Download Electromagnetic Transients Simulation Models for Accurate

1
Electromagnetic Transients Simulation Models for
Accurate Representation of Switching Losses and
Thermal Performance in Power Electronic Systems
A.D. Rajapakse, Member, IEEE, A.M. Gole, Member, IEEE, and P. L. Wilson, Member, IEEE
Abstract-- This paper presents an electro-thermal model of an
Insulated Gate Bipolar Transistor (IGBT) switch suitable for the
simulation of switching and conduction losses in a large class of
Voltage Sourced Converter (VSC) based FACTS devices. The
model is obtained by mathematical derivation of loss equations
from
the
known
sub-microsecond
device
switching
characteristics; and through the selection of appropriate
differential equation parameters for representing the thermal
performance. The model is useful in determining the device’s
heat generation, its junction temperature as well the cooling
performance of the connected heat sinks. The model provides
accurate results without recourse to an unreasonably small timestep.
Index Terms-- IGBT, switching losses, thermal performance,
electromagnetic transient simulation, voltage-sourced converter
I. INTRODUCTION
T
HE insulated gate bipolar transistor (IGBT) is widely used
in many modern power-electronic applications in power
transmission and distribution systems. Estimation of power
loss and junction temperature of power semiconductor devices
has become a major issue with the growth of high switching
frequency applications such as pulse width modulated
(PWM) inverters, where switching losses constitute a
significant portion of the power dissipation in the
semiconductor device. Power electronic system manufacturers
can utilize the relatively low but significant thermal capacity
of the power semiconductors to obtain short duration
overloading well in excess of continuous ratings [1]. Tools for
accurate prediction of device power dissipation and junction
temperature become important in achieving optimized
solutions in terms of performance, thermal management and
packaging.
Most electromagnetic transient programs (emtp-type)
model power electronic devices as on-off switches or two state
resistances [2]. This simple representation is sufficiently
accurate to simulate the system-level electrical behaviour of
power electronic circuits [3]. However, the determination of
switching and conduction losses requires the consideration of
the physics of the switching process, which lasts only about
several hundreds of nanoseconds. To model this process in
detail would require a very small time-step which would result
in an unacceptably large CPU time when simulating large
multi-device power electronic systems (such as FACTS
devices).
Previous efforts to address the issue of accurate estimation
of power losses include using specially defined switching
functions obtained through measurements [5] or the use of
lookup tables or fitted curves to define power losses as a
function of voltage, current and junction temperature
[4],[6],[7]. The first method requires very small time steps,
whereas the second is approximate.
Another approach that has been proposed is the use of
simple functions derived for losses based on the typical
switching waveforms [8],[9],[10]. The method presented in
this paper extends the above approach by ‘filling-in’ the
device’s current and voltage waveforms in between the
simulation time step to conform to the physics of the
switching process. With these estimated waveforms it
becomes possible to calculate the losses.
Once the losses are estimated, it becomes necessary to
solve the heat-flow problem in order to determine
temperatures and cooling requirements. The most accurate
method for doing so is through three dimensional finiteelement based modeling [11], which is again impractical in
system level simulations. The more acceptable and commonly
used approach is to model the thermal behaviour by using
equivalent network of thermal resistances and capacitances
[1],[12],[13].
This paper describes a complete electro-thermal model of
IGBT and parameter extraction method. Effort has made to
obtain most model parameters from the published data sheets.
The dependency of the switching losses on various factors
such as switching voltage, switching current, reverse recovery
of freewheeling diode, stray inductance and capacitance are
taken into account. The model was implemented in
PSCAD/EMTDC™, a well known emtp-type program.
Validation of the model was conducted using a simple
laboratory set-up and by comparison with published loss
curves by the manufacturer. The paper concludes with an
application example for loss determination in a PWM inverter.
II. DEVELOPMENT OF A SUITABLE SWITCH MODEL FOR EMTPTYPE PROGRAMS
A. Method for Interfacing
The majority of emtp-type programs are used for large
system studies, and therefore usually employ simple on/off
type representations for devices such as diodes, thyristors,
GTOs and IGBTs. For such studies, a detailed representation
of the physics of the switching device, which requires time-
2
steps in order of several nanoseconds, would be overly time
consuming.
Rest of
the
Electrical
Network
Electrical
parameters
Device Loss
Model
Parameter
Calculation
Simple
Switch
Model
model
parameter
Operating
conditions
Loss
Estimation
Device
temperature
Ambient
Thermal conditions
Path
Model
Power loss
Fig. 1. Interface between the electro-thermal device model and the network
model
The approach presented in this paper and depicted
schematically in Fig.1, adds an additional layer to this simple
device model which only makes minor dynamic updates to the
parameters within the host emtp program. The losses in the
device are estimated by observation of the pre- and postswitching currents and voltages using the algorithm described
below. These losses become the inputs to a dynamic model of
the heat management system (thermal path) which computes
the temperature changes in various parts of the system.
Because the device losses are functions of temperature, the
computed device temperature is then used to change the
parameters of the switch loss model for the next time-step.
B. Modelling of Device Losses
The losses in a power-switching device can be classified as
conduction losses, turn-on switching losses, turn-off switching
losses and off-state blocking losses. The conduction loss is
calculated in a straightforward manner as the product of the
device current and the forward saturation voltage; and the
blocking loss is the product of the blocking voltage and the
leakage current.
However, the determination of switching losses is a
challenge because the duration of the switching process is in
the order of a few hundred nanoseconds. The emtp-type
program typically uses a much larger time-step (tens of
microseconds) in order to achieve a reasonable CPU time for
simulating the entire network. This paper proposes a
workaround to this apparently impossible situation by
developing algebraic equations that represent the voltage and
current waveforms during the switching event based on the
fact that the current and voltage waveforms during switching
are principally a function of the pre- and post- switching
voltage and current. These equations ‘fill-in’ the intermediate
sub-microsecond values of voltage and current in between the
larger sampling instants dictated by the emtp time-step of
several microseconds. The parameters of these equations are
derivable from the pre- and post-switching voltages, currents
and other physical data. The energy loss can then be
calculated analytically (not numerically!) by integrating the
product of developed voltage and current equations resulting
in a formula for the switching loss. Thus the emtp-type
simulation can be conducted with a larger time-step, with the
developed formula providing an estimate of the loss at each
switching.
The switching loss model developed in this paper is
applicable to IGBT devices subject to ‘hard switching’ which
are widely used in today’s FACTS devices. Each switch
consists of an IGBT in anti-parallel with a freewheeling diode.
The turn-on of the IGBTs (and hence the turn-on switching
loss) is significantly affected by the reverse recovery
behaviour of the freewheeling diode and the parasitic
inductances. Although the discussion below is specific to
hard-switched IGBTs, as shown in the test circuit of Fig. 2,
the proposed concepts are readily extendable to other device
types.
Same as
(D.U.T.)
L
R
Vcc
Device Under
Test (D.U.T.)
Ic
Vce
Fig. 2. Inductive switching loss test circuit
1) Diode Turnoff Loss Formula
As mentioned above, the IGBT turn-on losses are affected
by the reverse recovery performance of the diode, which is
now discussed. The turn-off waveforms of a diode are shown
in Fig. 3. As the diode current falls, part of its stored charge is
removed due to recombination. The amount of the charge
removed is a function of the rate of current change dId/dt. This
rate is determined by the turn-on speed of the IGBT in the
opposite leg. The remaining part of the stored charge is
actively removed by a negative current through the diode.
During the initial period of this process known as reverse
recovery, the negative current increases; with the development
of a reverse voltage occurring only when the current attains a
value of Irrm, - the peak reverse recovery current. The
developed model uses the parameters Irrm, and trr (the time
taken for reverse recovery) as inputs.
The turn-off curves of the diode voltage and the current are
fitted considering three distinct intervals of Fig. 3. In the
interval [t0(rec), t1(rec)], Id is modeled as a linear slope, with
Vd=Vds (forward voltage drop). In the period [t1(rec),t2(rec)], it is
modeled by:
I d (t ) = − I1′( rec ) (t − t1( rec ) ) e
(
−α 1( rec ) t − t1( rec )
)2
(1)
The unknown parameters in (1) are computed from
datasheet information considering the defined points and the
initial slope of the Id curve as:
Id0
Id(t)
trra
Vds
trrb
trr
t
Irrm
0.1Irrm
Vd(t)
-Vd0
t0(rec)
t1(rec)
t2(rec)
t3(rec)
3
Fig. 4. Hard switching turn-on transient waveforms for loss calculation
Fig. 3. Idealized waveforms of diode turn-off transient
1
k D = I rrm e 2 t rr
(
dI d
dt
t0 ( rec )
)
1
α1( rec ) = 1 2( k D t rr ) 2 ; I1′( rec ) = 2α1( rec ) I rrm e 2
(2)
In the region t > t2(rec) the current and voltage are modeled
by:
I d (t ) = I rrm e
(
−α 2 ( rec ) t −t2 ( rec )
Vd (t ) ≈ V1( rec ) e
)2
(3)
(
−α 2 ( rec ) t −t2 ( rec )
)2 − V
d0
Won = ∫
(4)
The energy lost can now be computed as:
t 3( rec )
t 0 ( rec )
t 2 ( rec )
∫ Vd (t ) I d (t )dt + ∫ Vd (t ) I d (t )dt
Wrec =
≈
I d20Vds
2 I1( rec )
I
+ rrm
2
π
2α 2( rec )
(
2Vd 0 − V1( rec )
(6)
)
Note that the particular forms of the functions chosen to
represent the current and voltage variations are very
important; these functions should not only follow the desired
variations within the applicable region, but also facilitate the
analytical integration of the voltage-current product to arrive
at the formula for Wrec; and be amenable to extraction of the
values of parameters from the datasheet information.
2) IGBT Turn-on Loss Formula
Fig. 4 shows waveforms for the hard turn-on transient of an
IGBT. In data sheets, the turn-on behaviour is characterized
by the turn on delay time, td(on), the rise time, tr, and the turnon energy, Won.
The turn-on gate pulse is applied at t0(on) resulting in the
gradual rise of the gate voltage Vge (due to the input
capacitance of the IGBT). After a time td(on), when Vge reaches
a threshold voltage Vth, the collector current, Ic, starts to rise
almost linearly and the load current in the freewheeling diode
(of the opposite leg) gradually transfers to the IGBT. During
this rise, the device (collector-emitter) voltage Vce(t)
experiences a drop primarily due to parasitic inductance (Lp).
Vth
t 4 ( on )
t1( on )
where V1(rec) = Vd0+Vds. The condition that the reverse recovery
current decays to 10% of Irrm after time trr gives
ln | 10 |
ln | 10 |
=
α 2( rec ) = 2
(5)
t rrb
(1 − k D ) 2 t rr2
t1( rec )
The overshoot in Ic during [t2(on) – t4(on)] is due to the
reverse recovery current of freewheeling diode. The collectoremitter voltage Vce begins to fall when the diode reverse
recovery current reaches its peak value at t3(on).
As with the case for the diode turnoff discussed above,
applicable equations for the current and voltage waveforms
can be derived for the various intervals, and the energy loss
Won is calculated as:
Vge(t)
Vce (t ) I c (t )dt
⎛
≈ (Vc 0 − V1( on ) ) I1( on ) ⎜1.25t r +
⎝
(1− e
−1.25α1( on )t r
α 1( on )
)⎞
⎟
⎠
⎛ (1− e −1.25λ1( on )tr ) (1− e −1.25(α1( on ) +λ1( on ) ) tr ) ⎞
+ V1( on ) I1(on ) ⎜
+
⎟
λ1 ( on )
α 1 ( on ) + λ1( on )
⎝
⎠
(7)
2
(
k
t
)
−
α
2
(
rec
)
D
rr
⎛
I 1( rec ) (1− e
)⎞
⎟
⎜
+ Vcep I c 0 k D t rr +
2α 2 ( rec )
⎟
⎜
⎠
⎝
+ V2( on ) ⎛⎜ I c 0 4α π + I rrm 8α π ⎞⎟
2 ( rec )
2 ( rec ) ⎠
⎝
+ V3(on ) ⎛⎜ I c 0 4λπ + I rrm 4(α π+ λ ) ⎞⎟
3 ( on )
2 ( rec )
3 ( on ) ⎠
⎝
Appendix 1 provides an outline of the derivation and
definitions for the parameters in (7).
3) IGBT Turn-off Loss Formula
The IGBT’s turn-off behaviour shown in Fig. 5 is
characterized in data sheets by the turn-off delay time, td(off),
fall time, tf, and turn-off energy, Woff. The turn-off process
starts following the application of negative gate voltage at
time t0(off). The input capacitance of the IGBT discharges
gradually reducing gate-emitter voltage, Vge, but collectoremitter voltage, Vce, remains essentially unchanged until Vge
drops sufficiently to drive the IGBT out of saturation. This
initial period is denoted by tvd(off) in the Fig. 5. Thereafter, the
collector-emitter voltage rises rapidly. When Vce reaches the
forward blocking voltage Vce0, at t2(off), the freewheeling diode
become forward biased and starts to take over the load
current.
Vge(t)
Lp
Vce0
( )
dIc
dt max
Vce(t)
Ic0
0.9Ic0
kDtrr
Vce0
Lp
( )
Irrm
dI c
dt
tVd(off)
0.1Irrm
td(off)
tr
0.1Vce0
trr
tvtail
t1(on)
t2(on)
t0(off)
t3(on)
0.1Ic0
Itail
t1(off)
t2(off)
Ic(t)
t3(off)
t
Vces
Vce(t)
Vtail
0.1Ic0
t0(on)
titail
Vces
0.9Ic0
td(on)
tf
Ic(t)
Ic0
Fig. 5. Typical hard switching turn-off transient waveforms
t4(on)
t
The IGBTs internal construction includes a MOSFET
4
t2 ( off )
t0 ( off )
Vce (t ) I c (t )dt
α1(off )
Vce 0 I 2(off )
π
2
α 2(off )
)
C. Validation of Switching Energy Models
The approach developed above was validated by
comparison with published results from manufactures’ data
sheets as well as with a laboratory setup of the circuit in Fig.
2.
1) Comparison with Manufactures Data Sheets
The possibility of using the derived expression for
switching energies with data sheet parameters was studied by
computing switching energy verses collector current curves
for several IGBTs. The parameters that are not available in the
data sheets were estimated by adjusting their values to match
with the switching energy at the rated current. Those
parameter values are then used to predict the turn-on and turnoff losses at different collector currents. Two commercially
available IGBTs (with anti-parallel diodes) from different
manufacturers were considered, the SNR13H2500 from ABB,
rated at 2.5 kV, 1300 A and the IXGK50N60BD1 from IXYS
rated at 600 V, 65 A. The variation of calculated turn-on and
turn-off energy losses (as in (7) and (8)) for these two devices
are shown in Figs. 6 and 7 respectively; which also shows the
loss curves supplied on the manufacturers’ data sheets.
(mJ)
off
100
Vce (meas)
I c (meas)
I c (ideal)
Vce (ideal)
75
50
0
-200
kD = 0.5
kvtail = 0.15
-100
0
100
200
300
400
500
750
600
Fig. 8. Measured and fitted turn-on waveforms
Vce (meas)
Ic (meas)
Ic (ideal)
Vce (ideal)
c
200
150
100
kitail = 0.16
kvd = 0.64
50
1
250
500
time (ns)
ce
2
0
100
125
250
3
0
80
25
(V), 5.I (A)
4
60
150
V
on
W , Woff (J)
5
Ic (A)
300
ABB SNR 13H2500 @ 125 oC
W on (data)
W on (cal)
W off (data)
W off (cal)
6
40
175
c
(V2( off ) I 2(off ) + V3(off ) I 1(off ) ) ⎛
− 2 (α 4 +α 5 )( t f + titail ) 2 ⎞
⎟
⎜1 − e
2(α 1(off ) + α 2(off ) )
⎠
⎝
2
20
As can be seen, the equations developed in this paper
capture with reasonable accuracy, the variation of losses with
current.
2) Experimental Confirmation
The test circuit as in Fig. 2 was set up in a laboratory. A 20
mH inductance was selected to ensure negligible current
ripple; and the 4500 µF capacitor across the source was
selected to ensure ripple free dc voltage. The on-state current
in the device was adjusted by selecting the resistance R
appropriately. The IGBT (the anti-parallel diode being
included in the package) was rated at 600 V, 25 A
(IRG4PC40KD). The voltage and current waveforms were
measured and plotted for comparison with the piecewise
fitting formulae derived in this paper (see Appendix 1) from
which (7) and (8) are obtained. The plots for turn-on and turnoff are shown in Figs. 8 and 9 respectively and show good
agreement.
The calculated energy loss from (7) and (8) was also
compared with the measured energy loss; obtained by
integrating the product of the measured voltage and current
during switching.
5.I (A)
+
+
0
Fig 7 Variations of Eon and Eoff with Ic for IXYS IXGK50N60BD1 IGBT
ce
V3(off ) I 2(off ) ⎛
− 2α 2 ( off ) ( t f + titail ) 2 ⎞
⎜1 − e
⎟
4α 2(off ) ⎝
⎠
π
0
(8
+
Vce 0 I 1( off )
4
2
V2(off ) I c 0 ⎛
− 2α1( off ) ( td ( off ) − 81 t f ) 2 ⎞
+
⎜1 − e
⎟
4α 1(off ) ⎝
⎠
7
6
I c 0V1'(off ) (t d (off ) − 18 t f ) 2
2
I c 0Vces ⎛ λ1( off ) (1−kvd )( td ( off ) − 18 t f )
−λ
−1t )
k (t
+
− e 1( off ) vd d ( off ) 8 f ⎞⎟
⎜e
⎠
λ1(off ) ⎝
+
IXYS IXGK 50N60BD1 @125 oC
W on (data)
W on (cal)
W off (data)
W off (cal)
8
V (V),
≈
10
on
Woff = ∫
Fig. 6. Variations of Won and Woff with Ic for ABB SNR13H2500 IGBT
W ,W
driving a bipolar transistor, and due to the mechanisms
involved in these devices, the collector current Ic initially has a
rapid fall; followed by a more gentle drop towards extinction
at time t3(off). The rapid drop in current through the parasitic
inductance produces an overshoot in the voltage Vce .
Again, using suitable expressions for the current and
voltage over the various intervals (with details and parameters
in Appendix 1); the following expression is obtained for the
energy loss during turnoff Woff:
1000
1250
Ic (A)
1500
1750
2000
0
-400 -300 -200 -100
0
100
time (ns)
200
300
400
500
600
5
Fig. 9. Measured and fitted turn-off waveforms
Fig. 10. Equivalent thermal network of a semiconductor device and heat sink
TABLE I: COMPARISON OF MEASURED AND CALCULATED POWER LOSSES FOR
IRG4PC40KD IGBT
Vce0
Error
Error
Ic0
Won
Woff
(mJ)
(mJ)
(A)
(%)
(%)
(V)
Meas
Cal
Meas
Cal
150
15
0.193
0.216
11.9
0.183
0.203
10.9
150
20
0.274
0.312
13.9
0.289
0.318
10.0
150
25
0.353
0.417
18.1
0.394
0.478
21.3
120
120
120
15
20
25
0.155
0.221
0.310
0.173
0.242
0.325
11.6
9.5
4.8
0.112
0.183
0.289
0.125
0.205
0.321
11.6
12.0
11.1
III. MODELLING THE THERMAL PATH
The models developed in this paper are intended for
analyzing the thermal performance of the power electronic
circuit when operating into an electrical network. The junction
temperature of the device is an important parameter; an
excessive value can damage the device. The mounting of the
device and the heat-sink become important in determining the
heat removal performance, and hence must be modeled
accurately. The following section deals with this aspect.
A. Thermal Model of the IGBT
1) Thermal Equivalent Circuit
From a thermal point of view, the IGBT can be represented
by a lumped parameter equivalent circuit as in Fig. 10. PLj is
the power loss in the device with Tj and Tc being the junction
and case temperatures respectively. The nodal voltages
correspond to intermediate temperatures within the device. Rthi
and Cthi represent the thermal resistance and capacitance of
various layers of the semiconductor device. The number of RC
stages is usually determined by the number of materially
different layers in the thermal path. It is often sufficient to
model the heat sink as a single lumped thermal capacitance
and resistance from the sink to the ambient temperature (Ta).
If many devices are mounted on a common heat sink, the
IGBT thermal equivalent circuit can be connected in tandem
with the thermal equivalent of the heat sink as shown in Fig
10.
IGBT
PLj
+
Tj
-
Rth1
Rth2
Rthn
Cth1
Cth2
Cthn
Rc1s
Ta
+
Tc
PLc1
Tc1
Heat sink
Rsa
PLc
Rc2s
PLc2
Tc2
PLc
Cs
+
Ts
-
Rcms
PLcm
Tcm
In Fig. 10, Tci represents the case temperature of the ith
device mounted on the heat sink and Rcis are the corresponding
thermal resistances between the case and heat sink.
State space equations of the above thermal equivalent
circuit are set up and numerically solved to obtain the junction
temperatures. To calculate the average loss power PLj over a
small
measurement
period,
the
total
energy
(Wcond+Won+Woff+Wblok) as described in section IIb is
continuously calculated and divided by this measurement
period. This measurement period is effectively the ‘simulation
time-step’ of the thermal equivalent circuit of Fig. 10.
2) Extraction of Model Parameters
Although, some manufacturers provide the values of Rth
and Cth values in their device specification sheets, the
information required to obtain thermal network parameters is
commonly given in the form of a single-pulse junction to case
transient thermal impedance (Zth) curve shown in Fig. 11. This
curve is first approximated by an analytical function having
the form:
n
Z th (t ) = A0 + ∑ Ai e − a i t
(9)
i =1
where A0…An and a1…an are constants to be found through
an appropriate curve fitting technique. The Rthi and Cthi values
are then obtained from the Ai and ai as shown in Appendix 2.
The derived Ai and ai constants and the corresponding Rthi and
Cthi for IXER 35N120D1 IGBT/Diode module are shown in
Table II. As can be seen from Fig. 11, the Zth curves obtained
from the fitted thermal models (with 2 stages) show good
agreement with the corresponding data sheet curves.
1.4
Transient Z th (oC/W)
The results, which were generated considering various
combinations of two different voltages (150 V and 120 V) and
currents (15 A, 20A and 25 A) are shown in Table I. It can be
seen that the maximum error is 21%, although in most cases
the error is within 15%.
1.2
1
0.8
0.6
Zth
Zth
Zth
Zth
0.4
0.2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(IGBT) data
(Diode) data
(IGBT) cal
(Diode) cal
0.8
0.9
1
time (s)
Fig. 11. Transient thermal impedance curves of IXER 35N120D1 [14]
TABLE II: THERMAL PATH MODEL PARAMETERS OF IGBT
Parameters of fitted Zth curve
Calculated Rth and Cth
IGBT
Diode
IGBT
Diode
A0 = 0.600
A1 = -0.499
A2 = -0.101
a1 = 7.772
a2 = 69.518
A0 = 1.300
A1 = -1.099
A2 = -0.212
a1 = 6.901
a2 = 40.212
Rth1 = 0.238 K/W
Rth2 = 0.362 K/W
Cth1 = 0.095 J/K
Cth2 = 0.240 J/K
Rth1 = 0.650 K/W
Rth2 = 0.650 K/W
Cth1 = 0.064 J/K
Cth2 = 0.133 J/K
6
IV. APPLICATIONS
T1
E
T3
T4
T5
D3
D1
E
T6
D5
T2
R
L
40
Ia
Ib
0.0223
0.0278
Ia(ref)
Ic
Current (A)
20
0
-20
-40
0.0167
0.0334
time (s)
0.039
0.0445
0.0501
Fig. 13. Load and reference currents
6
IGBT (T1)
Diode (D1)
5
Energy loss (mJ)
B. Example: VSC with Hysteresis Current Control
The methods developed above were used in the loss and
thermal evaluation of the voltage source converter (VSC) of
Fig. 12. The converter is controlled using hysteresis current
control, which maintains the current in any phase within a
specified tolerance band around the reference current setting.
This is achieved by switching on the IGBT in the upper bridge
arm when the current is below the lower tolerance level; and
switching on the lower IGBT when the current is larger than
the upper tolerance level. Unlike conventional sinusoidal
PWM, the switching events and their frequency are highly
load dependent and so an a-priori estimation of switching
losses is difficult.
The inverter uses using six IXER 35N120D1 IGBT/Diode
modules and parameters required for the models were
obtained from its datasheet [14]. Fig. 13 shows the reference
current of Phase-A and the actual load currents in all three
phases. The relatively large hysterisis band seen in the load
current (∆I=10A) was deliberately set in order to clearly
observe the waveforms.
Fig. 14 shows the total energy loss as a function of time.
The conduction loss is proportional to the magnitude of the
current. The spikes at the beginning and end of conduction
periods correspond to turn-on and turn-off losses respectively.
In the diode, reverse recovery energy losses appear as spikes
at the end of conduction periods.
The variations of the junction temperatures of the IGBT
(T1) and diode (D1), and the module case temperature for an
ambient temperature of 25o C are shown in Fig. 15. The
depicted waveforms are for a transient state in which the
temperatures are still increasing enroute to their steady state
values (average 87oC for the IGBT junction temperature)
which are attained in approximately 10 s. Peaks of the ripples
appearing in the junction temperatures coincide with the
respective device current peaks, and their influence on
temperatures is smoothed out due to thermal capacitance.
Fig. 12. Hysteresis controlled voltage source inverter
4
3
2
1
0
0.12
0.125
time (s)
0.13
0.135
Fig. 14. Variation of energy losses (per simulation time step) in T1 and D1
60
Temperature ( oC)
A. The composite electro-thermal model
The power loss estimation model and the thermal models of
the device and heat sink were implemented in the
PSCAD/EMTDC program. As discussed in Section IIa and
shown in Fig. 1, the existing semiconductor switch model was
modified to include the loss calculations of section IIb. The
loss model calculates and outputs power dissipation (including
conduction, blocking and switching losses) in the switching
device during a simulation time step. The power dissipation is
input to the thermal model discussed in section III, which in
turn calculates the junction (and other) temperatures. The
junction temperature is fed back to the device power loss
calculation in the following time-step so that the temperature
dependent parameters (Vces and switching times) can be
updated.
40
Tj (IGBT)
Tcase
Tj (Diode)
Tamb
20
0
0.8
0.82
0.84
0.86
time (s)
Fig.15. Variation of junction and case temperatures
0.88
0.9
Table IV shows numerical values of the losses for two
different hysteresis band widths. As can be seen, the switching
losses increase with a smaller hysteresis band (i.e. higher
operating frequency), with the conduction losses remaining
fairly constant. The breakdown of the losses into various
components is also shown in the table.
TABLE IV: LOSS BREAKDOWN AND VARIATION WITH HYSTERESIS
BANDWIDTH
Type of loss per device
R=5.0Ω, L=0.005H
( 60 Hz load current)
∆I=10.0A
∆I=2.0A
Diode
IGBT
7
Conduction (W)
Turn-on (W)
Turn-off (W)
Blocking (W)
Conduction (W)
Reverse rec.(W)
Blocking (W)
17.77
(77.84%)
16.57
(62.01%)
3.16
(13.84%)
6.99
(26.16%)
1.79
(7.84%)
3.04
(11.38%)
0.11
(0.48%)
0.12
(0.45%)
5.84
(80.11%)
5.60
(68.71%)
1.34
(18.38%)
2.44
(29.94%)
0.11
(1.51%)
0.11
(1.35%)
This paper introduces modifications to the existing models
of semiconductor switches in electromagnetic transients
programs to account for losses. The approach, which is based
on interpolating analytically integrable equations to the
voltage and currents during the switching event, is reasonably
accurate without requiring excessively small time-steps. All
necessary parameters of the models can be estimated from
manufacturer’s data sheets or more accurately determined
from test waveforms where available.
The accuracy of the loss calculation formulae were
confirmed by comparison with a simple laboratory setup.
A method for calculation of temperature increase in the
semiconductor devices and the procedure of extracting the
required parameters from transient thermal impedance curves
was also presented.
Although the devices considered here were the IGBT and
the diode, the procedure is easily generalizable to most other
power electronic systems.
The applicability of the procedure was demonstrated by
considering the losses of a hysteresis controlled current
reference PWM inverter. The procedure yielded the different
components of the losses, as well as the dynamics of the
variations of junction temperatures. The example clearly
demonstrates that the developed approach would be useful in
the design of thermal management systems for power
electronic converters embedded in a large electrical network.
VI. APPENDIX 1
A. Turn-on Transient
The turn-on transient period is divided into three sections,
[t1(on) – t2(on)], [t2(on) – t3(on)] and [t3(on) – t4(on)] (see Fig. 4) to
derive the voltage and the current curves with:
t1( on ) = t0( on ) + td ( on ) − 18 t r , t2(on ) = t1(on ) + 10
t
8 r
(A1)
During [t1(on) – t2(on)], Ic and Vce are defined as
(
I c (t ) = I1(on ) 1 − e
−α1( on ) ( t − t1( on ) )
(
Vce (t ) = Vce 0 − V1(on ) 1 − e
)
− λ1( on ) ( t − t1( on ) )
)
(A2)
(A3)
Considering the almost linear rise of current, it is assumed
that I1(on) ≈ (100Ic0) where Ic0 is the on state current. Then
α1(on ) =
1
1.25t r
ln
1
0.99
V1( on ) =
8I c0
9t r
(A5)
Lp
Factor λ1(on) is obtained assuming 90% decay of V1(on)
during the considered period:
λ1(on ) = 1.251 t ln | 10 |
(A6)
r
During [t2(on) – t3(on)], the collector current is the sum of
load current and the reverse recovery current given in (1)
while Vce remains at plateau voltage Vcep defined below:
V. CONCLUSIONS
t3( on ) = t2( on ) + k D trr , t4(on ) = t2( on ) + t rr + tvtail
L p.
(A4)
An approximate value for V1(on) can be obtained
considering the average dIc/dt across the parasitic inductance
I c (t ) = I c 0 + I1′( rec ) (t − t2(on ) )e
Vcep = Vce0 − L p
−α 1( rec ) ( t − t 2 ( on ) ) 2
(A7)
0.8 I c 0
tr
(A8)
After t3(on), the reverse recovery current gradually decays
according to (3) while Vce falls towards its saturation value
Vces. It is assumed that Vce consist of two components decaying
at different rates:
I c (t ) = I c 0 + I rrm e
Vce (t ) = V2(on ) e
−α 2 ( rec ) ( t − t 3( on ) ) 2
−α 2 ( rec ) ( t − t 3( on ) )
2
+ V3(on ) e
(A9)
− λ 3( on ) ( t − t 3( on ) )
2
(A10)
The coefficient V3(on) of the slow decaying component of
Vce is equal to the tail voltage Vtail shown in Fig. 4, and
appears approximately proportional to plateau voltage Vcep.
Thus the factor, kv∞ [0-1], which characterizes the tail size is
defined such that:
Vtail = k v∞Vcep
(A11)
Then the magnitude of the fast decaying component (which
decays at the same rate as diode reverse recovery current) is
V2(on ) = (1 − k v∞ )Vcep
(A12)
The fact that the tail voltage drops to Vces, at t4(on) gives
k v∞Vcep
1
ln
λ3(on ) =
(A13)
2
Vces
[(1 − k D )trr + tvtail ]
B. Turn-off Transient
Expressions for the current and the voltage during the turnoff are defined considering two intervals, [t0(off) – t2(off)] and
[t2(off) – t3(off)] (see Fig.5) where:
t2( off ) = t0(off ) + td ( off ) − 18 t f
t3( off ) = t1( off ) + 98 t f + titail
(A14)
During [t0(off) – t2(off)], Ic remains at Ic0, while Vce rises
starting from its saturation value according to:
Vce (t ) = V1'( off ) t + Vces e
λ1( off ) ( t −t1( off ) )
where
t1( off ) = t0( off ) + k vd (td (off ) − 18 t f )
V1'( off ) =
λ1(off ) =
0.1Vce 0 − Vces
k vd (t d ( off ) − 18 t f )
ln (Vce 0 − V1( off ) tdf ) / Vces
(1 − k vd )(td ( off ) − 18 t f )
k vd ≈ tvd ( off ) / td ( off )
During [t2(off) – t3(off)], the Ic falls according to
(A15)
(A16)
(A17)
(A18)
(A19)
8
I c (t ) = I 1( off ) e
−α1( off ) ( t − t2 ( off ) ) 2
+ I 2(off ) e
−α 2 ( off ) ( t −t2 ( off ) ) 2
(A20)
Magnitude of the slowly decaying BJT component of the
current I2(off) is equal to the tail current Itail shown in Fig 5.
Assuming that Itail is proportional to Ic0, it is expressed as
I tail = ki∞ I co
(A20)
where ki∞ [0-1] is factor depend on the design (relative
gains of MOSFET and BJT) and the type (punch through or
non punch through) of IGBT. The magnitude of MOSFET
component of Ic is
I1(off ) = (1 − ki∞ ) I c 0
(A21)
The coefficients α1(off) and α2(off) are found considering the
defined point of current curve as:
α1(off ) ≈
64
t 2f
1− k
ln 0.9 − ki∞ , α 2( off ) ≈
i∞
1
( t f + t itail ) 2
ln 100ki∞
(A22)
The variation of Vce in this period is obtained considering
the induced voltage in parasitic inductance due to initial rapid
fall of Ic.
Vce (t )
dI ( t )
= Vce0 − Lp dtc
= Vce0 + V2(off )t ⋅ e
+ V3(off )t ⋅ e
−α 2( off ) ( t − t 2 ( off ) ) 2
Cth1 = s / q , Cth 2 = ( qr − ps) 2 / q( pqr − p 2 s − b 2 ) (A26)
where,
r=
1
a1
+
1
a2
, s=
+
1
a1
)+ A ( )+ A ( )
1
1 a1
1
2 a2
1
a1 a 2
(A27)
VIII. REFERENCES
[1]
[2]
[3]
[8]
[9]
[10]
[12]
[13]
[14]
A. Extraction of Thermal Model Parameters
The values of Rthi and Cthi values are calculated from the
coefficients of (9) as shown below. Generally, two
exponential terms (i.e. n =2 in (9)) can sufficiently accurately
approximate the Zth curve. For n=2, the values of Rthi and Cthi
are:
Rth1 = q 2 /( qr − ps ) , Rth 2 = p − q 2 /( qr − ps)
1
a1
[7]
[11]
VII. APPENDIX 2
(
[6]
(A24)
Again, the particular functions representing the voltage and
current at the different intervals of turn-on and turn-off were
chosen so that the product of the voltage and current is
analytically integrable.
q = A0
[5]
−α1( off ) ( t − t 2( off ) ) 2
where
V2(off ) = 2α1( off ) I1(off ) L p , V3(off ) = 2α 2(off ) I 2(off ) L p . (A25)
p = A0
[4]
G.L. Skibinski and W.A. Shthares, “Thermal Parameter Estimation
Using Recursive Identification, IEEE Trans. Power Electronics,” vol. 6,
pp. 228-239, Apr. 1991.
H. Selhi, and C. Christopouls, “Generalized TLM Switch Model for
Power Electronics Applications,” IEE Proc. Scientific Measuring
Technology, vol. 145, no.3, May 1998.
A.M. Gole, A. Keri, C. Kwankpa, E.W. Gunther, H.W. Dommel, I.
Hassan, J.R. Marti, J.A. Martinez, K.G. Fehrle, L. Tang, M.F.
McGranaghan, O.B. Nayak, P.F. Ribeiro, R. Iravani, and R. Lasseter,
“Guidelines for modeling power electronics in electric power
engineering applications,” IEEE Trans. Power Delivery, vol.12, pp. 505
–514, Jan. 1997.
S. Azuma, M. Kimata, M. Seto, X. Jiang, H. Lu, D. Xu, and L. Huang,
“Research on the power loss and junction temperature of power
semiconductor devices for inverter,” in Proc. of the IEEE International
Vehicle Electronics Conference, 6-9 Sept. 1999, vol.1, pp. 183 -187
C. Wong, “EMTP modeling of IGBT dynamic performance for power
dissipation estimation,” IEEE Trans. Industry Applications, vol. 33, pp
64 –71, Jan.-Feb. 1997.
S. Munk-Nielsen, L.N. Tutelea and U. Jaeger, “Simulation with ideal
switch models combined with measured loss data provides a good
estimate of power loss,” in Conference Record of the 2000 IEEE
Industry Applications Conference, vol.5, pp. 2915 –2922.
F. Blaabjerg, U. Jaeger, S. Munk-Nielsen, and J.K. Pedersen,
“Comparison of NPT and PT IGBT-devices for hard switching
applications,” in Conference Record of the 1994 IEEE Industry
Applications Society Annual Meeting, vol.2, pp. 1174 –1181.
J. Qian, A. Khan, A. I. Batarseh, “ Turn-off switching loss model and
analysis of IGBT under different switching operation modes,” in Proc.
21st International Conference on Industrial Electronics, Control, and
Instrumentation, 6-10 Nov. 1995, vol.1, pp. 240 –245.
M. Bland, P. Wheeler, J. Clare and L. Empringham, “Comparison of
calculated and measured losses in direct AC-AC converters,” in Proc.
IEEE 32nd Annual Power Electronics Specialists Conference, 17-21
June 2001, vol.2, pp. 1096 –1101.
K. Sheng, S.J. Finney, B.W. Williams, X. N. He and Z. M. Qian, “IGBT
switching losses,” in Proc. of the 2nd International Conference on Power
Electronics and Motion Control, Hangzhou, China, 1997, vol.1, pp. 27427.
A. Lakhsasi, Y. Hamri and A. Skorek, “Partially Coupled ElectroThermal Analysis for Accurate Prediction of Switching Devices,” in
Proc. Canadian Conference on Electrical and Computer Engineering,
13-16 May 2001, vol.1, pp. 375 –380.
J.H. Lee and B.H. Cho, “Large Time-Scale Electro-Thermal Simulation
for Loss and Thermal Management of Power MOSFET,”in Proc. IEEE
34th Annual Conference of Power Electronics Specialists, June 15-19,
2003, vol.1, pp. 112 –117.
J. Sigg, P. Türkes, and R. Kraus, “Parameter Extraction Methodology
and Validation for an Electro-Thermal Physics-Based NPT IGBT
Model,” in Proc. IEEE Industry Applications Society Annual Meeting,
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IXYS Semiconductor GmbH, Lampertheim, Germany, (2003), IXER
35N120D1 Product Specification Sheet,
IX. BIOGRAPHIES
A.D. Rajapakse (M,99) obtained his B.Sc. (Eng)
degree from the University of Moratuwa, Sri Lanka in
1990, M.Eng. degree from the Asian Institute of
Technology, Thailand in 1993 and Ph.D. degree from
the University of Tokyo in 1998. He is currently a
Visiting Professor at the University of Manitoba. Dr.
Rajapakse’s research interests are transient simulation
of power and power electronic systems, application of
fuzzy logic, neural networks and genetic algorithms
in modeling and control of dynamic systems,
renewable energy systems and energy conservation.
A. M. Gole (M’82) obtained the B.Tech. (EE) degree from IIT Bombay, India
in 1978 and the Ph.D. degree from the University of
Manitoba, Canada in 1982. He is currently a
Professor of Electrical and Computer Engineering at
the University of Manitoba. Dr. Gole’s research
interests include the utility applications of power
electronics and power systems transient simulation.
As an original member of the design team, he has
made important contributions to the PSCAD/EMTDC
simulation program. Dr. Gole is active on several
working groups of CIGRE and IEEE and is a
Registered Professional Engineer in the Province of Manitoba.
P. L. Wilson (M’00) graduated from the University
of Manitoba in 1987 in Electrical Engineering where
he joined Manitoba Hydro. In his professional career
he has held several positions including distribution
9
engineer, protection design engineer, maintenance engineer, and project
manager. Paul became the Managing Director of the Manitoba HVDC
Research Centre, November 1999. Along with his general duties, Paul is an
active member of the IEEE and CIGRE, and practicing member of the
APEGM. Paul Wilson lives in Winnipeg, Manitoba with his spouse Colleen
and two children.