2013 Electrical Insulation Conference, Ottawa, Ontario, Canada, 2 to 5 June 2013
Modelling of partial discharge pulses in high voltage cable insulation using finite element analysis software 1
H.A. Illias1,2, H.R. Yon1, A.H.A. Bakar2, H. Mokhlis1,2, G. Chen3, P.L. Lewin3 and A.M. Ariffin4 Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia 2 UM Power Energy Dedicated Advanced Centre, University of Malaya, 50603 Kuala Lumpur, Malaysia 3 The Tony Davies High Voltage Laboratory, University of Southampton, Southampton, SO17 1BJ, United Kingdom 4 College of Engineering, Universiti Tenaga Nasional, 43000 Selangor, Malaysia Email:
[email protected] sensitivity of PD measuring equipment was determined for any parameters of interest. It was also reported that the PD detection sensitivity under noisy conditions is around 30-100 pC at 1000 m, depending on the method of PD detection.
Abstract- Measurement of partial discharge (PD) in high voltage equipment is widely used in condition assessment and performance maintenance of the insulation system. One of the methods to evaluate PD data from condition monitoring activities is by analysing PD signals captured from the PD detection equipment. In high voltage power cable, PD pulses originated from defect sites within cable insulation can propagate along the insulation. A better understanding of PD pulse propagation along cable insulation can be attained through simulation work. Therefore, in this paper, the propagation of PD pulses within cable insulation was simulated using finite element analysis (FEA) software and its velocity of propagation was calculated. The result was compared with the theoretical value and simulation results using PSCAD software. The effect of cable insulation parameters on the PD pulse propagation was also studied through the FEA model; these include variation of the permittivity and conductivity of the insulation material.
Many works have reported on the application of PD pulse propagation in the field PD measurements in cable [3, 4, 610]. Most of the measurements were on high-frequency attenuation of shielded power cable. The attenuation constant generally increases with the frequency and length of the cable. This information is very important in field PD measurement because the factors which influence PD pulse propagation can be identified. PD pulses are also arbitrary in shape, depending on the sources of PD and the length of the cable. Several works on simulation of frequency-dependent attenuation in power cables were also reported, such as simulation using finite element analysis (FEA), ATP and EMTP simulation software [3, 6, 11, 12]. Majority of the comparisons of the simulation with the measurement results show a good agreement. In [11], simulation was employed using finite element method and ATP. The results from ATP simulation were found to have higher deviation from the measured results than FEA method. It was concluded that the reason was due to ATP is not able to include complex geometries and material physical constants of the cables. Thus, a more appropriate simulation tool for study on wave propagation characteristics of a cable is finite element analysis.
I. INTRODUCTION Power cable is commonly used in electrical utilities and transmission system in delivering electric power. Due to the highly usage of power cables, cable insulation must not deteriorate to ensure its good performance. The insulation is an important component in power cables as its breakdown may cause failure of the whole component. The deterioration is primarily caused by the aging, imperfection of insulation properties and partial discharge (PD) occurrences at the defect sites. Cable failures will cause power outages and lead to costly maintenance work and repairs. Therefore, early detections and diagnosis of cable insulation condition can prevent the cable failures.
Although numerous simulation works have been performed on PD pulse propagation, simulation using FEA method is less likely to be found. Therefore, in this work, simulation of PD pulse propagation within cable insulation was performed using FEA software. From the model developed, the velocity of propagation of a PD pulse was calculated and compared with the theoretical value and simulation using PSCAD software. Using the same FEA model, the effect of different cable insulation parameters such as permittivity and conductivity of the insulation material, was studied on the PD pulse propagation. The attenuation characteristics and comparison with the actual measurement results will be performed in the future.
The characteristics of wave propagation in cable insulation are determined by the length of the cable, load condition and cable propagation characteristics, such as attenuation and velocity of propagation [1]. These factors affect the PD pulse signals which propagate along the cable insulation from the defect site to the measuring point. Numerous works on analysis of PD pulse propagation have been performed in the past [2-4]. A general analytic approach for the propagation characteristics of arbitrary PD pulses prediction has been developed in [5]. A narrow Gaussian and asymmetric pulses were applied in this approach. For such PD pulse waveforms, PD propagation characteristics and detection
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overlapping with the injected pulse. Thus, α and β were chosen as 7x108 and 3x109 respectively. At the other end of the cable (boundary 2 in Fig.1), lumped port without excitation was assigned to model it as a receiving end of the propagated PD pulse. A perfect electric conductor boundary condition was assigned on the inner and outer radius of the insulation (boundary 3 in Fig.1). This condition is appropriate when both skin depth and losses in the conductors are neglected. After assigning all the boundary conditions, the model was meshed and simulated.
II. FEA MODEL The partial differential equation (PDE) used by the finite element analysis (FEA) software to solve the electric field distribution in the cable insulation model due to partial discharge (PD) pulse propagation along the cable insulation is governed by
0
A A 1 0 0 r ( A) 0 t t t r
(1)
III. SIMULATION RESULTS FROM FEA MODEL
where μ0 is the vacuum permeability, ε0 is the vacuum permittivity, A is the magnetic potential, μr is the permeability and σ is the conductivity.
The cable geometry in the FEA model was simulated and the electric field distribution in the cable insulation was obtained. Fig. 2 shows the electric field distribution in cable insulation at t = 0 to 10 ns during PD pulse propagation along the cable insulation.
Fig. 1 shows a three-dimensional (3D) cable model geometry that was drawn using FEA software, which is COMSOL Multiphysics. To reduce the computation time and as an initial study, a simplified cable model geometry was developed, which consists of a conductor (radius of 14.95 mm) and insulation (radius of 24.45 mm) only. The insulation has a relative permittivity of 2.3, relative permeability of 1 and conductivity of 1x10-18 Sm-1. The length of the cable was set as 1 m. The model was drawn in ‘Electromagnetic Waves’ module to simulate PD pulse propagation in cable insulation.
From the results obtained, we can observe that PD pulse propagates from one end of the cable through the cable insulation. At t = 0 s, the electric field is zero throughout the cable insulation. At t = 1 ns, the electric field magnitude can be seen higher at the region near to the PD pulse injected point. This is due to the PD pulse has started to propagate along the cable insulation from the injected point. From t = 1 to 5 ns, when the PD pulse was propagating along the cable insulation, high electric field portion can be seen moving further from the injection point of the PD pulse towards the other end of the insulation. At t = 6 ns, the PD pulse reaches the other end of the cable and was reflected at the receiving end. From t = 7 ns onwards, the reflected pulse propagated back towards the location of the injection point.
2
3 z (mm)
1 y (mm)
The electric field magnitude along the cable insulation during PD pulse propagation can be seen clearly in Fig. 3. It can be observed that after t = 8 ns, the reflected PD pulse from the cable receiving end has a lower peak electric field magnitude than the original injected pulse. This is due to the energy loss during the reflection at the end of the cable insulation.
x (m)
Fig. 1. Simplified cable model geometry drawn using COMSOL Multiphysics
At one end of the cable insulation (boundary 1 in Fig. 1), a lumped port boundary condition with a PD pulse of nanoseconds width was assigned. It was assumed that the PD pulse was originated from this end, which is called as the PD pulse injected point. Since the waveform of PD pulses are near to that of impulse voltage waveform, the injected PD pulse, V(t) can be represented by [9] V (t ) V0 exp( t ) exp( t )
Referring to Fig. 4 which shows the electric field magnitude at the PD pulse excitation point and the receiving end, the PD pulse reached the other end of the cable within 5.1 ns. Since the cable length is 1 m, the velocity of propagation can be easily obtained by dividing the cable length with the time of propagation. The velocity of propagation was found to be 1.96x108 ms-1. This value is considered reasonable because the velocity of wave propagation within cross-linked polyethylene (XLPE) cable insulation from theoretical calculation was reported to be 1.76x108 ms-1 [1]. The electric field magnitude at the receiving end of the insulation is slightly different than the injected PD pulse, where the width is comparatively larger. This could be due to less number of meshing elements used and simplified cable geometry in the FEA model in order to reduce the computational time.
(2)
where V0 is the amplitude and α and β are time constants related to the wave-shaping. The time width of the PD pulse was limited to 10 ns. This is due to the length of the cable used was only 1 m. If a longer pulse time width was used, most of the reflected pulse from the other end of the cable will be
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(e) t = 4 ns
(a) t = 0 s (f) t = 5 ns
(b) t = 1 ns
(g) t = 6 ns
(h) t = 7 ns
(c) t = 2 ns
(i) t = 8 ns
(d) t = 3 ns
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(j) t = 9 ns
cable length was set as 1 m. The relative permittivity of XLPE insulation was calculated based on equation in [11]. TABLE I PARAMETERS OF THE CABLE MODEL GEOMETRY Layer Outer radius Resistivity Relative (m) (Ωm) permittivity Conductor, r1 0.01495 3.1844x10-8 XLPE insulation, r2 0.02495 2.561 Wire screen, r3 0.030659 1.724x10-8 Outer sheath, r4 0.035659 4.55
The voltage amplitude captured at both ends of the cable as a function of time is shown in Fig. 6. The velocity of the propagated pulse determined from the simulation results using PSCAD model is 1.896x108 ms-1. This value is somewhat in reasonable agreement with the theoretical value (1.76x108 ms1 ) and also the FEA model. Therefore, it can be concluded that the models developed using FEA and PSCAD software are acceptable. Further validation of these models using actual measurement data will be performed in the future.
(k) t = 10 ns
Fig. 2. Electric field distribution from the FEA model (normalised magnitude) and magnitude colour bar t=0s
Normalised amplitude
1
t=2ns
t=4ns
t=6ns
t=8ns
t=10ns
0.8 0.6 0.4 0.2 0 0
0.2
0.4 0.6 Location (m)
0.8
1
Fig. 3. Electric field magnitude along x = 0 to 1 m, y = 0 and z = 14.95 mm from the FEA cable model geometry Vin Vout
0.8
Fig.5. Cirucit arrangement in PSCAD software
0.6
1
0.4
0.8
Normalised amplitude
Normalised amplitude
1
0.2 0 0
2
4
6
8 Time (ns)
10
12
14
16
Fig. 4. Electric field magnitude at the PD pulse excitation point (Vin) and the receiving end (Vout) from the FEA model
III.
SIMULATION
0.6 0.4 0.2 0 0
RESULTS FROM PSCAD MODEL
Vin Vout
2
4
6
8 Time (ns)
10
12
14
16
Fig. 6. Voltage amplitude as a function of time from PSCAD software
In order to compare the simulation results that have been obtained using FEA software, simulation of PD pulse propagation along a cable was also performed using PSCAD software. Fig. 5 shows the circuit arrangement, which consists of a PD pulse source and a cable model. The cable model parameters are shown in Table I. The cable consists of conductor, XLPE insulation, wire screen and outer sheath. The
IV. EFFECT OF CABLE PARAMETERS ON PD PULSE PROPAGATION The velocity of propagation as a function of relative permittivity, εr of the insulation material from the FEA and PSCAD models is shown in Fig. 7. The material permittivity depends on the insulation type and could be due to different
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compositions in the insulation, such as addition of nanofillers or combination of different materials. When the relative permittivity of insulation is higher, the velocity of propagation of the PD pulse becomes lower, which follows the relation of 1 / r . This shows that the pulse is harder to propagate along
reasonable agreement compared with the theoretical value and simulation using PSCAD software. The velocity of propagation decreases with the permittivity of cable insulation but does not change with its conductivity. Thus, certain properties of cable insulation can influence the PD pulse propagation and may affect the sensitivity of PD measuring equipment.
the insulation of higher εr. A higher insulation permittivity indicates more electric flux exists in the material per unit volume, which in turn reduces the velocity of propagation of a pulse.
Future work will consider measurement and simulation of high-frequency attenuation effect on PD pulse propagation and its application on cable fault location. The effect of a conductive path in cable insulation due to a fault on pulse propagation can also be simulated using FEA method. A detailed cable model geometry with finer meshing elements using FEA method will be considered in future simulation.
2.5
VI. ACKNOWLEDGEMENT The authors thank the Malaysian Ministry of Higher Education (MOHE) and University of Malaya, Malaysia for supporting this work through the FRGS research grant (Grant no: FP026-2012A). REFERENCES
PSCAD model FEA model
8
-1
Velocity of propagation (x10 ms )
Fig. 8 shows the velocity of propagation as a function of conductivity of the insulation material from the FEA model. In practice, the increase in insulation conductivity from its initial value could be due to ageing, deterioration in insulation as a result of electrical treeing or PD and an increase in insulation temperature. Referring to Fig. 8, from the simulation using FEA model, the velocity of propagation does not change with the insulation conductivity. This could be due to the conductivity values used are not large enough to influence the pulse propagation. Insulation with conductivity of higher than 1x10-5 Sm-1 may not exist in practical as the insulation will behave as a conductor beyond this value.
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2
1.5
1 2
3
4 5 Relative permittivity
6
7
3
8
-1
Velocity of propagation (x10 ms )
Fig. 7. Velocity of propagation of a PD pulse as a function of cable insulation permittivity from the simulation
2.5 2 1.5 1 0.5
10
-15
-10
10 Insulation conductivity (Sm-1)
10
-5
Fig. 8. Velocity of propagation of a PD pulse as a function of cable insulation conductivity from the FEA simulation
V. CONCLUSIONS Partial discharge (PD) pulse propagation along cable insulation was successfully modeled using finite element analysis (FEA) method in this work. From the model, the calculated velocity of propagation was found to be in
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