Example $3$

A $208-$V$,60$Hz$,$ three$-$phase, Y$-$connected, salient$-$pole, synchronous motor operates at its full load and

draws a current of $40$ A at $0\mathrm{.}8$ pf lagging. The d $-$ and q$-$axis reactance are $2\mathrm{.}7(\backslash$Omega $)/()$ phase and $1\mathrm{.}7(\backslash$Omega $)/()$ phase,

respectively. The armature winding resistance is negligible, and the rotational loss is $5\%$ of the power

developed by the motor. Determine:

a$->$P$\_($df$)=$Asin$\backslash$alpha

c$->$P$\_($ds$)=$Bsin$2\backslash$alpha

d$->$P$\_($df$)+$P$\_($ds$)$

V$=$E$\_($b$)+$K$\_($a$)$I$\_($a$)+$jx$\_($q$)$I$\_($a$)+$jI$\_($d$)($x$\_($d$)-$x$\_($q$))$

e$->$ @ $\backslash$alpha $\_($m$)->\backslash$alpha $\_($m$)=-$cos$^(-1)[(-$A$+\backslash$sqrt$($A$^(2)+32$B$^(2)))/(8$B$)]$