2019 IEEE

5.3.1 Winding short-circuit emulation

The transformer winding short-circuit scenario is emulated via installation of the

variable resistance rheostat in parallel to winding terminals. The maximum value of the

rheostat represents the open circuit scenario, since it significantly exceeds the winding

impedance and all the current coming from the source will flow the structure of the winding

(see Figure 5.2(a) [110] ©2019 IEEE). The open circuit scenario corresponds to the healthy

working mode of the transformer. In this work, the maximum value of the rheostat is 5 kΩ

and 5 MΩ for distribution and power transformers, respectively, and both values are high

enough to be compatible with windings’ total impedance. The worst-case scenario

corresponds to the full short-circuit of the transformer winding, where all the current

coming from the source flows through the rheostat as illustrated in Figure 5.2(b) [110]

Figure 5.3. Circuit representation of the winding short-circuit emulation The paralleled resistance is decreased with 500 Ω from highest (either 5 kΩ or 5 MΩ) to lowest (~Zero Ω) resistance. Generally, the relationship between input and output signal can be expressed in terms of the impedances as following:

V

out

/V

in

= Z

out

/(Z

w

+ Z

out

) (54) V

out

/V

in

= Z

out

/(Z

w

|| Z

R

+ Z

out

) (55) where V

in

and V

out

represent the input and output voltages, correspondingly, Z

out

is the cable impedance, Z

R

is the rheostat’s value, and Z

w

represents the winding impedance. Therefore, it is observed that the transfer function becomes the function of the new equivalent impedance.

Figure 5.4 illustrates the behavior of the frequency response signature towards the different short-circuit scenarios, where 5 kΩ parallel resistance corresponds to the 0%

short-circuit (healthy state) and 1 Ω corresponds to 100% short-circuit (critical). One of the major observations is that the magnitude of the transfer function increases along with severity of the winding short-circuit, which results in flattening of the signature around the first anti-resonance point (depicted by blue vertical line in Figure 5.4 [110] ©2019 IEEE).

The first anti-resonant peak corresponds to the frequency at which the winding self- inductance L resonates with the equivalent capacitance C, represented via following expression [175]:

f

anti-resonance

= 1/2π√LC (56)

Figure 5.4. FRA signatures for different short-circuit severities 5.3.2 Green-to-yellow decision boundary

The green-to-yellow decision boundary B

G|Y

corresponds to the transition point from healthy (green) to suspicious (yellow) working mode. In this work, the boundary B

G|Y

represents the case where the short circuit current starts to flow in the system and is expressed in terms of the SIs values estimated from the corresponding FRA measurement.

For each iteration step, short-circuit monitoring and FRA signature measurement is conducted via experimental setup depicted in Figure 5.5(a)-(b), respectively [20] ©2022 IEEE.

(a) (b)

Figure 5.5. Practical setup for: (a) short-circuit current monitoring and (b) FRA test

The short circuit current monitoring results given in Table 6 [181] ©2022 IEEE

demonstrate the transition point (green colored) from green to yellow working mode. In

the next short-circuit scenario the current flowing through the rheostat becomes measurable

by the ammeter. Hence the following observations, in particular, T1-12V at 500 Ω, T1-

24V at 1.5 kΩ, T2-22V at 500 Ω, T2-42V at 1.5 kΩ, T3-24V at 500 Ω, and T3-36V at 1 kΩ, are considered as the green-to-yellow boundary B

G|Y

. It was mentioned above, that for each fault scenario the FRA measurements are conducted to calculate 12 statistical indicators.

Table 7 [181] ©2022 IEEE illustrates the corresponding CC values for the scenarios presented in Table 6. Similarly, the green colored observations represent the critical CC value, i.e. the green-to-yellow B

G|Y

decision boundary. All collected B

G|Y

sample points expressed by other statistical indicators are also estimated from the obtained FRA signatures and presented in the Appendix H.

Table 6 – Short-circuit current monitoring results for different fault scenarios

Rating Taps Winding % 5 kΩ 4.5 kΩ 4 kΩ 3.5 kΩ 3 kΩ 2.5 kΩ 2 kΩ 1.5 kΩ 1 kΩ 500 Ω 200 Ω 0 Ω

400 VA T1 12V 33.33% 0 0 0 0 0 0 0 0 0 0 0.034 -

T1 24V 66.67% 0 0 0 0 0 0 0 0 0.024 0.031 0.054 -

630 VA T2 22V 10.00% 0 0 0 0 0 0 0 0 0 0 0.022 -

T2 42V 19.10% 0 0 0 0 0 0 0 0 0.027 0.041 0.218 -

1 kVA T3 24V 10.90% 0 0 0 0 0 0 0 0 0 0 0.022 -

T3 36V 16.36% 0 0 0 0 0 0 0 0 0 0.027 0.215 -

Table 7 – Estimated CC values for the emulated fault scenarios

Rating Taps Winding % 5 kΩ 4.5 kΩ 4 kΩ 3.5 kΩ 3 kΩ 2.5 kΩ 2 kΩ 1.5 kΩ 1 kΩ 500 Ω 200 Ω 0 Ω 400 VA T1 12V 33.33% 0.9997 0.9997 0.9997 0.9998 0.9999 0.9997 0.9998 0.9997 0.9998 0.9997 0.9992 0.8983

T1 24V 66.67% 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9995 0.9985 0.9939 0.8985 630 VA T2 22V 10.00% 1.0000 1.0000 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9992 0.8296 T2 42V 19.10% 1.0000 1.0000 0.9997 0.9999 0.9999 0.9999 0.9999 0.9998 0.9996 0.9987 0.9953 0.7701 1 kVA T3 24V 10.90% 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.8472 T3 36V 16.36% 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9997 0.9992 0.9966 0.7446

In this work, the list of statistical indicators used to estimate the numerical difference between reference and new frequency response includes 12 indices mostly used in the literature. The comprehensive details regarding utilized indices is presented in the next section of this thesis.

5.3.3 Yellow-to-red decision boundary

The yellow-to-red decision boundary B

Y|R

corresponds to the transition point from suspicious (yellow) to critical (red) working mode. In this work, the boundary B

Y|R

represents the maximum tolerable short-circuit current in the system and is also expressed

in terms of the statistical indicators values estimated from the respective FRA

measurements. Basically, the differential relay system of the transformer under the test is set to 0.5% of the nominal current [176]. The rheostat value corresponding to this short- circuit current is found via decreasing the resistance from the highest to the lowest and measuring the current through the rheostat. Once the measured current value matches the desired value (0.5% of the nominal), the paralleled resistance is recorded and FRA signature of the given configuration is obtained. Similarly, decision boundary B

Y|R

is expressed in terms of the critical values of 12 statistical indicators calculated from the FRA data.

Table 8 [180] ©2021 IEEE provides the rheostat values corresponding to yellow-to- red decision boundary and the CC value of that given short-circuit condition. B

Y|R

sample points expressed by other statistical indicators are also estimated from the obtained FRA signatures. Table 9 [181] ©2022 IEEE illustrates the summary of the decision boundary identification, where 6 observations of B

G|Y

and 3 observations of B

Y|R

are collected for the index CC and Table 10 summarizes the calculated critical values for all SIs indicating two decision boundaries [20] ©2022 IEEE.

Table 8 – Current and paralleled rheostat values of B

Y|R

boundary Transformer under test T1-0.4 kVA T2-0.63 kVA T3-1 kVA

Nominal current (A) 11.00 2.86 4.54

Critical current (A) 0.055 0.0143 0.0227

Rheostat (kΩ) 4.6 15.4 10.5

CC 0.9990 0.9991 0.9989

Table 9 – Collected critical CC values for B

G|Y

and B

Y|R

boundaries Green-to-yellow boundary, B

G|Y

Yellow-to-red boundary, B

Y|R

0.9997 0.9998 0.9998

0.9998 0.9999 0.9997

0.9990

0.9991

0.9989

Table 10 – Critical values of statistical indicators