USER MANUAL

1
USER MANUAL FOR THE LONG-TERM MODEL Purdue
University Edition 7 February 2001 As Supplied
to ECOWAS onWeb-Site at http//fairway.ecn.pur
due.edu/iies/ppdg
2
MODELING DEMAND (U.M. Ed.7
p.46) Within each day type, six hours are
modeled one off-peak hour, taken to be hour 9,
three peak hours, hours 19, 20 and 21, two
average hours, one average night hour (avnt),
representing 8 night hours and one average day
hour (avdy), representing 12 average day hours,
peaks excluded. All this comes together in
creating the demand driver for the model,
parameter Dyr(ty,ts,td,th,z) (Section 2 of
Appendix VII), which is country zs MW demand in
year ty in season ts (ts winter, summer) in
day td (td peak, off-peak, average) in hour th
(th hr9, avnt, hr19, hr20, hr21, and avdy)
Combining the yearly growth assumptions with the
base year day type demand data found in Table
Base(ts,td,th,z), we have   Dyr(ty,ts,td,th,z)
Base(ts,td,th,z)dgr(z,ty)
3
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
/
4
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
5
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
6
The Supply Side (U.M. Ed.7, p.48) The
demand in a given region can be met from a
variety of energy sources (a) existing thermal
sites, (b) new thermal sites, (c) existing hydro
sites, (d) new hydro sites, (e) pumped storage,
(f) net imports (imports less exports), (g)
paying an unserved energy cost. Within each
region, generating sites are identified which
contain generating plants. For purposes of
dispatch, all plants at a site are collectively
dispatched. Generation variables, in MW, for
the sites are   PG(ty,ts,td,th,z,i)
generation from existing thermal site i
PGNT(ty,ts,td,th,z,ni) generation from new gas
turbines at site ni PGNSC(ty,ts,td,th,z,ni)
generation from new small coal plants at site ni
PGNCC(ty,ts,td,th,z,ni) generation from new
combined cycle plants at site ni
PGNLC(ty,ts,td,th,z,ni) generation from new
large coal plants at site ni
H(ty,ts,td,th,z,ih) generation from existing
hydro site ih Hnew(ty,ts,td,th,z,nh)
generation from new hydro site nh
PGPSO(ty,ts,td,th,z) - PUPSO(ty,ts,td,th,z) net
generation from old pumped
hydro sites etc etc
7
NET IMPORTS (U.M. Ed.7,
p.54) MW power flows from country z to zp on old
lines are given by the variables
PF(ty,ts,td,th,z,zp) while flows on the new
lines are given by the variables
PFnew(ty,ts,td,th,z,zp). Using this notation,
and accounting for line losses reducing the
amount of power arriving at country z, net
imports for country z in a given hour would
be   Imports
arriving on old lines exports sent on old
lines ? zpPF(ty,ts,td,th,zp,z)(1-PFOloss(zp,z)P
F(ty,ts,td,th,z,zp)
Imports arriving on new lines
? zpPFnew(ty,ts,td,th,zp,z)(1-PFOloss(zp,z)
exports sent on new lines
PFnew(ty,ts,td,th,z,zp)
8
UNSERVED ENERGY U.M. Ed.7, p.55
(Distributed Generation) Each country
can choose not to meet hourly demand by allowing
unserved energy to enter the supply side of the
demand/supply balance equation. The variable
UE(ty,ts,td,th,z) gives the MW value of the
amount. The scalar UEcost, Section 1 of
Appendix II, sets the cost/MWh of unserved
energy. The nominal value is 140/MWh, but it
can be set at whatever value users want to
adopt.
9

• Full System Load Balance Equation U.M.
  Ed.7, p.56
• The load balance equation - Equation
  Demand in the
• model - requires that for all time periods
  for each country z,
• the sum of MW generation from
• ? existing thermal sites - PG(ty,ts,td,th,z,i)
• ? new thermal sites - 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)
• ? net firm and non-firm imports over existing
• transmission lines
• PF(ty,ts,td,th,zp,z)(1-PFOloss(zp,z) -
  PF(ty,ts,td,th,z,zp)
• ? net firm and non-firm imports over new
  transmission lines -
• PFnew(ty,ts,td,th,zp,z)(1-PFNloss(zp,z)) -
  PFnew(ty,ts,td,th,z,zp)

10

• Full System Load Balance Equation (Continued)
• ? existing hydro sites - H(ty,ts,td,th,z,ih)
• new hydro sites - Hnew(ty,ts,td,th,z,nh)
• old pumped storage - PGPSO(ty,ts,td,th,z)
• - PUPSO(ty,ts,td,th,z)
• new pumped storage - PGPSN(ty,ts,td,th,z,phn)
• - PUPSN(ty,ts,td,th,z,phn)
• plus unserved energy
• UE(ty,ts,td,th,z)
• Must equal
• Yper(ty)DLC(z)Dyr(ty,ts,td,th,z)
  LM(z,th)
• dumped energy DumpEn(ty,ts,td,th,z)

11
Old Thermals Expansion as Fixed
Multiples U.M. Ed.7, p.61

12
Old Thermals Expansion as a Continuous
Variable U.M. Ed.7 P.62
13
New Plant Initial Construction, with Expansion
as Fixed Multiples of a Given Size, U.M. Ed.7,
p.76 e.g., PGNCCexp(tyb,z,ni)0,1,2,3
14
New Plant Initial Construction, with Continuous
Expansion U.M. Ed.7, p.76 e.g.,
PGNCCexp(ty,z,ni)? 0
15
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.
16
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.
17
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.
18

• 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

19

• 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.

20

• 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.

21

• 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)
•  

22
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.
23
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
24
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.