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POWER SYSTEMS LAB, A.U.TH. EEM08
1
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Costas G. Baslis, Anastasios G. Bakirtzis
Power Systems Laboratory Dept. of Electrical & Computer Engineering
Aristotle University of Thessaloniki
EEM 2008 ▪▪▪ Lisbon, Portugal ▪▪▪ 28-30 May 2008
POWER SYSTEMS LAB, A.U.TH. EEM08
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Introduction
Objective
Model formulation
Test results
Conclusions
Outline
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
POWER SYSTEMS LAB, A.U.TH. EEM08
3
Hydrothermal scheduling
Time scope
Long-term (more than 3 years)
Medium-term (few months to 3 years)
Short-term (1 day to 1 week)
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Introduction
Optimal operation decisions
Physical resources allocation
• Reservoir management, target values for short-term operation
• Stochasticity (load, inflows, prices)
• Load/price duration curves, weekly/monthly time intervals
• Hourly operation decisions, system security constraints
• Deterministic approach, detailed system representation
• Chronological load/price curves, hourly time intervals
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
POWER SYSTEMS LAB, A.U.TH. EEM08
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Introduction
Objective
Model formulation
Test results
Conclusions
Outline
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
POWER SYSTEMS LAB, A.U.TH. EEM08
5
Yearly hydrothermal scheduling model with hourly time
step intervals
Medium-term goals (stored water management)
Short-term decisions (thermal unit commitment)
Detailed system representation
Perfectly competitive market
Objective
Chronological load curve
Thermal unit minimum output
Cost minimization problem
Large-scale mixed integer programming model solved under
GAMS/CPLEX
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
POWER SYSTEMS LAB, A.U.TH. EEM08
6
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Introduction
Objective
Model formulation
Test results
Conclusions
Outline
POWER SYSTEMS LAB, A.U.TH. EEM08
7
Power system
Yearly planning horizon
Deterministic approach; predictions over:
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Model formulation
Thermal units
Hydroplants / Pumped storage plants
Successive hourly time intervals
Load demand
Reservoir inflows
Fuel prices
Unit availability
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
POWER SYSTEMS LAB, A.U.TH. EEM08
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Thermal Units
Minimum (and maximum) operating limits
Stepwise incremental cost curve
Start-up cost, minimum up/down times ignored
Predefined maintenance program
Hourly unit commitment
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Binary variables
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
POWER SYSTEMS LAB, A.U.TH. EEM08
9
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Hydroplants / Reservoirs
Explicit modeling of hydraulic coupling
Hydro unit output proportional to turbine discharge rate
One equivalent hydro unit per hydroplant
Predefined maintenance program
Optimal pumping schedule
Obtained as a result
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
POWER SYSTEMS LAB, A.U.TH. EEM08
10
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Energy Market
Day-ahead (DA) energy market
Perfect competition
Market clearing
Objective
Total annual thermal cost minimization
Thermal producers bid their marginal
cost
Bid-cost minimization
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
(Hydro producer bidding is ignored)
POWER SYSTEMS LAB, A.U.TH. EEM08
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A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
Constraints
Power balance
System tertiary reserve
Thermal unit, hydroplant, pumped storage plant and reservoir
bounds
Reservoir target volume
Reservoir balance
(all hydro units and only committed thermal
units may contribute)
Initial volume is considered known
Target volume = Initial volume
Hourly
Monthly (Reduced Model)
POWER SYSTEMS LAB, A.U.TH. EEM08
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A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Introduction
Objective
Model formulation
Test results
Conclusions
Outline
POWER SYSTEMS LAB, A.U.TH. EEM08
13
Thermal unit data
Hydro system data
Load profile
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Fuel type Lignite Nat.Gas (CC) Nat.Gas (SC) Oil
No. of units 20 3 4 2
Capacity (GW) 4.7 1.1 0.7 0.4
Total
29
6.9
Inflows (GWh) 4.1
No. of plants 13 (2)
Capacity (GW) 3 (0.7)
Winter 40%
Spring 39%
Annual demand
(GWh)
Peak load
(GW)
Base load
(GW) Load factor
46,089 8.5 2.6 0.62
(Greek ISO data for 2004)
observed in summer
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
POWER SYSTEMS LAB, A.U.TH. EEM08
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GAMS model parameters and results
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Hourly
water balance
Monthly
water balance
Equations 611,953 498,097
Variables 1,338,684 1,110,792
Integer variables 240,096 240,096
Objective (million €) 1497.22 1498.65
Total run time (sec) 1430 1112
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
POWER SYSTEMS LAB, A.U.TH. EEM08
15
-1000
0
1000
2000
3000
4000
5000
6000
7000
8000
0 24 48 72 96 120 144 168
Time (Hours)
Dem
and (
MW
)
20
30
40
50
60
70
80
90
100
110
Price (
€/M
Wh)
Demand Thermal Units Hydro Units SMP
Hydrothermal scheduling for a week of the planning period
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
3 GW ~0.8 GW
λ = = 0.75 min SMP
max SMP
pumping cycle efficiency
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
POWER SYSTEMS LAB, A.U.TH. EEM08
16
0
100
200
300
400
500
600
700
800
J F M A M J J A S O N D
Months
Hydro
Pro
duction (
GW
h)
0
1
2
3
4
5
6
7
Volu
me (
GC
M)
Hydro Production Volume
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Monthly hydro production and daily stored water volume
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
Vmax filling discharge Reservoir filling
period:
• Low demand
• High inflows
Volume increases
Reservoir discharge
period:
• Summer peak
• Low inflows
Volume decreases
POWER SYSTEMS LAB, A.U.TH. EEM08
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0
1
2
3
4
5
6
7
J F M A M J J A S O N D
Months
Volu
me (
GC
M)
0
10
20
30
40
50
60
70
80
90
SM
P (
€/M
Wh)
Volume SMP
0
1
2
3
4
5
6
7
J F M A M J J A S O N D
Months
Volu
me (
GC
M)
0
10
20
30
40
50
60
70
80
90
SM
P (
€/M
Wh)
Volume SMP
Daily maximum SMP and stored water volume
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Hourly water balance Monthly water balance
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
filling discharge Vmax
• Lower SMP is observed during the filling period
• After volume ‘hits’ its upper bound
• Similar results from the reduced model
SMP gets a higher value
Vmax
POWER SYSTEMS LAB, A.U.TH. EEM08
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0
10
20
30
40
Poly
fyto
Sfikia
Asom
ata
Kre
masta
Kastr
aki
Str
ato
s
Thesavro
s
Pla
tanovrisi
Aliakmon Aheloos Nestos
Wate
r valu
e (
€/K
CM
)A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Water value in cascaded reservoirs
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
• Water value (€/KCM)
decreases as we move
downstream to the river
• It expresses the value of
using water in a reservoir
and all its downstream
reservoirs, as well
POWER SYSTEMS LAB, A.U.TH. EEM08
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A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Introduction
Objective
Model formulation
Test results
Conclusions
Outline
POWER SYSTEMS LAB, A.U.TH. EEM08
20
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions
A MIP approach to the yearly hydrothermal scheduling with hourly
time intervals, in a perfectly competitive market, under deterministic
assumptions
Tested on a system similar to the Greek Power System
Test results include:
Thermal unit commitment
Thermal and hydro generation and pumping
System marginal price and reservoir water values
Straightforward coordination of medium and short-term decisions
Simple and compact formulation of the problem
Conclusions
POWER SYSTEMS LAB, A.U.TH. EEM08
21
Future work:
A more detailed representation of the short-term operation
Stochastic nature of uncertain system parameters
Modeling of imperfect markets
Conclusions
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions