14

Insulation Coordination

Stephen R. Lambert

Shawnee Power Consulting, LLC

14.1    Insulation Coordination

14.2    Insulation Characteristics

14.3    Probability of Flashover

Multiple Gaps per Phase • Multiple Gaps and Multiple Phases

14.4    Flashover Characteristics of Air Insulation

Voltage Waveshape • Electrode Configuration • Effect of Insulator • Effect of Atmospheric Conditions on Air Insulation • Altitude • Insulator Contamination • Application of Surge Arresters • Examples of Surge Arrester Application (Nonself-Restoring Insulation)

References

14.1  Insulation Coordination

The art of correlating equipment electrical insulation strengths with expected overvoltage stresses so as to result in an acceptable risk of failure while considering economics and operating criteria (McNutt and Lambert, 1992).

Insulation properties can be characterized as self-restoring and nonself-restoring. Self-restoring insulation has the ability to “heal” itself following a flashover, and such insulation media is usually associated with a gas—air, SF₆, etc. Examples include overhead line insulators, station buswork, external bushing surfaces, SF₆ buswork, and even switchgear insulation. With self-restoring insulation, some flashovers are often acceptable while in operation. An EHV transmission line, for example, is allowed to experience occasional line insulator flashovers during switching operations such as energizing or reclosing, or as a result of a lightning flash striking the tower, shield wires, or phase conductors.

Nonself-restoring insulation is assumed to have permanently failed following a flashover, and repairs must be effected before the equipment can be put back into service. Insulation such as oil, oil/paper, and solid dielectrics such as pressboard, cross-link polyethylene, butyl rubbers, etc., are included in this insulation class. Any flashover of nonself-restoring insulation, say within a transformer or a cable, is unacceptable as such events usually result in lengthy outages and costly repairs.

The performance level of self-restoring insulation is usually addressed and defined in terms of the probability of a flashover. Thus, for a specific voltage stress, a given piece of insulation has an expected probability of flashover (pfo), e.g., a 1-m conductor-to-conductor gap exposed to a 490-kV switching surge would be expected to have a 50% chance of flashover; with a 453-kV surge, the gap would be expected to have a 10% chance of flashover, etc. Consequently, when self-restoring insulation is applied, the procedure is to select a gap length that will give the overall desired performance (pfo) as a function of the stress (overvoltages) being applied.

For nonself-restoring insulation, however, any flashover is undesirable and unacceptable, and consequently for application of nonself-restoring insulation, a capability is selected such that the “100%” withstand level (effectively a 0% chance of flashover) of the insulation exceeds the highest expected stress by a suitable margin.

14.2  Insulation Characteristics

Self-restoring (as well as nonself-restoring) insulation has, when exposed to a voltage, a pfo which is dependent on

•  Dielectric material (air, SF₆, oil…)

•  Waveshape of the stress (voltage)

•  Electrode or gap configuration (rod–rod, conductor to structure…)

•  Gap spacing

•  Atmospheric conditions (for gases)

14.3  Probability of Flashover

Assuming the flashover characteristics of insulation follow a Gaussian distribution, and this is a good assumption for most insulation media (air, SF₆, oil, oil/paper), the statistical flashover characteristics of insulation can be described by the V₅₀ or mean value of flashover, and a standard deviation. The V₅₀ is a function of the rise time of the applied voltage, and when at a minimum, it is usually known as the CFO or critical flashover voltage.

Consequently, for a given surge level and insulation characteristic, the pfo of a single gap can be described by p, and can be determined by first calculating the number of standard deviations the stress level is above or below the mean:

$\text{\#}\delta =\frac{V_{\mathrm{stress}}-V_{50}}{1\text{standard}\text{deviation}}$

(14.1)

For air insulation, 1 standard deviation is either 3% of the V₅₀ for fundamental frequency (50–60 Hz) voltages and for lightning impulses or 6% of the V₅₀ for switching surge impulses. That the standard deviation is a fixed percentage of the V₅₀ and is not a function of gap length is very fortuitous and simplifies the calculations. Once the number of standard deviations away from the mean has been found, then by calculation or by entering a table, the probability of occurrence associated with that number of standard deviations is found.

Example: Assume that an insulator has a V₅₀ of 1100 kV with a standard deviation of 6%, and a switching overvoltage of 980 kV is applied to the insulation. The stress is 1.82 standard deviations below the mean:

$\begin{array}{ll}\text{\#}\delta \hfill & =\frac{980-1100}{0.06\times 1100}\hfill \\ \hfill & =-1.82\text{standard}\text{deviations}\text{below the mean}\hfill \end{array}$

(14.2)

By calculation or table, the probability associated with −1.82 standard deviations below the mean (for a normal distribution) is 3.4%. Thus, there is a 3.4% chance of insulation flashover every time the insulation is exposed to a 980-kV surge.

The physics of the flashover mechanism precludes a breakdown or flashover below some stress level, and this is generally assumed to occur at 3.5–4 standard deviations below the mean.

14.3.1  Multiple Gaps per Phase

The pfo, P_n, for n gaps in parallel (assuming the gaps have the same characteristics and are exposed to the same voltage) can be described by the following equation where p is the pfo of one gap. This mathematical expression defines the probability of one or more gaps flashing over, but practically only one gap of the group will flashover as the first gap to flashover reduces the voltage stress on the other gaps:

$P_n=1-{\left(1-p\right)}^n$

(14.3)

14.3.2  Multiple Gaps and Multiple Phases

Analysis of some applications may not only require consideration of multiple gaps in a given phase but also of multiple phases. Consider the pfo analysis of a transmission line; during a switching operation for example, multiple towers are exposed to surges and at each tower, each of the three phases is stressed (typically by different surge magnitudes). Thus it is important to consider not only the multiple gaps associated with the multiple towers, but also all three phases often need to be considered to determine the overall line pfo. The overall pfo for a given surge, PFO, can be expressed as

$\text{PFO}=1-{\left(1-{\text{pfo}}_{n,a}\right)}^g{\left(1-{\text{pfo}}_{n,g}\right)}^g{\left(1-{\text{pfo}}_{n,c}\right)}^g$

(14.4)

where

pfo_n,x is the pfo of the x phase for the given surge

n, g is the number of towers (gaps in parallel)

The simultaneous analysis of all three phases can be important especially when various techniques are used to substantially suppress the surges (Lambert, 1988).

14.4  Flashover Characteristics of Air Insulation

14.4.1 Voltage Waveshape

Waveshapes used for testing and for determining the flashover response of insulation have been standardized by various groups and while there is not 100% agreement, the waveshapes used generally conform to the following:

Fundamental frequency	50 or 60 Hz sine wave (8000 μs rise time)
Switching impulse	200–250 μs by 2000 μs
Lightning impulse	1.2 μs by 50 μs

The impulse waveshapes are usually formed by a double exponential having the time to crest indicated by the first number and the time to 50% of the crest on the tail of the wave indicated by the second number. Thus, a lightning impulse would crest at 1.2 μs and following the crest would fall off to 50% of the crest at 50 μs.

Fundamental frequency characteristics have been published, and typical values are indicated on Figure 14.1 (Aleksandrov et al., 1962; EPRI, 1982).

Equations have also been published or can be developed which define the typical responses to positive polarity switching and lightning impulses (see Figure 14.2). Insulation usually has a lower withstand capability when exposed to positive polarity impulses than when exposed to negative impulses; thus, designs are usually based on positive magnitude impulses.

FIGURE 14.1  V₅₀ for fundamental frequency waveshapes. (From Transmission Line Reference Book, 345 kV and Above, 2nd edn., Electric Power Research Institute, Palo Alto, CA, 1975.)

FIGURE 14.2  V₅₀ for impulses—positive polarity, rod-plane gap. (From EHV Transmission Line Reference Book, Edison Electric Institute, New York, 1968; Gallet, G. et al., IEEE Trans. Power Appar. Syst., PAS-95, 580, 1976.)

For switching surge impulses (gaps ≤ 15 m) (Gallet et al., 1976):

$V_{50}=k\frac{3400}{1+\left(8/d\right)}\text{kV}$

(14.5)

For lightning impulses, the following equation can be developed from EEI (1968):

$V_{\text{50}}=k\star 500{}^{\star }d\text{kV}$

(14.6)

where

k is an electrode factor reflecting the shape of the electrodes (Paris, 1967)

d is the electrode gap spacing in meters

14.4.2  Electrode Configuration

Electrode configuration has a pronounced effect on the V₅₀ characteristics, and this is reflected as a gap or electrode factor, k (Paris, 1967). Examples of k are

Rod–plane	1.00
Conductor–structure	1.30
Rod–rod	1.30
Conductor–rope	1.40
Conductor–rod	1.65

14.4.3  Effect of Insulator

The presence of an insulator in a gap tends to reduce the gap factor from those given above, mainly due to the terminal electrode configuration (and intermediate flanges for multiunit column bus support insulators). The reduction increases with increased gap factor and typical correction values may be found on Figure 14.3. Note that these corrections are subject to variations (Thione, 1984).

Rain has little effect on a gap without an insulator; however, rain does reduce the gap factor when an insulator is present. Reductions as high as 20% have been noted; but, in general a reduction of 4%–5% is typical (Thione, 1984).

14.4.4  Effect of Atmospheric Conditions on Air Insulation

V₅₀ for gases is affected by temperature, atmospheric pressure, and humidity, and for air the correction can be expressed as

$V_{50,\text{ambient}}=V_{50,\text{NTP}}{\left(\frac{\delta }{H_{\text{o}}}\right)}^n$

(14.7)

where

NTP is the normal temperature and pressure (20°C, 101.3 kPa)

H_o is the humidity correction factor

n is a gap length correction factor

δ is the relative air density correction factor

FIGURE 14.3  Gap factor correction for presence of insulator. (From Thione, L., ELECTRA, 94, 77, 1984.)

The correction for temperature and pressure, “δ,” is known as the RAD (relative air density) correction factor and is expressed by

$\delta =\frac{0.386H_{\text{mm}\text{of}\text{Hg}}}{273+T}$

(14.8)

where

H_{mm of Hg} is the atmospheric pressure in mm of Hg

T is the temperature in °C

The humidity correction factor, H_o, is given in IEEE 4 (1978) and can be expressed approximately by

$\begin{array}{cc}{H}_{\text{o}}& \cong 1.1-0.00820\star H_{\text{AB}}\\ & \cong 1.1-0.008071\star \text{VP}\end{array}$

(14.9)

where

H_AB is the absolute humidity in g/m³

VP is the vapor pressure in mm of Hg

For switching impulses (and fundamental frequency) the effect of the RAD and humidity on V₅₀ is, however, a function of the gap length and has less effect on longer gap than on shorter gap lengths. For lengths of 0–1 m the n correction factor is 1.0; from 1 to 6 m, the correction decreases linearly from 1.0 to 0.4; and for lengths greater than 6 m, the factor is 0.4. There is no gap length correction for positive lightning impulses (EEI, 1968; EPRI, 1975, 1982). Other approaches for humidity corrections can be found in Menemenlis et al. (1988), Thione (1984), Feser and Pigini (1987).

14.4.5  Altitude

Corrections for altitude are also important as the insulation capability drops off about 10% per 1000 m as shown in Figure 14.4. There are various equations for the altitude correction factor (ACF) and the following expression is representative of most in use (IEEE 1312, 1999):

$\text{ACF}={\left({\text{e}}^{-H_{\text{t}}/8600}\right)}^n$

(14.10)

where

H_t is the altitude in meters

n is a gap length correction factor

Insulator contamination is an important issue for fundamental frequency voltage considerations, and the equivalent salt density, ESDD, approach is extensively used as a design tool. The contamination severity is defined by the ESDD in mg/cm², and an insulator creepage distance, in terms of mm/kV_{rms, phase to phase}, can then be selected (IEC 815, 1986). Note that insulator/bushing shed/skirt design has a significant impact on the performance, and some past designs performed poorly due to skirt configuration even though they had large creepage distances. With the ESDD approach insulators are tested to define their expected performance. Table 14.1 shows the relationship between contamination level, ESDD, and recommended creepage distances.

FIGURE 14.4  Altitude correction factors. (From Mizuno, Y. et al., IEEE Trans. Dielectr. Electr. Insul., 4, 286, 1997; IEEE Standard for Insulation Coordination—Part 2, Application Guide, Institute of Electrical and Electronic Engineers (IEEE), 1312, 1999.)

14.4.6  Insulator Contamination

TABLE 14.1 Recommended Creepage Distances

Contamination Level	Example	ESDD (mg/cm2)	Minimum Recommended Creepage Distance (mm/kVrms, phase to phase)
Light	Low industrial activity	0.03–0.06	16
Medium	Industrial activity—some exposure to wind from the sea	0.1–0.2	20
Heavy	Industrial area and areas close to the sea	0.3–0.6	25
Very heavy	Heavy industrial or sea coast area	>0.6	31

Altitude also has an effect on the performance of contaminated insulation, and the degradation of capability as a function of altitude may be found in Figure 14.4 (Mizuno et al., 1997).

14.4.7  Application of Surge Arresters

Surge arresters are used to limit overvoltages and as a result, allow reductions in the clearances required for self-restoring gaps (e.g., transmission line towers) as well as the capability required for nonselfrestoring insulation such as transformer windings. In most applications the proper approach is to determine the minimum arrester rating, which can be applied without resulting in damage to the arrester and then to define the insulation level required so as to result in an acceptable pfo or risk of failure.

For a transmission line application, for example, although the arrester reduces higher magnitude surges to lower levels, the line is still allowed to have a finite, albeit low, pfo for a specific switching operation. Thus, the arrester, by limiting the higher magnitude surges, allows smaller conductor to tower clearances.

However, when arresters are used to protect a transformer for example, an insulation level, which has a significantly higher capability than the maximum surge allowed by the arrester, is selected. This margin between the arrester protective levels (lightning or switching surge) is a function of various considerations as well as the conservatism of the person applying the arrester/insulation system.

Today, for new applications, only metal oxide (ZnO) arresters are being applied. Although there are certainly many of the gapped, silicon carbide type arresters still in service and which still perform effectively, in what follows, only metal oxide arresters will be considered to protect insulation. Successful application requires that the arrester survives the electrical environment in which it is placed, and the following arrester capabilities must be carefully considered:

MCOV—maximum fundamental frequency continuous operating voltage applied to the arrester
TOV—temporary fundamental frequency overvoltages to which the arrester may be exposed
Energy—the energy which must be absorbed by the arrester when limiting switching surges

14.4.7.1  MCOV

The highest system voltage, which can be continuously applied to the arrester, needs to be determined and the arrester capability, its MCOV rating, should at least be equal to and should usually exceed the highest continuous system voltage by some small margin. For example, if a nominal 345-kV system is never operated above 352 kV, then the maximum continuous voltage, which would be expected to be applied to a line to ground arrester, would be $352\text{kV/}\sqrt{3}=203.2\text{kV}$. With today’s typical arresters, the next highest available MCOV capability would be 209 kV and is associated with an arrester rated 258 kV.

14.4.7.2  TOV

On occasion, the fundamental-frequency voltage applied to an arrester will exceed the expected MCOV. Examples include fault conditions during which line to ground voltages on unfaulted phases can rise significantly (as high as phase-to-phase voltage for ungrounded systems); rise in line voltage when energizing a transmission line (Ferranti effect) and voltages which occur during load rejection events—these are usually associated with voltages experienced on a radial transmission line emanating from a generating plant when the load terminal of the line opens unexpectedly.

14.4.7.3  Energy

When an arrester limits switching surges on a transmission line, it can absorb a significant amount of energy, and it can be important to examine events and determine the energy which could be absorbed. Exceeding the arrester’s capability could result in immediate damage to the arrester and failure. It is also important to the arrester’s TOV capability as absorbing energy heats the arrester material, and application of a significant temporary overvoltage immediately following absorption of a significant amount of energy could result in thermal runaway and arrester failure.

Following selection of an arrester which would be expected to survive the electrical environment (i.e., the minimum rated arrester), the protective levels of the arrester must be correlated with the insulation capability and acceptable margins between the protective levels and the insulation capability achieved.

The protective level or discharge voltage of an arrester is the voltage magnitude to which the arrester will limit the voltage while discharging a surge, and these levels are a function of the waveshape and rise time of the surge as well as the current magnitude of the discharge. In general, the discharge or protective levels considered for coordination with insulation capability are

•  A 10-kA, 8 × 20-μs discharge for coordination with the insulation full wave or lightning impulse (BIL) capability and

•  A 0.5–2.0-kA, 36 × 90-μs discharge for coordination with the switching impulse capability

There should always be margin between the protective level of the arrester and the insulation capability to allow for uncertainties in arrester protective levels due to surge rise times, discharge currents, and arrester separation distance (faster rise times, higher currents, and longer separation distance or lead lengths generate higher protective levels). Uncertainties in insulation capability include reduced insulation strength due to aging (especially for paper insulation in transformers for example) and limitations of the ability of laboratory dielectric testing to accurately relate to field conditions.

In the author’s opinion, a margin of at least 40% is appropriate unless all the uncertainties and the risks are carefully evaluated.

14.4.8  Examples of Surge Arrester Application (Nonself-Restoring Insulation)

14.4.8.1 34.5-kV System application

Surge arresters are to be applied line to ground at the terminals of a circuit breaker (38-kV rating, 150-kV BIL) used on a solidly grounded 34.5-kV system. The highest expected continuous system voltage is 37 kV, and during fault conditions, the phase to ground voltage can rise to 1.4 pu or 27.9 kV. Faults can persist for 20 cycles.

The maximum line to ground voltage is $\text{37/}\sqrt{3}=21.4\text{kV}$ and the MCOV of the arrester must meet or exceed this value. An arrester rated 27 kV would be acceptable as it has an MCOV of 22.0 kV. The 1 s TOV capability of the arrester is 31.7 kV, and as this exceeds the 27.9 kV phase to ground voltage expected during faults, the 27-kV arrester meets the TOV criteria as well.

A 27-kV arrester has a 10-kA discharge level of 67.7 kV, and thus the margin between the discharge or protective level and the insulation BIL is (150/67.7 × 100–100) or 121%. This margin is obviously more than adequate, and selection of an arrester rated 27 kV would be appropriate.

14.4.8.2  500-kV System Application

A 500-kV shunt reactor (solidly grounded neutral) is being applied at the end of a 300 km, 500-kV transmission line, and arresters are to be applied line to ground on the terminals of the reactor to limit surges to reasonable levels. The reactor is solidly connected to the line and is switched with the line, and the substation at which the reactor resides is at an altitude of 1800 m. The highest expected continuous system voltage is 550 kV. During line switching operations, the circuit breaker at the reactor terminal may not be closed for some period following energizing of the line/reactor from the other terminal, and the phase to ground voltage at the reactor can be as high as 1.15 pu for as long as 5 min. Arrester energy requirements were determined (by EMTP or TNA simulations of switching operations) to be well within the capability of an arrester rated 396 kV.

The minimum required MCOV is $\text{550/}\sqrt{3}=317.5\text{kV}$. The minimum required TOV is $\text{1}\text{.15}\times \text{500/}\sqrt{3}=332\text{kV}$ for 300 s, and for most arresters, such a requirement would correlate with a 1 s TOV rating of 451 kV. An arrester rated 396 kV has a 318-kV MCOV and a 1 s TOV rating of 451 kV; thus, a 396-kV arrester would be the minimum rating that could be used. Of course any arrester rated higher than 396 kV could also be used. The 10-kA lightning (8 × 20 μs waveform) and switching surge (2 kA, 36 × 90 μs) discharge levels for a 396-kV and a 420-kV arrester are

Discharge Levels
Rating (kV)	10 kA (kV)	Switching Surge (kV)
396	872	758
420	924	830

BIL values of 1300 and 1425 kV for the reactor’s internal insulation (i.e., insulation not affected by altitude) could be considered as reasonable candidates for a specification. The corresponding switching impulse levels (SIL) would be 1080 and 1180 kV, respectively, and the following table indicates the margin between the arrester protective levels and the insulation level.

	1300-kV BIL		1425-kV BIL
Arrester	396 kV (%)	420 kV (%)	396 kV (%)	420 kV (%)
SIL	42	30	56	42
BIL	49	41	63	54

Application of a 420-kV arrester for a 1300-kV BIL insulation level results in margins below 40%, and unless the application is very carefully considered from the point of view of arrester separation distance and lead length, expected maximum discharge current level, wave rise time, etc., a 396-kV arrester would be a better choice. For a 1425-kV BIL, either the 396-kV or the 420-kV arrester would result in sufficient margins.

For external insulation, i.e., the reactor bushings, the effect of altitude on the insulation capability needs to be considered. At 1800 m, the insulation has only 81% of the withstand capability demonstrated at sea level or 0 m. For example, the SIL of a 1425-kV bushing (1180 kV at sea level) would be reduced to 956 kV at 1800 m (1180 × 0.81 = 956 kV), and application of even a 396-kV arrester would result in a margin of 26%—hardly acceptable.

Assume that a 420-kV arrester was selected to protect the reactor (the arrester itself is rated for application to 3000 m). The switching surge and 10 kA protective levels are 830 and 924 kV, respectively. With a desired minimum margin of 40%, and correcting for altitude, the minimum SIL and BIL at sea level (0 m) should be

$\begin{array}{c}\text{Minimum}\text{SIL}=\frac{830\times 1.4}{0.81}=1435\text{kV}\\ \text{Minimum}\text{BIL}=\frac{924\times 1.4}{0.81}=1597\text{kV}\end{array}$

A 1550-kV BIL bushing would have a 1290-kV SIL, and even if one would accept the slightly less than a 36% margin for the BIL, the SIL margin would only be 26%. A 1675-kV BIL bushing would be expected to have a 1390-kV SIL capability, and so the SIL margin would be 36% with a BIL margin of 47%. The next higher rated bushing (1800-kV BIL) would mean applying 800-kV system class bushings, and their increased size and cost would likely not make for a reasonable design. Consequently, specifying a 1675-kV BIL bushing and accepting the slightly reduced SIL margin would be a reasonable compromise.

14.4.8.3  Effect of Surge reduction techniques on Overall PFO

Application of surge arresters to significantly reduce switching surge levels on transmission line and substation insulators can be effective, however, the designer should be aware that the overall PFO of all three phases needs to be considered as it will usually be higher than that found for a single phase by a factor often approaching three. Also for long transmission lines, application of arresters at the line terminals will certainly limit the surges at the terminals but will not limit the surges at other points on the line to the same level. Consequently, the surge distribution along the line may need to be considered (Lambert, 1988; Ribiero et al., 1991).

References

Aleksandrov, G.N., Kizvetter, V.Y., Rudakova, V.M., and Tushnov, A.N., The AC flashover voltages of long air gaps and strings of insulators, Elektrichestvo, 6, 27–32, 1962.

EHV Transmission Line Reference Book, Edison Electric Institute, New York, 1968.

Feser, K. and Pigini, A., Influence of atmospheric conditions on the dielectric strength of external insulation, ELECTRA, 112, 83–93, 1987.

Gallet, G., Bettler, M., and Leroy, G., Switching impulse results obtained on the outdoor testing area at Renardieres, IEEE Transactions on Power Apparatus and Systems, PAS-95(2), 580–585, 1976.

Guide for the Selection of Insulators in Respect of Polluted Conditions, The International Electrotechnical Commission Publication 815, 1986.

IEEE Standard for Insulation Coordination—Part 2, Application Guide, Institute of Electrical and Electronic Engineers (IEEE) 1312, 1999.

IEEE Standard Techniques for High-Voltage Testing, Institute of Electrical and Electronic Engineers (IEEE) 4-1978.

Lambert, S.R., Effectiveness of zinc oxide surge arresters on substation equipment probabilities of flash-over, IEEE Transactions on Power Delivery, 3(4), 1928–1934, 1988.

McNutt, W.J. and Lambert, S.R., Transformer Concepts and Applications Course, Power Technologies, Inc., Schenectady, NY, 1992.

Menemenlis, C., Carrara, G., and Lambeth, P.J., Application of insulators to withstand switching surges in substations, part I: Switching impulse insulation strength, 88 WM 077-0, IEEE/PES Winter Meeting, New York, January 31–February 5, 1988.

Mizuno, Y., Kusada, H., and Naito, K., Effect of climatic conditions on contamination flashover voltage of insulators, IEEE Transactions on Dielectrics and Electrical Insulation, 4(3), 286–289, 1997.

Paris, L., Influence of air gap characteristics on line-to-ground switching surge strength, IEEE Transactions on Power Apparatus and Systems, PAS-86(8), 936–947, 1967.

Ribeiro, J.R., Lambert, S.R., and Wilson, D.D., Protection of compact transmission lines with metal oxide arresters, CIGRE Leningrad Symposium, 400-6, S33–S91, 1991.

Thione, L., Evaluation of the switching impulse strength of external insulation, ELECTRA, 94, 77–95, 1984.

Transmission Line Reference Book, 345 kV and Above, 1st edn., Electric Power Research Institute, Palo Alto, CA, 1975.

Transmission Line Reference Book, 345 kV and Above, 2nd edn., Electric Power Research Institute, Palo Alto, CA, 1982.