Design of LCL Filter and pre-Test for stability with PI-controller
In my simulation, I used LCL filter to reduce harmonic current and voltage. Most electric devices have inductors and capacitors. They will be had unnecessary loss of energy by harmonic voltage and current. So we need to make a clean sinus wave voltage and current to using our devices safely. In the Power system, They have criteria to make sure, the electric grid stay stable. That called THD (Total Harmonic Distortion). THD is a measurement of the harmonic distortion present in a signal and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency. It should be less than 5 %. For calculation of LCL filter, I assumed, that the design of the filter has a symmetry behavior and compensate mutual inductance active.
For calculation, I post the equations down below in this script which I found from IEEE. Also, I upload the MATLAB file and python script that I used for simulation.
I also tested for stability of LCL filter. The process is stable, but we need to consider the stability, when the system has some interruption. So I connected PI Controller and plot the result. The both system have some overshot and that can make some damage to electric device. So we need to cover up the overshot.
I connected a PI controller and make some variable value of kp and ki. The all kp and ki values are large enough to reduce overshot, but we can see in the graphic, that the bigger kp and ki value are, the faster output signal reach the reference value of 1. I also simulated with input data 400 V at 20 sec. In this graphic, we can clearly notice, that PI controller do very well.
Also, we can test stability with bode diagram. At -180°, the Magnitude is almost -45 so this system is stable.
