Example $5-2.$ A $480-$V$,60-$Hz$,-$connected, four$-$pole synchronous generator has the OCC shown in Figure $.$This generator has a synchronous reactance of $0\mathrm{.}1$ and an armature resistance of $0\mathrm{.}015.$ At full load, the machine supplies $1200$ A at $0\mathrm{.}8$ PF lagging. Under full$-$load conditions, the friction and windage losses are $40$ kW $,$ and the core losses are $30$ kW $.$ Ignore any field circuit losses.

$($a$)$ What is the speed of rotation of this generator?

$($b$)$ How much field current must be supplied to the generator to make the terminal voltage $480$ V at no load?

$($c$)$ If the generator is now connected to a load and the load draws $1200$ A at $0\mathrm{.}8$ PF lagging, how much field current will be required to keep the terminal voltage equal to $480$ V $?$

$($d$)$ How much power is the generator now supplying? How much power is supplied to the generator by the prime mover? What is this machine's overall efficiency?

$($e$)$ If the generator's load were suddenly disconnected from the line, what would happen to its terminal voltage?

$($f$)$ Finally, suppose that the generator is connected to a load drawing $1200$ A at $0\mathrm{.}8$ PF leading. How much field current would be required to keep $V_T$ at $480$ V $?$