OPTIMIZATION OF ANGULAR FREQUENCY OF ENERGY CONVERTER FOR FRICTIONLESS WAVE POWER ENERGY GENERATION-PENDULUM SYSTEM USING THE EULER-LAGRANGE EQUATION AND THE RUNGE-KUTTA METHOD

 ABSTRACT

A research about optimization of angular frequency of energy converter for frictionless Wave Power Energy Generation-Pendulum System (WPEG-PS) has been carried out. This research aims to determine the dimension of the pendulum components and wheel system. Optimization is done to obtain the size of the system components that produce optimum angular frequency of the generator. This determination is carried out through four main stages which are preliminary design, formulation of equations of motion, numerically solving the equations of motion and power system optimization. Preliminary design refers to the design of an integrated system consisting of pendulum motion, double freewheel and wheel system. The equations of motion of the generating system is derived from a Lagrange function which is a formulation of rotational kinetic and potential energy of the systems. The Lagrange function is subsequently solved using the Euler-Lagrange equation with an assumption that the system does not experience friction force. The solution to equation of motion is sought numerically using the Runge-Kutta method using 7.01 Matlab software. Numerical solutions of the equations of motion is sought by programming and variying parameters. The variations is carried through until the optimum angular frequency of the fourth wheel is found. The optimization results in the angular frequency of the fourth wheel is 138.11 rad/s. This angular frequency value is obtained after entering input values by the mass, the center of mass, and the inertia of the pendulum 8 kg, 0.9 m, 1.4 kgm2 but radius and inertia of wheels 1, 2, 3, and 4 are 0.4 , 0.25, 0.05, 0.02m, and 0.4, 0.125, 0.001875, 0.00005 kgm2.