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Power cable joint model in high frequency

Citation for published version (APA):

Li, Y., Wouters, P. A. A. F., Wagenaars, P., Wielen, van der, P. C. J. M., & Steennis, E. F. (2012). Power cable joint model in high frequency. In Proceedings of the 2012 IEEE International Conference on Condition

Monitoring and Diagnosis, 23-27 September 2012, Bali, Indonesia (pp. 76-79). Institute of Electrical and Electronics Engineers.

Document status and date: Published: 01/01/2012 Document Version:

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Power Cable Joint Modelin High Frequency

Yan Li, Peter A. A. F. Wouters

Electrical Energy Systems Eindhoven University of Technology

Eindhoven, the Netherlands y.li.4@tue.nl

Paul Wagenaars, Peter C. J. M. van der Wielen,

E. Fred Steennis

DNV KEMA Energy & Sustainability Arnhem, the Netherlands Abstract—Models in high frequency range for underground

power cabling system are the basis for the analysis of many condition diagnostic techniques, for instance, partial discharge (PD) monitoring. This paper focuses on modeling of power cable joints. A cascaded transmission line model is proposed for 10kV oil-filled PILC-PILC straight power cable joint in thefrequency range of 300 kHz-800 MHz.It can be applied to interpret PD signal transmission and reflection behavior in power cable connections. The model is verified by S-parameter measurement.

Keywords-monitoring, parameter estimation, partial discharges,power cable insulation, transmission lines

I. INTRODUCTION

The propagation characteristics of high frequency signals in underground power cabling system are the basis for many power cable diagnostic techniques [1-3]. The traveling signal will be affected by its propagation path, namely the underground cable connection, which mainly consists of cables, cable joints and Ring-Main-Units (RMUs). Each of these components has influence on high frequency signal propagation. For high frequency signals, the underground power cable can be modeled as a transmission line [4]. References [5-7] provide a model for RMU for high frequency phenomena. However, literature on models for a power cable joint for high frequency signals is relatively scarce.

There are different types of power cable joints, such as the straight joint for paper-insulated lead-covered (PILC) cable, the straight joint for cross-linked polyethylene (XLPE) insulated cable, the transition joint, etc. However, they share similar design: a metallic connector to connect the cable cores; insulation material around the connector; a flexible metallic braid to connect the metallic out layer of the cable on each end. This implies that a generic cable joint model can be designed in which the parameters can be adjusted to match measured behavior.

II. THEORY REVIEW

Figure 1 shows the concept of transmission line modeling [8]. It can be characterized by two parameters: the characteristic impedance Zcand the propagation coefficientγ.

Figure 1. Transmission line model.

The voltage and current waves are defined as:

z c z c z z S z z S Z V Z V I I z I V V z V       e e e e ) ( e e ) ( 0 0 0 0 0 0                (1) Figure 2 shows a typical two-port network. The matrix elements

S11, S12, S21 andS22 are referred to as the scattering parameters

or the S-parameters of the device under test (DUT). They are defined as:                    2 1 22 21 12 11 2 1 a a S S S S b b (2)

Figure 2. Two-port network.

In practice, the reference impedance is chosen to be

Z0 = 50Ω. Assume that the transmission line in Figure 1 is the

DUT, Z0 = Zg = ZL.The S-parameter can be expressed in terms

of transmission line parameters:

         l Z Z Z Z Z Z l Z Z D S c c c c S   sinh ) ( 2 2 sinh ) ( 1 ] [ 2 0 2 0 0 2 0 2 (3) where DS=2ZcZ0coshγl+( Zc2+ Z02)sinhγl.

The disadvantage of S-parameters is that they are not convenient to be used to model cascaded systems. However, S-parameter can be converted to [ABCD] matrix form which is suitable for cascaded modeling. The [ABCD] matrix is defined as:                    2 2 1 1 I V D C B A I V (4)

also it can be expressed in terms of characteristic impedance and propagation coefficient,

                           dS S S Z dS S S Z dS S S dS S S S D C B A 22 11 0 22 11 0 22 11 22 11 21 1 1 ) 1 ( 1 2 1 (5) where dS=S11S22- S12S21.

III. CABLE JOINT MODELING

The power cable joint has basically a similar structure as a power cable, except that its dimension changes along the length. Because of the inhomogeneous shape of power cable joint, compared with power cable, it is non-uniformregarding to the electric-magmatic field distribution. However, it

A-17 2012 IEEE International Conference on Condition Monitoring and Diagnosis

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remains a symmetric and enclosed design. Since the diameter changes relatively slowly over the joint length, a cascaded transmission line is adopted, as shown in Figure 3. The non-uniform cable joint is divided into msections. Each part is modeled as a separate transmission line with its own characteristic impedance,Zi(1≤i≤m) and propagation

coefficient, γi(1≤i≤m); the length for each section is Δxi

(1≤i≤m). All parameters (m, Zi, γi,Δxi) are dependent on the

specific power cable joint geometry and material. If m increases,the model approximates more closely reality. However, with a higher value of m, the computation effort increases and the difference betweenZi-1,γi-1 and Zi,γi decreases,

whichmeans it is more difficult to verify by experiment. So the final model is a balance between accuracy and effort.

Figure 3. Cascaded model for non-uniform transmission line. IV. 10KV3-CORE PILC STRAIGHT CABLE JOINT

MEASUREMENT

In order to verify the proposed models in section III, the S-parameters of a 10kV oil-filled 3-core PILC-PILC straight joint are measured and approximated with the model. The schematic drawing and the geometry of the joint are depicted inFigure 4. The whole cable joint construction is based on an inner and outer joint. The inner joint was made of white BMC polyester. The connectors in the joint were separated by tubes and spacers, both made of PTFE. The space between the innerjoint and the cast iron outer joint was filled with 2-component polyurethane. The lead sheath of the PILC cables is connected by 50 mm2 copper.

(a) Schematic drawing of the 10 kV oil-filled straight joint.

(b) Geometry of the 10 kV oil-filled straight joint. Figure 4.Illustration of DUT.

A Network Analyzer (NA) with S-parameter set is used for the S-parameter test. The vector network analyzer is connected to both sides of the joint under test with a 50Ω coaxial cable. The S-parameters are measured for the cable joint for the frequency range of 300 kHz-800 MHz. As discussed in [7], two propagation modes exist in the three-core power cable, namely shield-to-phase (SP) mode between conductors and earth screen and phase-to-phase (PP) mode between conductors. This paper focuses on the SP mode since it is the detectable signal mode at the earth screen of the cable. On-line measurement device detect this mode since PD sensors can be installed there without safety hazards [10]. Therefore, in the experiment three cable conductors are connected together. The test set up and the connection between the NA measurement cable and the power cable joint is illustrated in Figure 5.

(a)

(b)

Figure 5. (a) Power cable joint S-parameters measurement system.(b) Transitional connection from the coaxial measurement cable to the power

cable joint.

For the experiment, a 50Ω coaxial cable is used to connect the NA and DUT; furthermore, an adaptor is needed to connect the coaxial cable and the power cable joint. This coaxial cable and the transitional adaptor connection will distort the measured S-parameters [9, 11]. According to [11], the effect of the measurement cable is a phase shift in measured S-parameters. If the measured ports are at distance

l1,2from the DUT, the corresponding electrical phase shift for

measured S parameter is θ1,2= β1,2l1,2, where β1,2 is the phase

coefficient (imaginary part of propagation coefficient). Reference [9] pointed out that the combined effect of the measurement cable and the adaptor can be modeled as a piece of lossless transmission line plus a series inductance or a shunt capacitance depending on its influence. This is shown in Figure 6, where Δladl and Δladr are the equivalent transmission line

additions accounting for the adaptor together with the inductance and capacitance. Here, a shunt capacitance suits the measurement result best. The optimum values for the left measurement cable length and left side capacitance are 4.26 cm, 2.36 pF and the right cable length and capacitance

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Figure 6.Modeling the combination effect of measurement cable and adaptor.

Figure 7.Comparison of S-parametersbefore and after correction.

are5.01 cm, 9.23 pF. These correction parameters are obtained in such a way that maximum repetition of the S-parameters phase from -π to π is achieved,since the repetition phase indicates a cascaded transmission line configuration.The measured and corrected S-parameters are shown in

Figure 7. It can be seen from the comparison that the measurement error is mainly in the phase shift but hardly in the amplitude.

V. MODEL APPROXIMATION

Based on the analysis in SectionsII and III, the cascaded transmission line model is adjusted to the measurement result. A three cascaded transmission line model is proposed to model the power cable joint under test. The first and third part of the transmission line represent the connected power cable at both ends, while the second transmission line in middle represents the connecting part of the joint, since the most noticeable impedance change appears at the connection point. The characteristic impedance and propagation coefficient of the 10kV three-phase-PILC power cable are known from previous described in [6]. The characteristic impedance is 10Ω (Zc) and the propagation coefficient (γ) is frequency

dependent. Thus, Z1 = Z3 = Zc; γ1 = γ3 = γ are known as they

are in fact PILC power cable. Only l1, l3 and Z22, l2 are still to

be determined (Zis the characteristic impedance,γis the propagation coefficient, lis the length; the subscript number indicates the corresponding section of the cascaded transmission line). The best fit results are shown in Table 1. The section length and impedance are chosen such that the model can match the measured S-parameters. Concerning the propagation constant, since the insulation material permittivity for the power cable joint does not differ too much from the power cable, the phase constant (β) is taken equal to the value for the cable. For the attenuation, the relatively thicker insulation layer radius will increase the losses. The attenuation coefficient (α) is modified for the joint compared to the cable.

TABLE 1BEST FITTING RESULTS FOR CASCADED TRANSMISSION LINE MODEL

l1(m) l3 (m) Z2(Ω) γ2 l2(m)

0.35 0.34 111.4 8.6α+β 0.36

The modeled S-parameters and the measured values are shown in Figure 8. There is an artifact in all measured S-parameters around 125MHz, which might be caused by the NA [9]. 0 100 200 300 400 500 600 700 800 0 0.5 1 frequency MHz S-param et er am plit ude S11 correction measured S11 corrected S11 0 100 200 300 400 500 600 700 800 - -½ 0 ½  frequency MHz Phas e 0 200 400 600 800 0 0.5 1 frequency MHz S-param et er am plit ude S12 correction measured S12 corrected S12 0 200 400 600 800 - -½ 0 ½  frequency MHz Phas e 0 200 400 600 800 0 0.5 1 frequency MHz S-param et er am plit ude S21 correction measured S21 corrected S21 0 200 400 600 800 - -½ 0 ½  frequency MHz Phas e 0 100 200 300 400 500 600 700 800 0 0.5 1 frequency MHz S-param et er am plit ude S22 correction measured S22 corrected S22 0 100 200 300 400 500 600 700 800 - -½ 0 ½  frequency MHz Phas e

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Figure 8.Comparison between measured S-parameters and modeled values for the cascaded transmission line model.

Based on the above analysis, it can be concluded that the cascaded transmission line model can cover the frequency range from 300 kHz to 800 MHz.

VI. CONCLUSION

This paper proposes a cascaded transmission line model for power cable joint. The frequency range is from 300 kHz to 800 MHz. However, the frequency range may depend on the cable joint’s parameters and measurement device and method. The joint model is developed based on a measurement of a 10 kV 3-core PILC straight joint, however because of similar

design structure of power cable joint this model can be applied to other types of straight joints.

VII. REFERENCES

[1] P.C.J.M. Van der Wielen, J. Veen, P.A.A.F. Wouters, E.F. Steennis, “On-line partial discharge detection of MV cables with defect localization (pdol) based on two time synchronized sensors,” Proc. Int. Conf. Electricity Distrib. (CIRED), session no. 1, Turin, Italy, June 2005.

[2] P.C.J.M. Van der Wielen, E.F. Steennis, “Experiences with continuous condition monitoring of in-service mv cable connections,” Proc. Power Eng. Soc. (PES) Power Systems Conf. & Exp. (PSCE), Seattle, WA, USA, March 2009.

[3] M. Michel, “Innovative asset management and targeted investments using on-line partial discharge monitoring & mapping techniques,” Proc. 19th Int. Conf. Electricity Distrib. (CIRED), Vienna, Austria,p. 0551, May 2007.

[4] Matthew N.O. Sadiku, Sophocles J. Orfanidis, “Elements of electromagnetics,” 2007, pp. 512-515.

[5] P. Wagenaars, P.A.A.F. Wouters, P.C.J.M. van der Wielen and E.F. Steennis, “Influence of Ring Main Units and Substations on Online Partial-Discharge Detection and Location in Medium-Voltage Cable Networks,” IEEE Trans. Power Delivery, vol. 26, no. 2, Apr. 2011. [6] Paul Wagenaars, “Integration of Online Partial Discharge Monitoring

and Defect Location in Medium-Voltage Cable Networks,” PHD thesis, Eindhoven, The Netherlands, 2010, pp. 42-49.

[7] P.Wagenaars, P.A.A.F.Wouters, P.C.J.M.van der Wielen, E.F. Steennis, “Measurement of transmission line parameters of three-core power cables with common earth screen,” Science, Measurement & Technology, IET, vol.4, no.3, pp.146-155, May 2010.

[8] Sophocles J. Orfanidis, “Electromagnetic Waves and Antennas,” 2008,pp. 526-532.

[9] R.Papazyan, P.Pettersson, H.Edin, R.Eriksson, U.Gafvert, “Extraction of high frequency power cable characteristics from S-parameter measurements,”IEEE Transactions on Dielectrics and Electrical Insulation, vol.11, no.3, pp. 461- 470, Jun 2004.

[10] P.C.J.M. van der Wielen, “On-line Detection and Location of Partial Discharges in Medium-Voltage Power Cables,”PHD thesis, Eindhoven, The Netherlands,2005, pp. 52-53.

[11] N. Ed. Marcuvitz, Waveguide Handbook, New York: McGrawHill, 1951,pp. 310-312. 0 100 200 300 400 500 600 700 800 0 0.5 1 frequency MHz Am plit ude

S11 comparison between measurement(after compensation) and model

S11 after correction Modeled S11 0 100 200 300 400 500 600 700 800 - -½ 0 ½  frequency MHz Phas e 0 100 200 300 400 500 600 700 800 0 0.5 1 frequency MHz Am plit ude

S12 comparison between measurement(after compensation) and model

S12 after correction Modeled S12 0 100 200 300 400 500 600 700 800 - -½ 0 ½  frequency MHz Phas e 0 100 200 300 400 500 600 700 800 0 0.5 1 frequency MHz Am plit ude

S21 comparison between measurement(after compensation) and model S21 after correction Modeled S21 0 100 200 300 400 500 600 700 800 - -½ 0 ½  frequency MHz Phas e 0 100 200 300 400 500 600 700 800 0 0.5 1 frequency MHz Am plit ude

S22 comparison between measurement(after compensation) and model

S22 after correction Modeled S22 0 100 200 300 400 500 600 700 800 - -½ 0 ½  frequency MHz Phas e 79

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