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Diffstat (limited to 'glpk-5.0/examples/powpl25h.mod')
| -rw-r--r-- | glpk-5.0/examples/powpl25h.mod | 203 |
1 files changed, 203 insertions, 0 deletions
diff --git a/glpk-5.0/examples/powpl25h.mod b/glpk-5.0/examples/powpl25h.mod new file mode 100644 index 0000000..bdeefb9 --- /dev/null +++ b/glpk-5.0/examples/powpl25h.mod @@ -0,0 +1,203 @@ +/* Power plant LP scheduler, example data with 25hrs for daylightsavings */ + +/* Implemented, inspected, written and converted to GNU MathProg + by NASZVADI, Peter, 199x-2017 <vuk@cs.elte.hu> */ + +/* + Fast electric power plant scheduler implementation based on new + results in author's Thesis. + + The base problem is: + * given some power plants + * a short time scale partitioned to equidistant intervals + * the task is to yielding the cheapest schedule for the plants + * the daily demand forecast is usually accurate and part of the input + + The power plants has technical limitations: + * upper and lower bounds of produced energy + * and also a gradient barrier in both directions + (can depend on time, but this GMPL implementation is simplified) + * Also units with same properties (technical and price) should be + scheduled together usually with near same performance values + * Assumed a simplified network topology, which is contractive, so + keeping Kirchhoff's laws is a necessary constraint too + * All solutions must be integer + + The LP relaxation is equivalent with the MIP problem due to the + model's matrix interesting property: it is Totally Unimodular + (proven in 2004 by author) and also a Network Matrix (2006, + presented at OTDK 2016, Szeged, Hungary) so: + * it is strictly polynomial if it is solved by most simplex algs + * all base solutions become integer if the RHS vector is integer + (it is in real life, so this is an acceptable assumption) + * The transposed matrix is NOT a Network Matrix in most cases! + + However, adding several other constraints easily turns the problem + to be NP-hard, which is also pinpointed and discussed in the Thesis. + + See more about electric power plants' scheduling in the + author's Thesis (in Hungarian): + http://www.cs.elte.hu/matdiploma/vuk.pdf + + It is possible to run with custom parameters, what is needed + to define is: + * TIME set (daylightsaving cases or other than hour intervals) + * PLANTS set (the 'Demand' is mandatory and usually negative) + * PRICE parameter (can be negative if energy is sold to a consumer) + * BOUND parameter (technical bounds) + * MAXGRAD parameter (technical bounds) + + Then generate a pretty-printed solution by typing: + glpsol --math powpl25h.mod +*/ + +set TIME, default { + '00:00', '01:00', '02:00', '03:00', '04:00', + '05:00', '06:00', '07:00', '08:00', '09:00', + '10:00', '11:00', '12:00', '13:00', '14:00', + '15:00', '16:00', '17:00', '18:00', '19:00', + '20:00', '21:00', '22:00', '23:00', '24:00' +}; +/* Time labels, assumed natural ordering. daylightsaving's bias + can be inserted p.ex. in Central Europe like: + ... '01:00', '02:00', '02:00b', '03:00', ... */ + +set TADJ := setof{(r, s) in TIME cross TIME: r < s}(r, s) diff + setof{(t, u, v) in TIME cross TIME cross TIME: t < u and u < v}(t, v); +/* Tricky adjacent time label generator because GMPL lacks order determination + of set elements (except intervals composed of equidistant numbers) */ + +set PLANTS, default {'Demand'}; +/* Demand is a promoted, mandatory one, usually filled + with negative MW values in data section */ + +set DIRECTION, default {'Up', 'Down'}; +/* All possible directions of gradients, do not touch */ + +param MAXINT, default 10000; +/* A "macro" for bounding absolute value of all used numbers + and used as default value */ + +param PRICE{PLANTS}, default MAXINT; +/* Should be specified in data section, self-explanatory. + can be negative if there are energy buyers */ + +param BOUND{(p, t, d) in PLANTS cross TIME cross DIRECTION}, + default if t = '00:00' then if d = 'Down' then BOUND[p, t, 'Up'] else 0 else + if p <> 'Demand' or d = 'Up' then sum{(u, v) in TADJ: v = t} BOUND[p, u, d] + else BOUND[p, t, 'Up']; +/* Obvious, technical bounds of each power plant unit (real or virtual like + 'Demand'). If some parts are not given in data section, calculated + from preceeding values. Also for time '00:00', its 'Down' values by + default are the same as denoted with 'Up' */ + +param MAXGRAD{(p, d) in PLANTS cross DIRECTION}, default MAXINT; +/* Usually nonnegative integer, might differ in distinct directions per unit + in the cited thesis, it is allowed to gradient bounds to depend on time, + but this is a simplified model */ + +var x{(t, p) in TIME cross PLANTS}, <= BOUND[p, t, 'Up'], >= BOUND[p, t, 'Down']; +/* The schedule, dimension is MW */ + +s.t. kirchhoff{t in TIME: t <> '00:00'}: sum{p in PLANTS} x[t, p] = 0; +/* Conservative property */ + +s.t. gradient{(p, t, u) in PLANTS cross TADJ}: + -MAXGRAD[p, 'Down'] <= x[t, p] - x[u, p] <= MAXGRAD[p, 'Up']; +/* Technical limitations, each unit usually cannot change performance + arbitrarily in a short time, so limited in both directions per time unit*/ + +minimize obj: sum{(t, p) in TIME cross PLANTS}(x[t, p] * PRICE[p]); +/* The objective is the cost of the schedule */ + +solve; + +/* Pretty print solution in table */ + +printf '+--------+'; +for{p in PLANTS}{ + printf '-% 6s-+', '------'; +} +printf '\n'; +printf '|%7s |', ' '; +for{p in PLANTS}{ + printf ' % 6s |', p; +} +printf '\n'; +printf '+--------+'; +for{p in PLANTS}{ + printf '-% 6s-+', '------'; +} +printf '\n'; +for{t in TIME}{ + printf '|%7s |', t; + for{p in PLANTS}{ + printf ' % 6s |', x[t, p].val; + } + printf '\n'; +} +printf '+--------+'; +for{p in PLANTS}{ + printf '-% 6s-+', '------'; +} +printf '\n'; + +data; + +set TIME := + '00:00', '01:00', '02:00', '02:00b', '03:00', '04:00', + '05:00', '06:00', '07:00', '08:00', '09:00', + '10:00', '11:00', '12:00', '13:00', '14:00', + '15:00', '16:00', '17:00', '18:00', '19:00', + '20:00', '21:00', '22:00', '23:00', '24:00'; + +/* + Generated random default values and names, the demand is the sum of + 2 sinewaves. + Also specified a treshold for nuclear plants from 15:00 till 19:00 + The sun is shining only morning and in the afternoon: 07:00-18:00, so + solar plant cannot produce electric energy after sunset. + + Only touch this section, or export it to a data file! +*/ + +set PLANTS 'Demand', 'Atom1', 'Atom2', 'Coal', 'Gas1', 'Gas2', 'Green', 'Oil', 'Solar', 'Dam'; + +param PRICE := + 'Demand' 0 + 'Atom1' 2 + 'Atom2' 2 + 'Coal' 15.6 + 'Gas1' 12 + 'Gas2' 11.5 + 'Green' 8.8 + 'Oil' 23.3 + 'Solar' 7.6 + 'Dam' 3; +/* price per MW */ + +param BOUND := + [*, *, 'Up'] (tr): 'Atom1' 'Atom2' 'Coal' 'Gas1' 'Gas2' 'Green' 'Oil' 'Solar' 'Dam' := + '00:00' 240 240 100 150 150 20 90 0 20 + '01:00' 240 240 155 192 208 35 230 0 20 + [*, *, 'Up'] (tr): 'Atom1' 'Atom2' := + '15:00' 200 200 + '19:00' 235 235 + [*, *, 'Up'] (tr): 'Solar' := + '07:00' 20 + '18:00' 0 + [*, *, 'Down'] (tr): 'Atom1' 'Atom2' 'Coal' 'Gas1' 'Gas2' 'Green' 'Oil' 'Solar' 'Dam' := + '01:00' 100 100 50 62 68 0 75 0 20 + [*, *, 'Up'] : '01:00' '02:00' '02:00b' '03:00' '04:00' '05:00' '06:00' '07:00' '08:00' := + 'Demand' -868 -851 -842 -837 -791 -887 -912 -1046 -1155 + [*, *, 'Up'] : '09:00' '10:00' '11:00' '12:00' '13:00' '14:00' '15:00' '16:00' := + 'Demand' -945 -873 -797 -990 -1241 -1134 -815 -782 + [*, *, 'Up'] : '17:00' '18:00' '19:00' '20:00' '21:00' '22:00' '23:00' '24:00' := + 'Demand' -772 -827 -931 -1105 -1215 -1249 -1183 -952; + +param MAXGRAD (tr) + : 'Atom1' 'Atom2' 'Coal' 'Gas1' 'Gas2' 'Green' 'Oil' 'Solar' 'Dam' := + 'Up' 30 30 35 89 95 5 56 2 4 + 'Down' 30 30 45 96 102 5 56 2 4; + +end; |