Power Electronics
Power Electronics
Power Electronics
Contents
1 Introduction
1.1 Flyback transfer
1.2 Forward transfer
2 Buck Converter
3 Flyback Converter-Discontinuous Flux Mode
4 Flyback Converter-Continuous Flux Mode
5 Core Identification
6 Gapped Flyback Transformer
7 AC/DC Stage
8 Information on gEDA and PCB software
8.1 Configuring gEDA
9 Assignments
9.1 Final Project
9.2 AC/DC Rectifier Design
9.3 Core Identifcation
Course definition: Basics of DC/DC conversion, inductors,
transformers, switching characteristics of semiconductor devices,
elements of electromagnetic compatibility.
Syllabus
Repository of Spice simulations: SpiceRepo
Available SPICE simulators:
LTspice,
TopSpice.
1 Introduction
1.1 Flyback transfer
Figure 1: Flyback transfer: Single pulse of energy moves from primary to secondary side of the transformer.
1.2 Forward transfer
Figure 2: Forward transfer: Single pulse of energy moves from primary to secondary side of the transformer.
2 Buck Converter
The final project in this course is to design and build a 12V, 10A
power supply. The power supply is to be connected to the AC outlet,
which means that the rectified input voltage is high, 170V if
single diode rectification is used. One of possible choices for the
DC/DC step-down stage is the buck converter. The principle of
operation of this circuit is to periodically connect/disconnect the
load R0 to the 170V input voltage with a duty cycle just
enough to draw only 10A of current. With the load resistance of
1.2Ohm, the load voltage will then be 12V. The load current
has to be continuous and sufficiently smooth, therefore a 50uH
inductor is used to maintain continuouity of load current. As a
result, however, the dynamic response of the DC/DC converter is with
the time constant of (50/1.2)us, which will limit how fast the
power supply can respond to changing load. The faster the switching
frequency, the smaller the inductance necessary to limit the current
ripple. Therefore, the switching frequency is selected to be quite
high, 200kHz. On the other hand, too high of a frequency would
make it difficult to find practical components for the design.
Figure 3: Buck converter steps voltage down.
Inspecting the voltage and current waveforms, the minimum ratings for
the circuit components can be found. Maximum voltage across the
transistor excedes 170V due to spiking activity. Maximum current
excedes 10A due to the ripple magnitude. It seems a 200V,
18A mosfet and 200V, 20A diode are reasonable choices
of parts, in consultation with DigiKey pricing and availability of Spice
models for simulations. The inductor is usually custom-made in the
lab. For now, an estimated 10mOhm winding resistance is included in
the circuit. This can be updated later once the inductor design is
known. Having selected the parts, the circuit is simulated to find out
about its performance, especially the power efficiency. It is
important to know power loss in each of the circuit components. The
power supply has to be good for 100W of power into the load. It
should perhaps be designed to handle more than that to accomodate
possible transients if the load varies.
Using behavioral modeling the average power in each of the circuit
components can be found, as well as the overall input and output
power. Instantenous power is the product of voltage and current. The
average power can be found by low-pass filtering the waveform of
instanteneous power. To be able to see the average value, the time constant
of low-pass filtration is selected to be a quarter of the simulation
time.
Figure 4: Efficiency evaluation.
The power efficiency Po/Ps is about 60% in this
circuit. Such a low efficiency outcome is not satisfactory to be
practical. By inspecting all individual power losses, it is evident
that the mosfet losses are the highest, over 60W of power. Prior
to fixing the problem in this circuit, perhaps other types of DC/DC converters
should be considered since they may offer better performance in the
first place. (Point of interest: reverse recovery of diode)
3 Flyback Converter-Discontinuous Flux Mode
Figure 5: Flyback converter steps voltage down with the transformer
turn ratio.
4 Flyback Converter-Continuous Flux Mode
Figure 6: Flyback converter steps voltage down with the transformer
turn ratio.
Figure 7: Simple snubbers attenuate excessive ringing at switching devices.
5 Core Identification
In a coil with n turns, dynamic relationship between voltage and
current is analytically represented with the help of current-dependent
magnetic flux Φ(i). Voltage is the direct result of changes of
magnetic flux magnified through turn linkage v=n[(d Φ)/(d t)]. Flux
is uniformly distributed in the crossectional area A of the inductor
core and it is meaningful to introduce magnetic flux density
B=Φ/A.
Magnetic flux in the core nonlinearly responds to the current
excitation (ni) through the coil. In a regularly-shaped continuous
magnetic core, the current excitation is uniformly distributed along
the magnetic path of length l. The "density" of this excitation is
the magnetic field H=ni/l. Core manufacturers will provide
engineers with a description of the nonlinear relationship B(H) for
the magnetic material used in the core. Formally, this relationship is
not even a function, but is usually graphed as such as a family
of curves.
Figure 8: The B(H) curves for the Ferroxcube 3F3 ferrite material
In Spice, saturating cores with hysteresis can be modeled using the
core model. It takes 5 material parameters and 2 geometrical
dimensions: AREA and PATH which are the
crossectional area A and magnetic path length l. The parameters
are in fixed units with embedded prefix. Therefore, care must be taken
to avoid colosal scaling errors.
Figure 9: Parameters of the Spice core model
In TopSpice, the proper place to put the core model is the *.mis
file. Typically, core models are not readily available. It is
possible, however, to perform simple identification of core parameters
by hand using a simple circuit and graphing the B(H) curves. This can
be done more effectively if each of the parameters is varied using
the STEP command in Spice. The STEP command repeats all scheduled
simulations substituting the declared parameter value with a given
list.
* Core Identification circuit.mis
.param Pa = 22
.param Palpha = 100u
.param Pc = 0.5
.param Pk = 18
.param Pms = 368k
*.step PARAM Pa LIST 16 18 20 22
*.step PARAM Palpha LIST 80u 100u 120u
*.step PARAM Pc LIST 0.5 1 2
*.step PARAM Pk LIST 16 18 20
*.step PARAM Pms LIST 350k 360k 370k 380k
.model ferrite3F3 core(a={Pa} alpha={Palpha} area=5.11 c={Pc} k={Pk} ms={Pms} path=7.96)
The simplest circuit to identify the core parameters is an inductor
driven by triangular waveform of current. This induces two-directional
magnetic flux in the core. In TopSpice, the B(H) can be graphed
directly by choosing H(K1) for the x-coordinate of the graph, and
B(K1) for the y-coordinate. TopSpice uses historic units for both
magnetic field strength (oersted) and the flux density (Gauss). They
can be scaled back to the SI-compatible units of A/m and Tesla
according to the following conversion equations:
Note that some magnetic material manufacturers will still use the old
units in their detasheets. The datasheet curves can be graphed
together with the simluated B(H) curves for comparison using the
look-up table capability of the behavioral voltage source. (This is a
pure coincidence that the analyzed Ferroxcube core path length is
79.6mm, a number similar to the oersted conversion factor
79.57)
Figure 10: Identification of ferrite core.
Adjusting core model parameters by hand may be enjoyable for a while,
but the accuracy of such parameter extraction method is
limited. Moreover, when a large number of material types needs to be
analyzed, an automatic method of parameter extraction is
necessary. Following the equations of the
Jiles-Atheron model [1], which is used in
TopSpice, the hysteresis loop can be graphed in a numerical package of
choice, using first the starting guess for the model parameters. Then
with the help of a nonlinear curve fitting routine, the parameters can
be fine-tuned so that the B-H curve lines up better with the
datapoints copied from the manufacturer's datasheet.
Figure 11: Fine-tuning of core model parameters using nonlinear curve
fitting: Initial parameters (on left), tuned parameters (on right).
6 Gapped Flyback Transformer
Figure 12: The actual transformer core with the gap.
7 Identification of the Converter Dynamics
Figure 13: Step response of the Flyback converter.
Figure 14: Zero identification of the Flyback converter.
8 Pulse-Width Modulator
Figure 15: Flyback converter with an PWM controller.
9 AC/DC Stage
The power supply to be designed as final project will contain two
stages: AC/DC and DC/DC. The intermediate voltage between the two
stages is called the link voltage. In our case the link voltage will
be close to 170V, the peak value of the AC line. For the AC/DC a
half-bridge rectifier is chosen. Despite all its disadvantages, the
reason for this choice is that the ground of the power supply circuit
including its output and the ground of the AC line are the same. This
will enable measurements with the lab equipment, which is naturally
AC-grounded for safety.
Figure 16: Half-wave rectifier.
10 Information on gEDA and PCB software
Students need to have a working account on the ECE Department Unix
system in the Scadlab. To enable your account, talk to the ECE Lab Manager.
10.1 Configuring gEDA
By default, student accounts are set up to use TSCH as the primary
shell. Define three environment variables by including three extra
lines in your .cshrc.user file:
setenv PATH /usr/share/geda/bin:$PATH
setenv LD_LIBRARY_PATH /usr/share/geda/lib
Close and reopen the terminal window to activate the changes. Now
set up your project files:
mkdir gaf
cd gaf
mkdir gschem-sym
mkdir pcb-elements
cat (component-library "${HOME}/gaf/gschem-sym") > gafrc
11 Assignments
11.1 Final Project
Design and build a switch-mode power supply according to the following
specification:
- Output power: 100W
- Output voltage: 12V
- Input: 120V, 60Hz
- Minimum efficiency: 80%
11.2 AC/DC Rectifier Design
Design the AC/DC stage of the final project. In your submission
include the following deliverables:
- Schematic of the simlated circuit. Circuit components must be
physical parts available from a vendor. Nontrivial elements, such as
diodes, must be simulated using a valid model.
- Output voltage and current waveforms under 120W DC load.
- Evaluation of power factor.
- Evaluation of THD (total harmonic distortion coefficient) at the AC input.
11.3 Core Identifcation
Perform a detailed identification of the Ferroxcube 3F3 ferrite material
based on the 511mm2 E-core. All participants in the Power
Electronics course are to submit the parameters of their core model as a
library file Xxxxx.lib. The file should contain the following line:
.model Xxxxx3F3 core(a=111 alpha=222 area=5.11 c=444
k=555 ms=666 path=7.96). The Xxxxx is the last name of
participant. Numbers 111, 222,... naturally should be replaced with
the actual extracted model parametrs values.
References
- [1]
-
D. C. Jiles, J. B. Thoelke, and M. K. Devine,
"Numerical determination of hysteresis parameters for the modeling
of magnetic properties using the theory of ferromagnetic hysteresis",
IEEE Transactions on Magnetics, vol. 28, no. 1, pp. 27-35,
1992.
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On 23 Apr 2009, 19:41.
