Question: 5.24 | Electric Machinery Consider a synchronous generator operating a

Question

Question: 5.24 | Electric Machinery

Consider a synchronous generator operating at its rated terminal voltage whose synchronous reactance is 2.0 per unit, whose terminal current cannot exceed its rated value and whose maximum field current is limited to 1.75 times that required to achieve rated terminal voltage under open-circuit conditions. a. What is the maximum per-unit real power which can be supplied by the machine such that the machine can continue to operate at its rated armature current? What is the corresponding per-unit reactive power and power factor? b. What is the maximum per unit reactive power that can be supplied by this machine?

Explanation / Answer

Let

Terminal Voltage of generator V = 1 p.u

Rated armature current I = 1 p.u

Synchronuous rectance Xs = 2 p.u

Excitation Voltage E = V + (jXs)*I = 1 + (j2)*1 = 1+j2

Magnitude of excitation voltage Emag = 2.236

delta = 63.430

a)

Maximum real power supplied by generator is Pm = E*V/Xs = 2.236 *1/2 = 1.118 p.u i.e when delta = 900

Real power supplied by this generator P = (E*V/Xs) *sin(delta) = (2.236*1/2)*sin(63.43) = 0.999 p.u

Reactive power supplied by generator is Q = E2 / Xs - (E*V/Xs) cos(delta) = 2.2362 / 2 - ((2.236*1)/2) * cos(delta)

= 2.4999 - 0.5 = 1.999 p.u

Power factor pf = cos(tan-1 (Q/P) ) = cos ( 63.43) = 0.44

b)

Maximum reactive power supplied by this generator is Qmax = 2.4999 p.u

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.