Methods and Processes for Hydro-thermal Scheduling Prof. Olav Bjarte Fosso Dept of Electrical Power Engineering Norwegian University of Science and Technology (NTNU)

Hydro Power’s role in an Integrated Energy System?

Hydro Power in Norway

• Electricity: ~ 100% hydro power • Largest in Europe, nr 6 in the world • 30% of hydro power cap. In European Union (50 % of storage) • Installed capacity : ~ 29000 MW • Generation average,: ~ 125 TWh • Consumption: ~ 124 TWh • Average inflow +- 20 %

Real-world problems characterized by • •

Large physical models (Geographical and time horizon) Non-linear and non-convex with many local optimums – Final solution may depend on the starting point – Global optimal solution never guaranteed

• •

•

4

Binary variables complicates the solution process and may in some parts of the complete problem be important User-experience and ”non-mathematical” constraints (rulebased and state dependent) may be important Hydro scheduling is no exception regarding these problems

Challenges in hydro scheduling •

Cascaded reservoir systems with different storage capacity couples the decisions between the generation plants

•

The storage capacity and variable inflow couples the decisons over time – Inflow range in Norwegian system: 95 – 140 TWh (Average load 125 TWh) – Significant storage capacity requires long planning horizons (Typical up to 5 years) – Other system characteristics dictates the time resolution

•

5

The relative size of the hydro system compared to the thermal system call for different co-ordination principles (Peak shaving – similar size – hydro-dominated)

Large scale stochastic dynamic optimization •

•

•

•

Multi state • Typical more than 1000 different storages in an fundamental market model • Very varying storage size ( from about three years to hours) Stochastic multidimensional • Inflow, wind, radiation • Correlated in time an space • Historical observations • Short-term forecast, snow pack information • Exogenous prices Multi stage • Weekly (split into intraweek time step) • Several year long planning horizon Transmission constrained • Several thousand nodes

F in

Multi-area model of Nordic countries

T ro

Hel

N ord S v e r ig e

N -M I V -M I

F in la n d

G /L HAL V -S Ø

Ø -L S -Ø -L

Tel

S yd S v e r ig e

S -L

E s tla n d

L a tv ia DK vest DK øst

L ita u e n

P o le n Ned

T y s k la n d EFI

Scheduling Hierarchy (Norway – present practice) Long term scheduling ( 1-5 years) Stochastic models for optimazation and simulation Reservoir levels Marginal water values

Seasonal scheduling (3-18 months) Multi-scenario Deterministic optimization models Marginal water values Reservoir boundaries

Short term scheduling (1-2 weeks) Deterministic optimization models

Plans

Detailed simulation (1 -12 weeks) Verification of plans with non-linear simulation

Methods in use •

SDP (Long-term) – Aggregated – Stochastic

•

SDDP

(Long / Mid-term)

– Detailed – Stochastic

•

Scenario-based (Mid-term) – Deterministic

•

Deterministic(Short-term) – – – –

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LP MIP DP Lagrange relaxation

Longer-term scheduling

Simulation of markets with storages and weather uncertainty Storage possibilities

Strategy by (SDP/SDDP)

Markets and prices Supply/demand data

Water value

Stochastic, inflow solar, wind etc

Simulating markets (LP)

Storage utilization

Simulation

System operation

Courtesy: Birger Mo, SINTEF

Marginal water values calculated for all points over the time horizon Reservoir [%] Iterate over the time horizon (n-52, n)

0,0

100

0,0 0,5 0,8 1,0 1,5

98 96 94 92

n-51

4 2 0

60

n-1

n

51

52

2,0

20 Tm1 28 Tm2 30 Tm3 35 Tm4 40 Tm5

70 1 Tm6 2 Tm7

48

49

50

uke

20·1 + 28·5 + 30·9 + 35·20 + 40·9 + 60·5 + 70·1 VV4 = = 37,2 [øre/kWh] (1+ 5 + 9 + 20 + 9 + 5 + 1)

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Illustration of water values Reservoir content [GWh] 1,2

øre/kWh 0

1,0

10 20

0,8 0,6 0,4

30 40

0,2 0 0

50

100

150

200

week

13

Application example – Integration of balancing markets Fundamental model

Detailed water course description About 300 thermal power plants Transmission corridors (NTC)

Northern Europe

Denmark, Finland, Norway, Sweden Germany, Netherlands, Belgium

System scenarios

2010 – current state of the system 2020 – a future state of the system

Several climatic years

Hydrology (Inflow) Temperature Wind speed

Coupling between models and planning levels

Coupling between planning levels •

Different models at different planning levels complicates the coupling and information flow

•

The next level of analysis does not necessarily get input data of sufficient precision

•

Aggregation / disaggregation challenges

•

Coupling principles: – Price coupling (individual / aggregated) – Volume coupling

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Aggregation / disaggregation challenges

Longer-term

Shorter-term

Coupling principle Incremental water values Reservoir level

Flexible reservoir drawdown with possibility to move water between periods

Shorter-term

Longer-term

Puts certain requirements on the methods used in both periods

Short-term scheduling

Network formulation – short-term Reservoir content

Inflow

Reservoir balances Discharge

Time intervalls Short-term hydro power optimization 20

THANKS FOR YOUR ATTENTION More information: http://www.ntnu.edu/energy

Linear programming • • •

Linear models are fundamental for most the modeling and simulation The experience shows that most of the physical problems can be solved by using linear models as building blocks Non-linearities can be handles by: – Piece-wise linear segments – Iteration for successive refinement – Integer variable and to check combinations

•

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Algorithms are available to solve very large problems fast

Coupling principle Volume coupling Reservoir level

Specified reservoir endpoint level

Shorter-term

Longer-term

Less requirements to the methods used

Linearization Q

Q

1. iteration

2. iteration

Pmax

Pmin

P Pbest

Full description

Q

n. iteration

Pmax

Pmax

Pmin

P P1

Full description Short-term hydro power optimization

Pmin

P(n-1)

Incremental description

P

Norway - an energy nation…….

3 generations of energy development: Hydro Power, Petroleum, Renewables

Resource – demand profiles GWh/week 7000

Problem:

Max. inflow

6000

5000

Mean inflow

4000

Optimal use of reservoirs with: • stochastic precipitation, inflow, prices • seasonal variations • reservoirs with multiple years storage

Demand 3000

2000

Min. inflow

1000

0

Week

Complementarity: Wind Power / Hydro vs. Demand

6

H y d r o in flo w M id tn o r g e H y d r o in flo w N o r w a y D e ma n d N o rw a y D e m a n d M id tn o r g e W in d E n e r g y

Normalised weekly data [%]

5

4

3

2

1

5

10

15

20

25 30 W eek no.

35

40

45

50

Norwegian hydropower for balancing •

The reservoirs are natural lakes • Multi-year reservoirs • Largest lake stores 8 TWh • Total 84 TWh reservior capacity

•

Balancing capacity estimates 2030 • 29 GW installed at present • + 10 GW with larger tunnels and generators • + 20 GW pumped storage • 30 GW total new capacity • Within todays environmental limits • Requires more transmission capacity

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Courtesy: Birger Mo / CEDREN

Price difference between Norway and Germany – average week