Investment problem generation

The goal of this step is to modify the .mps files of the weekly Antares problems to create the so-called satellite problems of the investment problem. The master problem is also generated in this step.

Python orchestrator get_names

Before changing the .mps file, a post-processing of the files created by antares-solver must be done.

The goal is to produce a file mps.txt containing each .mps with his associated variables.txt file (defining the mapping between the column IDs and variable names). Each line of the mps.txt file looks as follows:

problem-1-1-20210713-163528.mps variables-1-1-20210713-163528.txt constraints-1-1-20210713-163528.txt

!!! Note constraints.txt files are still defined in the file but not used in later steps.

Then:

• The area-<mc_year>-<week>-<timestamp>.txt file produced by antares-solver is copied as area.txt.
• The interco-<mc_year>-<week>-<timestamp>.txt file produced by antares-solver is also copied as interco.txt.

Modification of weekly problems with lp_namer

Here are the main steps of problem modification with lp_namer, that lead to the creation of the satellite problems.

1- Read candidates and get link column ID

Each investment link corresponds to a variable in the weekly optimization problem. The first step is to retrieve the column ID of each investment candidate link from its name specified in candidates.ini:

• The area.txt and interco.txt files are used to map area names to link IDs.
• Candidates defined in candidates.ini and the associated link profile (if defined) are read.

2- Modification of .mps file

In order to create the satellite problems, some contraints of the weekly problems must be changed and some variables must be added.

Initial weekly problems

In the initial weekly problems, we have the following variables:

Notation	Description	Label
\(F_{l,t}\)	Total power flow through link \(l\) at time \(t\).	ValeurDeNTCOrigineVersExtremite
\(F_{l,t}^{+}\)	Power flow through link \(l\) in the forward direction at time \(t\).	CoutOrigineVersExtremiteDeLInterconnexion
\(F_{l,t}^{-}\)	Power flow through link \(l\) in the backward direction at time \(t\).	CoutExtremiteVersOrigineDeLInterconnexion

| \(\bar{C}_{l,t}^{+}\) | Maximum transmission capacity through link \(l\) in the forward direction at time \(t\). | | \(\bar{C}_{l,t}^{-}\) | Maximum transmission capacity through link \(l\) in the backward direction at time \(t\). |

The bounds on the variables are as follows: $$ F_{l,t} \leq \bar{C}_{l,t}^{+} $$

$$ F_{l,t} \geq -\bar{C}_{l,t}^{-} $$

$$ 0 \leq F_{l,t}^{+} \leq \bar{C}_{l,t}^{+} $$

$$ 0 \leq F_{l,t}^{-} \leq \bar{C}_{l,t}^{-} $$

There are also constraints linking the forward and backward flows:

$$ F_{l,t} = F_{l,t}^{+} - F_{l,t}^{-} $$

Modifications for satellite problems

In order to create the satellite problems, the constraints must be changed as follows:

$$ -\infty \leq F_{l,t} \leq +\infty $$

$$ 0 \leq F_{l,t}^{+} \leq +\infty $$

$$ 0 \leq F_{l,t}^{-} \leq +\infty $$ with the same additional constraints:

$$ F_{l,t} = F_{l,t}^{+} - F_{l,t}^{-} $$

We also need to add the investment variables \(x_{l}\) that represent the invested capacity on link \(l\). We suppose that the link has a direct (resp. indirect) temporal profile denoted by \(\Lambda_{l,t}^{+}\) (resp. \(\Lambda_{l,t}^{-}\)). The already installed capacity is \(\widetilde{C}_{l}^{+}\) in the forward direction (resp. \(\widetilde{C}_{l}^{-}\) in the backward direction) and the already installed direct (resp. indirect) temporal profile is denoted by \(\widetilde{\Lambda}_{l,t}^{+}\) (resp. \(\widetilde{\Lambda}_{l,t}^{-}\)). Then the following constraints must be added:

$$ F_{l,t} + \Lambda_{l,t}^{-} \cdot x_{l} \geq -\widetilde{\Lambda}_{l,t}^{-}\cdot\widetilde{C}_{l}^{-} $$

$$ F_{l,t} - \Lambda_{l,t}^{+} \cdot x_{l} \leq \widetilde{\Lambda}_{l,t}^{-}\cdot\widetilde{C}_{l}^{+}\ $$

$$ F_{l,t}^{-} - \Lambda_{l,t}^{-} \cdot x_{l} \leq \widetilde{\Lambda}_{l,t}^{-}\cdot\widetilde{C}_{l}^{-} $$

$$ F_{l,t}^{+} - \Lambda_{l,t}^{+} \cdot x_{l} \leq \widetilde{\Lambda}_{l,t}^{+}\cdot\widetilde{C}_{l}^{+} $$

This translates into the following steps for the modification of .mps files:

• Remove bounds for ValeurDeNTCOrigineVersExtremite variables (only for link with candidate),
• Change upper bounds to Inf for CoutOrigineVersExtremiteDeLInterconnexion and CoutExtremiteVersOrigineDeLInterconnexion variables (only for link with candidate),
• Add a new column for each candidate,
• Add the constraints on ValeurDeNTCOrigineVersExtremite,
• Add the constraints on CoutOrigineVersExtremiteDeLInterconnexion,
• Add the constraints on CoutExtremiteVersOrigineDeLInterconnexion.

3- Read additional candidate constraints

The additional-constraints parameter, that specifies the path to file, may be defined in the settings.ini. This is used to define linear constraints between the invested capacities of investment candidates, and is read at this stage of Antares-Xpansion process. For more information on the file format, see the corresponding part of the user guide.

4- Creation of master problem

The master problem is created from the list of candidates in the following way:

• Add a new column (= variable) for each candidate with lower bound 0 and upper bound max-investment or max-units \(\times\) unit-size.
• If the investment on the candidate has integer constraints (use of the unit-size parameter):
  • Add a new (integer) column for the number of built units, with lower bound 0 and upper bound max-units.
  • Add a constraint that links the number of units to the invested capacity.
• If additional constraints are defined:
  • Create binary constraints, that represent for example exclusion constraints, see Figure 13.
  • Create the other linear constraints between invested capactities of the candidates.

5- Creation of a variable / column ID mapping file

A file (structure.txt) is created, containing for each satellite problem and the master, the associated column ID for the candidates.

!!! Example master battery 0 master peak 1 master pv 2 master semibase 3 master transmission_line 4 problem-1-1-20210713-163528.mps battery 5547 problem-1-1-20210713-163528.mps peak 5545 problem-1-1-20210713-163528.mps pv 5548 problem-1-1-20210713-163528.mps semibase 5546 problem-1-1-20210713-163528.mps transmission_line 5544

Here:

• In master.mps, the candidate battery has column ID 0,
• In problem-1-1-20210713-163528 corresponding file problem-1-1-20210713-163528.mps, the candidate peak has column ID 5545.

!!! Note The column ID is no longer used by benders. This file must still be created so that benders knows the list of candidate for each problem.