1. Short-term uncertainty in investment models
Pernille Seljom & Asgeir Tomasgard
CREE 3rd research workshop

2. Introduction
Research project founded by the Research Council of Norway (2011 – 2014)
“The future Norwegian energy system in an European context”
Long-term TIMES model of Northern Europe
Some research questions:
How will the different global and European energy scenarios affect Norway?
What will be the future role of Norwegian hydropower?
Important premise
Proper modelling of unpredictable wind power = short-term uncertainty of supply
Research project at IFE, PhD position at NTNU
Today – Work from 1st paper presented – unpredictable characteristics of wind power in a case study of the Danish heat and electricity sector

3. Introduction Short-term uncertainty = availability of wind power
Mismatch supply and demand
Back-up capacity, transmission, storage
Long-term investment models as TIMES
More wind power = more short-term uncertainty
How to model?
Stochastic modelling of short-term uncertainty
Operational models - state of the art
Investment models - not as common
We use stochastic programming
Case study: TIMES model of the Danish heat and electricity sector
Operational models = Unit Commitment

4. Denmark- some energy facts
Wind power
Combines Heat and Power (CHP)
Highly interconnected
Data: Energistyrelsen
Interconnected to Norway, Sweden, Germany
Two physical separated grids until August 2010 were the two Nord Pool regions were connected (600 MW)
In EU, Denmark largest share if electricity production from CHP – 49 % in 2010, 12 % EU average
Denmark is the country with largest share of electricity production from wind power, 28 % in 2011
Figure: Nord Pool Spot

5. Model description TIMES (The Integrated MARKAL-EFOM system)
Modelling tool developed by ETSAP, an implementing agreement of IEA
Used by individuals/ teams in 63 countries
Work Shop twice a year
Model support and continuous development
Investment model of the Danish heat and electricity sector
Linear Programming model
Model regions Denmark East (DK-E) and Denmark West (DK-W)
Model horizon – 2050
Model periods 2010, 2015, 2020, 2030, 2040, 2050
Period split 4 seasons, 12 two-hour periods
Obj. function minimize total energy system costs
Perfect foresight
IEA – International Energy Agency
Work shop : Share experiences and discuss needs for further improvement

6. Model description

7. Model description
Traditionally in TIMES, wind power is modelled with a deterministic electricity peak reserve constraint
Sufficient capacity such that wind power only can contribute to a part of peak electricity demand
Possible wind contribution to the peak electricity demand
30 % typical value used
0 % most conservative value
What is the right value ???
Deterministic electricity prices in external trading regions
Germany, Sweden and Norway
This constraint can ensure sufficient capacity.
The right value is dependent on the energy system characteristics – how much wind power, how the wind power is correlated, and so on…….

8. Model description We do Stochastic modelling of wind availability
Stochastic modelling of electricity prices in trading regions
Not previously done in TIMES!
Future scenarios based on hourly historical data ( )
Hourly wind power production in DK-E and DK-W
Wind turbine capacity in DK-E and DK-W
Electricity prices in Germany, Sweden and Norway
Stochastic sub-annual trade prices
- Wind power data – include both onshore and offshore production and capacity data
Danish electricity prices are endogenous generated in the model but the electricity prices outside Denmark are exogenously given
Projected prices for biomass, fossil fuels, CO2 and annual electricity prices are from a Energinet study
We use historical data to present possible future scenarios – not necessarily a valid assumption but it is considered the best available basis
Not sufficient with annual electricity prices since the price tend to vary with season and time of day

9. Modelling uncertainty
Optimal investments given short-term uncertainty
Wind availability = wind production / max theoretical production
1 stage= investment decisions
wind availability and electricity price unknown
2 stage = operational decisions
wind availability and electricity price in known
Max theoretical production: 1 MW turbine can max produce 1 MWh in a given hour
Two-stage scenario tree
Scenario tree – discrete description of the outcomes of the uncertain parameter
Stage – where new information is revealed
Path – possible realisations of the uncertain parameter
Model returns scenario independent investment decisions and scenario dependent operational decisions

10. Wind power characteristics
Average wind availability ( )
Winter and spring shown in figure. Average is highest in winter and smallest in summer for both regions. Wind availability tend to be higher in the middle of the day compared to at night for all seasons except winter where the availability is more flat throughout the day. Figure spring show large variations within a season.
30/11/2018

11. Wind power characteristics
Variance in wind availability ( )
Variance show that wind availability is not predictable!!!

12. Wind power characteristics
Figure – Hourly wind availability of the first week of 2008 – Figure show 1. The wind is highly stochastic; 2. The wind is correlated in time; 3 The wind is correlated between the two model regions

13. Electricity trade prices
Average sub- annual electricity prices Germany ( )
Price vary significant with time of day with peaks in the middle of the day and in the afternoon

14. Electricity trade prices
Average sub- annual electricity prices Norway/ NO2 ( )
Norway – The price profile is more flat throughout the day. Higher prices in Winter than Summer
- The prices are also stochastic!!!

15. Modelling uncertainty
Every second hour from historical data is used
A scenario consist of 12 chronological two-hour wind availability data for DK-E and DK-W
Correlation in time
Correlation between model regions
A scenario consist of 12 chronological electricity price data for Germany, Norway and Sweden
Consistent electricity price and wind data
All historical data = computational challenges
Select a subset of historical data
1 day = 24 h and 1 model period = 12 daily periods
Same period selected for wind and electricity price data - automatic correlation
Subset – represent possible future scenarios!

16. Scenario generation Model input: Subset of historical data
Scenario reduction = solvable model
T scenario trees are randomly generated
Model input = best scenario tree
Least deviation of the four moments between sub-set and the historical data on wind availability
Scenario generation stability
Stability on number of scenarios/ size of sub-set
Sub-set selection, partly random process
In-sample stability
Out-if sample stability

17. Results – model options

18. Result 1 – In-sample stability
Show ????

19. Result 2 – Electric capacity 2030

20. Result 3 – Electric capacity 2050

21. Result 4 – Electric trade 2050

22. Result 5 – Exp. fuel consump. 2050

23. Results 6 – Value of Stochastic solution
« Cost of disregarding uncertainty»
Fixed investment - Det_30 → Infeasible
Fixed investment - Det_0 → More costly solution
Stoch 5.0 %
Stoch* %
VSS = (RP – EEV)/ EEV

24. Conclusions
Competiveness of wind power depend on the method used to model the unpredictable characteristics of wind power
Deterministic model approach overestimate competiveness of wind power
Deterministic investment decisions
Can give infeasible solutions
Or give more costly solutions
Stochastic modelling of short-term uncertainty gives cost effective investment decisions
Proper modelling of unpredictable wind power is essential to model the value of Norwegian hydro power