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@@ -11,7 +11,7 @@ An instance of the stochastic security-constrained unit commitment (SCUC) proble
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- [Reserves](#Reserves)
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- [Contingencies](#Contingencies)
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Each section is described in detail below. See [case118/2017-01-01.json.gz](https://axavier.org/UnitCommitment.jl/0.3/instances/matpower/case118/2017-01-01.json.gz) for a complete example.
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Each section is described in detail below. See [case118/2017-01-01.json.gz](https://axavier.org/UnitCommitment.jl/0.4/instances/matpower/case118/2017-01-01.json.gz) for a complete example.
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### Parameters
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@@ -31,7 +31,7 @@ This section describes system-wide parameters, such as power balance penalty, an
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```json
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{
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"Parameters": {
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"Version": "0.3",
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"Version": "0.4",
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"Time horizon (h)": 4,
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"Power balance penalty ($/MW)": 1000.0,
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"Scenario name": "s1",
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@@ -616,65 +616,3 @@ y^\text{flow}_{slt} = \sum_{b \in B} \delta_{sbl} y^\text{inj}_{sbt}
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\end{align*}
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```
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## 8. Transmission interfaces
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In some applications, such as energy exchange studies, it is important to
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enforce flow limits not only on individual lines, but also on groups of
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transmission lines. These groups are known as _interfaces_. More precisely, an
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interface is composed by two sets of lines: the _inbound_ and the _outbound
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lines_. The flow across the interface is defined as the sum of the flow in all
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inbound lines minus the sum of the flow in all outbound lines. An upper and a
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lower limit may be imposed on the flow across the interface, and a penalty is
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imposed if the limit is exceeded.
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### Sets and constants
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| Symbol | Unit | Description |
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| :-------------------------- | :---- | :----------------------------------------------------------------------------------------- |
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| $L^\text{inbound}_{si}$ | | Set of inbound lines for interface $i$ in scenario $s$. |
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| $L^\text{outbound}_{si}$ | | Set of outbound lines for interface $i$ in scenario $s$. |
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| $M^\text{limit-down}_{sit}$ | MW | Lower flow limit for interface $i$ at time at time $t$ and scenario $s$ (negative number). |
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| $M^\text{limit-up}_{sit}$ | MW | Upper flow limit for interface $i$ at time at time $t$ and scenario $s$ (positive number). |
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| $Z^\text{overflow}_{sit}$ | \$/MW | Overflow penalty for interface $l$ at time $t$ and scenario $s$. |
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| $\text{IF}$ | | Set of transmission interfaces. |
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### Decision variables
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| Symbol | JuMP name | Unit | Description | Stage |
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| :-------------------------- | :-------------------------- | :--- | :--------------------------------------------------------------- | :---- |
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| $y^\text{i-flow}_{sit}$ | `interface_flow[s,i,t]` | MW | Flow across interface $i$ at time $t$ and scenario $s$. | 2 |
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| $y^\text{i-overflow}_{sit}$ | `interface_overflow[s,i,t]` | MW | Flow above limit for interface $i$ at time $t$ and scenario $s$. | 2 |
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### Objective function terms
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- Penalty for exceeding interface limits:
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```math
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\sum_{s \in S} p(s) \left[
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\sum_{i \in \text{IF}} \sum_{t \in T} y^\text{i-overflow}_{sit} Z^\text{overflow}_{sit}
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\right]
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```
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### Constraints
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- Definition of interface flow (`eq_if_flow`):
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```math
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y^\text{i-flow}_{sit} = \sum_{b \in B} y^\text{inj}_{sbt} \left[
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\sum_{l \in L^\text{outbound}_{si}} \delta_{sbl} -
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\sum_{l \in L^\text{inbound}_{si}} \delta_{sbl}
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\right]
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```
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- Interface flow limits (`eq_if_limit_up` and `eq_if_limit_up`)
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```math
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\begin{align*}
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y^\text{i-flow}_{sit} & \leq M^\text{limit-up}_{sit} + y^\text{i-overflow}_{sit} \\
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-y^\text{i-flow}_{sit} & \leq -M^\text{limit-down}_{sit} + y^\text{i-overflow}_{sit}
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\end{align*}
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```
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## 9. Contingencies
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## 10. Reserves
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