parametric analyses on impulse voltage generator and ... power transformer winding for virtual high...

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Parametric Analyses on Impulse Voltage Generatorand Power Transformer Winding for Virtual High

Voltage Laboratory EnvironmentSachin Kumar, N K Kishore and B Hemalatha

Indian Institute of Technology KharagpurKharagpur-721302, India.

Abstract—This paper presents the development work donefor virtualization of a typical high voltage laboratory, especiallynamed as virtual high voltage laboratory. The main objective ofthe paper is to develop an understanding of impulse voltagegenerator’s ciruit parameters’ effect on the standard outputwaveforms. The most significant part includes analyses of variousinternal constraints which cannot be easily estimated in a highvoltage laboratory. The motive is to - analyze the effects ofdifferent parameters involved in the respective impulse voltagegenerator and equivalent power transformer winding circuitsand show the results graphically. To accomplish this motto,parametric analyses are carried out on the effects of differentparameters for impulse voltage generator and power transformerwinding, along with desired outputs.

Index Terms—Impulse voltage generator, marx generator,parametric analyses, power transformer winding, virtual highvoltage laboratory.

I. INTRODUCTION

COMPUTER simulation plays an important role in en-gineering course teaching. Nowadays, a variety of soft-

wares like MATLAB, AutoCAD, and PSCAD are availableto simulate electrical circuits; but fail to provide the actualfeel of a physical laboratory. Also most of these softwarescome with commercial license at a high price, thus restrictingtheir availability but virtual high voltage laboratory (VHVL)is a web based [1,2,3,4,5] application which not only servesas a good tool for teaching but also enables a student tounderstand the influence of the circuit parameters on the outputof the various experiments. VHVL can also act as a guidefor the testing engineer to arrive at the values of the desiredparameters to get a standard output waveform as listed inTable I [6]. VHVL prompts user to achieve the standardLightning Impulse (LI) or Switching Impulse (SI) parametersby providing facility to vary the circuit parameters throughgraphical user interface (GUI).

Fig. 1 presents a proposed scheme of VHVL which consti-tutes home page links for various experiments. By selecting

Sachin Kumar is a recent graduate of M.Tech. in Electrial Engineering fromIndian Instutute of Technology Kharagpur, Kharagpur 721302 India (email:[email protected]).

N K Kishore is Professor of Electrical Engineering with Indian Institute ofTechnology Kharagpur, Kharagpur 721302 India (email: [email protected]).

B Hemalatha is Principal System Manager with Indian Institute of Tech-nology Kharagpur (email: [email protected]).

Table ITIME PARAMETERS WITH TOLERANCES FOR SOME STANDARD IMPULSE

WAVEFORMS

Type of impulse Front Time Tf (µs) Tail Time Tt(µs)LI voltage 1.2±30% 50±20%SI voltage 250±30% 2500±20%

Impulse current 4.0±10% 10±10%Impulse current 8.0±10% 20±10%

particular experiment from the list, GUI prompts input val-ues. After submitting the input values mathematical analysesalgorithm of impulse voltage generator (IVG) circuit in thisparticular case is run and displays output waveform with thehelp of JAVA programming. So, present paper deals with theparametric analyses of IVG and impulse testing on powertransformer winding equivalent which is useful in VHVLenvironment to get the standard waveforms.

Figure 1. Proposed Scheme of VHVL.

II. IMPULSE VOLTAGE GENERATOR

A. Marx generator

Marx generators [7] are at the core of impulse voltage testsof HV equipment. The classical Marx generator nominallyproduces a pulse in the form of a double exponential function.

V (t) = V [exp(−αt) − exp(−βt)] (1)

where V(t) is the instantaneous value of output impulsevoltage, and V is the voltage that is stored across the generatorcapacitor (Cg) (for a multistage generator V is the sum ofthe charging voltages of all stages), α and β are inverse timeconstants in µs. Fig. 2 [8] shows an equivalent of n ≤ 20stage Marx generator which generates the impulse voltage for

16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 523

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.

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testing of transformers, where the front and tail time of theimpulse voltage are important; therefore one must observe theeffect of the wave-shaping control elements on the voltagewaveform. The dependence of the shape of the waveformon the resistors Rf (front resistor) and Rt (tail resistor) canbe checked by changing the values of these resistors. Theseresistors control the wave-front and wave-tail of the outputimpulse voltage waveform. The basic principle of operation ofthe Marx generator is that the generator capacitors are chargedin parallel with a HV dc source and discharged in seriesthrough load (here capacitive, Cl) with the means of triggeringspark gaps (SG). Hence an impulse voltage is obtained acrossthe load which is standardised as shown in Fig. 3.

Figure 2. Typical Scheme of a Marx Generator.

Referring to the waveshape in Fig. 3, the peak value A isfixed and referred to as 100% value. The point correspondingto 10% and 90% of the peak values are located on the frontportion (points C and D). O’ is taken as the virtual origin.1.25 times the interval between times t1 and t2 correspondingto points C and D is defined as the front time (Tf ), i.e.1.25*(O’t1-O’t2).1 The point E is located on the wave tail

1Due to oscillation in the initial portion, front is defined this way.

corresponding to 50% of the peak value, and it is t4. O’t4 isdefined as fall or tail time (Tt).

Figure 3. Standard waveform of an impulse voltage generator.

B. Single stage impulse voltage generator circuit

Fig. 5 shows single – stage equivalent of IVG circuit.Circuit contains front resistor (Rf ) and tail resistor (Rt)with small internal inductancesLf and Lt offered by Rf andRt respectively. These inductances are incorporated in theequivalent circuit to give the VHVL a more realistic feel.Solution for the circuit is obtained using differential equationsapproach and then the corresponding algorithm is developed.Differential equations and appropriate boundary conditionsV(t=0) = 0 and (dV

dt )(t=0) = 0 are formulated as follows:Loop i1 :

1

Cg

∫i1dt+ Lf

di2dt

+Rf ∗ i2 +1

Cl

∫i2dt = V (2)

Loop i2 :

Lfdi2dt

+Rf ∗ i2 +1

Cl

∫i2dt = Lf

d(i1 − i2)

dt+Rt ∗ (i1− i2)

(3)output voltage:

V (t) =1

Cl

∫i2dt (4)

After solving Eqn. 2 and Eqn. 3 for current i2 and puttingi2’s value in Eqn. 4 output voltage is obtained. The algorithmfor single-stage IVG for generation of impulse voltage isshown in Fig. 4, is employed in virtual laboratory environment[14].

1) Single stage impulse voltage generator - Algorithm :Based on the mathematical analyses of circuit shown in Fig.4, algorithm for the implementation of the VHVL is developed.The flowchart shown in Fig. 4 explains the algorithm ofparametric analyses for impulse voltage generation. The firsttask is to track peak voltage of waveform which is accom-plished by comparing present and previous sample valueswhich are continuously stored. At an instant when previousvalue is greater than the present value, the sample data of



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Figure 4. Algorithm for generation and parametric analyses of single-stage impulse voltage generator.

previous value is stored as the value of peak voltage. Aftertracking peak voltage, time for 10%, 90% and 50% of peakvoltage are determined. This provides waveform parametersto be compared with standard listed in Table I. Finally, a plotbetween voltage vs. time with front and tail time values isdisplayed with the help of JAVA programming.

Figure 5. Equivalent circuit of single stage impulse voltage generator.

III. IMPULSE VOLTAGE GENERATOR APPLICATION

A power transformer [9], a vital and expensive pieceof equipment in a power system, requires critical attentionfrom the standpoint of its insulation design and performanceunder both steady state and transient stress. Therefore, thisassessment is carried out through impulse tests. This studyis carried out using transformer model to be incorporatedin VHVL. Since, the virtualization involves simulation so,

transformer winding models are taken and analyzed throughsimulation. The results enable students to test a transformer invitual laboratory environment, and a test engineer to arrive atrequired configuration of the generator for an impulse test.

To accomplish the above discussion present paper deals withthe parametric analyses of an equivalent model of a powertransformer winding with an application of impulse voltage.

A. Power transformer winding equivalent

Fig. 6 shows an equivalent of one phase winding of athree-phase transformer [11]. In this model 2, each stage (oneturn of winding) is modeled by series resistance (Rs), self-inductance (Ls), shunt resistance (Rsh), series capacitance(Cs) and ground capacitance (Cg). The typical voltage and theneutral current waveform for A phase during impulse voltagetesting is shown in Fig. 7 and Fig. 8 respectively.

Cg represents the equivalent capacitance of primary andsecondary windings; Csh is the capacitance between primaryand secondary windings; Ls is equivalent leakage inductanceof the primary and secondary windings; Rs is equivalentresistance of the primary and secondary windings; Rsh isthe core exciting impedance-composed of a resistance andinductance.

2This paper presents transformer winding model of the frequency rangeof 10 kHz to few MHz which is helpful in internal resonance studies. Andthe experiments in this frequency range reveal remarkable overvoltages. So,necessary to model a transformer accordingly, as explained in [12].



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Figure 6. Equivalent model for a Power Transformer winding.

Figure 7. Typical voltage waveform at A phase terminal during impulsevoltage testing for power transformer.

Figure 8. Typical neutral current waveform at A phase terminal duringimpulse voltage testing for power transformer.

In the present paper, the data [12,13] for one phase ofa 220 kV/35 kV, 50 MVA three phase transformer are asfollows:

• series resistance per turn = 1 Ω;• self inductance per turn = 1.65 mH;• shunt resistance per turn = 1 kΩ;• series capacitance per turn = 2 nF;• ground capacitance per turn = 2 pF.

IV. RESULTS

A. Marx Generator

Fig. 9 shows the impulse voltage waveforms of Marxcircuit for different front resistor values. Small increment infront resistor value leads to negligible increment in tail timebut a significant change in peak voltage and front time assummarised in Table II.

Fig. 10 shows the impulse voltage waveforms of Marxcircuit for different values of tail resistor. Significant change in

tail resistor value only leads to increment in tail time but thereis no change in peak voltage and front time as summarised inTable III.

Fig. 11 shows the impulse voltage waveforms of Marxcircuit for different values of load capacitor. Slight changein load capacitor value leads to increment in peak voltage andtail time but there is no change in front time as summarisedin Table IV.

Figure 9. Variation of impulse voltage with front resistance Rf .

Figure 10. Variation of impulse voltage with tail resistance Rt.

Figure 11. Variation of impulse voltage with load capacitance Cl.



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Table IIVARIATION OF OUTPUT VOLTAGE WAVEFORM OF MARX GENERATOR WITH

FRONT RESISTANCE Rf

curve V(kV)

Cg

(µF )Rf

(Ω)Rt

(Ω)Cl

(nF)Vp

(kV)Tf

(µs)Tt

(µs)a 50 0.6 10 120 2 143.60 1.39 45.40b 50 0.6 11 120 2 143.30 1.43 45.45c 50 0.6 12 120 2 143 1.47 45.46d 50 0.6 13 120 2 142.85 1.51 45.52e 50 0.6 14 120 2 142.65 1.55 45.54

Table IIIVARIATION OF OUTPUT VOLTAGE WAVEFORM OF MARX CIRCUIT WITH

TAIL RESISTANCE Rt

curve V(kV)

Cg

(µF )Rf

(Ω)Rt

(Ω)Cl

(nF)Vp

(kV)Tf

(µs)Tt

(µs)a 50 0.6 10 120 2 143.60 1.39 45.40b 50 0.6 10 122 2 143.60 1.39 46.10c 50 0.6 10 124 2 143.60 1.39 46.76d 50 0.6 10 126 2 143.60 1.39 47.37e 50 0.6 10 128 2 143.60 1.39 48

Table IVVARIATION OF OUTPUT VOLTAGE WAVEFORM OF MARX GENERATOR

CIRCUIT WITH LOAD CAPACITANCECl

curve V(kV)

Cg

(µF )Rf

(Ω)Rt

(Ω)Cl

(nF)Vp

(kV)Tf

(µs)Tt

(µs)a 50 0.6 10 120 2 143.60 1.39 45.40b 50 0.6 10 120 2.2 143.30 1.43 45.50c 50 0.6 10 120 2.4 143.10 1.45 45.57d 50 0.6 10 120 2.6 142.90 1.49 45.72e 50 0.6 10 120 2.8 142.70 1.53 45.80

B. Single stage Impulse Voltage Generator

Fig. 12 shows the impulse voltage waveforms for the differ-ent values of front inductance. It is an important considerationto avoid output waveform distortion. Slight change in frontinternal inductance value does not affect peak voltage, fronttime and tail time, however, for a large change in inductancevalue output waveform shows oscillations as shown in Fig. 10and summarised in Table V.

It is also an important consideration for getting an errorfree standard output waveforms. Fig. 13 shows the impulsevoltage waveforms for the different values of tail inductance.As inductance increases slightly there is negligible change inpeak voltage, front time and tail time but due to a large changein inductance value there is a significant change in Vp, Tf andTt as summarised in Table VI.

Figure 12. Variation of impulse voltage for single stage impulse voltagegenerator with front inductance Lf .

Figure 13. Variation of impulse voltage for single stage impulse voltagegenerator with tail inductance Lt.

Table VVARIATION OF IMPULSE VOLTAGE FOR SINGLE STAGE IMPULSE VOLTAGEGENERATOR WITH FRONT INDUCTANCE Lf (CHARGING VOLTAGE = 100

KV)

curve Cg

(µF )Rf

(Ω)Lf

(nH)Rt

(Ω)Lt

(nH)Cl

(nF)Vp

(kV)Tf

(µs)Tt

(µs)a 1 112 1 70 1 2 97.03 1.22 45.30b 1 112 10 70 1 2 97.03 1.27 46.10

c 1 112 102 70 1 2 97.03 1.28 50.14d 1 112 103 70 1 2 97.09 1.34 53.70f 1 112 105 70 1 2 - - -e 1 112 106 70 1 2 - - -

Table VIVARIATION OF IMPULSE VOLTAGE FOR SINGLE STAGE IMPULSE VOLTAGEGENERATOR WITH FRONT INDUCTANCE Lf (CHARGING VOLTAGE = 100

KV)

curve Cg

(µF )Rf

(Ω)Lf

(nH)Rt

(Ω)Lt

(nH)Cl

(nF)Vp

(kV)Tf

(µs)Tt

(µs)a 1 112 1 70 1 2 97.03 1.28 50.14b 1 112 1 70 10 2 97.03 1.28 50.11

c 1 112 1 70 103 2 97.05 1.33 50.21

d 1 112 1 70 106 2 98.66 1.65 56.78

e 1 112 1 70 107 2 98.79 2.17 121

C. Power TransformerIn order to get power transformer testing analyses results,

simulation studies are carried out by using a MATLAB simu-lation model. The number of stages is chosen by the user,



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dependent on the number of coils of transformer winding,to simulate the transformer windings (here, it is 3), and theladder network for the transformer is constructed in MATLABby choosing proper values of the ladder parameters that areobtained from test results for the transformer. The transformeris connected to the output of the IVG as the test object asshown in Fig. 6.

Series inductance and shunt resistor having significant valueaffect the output voltage across transformer winding. So,present paper analyses the variation of these two only. Fig. 12and Fig. 13 show the voltage waveforms for different valuesof shunt resistor and series inductance respectively. As shuntresistor value is increased the voltage increment is more and asseries inductance value is increased the winding voltage hasvery little increment as summarised in Table VII and TableVIII respectively. The analyses on number of coils are alsodone which shows an increment in voltage across transformerwinding as shown and summarised in Fig. 14 and Table IXrespectively.

Figure 14. Variation in output voltage with shunt resistance Rsh.

Figure 15. Variation in output voltage with series inductance Ls.

Figure 16. Variation in output voltage with number of turns.

Table VIIVARIATION OF OUTPUT VOLTAGE WAVEFORM OF POWER TRANSFORMER

WITH Rsh

Curve Rs

(Ω)Ls

(mH)Csh

(nF)Rsh

(kΩ)Cg

(pF)

Numberof

turns

peakvoltage(kV)

a 1 1.65 2 1 2 1 134.20b 1 1.65 2 1.5 2 1 142.47c 1 1.65 2 2 2 1 146.63

Table VIIIVARIATION OF OUTPUT VOLTAGE WAVEFORM OF POWER TRANSFORMER

WITH Ls

Curve Rs

(Ω)Ls

(mH)Csh

(nF)Rsh

(kΩ)Cg

(pF)

Numberof

turns

peakvolt-age

(kV)a 1 1.65 2 1 2 1 134.20b 1 1.75 2 1 2 1 135.38c 1 1.85 2 1 2 1 135.90

Table IXVARIATION OF OUTPUT VOLTAGE WAVEFORM OF POWER TRANSFORMER

WITH NUMBER OF TURNS

Curve Rs

(Ω)Ls

(mH)Csh

(nF)Rsh

(kΩ)Cg

(pF)

Numberof

turns

peakvolt-age

(kV)a 1 1.65 2 1 2 1 134.20b 1 1.65 2 1 2 2 157.90c 1 1.65 2 1 2 3 166.70

V. CONCLUSIONS

The mutual coordination between present work and VHVLis to provide a remote access of virtual laboratory withaccomplished parametric analyses, which is most importantfor the learning perspective.

This paper is outlined and illustrated a MATLAB model togenerate standard output impulse voltage waveforms of 1.2/50µs which leads to the simulation analyses on impulse voltagetesting of power transformer winding equivalent.

Students may use power transformer winding equivalentmodel to learn about impulse voltage testing, and can simulate



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different kinds of winding parameters during impulse voltagetesting.

The method considerably reduces the time and cost neededto teach impulse testing of power transformers. Therefore, itis very useful for educational purposes where the budget islimited.

ACKNOWLEDGMENT

Sachin Kumar whole heartedly thanks Professor N.K.Kishore for providing an opportunity to compose a conferencepaper on M.Tech project work, which is one of the mostemerging technology in the field of virtualization. Author takesthis opportunity to express his gratitude to Ministry of HumanResource development (MHRD), Government of India (GoI)for sponsoring the project. Author would like to thank Mr.N.C. Santhosh (Electrical Engineer, Tata Consulting EngineersLimited, Jamshedpur), Mr. Debasish Mukherjee (Jr. Program-mer, Electrical Engineering Department, IIT Kharagpur), MissS. Poornima Rao (Web Developer, Electrical EngineeringDepartment, IIT Kharagpur) and all his colleagues for theirsupport. Finally, the Department of Electrical Engineering, IITKharagpur for their encouragement.

REFERENCES

[1] Christof Rohrig and Andreas Jochheim, “The Virtual Lab for ControllingReal Experiments via Internet,” Proceedings of the 1999 IEEE Interna-tional Symposium on Computer Aided Control System Design KohalaCoast-lsland of Hawaii, Hawaii, USA, 1999.

[2] Hess Hodge, H.Scott Hinton and Micheal Lightner, “Virtual CircuitLaboratory,” 30th ASEE/IEEE Frontier Education Conference, KansasCity, Missouri, 2000.

[3] N Liester and W Schufft, “Virtual ASP based Impulse Generator,”presented at the 12th Int. Symposium on High Voltage Engineering,Netherlands, 2003.

[4] B. Hemalatha, Dipak Kumar Pal and Swati Sinha, “A web based sim-ulator for Impulse Voltage Generation,” First International Conferenceon Industrial and Information Systems, ICIIS 2006, 8-10 August 2006,Sri Lanka.

[5] Prashant Kr. Agrawal, Chandan and N. K. Kishore, “Development ofVirtual Impulse Laboratory,” IEEE Conference on Industrial Electronicsand Applications (ICIEA-2006), Singapore.

[6] IS 2071, Indian Standard specifications for “High Voltage Test Tech-niques,” Bureau of Indian Standards, New Delhi, November 1996.

[7] (Late) M. S. Naidu and V. Kamaraju, “High Voltage Engineering,” 3rdEd. New Delhi: Tata McGraw Hill, 2003, p.141-203 (book).

[8] Steven E. Meiners, “An Impulse Generator Simulation Circuit,” thisthesis was defended on November 25, 2002, University of Pittsburgh,USA (Thesis Chapter 6).

[9] W. Hauschild, H. Bachmann and M. Baronick, “Computer aidedImpulse-Voltage testing,” IEEE transaction on Electrical Insulation,Volume 26 Number 3, June 1991.

[10] Tilman Wolf, “Assessing Student Learning in a Virtual LaboratoryEnvironment,” Education, IEEE Transactions on: Accepted for futurepublication Volume PP, Forthcoming, 2009.

[11] Behrooz Vahidi and Jamal Beiza, “Using Pspice in teaching ImpulseVoltage testing of Power Transformers to Senior Graduate students,”IEEE Transaction on Education, Vol. 48, No. 2, May 2005.

[12] G. B. Gharehpetian, H. Mohseni, and K. Moller, “Hybrid modeling ofinhomogeneous transformer windings for very fast transient overvoltagestudies,” IEEE Trans. Power Del., vol. 13, no. 1, pp. 157–163, Jan. 1998.

[13] Youyuan Wang, Weigen Chen, Chaisheng Wang, Lin Du and Jinx-ing Hu, “A Hybrid Model of Transformer Windings for Very FastTransient Analysis Based on Quasi-stationary Electromagnetic Fields,”Electric Power Components and Systems, 36:5, 540-554 (Article: DOI:10.1080/15325000701735520), September 2007.

[14] Virtual High Voltage Laboratory (VHVL) web domain,“http://203.110.240.54/VHVL.”



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