A. Power (P): 100 kW
B. Voltage (V): 11 kV
C. Power Factor: 0.9
D. Length of Transmission Line (L): 10 km
E. Resistance of Conductor (R): 0.05 ohms/km
F. ConducÆŸvity of Material (σ): 58 x 10^6 Siemens/m (for copper) G. Allowable Current Density: 1.2 A/mm²
Single-Phase System
1. Current Carrying Capacity (Ampacity)
I = P / (V x Power Factor)
P = 100 kW = 100,000 W
V = 11 kV = 11,000 V
Power Factor = 0.9
I = 100,000 W / (11,000 V x 0.9)
I = 100,000 W / 9,900
I ≈ 10.1 A
Why Calculate Current Carrying Capacity (Ampacity)?
Calculating the current carrying capacity, or ampacity, is crucial to ensure that the transmission line can handle the maximum current without overheating or causing damage. It helps determine the required conductor size and material.
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2. Voltage Drop
Voltage Drop = (L x I x R) / 1000
L = 10 km
I = 10.1 A
R = 0.05 ohms/km
Voltage Drop = (10 km x 10.1 A x 0.05 ohms/km) / 1000 Voltage Drop = (10 x 10.1 x 0.05) / 1000
Voltage Drop = 0.505 V
Why Calculate Voltage Drop?
Calculating the voltage drop is essential to ensure that the transmission line can deliver the required voltage to the load. A high voltage drop can result in reduced power quality and efficiency.
3. Conductor Sizing
A = I / (σ x Allowable Current Density)
I = 10.1 A
σ = 58 x 10^6 Siemens/m = 58,000 Siemens/mm²
Allowable Current Density = 1.2 A/mm²
A = 10.1 A / (58,000 Siemens/mm² x 1.2 A/mm²)
A = 10.1 A / 69,600
A ≈ 0.145 mm²
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Why Calculate Conductor Sizing?
Calculating the conductor sizing is necessary to determine the required cross-sectional area of the conductor to carry the maximum current without overheating or causing damage.
Three-Phase System
1. Current Carrying Capacity (Ampacity)
I = P / (√3 x V x Power Factor)
P = 100 kW = 100,000 W
V = 11 kV = 11,000 V
Power Factor = 0.9
I = 100,000 W / (√3 x 11,000 V x 0.9)
I = 100,000 W / 17,124.8
I ≈ 5.87 A
Why Calculate Current Carrying Capacity (Ampacity)?
Calculating the current carrying capacity for a three-phase system ensures that each phase can handle the maximum current without overheating or causing damage. This is crucial for maintaining power quality and efficiency in three-phase systems.
2.Voltage Drop
Voltage Drop = (2 x L x I x R) / 1000
L = 10 km
I = 5.87 A
R = 0.05 ohms/km
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Voltage Drop = (2 x 10 km x 5.87 A x 0.05 ohms/km) / 1000 Voltage Drop = (2 x 10 x 5.87 x 0.05) / 1000
Voltage Drop = 0.587 V
Why Calculate Voltage Drop?
Calculating the voltage drop in a three-phase system ensures that the transmission line can deliver the required voltage to the load, taking into account the increased current and resistance in three phase systems.
3. Conductor Sizing
A = I / (σ x Allowable Current Density)
I = 5.87 A
σ = 58 x 10^6 Siemens/m = 58,000 Siemens/mm²
Allowable Current Density = 1.2 A/mm²
A = 5.87 A / (58,000 Siemens/mm² x 1.2 A/mm²)
A = 5.87 A / 69,600
A ≈ 0.084 mm²
Why Calculate Conductor Sizing?
Calculating the conductor sizing for a three-phase system determines the required cross-sectional area of each conductor to carry the maximum current without overheating or causing damage, ensuring reliable operation.
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