Abstract:
The depletion of oil reserves, demand for electricity, frequent power shortage and the need to have
an environmentally friendly power have led to a number of research geared towards this course.
This study employs the use of a motor to run the generator instead of diesel which causes global
warming due to gas emission to the environment. A mathematical model of the motor-generator
coupled power system is formulated and used to amplify and rectify the solar voltage for
commercial purposes. Detailed mathematical derivations have been presented and represented in
the transfer function within the Simulink. Nonlinear least square, gradient descent and the simplex
search were the methods used to determine the effective parameters of the system. From the
simulation of the parameters, it was found that the curve of the gradient descent converges to that
of the experimental data and the values obtained from the gradient descent were taken for stability
analysis. Routh-Hurwitz, Nyquist criterion and Bode plot were used to test system the stability.
Routh-Hurwitz method confirmed that the system was stable for a third order system while the
Nyquist criterion showed that the number of poles with positive real parts were zero and the
number of counter clockwise encirclement of (-1,0) was zero. The Bode plot phase margin was
99.5o
and the gain margin was 51.6 db. The gear ratio that maintained the stability of the system
was found to be 1 < 𝐺𝑟 < 35 and the excess voltage was achieved when the 𝐺𝑟 > 2 . This
work contributed to the field of control system, system identification and stability analysis where
the accuracy of parameter identification in control system are needed.
