Abstract—Power transformers can experience large inrush

currents upon energization, the severity of which depends on the source strength, the angle of the applied voltage at energization, and the residual flux of the transformer. A novel inrush current reduction strategy has been investigated which involves setting the transformer’s residual flux. Testing of this strategy required a measurement system capable of measuring transformer residual flux. This paper details the construction of the flux measurement system, based on LabVIEW software, and presents test results which confirmed properly measured residual flux values.

Index Terms—Transformer, Residual Flux Measurement,

LabVIEW, Inrush Current

I. INTRODUCTION HEN a transformer is energized, it will often draw a non-symmetrical magnetizing current, referred to as inrush

current. These inrush currents can be very large, in some cases exceeding 10 p.u. The magnitude of the inrush current drawn by the transformer depends on the source strength, the angle of the applied voltage at the time of energization, and the residual flux stored in the transformer’s core. A transformer’s residual flux is determined by the de-energizing conditions of the transformer and is the flux retained in the transformer core in the absence of a magnetizing current.

The integral form of Faradays Law, which relates the flux of a transformer core to the EMF, e, is given in (1).

Φ(t) = 1N ⌡⌠

t0

te(t) dt + Φ0 (1)

Where: Φ0 is the transformer’s residual flux and N is the number of turns of the winding associated with the EMF.

Fig. 1 illustrates how the inrush current magnitude is dependent upon the residual flux and the angle of the system voltage at the time of energization. The waveforms on the left of Fig. 1 are the system voltage, represented by a dotted (red) trace, the prospective flux, represented by a dashed (green) trace, and finally the actual transformer flux, represented by a solid (blue) trace. The prospective flux is the flux that will circulate in the transformer core under steady state conditions

This work was supported in part by Schweitzer Engineering Labs. Douglas I. Taylor, and Normann Fischer are with Schweitzer Engineering

Labs, Pullman, WA 99163 USA (email: Doug_Taylor@selinc.com). Joseph D. Law and Brian K. Johnson are with the University of Idaho,

Moscow, ID 83844 USA (email: Joel@uidaho.edu).

[1]. Equation (1) indicates the prospective flux waveform of Fig. 1 is obtained by integrating the system voltage waveform and setting the residual flux term, Φ0, to zero, since the prospective flux is by definition the steady state flux.

Fig. 1. Depiction of the influence that transformer residual flux and the

applied voltage angle at energization have on inrush current magnitude.

Fig. 1 depicts a transformer that has a positive residual flux of 1 p.u. and is energized at a system voltage angle of zero degrees, when the prospective flux of the transformer is −1 p.u. By (1), the actual transformer flux is then the sum of the prospective flux and the residual flux, which results in a worst-case peak transformer flux of 3 p.u. Tracing this value of peak flux over to the flux-current (ΦI) curve shown on the right of Fig. 1 indicates that a large, unsymmetrical magnetizing current is required to support this level of flux in the transformer core, because the transformer core operates in saturation at this level of flux. The magnitude of the transformer inrush current diminishes as the value of the prospective flux approaches that of the transformer’s residual flux at the instant of energization.

This paper describes the construction of a system for measuring transformer residual flux. The residual flux measurements were used to verify an inrush current reduction strategy which actively sets the residual flux of a transformer in a method known as ‘Pre-Fluxing’. Section II describes the pre-fluxing method and the laboratory transformer used for experimentation. Section III briefly discusses LabVIEW and the reasons for its selection. Section IV details the measurement of the transformer’s ΦI curve. Section V describes the measurement of the transformer’s residual flux when pre-fluxing the transformer. Section VI presents the results verifying the correctly measured residual flux value, and section VII summarizes the results of the paper.

Using LabVIEW to Measure Transformer Residual Flux for Inrush Current Reduction

Douglas I. Taylor, Normann Fischer, Joseph D. Law, Brian K. Johnson

W

II. INRUSH CURRENT REDUCTION STRATEGY The scenario in Fig. 1, when the transformer’s residual and

prospective fluxes are equal in magnitude but opposite in polarity when the transformer is energized, represents the worst-case inrush current condition. A strategy to reduce transformer inrush current has been proposed which sets the transformer flux prior to energizing the transformer by a method known as pre-fluxing [2].

The method involves setting the transformer flux to a large magnitude in either the positive or negative polarity and energizing the transformer at either an angle of 210deg for positive residual flux, or 330 deg, for negative residual flux. At these two system voltage angles, the prospective flux is equal to either 0.87 p.u., for 210 deg, or −0.87 p.u for 330 deg. Thus, depending on the energization angle, the closer the residual flux can be pre-fluxed to the appropriate prospective flux p.u. value, the smaller the magnitude of the transformer inrush current when the transformer is energized.

To test the pre-fluxing method, a 55kVA laboratory transformer, shown in Fig. 2, was used. The transformer is a three phase, three winding, three leg transformer; the yard stick in Fig. 2 shows the relative size of the transformer. Table I contains the pertinent transformer specifications. As is labeled in Fig. 2, the secondary and tertiary winding connection points are shown. The primary winding connection points are located on the opposite side of the transformer.

Fig. 2. Three phase 55kVA laboratory transformer used for measurements.

Only a single phase of the transformer was energized, the center phase.

Table I – 55kVA Lab Transformer Design Parameters Winding Number of

Turns

Power

Rating

(kVA)

Voltage

Rating

(VRMS)

Current

Rating

(ARMS)

Primary 48 55 230 80

Secondary 48 50 230 72

Tertiary 5 5 25 67

This specific transformer was built to research interwinding faults, hence each phase of the secondary winding was constructed with multiple taps occurring at various percentages of the secondary winding. All of the testing performed on the secondary winding for the research presented here was done using the full percentage winding. Additionally, while this is a three-phase transformer, for the purposes of the research presented in this paper, only the center phase of the transformer was energized; the remaining two outer phases were left open-circuited.

Having identified an inrush current reduction strategy and obtained an adequate lab transformer for testing the strategy, it was necessary to create a system for measuring the transformer’s residual flux. The construction and verification of this measurement system is the focus of this paper.

III. LABVIEW The measurement system required flexibility in its input

capabilities as well as its output capabilities. Specifically, the system needed to be able to accept multiple different inputs and also needed to present the measurements in a variety of formats. For these reasons, LabVIEW [3] was selected as the core of the measurement system.

LabVIEW is a hardware/software package which takes analog signals fed into a data acquisition (DAQ) card, converts them into their digital representations, and displays them on a computer. LabVIEW is fairly intuitive and simple to learn because of its graphical user interface. The program executes user-constructed Virtual Instrument (VI) files. A VI contains all the desired signal inputs and data manipulation operations, such as arithmetic operators, signal filters, data recorders, and waveform viewers. The VIs make editing and file reuse very easy which was handy for this research because of the similarities between the various required measurements as will be discussed in the proceeding sections.

IV. REAL-TIME ΦI CURVE MEASUREMENT Transformer iron is limited to some maximum residual flux

value, the value of which depends on the material used and the construction process. A measurement of the transformer’s maximum residual flux was needed to properly gauge the levels of residual flux obtained from the pre-fluxing process. The value of a transformer’s maximum residual flux can be acquired from the hysteretic ΦI curve when the transformer is operating at or above rated voltage levels. The ΦI curve shown in Fig. 1 is a single valued curve. The single-valued curve does not contain the maximum residual flux information because it is constructed by measuring the peak flux and magnetizing current values corresponding to a varying range of voltage magnitudes and then connecting the points with a smooth line. However, a real-time ΦI curve does contain the hysteretic and maximum residual flux information. Thus, the first task in constructing the measurement system was to create a method to measure a real-time ΦI curve.

The principle behind measuring a transformer’s ΦI curve is relatively simple: the transformer’s magnetizing current is

Search Coil

Tertiary Winding

Secondary Winding

plotted along the abscissa and the transformer flux is plotted along the ordinate as shown in Fig. 1.

Current measurements can be readily obtained using a variety of methods and instrumentation. A through-hole Hall-Effect sensor was selected because of the electrical isolation it provided from the transformer itself.

The output of the LEM device is a voltage signal proportional to the current flowing in the conductor placed through the LEM device. This output voltage signal was fed into the DAQ card making it available in digital form for use within the LabVIEW VI.

Measurement of magnetic flux can also be performed with many different methods and instrumentation, broadly ranging in complexity. The easiest method, and the method chosen for the measurement system, was to measure the EMF signal existing across an open-circuited winding on the transformer, integrating this EMF signal, and dividing by the number of turns of the winding, as indicated in (1), to obtain the flux waveform.

While any open-circuited winding will produce an adequate EMF signal to measure flux, a search coil added around the middle leg of the lab transformer, shown in Fig. 2, allowed for control of the voltage magnitude of the EMF signal fed into the DAQ card, which had a maximum tolerable input of 15Vpk. Given the rated voltage levels and the number of turns of the various transformer windings shown in Table I, the EMF magnitude induced in the search coil would exceed the maximum input of the DAQ card unless the search coil was limited to one turn. To protect the DAQ card from any transient voltage spikes appearing across the search coil, two anti-parallel 15Vpk Zener diodes were placed in parallel with the search coil at the input to the DAQ card. A block diagram of the lab implementation used for the real-time ΦI curve is shown in Fig. 3.

Fig. 3. Lab implementation used for real-time ΦI curve. The variac was used

for varying the voltage applied to the tertiary winding

In Fig. 3, the source for the transformer was a variac capable of supplying between 0–100VRMS. Because the variac output couldn’t supply the 230VRMS rated voltage of the transformer primary or secondary winding, the variac was applied to the tertiary winding, which was rated for 25VRMS.

Once the magnetizing current and EMF signals were available within LabVIEW via the DAQ card, a VI was constructed which handled the appropriate signal conditioning and plotting of the ΦI curve. The magnetizing current signal needed to be corrected for the attenuation introduced by the Hall-Effect device, which involved multiplying the current waveform by 20 to adjust it to the actual values.

The EMF signal measured from the search coil was referred to the tertiary winding using the turns ratio, and is the voltage labeled in Fig. 3. Because the tertiary winding had five turns and the search coil had one turn, this meant multiplying the EMF signal by five.

The flux waveform is derived by integrating the EMF signal and dividing by the turns ratio, as indicated in (1). LabVIEW offers a pre-defined integrator block that makes this task easy. Dividing the integrated signal by the five turns on the tertiary winding produced the flux waveform. Because any DC offset present in the EMF signal would lead to integrator drift [4], the EMF signal was put through LabVIEW’s filter block prior to being integrated. The filter was configured as a third order Butterworth, high pass filter with a cutoff frequency of 1Hz. This filtering removed any DC in the EMF signal and prevented drift in the flux waveform. Having completed the signal conditioning of the magnetizing current and flux waveforms, the signals were then fed into an XY graphing block; the magnetizing current was the X input and the flux was the Y input.

To enable the LabVIEW VI to measure the ΦI Curve in real-time, the VI contained a while loop that continually executed all the measurement, signal computation, and display processes contained within the VI. The ΦI Curve VI is shown in Fig. 11 located in the Appendix.

With the completion of the LabVIEW ΦI Curve VI, the maximum residual flux was measured. This measurement was performed by applying the rated voltage to the transformer’s tertiary winding using the variac shown in Fig. 3. The ΦI curve shown on the left of Fig. 4 is with the rated 25VRMS appearing across the tertiary winding. The hysteretic ΦI curve shows the lab transformer has a maximum residual flux of 12mWb and a rated peak flux of 18.5mWb. The curve on the right of Fig. 4 is the ΦI curve with 28V applied across the tertiary winding. Because applying an above-rated voltage to the transformer causes the iron to operate in the saturated region, the magnetizing current increases from roughly 50Apk to 75Apk for only a 3VRMS increase in/ the applied voltage. The operation at 28VRMS shows the peak flux is roughly 20mWb, but the maximum residual flux is still 12mWb.

Fig. 4. ΦI curves of the lab transformer. The ΦI curve on the left is with the

rated 25VRMS applied across the tertiary winding. The ΦI curve on the right is with 28VRMS applied across the tertiary.

LabVIEW also allowed for the voltage, transformer flux, and magnetizing current waveforms to be plotted together, which was helpful for visualization purposes. Several cycles of these waveforms with the transformer operating unloaded at

rated tertiary voltage are plotted in Fig. 5. The top waveform is the voltage, the middle waveform the flux, and the bottom waveform is the magnetizing current. The maximum residual flux shown in Fig. 4 is also labeled in Fig. 5. From Fig. 5 it is evident that the magnetizing current is zero when the flux is at its maximum residual flux value as one would expect.

Fig. 5. Transformer waveforms at rated tertiary voltage. Beginning with the

top, the waveforms are voltage, flux, and magnetizing current.

V. RESIDUAL FLUX MEASUREMENT Having measured the transformer’s maximum residual flux,

the next task was to measure the transformer’s residual flux when pre-fluxing the lab transformer. This measurement was very similar to that of the ΦI curve, which enabled substantial reuse of the ΦI Curve VI, with some minor differences.

The first difference between the Residual Flux VI and the ΦI Curve VI was the Residual Flux VI needed to measure the transformer flux just during the pre-fluxing of the transformer, which, because of the device used for pre-fluxing, was between 0.1–1s in duration. Removing the while loop from the VI, and adjusting LabVIEW’s sample rate and number of recorded samples appropriately controlled the length of time that the Residual Flux VI measured data. Also, the Residual Flux VI did not use a high-pass filter as the ΦI Curve VI had because residual flux is a DC quantity.

The final difference between the two VIs is the Residual Flux VI required an external trigger fed into the DAQ card to synchronize the start of the pre-fluxing process and the residual flux measurement. The device used for pre-fluxing consists of a capacitor, two diodes, and a switch and its operation is detailed in [2]. For the switch, a two-pole knife switch was used with one-pole completing the circuit of the pre-fluxing device and the transformer and the other pole completing the path of the trigger circuit. The trigger command was a 5V DC signal fed into the DAQ card. When the switch was closed, the DAQ card trigger input changed from its previous state of 0V to 5V. LabVIEW was configured to start measuring the residual flux on this rising voltage edge.

Other than these three changes, the Residual Flux VI used the same signal conditioning and graphing methods that the ΦI Curve VI had. A block diagram of the lab implementation

used for the residual flux measurements is shown in Fig. 6. Because pre-fluxing should be performed on the highest voltage winding [2], and the lab transformer was rated for the same voltage on both the primary and the secondary winding, the transformer was pre-fluxed on the secondary winding because of its accessibility.

Fig. 6. Lab implementation used for residual flux measurement. When the

knife switch closed, it synchronized the pre-fluxing process and the measurement system.

A final detail requiring attention when performing a residual flux measurement is the initial residual flux already stored in the transformer, the Φ0 term in (1). While not required for the proposed pre-fluxing process [2], this initial residual flux must be known in order to measure the proper residual flux value. The simplest method for setting the residual flux to a known value is to set the residual flux to zero by demagnetizing the transformer. Demagnetization occurs when reducing a magnetic material’s flux density from its rated value to zero [5]. For a transformer, this process is performed by applying rated voltage to the transformer winding and reducing it to zero, a task suitable for a variac. As mentioned previously, because of the output voltage limitations of the variac, the demagnetization of the lab transformer was performed on the lab transformer’s tertiary winding. The completed Residual Flux VI is shown in Fig. 12 located in the Appendix.

With the Residual Flux VI finished, it could be used to measure the residual flux during the pre-fluxing process. The measurement from a pre-fluxing operation is shown in Fig. 7.

Fig. 7. ΦI Curve produced with the Residual Flux VI. The residual flux left

in the transformer after the pre-fluxing process was approximately 9mWb.

Fig. 7 shows that the transformer was initially demagnetized, and after application of the pre-fluxing device,

the residual flux of the transformer was set to approximately 9mWb, or, in terms of the transformer’s rated peak flux of 18.5mWb, 0.49 p.u. This value of residual flux is slightly below the transformer’s maximum residual flux of 12mWb, shown in Fig. 4. Notice that because the pre-fluxing was performed on the secondary winding of the transformer, which has many more turns than the tertiary winding, the magnetizing current magnitude is much less than that of the tertiary winding shown in Fig. 4. Section VI will describe how the residual flux measurements were verified.

VI. VERIFICATION OF RESIDUAL FLUX MEASUREMENT As was described in section I, the magnitude of the

transformer inrush current diminishes as the value of the prospective flux approaches that of the transformer’s residual flux at the instant a transformer is energized. If the prospective flux of the transformer is exactly equal to the residual flux of the transformer at energization, the transformer will not draw any inrush current and the magnetizing current will be perfectly symmetrical. This condition is depicted in Fig. 8.

Fig. 8. Depiction of ideal energization of a transformer when the residual flux

equals the prospective flux.

In Fig. 8, because the residual and prospective flux are equal at the moment of energization, by (1), the transformer flux exactly follows the prospective flux waveform, which results in peak flux values of ±1 p.u., and when the transformer flux oscillates about these peak steady state values, the magnetizing current is symmetrical, as shown by the symmetrical set of dotted lines intersecting the ΦI curve in Fig. 1. Thus, if the lab transformer is energized at the exact system voltage angle when the prospective flux is equal to the measured residual flux, the transformer’s magnetizing current should be symmetrical.

Using a specially constructed switch capable of closing at any specified system voltage angle, the transformer’s secondary winding was energized at the angle when the prospective and measured residual fluxes were equal. For the residual flux of 9mWb, shown in Fig. 7, the system voltage angle when the prospective flux is equal to this value of

residual flux is 119deg. The transformer’s voltage and magnetizing current waveforms when energizing the transformer at this angle are shown in Fig. 9.

Fig. 9. Transformer voltage (top) and magnetizing current (bottom)

waveforms when energizing the transformer at a system voltage angle of 119deg. Because the prospective flux equaled the residual flux, the magnetizing current was symmetrical, which verified the residual flux measurement.

Fig. 9 shows that when the transformer was energized at a system voltage angle of 119deg, the magnetizing current waveform was symmetrical with a peak value of 5.5A. The symmetry of the current waveform verified the residual flux measurement in Fig. 7 was correct. If the measured residual flux had been different from the actual residual flux, then closing in at 119deg would cause an initial asymmetry in the magnetizing current as shown in Fig. 10, where the current peaks at 8A in the positive polarity but only 3A in the negative polarity.

Fig. 10. Transformer voltage (top) and magnetizing current (bottom)

waveforms when energizing the transformer at a system voltage angle of 119deg. Because the prospective flux did not equal the residual flux, the magnetizing current wasn’t symmetrical, which indicates an error in the residual flux measurement.

VII. SUMMARY This paper discussed a transformer flux measurement

system using LabVIEW. The flux measurement system was used during an investigation of a method for reducing transformer inrush current by pre-fluxing a transformer prior to its energization. The measurement system used to produce a real-time ΦI curve was described. This curve provided the value of the transformer’s maximum residual flux and rated peak flux, which helped quantify the value of residual flux achieved with the pre-fluxing method. The measurement system used in measuring the residual flux during pre-fluxing was also described. This system was very similar to that used to measure the real-time ΦI Curve, with some minor changes. The values of the measured residual flux were verified by energizing the transformer at the system voltage angle when

the prospective and measured residual fluxes were equal, which was indicated by a symmetrical magnetizing current.

REFERENCES [1] J. H. Brunke, Elimination of Transient Inrush Currents when Energizing

Unloaded Power Transformers, Ph.D. dissertation, Swiss Federal Institute of Technology, Zurich, Switzerland, 1998.

[2] D. I. Taylor, Single Phase Transformer Inrush Current Reduction Using Pre-Fluxing, Masters Thesis, University of Idaho, Moscow, Idaho, 2009.

[3] National Instruments, LabVIEW User Manual, 2009 [cited 2009, June 11] Available at HTTP: http://digital.ni.com/manuals.nsf/websearch/790127B60590AD0C86256D2C005DCE0F

[4] Y. Husianycia, M. Rioual, “Determination of the Residual Fluxes when De-Energizing a Power Transformer / Comparison with On-Site Tests,” Power Engineering Society General Meeting, 2005, IEEE, 12-16 June 2005, pp 449-454.

[5] M. Enokizono, T. Todaka; K. Ikeshita, “Analysis of Residual Flux Distribution and Consideration of Demagnetizing Conditions of Mild Steel,” IEEE Translation Journal on Magnetics in Japan, Vol 2, No. 11, Nov. 1987, pp 963-972.

APPENDIX – LABVIEW VIS

Fig. 11. ΦI Curve VI. The VI is contained within a While loop (shown) that continually executes all the processes.

Fig. 12. Residual Flux VI. While similar to the ΦI Curve VI, the Residual Flux VI removed the filter and the While loop. The VI was configured to trigger on a

rising edge within the DAQ Assistant block.