MCQs on Power Systems

01․ Find the surge impedance of a line when inductance is 160 mH and capacitance is 1µF?

Characteristic impedance Zc = V(x)/I(x) = √(Z/Y) = √(R + jωL)/(G + jωC) For loss less line. R = G = 0 Surge impedance Zs = √(L/C) Zs = √((160 * 10^-3)/(1*10^-6)) Zs = 400 Ω

02․ A transmission line has a surge impedance of 400 Ω is connected with the cable having surge impedance of 40 Ω, a surge magnitude of 100 kV is travelling from the transmission line towards the cable. Find the transmitted voltage?

Transmitted voltage V" = V + V' Transmitted current I" = I + I' Where, V' = Reflected voltage V = Incident voltage I' = Reflected current I = Incident current Transmission or reflection coefficient of voltage T_v = V"/V Transmission or reflection coefficient of current T_i = I"/I T_v = V"/V = 2Zl/(Z_l+Z_s) Where, Z_l = Surge impedance of load Z_s = Surge impedance of line Therefore, V" = 100*10³*2*40/440 = 18.18 kV

03․ A transmission line has a surge impedance of 400 Ω is connected with the cable having surge impedance of 40 Ω, a surge magnitude of 100 kV is travelling from the transmission line towards the cable. Find the incident current?

The voltage or current signals transmitting or travelling from source to load the load through the line are called incident waves. Incident current I = V/Z_s I = 100*10³/400 I = 250 A

04․ Counter poise is used for

Counter poise is connected to the ground wire and it is having parallel paths to discharge faster rate. For proper discharging of lightning surges from the top of the tower to the ground, earth wire is used which has low resistance and this earth wire is terminated with parallel paths of copper conductors which has impedance equal to surge impedance . This is called counter poise. It is used in sub stations which are connected between one tower to the other tower.

05․ Surge impedance loading (SIL) is represented by

Surge impedance loading SIL = 3*V_ph*I_ph Where, V_ph = Phase voltage I_ph = Phase current V_l = Line voltage SIL = 3*(V_l/√3)²/Z_s SIL = Vl²/Z_s Surge impedance Z_s = √(L/C) Therefore, SIL = V_l²*√(C/L)

06․ Surge impedance loading can be increased by

Surge impedance loading SIL = 3*V_ph*I_ph Where, V_ph = Phase voltage I_ph = Phase current V_l = Line voltage SIL = 3*(Vl/√3)²/Z_s SIL = Vl²/Z_s Surge impedance Z_s = √(L/C) Therefore, SIL = Vl²*√(C/L) Surge impedance loading can be increased by, 1. Increasing of voltage level 2. Increasing of capacitance value 3. Decreasing of inductance value

07․ A transmission line is compensated with shunt capacitance C_sh. If the uncompensated transmission line surge impedance is Z_s, then find the new surge impedance Z_n after shunt compensation?

Surge impedance Z_s = √(L/C) After shunt compensation new surge impedance Z_n = √(L/C(1 + K_csh)) Where K_csh = Degree of shunt capacitance = C_sh/C Therefore, new surge impedance Z_n = Z_s/√(1 + K_csh)

08․ A transmission line is compensated with shunt capacitance Csh. After shunt compensation surge impedance loading will

Surge impedance Zs = √(L/C) Surge impedance loading SIL = Vl² *√(C/L) After shunt compensation new surge impedance Zn = √(L/C(1 + Kcsh)) Where Kcsh = Degree of shunt capacitance = Csh/C Therefore, new surge impedance Zn = Zs/√(1 + Kcsh) New surge impedance loading SILn = SIL*√(1 + Kcsh) Therefore after compensation surge impedance loading will increase and surge impedance will decrease.

09․ Which of the following represents the transmission or reflection coefficient of voltage Tv? (Zl = Surge impedance of load, Zs = Surge impedance of line)

Transmitted voltage V" = V + V' Transmitted current I" = I + I' Where, V' = Reflected voltage V = Incident voltage I' = Reflected current I = Incident current I" = V"/Zl, I = V/Zs, I' = -V'/Zs V"/Zl = V/Zs - V'/Zs V' = V" - V Therefore, Tv = V"/V = 2Zl/(Zl + Zs)

10․ Reflection coefficient of voltage is Rv

Transmitted voltage V" = V + V' Transmitted current I" = I + I' Where, V' = Reflected voltage V = Incident voltage I' = Reflected current I = Incident current Transmission or reflection coefficient of voltage Tv = V"/V Transmission or reflection coefficient of current Ti = I"/I I" = V"/Zl, I = V/Zs, I' = -V'/Zs V"/Zl = V/Zs - V'/Zs V' = V" - V Therefore, Tv = V"/V = 2Zl/(Zl + Zs) Tv = V"/V = 2Zl/(Zl+Zs) Reflection coefficient of voltage is Rv = Tv - 1 Rv = (Zl - Zs)/(Zs + Zl)