1. Effects of Changes in Shaft Load Shaft load is doubled – I a cosθ i and E f sinδ must double

2. Effects of Changes in Shaft Load Since Field Excitation is constant, E f traces a circular arc, δ increases θ i decreases, increasing the power factor – continues until δ=90  -- pullout

3. Effects of Changes in Field Excitation Voltage on Synchronous-Motor Performance Apply step changes to E f

4. Effects of Changes in Field Excitation Voltage on Synchronous-Motor Performance Apply step changes to E f E f sinδ must be constant

5. Effects of Changes in Field Excitation Voltage on Synchronous-Motor Performance Increasing the strength of the magnets should cause a closer pole alignment and a smaller power angle. Assuming a constant shaft load, –apply a step increase to E f –E f sinδ increases, the rotor accelerates –angle δ decreases until E f sinδ has the same value as before (synchronous speed)

6. Effects of Changes in Field Excitation Voltage on Synchronous-Motor Performance Apply step changes to E f E f sinδ constant I a cosθ constant

7. Effects of Changes in Field Excitation Voltage on Synchronous-Motor Performance For constant shaft load, –P is proportional to E f sinδ –E f1 sinθ 1 = E f2 sinθ 2 = E f3 sinθ 3 = E f sinθ –Locus of the tip of the E f phasor is parallel to the V T phasor –P is proportional to I a cosθ –I a1 cosθ 1 = I a2 cosθ 2 = I a3 cosθ 3 = I a cosθ –Locus of tip of the I a phasor is perpendicular to the V T phasor

8. Effects of Changes in Field Excitation Voltage on Synchronous-Motor Performance Apply step changes to E f E f sinδ constant I a cosθ constant

9. Effects of Changes in Field Excitation Voltage on Synchronous-Motor Performance IMPORTANT!!!! –Increasing the excitation from E f1 to E f3 caused the angle if the current phasor (and hence the power factor) to go from lagging to leading! –Normal excitation when power factor = 1 –Excitation greater than normal is known as overexcitation –Excitation less than normal is known as underexcitation

10. Effects of Changes in Field Excitation Voltage on Synchronous-Motor Performance Apply step changes to E f E f sinδ constant I a cosθ constant Power factor changes from lagging to leading

11. V Curves Plot armature current as a function of field current or armature current as a function of excitation voltage.

12. V-Curves

13. Stability Limit is where angle δ = -90° -- the rotor is still synchronized

14. V-Curves continued Constant-Load V-Curves can be plotted from laboratory data, phasor diagrams, or from the following expression

15. Example 8.2 Referring to the V-curve for 100% load, determine –a) the minimum value of excitation that will maintain synchronism 98V 100% rated load

16. Example 8.2 continued b) using Eq. (8 – 16)

17. Example 8.2 continued Repeat (a) using Eq. (8-21) Make the quantity under the radical = 0 for minimum excitation

18. Example 8.2 continued

19. d) the power angle if the field excitation voltage is increased to 175% of the stability limit determined in (c).