Phase-Phase and Phase-Ground

Phase-Phase Switching Overvoltages, Transmission Lines

2.4 Phase-Phase and Phase-Ground

In the practical case, a phase-phase insulation always exists with a phase-to-ground insulation. For example, for a transmission line, there exists a strike distance to ground and a strike distance between phases. This general case may be easily por- trayed by the V - v diagram as illustrated in Fig. 8. The diagram is composed of three straight line segments: (1) the horizontal line at the positive polarity phase-to- ground CFO, CFO;, (2) the linearly falling line representing the phase-phase CFO, CFO', and (3) the vertical line representing the negative polarity CFO to ground, CFO;. For low and high values of V , flashover to ground is more probable than

Figure 8 Switching impulse strength characteristics for phase-phase and phase-ground.

Phase-Phase SOVs, Transmission Lines 143

flashover between phases. However, between these high and low values of V , flash- over between phases is most probable.

As noted from this portrayal, phase-phase flashover can be essentially elimi- nated if the phase-ground strike distance is sufficiently lowered-or the phase-to- ground flashover can be essentially eliminated if the phase-to-ground strike distance is increased. Thus the

v + - v

method can handle both phase-phase and phase- ground insulations simultaneously.

The diagram of Fig. 8 is general in nature in that it can also be used to portray the insulation strength of internal gas or solid insulation such as is employed in a transformer, GIs, or cable. In this case, the strength of the insulation is only depen- dent on the magnitude of the phase-phase voltage and not on the division of the phase-phase voltage into positive and negative components. Therefore K = 1.0, and from Eq. 15, the phase-phase CFO, CFOp, is equal to CFOo.

In general, for small air gaps of less than about 2 to 3meters, i.e., for nominal system voltages less than 500 kV, K is also equal to one. Thus only for large air clearance does the separation of the phase-phase voltage into separate components become important, and for this case KL is less than one.

Effect of

So

^{on CFOg}

In Ref. 6.2, the authors evaluate the effect of the strike distance between phases on the positive CFO to ground, CFO; The indicate that as Sp/h decreases below 1.0, the CFO; decreases. For example, if Sp/h is 0.5, then the CFO; decreases by about 20 to 25%.

Using the data from Ref. 6.2 for the conductor-conductor gap when V = 0 and all flashovers are to ground, Table 2 indicates that the CFO; remains constant for Sp/h of 0.89 and 0.23. that is, the phase-ground gap factor remains constant at

1.17.

The authors also consider the phase-phase gap called screen to screen with a phase-ground gap to pedestals with a pedestal height of 2.5 meters. For V = 0, all flashovers are to ground. From the CFO;, the phase-ground gap factor is found.

Then using Eq. 32 of Chapter 2 with A = 0, the phase-ground gap factor is calcu- lated. Since the calculated and actual gap factor are equal, the conclusion is that the C F O ~ is not affected by the values of Sp/h of from 0.81 to 1.0; see Table 3.

Thus the overall conclusion is that using the presently available data, the CFO;

is unchanged for Sp/h as low as 0.23. It is to be hoped that future laboratory studies will closely study this issue.

Table 2 Effect of Sp/h on CFO; on Conductor-Conductor-to-Ground Gap

h, meters Sp, meters

sdh

CFO;, kV k g

4 44 Chapter 4

Table 3 Effect of S p / h on CFO; for Screen-Screen-to-Grounded-Pedestal Gap h, meters S p , meters S g , meters S p / h CFO;, kV kg Calc kg

7 7 4.5 1 .O 1810 1.48 1.41

9 9 6.5 1 .OO 1524 1.34 1.33

11 9 8.5 0.81 1752 1.29 1.30

Effect of the Third Phase

To simplify the presentation, only two phases were considered. The effect of the third phase is minor, since for the higher SOVs the voltage on this phase will be signifi- cantly less than that on the negative polarity second phase [6.4].

Effect of Time Delay Between Times to Crest

One other point needs some discussion. The data presented assumes that the two impulse waveshapes have the same time to crest and are synchronized so that they are applied at the same instant. That is, viewing Fig. 9, AT is zero. If the positive voltage precedes the negative voltage as in Fig. 9, AT has no effect, i.e., there is no decrease in the CFO. However, if the negative voltage precedes the positive voltage, a decrease may occur, this decrease being from 10 to 15% if AT is several milli- seconds. For the higher SOVs which are of primary importance, AT is small or nonexistent, and therefore this decrease is normally not considered [6.4, 81.

The Value of KL

For transmission lines there exist several values of Sp/h. Since h is highest at the tower, the minimum value occurs at this location, whereas since h is lowest at the midspan, the maximum values occur there. For present designs of 500- and 765-kV transmission lines at the tower, Sn/h ranges from about 0.23 to 0.43 with an average of about 0.40. At the midspan, the ratio S p / h ranges from about 0.70 to 1.45 and averages about 0.95. Using Eqs. 9 and 12, K at the tower is about 0.64 to 0.68 and at the

>

$ - y

^0.0

¤

midspan is 0.24 to 0.34.

r

Figure 9 Non-synchronous impulses may decrease the CFO.

Phase-Phase SOVs, Transmission Lines 145

For present substations Sp/h is about 1.2, although future substations may decrease this to about 0.80. Also, Sp/Sg is about 2.0 for present stations but may decrease to 1.4 for future substations. If Eqs. 9 and 12 are used, Ki becomes less than zero, an unrealistic value.

In view of these inconsistencies and those regarding the effect of Sp/h on the CFO to ground, it is recommended that KL be selected from Table 1, i.e., independently of Sp/h. It goes without saying that for any future installation, tests should be made, since the values of Table 1 are to be considered as estimates. From Table 1, for transmission lines whose span lengths are in the range of 300 to 400 meters, the average value of KL is 0.68, the average value of opp/CFOo is 0.02, and the average value of KGp is about

1.26. These values are recommended for use for transmission lines.

More on the CFOo

When V is equal to zero, the CFOo is the phase-phase CFO with the second phase grounded. That is, assume a conductor-conductor-to-ground arrangement. V = 0 means that one of the conductors is grounded. Thus the CFOo is the same as a phase-to-ground CFO of a conductor-to-grounded conductor gap. Thus the value of KGp is equal to k g . For example, for a rod-rod phase-phase arrangement, Table 1 shows that Key is 1.35. From Eq. 34 of Chapter 2, for h' = 0

which is practically identical to KGp. This attribute or equality is used in IEC Standard 71-2 [5], which is discussed in Chapter 5. This also indicates that CT~/CFO; is equal to opp/CFOo, which is assumed in Table 1.

3 PHASE-PHASE SWITCHING OVERVOLTAGES

As for phase-ground overvoltages, there exist three phase-phase overvoltages. For simplicity of presentation, two of these are shown in Fig. 10. At each instant in time, the insulation is stressed by a different overvoltage. Therefore, ideally or theoreti- cally, the insulation strength and the probability of flashover should be evaluated at each instant in time. From this, the total probability of flashover is 1 minus the probability of no flashover at each of the time instants.

To circumvent this laborious procedure, only two time instants are usually considered: (1) the time T', at which the maximum positive ground-ground voltage occurs and (2) time Tn, at which time the maximum phase-phase voltage occurs.

The SSFOR is then calculated for each of these time instants and the larger SSFOR is used.

In general, for air clearances greater than bout 3meters (500-kV systems and above), the time of the maximum positive SOV is more severe, whereas for non-self- restoring insulations, such as transformer insulation, cables, for GIs, and for small air clearances (below 500 kV systems), the time for the maximum phase-phase SOV is more severe.

At present, the digital transient programs, EMTP or ATP, are not equipped to obtain these data conveniently. That is, the programs easily obtain the maximum phase-ground voltage at T^ and the maximum phase-phase voltage at TI2.

Chapter 4

TIME OF TIME OF MAX V + MAX vp

Figure 10 The voltages at two time instants, T' and TI2 are considered to evaluate the SSFOR.

Therefore engineers are prone to collect this mixture of data. That is, the maximum phase-phase SOVs are collected, i.e., using time T I 2 , and the maximum p h a s e ground SOVs are collected using time T'. Again, collecting the data in this manner is incorrect. However, this method is inherently conservative since it involves collec- tion of the "worst" data at each time instant.

Further, in many cases, the SOV densities for the higher SOVs, which are of primary interest, are sufficiently close for both time instants so that, as an approx- imation, either time instant may be employed.

For further development of the methodology, the simple assumption is made that the SOV distribution is composed of voltages V' and V- or voltages V' and Vp-and that these are obtained at one of the two time instants, or in any manner.

Since there are three voltages of interest, Vp, v', and V-, any two of these can be collected, and from the distribution of the two voltages, the distribution of the third can be obtained. Today the trend is to collect the V' data, since it is necessary for evaluation of the SSFOR for phase-ground insulations and to collect also the Vp data. The other option of collecting the V' and V- data is infrequently employed.

In most cases, the Gaussian or normal distribution is used to approximate the random values of SOVs. In this case, the following sections apply.

3.1 Gaussian SOV Distributions, Vp and V +