$1.$ A three phase, four pole, $50$ Hz$,$ delta connected induction machine$$s parameters are given below; Vrated$=400$ V nrated$=1450$ rpm Tfriction$=2$ Nm R$1=0\mathrm{.}45$ X$1$$0=1\mathrm{.}85$ R$2=0\mathrm{.}55$ X$2$$0=2\mathrm{.}2$ Rfe $=400$ Xm $=150$ Using T$-$equivalent circuit and considering steady state, plot the following from zero to double the synchronous speed.

a$)$ Calculate and plot the torque$-$speed curve of the machine. Specify the breakdown torques for different regions. b$)$ Plot the input current $$ speed curve. c$)$ Plot the variation of the rms induced voltage with respect to speed. d$)$ Plot the copper losses, iron losses and total losses with respect to speed. e$)$ Plot the total input active power and reactive power with respect to speed. f$)$ Plot the efficiency versus speed. g$)$ Plot the power factor versus speed. h$)$ Calculate the prime mover torque and speed for generating $($supersynchronous operation$)10$ kW of power. Find the current, power factor and efficiency for that case. PS$.$ Please use MATLAB to write your scripts and draw your graphs for this question.