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# Small Distribution Grid with Multiple Fault Test Capability with Mutual Inductances

This model is a small distribution grid used to test faults and possibly relays. It is a fully lumped network with many fault insertions. SSN is notably useful in this model because it puts switches in differents SSN groups without memory overflow and allows HIL simulation.

### Coupled inductances or full pi-line choice

This demo exists also with pi-lines instead of mutual inductances used for transmission lines. Although a pi-line seems a more accurate choice to model a short transmission line, it may not always be the best choice in terms of numerical stability and effectiveness. We exclude Bergeron-type transmission lines of this discussion with the 'short' qualitative.

The mutual inductance is obviously more efficient in terms of calculation speed because the same pi-line adds a lot of states into the SSN group calculations.

Typical transmission line capacitance values are in the range of 1e-8 to 1e-9 F/km. (See https://www.unioviedo.es/pcasielles/uploads/proyectantes/cosas_lineas.pdf for example)

If your model data does not comprise line capacitance values, you should either add realistic values of capacitance or simply use mutual inductance values. The worst choice is to use a pi-line with very small capacitances (ex: 1e-11 F total). These may trigger numerical issues (ex: MATLAB Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 7.288285e-22). These types of warnings are usually caused by extreme values small (Line capacitance <= 1e-12F or Breaker resistance <=1e-5 Ohms or large transformer core inductance >= 1000 p.u. for examples)

It is much better numerically to use null or infinite values in these cases; this forces the solver to symbolically resolve the dependencies of the model. Using a mutual inductance in place of a pi-line also does this.

Fig.1 Node reduction feature of SSN compared to EMTP

The model features blocks from the ARTEMiS fault library which allow the model to be compiled only once; fault location and activation is then selected during the real-time simulation from the opElectricFaultSelector block.

opPOWFaultControl: the main block to generate synchronized faults and acquisition trigger with Point-on-Wave (POW)

opElectricFault: This is an SPS breaker block that fault capability is enabled from the RT-LAB Console using the opElectricFaultSelector

opElectricFaultSelector: block that is used to select fault location, fault period and POW parameters during real-time simulation.

### Demonstration

The model OpElectricFaultSelector (in SC_Console) is set to activate a 3-phase to ground fault at location ID=1 (OpElectricFault block near the GENERATOR_0 source in SM_grid). OpElectricFaultSelector also set the fault to be POW-synchronized on GENERATOR_0, sync on the rising edge of A-phase voltage (in opPOWFaultControl). The period of the fault (set in OpElectricFaultSelector) is 10 seconds.

Note: ssn_distributiongrid_A1 is a version with pi-lines. ssn_distributiongrid_A2 is a version with mutual inductance.

### References

This model is featured in the following transaction paper: C. Dufour, J. Mahseredjian , J. Belanger, "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

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