[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

ate of rise of transient-recovery voltage can also occur. It is recommended that a TRV study be conducted
prior to selection of a circuit breaker and/or prior to installation of a current-limiting reactor.
2.9.5.2 Circuit-Breaker TRV Capabilities
Rated circuit-breaker TRV capabilities can be obtained from the manufacturer or from various standards
such as ANSI C37.06 [15] or IEC 62271-100. [16] Circuit breaker TRV capabilities are normally defined
by two sets of parameters. One indicates the maximum voltage peak that the circuit breaker can withstand,
and the other one represents the rate of rise of the voltage, i.e., the minimum time to the voltage peak.
Parameters introduced in ANSI C37.06 define the TRV capability of a circuit breaker by means of two
types of envelopes. For circuit breakers rated 123 kV and above, the envelope has an exponential-cosine
shape if the symmetrical short-circuit current is above 30% of the circuit breaker short-circuit capability
(see Figure 2.9.35). At 30% and below, the envelope has a 1-cosine shape. For circuit breakers rated 72.5
kV and below, the envelope has a 1-cosine shape over the entire fault-current range. Circuit breakers are
also required to withstand line-side TRV originating from a “kilometric” or short-line fault (SLF). This
type of TRV normally reaches its peak during the delay time of the source-side TRV (see Figure 2.9.35).
When the actual fault current is less than the circuit-breaker rated fault current, circuit breakers can
withstand higher TRV voltages in a short rise time versus their rated value. As shown in Figure 2.9.35,
when the actual fault current is 60% of rated value, the circuit breaker can withstand a TRV of 7% higher
voltage for a duration 50% shorter than rated time. Therefore when using reactors to reduce the shortcircuit
level at a substation, it might be more beneficial, from the TRV point of view, to install currentlimiting
reactors at the upstream feeding substation, where circuit breakers are rated for higher shortcircuit
level.
2.9.5.3 TRV Evaluation
Computer simulation, or even manual calculation using the current-injection method, can be employed
to evaluate the TRV across the circuit-breaker terminals. IEEE C37.011-1994 [17] also provides some
guidance for evaluating the TRV. To conduct the study, the electrical characteristics of all the equipment
involved in the TRV circuit is required. Equipment characteristics can normally be obtained from the
equipment nameplate. However, stray capacitances or inductances are not normally shown on the
nameplates. To obtain this information, the equipment manufacturer should be consulted. When dealing
with TRV associated with fault current limited by a current-limiting reactor, normally the first pole to
open, during an ungrounded three-phase fault at the terminal, experiences the highest peak of TRV. (For
certain conditions during a two-phase-to-ground fault, higher TRV can be experienced [11]). The shape
of TRV when fault current is limited by a reactor is oscillatory (underdamped) and is very similar to the
TRV generated when fault current is limited by a transformer impedance.
When modeling a reactor for TRV studies, the following items shall be considered:
• All types of reactors have stray capacitances, whose values can be obtained from the manufacturer.
Generally, the stray capacitance of a dry-type reactor is on the order of a few hundred pF and that
of an oil-filled reactor is on the order of a few F (see Figure 2.9.36).
• Reactor losses at power frequency are very small and insignificant. However, as a result of skin
effect and eddy losses at high frequencies (in the range of kHz), the reactor losses are significant
(see Figure 2.9.36).
This characteristic of the reactor can help to damp the transients and shall be reflected in the model
by including a frequency-dependent resistance in series with the reactance.
2.9.5.4 TRV Mitigation Methods
Should the system TRV exceed the circuit breaker capability, one or a combination of the following
mitigation methods can be employed:
1. Installation of a capacitor across the reactor terminals
2. Installation of a capacitor to ground from the reactor terminal connected to the circuit breaker.
For bus-tie reactors, capacitors shall be installed to ground at both reactor terminals.
From a TRV point of view, either of the previous mitigation methods is acceptable. However, from
an economic point of view, it is more cost-effective to install the capacitor between the reactor terminals,
since the steady-state voltage drop across the reactor is significantly lower than the line-to-ground voltage.
Consequently, a lower voltage capacitor can be used.
Figure 2.9.37 shows the result of a TRV study for a subtransmission substation. Curve b in this figure
shows the system TRV prior to installation of a current-limiting reactor. It slightly exceeds the circuit
breaker capability, as seen in Curve a. After installation of a current-limiting reactor, the system TRV
exceeds the circuit breaker capability significantly, as seen in Curve c. To reduce the rate of rise of TRV,
a capacitor was installed across the reactor terminals. As seen in Curve d, the system TRV has been
modified to an acceptable level.
FIGURE 2.9.35 Typical TRV capability envelopes for 123-kV-class circuit breaker at (a) 60% and (b) 100% of rated
fault current.
FIGURE 2.9.36 Reactor model for TRV studies, where: C gl and C g2 = stray capacitance of reactor terminals to
ground, C t = terminal-to-terminal stray capacitance, L = reactor inductance, and R (f) = reactor-frequency-dependent
resistance.
© 2004 by CRC Press LLC
© 2004 by CRC Press LLC