1. POWER SYSTEMS LAB, A.U.TH. EEM08
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
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2. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Outline
 Introduction
 Objective
 Model formulation
 Test results
 Conclusions
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3. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Introduction
 Hydrothermal scheduling Optimal operation decisions
Physical resources allocation
 Time scope
 Long-term (more than 3 years)
• Reservoir management, target values for short-term operation
 Medium-term (few months to 3 years)
• Stochasticity (load, inflows, prices)
 Short-term (1 day to 1 week)
• 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
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

4. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Outline
 Introduction
 Objective
 Model formulation
 Test results
 Conclusions
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5. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Objective
 Yearly hydrothermal scheduling model with hourly time
step intervals
 Medium-term goals (stored water management)
 Short-term decisions (thermal unit commitment)
 Detailed system representation Chronological load curve
Thermal unit minimum output
 Perfectly competitive market Cost minimization problem
Large-scale mixed integer programming model solved under
GAMS/CPLEX
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

6. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Outline
 Introduction
 Objective
 Model formulation
 Test results
 Conclusions
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7. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Model formulation
 Power system Thermal units
Hydroplants / Pumped storage plants
 Yearly planning horizon Successive hourly time intervals
 Deterministic approach; predictions over:
 Load demand
 Reservoir inflows
 Fuel prices
 Unit availability
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

8. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
 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 Binary variables
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

9. POWER SYSTEMS LAB, A.U.TH. EEM08
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
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

10. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
 Energy Market
 Day-ahead (DA) energy market
 Perfect competition Thermal producers bid their marginal
cost (Hydro producer bidding is ignored)
 Market clearing Bid-cost minimization
 Objective Total annual thermal cost minimization
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

11. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
 Constraints
 Power balance
 System tertiary reserve (all hydro units and only committed thermal
units may contribute)
 Thermal unit, hydroplant, pumped storage plant and reservoir
bounds
 Reservoir target volume Initial volume is considered known
Target volume = Initial volume
 Reservoir balance Hourly
Monthly (Reduced Model)
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

12. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Outline
 Introduction
 Objective
 Model formulation
 Test results
 Conclusions
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13. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
 Thermal unit data
Fuel type Lignite Nat.Gas (CC) Nat.Gas (SC) Oil Total
No. of units 20 3 4 2 29
Capacity (GW) 4.7 1.1 0.7 0.4 6.9
 Hydro system data
Inflows (GWh) 4.1 Winter 40%
No. of plants 13 (2) Spring 39%
Capacity (GW) 3 (0.7)
 Load profile (Greek ISO data for 2004)
Annual demand Peak load Base load
Load factor
(GWh) (GW) (GW)
46,089 8.5 2.6 0.62
observed in summer
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

14. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
 GAMS model parameters and results
Hourly Monthly
water balance 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
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

15. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Hydrothermal scheduling for a week of the planning period
8000 110
7000 100
6000 90
3 GW
5000 80 ~0.8 GW
Demand (MW)
Price (€/MWh)
4000 70
3000 60 min SMP
λ= = 0.75
2000 50 max SMP
1000 40
0 30 pumping cycle efficiency
-1000 20
0 24 48 72 96 120 144 168
Time (Hours)
Demand Thermal Units Hydro Units SMP
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

16. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Monthly hydro production and daily stored water volume
filling Vmax discharge Reservoir filling
800 7
period:
Hydro Production (GWh)
700 6
• Low demand
600
Volume (GCM)
5 • High inflows
500
4
400 Volume increases
3
300
200 2 Reservoir discharge
period:
100 1
• Summer peak
0 0
J F M A M J J A S O N D • Low inflows
Months
Volume decreases
Hydro Production Volume
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

17. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Daily maximum SMP and stored water volume
Hourly water balance Monthly water balance
7 filling Vmax discharge 90 7 Vmax 90
6 80 6 80
70 70
Volume (GCM)
SMP (€/MWh)
5
Volume (GCM)
5
SMP (€/MWh)
60 60
4 50 4 50
3 40 3 40
30 30
2 2
20 20
1 10 1 10
0 0 0 0
J F M A M J J A S O N D J F M A M J J A S O N D
Months Months
Volume SMP Volume SMP
• Lower SMP is observed during the filling period
• After volume ‘hits’ its upper bound SMP gets a higher value
• Similar results from the reduced model
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

18. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Water value in cascaded reservoirs
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Water value (€/KCM)
• Water value (€/KCM)
30 decreases as we move
downstream to the river
20 • It expresses the value of
using water in a reservoir
10 and all its downstream
reservoirs, as well
0
Platanovrisi
Thesavros
Kremasta
Asomata
Kastraki
Sfikia
Stratos
Polyfyto
Aliakmon Aheloos Nestos
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

19. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Outline
 Introduction
 Objective
 Model formulation
 Test results
 Conclusions
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20. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
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
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

21. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Conclusions
 Future work:
 A more detailed representation of the short-term operation
 Stochastic nature of uncertain system parameters
 Modeling of imperfect markets
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Introduction ▪ Objective ▪ Model formulation ▪ Test results ▪ Conclusions

22. POWER SYSTEMS LAB, A.U.TH. EEM08
A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System
Thank you for your attention!
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