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