Power Flow within a Synchronous Motor
Power Flow within a Synchronous Motor:
- Different power stages in a synchronous motor are as under:
- Let R_{a} = armature resistance / phase ; X_{S} = synchronous reactance / phase, then
- The angle θ (known as internal angle) by which I_{a} lags behind E_{R} is given by tan θ = X_{S} / R_{a}.
- If Ra is negligible, then θ = 90º. Motor input = V I_{a} cos φ —per phase
Here, V is applied voltage / phase.
Total input for a star-connected, 3-phase machine is, P = √3 V_{L} . I_{L} cos φ.
- The mechanical power developed in the rotor is
P_{m} = back e.m.f. × armature current × cosine of the angle between the two i.e., angle between I_{a} and E_{b} reversed.
= E_{b} I_{a} cos (α − φ) per phase
Out of this power developed, some would go to meet iron and friction and excitation losses. Hence, the power available at the shaft would be less than the developed power by this amount. Out of the input power / phase V I_{a} cos φ, and amount I_{a}^{2} R_{a} is wasted in armature, the rest (V. I_{a} cos φ − I_{a}^{2} R_{a} ) appears as mechanical power in rotor; out of it, iron, friction and excitation losses are met and the rest is available at the shaft. If power input / phase of the motor is P, then
- The per phase power development in a synchronous machine is as under: