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
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 ◦ CO 2 -Emissions: caused by fossil energy ◦ Pricing of Emissions: CO 2 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
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
What is the Research Question? Question to Be Answered in This Presentation What does a cost-optimal electricity generation portfolio consist of, 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
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 ◮ input: LCOE or CF ◮ weights: + und − ◮ weights: + ◮ problem: ◮ problem: w ⊤ µ − β w ⊤ µ + β 2 w ⊤ Σ w 2 w ⊤ Σ w max min w w e ⊤ w = 1 , e ⊤ w = 1 , s.t. s.t. w ≥ 0 . Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 5 / 22
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
Data Input Costs Evolution of the Input Prices in Germany (January 1999 − May 2017) 70 Gas Coal Uranium 60 Input Prices [EUR/MWh] 50 40 30 20 10 0 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 Time [Years] Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 7 / 22
Data System Costs Balancing Costs Assumptions (Reliability Costs Identical) ◮ linear or quadratic growth in the share of wind generation. Additional Balancing Costs via Wind Integration 5 Balancing Costs [Euro/MWh] 4 3 2 linear −intercept linear +intercept 1 quadratic −intercept quadratic +intercept 0 10 20 30 40 Share of Wind Production [%] Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 8 / 22
Data Wind Availability – Part 1 Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 9 / 22
Data Wind Availability – Part 2 Kernel Density Estimation at Different Locations in Germany Fehmarn−Mitte (North) 0.5 Goerlitz (East) Konstanz (South) 0.4 Roth bei Prüm (West) 0.3 Density 0.2 0.1 0.0 0 5 10 15 20 25 Wind Speed [m/s] Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 10 / 22
Data Wind Availability – Part 3 Kernel Density Estimation at Different Locations in Germany Fehmarn−Mitte (North) 0.5 Goerlitz (East) Konstanz (South) 0.4 Roth bei Prüm (West) 0.3 Density 0.2 0.1 0.0 0 5 10 15 20 25 Wind Speed [m/s] Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 11 / 22
Data Wind Availability – Part 4 Availability of Wind in Germany − Linear Approach Fehmarn Mitte (North) 80 Görlitz (East) Konstanz (South) Roth bei Prüm (West) Weighted Average − Federal States 60 density 40 20 0 0.0 0.1 0.2 0.3 0.4 Yearly Availability Factor Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 12 / 22
Data Load and Load Duration Curve – Part 1 Load Germany 2015 70000 60000 Load [MW] 50000 40000 0 2000 4000 6000 8000 Time [h] Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 13 / 22
Data Load and Load Duration Curve – Part 2 � ℓ n N � min ( ℓ n − ℓ n − 1 ) D ( ℓ n − 1 ) − D ( l ) d l ℓ n ℓ n − 1 n =1 � ℓ n N ( ℓ n − ℓ n − 1 ) D ( ℓ n − 1 ) + D ( ℓ n ) � s.t. D ( l ) d l ≈ 2 ℓ n − 1 n =1 ℓ 0 = 0 ≤ ℓ n ≤ 1 = ℓ N , Empirical LDC, Its Polynomial Estimate and Optimally Discretized Blocks − Germany 2015 1.0 Empirical LDC Polynomial LDC 0.9 Noramlized Load [MW] 0.8 0.7 0.6 0.5 0.0 0.2 0.4 0.6 0.8 1.0 Load Factor Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 14 / 22
Data Load and Load Duration Curve – Part 3 Load Germany 2015 70000 60000 Load [MW] 50000 40000 0 2000 4000 6000 8000 Time [h] Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 15 / 22
Mathematical Optimization Model β � c LCOE � � c LCOE � min E + V ar xi,j ,i ∈ I,j ∈ J 2 1 x 1 , 1 . . . x 1 ,J − 1 x 1 ,J ℓ N D ( ℓ N − 1 ) . . . . . ... = s.t. . . . . . . . . . . � � x I, 1 . . . x I,J − 1 x I,J A ( s ) ℓ 1 ( D max − D ( ℓ 1 )) E � �� � X X ≥ 0 , ◮ ◮ I . . . = 3 number of load blocks consideration of the load via the Load Duration Curve (LDC) base, intermediate, peak ◦ ◮ 2 random variables ◮ J . . . = 4 number of technologies ◦ A . . . availability factor wind thermal: coal, gas, nuclear ◦ C Fuel . . . input prices renewable: wind ◦ ◦ ◮ x ij ∈ X ◮ system costs function f ( AX W ) ◦ electricity generation load block i with ◦ none technology j ◦ linear in share of wind generation ◦ decision variable Magda Mirescu Optimal Electricity Generation Portfolios in the Presence of Fuel Price and Availability Risks 16 / 22
Results Without the Consideration of System Costs Optimal Portfolios with System Costs 1.0 Share in Generation/Year [in %] 0.8 wind 0.6 coal 0.4 0.2 gas 0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Risk Aversion Beta ◮ 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
Results With the Consideration of System Costs Optimal Portfolios with System Costs 1.0 Share in Generation/Year [in %] wind 0.8 0.6 nuclear coal 0.4 0.2 gas 0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Risk Aversion Beta ◮ 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
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 optimization 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
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
Recommend
More recommend
