OPAL-RT - RT13 Conference, State-Space Nodal
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Transcript of OPAL-RT - RT13 Conference, State-Space Nodal
ARTEMiS-SSN
State-Space Nodal (SSN)
A nodal admittance solver for
SimPowerSystems
ARTEMiS, SSN and SimPowerSystems
– SimPowerSystems (SPS) is the main blockset of Simulink to simulate electric circuits and power systems
– ARTEMiS is a real-time enabler for SPS, its adds adapted real-time solvers like SSN (State-Space Nodal)
Simulink
SimPowerSystems
Rea
l-Ti
me
ARTEMiS
eMEGAsim
Simulation challenges of large power grids
• Grids represent a very large simulation problem
• Simulation can be parallelized by using the line propagation delays (-> maps into inter-core delays!)
6-core eMEGAsimGrid model
1 2
3 4
5 6
Simulation challenges of large power grids
• So what do we do to parallelize the simulation when no transmission lines?
• Ex: distribution systems, on-board power systems…
Example of renewable integrationinto an existing distribution grid
ARTEMiS for the historians (before SSN)• ARTEMiS was based on state-space equations of power
systems. Like SimPowerSystems.
• Uses precalculation of all possible state-space matrices for all switch possibilities.
• With 22 switches, we end up with 4 millions possibilities!
Def_F
Def_A Def_E
Brk0 Brk111 km 9 km 9 km 11 km
3 kmCT1CT0
Def_D
State-space vs. ‘Nodal method’• Directly find the state-space
equations (‘ABCD’ equations)
• not so easy to do in general, many special cases exists.
• 1st , make small pieces (groups!) of the network
• Find the equation of each one (VERY EASY!)
• Solve the common voltages/currents with nodal admittance equation VY=I
Advantages of nodal admittance methods.• Let’s add 9 nodes to our model in SSN. Note that it
defines groups boundaries, in colors.
• The 5 groups contribute independently to the nodal matrix, even if we precompute the switches in each groups. Here, each group has only 3-4 switches!
• All groups solved in the VY=I (by LU method).
Def_F
Def_A Def_E
Brk0 Brk111 km 9 km 9 km 11 km
3 kmCT1CT0
Def_D
333
Advantages of nodal admittance methods.
• OK. What would do HYPERSIM or RTDS then?
• Answer: the same thing, except that the groups are simpler. It results in larger nodal matrix, here of size 24.
• Smaller groups, bigger admittance matrix, which one is faster? I don’t know. It depends...
Def_F
Def_A Def_E
Brk0 Brk111 km 9 km 9 km 11 km
3 kmCT1CT0
Def_D
33
3
3 3 3 3 3
SSN example: bipolar HVDC withswitched filter banks.
• On each station: 42 switches, 19 nodes
• Time step: 48µs
• Firing interpolation included for free!
SSN example: High-current converter
• 124 states, 448 inputs, 389 outputs and…
• 162 coupled switches!!!
• Real-time integration step=57 µs
SSN example: Motor drive with Triple3-level NPC rectifiers
• ~100 coupled IGBT/switches!!!
• Real-time integration step=25 µs
SSN example: More-Electric Aircraft power system management
• 109 switches. 25 SSN partitions, nodal admittance matrix of rank 48, which is 80% sparse.
• Real time step=39 µs
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
20
25
30
35
40
45
Time (s)
Voltage (
VD
C)
BATT Bus
VFG 1 supplies
AC Bus 4
14.31 VDC
43.06 VDC
29.4 VDC
18.7 VDC
29.11 VDC
VFG 4 on
(28.01 VDC)
SSPC supplies
25.08 VDC
SSPC supplies
25.08 VDC
VFG 4 failure
(off)
Generator #4 failure test case
SSN example: Military navy ship
• 885 states in total
• Real-time step= 280 µs (2 cores), 338 us (6 cores)
(this is not a PPT error! )
Cause of this: difficulty in making effectiveparallelisation of theSSN algorithm.
Load Center 2Load Center 1
Load Center 3
Switchboard 1
Load Center 5
Switchboard 2
Sw
itch
bo
ard
3
Load Center 4
Generator 1
450 V, 60 Hz, 900 RPM
3.125 MVA, 0.8 PF
Generator 2
450 V, 60 Hz, 900 RPM
3.125 MVA, 0.8 PF
L0635 kVA
L0535 kVA
L037 kVA
L13333 kVA
L01333 kVA
L027 kVA
L0938 kVA
L0412 kVA
L11191 kVA
L1070 kVA
M15139 kVA
M18214 kVA
M0991 kVA
M0891 kVA
M025 kVA
L0838 kVA
M16214 kVA
M12139 kVA
M015 kVA
M0555 kVA
M0455 kVA
M17214 kVA
M14139 kVA
M13139 kVA
M11139 kVA
M0346 kVA
M10139 kVA
L0938 kVA
T0175 kVA
T0275 kVA
T0375 kVA
T0475 kVA
T0575 kVA
T0775 kVAT08
75 kVA
T0975 kVA
T1075 kVA
Cable (alternate supply)
Bus transfer switch
Transformer (450:120 V)
Low-voltage protective device
Synchronous generator
Bus
Cable (primary supply)
Circuit breaker
Load (kVA values approximate)
L12316 kVA
T1175 kVA
M0655 kVA
M0755 kVA
M19214 kVA
T0675 kVA
H
G
F
E
D
C
B
A
8 7 6 5 4 3 2 1
H
G
F
E
D
C
B
A
8 7 6 5 4 3 2 1
Node Tearing Case Study
Three-phase a-b-c fault
(Rf =1 mΩ)
t = 10 ms: fault applied
t = 25 ms: fault clears
All measurements made
at this circuit breaker
State-Space Nodal Case Study
Three-phase a-b-c fault (Rf =1 mΩ)
t = 111 ms: fault applied
t = 113 ms: breaker at GEN1 opens
t = 115 ms: fault clears
t = 130 ms: breaker at GEN1 opens
SSN: still place for improvements
• SSN groups are computed in parallel with a simple computation load balancing among cores.
• We can make this load allocation more intelligent by making SSN super-groups.
GRID
F1
F2
F5
F3
F4
Transformer + OLTC
63 kV / 20 kV
36 MVA
OLTC connectedDistribution system case
ARTEMiS-SSN L-stable discretization(for more stable simulations)
y’=ly
Re{l}
Im{l}
Laplace map
y(n+1)=zy(n)
Re{z}
Im{z}Z- domain map
-1
12/
2/lim
ATI
ATIAT
Trapeze (A-stable)
0)()(
)(lim
3
6012
203
53
2
201
52
ATATATI
ATATIAT
ARTEMiS art5 (L-stable)
z mapping near -1means oscillations
This mode isgetting faster!
Frequency Dependant Transmission Line in SSN
• Frequency-Dependant (Marti-type) and WideBand line models are much more accurate than Bergeron CP-line
• These line model are coded with nodal method with a Norton-Type interface compatible with SSN
Ir Z V2 +-
W2k2
IsZ
Line model nodal interface
Why are frequency dependant line model more accurate?
• Frequency-Dependant lines include the attenuation of the line propagation effects with regards to frequency– Bergeron CP-line only include lumped resistive losses
– FD/WB models will better damp high-frequency components of the line.
– WB better suited mathematically for cables
• Impulse response compared below: FD includes real line effects like dispersion, attenuation, etc…
Line
Impulse step
propagation propagation
FD/WB-LineCP-Line
User’s coded SSN models
• It’s possible for the user to code his own SSN model. Why would you do this?
– To optimize models for RT.
– To change electric parameters on-line
• Many examplesavailable inARTEMiS-SSNdemos
Conclusion
• SSN has brought ARTEMiS & eMEGAsim in the major league of power system simulation
• Future work and evolution of SSN
1: On-line electric parameter change (now only doable with SSN external models)
2: Better parallelisation algorithm
3: Automatic partitioning & task parallelisation
• HYPERSIM makes partionining & task parallelisation. Not so easy to do within the Simulink environment
Selected References
• C. Dufour, J. Mahseredjian , J. Bélanger, “A Combined State-Space Nodal Method for the Simulation of Power System Transients”, IEEE Transactions on Power Delivery, Vol. 26, no. 2, April 2011 (ISSN 0885-8977), pp. 928-935
• Ramos-Leanos, O.; Naredo, J. L.; Mahseredjian, J.; Dufour, C.; Gutierrez-Robles, J. A.; Kocar, I.; "A Wideband Line/Cable Model for Real-Time Simulations of Power System Transients," Power Delivery, IEEE Transactions on , vol.27, no.4, pp.2211-2218, Oct. 2012.
• W.Wang, L. Bakay, C. Dufour, “Hardware-In-the-Loop Simulation of a Complex AC-fed Motor Drive with Triple Active Front-End 3-level Rectifiers and Induction Motor Drive using an Intra-Step-Parallel State-Space-Nodal Solver”, Proceedings of the 14th European Conference on Power Electronics and Applications (EPE-2011), Birmingham, England, Aug. 30- Sept. 1, 2011
• C. Dufour, L.-A. Grégoire, J. Bélanger, “Solvers for Real-Time Simulation of Bipolar Thyristor-Based HVDC and 180-cell HVDC Modular Multilevel Converter for System Interconnection and Distributed Energy Integration”, 2011, CIGRÉ conference proceedings, Recife, Brazil, April 3-8, 2011.
• L. Montealegre Lobo, C. Dufour, J. Mahseredjian, “Real-time Simulation of More-Electric Aircraft Power Systems”, Proceedings of the 15th European Conference on Power Electronics and Applications (EPE’13 ECCE Europe), Lille, France, Sept. 3-5, 2013