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# ARTEMiS Distributed Parameters Line with Variable Internal Fault Distance

# Description

Since ARTEMiS v. 7.3.5, a new DPL model with fault is available in the SSN section of ARTEMiS. This new SSN-based DPL with fault model is more precise because it distributes the line losses proportionally to the fault distance.

It, along with all other ARTEMiS models, can be opened from within the software.

The ARTEMiS Distributed Parameters Line with Variable Internal Fault Distance block implements an 3-phases distributed parameters transmission line model with an on-line modifiable internal fault capability.

The ARTEMiS Distributed Parameters Line with Variable Internal Fault Distance (ADPLF) block is based on the Bergeron's travelling wave method used by the Electromagnetic Transient Program (EMTP) **[4]**. The model implement two DPL lines in series with an internal mid-point to connect faults.

The fault type is specified inside the model (see the example at the end). The fault location is entered as a signal input and can be change during the simulation without recompiling the models. An error signal is set if the fault location is to short. Otherwise, the fault distance can be arbitrarily set to any value.

For the model to have a fault distance that is variable during real-time simulation, an approximation is made in the distribution of the line losses. This is explained next:

A standard Bergeron-type line is a lossless line to which lumped resistances are added to represent the line losses. This is the case of the EMTP and Simscape Electrical Specialized Power Systems (SPS) DPL models.

Normally, when using two lines in series, the losses should be distributed in proportion of the respective line lengths. However, if we do this, the total surge impedance of the line would vary with the line length (i.e. the fault location). This in return would force the recalculation of state-space matrices, and it is not acceptable during real-time simulation.

The ADPLF model therefore fixes the losses distribution without regards to the fault location. By default, the losses are split in half between the two lines.

Refer to the SPS Distributed Parameter Line block Reference page for more details on the mathematical model of the distributed parameters line. This may induce some error when the fault distance is very short.

The * Maximum fault distance from ABC terminal (%) *parameter can help to minimize this error if the maximum fault distance is known. For example, if the fault location is located in the first half of the complete line, the losses would be distributed in a {25%, 75%} way, so to obtain the exact losses reparation of the average distance of the fault.

**Table of Contents**

# Mask and Parameters

| Currently, only 3-phase lines are supported |
---|---|

| Specifies the frequency used to compute the resistance R, inductance L, and capacitance C matrices of the line model. |

| The resistance R per unit length, as an N-by-N matrix in ohms/km. For a symmetrical line, you can either specify the N-by-N matrix or the sequence parameters. For a two-phase or three-phase continuously transposed line, you can enter the positive and zero-sequence resistances [R1 R0]. For a symmetrical six-phase line you can set the sequence parameters plus the zero-sequence mutual resistance [R1 R0 R0m]. For asymmetrical lines, you must specify the complete N-by-N resistance matrix. |

| The inductance L per unit length, as an N-by-N matrix in henries/km (H/km). For a symmetrical line, you can either specify the N-by-N matrix or the sequence parameters. For a two-phase or three-phase continuously transposed line, you can enter the positive and zero-sequence inductances [L1 L0]. For a symmetrical six-phase line, you can enter the sequence parameters plus the zero-sequence mutual inductance [L1 L0 L0m]. For asymmetrical lines, you must specify the complete N-by-N inductance matrix. |

| The capacitance C per unit length, as an N-by-N matrix in farads/km (F/km). For a symmetrical line, you can either specify the N-by-N matrix or the sequence parameters. For a two-phase or three-phase continuously transposed line, you can enter the positive and zero-sequence capacitances [C1 C0]. For a symmetrical six-phase line you can enter the sequence parameters plus the zero-sequence mutual capacitance [C1 C0 C0m]. For asymmetrical lines, you must specify the complete N-by-N capacitance matrix. |

| The line length, in km. This length is the total length of the line, not the individual length of the 2 line sections used by the model. |

| This parameter is used to indicate the maximum fault distance from the ABC side of the line (the side with the fault distance inport). A 100% is the default value for which the losses are distributed evenly between the two line section (independently of each section line length). If the maximum fault distance is known, the losses are then distributed differently to better approximate the average fault distance. |

# Inputs and Outputs

## Inputs

| this signal value is the location of the fault in per unit of total line length with regards to the side of the input connector on the block. N-Phases voltage-current signals (Physical Connection) |
---|

## Outputs

| when equal to 1, this signal output indicates that the fault distance is too short for the selected simulation sample time. The model requires that the line transmission delay be at least one sample time of the model. In that case, the user has the option of either lowering the simulation sample time or increasing the line length or fault distance. N-Phases delayed voltage-current signals (Physical connection). |
---|

## Characteristics and Limitations

The ARTEMiS Distributed Parameters Line with Variable Internal Fault Distance block does not initialize in steady-state so unexpected transients at the beginning of the simulation may occur.

The use of the ARTEMiS Distributed Parameters Line with Variable Internal Fault Distance disable the ‘Measurements’ option of the regular Distributed Parameter Line. Usage of regular voltage measurement blocks is a good alternative.

| No |
---|---|

| Yes, defined in the ARTEMiS guide block. |

| Yes |

| Yes |

# Example

The following example compare the ARTEMiS Distributed Parameters Line with Variable Internal Fault Distance with a line fault modeled with two distinct line section. The example helps to put in context the error introduced by the model with regards to the normal ARTEMiS line model, that implement the standard Bergeron line model with lumped loss.

Inside the ADPLF, the user can implement its own fault scheme as seen in the following figure. In our case, a single-phase fault to ground is implemented.

The main error will arise for faults near the line terminal because a lumped loss of R/8 instead of R/4*fault_length/line_length. Remember that a normal Bergeron line with loss has R/4 loss at each end and R/2 in the middle with losses proportional to line length section. In the case of the ADPLF, this loss is fixed and no more proportional to section length.

The line used for the test is 100 km in length and has a 0.01273 (direct) and 0.3864 (homopolar) Ohms/km series losses. The line has a minimum transmission delay of approximately 333 µs and the minimum fault distance is approximately 15 km for a simulation time step of 50 µs (50/3.33, see **Limitations**). The user must use pi-line to simulate shorter faults. The test consists on a 4-cycle single-phase to ground fault on the line from steady-state.

The line is completely opened at 0.11 seconds. Because the line is not loaded, the per-fault steady-state current is quite small.

The next two figure shows the results for a very short and a mid-line fault. On the short fault, one can observe that the input current during the fault is smaller than the reference. This is caused by the lumped losses of the line end which is bigger than normal.

If we now make a fault at mid-line point, the two results are exactly the same. This is normal because the ADPLF assume a fixed losses distribution corresponding to a mid-line separation. Fault current is lower in this case also as expected for a fault occurring farther from the power source.

# Limitations

**Usage in RT-LAB as task decoupling elements**

The ADPLF model cannot be used as a separating element in RT-LAB.

**Short distance fault limit**

The ADPLF model can only implement a fault occurring at a distance corresponding to one time step of propagation of the line (the fastest mode for the 3-phase line). If a shorter fault distance needs to be implemented, a pi-line model is recommended. As a quick rule of the thumb, considering the speed of light of 300000km/s, a 3.33µs/km relation exists between the minimum time step and minimal fault distance of the model.

# Related Items

Since ARTEMiS 7.3.5, a new DPL models with fault is available in the SSN section of ARTEMiS. This new SSN-based DPL with fault model is more precise because it distributes the line losses proportionally to the fault distance.

# References

[4] Dommel, H., “Digital Computer Solution of Electromagnetic Transients in Single and Multiple Networks”. IEEE Transactions on Power Apparatus and Systems, Vol. PAS-88, No. 4, April, 1969.

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