# Objective

This document's objective is to explain the usage of the damping feature of the new ARTEMiS Compensated Stubline model[1][2]. The ARTEMiS Compensated Stubline is Bergeron traveling wave line model, with phase couplings, that are adjusted to provide an exact one-time-step propagation delay. As a standard stubline substitution of a very short line adds spurious capacitance to the network, the Compensated Stubline also compensates for the added reactive power that it creates.

# Software Requirements

To perform the parameter modification using the method described in this documentation, the following software is required to properly install on a computer that is used to conduct this operation.

**Software required **

Software Names | Version |
---|---|

MATLAB | R2017b |

# Introduction

The ARTEMiS Compensated Stubline (ACS) implements a 1-time-step delay distributed parameters line model with interphase couplings. The ACS is typically used to obtain equation decoupling in large grids that only contain short lines.

The use of stublines will typically increase the equivalent capacitance at the point of insertion because the underlying Bergeron line model will have an equivalent length consequent with simulation sample time. The ACS compensates for this increase of reactive power by adding a corresponding shunt inductance.

In some cases, despite the correction of reactive power made by the ACS model, transient behavior can still be oscillatory, depending on usage.

The current document objective is to explain the Damping Option of the ACS model, an option that is provided to decrease some unwanted transient oscillations while using the ACS.

# ARTEMiS Compensated Stubline Damping Basics

At the point of the measurement, the additional capacitance may cause a complex oscillatory response. However if it possible to discern a simplified single oscillation in the fault current waveform or recovery voltage to ground waveform, then that waveform may be a suitable target for damping.

**Simplified representations for recovery voltage (a) and faulted current (b) equivalent circuits**

**Above**, simplified circuits that would give rise to single-frequency oscillation phase components. For the purposes of transient analysis, both circuits (a) and (b) above reduce to a simple parallel LC circuit with regards to the point of measurement. The problem then becomes how to introduce damping for the transient oscillatory component without offsetting steady-state accuracy. A possible solution is to introduce a damping resistance in parallel with the added capacitance and compensating inductance for each phase through a coupling capacitance that effectively cuts off the damping resistance at power frequency.

**Adding damping to the simple LC circuit**

**Above**, the added damping circuit. A rigorous analysis of the circuit [1] gives the maximum damping as

The resistance necessary to achieve this damping is given as

is the observed oscillatory frequency.

However, an additional constraint is that the compensating circuit (enclosed within the dashed box) should appear as a single inductor Lcomp at steady-state frequency.

The frequency response for the impedance of an example circuit of this type is performed and is shown.

If the peak of the magnitude at the frequency Wpeak is chosen to coincide with 100 Hz then a phase angle of close to 90 degrees is realized at power frequency (50-60 Hz), consistent with a pure inductance.

In the region of transient switching frequencies (200-4000Hz), the response appears to represent an RC circuit with a negative angle that becomes progressively smaller, which is appropriate for damping.

It is found that selecting Wpeak at less than 100 gives better damping but at the expense of the departure of the steady-state impedance angle from 90 degrees.

The equations necessary for design of the compensating circuit find the values for L'comp, Ccoupling, and Rdamping given C and Lcomp as follows (abbreviating L'comp as L'c, Rdamping as Rd, and Ccoupling as Cc).

The three equations are solved numerically, all non-real solutions are discarded, and the real solution which offers L'comp as close as possible to Lcomp is selected.

# Usage examples

In this section, we will explain the usage of the ACS damping option, with benefits and drawbacks, on 2 demo models: IEEE 13 node test feeder and IEEE 123 node test feeder. The original demos are available in the ARTEMiS help section.

**IEEE 13 node test feeder**

**IEEE 13 node feeder diagram with line 632-671 divided into two segments**

In the ARTEMiS help section, the IEEE 13 node system was used to demonstrate the novel decoupling method of the Compensated Stubline. In this application note, we will use the system again to demonstrate the Compensated Stubline with the damping option. However, the original line used for decoupling between nodes 632 and 671 is too long at 2000 ft for the added capacitance to make an appreciable effect on dynamics. We thus make the decoupling line much shorter by dividing the lines into two segments of lengths 1900 ft and 100 ft as shown in Fig 4.0. The shorter 100 ft segment is used for decoupling.

A line to ground fault on phase (b) at bus 671 is applied for 3 cycles and removed. Using the ARTEMiS-based SSN solver with Compensated Stubline decoupling will lead to observed oscillations on the incipient fault-current waveform. The original SPS solution for the complete system does not contain these oscillations – therefore they are attributed to the effect of the large capacitance required to implement Stubline decoupling for the 100 ft line segment. The oscillations are very lightly damped and have a frequency of around 1600 Hz.

To attempt damping these oscillations according to the theory discussed in section 4.0, the mask of the Compensated Stubline has the option to include damping as shown in Fig 5. The user will check the box <Damping required?> and is then presented with the option for entering the observed <Undamped Frequency> and <Peak Frequency> (Wpeak), which has a default of 100 Hz.

Upon entering the values and hitting the <Apply> button, the corresponding compensation block must be updated (using <Update stub compensation block>). A look under the mask of the compensation block (Fig 6.) reveals the damping resistors in series with coupling capacitors on all phases.

For the IEEE 13 node system, damping was implemented as described above. Fig 7. presents the waveforms of the incipient fault current for three simulations: (1) SPS-based intact system, (2) SSN-based decoupled system using a 3-phase Coupled Stubline (2 modes), and (3) Same SSN-based system in (2), but with the damping option selected and implemented. The damped waveforms (shown dashed) are seen to quickly settle down to the path of the original waveform.

**ARTEMiS 3-phase Coupled Stubline mask with ‘Damping’ option**

**Looking under the mask of the ARTEMiS 3-phase Coupled Stubline Compensation Block**

**Line–Ground fault on bus 671 of the IEEE 13 bus system; Original, Undamped, and Damped simulations**

# IEEE 123 node test feeder

**IEEE 123 node test feeder diagram with ACS locations**

**Above**, ARTEMiS Compensated Stubline locations for the IEEE 123 node test feeder. In this model, no modifications are made to demonstrate the need for oscillation damping, since the line is already short (ranging from 700 and 1000 ft) and decoupling will introduce some oscillatory behavior. A comparison is made between an SPS-based simulation for the complete system for a line–line fault (phase’s b & c) at bus 23 and an SSN-decoupled simulation for the same fault. The fault is applied for 3 cycles and when removed transient oscillatory behavior in the recovery voltage appears in the SSN simulation as shown in Fig. 9. The incipient fault current also shows brief oscillations, but they are mostly insignificant. Both simulations are solved with the Backward Euler method and no damping is applied in the ACS decoupling lines compensation blocks.

**IEEE 123 node voltage recovery waveforms – SPS-based and SNN undamped.**

It is possible to reduce these oscillations by selecting the damping option in the ARTEMiS Compensated Stublines and entering relevant damping information. The observed oscillation has a frequency around 900 Hz, and with the default value of =100 Hz, the oscillation damping improves. Reducing the values of Wpeak improves damping further, and Fig 10. shows resulting waveforms for values of Wpeak of 100, 80, and 70 Hz. The best damping is seen with =70Hz, shown dotted. The problem with the reduction of Wpeak even further is that it leads to the departure of the compensating block from presenting a pure shunt inductance under steady-state (power frequency) conditions, as it should do. The angles of the shunt component in the compensating block corresponding to the values of Wpeak above for the first decoupling line (between bus 13 and 18) are 87 deg, 81 deg, and 67 deg under steady-state conditions. If Wpeak is set equal to the power frequency (60 Hz for this system) the angle goes all the way down to about 13 deg, resulting in a largely resistive component instead of inductive. This will lead to inaccurate steady-state conditions.

** IEEE 123 node voltage recovery waveforms – different values for Wpeak**

** 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, J. L. Naredo, “An Advanced Real-Time Electro-Magnetic Simulator for Power Systems with a Simultaneous State-Space Nodal Solver”, IEEE/PES T&D 2010 - Latin America, São Paulo, Brazil, Nov. 8-10, 2010