B.4.1 Application design procedure for masts
Application of the electrogeometric theory by the rolling sphere method involves rolling an imaginary sphere of radius S over substation lightning terminals such as lightning masts, shield wires, and metal support structures as described in 6.3. Therefore, to apply the method to the example substations requires the computation of the radius S, and this will first require the calculation of Zs, the surge impedance, and Is, the allowable stroke current for the various buses within the substation.
Annex C gives a method of calculating surge impedance under corona. Corona radius can be taken from Figure C.1 or calculated from Equation (C.1) or Equation (C.2). The engineer who designs protection
systems on a regular basis could write a simple computer program to perform these calculations. Once the corona radius is determined, it is an easy matter to calculate the surge impedance. The surge impedance will be required for each bus of a different height and conductor type.
Next, the designer will calculate the allowable stroke current from Equation (18) using the above values.
The striking distance then can be calculated from Equation (17). In the examples, k = 1.2 has been used for the mast example, and k = 1 has been used for the shield wire example. For a combination of masts and wires, the designer can use k = 1, which will give a conservative result. 6.3.1 states that the usual practice is to assume that the striking distance to a mast, a shield wire, or the ground is the same. This suggests the use of only one k value. The example calculations demonstrate that a different k can be used for masts resulting in a more economical design.
The designer is now ready to roll the imaginary sphere over the example substation. If the sphere remains above the equipment and busses to be protected as seen in the center of Figure 24, the design is satisfactory.
If the equipment touches or enters the sphere as seen in the right side of Figure 24, the equipment is not protected and the design must be revised.
The designer can determine if some areas of the station are protected by simply striking arcs on a scale drawing of the substation. Further calculation is necessary, however, to determine the maximum separation of wires and masts to prevent the sphere from sinking between them and touching the equipment to be protected. The following examples illustrate how to calculate these quantities.
B.4.2 Nomenclature used in the calculations
The nomenclature listed below are used in the following calculations: For calculations when using masts:
S Sphere radius
H Mast height (calculations use an assumed height; designers typically pick a mast height suitable for the design)
A Bus height
W&C Horizontal distance from origin of sphere (OOS) to bus T Maximum separation from mast to bus for protection Y Minimum phase to steel clearance
Z Horizontal distance between OOS and line drawn between two masts L Half the separation between two masts
X Maximum separation between two masts D Elevation difference between mast and bus E Elevation difference between mast and OOS J Horizontal distance between OOS and mast
K Diagonal distance between masts when four masts support the sphere P Distance between masts when four masts support the sphere
Q Distance between masts when three masts support the sphere For calculations using shield wires:
S Sphere radius
H Wire height (calculations use assumed heights; designers typically pick mast height suitable for his/her design)
A Bus height
X Maximum separation between two wires D Elevation difference between wire and bus E Elevation difference between wire and OOS R Horizontal distance between OOS and wire T Horizontal distance between OOS and bus C Horizontal distance between shield wire and bus The resulting lay out is found in Figure B.19 and Figure B.20.
Figure B.19—Mast protection for a 69 kV substation
Figure B.20—Mast protection for a 69 kV substation
B.4.3 Calculations for mast protection of 69 kV substation 69 kV Substation example—protection by mast
m
These values are the maximum separation between the mast and protected bus for the two bus heights A.
Maximum distance between two masts for side stroke
2
These values are the maximum separation of two masts for protection of bus at the two heights A.
Maximum distance between masts for vertical stroke sphere supported by four masts
These values are the maximum spacing of four masts for protection of bus at the two heights A.
Maximum distance between masts for vertical stroke sphere supported by three masts
1
1
180
cos 30
2 J
Q
2
2
180
cos 30
2 J
Q
m
Q1 29.32 Q2 30.02m
These values are the maximum spacing of three masts for protection of bus at the two heights A.
However, Q shall not be greater than X (the maximum separation of two masts).
B.4.4 Calculations for shield wire protection of a 69 kV substation
The procedure for designing a shield wire system follows a similar routine. For parallel wires, only two calculations are required: the horizontal distance C, to prevent side strokes and the distance X, the maximum separation to prevent vertical strokes.
The 14 ft bus (or the transformer that is at the same height) can extend 13 ft beyond the shield wire and still be protected from side strokes. Since the transformer does not extend beyond the shield wire it is protected.
The high bus can extend 9 ft beyond the shield wire and be protected. Since it extends only 6 ft beyond, it is protected.
Calculations are also included for a 60 ft shield wire height. Notice that the values for C are slightly less than for a 40 ft wire height. This illustrates that a 60 ft wire height would give less protection from side stroke. A study of Figure B.23 will show why this is true.
The calculations for maximum shield wire separation for the 14 ft bus yield a value of 86 ft. Since the actual separation is 84 ft, the bus is protected. A maximum separation of 80 ft is permitted for the 19 ft bus and it is protected since the separation is 79 ft. The set of shield wires actually protects the low bus as well, and the other set is needed only for side stroke protection. The incoming line conductors are fully shielded by the existing shield wires. This completes the protection of the substation. The resulting layout is found in Figure B.21, Figure B.22, and Figure B.23.
69 kV substation example—protection by shield wire (height = 18.25 m)
m
These values are the maximum horizontal separation of shield wire and bus for protection at bus height A.
Maximum distance between two wires for vertical stroke (D must be less than or equal H – A for protection at height A).
1
These values are the maximum separation of shield wires for protection of bus at height A.
69 kV substation example—protection by shield wires (height = 19.19 m)
Maximum distance between two wires for vertical stroke (D must be less than or equal H – A for protection at height A).
1
1 H A
D D2 H A2
m
D1 6.4 D2 7.92m
1
1 S D
E E2 SD2
m
E1 8.36 E2 6.84m
2 1 2
1
S E
L L
2 S
2 E
22m
L1 12.16 L2 13.08m
1
1 2L
X X2 2L2
m
X1 24.32 X2 26.16m
These values are the maximum separation of shield wires for protection at bus height A.
Figure B.21—Shield wire protection for 69 kV substation
Figure B.22—Shield wire protection for 69 kV section AA
Figure B.23—Shield wire protection for 69 kV section BB
B.4.5 The 500/230 kV switchyard—dealing with multiple voltages
The procedure of applying the rolling sphere method when there are multiple voltages in a substation is quite simple, as illustrated by the sample substation. The designer simply makes a separate calculation for each voltage level in the station using the appropriate BIL and surge impedance. At the voltage interface (usually the transformer) the designer should determine whether the lower voltage equipment is protected by using the appropriate lower striking distance. If low voltage busses are present, it might be appropriate to use a minimum stoke current of 2 kA for the design calculations in these areas see 6.3.6.
The procedure for the 500 kV portion of the switchyard and for the 230 kV portion taken separately follow the same routine as has been previously discussed for the 69 kV example. Calculations for mast placement in the 500 kV portion of the station are in B.4.5.1. The 230 kV calculations are in B.4.5.2. The resulting layout is shown in Figure B.24. 500 kV shield wire calculations are in B.4.5.3 with the 230 kV shield wire calculations in B.4.5.4. The resulting layout from those calculations is shown in Figure B.25.
A summary of the rolling sphere method results can be found in Table B.5 and Table B.6.
B.4.5.1 Calculations for 500 kV substation with masts
1
1 R C
T T2 RC2
m
T1 8.19 T2 16.41m
These values are the maximum separation between the mast and protected bus for the two bus heights A.
Maximum distance between two masts for side stroke
2
These values are the maximum separation of two masts for protection of bus at the two bus heights A.
Maximum distance between two masts for vertical stroke sphere supported by four masts
These values are the maximum spacing of four masts for protection of bus at the two heights A.
Maximum distance between two masts for vertical stroke sphere supported by three masts
1
These values are the maximum spacing of three masts for protection at the two bus heights A.
However, Q shall not be greater than X.
B.4.5.2 Calculations for 230 kV substation with masts
230 kV substation example—protection by masts
1
1 S C
T T2 SC2
T
3 S C
3 mT1 9.29 T2 12.18m
T
3 6 . 29 m
These values are the maximum separation between the mast and protected bus for the two bus heights A.
Maximum distance between two masts for side stroke
2
These values are the maximum separation of two masts for protection of bus at the three heights A.
Maximum distance between masts for vertical stroke sphere supported by four masts
Maximum distance between masts for vertical strike sphere supported by three masts
However, Q shall not be greater than X.
Figure B.24—Shielding a 500/230 kV substation using the rolling sphere method
B.4.5.3 Calculations for a 500 kV substation with shield wires 500 kV substation example—protection by shield wires (30.48 m)
These values are the maximum horizontal separation of shield wire and bus for protection at bus height A.
Maximum distance between two wires for vertical stroke D must be less than or equal to H – A for protection at height A.
1
1 H A
D D2 H A2
m
D1 13.72 D2 21.31m
1
1 S D
E E2 SD2
m
E1 26.04 E2 18.45m
2 1 2
1
S E
L L
2 S
2 E
22m
L1 30.05 L2 35.22m
1
1 2L
X X2 2L2
m
X1 60.1 X2 70.44m
These values are the maximum separation of shield wires for protection at bus height A.
B.4.5.4 Calculations for a 230 kV substation with shield wires 230 kV substation example—protection by shield wires (30.48 m)
These values are the maximum horizontal separation of shield wire and bus for protection at bus height A.
Maximum distance between two wires for vertical stroke D must be less than or equal to H – A for protection at height A.
1
1 H A
D D2 H A2
D
3 H A
3 mD1 21.95 D2 24.41m
D
3 18 . 59 m
1
1 S D
E E2 SD2
E
3 S D
3 mE1 3.39 E2 0.93m
E
3 6 . 75 m
2 1 2
1
S E
L L
2 S
2 E
22 L3 S2 E32 mL1 25.11 L2 25.32m
L
3 24 . 42 m
1
1 2L
X X2 2L2
X
3 2L
3m
X1 50.22 X2 50.64m
X
3 48 . 84 m
These values are the maximum separation of shield wires for protection at bus height A.
Figure B.25—Shielding a 500/230 kV substation with shield wires using the rolling sphere method
Table B.5—Summary of lightning protection calculations by the rolling sphere method shield wires—30.48 m (100 ft) high wire: separation of wires for
protection against vertical strikes Calculations Shield wire
height (m/ft) Collector
(m/ft) Wire separation for
high bus (m/ft) Wire eparation
for low bus (m/ft) Type of stroke
B.4.5.3 30.48/100 - 60.05/197 70.41/231 Vertical
B.4.5.3 30.48/100 - 6.10/20 13.41/44 Side
B.4.5.3 30.48/100 48.77/160 50.29/165 50.60/166 Vertical
B.4.5.3 30.48/100 3.35/11 5.79/19 8.23/27 Side
B.4.5.4 18.29/60 - 29.26/96 29.57/97 Vertical
B.4.5.4 18.29/60 - 2.74/9 3.96/13 Side
B.4.5.4 12.19/40 - 24.38/80 26.21/86 Vertical
B.4.5.4 12.1940 - 2.74/9 2.27/14 Side
Table B.6—Summary of lightning protection calculations by the rolling sphere method masts. Separation of masts for protection against vertical strikes.
Calculations Mast height (m/ft)
B.4.5.1 30.48/100 - 67.10/220 79.55/261 Vertical
(4 masts)
B.4.5.1 30.48/100 - 57.91/190 68.88/226 Vertical
(3 masts)
B.4.5.2 30.48/100 41.45/136 46.94/154 51.21/168 Side
B.4.5.2 30.48/100 56.08/184 58.52/192 59.74/196 Vertical (4 masts) B.4.5.2 30.48/100 48.46/159 50.60/166 51.51/169 Vertical (3 masts)