Consider the AC Power transmission system sketched in Fig. 3. The RMS generator

Question

Consider the AC Power transmission system sketched in Fig. 3. The RMS generator AC voltage is y1 110 V and the number of windings on the primary coil of the ideal transformer N1 = 5(n). The transmission line (between the transformers) is made of copper wire with a radius of 1 cm and has a total length of 50 km The resistivity of copper is p= 1.7x10^-8 Omega m. (a) Determine the resistance of the transmission line. (b) There is a total power consumption of 200 kW by consumers. Determine the load resistance RL (c) Determine N3 and the voltage of the transmission line required to keep the transmission losses in RT below 10% of the power delivered to the load RL. Use that i1v1 it across each transformer, (d) Determine the fraction of power delivered by the source that would go to the consumer if there were no transformers and the generator was connected to the load directly with the copper transmission lines.

Explanation / Answer

Apply in a transforner   Ns/Np = Vs/Vp = Ip/Is

where NS ans Np are seconda dr and primary tunrs

Vs and Vp are secondary and primary volatges

Is and Ip are secondary and prianry currents

also in ideal tansformer output P = input P

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here for Resistance we use R = rho L/A

where rho is resistivity of copper =1.67 e -8 ohm m

so

R = 50000 * 1.67 e-8/(3.14 * 0.01* 0.01)

R = 2.659 Ohms

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apply In put Power = out put power

V1i1 = V2^2/R

RL = 110*110/ 200000

Rl = 0.0605 ohms

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