Angular displacement is defined as the phase angle in degrees between the line-to-neutral voltage of the reference-identified high-voltage terminal and the line-to-neutral voltage of the corresponding identified low-voltage terminal.
The angle is positive when the low-voltage terminal lags the high-voltage terminal. The convention for the direction of rotation of the voltage phasors is taken as counterclockwise.
Since the bulk of the electric power generated and transmitted is three-phase, the grouping of transformers for three-phase transformations is of the greatest interest. Connection of three-phase transformers or three single phase transformers in a three-phase bank can create angular displacement between the primary and secondary terminals.
The standard angular displacement for two-winding transformers is shown in Figure above. The references for the angular displacement are shown as dashed lines.
The angular displacement is the angle between the lines drawn from the neutral to H1 and from the neutral to X1 in a clockwise direction from H1 to X1.
The angular displacement between the primary and secondary terminals can be changed from 0 to 330 degrees in 30deg steps simply by altering the three-phase connections of the transformer.
Therefore, selecting the appropriate three-phase transformer connections will permit connection of systems with different angular displacements.
Figure shows angular displacement for common double-wound three-phase transformers. Multicircuit and autotransformers are similarly connected.
POWER TRANSFORMER | DISTRIBUTION TRANSFORMER | TRANSFORMER DESIGN | TRANSFORMER PRINCIPLES | TRANSFORMER THEORY | TRANSFORMER INSTALLATION | TRANSFORMER TUTORIALS
TRANSFORMER BUSHINGS FOR SPECIAL APPLICATIONS
High-Altitude Applications
Bushings intended for application at altitudes higher than 1000 m suffer from lower air density along the outer insulator. Standards specify that, when indicated, the minimum insulation necessary at the required altitude can be determined by dividing the standard insulation length at 1000 m by the correction factor given in Table 3.2.2.
For instance, suppose that the required length of the air insulator on a bushing is 2.5 m at 1000-m altitude. Further, suppose that this bushing is to be applied at 3000 m. Hence, the air insulator must be at least 2.5/0.8 = 3.125 m in length.
The air insulator on the bushing designed for 1000 m must be replaced with a 3.125-m-long insulator, but the remainder of the bushing, i.e., the central core and the oil insulator, will remain the same as the standard bushing because these parts are not affected by air insulation. These rules do not apply to altitudes higher than 4500 m.
Highly Contaminated Environments
Insulators exposed to pollution must have adequate creep distance, measured along the external contour of the insulator, to withstand the detrimental insulating effects of contamination on the insulator surface. Figure 3.2.2 shows the undulations on the weather sheds, and additional creep distance is obtained by adding undulations or increasing their depth. Recommendations for creep distance are shown in
Table 3.2.3 according to four different classifications of contamination. For example, a 345-kV bushing has a maximum line-to-ground voltage of 220 kV, so that the minimum creep is 220 X 28 = 6160 mm for a light contamination level and 220 X 44 = 9680 mm for a heavy contamination level. The term ESDD (equivalent salt-density deposit) used in Table 3.2.3 is
TABLE 3.2.2 Dielectric-Strength Correction Factors for Altitudes
Greater than 1000 m
Altitude, m Altitude Correction Factor for Dielectric Strength
1000 1.00
1200 0.98
1500 0.95
1800 0.92
2100 0.89
2400 0.86
2700 0.83
3000 0.80
3600 0.75
4200 0.70
4500 0.67
Source: ANSI/IEEE, 1997 [1]. With permission.
TABLE 3.2.3 Recommended Creep Distances for Four Contamination Levels
Contamination Level
Equivalent Salt-Deposit
Density (ESDD), mg/cm2
Recommended Minimum Creep
Distance, mm/kV
Light 0.03–0.08 28
Medium 0.08–0.25 35
Heavy 0.25–0.6 44
Extra heavy above 0.6 54
Source: IEEE Std. C57.19.100-1995 (R1997) [8]. With permission.
the conductivity of the water-soluble deposits on the insulator surface. It is expressed in terms of the density of sodium chloride deposited on the insulator surface that will produce the same conductivity.
Following are typical environments for the four contamination levels listed:
Light-contamination areas include areas without industry and with low-density emission-producing residential heating systems, and areas with some industrial areas or residential density but with frequent winds and/or precipitation. These areas are not exposed to sea winds or located near the sea.
Medium-contamination areas include areas with industries not producing highly polluted smoke and/ or with average density of emission-producing residential heating systems, areas with high industrial and/or residential density but subject to frequent winds and/or precipitation, and areas exposed to sea winds but not located near the sea coast.
Heavy-contamination areas include those areas with high industrial density and large city suburbs with high density emission-producing residential heating systems, and areas close to the sea or exposed to strong sea winds.
Extra-heavy-contamination areas include those areas subject to industrial smoke producing thick, conductive deposits and small coastal areas exposed to very strong and polluting sea winds.
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