When a circuit breaker opens to interrupt a fault current in a power system, the voltage across the breaker contacts does not simply return to normal operating voltage. Instead, it oscillates and overshoots before settling down. This voltage behavior is what we call Transient Recovery Voltage or TRV.
For electrical engineers working with high voltage systems and switchgear, TRV is one of the most demanding aspects of circuit breaker design and selection. If you do not account for TRV properly, the circuit breaker may fail to interrupt the current successfully. This can lead to equipment damage and system failures.
In this technical guide, we will discuss everything you need to know about Transient Recovery Voltage. We will explain what it is, how it develops, the factors that affect it, and how to manage it in real power systems.
1. What is Transient Recovery Voltage?
Transient Recovery Voltage is the voltage that appears across the contacts of a circuit breaker immediately after the current has been interrupted. When a circuit breaker opens and the arc is extinguished at current zero, the voltage across the open contacts does not instantly become the normal system voltage. Instead, it goes through a transient phase.
During this transient phase, the voltage can oscillate at high frequencies and reach peak values that are much higher than the normal operating voltage. This happens because of the stored energy in the inductances and capacitances of the power system. When the current is suddenly interrupted, this energy needs to redistribute itself and it does so through oscillations.
Think of it like a spring that has been compressed and suddenly released. The spring does not simply return to its resting position. It oscillates back and forth several times before settling down. Similarly, the voltage across the circuit breaker contacts oscillates before reaching a steady state.
2. Why Does TRV Occur?
To understand why TRV occurs, we need to look at what happens during current interruption. When a fault occurs in a power system, current flows through the circuit breaker. This current is alternating in nature and passes through zero twice every cycle.
Modern circuit breakers are designed to extinguish the arc at the moment when current passes through zero. At this instant, the arc power is momentarily zero, which gives the breaker a chance to interrupt the current. However, while the current has become zero, the voltage across the circuit does not become zero at the same instant.
In an inductive circuit (which most power systems are), the voltage and current are out of phase. When current is at zero, the voltage is near its peak value. This means that immediately after the current is interrupted, the circuit breaker contacts must withstand this recovery voltage.
The situation becomes more complex because of the distributed inductances and capacitances in the system. These elements form oscillating circuits that cause the voltage to swing beyond the steady-state value before settling down.
3. The Physics Behind TRV Formation
Let us take a simple example to understand TRV formation. Consider a circuit with a source voltage, a line inductance L, and a fault. When the circuit breaker opens and interrupts the fault current at current zero, the magnetic energy stored in the inductance needs somewhere to go.
Before the interruption, the energy was cycling between the inductance (magnetic field) and the source. When the current path is suddenly broken, this energy cannot simply disappear. It has to be absorbed by the circuit in some way.
The stray capacitances in the system (capacitance between conductors, bushing capacitances, winding capacitances, etc.) provide a path for this energy redistribution. The inductance and capacitance together form an LC circuit that oscillates at its natural frequency.
This oscillation causes the voltage across the breaker to swing from zero (at the moment of interruption) to a peak value that can be 1.5 to 3 times the peak value of the normal system voltage. In some cases, with multiple reflections and superpositions the peak can be even higher.
4. Mathematical Representation of TRV
For a simple single-frequency TRV, the voltage across the circuit breaker after current interruption can be represented as:
\(v(t) = V_m \times (1 – cos \omega t)\)
Where:
- \(v(t)\) is the transient recovery voltage at time \(t\)
- \(V_m\) is the peak value of the system voltage
- \(\omega\) is the natural angular frequency of the circuit
- \(t\) is time after current zero
The natural frequency of oscillation is given by:
\(f = \frac{1}{(2\pi \sqrt{LC})}\)
Where:
- \(L\) is the system inductance
- \(C\) is the total capacitance
From this equation, you can see that a system with low capacitance will have a high natural frequency. This means the voltage will rise very quickly after current zero. This rapid voltage rise is one of the main challenges in TRV management.
5. Rate of Rise of Recovery Voltage (RRRV)
One of the most important parameters associated with TRV is the Rate of Rise of Recovery Voltage, commonly abbreviated as RRRV. This parameter tells us how fast the voltage across the breaker contacts is increasing after current interruption.
RRRV is measured in volts per microsecond \((V/µs)\) or kilovolts per microsecond \((kV/µs)\). A high RRRV is more dangerous for the circuit breaker than a high peak TRV value alone. This is because the dielectric strength of the gap between the opening contacts also builds up with time.
When the contacts first separate, the gap is small and its dielectric strength is low. As the contacts move apart and as the arc plasma cools down and de-ionizes, the dielectric strength increases. If the TRV rises faster than the dielectric strength of the gap the arc will re-strike and the interruption will fail.
For example, if a circuit breaker contact gap can withstand 10 kV after 5 microseconds, but the TRV reaches 15 kV in that time, the gap will break down and the arc will re-establish. This is called a re-strike and it represents a failure of the interruption process.
6. Types of TRV Waveshapes
Based on the system configuration and type of fault, TRV can have different waveshapes. The main types are:
6.1 Exponential-Cosine TRV
This type of TRV occurs in systems where the fault is far from the circuit breaker or where the system has high capacitance. The TRV rises relatively slowly and has a single frequency component. The waveshape looks like a damped cosine function offset from zero.
6.2 Oscillatory TRV
In systems with multiple frequency components, the TRV can show multiple oscillations superimposed on each other. This occurs when there are several LC circuits interacting in the network. The waveshape is more complex and the peak value can be higher than a single frequency TRV.
6.3 Saw-tooth or Triangular TRV
This type occurs during short line faults. When a fault occurs relatively close to the circuit breaker but on a transmission line (typically between 100 meters and a few kilometers), traveling wave effects dominate the TRV. The voltage waves travel down the line, reflect from the fault, and return to the breaker. This creates a triangular waveshape with very steep initial rise.
6.4 Exponential TRV
In heavily damped circuits or circuits with resistive elements, the TRV may rise exponentially toward the recovery voltage without significant oscillation.
7. TRV in Different Switching Conditions
The TRV behavior varies with different switching conditions. Let us look at the main scenarios:
7.1 Terminal Faults
A terminal fault is a short circuit that occurs at or very near the terminals of the circuit breaker. For this type of fault, the TRV is determined by the source side of the system. The frequency of the TRV depends on the source inductance and the stray capacitances.
Terminal faults generally produce TRV with moderate RRRV but can produce high peak values. The peak can reach 1.5 to 2 times the peak of the normal voltage.
7.2 Short Line Faults (SLF)
Short line faults are one of the most severe conditions for circuit breaker TRV duties. These faults occur on transmission lines at a distance of a few hundred meters to a few kilometers from the circuit breaker.
When such a fault is interrupted, two TRV components appear. One component comes from the source side and rises relatively slowly. The second component comes from the line side and rises extremely fast due to traveling wave effects.
The initial RRRV from the line side can be very high, sometimes exceeding 10 kV/µs for high voltage systems. This makes short line faults one of the most demanding duties for circuit breakers.
7.3 Out-of-Phase Switching
When a circuit breaker has to interrupt current while two parts of the system are out of phase with each other, the TRV can be very severe. In the worst case, when the two systems are 180 degrees out of phase, the TRV can reach values close to 4 times the peak of the normal phase voltage.
This condition can occur during system disturbances or incorrect synchronization. Circuit breakers that may be required to interrupt current under such conditions must be rated for out-of-phase switching duty.
7.4 Capacitor Switching
Switching capacitor banks presents unique TRV challenges. When disconnecting a capacitor bank, the capacitor retains its charge at the peak voltage. Meanwhile, the source voltage continues to alternate. This can result in very high voltage across the breaker contacts.
If a re-strike occurs during capacitor switching, voltage escalation can happen, leading to even higher voltages across the breaker and the capacitor.
7.5 Reactor Switching
Switching shunt reactors creates high TRV due to the stored energy in the reactor. When current is interrupted, the energy in the reactor inductance interacts with stray capacitances to produce high frequency oscillations. This can result in high peak TRV values.
7.6 Transformer Limited Faults
When a fault occurs on the secondary side of a transformer and is fed through the transformer from the primary side, the TRV is influenced by the transformer characteristics. The transformer leakage inductance and winding capacitances affect the TRV waveshape and peak value.
8. TRV and Circuit Breaker Design
Circuit breaker manufacturers design their products to handle specific TRV duties. When you purchase a circuit breaker, it comes with TRV ratings that specify what TRV conditions the breaker can successfully withstand.
8.1 TRV Capability Curve
Each circuit breaker has a TRV capability curve or envelope. This curve shows the voltage that the breaker can withstand as a function of time after current zero. The breaker can successfully interrupt currents only if the actual TRV stays below this capability curve.
The capability curve starts from zero at the moment of current zero and rises with time. Initially, the rise is slow because the contacts are close together and the gap is still filled with hot arc plasma. As the contacts separate and the plasma cools, the dielectric strength increases more rapidly.
8.2 TRV Rating Parameters
International standards (IEC and IEEE) specify TRV requirements using specific parameters:
- Peak TRV value (Uc): The maximum voltage the breaker must withstand
- Time to peak (T3): The time at which the peak TRV value is reached
- Rate of rise (U/T or RRRV): The steepness of the TRV rise
- First reference voltage (U1) and time (T1): For two-parameter envelope specifications
- Delay time (Td): Time before TRV starts to rise appreciably
These parameters define an envelope within which the actual TRV must remain for successful interruption.
9. How to Manage and Limit TRV
Engineers have several methods to manage TRV in power systems. These methods aim to reduce either the peak TRV value or the RRRV or both.
9.1 Adding Capacitance
One of the most common methods is to add capacitance across the circuit breaker or on the line side. Added capacitance reduces the natural frequency of the circuit and therefore reduces the RRRV. It also provides a low impedance path for the initial current flow after current zero, which reduces voltage buildup.
Capacitance can be added in the form of:
- Grading capacitors across the breaker contacts
- Surge capacitors on the line side
- Shunt capacitor banks nearby
9.2 Resistor Switching
Many high voltage circuit breakers use resistors as part of the interrupting process. Opening resistors are connected in parallel with the main contacts. When the main contacts open, current flows through the resistor. This resistor damps the TRV oscillations and reduces both the peak TRV and RRRV.
After the main arc is extinguished, the resistor contacts open to complete the interruption. By this time, the system has settled and the TRV is no longer a problem.
9.3 Metal Oxide Surge Arresters
Surge arresters placed near circuit breakers can limit the peak TRV value by clamping any voltage that exceeds their protective level. While arresters are primarily designed for lightning and switching surge protection they also help limit TRV peak values.
10. TRV Testing of Circuit Breakers
Circuit breakers undergo extensive testing to verify their TRV capability. These tests are performed at specialized high power laboratories that can generate the required short circuit currents and create controlled TRV conditions.
10.1 Synthetic Testing
For very high voltage circuit breakers, direct testing may not be practical because no single laboratory can provide the required power. In such cases, synthetic testing methods are used.
In synthetic testing, a high current source provides the current during the arcing period. At the moment of current zero, a separate high voltage source takes over to apply the TRV across the breaker. Through precise timing and coordination, the breaker sees conditions equivalent to actual service.
10.2 TRV Test Duties
Standard test duties for TRV verification include:
- Terminal fault tests (T10, T30, T60, T100 representing different percentages of rated breaking current)
- Short line fault tests
- Out-of-phase tests
- Capacitor switching tests (where applicable)
- Reactor switching tests (where applicable)
Each duty has its own TRV requirements, and the breaker must pass all applicable duties to receive its rating.
11. Conclusion
Transient Recovery Voltage is a fundamental concept in high voltage circuit breaker engineering. It describes the voltage that appears across breaker contacts immediately after current interruption. This voltage can oscillate at high frequencies and reach peak values well above normal system voltage.
The rate at which TRV rises (RRRV) and the peak TRV value both determine whether a circuit breaker can successfully interrupt current. If TRV rises faster than the gap’s dielectric strength recovers, the arc will re-strike and interruption fails.
12. Frequently Asked Questions (FAQs)
Normal recovery voltage is the steady-state voltage that appears across the circuit breaker contacts after all transients have died out. TRV is the voltage during the transient period immediately after current interruption. TRV can be much higher than normal recovery voltage due to oscillations.
A: Short line faults create traveling waves on the transmission line. These waves reflect from the fault point and return to the breaker very quickly, causing an extremely fast initial rate of rise of TRV. Terminal faults do not have this traveling wave component.
A: Repeated failure to interrupt current due to TRV can lead to excessive energy absorption in the breaker. This can cause overheating, gas pressure buildup (in SF6 breakers), and in extreme cases, mechanical failure or explosion. Modern breakers have protective features to minimize this risk.
A: Capacitors provide a low impedance path at high frequencies. When connected across the breaker or on the line side, they slow down the rate of rise of voltage because current flows into the capacitor instead of building up voltage immediately. They also reduce the natural frequency of the TRV oscillation.
A: If TRV exceeds the breaker’s dielectric capability at any point, the arc will re-strike between the contacts. The current will continue to flow, and the breaker will attempt interruption again at the next current zero. This may succeed or fail depending on conditions.
A: TRV is measured using high frequency voltage dividers connected across the circuit breaker terminals. These dividers scale down the voltage to levels that can be recorded by oscilloscopes or digital recording equipment with sufficient bandwidth.
A: Yes, TRV occurs in all circuit breakers. However, at low voltage levels, the absolute values of TRV are low and are usually not a major concern.
A: The TRV seen by the breaker is determined by the power system, not the breaker technology. However, SF6 and vacuum breakers have different dielectric recovery characteristics after arc extinction. This affects their ability to withstand TRV. Each technology has its strengths for different applications.