2d_constraints.gms 131 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
$ontext
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/>.
$offtext

18

19
* =============================================================================
20
* --- Constraint Equation Definitions -----------------------------------------
21
22
23
24
* =============================================================================

* --- Energy Balance ----------------------------------------------------------

25
26
27
q_balance(gn(grid, node), msft(m, s, f, t)) // Energy/power balance dynamics solved using implicit Euler discretization
    ${  not p_gn(grid, node, 'boundAll')
        } ..
28
29
30
31

    // 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)
        * [
32
33
            + v_state(grid, node, s, f+df_central(f,t), t)                   // The difference between current
            - v_state(grid, node, s+ds_state(grid,node,s,t), f+df(f,t+dt(t)), t+dt(t))       // ... and previous state of the node
34
35
36
37
38
39
40
41
            ]

    =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
        * (
            // Self discharge out of the model boundaries
42
            - p_gn(grid, node, 'selfDischargeLoss')${ gn_state(grid, node) }
43
                * v_state(grid, node, s, f+df_central(f,t), t) // The current state of the node
44
45

            // Energy diffusion from this node to neighbouring nodes
46
            - sum(gnn_state(grid, node, to_node),
47
                + p_gnn(grid, node, to_node, 'diffCoeff')
48
                    * v_state(grid, node, s, f+df_central(f,t), t)
49
50
51
                ) // END sum(to_node)

            // Energy diffusion from neighbouring nodes to this node
52
            + sum(gnn_state(grid, from_node, node),
53
                + p_gnn(grid, from_node, node, 'diffCoeff')
54
                    * v_state(grid, from_node, s, f+df_central(f,t), t) // Incoming diffusion based on the state of the neighbouring node
55
56
57
                ) // END sum(from_node)

            // Controlled energy transfer, applies when the current node is on the left side of the connection
58
            - sum(gn2n_directional(grid, node, node_),
59
                + (1 - p_gnn(grid, node, node_, 'transferLoss')) // Reduce transfer losses
60
                    * v_transfer(grid, node, node_, s, f, t)
61
                + p_gnn(grid, node, node_, 'transferLoss') // Add transfer losses back if transfer is from this node to another node
62
                    * v_transferRightward(grid, node, node_, s, f, t)
63
64
65
                ) // END sum(node_)

            // Controlled energy transfer, applies when the current node is on the right side of the connection
66
            + sum(gn2n_directional(grid, node_, node),
67
                + v_transfer(grid, node_, node, s, f, t)
68
                - p_gnn(grid, node_, node, 'transferLoss') // Reduce transfer losses if transfer is from another node to this node
69
                    * v_transferRightward(grid, node_, node, s, f, t)
70
71
72
73
                ) // END sum(node_)

            // Interactions between the node and its units
            + sum(gnuft(grid, node, unit, f, t),
74
                + v_gen(grid, node, unit, s, f, t) // Unit energy generation and consumption
75
                )
76
77

            // Spilling energy out of the endogenous grids in the model
78
            - v_spill(grid, node, s, f, t)${node_spill(node)}
79
80

            // Power inflow and outflow timeseries to/from the node
81
            + ts_influx_(grid, node, f, t, s)   // Incoming (positive) and outgoing (negative) absolute value time series
82
83

            // Dummy generation variables, for feasibility purposes
84
85
            + vq_gen('increase', grid, node, s, f, t) // Note! When stateSlack is permitted, have to take caution with the penalties so that it will be used first
            - vq_gen('decrease', grid, node, s, f, t) // Note! When stateSlack is permitted, have to take caution with the penalties so that it will be used first
86
    ) // END * p_stepLength
87
;
88
89

* --- Reserve Demand ----------------------------------------------------------
90
91
// NOTE! Currently, there are multiple identical instances of the reserve balance equation being generated for each forecast branch even when the reserves are committed and identical between the forecasts.
// NOTE! This could be solved by formulating a new "ft_reserves" set to cover only the relevant forecast-time steps, but it would possibly make the reserves even more confusing.
92

93
q_resDemand(restypeDirectionNode(restype, up_down, node), sft(s, f, t))
94
95
    ${  ord(t) < tSolveFirst + p_nReserves(node, restype, 'reserve_length')
        and not [ restypeReleasedForRealization(restype)
96
                  and sft_realized(s, f, t)]
97
        } ..
98

99
100
    // Reserve provision by capable units on this node
    + sum(nuft(node, unit, f, t)${nuRescapable(restype, up_down, node, unit)},
101
        + v_reserve(restype, up_down, node, unit, s, f+df_reserves(node, restype, f, t), t)
102
103
104
105
            * [ // Account for reliability of reserves
                + 1${sft_realized(s, f+df_reserves(node, restype, f, t), t)} // reserveReliability limits the reliability of reserves locked ahead of time.
                + p_nuReserves(node, unit, restype, 'reserveReliability')${not sft_realized(s, f+df_reserves(node, restype, f, t), t)}
                ] // END * v_reserve
106
107
        ) // END sum(nuft)

108
    // Reserve provision from other reserve categories when they can be shared
109
    + sum((nuft(node, unit, f, t), restype_)${p_nuRes2Res(node, unit, restype_, up_down, restype)},
110
        + v_reserve(restype_, up_down, node, unit, s, f+df_reserves(node, restype_, f, t), t)
111
            * p_nuRes2Res(node, unit, restype_, up_down, restype)
112
113
114
115
116
            * [ // Account for reliability of reserves
                + 1${sft_realized(s, f+df_reserves(node, restype, f, t), t)} // reserveReliability limits the reliability of reserves locked ahead of time.
                + p_nuReserves(node, unit, restype, 'reserveReliability')${not sft_realized(s, f+df_reserves(node, restype, f, t), t)}
                    * p_nuReserves(node, unit, restype_, 'reserveReliability')
                ] // END * v_reserve
117
118
        ) // END sum(nuft)

119
    // Reserve provision to this node via transfer links
120
    + sum(gn2n_directional(grid, node_, node)${restypeDirectionNodeNode(restype, up_down, node_, node)},
121
        + (1 - p_gnn(grid, node_, node, 'transferLoss') )
122
            * v_resTransferRightward(restype, up_down, node_, node, s, f+df_reserves(node_, restype, f, t), t) // Reserves from another node - reduces the need for reserves in the node
123
        ) // END sum(gn2n_directional)
124
    + sum(gn2n_directional(grid, node, node_)${restypeDirectionNodeNode(restype, up_down, node_, node)},
125
        + (1 - p_gnn(grid, node, node_, 'transferLoss') )
126
            * v_resTransferLeftward(restype, up_down, node, node_, s, f+df_reserves(node_, restype, f, t), t) // Reserves from another node - reduces the need for reserves in the node
127
128
129
130
131
132
133
134
        ) // 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')}

135
136
    // Reserve demand increase because of units
    + sum(nuft(node, unit, f, t)${p_nuReserves(node, unit, restype, 'reserve_increase_ratio')}, // Could be better to have 'reserve_increase_ratio' separately for up and down directions
137
        + sum(gnu(grid, node, unit), v_gen(grid, node, unit, s, f, t)) // Reserve sets and variables are currently lacking the grid dimension...
138
139
140
            * p_nuReserves(node, unit, restype, 'reserve_increase_ratio')
        ) // END sum(nuft)

141
    // Reserve provisions to another nodes via transfer links
142
    + sum(gn2n_directional(grid, node, node_)${restypeDirectionNodeNode(restype, up_down, node, node_)},   // If trasferring reserves to another node, increase your own reserves by same amount
143
        + v_resTransferRightward(restype, up_down, node, node_, s, f+df_reserves(node, restype, f, t), t)
144
        ) // END sum(gn2n_directional)
145
    + sum(gn2n_directional(grid, node_, node)${restypeDirectionNodeNode(restype, up_down, node, node_)},   // If trasferring reserves to another node, increase your own reserves by same amount
146
        + v_resTransferLeftward(restype, up_down, node_, node, s, f+df_reserves(node, restype, f, t), t)
147
148
149
        ) // END sum(gn2n_directional)

    // Reserve demand feasibility dummy variables
150
151
    - vq_resDemand(restype, up_down, node, s, f+df_reserves(node, restype, f, t), t)
    - vq_resMissing(restype, up_down, node, s, f+df_reserves(node, restype, f, t), t)${ft_reservesFixed(node, restype, f+df_reserves(node, restype, f, t), t)}
152
;
153

154
155
156
157
* --- N-1 Reserve Demand ----------------------------------------------------------
// NOTE! Currently, there are multiple identical instances of the reserve balance equation being generated for each forecast branch even when the reserves are committed and identical between the forecasts.
// NOTE! This could be solved by formulating a new "ft_reserves" set to cover only the relevant forecast-time steps, but it would possibly make the reserves even more confusing.

158
q_resDemandLargestInfeedUnit(grid, restypeDirectionNode(restype, 'up', node), unit_fail(unit_), sft(s, f, t))
159
    ${  ord(t) < tSolveFirst + p_nReserves(node, restype, 'reserve_length')
160
        and gn(grid, node)
161
162
163
        and not [ restypeReleasedForRealization(restype)
            and ft_realized(f, t)
            ]
164
        and p_nuReserves(node, unit_, restype, 'portion_of_infeed_to_reserve')
165
        } ..
166

167
168
    // Reserve provision by capable units on this node excluding the failing one
    + sum(nuft(node, unit, f, t)${nuRescapable(restype, 'up', node, unit) and (ord(unit_) ne ord(unit))},
169
        + v_reserve(restype, 'up', node, unit, s, f+df_reserves(node, restype, f, t), t)
170
171
172
173
            * [ // Account for reliability of reserves
                + 1${sft_realized(s, f+df_reserves(node, restype, f, t), t)} // reserveReliability limits the reliability of reserves locked ahead of time.
                + p_nuReserves(node, unit, restype, 'reserveReliability')${not sft_realized(s, f+df_reserves(node, restype, f, t), t)}
                ] // END * v_reserve
174
175
176
        ) // END sum(nuft)

    // Reserve provision from other reserve categories when they can be shared
177
    + sum((nuft(node, unit, f, t), restype_)${p_nuRes2Res(node, unit, restype_, 'up', restype)},
178
        + v_reserve(restype_, 'up', node, unit, s, f+df_reserves(node, restype_, f, t), t)
179
            * p_nuRes2Res(node, unit, restype_, 'up', restype)
180
181
182
183
184
            * [ // Account for reliability of reserves
                + 1${sft_realized(s, f+df_reserves(node, restype, f, t), t)} // reserveReliability limits the reliability of reserves locked ahead of time.
                + p_nuReserves(node, unit, restype, 'reserveReliability')${not sft_realized(s, f+df_reserves(node, restype, f, t), t)}
                    * p_nuReserves(node, unit, restype_, 'reserveReliability')
                ] // END * v_reserve
185
186
187
188
189
        ) // END sum(nuft)

    // Reserve provision to this node via transfer links
    + sum(gn2n_directional(grid, node_, node)${restypeDirectionNodeNode(restype, 'up', node_, node)},
        + (1 - p_gnn(grid, node_, node, 'transferLoss') )
190
            * v_resTransferRightward(restype, 'up', node_, node, s, f+df_reserves(node_, restype, f, t), t) // Reserves from another node - reduces the need for reserves in the node
191
192
193
        ) // END sum(gn2n_directional)
    + sum(gn2n_directional(grid, node, node_)${restypeDirectionNodeNode(restype, 'up', node_, node)},
        + (1 - p_gnn(grid, node, node_, 'transferLoss') )
194
            * v_resTransferLeftward(restype, 'up', node, node_, s, f+df_reserves(node_, restype, f, t), t) // Reserves from another node - reduces the need for reserves in the node
195
196
197
198
199
        ) // END sum(gn2n_directional)

    =G=

    // Demand for reserves of the failing one
200
    v_gen(grid,node,unit_,s,f,t) * p_nuReserves(node, unit_, restype, 'portion_of_infeed_to_reserve')
201
202

    // Reserve provisions to another nodes via transfer links
203
    + sum(gn2n_directional(grid, node, node_)${restypeDirectionNodeNode(restype, 'up', node, node_)},   // If trasferring reserves to another node, increase your own reserves by same amount
204
        + v_resTransferRightward(restype, 'up', node, node_, s, f+df_reserves(node, restype, f, t), t)
205
        ) // END sum(gn2n_directional)
206
    + sum(gn2n_directional(grid, node_, node)${restypeDirectionNodeNode(restype, 'up', node, node_)},   // If trasferring reserves to another node, increase your own reserves by same amount
207
        + v_resTransferLeftward(restype, 'up', node_, node, s, f+df_reserves(node, restype, f, t), t)
208
209
210
        ) // END sum(gn2n_directional)

    // Reserve demand feasibility dummy variables
211
212
    - vq_resDemand(restype, 'up', node, s, f+df_reserves(node, restype, f, t), t)
    - vq_resMissing(restype, 'up', node, s, f+df_reserves(node, restype, f, t), t)${ft_reservesFixed(node, restype, f+df_reserves(node, restype, f, t), t)}
213
;
214
215
* --- Maximum Downward Capacity -----------------------------------------------

216
q_maxDownward(gnu(grid, node, unit), msft(m, s, f, t))
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
    ${  gnuft(grid, node, unit, f, t)
        and {
            [   ord(t) < tSolveFirst + smax(restype, p_nReserves(node, restype, 'reserve_length')) // 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)]
                ]
        }} ..

236
    // Energy generation/consumption
237
    + v_gen(grid, node, unit, s, f, t)
238
239

    // Considering output constraints (e.g. cV line)
240
241
    + sum(gngnu_constrainedOutputRatio(grid, node, grid_output, node_, unit),
        + p_gnu(grid_output, node_, unit, 'cV')
242
            * v_gen(grid_output, node_, unit, s, f, t)
243
244
245
        ) // END sum(gngnu_constrainedOutputRatio)

    // Downward reserve participation
246
    - sum(nuRescapable(restype, 'down', node, unit)${ord(t) < tSolveFirst + p_nReserves(node, restype, 'reserve_length')},
247
        + v_reserve(restype, 'down', node, unit, s, f+df_reserves(node, restype, f, t), t) // (v_reserve can be used only if the unit is capable of providing a particular reserve)
248
249
250
251
252
253
        ) // 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')
254
        * sum(suft(effGroup, unit, f, t), // Uses the minimum 'lb' for the current efficiency approximation
255
256
257
258
            + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
            + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
            ) // END sum(effGroup)
        * [ // Online variables should only be generated for units with restrictions
259
260
            + v_online_LP(unit, s, f+df_central(f,t), t)${uft_onlineLP(unit, f+df_central(f,t), t)} // LP online variant
            + v_online_MIP(unit, s, f+df_central(f,t), t)${uft_onlineMIP(unit, f+df_central(f,t), t)} // MIP online variant
261
262
            ] // END v_online

263
264
265
266
    // Units in run-up phase neet to keep up with the run-up rate
    + p_gnu(grid, node, unit, 'unitSizeGen')
        * sum(unitStarttype(unit, starttype)${uft_startupTrajectory(unit, f, t)},
            sum(runUpCounter(unit, counter)${t_active(t+dt_trajectory(counter))}, // Sum over the run-up intervals
267
268
                + [
                    + v_startup_LP(unit, starttype, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
269
                        ${ uft_onlineLP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
270
                    + v_startup_MIP(unit, starttype, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
271
                        ${ uft_onlineMIP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
272
                    ]
273
                    * p_uCounter_runUpMin(unit, counter)
274
275
276
277
278
279
                ) // END sum(runUpCounter)
            ) // END sum(unitStarttype)

    // Units in shutdown phase need to keep up with the shutdown rate
    + p_gnu(grid, node, unit, 'unitSizeGen')
        * sum(shutdownCounter(unit, counter)${t_active(t+dt_trajectory(counter)) and uft_shutdownTrajectory(unit, f, t)}, // Sum over the shutdown intervals
280
281
282
283
284
285
            + [
                + v_shutdown_LP(unit, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
                    ${ uft_onlineLP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
                + v_shutdown_MIP(unit, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
                    ${ uft_onlineMIP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
                ]
286
                * p_uCounter_shutdownMin(unit, counter)
287
            ) // END sum(shutdownCounter)
288

289
290
291
292
293
    // Consuming units, greater than maxCons
    // Available capacity restrictions
    - p_unit(unit, 'availability')
        * [
            // Capacity factors for flow units
294
            + sum(flowUnit(flow, unit),
295
                + ts_cf_(flow, node, f, t, s)
296
297
298
299
300
301
                ) // 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
302
303
304
305
306
307
            // !!! TEMPORARY SOLUTION !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
            + [
                + p_gnu(grid, node, unit, 'unitSizeCons')
                + p_gnu(grid, node, unit, 'maxCons')${not p_gnu(grid, node, unit, 'unitSizeCons') > 0}
                ]
            // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
308
                * [
309
                    // Capacity online
310
311
                    + v_online_LP(unit, s, f+df_central(f,t), t)${uft_onlineLP(unit, f, t)}
                    + v_online_MIP(unit, s, f+df_central(f,t), t)${uft_onlineMIP(unit, f, t)}
312
313
314
315
316
317
318
319

                    // 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)
320
321
                    ] // END * p_gnu(unitSizeCons)
            ] // END * p_unit(availability)
322
;
323
324
325

* --- Maximum Upwards Capacity ------------------------------------------------

326
q_maxUpward(gnu(grid, node, unit), msft(m, s, f, t))
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
    ${  gnuft(grid, node, unit, f, t)
        and {
            [   ord(t) < tSolveFirst + smax(restype, p_nReserves(node, restype, 'reserve_length')) // 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))
                ]
        }}..

345
    // Energy generation/consumption
346
    + v_gen(grid, node, unit, s, f, t)
347
348
349
350

    // Considering output constraints (e.g. cV line)
    + sum(gngnu_constrainedOutputRatio(grid, node, grid_output, node_, unit),
        + p_gnu(grid_output, node_, unit, 'cV')
351
            * v_gen(grid_output, node_, unit, s, f, t)
352
353
354
        ) // END sum(gngnu_constrainedOutputRatio)

    // Upwards reserve participation
355
    + sum(nuRescapable(restype, 'up', node, unit)${ord(t) < tSolveFirst + p_nReserves(node, restype, 'reserve_length')},
356
        + v_reserve(restype, 'up', node, unit, s, f+df_reserves(node, restype, f, t), t)
357
358
359
360
361
        ) // END sum(nuRescapable)

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

    // Consuming units
362
    - p_gnu(grid, node, unit, 'unitSizeCons')
363
        * sum(suft(effGroup, unit, f, t), // Uses the minimum 'lb' for the current efficiency approximation
364
365
366
367
            + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
            + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
            ) // END sum(effGroup)
        * [
368
369
            + v_online_LP(unit, s, f+df_central(f,t), t)${uft_onlineLP(unit, f, t)} // Consuming units are restricted by their min. load (consuming is negative)
            + v_online_MIP(unit, s, f+df_central(f,t), t)${uft_onlineMIP(unit, f, t)} // Consuming units are restricted by their min. load (consuming is negative)
370
371
372
373
374
375
376
            ] // 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
377
            + sum(flowUnit(flow, unit),
378
                + ts_cf_(flow, node, f, t, s)
379
380
381
382
383
384
385
386
                ) // 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')
                * [
387
                    // Capacity online
388
389
                    + v_online_LP(unit, s, f+df_central(f,t), t)${uft_onlineLP(unit, f ,t)}
                    + v_online_MIP(unit, s, f+df_central(f,t), t)${uft_onlineMIP(unit, f, t)}
390
391
392
393
394
395
396
397

                    // 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)
398
399
                    ] // END * p_gnu(unitSizeGen)
            ] // END * p_unit(availability)
400

401
402
403
404
    // Units in run-up phase neet to keep up with the run-up rate
    + p_gnu(grid, node, unit, 'unitSizeGen')
        * sum(unitStarttype(unit, starttype)${uft_startupTrajectory(unit, f, t)},
            sum(runUpCounter(unit, counter)${t_active(t+dt_trajectory(counter))}, // Sum over the run-up intervals
405
406
                + [
                    + v_startup_LP(unit, starttype, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
407
                        ${ uft_onlineLP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
408
                    + v_startup_MIP(unit, starttype, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
409
                        ${ uft_onlineMIP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
410
                    ]
411
                    * p_uCounter_runUpMax(unit, counter)
412
413
414
415
416
417
                ) // END sum(runUpCounter)
            ) // END sum(unitStarttype)

    // Units in shutdown phase need to keep up with the shutdown rate
    + p_gnu(grid, node, unit, 'unitSizeGen')
        * sum(shutdownCounter(unit, counter)${t_active(t+dt_trajectory(counter)) and uft_shutdownTrajectory(unit, f, t)}, // Sum over the shutdown intervals
418
419
420
421
422
423
            + [
                + v_shutdown_LP(unit, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
                    ${ uft_onlineLP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
                + v_shutdown_MIP(unit, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
                    ${ uft_onlineMIP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
                ]
424
                * p_uCounter_shutdownMax(unit, counter)
425
            ) // END sum(shutdownCounter)
426
;
427

428
429
* --- Reserve Provision of Units with Investments -----------------------------

430
431
432
433
434
435
436
q_reserveProvision(nuRescapable(restypeDirectionNode(restype, up_down, node), unit), sft(s, f, t))
    ${  ord(t) <= tSolveFirst + p_nReserves(node, restype, 'reserve_length')
        and nuft(node, unit, f, t)
        and (unit_investLP(unit) or unit_investMIP(unit))
        and not ft_reservesFixed(node, restype, f+df_reserves(node, restype, f, t), t)
        } ..

437
    + v_reserve(restype, up_down, node, unit, s, f+df_reserves(node, restype, f, t), t)
438
439
440
441
442
443
444
445
446
447
448
449
450

    =L=

    + p_nuReserves(node, unit, restype, up_down)
        * [
            + sum(grid, p_gnu(grid, node, unit, 'maxGen') + p_gnu(grid, node, unit, 'maxCons') )  // Reserve sets and variables are currently lacking the grid dimension...
            + sum(t_invest(t_)${ ord(t_)<=ord(t) },
                + v_invest_LP(unit, t_)${unit_investLP(unit)}
                    * sum(grid, p_gnu(grid, node, unit, 'unitSizeTot')) // Reserve sets and variables are currently lacking the grid dimension...
                + v_invest_MIP(unit, t_)${unit_investMIP(unit)}
                    * sum(grid, p_gnu(grid, node, unit, 'unitSizeTot')) // Reserve sets and variables are currently lacking the grid dimension...
                ) // END sum(t_)
            ]
451
452
453
454
        * p_unit(unit, 'availability') // Taking into account availability...
        * [
            // ... and capacity factor for flow units
            + sum(flowUnit(flow, unit),
455
                + ts_cf_(flow, node, f, t, s)
456
457
                ) // END sum(flow)
            + 1${not unit_flow(unit)}
458
459
460
            ] // How to consider reserveReliability in the case of investments when we typically only have "realized" time steps?
;

461
462
* --- Unit Startup and Shutdown -----------------------------------------------

463
464
465
466
q_startshut(ms(m, s), uft_online(unit, f, t))
    ${  msft(m, s, f, t)
        }..

467
    // Units currently online
468
469
    + v_online_LP (unit, s, f+df_central(f,t), t)${uft_onlineLP (unit, f, t)}
    + v_online_MIP(unit, s, f+df_central(f,t), t)${uft_onlineMIP(unit, f, t)}
470
471

    // Units previously online
472
    // The same units
473
    - v_online_LP (unit, s+ds(s,t), f+df(f,t+dt(t)), t+dt(t))${ uft_onlineLP_withPrevious(unit, f+df(f,t+dt(t)), t+dt(t))
474
                                                             and not uft_aggregator_first(unit, f, t) } // This reaches to tFirstSolve when dt = -1
475
    - v_online_MIP(unit, s+ds(s,t), f+df(f,t+dt(t)), t+dt(t))${ uft_onlineMIP_withPrevious(unit, f+df(f,t+dt(t)), t+dt(t))
476
477
478
479
                                                             and not uft_aggregator_first(unit, f, t) }

    // Aggregated units just before they are turned into aggregator units
    - sum(unit_${unitAggregator_unit(unit, unit_)},
480
481
        + v_online_LP (unit_, s, f+df(f,t+dt(t)), t+dt(t))${uft_onlineLP_withPrevious(unit_, f+df(f,t+dt(t)), t+dt(t))}
        + v_online_MIP(unit_, s, f+df(f,t+dt(t)), t+dt(t))${uft_onlineMIP_withPrevious(unit_, f+df(f,t+dt(t)), t+dt(t))}
482
        )${uft_aggregator_first(unit, f, t)} // END sum(unit_)
483

484
485
    =E=

486
    // Unit startup and shutdown
487

488
    // Add startup of units dt_toStartup before the current t (no start-ups for aggregator units before they become active)
489
    + sum(unitStarttype(unit, starttype),
490
        + v_startup_LP(unit, starttype, s, f+df(f,t+dt_toStartup(unit, t)), t+dt_toStartup(unit, t))
491
            ${ uft_onlineLP_withPrevious(unit, f+df(f,t+dt_toStartup(unit, t)), t+dt_toStartup(unit, t)) }
492
        + v_startup_MIP(unit, starttype, s, f+df(f,t+dt_toStartup(unit, t)), t+dt_toStartup(unit, t))
493
            ${ uft_onlineMIP_withPrevious(unit, f+df(f,t+dt_toStartup(unit, t)), t+dt_toStartup(unit, t)) }
494
        )${not [unit_aggregator(unit) and ord(t) + dt_toStartup(unit, t) <= tSolveFirst + p_unit(unit, 'lastStepNotAggregated')]} // END sum(starttype)
495

496
497
498
499
    // NOTE! According to 3d_setVariableLimits,
    // cannot start a unit if the time when the unit would become online is outside
    // the horizon when the unit has an online variable
    // --> no need to add start-ups of aggregated units to aggregator units
500

501
    // Shutdown of units at time t
502
503
504
505
    - v_shutdown_LP(unit, s, f, t)
        ${ uft_onlineLP(unit, f, t) }
    - v_shutdown_MIP(unit, s, f, t)
        ${ uft_onlineMIP(unit, f, t) }
506
;
507

508
*--- Startup Type -------------------------------------------------------------
509
// !!! NOTE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
510
511
512
// 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.
513

514
515
516
517
q_startuptype(ms(m, s), starttypeConstrained(starttype), uft_online(unit, f, t))
    ${  msft(m, s, f, t)
        and unitStarttype(unit, starttype)
        } ..
518
519

    // Startup type
520
521
    + v_startup_LP(unit, starttype, s, f, t)${ uft_onlineLP(unit, f, t) }
    + v_startup_MIP(unit, starttype, s, f, t)${ uft_onlineMIP(unit, f, t) }
522
523
524
525

    =L=

    // Subunit shutdowns within special startup timeframe
526
527
528
529
530
531
532
    + sum(unitCounter(unit, counter)${  dt_starttypeUnitCounter(starttype, unit, counter)
                                        and t_active(t+(dt_starttypeUnitCounter(starttype, unit, counter)+1))
                                        },
        + v_shutdown_LP(unit, s, f+df(f,t+(dt_starttypeUnitCounter(starttype, unit, counter)+1)), t+(dt_starttypeUnitCounter(starttype, unit, counter)+1))
            ${ uft_onlineLP_withPrevious(unit, f+df(f,t+(dt_starttypeUnitCounter(starttype, unit, counter)+1)), t+(dt_starttypeUnitCounter(starttype, unit, counter)+1)) }
        + v_shutdown_MIP(unit, s, f+df(f,t+(dt_starttypeUnitCounter(starttype, unit, counter)+1)), t+(dt_starttypeUnitCounter(starttype, unit, counter)+1))
            ${ uft_onlineMIP_withPrevious(unit, f+df(f,t+(dt_starttypeUnitCounter(starttype, unit, counter)+1)), t+(dt_starttypeUnitCounter(starttype, unit, counter)+1)) }
533
534
535
        ) // END sum(counter)

    // NOTE: for aggregator units, shutdowns for aggregated units are not considered
536
;
537

538

539
540
*--- Online Limits with Startup Type Constraints and Investments --------------

541
542
543
544
545
546
547
548
549
q_onlineLimit(ms(m, s), uft_online(unit, f, t))
    ${  msft(m, s, f, t)
        and {
            p_unit(unit, 'minShutdownHours')
            or p_u_runUpTimeIntervals(unit)
            or unit_investLP(unit)
            or unit_investMIP(unit)
        }} ..

550
    // Online variables
551
552
    + v_online_LP(unit, s, f+df_central(f,t), t)${uft_onlineLP(unit, f, t)}
    + v_online_MIP(unit, s, f+df_central(f,t), t)${uft_onlineMIP(unit, f ,t)}
553
554
555
556
557
558

    =L=

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

559
    // Number of units unable to become online due to restrictions
560
561
562
563
564
565
566
    - sum(unitCounter(unit, counter)${  dt_downtimeUnitCounter(unit, counter)
                                        and t_active(t+(dt_downtimeUnitCounter(unit, counter) + 1))
                                        },
        + v_shutdown_LP(unit, s, f+df(f,t+(dt_downtimeUnitCounter(unit, counter) + 1)), t+(dt_downtimeUnitCounter(unit, counter) + 1))
            ${ uft_onlineLP_withPrevious(unit, f+df(f,t+(dt_downtimeUnitCounter(unit, counter) + 1)), t+(dt_downtimeUnitCounter(unit, counter) + 1)) }
        + v_shutdown_MIP(unit, s, f+df(f,t+(dt_downtimeUnitCounter(unit, counter) + 1)), t+(dt_downtimeUnitCounter(unit, counter) + 1))
            ${ uft_onlineMIP_withPrevious(unit, f+df(f,t+(dt_downtimeUnitCounter(unit, counter) + 1)), t+(dt_downtimeUnitCounter(unit, counter) + 1)) }
567
568
569
        ) // END sum(counter)

    // Number of units unable to become online due to restrictions (aggregated units in the past horizon or if they have an online variable)
570
    - sum(unitAggregator_unit(unit, unit_),
571
572
573
574
575
576
577
        + sum(unitCounter(unit, counter)${  dt_downtimeUnitCounter(unit, counter)
                                            and t_active(t+(dt_downtimeUnitCounter(unit, counter) + 1))
                                            },
            + v_shutdown_LP(unit_, s, f+df(f,t+(dt_downtimeUnitCounter(unit, counter) + 1)), t+(dt_downtimeUnitCounter(unit, counter) + 1))
                ${ uft_onlineLP_withPrevious(unit_, f+df(f,t+(dt_downtimeUnitCounter(unit, counter) + 1)), t+(dt_downtimeUnitCounter(unit, counter) + 1)) }
            + v_shutdown_MIP(unit_, s, f+df(f,t+(dt_downtimeUnitCounter(unit, counter) + 1)), t+(dt_downtimeUnitCounter(unit, counter) + 1))
                ${ uft_onlineMIP_withPrevious(unit_, f+df(f,t+(dt_downtimeUnitCounter(unit, counter) + 1)), t+(dt_downtimeUnitCounter(unit, counter) + 1)) }
578
579
            ) // END sum(counter)
        )${unit_aggregator(unit)} // END sum(unit_)
580
581
582

    // Investments into units
    + sum(t_invest(t_)${ord(t_)<=ord(t)},
583
584
        + v_invest_LP(unit, t_)${unit_investLP(unit)}
        + v_invest_MIP(unit, t_)${unit_investMIP(unit)}
585
586
587
        ) // END sum(t_invest)
;

588
589
590
591
*--- Both q_offlineAfterShutdown and q_onlineOnStartup work when there is only one unit.
*    These equations prohibit single units turning on and off at the same time step.
*    Unfortunately there seems to be no way to prohibit this when unit count is > 1.
*    (it shouldn't be worthwhile anyway if there is a startup cost, but it can fall within the solution gap).
592
593
594
595
q_onlineOnStartUp(s_active(s), uft_online(unit, f, t))
    ${  sft(s, f, t)
        and sum(starttype, unitStarttype(unit, starttype))
        }..
596
597

    // Units currently online
598
599
    + v_online_LP(unit, s, f+df_central(f,t), t)${uft_onlineLP(unit, f, t)}
    + v_online_MIP(unit, s, f+df_central(f,t), t)${uft_onlineMIP(unit, f, t)}
600
601
602
603

    =G=

    + sum(unitStarttype(unit, starttype),
604
        + v_startup_LP(unit, starttype, s, f+df(f,t+dt_toStartup(unit, t)), t+dt_toStartup(unit, t)) //dt_toStartup displaces the time step to the one where the unit would be started up in order to reach online at t
605
            ${ uft_onlineLP_withPrevious(unit, f+df(f,t+dt_toStartup(unit, t)), t+dt_toStartup(unit, t)) }
606
        + v_startup_MIP(unit, starttype, s, f+df(f,t+dt_toStartup(unit, t)), t+dt_toStartup(unit, t)) //dt_toStartup displaces the time step to the one where the unit would be started up in order to reach online at t
607
            ${ uft_onlineMIP_withPrevious(unit, f+df(f,t+dt_toStartup(unit, t)), t+dt_toStartup(unit, t)) }
608
609
610
      ) // END sum(starttype)
;

611
612
613
614
q_offlineAfterShutdown(s_active(s), uft_online(unit, f, t))
    ${  sft(s, f, t)
        and sum(starttype, unitStarttype(unit, starttype))
        }..
615

616
617
618
619
620
    // Number of existing units
    + p_unit(unit, 'unitCount')

    // Investments into units
    + sum(t_invest(t_)${ord(t_)<=ord(t)},
621
622
        + v_invest_LP(unit, t_)${unit_investLP(unit)}
        + v_invest_MIP(unit, t_)${unit_investMIP(unit)}
623
624
        ) // END sum(t_invest)

625
    // Units currently online
626
627
    - v_online_LP(unit, s, f+df_central(f,t), t)${uft_onlineLP(unit, f, t)}
    - v_online_MIP(unit, s, f+df_central(f,t), t)${uft_onlineMIP(unit, f, t)}
628
629
630

    =G=

631
632
633
634
    + v_shutdown_LP(unit, s, f, t)
        ${ uft_onlineLP(unit, f, t) }
    + v_shutdown_MIP(unit, s, f, t)
        ${ uft_onlineMIP(unit, f, t) }
635
636
;

637
638
*--- Minimum Unit Uptime ------------------------------------------------------

639
640
641
642
q_onlineMinUptime(ms(m, s), uft_online(unit, f, t))
    ${  msft(m, s, f, t)
        and  p_unit(unit, 'minOperationHours')
        } ..
643
644

    // Units currently online
645
646
    + v_online_LP(unit, s, f+df_central(f,t), t)${uft_onlineLP(unit, f, t)}
    + v_online_MIP(unit, s, f+df_central(f,t), t)${uft_onlineMIP(unit, f, t)}
647
648
649
650

    =G=

    // Units that have minimum operation time requirements active
651
652
653
    + sum(unitCounter(unit, counter)${  dt_uptimeUnitCounter(unit, counter)
                                        and t_active(t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)) // Don't sum over counters that don't point to an active time step
                                        },
654
        + sum(unitStarttype(unit, starttype),
655
            + v_startup_LP(unit, starttype, s, f+df(f,t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)), t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1))
656
                ${ uft_onlineLP_withPrevious(unit, f+df(f,t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)), t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)) }
657
            + v_startup_MIP(unit, starttype, s, f+df(f,t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)), t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1))
658
                ${ uft_onlineMIP_withPrevious(unit, f+df(f,t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)), t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)) }
659
            ) // END sum(starttype)
660
661
662
        ) // END sum(counter)

    // Units that have minimum operation time requirements active (aggregated units in the past horizon or if they have an online variable)
Topi Rasku's avatar
Topi Rasku committed
663
    + sum(unitAggregator_unit(unit, unit_),
664
665
666
        + sum(unitCounter(unit, counter)${  dt_uptimeUnitCounter(unit, counter)
                                            and t_active(t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)) // Don't sum over counters that don't point to an active time step
                                            },
667
            + sum(unitStarttype(unit, starttype),
668
                + v_startup_LP(unit, starttype, s, f+df(f,t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)), t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1))
669
                    ${ uft_onlineLP_withPrevious(unit, f+df(f,t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)), t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)) }
670
                + v_startup_MIP(unit, starttype, s, f+df(f,t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)), t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1))
671
                    ${ uft_onlineMIP_withPrevious(unit, f+df(f,t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)), t+(dt_uptimeUnitCounter(unit, counter)+dt_toStartup(unit, t) + 1)) }
672
673
674
                ) // END sum(starttype)
            ) // END sum(counter)
        )${unit_aggregator(unit)} // END sum(unit_)
675
676
;

677
678
* --- Cyclic Boundary Conditions for Online State -----------------------------

679
680
681
682
683
q_onlineCyclic(uss_bound(unit, s_, s), m)
    ${  ms(m, s_)
        and ms(m, s)
        and tSolveFirst = mSettings(m, 't_start')
        }..
684
685
686
687

    // Initial value of the state of the unit at the start of the sample
    + sum(mst_start(m, s, t),
        + sum(sft(s, f, t),
Topi Rasku's avatar
Topi Rasku committed
688
689
690
691
            + v_online_LP(unit, s, f+df(f,t+dt(t)), t+dt(t))
                ${uft_onlineLP_withPrevious(unit, f+df(f,t+dt(t)), t+dt(t))}
            + v_online_MIP(unit, s, f+df(f,t+dt(t)), t+dt(t))
                ${uft_onlineMIP_withPrevious(unit, f+df(f,t+dt(t)), t+dt(t))}
692
693
694
695
696
697
698
699
700
701
702
703
704
705
            ) // END sum(ft)
        ) // END sum(mst_start)

    =E=

    // State of the unit at the end of the sample
    + sum(mst_end(m, s_, t_),
        + sum(sft(s_, f_, t_),
            + v_online_LP(unit, s_, f_, t_)${uft_onlineLP(unit, f_, t_)}
            + v_online_MIP(unit, s_, f_, t_)${uft_onlineMIP(unit, f_, t_)}
            ) // END sum(ft)
        ) // END sum(mst_end)
;

706
* --- Ramp Constraints --------------------------------------------------------
707

708
709
710
711
q_genRamp(ms(m, s), gnuft_ramp(grid, node, unit, f, t))
    ${  ord(t) > msStart(m, s) + 1
        and msft(m, s, f, t)
        } ..
712

713
714
    + v_genRamp(grid, node, unit, s, f, t)
        * p_stepLength(m, f, t)
715

716
    =E=
717

718
    // Change in generation over the interval: v_gen(t) - v_gen(t-1)
719
    + v_gen(grid, node, unit, s, f, t)
720

721
    // Unit generation at t-1 (except aggregator units right before the aggregation threshold, see next term)
722
    - v_gen(grid, node, unit, s+ds(s,t), f+df(f,t+dt(t)), t+dt(t))${not uft_aggregator_first(unit, f, t)}
723
724
    // Unit generation at t-1, aggregator units right before the aggregation threshold
    + sum(unit_${unitAggregator_unit(unit, unit_)},
725
        - v_gen(grid, node, unit_, s+ds(s,t), f+df(f,t+dt(t)), t+dt(t))
726
      )${uft_aggregator_first(unit, f, t)}
727
;
728

729
* --- Ramp Up Limits ----------------------------------------------------------
730

731
732
733
734
735
736
737
738
739
740
741
742
q_rampUpLimit(ms(m, s), gnuft_ramp(grid, node, unit, f, t))
    ${  ord(t) > msStart(m, s) + 1
        and msft(m, s, f, t)
        and p_gnu(grid, node, unit, 'maxRampUp')
        and [ sum(restype, nuRescapable(restype, 'up', node, unit))
              or uft_online(unit, f, t)
              or unit_investLP(unit)
              or unit_investMIP(unit)
              ]
        } ..

    // Ramp speed of the unit?
743
    + v_genRamp(grid, node, unit, s, f, t)
744
    + sum(nuRescapable(restype, 'up', node, unit)${ord(t) < tSolveFirst + p_nReserves(node, restype, 'reserve_length')},
745
        + v_reserve(restype, 'up', node, unit, s, f+df_reserves(node, restype, f, t), t) // (v_reserve can be used only if the unit is capable of providing a particular reserve)
746
747
748
749
750
        ) // END sum(nuRescapable)
        / p_stepLength(m, f, t)

    =L=

751
    // Ramping capability of units without an online variable
752
753
754
755
756
757
758
759
760
761
762
763
    + (
        + ( p_gnu(grid, node, unit, 'maxGen') + p_gnu(grid, node, unit, 'maxCons') )${not uft_online(unit, f, t)}
        + sum(t_invest(t_)${ ord(t_)<=ord(t) },
            + v_invest_LP(unit, t_)${not uft_onlineLP(unit, f, t) and unit_investLP(unit)}
                * p_gnu(grid, node, unit, 'unitSizeTot')
            + v_invest_MIP(unit, t_)${not uft_onlineMIP(unit, f, t) and unit_investMIP(unit)}
                * p_gnu(grid, node, unit, 'unitSizeTot')
          )
      )
        * p_gnu(grid, node, unit, 'maxRampUp')
        * 60   // Unit conversion from [p.u./min] to [p.u./h]

764
    // Ramping capability of units with an online variable
765
    + (
Topi Rasku's avatar
Topi Rasku committed
766
767
768
769
        + v_online_LP(unit, s, f+df_central(f,t), t)
            ${uft_onlineLP(unit, f, t)}
        + v_online_MIP(unit, s, f+df_central(f,t), t)
            ${uft_onlineMIP(unit, f, t)}
770
771
772
773
774
      )
        * p_gnu(grid, node, unit, 'unitSizeTot')
        * p_gnu(grid, node, unit, 'maxRampUp')
        * 60   // Unit conversion from [p.u./min] to [p.u./h]

775
776
777
778
779
780
781
782
783
784
785
786
787
    // Generation units not be able to ramp from zero to min. load within one time interval according to their maxRampUp
    + sum(unitStarttype(unit, starttype)${   uft_online(unit, f, t)
                                             and gnu_output(grid, node, unit)
                                             and not uft_startupTrajectory(unit, f, t)
                                             and ( + sum(suft(effGroup, unit, f, t), // Uses the minimum 'lb' for the current efficiency approximation
                                                       + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
                                                       + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
                                                     ) // END sum(effGroup)
                                                       / p_stepLength(m, f, t)
                                                   - p_gnu(grid, node, unit, 'maxRampUp')
                                                       * 60 > 0
                                                   )
                                             },
788
789
790
791
        + v_startup_LP(unit, starttype, s, f, t)
            ${ uft_onlineLP(unit, f, t) }
        + v_startup_MIP(unit, starttype, s, f, t)
            ${ uft_onlineMIP(unit, f, t) }
792
793
794
795
796
797
798
799
800
801
802
803
      ) // END sum(starttype)
        * p_gnu(grid, node, unit, 'unitSizeTot')
        * (
            + sum(suft(effGroup, unit, f, t), // Uses the minimum 'lb' for the current efficiency approximation
                + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
                + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
              ) // END sum(effGroup)
                / p_stepLength(m, f, t)
            - p_gnu(grid, node, unit, 'maxRampUp')
                * 60   // Unit conversion from [p.u./min] to [p.u./h]
          ) // END * v_startup

804
805
806
807
    // Units in the run-up phase need to keep up with the run-up rate
    + p_gnu(grid, node, unit, 'unitSizeTot')
        * sum(unitStarttype(unit, starttype)${uft_startupTrajectory(unit, f, t)},
            sum(runUpCounter(unit, counter)${t_active(t+dt_trajectory(counter))}, // Sum over the run-up intervals
808
809
                + [
                    + v_startup_LP(unit, starttype, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
810
                        ${ uft_onlineLP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
811
                    + v_startup_MIP(unit, starttype, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
812
                        ${ uft_onlineMIP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
813
                    ]
814
815
816
817
818
819
820
821
                    * [
                        + p_unit(unit, 'rampSpeedToMinLoad')
                        + ( p_gnu(grid, node, unit, 'maxRampUp') - p_unit(unit, 'rampSpeedToMinLoad') )${ not runUpCounter(unit, counter+1) } // Ramp speed adjusted for the last run-up interval
                            * ( p_u_runUpTimeIntervalsCeil(unit) - p_u_runUpTimeIntervals(unit) )
                        ]
                    * 60 // Unit conversion from [p.u./min] into [p.u./h]
                ) // END sum(runUpCounter)
            ) // END sum(unitStarttype)
822

823
    // Shutdown of consumption units according to maxRampUp
824
825
826
827
828
829
    + [
        + v_shutdown_LP(unit, s, f, t)
            ${uft_onlineLP(unit, f, t) and gnu_input(grid, node, unit)}
        + v_shutdown_MIP(unit, s, f, t)
            ${uft_onlineMIP(unit, f, t) and gnu_input(grid, node, unit)}
        ]
830
        * p_gnu(grid, node, unit, 'unitSizeTot')
831
832
833
        * p_gnu(grid, node, unit, 'maxRampUp')
        * 60   // Unit conversion from [p.u./min] to [p.u./h]
    // Consumption units not be able to ramp from min. load to zero within one time interval according to their maxRampUp
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
    + [
        + v_shutdown_LP(unit, s, f, t)
            ${ uft_onlineLP(unit, f, t) }
        + v_shutdown_MIP(unit, s, f, t)
            ${ uft_onlineMIP(unit, f, t) }
        ]
        ${  gnu_input(grid, node, unit)
            and ( + sum(suft(effGroup, unit, f, t), // Uses the minimum 'lb' for the current efficiency approximation
                      + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
                      + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
                      ) // END sum(effGroup)
                      / p_stepLength(m, f, t)
                  - p_gnu(grid, node, unit, 'maxRampUp')
                      * 60 > 0
                  )
            }
850
851
852
853
854
855
856
857
858
        * p_gnu(grid, node, unit, 'unitSizeTot')
        * (
            + sum(suft(effGroup, unit, f, t), // 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)
                / p_stepLength(m, f, t)
            - p_gnu(grid, node, unit, 'maxRampUp')
                * 60   // Unit conversion from [p.u./min] to [p.u./h]
859
          ) // END * v_shutdown
860
;
861

862
* --- Ramp Down Limits --------------------------------------------------------
863

864
865
866
867
868
869
870
871
872
873
874
875
q_rampDownLimit(ms(m, s), gnuft_ramp(grid, node, unit, f, t))
    ${  ord(t) > msStart(m, s) + 1
        and msft(m, s, f, t)
        and p_gnu(grid, node, unit, 'maxRampDown')
        and [ sum(restype, nuRescapable(restype, 'down', node, unit))
              or uft_online(unit, f, t)
              or unit_investLP(unit)
              or unit_investMIP(unit)
              ]
        } ..

    // Ramp speed of the unit?
876
    + v_genRamp(grid, node, unit, s, f, t)
877
    - sum(nuRescapable(restype, 'down', node, unit)${ord(t) < tSolveFirst + p_nReserves(node, restype, 'reserve_length')},
878
        + v_reserve(restype, 'down', node, unit, s, f+df_reserves(node, restype, f, t), t) // (v_reserve can be used only if the unit is capable of providing a particular reserve)
879
880
881
882
883
        ) // END sum(nuRescapable)
        / p_stepLength(m, f, t)

    =G=

884
    // Ramping capability of units without online variable
885
    - (
Topi Rasku's avatar
Topi Rasku committed
886
887
        + ( p_gnu(grid, node, unit, 'maxGen') + p_gnu(grid, node, unit, 'maxCons') )
            ${not uft_online(unit, f, t)}
888
        + sum(t_invest(t_)${ ord(t_)<=ord(t) },
Topi Rasku's avatar
Topi Rasku committed
889
890
            + v_invest_LP(unit, t_)
                ${not uft_onlineLP(unit, f, t) and unit_investLP(unit)}
891
                * p_gnu(grid, node, unit, 'unitSizeTot')
Topi Rasku's avatar
Topi Rasku committed
892
893
            + v_invest_MIP(unit, t_)
                ${not uft_onlineMIP(unit, f, t) and unit_investMIP(unit)}
894
895
896
897
898
899
                * p_gnu(grid, node, unit, 'unitSizeTot')
          )
      )
        * p_gnu(grid, node, unit, 'maxRampDown')
        * 60   // Unit conversion from [p.u./min] to [p.u./h]

900
    // Ramping capability of units that are online
901
    - (
Topi Rasku's avatar
Topi Rasku committed
902
903
904
905
        + v_online_LP(unit, s, f+df_central(f,t), t)
            ${uft_onlineLP(unit, f, t)}
        + v_online_MIP(unit, s, f+df_central(f,t), t)
            ${uft_onlineMIP(unit, f, t)}
906
907
908
909
910
      )
        * p_gnu(grid, node, unit, 'unitSizeTot')
        * p_gnu(grid, node, unit, 'maxRampDown')
        * 60   // Unit conversion from [p.u./min] to [p.u./h]

911
    // Shutdown of generation units according to maxRampDown
912
913
914
915
916
917
918
919
920
    - [
        + v_shutdown_LP(unit, s, f, t)
            ${  uft_onlineLP(unit, f, t) }
        + v_shutdown_MIP(unit, s, f, t)
            ${  uft_onlineMIP(unit, f, t) }
        ]
        ${  gnu_output(grid, node, unit)
            and not uft_shutdownTrajectory(unit, f, t)
            }
921
        * p_gnu(grid, node, unit, 'unitSizeTot')
922
923
924
        * p_gnu(grid, node, unit, 'maxRampDown')
        * 60   // Unit conversion from [p.u./min] to [p.u./h]
    // Generation units not be able to ramp from min. load to zero within one time interval according to their maxRampDown
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
    - [
        + v_shutdown_LP(unit, s, f, t)
            ${  uft_onlineLP(unit, f, t) }
        + v_shutdown_MIP(unit, s, f, t)
            ${  uft_onlineMIP(unit, f, t) }
        ]
        ${  gnu_output(grid, node, unit)
            and not uft_shutdownTrajectory(unit, f, t)
            and ( + sum(suft(effGroup, unit, f, t), // Uses the minimum 'lb' for the current efficiency approximation
                      + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
                      + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
                    ) // END sum(effGroup)
                    / p_stepLength(m, f, t)
                  - p_gnu(grid, node, unit, 'maxRampDown')
                      * 60 > 0
                )
        }
942
943
944
945
946
947
948
949
950
951
        * p_gnu(grid, node, unit, 'unitSizeTot')
        * (
            + sum(suft(effGroup, unit, f, t), // 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)
                / p_stepLength(m, f, t)
            - p_gnu(grid, node, unit, 'maxRampDown')
                * 60   // Unit conversion from [p.u./min] to [p.u./h]
          ) // END * v_shutdown
952

953
954
    // Units in shutdown phase need to keep up with the shutdown ramp rate
    - p_gnu(grid, node, unit, 'unitSizeGen')
955
956
        * [
            + sum(shutdownCounter(unit, counter)${t_active(t+dt_trajectory(counter)) and uft_shutdownTrajectory(unit, f, t)}, // Sum over the shutdown intervals
957
958
959
960
961
962
                + [
                    + v_shutdown_LP(unit, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
                        ${ uft_onlineLP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
                    + v_shutdown_MIP(unit, s, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter))
                        ${ uft_onlineMIP_withPrevious(unit, f+df(f, t+dt_trajectory(counter)), t+dt_trajectory(counter)) }
                    ]
963
                    * [
964
965
966
                        + p_gnu(grid, node, unit, 'maxRampDown')${ not shutdownCounter(unit, counter-1) } // Normal maxRampDown limit applies to the time interval when v_shutdown happens, i.e. over the change from online to offline (symmetrical to v_startup)
                        + p_unit(unit, 'rampSpeedFromMinLoad')${ shutdownCounter(unit, counter-1) } // Normal trajectory ramping
                        + ( p_gnu(grid, node, unit, 'maxRampDown') - p_unit(unit, 'rampSpeedFromMinLoad') )${ shutdownCounter(unit, counter-1) and not shutdownCounter(unit, counter-2) } // Ramp speed adjusted for the first shutdown interval
967
968
969
                            * ( p_u_shutdownTimeIntervalsCeil(unit) - p_u_shutdownTimeIntervals(unit) )
                        ]
                ) // END sum(shutdownCounter)
970
            // Units need to be able to shut down after shut down trajectory
971
972
973
974
975
976
977
            + [
                + v_shutdown_LP(unit, s, f+df(f, t+dt_toShutdown(unit, t)), t+dt_toShutdown(unit, t))
                    ${ uft_onlineLP_withPrevious(unit, f+df(f, t+dt_toShutdown(unit, t)), t+dt_toShutdown(unit, t)) }
                + v_shutdown_MIP(unit, s, f+df(f, t+dt_toShutdown(unit, t)), t+dt_toShutdown(unit, t))
                    ${ uft_onlineMIP_withPrevious(unit, f+df(f, t+dt_toShutdown(unit, t)), t+dt_toShutdown(unit, t)) }
                ]
                ${uft_shutdownTrajectory(unit, f, t)}
978
979
980
981
982
                * [
                    + p_unit(unit, 'rampSpeedFromMinload')
                    + ( p_gnu(grid, node, unit, 'maxRampDown') - p_unit(unit, 'rampSpeedFromMinLoad') )${ sum(shutdownCounter(unit, counter), 1) = 1 } // Ramp speed adjusted if the unit has only one shutdown interval
                        * ( p_u_shutdownTimeIntervalsCeil(unit) - p_u_shutdownTimeIntervals(unit) )
                    ]
983
984
            ]
        * 60 // Unit conversion from [p.u./min] to [p.u./h]
985
986
987
988
989
990
991
992
993
994
995
996
997

    // Consumption units not be able to ramp from zero to min. load within one time interval according to their maxRampDown
    - sum(unitStarttype(unit, starttype)${   uft_online(unit, f, t)
                                             and gnu_input(grid, node, unit)
                                             and ( + sum(suft(effGroup, unit, f, t), // Uses the minimum 'lb' for the current efficiency approximation
                                                       + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
                                                       + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
                                                     ) // END sum(effGroup)
                                                       / p_stepLength(m, f, t)
                                                   - p_gnu(grid, node, unit, 'maxRampDown')
                                                       * 60 > 0
                                                   )
                                             },
998
999
1000
        + v_startup_LP(unit, starttype, s, f, t)
            ${ uft_onlineLP(unit, f, t) }
        + v_startup_MIP(unit, starttype, s, f, t)