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Bob S Potatoe

on 6 April 2014

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Steven Colussi
Cameron Collie
Bachelor of Electrical Engineering
Degree Project
Digital Power Factor Correction Boost Converter

Design of a digital boost rectifier with power factor control system scoped for a US/Canadian line voltage range (90-132V, AC) with an easy transition to European line range (180-264V, AC).

Using a Microprocessor as the PI controller, it will monitor the input and output of the converter and keep these ranges boosted at a constant 400V DC with a varying voltage of the ranges mentioned above.

Due to High Currents and for safety the design will be scaled down to 24V AC source boosted to a maximum of 40V DC with a 3700ohm load for testing.


Boost Converters

Also known as step-up converters, are used in the industry to boost from a DC input and steps up to a higher DC output.

Became widely used in the 1960’s as better switches were available with higher switching frequency with minimum switching power losses.

Boost Converter

Theory and Application

Used today to achieve more voltage while using fewer cells, able to achieve more power with less space and weight.

Ideal for
Electric and hybrid cars.
Inverters to raise the DC bus voltage
power factor correction.

With the switch open the Inductor forms a magnetic field to resist changes in current.

When the switch closes, a very high current will flow through the inductor, at this point the voltage right of the inductor is negative.

As the switch opens again the inductor’s magnetic field resists the current change causing a back flow of current and makes the voltage to the right of the inductor become positive.

Causing the diode to see a higher voltage drop then what is at the source, and causes the capacitor to be charged above source voltage. With precise switching speeds current and voltage can be controlled.

The switch is controlled using a feedback PI or PID controller

Traditionally the controller is analog but the advances of technology, using a digital controller makes the control and power factor correction(pfc) efficient over many systems and specifications.

The ratio of the real power to the load and the apparent power in the system.

Real power is the capacity of the circuit for performing work over time.

Apparent power is the product of the current and voltage.

A low power factor draws more current than a load with a high power factor for the same amount of useful power transferred.

If the power factor is .7 the apparent power would be 1.4 times the real power used by the load and losses would be doubled.

Power companies charge more to companies who have equipment running at low power factors or only allow equipment to be above a certain power factor limit, usually .90-.95. So companies need to use power factor correction to stay within these limits.

Power Factor Correction

Traditional methods is to have a PID controller that compares the voltage upstream of the inductor to the output of the current downstream of the inductor and adjusts for correction.

At unity power factor the two values should be linearly proportional.

This is considered automatic power factor correction.

An AC source of the universal line range from 90 to 285V

A diode full-bridge rectifier needed to rectify the AC signal to a DC Signal inverting it negative component.

Boost Converter

Inductor (L) and the capacitor (C) need to be designed around the switching frequency and the amount of output voltage ripple required.

Controlled with a PWM signal that duty cycles the MOSFET of the circuit, the switching frequency (fs) to be used is 100KHZ.

Simulating the max universal line voltage of 90-286 input voltage (Vin) and the output of 385V(Vo) keeping within a 400W output with a max load of 3700ohms.
Inductor current and the minimum inductor values:

To calculate the capacitor value the percentage of the maximum output voltage ripple is needed which is 2%.

To operate, the microprocessor must be able to read voltage just upstream of the inductor, and voltage at the load resistor output.

The circuit uses a 10 bit ADC with max 5 volt analog input. Identical voltage dividers step down the voltage to a value below the 5 volt limit.
ADC Conversion

Voltages will be stored as a 10-bit binary numbers.
2^10 = 1024 possible values 1023 steps

5 volts will register as 1023, and 0 volts will register as 0, and all in-between should be calculated as:
ADC output = Voltage (5V / 1023).

Power Factor Correction

Let the voltage just upstream of the inductor be Vi and the voltage at the output be Vo. From this we define duty cycle (D) and decay interval (D2). 

The boost converter inductor current iL(t) and Diode current id(t) will approximately follow the following patterns: 

We must condition the duty cycle to validate the average current sources.

You get the linear relation between input current and voltage that would accommodate a unity power factor.
The Single-pole transfer function is given below:

With this equation we need to find the proportional and integral gains of the transfer function, using the following equations:

Pole Frequency:

PI controller Zero:

Crossover Frequency of the voltage loop:
Inputs to the ADC:

Analog to Digital conversion:

Feed Forward Gain:

Pulse Wave Modulator (PWM):

Dc Gain:

Simulated in MATLAb’s Simulink.  

Powerlib add on to MATlab 

If changes to the design became necessary, they were added to the simulink model and tested
Values were calculated using previous eqns.

Ways in which this model does not fairly represent the actual system are as follows:

The generator, line, and transformer impedances are all simplified to an idealized one ohm resistor.

The analog to digital converter ADC is modeled as a gain rather than a conversion to 10 bit space.

Laplace transforms are used to predict the outcome of a unilateral z transfrom.
The pwm is modeled by a simple comparator and sawtooth.
Concept Design

a) Voltage At Source
b) Current At Source
c) Voltage At Output
d) Current At Output
Simulation Results
sqrt( 1 - Vi / Vo )
Error Signal
Ouput of PI Controller

The design used was based on a boost rectifier which converts 120 VAC to 400 VDC.
A lower voltage model was built. The lower voltage system is of equal complexity and follows the same principles. It allows us to lower currents, making the system safer to troubleshoot, as well as less expensive and more versatile.

The highest currents in the system occur across the mosfet. Current reaches 1.5 amps and can increase for changes in the load or source. Moreover, the gate floats high. If the gate of the mosfet is not properly grounded or connected to the pwm, then the transformer could short. This is essentially the most dangerous part of the circuit.

Interlocks are placed in the software for safety through control of the mosfet currents.

To protect from inrush currents the gate is held at ground until the output voltage goes above 5 volts for a full second. To protect from an over-voltage, the pwm goes to zero whenever the output voltage is above 50 volts.

In addition, a heat sink protects the mosfet itself from overheating.


The transformer is isolated in a metal enclosure. It’s primary has an isolating switch and a 2 amp fuse.


Parts were sized to tolerate the currents and voltages they endure.

Lab procedures were followed during fabrication. i.e. glasses and fume dispelling fan used when soldering, always mindful of proper grounding, etc....

Concept Design

Health And Safety

In analog implementation the PI controller would feed the signal into parallel proportional and integral op amp circuits, then sum them back together.

Need to simulate this with programming of a microprocessor.

Implemented Design

Programming and Code

ADC Readings


//Initaliazing pins as outputs
pinMode(A1, INPUT);
pinMode(A2, INPUT);
//Reading the analog value at the pins
InV = (analogRead(A2));
OutV = (analogRead(A1));


PWM signal of 100khz

Achieved by setting a 16MHz clock to have a top over flow of 159

Setting the output pin (OCR2B) between 0 and 159 will respectively give you 0-100% duty cycle.


TCCR2A = 0x23; // set pin high on overflow,clear on match
TCCR2B = 0x09; // select timer2 clock as unscaled 16 MHz
OCR2A = 159; //top/overflow value is 159
OCR2B=0; //start the duty cycle 0%

Constantly reading the Output Voltage (pin A1)

Comparing with the targeted output value

Ki value is multiplied by the error first and compared

Kp value gets multiplied by this error and then sums both these values added together.

double error = *mySetpoint - Vo; //computing error
ITerm+= (ki * error);
if(ITerm>outMax) ITerm = outMax; //compare with limits
else if(ITerm<outMin) ITerm = outMin;
double vc = kp * error + ki * error; //computing PI Value
Compute PI


double x = 1 - (VI/VO); //input and output voltages compared

double Compare = sqrt(x) * kf; // square rooted and multiplied by the gain

if(output >outMax) output = outMax;
else if(output <outMin) output = outMin
*myOutput = output; //set the final output duty cycle

if (voltage >targetVoltage) //comparing voltage with targeted
OCR2B=0; //output 0% duty cycle
else if(voltage <= targetVoltage)
OCR2B = output; //output duty cycle




AC source effectively have its voltage boosted and rectified by the method outlined in this report.

Semi-automatic method of power factor correction employed will indeed correct the power factor.
The simulation was successful in predicting the behavior of the boost rectifier.

Ripple was within acceptable parameters.
Applying to large scale model

Potential Future Work
PI to PID 

Adjust the kp and Ki when the voltage is within a certain dead band of it’s target range.  

Scaling Up the system 

More research could be done on how to adapt the existing system to a more specific application or even increase its versatility so it could be directed to multiple applications. (i.e electric cars)

High Currents initial design
High Floating Gate on Mosfet

Jump and Spikes
Bad Information
Software Issues
FPGA or Microprocessor

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