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Transient Recovery Voltage (TRV) Study:

An Overview, Characteristics, Rating Considerations, Calculation & Mitigation Techniques

1. Transient Recovery Voltage (TRV) and Rate of Rise of Recovery Voltage (RRRV)

A Transient Recovery Voltage (TRV) study is essential for determining the HV circuit breaker capability limits. The TRV is the voltage across the circuit breaker terminal after the circuit is disconnected. When the breaker disconnects the circuit, the current stops flowing through it. The power network response to the current interruption (due to the breaker opening) can generate the TRV. The TRV is the voltage difference between the source side and load side of the circuit breaker. Figure 1 shows the TRV scenario in power systems.

Normally, the circuit breaker operation is successful when the breaker interrupts the fault current and withstands the TRV limits. The most severe TRV occur across the first pole of a circuit breaker interrupting the three-phase symmetrical fault when the system voltage is at peak. The Rate of Rise of Recovery Voltage (RRRV) is the speed at which the TRV increases (dV/dt) after the circuit breaker has been interrupted.

Figure 1: The TRV scenario in power systems.

2. TRV Characteristics

The nature of TRV depends on the connected circuit where the breaker is being interrupted. Mostly, the system TRV characteristics can be exponential, oscillatory, and triangular type wave-shapes. The TRV waveforms can be single-frequency oscillations produced by a lumped RLC circuit, or they can be various oscillatory components and travelling wave reflections.

An exponential (over-damped) TRV occurs when at least one transformer and transmission line are connected on the unfaulted side of the circuit breaker when it clears the three-phase fault. The exponential TRV is shown in Figure 2. Assume that the network is reduced to a parallel RLC circuit, the TRV is exponential when R ≤ [(1/2)×√(L/C)].

An oscillatory (under-damped) TRV occurs when the fault is limited by the transformer or series reactor, and there is no transmission line or cable connected with the breaker to provide the damping. The oscillatory TRV is shown in Figure 3. The TRV in the RLC parallel circuit is oscillatory when R > [(1/2)×√(L/C)].

For the short line faults, the nature of the TRV depends on the transmission line surge impedance. The triangular-shaped TRV is shown in Figure 4. The rate of rise of the sawtooth or triangular-shaped TRV is higher than exponential or oscillatory wave-shape.

Figure 2: Exponential TRV characteristics.

Figure 3: Oscillatory TRV characteristics.

Figure 4: Triangular TRV characteristics.

3. TRV Rating Considerations

For the system with rated voltages up to 100 kV, all the circuit breakers should interrupt the three-phase ungrounded faults. So, for the circuit breakers used in the systems below 100 kV, the TRV rating assumes that the system can be operated in an ungrounded situation.
For the systems with rated voltages from 100 kV to 170 kV, the three-phase ungrounded faults occur, but are less common (may not occur frequently), therefore, the user can select the circuit breakers, whether the breaker limit should consider three-phase ungrounded faults as well. For the circuit breakers used in the systems from 100 kV to 170 kV, the TRV rating shall be available for the systems operated in ungrounded and effectively grounded situations.
For the systems with rated voltages higher than 170 kV, most of the systems have neutral grounded. The three-phase-ungrounded faults occur less frequently (less than 1.3 % of all faults) in this system. Also, the three-phase ungrounded faults can produce the highest TRV peak values. Considering the probability of occurrence, the CIGRE working group, IEEE-C37.04 & IEC-62271 recommend considering the three-phase grounded faults for the circuit breaker rating selection for an effectively grounded system. Moreover, IEEE-C37.04 suggested that the user can consider the three-phase ungrounded faults (as the base for the breaker rating) where the user finds that the higher TRV capability is necessary. National Electrical Code (NEC) Clause 171 suggests that the user can judge the most suitable one whether three-phase ungrounded faults or three-phase grounded faults are used for the TRV rating selection for a given system. Also, NEC Clause 171 states that the circuit breaker should interrupt the maximum short circuit current. Therefore, for the systems above 170 kV, the TRV ratings assume that the systems are operated with effective grounding.
IEEE C37.011 refers that the terminal fault, short line fault and out-of-phase fault scenarios should be studied and considered for the breaker rating determination because these three cases are the worst-case situations to produce severe voltage stress that can cause breaker failure.

4. TRV Calculation

For TRV calculation, IEEE standard C37.011.2019 refers to the following two types of TRV waveforms at rated short circuit current, which are used based on the voltage class of the equipment.

Four-parameter TRV is used for rated voltages of 100 kV and above.
Two-parameter TRV is used for rated voltages less than 100 kV.

The two-parameter TRV can be used for all the rated voltages for the fault currents 30% or less of the rated short circuit current. An earlier version of IEEE standard C37.04 refers to the 1-cosine wave as the standard TRV wave-shape.

Both the initial rate of rise and peak values are essential for the selection of circuit breaker capability. So, every part of the TRV wave-shape is considered for the study.

The TRV parameters are influenced by the following factors:

Rated voltage (Vrated)
The first-pole-to-clear factor (kpp)
The amplitude factor (kaf)

The consideration between the three-phase grounded and three-phase ungrounded conditions is depending on the value of the first-pole-to-clear factor (kpp) for the TRV peak calculation.

4.1. Four-parameter TRV Wave-Shape

The four-parameter TRV is used for the rated voltages of 100 kV and above, and its shape is shown in Figure 5. For the systems above 100 kV, the TRV has a higher rate of rise in the initial period and a lower rate of rise for the later period. The initial part of the transients is mostly an exponential waveform which is produced by the inductance and resistance of the transmission line surge impedance. The later part of the TRV can be formed by the return of the traveling wave from the connected lines.

Here, V1 is the first reference voltage in kV, and t1 is the time to reach V1 in microseconds. VC is the second reference voltage (TRV peak) in kV, and t2 is the time to reach V2 in microseconds. VR is the reference voltage for the delay line in kV, tR is the time to reach VR in microseconds, and td is the time delay in microseconds.

The magnitude of first reference voltage (V1), the rate of rise of TRV (RRRV) and the magnitude of TRV peak (VC) are given in equations (1) - (3).

Figure 5: Four-parameter TRV shape.

kaf is the amplitude factor. For terminal and short line faults, kaf = 1.4. For out-of-phase switching conditions, kaf = 1.25.

kpp is the first-pole-to-clear factor.

For terminal fault, kpp = 1.3 (or) 1.5.

For short line fault, kpp = 1.0.

For out-of-phase conditions in grounded systems, kpp = 2.0.

For out-of-phase conditions in ungrounded systems, kpp = 2.5.

For terminal and short line faults, the rated time to reach VC, t2 = 4×t1 = t2(T100)

For out-of-phase switching conditions, rated time, t2 = 2×t2(T100)

The test duties are considered as T100 (1×ISC) and T60 (0.6×ISC). Here, ISC is the short circuit current rating.

4.2. Two-parameter TRV Wave-Shape

For rated voltages less than 100 kV, the two-parameter TRV shape is used, and the TRV wave-shape is approximately a damped single-frequency oscillation. The two-parameter TRV shape is shown in Figure 6. Where, VC is the reference voltage (TRV peak) in kV, and t3 is the time to reach VC. VR is the reference voltage for the delay line in kV, and tR is the time to reach VR in microseconds. td is the time delay in microseconds.

IEEE C37.011-2019 defines the two classes of circuit breakers for systems below 100 kV. Class S1 is used for the cable systems, and Class S2 is used for the line system. IEEE C37.04 shows that the peak TRV is higher and the RRRV is two times faster in the line system when compared to the cable systems. The RRRV is affected by the amount of capacitance. The overhead line systems have a small amount of capacitance when compared to the cable systems, and hence, the RRRV is faster in overhead line systems. The comparison of the two-parameter TRV shape for line and cable systems is shown in Figure 7.

The magnitude of TRV peak (VC), and the rate of rise of TRV (RRRV) are given in equations (4) & (5).

Figure 6: Two-parameter TRV wave-shape.

Figure 7: Comparison of Two-parameter TRV shape for Line and Cable systems.

For overhead line systems, kaf = 1.54 (terminal and short line faults). For cable systems, kaf = 1.4 (terminal fault). For cable and overhead line systems, kaf = 1.25 (out of phase).

For line systems, td = 0.05×t3. For cable systems, td = 0.15×t3.

The test duties are considered as T100 (1×ISC), T60 (0.6×ISC), T30 (0.3×ISC), T10 (0.1×ISC). Here, ISC is the short circuit current rating.

4.3. First-Pole-to-Clear Factor

The first pole-to-clear factor is the ratio of power frequency voltage across the first interrupting pole (before the current interruption in other poles) to the power frequency voltage across the pole/s after the current interruption in all 3 poles.

X0 & X1 are the zero and positive sequence reactances.

For ungrounded neutral systems (X0 >> X1), the value of kpp is 1.5. For effectively grounded neutral systems (X0 ≤ 3X1), the value of kpp is 1.3.

Note: As per IEEE C37.011-2019, for the rated voltages less than 170 kV, the system can be operated either grounded or ungrounded. For the rated voltages higher than 170 kV, effective grounding is necessary. For the effective grounded systems, the X0/X1 ratio is lower than 3.

4.4. Delay Line

The delay line in Figure 2 and Figure 3 is the initial delay (td) in the TRV. The local capacitance on the source side of the CB can slow down the voltage change rate during the initial period. Therefore, the delay line is accounted for the four-parameter and two-parameter TRV shape. For the systems 100 kV and above, the reference time delay (td) shall be longer than 2 µs at the rated short circuit current as per IEEE C37.011-2019.

4.5. Initial Transient Recovery Voltage (ITRV)

The initial transient recovery voltage (ITRV) mainly depends on the substation bus-bar and line bay configuration. The ITRV occurs due to the reflections from the first major discontinuity from the bus bar. The time to reach the first peak for ITRV is extremely short (within the first microsecond after the current zero) when compared to the short line fault. The ITRV applies to the CB rated 100 kV and above because the bus length is too short for lower voltages. The ITRV is proportional to the bus-bar surge impedance and to the current (it is considered significant for the currents above 31.5 kA as per IEEE C37.011.2019). For the CB in gas-insulated substations, the ITRV can be neglected due to low surge impedance and small distance to the first major discontinuity.

5. TRV Mitigation Techniques

When the system TRV exceeds the standards or breaker capability, the following methods can help to reduce the TRV.

Use of a higher rating circuit breaker.
The capacitance (capacitors to ground) shall be added to the circuit breaker terminal. Adding capacitance will reduce the natural frequency of the system, and hence, the rate of rise of recovery voltage (RRRV) will be reduced.
Use of surge arresters near the circuit breaker.
Reconfiguring the system / network.
Pre-insertion resistors are connected in parallel with the CB contacts.

References

IEEE Std C37.011.2019 – IEEE Guide for the application of transient recovery voltage for AC high voltage circuit breakers with rated maximum voltage above 1000 V.
IEEE Std C37.04.2018 – IEEE standard for ratings and requirements for AC high voltage circuit breakers with rated maximum voltages above 1000 V.