ACCURATE SIMULATION OF THYRISTOR CONTROLLED REACTOR
WITH SWITCHING EVENT COMPENSATION IN ARTEMIS
C. Dufour, J. Bélanger, S. Abourida
OPAL-RT Technologies, www.opal-rt.com, christian.dufour@opal-rt.com
This paper presents new simulation software that allows
the efficient and accurate fixed-time-step simulation of
complex switched electrical systems. The software, named
ARTEMIS accurately simulates time-segment linear
systems with discontinuities occurring anywhere between
time-steps. This paper focuses on the simulation of a
thyristor controlled reactor by the ARTEMIS DTCSE
(Discrete Time Compensation of Switching Events)
algorithm and the RT-Events algorithm, showing the
accuracy of the software.
1 SIMULATION CASE: 1-PHASE THYRISTOR
CONTROLLED REACTOR (TCR)
The simulated circuit, a 3-phase static voltage compensator
composed of a 1-phase AC source feeding a thyristorcontrolled reactor (TCR) controlled by a phase-locked
(PLL) firing pulse unit (FPU), is shown in Figure 1. The
snubber was needed only for the Tustin simulation, since
without it the simulation missed some thyristor firings.
ARTEMIS-DTCSE method while Tustin method produces
spurious low-frequency jitter of about 5% in amplitude. In
both cases the same 50 µs time step was.
TCR current (firing angle: 135°)
0.292
DTCSE
0.29
jitter=0.1%
0.288
0.286
Current (A)
ABSTRACT
0.284
0.282
Tustin
0.28
jitter=5%
0.278
0.276
0.274
0.272
Ts=50µs
0.71
0.72
0.73
0.74
Time (s)
0.75
0.76
Figure 2. Comparison of DTCSE and Tustin simulation
results showing that the Tustin method produces
spurious low-frequency jitter.
Figure 1. Thyristor Controlled Reactor and controller.
1.2 Frequency domain analysis
The effect of firing angle on open-loop current were
investigated and are displayed in Figures 3 and 4. For
comparison purposes, the results calculated using the
ARTEMIS DTCSE/RT-Events and the Tustin algorithms
are superimposed on a reference result calculated using the
more accurate variable-time-step method (which
unfortunately cannot be used in real-time systems due to its
non-deterministic calculation time). The ARTEMIS
algorithms provide continuous small signal linearity in
fixed time step. This linearity can have a great impact on
the design of closed-loop controls.
Figures 6 and 7 compare the results with respect to the 3rd
and 5th harmonics, again showing that the ARTEMIS
algorithms produce visibly better results than the Tustin
method. Close examination of Figure 4 reveals that the
Tustin method produces an 2°-equivalent backlash in its
characteristic.
1.1 Time domain analysis
Simulation results for the TCR obtained using the
ARTEMIS DTCSE algorithm are compared with those
obtained using the standard Tustin algorithm in Figure 2. A
jitter-free TCR current is correctly calculated by the
c:\documents and settings\davidm\local settings\temporary internet files\olk58b\tn-art-08 tcr 1-ph.doc
1
Fundamental componant TCR current
5e harmonic of TCR current
1
0.06
Tustin
0.9
DTCSE
variable time step solver
0.05
0.8
DTCSE &
variable time step solver
0.7
Current (A)
Current (A)
0.04
0.6
0.5
0.4
Tustin
Ts=104µs
0.03
0.02
0.3
0.2
0.01
0.1
0
90
100
110
120
130
140
150
160
170
180
0
90
100
110
120
Angle (degres)
Figure 3. Comparison of simulation results showing effect of
130
140
Angle (degres)
150
160
170
180
Figure 6. Comparison of simulation results showing effect of
th
Tustin quantization errors.
Tustin quantization errors on the 5
harmonic of
TCR branch current.
2 RT-EVENT TOOLBOX FOR EASY EVENTBASED CONTROL DESIGN
The simulation of the thyristor-controlled reactor with
DTCSE requires the use of the RT-Events toolbox to
provide the DTCSE algorithm with precise intra-step
timing of switching events. The RT-Events toolbox is easy
to use and leaves standard alpha-controlled firing scheme
techniques unmodified, as shown in Figure 7.
0.7
DTCSE &
variable time step solver
Current (A)
0.65
0.6
0.55
0.5
Tustin
synchonization
voltages
Simulink subsystems
band-pass filter and/or
phase-lock loop
Ts=104µs
104
106
108
110
112
114
116
firing angle α
Rt-Event blocs
>0.0
Rt-Event
Rt-Event
level detector triggered
integrator
α
To switch
gates
Rt-Event
pulse logic
Angle (degres)
Figure 7. RT-Events blocks alpha-controlled firing control
Figure 4. Detail of Figure 3.
The RT-Events blocks have the same functionality as their
Simulink counterparts except they output additional timing
information on intra-step events like zero-crossings.
3e harmonic of TCR current
0.16
0.14
Tustin
DTCSE &
variable time step solver
3 CONCLUSION
The simulation of the TCR by ARTEMIS with DTCSE has
eliminated sub-synchronous jitter and provided small
signal linearity of the TCR characteristic in fixed time step.
The software can be use for the design of digital controller,
with the use of RT-Events, a Simulink Blockset, for realtime simulation, hardware-in-the-loop design and other
simulation applications.
0.12
Current (A)
0.1
0.08
Ts=104µs
0.06
0.04
0.02
0
90
100
110
120
130
140
150
160
170
180
Angle (degres)
Figure 5. Comparison of simulation results showing effect of
Tustin quantization errors on the 3
rd
harmonic of
TCR branch current.
c:\documents and settings\davidm\local settings\temporary internet files\olk58b\tn-art-08 tcr 1-ph.doc
2