FREQUENCY RESPONSE ANALYSIS FOR EXACT POWER TRANSFORMER IMPEDANCE

The frequency response analysis (FRA) of the transformer impedance is known as a diagnosis method for the damages in a transformer. It is reported the transfer function as frequency response analysis. But the impedance of the transformer cannot be measured correctly in the high frequency range when the influence by the stray capacitance becomes large. And, it is not obvious the influences of residual flux to the transfer function or the impedance. In this paper, the exact measurement method for the FRA of transformer impedance is described. We proposed the measurement circuit diagram in which the influence of the stray capacitance to the earth can be included. In the circuit diagram, the resistance for the current measurement is connected between the power supply and the transformer terminal. Therefore, it can be measure the exact transformer impedance. The magnetic flux remains in the iron core after the transformer was switched off. In the FRA measurement, the residual flux has an effect on the impedance. The residual flux can be removed by supplying attenuated rectangle voltage waveform. It is cleared the difference of the impedance at the frequency range from DC to resonance point. The exact transformer impedance will be derived by this proposed measurement method and demagnetizing.


INTRODUCTION
There are several failure modes in the power transformer.They are damages caused during the transportations, due to the electromagnetic forces caused by a short-circuit current, caused on conductors and insulating materials by over-voltages and due to ages.When the damage is seen from outside and is judged as a failure, it can be removed by repairing.However, the large capacity transformer has an iron core and a coil in a tank and the medium and low capacity transformer has a molded coil.The constructions make the recognition of the damages difficult.
The frequency response analysis (FRA) of the transformer impedance is known as a diagnosis method for the damages in a transformer [1].The measured result is acquired for the sound one and compared to the result measured after a transporting, a commissioning test or an operation.The comparison will be the possible diagnosis of transformer.It is known for measuring the transformer impedance that the circuit diagram is constructed with a resistor of 50 ohms between the terminal of transformer and the earth and the power source of the function generator is connected to the other terminal of transformer and the earth [2] [3].The impedance is derived from the current deduced from the voltage drop of the resistor and the terminal voltage drop of the transformer.In the circuit diagram, the current which flows through the stray capacitance of transformer does not flow through the 50 ohm resistance.Therefore by the circuit diagram the impedance cannot be measured correctly in the high frequency range when the influence by the stray capacitance becomes large.
In this paper, the measurement method for the FRA of transformer impedance and the measured result for the two winding transformer as an example are described.The measurement was conducted by applying the sinusoidal wave with changing the frequency from the function generator and deducing the impedance from the voltage and the current.This is called as FRA hereafter.The measurement was also conducted by the LCR meter.This is called as LCR hereafter.The results of two methods will be compared.The new circuit diagram for the FRA measurement is proposed.In the new one, the resistor for the current measurement is connected to the transformer terminal of the voltage application and the resistance value is changed.Furthermore, On FRA measurement, it is necessary to take into consideration the influence of residual magnetic flux in the measurement using the open-circuit of FRA.The experimental result about the influence of residual

TRANSFORMER FAILURE WITH REFEREN-CE TO FREQUENCY DOMAIN
There are several failure modes for the transformer.The appearances differ dependently on the frequency.The failure appearances are summarized for the frequency region in Table 1 [3][8].The failure mode of transformer might possibly be estimated by comparing the frequency response of the measured impedance to one measured for the sound transformer.This method can contribute to the diagnosis of the transformer soundness.

Transformer equivalent circuit
Figure 1 shows the equivalent circuit for the two winding transformer.From figure 1, it can be seen that the magnetizing characteristics are measured when the secondary winding is open and the voltage applied to the primary winding.This is deduced as the inductance L 0 is far large compared to the leakage impedance l 1 , due to magnetizing characteristics.
On the other hand, the leakage impedance and the coil resistance can be measured when the secondary winding is short-circuited, as the voltage is hardly applied to the iron core.

Measurement method of impedance
of impedance.The impedance is calculated by (1) from the voltages V 1 and V 2 measured by the circuit shown in figure 3. The impedance change along the frequency is obtained by repeating the measurement at the different frequencies.From (1), the ratio of k between V 1 and V 2 is obtained.In the low frequency domain, (1) is proved correct as the influence of the stray capacitances are limited [4] [5].
The signal of V 2 in figure 2 is input to an oscilloscope with the input impedance of 50 ohms.It can be converted to the current.When V 1 is measured by the same way, the impedance can be calculated.
However in the high frequency domain, the error becomes large in the calculation by (1), as the impedance is a few to 10s kHz near the resonance frequency domain.

Experimental results
Figure 4 shows the measured result of the impedance on the single phase transformer of 110V-3kV and 60 VA, when the 110V winding is short-circuited and the high voltage winding is connected to the function generator.The measurement diagram is shown in figure 3. The frequency was changed from 10Hz to 1MHz.The measured result by using the LCR meter (NF/ZM2376) is shown in figure 4 as well.
Following observations are deduced from figure 4. a) Below 100Hz the impedance value is constant along with the frequency in both measurements.This will be caused by the winding resistance.b) The impedance increases along with the frequency above 200Hz.It is caused by the inductance.

c)
The local resonances are seen at 20 and 40 kHz.The resonance appears at 300 kHz, above which the impedance decreases.This is caused due to the capacitance which becomes dominant.e) The measured data by two methods coincide with each other.The impedance at the resonance frequency 300 kHz differs.The circuit diagram was basically same as one shown in figure 3 for the LCR measurement.The reason is considered as follows.The resistance for the current measurement is changed according to the measured impedance value in the LCR meter measurement case.However the resistance is constant as 50 ohms in the measurement case by the function generator.

Discussion
The influence of the stray capacitance of transformer is discussed for the measurement by the function generator shown in figure 3. The impedance of the transformer measured from the primary terminal is calculated by the Frequency Scan software in the Electro Magnetic Transient Program, EMTP for the circuit of figure 5, where the transformer circuit is expressed by the inductance, the stray capacitance between the windings and the stray capacitance from winding to the earth.The result is shown in figure 6, in which the transformer impedance is shown when it is measured without the resistance of 50 ohms.
Following facts can be deduced from figure 6. a) The impedance shows same tendency for the two conditions.b) The results are same at the resonance frequency of 'A'.c) The results differ significantly at the resonance frequency of 'B'.When the resistance of 50 ohms is connected from the transformer terminal to the earth, the resonance becomes unclear.d) The results by two ways differ in the 'C' frequency domain.The reason is that the current flow through the resistance of 50 ohms becomes small as the large current flows through the stray capacitance to the earth of 100pF.From the facts it can be said that the measurement way does not give a correct value for the impedance near and above the resonance frequency.

Proposed method
As is shown in figure 5 and discussed previously, the known measurement way restricts the current through the resistance as the current flows through the stray capacitance to the earth.As a result, the impedance is not correct near and above the resonance frequency for the transformer used in the experiment of figure 4. The measurement way is basically same as one shown in figure 3 for the LCR meter.This means that the impedance measurement will not be correct in the high frequency domain for the LCR meter measurement.
Figure 7 shows the measurement circuit diagram in which the influence of the stray capacitance to the earth can be included.In the diagram, the resistance for the current measurement is connected between the power supply and the transformer terminal.In addition the resistance value is increased along with the increment of the transformer impedance.The current flows through the capacitance to the earth can flow the resistance and the measurement error is made small around the resonance frequency when the transformer impedance is big.
The relationship of V 1 and V 2 is shown in figure 8 in the circuit of figure 7. The equation to calculate the transformer impedance is described in (2).The transformer impedance can be calculated by measuring V 1 and V 2 with the phase difference between them.

Experiment
The measured results of impedance along with the frequency are shown in figure 9 as R input side where the resistance for the current measurement is connected between the function generator and the transformer terminal and its value is varied as 50, 470 and 1k ohms.The results of figure 4 are also shown as R earth side in figure 9.
The followings are seen from figure 9. a) Both data agree almost in the frequency range below 10 kHz.b) The impedance by the resistance of the generator side is lower than that of the earth side.c) The tendency of (b) was obtained since the impedance is calculated correctly by changing the resistance according to the impedance value with the resister of the generator side.d) In the frequency domain above the resonance frequency the impedance is smaller with the resistance of the generator side than that with the resister of the earth side.This means that the current through the stray capacitance to earth is measured correctly.e) The resonance frequency differs in both cases.One with the resistance of the earth side is larger than that of the generator side.The resonance frequency is decided by the transformer inductance L and the stray capacitance C as shown in figure 10.When the resistance is connected to the earth, the current through the stray capacitance does not flow in the resistance.The stray capacitance is small equivalently and the resonance frequency becomes large.

DEMAGNETIZATION OF RESIDUAL MAG-NETIC FLUX
The influence on the impedance measurement by residual magnetic flux (RMF) is described.The test transformer is 110V-3kV, 60VA and single phase type.Voltage injection to a transformer was taken as high voltage winding, and low voltage winding was set to the open-circuit.Moreover, the state of iron core was set to two types, those were "without RMF" and "with RMF".The RMF can be removed by supplying attenuated rectangle voltage waveform shown in figure 11 [9].The state "with RMF" of an iron core was made by injecting DC+5V into low voltage winding for about 60 seconds.The results of FRA is shown in figure 12.The followings are seen from figure 12. a) In the range from 10 Hz to the resonance frequency, if frequency is the same, the impedance with RMF is smaller than the impedance without RMF.b) The resonance frequency in a state with RMF is higher than a state without RMF.The reason why the resonance frequency in a state with RMF is higher than a state without RMF was reduction of magnetization inductance.That is, in the equation (3), since the inductance L became small, the resonance frequency f r became high.

CONCLUSIONS
The measuring system is investigated for the frequency response of transformer impedance.The following conclusions are deduced.1) The current through the stray capacitance cannot be measured by the conventional measuring system.2) The measurement of the impedance is not sufficiently correct in the high frequency domain where the influence of stray capacitance becomes negligible.
3) The new measuring system is proposed, where the current through the stray capacitance can be measured.4) The resistance for the current measurement is inserted between the function generator and the transformer terminal instead between the earth and the terminal.5) The resistance value is varied according to the transformer impedance value.The system gives the correct measurement of the transformer impedance in all frequency domain.6) Magnetic inductance with RMF is smaller than that without RMF.In the range from 10 Hz to resonance frequency, if frequency is the same, the impedance with RMF is smaller than impedance without RMF.The resonance frequency in a state with RMF is higher than a state without RMF.7) In order to measure the accurate impedance, demagnetizing before the measurement is desirable.8) The exact transformer impedance will be derived by this proposed measurement method and demagnetizing.
the impedance measurement using the open-circuit of FRA is described.

Figure 2
Figure2shows the measuring methods schematically.In the IEEE guide[3], the diagram shown in figure3is adopted as a circuit measuring the frequency response

Fig. 4 .
Fig.4.Measurement results by FRA and LCR meter d) The resonance appears at 300 kHz, above which the impedance decreases.This is caused due to the capacitance which becomes dominant.e)The measured data by two methods coincide with each other.The impedance at the resonance frequency 300 kHz differs.The circuit diagram was basically same as one shown in figure3for the LCR measurement.The reason is considered as follows.The resistance for the current measurement is changed according to the measured impedance value in the LCR meter measurement case.However the resistance is constant as 50 ohms in the measurement case by the function generator.

Table . 1
. Frequency and failure mode.