set as.5 mm for any size of the void. The void surface conductivity was assigned at the volume of the void surface in the FEA model. The void surface was used to model surface charge decay through conduction along the void surface. The governing partial differential equation (PDE) that is used to solve the electric field distribution in the model is given by ( σv ) ε V t Top electrode h mat Bottom electrode Material temperature, T mat ( C) , 16, 18, , 35, 5, ,5, 1, 2, 5 2 where ε is the permittivity, σ is the conductivity and V is the electric potential. In order to simplify the model, some assumptions have been made as follows: a) A PD affects the whole void space. This is due to the size of the void being considerably small (the void radius is less than 1 mm). (1)

3 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 22, o. 1; February where es is the EGR due to surface emission and ev is the EGR due to volume ionization. The surface emission is due to charge detrapping from the void surface, charge injection from the electrode and the available free charges on the void surface due to previous PD. es is defined as [11] es PD t t exp PD decay Evoid T exp Einc T mat amb (5) Figure 2. PD model using FEA software. b) To model a PD event, the conductivity of the whole void, σ void is increased from a very low value, σ voidl, to a higher value, σ voidh. PD is modeled in this manner because PD occurs within a very short time, thus the conductivity changes very quickly when a PD occurs. The time taken for this change can be neglected. Increasing the void conductivity represents the flow of charges in the void during a PD event, resulting in the electric field in the void to decrease. σ void can be written as voidl, when no PD occurs (2) void voidh, when PD occurs c) In a spherical void, PD events only occur along the symmetry axis of the void (along r = line) and charges from PD propagate along the top and bottom surfaces symmetrically once they reached the void surface d) Only one PD occurs at a time in a spherical void. The inception field, E inc, is defined as the minimum electric field in a void for a PD to occur. The inception field has been defined as [16, 17] 8.6 E 24.2 p1 (3) inc. 5 (2 pr) where p is the pressure in the void (in Pa) and r is the void radius (in m). Rapid increase in the current during PD is considered as an avalanche process; therefore, the occurrence of initial electron is essential for such process. Even though the electric field in the void has exceeded E inc, PD could not occur if there is no initial free electron available. When the electric field in the void, E void is higher than the inception field, E inc, the total electron generation rate (EGR), et, at instantaneous time, t, is calculated using [11] et (4) es ev where t PD is the time elapsed since previous PD occurrence and τ decay is the effective charge decay time constant [13, 14, 18]. Equation (5) shows that the surface emission depends on the temperature and electric field in the void. The surface emission also decays with time because some charges accumulated on the void surface may not remain there for a long time. PD, the initial EGR immediately after a previous PD has occurred is calculated using E ( t ) / E (6) PD es void PD inc where es is the initial EGR due to surface emission at E inc and E void (t PD ) is the electric field in the void at which a previous PD has occurred. Equation (6) shows that the occurrence of the next PD depends on the previous PD occurrence. This is due to the amount of charge presented on the void surface from previous PD event determines the availability level of free electron to initiate the next PD. es is assigned with two values, esl, when Evoid / Evoid ( tpd) (7) es esh, when Evoid / Evoid ( tpd) where esl and esh are lower and higher es values, which depends on the polarity of E void of the current PD occurrence and the previous PD occurrence at time t PD [13, 14]. This is due to the polarity of charge accumulated along the void surface influences the difficulty of free electron to be detrapped from the void surface to initiate the next PD. When positive charges are accumulated on the void surface, electron detrapping from the void surface is easier compared to when negative charges are accumulated. The probability, P, of a PD occurrence is calculated using P et dt, when E, when E void void E E where dt is the time step used in the simulation. Equation (8) calculates the probability within time interval dt. The PD charge magnitude is calculated by integration of inc inc (8)

4 466 H. A. Illias et al.: Determination of Partial Discharge Time Lag in Void using Physical Model Approach current through the void with time during the occurrence of a PD event. Charge decay along the void surface is modeled by changing the void surface conductivity, σ s from a lower, σ sl to a higher value, σ sh, depending on the signs of E void and the electric field due to the surface charge, E q [11], sl, when Eq / Evoid (9) s sh, when Eq / Evoid conductivity, σ voidh is chosen as 5x1-3 Sm -1 so that the change of E void during PD occurrence does not take too long or short time period. The value of higher void surface conductivity, σ sh is assigned based on the measured maximum charge magnitude. Start Clear workspace Equation (9) is considered because charges accumulated along the void surface after a PD event may decay through surface conduction, which depends on the void surface conductivity, σ s. Hence, higher σ s leads to a faster surface charge reduction. Figure 3 shows a flowchart of the simulation program that has been written in MATLAB, which is interfaced with the FEA model in Figure 2. Initially, the workspace is cleared. The FEA model is assigned with its initial boundary and subdomain settings. At each time step, the boundary and subdomain of the FEA model; such as the conductivity of the void and void surface, are updated. When the electric field in the void, E void is higher than the inception field, E inc, the total electron generation rate (EGR) at instantaneous time, t, et and probability of PD occurrence, P are calculated using equations (4) to (8). Then, P is compared with a random number, R which lies between and 1. R is a decimal number randomly generated by MATLAB software every time after P is calculated. If P is larger than R, a PD will occur, where the void conductivity is increased to a higher value using equation (2). PD stops when E void becomes less than the extinction field, E ext. After PD stops, the charge accumulated along the void surface is determined whether they decay or not by comparing the polarity of electric field due to surface charge, E q with E void. The void surface conductivity is determined using equation (9), whether lower or higher value is assigned. The same process is repeated for each time step. The program stops once the specified cycles of simulation have been reached. All simulation results are stored in the workspace and various result analyses are done. Table 2 shows the parameter values that have been used in the simulation for different conditions of the applied stress. The values for τ decay, esh, esl and ev were chosen by adjusting their values until the total difference (TD) between the simulation (sim) and measurement (meas) results of the number of PDs per cycle, S PD and the average time and voltage differences between consecutive PDs (Δt n and ΔU n ), is the lowest. TD is calculated using TD S PD( meas) U S n( meas) PD( sim) U t n( sim) n( meas) t n( sim) (1) Define constants Assign initial subdomain and boundary conditions Increase time step Update boundary and subdomain settings Solve FEA model E void >E inc? Calculate et and P P>R? Increase σ void to σ voidh Solve FEA model E void <E ext? Reset σ void to σ voidl E q /E void >? Set σ s to σ sl Cycles complete? Save results in workspace End Set σ s to σ sh The lower void and void surface conductivity were assigned as Sm -1 because there is no charge movement in the void and the void surface. The value for higher void a = es, = o Figure 3. Flowchart of the MATLAB programming code.

5 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 22, o. 1; February Table 2. Parameter values used in the simulation. Parameter Value Table 3. Measurement and Simulation Results From Test Sample 1. Applied voltage, V app (kv) Ambient temperature, T amb (K) 293 (2 C) Lower void conductivity, σ voidl (Sm -1 ) Higher void conductivity, σ voidh (Sm -1 ) 5x1-3 Lower void surface conductivity, σ sl (Sm -1 ) Higher void surface conductivity, σ sh (nsm -1 ) Inception field, E inc (kvmm -1 ) Extinction field, E ext (kvmm -1 ) Lower initial EGR due to surface emission, esl (s -1 ) Higher initial EGR due to surface emission, esh (s -1 ) S1:.2,.4,.9, 2. S2:.8, 1.7, 3.3, 6. S3:.2,.1,.2,.4, 1.1 S1: 3.35 S2: 3.53, 3.69, 3.86, 4.2 S3: 3.2 S1:.88 S2:.76,.8, 1.21, 1.81 S3:.64 S1: 15 S2: 1, 15, 2, 25 S3: 3 S1: 3 S2: 135, 42, 75, 99 S3: 21 EGR due to volume ionization, ev (s -1 ) S1: 55, 7, 8, 85 S2: 1, 2, 3, 4 S3: 5, 2, 35, 6, 12 Effective charge decay time constant, τ decay (ms) S1: 2 S2: 1.8, 3.4, 6.4, 12.1 S3: 2 a S1, S2 and S3 are test samples 1, 2 and 3 respectively 5 COMPARISO BETWEE MEASUREMET AD SIMULATIO RESULTS Figure 4 shows simulation of electric fields against time of the applied voltage obtained from the FEA model. The statistical time lag, τ stat of each PD event is calculated from the time when the electric field in the void, E void exceeds the inception field, E inc to the time when a PD occurs (shown by the sharp field reduction in Figure 4). E q is the field due to the surface charge and E void is the field in the void in the absence of E q. The average statistical time lag, τ statave equals to summation of each τ stat divided by the total number of PDs. The time and voltage differences between consecutive PDs, Δt n and ΔU n are also shown in Figure TEST SAMPLE 1 Table 3 shows comparison between measurement and simulation results for test samples 1 at different applied voltage amplitudes. Most of the % differences can be considered Electric field (kvmm -1 ) U n t n E void E void E q E inc -1 stat stat Time (ms) Figure 4. Simulation of electric fields against time of the applied voltage. Measured average Δt n (ms) Simulated average Δt n (ms) % difference in Δt n 3.8% 2.13% 2.86% 3.57% Measured average ΔU n (V) Simulated average ΔU n (V) % difference in ΔU n.4%.%.%.% Measured S PD Simulated S PD % difference in S PD % % % % Simulated average statistical time lag, τ statave (ms) reasonably small, which indicates that the simulation results are in good agreement with the measurement data. When the applied voltage is higher, the number of PDs per cycle is higher. Thus, the measured average time difference between consecutive PDs, t n and the average statistical time lag, τ statave becomes shorter. The measured average voltage difference between consecutive PDs, U n increases due to a higher applied voltage amplitude. Figure 5 shows cycle to cycle behavior of PD events from measurement and simulation results at 5 Hz, 2 kv ac sinusoidal voltage. Referring to Figure 5a, a large PD charge magnitude is obtained from the measurement when the PD charge sign changes from that of previous PD charge. However, PD charge magnitudes are lower when there is no change of PD charge sign between consecutive PDs. These behaviors were reproduced in the simulation results. The polarity of the charge magnitude indicates the polarity of field in the void, E void at which a PD occurs. Referring to Figure 6 which shows simulation of electric fields against time of 2 kv ac sinusoidal voltage for test sample 1, when there is no polarity change of E void between consecutive PDs, PD occurs almost immediately when E void exceeds E inc. This results in smaller PD charge magnitude, since the charge magnitude depends Charge magnitude (nc) Charge magnitude (nc) Cycle number (a) Cycle number (b) Figure 5. Measured (a) and simulated (b) cycle to cycle behaviour of PD events for test sample 1 at 2 kv applied voltage.

6 468 H. A. Illias et al.: Determination of Partial Discharge Time Lag in Void using Physical Model Approach on the reduction of E void. This also indicates that the statistical time lag, τ stat is shorter, i.e. close to ms. From Figure 6, when the polarity of E void changes between consecutive PDs, it can be seen that many PDs do not occur immediately when E void exceeds E inc. This results in larger PD charge magnitude. This also indicates that the statistical time lag, τ stat is longer, i.e. more than 1 ms. The occurrence is caused by the variation of the electron generation rate due to surface emission, es (t). When the polarity of E void changes from that of previous PD, the time interval between consecutive PDs is longer, resulting in more charges on the void surface to decay within that time interval. Hence, es (t) becomes lower when the next PD is likely to occur [13, 14]. This reduces the probability of PD to occur, resulting in PD does not occur immediately when E void exceeds E inc. From the simulation results in Table 3, the average statistical time lag, τ statave in general can be represented as a function of applied voltage amplitude, V app by ( ) [ s] (11) statave V app zero, τ statave is also approaching zero. Higher applied voltage amplitude reduces t n, which in turn reduces τ statave [ms] (12) statave t n Figure 7 shows the distribution of τ stat for different applied voltage. It can be seen that when the applied voltage increases, more τ stat become shorter, which results in smaller average of τ stat, as shown by equation (11). stat (ms) where V app is in kv. Therefore, equation (11) shows in general that the average statistical time lag decreases with the amplitude of the applied voltage. This finding agrees with the fact that higher applied voltage increases the electron generation rate, which reduces the time waiting for a free initial electron available to generate a PD event after the inception field is exceeded [11]. When the applied voltage is increased to a very high value, τ statave is approaching zero because most of PDs occur immediately after the inception field is exceeded. Referring to model parameters in Table 2 for S1 (stressed with variable voltage amplitude) and Table 3, it can be concluded that the void surface conductivity and electron generation rate due to volume ionization are influencing the τ statave under different applied voltage. A general equation which can represent the relation between τ statave and t n is given by equation (12). It shows that in general, the average statistical time lag increases with the average time difference between consecutive PDs. When t n is approaching Electric field (kvmm -1 ) E void E void E q E inc Time (ms) Figure 6. Simulation of electric fields against time of the applied voltage for certain voltage cycles Applied voltage (kv) Figure 7. Distribution of τ stat for different applied voltage. 5.2 TEST SAMPLE 2 The cycle to cycle behaviour of PD events from the measurement and simulation results at temperature 2 C for test sample 2 is shown in Figure 8, while comparison between both results is shown in Table 4. The applied voltage was 5 Hz, 2 kv AC sinusoidal. Most of the % differences are within acceptable values. The explanations for Figure 8 are similar with Figure 5. From Table 4, the number of PDs per cycle is higher at material temperature. Hence, the measured t n and τ statave are shorter at higher material temperature. U n does not change significantly with material temperature because the applied voltage amplitude is unaltered. From the simulation results shown in Table 4, it is possible to represent τ statave as a function of material temperature using ( ) [ s] (13) statave T mat where T mat is in K. Therefore, equation (13) shows in general that the average statistical time lag decreases with the material temperature. This agrees with the fact that higher material temperature enhances the electron generation rate, reducing the time waiting for a PD to occur after the inception field has been exceeded. ote that τ statave is approaching zero when the material temperature is very high due to most of PDs occur immediately after the inception field has been exceeded.

7 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 22, o. 1; February Charge magnitude (nc) Charge magnitude (nc) From Table 2 for sample 2, τ statave as a function of the material temperature is dependent on the void surface conductivity, inception and extinction fields and all parameters to the electron generation rate. A function which can be used to represent the relationship between τ statave and the measured t n is [ms] (14) statave t n Figure 9 shows the distribution of τ stat for different material temperature. It can be seen that when the material temperature increases, more τ stat become shorter, which results in smaller average of τ stat, as shown by equation (13). stat (ms) Cycle number (a) Cycle number (b) Figure 8. Measured (a) and simulated (b) cycle to cycle behaviour of PD events for test sample 2 at material temperature of 2 C. Table 4. Measurement and Simulation Results From Test Sample 2. Material temperature, T ( C) Measured average Δt n (ms) Simulated average Δt n (ms) % difference in Δt n 3.33% 4.55% 11.76% 6.67% Measured average ΔU n (V) Simulated average ΔU n (V) % difference in ΔU n.8%.8%.8%.5% Measured S PD Simulated S PD % difference in S PD % 1.18%.94% % Simulated average statistical time lag, τ statave (ms) Temperature ( o C) Figure 9. Distribution of τ stat for different material temperature. 5.3 TEST SAMPLE 3 Comparison between measurement and simulation results from test sample 3 as a function of applied frequency is shown in Table 5. The applied voltage was 14 kv AC sinusoidal while the material temperature was 2 C. The measurement and simulation results are in general agreement compared to each other. The average statistical time lag, τ statave can be seen to be strongly dependent on the frequency of the applied voltage, f. From the simulation results, a function which can be used to represent the relationship between τ statave and f is f [ s] (15) statave where f is in Hz. Therefore, equation (15) shows in general that the average statistical time lag decreases with the frequency of the applied voltage. When the applied frequency is higher, the time interval between previous PD occurrence and the next PD which is likely to occur is shorter. Thus, the amount of charge due to previous PD which still left when the next PD is likely to occur is higher. This causes the electron generation rate to be higher, reducing the statistical time lag. Hence, PD occurs immediately after the inception field has been exceeded [11]. This also causes the number of PDs per cycle, S PD to be larger when the applied frequency is higher. Also, if τ statave is expressed in terms of the measured t n, the equation which fits the relationship is [ms] (16) statave t n Figure 1 shows the distribution of τ stat for different applied frequency. It can be seen that when the applied frequency increases, more τ stat become shorter, which results in smaller average of τ stat, as shown by equation (15). stat (ms) Applied frequency (Hz) Figure 1. Distribution of τ stat for different applied frequency. From the simulation results of PD events for different applied voltage amplitude and frequency and material temperature, a general equation which can be used to represent the average statistical time lag, τ statave as a function of the applied stress is [s] (17) statave where α and β are constants, depending on the applied stress and θ is the applied stress parameter, i.e. applied voltage amplitude, applied frequency and material temperature. From the simulation results in this work, τ statave decreases with amplitude and frequency of the applied voltage and material temperature.

8 47 H. A. Illias et al.: Determination of Partial Discharge Time Lag in Void using Physical Model Approach The statistical time lag, τ statave as a function of the time difference between consecutive PDs, t n can be generally defined using statave ( t (18) n ) where χ and γ are constant depending on the applied stress. The τ statave decreases with t n for higher amplitude and frequency of the applied voltage and material temperature. The proposed method of determining the statistical time lag has been tested on epoxy resin insulation materials. The results might be different for other insulation materials since different materials exhibit different electrical, thermal and mechanical properties. The shape of the void within insulation material may also affect the statistical time lag as a function of applied stress. Therefore, future work may consider tests on other insulation materials and different void shape using the proposed method in this work. Table 5. Measurement and Simulation Results From Test Sample 3. Applied frequency, f (Hz) Measured average Δt n (ms) Simulated average Δt n (ms) % difference in Δt n 2.74% 1.2% % 2.8% 2.74% Measured average ΔU n (V) Simulated average ΔU n (V) % difference in ΔU n.11%.4% %.4%.11% Measured S PD Simulated S PD % difference in S PD % % % 2.86% % Simulated average statistical time lag, τ statave (ms) COCLUSIOS A physical model of PD using finite element analysis (FEA) method has been successfully developed and used to determine the relationship of statistical time lag with different applied stresses for epoxy resin insulation material. The statistical time lag was modeled as the time interval between the field in the void exceeding the inception field and the occurrence of a PD and determined through comparison of simulation results with measurement data. It was found that higher applied voltage amplitude, material temperature and applied frequency reduce the statistical time lag. Therefore, the proposed experimentalmodeling approach is able to determine the partial discharge time lag in void, which can also enhance the understanding and interpretation of PD activity. Since the current work is limited to epoxy resin insulation material, future work will consider similar experiment and simulation approach on other insulation materials, such as impregnated paper, XLPE, PPL and polycarbonate. In general, it is expected that the proposed model can be used for any types of insulation material, void shapes and void conditions. ACKOWLEDGEMET The authors thank the staff of Tony Davies High Voltage Laboratory, University of Southampton, UK for providing the test facilities and technical knowledge and also the Malaysian Ministry of Education (MOE) and the University of Malaya for supporting this work through HIR, FRGS and UMRG research grants (grant no. H-161-D48, FP26-212A and RG135/11AET). REFERECES [1] A. Bui, A. Khedim, A. Loubière, and M. B. 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Lewin, "Partial Discharge Behavior within a Spherical Cavity in a Solid Dielectric Material as a Function of Frequency and Amplitude of the Applied Voltage," IEEE Trans. Dielectr. Electr. Insul., Vol. 18, pp , 211. [12]. Wiegart, L. iemeyer, F. Pinnekamp, W. Boeck, J. Kindersberger, R. Morrow, W. Zaengl, M. Zwicky, I. Gallimberti, and S. A. Boggs, "Inhomogeneous field breakdown in GIS-the prediction of breakdown probabilities and voltages. II. Ion density and statistical time lag," IEEE Trans. Power Delivery, vol. 3, pp , [13] L. iemeyer, "A generalized approach to partial discharge modeling," IEEE Trans. Dielectr. Electr. Insul., Vol. 2, pp , [14] F. Gutfleisch and L. iemeyer, "Measurement and simulation of PD in epoxy voids," IEEE Trans. Dielectr. Electr. Insul., Vol. 2, pp , [15] H. Illias, G. Chen, and P. L. Lewin, "Modeling of partial discharge activity in spherical cavities within a dielectric material," IEEE Electr. Insul. Mag., Vol. 27, o. 1, pp , 211. [16] R. Schifani, R. Candela, and P. Romano, "On PD mechanisms at high temperature in voids included in an epoxy resin," IEEE Trans. Dielectr. Electr. Insul., Vol. 8, pp , 21. [17] S. A. Boggs, "Partial discharge. III. Cavity-induced PD in solid dielectrics," IEEE Electr. Insul. Mag., Vol. 6, pp , 19-2, 199. [18] E. Kuffel, W. S. Zaengl, and J. Kuffel, High Voltage Engineering: Fundamentals (2nd. ed.), ewnes, 2. H.A. Illias was born in Kuala Lumpur, Malaysia in He received the Bachelor s Degree in Electrical Engineering from the University of Malaya, Malaysia in May 26 and the PhD degree in Electrical Engineering from the University of Southampton, United Kingdom in May 211. He worked as a product engineer in Freescale Semiconductor Malaysia from June 26 to December 27. Since August 211, he has been a Senior Lecturer in the University of Malaya. His main research interests include modeling and measurement of partial discharge phenomena in solid dielectric insulation and condition monitoring.

9 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 22, o. 1; February M.A. Tunio received his B.Eng. degree in electrical engineering in 29 from Quaid-e-Awam University of Engineering, Science & Technology, Pakistan and the M.Eng. degree in power system in 212 from the University of Malaya, Malaysia. Since 212, he has been a Research Assistant and Ph.D. degree student in the Department of Electrical Engineering, University of Malaya. A.H.A. Bakar received his B.Sc. degree in electrical engineering in 1976 from Southampton University, UK and the M.Eng. and Ph.D. degrees from University Technology Malaysia in 1996 and 23. He has 3 years of utility experiences in Malaysia before joining academia. Since 29, he has been a Lecturer in the Department of Electrical Engineering, University of Malaya, Malaysia. G. Chen was born in China in He received the BEng (1983) and MSc (1986) degrees in electrical engineering from Xi an Jiaotong University, China. After he obtained the Ph.D. degree (199) from the University of Strathclyde, UK, he joined the University of Southampton as a postdoctoral research fellow and became a senior research fellow subsequently. In 1997 he was appointed as a research lecturer and promoted to a Reader in 22. He is now the professor of high voltage engineering at the University of Southampton and a visiting professor of Xi an Jiaotong University. His main research interests are electrical characterisation of dielectric materials and electrical ageing. In last twenty years, one of his key areas of research has been developing techniques for space charge measurement in polymeric materials and understanding its role in electrical ageing and breakdown. He is recognised as one of the leading experts in space charge measurement technique internationally and has been given keynote lectures and invited talks on the topic at many international conferences. Over the years, he has attracted financial support from both EPSRC and UK industry, has been actively involved in IEEE, IEC and CIGRE activities and has authored over 1 journal papers and 25 international conference papers. H. Mokhlis received his BEng in Electrical Engineering in 1999 and MEng Sc in 22 from University of Malaya, Malaysia. He obtained the PhD degree from the University of Manchester, UK in 29. In 29, he became a Senior Lecturer and since 213, he has been promoted as an Associate Professor in the Department of Electrical Engineering, University of Malaya.