Minor fixes

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2024-05-21 10:56:24 -05:00
parent b928baeeda
commit 4f04f0dd66
4 changed files with 4 additions and 66 deletions

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