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Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks Magda Mirescu University of Vienna and Vienna University of Technology September 6, 2017 Magda Mirescu Optimal Electricity Generation Portfolios

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SLIDE 1

Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks

Magda Mirescu

University of Vienna and Vienna University of Technology

September 6, 2017

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

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SLIDE 2

Why Look Into Electricity Generation?

◮ Europe-Wide: considerable national and supranational measures for the

composition 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

◮ Climate Change: ecological motivation or pressure factor

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

◮ Worldwide: projected growing demand

= ⇒ What is an optimal electricity generation portfolio?

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 2 / 22

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SLIDE 3

What is the Setting?

General (Research) Assumptions

◮ national decision maker ◮ economical decision criteria with technical considerations ◮ several technologies available:

  • thermal and
  • renewable → wind

◮ each technology type has both advantages and disadvantages

  • thermal: dispatchable but

dirty and dependent on variable input prices

  • renewable: clean but

non-dispatchable and with variable availability

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 3 / 22

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SLIDE 4

What is the Research Question? Question to Be Answered in This Presentation

What does a cost-optimal electricity generation portfolio consist

  • f, if the decision-maker were to take into account:

◮ volatility of input prices, ◮ volatility of (wind) availability and with that coupled higher system

costs?

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 4 / 22

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SLIDE 5

How to Tackle the Research Question?

Portfolio Optimization

The process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other according to some criterion.

Distinction Finance – Electricity Economics

◮ input: return ◮ weights: + und − ◮ problem:

max

w

w⊤µ − β 2 w⊤Σw s.t. e⊤w = 1,

◮ input: LCOE or CF ◮ weights: + ◮ problem:

min

w

w⊤µ + β 2 w⊤Σw s.t. e⊤w = 1, w ≥ 0.

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 5 / 22

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SLIDE 6

Data

Overview

◮ Cost Structure:

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

  • Additional System Costs:
  • Balancing Costs: short-term operational costs a system

incurs through output variability and uncertainty.

  • Capacity Costs: costs associated with the required capacity

that enables a system to provide system reliability at any time.

◮ Availability Factors: wind speeds → Germany

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 6 / 22

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SLIDE 7

Data

Input Costs

Evolution of the Input Prices in Germany (January 1999 − May 2017) Time [Years] Input Prices [EUR/MWh]

99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 10 20 30 40 50 60 70 Gas Coal Uranium

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 7 / 22

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SLIDE 8

Data

System Costs

Balancing Costs Assumptions (Reliability Costs Identical)

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

10 20 30 40 1 2 3 4 5

Additional Balancing Costs via Wind Integration Share of Wind Production [%] Balancing Costs [Euro/MWh]

linear −intercept linear +intercept quadratic −intercept quadratic +intercept

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 8 / 22

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SLIDE 9

Data

Wind Availability – Part 1

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 9 / 22

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SLIDE 10

Data

Wind Availability – Part 2

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

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 10 / 22

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SLIDE 11

Data

Wind Availability – Part 3

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

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 11 / 22

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SLIDE 12

Data

Wind Availability – Part 4

0.0 0.1 0.2 0.3 0.4 20 40 60 80 Availability of Wind in Germany − Linear Approach Yearly Availability Factor density Fehmarn Mitte (North) Görlitz (East) Konstanz (South) Roth bei Prüm (West) Weighted Average − Federal States

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 12 / 22

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SLIDE 13

Data

Load and Load Duration Curve – Part 1

2000 4000 6000 8000 40000 50000 60000 70000 Load Germany 2015 Time [h] Load [MW]

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 13 / 22

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SLIDE 14

Data

Load and Load Duration Curve – Part 2

min

ℓn N

  • n=1

(ℓn − ℓn−1)D(ℓn−1) − ℓn

ℓn−1

D(l)dl s.t. ℓn

ℓn−1

D(l)dl ≈

N

  • n=1

(ℓn − ℓn−1) D(ℓn−1) + D(ℓn) 2 ℓ0 = 0 ≤ ℓn ≤ 1 = ℓN,

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 Noramlized Load [MW]

Empirical LDC Polynomial LDC

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 14 / 22

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SLIDE 15

Data

Load and Load Duration Curve – Part 3

2000 4000 6000 8000 40000 50000 60000 70000 Load Germany 2015 Time [h] Load [MW]

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 15 / 22

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SLIDE 16

Mathematical Optimization Model

min

xi,j ,i∈I,j∈J

E

  • cLCOE

+ β 2 Var

  • cLCOE

s.t.     x1,1 . . . x1,J−1 x1,J . . . ... . . . . . . xI,1 . . . xI,J−1 xI,J    

  • X

    1 . . . E

  • A(s)

   =     ℓN D(ℓN−1) . . . ℓ1(Dmax − D(ℓ1))     X ≥ 0,

◮

I . . . = 3 number of load blocks

  • base, intermediate, peak

◮

J . . . = 4 number of technologies

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

◮

xij ∈ X

  • electricity generation load block i with

technology j

  • decision variable

◮

consideration of the load via the Load Duration Curve (LDC)

◮

2 random variables

  • A . . . availability factor wind
  • CFuel . . . input prices

◮

system costs function f(AXW )

  • none
  • linear in share of wind generation

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 16 / 22

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SLIDE 17

Results

Without 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 Share in Generation/Year [in %] gas coal wind

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

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 17 / 22

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Results

With 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 Share in Generation/Year [in %] gas coal nuclear wind

◮ Gas: unchanged ◮ Coal: slightly more ◮ Nuclear: additional diversification mean → base and intermediate load ◮ Wind: clearly less → base load only

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 18 / 22

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Conclusion

◮ A simultaneous consideration of both risk factors appears to be

indispensable.

◮ The diversification effect of wind is

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

◮ The consideration of system costs leads to a non-linear, non-quadratic

  • ptimization problem → curse of dimensionality.

⇒ ∃ trade-off between precision and solvability.

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 19 / 22

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Outlook

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

  • hydro,
  • solar,
  • lignite.

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

Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 20 / 22

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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 Control Systems (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 magda.mirescu@univie.ac.at Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 21 / 22