Modelling for On-Line Partial Discharge Monitoring on MV Cables by Using a Modified Universal Line Model A. N. Milioudist and D. P. Labridist tDepartment of Electrical and Computer Engineering Aristotle University of Thessaloniki, Greece Email:
[email protected]@auth.gr
Abstract-The overall cable insulation condition can be mon itored continuously by the implementation of an on-line partial discharge (PD-OL) monitoring system. It can both detect and locate the sources of PDs and also assess the insulation condition by using past data. The utilization of an accurate electromagnetic transient model
is crucial for
the accuracy
of
the
system.
Therefore, the well known Universal Line Model (ULM) is chosen to be used for the modelling of PDs propagation through underground medium voltage (MV) cables. For that purpose the ULM is properly modified in order to be able to take into account the PDs occurring among the two terminals of a cable section. The proposed approach also indicates the way that frequency dependent cable terminations can be included as well as the time varying noise existent at the points of measurements.
Index Terms-Partial discharges (PDs), condition based main tenance, electromagnetic transients modelling, insulation degra dation.
I.
INTRODUCTION
Underground distribution networks constitute one of the major parts of the power grid, while underground cables cover vast areas and deliver large amounts of power. The normal operation of underground cables is crucial for system reliability. Partial discharges (PDs) are one of the major causes of insulation degradation and can finally lead to destructive faults [1]. Continuous on-line PD (PD-OL) monitoring, in the context of continuous based maintenance, of medium voltage (MV) underground cables can improve the reliability of the distribution system and reduce maintenance costs [2]. PD OL systems do not require the disconnection of the cable under study, while they diagnose the cable condition under real operational conditions. Furthermore, usually they do not require maintenance costs and the total costs is equal to the initial installation cost. Moreover, the continuous measurement can provide information regarding the progression of a defect in time and can prevent the occurrence of destructive faults enabling the utility to proceed with the repairment of defective cable parts before final breakdown [3]. The operation of such a system requires the synchronized on-line measurements of current at both ends of the monitored The work of A.N. Milioudis is supported by the "IKY Fellowships of Excellence for P ostgraduate Studies in Greece - Siemens Program".
cable. The accurate modelling of all involved quantItIes is essential for the design of an effective PD-OL system. The frequency dependent behavior of cables under study and terminations were studied by the utilization of a model in frequency domain (FD) focusing only on the first pulse arriv ing at measuring ends [4]. The occurring noise significantly affects the denoising process and has to be taken seriously into account [5]-[7]. The denoising processes that have been proposed in the literature are based on the same principal, whereas the measured signals are compared with a library of pulse-like waveforms that resemble the PD signals, and the outcome corresponds to the reduction of noise levels. More concretely, the utilization of matched filters [5], [8] and discrete wavelet transform (DWT) [7], [9] have been proposed for denoising at PD-OL monitoring systems. Consequently, with an effective design of a denoising scheme the pulses associated to PD activity can be detected and by utilizing time synchronized current measurement from both cable ends the location can be derived. Is is essential that the charge of the PD can be computed in order to be stored for PD progression information extraction. Accurate modelling leads to better system design and for that reason, the well known universal line model (ULM) is chosen for the modelling and propagation of PD pulses, due to the fact that it is the most numerically accurate and robust line/cable model capable of handling wide frequency spectrum phenomena [10]. The ULM can be incorporated into EMTP-type programs while it includes the connection among the voltages and currents of both line ends. However, since PD pulses are originated among cable ends a modification to ULM basic equations has to be made in order for PD pulses to be included to the modelling. This modification along with the way that frequency dependent terminations and noise incorporation can be modelled are presented. In Section II the model is thoroughly presented, including the necessary modification to the core equations of ULM in order to incorporate PDs, and the incorporation of frequency dependent terminations and noise levels at both cable ends. In Section III the case study is presented together with conducted simulations indicating the efficacy of the proposed model.
Finally, important conclusions are included in Section IV. II.
MODEL DESCRIPTION
y(t)
A. General Formulation
The ULM incorporates incident and reflected current waves at the two line ends, k and m, in order to calculate the unknown voltages and currents. The general formulation for a single phase approach in time domain is
=
Ne L {eae'D.ty(t_llt) + Tie [AeiUk(t) +J.Leiuk(t-llt)]}
n=l
(7) with llt being the time step of the simulation and Aei and J.Lei (8)
(1) (9) (2) where ik and iki are the current and incident current at line end k, respectively. Ye is the characteristic admittance, H is the transfer function between line ends, Vk is the voltage at line end k and imr the reflected current from line end m [10]. Equations (1) and (2) are expressed for the other line end accordingly. Functions Ye(s) and H (s) can be approximated through rational functions in frequency domain as shown in [11] and equations (3) and (4)
H(s)
=
(
Nh L� n=l S + ahi
)
(3)
·e-sT
(4)
where Ne and Nh are the orders of approximation for each function, D is a constant term corresponding to the value of characteristic impedance for high frequencies, Tei and aei are the residues and poles respectively for the ith term of approximation of Ye(s) function, Thi and ahi are the residues and poles respectively for the ith term of approximation of H (s) function and T corresponds to the propagation time of the highest considered frequency through the entire line length for the back winding process in order to reduce the approximation order [12]. The rational function approximation allows the implementa tion of recursive convolution technique for the computations of the time domain convolutions [13]. Considering the convolu tion y(t) Ye(t)*Uk(t) where the time domain representation Ye(t) is given by equation (5) the overall result is given by equation (6)
Similarly, for the convolution of (2) the same approach yields
iki(t)
=
Nh L {eahiD.tiki(t -llt)+
n=l
+ ThdAhiimr(t - T) + J.Lhiimr(t - T -llt)]}
(10)
with Ahi and J.Lhi being computed as in (8) and (9) but incor porating the residues and poles from function approximation of the transfer function as shown in (4). Let us consider that N PD sources exist throughout the entire length of the line. Each PD source is modelled as a current source iPDi(t), where i E [1, N]. Furthermore, the ith PD source is located at distance Xki and Xmi from the line ends k and m, respectively. Therefore, two transfer functions, HpDk,(S) and HpD=i(S), can be defined in order to model the effect of the PD source to the voltages and currents of line end k and m, respectively (11)
(12) where L corresponds to the line length. Hence, a modification to the main equations of the ULM has to be made in order for the effect of all PD sources to the incident current waves at line ends to be incorporated. The incident current wave from the ith PD source at line end k is
=
Ye(t)
y(t)
=
=
Nc LYei(t)
=
n=l
Ne LYi(t)
n=l
=
Nc L Teie-ae,t
n=l
Ne LYei(t) * Uk(t).
n=l
Therefore the total effect of PD sources are taken into account in the modified formula for the ULM
(5)
iki(t)
=
1 N H(t) * imr(t) + "2 . LHpDk, (t) * ipDi(t)
i=l
(14)
(6)
After computing the contribution of each part of the rational approximation, function y(t) is
imi(t)
=
1 N H(t) * ikr(t) + "2 . LHpD=i (t) * iPDi(t). (15)
i=l
The current at cable end k consists of three parts, i.e. the noise current entering the cable from that end, nk(t), the transferred noise current entering from the other cable end, hmk(t) * nm(t), and the current from the N PD sources as in equation (17). Similarly, the measured current at cable end m is given from equation (18)
TABLE I EXAMINED CONFIGURATION DETAILS Cable property
Value
Core conductor radius (mm) Inner insulation radius (mm) Screen outer radius (mm) Outer insulation radius (mm) Core conductor resistivity (Om) Inner insulation relative permittivity Screen resistivity (Om) Outer insulation relative permittivity Earth resistivity (Om) Earth relative permittivity Relative permeability of all elements Cable depth (m) Total length (m)
1l.9 18.55 19.75 22.75 l.68·10-8 2.6 1.68·lO-8 6 100 10 1 0.7 1000
im(t)
=
nm(t) + hkm(t) * nk(t) + ipD(t)
(18)
where hmk(t) and hkm(t) correspond to the impulse responses in the time domain, from cable end m to k, and from k to m, respectively. Moreover, sign * denotes convolution. Consequently, the total noise at each cable end is
B. Incorporating Terminations
Each underground cable under study is connected at both ends either to a ring main unit (RMU) or a substation. As described in [4] the cable terminations can be measured on line and their frequency-dependency can be known. Once, the termination impedance per frequency is measured, it can be incorporated into the proposed model. This can be achieved through an appropriate interface with the EMTP-type simulation engine using the Norton equivalent. This equivalent includes at each end a fixed conductance matrix and a vector of current sources. Let us consider that both terminations can be expressed by their admittance parameters in frequency domain, Yk(s) and Ym(s) for k and m ends respectively. Naturally, the relation among voltage and current at cable ends is
ij(s)
=
0(s) . Vj(s)
(16)
where j corresponds to cable end indication k or m. The multiplication shown in equation (16) is transformed to con volution in time domain. Therefore, the admittance parameters Yk(s) and Ym(s) have to be approximated using rational functions. By doing so the convolutions can be computed. The frequency dependency is transformed to the computation of a fixed conductance matrix and current history terms and can be incorporated for voltage and current calculations as described in [14]. C. Incorporating Noise
The efficacy of PD-OL systems depends drastically on the ability to efficiently reduce noise levels. The low energy pulses corresponding to PDs can be hidden in occurring noise levels, hence the proper modelling of noise is of crucial importance. The existing noise on a PD-OL system is composed of two main parts, which are the noise levels at both line ends. The incorporation of noise into the proposed model can be done considering the noise at each end as a source of noise for the other and vise versa. Consequently, the overall measured signals at both line ends can be computed through the implementation of the superposition theorem.
and can be calculated by considering the noise source of the other cable end as input and after that add the result to the noise source of the studied cable end as described in equations (19) and (20). As shown in equations (17) and (18) the current correspond ing to PD activity is added to the occurring noise. These terms are calculated as described in subsection II-A. III.
SIM ULATIONS
The system configuration under study is comprised of a three-phase system of underground single core (SC) MV cables, thus forming a multi-conductor arrangement. However, a pulse corresponding to a PD on a single core underground cable excites only the coaxial mode and hence the modelling of the PD pulse propagation can be conducted via a single phase consideration, because the presence of the other ca bles/conductors has no significant effect. All the necessary details regarding the chosen SC cable configuration are shown in Table I and Fig. l. Firstly, a model for ULM without taking into account PD sources was developed in MATLAB® in order to test its results compared to those from PSCADIEMTDC® for a cable impulse response for a current pulse of 1 A. Both line ends were connected to constant resistances of 100 rl. The results obtained by PSCADIEMTDC® and from the developed model in MATLAB® are illustrated in Fig. 2 and 3, respectively. The respective mean squared error (MSE) among the two curves is equal to 5· 10-10, therefore the developed model can be considered reliable for the inclusion of PD sources. The developed modified ULM with the inclusion of a PD source corresponding to charge of 10 nC located at 400 m from cable end k was tested. The resulting measured currents from both line ends are included in Fig. 4. The sum of both measured currents integrals, taking into account the sampling frequency, is a reliable performance metric since it has to add up to the charge of the PD. The respective sum for the tested
0.08,-------,--,---, Earth 0.06
Outer insulation
Screen
$ � 0.04
O.7m
= U v
0.02
l
Core Inner insulation
0.1
0.06
� " � 0.05
$" 0.04 0.05
0-
a 0.03 0.02
-0.05 0 20
30
25
20
40
50 60 Time (�sec)
70
80
90
[00
[J
i
I I I I I I I I
;;.
!:
l
[5
-um
"0
[0
\.
0.15
0.07
o
l Time (�sec)
Fig. 4. Currents at both line ends for one PO source.
Fig. I. Single core underground cable configuration.
0.0[
10
��
l�
lu', " � I ,
4
�
1"1
:,I::V
,
'
" ,
6 8 Time (�sec)
I�V 10
12
�AV�
14
Fig. 5. Measured voltage at both line ends corresponding to PO source located at 800 m from k cable end.
Fig. 2. Impulse response using PSCAO/EMTOC software.
0.07 0.06
$" 0.04 0.05
t: a 0.03 0.02 0.01 o
10
l 20
l
30
40
50 60 Time(�sec)
70
80
90
100
Fig. 3. Single core underground cable configuration.
case equals the amount of 10 ne leading to the conclusion that the developed model is accurate. Furthermore, the incorporation of frequency dependent ter minations was tested. The cable under study was considered to connect two RMUs. Assuming that both RMUs are associated to the same impedance per frequency, it was calculated by adopting the process and values given in [4]. Moreover, Rogowski coils were considered to be used for PD associated signals measurement, transforming currents associated to PD activity to voltage signals. The corresponding voltage signals as measured at both cable ends for a lOne PD source located
at 800 m away from cable end k are illustrated in Fig. 5. It is deduced that reflections are also recorded and they can be considered as noticeable compared to the first arriving pulses. For that, reflections corresponding to PD activities can be of interest towards designing a complete and accurate detecting and locating system. In the case that reflections are not recognized as such by a monitoring system they can be regarded as new PD activity of different apparent charge which can deteriorate the efficacy of the overall system. Therefore, all pulses corresponding to the same PD source have to be recognized and associated to that same source. The next test case investigates the effect of the PD source location to the measured voltage at one cable end. More specifically, a 10 ne PD source is simulated at various distances from cable end k and the computed first arrived pulses to cable end k are included into Fig. 6. The various locations correspond to 50, 200, 500, 700 and 950 m from cable end k. It is deduced that the shape of the calculated waveforms is not significantly changed, however the peak is notably changed due to the attenuation introduced by the cable. This observation for the tested cable leads to the conclusion that the same wavelet can be used for the detection of all possible PD sources that can occur along the cable's length, regardless of its actual location. This can greatly simplify the monitoring system since the best suited wavelet to be used can easily be determined.
0.15�-'------'----'------r �- " 0=0� �'� � � � m� _ - C"" m � l _�_ 2�00 70=0 50 m ' 50O m ' 0 0 m -=O= =O=950 ,
0.15�--�--�--,-----,---c=�
I I
, , " " "
0.1
�
IL
0.05
� S
0.1
�
I
,,, , " , " " I
�
,f\.. v
-
" " " " �
-0.05
� S
�
-0.05
3 Time (Ilsec)
4
Fig. 6. Measured voltage at cable end k for various locations of a PD source.
" "
�-"
5
� ������������1 Time (Ilsec)
OO
-0. 020
I
2
0.05
3
4
5
Time (Ilsec)
6
7
8
9
10
Fig. 7. Components and overall occurring noise at cable end k.
The proposed model can incorporate noise occurring at both cable ends and additionally takes into account the effect of the noise levels occurring at one cable end to the noise occurring at the other. In order to illustrate the capability of the model the next test case focuses on noise levels. In particular, Fig. 7 includes the total noise levels at cable end k, iroise, along with noise coming outside the cable under test to cable end k, i.e. nk, and the transferred noise from the other cable end, hmk * nm. The last term corresponds to the transferred noise coming from outside the cable's under test end m as seen from cable end k. For that reason, as seen in Fig. 7 the term hmk*nm is equal to zero for the time period, that is approximately 5.5 J.Lsec, which corresponds to the propagation time among cable ends. It has to be mentioned that the noise coming outside the cable under study is considered to correspond to uniform distribution from range [-0.01, 0.01]. Consequently, the transferred noise from end m added to the noise coming outside the cable and towards cable end k gives the total occurring noise at k, iroise. It can be observed that there is a slight increase to the total noise levels after the transferred noise from other cable end has arrived. Subsequently, a complete test case has been simulated at which a 10 nC PD source was located at 800 m away from cable end k. The noise coming outside of both cable under study ends was considered to uniform distribution from range [-0.01, 0.01]. As illustrated in Fig. 8 the waveform shapes corresponding to PD activity are noticeable, due to the fact
8 6 Time (Ilsec)
10
12
14
Fig. 8. Measure voltage at both cable ends corresponding to one PD source located at 800 m from cable end k with noise.
that the signal to noise ratio (SNR) is quite high. Therefore, an effective denoising scheme could separate the PD associated waveforms from the noise. After that the charge of the PD can be calculated in order to be stored and be used with the rest of available historical data to assess the condition of the insulation. DWT has been widely used for denoising in several fields as well as in PD detection [6], [7], [9], [15]. In order to be used the optimal wavelet has to be chosen, along with the method of thresholding and the threshold values for all studied levels of decomposition. DWT was used in order to denoise the PD associated waveforms from noise corresponding to the last described test case for both line ends. Adopting the procedure proposed in the literature [6] the obtained results are shown in Fig. 9 and 10, for cable end k and m respectively. As it can easily be deduced the denoising process can be regarded as quite effective, while all PD associated pulses are extracted from noise by using the same wavelet even though first and reflected arriving pulses are quite different in shape. Moreover, the extracted signals significantly resemble the original pulses as illustrated in Fig. 5 resulting to apparent charge computations close to the real values, hence to effective operation of the studied PD-OL monitoring system. Furthermore, as seen from Fig. 9 and 10 the utilization of a single wavelet can extract the first arriving pulses as well as reflected pulses associated to the same PD source, at least for high SNR case studies. This observation strengthens the aforementioned conclusion that specialized algorithms have to be implemented in order to associate all recorded pulses with the correct PD source, taking into account reflected pulses. IV.
CONCL USIONS
The implementation of a very precise model is necessary in order to cope with the wide frequency range of PD propagation over MV cables. For that reason a modification to the well known ULM is made in order to incorporate PDs. The core formulas of ULM incorporate voltages and currents of a transmission line ends, hence the are properly modified in order to include PD activity. After calculating the per unit length electrical parameters of the cable under study the proposed model can be implemented for every MV
0.15
-uk _Denoised U
k
0.1
E 0.05 � !:l "0 ;;.
-0.05 -0.1 0
4
6 8 Time (Ilsec)
10
12
14
Fig. 9. Denoising measured voltage at cable end k implementing DWT.
0.12
-Um -Denoised ll
0.1 0.08
m
0.06
E 0.04 � !:l "0 ;;.
4
8 6 Time (Ilsec)
Fig. 10. Denoising measured voltage at cable end
10
m
12
14
implementing DWT.
underground cable configuration. Furthermore, the model is applied to impulse response as well as PD propagation over a MY underground cable and the results are very accurate. The way that frequency dependent terminations can be included is explained, as well as proper modelling of noise sources is included. Moreover, several test cases have been simulated and important results are deduced. It is shown that the first arriving pulses associated to PD sources at various locations exhibit a significant resemblance leading to the conclusion that one wavelet can be used for extracting PD activity for all locations. Apart from that DWT denoising procedure was implemented and really efficient results have been illustrated. Moreover, the implementation of a single wavelet was able to extract first arriving pulses as well as reflected pulses making the utilization of specialized algorithms to associate all measured pulses with the correct PD source necessary. Experimental validation of the proposed approach will be presented in future work by the authors. REFERENCES
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