This paper presents the state space modeling and simulation of different micro electrostatic energy harvesters – in plane overlap, in plane gap closing and their compound structures – with freedom of movement in x, x-y and x-y-z axis. The structures are specially designed for energy harvesting of vibrations whose frequencies are lower than 100 Hz to be suitably applied for heartbeat energy harvesting. The detail models of both electrical and mechanical subsystems including stopper function, motion drag, parasitic capacitors and multi directional transducing capacitors are developed in the format of state space equations. To reach the optimal heartbeat energy harvesting, the system behavior is simulated under different parameters by numerical solution of nonlinear state space equation set.

A two-dimensional analytical model is proposed for slotless brushless machines with arc-shaped spoke permanent magnets assisted by hub magnets to calculate the magnetic field distribution due to magnets and armature reaction, the electromagnetic torque, and back electromotive force. To verify the model, the analytical results of the field distribution, electromagnetic torque and back electromotive force have been compared with those achieved from finite element method. Moreover, this model is used as an equivalent analytical model for a cubic spoke motor, and it is shown that the proposed equivalent sub domain model satisfactorily estimates the electromagnetic quantities.