2b_equations.gms 87.1 KB
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This file is part of Backbone.

Backbone is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

Backbone is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License
along with Backbone.  If not, see <http://www.gnu.org/licenses/>.
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* =============================================================================
* --- Penalty Definitions -----------------------------------------------------
* =============================================================================

$setlocal def_penalty 1e6
Scalars
    PENALTY "Default equation violation penalty" / %def_penalty% /
;
Parameters
    PENALTY_BALANCE(grid) "Penalty on violating energy balance eq. (EUR/MWh)"
    PENALTY_RES(restype, up_down) "Penalty on violating a reserve (EUR/MW)"
;
PENALTY_BALANCE(grid) = %def_penalty%;
PENALTY_RES(restype, up_down) = %def_penalty%;


* =============================================================================
* --- Equation Declarations ---------------------------------------------------
* =============================================================================

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equations
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    // Objective Function, Energy Balance, and Reserve demand
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    q_obj "Objective function"
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    q_balance(grid, node, mType, f, t) "Energy demand must be satisfied at each node"
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    q_resDemand(restype, up_down, node, f, t) "Procurement for each reserve type is greater than demand"
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    // Unit Operation
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    q_maxDownward(mType, grid, node, unit, f, t) "Downward commitments will not undercut power plant minimum load constraints or maximum elec. consumption"
    q_maxUpward(mType, grid, node, unit, f, t) "Upward commitments will not exceed maximum available capacity or consumed power"
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    q_startup(unit, f, t) "Capacity started up is greater than the difference of online cap. now and in the previous time step"
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    q_startuptype(mType, starttype, unit, f, t) "Startup type depends on the time the unit has been non-operational"
    q_onlineLimit(mType, unit, f, t) "Number of online units limited for units with startup constraints and investment possibility"
    q_onlineMinUptime(mType, unit, f, t) "Unit must stay operational if it has started up during the previous minOperationTime hours"
*    q_minDown(mType, unit, f, t) "Unit must stay non-operational if it has shut down during the previous minShutDownTime hours"
*    q_genRamp(grid, node, mType, s, unit, f, t) "Record the ramps of units with ramp restricitions or costs"
*    q_genRampChange(grid, node, mType, s, unit, f, t) "Record the ramp rates of units with ramping costs"
*    q_rampUpLimit(grid, node, mType, s, unit, f, t) "Up ramping limited for units"
*    q_rampDownLimit(grid, node, mType, s, unit, f, t) "Down ramping limited for units"
    q_outputRatioFixed(grid, node, grid, node, unit, f, t) "Force fixed ratio between two energy outputs into different energy grids"
    q_outputRatioConstrained(grid, node, grid, node, unit, f, t) "Constrained ratio between two grids of energy output; e.g. electricity generation is greater than cV times unit_heat generation in extraction plants"
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    q_conversionDirectInputOutput(effSelector, unit, f, t) "Direct conversion of inputs to outputs (no piece-wise linear part-load efficiencies)"
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    q_conversionSOS2InputIntermediate(effSelector, unit, f, t)   "Intermediate output when using SOS2 variable based part-load piece-wise linearization"
    q_conversionSOS2Constraint(effSelector, unit, f, t)          "Sum of v_sos2 has to equal v_online"
    q_conversionSOS2IntermediateOutput(effSelector, unit, f, t)  "Output is forced equal with v_sos2 output"
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    q_fixedGenCap1U(grid, node, unit, t) "Fixed capacity ratio of a unit in one node versus all nodes it is connected to"
    q_fixedGenCap2U(grid, node, unit, grid, node, unit, t) "Fixed capacity ratio of two (grid, node, unit) pairs"

    // Energy Transfer
    q_transfer(grid, node, node, f, t) "Rightward and leftward transfer must match the total transfer"
    q_transferRightwardLimit(grid, node, node, f, t) "Transfer of energy and capacity reservations to the rightward direction are less than the transfer capacity"
    q_transferLeftwardLimit(grid, node, node, f, t) "Transfer of energy and capacity reservations to the leftward direction are less than the transfer capacity"
    q_resTransferLimitRightward(grid, node, node, f, t) "Transfer of energy and capacity reservations are less than the transfer capacity to the rightward direction"
    q_resTransferLimitLeftward(grid, node, node, f, t) "Transfer of energy and capacity reservations are less than the transfer capacity to the leftward direction"

    // State Variables
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    q_stateSlack(grid, node, slack, f, t) "Slack variable greater than the difference between v_state and the slack boundary"
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    q_stateUpwardLimit(grid, node, mType, f, t) "Limit the commitments of a node with a state variable to the available headrooms"
    q_stateDownwardLimit(grid, node, mType, f, t) "Limit the commitments of a node with a state variable to the available headrooms"
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*    q_boundState(grid, node, node, mType, f, t) "Node state variables bounded by other nodes"
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    q_boundStateMaxDiff(grid, node, node, mType, f, t) "Node state variables bounded by other nodes (maximum state difference)"
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    q_boundCyclic(grid, node, mType, s, s_) "Cyclic bound for the first and the last states of samples"
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*    q_boundCyclicSamples(grid, node, mType, s, f, t, s_, f_, t_) "Cyclic bound inside or between samples"
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    // Policy
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    q_capacityMargin(grid, node, f, t) "There needs to be enough capacity to cover energy demand plus a margin"
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    q_emissioncap(gngroup, emission) "Limit for emissions"
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    q_instantaneousShareMax(gngroup, group, f, t) "Maximum instantaneous share of generation and controlled import from a group of units and links"
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    q_energyShareMax(gngroup, group) "Maximum energy share of generation and import from a group of units"
    q_energyShareMin(gngroup, group) "Minimum energy share of generation and import from a group of units"
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    q_inertiaMin(gngroup, f, t) "Minimum inertia in a group of nodes"
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;

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* =============================================================================
* --- Equation Definitions ----------------------------------------------------
* =============================================================================

* --- Objective Function ------------------------------------------------------
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q_obj ..
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    + v_obj * 1000000

    =E=

    // Sum over all the samples, forecasts, and time steps in the current model
    + sum(msft(m, s, f, t),
        // Probability (weight coefficient) of (s,f,t)
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        + p_msft_Probability(m, s, f, t)
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            * [
                // Time step length dependent costs
                + p_stepLength(m, f, t)
                    * [
                        // Variable O&M costs
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                        + sum(gnuft(gnu_output(grid, node, unit), f, t),  // Calculated only for output energy
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                            + v_gen(grid, node, unit, f, t)
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                                * p_unit(unit, 'omCosts')
                            ) // END sum(gnu_output)

                        // Fuel and emission costs
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                        + sum(uFuel(unit, 'main', fuel)${uft(unit, f, t)},
                            + v_fuelUse(fuel, unit, f, t)
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                                * [ // !!! NOTE !!! Sum over tFull is needlessly time consuming. Price time series could be calculated beforehand.
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                                    + sum(tFull(tFuel)$[ord(tFuel) <= ord(t)], // Fuel costs, sum initial fuel price plus all subsequent changes to the fuelprice
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                                        + ts_fuelPriceChange(fuel, tFuel)
                                        )
                                    + sum(emission, // Emission taxes
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                                        + p_unitFuelEmissionCost(unit, fuel, emission)
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                                        )
                                    ] // END * v_fuelUse
                            ) // END sum(uft)

                        // Node state slack variable penalties
                        + sum(gn_stateSlack(grid, node),
                            + sum(slack${p_gnBoundaryPropertiesForStates(grid, node, slack, 'slackCost')},
                                + v_stateSlack(grid, node, slack, f, t)
                                    * p_gnBoundaryPropertiesForStates(grid, node, slack, 'slackCost')
                                ) // END sum(slack)
                            ) // END sum(gn_stateSlack)

                        // Dummy variable penalties
                        // Energy balance feasibility dummy varible penalties
                        + sum(inc_dec,
                            + sum(gn(grid, node),
                                + vq_gen(inc_dec, grid, node, f, t)
                                    * PENALTY_BALANCE(grid)
                                ) // END sum(gn)
                            ) // END sum(inc_dec)

                        // Reserve provision feasibility dummy variable penalties
                        + sum(restypeDirectionNode(restype, up_down, node),
                            + vq_resDemand(restype, up_down, node, f, t)
                                * PENALTY_RES(restype, up_down)
                            ) // END sum(restypeDirectionNode)

                        ] // END * p_stepLength

                // Start-up costs
                + sum(uft_online(unit, f, t),
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                    + sum(unitStarttype(unit, starttype),
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                        + v_startup(unit, starttype, f, t) // Cost of starting up
                            * [ // Startup variable costs
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                                + p_uStartup(unit, starttype, 'cost', 'unit')
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                                // Start-up fuel and emission costs
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                                + sum(uFuel(unit, 'startup', fuel),
                                    + p_uStartup(unit, starttype, 'consumption', 'unit')${not unit_investLP(unit)}
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                                        * [
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                                            + sum(tFull(tFuel)$[ord(tFuel) <= ord(t)], // Fuel costs for start-up fuel use
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                                                + ts_fuelPriceChange(fuel, tFuel)
                                                ) // END sum(tFuel)
                                            + sum(emission, // Emission taxes of startup fuel use
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                                                + p_unitFuelEmissionCost(unit, fuel, emission)
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                                                ) // END sum(emission)
                                            ] // END * p_uStartup
                                        ) // END sum(uFuel)
                                ] // END * v_startup
                        ) // END sum(starttype)
                    ) // END sum(uft_online)
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                // !!! PENDING CHANGES !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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                // Ramping costs
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                + sum(gnuft_ramp(grid, node, unit, f, t)${  p_gnu(grid, node, unit, 'rampUpCost')
                                                            or p_gnu(grid, node, unit, 'rampDownCost')
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                                                            },
                    + p_gnu(grid, node, unit, 'rampUpCost') * v_genRampChange(grid, node, unit, 'up', f, t)
                    + p_gnu(grid, node, unit, 'rampDownCost') * v_genRampChange(grid, node, unit, 'down', f, t)
                    ) // END sum(gnuft_ramp)
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                ]  // END * p_sft_probability(s,f,t)
        ) // END sum over msft(m, s, f, t)

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    // Value of energy storage change
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    + sum(gn_state(grid, node),
        + sum(mftStart(m, f, t)${   p_storageValue(grid, node, t)
                                    and active(m, 'storageValue')
                                    },
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            + v_state(grid, node, f, t)
                * p_storageValue(grid, node, t)
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                * sum(ms(m, s)${ p_msft_probability(m, s, f, t) },
                    + p_msft_probability(m, s, f, t)
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                    ) // END sum(s)
            ) // END sum(mftStart)
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        - sum(mftLastSteps(m, f, t)${   p_storageValue(grid, node, t)
                                        and active(m, 'storageValue')
                                        },
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            + v_state(grid, node, f, t)
                * p_storageValue(grid, node, t)
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                * sum(ms(m, s)${p_msft_probability(m, s, f, t)},
                    + p_msft_probability(m, s, f, t)
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                    ) // END sum(s)
            ) // END sum(mftLastSteps)
        ) // END sum(gn_state)

    // Investment Costs
    + sum(t_invest(t),
        // Unit investment costs
        + sum(gnu(grid, node, unit),
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            + v_invest_LP(unit, t)${ unit_investLP(unit) }
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                * p_gnu(grid, node, unit, 'invCosts')
                * p_gnu(grid, node, unit, 'annuity')
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            + v_invest_MIP(unit, t)${ unit_investMIP(unit) }
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                * p_gnu(grid, node, unit, 'unitSizeTot')
                * p_gnu(grid, node, unit, 'invCosts') * p_gnu(grid, node, unit, 'annuity')
            ) // END sum(gnu)

        // Transfer link investment costs
        + sum(gn2n_directional(grid, from_node, to_node),
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            + v_investTransfer_LP(grid, from_node, to_node, t)${ not p_gnn(grid, from_node, to_node, 'investMIP') }
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                * [
                    + p_gnn(grid, from_node, to_node, 'invCost')
                        * p_gnn(grid, from_node, to_node, 'annuity')
                    + p_gnn(grid, to_node, from_node, 'invCost')
                        * p_gnn(grid, to_node, from_node, 'annuity')
                    ] // END * v_investTransfer_LP
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            + v_investTransfer_MIP(grid, from_node, to_node, t)${ p_gnn(grid, from_node, to_node, 'investMIP') }
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                * [
                    + p_gnn(grid, from_node, to_node, 'unitSize')
                        * p_gnn(grid, from_node, to_node, 'invCost')
                        * p_gnn(grid, from_node, to_node, 'annuity')
                    + p_gnn(grid, to_node, from_node, 'unitSize')
                        * p_gnn(grid, to_node, from_node, 'invCost')
                        * p_gnn(grid, to_node, from_node, 'annuity')
                    ] // END * v_investTransfer_MIP
            ) // END sum(gn2n_directional)
        ) // END sum(t_invest)

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    // "Value" of online units, !!! TEMPORARY MEASURES !!!
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  - sum([s, m, uft_online(unit, ft_dynamic(f,t))]$mftStart(m, f, t),
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        + p_sft_probability(s, f, t) * 0.5
            * (
                + v_online(unit, f+cf(f,t), t) * p_unit(unit, 'startCost')
                + v_online_LP(unit, f+cf(f,t), t) * p_unit(unit, 'startCost_MW')
              )
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        ) // minus value of avoiding startup costs before
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  - sum((s, uft_online_last(unit, ft_dynamic(f,t))),
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        + p_sft_probability(s, f, t) * 0.5
            * (
                + v_online(unit, f+cf(f,t), t) * p_unit(unit, 'startCost')
                + v_online_LP(unit, f+cf(f,t), t) * p_unit(unit, 'startCost_MW')
              )
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        ) // or after the model solve
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;
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* --- Energy Balance ----------------------------------------------------------

q_balance(gn(grid, node), mft(m, f, t))${   not p_gn(grid, node, 'boundAll')
                                            } .. // Energy/power balance dynamics solved using implicit Euler discretization

    // The left side of the equation is the change in the state (will be zero if the node doesn't have a state)
    + p_gn(grid, node, 'energyStoredPerUnitOfState')${gn_state(grid, node)} // Unit conversion between v_state of a particular node and energy variables (defaults to 1, but can have node based values if e.g. v_state is in Kelvins and each node has a different heat storage capacity)
        * [
            + v_state(grid, node, f+df_central(f,t), t)                   // The difference between current
            - v_state(grid, node, f+df(f,t+dt(t)), t+dt(t))                     // ... and previous state of the node
            ]

    =E=

    // The right side of the equation contains all the changes converted to energy terms
    + p_stepLength(m, f, t) // Multiply with the length of the timestep to convert power into energy
        $$ifi '%rampSched%' == 'yes' / 2    // Averaging all the terms on the right side of the equation over the timestep here.
        * (
            // Self discharge out of the model boundaries
            - p_gn(grid, node, 'selfDischargeLoss')${gn_state(grid, node)}
                * [
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                    + v_state(grid, node, f+df_central(f,t), t) // The current state of the node
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                    $$ifi '%rampSched%' == 'yes' + v_state(grid, node, f+df(f,t+dt(t)), t+dt(t)) // and possibly averaging with the previous state of the node
                    ]

            // Energy diffusion from this node to neighbouring nodes
            - sum(to_node${gnn_state(grid, node, to_node)},
                + p_gnn(grid, node, to_node, 'diffCoeff')
                    * [
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                        + v_state(grid, node, f+df_central(f,t), t)
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                        $$ifi '%rampSched%' == 'yes' + v_state(grid, node, f+df(f,t+dt(t)), t+dt(t))
                        ]
                ) // END sum(to_node)

            // Energy diffusion from neighbouring nodes to this node
            + sum(from_node${gnn_state(grid, from_node, node)},
                + p_gnn(grid, from_node, node, 'diffCoeff')
                    * [
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                        + v_state(grid, from_node, f+df_central(f,t), t) // Incoming diffusion based on the state of the neighbouring node
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                        $$ifi '%rampSched%' == 'yes' + v_state(grid, from_node, f+df(f,t+dt(t)), t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                        ]
                ) // END sum(from_node)

            // Controlled energy transfer, applies when the current node is on the left side of the connection
            - sum(node_${gn2n_directional(grid, node, node_)},
                + (1 - p_gnn(grid, node, node_, 'transferLoss')) // Reduce transfer losses
                    * [
                        + v_transfer(grid, node, node_, f, t)
                        $$ifi '%rampSched%' == 'yes' + v_transfer(grid, node, node_, f, t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                        ]
                + p_gnn(grid, node, node_, 'transferLoss') // Add transfer losses back if transfer is from this node to another node
                    * [
                        + v_transferRightward(grid, node, node_, f, t)
                        $$ifi '%rampSched%' == 'yes' + v_transferRightward(grid, node, node_, f, t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                        ]
                ) // END sum(node_)

            // Controlled energy transfer, applies when the current node is on the right side of the connection
            + sum(node_${gn2n_directional(grid, node_, node)},
                + [
                    + v_transfer(grid, node_, node, f, t)
                    $$ifi '%rampSched%' == 'yes' + v_transfer(grid, node_, node, f, t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                    ]
                - p_gnn(grid, node_, node, 'transferLoss') // Reduce transfer losses if transfer is from another node to this node
                    * [
                        + v_transferRightward(grid, node_, node, f, t)
                        $$ifi '%rampSched%' == 'yes' + v_transferRightward(grid, node_, node, f, t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                        ]
                ) // END sum(node_)

            // Interactions between the node and its units
            + sum(gnuft(grid, node, unit, f, t),
                + v_gen(grid, node, unit, f, t) // Unit energy generation and consumption
                $$ifi '%rampSched%' == 'yes' + v_gen(grid, node, unit, f, t+dt(t))
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                )
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            // Spilling energy out of the endogenous grids in the model
            - v_spill(grid, node, f, t)${node_spill(node)}
            $$ifi '%rampSched%' == 'yes' - v_spill(grid, node, f, t)${node_spill(node)}

            // Power inflow and outflow timeseries to/from the node
            + ts_influx_(grid, node, f, t)   // Incoming (positive) and outgoing (negative) absolute value time series
            $$ifi '%rampSched%' == 'yes' + ts_influx_(grid, node, f, t+dt(t))

            // Dummy generation variables, for feasibility purposes
            + vq_gen('increase', grid, node, f, t) // Note! When stateSlack is permitted, have to take caution with the penalties so that it will be used first
            $$ifi '%rampSched%' == 'yes' + vq_gen('increase', grid, node, f, t+dt(t))
            - vq_gen('decrease', grid, node, f, t) // Note! When stateSlack is permitted, have to take caution with the penalties so that it will be used first
            $$ifi '%rampSched%' == 'yes' - vq_gen('decrease', grid, node, f, t+dt(t))
    ) // END * p_stepLength
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;
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* --- Reserve Demand ----------------------------------------------------------

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q_resDemand(restypeDirectionNode(restype, up_down, node), ft(f, t))${   ord(t) < tSolveFirst + sum[mf(m, f), mSettings(m, 't_reserveLength')]
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                                                                        } ..
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    // Reserve provision by capable units on this node
    + sum(nuft(node, unit, f, t)${nuRescapable(restype, up_down, node, unit)},
        + v_reserve(restype, up_down, node, unit, f+df_nReserves(node, restype, f, t), t)
        ) // END sum(nuft)

    // Reserve provision to this node via transfer links
    + sum(gn2n_directional(grid, node_, node)${restypeDirectionNode(restype, up_down, node_)},
        + (1 - p_gnn(grid, node_, node, 'transferLoss') )
            * v_resTransferRightward(restype, up_down, node_, node, f+df_nReserves(node_, restype, f, t), t)             // Reserves from another node - reduces the need for reserves in the node
        ) // END sum(gn2n_directional)
    + sum(gn2n_directional(grid, node, node_)${restypeDirectionNode(restype, up_down, node_)},
        + (1 - p_gnn(grid, node, node_, 'transferLoss') )
            * v_resTransferLeftward(restype, up_down, node, node_, f+df_nReserves(node_, restype, f, t), t)             // Reserves from another node - reduces the need for reserves in the node
        ) // END sum(gn2n_directional)

    =G=

    // Demand for reserves
    + ts_reserveDemand_(restype, up_down, node, f, t)${p_nReserves(node, restype, 'use_time_series')}
    + p_nReserves(node, restype, up_down)${not p_nReserves(node, restype, 'use_time_series')}

    // Reserve provisions to another nodes via transfer links
    + sum(gn2n_directional(grid, node, node_)${restypeDirectionNode(restype, up_down, node_)},   // If trasferring reserves to another node, increase your own reserves by same amount
        + v_resTransferRightward(restype, up_down, node, node_, f+df_nReserves(node, restype, f, t), t)
        ) // END sum(gn2n_directional)
    + sum(gn2n_directional(grid, node_, node)${restypeDirectionNode(restype, up_down, node_)},   // If trasferring reserves to another node, increase your own reserves by same amount
        + v_resTransferLeftward(restype, up_down, node_, node, f+df_nReserves(node, restype, f, t), t)
        ) // END sum(gn2n_directional)

    // Reserve demand feasibility dummy variables
    - vq_resDemand(restype, up_down, node, f, t)

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* --- Maximum Downward Capacity -----------------------------------------------

q_maxDownward(m, gnuft(grid, node, unit, f, t))${   [   ord(t) < tSolveFirst + mSettings(m, 't_reserveLength') // Unit is either providing
                                                        and sum(restype, nuRescapable(restype, 'down', node, unit)) // downward reserves
                                                        ]
                                                    // NOTE!!! Could be better to form a gnuft_reserves subset?
                                                    or [ // the unit has an online variable
                                                        uft_online(unit, f, t)
                                                        and [
                                                            (unit_minLoad(unit) and p_gnu(grid, node, unit, 'unitSizeGen')) // generators with a min. load
                                                            or p_gnu(grid, node, unit, 'maxCons') // or consuming units with an online variable
                                                            ]
                                                        ] // END or
                                                    or [ // consuming units with investment possibility
                                                        gnu_input(grid, node, unit)
                                                        and [unit_investLP(unit) or unit_investMIP(unit)]
                                                        ]
                                                    } ..

    // Energy generation/consumption
    + v_gen(grid, node, unit, f, t)

    // Considering output constraints (e.g. cV line)
    + sum(gngnu_constrainedOutputRatio(grid, node, grid_, node_, unit),
        + p_gnu(grid_, node_, unit, 'cV')
            * v_gen(grid_, node_, unit, f, t)
        ) // END sum(gngnu_constrainedOutputRatio)

    // Downward reserve participation
    - sum(nuRescapable(restype, 'down', node, unit)${ord(t) < tSolveFirst + mSettings(m, 't_reserveLength')},
        + v_reserve(restype, 'down', node, unit, f+df_nReserves(node, restype, f, t), t) // (v_reserve can be used only if the unit is capable of providing a particular reserve)
        ) // END sum(nuRescapable)

    =G= // Must be greater than minimum load or maximum consumption  (units with min-load and both generation and consumption are not allowed)

    // Generation units, greater than minload
    + p_gnu(grid, node, unit, 'unitSizeGen')
        * sum(effGroup, // Uses the minimum 'lb' for the current efficiency approximation
            + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
            + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
            ) // END sum(effGroup)
        * [ // Online variables should only be generated for units with restrictions
            + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)} // LP online variant
            + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)} // MIP online variant
            ] // END v_online

    // Consuming units, greater than maxCons
    // Available capacity restrictions
    - p_unit(unit, 'availability')
        * [
            // Capacity factors for flow units
            + sum(flow${flowUnit(flow, unit)},
                + ts_cf_(flow, node, f, t)
                ) // END sum(flow)
            + 1${not unit_flow(unit)}
            ] // END * p_unit(availability)
        * [
            // Online capacity restriction
            + p_gnu(grid, node, unit, 'maxCons')${not uft_online(unit, f, t)} // Use initial maximum if no online variables
            + p_gnu(grid, node, unit, 'unitSizeCons')
                * [
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                    // Capacity online
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                    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
                    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
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                    // Investments to additional non-online capacity
                    + sum(t_invest(t_)${    ord(t_)<=ord(t)
                                            and not uft_online(unit, f, t)
                                            },
                        + v_invest_LP(unit, t_)${unit_investLP(unit)} // NOTE! v_invest_LP also for consuming units is positive
                        + v_invest_MIP(unit, t_)${unit_investMIP(unit)} // NOTE! v_invest_MIP also for consuming units is positive
                        ) // END sum(t_invest)
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                    ] // END * p_gnu(unitSizeCons)
            ] // END * p_unit(availability)
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* --- Maximum Upwards Capacity ------------------------------------------------

q_maxUpward(m, gnuft(grid, node, unit, f, t))${ [   ord(t) < tSolveFirst + mSettings(m, 't_reserveLength') // Unit is either providing
                                                    and sum(restype, nuRescapable(restype, 'up', node, unit)) // upward reserves
                                                    ]
                                                or [
                                                    uft_online(unit, f, t) // or the unit has an online variable
                                                        and [
                                                            [unit_minLoad(unit) and p_gnu(grid, node, unit, 'unitSizeCons')] // consuming units with min_load
                                                            or [p_gnu(grid, node, unit, 'maxGen')]                          // generators with an online variable
                                                            ]
                                                    ]
                                                or [
                                                    gnu_output(grid, node, unit) // generators with investment possibility
                                                    and (unit_investLP(unit) or unit_investMIP(unit))
                                                    ]
                                                }..
    // Energy generation/consumption
    + v_gen(grid, node, unit, f, t)

    // Considering output constraints (e.g. cV line)
    + sum(gngnu_constrainedOutputRatio(grid, node, grid_output, node_, unit),
        + p_gnu(grid_output, node_, unit, 'cV')
            * v_gen(grid_output, node_, unit, f, t)
        ) // END sum(gngnu_constrainedOutputRatio)

    // Upwards reserve participation
    + sum(nuRescapable(restype, 'up', node, unit)${ord(t) < tSolveFirst + mSettings(m, 't_reserveLength')},
        + v_reserve(restype, 'up', node, unit, f+df_nReserves(node, restype, f, t), t)
        ) // END sum(nuRescapable)

    =L= // must be less than available/online capacity

    // Consuming units
    + p_gnu(grid, node, unit, 'unitSizeCons')
        * sum(effGroup, // Uses the minimum 'lb' for the current efficiency approximation
            + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
            + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
            ) // END sum(effGroup)
        * [
            + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)} // Consuming units are restricted by their min. load (consuming is negative)
            + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)} // Consuming units are restricted by their min. load (consuming is negative)
            ] // END * p_gnu(unitSizeCons)

    // Generation units
    // Available capacity restrictions
    + p_unit(unit, 'availability') // Generation units are restricted by their (available) capacity
        * [
            // Capacity factor for flow units
            + sum(flow${flowUnit(flow, unit)},
                + ts_cf_(flow, node, f, t)
                ) // END sum(flow)
            + 1${not unit_flow(unit)}
            ] // END * p_unit(availability)
        * [
            // Online capacity restriction
            + p_gnu(grid, node, unit, 'maxGen')${not uft_online(unit, f, t)} // Use initial maxGen if no online variables
            + p_gnu(grid, node, unit, 'unitSizeGen')
                * [
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                    // Capacity online
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                    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f ,t)}
                    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
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                    // Investments to non-online capacity
                    + sum(t_invest(t_)${    ord(t_)<=ord(t)
                                            and not uft_online(unit, f ,t)
                                            },
                        + v_invest_LP(unit, t_)${unit_investLP(unit)}
                        + v_invest_MIP(unit, t_)${unit_investMIP(unit)}
                        ) // END sum(t_invest)
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                    ] // END * p_gnu(unitSizeGen)
            ] // END * p_unit(availability)
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* --- Unit Startup and Shutdown -----------------------------------------------

q_startup(uft_online(unit, f, t)) ..

    // Units currently online
    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}

    =E=

    // Units previously online
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    + v_online_LP(unit, f+df(f,t+dt(t)), t+dt(t))${uft_onlineLP(unit, f+df(f,t+dt(t)), t+dt(t))} // This reaches to tFirstSolve when pt = -1
    + v_online_MIP(unit, f+df(f,t+dt(t)), t+dt(t))${uft_onlineMIP(unit, f+df(f,t+dt(t)), t+dt(t))}

    // Unit online history (solve initial value), required because uft_online doesn't extend to before active modelling
    + r_online(unit, f+df(f,t+dt(t)), t+dt(t))${    not uft_onlineLP(unit, f+df(f,t+dt(t)), t+dt(t))
                                                    and not uft_onlineMIP(unit, f+df(f,t+dt(t)), t+dt(t))
                                                    }
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    // Unit startup and shutdown
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    + sum(unitStarttype(unit, starttype),
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        + v_startup(unit, starttype, f, t)
        ) // END sum(starttype)
    - v_shutdown(unit, f, t)
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*--- Startup Type -------------------------------------------------------------
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// !!! NOTE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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// This formulation doesn't work as intended when unitCount > 1, as one recent
// shutdown allows for multiple hot/warm startups on subsequent time steps.
// Pending changes.
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q_startuptype(m, starttypeConstrained(starttype), uft_online(unit, f, t))${ unitStarttype(unit, starttype) } ..
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    // Startup type
    + v_startup(unit, starttype, f, t)

    =L=

    // Subunit shutdowns within special startup timeframe
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    + sum(counter${dt_starttypeUnitCounter(starttype, unit, counter)},
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        + v_shutdown(unit, f+df(f,t+dt_starttypeUnitCounter(starttype, unit, counter)), t+dt_starttypeUnitCounter(starttype, unit, counter))
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    ) // END sum(t_)
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*--- Online Limits with Startup Type Constraints and Investments --------------

q_onlineLimit(m, uft_online(unit, f, t))${  p_unit(unit, 'minShutDownTime')
                                            or unit_investLP(unit)
                                            or unit_investMIP(unit)
                                            } ..
    // Online variables
    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f ,t)}

    =L=

    // Number of existing units
    + p_unit(unit, 'unitCount')

    // Number of units unable to start due to restrictions
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    - sum(counter${dt_downtimeUnitCounter(unit, counter)},
        + v_shutdown(unit, f+df(f,t+dt_downtimeUnitCounter(unit, counter)), t+dt_downtimeUnitCounter(unit, counter))
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    ) // END sum(t_)

    // Investments into units
    + sum(t_invest(t_)${ord(t_)<=ord(t)},
        + v_invest_LP(unit, t_)
        + v_invest_MIP(unit, t_)
        ) // END sum(t_invest)
;

*--- Minimum Unit Uptime ------------------------------------------------------

q_onlineMinUptime(m, uft_online(unit, f, t))${  p_unit(unit, 'minOperationTime')
                                                } ..

    // Units currently online
    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}

    =G=

    // Units that have minimum operation time requirements active
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    + sum(counter${dt_uptimeUnitCounter(unit, counter)},
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        + sum(unitStarttype(unit, starttype),
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            + v_startup(unit, starttype, f+df(f,t+dt_uptimeUnitCounter(unit, counter)), t+dt_uptimeUnitCounter(unit, counter))
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            ) // END sum(starttype)
    ) // END sum(t_)
;

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* --- Ramp Constraints --------------------------------------------------------
// !!! CURRENTLY REMOVED, PENDING CHANGE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
$ontext
q_genRamp(gn(grid, node), m, s, uft(unit, f, t))${  gnuft_ramp(grid, node, unit, f, t)
                                                    and ord(t) > msStart(m, s)
                                                    and ord(t) <= msEnd(m, s)
                                                    } ..

    + sum(ramp, // Sum over the ramp categories
        + v_genRamp(ramp, grid, node, unit, f, t)
            * p_stepLength(m, f, t)
        ) // END sum(ramp)

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    =E=
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    // Change in generation over the time step
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    + v_gen(grid, node, unit, f, t)
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    - v_gen(grid, node, unit, f+df(f,t), t+dt(t))
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$offtext
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* -----------------------------------------------------------------------------
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$ontext
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q_genRampChange(gn(grid, node), m, s, unit, ft(f, t))${ gnuft_ramp(grid, node, unit, f, t)
*                                                     and ord(t) > mSettings(m, 't_start')
                                                     and ord(t) > msStart(m, s)
                                                     and ord(t) <= msEnd(m, s)
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                                                     and [ p_gnu(grid, node, unit, 'rampUpCost')
                                                           or p_gnu(grid, node, unit, 'rampDownCost')
                                                           ]
                                                     } ..
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    + v_genRampChange(grid, node, unit, 'up', f+pf(f,t), t+pt(t))
    - v_genRampChange(grid, node, unit, 'down', f+pf(f,t), t+pt(t))
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    =E=
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    + v_genRamp(grid, node, unit, f, t)
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    - v_genRamp(grid, node, unit, f+pf(f,t), t+pt(t));
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$offtext

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* --- Ramp Up Limits ----------------------------------------------------------
// !!! PENDING CHANGES !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// The way ramp limits are defined are waiting changes, so these equations have
// to be rewritten in the future.
$ontext
q_rampUpLimit(gn(grid, node), m, s, unit, ft(f, t))${ gnuft_ramp(grid, node, unit, f, t)
                                                   and ord(t) > msStart(m, s)
                                                   and msft(m, s, f, t)
                                                   and p_gnu(grid, node, unit, 'maxRampUp')
                                                   and (uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))
                                                           or unit_investLP(unit)
                                                           or unit_investMIP(unit))
                                                   } ..
  + v_genRamp(grid, node, unit, f, t+pt(t))
  =L=
    // Ramping capability of units without online variable
  + (
      + ( p_gnu(grid, node, unit, 'maxGen') - p_gnu(grid, node, unit, 'maxCons') )${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      + sum(t_$(ord(t_)<=ord(t)),
          + v_invest_LP(grid, node, unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t)) and p_gnu(grid, node, unit, 'maxGenCap')}
          - v_invest_LP(grid, node, unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t)) and p_gnu(grid, node, unit, 'maxConsCap')}
          + v_invest_MIP(unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
              * p_gnu(grid, node, unit, 'unitSizeGenNet')
        )
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      * p_gnu(grid, node, unit, 'maxRampUp')
      * 60 / 100  // Unit conversion from [p.u./min] to [MW/h]
    // Ramping capability of units that were online both in the previous time step and the current time step
  + (
      + v_online_LP(unit, f+cpf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      + v_online(unit, f+cpf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      - v_shutdown(unit, f+cf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
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      * p_gnu(grid, node, unit, 'unitSizeGenNet')
      / {
          + 1${  not unit_investLP(unit)
                 or not p_gnu(grid, node, unit, 'unitSizeGenNet')
              }
          + sum(gnu(grid_, node_, unit)${ unit_investLP(unit)
                                          and p_gnu(grid, node, unit, 'unitSizeGenNet')
                }, p_gnu(grid_, node_, unit, 'unitSizeTot')
            )
        } // Scaling factor to calculate online capacity in gn(grid, node) in the case of continuous investments
      * p_gnu(grid, node, unit, 'maxRampUp')
      * 60 / 100  // Unit conversion from [p.u./min] to [MW/h]
  // Newly started units are assumed to start to their minload and
  // newly shutdown units are assumed to be shut down from their minload.
  + (
      + sum(starttype, v_startup(unit, starttype, f+cf(f,t), t+pt(t)))
      - v_shutdown(unit, f+cf(f,t), t+pt(t))
    )${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      * p_gnu(grid, node, unit, 'unitSizeGenNet')
      / {
          + 1${not unit_investLP(unit) or not p_gnu(grid, node, unit, 'unitSizeGenNet')}
          + sum(gnu(grid_, node_, unit)${ unit_investLP(unit)
                                          and p_gnu(grid, node, unit, 'unitSizeGenNet')
                }, p_gnu(grid_, node_, unit, 'unitSizeTot')
            )
        } // Scaling factor to calculate online capacity in gn(grid, node) in the case of continuous investments
      * sum(suft(effGroup, unit, f+cf(f,t), t), p_effGroupUnit(effGroup, unit, 'lb'))
// Reserve provision?
// Note: This constraint does not limit ramping properly for example if online subunits are
// producing at full capacity (= not possible to ramp up) and more subunits are started up.
// Take this into account in q_maxUpward or in another equation?:
// v_gen =L= (v_online(t-1) - v_shutdown(t-1)) * unitSize + v_startup(t-1) * unitSize * minLoad
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* --- Ramp Down Limits --------------------------------------------------------
q_rampDownLimit(gn(grid, node), m, s, unit, ft(f, t))${ gnuft_ramp(grid, node, unit, f, t)
                                                     and ord(t) > msStart(m, s)
                                                     and msft(m, s, f, t)
                                                     and p_gnu(grid, node, unit, 'maxRampDown')
                                                     and (uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))
                                                             or unit_investLP(unit)
                                                             or unit_investMIP(unit))
                                                     } ..
  + v_genRamp(grid, node, unit, f, t+pt(t))
  =G=
    // Ramping capability of units without online variable
  - (
      + ( p_gnu(grid, node, unit, 'maxGen') - p_gnu(grid, node, unit, 'maxCons') )${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      + sum(t_$(ord(t_)<=ord(t)),
          + v_invest_LP(grid, node, unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t)) and p_gnu(grid, node, unit, 'maxGenCap')}
          - v_invest_LP(grid, node, unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t)) and p_gnu(grid, node, unit, 'maxConsCap')}
          + v_invest_MIP(unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
              * p_gnu(grid, node, unit, 'unitSizeGenNet')
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      * p_gnu(grid, node, unit, 'maxRampDown')
      * 60 / 100  // Unit conversion from [p.u./min] to [MW/h]
    // Ramping capability of units that were online both in the previous time step and the current time step
  - (
      + v_online_LP(unit, f+cpf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      + v_online(unit, f+cpf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      - v_shutdown(unit, f+cf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
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      * p_gnu(grid, node, unit, 'unitSizeGenNet')
      / {
          + 1${  not unit_investLP(unit)
                 or not p_gnu(grid, node, unit, 'unitSizeGenNet')
              }
          + sum(gnu(grid_, node_, unit)${ unit_investLP(unit)
                                          and p_gnu(grid, node, unit, 'unitSizeGenNet')
                }, p_gnu(grid_, node_, unit, 'unitSizeTot')
            )
        } // Scaling factor to calculate online capacity in gn(grid, node) in the case of continuous investments
      * p_gnu(grid, node, unit, 'maxRampDown')
      * 60 / 100  // Unit conversion from [p.u./min] to [MW/h]
  // Newly started units are assumed to start to their minload and
  // newly shutdown units are assumed to be shut down from their minload.
  + (
      + sum(starttype, v_startup(unit, starttype, f+cf(f,t), t+pt(t)))
      - v_shutdown(unit, f+cf(f,t), t+pt(t))
    )${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      * p_gnu(grid, node, unit, 'unitSizeGenNet')
      / {
          + 1${not unit_investLP(unit) or not p_gnu(grid, node, unit, 'unitSizeGenNet')}
          + sum(gnu(grid_, node_, unit)${ unit_investLP(unit)
                                          and p_gnu(grid, node, unit, 'unitSizeGenNet')
                }, p_gnu(grid_, node_, unit, 'unitSizeTot')
            )
        } // Scaling factor to calculate online capacity in gn(grid, node) in the case of continuous investments
      * sum(suft(effGroup, unit, f+cf(f,t), t), p_effGroupUnit(effGroup, unit, 'lb'))
// Reserve provision?
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$offtext

* --- Fixed Output Ratio ------------------------------------------------------

q_outputRatioFixed(gngnu_fixedOutputRatio(grid, node, grid_, node_, unit), ft(f, t))${  uft(unit, f, t)
                                                                                        } ..

    // Generation in grid
    + v_gen(grid, node, unit, f, t)
        / p_gnu(grid, node, unit, 'cB')

    =E=

    // Generation in grid_
    + v_gen(grid_, node_, unit, f, t)
        / p_gnu(grid_, node_, unit, 'cB')
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* --- Constrained Output Ratio ------------------------------------------------

q_outputRatioConstrained(gngnu_constrainedOutputRatio(grid, node, grid_, node_, unit), ft(f, t))${  uft(unit, f, t)
                                                                                                    } ..

    // Generation in grid
    + v_gen(grid, node, unit, f, t)
        / p_gnu(grid, node, unit, 'cB')

    =G=

    // Generation in grid_
    + v_gen(grid_, node_, unit, f, t)
        / p_gnu(grid_, node_, unit, 'cB')
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* --- Direct Input-Output Conversion ------------------------------------------

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q_conversionDirectInputOutput(suft(effDirect(effGroup), unit, f, t)) ..
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    // Sum over endogenous energy inputs
    - sum(gnu_input(grid, node, unit),
        + v_gen(grid, node, unit, f, t)
        ) // END sum(gnu_input)

    // Sum over fuel energy inputs
    + sum(uFuel(unit, 'main', fuel),
        + v_fuelUse(fuel, unit, f, t)
        ) // END sum(uFuel)

    =E=

    // Sum over energy outputs
    + sum(gnu_output(grid, node, unit),
        + v_gen(grid, node, unit, f, t)
            * [ // Heat rate
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                + p_effUnit(effGroup, unit, effGroup, 'slope')${not ts_effUnit(effGroup, unit, effGroup, 'slope', f, t)}
                + ts_effUnit(effGroup, unit, effGroup, 'slope', f, t)
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                ] // END * v_gen
        ) // END sum(gnu_output)

    // Consumption of keeping units online
    + sum(gnu_output(grid, node, unit),
        + p_gnu(grid, node, unit, 'unitSizeGen')
        ) // END sum(gnu_output)
        * [
            + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
            + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
            ] // END * sum(gnu_output)
        * [
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            + p_effGroupUnit(effGroup, unit, 'section')${not ts_effUnit(effGroup, unit, effDirect, 'section', f, t)}
            + ts_effUnit(effGroup, unit, effGroup, 'section', f, t)
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            ] // END * sum(gnu_output)
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* --- SOS2 Efficiency Approximation -------------------------------------------

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q_conversionSOS2InputIntermediate(suft(effLambda(effGroup), unit, f, t)) ..

    // Sum over endogenous energy inputs
    - sum(gnu_input(grid, node, unit),
        + v_gen(grid, node, unit, f, t)
        ) // END sum(gnu_input)

    // Sum over fuel energy inputs
    + sum(uFuel(unit, 'main', fuel),
        + v_fuelUse(fuel, unit, f, t)
        ) // END sum(uFuel)

    =E=

    // Sum over the endogenous outputs of the unit
    + sum(gnu_output(grid, node, unit), p_gnu(grid, node, unit, 'unitSizeGen'))
        * [
            // Consumption of generation
            + sum(effSelector${effGroupSelectorUnit(effGroup, unit, effSelector)},
                + v_sos2(unit, f, t, effSelector)
                    * [ // Operation points convert the v_sos2 variables into share of capacity used for generation
                        + p_effUnit(effGroup, unit, effSelector, 'op')${not ts_effUnit(effGroup, unit, effSelector, 'op', f, t)}
                        + ts_effUnit(effGroup, unit, effSelector, 'op', f, t)
                        ] // END * v_sos2
                    * [ // Heat rate
                        + p_effUnit(effGroup, unit, effSelector, 'slope')${not ts_effUnit(effGroup, unit, effSelector, 'slope', f, t)}
                        + ts_effUnit(effGroup, unit, effSelector, 'slope', f, t)
                        ] // END * v_sos2
                ) // END sum(effSelector)

            // Consumption of keeping units online
            + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
                * p_effGroupUnit(effGroup, unit, 'section')
            ] // END * sum(gnu_output)
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* --- SOS 2 Efficiency Approximation Online Variables -------------------------

q_conversionSOS2Constraint(suft(effLambda(effGroup), unit, f, t)) ..

    // Total value of the v_sos2 equals the number of online units
    + sum(effSelector${effGroupSelectorUnit(effGroup, unit, effSelector)},
        + v_sos2(unit, f, t, effSelector)
        ) // END sum(effSelector)

    =E=

    // Number of units online
    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
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* --- SOS 2 Efficiency Approximation Output Generation ------------------------

q_conversionSOS2IntermediateOutput(suft(effLambda(effGroup), unit, f, t)) ..

    // Endogenous energy output
    + sum(gnu_output(grid, node, unit),
        + p_gnu(grid, node, unit, 'unitSizeGen')
        ) // END sum(gnu_output)
        * sum(effSelector${effGroupSelectorUnit(effGroup, unit, effSelector)},
            + v_sos2(unit, f, t, effSelector)
            * [ // Operation points convert v_sos2 into share of capacity used for generation
                + p_effUnit(effGroup, unit, effSelector, 'op')${not ts_effUnit(effGroup, unit, effSelector, 'op', f, t)}
                + ts_effUnit(effGroup, unit, effSelector, 'op', f, t)
                ] // END * v_sos2
            ) // END sum(effSelector)

    =E=

    // Energy output into v_gen
    + sum(gnu_output(grid, node, unit),
        + v_gen(grid, node, unit, f, t)
        ) // END sum(gnu_output)
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*--- Fixed Investment Ratios --------------------------------------------------
// !!! PENDING FIX !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// v_invest(unit) instead of the old v_invest(grid, node, unit)
// Are these even necessary anymore, if investment is unitwise?
// Maybe for batteries etc?
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q_fixedGenCap1U(gnu(grid, node, unit), t_invest(t))${   unit_investLP(unit)
                                                        } ..
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    // Investment
    + v_invest_LP(unit, t)
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    =E=

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    // Capacity Ratios?
    + sum(gn(grid_, node_),
        + v_invest_LP(unit, t)
        ) // END sum(gn)
        * p_gnu(grid, node, unit, 'unitSizeTot')
        / sum(gn(grid_, node_),
            + p_gnu(grid_, node_, unit, 'unitSizeTot')
            ) // END sum(gn)
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*--- Fixed Investment Ratios 2 ------------------------------------------------
// !!! PENDING FIX !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// See notes in the above equation
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q_fixedGenCap2U(grid, node, unit, grid_, node_, unit_, t_invest(t))${   p_gnugnu(grid, node, unit, grid_, node_, unit_, 'capacityRatio')
                                                                        } ..
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    // Investment
    + v_invest_LP(unit, t)
    + v_invest_MIP(unit, t)

    =E=

    // Capacity Ratio?
    + p_gnugnu(grid, node, unit, grid_, node_, unit_, 'capacityRatio')
        * [
            + v_invest_LP(unit_, t)
            + v_invest_MIP(unit_, t)
            ] // END * p_gngnu(capacityRatio)
;

* --- Total Transfer Limits ---------------------------------------------------

q_transfer(gn2n_directional(grid, node, node_), ft(f, t)) ..

    // Rightward + Leftward
    + v_transferRightward(grid, node, node_, f, t)
    - v_transferLeftward(grid, node, node_, f, t)

    =E=

    // = Total Transfer