SIMULATION OF A DC-DC BOOST CONVERTER(USING MATLAB) (ELEC5564 COURSEWORK 2)

WRITTEN BY

OLADAPO Opeoluwa Ayokunle(200581534)

SUBMITTED TO

Dr. Li ZHANG

SCHOOL OF ELECTRONIC & ELECTRICAL ENGINEERING THE UNIVERSITY OF LEEDS LEEDS LS2 9JT

24 November 2010

AIMS AND OBJECTIVESThe aims of the exercise include; To improve the understanding of a DC-DC Boost converter by practising converter design

calculations To understand and describe the equations, methods and/or algorithms that are commonly

used in modelling and analyzing a DC-DC Boost converter To simulate the output voltage/current, input voltage/current variation with time at

different operating conditions To study the effects of sampling step on the precision and accuracy of the program

simulation To study the effects of various parameters including; output capacitor value, input inductor

value and duty ratio on the current ripple, voltage ripple, variations from transient state to steady state and generally, the behaviour of a DC-DC Boost converter

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PRINCIPLES OF OPERATION OF A DC-DC BOOST CONVERTERThe DC-DC boost converter is an example of a classical switched-mode power supply circuit which is mostly used for power applications having the output voltages higher than the input voltages. The DC-DC converter is also used to regulate the dc output voltage under varying load and input voltages.

Equivalent Circuit model of a DC-DC Boost converterThe circuit of a boost converter is shown in figure 1 below; L + VL Vi + VSW C iL D iC VC VO R iO

Figure 1: DC-DC Boost converter circuit

The switching signal to the switch (typically a MOSFET switch) is usually a pulse-width modulated (PWM) signal which consequently turns the switch ON and OFF. The duration of the ON and OFF (i.e. the switching sequence) is determined by the duty ratio of the PWM signal and their sum is equal to the switching period. The circuit goes from its initial transient state when the inductor current and capacitor voltage build up to a steady state. When the switch is ON, the diode is reverse bias and the circuit is separated into two parts as shown in figure 2.The left part of the circuit shows the dc supply voltage charging the inductor while the right shows that the output capacitor maintains the output voltage using previously stored energy. When the switch is OFF as seen in figure 3, both the dc supply voltage and energy stored in the inductor will charge the output capacitor and also supply power to the load hence the output voltage is boosted1 as shown by equation 1.

where

is output voltage,

is input voltage and

is the duty ratio.

Once more, the output voltage can be maintained at the constant required level by changing the duty ratio and consequently controlling the switching sequence.

1

http://fayazkadir.com/blog/?page_id=460

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Ned Mohan, Tore M. Undeland and William P. Robbins, Power Electronics: Converters, Application and Design

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L + vL VIL1

iL ic vc

io

C VoL2

R

Figure 2: DC-DC Boost converter circuit (when switch is ON)

L + vL VIL3

iL

D ic

P+v

io

C

c -

VoL4

R

Figure 3: DC-DC Boost converter circuit (when switch is OFF)

State-Space model for a DC-DC Boost ConverterThe switching devices are assumed to be ideal thus the dc-dc boost converter circuit varies as a function of time as a result of the switching action. The state of a system is defined by the values of fundamental variables (the state variables) describing its state-space model. For the dc-dc boost converter being considered, the state variables defining the system are the capacitor voltage VC and the inductor current iL. The other variables being considered are the output current and the input voltage. The state-space describing the ON and OFF states are enumerated as follows; SWITCH ON

Handout ELEC5564 Power Generation By Renewable Sources, Section 2, Power Converters and Applications to Renewable Generation

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4

SWITCH OFF

SWITCHED STATE-SPACE MODEL The equations 4 and 8 can be combined to give a state-space model equation which describes the circuit operation. This resulting equation in equation 10 is referred to as a switched state-space model.

where D(t)=0 at switch off and D(t)=1 at switch on. The equations 9 and 10 can be compared to equations 11 and 12 respectively;

where

,

,

,

,

,C=

,

.

Numerical Solution of Ordinary Differential Equations (ODE)The fundamental concept of the numerical solution of ordinary differential equations is that of combining evaluated function values at different times in order to approximate the derivatives of the required equation. The mode of combining these evaluated function value is determined by a

Li Zhang (2010): Handout ELEC5564 Power Generation By Renewable Sources, Section 2, Power Converters and Applications to Renewable Generation

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5

finite difference approximation scheme. For this modelling exercise the Improved Euler method otherwise known as the Trapezoidal method is used. Principle of Trapezoidal method of solving ordinary differential equations This method uses the forward Euler as the predictor;

)

where,

This calculates the next value of the state variables (inductor current, iL and capacitor voltage, Vc) by using the present value of these state variables, the sampling time and the derivative of these state variables. Then it uses the backward Euler as a corrector to give correction to the estimation of the forward Euler method;

)

This calculates the next value of the state variables (inductor current, iL and capacitor voltage, Vc) by using the estimated value of these state variables given by the forward Euler (or predictor), the sampling time, the next time and the derivative of these state variables given by the forward Euler. The final solution is calculated by taking the mean of the two previously calculated values from the predictor and the corrector as shown below;

Since the two values being added have been estimated using equations 13 and 14, the final solution can be re-written in terms of present state variable value, sampling time, derivative of the state variable evaluated at the present variable value and derivative of the state variable evaluated at the next variable value. The described method is represented graphically in figure 4;f(t) f(t+h)

f(t) h

t+h t time Figure 4: Trapezoidal method for calculating integration

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PROGRAM LISTING FOR THE SIMULATION OF A DC-DC BOOST CONVERTERFLOWCHARTStart Enter circuit parameters and initial conditions

While t