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# ARTEMiS Distributed Parameters Line

# Description

The ARTEMiS distributed parameters line block implements an N-phases distributed parameters transmission line model optimized for real-time simulation.

The ARTEMiS Distributed Parameters Line block implements an N-phases distributed parameters line model with lumped losses. The model is based on Bergeron's travelling wave method used by the Electromagnetic Transient Program (EMTP) ** ^{[1]}**. This block is similar to the SPS distributed parameters line block but is optimized for discrete real-time simulation and allows network decoupling. It also allows multi-CPU simulation on an RT-LAB simulator.

Refer to the SPS Distributed Parameter Line block Reference page for more details on the mathematical model of the distributed parameters line.

## Network Decoupling

One of the main advantages of the ARTEMiS line blocks (Distributed parameters lines and Stublines), by opposition to the SPS lines, is the decoupling of the electric circuit into smaller subnetworks. This important property allows ARTEMiS to simulate, in real-time, circuits with more switching elements.

SPS and ARTEMiS solve electric circuits using the common state-space method. One of the main limitations of this method is related to the switch elements. When an event occurs that changes the topology of the circuit (or changes the state of a switch), SPS and ARTEMiS need to compute a new state-space matrix. This calculation causes unacceptable overhead when simulating a circuit in real-time.

To solve this problem, ARTEMiS stores the state-space matrices of a given set of topologies, normally the steady-state topologies, in cached memory and uses them when necessary without having to recalculate the matrices. However, the number of matrices required to cover all topologies of the system depends on the number of switch elements. When a circuit contains a lot of switch elements, the number of required topologies is high and it is not possible to store all matrices in cached memory because of the size of the matrices.

The decoupling property of the line allows ARTEMiS to divide the state-space system into two different state-space systems and reduce the total size of the state-space matrices in memory. It also reduces the maximum number of topologies by an important factor.

## RT-LAB Simulation Using a Cluster of PCs

The distributed configuration of RT-LAB allows for complex models to be distributed over a cluster of PCs running in parallel. The target nodes in the cluster communicate between each other with low latency protocols such as shared memory, FireWire, SignalWire or InfiniBand, fast enough to provide reliable communication for real-time applications.

However, electrical circuits cannot be easily distributed over a cluster of PCs without changing the dynamic behaviors of the system. The communication delays degrade the computation.

ARTEMiS lines (Distributed Parameters Lines and Stublines) can be used to distribute a circuit over a cluster of PCs. ARTEMiS used the intrinsic delay of the line to split the circuit without affecting the dynamic property of the system. Moreover, SPS and ARTEMiS use physical modelling lines and connectors to model the circuit.

This type of signals cannot be used by RT-LAB to communicate signals between subsystems, because the RT-LAB opcomm block only supports basic Simulink signals. The only exception to this rule is the ARTEMiS **Distributed Parameters Line** block and the **ARTEMiS Stubline** block. RT-LAB allows the insertion of a line block at the root level of the block diagram and the connection of the physical modelling ports of the block to the real-time subsystems.

Also, note that the physical modelling signals and ports do not have to pass through the OpComm block. The Example in the **Characteristics and Limitations** section illustrates how to use the block with RT-LAB.

# Mask and Parameters

| Defines the mathematical models of the distributed parameters line used by ARTEMiS and SPS. Here are the available options: |
---|---|

• | |

| Specifies the number of phases, N, of the model. The block dynamically changes according to the number of phases that you specify. When you apply the parameters or close the dialogue box, the number of inputs and outputs is updated. |

| 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. |

| Line current and voltage measurement are not working. |

# Inputs and Outputs

## Inputs

N-Phase voltage-current signals

## Outputs

N-Phase delayed voltage-current signals.

# Characteristics and Limitations

The ARTEMiS distributed parameters line block does not initialize in steady-state so unexpected transients at the beginning of the simulation may occur.

The use of the ARTEMiS Distributed Parameter Line disables the **Measurements** option of the regular Distributed Parameter Line. Usage of regular voltage measurement blocks is a good alternative.

Direct Feedthrough | No |
---|---|

Discrete sample time | Yes, defined in the ARTEMiS guide block. |

XHP support | Yes |

Work offline | Yes |

# Example

The example shows how to use the ARTEMiS distributed parameters line to decouple an electrical network into two distinct subnetworks and consequently to optimize the time to simulate the system in real-time. This property also allows ARTEMiS to simulate systems that contain more switching elements and consequently more complex **systems.**

**Note:** The procedure shown below can also be applied to ARTEMiS Stubline block to decouple subnetworks and optimize real-time simulation.

Open the SPS demo power_monophaseline model by typing the following command in the command prompt of Matlab: power_monophaseline;

To become familiar with the example, consult the help and perform simulation and check the results. The next steps will modify the demo to use the ARTEMiS solver instead of the normal SPS solver.

Drag an ARTEMiS Guide block from the ARTEMiS library into the model and set it sample time to 50e-6 seconds.

Set the SPS PowerGUI block to <Discrete> mode with a sample time equal to ARTEMiS

Change the SPS Distributed Parameter Line line to an ARTEMiS Distributed Parameter Line block by chaning the corresponding option in the ARTEMiS GUIde block:

The model must be similar to the following figure. Save the model under the following name: power_monophaseline_artemis.mdl.

Simulate the model and analyze the results. You will see that the results are similar to the original model.

The next steps will show you how to run the model on a cluster of PCs running RT-LAB. The general idea is to benefit from the intrinsic delay of the transmission line to split the model into subnetworks. The mathematical model of the distributed parameters line of ARTEMiS, contrary to the SPS model, allows distribution of the line onto two different CPUs. This property also allows ARTEMiS to simulate systems containing more switching elements and consequently more complex systems.

Select all blocks located in the subnetwork 1 in the figure above and press Ctrl-G to create a new subsystem.

Move the ARTEMiS block inside the subsystem.

Rename this subsystem to SM_Subnetwork_1. The following figure displays the content of the SS_Subnetwork_1 subsystem.

Select all blocks located in the subnetwork 2 and press Ctrl-G to create a new subsystem.

Add an ARTEMiS Guide block inside the subsystem.

Rename this subsystem to SS_Subnetwork_2. The following figure illustrates the content of the SS_Subnetwork_2 subsystem.

Select the 3 remaining blocks, normally the two scopes blocks and the Mux1 block and press Ctrl-G to create a new subsystem.

Rename this subsystem to SC_Console.

Add the RT-LAB opcomm block between the inports blocks and the content of the subsystem. Don’t forget to set the number of inports of the OpComm blocks to 3. Refer to the RT-LAB user guide for more help.

The following figure illustrates the content of the SC_Console subsystem after the modifications described above have been made.

Modify the solver parameters of the model; select one of the fixed-step solver, like ode3 for example, and change the fixed-step size to 50e-6.

Organize the top level blocks according to the following figure. IMPORTANT: the powerGUI block must be at the top level.

Save your model.

Your model is now ready to be compiled with RT-LAB. Refer to the RT-LAB User Guide for more help. If you have set the sample times of your model with a variable set in the workspace (ex: Ts), you should set the model initialization function with <Ts=50e-6;> in

**File->Model Properties->Callbacks→InitFcn**

## Limitations

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

**When used in RT-LAB to decouple and separate computational tasks on different cores/CPUs, the following connection restriction are applicable to the ARTEMiS distributed parameters line model:**

The ARTEMiS distributed parameters line must be located on the top-level of the RT-LAB compatible Simulink model

Each ARTEMiS distributed parameters line outports can be connected only to SimPowerSystems component located

*inside the*RT-LAB top-level subsystem (names beginning with ’SS’ or ’SM’ prefixes)No connection between ARTEMiS distributed parameters lines is allowed on the top-level. If such a connection is required, the ARTEMiS distributed parameters block connection lines must be first routed inside the subsystems individually and the connection between the ARTEMiS distributed parameters line ports can be made inside the subsystem. The following figure shows an example of illegal ARTEMiS DPL connection at the RT-LAB top-level and how to connect the line inside an RT-LAB top-level subsystem.

# References

[1] 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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