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356 lines
12 KiB
Plaintext
356 lines
12 KiB
Plaintext
# Mini Manitoba Hydro LP Model
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# Written for zimpl 3.0.0a
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# Licensed under the MIT license
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# Developed for fun using publicly available sources.
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# This software comes with no guarantees and no claims that it is fit for any purpose.
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# john howard, 1 Dec 2009
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# Inflows:
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# CR churchill river
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# LT lower nelson tribs
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# SL south indian lake
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# RR red river
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# WR winnipeg river
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#
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# Major Storages:
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# LW lake winnipeg
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# CL cedar lake
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#
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# Controlled Channels:
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# MF missi falls
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# NT notigi
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# EC east channel
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# WC west channel
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#
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# Generation Projects:
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# GR grand rapids
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# JP jenpeg
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# KE kelsey
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# LN lower nelson projects
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# variables and constraints are named the following way:
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# Type Subtype 2LetterName Kind Modifier
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# (v|k) [c] (..) (q|i|o|p|v|e|s|hk|ss|tw|mb|rc|os|ur) [ Start | End | Max | Min | Adj | Fact | Offset ]
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param kTS := 662;
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set sTime := { 1 .. kTS };
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# for 5 day averaging requires indices spaced 3 apart
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set sTime5 := { <t> in sTime with t < (kTS - 1) and t mod 3 == 0 };
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param kCMSd2KCFSdFact := 35.315 / 1000;
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# column 8 is month
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param vMONTH[ sTime ] := read "historical.csv" as "8n" skip 1;
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set sMonth := { 1 .. 12 };
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#########################
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### Inital Conditions ###
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# South Indian Lake
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param kSLeMin := 840.0;
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param kSLeMax := 847.9;
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param kSLssFactor := 283.7;
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param kSLvMax := (kSLeMax - kSLeMin) * kSLssFactor;
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# Grand Rapids Pond (Cedar Lake)
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param kGReMin := 830.0;
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param kGReMax := 841.5;
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param kGRssFactor := 330.9;
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param kGRvMax := (kGReMax - kGReMin) * kGRssFactor;
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# Lake Winnipeg
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param kLWeMin := 709.0;
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param kLWeMax := 714.75;
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param kLWssFactor := 3040.0;
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param kLWvMax := (kLWeMax - kLWeMin) * kLWssFactor;
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# Kelsey Pond
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param kKEeMin := 0.0;
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param kKEeMax := 0.1; # as modelled
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param kKEssFactor := 902.0;
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param kKEvMax := (kKEeMax - kKEeMin) * kKEssFactor;
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# Storage at aggregate Lower Nelson Projects
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param kLNeMin := 0.0;
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param kLNeMax := 3.0; # as modelled
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param kLNssFactor := 200.0;
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param kLNvMax := (kLNeMax - kLNeMin) * kLNssFactor;
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param kLNvStart := kLNvMax / 2;
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####################################################################
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### Churchill River through South Indian Lake and Notigi Control ###
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param kNToMin := 15; # control discharge limits (KCFS)
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param kNToMax := 35;
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param kMFoMin := 0; # control discharge limits (KCFS)
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param kMFoMax := 10; # as modelled
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param kMFoFact := 0.001; # adjustments (calibrated for 92-94 peroid)
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var vMFo[ sTime ] >= 1 <= kMFoMax; # Missi Falls acts as spill
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var vNTo[ sTime ] >= kNToMin <= kNToMax;
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var vSLv[ sTime ] >= 0 <= kSLvMax;
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# 2nd column for Churchill River
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param vCRq[ sTime ] := read "historical.csv" as "2n" skip 1;
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param kSLiAdj := 2.3; # adjustments (calibrated for 92-94 peroid)
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param kSLvStart := kSLvMax / 2;
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# refill
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subto kcSLvEnd: vSLv[ kTS ] >= kSLvStart;
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# change-in-storage + outflow == inflow
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subto vcSLmb:
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forall <t> in sTime do
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if ( t == 1 ) then vSLv[ 1 ] - kSLvStart + vMFo[ 1 ] + vNTo[ 1 ]
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else vSLv[ t ] - vSLv[ t - 1 ] + vMFo[ t ] + vNTo[ t ]
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end
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== kCMSd2KCFSdFact * vCRq[ t ] + kSLiAdj;
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# Notigi within-week outflow shaping
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param kNTosFact := 0; # as modelled
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subto vcNTosA: forall<t> in sTime5 do vNTo[ t - 2 ] >= vNTo[ t ] - kNTosFact;
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subto vcNTosB: forall<t> in sTime5 do vNTo[ t - 2 ] <= vNTo[ t ] + kNTosFact;
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subto vcNTosC: forall<t> in sTime5 do vNTo[ t - 1 ] >= vNTo[ t ] - kNTosFact;
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subto vcNTosD: forall<t> in sTime5 do vNTo[ t - 1 ] <= vNTo[ t ] + kNTosFact;
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subto vcNTosE: forall<t> in sTime5 do vNTo[ t + 1 ] >= vNTo[ t ] - kNTosFact;
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subto vcNTosF: forall<t> in sTime5 do vNTo[ t + 1 ] <= vNTo[ t ] + kNTosFact;
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subto vcNTosG: forall<t> in sTime5 do vNTo[ t + 2 ] >= vNTo[ t ] - kNTosFact;
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subto vcNTosH: forall<t> in sTime5 do vNTo[ t + 2 ] <= vNTo[ t ] + kNTosFact;
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###########################################################
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### Sask River into Cedar Lake and through Grand Rapids ###
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param kGRoMin := 5; # plant/control discharge limits (KCFS)
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param kGRoMax := 53;
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param kGRsMin := 0;
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param kGRsMax := 40;
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param kGRpMax := 472; # generation limits (MW)
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var vGRv[ sTime ] >= 0 <= kGRvMax;
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var vGRs[ sTime ] >= kGRsMin <= kGRsMax;
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var vGRo[ sTime ] >= kGRoMin <= kGRoMax;
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var vGRp[ sTime ] >= 0 <= kGRpMax;
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# 1st column for Sask River
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param vSKRq[ sTime ] := read "historical.csv" as "1n" skip 1;
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param kGRhk := 9.2; # plant HK factors (MW/KCFS)
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param kGRiAdj := -0.6; # adjustments (calibrated for 92-94 peroid)
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param kGRvStart := kGRvMax / 2;
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# refill
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subto kcGRvEnd: vGRv[ kTS ] >= kGRvStart;
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# change-in-storage + outflow == inflow
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subto vcGRmb:
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forall <t> in sTime do
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if ( t == 1 ) then vGRv[ 1 ] - kGRvStart + vGRo[ 1 ] + vGRs[ 1 ]
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else vGRv[ t ] - vGRv[ t - 1 ] + vGRo[ t ] + vGRs[ t ]
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end
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== kCMSd2KCFSdFact * vSKRq[ t ] + kGRiAdj;
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# compute power from discharge
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subto vcGRp:
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forall <t> in sTime do
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vGRp[ t ] == kGRhk * vGRo[ t ];
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# Grand Rapids within-week outflow shaping
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param kGRosFact := 10; # as modelled
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subto vcGRosA: forall<t> in sTime5 do vGRo[ t - 2 ] >= vGRo[ t ] - kGRosFact;
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subto vcGRosB: forall<t> in sTime5 do vGRo[ t - 2 ] <= vGRo[ t ] + kGRosFact;
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subto vcGRosC: forall<t> in sTime5 do vGRo[ t - 1 ] >= vGRo[ t ] - kGRosFact;
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subto vcGRosD: forall<t> in sTime5 do vGRo[ t - 1 ] <= vGRo[ t ] + kGRosFact;
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subto vcGRosE: forall<t> in sTime5 do vGRo[ t + 1 ] >= vGRo[ t ] - kGRosFact;
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subto vcGRosF: forall<t> in sTime5 do vGRo[ t + 1 ] <= vGRo[ t ] + kGRosFact;
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subto vcGRosG: forall<t> in sTime5 do vGRo[ t + 2 ] >= vGRo[ t ] - kGRosFact;
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subto vcGRosH: forall<t> in sTime5 do vGRo[ t + 2 ] <= vGRo[ t ] + kGRosFact;
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##############################################################################
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### Lake Winnipeg Storage as operated by JENPEG and effect of Each Channel ###
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param kJPoMin := 0; # plant/control discharge limits (KCFS)
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param kJPoMax := 93;
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param kJPsMin := 0; # plant/control discharge limits (KCFS)
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param kJPsMax := 9e9; # as modelled
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param kJPpMax := 97; # generation limits (MW)
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var vLWv[ sTime ] >= 0 <= kLWvMax;
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var vECo[ sTime ] >= 0; # upper bound determined by rating curve
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var vJPo[ sTime ] >= kJPoMin <= kJPoMax;
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var vJPs[ sTime ] >= kJPsMin <= kJPsMax;
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var vJPp[ sTime ] >= 0 <= kJPpMax;
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# 3rd column for Red River and 4th column for Winnipeg River
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param vRRq[ sTime ] := read "historical.csv" as "3n" skip 1;
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param vWRq[ sTime ] := read "historical.csv" as "4n" skip 1;
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param kLWiAdj := 11.7; # adjustments (calibrated for 92-94 peroid)
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param kLWvStart := kLWvMax / 2;
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param kJPhk := 1; # plant HK factors (MW/KCFS)
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param kJPoNovMaxFact := 0; # curves
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param kJPoNovMaxOffset := 0;
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param kJPtwFact := 0; # TODO
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param kJPtwOffset := 0;
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# refill
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subto kcLWvEnd: vLWv[ kTS ] >= kLWvStart;
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# change-in-storage + outflow == inflow
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subto vcLWmb:
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forall <t> in sTime do
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if ( t == 1 ) then vLWv[ 1 ] - kLWvStart + vJPo[ 1 ] + vJPs[ 1 ] + vECo[ 1 ]
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else vLWv[ t ] - vLWv[ t - 1 ] + vJPo[ t ] + vJPs[ t ] + vECo[ t ]
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end
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== kCMSd2KCFSdFact * vRRq[ t ] + kCMSd2KCFSdFact * vWRq[ t ] + vGRo[ t ] + vGRs[ t ] + kLWiAdj;
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# compute power from discharge
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subto vcJPp:
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forall <t> in sTime do
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vJPp[ t ] == kJPhk * vJPo[ t ];
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# West Channel Max Discharge
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param vWCoMax[ sMonth ] := <1> 8.6440678, <2> 7.79661017, <3> 7.11864407, <4> 6.61016949, <11> 10.3389831, <12> 9.3220339 default 12.5423729;
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subto vJPoA:
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forall <t,m> in sTime cross sMonth with m == vMONTH[ t ] do
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vJPo[ t ] <= vLWv[ t ] * vWCoMax[ m ] / kLWssFactor;
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# East Channel Discharge
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subto vcECo:
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forall <t> in sTime do
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vECo[ t ] == vLWv[ t ] * 4.67463938 / kLWssFactor; # convert q/ft (from historical 92-94 period data) to q/v
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# Jenpeg within-week outflow shaping
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param kJPosFact := 2; # as modelled
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subto vcJPosA: forall<t> in sTime5 do vJPo[ t - 2 ] >= vJPo[ t ] - kJPosFact;
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subto vcJPosB: forall<t> in sTime5 do vJPo[ t - 2 ] <= vJPo[ t ] + kJPosFact;
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subto vcJPosC: forall<t> in sTime5 do vJPo[ t - 1 ] >= vJPo[ t ] - kJPosFact;
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subto vcJPosD: forall<t> in sTime5 do vJPo[ t - 1 ] <= vJPo[ t ] + kJPosFact;
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subto vcJPosE: forall<t> in sTime5 do vJPo[ t + 1 ] >= vJPo[ t ] - kJPosFact;
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subto vcJPosF: forall<t> in sTime5 do vJPo[ t + 1 ] <= vJPo[ t ] + kJPosFact;
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subto vcJPosG: forall<t> in sTime5 do vJPo[ t + 2 ] >= vJPo[ t ] - kJPosFact;
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subto vcJPosH: forall<t> in sTime5 do vJPo[ t + 2 ] <= vJPo[ t ] + kJPosFact;
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# Jenpeg intra-week shaping
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subto vcJPosI: forall<t> in sTime5 without { kTS - 2 } do vJPo[ t + 3 ] >= vJPo[ t ] - kJPosFact * 2;
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subto vcJPosJ: forall<t> in sTime5 without { kTS - 2 } do vJPo[ t + 3 ] <= vJPo[ t ] + kJPosFact * 2;
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#########################
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### Kelsey Operations ###
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param kKEoMin := 0; # plant/control discharge limits (KCFS)
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param kKEoMax := 55.4;
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param kKEsMin := 0; # as modelled
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param kKEsMax := 9e9; # as modelled
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param kKEpMax := 211; # generation limits (MW)
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var vKEv[ sTime ] >= 0 <= kKEvMax;
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var vKEs[ sTime ] >= kKEsMin <= kKEsMax;
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var vKEo[ sTime ] >= kKEoMin <= kKEoMax;
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var vKEp[ sTime ] >= 0 <= kKEpMax;
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# 5th column for Gunisao River
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param vGUNq[ sTime ] := read "historical.csv" as "5n" skip 1;
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param kKEhk := 3.8; # plant HK factors (MW/KCFS)
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param kKEiFact := 1; # adjustments (calibrated for 92-94 peroid)
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param kKEtwFact := 0; # curves
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param kKEtwOffset := 0;
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param kKEiAdj := 3; # adjustments (calibrated for 92-94 peroid)
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param kKEvStart := kKEvMax / 2;
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# refill
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subto kcKEvEnd: vKEv[ kTS ] >= kKEvStart;
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# change-in-storage + outflow == inflow
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subto vcKEmb:
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forall <t> in sTime do
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if ( t == 1 ) then vKEv[ 1 ] - kKEvStart + vKEo[ 1 ] + vKEs[ 1 ]
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else vKEv[ t ] - vKEv[ t - 1 ] + vKEo[ t ] + vKEs[ t ]
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end
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== kKEiFact * kCMSd2KCFSdFact * vGUNq[ t ] + kKEiAdj + vECo[ t ] + vJPo[ t ] + vJPs[ t ];
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# compute power from discharge
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subto vcKEp:
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forall <t> in sTime do
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vKEp[ t ] == kKEhk * vKEo[ t ];
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#########################################################################
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### Lower Nelson Operations with inflows from Upper Nelson and Notigi ###
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param kLNoMin := 0; # plant/control discharge limits (KCFS)
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param kLNoMax := 165.7;
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param kLNsMin := 0; # plant/control discharge limits (KCFS)
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param kLNsMax := 150; # kpill limits (KCFS)
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param kLNpMax := 3583; # generation limits (MW)
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var vLNv[ sTime ] >= 0 <= kLNvMax;
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var vLNs[ sTime ] >= kLNsMin <= kLNsMax;
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var vLNo[ sTime ] >= kLNoMin <= kLNoMax;
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var vLNp[ sTime ] >= 0 <= kLNpMax;
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# 6th column for Lower Nelson Tribs
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param vLTq[ sTime ] := read "historical.csv" as "6n" skip 1;
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param kLNhk := 21.7; # plant HK factors (MW/KCFS)
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param kLNiAdj := 5; # adjustments (calibrated for 92-94 peroid)
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param kLTiFact := 3; # adjustments (calibrated for 92-94 peroid)
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# refill
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subto kcLNvEnd: vLNv[ kTS ] >= kLNvStart;
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# Routed discharges from Notigi to Lower Nelson
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var vNTor[ sTime ] >= 0;
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set sUIR := { 1, 2, 3, 4 };
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param kNTur[ sUIR ] := <1> 0.0, <2> 0.05, <3> 0.80, <4> 0.15; # as modelled
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subto vcNTorA:
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forall <t> in sTime without { 1, 2, 3 } do
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vNTor[ t ] == vNTo[ t - 0 ] * kNTur[ 1 ] + vNTo[ t - 1 ] * kNTur[ 2 ] + vNTo[ t - 2 ] * kNTur[ 3 ] + vNTo[ t - 3 ] * kNTur[ 4 ];
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# change-in-storage + outflow == inflow
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subto vcLNmb:
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forall <t> in sTime do
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if ( t == 1 ) then vLNv[ 1 ] - kLNvStart + vLNo[ 1 ] + vLNs[ 1 ]
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else vLNv[ t ] - vLNv[ t - 1 ] + vLNo[ t ] + vLNs[ t ]
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end
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== kLTiFact * kCMSd2KCFSdFact * vLTq[ t ] + kLNiAdj + vNTor[ t ] + vKEo[ t ] + vKEs[ t ];
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# compute power from discharge
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subto vcLNp:
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forall <t> in sTime do
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vLNp[ t ] == kLNhk * vLNo[ t ];
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# Lowern Nelson within-week outflow shaping
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param kLNosFact := 10; # as modelled
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subto vcLNosA: forall<t> in sTime5 do vLNo[ t - 2 ] >= vLNo[ t ] - kLNosFact;
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subto vcLNosB: forall<t> in sTime5 do vLNo[ t - 2 ] <= vLNo[ t ] + kLNosFact;
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subto vcLNosC: forall<t> in sTime5 do vLNo[ t - 1 ] >= vLNo[ t ] - kLNosFact;
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subto vcLNosD: forall<t> in sTime5 do vLNo[ t - 1 ] <= vLNo[ t ] + kLNosFact;
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subto vcLNosE: forall<t> in sTime5 do vLNo[ t + 1 ] >= vLNo[ t ] - kLNosFact;
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subto vcLNosF: forall<t> in sTime5 do vLNo[ t + 1 ] <= vLNo[ t ] + kLNosFact;
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subto vcLNosG: forall<t> in sTime5 do vLNo[ t + 2 ] >= vLNo[ t ] - kLNosFact;
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subto vcLNosH: forall<t> in sTime5 do vLNo[ t + 2 ] <= vLNo[ t ] + kLNosFact;
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# Lowern Nelson inter-week outflow shaping
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subto vcLNosI: forall<t> in sTime5 without { kTS - 2 } do vLNo[ t + 3 ] >= vLNo[ t ] - kLNosFact * 2;
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subto vcLNosJ: forall<t> in sTime5 without { kTS - 2 } do vLNo[ t + 3 ] <= vLNo[ t ] + kLNosFact * 2;
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########################################################
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# 7th column for Load
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param vLOAD[ sTime ] := read "historical.csv" as "7n" skip 1;
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var sLOAD >= 0;
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subto vcLOAD:
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forall <t> in sTime do
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vGRp[ t ] + vJPp[ t ] + vKEp[ t ] + vLNp[ t ] >= vLOAD[ t ];
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minimize kSPILL:
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sum <t> in sTime do vMFo[ t ] +
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sum <t> in sTime do vGRs[ t ] +
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sum <t> in sTime do vJPs[ t ] +
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sum <t> in sTime do vKEs[ t ] +
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sum <t> in sTime do vLNs[ t ];
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