MANUEL DUTILISATION

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MANUEL DUTILISATION DU MODELE A
LONG-TERME Purdue University Edition 7 February
2001 Pour lUtilisation des Pays Membres de la
CEDEAO http//fairway.ecn.purdue.edu/iies/ppdg
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MODELISATION DE LA DEMANDE
(U.M. Ed.7 p.46) Six heures ont été modélisées
pour chaque type de jour une heure de demande
hors-pointe, (heure 9), trois heures de demande
de pointe, heures 19, 20 et 21, deux heures de
demande moyenne, une heure de demande moyenne
nocturne (avnt), sur 8 heures nocturnes et une
heure de de demande moyennne dans la journée
(avdy), représentant une moyenne de 12 heures de
la journée, en dehors des heures de pointe.
Ensemble ces éléments forment le facteur de
variation de la demande dans le modèle, le
paramètre Dyr(ty,ts,td,th,z) (Section 2 de
lAppendice VII), qui est la demande en MW du
pays z pour lannée ty durant la saison ts (ts
hiver, été) et le jour td (td pointe,
hors-point, moyenne) à lheure th (th hr9,
avnt, hr19, hr20, hr21, et avdy) Sur la base
des des hypothèses de croissance annuelles, et
des données de demande de lannée de base
présentées dans le tableau Base(ts,td,th,z), nous
avons   Dyr(ty,ts,td,th,z)
Base(ts,td,th,z)dgr(z,ty)
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Sixhr.inc Input File (U.M. Ed.7,
P.162) Parameter Mday(td) number of days in a
year /offpeak 104 peak 52 average 209
/ Parameter Mseason(ts) Multiplier of seasons
per year / summer 0.750 9/12 winter 0.250
3/12 / set th Hours index / hr9
1 avnt 8 hr19 1 hr20
1 hr21 1 avdy 12 /
Parameter Mtod(th) Assigns weight to each type
of hour in a day (fraction) / hr9
1 avnt 8 hr19
1 hr20 1 hr21
1 avdy 12
/
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Sixhr.inc Input File (U.M. Ed.7,
P.162) Parameter PeakD(z) Parameter
Base(ts,td,th,z) Sets wk / week1
week52 / dy / sun, mon, tues, wed, thur,
fri, sat / hr / hour1 hour24
/ parameter upeak(z) annual peak demand of the
base year / gui 251.3 mal 78.6 gha
1075.0 gam 15.0 tog 109.0 lib 7 bfa 80.1
ben 73.0
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Sixhr.inc Input File (U.M. Ed.7,
P.163) Table uhour(z,hr,dy) thur
tues fri mon wed sun sat
mal.hour14 72.44 72.44 66.71 71.7 73.92
49.52 50.66 mal.hour13 71.5 71.5 65.84
70.77 72.96 47.59 48.68 mal.hour12 72.22
72.22 66.51 71.49 73.7 46.3 47.37
mal.hour11 71.38 71.38 65.74 70.66 72.84
45.66 46.71 mal.hour10 70.43 70.43 64.86
69.71 71.87 45.02 46.05 sle.hour24 51.11
55.4 51.22 52.5 54.12 56.45 59.71
sle.hour23 57.17 57.4 61.54 56.9 59.47
57.94 62.54 sle.hour22 58.74 60.3 62.62
63.1 62.36 58.85 66.16 sle.hour21 59.71
62.5 63.07 64.4 63.61 59.04 67.81
sle.hour20 59.37 60.9 60.83 32.2 61.28
53.09 62.76 sle.hour19 58.61 51.9 55.23
30.6 56.73 50.23 56.38 sle.hour18 46.35
39.1 48.22 41.0 42.37 49.88 51.16
sle.hour17 43.6 36.5 43.8 42.9 43.81
49.37 44.01 sle.hour16 39.61 36.3 38.65
4.0 41.68 51.2 46.88 sle.hour15 40.92
35.6 32.42 40.4 40.13 47.8 49.33
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Modélisation de lOffre (U.M. Ed.7,
p.48) Différentes sources dénergie peuvent être
utilisées pour satisfaire la demande au niveau
dune région donnée (a) centrales thermiques
existantes, (b) nouvelles centrales thermiques,
(c) centrales hydroélectriques existantes, (d)
nouvelles centrales hydro, (e) pumped storage,
(f) importation nette (importation moins
exportation), (g) coût de la demande non
satisfaite (unserved energy). Les sites
(centrales) de production sont identifiés pour
chaque région. Toutes les centrales dune même
localité utilisent les lignes de transport.
Variables de production, en MW, par centrale  
PG(ty,ts,td,th,z,i) production de la centrale
thermique existante i PGNT(ty,ts,td,th,z,ni)
production des nouvelles turbines à gaz de la
centrale ni PGNSC(ty,ts,td,th,z,ni)
production de petites unités à charbon de la
centrale ni PGNCC(ty,ts,td,th,z,ni)
production des unités à cycle combiné de la
centrale ni PGNLC(ty,ts,td,th,z,ni)
production des nouvelles grandes unités à charbon
de ni H(ty,ts,td,th,z,ih) production des
centrales hydroélectriques existantes ih
Hnew(ty,ts,td,th,z,nh) production des nouvelles
centrales hydroélectriques nh
PGPSO(ty,ts,td,th,z) - PUPSO(ty,ts,td,th,z)
production nette des centrales de
pompage hydro existantes etc etc
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IMPORTATION NETTE (U.M. Ed.7, p.54) Les flux
dénergie (MW) du pays z à zp par les lignes de
transport existantes sont donnés les variables
PF(ty,ts,td,th,z,zp) tandis que les sur les
nouvelles lignes sont donnés par les variables
PFnew(ty,ts,td,th,z,zp). Utilisant cette
notation, et en tenant compte des pertes au cours
du transport qui reduisent la quantité dénergie
reçu par z, les importations nettes du pays pour
une heure donnée seraient de  
Importation à partir des lignes
existantes exportations via lignes existantes
? zpPF(ty,ts,td,th,zp,z)(1-PFOloss(zp,z)PF(ty,t
s,td,th,z,zp) Importations via
nouvelles lignes ? zpPFnew(ty,ts,td,th,zp,z)
(1-PFOloss(zp,z) exportations
via nouvelles lignes PFnew(ty,ts,td,th,z,
zp)
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Demande non-satisfaite U.M. Ed.7, p.55
(Production délectricité à titre
privé) La demande non-satisfaite par heure dans
chaque pays peut être modéliser, en lincorporant
dans le terme de loffre de léquation
demande/offre. La variable UE(ty,ts,td,th,z)
donne la quantité de MW de cette demande
non-satisfaite. Le scalaire UEcost, Section 1 de
lAnnexe II, représente le coût/MWh de la
demande non satisfaite. Sa valeur nominale est
de 140/MWh, mais elle peut être fixée à la
valeur de choix de lutilisateur.
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• Equation de la Capacité Totale (Load Balance) du
  Système U.M. Ed.7, p.56
• Léquation de la capapcité totale -
  LEquation de la Demande dans
• le modèle exige que pour chaque pays z, la
  production totale dénergie
• (MW) sur toute la période de plannification
  à partir des
• ? centrales thermiques existantes -
  PG(ty,ts,td,th,z,i)
• ? nouvelles centrales thermiques -
  PGNT(ty,ts,td,th,z,ni),
• PGNCC(ty,ts,td,th,z,ni), PGNSC(ty,ts,td,th,z,ni),
  
• PGNLC(ty,ts,td,th,z,ni)
• ? importations nettes via les Lignes de
  transmission existantes
• PF(ty,ts,td,th,zp,z)(1-PFOloss(zp,z) -
  PF(ty,ts,td,th,z,zp)
• ? importations nettes via les nouvelles
  lignes de transmission -
• PFnew(ty,ts,td,th,zp,z)(1-PFNloss(zp,z)) -
  PFnew(ty,ts,td,th,z,zp)

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• Equation de la Capacité Totale (suite)
• ? centrales hydro existantes -
  H(ty,ts,td,th,z,ih)
• nouvelles centrales hydro - Hnew(ty,ts,td,th,z,n
  h)
• centrale de pompage existante -
  PGPSO(ty,ts,td,th,z)
• - PUPSO(ty,ts,td,th,z)
• nouvelles centrale de pompage -
  PGPSN(ty,ts,td,th,z,phn)
• - PUPSN(ty,ts,td,th,z,phn)
• plus la demande dénergie non satisfaite
• UE(ty,ts,td,th,z)
• Doit être égale à
• Yper(ty)DLC(z)Dyr(ty,ts,td,th,z)
  LM(z,th)
• énergie dumped DumpEn(ty,ts,td,th,z)

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Old Thermals Expansion as Fixed
Multiples U.M. Ed.7, p.61

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Old Thermals Expansion as a Continuous
Variable U.M. Ed.7 P.62
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New Plant Initial Construction, with Expansion
as Fixed Multiples of a Given Size, U.M. Ed.7,
p.76 eg PGNCCexp(tyb,z,ni)0,1,2,3
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New Plant Initial Construction, with Continuous
Expansion U.M. Ed.7, p.76 eg
PGNCCexp(ty,z,ni)? 0
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Critical Capacity Constraint
Parameters U.M. Ed.7, p.77 additional
generating units can be added to the new sites
at any time, as long as the capacity of the
plants to add units is not exceeded. Each new
plant at a site, then, has three
parameters critical to the capacity
constraints ? PGNCCinit(z,ni) and
PGNLCinit(z,ni), the initial plant
capacity installed when the new site is first
constructed. ? NCCexpstep(z,ni) and
NLCexpstep(z,ni), the MW size of units
added to a plant, once one is built at site
ni. ? PGNCCmax(z,ni) and PGNLCmax(z,ni), the
upper limit on the total MW
capacity, which can be added by additional units
to the plant.
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Transmission Capacity Constraint U.M. Ed.7,
p.98 The flow variables for old and new lines -
PF(ty,ts,td,th,z,zp) and PFnew(ty,ts,td,th,z,zp)
- power flows from country z to country zp in a
given time slice give the total flow between
two countries consisting of the sum of all firm
and non-firm power trades. Thus, the
transmission capacity flow constraints for old
lines involve only PF(ty,ts,td,th,z,zp) and the
current capacity of the old lines connecting z
to zp e.g., for old lines (ignoring decay and
forced outages)   PF(ty,ts,td,th,z,zp)?
Pfinit(z,zp) ?tye1,tyPFOexp(tye,z,zp) a
similar equation holds for new lines.
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Firm Non-Firm Power in the Load Balance
Constraints U.M. Ed.7, p.99 The hourly load
balances which require that supplies must equal
demands, involve only domestic generation, power
imports, power exports, and demand. Ignoring
both unserved and dumped energy the load balance
equation for the time slice (ty,ts,td,th) is
simply Sum of all Domestic Generation in
(ty,ts,td,th) ?zpPF(ty,ts,td,th,zp,z)(1-linelo
ss) Demand in (ty,ts,td,th,z,zp)
?zpPF(ty,ts,td,th,z,zp)   No distinction is made
between firm and non-firm power in meeting
demand, nor should there be both can
interchangeably satisfy the load balance
equation.
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• Reliability Constraints, U.M. Ed.7, p.99
• The reserve capacity obligation of each country
  can be
• expressed as
• Thermal Capacity Hydro Capacity 
• 1.19 1.10
• Peak Demand Firm Power Purchases Firm Power
  Sales

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• Objective Function Variable Operating Costs
• U.M. Ed.7, p101
• Thermal units In a given year the costs for
  old(existing)
• thermals (PG), new turbines (NT), new combined
  cycle (CC),
• new small coal (SC), and new large coal (LC) are
  of the generic
• form
• Power Generation Heat Rate Fuel
  Cost Fuel Escalation
• ? ts,td,th,z ? iPG(ty,ts,td,th,z,i) HR(z,i)
  fp(z,i) Fpesc(z,i)n(ty)-1
• Variable OM Costs
• OM(z,i)
• One each for each unit type, with appropriate
  modifications
• in notation made for each since generation is
  MWh, the costs
• are /MWh.

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• Objective Function Variable Operating Costs for
  NT
• U.M. Ed.7, p103
• . the full equation reflecting fuel and variable
  costs for
• combustion turbine (NT) in a given year would be
• ? ts,td,th,z,ni (Mseason(ts))(Mday(td))(Mtod(th))
  
• PGNT(ty,ts,td,th,z,ni)HRNT(z,ni)(fpNT(z,ni))
• (FpescNT(z)) n(ty)-1 OMT(z,ni)
• Similar terms appear in the objective function
  for old
• Plants and other new technologies.

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• Objective Function Variable Operating Costs for
  Hydropower
• U.M. Ed.7, p103
• The only operating costs for hydropower are the
  cost of water
• wcost(z,ty), now set at 0.50/MWh, which can be
  altered by
• changing scalar wcost in the appendix, and
  variable cost for old
• VarOMoh(z,ih) and new VarOMnh(z,nh) hydro plants.
  (Fixed
• OM costs for new plants are annualized, and will
  be included in
• the capital cost of the plants.) Hence, the
  operating costs for new
• and old hydros in year ty are simply
• ? ts,td,th,z,ih,nh H(ty,ts,td,th,z,ih)(Mseason(ts
  ))(Mday(td))
• wcost(z,ty) VarOMoh(z,ih)
• Hnew(ty,ts,td,th,z,ih)(Mseason(ts))(Mday
  (td))
• wcost(z,ty) VarOMnh(z,nh)
•  

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SUNK CAPITAL COSTS U.M. Ed.7, p.105 .
since the model is an economic decision model,
the sunk costs involved in recovering the
capital investment and fixed OM costs of
existing units is not included in the model,
since they should have no impact on the optimal
expansion and operation plan. Their omission
does, however, create a problem in comparing the
average cost/MW that arises from the model with
the average costs/MWh that users might have
become accustomed to dealing with in everyday
use. The costs/MWh reported here for a
representative year, particularly during the
early part of the horizon, will be significantly
lower than standard costs, since only the
out-of-pocket costs of old units are included,
not their capital costs.
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OLD THERMAL CAPITAL COSTS U.M. Ed.7,
p.105/6 For new construction expansion of old
sites, both capital fixed operating costs are
involved, since they both represent real
out-of-pocket avoidable costs to decision
makers. Eg The annualized cost of expanding
existing thermal facilities (which must be
charged to the objective function each
year Subsequent to the expansion date)
is PGOcapcost(ty) ? z,i ? tyb1-tyPGOexp(tyb,
z,i)PGOexpstep(z,i)Oexpcost(z,i)crfi(z,i) (1d
isc)ty-1
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NEW THERMAL CAPITAL COSTS U.M. Ed.7,
p.107/8 The generic equation for capital expenses
in year ty for a given technology at site ni in
country z is PGNcapcost(ty) ?
ty1,tyNFcost(z,ni)Y(tya,z,ni)
PGNexp(tya,z,ni)Nexstep(z,ni)
Nexpcost(z,ni)(crfn(z,ni)) (1 disc)ty-1
? tya1,tyPGNinit(z,ni)Y(tya,z,ni)
PGNexp(tya,z,ni) Nexpstep(z,ni)FIXOM(z,ni)
(1 disc)ty-1 NFcost(z,ni) Fixed cost of
initial plant at site ni. Y(tya,z,ni)
Binary decision variable which is 1 if a new
plant is built at site ni is tya, otherwise it
is 0. PGNexp(tya,z,ni) Continuous or integer
variable which gives the amount of site
expansion in tya.