Transcript Fundamentals of Power Electronics

Announcements
Homework #2 due today for on-campus students. Off-campus students
submit according to your own schedule.
Homework #3 is posted and is due NEXT Friday for on-campus students
(Friday Feb. 8)
Fundamentals of Power Electronics
1
Chapter 19: Resonant Conversion
19.4
Load-dependent properties
of resonant converters
Resonant inverter design objectives:
1. Operate with a specified load characteristic and range of operating
points
• With a nonlinear load, must properly match inverter output
characteristic to load characteristic
2. Obtain zero-voltage switching or zero-current switching
• Preferably, obtain these properties at all loads
• Could allow ZVS property to be lost at light load, if necessary
3. Minimize transistor currents and conduction losses
• To obtain good efficiency at light load, the transistor current should
scale proportionally to load current (in resonant converters, it often
doesn’t!)
Fundamentals of Power Electronics
2
Chapter 19: Resonant Conversion
Inverter output characteristics
General resonant inverter
output characteristics are
elliptical, of the form
with
This result is valid provided that (i) the resonant network is purely reactive,
and (ii) the load is purely resistive.
Fundamentals of Power Electronics
3
Chapter 19: Resonant Conversion
A Theorem relating transistor current variations to
load resistance R
Theorem 1: If the tank network is purely reactive, then its input impedance
|| Zi || is a monotonic function of the load resistance R.




So as the load resistance R varies from 0 to , the resonant network
input impedance || Zi || varies monotonically from the short-circuit value
|| Zi0 || to the open-circuit value || Zi ||.
The impedances || Zi || and || Zi0 || are easy to construct.
If you want to minimize the circulating tank currents at light load,
maximize || Zi ||.
Note: for many inverters, || Zi || < || Zi0 || ! The no-load transistor current
is therefore greater than the short-circuit transistor current.
Fundamentals of Power Electronics
4
Chapter 19: Resonant Conversion
Example: || Zi || of LCC
• for f < f m, || Zi ||
increases with
increasing R .
• for f > f m, || Zi ||
decreases with
increasing R .
• for f = fm, || Zi || constant
for all R .
• at a given frequency f,
|| Zi || is a monotonic
function of R.
• It’s not necessary to
draw the entire plot: just
construct || Zi0 || and
|| Zi ||.
Fundamentals of Power Electronics
5
Chapter 19: Resonant Conversion
A Theorem relating the ZVS/ZCS boundary to load
resistance R
Theorem 2: If the tank network is purely reactive, then the boundary between
zero-current switching and zero-voltage switching occurs when the load
resistance R is equal to the critical value Rcrit, given by
It is assumed that zero-current switching (ZCS) occurs when the tank input
impedance is capacitive in nature, while zero-voltage switching (ZVS) occurs when
the tank is inductive in nature. This assumption gives a necessary but not sufficient
condition for ZVS when significant semiconductor output capacitance is present.
Fundamentals of Power Electronics
6
Chapter 19: Resonant Conversion
LCC example




f > f: ZVS occurs for all R
f < f0: ZCS occurs for all R
f0 < f < f, ZVS occurs for
R< Rcrit, and ZCS occurs for
R> Rcrit.
Note that R = || Zo0 ||
corresponds to operation at
matched load with maximum
output power. The boundary
is expressed in terms of this
matched load impedance,
and the ratio Zi / Zi0.
Fundamentals of Power Electronics
7
Chapter 19: Resonant Conversion
LCC example, continued
Typical dependence of Rcrit and matched-load
impedance || Zo0 || on frequency f, LCC example.
Fundamentals of Power Electronics
Typical dependence of tank input impedance phase
vs. load R and frequency, LCC example.
8
Chapter 19: Resonant Conversion
19.4.4 Design Example
Select resonant tank elements to design a resonant inverter that meets the
following requirements:
• Switching frequency fs = 100 kHz
• Input voltage Vg = 160 V
• Inverter is capable of producing a peak open circuit output voltage
of 400 V
• Inverter can produce a nominal output of 150 Vrms at 25 W
Fundamentals of Power Electronics
9
Chapter 19: Resonant Conversion
Solve for the ellipse which meets requirements
Fundamentals of Power Electronics
10
Chapter 19: Resonant Conversion
Calculations
The required short-circuit current can be found by solving the elliptical
output characteristic for Isc:
hence
Use the requirements to evaluate the above:
Fundamentals of Power Electronics
11
Chapter 19: Resonant Conversion
Solve for the open circuit transfer function
The requirements imply that the inverter tank circuit have an open-circuit
transfer function of:
Note that Voc need not have been given as a requirement, we can solve
the elliptical relationship, and therefore find Voc given any two required
operating points of ellipse. E.g. Isc could have been a requirement
instead of Voc
Fundamentals of Power Electronics
12
Chapter 19: Resonant Conversion
Solve for matched load
(magnitude of output impedance )
Matched load therefore occurs at the operating point
Hence the tank should be designed such that its output impedance is
Fundamentals of Power Electronics
13
Chapter 19: Resonant Conversion
Solving for the tank elements
to give required ||Zo0|| and ||Hinf||
Let’s design an LCC tank network for this example
The impedances of the series and shunt branches can be represented by
the reactances
Fundamentals of Power Electronics
14
Chapter 19: Resonant Conversion
Analysis in terms of Xs and Xp
The transfer function is given by the voltage divider equation:
The output impedance is given by the parallel combination:
Solve for Xs and Xp:
Fundamentals of Power Electronics
15
Chapter 19: Resonant Conversion
Analysis in terms of Xs and Xp
Fundamentals of Power Electronics
16
Chapter 19: Resonant Conversion
||Hinf||
Fundamentals of Power Electronics
17
Chapter 19: Resonant Conversion
||Zo0||
Fundamentals of Power Electronics
18
Chapter 19: Resonant Conversion
||Zo0||
Fundamentals of Power Electronics
19
Chapter 19: Resonant Conversion
Analysis in terms of Xs and Xp
Fundamentals of Power Electronics
20
Chapter 19: Resonant Conversion
Analysis in terms of Xs and Xp
The transfer function is given by the voltage divider equation:
The output impedance is given by the parallel combination:
Solve for Xs and Xp:
Fundamentals of Power Electronics
21
Chapter 19: Resonant Conversion
Evaluate tank element values
Fundamentals of Power Electronics
22
Chapter 19: Resonant Conversion
Discussion
Choice of series branch elements
The series branch is comprised of two elements L and Cs, but there is only
one design parameter: Xs = 733 Ω. Hence, there is an additional
degree of freedom, and one of the elements can be arbitrarily chosen.
This occurs because the requirements are specified at only one operating
frequency. Any choice of L and Cs, that satisfies Xs = 733 Ω will meet
the requirements, but the behavior at switching frequencies other than
100 kHz will differ.
Given a choice for Cs, L must be chosen according to:
For example, Cs = 3Cp = 3.2 nF leads to L = 1.96 mH
Fundamentals of Power Electronics
23
Chapter 19: Resonant Conversion
Requirements met at one frequency
Fundamentals of Power Electronics
24
Chapter 19: Resonant Conversion
What if Cs = infinity?
Fundamentals of Power Electronics
25
Chapter 19: Resonant Conversion
Discussion
Choice of series branch elements
The series branch is comprised of two elements L and Cs, but there is only
one design parameter: Xs = 733 Ω. Hence, there is an additional
degree of freedom, and one of the elements can be arbitrarily chosen.
This occurs because the requirements are specified at only one operating
frequency. Any choice of L and Cs, that satisfies Xs = 733 Ω will meet
the requirements, but the behavior at switching frequencies other than
100 kHz will differ.
Given a choice for Cs, L must be chosen according to:
For example, Cs = 3Cp = 3.2 nF leads to L = 1.96 mH
Fundamentals of Power Electronics
26
Chapter 19: Resonant Conversion
Rcrit
For the LCC tank network chosen, Rcrit is determined by the parameters of
the output ellipse, i.e., by the specification of Vg, Voc, and Isc. Note that
Zo is equal to jXp. One can find the following expression for Rcrit:
Since Zo0 and H  are determined uniquely by the operating point
requirements, then Rcrit is also. Other, more complex tank circuits may have
more degrees of freedom that allow Rcrit to be independently chosen.
Evaluation of the above equation leads to Rcrit = 1466 Ω. Hence ZVS for
R < 1466 Ω, and the nominal operating point with R = 900 Ω has ZVS.
Fundamentals of Power Electronics
27
Chapter 19: Resonant Conversion
Rcrit
Fundamentals of Power Electronics
28
Chapter 19: Resonant Conversion
Ellipse again with Rcrit, Rmatched, and Rnom
Showing ZVS and ZCS
Fundamentals of Power Electronics
29
Chapter 19: Resonant Conversion
Converter performance
For this design, the salient tank frequencies are
(note that fs is nearly equal to fm, so the
transistor current should be nearly
independent of load)
The open-circuit tank input impedance is
So when the load is open-circuited, the transistor current is
Similar calculations for a short-circuited load lead to
Fundamentals of Power Electronics
30
Chapter 19: Resonant Conversion
Extending ZVS range
Fundamentals of Power Electronics
31
Chapter 19: Resonant Conversion
Extending ZVS range
Fundamentals of Power Electronics
32
Chapter 19: Resonant Conversion
Extending ZVS range
Fundamentals of Power Electronics
33
Chapter 19: Resonant Conversion
Discussion wrt ZVS and transistor current scaling
Series and parallel tanks
•
•
•
•
•
Fundamentals of Power Electronics
34
fs above resonance:
•
No-load transistor current = 0
•
ZVS
fs below resonance:
•
No-load transistor current = 0
•
ZCS
fs above resonance:
•
No-load transistor current greater than short circuit current
•
ZVS
fs below resonance but > fm :
•
No-load transistor current greater than short circuit current
•
ZCS for no-load; ZVS for short-circuit
fs < fm:
•
No-load transistor current less than short circuit current
•
ZCS for no-load; ZVS for short-circuit
Chapter 19: Resonant Conversion
Discussion wrt ZVS and transistor current scaling
LCC tank
•
•
•
•
Fundamentals of Power Electronics
35
fs > finf
•
No-load transistor current greater than short circuit current
•
ZVS
fm < fs < finf
•
No-load transistor current greater than short circuit current
•
ZCS for no-load; ZVS for short-circuit
f0 < fs < f m
•
No-load transistor current less than short circuit current
•
ZCS for no-load; ZVS for short-circuit
fs < f0
•
No-load transistor current less than short circuit current
•
ZCS
Chapter 19: Resonant Conversion