A small town with a demand of 800 kW of electric power at 220 V issituated 15 km away from an electric plant generating power at 440 V.The resistance of the two wire line carrying power is 0.5 W per km.The town gets power from the line through a 4000-220 V step-downtransformer at a sub-station in the town. (a) Estimate the line power loss in the form of heat. (b) How much power must the plant supply, assuming there isnegligible power loss due to leakage? (c) Characterise the step up transformer at the plant.
Given: The total electric power required is 800 kW , the applied voltage is 220 V , the generating voltage is 440 V , the distance between the town and power generating station is 15 km , the resistance of two wire lines is 0.5 Ω / km , the input voltage is 4000 V and the output voltage is 220 V .
The total resistance of the wires is given as,
R = 2 d × r
Where, the distance between the town and power generating station is d and the resistance of two wire per km is r .
By substituting the given values in the above equation, we get
R = ( 2 × 15 ) × 0.5 = 15 Ω
The rms value of current flowing in the wire lines is given as,
I = P V 1
Where, the total required electric power is P , the input voltage is V 1 .
By substituting the given values in the above equation, we get
I = 800 × 10 3 4000 = 200 A
a)
The line power loss is given as,
P 1 = I 2 R
By substituting the given values in the above equation, we get
P 1 = ( 200 ) 2 ( 15 ) = 600 × 10 3 W = 600 kW
Thus, the line power loss in the form of heat is 600 kW .
b)
Since, due to the leakage current the power loss is negligible.
The total power supplied by the plant is given as,
P 2 = P + P 1
By substituting the given values in the above equation, we get
P 2 = 800 + 600 = 1400 kW
Thus, the power supply from the plant is 1400 kW .
c)
The voltage drop in the power line is given as,
V = I R
By, substituting the given values in the above equation, we get
V = 200 × 15 = 3000 V
The total voltage transferred from the plant is given as,
V t = V + V 1
By substituting the given values in the above equation, we get
V t = 3000 + 4000 = 7000 V
Thus, the rating of the step up transformer at the power plant is 440 V − 7000 V .
Given: The total electric power required is
The total resistance of the wires is given as,
Where, the distance between the town and power generating station is
By substituting the given values in the above equation, we get
The rms value of current flowing in the wire lines is given as,
Where, the total required electric power is
By substituting the given values in the above equation, we get
a)
The line power loss is given as,
By substituting the given values in the above equation, we get
Thus, the line power loss in the form of heat is
b)
Since, due to the leakage current the power loss is negligible.
The total power supplied by the plant is given as,
By substituting the given values in the above equation, we get
Thus, the power supply from the plant is
c)
The voltage drop in the power line is given as,
By, substituting the given values in the above equation, we get
The total voltage transferred from the plant is given as,
By substituting the given values in the above equation, we get
Thus, the rating of the step up transformer at the power plant is
