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add Lossless line and converter
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rodrigomha committed Sep 24, 2024
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# DC Models formulations

!!! note
Multi-terminal DC models are still in early stages of development and future versions will add a more comprehensive list of formulations

---

## LossLessLine

`LossLessLine` models are used with `PSY.DCBranch` models.

```@docs
LossLessLine
```

**Variables:**

- [`FlowActivePowerVariable`](@ref):
- Bounds: ``(R^\text{min},R^\text{max})``
- Symbol: ``f``

**Static Parameters**

- ``R^\text{from,min}`` = `PowerSystems.get_active_power_limits_from(branch).min`
- ``R^\text{from,max}`` = `PowerSystems.get_active_power_limits_from(branch).max`
- ``R^\text{to,min}`` = `PowerSystems.get_active_power_limits_to(branch).min`
- ``R^\text{to,max}`` = `PowerSystems.get_active_power_limits_to(branch).max`

Then, the minimum and maximum are computed as `R^\text{min} = \min(R^\text{from,min}, R^\text{to,min})` and `R^\text{max} = \min(R^\text{from,max}, R^\text{to,max})`

**Objective:**

No cost is added to the objective function.

**Expressions:**

The variable `FlowActivePowerVariable` ``f`` is added to the nodal balance expression `ActivePowerBalance` for DC Buses, by adding the flow ``f`` in the receiving DC bus and subtracting it from the sending DC bus.

**Constraints:**

No constraints are added to the function.

---

## LossLessConverter

Converters are used to interface the AC Buses with DC Buses.

```@docs
LossLessConverter
```

**Variables:**

- [`ActivePowerVariable`](@ref):
- Bounds: ``(P^\text{min},P^\text{max})``
- Symbol: ``p``


**Static Parameters:**

- ``P^\text{min}`` = `PowerSystems.get_active_power_limits(device).min`
- ``P^\text{max}`` = `PowerSystems.get_active_power_limits(device).max`


**Objective:**

No cost is added to the objective function.

**Expressions:**

The variable `ActivePowerVariable` ``p`` is added positive to the AC balance expression `ActivePowerBalance` for AC Buses, and added negative to `ActivePowerBalance` for DC Buses, balancing both sides.

**Constraints:**

No constraints are added to the function.

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