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

A comprehensive explanation of PLL together with its design using Matlab Simulink

New

Created bySiva Sylesh

Last updated 6/2026

English

What you'll learn

A concise understanding of a Phase locked loop
Physics and Mathematics behind the design of a PLL
Design of the Phase locked loop using Matlab Simulink
Use cases of PLL in different inverters and OBCs of EVs

Course content

1 section • 5 lectures • 1h 14m total length

Introduction22:49
The lecture 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.
PLL Controller Design17:20
A detailed explanation on the control strategy of the PLL is explained in this lecture. How the abc phases are converted into a stationary alpha, beta frame and how a rotating frame is then designed using a PI controller to monitor and lock the grid frequency and phase.
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.
Design of a PLL using Matlab Simulink26:09
A comprehensive design of a PLL to monitor a 50Hz and 60Hz frequency AC Grid is designed and simulated using matlab Simulink.
A simulink model is created from the scratch to illustrate the design of each element in the PLL. The model is simulated and the results are illustrated.
The lecture also focuses on the tuning of the PID controller for a faster response of the PLL.
This lecture also acts as a simulink modelling lecture.
PLL Use case 1: Solar PV3:17
In this lecture , a use case of Solar PV installation is given wherein the use of PLL is illustrated while feeding the solar energy back to the grid.
The MPPT or the maximum power point transfer is explained. The use of an intermediary DCD converter and then the method of converting DC to the AC is mentioned.
The significance of the PLL in the solar PV is this illustrated.
PLL use Case 2: OBC in EVs with V2G capabilities4:59
A use case of an EV with bidirectional charging capability to support V2G functionality has been explained in this lecture and also the significance of the PLL in the On Board charger of such an EV is illustrated.
The design of the OBC is shown as an outline.
The example of the OBC design in the Charging scenario as wall as the reuse of this architecture in the discharging scenrio together with the PLL is thus illustrated.

Requirements

You will learn everything in this course about PLL

Description

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.

Who this course is for:

Electrical Engineers, Physics Grads,