optimal electricity generation portfolios in the presence ...€¦ · optimal electricity...

Optimal Electricity Generation Portfoliosin the Presence of Fuel Price and

Availability Risks

Magda Mirescu

University of Viennaand

Vienna University of Technology

September 6, 2017

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 1 / 22

Why Look Into Electricity Generation?

I Europe-Wide: considerable national and supranational measures for thecomposition of national electricity generation portfolios(announced or partially implemented already):

◦ Nuclear Phase-Out: Italy, Germany, Belgium, Switzerland etc.◦ Subsidies: wind, solar, biomass, combined heat and power

plants/systems◦ Targets: 27% renewables by 2030

I Climate Change: ecological motivation or pressure factor

◦ CO2-Emissions: caused by fossil energy◦ Pricing of Emissions: CO2 European Emission Allowances

I Worldwide: projected growing demand

=⇒ What is an optimal electricity generation portfolio?


What is the Setting?

General (Research) Assumptions

I national decision makerI economical decision criteria with technical considerationsI several technologies available:

◦ thermal and◦ renewable→ wind

I each technology type has both advantages and disadvantages

◦ thermal: dispatchable butdirty and dependent on variable input prices

◦ renewable: clean butnon-dispatchable and with variable availability


What is the Research Question?

Question to Be Answered in This Presentation

What does a cost-optimal electricity generation portfolio consistof, if the decision-maker were to take into account:

I volatility of input prices,

I volatility of (wind) availability and with that coupled higher systemcosts?


How to Tackle the Research Question?

Portfolio OptimizationThe process of choosing the proportions of various assets to beheld in a portfolio in such a way as to make the portfolio betterthan any other according to some criterion.

Distinction Finance – Electricity Economics

I input: returnI weights: + und −I problem:

maxw

w>µ− β

2w>Σw

s.t. e>w = 1,

I input: LCOE or CFI weights: +

I problem:

minw

w>µ+β

2w>Σw

s.t. e>w = 1,

w ≥ 0.


DataOverview

I Cost Structure:

IC, FOM, VOM, Fuel Costs, Additional System Costs→ Germany

◦ Additional System Costs:

• Balancing Costs: short-term operational costs a systemincurs through output variability and uncertainty.

• Capacity Costs: costs associated with the required capacitythat enables a system to provide system reliability at anytime.

I Availability Factors: wind speeds→ Germany


DataInput Costs

Evolution of the Input Prices in Germany (January 1999 − May 2017)

Time [Years]

Inpu

t Pric

es [E

UR

/MW

h]

99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

010

2030

4050

6070 Gas

CoalUranium


DataSystem Costs

Balancing Costs Assumptions (Reliability Costs Identical)

I linear or quadratic growth in the share of wind generation.

10 20 30 40

01

23

45

Additional Balancing Costs via Wind Integration

Share of Wind Production [%]

Bal

anci

ng C

osts

[Eur

o/M

Wh]

linear −interceptlinear +interceptquadratic −interceptquadratic +intercept


DataWind Availability – Part 1



0 5 10 15 20 25

0.0

0.1

0.2

0.3

0.4

0.5

Kernel Density Estimation at Different Locations in Germany

Wind Speed [m/s]

Den

sity

Fehmarn−Mitte (North)Goerlitz (East)Konstanz (South)Roth bei Prüm (West)



0.0 0.1 0.2 0.3 0.4

020

4060

80

Availability of Wind in Germany − Linear Approach

Yearly Availability Factor

dens

ity

Fehmarn Mitte (North)Görlitz (East)Konstanz (South)Roth bei Prüm (West)Weighted Average − Federal States


DataLoad and Load Duration Curve – Part 1

0 2000 4000 6000 8000

4000

050

000

6000

070

000

Load Germany 2015

Time [h]

Load

[MW

]



min`n

N∑n=1

(`n − `n−1)D(`n−1)−∫ `n

`n−1

D(l)dl

s.t.∫ `n

`n−1

D(l)dl ≈N∑n=1

(`n − `n−1)D(`n−1) +D(`n)

2

`0 = 0 ≤ `n ≤ 1 = `N ,

0.0 0.2 0.4 0.6 0.8 1.0

0.5

0.6

0.7

0.8

0.9

1.0

Empirical LDC, Its Polynomial Estimate and Optimally Discretized Blocks − Germany 2015

Load Factor

Nor

amliz

ed L

oad

[MW

]

Empirical LDCPolynomial LDC



0 2000 4000 6000 8000

4000

050

000

6000

070

000

Load Germany 2015

Time [h]

Load

[MW

]


Mathematical Optimization Model

minxi,j ,i∈I,j∈J

E[cLCOE]

+β

2Var[cLCOE]

s.t.

x1,1 . . . x1,J−1 x1,J

.

.

.. . .

.

.

....

xI,1 . . . xI,J−1 xI,J

︸︷︷︸

X

1

.

.

.E[A(s)

] =

`ND(`N−1)

.

.

.`1(Dmax −D(`1))

X ≥ 0,

I I . . . = 3 number of load blocks

◦ base, intermediate, peak

I J . . . = 4 number of technologies

◦ thermal: coal, gas, nuclear◦ renewable: wind

I xij ∈ X

◦ electricity generation load block i withtechnology j

◦ decision variable

I consideration of the load via the Load DurationCurve (LDC)

I 2 random variables

◦ A . . . availability factor wind

◦ CFuel

. . . input prices

I system costs function f(AXW )

◦ none◦ linear in share of wind generation


ResultsWithout the Consideration of System Costs

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0

0.2

0.4

0.6

0.8

1.0

Optimal Portfolios with System Costs

Risk Aversion Beta

Sha

re in

Gen

erat

ion/

Year

[in

%]

gas

coal

wind

I Gas: due to low CF and volatile input costs→ peak load for high βI Coal: lower volatility than gas→ replaced by wind for high β (base load)I Nuclear: too expensive to be a part of the portfolioI Wind: covers base load only


ResultsWith the Consideration of System Costs

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0

0.2

0.4

0.6

0.8

1.0

Optimal Portfolios with System Costs

Risk Aversion Beta

Sha

re in

Gen

erat

ion/

Year

[in

%]

gas

coal

nuclear

wind

I Gas: unchangedI Coal: slightly moreI Nuclear: additional diversification mean→ base and intermediate loadI Wind: clearly less→ base load only


Conclusion

I A simultaneous consideration of both risk factors appears to beindispensable.

I The diversification effect of wind is

◦ overestimated, without considering system costs◦ smaller, with the consideration of system costs.

I The consideration of system costs leads to a non-linear, non-quadraticoptimization problem→ curse of dimensionality.⇒ ∃ trade-off between precision and solvability.


Outlook

I Find a better algorithm to compute the solutions.I Add several technologies:

◦ hydro,◦ solar,◦ lignite.

I Think of a way of modeling the intermittency problem.I Implement a higher degree system costs function.


Thank You for Your Attention!

Dipl.-Ing. Magda Mirescu

PhD Student

Vienna University of Technology

Faculty of Mathematics and Geoinformation

Research Group Operations Research and ControlSystems (ORCOS)

Wiedner Hauptstraße 8, 1040 Wien

I

Research and Teaching Assistent

University of Vienna

Faculty of Business, Economics and Statistics

Chair of Industry, Energy und Environment (IEE)

Oskar-Morgenstern-Platz 1, 1090 Wien

[email protected]


https://www.tuwien.ac.at/de/

http://orcos.tuwien.ac.at/

http://orcos.tuwien.ac.at/

https://www.univie.ac.at/de/

http://bwl.univie.ac.at/ieu/home/

mailto:[email protected]

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