**6. Experimental tests of voltage transformer transfer characteristic**

Experimental investigations have been done for voltage transformers typically used in MV power system with primary and secondary windings grounded. Exemplary measurement results presented in this chapter have been obtained for VT of *50 VA* rated power and *20 kV/0.1 kV* nominal transformation ratio. Parameters of the proposed VT circuit model for simulation have been identified by analysis of secondary windings impedance-frequency characteristics measured for no load condition (magnetizing inductance – Fig.10) and short circuit condition (leakage inductance – Fig.11). Measurements have been done in frequency range from *10 Hz* up to *30 MHz*, which is a range typically used for the analysis of conducted disturbances in power system. Particular attention has been paid to the frequency range below *10 kHz* which is obligatory for power quality analysis, especially for analysis of power system voltage harmonics related phenomena.

The measured voltage transfer characteristics of evaluated VT for nominal load and no load conditions are presented in Fig. 17. Based on these results the *3 dB* high frequency pass band of the evaluated VT can be estimated to be about *2 kHz*. For frequencies higher than 2 kHz a number of less meaningful resonances are clearly visible on the VT voltage transfer characteristic which are not adequately characterized by the evaluated circuit model. This inadequacy is associated with extra internal resonances appearing in windings which cannot be properly represented by lumped parasitic capacitances referenced only to windings terminals. In order to model these phenomena more complex circuit model are required which take into account more detailed distributed representation of partial parasitic capacitance of VT primary winding.

Fig. 17. Normalized voltage transfer ratio of the VT for no load and nominal resistive load

Voltage Harmonics Measuring Issues in Medium Voltage Systems 105

Accurateness of magnitude and phase voltage transfer characteristics of VT is a fundamental aspect for identification and measurement of power quality related phenomena in power system. For the investigated VT the voltage transfer ratio and voltage phase shift characteristics have been measured to reveal measurement accuracy problems of power quality assessment in MV systems. Magnitudes versus phase transfer characteristic of VT measured for different frequency ranges typically used in power quality measurement systems (up to 40th harmonic and up to *9 kHz*) are presented in Fig. 19 and Fig. 20. Experimental investigations prove that magnitude and phase errors increase noticeably with frequency. In frequency range up to *2 kHz*, the highest magnitude error of about *11 %* and

that voltage harmonics measurement in MV grids by using VT can be not accurate enough

**1 k**

**Hz**


Phase shift [Degrees]

, which cannot be accepted in

Fig. 19. Normalized VT voltage ratio vs. phase shift angle for frequency band up to 2 kHz Magnitudes and phase inaccuracy of VT obtained in frequency range from *2 kHz* up to *9 kHz* (Fig. 20) are evidently greater and its frequency dependence is more complex, therefore more difficult to model using simplified circuit models. Magnitude errors in this frequency

in applications with noticeable harmonic content above approximately *1 kHz*.

**1.5**

**1.8**

range reach almost 180% and phase shift error almost *80*

power quality measurement applications.

**2**

**kHz**

**kHz**

**kHz**

, have been obtained for frequency *2 kHz*. These results confirm

**10**

**50**

**250**

**Hz**

**Hz**

**Hz**

phase shift error almost *8*

0.88

0.90

0.92

0.94

0.96

Modulus of normalized voltage transfer ratio [-]

0.98

1.00

1.02

1.04

Comparison of voltage transfer characteristic measured for no load and nominal resistive load condition confirms that the influence of the level of the resistive load is mostly observable for frequencies close to the resonance frequencies. For these frequency ranges the voltage transfer ratio can vary even few times due to the VT load change.

Comparison of VT leakage and magnetizing impedances allow for preliminary approximation of the VT pass band cut-off frequency. In Fig. 18 correlation between VT impedances and the measured voltage transfer ratio is presented. Based on this comparison it can be noticed that:


Additional effects of parasitic capacitance distribution, which are not sufficiently represented by evaluated simplified circuit model, justify narrower pass band of VT obtained by experimental investigation (about *2 kHz*) with comparison to simulation results (about *20 kHz*).

Fig. 18. Correlation between measured VT voltage transfer characteristic and magnetizing and leakage impedance-frequency characteristics

Comparison of voltage transfer characteristic measured for no load and nominal resistive load condition confirms that the influence of the level of the resistive load is mostly observable for frequencies close to the resonance frequencies. For these frequency ranges the

Comparison of VT leakage and magnetizing impedances allow for preliminary approximation of the VT pass band cut-off frequency. In Fig. 18 correlation between VT impedances and the measured voltage transfer ratio is presented. Based on this comparison

 firstly, for the frequency range where magnetizing inductance is evidently higher than leakage impedance (Band 1 according to Fig. 12) the magnetic coupling between VT windings is tough, the VT voltage transfer characteristic is nearly flat and relatively

 secondly, for the frequency range where magnetizing and leakage inductances are comparable (Band 2 according to Fig. 12) the VT voltage transfer characteristic is hardly dependent of VT load character and the influence of internal distribution of parasitic capacitances of winding is manifested by extra local parasitic resonance

Additional effects of parasitic capacitance distribution, which are not sufficiently represented by evaluated simplified circuit model, justify narrower pass band of VT obtained by experimental investigation (about *2 kHz*) with comparison to simulation results

10 100 1k 10k 100k

Frequency [Hz]

Fig. 18. Correlation between measured VT voltage transfer characteristic and magnetizing

Nominal load

 Magnetizing impedance Leakage impedance

voltage transfer ratio can vary even few times due to the VT load change.

it can be noticed that:

occurrence.

(about *20 kHz*).

0.0 0.5 1.0 1.5 2.0 2.5 100m 1 10 100 1k 10k

and leakage impedance-frequency characteristics

Normalized voltage

transfer ratio [-]

Impedance (Absolut) (

)

weakly dependent on load,

Accurateness of magnitude and phase voltage transfer characteristics of VT is a fundamental aspect for identification and measurement of power quality related phenomena in power system. For the investigated VT the voltage transfer ratio and voltage phase shift characteristics have been measured to reveal measurement accuracy problems of power quality assessment in MV systems. Magnitudes versus phase transfer characteristic of VT measured for different frequency ranges typically used in power quality measurement systems (up to 40th harmonic and up to *9 kHz*) are presented in Fig. 19 and Fig. 20. Experimental investigations prove that magnitude and phase errors increase noticeably with frequency. In frequency range up to *2 kHz*, the highest magnitude error of about *11 %* and phase shift error almost *8*, have been obtained for frequency *2 kHz*. These results confirm that voltage harmonics measurement in MV grids by using VT can be not accurate enough in applications with noticeable harmonic content above approximately *1 kHz*.

Fig. 19. Normalized VT voltage ratio vs. phase shift angle for frequency band up to 2 kHz

Magnitudes and phase inaccuracy of VT obtained in frequency range from *2 kHz* up to *9 kHz* (Fig. 20) are evidently greater and its frequency dependence is more complex, therefore more difficult to model using simplified circuit models. Magnitude errors in this frequency range reach almost 180% and phase shift error almost *80*, which cannot be accepted in power quality measurement applications.

Voltage Harmonics Measuring Issues in Medium Voltage Systems 107

The use of VT in power quality monitoring MV grids influence essentially finally obtained measurement accuracy. In power quality measurement applications where dominating harmonics emission is expected only in frequency range below *2 kHz* VTs can provide sufficient accuracy in many applications, nevertheless its voltage transfer characteristic should be carefully verified with taking into account particular operating conditions. Nowadays, much wider than up to *2 kHz* harmonics emission spectrum can be injected into the power system, especially by contemporary high power electronic applications. In this frequency range from *2 kHz* up to *9 kHz*, which is already well specified by harmonic emission limitation standards, typically used VT are not reliable enough. Measurement errors in frequency range up to *9 kHz* are usually not acceptable, because of resonance

Islam, S.M.; Coates, K.M.; Ledwich, G.; Identification of high frequency transformer

Kadar, L.; Hacksel, P.; Wikston, J.; The effect of current and voltage transformers accuracy

Klatt, M.; Meyer, J.; Elst, M.; Schegner, P.; Frequency Responses of MV voltage transformers

Łuszcz J.; Conducted EMI propagation modelling in the wound components. Seventeenth

Łuszcz J.; Iron Core Inductor High Frequency Circuit Model for EMC Application. Coil Winding International & Electrical Insulation Magazine. Volume 28, Issue 1, 2004 Mahesh, G.; George, B.; Jayashankar, V.; Kumar, V.J.; Instrument transformer performance

Mohamed, R.; Markovsky, I.; Lewin, P.L.; Modeling and Parameter Estimation of High

Seljeseth, H.; Saethre, E.A.; Ohnstad, T.; Lien, I.; Voltage transformer frequency response.

Shibuya, Y.; Fujita, S.; High frequency model and transient response of transformer windings, Transmission and Distribution Conference 2002: 6-10 Oct. 2002 Vermeulen, H.J.; Dann, L.R.; van Rooijen, J.; Equivalent circuit modelling of a capacitive

Applications, Volume 33, Issue 3, May-June 1997 Page(s):780 - 783

equivalent circuit using Matlab from frequency domain data. Thirty-Second IAS Annual Meeting, IAS '97., Conference Record of the 1997 IEEE Industry

on harmonic measurements in electric arc furnaces., IEEE Transactions on Industry

in the range of 50 Hz to 10 kHz. 14th International Conference on Harmonics and

International Wrocław Symposium and Exhibition on Electromagnetic

under distorted-conditions. India Annual Conference, 2004. Proceedings of the

Voltage Transformer Using Rational Transfer Function State Space Approach. Annual Report Conference on Electrical Insulation and Dielectric Phenomena, 2008.

Measuring harmonics in Norwegian 300 kV and 132 kV power systems., 1998. Proceedings. 8th International Conference on Harmonics And Quality of Power.

voltage transformer for power system harmonic frequencies, IEEE Transactions on

effects which commonly appear and are difficult to predict.

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Compatibility, EMC 2004

CEIDP 2008

**7. References** 

Fig. 20. Normalized VT voltage ratio vs. phase shift angle for frequency band up to 9 kHz

### **6. Conclusions**

Modelling of VT voltage transfer characteristic in wide frequency range is rather challenging. Main problems with accurate modelling using circuit models are related to windings' parasitic capacitances and especially identification of its unequal distribution along windings. To model the influence of parasitic capacitive couplings existing in a typical VT several simplifications should be considered. The method of VT parasitic capacitances analysis based on the lumped representation is often used and particularly rational, nevertheless limits the frequency range within which acceptable accuracy can be obtained.

Its parameters can be determined based only on wideband measurement of leakage and magnetizing impedances, unfortunately it can be successfully used only in the limited frequency range. For typical VT used in MV grids the flatten fragment of transfer characteristic can be obtained usually only up to few kHz. Above this frequency VT usually exhibit a number of resonances which change evidently its transfer characteristic and cannot be reflected adequately by simplified circuit models. Wideband performance of VT in a particular application is also noticeably related to its load level and character (inductive or capacitive). For typical VT it is possible to improve slightly its wideband performance by lowering its load level or by changing its character into inductive, but it usually requires laborious experimental verification. Despite of recognized restrictions and limited accuracy of the developed circuit model it can be successfully used for approximate assessment of VT pass band.

The use of VT in power quality monitoring MV grids influence essentially finally obtained measurement accuracy. In power quality measurement applications where dominating harmonics emission is expected only in frequency range below *2 kHz* VTs can provide sufficient accuracy in many applications, nevertheless its voltage transfer characteristic should be carefully verified with taking into account particular operating conditions. Nowadays, much wider than up to *2 kHz* harmonics emission spectrum can be injected into the power system, especially by contemporary high power electronic applications. In this frequency range from *2 kHz* up to *9 kHz*, which is already well specified by harmonic emission limitation standards, typically used VT are not reliable enough. Measurement errors in frequency range up to *9 kHz* are usually not acceptable, because of resonance effects which commonly appear and are difficult to predict.
