This document presents a mixed integer programming approach for the yearly scheduling of a mixed hydrothermal power system. The model schedules thermal generating units on an hourly basis while considering reservoir levels and pumping operations for hydro units on both an hourly and monthly basis. The objective is to minimize total annual thermal generation costs given load predictions and constraints for the power balance, reserve requirements, and hydro plant and reservoir operations. The model is tested on a power system based on Greek electricity data from 2004 consisting of 29 thermal units totaling 6.9 GW of capacity and 13 hydro plants with 3 GW of capacity.

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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