0195136047.pdf

470 AC POWER SYSTEMS

IR

+

−

+

−

VS = VS ∠δ VR = VR ∠^0 °

IS Z = jX

Figure P10.3.1Simple model of loss-

less transmission line.

IR

+

−

+

−

VS VR

IS

Two-port

network

Sending end Receiving end

Figure P10.3.3

10.3.10On a per-phase basis, letv=

√

2 Vcosωtand

i=

√

2 Icos(ωt−θ).

(a) Express the instantaneous powers(t) in terms

of real powerPand reactive powerQ.

(b) Now consider the energyEassociated with

the instantaneous power and show thatE=

Pt, wheretis the duration of the time interval

in seconds.

10.3.11A 60-Hz, three-phase transmission line has a total
per-phase series impedance of 35+j 140 .Ifit
delivers 40 MW at 220 kV and 0.9 power factor
lagging, find:

(a) The voltage, current, and power factor at the

sending end of the line.

(b) The voltage regulation and efficiency of the

line.

10.3.12A three-phase, 60-Hz transmission line has a total

series impedance of 22. 86  62 .3°per phase. It

delivers 2.5 MW at 13.8 kV to a load connected

to its receiving end. Compute the sending-end

voltage, current, real power, and reactive power

for the following conditions:

(a) 0.8 power factor lagging.

(b) Unity power factor.

(c) 0.9 power factor leading.