Modelling and Transient Performance of Buck Ch-4

8/12/2019 Modelling and Transient Performance of Buck Ch-4

1/16

Chapter4

SIMULATION AND ANALYSIS OF OPEN LOOP BUCK CONVERTER

4.1 Introduction

In the previous chapter we have derived the various transfer function of Buck converter. We

have also calculated the parameters of Buck converter for the given specification. In this

chapter we will simulate the converter using Matlab coding and Matlab Simulink in open

loop and close loop mode. Then we will find the effect of variation of change in input

voltage, load current and effect of variation of switching frequency. For the purpose we will

calculate the Buck converter parameter for ideal condition and output of ideal converter will

be compared with a fix parameter converter and comparative results will be analyzed.

4.2 Matlab Programme to Calculate Buck Converter Parameters and Transfer

Function

Modeling of Buck Converter%...Model of BuckConverterclc;clear all;disp('parameterts of buck converter');% User specification of Buck ConverterVi=input('input voltage=');Vo=input('output voltage=');Vripple = input(' Enter allowed percentage ripple in voltage= ');Iripple=input('Enter allowed percentage ripple in current=');D=Vo/Vi;fs=input('switching frequency=');Po=input('output power=');Io=Po/Vo; % AmperedelIo=(Iripple*Io)/100;L=(D*(Vi-Vo))/(delIo*fs)delVo=(Vripple*Vo)/100;C=(100*(1-D)*Vo)/(8*L*Vripple*(fs^2))

Ro=(Vo^2)/PoRL=10e-3; %OhmRC=30e-3; %Ohm%Buck Models=tf('s');

Nr=1+s*(RC*C);Dr=1+s*(L/(Ro+RL) + (C*Ro*RL)/(Ro+RL) + C*RC) + (s^2)*L*C*((Ro+RC)/(Ro+RL));Buck=Vi*(Nr/Dr)


2/16

The parameters of Buck converter for given input voltage and output specifications can be

calculated using the above matlab program. Parameters and required transfer function of

others converter can be calculated.

4.2.1 DC-DC Buck Converter Circuit Parameters

Using the program given in 4.2 we can calculate the parameters of buck converter as per

variation of input, output specifications for a fixed output voltage of 12 volt.

4.2.1.1 DC-DC Buck Converter Circuit Parameters with Input Voltage 24 V

For input voltage of 24 V and constant output voltage of 12 V, 20 watt output power the

various parameters calculated using matlab are

Output from Matlabinput voltage=24 volt, output voltage=12 volt, ripple current=2%, ripple voltage=1%,

switching frequency=100000, output power=20 watt, Rload= 7.2 , L = 3.6 mH,

C = 2.09f.

From datasheet for calculated value of inductor and capacitor resistance of inductor and ESR

of capacitor are RL= 6m, RC=2m respectively.





switching frequency=100000, output power=20 watt, Rload = 7.2 , L = 3.3 mH, C =

2.09f.


of capacitor are RL= 6.8m, RC=2.9m respectively.


3/16





switching frequency=100000, output power=20 watt, Rload= 7.2 , L = 2.2 mH,

C = 4.09f.


of capacitor are RL= 6m, RC=2m respectively.

4.3 Simulink Models

4.3.1 Introduction

The complexity of device models and switching nature of switching converters make

simulation difficult due to converge in PSPICE. Simulink is a windows oriented dynamic

modeling package that is an extension to Matlab. The advantage is that models are entered as

block diagrams after corresponding mathematical equations are developed for the target

system.

Matlab uses ordinary differential equation solver (ode45) to solve sets of linear and non-

linear differential equations which in this case are emulated by block diagrams. Thus to

simulate an electrical system such as DC/DC converter, one has to write equations for various

blocks in the system and construct an equivalent block diagram using icons in simulink. The

parameters for individual icons can be set for the process. Finally, a choice of equation solver

and simulation time is made. The output of system could be observed or recorded into file.

4.3.2 Simulink Model of Buck Converter

Figure 4.1 show the matlab based electrical model of Buck converter. In the shown model

capacitor is shown with ESR, we have considered inductor as non-ideal and has series

resistance. To facilitate subsequent simulation, and feedback controller design and


4/16

verification, the inputs to buck converter sub-block are input voltage Vi and duty ratio d. The

outputs are inductor current, capacitor voltage and output voltage.

Fig. 4.1 Simulink Model of Buck Converter

The non-idealities of transistor ON resistance and inductor series resistance are appropriately

included.

4.3.3 PWM

The output of the switching converter is subtracted from the reference signal to generate an

error signal.

Fig. 4.2 Simulink Model of PWM Scheme

This error signal is compared with a ramp signal to generate a pulse to switch on the

MOSFET and maintain a steady state duty cycle. For any variations in the input voltage or

output load current, the error signal either increases or decreases. If the output voltage

increases, the error signal increases and the reset pulse is generated earlier to reduce the duty


5/16

cycle and eventually lower the output voltage. Similarly, if the output voltage decreases, the

error signal decreases and the reset pulse is generated at later duration to increase the duty

cycle and bring the output voltage back into equilibrium.

4.4 Open Loop Response of Buck Converter

Using the above described model and with calculated parameters using program, we find the

effect of variation of input voltage, switching frequency and load on transient and steady state

performance of buck converter.

4.4.1 Effect of Variation of Input Voltage

To observe the effect of variation input voltage we analyze the output waveforms of

converter at one higher and a lower input voltage.

4.4.1.1 Simulation Result without Disturbance at Vi = 24 Volts

The below graph Figure 4.3, is the output of the model in open loop at rated input voltage.

Fig. 4.3 Simulation response open loop buck converter without disturbance


6/16

We can observe from the graph shown in fig.4.3 that rise time is around 2ms, steady state

error of 4.5% in voltage.

4.4.1.2 Simulation Result with Lower Input Voltage at Vi = 20 Volts

The below graph Fig. 4.4, is the output of the model in open loop at below the rated input

voltage. Comparing the graph shown in fig. 4.3 and 4.4, it is seen that system takes more time

to reach steady state value. We can observe from the graph shown in fig.4.4 that rise time is

more than 2ms, steady state error of 5% in voltage.

Fig. 4.4 Simulation Response open loop Buck converter with lower input voltage


7/16

4.4.1.3 Simulation Result with Higher Input Voltage at Vi = 28 Volts

The below graph fig. 4.5, is the output of the model in open loop at below the rated input

voltage.

We can observe from the graph shown in fig.4.4 that rise time is 1ms, steady state error of

5% in voltage.

Further we have calculated the steady state error, transient time and efficiency of the circuit

for a range of input voltage from 14 volts to 34 volts, a drawn graph between various

parameters versus change in input voltage.

Fig. 4.5 Simulation Response open loop Buck converter with higher input voltage


8/16

Below table shows the variation of rise time steady state error with change in input voltage

Table 4.1

COMPARISONS OF VARIOUSPID TUNING METHODS

S. No. Input Voltage

(Volt)

Rated Vi=24

Output Voltage

(Volt)

Transient

Time

(milli-sec)

Steady

state error

(%)

1 14 6.55 1.67 45.41

2 16 7.65 1.65 36.25

3 18 8.51 1.61 29

4 20 9.48 1.55 21

5 22 10.52 1.61 12.33

6 24 11.5 1.68 4.2

7 26 12.47 1.75 -3.92

8 28 13.48 1.69 -12.33

9 30 14.48 2.01 -20.66

10 32 15.45 0.87 -28.75

11 34 16.46 1.94 -45.17


9/16

A graph below shows the variation of output voltage its transient time and steady state error

with input voltage.

Fig.4.6 Graph percentage Steady state error with variation of input voltage

From fig.4.6 we find that steady state error is high as we work at lower or higher input

voltage. Percentage Steady state error rises as we go away from input rated voltage.

From fig. 4.7 is nearly constant for lower and around rated input voltage but sudden changes

are there at higher input voltages, circuit response is faster at high voltages.


10/16

Fig.4.7 Graph transient time with variation of input voltage

4.4.2 Effect of Variation of Switching Frequency

To observe the effect of variation of switching frequency, we analyze the output waveforms

of converter at some higher and lower switching frequencies. The output waveforms are

shown for one higher and lower switching frequencies.

4.4.2.1 Simulation Result without Disturbance at Frequency = 100KHz

The below graph Figure 4.7, is the output of the model in open loop at rated input voltage


11/16

Fig. 4.7 Simulation Response open loop Buck converter with standard rated switching frequency


The below graph Figure 4.7, is the output of the model in open loop at rated input voltage

Fig.4.7 Simulation Response open loop Buck converter with higher switching frequency


12/16

. Fig.4.8 Simulation Response open loop Buck converter with higher switching frequency showing ripples in

output voltage


The below graph Figure 4.7, is the output model in open loop at rated input voltage.

. Fig.4.9 Simulation Response open loop Buck converter with lower switching frequency


13/16

As from fig. 4.9 we can see with the operation at lower switching frequency results in higher

ripple voltage and total harmonic content has increased.

To get a better picture we will find the output voltage for a range of frequency from 50 Khz

to 200 KHz and we will plot a graph output voltage versus variable switching frequency.

Fig.4.10 Simulation Response open loop Buck converter with lower switching frequency showing ripples in

output voltage

4.4.3 EFFECT OF VARIATION OF LOAD

To observe the effect of variation of output voltage with change of load we analyze the output

voltage waveforms of converter at one higher and a lower load. For the simulation we have

design our buck converter for 20Watt rated load. First we find the output voltage response at

at 50% reduced load than rated load i.e. 10Watt and 200% of rated load i.e. at 40Watt. The


14/16

graph for variation of output voltage with time is drawn with the help of MATLAB simulink

model.

Table 4.2

COMPARISONS OF VARIOUSPID TUNINGMETHODS

4.4.3.1 Simulation Result without Disturbance at Vi = 24 Volts and Rated Load

The below graph Figure 4.12, is the output model in open loop at rated input voltage

S. No. Load (%) at

Rated Voltage

Output Voltage

(Volt)

Transient

Time

(milli-sec)

Steady

state error

(%)

1 50 14.25 5 -18.25

2 80 13.8 4.7 -15

4 90 13.1 1.8 -9.167

5 100 (rated

load)

12.5 1.6 -4.17

6 120 13 2.5 -8.33

7 140 12.25 3 -2.08

8 160 12.2 3.1 -1.67

9 180 12.2 3.6 -1.67

10 200 12.4 4 -3.33


15/16

Fig. 4.12 Simulation Response open loop Buck converter with standard rated switching frequency at rated load.

4.4.3.2 Simulation Result without Disturbance at Vi = 24 Volts and 50% of Rated Load

The below graph Figure 4.13, is the output of the model in open loop at 50% of rated load

Fig. 4.13 Simulation Response open loop Buck converter at half rated load.


16/16

4.4.3.3 Simulation Result without Disturbance at Vi = 24 Volts and 200% of Rated Load

The below graph Figure 4.13, is the output of the model in open loop at 200% of rated load

Fig. 4.14 Simulation Response open loop Buck converter at double the rated load

From the graph shown above variation of output voltage at rated, reduced and double load the

rated load, we can draw following conclusions:

For the load lower than the rated load response of the system is fast, transient time is small,but the steady state error is large, in our particular case we find it is 15% approx., and our

specification is only 1%. Output voltage is higher than the specified rated voltage.

At higher load system become slow and transient time is more, further steady state error

increases, as in our case it is 18% approx. also at higher load than rated, harmonics content in

output voltage has increased.

Documents

Modelling and Transient Performance of Buck Ch-4