POWER SYSTEMS LAB, A.U.TH. EEM08

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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

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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

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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

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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

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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

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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

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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

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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

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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)

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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)

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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

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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

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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

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-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

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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

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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

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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

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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

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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

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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

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Thank you for your attention!

A MIP Approach to the Yearly Scheduling Problem of a Mixed Hydrothermal System