Section 14.7: Performance of a Round-Rotor Synchronous Motor cont.
3810/d V. = 3810/0° V. + 10.4/89.6° W ´ 218.7/q A.
3810/d = 3810/0° + 2274.48/89.6°+ q
3810/d = [3810 + 2274.48 cos(89.6°+ q)] +j 2274.48 sin(89.6°+ q)
Then by the Pythagorean Theorem,
38102 = [3810 + 2274.48 cos(89.6°+ q)]2 + [2274.48 sin(89.6°+ q)]2
Which yields cos(89.6°+ q) = -0.2984 ergo,
89.6°+ q = cos-1(-0.2984) = 107.4° \
q = +17.76° so that cosq = 0.952 and the power factor is …
0.952 Lead (since Ia leads Vt by q = +17.76° )