- 2068 Magh · 6 marks
Active power between machines, 200∠0° and 200∠15° V
Short answer
Active power per phase P = (200×200/10) sin(0°−15°) = −1035.28 W, so 1.035 kW flows from machine B to A (three-phase 3.106 kW). B is generator, A motor because V_B leads V_A by 15°.
Two 3-phase synchronous machines A and B are connected by a link having series impedance of 0 + j10 Ohms/phase. The terminal voltages at machines A and B are 200∠0° V and 200∠15° V respectively. Compute the magnitude and direction of active power flow through the link.
For a purely reactive link the real power transfer is
and it flows from the machine with the leading angle to the one with the lagging angle.
Calculation (per phase)
The negative sign means the power actually flows from B to A.
Check with phasors:
So A receives 1035.28 W and B delivers 1035.28 W. The link has no resistance, so there is no real-power loss. Each machine supplies 136.30 var to the link ( var).
| Quantity | Per phase | Three-phase |
|---|---|---|
| Real power B → A | 1035.28 W | 3105.83 W |
| Reactive loss in link | 272.59 var | 817.78 var |
Answer: About 1.035 kW per phase (3.106 kW three-phase) flows from machine B to machine A. B acts as the generator and A as the motor, because leads by 15°.
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Reactive power flow between machines via j10 Ω · Power System Analysis I, chapter 3
- Two machines 3.81∠0° and 3.81∠-18° kV · Power System Analysis I, chapter 3
- Direction of active and reactive power flow · Power System Analysis I, chapter 6
- Two generators 200∠30° and 210∠50° V · Power System Analysis I, chapter 3
- Two machines 100∠0° and 120∠30° V via j5 Ω · Power System Analysis I, chapter 3
- Two sources via 0 - j5 Ω: power flow · Power System Analysis I, chapter 3
- Reverse power flow in bipolar HVDC link · Power Electronics, chapter 7
- Resultant magnitude, direction and position of forces · Applied Mechanics, chapter 3
- Two-port impedance model and series connection · Filter Design, chapter 4
- L-G fault through Zf: currents and voltages · Power System Analysis II, chapter 5