12

Transient Recovery Voltage

Thomas E. McDermott

Meltran, Inc.

12.1    Fault Interruption Process

12.2    Analysis Principles

12.3    TRV for Transformer-Fed Faults

12.4    TRV for Capacitor Bank Switch Opening

12.5    TRV for Line-Fed Faults

12.6    TRV for Current-Limiting Reactor Faults

12.7    Switchgear Tests and Standards

12.8    TRV Mitigation

References

Transient recovery voltage (TRV) refers to the voltage appearing across circuit breaker contacts after it interrupts current. The circuit breaker must withstand TRV in order to complete the current interruption process. For circuit breakers rated above 1 kV, the TRV is a crucial application criterion, along with several other important factors:

1.  Voltage rating

2.  Interrupting current ratings

3.  Capacitive current switching (inrush, outrush, close-and-latch ratings)

4.  Out-of-phase switching

5.  Generator breakers pose a special case due to asymmetrical current interruption

TRV is not a consideration for low-voltage circuit breakers rated 1 kV or less, but above 1 kV, every circuit breaker application should include TRV analysis. The rest of this section introduces TRV calculations and mitigation, at a level sufficient for educational purposes. For actual design work, the user should have access to one of the standard application guides (IEEE C37.011-2005, 2005; IEC 62271-100, 2008). In some cases, time-domain simulation in an electromagnetic transients (EMT) program is necessary.

12.1  Fault Interruption Process

As a circuit breaker opens to interrupt current, an arc develops between the separating contacts. The current continues to flow through this arc, with a nonlinear voltage drop that produces heat. In AC steady state, the current approaches each zero crossing with approximately linear slope, and when it passes through zero, there is a chance for current interruption. During the first few microseconds after interruption, a post-arc current may flow and produce more heat. At the same time, the arc dissipates heat through radiation, convection, and conduction according to the breaker design. During this initial energy balance period, the arc must lose heat faster than it gains heat. Otherwise, a reignition occurs and interruption cannot occur until the next natural current zero crossing.

Beyond the energy balance period, recovery voltage continues to build up across the still opening breaker contacts. The dielectric strength, which depends on contact separation, must exceed the recovery voltage stress throughout the dielectric stress period. If not, a reignition or restrike occurs and interruption must wait for the next natural current zero crossing.

The circuit breaker must pass both the energy balance and dielectric stress periods, in order to complete a current interruption. Detailed arc physics models have been developed to analyze these processes, but these models are of most use to circuit breaker designers. In applications, the TRV is usually calculated based on the electrical system model only, ignoring interactions between the arc and system models. This calculated TRV stress is then compared to standard TRV test results, which are performed in the lab and already encompass the arc behavior. There may be system TRV studies that require detailed arc models, but they are beyond the scope of this chapter.

There are consequences when the breaker fails to interrupt because of TRV. At a minimum, each reignition or restrike produces a transient overvoltage, until the breaker finally interrupts. If the breaker never succeeds to interrupt, it will require inspection and repair because of thermal damage or dielectric breakdown. TRV failures usually occur when interrupting fault current, in which case a backup circuit breaker will have to interrupt the fault. Backup clearing takes longer, which allows more time for equipment damage to occur from heating or short-circuit forces during the fault. Backup clearing also removes more of the system from service, which may lead to cascading outages. If the TRV failure occurs during a normal (i.e., nonfault) opening, it probably leads to a short circuit in the failed breaker, which also leads to backup clearing and possible cascading effects. TRV analysis is important because it affects protection of the power system.

12.2  Analysis Principles

Hand calculation and computer simulation both play roles in TRV studies. First, a simplified circuit analysis provides guidance on how much of the power system to model, which component parameters are most important, and what results to expect. Second, computer simulation with an EMT model should provide more realistic results and precise evaluation of all important cases. Third, reanalysis of an equivalent circuit can help explain the results and correct modeling errors. IEEE Std. C37.011 is a good source of typical data for equipment capacitance and other important parameters. Circuit breaker modeling guidelines are found in (IEEE PES Task Force, 2005). Guidelines for modeling the balance-of-system are found in (IEC TR 60071, 2004).

TRV phenomena may consist of high-frequency transients in lumped-parameter circuits, along with traveling wave transients in distributed-parameter overhead lines and cables. It is also necessary to consider all three phases, and neutral grounding. These factors make TRV, or any transient analysis, more complicated than steady-state calculations at power frequency.

Figure 12.1 shows a simplified three-phase equivalent circuit on the source side of a circuit breaker, which is interrupting a three-phase grounded fault on its terminals. The three phases do not interrupt simultaneously, and Figure 12.1 shows just the first phase opening. The most severe TRV usually appears on the first phase of the last circuit breaker to clear a fault. The source inductance often has unequal zero sequence and positive sequence values, as in Figure 12.1, which affects the equivalent inductance for TRV analysis:

$L_{eq}=\frac{3L_0{L}_1}{L_1+2L_0}$

(12.1)

FIGURE 12.1  Three-phase equivalent circuit for first pole to clear.

FIGURE 12.2  Single-phase equivalent circuits for the first pole to clear, L₀ = L₁.

The equivalent capacitance, C, comes from buswork, power transformers, instrument transformers, bushings, and other equipment. This stray capacitance is usually grounded for the purpose of TRV calculations. The most important capacitance values come from power transformers, coupling capacitor voltage transformers (CCVT), and capacitive voltage transformers (CVT). Because capacitance mitigates TRV, the study should make conservative assumptions about which capacitive equipment will be in service when the breaker opens. In many cases, it is not necessary to explicitly model the buswork between equipment, but Section 12.6 describes one exception to that guideline.

The left-hand side of Figure 12.2 shows the greatest possible simplification of Figure 12.1, with a grounded fault and equal sequence inductances. Each phase operates independently. This lumped circuit has transient response governed by the surge impedance and natural frequency:

$Z_{lump}=\sqrt{\frac{L}{C}}$

(12.2)

$f_0=\frac{1}{2\pi \sqrt{LC}}$

(12.3)

Z_lump is the ratio of peak transient voltage to peak transient current in the circuit. With no damping, the transient voltage and current will oscillate around their steady-state values, with 100% overshoot. A parallel resistance in Figure 12.2 will provide damping, and reduce the peak transient voltage and current. If the parallel R ≤ 0.5 Z_lump, then the circuit response will be critically damped or overdamped. This means the response is exponential rather than oscillatory. If the parallel R is approximately 4 Z_lump, the damping factor is 1.7. This means the first transient peak will be only 85% of the undamped peak. The generalized damping curves in Greenwood (1991) provide more detailed information. IEEE Std. C37.011 suggests that practical damping factors range from 1.6 to 1.9, based on measurements. In an EMT model, damping comes primarily from frequency-dependent line and transformer losses, which are sometimes burdensome to model in detail. As an alternative, series or shunt resistors may be added to the EMT model at strategic points, in order to provide high-frequency TRV damping.

The right-hand side of Figure 12.2 illustrates the use of circuit folding and phase symmetry, if the fault is ungrounded, but the sequence inductance values are still equal. The source-side parameters, L₁ and C, do not change. However, the fault current no longer flows to ground, but must return in the two unfaulted phases (top and bottom wires in Figure 12.1). These phases provide parallel paths, with equivalent inductance L₁/2 and capacitance 2C.

Overhead lines and cables connected to a bus would initially appear as shunt resistors in Figures 12.1 and 12.2. Some traveling wave effects are discussed in Section 12.5. For TRV studies, the surge impedances should be calculated at high frequency, or in EMT simulations, a frequency-dependent model can be used. Typical values of the positive sequence overhead line surge impedance are 350 Ω for single conductors and 275 Ω for bundled conductors. During faults, subconductor clashing may increase the effective surge impedance. Given the positive sequence surge impedance, Z₁, and the number of lines connected to a bus, the zero sequence and single-phase equivalent surge impedances are

FIGURE 12.3  Current injection to simulate fault interruption.

$Z_0\approx 1.6Z_1$

(12.4)

$Z_{eq}=\frac{3}{n}\frac{Z_0{Z}_1}{Z_1+2Z_0}$

(12.5)

A cable’s surge impedance, both positive sequence and equivalent, ranges from 20 to 75 Ω.

For hand calculation, the current injection method simulates TRV following fault interruption. Referring to the right-hand side of Figure 12.3, during the fault, current flows through the circuit breaker pole, and the “TRV” across that pole is 0. If the circuit is linear, then we can simulate fault interruption by injecting equal and opposite current through the breaker pole. In the left-hand side of Figure 12.3, interruption is simulated by injecting a current at π radians, and after that the sum of the two currents is 0. In the right-hand side of Figure 12.3, this is done by injecting currents on each side of the open pole. Each injected current source produces a transient voltage at its terminal, and the difference between them is the total TRV. If the fault is grounded, one of the current source terminal voltages may be 0. For hand calculation by Laplace transform, sometimes the injected currents are simplified to linear ramps, valid for a short period of time.

The current injection method is also useful in EMT simulation, because the time of fault interruption is precisely controlled. That helps control numerical oscillations, and also simplifies waveform evaluation when the TRV starts exactly at time zero. The injection current sources should be sinusoids instead of ramps. Of course, the EMT model must be linear in order for superposition to apply. That is not a serious restriction because most TRV studies are done without surge arrester models and without iron core saturation models. Exceptions might apply when studying surge arresters across the breaker terminals (i.e., not to ground), and when studying lower-frequency resonant or dynamic overvoltages, for which iron core saturation may become important.

The most severe TRV comes from a three-phase ungrounded fault, but those faults are quite rare. The standard TRV application for an effectively grounded system is based on a three-phase grounded fault at the breaker terminals.

With EMT simulation, the question will arise about how much of the surrounding power system to model. One of the classic rules of thumb has been “within two buses from the breaker under study.” A better rule accounts for the rated TRV time to peak, which increases with the breaker voltage level, and on typical wave travel times for overhead lines. As a guideline, include all buses within 0.48 * (system nominal kV). For example, for a 115 kV system, include all buses within 55 km of the studied bus, along with all transformer and generator sources connected to those buses. This ensures that all traveling wave and remote source effects appear at the station under study, before the breaker’s rated TRV reaches its peak value.

12.3  TRV for Transformer-Fed Faults

Transformer-fed faults occur quite often in medium-voltage facilities, and provide a good starting point for understanding TRV. Figure 12.4 shows a fault cleared by a breaker on the secondary of a transformer, with equivalent circuit parameters L_S and C_S. L_S primarily comes from the transformer inductance, while C_S comes primarily from transformer secondary capacitance, and secondary cables between the transformer and breaker. In this example, E is 11.3 kV peak line-to-ground (for a 13.8 kV system), L_S is 0.69 mH, and C_S is 0.11 μF. From Equation 12.3, the natural frequency is 18.3 kHz. The TRV will be a 1-cosine shape defined by Equation 12.6 and plotted in Figure 12.5:

${\text{TRV}}_S=2E\left[1-\cos \frac{t}{\sqrt{L_S{C}_S}}\right]$

(12.6)

In Figure 12.6, the same breaker interrupts a fault on the other side of a load transformer, as might occur during backup clearing. The source-side equivalent circuit does not change, but there is also a load-side equivalent circuit consisting of L_L and C_L, where L_L comes from the load transformer, and C_L comes from the load transformer and connected cable. In this example, L_L is 3.03 mH and C_L is 4 nF. A doublefrequency TRV will appear across the breaker pole. The source-side component frequency is 18.3 kHz as before, while the load-side frequency is 45.7 kHz from Equation 12.3. The faulted system voltage at the breaker is no longer zero at the time of interruption, because of the load transformer impedance between breaker and fault:

FIGURE 12.4  Single-frequency transformer fed fault TRV.

FIGURE 12.5  Single-frequency TRV.

FIGURE 12.6  Double-frequency transformer fed fault TRV.

FIGURE 12.7  Double-frequency TRV.

$E_{bus}=E\frac{L_L}{L_S+L_L}=9.2\left(\text{kV}\right)$

(12.7)

The load-side voltage will oscillate around zero, starting from E_bus. The source side voltage will oscillate around E = 11.3 kV, also starting from E_bus. These voltages and the TRV are provided in Equations 12.8 through 12.10 and plotted in Figure 12.7:

$E_{load}=9.2\cos \frac{t}{\sqrt{L_L{C}_L}}$

(12.8)

$E_{source}=9.2+2.1\left[1-\cos \frac{t}{\sqrt{L_S{C}_S}}\right]$

(12.9)

$E_{TRV}=E_{source}-E_{load}$

(12.10)

These examples illustrated single-frequency and double-frequency TRV, and the influence of impedance between breaker and fault. Damping was not considered. System resistance was also ignored, so the fault current and source voltage were 90° out of phase. Considering the actual phase shift would affect E.

12.4  TRV for Capacitor Bank Switch Opening

This example uses the case of capacitor bank de-energization to illustrate the importance of neutral voltage shifts in TRV. These phenomena occur at power frequency, so the voltage across breaker contacts is more properly termed recovery voltage, rather than transient recovery voltage. However, a restrike or reignition of the breaker will produce high-frequency transients. Capacitor banks are usually switched often. Special-purpose breakers or switches may be specified to minimize the possibility of restrikes.

FIGURE 12.8  One phase of grounded capacitor bank opening.

FIGURE 12.9  Grounded capacitor bank recovery voltage.

Figure 12.8 shows one phase of a three-phase grounded capacitor bank, so each phase may be considered independently, and the neutral voltage remains at zero. Figure 12.9 shows that the current leads the voltage by 90°, and when the current passes through zero at 1.5 π radians, the voltage on the bank is at its negative peak. This voltage is trapped on the disconnected capacitance, and will remain at this DC value for typically several minutes. Meanwhile, the source-side voltage continues to oscillate at power frequency. The peak voltage across the switch, V_a′–V_a, is 2 per unit. The switch should be able to withstand this.

Figure 12.10 shows a three-phase ungrounded capacitor bank. The neutral is actually grounded through stray capacitance, which may be on the order of 1 nF, but the bank neutral voltage is no longer held at zero. The bank neutral can shift and hold a nonzero voltage, supported by the stray capacitance. The actual value of this stray capacitance has little importance to the analysis.

Figure 12.11 shows the three-phase voltages on the bus, and Figure 12.12 shows the capacitor bank currents. Phase A opens first, at which time phases B and C are still energized in series, by the line-to-line voltage between phases B and C. The capacitor bank currents in phases B and C must be equal and opposite. Figure 12.12 shows these currents have equal and opposite values of 0.866 per unit, and their waveshapes change slope at the point of phase A interruption. The phase B and C currents remain equal and opposite, until they interrupt 1/4 cycle later.

FIGURE 12.10  Ungrounded capacitor bank opening.

FIGURE 12.11  Ungrounded capacitor bank source voltages.

FIGURE 12.12  Ungrounded capacitor bank opening currents.

Figure 12.13 shows the voltage on each of the four capacitors shown in Figure 12.10. After phase A interruption, 1/4 cycle into the event, the phase A-N capacitance has a trapped DC voltage of 1 per unit. This is similar to Figure 12.9 although opposite in polarity. The phase B-N and C-N capacitances have equal −0.5 per unit voltages at this time, but they continue to be charged or discharged by the phase B-C line-to-line voltage for another 1/4 cycle. Based on Figure 12.12, phase B-N receives positive current and charge for 1/4 cycle, while phase C-N receives negative current and charge over that 1/4 cycle. The change in voltage is 0.866 per unit instead of 1.0 per unit during that time, because each capacitor is now energized by half of the line-to-line voltage, rather than line-to-neutral voltage. When phase B and C interrupt at 1/2 cycle into the event, they have trapped capacitance voltages 0.366 and 1.366 per unit, respectively.

FIGURE 12.13  Ungrounded capacitor bank opening voltages.

FIGURE 12.14  Ungrounded capacitor bank recovery voltages.

The neutral point voltage has to increase during that second 1/4 cycle of unbalanced charging, and has 0.5 per unit trapped on it when phases B and C interrupt. Figure 12.14 shows the recovery voltage on each switch pole, evaluated from

$\begin{array}{c}{\text{TRV}}_A=V_A^{\prime }-\left(V_{AN}+V_N\right)\\ {\text{TRV}}_B=V_B^{\prime }-\left(V_{BN}+V_N\right)\\ {\text{TRV}}_C=V_C^{\prime }-\left(V_{CN}+V_N\right)\end{array}$

(12.11)

The peak recovery voltage on phase A is now 2.5 per unit because of the neutral shift, although the recovery voltages on the other two phases are less than 2.0 per unit. Again, the capacitor switching device should be able to withstand this. If phases B and C do not interrupt at their first chance, the neutral voltage may reach a peak of 1.0 per unit and increase the peak TRV to 3.0 per unit. If that causes a restrike, the switch should be designed to minimize the occurrence rate of restrikes.

The textbook (Greenwood, 1991) contains more detail on the effect of source impedance, the transient after a restrike, and the effect of neutral voltage shift on shunt reactor switching.

12.5  TRV for Line-Fed Faults

When interrupting a fault fed at least partially by overhead/underground lines, traveling wave effects and resistive surge impedances play a role in the TRV, which may no longer be oscillatory (Colclaser and Buettner, 1969; Colclaser, 1972). Figure 12.15 shows an example 115 kV substation bus, fed by three transmission lines and a transformer. Two fault scenarios are considered, one at the terminals of a line breaker and another one located a short distance, d, out on the line. These two scenarios are chosen to show the difference between terminal faults and short-line faults on the same breaker. This terminal fault does not produce the highest possible fault current; the highest bus fault is fed by all three lines plus the transformer. If it is possible for a breaker within the station to interrupt the total bus fault current, that case should be included in the study because higher fault current produces higher TRV.

The transformer inductance is 20 mH and the total bus capacitance is 10 nF. From Equation 12.2, the lumped circuit surge impedance is 1414 Ω. The effective surge impedance is 420 Ω for each line, and for two lines in parallel on the source side, the equivalent surge impedance Z = 210 Ω. This value is much less than half of the lumped circuit surge impedance, so the TRV will be an exponential waveform. The capacitance is small enough to be ignored for initial analysis.

If the fault current through the line breaker is 20 kA, then the TRV response is given in Equation 12.12, where the angular frequency ω is 377 for a 60 Hz power system (i.e., this case) and 314 for a 50 Hz power system:

$\begin{array}{c}\tau =\frac{L}{Z}=95\left(\mu s\right)\\ E_1=\sqrt{2}{I}_{flt}\omega L=213\left(\text{kV}\right)\\ \text{TRV}=E_1\left(1-\exp \left(\frac{t}{\tau }\right)\right)\end{array}$

(12.12)

This TRV is plotted in Figure 12.16. In a real power system, traveling wave reflections from nearby stations would modify this TRV, possibly increasing or decreasing the peak value. It is difficult to analyze these reflections by hand, because they are complicated by multiple line and inductive terminations.

On a 115 kV system, about 9 kA fault current would flow through the transformer, and the remaining 11 kA must come from the two unfaulted lines. If the fault current were higher, then the TRV would increase. On the other hand, higher fault current usually means more parallel source connections, and stronger source equivalents at nearby stations, both of which should help reduce the TRV. This is one of the main reasons for using EMT simulation to perform the study. The EMT model can be set up for transients only, and use current injection sources derived from a separate fault study. Alternatively, the EMT model can be set up and used for both steady-state fault analysis and transient analysis, avoiding the use of current injection. Either way, accurate fault current levels must be used in the study.

FIGURE 12.15  Bus terminal and short-line fault fed by lines and transformers.

FIGURE 12.16  Bus terminal fault TRV.

If there is no inductive source at the station in Figure 12.15, then the TRV will consist of a linearly rising ramp, until modified by traveling wave reflections from nearby stations. Cables have lower surge impedances than overhead lines, leading to longer time constants for exponential TRV, or lower slopes for linear TRV components.

The second fault location in Figure 12.15 is a distance d = 3.2 km from the line breaker terminals. The TRV is lower because the fault current is less, but a saw tooth component on the 3.2 km line segment produces a higher initial rate of rise. Years ago, short-line faults like this led to some breaker failures. Newer versions of the IEEE and IEC standards include short-line fault tests, so that the user does not have to explicitly evaluate them for applications. However, the case provides an instructive example, and the tested short-line fault capability can also be applied to other situations.

Assuming the maximum fault currents were evaluated at 1.05 per unit operating voltage, the first step is to estimate the breaker fault current during a short-line fault. (This could also be done using a separate short-circuit analysis.) Based on typical line reactance of 0.5 Ω/km in positive sequence and 1.2 Ω/km in zero sequence, the total line reactance to the fault is

$X_L=d\frac{2X_{1L}+X_{0L}}{3}=2.35\Omega$

(12.13)

The source-side equivalent reactance, from two lines and one transformer, comes from the 20 kA terminal fault current:

$X_S=\frac{1.05{}^{\star }115}{\sqrt{3}{}^{\star }20}=3.49\Omega$

(12.14)

Those two reactances now determine the reduced fault current:

$I_{SLF}=\frac{1.05{}^{\star }115}{\sqrt{3}{}^{\star }\left(2.35+3.49\right)}=11.9\text{kA}$

(12.15)

The bus voltage at the time of interruption is no longer zero, because of the line impedance out to the fault. After interruption, the source-side voltage will approach its 1.05 per unit peak prefault level according to an exponential waveform. Modifying Equation 12.12 accordingly,

$\begin{array}{c}\tau =\frac{L}{Z}=95\left(\mu \text{s}\right)\\ E_{1-SLF}=\left[115{}^{\star }{1.05}^{\star }\sqrt{\frac{2}{3}}-X_L{I}_{SLF}\sqrt{2}\right]=59\left(\text{kV}\right)\\ {\text{TRV}}_{1-SLF}=E_{1-SLF}\left(1-\exp \left(\frac{t}{\tau }\right)\right)\end{array}$

(12.16)

The source-side TRV component, plotted in Figure 12.17, has a lower prospective peak value but the same time constant.

Equation 12.17 defines the rate of rise of the line-side component; Z_eff = 420 Ω because it applies to the single faulted line segment

$R=\sqrt{2}\omega I_{SLF}{Z}_{eff}{}^{\star }{10}^{-6}=2.69\left(\text{kV/}\mu \text{s}\right)$

(12.17)

In IEEE standards, a damping factor of 1.6 applies to the line-side component of TRV, meaning that the damped peak reaches 1.6 per unit of the line-side breaker terminal voltage at the instant of interruption. Without damping, the peak would be 2.0 per unit of that line-side breaker terminal voltage. This damping factor is η, and the peak line-side TRV component is

$U_L=\eta X_L{I}_{SLF}\sqrt{2}=63.3\text{kV}$

(12.18)

FIGURE 12.17  Short-line fault TRV components.

The time to first peak is U_L/R = 23.5 μs. Figure 12.17 includes this damped line-side TRV component. The total TRV is the difference between the two waveforms in Figure 12.17. Compared to Figure 12.16, the peak TRV is lower but the initial rate of rise is more severe (note that for clarity, Figure 12.17 has a shorter timescale than Figure 12.16).

12.6  TRV for Current-Limiting Reactor Faults

Shunt capacitor banks and underground cables often have current-limiting reactors (CLR) installed in series. The CLR may be necessary to limit capacitor bank inrush and outrush currents, especially when multiple capacitors are connected to the same bus. CLR has also been used to reduce fault currents in low-impedance cable systems. The CLR can increase high-frequency TRV stresses on switchgear, and there have been cases of capacitor switch failure when trying to interrupt a CLR-limited fault. When this causes backup clearing of several lines and transformers connected to that bus, more widespread outages and disruptions can occur.

Figure 12.18 shows a simplified view of one station with a faulted capacitor bank at the node CAP, and a breaker at node BRKR tasked to clear that fault. A CLR between the capacitor and breaker has a series inductance, with relatively small shunt and series capacitances associated. The high-frequency lumped-circuit oscillations within the CLR produce high TRV rate of rise on the line side, and possibly lead to failure. Because of the fault location, the capacitor bank’s large capacitance provides no TRV mitigation. However, other buswork and equipment capacitance located between CLR and breaker may help in mitigating the TRV.

On the source side of the breaker, a total bus capacitance and external network of lines and transformers determine the source-side TRV, which would be similar to that produced by a bus terminal fault. If the CLR were moved to the source side of the breaker, it would still produce a high-frequency TRV component. That high-frequency TRV, now on the source side instead of load side, would still possibly lead to breaker failure.

Figure 12.19 shows a simplification of the model, by aggregating all capacitance between breaker and CLR into one value, ignoring the inductance of connections between them. The full external system network should still be part of the model, for accurate fault currents and source-side TRV components. The study can focus on changing CLR or breaker parameters to mitigate the TRV.

FIGURE 12.18  Model for current-limiting reactor fault TRV.

FIGURE 12.19  Reduced model for current-limiting reactor fault TRV.

12.7  Switchgear Tests and Standards

Both IEEE and IEC define circuit breaker test procedures, rating structures, preferred rating values, and TRV evaluation procedures in a set of standards that are updated periodically (IEEE C37, IEC 62271). Most North American utilities use IEEE standards, while other utilities in the world generally use IEC standards. The same choice would apply to medium-voltage and high-voltage industrial or commercial users, who might also need to do TRV studies.

Historically, there have been differences between IEEE and IEC standards, but the IEEE standards have been recently harmonized with IEC. That harmonization process is not yet complete. Even when harmonization is completed, circuit vendors can still offer products that were type-tested to earlier versions of IEEE standards. Circuit breakers can last for many decades in service, and they would have been tested to earlier standards. For both IEEE and IEC standards, there may be changes in procedures and ratings between updates. These are all good reasons to verify, at the beginning of a TRV study, which version of the standards applies to the breakers under evaluation.

At present, the standards mention that TRV evaluation can be based on three-phase grounded terminal faults, and that the vendor is responsible for testing breakers to withstand short-line fault TRV. There may be situations that still call for analysis of three-phase ungrounded faults, short-line faults, out-of-phase switching, or other examples not covered in this chapter.

Figure 12.20 shows the TRV rating for a 123 kV class circuit breaker, interrupting 100%, 60%, 30%, or 10% of its rated fault capability. These ratings apply to older IEEE standards; at 60% and higher, the TRV envelope is a composite 1-exponential and 1-cosine shape. At 30% and 10% interrupting rating, and for voltage ratings below 100 kV, only the 1-cosine shape is used. At fault current levels in between the defined four test levels, TRV rating envelopes may be interpolated. The calculated or simulated TRV stress should lie entirely under the applicable envelope in Figure 12.20 for a successful application. The user should also be aware of the TRV “delay line” as described in both IEEE and IEC standards.

FIGURE 12.20  Old IEEE TRV ratings.

TABLE 12.1 Interpolated TRV Ratings for IEEE and IEC Standards, Breakers Rated 100 kV and Higher

Given breaker rating values of E_m = 123 kV and T₂ = 260 μs, the curves in Figure 12.20 may be constructed from Equation 12.19 with interpolation factors from Table 12.1.

$\begin{array}{l}{K}_a=1.4\hfill \\ K_f=1.3\hfill \\ T_2\leftarrow T_{2}k{T}_2\hfill \\ U_r=E_m\sqrt{\frac{2}{3}}\hfill \\ E_2=K_a{K}_f{U}_{r}k{E}_2\hfill \\ \tau =\frac{E_1}{R_1}\hfill \\ E_{exp}=E_1\left[1-\exp \left(-\frac{t}{\tau }\right)\right]\hfill \\ E_{cos}=0.5E_2\left[1-\cos \left(\frac{\pi t}{T_2}\right)\right]\hfill \\ \text{TRV}=\max \left(E_{exp},E_{cos}\right)\hfill \end{array}$

(12.19)

R₁ is a rate of rise, to be interpolated from Table 12.1. If R₁ is 0, the E_exp term does not appear in the TRV, only the 1-cosine term, E_cos. Table 12.1 also provides multipliers to use with E₂ and T₂, at lower-than-rated fault currents.

Figure 12.21 shows corresponding IEC standard TRV ratings, for the same four test current levels, and the same 123 kV breaker voltage class. At 100% and 60% of rated interrupting current, the TRV envelope is a two-slope characteristic, defined by two points, or four parameters. At 30% and 10% of rated interrupting current, or for any breaker voltage rating below 100 kV, only one point defines the TRV. These are often called “4 parameter” and “2 parameter” TRV ratings. Newer versions of the IEEE standards will use TRV ratings presented as in Figure 12.21. With reference to interpolated values from Table 12.1, Figure 12.21 is constructed according to

FIGURE 12.21  IEC and harmonized IEEE TRV ratings.

$\begin{array}{l}{K}_{pp}=1.3\hfill \\ U_r=E_m\sqrt{\frac{2}{3}}\hfill \\ U_c=K_{pp}{K}_{af}{U}_r\hfill \end{array}$

(12.20)

If M ≤ 30% then Equation 12.21 applies

$\begin{array}{c}{T}_2=\frac{U_c}{ROR}\\ T_1=05T_2\\ U_1=0.5U_c\end{array}$

(12.21)

If M > 30% then Equation 12.22 applies, and T₂ is interpolated according to Table 12.1 after T₁ has been determined:

$\begin{array}{l}{U}_1=0.75K_{pp}{U}_r\hfill \\ T_1=\frac{U_1}{ROR}\hfill \end{array}$

(12.22)

The TRV is then constructed by linear interpolation between four points: (0, 0), (T₁, U₁), (T₂, U_c), and (2T₂, U_c). Equations 12.20 through 12.22 smoothly transition from two-parameter and four-parameter characteristics, when M increases from 30% to 60%.

FIGURE 12.22  Composite TRV rating based on short-line fault tests.

Figure 12.22 illustrates the aggregation of a breaker’s tested short-line fault TRV capability, with the base TRV rating. By IEEE standards, the short-line fault test may be performed at M values of 70%–95%. The standard test surge impedance Z = 450 Ω, and this breaker has rated frequency f = 60 Hz and rated interrupting current I_r = 40 kA. The short-line fault test verifies TRV withstand up to a point defined by the linear segment from (0, 0) to (T_slf, E_slf), as obtained from

$\begin{array}{l}{E}_{line}=1.6\left(1-\overline{M}\right)U_r\hfill \\ R_{slf}={8.8858}^{-6}f\overline{M}{I}_{r}Z\hfill \\ T_{slf}=\frac{E_{line}}{R_{slf}}\hfill \\ E_{srce}=\max \left[0,2\overline{M}\left(T_{slf}-2\right)\right]\hfill \\ E_{slf}=E_{line}+E_{srce}\hfill \end{array}$

(12.23)

After T_slf, the TRV rating extends horizontally at voltage E_slf, until it encounters the exponential TRV characteristic. The extra short-time TRV capability may be useful in applications that produce a fast-rising TRV.

12.8  TRV Mitigation

If the calculated TRV stress exceeds the breaker ratings, mitigation will be necessary:

1.  Consult the circuit breaker vendor, and provide the TRV stress waveform in electronic form. Sometimes the vendor has designed the breaker to withstand higher TRV, and is willing to state that the application is acceptable.

2.  Add capacitance to the circuit breaker terminals, or across the terminals. This slows down the TRV by reducing the rate of rise or oscillation frequency. It is one of the most common TRV mitigation techniques. However, the first peak in TRV can increase slightly with more capacitance, so that should be evaluated, too. The capacitance also has to be located close enough to the circuit breaker, and cannot be separated from the breaker through disconnect switch operation or station reconfiguration.

FIGURE 12.23  Mitigation of medium-voltage breaker TRV. (Reproduced with permission from McDermott, T.E. and Dafis, C., Cost-effective ship electrical system simulation, ISS IX Conference Paper. Philadelphia, PA, May 25–26, 2011. Copyright 2011 American Society of Naval Engineers.)

3.  When a current-limiting reactor is involved, capacitance can be added on the CLR terminals. It may also be possible for the CLR vendor to alter its design to have more internal capacitance.

4.  Use a circuit breaker of higher voltage rating. This can be expensive, but it works because the breaker will have significantly higher TRV capability for the same fault current.

5.  Use a circuit breaker of higher current rating. This can also be expensive, but it increases the TRV capability because the system fault current will be a lower portion of the breaker rating.

6.  Reduce the system fault current, either by splitting a bus or by adding fault current-limiting impedances. The system impedance changes may tend to increase TRV, but that is usually more than offset by the reduction in fault current level.

7.  Surge arresters across the breaker contacts have been considered, especially when the TRV comes from dynamic overvoltages. One must also check the arrester energy and temporary overvoltage ratings in this application.

8.  Some older circuit breakers have used grading resistors to limit TRV.

Any such measures that change the system response (e.g., items 2, 3, 6, 7, 8) call for a reevaluation of the TRV, with countermeasures in place. Figure 12.23 shows the TRV stress on an example 15 kV, 20 kA circuit breaker interrupting a 14 kA fault (Mc Dermott and Dafis, 2011). With 1 nF total bus capacitance, the TRV exceeds the breaker capability at 100% current interruptions, T100. By increasing the total capacitance to 40 nF, the peak TRV occurs later, and the stress waveform lies completely under the T100 rating. Because the 14 kA fault current is only 70% of the breaker’s interrupting capability, the TRV rating may be increased to T70. In that case, the TRV stress waveform lies completely under the T70 rating, even with 1 nF total capacitance.

References

ANSI Std. C37.06-2009, IEEE Standard for AC High-Voltage Circuit Breakers Rated on a Symmetrical Current Basis–Preferred Ratings and Related Required Capabilities for Voltages above 1000 V, The Institute of Electrical and Electronic Engineers, New York, 2009.

Colclaser, R. G., The transient recovery voltage application of power circuit breakers, IEEE Transactions on Power Apparatus and Systems, 91(5), 1941–1947, May 1972.

Colclaser, R. G. and D. E. Buettner, The traveling-wave approach to transient recovery voltage, IEEE Transactions on Power Apparatus and Systems, 88(7), 1028–1035, July 1969.

Greenwood, A. N., Electrical Transients in Power Systems, 2nd edn., John Wiley & Sons, New York, 1991.

IEC, Insulation co-ordination–Part 4: Computational guide to insulation co-ordination and modelling of electrical networks, Technical Report TR 60071-4, Edition 1, International Electrotechnical Commission, Geneva, Switzerland, June 2004.

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IEEE PES Task Force on Data for Modeling System Transients, Parameter determination for modeling system transients—Part VI: Circuit breakers, IEEE Transactions on Power Delivery, 20(3), 2079–2085, July 2005.

IEEE Std. C37.04-1999, IEEE Standard Rating Structure for AC High-Voltage Circuit Breakers, The Institute of Electrical and Electronic Engineers, New York, June 1999.

IEEE Std. C37.04-1999/Cor 1-2009, IEEE Standard for Rating Structure for AC High-Voltage Circuit Breakers Corrigendum 1, The Institute of Electrical and Electronic Engineers, New York, 2009.

IEEE Std. C37.04a-2003, IEEE Standard Rating Structure for AC High-Voltage Circuit Breakers Rated on a Symmetrical Current Basis: Amendment 1 Capacitance Current Switching, The Institute of Electrical and Electronic Engineers, New York, July 2003.

IEEE Std. C37.04b-2008, IEEE Standard for Rating Structure for AC High-Voltage Circuit Breakers Rated on a Symmetrical Current Basis Amendment 2: To Change the Description of Transient Recovery Voltage for Harmonization with IEC 62271-100, The Institute of Electrical and Electronic Engineers, New York, 2008.

IEEE Std. C37.09-1999, IEEE Standard Test Procedure for AC High-Voltage Circuit Breakers Rated on a Symmetrical Current Basis, The Institute of Electrical and Electronic Engineers, New York, January 2000.

IEEE Std. C37.09-1999/Cor 1-2007, IEEE Standard Test Procedure for AC High-Voltage Circuit Breakers Rated on a Symmetrical Current Basis–Corrigendum 1, The Institute of Electrical and Electronic Engineers, New York, September 2007.

IEEE Std. C37.09a-2005, IEEE Standard Test Procedure for AC High-Voltage Circuit Breakers Rated on a Symmetrical Current Basis: Amendment 1, Capacitance Current Switching, The Institute of Electrical and Electronic Engineers, New York, March 2005.

IEEE Std. C37.011-2005, IEEE Application Guide for Transient Recovery Voltage for AC High-Voltage Circuit Breakers, The Institute of Electrical and Electronic Engineers, New York, September 2005.