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Small Signal Gain
Small Signal Gain
This block is included only in the PLECS Standalone library.
Purpose
Measure loop gain of closed control loop using small-signal analysis
Library
Control / Small Signal Analysis
Description
This block uses the Small Signal Perturbation block see page 520 and the
Small Signal Response block see page 521 to inject a perturbation into a
feedback loop and measure the system response. To see the implementation
choose Look under mask from the Subsystem submenu of the block’s con-
text menu.
For detailed information regarding small-signal analysis see chapter “Analysis
Tools” (on page 143).
Parameter
Compensate for negative feedback
When set to
on
,the underlying Small Signal Response block inverts the
reference input in order to compensate for a negative unity gain that is
introduced when the feedback signal is subtracted from a reference signal.
When set to
off
,the reference input is taken as is.
519
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13
Component Reference
Small Signal Perturbation
This block is included only in the PLECS Standalone library.
Purpose
Generate perturbation signal for small-signal analysis
Library
Control / Small Signal Analysis
Description
During a small-signal analysis that references this block, it generates the ap-
propriate perturbation signal: a sinusoidal signal for an AC Sweep and a dis-
crete pulse for an Impulse Response Analysis. At all other times the perturba-
tion is zero.
For detailed information regarding small-signal analysis see chapter “Analysis
Tools” (on page 143).
Parameter
Show feed-through input
When set to
on
,the block displays an input port. The output signal is the
sum of the input signal and the perturbation. The default is
off
.
520
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Small Signal Response
Small Signal Response
This block is included only in the PLECS Standalone library.
Purpose
Measure system response for small-signal analysis
Library
Control / Small Signal Analysis
Description
During a small-signal analysis that references this block, it records the sig-
nal(s) that are connected to the block input(s) in order to calculate the trans-
fer function
G(s) =
Y(s)
U(s)
If the reference input is shown, U(s) is calculated from the signal that is con-
nected to it. Otherwise, U(s) is calculated from the perturbation signal gener-
ated by the corresponding Small Signal Perturbation block see page 520.
For detailed information regarding small-signal analysis see chapter “Analysis
Tools” (on page 143).
Parameters
Show reference input
Specifies whether or not the block shows the reference input port.
Invert reference input
Specifies whether or not the reference input signal is inverted, i.e. multi-
plied with -1.
521
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13
Component Reference
Space Vector PWM
Purpose
Generate PWM signals for 3-phase inverter using space-vector modulation
technique
Library
Control / Modulators
Description
The space vector modulator generates a reference voltage vector,
!
V
s
,at the ac
terminals of a three phase voltage source converter shown below. The refer-
ence vector is defined in the  coordinate system:
!
V
s
=V
+j V
.
Vdc
leg A
leg B
leg C
Vs
a
b
c
Operation
The construction of the reference voltage vector,
!
V
s
,is graphically depicted be-
low. Internally, the space vector modulator consists of a sector detection and
vector timing calculation function that is executed at the beginning of the
switching cycle. In this function, the operating sector and relative on-times
of the switching vectors are calculated. During a switching cycle, a vector gen-
eration and sequencing function is called at the switching instants to update
the switch output.
The sector detection calculation determines the sector in which the reference
voltage vector
!
V
s
resides. The relative on-times, 
a
;
b
;
0
,for the switching vec-
tors
!
V
a
;
!
V
b
and
!
V
0
are then calculated. In each sector, two unique switching
vectors named
!
V
a
and
!
V
b
are available. Two zero vectors, named
!
V
1
0
;
!
V
2
0
are
also available. The relationship between the relative on-times and the refer-
ence vector is shown below for an arbitrary sector. The relative on-times are
calculated by projecting the reference vector onto the vectors
!
V
a
and
!
V
b
.
The vector generation and sequencing function creates a switching cy-
cle by time-averaging the switching vectors according to their on-time
522
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Space Vector PWM
v
s
Sector 2
Sector 1
Sector 3
Sector 4
Sector 6
Sector 5
v
*
v
*
Construction of the reference vector
!
V
s
.
values. There are many possible switching sequences that can be imple-
mented since the order in which the vectors
!
V
a
;
!
V
b
;
!
V
0
are applied dur-
ing a switching cycle is arbitrary. In addition, one or both of the
!
V
0
vec-
tors can be used. For further information, please read the documenta-
tion that accompanies the demo model "Space Vector Control of a Three
Phase Rectifier using PLECS". This documentation can be found at
www.plexim.com/sites/default/files/plecs_svm.pdf
.
523
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13
Component Reference
V
b
V
a
v
s
V
0
V
0
V
a
V
b
V
0,
1
2
0
b
a
Relationship between relative on times, 
a
;
b
;
0
,switching vectors,
!
V
a
;
!
V
b
;
!
V
0
,
and reference vector,
!
V
s
.
Parameters
Modulation strategy
The modulation strategy can be set to ‘Alternating zero vector’ or ‘Symmet-
rical’ using a combo box. With alternating zero vector modulation, only one
of the two
!
V
0
switching vectors is used during a switching sequence. One
switch leg is always clamped to the positive or negative dc bus voltage and
only two of the three inverter legs are switched.
With symmetrical modulation, the two
!
V
0
switching vectors are used: one
at the beginning and one at the middle of a switching sequence. All three
inverter legs are switched during a switching sequence.
Switching frequency
The switching frequency in Hz.
Switch output values
The switch output values in the high and low state. The values should
be selected to match the inverter’s gate control logic so that a high value
turns on the upper switch in the leg and the low value turns on the lower
switch. The default values are [ 1 1].
Inputs and
Outputs
DC voltage
The input signal V
dc
is the voltage measured on the dc side of the inverter.
Reference voltage
This input, labeled V

,is a two-dimensional vector signal comprising the
elements [V
;V
].
524
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Space Vector PWM
Switch output
The output labeled sw is formed from three switch control signals,
[S
a
;S
b
;S
c
], which control the inverter legs A, B, and C. Each switch signal
controls the upper and lower switches in the respective leg.
Probe Signals
sector
Avalue in the set of [1::6] that indicates the sector in which the referer-
ence vector,
!
V
s
,is located.
tau
Avector signal comprising the three relative on-time values, [
a
;
b
;
0
].
sw
Avector signal consisting of the three gate signals for the inverter legs,
[S
a
;S
b
;S
c
].
525
13
Component Reference
Space Vector PWM (3-Level)
Purpose
Generate PWM signals for a 3-phase 3-level neutral-point clamped inverter
using space-vector modulation technique
Library
Control / Modulators
Description
The 3-level space-vector modulator generates a voltage vector on the ac ter-
minals of a neutral-point clamped 3-phase inverter according to a reference
signal provided in the stationary  reference frame.
-+- 
o+- 
+o- 
+-- 
+-o
+-+
o-+ 
--+ 
-o+ 
-++ 
-+o 
++- 
++o 
oo- 
+oo 
o-- 
+o+ 
o-o 
--o 
oo+ 
-oo 
o++ 
o+o 
-o- 
Sector 
Sector 
Sector 
Sector 
Sector 
Zone 
Zone 
Zone 
Zone 
The hexagon area can be divided in to six sectors (1 to 6), each of which has
four zones (1 to 4). As an example, consider the reference voltage
~
V
to be lo-
cated in zone 2 of sector 1. In order to generate the reference voltage
~
V
on
the ac terminals, the adjacent vectors
~
V
1
,
~
V
3
and
~
V
5
are selected and weighted
by time. The on-time of each vector with respect to the switching period is cal-
culated as:
a
=1  2k sin()
b
=2k sin
3
+
1
c
=1  2k sin
3
This block implements a symmetrical sequence to achieve minimum total har-
monic distortion (THD). The short vectors have redundant switch states, e.g.
~
V
1
can be either generated by the combination (+oo) or (o--). In order to keep
the dc link voltages balanced, both switch states must be applied for the same
527
13
Component Reference
V
0
V
1
V
2
V
5
V
4
V
3
V*
Sector 
τ
a
τ
b
τ
c
θ
duration during one switching period. The resulting switch pattern is illus-
trated below:
τ
c
4
τ
a
4
τ
b
4
τ
c
4
τ
a
4
τ
c
4
τ
b
4
τ
a
4
τ
c
4
S
a
S
b
S
c
Parameters
Switching frequency
The switching frequency in Hz.
Output values
The switch output values in the high, neutral and low state. The default
values are [-1 0 1].
Inputs and
Outputs
DC voltage
The input signal V
dc
is the sum of the two dc link voltages V
dc+
and V
dc 
.
528
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