Selection of optimal power plant generation mix: Case study

The main goal of the owners and operators of power plants is the use of different generation technologies to make the power supply not only secure and sustainable but also profitable. The selection of suitable technology mixes requires a robust analytical framework, such as the Mean-Variance Portfolio Theory. Under this framework, specific financial risks related to various technologies as well as the technical, economic and societal aspects of the plants can explicitly be considered.

The objective of this case study is to find out the efficient combination of selected electricity generation technologies currently operated. In the generation mix two conventional technologies such as hard-coal- and lignite-fired power plants as well as two renewable technologies: onshore wind power and hydro pumped storage are considered. The description of these technologies with some economic characteristics are presented in the Table 1.

Tab 1. Economic characteristics of technologies considered in the power generation mix

Type of technology	Brutto installed capacity [in MW]	Start-up year	Life time [in years]	Investment costs [€/kW]	Fixed O&M costs [€/kW]	WACC_real [%]
Hard coal	1,000	1998	40⁽¹⁾	820^{(6, 7)}	40.00⁽⁸⁾	6.9⁽²⁾
Hydro pumped storage	200	1983	100⁽¹⁾	1,750⁽⁴⁾	4.00⁽⁵⁾	4.98⁽³⁾
Lignite	900	2003	40⁽¹⁾	1,100⁽⁶⁾	40.00⁽⁸⁾	6.9⁽²⁾
Wind on shore	45	2012	20⁽¹⁾	1,000⁽²⁾	20.00⁽⁸⁾	3.8⁽²⁾

(1) Agora (2017). Erneuerbare vs. fossile Stromsysteme: ein Kostenvergleich. Öko-Institut e.V.

(2) Fraunhofer (2013). Levelized Cost of Electricity Renewable Energy Technologies. Fraunhofer-ISE, Freiburg

(3) WACC – Kalkulatorischer Zinssatz; URL: https://www.bfe.admin.ch/bfe/de/home/foerderung/erneuerbare-energien/wacc-kalkulatorischer-zinssatz.html

(4) https://www.rwe.com/der-konzern/laender-und-standorte/pumpspeicherkraftwerk-herdecke/ and https://de.wikipedia.org/wiki/Pumpspeicherkraftwerk_Herdecke

(5) Kloess M. (2012). Wirtschaftliche Bewertung von Stromspeichertechnologien. Energy Economics Group, TU Wien

(6) IEA (2005). Projected costs of generating electricity, IEA/OECD, Paris

(7) Roques, F.A., Newbery, D.M., Nuttall, W.J. (2007). Fuel mix diversification in liberalized electricity markets: A mean-variance portfolio theory approach, Energy Economics, 30(4), 1831-1849

(8) Agora (2017). Erneuerbare vs. fossile Stromsysteme: ein Kostenvergleich. Öko-Institut e.V.

The optimization is undertaken for a rational investor trying to attain either the power generation mix with the highest expected return at a prescribed risk level, or the least volatile expected return prescribed.

Within the framework of this case study the net present value (NPV) of power generation assets can be calculated/simulated (using Python or Oracle’s Crystal Ball® in Excel) as a measure for project evaluation (so-called portfolio selection criterion), in order to construct return-risk-optimized power generation mixes.

TASK 1

Using the technical characteristics of each technology (Table 2) as well as stochastic financial parameters (i.e., fuel, CO₂ and electricity prices – Table 3) for the selected power generation technologies, simulate mean values and standard deviations of the discounted cash flows per installed unit of capacity for each technology (so-called present value) as well as variance-covariance matrix of all selected technologies. The Monte Carlo simulation should be conducted applying Python, as shown in the presentation “Economics of power plants and example of power plants optimization in Python”.

Tab 2. Technical characteristics for each technology

Technology	(Typical) Capacity factor (lambda)[in %]	(Typical) Net thermal efficiency [in %]⁽¹⁾	Heating value⁽¹⁾	Conversion factor⁽¹⁾	Specific power plant CO₂ emissions [tCO₂/MWh]
Hard coal	0.60⁽²⁾	0.44⁽⁴⁾	8.06 MWh/tonne⁽⁹⁾	0.97	0.939⁽⁵⁾
Hydro	0.05⁽⁶⁾	0.80⁽⁷⁾	-	1	-
Lignite	0.82⁽²⁾	0.39⁽⁴⁾	4.17 MWh/tonne⁽⁹⁾	1	1.173⁽⁵⁾
Wind onshore	0.20⁽³⁾	1.00⁽⁸⁾	-	1	-

(1) Note: This parameter is needed for the calculation of fuel consumption

(2) Average capacity factor (forecast) for German conventional power plants; see Table 3.2.4.4-2 in: Prognos (2014) Entwicklung der Energiemärkte – Energiereferenzprognose (Projekt Nr. 57/12 Studie im Auftrag des Bundesministeriums für Wirtschaft und Technologie), Basel/Köln/Osnabrück, 2014

(3) Average capacity factor (forecast) for German renewable power plants see Table 3.2.4.6-1 in: Prognos (2014). Entwicklung der Energiemärkte – Energiereferenzprognose (Projekt Nr. 57/12 Studie im Auftrag des Bundesministeriums für Wirtschaft und Technologie), Basel/Köln/Osnabrück, 2014

(4) Umwelt Bundesamt (2022). Kraftwerke: konventionelle und erneuerbare Energieträger (Abb.6) URL: https://www.umweltbundesamt.de/daten/energie/kraftwerke-konventionelle-erneuerbare#kraftwerke-auf-basis-erneuerbarer-energien

(5) Specific Carbon Dioxide Emissions of Various Fuels URL: https://www.volker-quaschning.de/datserv/CO2-spez/index_e.php (online 21.03.2023)

(6) IRENA (2017). Electricity Storage and Renewables: Costs and Markets to 2030, International Renewable Energy Agency, Abu Dhabi

(7) https://www.rwe.com/der-konzern/laender-und-standorte/pumpspeicherkraftwerk-herdecke/ and https://de.wikipedia.org/wiki/Pumpspeicherkraftwerk_Herdecke

(8) Hasche B., Barth R., Swider D.J. (2006). Verteilte Erzeugung im deutschen Energiesystem. Universität Stuttgart, Institut für Energiewirtschaft und Rationelle Energieanwendung, Stuttgart, Germany

(9) https://agrarplus.at/heizwerte-aequivalente.html

Tab 3. Prices for fuels, CO₂ and electricity (normal distribution)

Prices of	Parameters (time series 2009-2012)	Parameters (time series 2016-2021)
Electricity	64.96 (12.85) €/MWh	45.36 (37.94) €/MWh
Hard coal	55.41 (10.16) €/t SKE	87.43 (26.03) €/t SKE
Lignite	92.50 (3.95) €/t	16.31 (0.67) €/t
CO₂	18.59 (6.50) €/t CO₂	18.42 (16.22) €/t CO₂

TASK 2

Using the simulated mean values of the discounted cash flows per installed unit of capacity for each technology (so-called present value) in Task 1, determine the feasible set and the efficiency frontier for selected power generation technologies. Portfolio optimization should be conducted using Python and applying theory from the presentations: “Portfolio optimization for power generation assets” and ”Economics of power plants and example of power plants optimization in Python”.

The prices for fuels, CO₂ and electricity in Table 3 are given for two different time periods. Conduct the portfolio optimization for these two different time series and discuss the differences and their reasons.

Present the results of the optimization for both time series graphically, as an efficiency frontier (e.g., in .png format) and in the form of a table (.csv or Excel data) with the shares of each technology in the efficient portfolio, its expected return, and its risk. The discussion of the differences should be provided in the form of text data. The obtained results are useful for both decision makers and managers.