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.