Theory and Physics of Phase locked loop (PLL) & Design

The course provides a detailed and comprehensive explanation of the PLLs used in Inverters, OBCs in EVs and any other Grid tied inverter use cases.

The course explains the mathematics behind the Clarke and the Park transforms used in the PLL.

A detailed mathematical matrix is created to explain how the 3 dimensional phase vectors are constituted into their 2 Dimensional stationary frame and further into a rotating frame of reference.

During the creation of the matrices, the resolution of the voltage vectors in to the respective alpha, beta during the Clarke transform and the d, q during the Park transform is clearly explaned.

A Matlab Simulation is then explained with design of the PLL from the scratch and to monitor a grid frequency of 50 and 60Hz in the two trials.

A PI controller is designed to lock the created rotational frame of referencee using the Park transform to the actual grid voltage vector. The PI controller is then tuned to ensure that the lock on happens quickly and as per the design requirements.

An example of the grid’s nature is explained through the physics of synchronous generators and how the real load effects the spped of the generator and how the designed PLL can take care of these change instantaneously to always remain grid locked.

In the Matlab simualtion , a short design of the frequency calculation was done to show the PLL locking on to the set grid frequencies of 50Hz and 60 Hz.

This illustration clearly explains how the PLL works in locking the grid frequency.

Two use cases of PLL i.e in Solar PV installations and also in the On board Chargers of Bi-directional capable EVs to support V2G functions are explained. The significance of PLL in each of those two use cases was illustrated.