Approximate Steady State Analytical Solution

Given the potential damage to line connected equipment, such as surge-arresters, instrument transformers, shunt reactors and circuit breakers, the circuit configurations leading to excessive over-voltages need to be identified.

The key questions to be resolved for any transmission line construction requiring shunt compensation are:

1. What are the particular reactor sizes that give rise to resonant conditions?

2. What is the induced open-phase voltage for any particular degree of shunt compensation?

A high level answer to those questions can be given using the simple formulae presented in sections 4.2.2.1 and 4.2.2.2 next. It should be noted that this is a steady-state analysis and higher temporary over-voltages can be expected during transient conditions.

For clarity, the equations are presented in terms of both, positive and zero, sequence capacitances as well as phase-to-ground and inter-phase capacitances. The relationship between these magnitudes (assuming symmetrical line construction) is as follows:

ph

The equations presented next (sections 4.2.2.1 and 4.2.2.2) are based on the assumptions made in section 4.2.1.

In particular, the assumptions of symmetrical line parameters, equal positive and zero sequence reactance for the shunt reactors and solidly earthed reactor neutral connection apply (see section 4.2.3.2 for the effect of a neutral reactor). Furthermore, it must be emphasised that losses and saturation effects have been ignored at this stage for simplicity. In practice, the theoretical steady-state over-voltages calculated with this approach may be limited by corona losses and/or reactor core saturation.

4.2.2.1 One Open-Phase

It is assumed that phases B and C are energized while phase A is disconnected (Figure 4-4 (a)). This circuit, as seen from disconnected phase A, can be simplified as Figure 4-4 (b). By applying the Thevenin theorem, this circuit can be reduced further as Figure 4-4 (c), which is a common series L-C circuit with a natural frequency of oscillation equal to fn_(1 open-phase):

)

Using circuit analysis to the equivalent shown in Figure 4-4 (c), the following expressions are derived:

Eq. 4-6

Induced open-phase voltage for a compensation degree k:

Eq. 4-7

Figure 4-4 Simplified circuit for the analysis of Line Resonance

4.2.2.2 Two Open-Phases

A similar approach can be used with the two open-phases scenario, resulting in another equivalent L-C circuit with a natural frequency of oscillation equal to fn_(2 open-phases):

)

Similarly to the one open-phase condition, the following expressions are derived:

˜ ˜

Eq. 4-9

Open-phase voltage for a compensation degree k:

2

As an illustrative example, the analytical “approximate” method presented above has been used to estimate the resonant conditions in a standard 400 kV transmission line design used in Ireland, as a function of the degree of shunt compensation. For this construction, the circuit capacitances are C+=11.59 nF/km and C0=7.77 nF/km. The line is assumed to be fully transposed and the neutral point of the shunt reactors is directly connected to ground.

Power frequency is 50 Hz.

Figure 4-5 shows the natural frequencies of oscillation for one and two open-phase(s) conditions, as a function of the degree of shunt compensation. It can be seen that the natural frequency increases with the degree of compensation. These frequencies reach values within ±0.5 Hz of power frequency for compensation degrees between 77% and 79% during operation with two open phases and between 88% and 91% during operation with one open-phase.

Figure 4-6 presents the steady-state open-phase voltages as a function of the shunt compensation degree, calculated using Eq. 4-7 and Eq. 4-10. These curves clearly show resonant conditions for shunt compensation degrees of 78% and 89% for the two open-phases and the one open-phase conditions, respectively. Shunt compensation degrees from 68% to 99% bring near-resonant conditions with steady-state open-phase voltages in excess of 1 pu.

It should be noted that this illustrative example is based on a number of stated simplifications and that the calculated voltages refer to steady-state conditions only. In practice, temporary conditions may lead to voltages in excess to those calculated using this analytical method. On the other hand, saturation or circuit losses may limit these over-voltages. Notwithstanding its limitations, this “approximate” method enables the engineer to carry-out a speedy estimation of the risk of power frequency resonance for a particular circuit configuration and degree of shunt compensation. Further detailed studies are required when it is envisaged to operate close to a resonant peak. This is typically done using time domain simulation, as shown in section 4.3.

The following can be concluded from this example:

1. A symmetrical shunt-compensated transmission circuit exhibits two resonant peaks: one for one open-phase and a second one for two open-phases conditions.

2. The two open-phases condition presents a resonant peak at a lower degree of shunt compensation than the one-open-phase condition.

3. Steady-state voltages in excess of 1 pu can be expected for a wide range of shunt compensation degrees.

0

Figure 4-5 Natural oscillation frequencies of a 400 kV shunt-compensated line under one and two open phase conditions

Figure 4-6 Steady-State open-phase voltage (approximate analytical solution) in a 400 kV line as a function of the Shunt Compensation Degree, k.

4.2.2.4 Field Measurements Showing 500kV Surge Arrester Failures During a Two-Open-Phase Condition

In April of 2012 a Canadian utility experienced failures of a 500 kV line terminal breaker and two 500 kV surge arresters on two different phases of a long EHV circuit during a prolonged two open-phase condition. Very high TOVs occurred from induced voltages and a resonant condition in the shunt compensated circuit, as discussed in section 4.2.2. The incident occurred during routine maintenance of protection at one terminal resulting in an inadvertent three-phase trip of the unfaulted line, initiated by line protection, followed by an automatic reclose, and then immediately followed by a protective re-trip of the line. This case provides a good example of hazardous TOVs that can occur due to capacitive coupling in the presence of series resonance on open phases of an EHV line equipped with shunt reactors that provide a high degree of shunt compensation.

Description of the case

Figure 4-7 shows a simplified single-line diagram of the 277 km 500 kV shunt (and series) compensated and transposed circuit 5L2 from GMS Station to WSN Station. The series capacitor bank does not play a role in this case because the bypass breaker was closed before the open phase condition occurred. The 500 kV shunt reactors (2040 Ohms/phase) 5RX2 at GMS end of the line and 5RX4 at WSN end provide 72.2% compensation of the positive sequence capacitance of the line. These reactors have solidly grounded neutrals hence the line is operated in three pole trip and reclose mode. The line originally went into service before single pole operation could be reliably achieved with the 500 kV breaker technology existing at the time. The GMS bus (part of a major hydroelectric installation) is the master end for high speed auto-reclose and the associated breakers 5CB5 and 5CB11 are equipped with POW closing. At the WSN (follow) end 5CB3 and 5CB4 are not equipped for POW closing. There is a set of surge arresters 5SA26 protecting 5RX2 and another set of arresters 5SA34 at 5RX4, as indicated in the diagram. Figure 4-8 shows a typical guyed-V tower for this flat-configuration circuit. The average height of the conductor above ground at the tower and the average conductor sag are 26.7 m and 10 m, respectively. Each phase comprises a bundle of four 316.1 mm² ACSR conductors in a 45.7 cm by 45.7 cm square arrangement.

Transmission Line Parameters:

Z1 = 7.26 + j92.54 (uncomp.) Y1 = 1356 µMho

Z0 = 56.86 + j342.4 Y0 = 780.5 µMho

Figure 4-7 500 kV Circuit Details For the Two Open-Phase Event

Figure 4-8 Details of Circuit 5L2 Typical 500 kV Guyed-V Structure

Sequence of events

On 16 April, 2012, during routine protection maintenance at GMS, one phase of a CT connected to 5L2 line protection was inadvertently shorted and isolated under load but without blocking the line protection. During a sequence of events (see Table 4-1) which lasted 7.6 seconds from initiation of the inadvertent trip to complete line isolation, one breaker (WSN 5CB4 Phase A) and two surge arresters (WSN 5SA34 Phase B and GMS 5SA26 Phase A) failed. The former arrester failed because of excessive and prolonged TOV while the latter arrester failed due to repeated high switching surges due to restriking within the failed breaker. The unintended isolation of the CT when 5L2 was under load initiated a three-phase trip of the line, first at GMS followed by the WSN end.

Table 4-1 Sequence of Events – 16 April 2012

Order Time-stamp - PST Event

1 15:24:27:93 hrs Unintentional Trip of 5L2 at GMS and WSN terminals 2 15:24:28:61 hrs Phases B and C automatically reclose at GMS 3 15:24:28:70 hrs Suboptimal Phase A POW reclose at GMS

4 - Reclose at WSN

5 15:24:28:71 hrs Trip initiation at GMS and DTT to WSN

6 WSN 5CB4 Pole A stuck closed on trip

7 WSN 5SA34 Phase B failure

8 15:24:33.75 hrs GMS 5SA26 Phase A failure causing ground fault 9 15:24:34:59 hrs Trip initiation at WSN by timed ground fault protection 10 15:24:35:71 hrs WSN 5CB4 breaker trip

Following the line trip, 5L2 line protection initiated automatic high speed reclose. The POW controller at GMS successfully reclosed phases B and C but delayed reclosing Phase A by about 6 cycles. Shortly after Phase A closed at the lead end, line protection transiently picked up and initiated a line re-trip and also sent a direct transfer trip (DTT) to the follow terminal, which, by this time had successfully reclosed three-phase. However, during the second line tripping operation, Pole A of WSN 5CB4 became stuck and failed to open. As a result, the circuit became single-phase energized from WSN. Phases B and C of 5L2, with the line-end reactors and associated surge arresters, were open but capacitively coupled to the energized Phase A. The induced overvoltages on the open phases caused failure of WSN 5SA34 Phase B. Pole A of 5CB4 in the stuck condition sustained uncontrolled multiple restrikes which, in about 6 seconds, led to the second surge arrester failure – Phase A of 5SA26 at GMS.

Figure 4-9 shows the instantaneous phase-to-ground voltages and 5L2 line currents at GMS (the upper three traces are the voltages, followed by the corresponding phase currents) and at WSN for a period of 680 ms, starting about 5 cycles before the auto-reclose of phases B and C at GMS. These traces were recorded by digital fault recorders at these two stations on 16 April. In examining these traces, the following two points must be kept in mind:

1. The voltage waveforms are NOT plotted on the same scale. The scaling of the voltage-axis for each plot is independently determined based on the maximum and minimum instantaneous values so that the entire plot fits within the bounds of the plotting area. The same applies for the line currents.

2. Inspection of the Phase B and Phase C voltage waveforms at WSN, during the two open-phase condition, indicates “flat topping”. This is NOT due to surge arrester conduction (or other non-linear phenomenon) during the excessive TOV but is because the overvoltages are so high that they have exceeded the pre-set range of the digital fault recorder. The recordings at GMS do not have this problem.

Prior to time T = 0, circuit 5L2 was isolated and all three phase-to-ground voltages at both line terminals exhibit ringdown oscillations as stored energy oscillates between the line capacitance and the shunt reactors as a result of the prior trip-out of the line. At time T = 10 ms the POW controller at GMS auto-reclosed Phases B and C (but not yet Phase A) while the remote end of the line was open. Thus, there was a one open-phase condition for about 5 cycles before Phase A reclosed (late). During these 5 cycles, the amplitude of the open Phase A voltage escalated dramatically and reached 669.5 kVp (1.64pu). When the POW controller reclosed Phase A at T = 110 ms, it did so near a voltage zero, a non-optimal point on the voltage wave, thereby initiating a large DC offset in the current due to the re-energization of the line-end reactors. However, about 2 cycles later there was a re-trip of the line but, since there was no zero crossing of the Phase A current at that time, this current continued uninterrupted.

However, at T = 190 ms the WSN end of the line reclosed three-phase. The disturbance created by closing the follow end of 5L2 Phase A created a current zero at GMS and the slowly decaying DC component in the current was transferred to the WSN Phase A breakers. A re-trip of the line at WSN occurred about 2 cycles later (T = 240 ms) but the Phase A current could not be interrupted until the next zero crossing, which occurred about 13 cycles later. Subsequently, there were multiple restrikes, which can be seen in the WSN Phase A line current indicating that one of the two breakers 5CB3 or 5CB4 had failed. Therefore, for more than 13 cycles, there was a two open-phase condition on 5L2 resulting in high TOVs on B and C phases of the line. The instantaneous Phase B voltage was about 668 kVp (1.64 pu) and Phase C voltage was about 697 kVp (1.71 pu), as measured at GMS.

The failure of the surge arrester on Phase B at WSN and on Phase A at GMS would have occurred some time beyond the time frame of Figure 3. Unfortunately, there were no time stamps for the switchings recorded at WSN because event logs were overwritten due to the large number of events.

Figure 4-9 Field Recordings of 16 April 2012 Two Open-Phase Event. Upper Three Traces are the Phase A, B, and C Voltages on 5L2 at GMS End Followed by the Corresponding Phase A, B and C Line Currents. The

Corresponding Voltages and Currents at WSN End Appear Below

One open-phase condition Auto-reclosure occurs near voltage zero

V-A GMS

V-B GMS

V-C GMS

V-A WSN

V-B WSN

V-C WSN Two open-phase condition

V-B 1.64 pu V-C 1.71 pu DC Offset

DC Offset Transferred to WSN Terminal Phase A recloses late

Phase B recloses

Phase C recloses

Line Re-trip at GMS

WSN Phase A Recloses

WSN Phase B Recloses

WSN Phase C Recloses

Line Re-trip at WSN

No Current Zero for 13 Cycles

WSN 5CB4 restriking

Steady State “Approximate” Analysis of the TOV

It is useful to calculate, analytically, the expected steady state TOVs during the open-phase conditions for 5L2 having two shunt reactors and compare these results to the field recordings. The positive and zero phase sequence line impedances and shunt susceptances are shown on Figure 4-7. At each 5L2 terminal there is a set of shunt reactors, each having a reactance of 2040 per phase (L+ = 2.706 H for two reactors in parallel per phase). Power frequency is 60 Hz.

From Eq. 4-3 and Eq. 4-4, Cph-ph = 1/3(C+ - C0) = 0.5087 µF and Cph-gr = C0 = 2.072 µF

From Eq. 4-1, the degree of shunt compensation, k, provided by two reactors on circuit 5L2 is 72.27%

One Open-Phase Condition:

From Eq. 4-5, the natural frequency of oscillation, fn, for 5L2 having two shunt reactors and one open phase is 55.0 Hz.

From Eq. 4-6, the shunt compensation degree that causes series resonance at fundamental frequency, k1, is 0.8586, which is well above the actual compensation level of 0.7227.

From Eq. 4-7, the induced open-phase voltage for 72.27% shunt compensation, k, for steady-state conditions is theoretically 1.04 pu.

Two Open-Phase Condition:

From Eq. 4-8, the natural frequency of oscillation, fn, for 5L2 having two shunt reactors and two open phases is 60.2 Hz, which is almost precisely the fundamental frequency.

From Eq. 4-9, the shunt compensation degree that causes series resonance at fundamental frequency, k2, is 0.7172, which is very close to the actual compensation level of 0.7227.

From Eq. 4-10, the induced open-phase voltage for 72.27% shunt compensation, k, for steady-state conditions is theoretically 26.0 pu, which is extremely high.

Discussion

For circuit 5L2, the degree of shunt compensation required to obtain series resonance at fundamental frequency for one open phase is 85.9% which is significantly more than the actual shunt compensation of 72.2%. This can be compared to the 89% shown on Figure 4-5 for the example 400 kV overhead circuit. For the two open-phase condition of 5L2 the natural frequency of this configuration is 60.2 Hz, indicating that this case is almost precisely resonant at fundamental frequency and high voltages on the two open phases can be expected. Alternatively, 71.72% shunt compensation is required to produce resonance at fundamental frequency, which is almost identical to the actual compensation of 72.2%. This can be compared to 78% compensation required for the 400 kV example circuit. From a theoretical perspective, a one open-phase condition of 5L2 having two shunt reactors will result in only a negligible induced steady state overvoltage whereas a two open-phase condition can be expected to produce a potentially hazardous temporary overvoltage.

The theoretical calculations of open-phase induced voltages assume steady-state conditions and ignore the nonlinear effects of surge arrester conduction, magnetic saturation of the shunt reactors, and corona losses on the conductors. They also assume that the line is balanced (i.e. the phase-to-phase capacitances are all identical). It should therefore not be surprising to find differences between the induced voltages calculated analytically and the voltages actually observed on 5L2 during the unusual phase conditions in April of 2012. For the two open-phase condition, both theory and field measurement indicated very high induced TOVs on the two open open-phases, but with only the (very understandable) disagreement in the severity of the overvoltage. It is also quite understandable that there was a surge arrester (WSN 5LA34) failure during the prolonged TOVs, although it might have been expected to occur on Phase C rather than Phase B. It is possible that the arrester on Phase B had a different V – I characteristic than the Phase C arrester. During the 4 to 5 cycles when Phase A was open but