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# ARTEMiS 3-phase Coupled Stubline and Compensation Block

# Library

ARTEMiS/Tools/Decoupling Blocks

# Blocks

# Description

The ARTEMiS 3-phase Coupled Stubline and Compensation Blocks are a recent advancement to achieve computational decoupling of grid equations composed of short transmission lines. This type of equation decoupling is very useful to achieve the required calculation speed for real-time simulations. The two blocks are used together and form what is called the ARTEMiS Compensated Stubline (ACS).

The ARTEMiS 3-phase Coupled Stubline implements by itself a 3-phase stubline with interphase coupling. Stublines are driven by the Bergeron line model with losses, in which the equivalent capacitance is adjusted to obtain exactly one time step of traveling delay. This model is particular in the way that it produces a coupled stubline in 3 different ways: three independent uncoupled modes (equivalent to 3 single-phase stublines), single-mode propagation (for which the 3 modes have exactly the same propagation time and two-mode propagation in which one of the modes has exactly 2 time-step of delay. The latter options with modal propagation modes represent distributed parameter lines with interphase coupling, a better approximation of the Bergeron line model (and real lines for that matter).

The Compensation Block for its part is used to compensate the extra equivalent capacitance added by the ARTEMiS 3-phase Coupled Stubline, and to include the remaining part of the line impedances not used in constructing the propagation modes. In typical usage of these blocks, the stubline will be used to replace a line of much lower capacitance and therefore equivalent propagation time. This is equivalent to say that the stubline adds some reactive power to the circuit it is used in. The Compensation Block is used to cancel out some of this extra reactive power. The reactive power canceling is correct at power frequency.

The Compensation Block also has the option to add some damping to the decoupled model. Added damping can be beneficial to increase the stability of the decoupled network under transient conditions, especially when the selected lines are very short.

# Mask

# Parameters

*Artemis 3-phase Coupled Stubline*

**Stubline type: **The type of stubline used.

- 3-phase coupled line (1 mode): stubline with LC coupling selected to produce a one-step delay on all modes.
- 3-phase coupled line (2 modes): stubline with LC coupling selected to produce a one-step delay on 2 modes plus two-step delay on the third mode.
- 3-phase line without couplings: stubline without LC coupling across phases. This is identical to using 3 single-phase stublines.

**Nominal Frequency (Hz): **The frequency used for internal calculations of compensation.

**Resistance (Ohms/km):** The 3x3 resistance matrix of the line in Ohms/km.

**Inductance (H/km):** The 3x3 inductance matrix of the line in Henry/km.

**Capacitance (F/km):** The 3x3 capacitance matrix of the line in Ohms/km.

**Length (km):** The length of the line in km.

**Sample Time (s):** The sample time of the model in seconds.

**Damping Required:** Check this box if damping is added in the corresponding Compensation Block.

**Undamped Frequency (Hz):** the maximum frequency for the computed damping, when damping is selected (one way to estimate this frequency is to observe performance without the option checked and to note transient oscillatory waveform introduced by stubline).

**Peak Frequency (Hz):** this is the damping resonance frequency. This value should always be greater than the power frequency.

**Corresponding stub compensation block name:** the name of the corresponding Compensation Block, which is normally connected in series with the *Artemis 3-phase Coupled Stubline*. This name includes the block path (when located in some subsystem) but __not__ the model name.

**Update stub compensation block (button): **When pressed, this button will transfer the compensation parameter from the *Artemis 3-phase Coupled Stubline* to the *Compensation Block*

*Artemis 3-phase Coupled Stubline Compensation Block*

*Artemis 3-phase Coupled Stubline Compensation Block*

This block is normally filled automatically from the *Artemis 3-phase Coupled Stubline*. The visible parameters consist of RLC values used to compute the reactive compensation.

# Input and Output signals

**Physical Modeling connection points**

Both block terminals have phase ‘abc’ on each side, representing the 3 phases of the line at each end. The model is symmetrical also as with most line models.

# Examples

The demo model ssn_IEEE13Node.slx is available in the ARTEMiS path. The demo model implements the IEEE 13 node standard demo with the *Artemis 3-phase Coupled Stubline* and *Compensation Block.*

The model also includes Commented blocks such as the original pi-line and SPS transformers for easy comparison with SPS.

**Above, IEEE 13 node standard model in SPS and ARTEMiS**

In the model, a Compensated Stubline is inserted in the place of the line between nodes 632 and 671 and splits the network equation into two halves. The selected line is 2000 ft (0.61 km). The stubline that replaces it has a one-time step delay and with the same total inductance, so it could be considered as having an equivalent length of ~7km at 25 us. A single-phase-to-ground fault is made at bus 671 for the test.

The figure compares SPS with the original pi-line to the SSN Stubline cases with and without the compensation for the main feeder input current (bus 632) and clearly shows that all curves match very well during the fault except for the non-compensated stubline case.

# Advanced damping options

The ACS damping option is available to diminish spurious oscillations of the ACS during transients.

Users are referred to the ARTEMiS Application Note entitled: ‘Using ARTEMiS Compensated Stubline Damping Option’ for further details.

# References

[1] B. Ahmed, A. Abdelgadir, N. Saied, and A. Karrar, "A Compensated Distributed-Parameter Line Decoupling Approach for Real-Time Applications," in IEEE Transactions on Smart Grid, DOI: 10.1109/TSG.2020.3033145.

[2] 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.

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