Active windows¶
Data can be reviewed, updated, deleted by selecting different possible active windows whose list and content are described hereafter. On launching Antares, the default active window is "System Maps".
DISCLAIMER: this section sometimes refers to the original interfaces of AntaresSimulator, which are deprecated. Please refer to the AntaresWeb online documentation for the description of the current interface.
System Maps¶
This window is used to define the general structure of the system, i.e. the list of areas and that of the interconnections. Only the area's names, location and the topology of the grid are defined at this stage. Different colors may be assigned to different areas. These colors may later be used as sorting options in most windows. They are useful to edit data in a fashion that has a geographic meaning (which the lexicographic order may not have). This window displays copy/paste/select all icons equivalent to the relevant EDIT menu commands.
The top left side of the window shows a "mouse status" field with three icons. These icons (one for nodes, one for links and one for binding constraints) indicate whether a selection made on the map with the mouse will involve or not the related elements. When a copy/paste action is considered, this allows for instance to copy any combination of nodes, links and binding constraints. Status can be changed by toggling the icons. Default is "on" for the three icons. Two other purely graphic icons/buttons (no action on data) allow respectively to center the map on a given set of (x , y) coordinates, and to prune the "empty" space around the current map. Multiple additional maps may be defined by using the crossshaped button located top right. A detailed presentation of all system map editor features can be found in the document "System Map Editor Reference Guide".
Simulation¶
The main simulation window is divided up in two parts. On the left side are the general parameters while the right side is devoted to the timeseries management.
These two parts are detailed hereafter.
LEFT PART: General parameters¶

Simulation
 Mode: Economy, Adequacy ^{1}
 First day: First day of the simulation (e.g. 8 for a simulation beginning on the second week of the first month of the year)
 Last day: Last day of the simulation (e.g. 28 for a simulation ending on the fourth week of the first month of the year) ^{2}

Calendar

Horizon: Reference year (static tag, not used in the calculations)

Year: Actual month by which the Timeseries begin (Jan to Dec, Oct to Sep, etc.)

Leap Year: (Yes/No) indicates whether February has 28 or 29 days

Week: In economy or adequacy simulations, indicates the frame (Mon Sun, SatFri, etc.) to use for the edition of weekly results

1st January: First day of the year (Mon, Tue, etc.)


MonteCarlo scenarios

Number: Number of MC years that should be prepared for the simulation (not always the same as the Number of MC years actually simulated, see "selection mode" below)

Building mode:
 Automatic For all years to simulate, all timeseries will be drawn at random
 Custom The simulation will be carried out on a mix of deterministic and probabilistic conditions, with some timeseries randomly drawn and others set to userdefined values. This option allows setting up detailed "what if" simulations that may help to understand the phenomena at work and quantify various kinds of risk indicators. To set up the simulation profile, choose in the main menu: Configure/ MC scenario builder
 Derated All timeseries will be replaced by their general average and the number of MC years is set to 1. If the TS are readymade or Antaresgenerated but are not to be stored in the INPUT folder, no timeseries will be written over the original ones (if any). If the timeseries are built by Antares and if it is specified that they should be stored in the INPUT, a single averageout time series will be stored instead of the whole set.

Selection mode:

Automatic All prepared MC years will actually be simulated.

Custom The years to simulate are defined in a list. To set up this list, choose in the main menu: Configure/ MC scenario playlist ^{3}.



Output profile

Simulation synthesis:
 True Synthetic results will be stored in a directory:
Study_name/OUTPUT/simu_tag/Economy/mcall
 False No general synthesis will be printed out
 True Synthetic results will be stored in a directory:

YearbyYear:
 False No individual results will be printed out
 True For each simulated year, detailed results will be printed out in an individual directory: `Study_name/OUTPUT/simu_tag/Economy/mcinumber

Geographic Trimming:
 None Storage of results for all areas, geographic districts, interconnections as well as all time spans (hourly, daily, etc.)
 Custom Storage of the results selected with the "Geographic Trimming" command of the "Configure"
option available in the main menu.
Filters on areas, interconnections and time spans may also be defined as follows:
 On the map, select area(s) and/or interconnection(s)
 Open the inspector module (Main menu, Windows)
 Set adequate parameters in the "output print status" group

Thematic Trimming:
 None Storage, for the geographic selection defined previously, of all variables defined in Output Files for Areas and Links.
 Custom Storage, for the geographic selection defined previously, of the variables selected with the "Thematic Trimming" command of the "Configure" option available in the main menu.

MC Scenarios:
 False No storage of the timeseries numbers (either randomly drawn or userdefined) used to set up the simulation
 True A specific OUTPUT folder will be created to store all the timeseries numbers drawn when
 preparing the MC years.

RIGHT PART: Timeseries management¶
For the different kinds of timeseries that Antares manages in a nondeterministic way (load, thermal generation, hydro power, hydro max power, wind power, solar power or renewable depending on the option chosen):

Choice of the kind of timeseries to use Either « readymade » or «stochastic » (i.e. Antaresgenerated), defined by setting the value to either "on" or "off". Exception is hydro max power that can only be « readymade ». Note that for Thermal timeseries, the clusterwise parameter may overrule this global parameter (see Thermal window description below).

For stochastic TS only:

Number Number of TS to generate

Refresh (Yes /No) ndicates whether a periodic renewal of TS should be performed or not

Refresh span Number of MC years at the end of which the renewal will be performed (if so required)

Seasonal correlation ("monthly" or "annual") Indicates whether the spatial correlation matrices to use are defined month by month or if a single annual matrix for the whole year should rather be used (see Timeseries analysis and generation)

Store in input
 Yes the generated timeseries will be stored in the INPUT in replacement of the original ones (wherever they may come from)
 No: the original timeseries will be kept as they were

Store in output
 Yes: the generated timesseries will be stored as part of the simulation results
 No: no storage of the generated timeseries in the results directories


General rules for building up the MC years
 Intramodal:
 Yes For each mode, the same number should be used for all locations (or 1 where there is only one TS), but this number may differ from one mode to another. For instance, solar power TS = 12 for all areas, while wind power TS number = 7 for all areas.
 No Independent draws
 Intermodal:
 Yes For all modes, the same number should be used but may depend on the location (for instance, solar and wind power TS = 3 for area 1, 8 for area 2, 4 for area 3, etc.)
 No Independent draws
 Intramodal:
A full meteorological correlation (for each MC year, one single number for all modes and areas) is, from a theoretical standpoint, accessible by activating "intramodal" and " intermodal" for all but the "thermal" kind of timeseries. The availability of an underlying comprehensive multidimensional Meteorological data base of readymade timeseries is the crux of the matter when it comes to using this configuration.
User's Notes¶
A builtin notepad for recording comments regarding the study. Such comments typically help to track successive input data updates (upgrading such interconnection, removing such plant, etc.). Another simple use is to register what has been stored in the "user" subfolder and why. Such notes may prove useful to sort and interpret the results of multiple simulations carried out at different times on various configurations of the power system.
Load¶
Documentation of the AntaresWeb interface for this section
This window is used to handle all input data regarding load. In Antares load should include transmission losses. It should preferably not include the power absorbed by pumped storage power plants. If it does, the user should neither use the "PSP" array (see window "Misc. Gen") nor the explicit modeling of PSP plants
The user may pick any area appearing in the list and is then given access to different tabs:

The "timeseries" tab display the "readymade" 8760hour timeseries available for simulation purposes. These data may come from any origin outside Antares, or be data formerly generated by the Antares timeseries stochastic generator, stored as input data on the user's request. Different ways to update data are :

direct typing

copy/paste a selected field to/from the clipboard

load/save all the timeseries from/to a file (usually located in the "user" subfolder)

Apply different functions (+,, *, /,etc.) to the existing (possibly filtered) values (e.g. simulate a 2% growth rate by choosing "multiplyallby1.02")

Handle the whole (unfiltered) existing dataset to either
 Change the number of columns (function name: resize)
 Adjust the values associated with the current first day of the year (function name: shift rows)
Versatile "Filter" functions allow quick access to userspecified sections of data (e.g. display only the load expected in the Wednesdays of January, at 09:00, for timeseries #12 to #19). Hourly load is expressed in round numbers and in MW. If a smaller unit has to be used, the user should define accordingly ALL the data of the study (size of thermal plants, interconnection capacities, etc.)

Note that:
 If the "intramodal correlated draw" option has not been selected in the simulation window, MC adequacy or economy simulations can take place even if the number of timeseries is not the same in all areas (e.g. 2 , 5 , 1 , 45 ,...)
 If the "intramodal correlated draws" option has been selected in the simulation window, every area should have either one single timeseries or the same given number (e.g. 25 , 25 , 1 , 25...)

The "spatial correlation" tab gives access to the interarea correlation matrices that will be used by the stochastic generator if it is activated. Different subtabs are available for the definition of 12 monthly correlation matrices and of an overall annual correlation matrix. A matrix A must meet three conditions to be a valid correlation matrix:
$$\forall i,\ \forall j,\ {A_{ii} = 100; 100 \le A_{ij} \le 100}; A\ symmetric; A\ positive\ semi\mbox{}definite$$
When given invalid matrices, the TS generator emits an infeasibility diagnosis

The "local data" tab is used to set the parameters of the stochastic generator. These parameters are presented in four subtabs whose content is presented in Timeseries analysis and generation.

The "digest" tab displays for all areas a short account of the local data

Thermal¶
Documentation of the AntaresWeb interface for this section
This window is used to handle all input data regarding thermal dispatchable power.
The user may pick any area appearing in the area list and is then given access to the list of thermal plants clusters defined for the area (e.g. "CCG 300 MW", "coal 600", etc.). Once a given cluster has been selected, a choice can be made between different tabs:

The "timeseries" tab displays the "readymade" 8760hour timeseries available for simulation purposes. These data may come from any origin outside Antares, or be data formerly generated by the Antares timeseries stochastic generator, stored as input data on the user's request. Different ways to update data are :
 direct typing
 copy/paste a selected field to/from the clipboard
 load/save all the timeseries from/to a file (usually located in the "user" subfolder)
 Apply different functions (+,, *, /,etc.) to the existing (possibly filtered) values (e.g. simulate a 2% growth rate by choosing "multiplyallby1.02")

Handle the whole (unfiltered) existing dataset to either

Change the number of columns (function name: resize)
 Adjust the values associated with the current first day of the year (function name: shift rows)
Versatile "Filter" functions allow quick access to userspecified sections of data (e.g. display only the generation expected on Sundays at midnight, for all timeseries).
Hourly thermal generation is expressed in round numbers and in MW. If a smaller unit has to be used, the user should define accordingly ALL the data of the study (Wind generation, interconnection capacities, load, hydro generation, solar, etc.)

Note that:

If the "intramodal correlated draws" option has not been selected in the simulation window, MC adequacy or economy simulations can take place even if the number of timeseries is not the same in all areas (e.g. 2, 5, 1, 45,etc.)

If the "intramodal correlated draws" option has been selected in the simulation window, every area should have either one single timeseries or the same given number (e.g. 25, 25, 1, 25, etc.). Note that, unlike the other timeseries (load, hydro, etc.), which depend on meteorological conditions and are therefore interareacorrelated, the thermal plants timeseries should usually be considered as uncorrelated. Using the "correlated draws" feature makes sense only in the event of having to play predefined scenarios (outside regular MC scope)


The "TS generator" tab is used to set the parameters of the stochastic generator. These parameters are defined at the daily scale and are namely, for each day: the average duration of forced outages (beginning on that day), the forced outage rate, the duration of planned outages (beginning on that day), the planned outage rate, planned outages minimum and maximum numbers. Durations are expressed in days and rates belong to [0 , 1].

The "Common" tab is used to define the cluster's technoeconomic characteristics :
 Name
 Fuel used
 Location (Area)
 Activity status
 false: not yet commissioned, mothballed, etc.
 true : the plant may generate
 Number of units
 Nominal capacity
 Full Mustrun status
 false: above a partial "mustrun level" (that may exist or not, see infra) plants will be dispatched on the basis of their market bids.
 true: plants will generate at their maximum capacity, regardless of market conditions
 Minimum stable power (MW)
 Minimum Up time (hours)
 Minimum Down time (hours)
 Default contribution to the spinning reserve (% of nominal capacity)
 tons of different pollutant types (CO2, SO2, etc.) emitted per electric MWh
 Fuel efficiency (%)
 Cost generation [Set manually / Use cost timeseries]
 Marginal operating cost (€/MWh)
 Volatility (forced): a parameter between 0 and 1, see section Timeseries generation (thermal)
 Volatility (planned): a parameter between 0 and 1, see section Timeseries generation (thermal)
 Law (forced): Probabilistic law used for the generation of the forced outage timeseries, can be set to either uniform or geometric
 Law (planned): Probabilistic law used for the generation of the planned outage timeseries, can be set to either uniform or geometric
 Generate TS: Parameter to specify the behavior of this cluster for TS generation. This clusterwise parameter takes priority over the studywide one. It can hold three values:
 Force generation: TS for this cluster will be generated
 Force no generation: TS for this cluster will not be generated
 Use global parameter: Will use the parameter for the study (the one in the Simulation Window).
 Fixed cost (NoLoad heat cost) (€ / hour of operation )
 Startup cost (€/startup)
 Market bid (€/MWh)
 Random spread on the market bid (€/MWh)
 Variable Operation&Maintenance cost (€/MWh, only used if Cost generation is set to use cost timeseries)
 Seasonal marginal cost variations (gas more expensive in winter, ...)
 Seasonal market bid modulations (assets costs charging strategy )
 Nominal capacity modulations (seasonal thermodynamic efficiencies, special overgeneration allowances, etc.). These modulations are taken into account during the generation of available power timeseries

Minimal generation commitment (partial mustrun level) set for the cluster

Note that:
 The optimal dispatch plan as well as locational marginal prices are based on market bids, while the assessment of the operating costs associated with this optimum are based on cost parameters. (In standard "perfect" market modeling, there is no difference of approaches because market bids are equal to marginal costs)

Note that:
 If
Cost generation
is set toSet manually
Marginal and Market bid costs (€/MWh) are specified directly inCommon
tab and have the same value for all timeseries and hours.  If
Cost generation
is set toUse cost timeseries
Marginal and Market bid costs (€/MWh) are calculated separately for all the timeseries and hours using the following equation:
Marginal_Cost[€/MWh] = Market_Bid_Cost[€/MWh] = (Fuel_Cost[€/GJ] * 3.6 * 100 / Efficiency[%]) + CO2_emission_factor[tons/MWh] * C02_cost[€/tons] + Variable_O&M_cost[€/MWh]
where Efficiency[%], CO2_emission_factor[tons/MWh] and Variable_O&M_cost[€/MWh] are specified in theCommon
tab under operating costs and parameters, while Fuel_Cost[€/GJ] and C02_cost[€/tons] are provided as timeseries in separate tabs.
 If
Storages¶
Documentation of the AntaresWeb interface for this section
This window is used to create and edit shortterm storage objects. An individual shortterm storage component is defined as an object with the following characteristics:
 Storage managed with a filling level which is identical at the start and end of each Antares optimization window;
 Rule curves that frame permissible storage levels hour by hour  the admissible range is a coefficient comprised between 0 and 1;
 Timeseries of hourly modulation of the maximum injection and withdrawal power;
 Timeseries of natural inflows (case of an opencycle PSP).
The user may pick any area appearing in the area list and is then given access to the list of shortterm storages defined for the area. Once a given storage has been selected, the following characteristics can be set:

General characteristics of the storage:
 Name
 Group: the type of storage, based on a predefined list of storages ("PSP_open", "PSP_closed", "Pondage", "Battery", "Other1", "Other2", ..., "Other5")
 Withdrawal (MW): the maximum withdrawal power for the storage  withdrawal refers to the flow from the storage to the power system
 Injection (MW): the maximum injection power for the storage  withdrawal refers to the flow from the power system to the storage
 Stock (MWh): the capacity of the storage in MWh
 Efficiency (%): the energy efficiency of the storage, i.e. the ratio for a given volume between the energy taken from the system to be injected into the storage and the energy returned to the system during its withdrawal. This efficiency factor is applied when injecting energy into the storage.
 Initial level (%): the imposed initial filling rate of the storage at the beginning of each optimisation period.
 Initial level optimal: if the parameter is activated, the "Initial level" parameter is ignored and the initial storage level is optimized by Antares for each optimization period to minimize its objective function.
Note: setting this parameter to "True" implies that there is no guarantee that the initial storage level of week N is the same as the final storage level of week N1. However, the final level of week N is always equal to the initial level of the same week N plus/minus the injections/withdrawals occuring at the last hour of week N.

"Injections/withdrawal capacities": a hourly timeseries of modulation factors of the injection and withdrawal capacity for each hour (between 0 and 1), reflecting a lower availability of the structures during certain periods. At a given hour, the overall injection/withdrawal capacities of the storage are the product of this modulation factor by the "Withdrawal" and "Injection" parameters in the General data.

"Rule curves": a hourly timeseries of rule curves (between 0 and 1), which are the lower and upper limits of the storage level imposed at each hour.

"Inflows": a hourly timeseries of inflows filling the storage (in MWh). The values can be negative, corresponding to withdrawals imposed on the storage for other uses.
Hydro¶
Documentation of the AntaresWeb interface for this section
This section of the AntaresWeb interface for this section is meant to handle all input data regarding hydro power, as well as any other kind of energy storage system of any size (from a small battery to a large conventional hydrostorage reservoir with or without pumping facilities, etc.): Hydro power being historically the first and largest form of power storage, it stood to reason that it should play in Antares the role of a "generic template" for all forms of storable power. This versatility, however, comes at the price of a comparatively more complex data organization than for other objects, which explains the comparatively long length of this chapter.
In the main Window, the user may pick any area appearing in the list and is then given access to different tabs:

The "timeseries" tab displays the "readymade" timeseries already available for simulation purposes. There are five categories of timeseries (displayed in five different subtabs): the Run of River (ROR) timeseries, the Storage power (SP) timeseries, the Minimum Generation power, the Maximum Generation power and the Maximum Pumping Power.
ROR timeseries are defined at the hourly scale; each of the 8760 values represents the ROR power expected at a given hour, expressed in round number and in MW. The SP timeseries are defined at the daily scale; each of the 365 values represents an overall SP energy expected in the day, expressed in round number and in MWh. These natural inflows are considered to be storable into a reservoir for later use. The Minimum Generation timeseries are defined at the hourly scale; each of the 8760 values represents the Minimum Generation power expected at a given hour expressed in round number and in MW. The Maximum Generation timeseries are defined at the hourly scale; each of the 8760 values represents the Maximum Generation power expected at a given hour expressed in round number and in MW. The Maximum Pumping timeseries are defined at the hourly scale; each of the 8760 values represents the Maximum Pumping power expected at a given hour expressed in round number and in MW.
ROR timeseries and SP timeseries may come from any origin outside Antares, or may have been formerly generated by the Antares timeseries stochastic generator and stored as input data on the user's request. Minimum Generation, Maximum Generation and Maximum Pumping may come from any origin outside Antares, but they can not be generated by the Antares timeseries stochastic generator. Different ways to update data are:
 direct typing
 copy/paste a selected field to/from the clipboard
 load/save all the timeseries from/to a file (usually located in the "user" subfolder)
 Apply different functions (+,, *, /,etc.) to the existing (possibly filtered) values (e.g. simulate a 2% growth rate by choosing "multiplyallby1.02")

Handle the whole (unfiltered) existing dataset to either
 Change the number of columns (function name: resize)
 Adjust the values associated with the current first day of the year (function name: shift rows)

Note that:
 For a given area, the number of ROR timeseries, SP timesseries and Minimum Generation must be identical
 For a given area, the number of Maximum Generation and Maximum Pumping must be identical
 If the "intramodal correlated draws" option was not selected in the simulation window, MC adequacy or economy simulations can take place even if the number of hydro timeseries is not the same in all areas (e.g. 2 , 5 , 1 , 45 ,...)
 If the "intramodal correlated draws" option was selected in the simulation window, every area should have either one single timeseries or the same given number (e.g. 25 , 25 , 1 , 25...)

The "spatial correlation" tab gives access to an annual interarea correlation matrix that will be used by the stochastic generator if it is activated. Correlations are expressed in percentages, hence to be valid this matrix must be symmetric, p.s.d, with a main diagonal of 100s and all terms lying between (100 ,+100)

The "Allocation" tab gives access to an annual interarea allocation matrix A(i,j) that may be used during a heuristic hydro preallocation process, regardless of whether the stochastic timeseries generator is used or not. This matrix describes the weights that are given to the loads of areas (i) in the definition of the monthly and weekly hydro storage generation profiles of areas (j). The way this is done in detailed in Miscellaneous.

The "local data" tab is used to set up the parameters of the stochastic generator_ AND _to define technoeconomic characteristics of the hydro system that are used in Economy and Adequacy optimizations. For the purpose of versatility (use of the hydro section to model storage facilities quite different in size and nature), this "local tab" is itself divided up into four different subtabs whose list follows and which are further described:
 Inflow Structure
 Reservoir Levels and water value
 Daily Power and Energy Credits
 Management options
Inflow Structure
This tab contains all the local parameters used for the stochastic generation of hydro timeseries. These are namely:
 The expectations, standard deviations, minimum and maximum values of monthly energies (expressed in MWh), monthly shares of Run of River within the overall hydro monthly inflow.
 The average correlation between the energy of a month and that of the next month (intermonthly correlation).
 The average daily pattern of inflows within each month. Each day is given a relative "weight" in the month. If all days are given the same weight, daily energy timeseries will be obtained by dividing the monthly energy in equal days. If not, the ratio between two daily energies will be equal to that of the daily weights in the pattern array.
Overall hydro energy is broken down into two parts: Run of River ROR and storage STOR
ROR energy has to be used on the spot, as it belongs to the general "mustrun" energy category.
STOR energy can be stored for use at a later time. The way how stored energy may actually be used depends on the options chosen in the "management options" Tab and of the values of the parameters defined in the other Tabs.
Reservoir Levels and Water Values
Reservoir levels (left side)
On the left side are defined 365 values for the minimum, average and maximum levels set for the reservoir at the beginning of each day, expressed in percentage of the overall reservoir volume. The lower and upper level timeseries form a pair of socalled lower and upper "reservoir rule curves"
Depending on the set of parameters chosen in the "management options" Tab, these rule curves may be used in different ways in the course of both heuristic seasonal hydro preallocation process and subsequent weekly optimal hydrothermal unitcommitment and dispatch process.
Water values (right side)
On the right side is a table of marginal values for the stored energy, which depends on the date (365 days) and of the reservoir level (101 round percentage values ranging from 0% to 100%). These values may have different origins; they theoretically should be obtained by a comprehensive (dual) stochastic dynamic programming study carried out over the whole dataset and dealing simultaneously with all reservoirs.
Depending on the set options chosen in the "management options" Tab, these values may be used or not in the course of the weekly optimal hydrothermal unitcommitment and dispatch process.
Daily Power and Energy Credits
Standard credits (Bottom part)
The bottom part displays two daily timeseries (365 values) defined for energy generation/storage (hydro turbines or hydro pumps). Both arrays represents the maximum daily energy (either generated or stored).
For the sake of clarity, maximum daily energies are expressed as a number of hours at maximum power and these values are used along with the Maximum Generation and Maximum Pumping TS's to calculate daily mean energy.
Credit modulation (Upper part)
The upper part displays two leveldependent (101 round percentage values ranging from 0% to 100%) timeseries of modulation coefficients defined for either generating or storing (pumping).
These modulations, which can take any positive value, may (depending on the options chosen in the management options Tab) be used to increase (value >1) or to decrease (value <1) the standard credits defined previously for the maximum daily power and energies.
Management Options
This Tab is a general dashboard for the definition of how storage units, whatever their size or nature, should be managed. It includes 15 parameters (out of which 7 are booleans) presented hereafter:

"Follow load" (yn): defines whether an "ideal" seasonal generation profile should somehow follow the load OR an "ideal" seasonal generation profile should remain as close as possible to the natural inflows (i.e. instant generation whenever possible)

"Interdaily breakdown" and "Intermonthly breakdown" : parameters used in the assessment, through a heuristic process, of an "ideal" seasonal generation profile, if the use of such a profile is required (the heuristic itself is presented in Miscellaneous)

"Intradaily modulation": parameter which represents, for the storage power, the maximum authorized value for the ratio of the daily peak to the average power generated throughout the day. This parameter is meant to allow simulating different hydro management strategies. Extreme cases are : 1 : generated power should be constant throughout the day 24 : use of the whole daily energy in one single hour is allowed

"Reservoir management"
yn
: defines whether the storage should be explicitly modeled or not.Choosing "No" implies that available data allow or require that, regardless of the reservoir characteristics:

The whole amount of STOR energy of each month MUST be used during this month (no longterm storage)

The actual daily generation should follow, during the month, an "ideal" profile defined by the heuristic defined in Miscellaneous
Choosing "Yes" implies that available data allow or require explicit modeling of the storage facility, regardless of whether a preallocation heuristic is used or not.


"Reservoir capacity": size of the storage facility, in MWh

"Initialize reservoir level on the 1^{st} of": date at which the reservoir level should be initialized by a random draw. The "initial level" is assumed to follow a "beta" variable with expectation "average level", upper bound U=max level, lower bound L= min level, standard deviation = (1/3) (UL)

"Use Heuristic Target" (yn): defines whether an "ideal" seasonal generation profile should be heuristically determined or not.
Choosing "No" implies that available data allow or require that full confidence should be put in water values determined upstream (through [dual] stochastic dynamic programming) OR that there are no "natural inflows" to the storage facility (battery or PSP, etc.)
Choosing "Yes" implies that available data allow or require the definition of an "ideal" generation profile, that can be used to complement –or replace– the economic signal given by water values AND that there are "natural inflows" on which a generation heuristic can be based.

"PowertoLevel modulations (yn)": defines whether the standard maximum daily energy and power credit should be or not multiplied by leveldependent modulation coefficients.

"Hard bounds on rule curves (yn)": states whether, beyond the preliminary heuristic stage (if any), lower and upper reservoir rule curves should still be taken into account as constraints in the hydrothermal unit commitment and dispatch problems.

"Use leeway (yn)", lower bound L, upper bound U: states whether the heuristic hydro ideal target (HIT) should be followed exactly or not.
Choosing "No" implies that, in optimization problems, the hydro energy generated throughout the time interval will be subject to an equality constraint, which may include shortterm pumping cycles independent of water value: sum{ 1,t,T} (hydro(t)) – sum{1,t,T} (r. pump(t))= *HIT
Choosing "Yes", with bounds L and U, implies that, in optimization problems, the hydro energy generated throughout the time span will be subject to inequality constraints: L_HIT <=sum{1,t,T} (hydro(t)) <= U*HIT
Independently, short or longterm pumping may also take place if deemed profitable in the light of water values.

"Use Water Value (yn)": states whether the energy taken from / stored into the reservoir should be given the reference value defined in the ad hoc table OR should be given a zero value.

"Pumping Efficiency Ratio": setting the value to r means that, for the purpose of storing 1 gravitational MWh, pumps will have to use (1/r) electrical MWh.
Wind¶
Documentation of the AntaresWeb interface for this section
This window is used to handle all input data regarding Wind power. This window is only accessible when the advanced parameter Renewable Generation modeling is set to "Aggregated".
The user may pick any area appearing in the list and is then given access to different tabs:

The "timeseries" tab display the "readymade" 8760hour timeseries already available for simulation purposes. These data may come from any origin outside Antares, or be data formerly generated by the Antares timeseries stochastic generator, stored as input data on user's request. Different ways to update data are :
 direct typing
 copy/paste a selected field to/from the clipboard
 load/save all the timeseries from/to a file (usually located in the "user" subfolder)
 Apply different functions (+,, *, /,etc.) to the existing (possibly filtered) values (e.g. simulate a 2% growth rate by choosing "multiplyallby1.02")
 Handle the whole (unfiltered) existing dataset to either
 Change the number of columns (function name: resize)
 Adjust the values associated with the current first day of the year (function name: shift rows)
Versatile "Filter" functions allow quick access to userspecified sections of data (e.g. display only the wind generation expected between 17:00 and 21:00 in February, for timeseries 1 to 100).
Hourly wind generation is expressed in round numbers and in MW. If a smaller unit has to be used, the user should define accordingly ALL the data of the study (size of thermal plants, interconnection capacities, load, etc.)

Note that:

If the "intramodal correlated draws" option has not been selected in the simulation window, MC adequacy or economy simulations can take place even if the number of timeseries is not the same in all areas (e.g. 2, 5, 1,45, ...)

If the "intramodal correlated draws" option has been selected in the simulation window, every area should have either one single timeseries or the same given number (e.g. 25, 25, 1, 25, ...)


The "spatial correlation" tab gives access to the interarea correlation matrices that will be used by the stochastic generator if it is activated. Different subtabs are available for the definition of 12 monthly correlation matrices and an overall annual correlation matrix.
A matrix A must meet three conditions to be a valid correlation matrix:
$$\forall i,\ \forall j,\ {A_{ii} = 100; 100 \le A_{ij} \le 100}; A\ symmetric; A\ positive\ semi\mbox{}definite$$
When given invalid matrices, the TS generator emits an infeasibility diagnosis

The "local data" tab is used to set the parameters of the stochastic generator. These parameters are presented in four subtabs whose content is presented in Timeseries analysis and generation.

The "digest" tab displays for all areas a short account of the local data
Solar¶
Documentation of the AntaresWeb interface for this section
This window is used to handle all input data regarding Solar power. Both thermal solar generation and PV solar generation are assumed to be bundled in this data section. This window is only accessible when the advanced parameter Renewable Generation modeling is set to "aggregated”.
The user may pick any area appearing in the list and is then given access to different tabs:

The "timeseries" tab display the "readymade" 8760hour timeseries available for simulation purposes. These data may come from any origin outside Antares, or be data formerly generated by the Antares timeseries stochastic generator, stored as input data on the user's request. Different ways to update data are :
 direct typing
 copy/paste a selected field to/from the clipboard
 load/save all the timeseries from/to a file (usually located in the "user" subfolder)
 Apply different functions (+,, *, /,etc.) to the existing (possibly filtered) values (e.g. simulate a 2% growth rate by choosing "multiplyallby1.02")

Handle the whole (unfiltered) existing dataset to either
 Change the number of columns (function name: resize)
 Adjust the values associated with the current first day of the year (function name: shift rows)
Versatile "Filter" functions allow quick access to userspecified sections of data (e.g. display only the solar power expected in August at noon, for all timeseries).
Hourly solar power is expressed in round numbers and in MW. If a smaller unit has to be used, the user should define accordingly ALL the data of the study (size of thermal plants, interconnection capacities, etc.)

Note that:

If the "intramodal correlated draws" option was not selected in the simulation window, MC adequacy or economy simulations can take place even if the number of timeseries is not the same in all areas (e.g. 2 , 5 , 1 , 45 ,...)

If the "intramodal correlated draws" option was selected in the simulation window, every area should have either one single timeseries or the same given number (e.g. 25 , 25 , 1 , 25...)


The "spatial correlation" tab gives access to the interarea correlation matrices that will be used by the stochastic generator if it is activated. Different subtabs are available for the definition of 12 monthly correlation matrices and of an overall annual correlation matrix.
A matrix A must meet three conditions to be a valid correlation matrix:
$$\forall i,\ \forall j,\ {A_{ii} = 100; 100 \le A_{ij} \le 100}; A\ symmetric; A\ positive\ semi\mbox{}definite$$
When given invalid matrices, the TS generator emits an infeasibility diagnosis

The "local data" tab is used to set the parameters of the stochastic generator. These parameters are presented in four subtabs whose content is presented in Timeseries analysis and generation.

The "digest" tab displays for all areas a short account of the local data
Renewable¶
Documentation of the AntaresWeb interface for this section
This window is used to handle all input data regarding renewable generation. This window is only accessible when the advanced parameter Renewable Generation modeling is set to "cluster” (default value).
The user may pick any area appearing in the area list and is then given access to the list of renewable clusters defined for the area (e.g. "Onshore Wind Farm 200MW", "Solar Rooftop 50MW", etc.). Once a given cluster has been selected, a choice can be made between different tabs:

The "timeseries" tab displays the "readymade" 8760hour timeseries available for simulation purposes. These data may come from any origin outside Antares, or be data formerly generated by the Antares timeseries stochastic generator, stored as input data on the user's request. Different ways to update data are :
 direct typing
 copy/paste a selected field to/from the clipboard
 load/save all the timeseries from/to a file (usually located in the "user" subfolder)
 Apply different functions (+,, *, /,etc.) to the existing (possibly filtered) values (e.g. simulate a 2% growth rate by choosing "multiplyallby1.02")

Handle the whole (unfiltered) existing dataset to either
 Change the number of columns (function name: resize)
 Adjust the values associated with the current first day of the year (function name: shift rows)
Versatile "Filter" functions allow quick access to userspecified sections of data (e.g. display only the generation expected on Sundays at midnight, for all timeseries).
Hourly thermal generation is expressed in round numbers and in MW. If a smaller unit has to be used, the user should define accordingly ALL the data of the study (Wind generation, interconnection capacities, load, hydro generation, solar, etc.)

Note that:

If the "intramodal correlated draws" option has not been selected in the simulation window, MC adequacy or economy simulations can take place even if the number of timeseries is not the same in all areas (e.g. 2, 5, 1, 45,etc.)

If the "intramodal correlated draws" option has been selected in the simulation window, every area should have either one single timeseries or the same given number (e.g. 25, 25, 1, 25, etc.). Note that, unlike the other timeseries (load, hydro, etc.), which depend on meteorological conditions and are therefore interareacorrelated, the thermal plants timeseries should usually be considered as uncorrelated. Using the "correlated draws" feature makes sense only in the event of having to play predefined scenarios (outside regular MC scope)


The "TS generator" tab is not accessible for this version.

The "Common" tab is used to define the cluster's technoeconomic characteristics :
 Name
 Group: The group can be any one of the following: Wind Onshore, Wind Offshore, Solar Thermal, Solar PV, Solar Rooftop, Other RES 1, Other RES 2, Other RES 3, or Other RES 4. If not specified, the renewable cluster will be part of the group Other RES 1.
 Location (Area)
 Timeseries mode:
 Power generation means that the unit of the timeseries is in MW
 Production factor means that the unit of the timeseries is in p.u. (between 0 and 1, 1 meaning the full installed capacity)
 Activity status
 false: not yet commissioned, mothballed, etc.
 true: the cluster may generate
 Number of units
 Nominal capacity (in MW per unit)
Misc. Gen.¶
Documentation of the AntaresWeb interface for this section
This window is used to handle all input data regarding miscellaneous non dispatchable generation.
On picking any area in the primary list, the user gets direct access to all data regarding the area, which amount to 8 readymade 8760hour timeseries (expressed in MW):

CHP generation

Bio Mass generation

Biogas generation

Waste generation

Geothermal generation

Any other kind of nondispatchable generation

A predefined timeseries for the operation of Pumped Storage Power plants, if they are not explicitly modeled. A positive value is considered as an output (generating) to the grid, a negative value is an input (pumping) to the station.
Note that the sum of the 8760 values must be negative, since the pumping to generating efficiency is lower than 1. The user may also use only the negative values (prescribed pumping), while transferring at the same time the matching generating credit on the regular hydro storage energy credit.

ROW balance: the balance with the rest of the world. A negative value is an export to ROW, a positive value is an import from ROW. These values acts as boundary conditions for the model. Different ways to update data are:
 direct typing
 copy/paste a selected field to/from the clipboard
 load/save all the timeseries from/to a file (usually located in the "user" subfolder)
 Apply different functions (+,, *, /,etc.) to the existing (possibly filtered) values (e.g. simulate a 2% growth rate by choosing "multiplyallby1.02")

Handle the whole (unfiltered) existing dataset to either
 Change the number of columns (function name: resize)
 Adjust the values associated with the current first day of the year (function name: shift rows)
Reserves / DSM¶
Documentation of the AntaresWeb interface for this section
This window is used to handle all input data regarding reserves and the potential of "smart" load management (when not modeled using "fake" thermal dispatchable plants). On picking any area in the primary list, the user gets direct access to all data regarding the area, which amount to four readymade 8760hour timeseries (expressed in MW). Those reserves are available in either "adequacy" or "economy" simulations:

Dayahead reserve: power accounted for in setting up the optimal unitcommitment and schedule of the following day(s), which must consider possible forecasting errors or lastminute incidents. If the optimization range is of one day, the reserve will be actually seen as "dayahead". If the optimization range is of one week, the need for reserve will be interpreted as "weekahead". (Adequacy and Economy simulations)

DSM: power (decrease or increase) to add to the load. A negative value is a load decrease, a positive value is a load increase. Note that an efficient demand side management scheme may result in a negative overall sum (All simulation modes).
Links¶
This window is used to handle all input data regarding the interconnections. On picking any interconnection in the primary list, the user gets direct access to all data regarding the link, which are five annual parameters, a set of six readymade 8760hour timeseries, and a flexible number of readymade 8760hour timeseries corresponding to the capacities of the links.

The five parameters, used in economy or adequacy simulations are displayed in the "Parameters" and in the "Transmission capacities" tab. They are namely:
 "Hurdle cost": set by the user to state whether (linear) transmission fees should be taken into account or not in economy and adequacy simulations
 "Transmission capacities": set by the user to state whether the capacities to consider are those indicated in 8760hour arrays or if zero or infinite values should be used instead (actual values / set to zero / set to infinite)
 "Asset type": set by the user to state whether the link is either an AC component (subject to Kirchhoff's laws), a DC component, or another type of asset
 "Account for loop flows": set by the KCG ^{4} to include (or not) passive loop flows in the formulation of the constraints enforcing Kirchhoff's laws
 "Account for PST": set by the KCG to include (or not) the settings of phaseshifting transformers in the formulation of the constraints enforcing Kirchhoff's laws

The "Parameters" tab displays six 8760hour timesseries, which are:

Hurdle cost direct: an upstreamtodownstream transmission fee, in €/MWh

Hurdle cost indirect: a downstreamtoupstream transmission fee, in €/MWh

Impedance: used in economy simulations to give a physical meaning to raw outputs, when no binding constraints have been defined to enforce Kirchhoff's laws (see "Output" section, variable "Flow Quad") OR used by the Kirchhoff's constraint generator to build up proper flow constraints (AC flow computed with the classical "DC approximation"). Since voltage levels are not explicitly defined and handled within Antares, all impedances are assumed to be scaled to some reference $ U_{ref} $

Loop flow: amount of power flowing circularly though the grid when all "nodes" are perfectly balanced (no import and no export). Such loop flows may be expected on any "simplified" grid in which large regions (or even countries) are modeled by a small number of "macro" nodes, and should accordingly be accounted for.

PST min (denoted $Y^$ in Kirchhoff Constraints Generator): lower bound of phaseshifting that can be reached by a PST installed on the link, if any (note : the effect of the active loop flow generated by the PST may be superimposed to that of the passive loop flow)

PST max (denoted $Y^+$ in Kirchhoff Constraints Generator): upper bound of phaseshifting that can be reached by a PST installed on the link, if any (note : the effect of the active loop flow generated by the PST may be superimposed to that of the passive loop flow)
For the sake of simplicity and homogeneity with the convention used for impedance, PST settings are assumed to be expressed in $ rad/U^2_{ref} $


The "Transmission capacities" tab displays "readymade" 8760hour timeseries already available for simulation purposes. In this tab, the table "Direct" describes the upstreamtodownstream capacity, in MW, and the table "Indirect" describes the downstreamtoupstream capacity, in MW. Please note that TimeSeries analysis and generation is not available for capacity TimeSeries. Different ways to update data are :
 direct typing
 copy/paste a selected field to/from the clipboard
 load/save all the timeseries from/to a file (usually located in the "user" subfolder)
 Apply different functions (+,, *, /,etc.) to the existing (possibly filtered) values (e.g. simulate a 2% growth rate by choosing "multiplyallby1.02")

Handle the whole (unfiltered) existing dataset to either:
 Change the number of columns (function name: resize)
 Adjust the values associated with the current first day of the year (function name: shift rows)
Versatile "Filter" functions allow quick access to userspecified sections of data (e.g. display only the generation expected on Sundays at midnight, for all timeseries).

Note that:

For a given link, the number of TimeSeries for the direct and indirect capacity must be equal. Otherwise, an issue will be raised when launching a simulation

If the "intramodal correlated draws" option was not selected in the simulation window, MC adequacy or economy simulations can take place even if the number of timeseries for direct/indirect capacity is not the same for all links (e.g. 2 , 5 , 1 , 45 ,...)

If the "intramodal correlated draws" option was selected in the simulation window, every link should have either one single timeseries for both the direct and indirect capacity, or the same given number of timeseries (e.g. 25 , 25 , 1 , 25...)

Binding constraints¶
This section of the AntaresWeb interface for this section is used to handle all data regarding special constraints that one may wish to include in the formulation of the optimization problems to solve.
The set of tabs described hereafter provides for that purpose all the means required to define arbitrary linear constraints on any subset of continuous variables involved in the modeling of the power system.
Since no limitation is set on the number and content of the constraints that may be defined that way, it is the user's sole responsibility to make sure that these socalled "binding constraints" are realistic and meaningful, be it from a technical or economic standpoint.
A typical situation in which this feature proves useful is, for instance, encountered when data at hand regarding the grid include an estimate of the impedances of the interconnections.
In such cases, assuming that:
 $Z_l$ denotes the impedance of interconnections $l=1, L$
 A preliminary study of the graph modeling the grid has shown that it can be described by a set of independent meshes $c=1, C$(cycle basis of the graph)
Then the DC flow approximation may be implemented, for each timestep of the simulation, by a set of C binding constraints between AC flows $F_l$:
$$ c= 1, ..., C : \sum_{i \in C}{sign(l,c)F_lZ_l = 0}$$
Note that such specific binding constraints can be automatically generated within Antares by using the auxiliary module "Kirchhoff's Constraints Generator" further described in Kirchhoff Constraints Generator.
Aside from such sets of constraints, which may help to give realistic geographic patterns to the flows, completely different sets of constraints may be also defined, such as those set up by the market organization, which may define precise perimeters for valid commercial flows ^{5}.
More generally, Antares allows to define three categories of binding constraints between transmission flows and/or power generated from generating units:

"hourly" binding constraints, which are applied to instant power (transmitted and/or generated)

"daily" binding constraints, that are applied to daily energies. This class makes more sense for commercial modeling (say: imports and exports from/to such and such area should be comprised between such and such lower bound and upper bound). Daily binding constraints are also commonly used to model specific facilities, such as pumped storage units operated on a daily cycle

"weekly" binding constraints, that are applied to weekly energies. Like the previous ones, these constraints may be used to model commercial contracts or various phenomena, such as the operation of a pumped storage power plant operated on a weekly cycle.
The Binding Constraints section of the AntaresWeb interface for this section involves six main tabs described hereafter:

TAB "summary" Creation, edition or removal of a binding constraint. A binding constraint is here defined by four macroscopic attributes that can be set by the edit command:
 Name (caption)
 Timerange (hourly, daily, weekly)
 Numerical type (equality, bounded above, below, on both sides)
 Status (active /enabled or inactive/disabled)

TAB "weights" Definition of the coefficients given to each flow variable or generation variable in the formulation of the constraints. Two subtabs make it possible to handle the coefficients associated with transmission assets (links) and those associated with generation assets (thermal clusters). In both cases:
 The lines of the tables show only the components (links or clusters) that are visible on the current map
 The columns of the tables show only the constraints that do not have nonzero weights attached to components that are nor visible on the current map

TAB "offsets" Definition of the timelag (in hours) assigned to each flow variable or generation variable in the formulation of the constraints. Two subtabs make it possible to handle the offsets associated with transmission assets (links) and those associated with generation assets (thermal clusters). In both cases:
 The lines of the tables show only the components (links or clusters) that are visible on the current map
 The columns of the tables show only the constraints that do not have nonzero weights attached to components that are nor visible on the current map

TAB "=" Definition of the righthand side of equality constraints. This RHS has either 8760 values (hourly constraints) or 365 values (daily or weekly constraints). Depending on the range actually chosen for the simplex optimization (see section Configure of the main menu), the weekly constraints RHS will either be represented by the sum of seven daily terms or by a set of seven daily terms (weekly constraint downgraded to daily status).

TAB ">" Definition of the righthand side of "bounded below" and "bounded on both sides" inequality constraints. This RHS has either 8760 values (hourly constraints) or 365 values (daily or weekly constraints). Depending on the range actually chosen for the simplex optimization (see section Configure of the main menu), the weekly constraints RHS will either be represented by the sum of seven daily terms or by a set of seven daily terms (weekly constraint downgraded to daily status).

TAB "<" Definition of the righthand side of "bounded above" and "bounded on both sides" inequality constraints. This RHS has either 8760 values (hourly constraints) or 365 values (daily or weekly constraints). Depending on the range actually chosen for the simplex optimization (see section Configure of the main menu), the weekly constraints RHS will either be represented by the sum of seven daily terms or by a set of seven daily terms (weekly constraint downgraded to daily status).
NOTE: The righthand side of a binding constraint can be set to "inf" (for "bounded above" constraints) or "inf" (for "bounded below" constraints) for any timestamp. In that case, the constraint will be ignored by the solver for this timestamp. Please note that it is the user's responsibility to ensure that these values are set in a consistent way.
WARNING: When some clusters are defined as being in mustrun ("mustrun" parameter set to "True"), these clusters are automatically removed from the binding constraints in order to avoid potential incompatibilities between these constraints and the power output imposed to the mustrun clusters. The clusters which are removed from binding constraints are visible in the "Summary" tab, in which they are multiplied by N/As in the binding constraints. In case a binding constraint only contains mustrun clusters, it will be ignored in the simulation and subsequently identified as "Skipped" in the summary tab. Please note that in the specific context of the adequacy simulation mode (in which all thermal clusters are considered as being fully mustrun), all thermal clusters will consequently be deactivated from the binding constraints. This can lead to incorrect adequacy indicators in Antares studies containing binding constraints.
When defining binding constraints between (hourly) power, daily or weekly (energy) flows, special attention should be paid to potential conflicts between them or with the "basic" problem constraints. Lack of caution may result in situations for which the optimization has no solution. Consider for instance a case in which three variables X1, X2, X3 (whatever they physical meaning) are involved in the following binding constraints:
$$X1 + X2 > 5$$
$$X2 < 3$$
$$X3 > 0$$
$$X1 + X3 < 7$$
These commitments are obviously impossible to meet and, if the economic simulator is run on a dataset including such a set of constraints, it will produce an infeasibility analysis that looks like the following.
[solver][notic] Solver: Starting infeasibility analysis...
[solver][error] The following constraints are suspicious (first = most suspicious)
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 124
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 128
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 137
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 140
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 133
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 139
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 136
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 130
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 142
[solver][error] Hydro reservoir constraint at area 'Germany' at hour 123
This report should help you identify constraints that generate infeasible linear optimization problems such what is presented above.
The advanced preference "Unfeasible Problems Behavior" gives to the user the ability to choose between four different strategies regarding these situations.
Economic Opt.¶
This window is used to set the value of a number of arearelated parameters that, aside from the costs of each generating plant, define the optimal solution that Antares has to find in economic simulations. These parameters are namely, for each area of the system:

The value of the unsupplied energy (also commonly denoted Value Of Lost Load,VOLL) , in €/MWh. This value should usually be set much higher than the cost of the most expensive generating plant of the area

The random spread within which the nominal unsupplied energy value is assumed to vary

The value of the spilled energy, in € /MWh. This value reflects the specific penalty that should be added to the economic function for each wasted MWh, if any. Note that even if this value is set to zero no energy will be shed needlessly

The random spread within which the nominal unsupplied energy value is assumed to vary

Three parameters named "shedding status" and related to different kinds of generation. If the system cannot be balanced without shedding some generation, these parameters give control on how each kind of generation ("Non dispatchable power","Dispatchable hydropower" and "Other dispatchable generating plants") should contribute to the shedding. Depending on the value chosen for the status, the generation can or cannot be shed to find a solution to the load/generation balance problem. Note that enforcing a negative status for all types of plants may lead to simulations scenarios for which there are no mathematical solutions.
On running the economic simulator, such situations produce an infeasibility diagnosis.
Miscellaneous¶
In all previous windows showing Input data, the content can be filtered so as to reflect only items that are associated with Areas and Links defined as "visible" in a particular map. In that regard, binding constraints are considered as visible if and only if all of their nonzero weight associated objects are visible on the map.

"Economy" simulations make a full use of Antares optimization capabilities. They require economic as well as technical input data and may demand a lot of computer resources. "Adequacy" simulations are faster and require only technical input data. Their results are limited to adequacy indicators. ↩

In Economy an Adequacy simulations, these should be chosen so as to make the simulation span a round number of weeks. If not, the simulation span will be truncated: for instance, (1, 365) will be interpreted as (1, 364), i.e. 52 weeks (the last day of the last month will not be simulated). ↩

changing the number of MC years will reset the playlist to its default values ↩

KCG : Kirchhoff's constraints generator (see section 7) ↩

A typical case is given by the "FlowBased" framework today implemented in a large portion of the European electricity market. ↩