Question $4$

A $23kw,230V,1500rpm$ DC shunt generator has an armature resistance $R_a=0\mathrm{.}2$ and shunt field winding resistance $R_{wf}=130.$ The number of turns of the shunt winding $N_f$ is $1200$ turns. Its rated field current is $1\mathrm{.}2$ A$.$ The magnetization curve at $1500$ rpm is shown in in Figure $5$

$($a$)$ The machine is operated as a separately excited DC generator.

$($i$)$ If the machine is rotating at $1500$ rpm $,$ determine its terminal voltage at full load condition and rated field current.

$($ii$)$ If the machine is rotating at $1000$ rpm $,$ determine its terminal voltage at full load condition and rated field current.

$($iii$)$ If armature reaction is equivalent to a reduction in the field current of $0\mathrm{.}05$ A $,$ determine the terminal voltage at operating condition similar to $($a$)($i$).$

$($b$)$ The machine is operated as a self$-$excited shunt DC generator and rotating at $1500$ rpm$.$

$($i$)$ Determine the field circuit control resistance $R_{fc}$ needed to generate a no$-$load voltage of $230$ V

$($ii$)$ Determine the terminal voltage at full load assuming an armature reaction is equivalent to a reduction in field current of $0\mathrm{.}05$ A $.$

$($c$)$ In order to improve the voltage regulation, the DC machine is connected as short shunt compound DC generator. Determine the required number of turns in the series winding to produce the no$-$load and full$-$load terminal voltages of $230$ V $.$ Assume the resistance of the series winding $R_{sr}=0\mathrm{.}1$

Figure $5$