Iterative Algorithmsof Surge Arrester
for Real-Time Simulators
Christian Dufour
OPAL-RT TECHNOLOGIES
Olivier Tremblay
Hydro-Québec’s research institute(IREQ)
Objective of the work
• Demonstrate how iterations within a real-time simulation can improve the accuracy of networks containing surge arresters
• Implementation in the State-Space-Nodal solver of ARTEMiS (OPAL-RT eMEGAsim RT-simulator)
• Compare performance with the existing iterative methods in HYPERSIM
– Implemented since 2012 in HYPERSIM**
**O. Tremblay, M. Fecteau, P. Prud’homme, “Precise Algorithm for Nonlinear Elements in Large-Scale Real-Time Simulator,” Proceedings of the 2012 CIGRÉ conference, Montréal, Qc, Canada, Sept. 24-26, 2013
OPAL-RT simulator line• OPAL-RT sells mainly 3 different power system
simulators– eMEGAsim: a MATLAB-Simulink-SimPowerSystems-based
real-time power system EMT simulator, aimed at researchers. It uses the State-Space Nodal solver.
– HYPERSIM: a integrated high-end power system EMT simulator, developed by a utility (Hydro-Québec) and aimed at utilities. It uses the standard nodal method.
– ePHASORsim: a real-time phasor-type simulator aimed at the Transient Stability simulator of very large network (+10000 busses)
• This work concerns eMEGAsim and HYPERSIM
The State-Space Nodal solver (SSN)• SSN** partition equations are derived from the partitions
(i.e. ‘SSN groups’) of the global state-space equations.
• With nodes , partition’s equations becomes decoupled
• Nodal admittance method used to solve the implicit common terms at the nodes
** 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
State-Space Nodal (SSN) vs. ‘Classic’ nodal
• Both use the nodal admittance method to solve the implicit terms of discretized branch equations.
• Standard nodal approach With SSN grouping
Y is rank 3 Y is rank 1
• Grouping of elements in SSN reduce the nodal admittance matrix size
• Since LU factorization is O3, we can obtain speed improvements in SSN
EMTP/EMTP-RV/HYPERSIM/RTDS
Y matrix automatically determined from branch connections
10 nodes/18 branches case (shown right)
State-Space Nodal solver
Y matrix nodes determined by the user partition selection
Examples: 1 node/2 partitions or…
2 nodes/3 partitions
Tends to classic nodal when node/partitions are increased
State-Space Nodal (SSN) vs. ‘Classic’ nodal
Surge Arrestersor Metal Oxide Varistors (MOV)
• MOVs are very non-linear devices used on a grid to protect from overvoltages
• Normally approximated by piecewise linear segments elements of function V=Vok+Rk*I (k is segment number, with very low R when conducting)
Characteristic of one of the 315 kV MOV of Gaspé network
Iterations in nodal admittance solvers
• Uses the standard EMTP algorithm
Algorithm modifications
1: Verify the validity of MOV segment AFTER the nodal voltage solution
2: Iterate on invalid segment
(i.e redo YV=I solution)
• This is possible because MOV have no LC states. Only contribute to YV=I
• MOV nodes have to be on the lowerright size of Y for optimal speed.
Iterations in nodal admittance solvers
• Oups…
• Let me correct the algorithm for the classicnodal method
• Basically, SSN is a nodal admittance algorithmlike EMTP in which he‘branch’ concept isgeneralized to ‘SSN groups’ or ‘SSN partitions’ branch
Branch equation
bra
nch
bra
nch
bra
nch
Parallelisation of SSN
• The branch/group ‘for’ loops can be parallelizedin all cases (EMPT, SSN)
• Practically however, parallelization of tinybranch equation will not be efficient on CPUs.
• In SSN, the group equations are big and parallelization is efficient(up to 50% speed up)
Case 1: Series-compensated network with MOV protection (SSN)
• Well-known SPS demo
• Fault at load, load overvoltage happens at fault clearance.
• 2 iterations are required on MOV2 to get accurate results
• MOV1 don’t need iteration(thanks to big capacitor)
Case 2: Gaspésie network (HYPERSIM)(a real network in Quebec, Canada)
• 103 nodes network, simulated on 4 CPUs.• 33 MOV approximated with 128 segments each• Saturable transformers also iterated in HYPERSIM
(but not explained in this paper)• Fault made on Bus 69, Voltage read on Bus 315
!
Case 2: Gaspésie network (HYPERSIM)
• 2 iterations required to avoid numerical oscillations (3rd trace)
• Achieved time step with 2 iterations: 24 µs
• Cost of iterations on time step: 25% (for this case)
Summary
• Iterations in real-time simulator are sometimes required to achieve accurate simulations for realistic networks.
• For surge arresters, this is possible at acceptable costs in terms of simulation time step.
– 24 µs for 103 node network achieved in this paper on HYPERSIM
• The iterative algorithm was also implemented successfully in SSN.– SSN real-time iterative MOVs (and Switches) to be
released in Q4/2014.
