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5.2.1 Transformer Terminated Transmission Line in Multi-Circuit Right of Way

A ferroresonant circuit can be formed when a transformer terminated transmission line is de-energized while there is an energized circuit running in parallel in the same right of way. A typical topology is illustrated in Figure 5-7 (a).

It shows a power transformer directly connected to a transmission line in “Substation 1”. Circuit breakers are only installed on the LV side of the transformer in “Substation 1” (CB1), whereas the HV side circuit breakers are installed in a remote location, at “Substation 2” (CB2). The transmission line between “Substation 1” and

“Substation 2” (cct A) shares a right of way with other transmission line(s) (cct B). Ferroresonance can occur after opening circuit breakers CB1 and CB2 if the parallel circuit remains energized.

In this case, an oscillation occurs between the non-linear magnetising inductance of the transformer and the capacitance of transmission line it is connected to. The energy required to sustain the ferroresonant condition is provided from the capacitive coupling with the parallel energized circuit. This topology can occur when circuit breakers are not installed on both sides of a transformer, for instance to reduce costs in the early stages of system development. It should be noted that even when circuit breakers are installed on both sides of the transformer, this topology can still arise if a circuit breaker fails to trip after a transformer fault and the back-up protection trips the circuit breaker at the remote end of the transmission circuit. Ferroresonance has also been reported to occur following uneven breaker pole operation (i.e. stuck circuit breaker pole). A similar network topology that has been reported to exhibit ferroresonance is a “tee” or “tapped” step-down transformer as illustrated in Figure 5-7 (b) where the transformer is tapped from one of the two parallel circuits.

A simplified equivalent circuit is shown in Figure 5-7 (c), where CA represents the capacitance to ground of Cct A, CA-B represents the inter-circuit capacitance between Cct A and Cct B, R represents the circuit losses and L represents the transformer magnetising inductance. It should be noted that this simplified equivalent circuit is only valid for banks of single phase transformers, where there is no coupling between phases. Otherwise, a three-phase equivalent circuit must be used. Notwithstanding the simplification, the equivalent circuit assists in the visualisation of the key parameters determining the likelihood of ferroresonance in this topology.

Various modes of ferroresonance, typically fundamental frequency and sub-harmonic ferroresonance can arise depending on the circuit parameters, initial conditions or switching sequence. Field measurements of a 150km, 400 kV double circuit line terminating in a 500MVA transformer are described in [29]. This reference work relates the length of the parallel coupling with the type of ferroresonant modes. Very short lines (i.e. less than 20km) do not experience ferroresonance. Fundamental frequency ferroresonance is observed for medium line lengths, while sub-harmonic ferroresonant oscillations are dominant in long circuit lengths (i.e. >150km). The result of the oscillations is normally an overvoltage stressing the line and transformer insulation and transformer overflux causing excessive heating and possible damage to the core and windings. It should be noted that no destructive failure of a power transformer due to ferroresonance has been reported to date, however sustained operation of a transformer in this condition is a main contributor to its accelerated aging.

Figure 5-7 Transformer terminated transmission line

5.2.2 Lightly Loaded Transformer Energized via Cable or Long Line from a Low Short-Circuit Capacity Network

A ferroresonant circuit can be formed when a large power transformer is energized from a weak source via a long overhead line or cable. This is a parallel ferroresonant topology where an oscillation arises between the non-linear magnetising inductance of the transformer and the capacitance of transmission line or cable it is connected to. The voltage source is located behind a large inductive source impedance. A typical network topology and its equivalent

Capacitive coupling with parallel energized circuit

Capacitive coupling with parallel energized circuit

such as during emergency switching operations or system restoration following a blackout. It is best avoided by proper system design and planning. An example of ferroresonance in this topology was experienced in France during a black-start restoration test where two 1080 MVA transformers were energized from a 90 MW hydro unit via a 360 km long overhead line [30]. Sustained non-periodic ferroresonant oscillations have been recorded in this incident.

Figure 5-8 Transformer energized from weak source via long transmission circuit

5.2.3 Transformer energized in one or two phases

Power transformer ferroresonance in this topology is more common in distribution systems due to the use of singe-phase switching or the deployment of fuses. The system neutral can be either grounded or ungrounded, although ungrounded neutrals are more susceptible to the phenomena. It is a series ferroresonant phenomenon with the voltage source coming from the back feed voltage induced on the open phase of the transformer (this is highly dependent on the core construction) as illustrated in Figure 5-9 for typical topologies. The non-linear inductance is a combination of the individual limbs in the transformer core and the capacitance comes from the connected network. It can be seen that series connections of a capacitance with the transformer’s reactance are possible when one or two phases are disconnected. This can be the result of fuses blowing, sequential operation of single-phase switches or accidental break in a single-phase conductor. It should be noted that the capacitance involved in this series ferroresonant circuit is not necessarily just the feeding network between the transformer and the open switch/fuse but it can also include other circuits still connected to the transformer terminals, such as capacitor banks and the stray capacitance of the transformer winding. This concept is illustrated in Figure 5-10 where for instance opening of one phase in S1 can leave a significant amount of circuit capacitance connected in series with the reactance of TX1 and TX2. It should be noted that, in the case of a capacitor bank, if both neutrals (cap bank and transformer) are grounded or both are ungrounded, then no series path exists and there is no clear possibility of ferroresonance.

The result of this series ferroresonant phenomenon is typically an overvoltage of 2 to 3 p.u. on the transformer windings and on the feeding network. This overvoltage imposes stress on the transformer insulation and on any feeding cable.

The following three conditions must be met for ferroresonance to occur:

At least one phase must be energized.

The maximum length of MV cable that can be connected to a distribution transformer energized in one or two phases can be calculated using the following formula [39]:

L = 0.6 I _% KVAr 1000

1.58 + CC 62.8 (kV ) C [m ] _{Eq. 5-2}

where Lcritical is the critical cable length in meters, Imag% is the transformer magnetising current (typically in the order of 0.8%), KVAr is the transformer rating in kva, kVR is the rated voltage in kV, C’CC is the cable’s core to core capacitance in F/km and C’CS is the cable’s core to sheath capacitance in F/km.

Figure 5-9 Transformer accidentally energized in one or two phases

Figure 5-10 Distribution Network Topologies Prone to Ferroresonance in single-phase switching

5.2.4 Transformer connected to a series compensated line

The installation of series capacitors in long transmission networks for voltage regulation purposes can increase the risk of ferroresonance in certain configurations.

A load rejection on a long transmission/distribution line with series compensation could initiate ferroresonance. This is a series ferroresonant circuit. If the load rejection was caused by opening the low voltage side circuit breakers, the temporary overvoltages would cause transformers to operate into the saturation region. With series compensation in-service, this line open condition could initiate a ferroresonance condition that would stress dielectric and thermal withstand capability of equipment.

Figure 5-11 – Series Compensated Distribution Circuit