This package works along with RTE's adequacy software ANTARES : https://antares.rte-france.com/

antaresXpansion is the package which optimizes the installed capacities of an ANTARES study. Typical uses of the package are for:

• long-term scenario building: build an economically consistent long-term generation mix
• transmission expansion planning : compute the network developement which maximizes social welfare

The investment decisions are optimized by running ANTARES' simulations iteratively. At each iteration, the installed capacity of the investments are updated, and the simulations are repeated until the total costs have converged to a minimum. The total cost evaluated in this problem are the sum of the expected operation cost during one year and the investment annuity.

antaresXpansion is currently under development. Feel free to submit any issue.

The user of the package defines investiment candidates. Each investment candidate is characterized with the following properties:

• name: name of the investment candidate
• link: link whose capacity will be invested
• annual cost per MW: investment cost, per year and per MW
• unit size: size, in MW, of an investment unit (e.g. one group of 300 MW)
• maximum units: maximum number of units which can be built

Concretely, the investiment decision will affect only the capacity of the ANTARES' links. Investing in interconnections can be made directly with the package, while investing in generation capacity or storage capacity can be made using the so-called concept of "virtual nodes" with ANTARES.

The definition of all the investment candidates is given in a new input file, located in the user folder of the study: ./user/expansion/candidates.ini. The syntax used within this file is illustrated in the example below.

An example with two investments candidates, one in semi-base generation and one in network capacity, is given below.

The invested semi-base generation in area 1 is shifted in the "virtual node" invest_semibase. Within the optimization process, the capacity of the link between area 1 and invest_semibase will be updated with the new invested capacity.

The candidates.ini file for this example will be the following one. This file has to be saved in the folder user/expansion/

[1]
name = semibase
link = area1 - invest_semibase
annual-cost-per-mw = 126000
unit-size = 200
max-units = 5

[2]
name = grid
link = area1 - area2
annual-cost-per-mw = 3000
unit-size = 500
max-units = 4

For the case of distributed generation and storage, the investment variables can be continuous, without steps of several MW. In that case, the properties unit-sizeand max-unitscan be replaced by the property max-investment, and the invested capacity will be able to take any real value between 0 and max-investment (in MW).

By default, the investment candidates offer a "perfect capacity". That is to say, when 1 MW is invested, this 1 MW will be fully available for all the hours of the year. However, by adding the property link-profile, one can define a time series (with an hourly time step) of the ratio between the invested capacity and the capacity which is actually available at a given hour. This feature can be used to model investments in (e.g.) intermittent generation or thermal generation with seasonalized maintenance shutdowns.

The property link-profile can be used as below :

[1]
name = solar_power
link = area1 - pv1
annual-cost-per-mw = 100000
max-investment = 10000
link-profile = pv1.txt

Where pv1.txt is a text file, located in the user/expansion/capa/ folder of the study, and which contains the load factor time series of the candidate (one column of 8760 values between 0 and 1). When x MW of the candidate solar_power will be invested, the actual time series of available power will be equal to the product of x and the time series pv1.txt.

The method used to perform the optimal expansion is a benders decomposition in which:

• The slave problem is an ANTARES simulation, where the installed capacities of the investment candidates are fixed,
• The master problem is a MILP, in which the decision variables are the installed capacities of each investment candidate.

The objective function which is minimized, is the sum of the expected annual operation cost (column OV. COST + column HURDLE COST of the outputs of ANTARES ) and the investment annuity (as defined in the candidates.ini file).

Concretely, the package will run ANTARES iteratively. Depending on the number of candidates, the convergence to the optimal solution can be quite long (several hundreds iterations, and so several hundreds ANTARES' simulations). Some algorithmic settings are however available and propose different tradeoffs between the accuracy of the solution and the computation time.

The different settings can be modified by the user of the package. All the settings are saved in a file settings.ini located in the folder user/expansion/.

• optimality_gap: The optimality gap can take any numeric value. The optimality gap is the maximum possible distance (in euros) between the solution returned by the method and the optimal solution.

• master: Can take two values, relaxed or integer. Defines whether or not should integer variables be used for the master problem.

• uc-type: The UC (Unit Commitment) type can take two different values, expansion_fast or expansion_accurate. It defines which mode will be used in ANTARES. expansion_fast correponds to the fast mode of ANTARES in which the minimum up/down and minimum stable power constraints are relaxed whereas expansion_accurate takes into account the technical constraints of the thermal power plants as well as their start-up costs.

An example of a settings.ini file with the appropriate syntax is given below.

uc_type = expansion_fast
master = integer
optimality_gap = 0

Note that the optimality gap can also be given relatively to be best found solution by entering a % after the numeric value of the setting. In that case, the optimality is between 0%and 100% and the decimal separator is a point (.).

In that case, if the optimal solutions are not returned by the package, the comparison of several variants can be tricky as the imprecision of the method might be in the same order of magnitude as the changes brought by the input variations.

It is therefore advised to be as closed as possile from the optimum of the expansion problem. To do so, the two following conditions should necessarily be fulfilled:

• set the optimality_gap to zero.

[Remark : even with the conditions mentionned above, the reslult might be slighty different from the optimum due to numeric approximations, this can be partly solved by putting to optimality gap to -Inf]

As the optimal solution is not more realistic than an approximate solution of the modelled expansion problem. The settings can be less constraining with :

• an optimality_gap of a few million euros

Load the package

library(antaresXpansion)

Select an ANTARES study using antaresRead package. As no outputs are needed, the simulation argument should be put to zero.

setSimulationPath("study_path", simulation = 0)

Create the candidate.ini and settings.ini files as explained above and store them in the directory study_path/user/expansion.

Enter the path of the ANTARES solver (for example).

path_solver <- "C:/Program Files/RTE/Antares/6.0.0/bin/antares-6.0-solver.exe"

Run the benders function.

benders(path_solver, display = TRUE, report = TRUE)

The expansion optimization can be quite long, intermediary results can be written in the console using display = TRUE. Moreover, if report = TRUE, the results of the function will be summarized in a html report saved in the directory study_path/user/expansion/report.

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