Session 3: Basic operation and analysis of a DC/DC converter
3.1 Aims and Objectives
The aim of this task is to develop a simple model of a Buck converter in Matlab / Simulink, while the objective is to better understand the operation of the Buck converter. The general principles behind developing this model can be applied to any power electronic converter system – boost converters, three phase inverters, rectifiers etc. used for your project.
3.2 Introduction to the Buck Converter
Vg
RL L RC + νo
C
–
Control Signal u
Figure 1: General model of Buck DC/DC converter
𝑽𝒈 =𝟏𝟐𝑽,𝑹𝑳 =𝟎.𝟓𝛀,𝑹𝒄(𝑬𝑺𝑹) =𝟓𝒎𝛀,𝑹𝑶 =𝟏𝟎𝛀,𝑳=𝟑𝟑𝒎𝑯,𝑪=𝟔𝟖𝟎𝝁𝑭
The general topology of a DC/DC Buck converter is shown in Figure 1. The operation of the Buck converter can be researched in Mohan, Undelands and Robbins [1]. [1] also contains useful information regarding other power electronic converter types. It is an excellent source of information.
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RO
The main purpose of a Buck converter is to step-down the DC input voltage to a lower DC voltage at the output. In a step down converter, the output voltage is always lower than the input voltage. This circuit is commonly used in many power conversion applications such as switch mode power supplies, renewable energy systems, and in electric systems within vehicles. In Fig. 1, the circuit includes the inductor body resistance (𝑅𝐿), and the capacitor equivalent series resistance (𝑅𝑐). The load (𝑅𝑂) is considered as part of the DC/DC converter to take account of the effect of any load change to the dynamic response of the system. It is assumed that the diode is characterized by an ideal diode. For now, the mathematics will be kept to a minimum.
3.3 Task 1: Developing the DC/DC converter model using Simulink.
With the help of the ‘Simscape: Power Systems’ (formerly ‘SimPowerSystems’) library, construct a Buck converter model in Simulink. On completion, the model
should look like Fig. 2. (Don’t panic – see following instructions for some useful guidance).
The following instructions assume you are using Matlab 2018a. Within Matlab open the Simulink library browser – this will give you a long list of libraries, each of which contains a large number of blocks which can be used to develop any given model. There are two options to open the library as shown in Fig. 3, either click on the button or type “Simulink” into the command window, this will open the “Simulink Start Page”. Choose “Blank Model”. A black model called “untitled” should appear; save this is a suitable place. To obtain the libraries, click the button as shown in Fig. 4, the library as shown in Fig. 5 should appear. Here, we are only going to work with a small number of libraries. For this model we are using blocks from the standard “Simulink” library and the “Simscape: Power Systems” library which contains most of the basic elements required for simulating power electronics and electric drives systems. Feel free to explore the full contents of this library in your own time. Here we will just focus on the small number of components required to construct the Buck Converter.
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Figure 2: Example Simulink model of a Buck converter, with simple open loop PWM control
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Figure 3: Simulink Library Browser Options
Figure 4: To open Simulink Library
Figure 5: Simulink Library Browser
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In the Simulink Library Browser, where is states “Enter Search term”, search for “powergui” (Environment block for “Simscape: Power Systems” models); right click on the “powergui” block selecting “Add block to…”, this will add the block to your system. We will alter this blocks parameters later.
For the “Ideal Switch”, navigate to the “Simscape: Power Systems: Specialized Technology: Fundamental Blocks: Power Electronics”. It is possible to choose one of a number of semiconductor devices – IGBT, MOSFET etc. The choice is usually determined by the voltage and power rating of the Buck converter. This is not a real concern at this stage. Therefore, for simplicity, use an “Ideal Switch” for the circuit. It is possible to modify the behaviour of the ideal switch, but here use the default parameters. As before, right click to add to your simulation.
The diode can be found in the same library, “Simscape: Power Systems: Specialized Technology: Fundamental Blocks: Power Electronics”. Add a “Diode” block to the simulation model. Again, it is possible to modify the behaviour of the diode, but for now do not change the default parameters
For all resistors, inductors and capacitors, go to the “Simscape: Power Systems: Specialized Technology: Fundamental Blocks: Elements” library. Use a “Series RLC branch” block for each of these passive components. Drag and drop one of these blocks into the simulation model. Double click on the symbol. In the pop-up window modify the parameters of the block to match the component of interest. The pop-up window should be fairly intuitive.
Set the component values as follows:
𝑹𝑳 =𝟎.𝟓𝛀,𝑳=𝟑𝟑𝒎𝑯,𝑹𝒄(𝑬𝑺𝑹) =𝟓𝒎𝛀,𝑪=𝟔𝟖𝟎𝝁𝑭,𝑹𝑶 =𝟏𝟎𝛀,
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For the input voltage source, use a “DC Voltage Source” block (“Simscape: Power Systems: Specialized Technology: Fundamental Blocks: Electrical Sources”). Drag and drop one of these into the simulation model. Double click on the symbol. In the pop- up window configure the voltage for 12Vdc.
At this stage, set the components out on the screen and simply join them together to form the Buck converter circuit as shown in Fig. 2. The circuit will not do anything yet until a control circuit is provided (this will be added next)
For the control signal, “u”, begin by considering an open loop system. Implement a simple Pulse Width Modulation (PWM) circuit as shown in the top left of Fig. 2. (See [1] for information on PWM).
The circuit comprises of the following blocks which can be found in the “Simulink” library
‘Constant’ (“Simulink: Commonly used Blocks”)
‘Repeating Sequence’ (“Simulink: Sources”)
‘Relational Operator’ (“Simulink: Commonly used Blocks”)
Set the constant to 0.5 – this is the modulation signal used to control the duty cycle of the PWM control signal, “u”. Set the repeating sequence block for 1 kHz PWM. To do this, the time values field must be set for a repetition of 1ms (the period of the PWM); [0 1e-3]. Set the output values to [0 1]. Finally, double click on the logic operator block and configure it to behave as a “>=” block. Connect the blocks together as shown in Fig. 2.
NOTE: You cannot directly connect a Scope to a “Simscape: Power Systems” circuit. To measure the parameters voltage and current measurement blocks are needed, these can be found in “Simscape: Power Systems: Specialized Technology: Fundamental Blocks: Measurements”. You will need both “Current Measurement”, and “Voltage Measurement” blocks. The “Scope” blocks can be found in “Simulink: Sinks”; add the Scope blocks to your model as shown in Fig. 2. “Scope” blocks can have a limitation with the number of data points they save, it is recommended that you remove this limit. As shown in Fig. 6, if you click on
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the “Configuration Properties” button (highlighted in red) and click on the “Logging” tab, you can remove the limitation.
Figure 6: Scope Parameters
It is recommended that you monitor the following signals
Signal Measurements:
PWM control signal, “u” – connect a Scope to the output of the PWM control circuitry.
Switching signal, “s” – connect a Scope to the output of the repeating sequence block
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Power Measurements:
3.4
Output Voltage – place a “voltage measurement” block in parallel with the load Diode Voltage – place a “voltage measurement” block in parallel with the diode, this will allow you to monitor the voltage applied to the LC circuit in the Buck converter. Inductor current – place a “current measurement” block in series with the inductor.
Task 2: Verifying the characteristics of the circuit
If your Simulation has been correctly implemented, it is now time to simulate the circuit. Set the simulation time to 0.2 seconds, and then run the simulation. The areas highlighted in Fig. 7 allow you to achieve this. You also need to set the simulation solver settings, these can be accessed in “Simulation: Model Configuration Parameters”. Set the solver options as shown in Fig. 8.
Figure 7: Run and Time Buttons
Figure 8: Simulation Settings
For the “powergui” settings, double click in the “powergui” block to open up further options, in the “Solver” options, choose “Simulation type: Discrete”, and set the “Sample Time” to “1e-6”; while in the “Preferences” options, set the “Discrete Solver” to “Tustin/Backward Euler (TBE)”.
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If necessary, fix any errors with the simulation, then proceed to study the circuit as follows:-
Initially, consider the PWM circuit. Observe the control signal, “u”, with 1 kHz switching and a constant modulation signal of 0.5. You should find that this signal is a square wave with 50% duty cycle.
Vary the magnitude of the constant within the range of 0 to 1. Comment on the effect on the control signal, “u”. Does the circuit behave as expected?
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Now, consider the PWM controlled Buck Converter. Observe the load voltage, inductor current, and voltage across the diode with 1 kHz switching and a constant modulation signal of 0.5
Draw a simple sketch of the load voltage and inductor current on the following axes.
Figure 9: Buck converter: output voltage. Vin = 12V, D = 0.5
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Figure 10: Buck converter: inductor current. Vin = 12V, D = 0.5
By varying the magnitude of the constant duty cycle ratio, “D” from 0.1 to 0.9, complete the following table:
D
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Vin
12
12
12
12
12
12
12
12
12
Vout (average), (steady. state)
IL (average)
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While using the axes provided below, plot a graph of D (x-axis) versus output voltage (y-axis)
Figure 11: Output Voltage vs. D
The ideal relationship between the input voltage and output voltage with respect to the applied modulation signal is:
𝑉 =𝐷×𝑉 (1) 𝑜𝑢𝑡 𝑖𝑛
Do the results generally* confirm this relationship? (*the simulated circuit includes parasitic components such as 𝑅𝐿 and 𝑅𝐶, so it will not be perfect, but should be close).
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3.5 Task 3: Taking a closer look at the circuit behaviour
Take a closer look at the voltage waveform across the load. Try to explain the characteristics of this waveform. You may need to zoom into the waveform to fully see the behaviour of the load voltage.
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Now, take a closer look at the current waveform in the inductor. Try to explain the characteristics of this waveform. You may need to zoom into the waveform to fully see the behaviour of the inductor current.
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Increase the value of the capacitor in the circuit – for example multiply it by 10. Then reduce the value of the capacitor – for example divide it by 10. In each case, take another look at the load voltage waveform and inductor current waveform. Explain this behaviour. ([1] may be useful here!). Note: if necessary, change the simulation time.
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Values shown in Table 1 below are from Figs. 12-15, using a fixed 33mH inductor and D = 0.5.
Max. Voltage (V)
Max. Current (A)
Max. Voltage Ripple (V) in steady state
Min. Voltage Ripple (V) in steady state
Max. Current Ripple (A) in steady state
Min. Current Ripple (A) in steady state
𝐶 = 680𝜇𝐹
𝐶 = 6800𝜇𝐹
𝐶 = 68𝜇𝐹
Table 1: Varying Capacitor Value Results
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Figure 12: Buck Converter Output Voltage, Varying Capacitor Values
Figure 13: Magnified Buck Converter Output Voltage Ripples, Varying Capacitor Values
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Figure 14: Buck Converter Inductor Current, Varying Capacitor Values
Figure 15: Magnified Buck Converter Inductor Current Ripples, Varying Capacitor Values
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Set the capacitor back to its original value. Increase the value of the inductor in the circuit – for example double it. Then reduce the value of the inductor – for example halve it. In each case, take another look at the load voltage waveform and inductor current waveform. Explain this behaviour. ([1] may be useful here!)
Values shown in Table 2 below are from Figs. 16-19, using a fixed 680μF capacitor and D = 0.5.
Max. Voltage (V)
Max. Current (A)
Max. Voltage Ripple (V) (0.14 – 0.15s)
Min. Voltage Ripple (V) (0.14 – 0.15s)
Max. Current Ripple (A) (0.14 – 0.15s)
Min. Current Ripple (A) (0.14 – 0.15s)
𝐿 = 33𝑚𝐻
𝐿 = 66𝑚𝐻
𝐿 = 16.5𝑚𝐻
Table 2: Varying Inductor Value Results
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Figure 16: Buck Converter Output Voltage, Varying Inductor Values
Figure 17: Magnified Buck Converter Output Voltage Ripple, Varying Inductor Values
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Figure 18: Buck Converter Inductor Current, Varying Inductor Values
Figure 19: Magnified Buck Converter Inductor Current Ripples, Varying Inductor Values
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Set the inductor and capacitor back to their original values. Now, change the switching frequency of the PWM circuit to 10 kHz. Re-run the simulation. Take another look at the inductor current and load voltage waveforms. What effect does increasing the PWM switching rate have on the performance of the circuit?
Reduce the switching frequency of the PWM circuit to 100Hz. Re-run the simulation. Take another look at the inductor current and load voltage waveforms. Explain the behaviour of the circuit.
Values shown in Table 3 below are from Figs. 20-23 when D = 0.5
Max. Voltage (V)
Max. Current (A)
Max. Voltage Ripple (V) in steady state
Min. Voltage Ripple (V) in steady state
Max. Current Ripple (A) in steady state
Min. Current Ripple (A) in steady state
𝑓 = 100𝐻𝑧
𝑓 = 1𝑘𝐻𝑧
𝑓 = 10𝑘𝐻𝑧
Table 3: Varying Frequency Value Results
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.
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Figure 20: Buck Converter Output Voltage, Varying Frequency Values
Figure 21: Magnified Buck Converter Output Voltage Ripple, Varying Frequency Values
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Figure 22: Buck Converter Inductor Current, Varying Frequency Values
Figure 23: Magnified Buck Converter Inductor Current Ripple, Varying Frequency Values
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3.6
Some general tips on simulation modelling
If it works first time, think yourself lucky! It is rare that a simulation model will work as expected first time round – like it or not, you are going to have to debug the simulation!
When debugging a simulation, consider the problem logically and where possible simplify things as much as possible. First try to confirm that the subsystems within the model behave properly.
No matter how small or obvious you think it is, never assume something is okay until you have checked it properly. E.g. Does the PWM actually generate 1 kHz PWM? Has this been verified on the scope?
Most important of all: A simulation model should generally be used to confirm your understanding of the system. It should not be used to generate answers to something you do not understand!! When questioned, you should be prepared to explain the result.
References
Mohan, Undelands, and Robbins, “Power Electronics, Converters. Applications and Design.” vol. 3rd Edition, Wiley, Ed., ed.
3.7
[1]
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