Effect of Load P.F. on Regulation and Efficiency

Effect of Load P.F. on Regulation and Efficiency

AU : Oct-96, 2000, May-06, 07, 08, Dec.-12, 17

The load p.f. has considerable effect on the regulation and efficiency of transmission line.

Consider the approximate expression for V_S

This expression is valid for lagging power factor. In case of leading power factor the expression for voltage regulation is given by,

When the load power factor is lagging or unity such that IR cos ϕ_R > IX_L sin ϕ_R then the voltage regulation is positive. It indicates that the receiving end voltage V_R is less than sending end voltage V_S.

With decrease in the power factor in case of lagging loads, the voltage regulation of the line increases for given values of V_R and I.

If the load power factor is such that IX_L sin ϕ_R > IR sin ϕ_R, then voltage regulation is negative which indicates that receiving end voltage VR is more than the sending end voltage V_S.

For leading power factor loads, the voltage regulation of the line decreases with decrease in p.f.

The phasor diagram for lagging load, unity p.f. load and leading p.f. load is shown in the Fig. 2.7.1.

The angle between V_R and V_S is called power angle and denoted as δ.

The power delivered to the load depends upon the power factor. For single phase circuit power is given by,

It can be seen that for a given power transmitted (P) at the voltage (VR) at the receiving end, the load current I is inversely proportional to the load power factor, cos ϕ_R. If the load p.f. is low then current and hence losses will be more which will decrease transmission efficiency.

Example 2.7.1 Find the distance over which a load of 15000 kW at a p.f. of 0.75 lagging can be delivered by a 3 phase transmission line having conductors each of resistance 2 Q per kilometer. The voltage at the receiving end is 132 kV and the loss in the transmission is to be 5 %. 

Solution : Load = 15000 kW, cos ϕ_R = 0.75 lagging, R per kilometer = 2 Ω

V_R = 132 kV

Loss in line = 5 % of power delivered

Example 2.7.2 A 15 km long 3 phase overhead line delivers 5 MW at 11 kV at 0.8 lagging p.f, line loss is 12 % of power delivered. Line inductance is 1.1 mH per km per phase. Find the sending end voltage and regulation.

Solution : Load p.f., cos ϕ_R = 0.8 lagging ϕ_R = 36.86°

Example 2.7. 3 A short 3-phase transmission line with an impedance of (6 + j8) Q per phase has sending and receiving end voltages of 120 kV and 110 kV respectively for some receiving end load at a pf of 0-9 lagging. Determine power output and sending end power factor.

AU : May-07, Marks 8

Solution :

Example 2.7.4 A three - phase transmission line having a series impedance of (20 + j30) Q delivers 7 MW at 33 kV and 0.8 lagging power factor. Find the sending end voltage, regulation and power angle. Neglect shunt capacitance.

Solution :

Review Questions

1. Explain the influence of power factor on the performance of a transmission line.

2. A single phase overhead transmission line delivers 1100 kW at 11 kV at 0.8 p.f. lagging. The total resistance and inductive reactance of the line are 8 and 16 respectively. Determine i) Sending end voltage ii) Sending end power factor iii) Transmission efficiency iv) Percentage regulation. 

[Ans : 13.038 kV 4.398,0.7518 lagging, 89.79 %, 18.52 %]

3. An overhead 3 phase transmission line delivers 3000 kW at a 0.8 pfl lagging to a load. The resistance and reactance of each conductor is 4 and 6 respectively. If the sending end voltage is 33 kV, determine i) Sending end voltage ii) Transmission efficiency.

[Ans.: 31.96 kV, 99.24 %]

4. A three phase, 11 kV, 50 Hz, transmission line 10 km long delivers a load of 5 MW at 0.8 pfl lag at the far end. The resistance and reactance per phase, per km are 0.1 and 0.2 ohm respectively. Find sending end voltage, current and pfl Also draw the phasor diagram. Treat the line as a short

AU : Oct.-96

[Ans.: 7.01 kV, 328.03 A, 0.7711 lag]

5. A 3-phase 5 km long transmission line, having resistance of 0.5 Ω / km and inductance of 1.76 mH/km is delivering power at 0.8 p.f. lagging. The receiving end voltage is 32 kV. If the supply end voltage is 33 kV, 50 Hz find 1) Line current 2) Regulation and 3) Efficiency of the transmission line.

[Ans.: 31.108 A, 3.156 %, 98.44 %]

6. Derive expressions for regulation and efficiency of a short transmission line. Draw required circuit and phasor diagram.

7. Draw the phasor representation of short transmission line.