SYSTEMS

SEMESTER GROUP PROJECT

Prepare your report in computer with all your study details.

The figure shows the $10$ MW wind generator system. The equation for aerodynamic torque from the wind $=12$p$..$R$3.$V$2$

The wind turbine in the figure has a radius of $45\mathrm{.}6$ m $,$ moment of inertia of $1\mathrm{.}26e7kg.m2,$ the friction coefficient of $1100Nm.\frac{s}{r}ad,$ torque coefficient of $0\mathrm{.}075,$ while the generator has a moment of inertia of $240kg.m2,$ friction coefficient of $0\mathrm{.}1Nm.\frac{s}{r}ad,$ load torque of $120{}^{}2Nm.$ The wind speed is $13\frac{m}{s}$ at $t=0.$ Gear $1$ and gear $2$ radiuses are $0\mathrm{.}93$ m and $0\mathrm{.}01$ m $,$ respectively.

a$)$ Obtain the mathematical model of given wind generator system $($mathematical equations, state space matrix form, block diagram$).$

b$)$ Calculate the constant angular velocities of the turbine and the generator at $t=0$ and find the transfer function of the turbine angular velocity. c$)$ If when $t=10s,$ the wind speed changes from $13\frac{m}{s}$ to $15\frac{m}{s}$ with a constant acceleration of $0\mathrm{.}25\frac{m}{s}2,$ obtain the angular velocities waveform of the turbine and the generator by using Simulink. Use the initial conditions calculated in $($b$).$