Overall, I find only minor differences in the samples’ distributions. There are slight deviations in the lower levels of wind speeds and production outputs. This makes the distribution of wind speed exposure wider for large turbines. Also, large turbines seem to produce low levels of power more often than small turbines. The results suggest that these power outputs come at a time of relatively high prices, putting larger turbines in a position of exploiting a higher average price.
That said, it must hold true that the distribution of production outputs by large turbines allocates at an overall more favorable place in the time series of electricity prices.
Table 6: Electricity production vs. prices in high-frequency environments
The table exhibits the regression results according to Equation (10). Also, I run the regression on changes to the previous period (∆) in dependent and independent variables. Specifically, I subset the data sample with regards to capacity levels. The dependent variable is the relevant hourly electricity price in area DK1 or DK2 of the individual turbine. Production estimates, also hourly, are standardized through Equation (1) and expressed in MWh. I control for lagged electricity prices (γ) as well as electricity consumption (κ) with the explanatory variable measured in GWh. Furthermore, I account for seasonality in price, production outputs and consumption estimates through monthly time fixed effects, weekday fixed effects as well as hourly fixed effects. Standard errors are clustered by time and documented in the brackets below the estimates.
Dependent variable:
Pt ∆Pt
Total Small Large Total Small Large
(1) (2) (3) (4) (5) (6)
β: Turbine productionM W h −2.094∗∗∗ −2.658∗∗∗ −1.698∗∗∗
(0.246) (0.265) (0.240) γ: El. pricePt−1 0.934∗∗∗ 0.927∗∗∗ 0.939∗∗∗
(0.009) (0.009) (0.009)
κ: El. consumptionGW h 1.106 1.194 1.048
(0.940) (0.947) (0.934)
β: Turbine production ∆M W h −2.198∗∗∗ −2.281∗∗∗ −2.129∗∗∗
(0.285) (0.334) (0.273)
γ: El. price ∆Pt−1 0.125∗∗∗ 0.130∗∗∗ 0.120∗∗∗
(0.040) (0.039) (0.040)
κ: El. consumption ∆GW h 12.658∗∗∗ 12.560∗∗∗ 12.743∗∗∗
(2.201) (2.206) (2.199)
Constantα −1.483 −1.237 −1.645 −0.333 −0.330 −0.337
(1.829) (1.838) (1.822) (0.271) (0.270) (0.271)
Month fixed effects? Yes Yes Yes Yes Yes Yes
Weekday fixed effects? Yes Yes Yes Yes Yes Yes
Hour fixed effects? Yes Yes Yes Yes Yes Yes
Observations 1,593,184 734,622 858,562 1,578,103 727,331 850,772
Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
small turbines. Also, the marginal additional production output tends to be compensated with less of a discount in the price of electricity for larger turbines. Magnitudes however, are significantly higher than the monthly data suggests, implying that the short-term dynamics of production and electricity prices largely matter.
6 Discussion: Is the bigger really the better?
This paper presents evidence that large turbines yield higher average prices of electricity in com-parison to their smaller peers. The empirical analysis suggests that this finding roots in the fact
that the production by large turbines is less negatively correlated to electricity prices. All else equal, an investor would therefore be better off owning a share in a large turbine.
This key finding of the bigger the better makes an important assumption however, which is that all other variables are equal. These other variables specifically refer to the cost side of such investments. In particular, investors are exposed to two main sources of costs. First, operational expenditures (OPEX), which occur throughout the lifetime of a project, and second, capital ex-penditures (CAPEX), which are due during the investment (or development) into a project depict the most relevant cost drivers.
To compare investment opportunities in energy assets and take into account both expected production as well as costs over time, decision-making typically relies on the concept of the levelized cost of energy (LCOE). Specifically, the LCOE depicts the ratio of total costs over time divided by the total energy output (Lai and McCulloch, 2017).28 Comparing this ratio among a subset of projects helps investors gain a quick overview of which ones seem most profitable. It is relevant to point out that the concept of LCOE does not inherently incorporate uncertainty drivers, however, it has proven to serve as a useful indicator in the industry to compare investment opportunities not only within but also across markets.
If and only if this ratio is the same across turbines, an investor is as a matter of fact better off owning a share in a larger one. If instead this ratio significantly differs across turbines, this can either strengthen or reverse profitability differences. For example, a small turbine that is more negatively correlated to energy prices than a large turbine and hence, ∆PS <∆PL, might still be the better investment opportunity ifLCOES < LCOELto an extent where it offsets the difference between ∆PS and ∆PL.
This paper does not offer any empirical background on distributions and levels of LCEOs across wind energy investment opportunities. Indeed, this could serve as another research venue and would help obtain a more complete picture on this asset class. The statement of the bigger the better therefor only holds true under the assumption of equal costs across turbines of different capacity levels and should be interpreted as such.
28LCOE derives from he ratio of costs over output over time. Specifically, it is:
LCEO= present value of costs over project lif etime
present value of energy production over project lif etime (11) The variable of costs take into consideration capital and operational expenditures. In the case of conventional energy investments, it further considers the cost of commodities that are required for production. The denominator only considers energy outpout over time. The present value of the ratio helps as an indication to compare investment opportunities.
7 Conclusion
This paper empirically examines wind energy production uncertainty and correlations to electricity prices. Next to comparing turbines with regards to absolute and relative production volatility, it investigates the relationship between production and electricity prices across capacity levels and sheds light on its monetary implications.
I find that production outputs by large-capacity turbines is higher while (relative) volatility is lower in comparison to smaller peers. I further document that large-capacity turbines are less negatively correlated to electricity prices, suggesting that they sell electricity outputs at higher prices on average. These findings have important implications. They suggest lower volatility in cash flows over time and higher risk-adjusted returns by large-capacity turbines. Additionally, these features could result in more favorable financing conditions.
Furthermore, results persist in a sample of high-frequency data, however, the magnitudes of estimates are significantly higher than monthly data suggests. This indicates that short-term dynamics largely matter for the valuation of investment opportunities.
These findings are important for investors to consider when allocating capital to the asset class of wind energy. All else equal, investors are better off following the dogma ofthe bigger the better!
Appendices
A Turbine Data
In this appendix section, I show more information on the turbine data used in the analysis.
Figure A.1: Wind turbine distribution by capacity
This figure shows the number of turbines in the data sample by the Danish Energy Agency and according to capacity levels as indicated by MW. Not all turbines shown in this plot are still in production today.
MW Frequency 05001000150020002500
0 1 2 3 4 5 6 7 8
Figure A.2: Turbine investments by vintage
The figure shows the number of added turbines according to capacity levels over time. Note that even though vintages date back to 1978, production data is only available from 2002. Not all turbines shown in this plot are still in production today. In fact, old turbines in this sample might have been replaced (re-powered) with newer and perhaps more powerful ones.
Frequency 0100200300400500600700
0 − 0.5MW 0.5 − 1MW 1 − 2MW 2 − 3MW 3+
1978 1983 1988 1993 1998 2003 2008 2013 2017
B Electricity Prices and Production
In this appendix section I show more information on electricity prices and their relationship to wind energy production.
Figure B.1: Electricity prices over time
Figure B.1a represents monthly averages of the electricity spot prices in the price areas of DK1 and DK2 as obtained by Nord Pool AS. Prices are denoted in EUR per MWh. The data goes from January 2002 until December 2017. The DK1 price area covers Jutland and Fyn (the western area), whereas the DK2 price area consists of Zealand and the Capital Region (the eastern area). Figure B.1b exhibits the differences in the electricity spot prices as denoted by the two price areas of DK1 and DK2.
(a) Electricity prices over time
2005 2010 2015
020406080100
Date
EUR per MWh
DK1 DK2
(b) Differences in DK1 and DK2 price areas
2005 2010 2015
−60−40−20020
Date
DK1 − DK2
Figure B.2: Production vs. price
This figure plots the average production of all the turbines in the sample over time as well as the SYS spot price of electricity. Production outputs for all turbines are adjusted according to Equation (1). The system (SYS) electricity spot price is the balanced price on the Nordic electricity market between the Nordic areas and is denoted in EUR per MWh.
2005 2010 2015
020406080100120
EUR per MWh MWh
0100200300400
SYS Spot Price Avg Production in MWh
Table B.1: Differences in production vs. prices
This table reports the results from Figure 4. ∆P in % depicts the average price deviation of turbines according to capacity levels and based on Equation (3). The difference (diff) is the delta between two adjacent capacity levels’ price difference. The t-test documents whether this delta is significantly different from zero.
Total 0-0.5MW 0.5-1MW 1-2MW 2-3MW 3+MW
∆P in % -1.824 -2.202 -1.929 -1.573 -1.120 -0.626
diff 0.273 0.356 0.453 0.494
t-test -3.197 -7.729 -7.934 -8.131
Panel B: DK2
∆P in % -1.179 -1.476 -1.086 -0.711 -0.858 -0.587
diff 0.389 0.376 -0.148 0.271
t-test -2.609 -1.210 0.466 -2.383
C Robustness Regressions and other Tests
C.1 Additional regressions
In this appendix section I show additional regression results based on variations of Equation (6).
Table C.1: Delta regressions of production vs. electricity prices The table shows the regression results of ∆Pi,t =α+β∆GW hi,t+γ∆Pi,t−1+κ∆T W ht+P11
j=1µjMj,t+i,t. Specifically, I subset the data sample with regards to capacity levels. The dependent variable is the relevant area price change in DK1 or DK2 of the individual turbine. Production estimates of turbineiand at timet are standardized through Equation (1) and documented in GWh. I control for lagged changes in electricity prices (γ) as well as changes in electricity consumption throughκwith the explanatory variable measured in TWh. Furthermore, I account for seasonality in price, production outputs and consumption estimates through monthly time fixed effects. Standard errors are clustered by time and documented in the brackets below the estimates.
Dependent variable:
∆Pt
Total 0-0.5MW 0.5-1MW 1-2MW 2-3MW 3+MW
(1) (2) (3) (4) (5) (6)
β: Turbine production ∆GW h −10.568 −9.588 −11.709 −9.876 −4.141 −3.700 (7.257) (6.667) (8.294) (6.275) (3.644) (4.820) γ: El. price ∆Pt−1 −0.111 −0.106 −0.105 −0.124 −0.228∗∗ −0.285∗∗∗
(0.092) (0.099) (0.092) (0.089) (0.089) (0.103) κ: El. Consumption ∆T W h 2.640∗∗∗ 2.880∗∗∗ 2.578∗∗∗ 2.422∗∗∗ 2.610∗∗∗ 2.085∗∗∗
(0.415) (0.411) (0.424) (0.404) (0.534) (0.548) Constantα −1.990∗∗∗ −2.405∗∗∗ −1.815∗∗∗ −1.773∗∗∗ −2.373∗∗∗ −2.406∗∗∗
(0.456) (0.463) (0.469) (0.400) (0.549) (0.684)
Time fixed effects? Yes Yes Yes Yes Yes Yes
Observations 580,848 144,895 373,279 36,081 17,511 9,082
Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
Table C.2: Real price regressions of production vs. electricity prices The table shows the regression results of Pi,t = α+βGW hi,t +γPi,t−1+κT W ht+P11
j=1µjMj,t+i,t. Specifically, I subset the data sample with regards to capacity levels. The dependent variable is the relevant nominal electricity price of area DK1 or DK2 of the individual turbine. Production estimates of turbineiat timetare standardized through Equation (1) and documented in GWh. I control for lagged electricity prices (γ) as well as electricity consumption (κ) with the explanatory variable measured in TWh. Furthermore, I account for seasonality in price, production outputs and consumption estimates through monthly time fixed effects. Standard errors are clustered by time and documented in the brackets below the estimates.
Dependent variable:
Pt
Total 0-0.5MW 0.5-1MW 1-2MW 2-3MW 3+MW
(1) (2) (3) (4) (5) (6)
β: Turbine ProductionGW h −13.464∗∗∗ −11.171∗∗∗ −19.379∗∗∗ −9.995∗∗∗ −4.658 −5.260
(3.412) (2.875) (5.476) (2.120) (3.056) (3.690)
γ: El. PricePt−1 0.761∗∗∗ 0.744∗∗∗ 0.772∗∗∗ 0.776∗∗∗ 0.723∗∗∗ 0.728∗∗∗
(0.068) (0.072) (0.067) (0.068) (0.064) (0.075)
κ: El. ConsumptionT W h 1.702∗∗∗ 1.885∗∗∗ 1.613∗∗∗ 1.624∗∗∗ 2.584∗∗∗ 2.851∗∗∗
(0.322) (0.340) (0.309) (0.332) (0.424) (0.580)
Constantα −24.056∗∗∗ −28.230∗∗∗ −21.221∗∗∗ −23.405∗∗∗ −40.559∗∗∗ −44.886∗∗∗
(5.958) (6.167) (5.813) (6.122) (7.701) (10.669)
Time fixed effects? Yes Yes Yes Yes Yes Yes
Observations 585,064 145,896 375,707 36,367 17,763 9,331
Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
C.2 Individual turbine exposure
In this appendix section I repeat the regression analysis according to Equation (6) on an individual turbine level. Specifically, I run regressions of every single turbine’s production on the relevant electricity price (DK1 or DK2), while adjusting for consumption, lagged prices, and month fixed effects. I only run the individual turbine regression if there are at least 10 observations for the individual unit.
I store all β-coefficients on production and plot the distributions according to capacity levels.
The results aim to provide an understanding on cross-sectional distribution in correlations to electricity prices. Figure C.1 shows the results.
Figure C.1 shows that the distribution mass of smaller turbines’β-coefficients tends to be more negative in comparison to that of large-scale turbines, which confirms previous results. A t-test on the distributions of each capacity level’s β-coefficients shows that all are significantly different from zero, however, large turbines deviate less from zero than their smaller peers when comparing means.
The distribution of 3+MW turbines’ β-coefficients is unique in comparison to others. The reason is that in this sample of turbines there is a number of wind parks. When listing wind parks, the sample distinguishes between individual turbines in the park, but lists the same production numbers for every turbine. This implies that single parks have an impact on the results within given categories as they represent higher weights than single turbines. Furthermore, there is also a small number of observations that are far from zero, suggesting that an individual turbine’s correlation to electricity prices can vary significantly and therefor resulting in much higher or lower returns.
In a nutshell, Figure C.1 confirms the results from Table 5. Smaller and individual turbines’
electricity production, on average, is more negatively correlated to electricity prices than their larger competitors. Furthermore, results under 3+MW capacity are partly driven by a number of wind parks as turbines in a given park exhibit the same production level data.
Figure C.1: Electricity vs. production
The histograms plot the distributions ofβi-coefficients obtained from the turbine-individual (i) regressions ofpi,t =α+βiGW hi,t+γpi,t−1+κT W hi,t+P11
j=1µjMi,t+i,t, grouped by capacity levels. The dependent variable is the log-price in the respective price area of DK1 or DK2 of the individual turbine. Production estimates of turbineiat timetare standardized through Equation (1) and documented in GWh. I adjust for lagged electricity log-prices and aggregated electricity consumption throughγ and κ(measured in TWh).
Furthermore, I account for seasonality in price, production outputs, and consumption estimates through monthly time fixed effects.
Total
−4 −3 −2 −1 0 1 2 3
050010001500
0−0.5MW
−4 −3 −2 −1 0 1 2 3
050100150200250300
0.5−1MW
−4 −3 −2 −1 0 1 2 3
020040060080010001200
1−2MW
−4 −3 −2 −1 0 1 2 3
020406080100
2−3MW
β
−4 −3 −2 −1 0 1 2 3
050100150
3+MW
−4 −3 −2 −1 0 1 2 3
020406080100120
C.3 Exposure over time
To further examine the results of Table 5, I investigate time-varying exposures of wind energy production to electricity prices through rolling regressions. In essence, I redo the analysis from Table 5 and based on Equation (6) but on a rolling basis of 24 months. This allows me to observe exposure throughout time. Figure C.2 shows the results.
Figure C.2: Rolling correlations between output and electricity spot prices
The figure exhibits the rolling beta estimates of the regression results of pi,t =α+βGW hi,t+γpi,t−1+ κT W ht+P11
j=1µjMj,t+i,t, grouped by the capacity of the turbines. The rolling window is 24 months.
Specifically, I subset the data sample with respect to capacity levels. The dependent variable is the relevant area log-price in DK1 or DK2, depending on where the individual turbine locates. Production estimates of turbine i at time t are standardized through Equation (1) and documented in GWh. I adjust for lagged electricity log-prices withγand aggregated electricity consumption throughκwith the explanatory variable measured in TWh. Furthermore, I account for seasonality in price, production outputs and consumption estimates through monthly time fixed effects. Standard errors are clustered by time. Gray intervals around the observations show 95% confidence intervals.
2008 2012 2016
−2.0−1.5−1.0−0.50.00.51.01.5
Total
β
2008 2012 2016
−2.0−1.5−1.0−0.50.00.51.01.5
0−0.5MW
2008 2012 2016
−2.0−1.5−1.0−0.50.00.51.01.5
0.5−1MW
2008 2012 2016
−2.0−1.5−1.0−0.50.00.51.01.5
1−2MW
β
2008 2012 2016
−2.0−1.5−1.0−0.50.00.51.01.5
2−3MW
2012 2014 2016 2018
−2.0−1.5−1.0−0.50.00.51.01.5
3+MW
It shows that correlation is volatile throughout time. Negative correlations are more likely
than not except for the 3+MW capacity level. Turbine production exposure to electricity prices is particularly volatile in the 0.5-1MW capacity bracket.
The results demonstrate another interesting observation when looking at the time horizon of 2007 until 2009. Almost all capacity level experience strong negative exposures to electricity prices.29 As this time-horizon is characterized by the financial crisis, this finding might have implications for times of economic distress. It suggests that wind energy production is more negatively exposed to electricity prices during crises, in which case investors need to anticipate even lower earnings due to higher than normal negative correlations. If true, the notion of real assets (as wind energy investments) offering a hedge against crises therefor loses some of its merit.
The next appendix section conducts additional analysis on whether times of crises are indeed of economic significance with regards to correlations.
29The 3+MW capacity bracket does not have any data available for the time of the financial crisis, because there were no turbines in operation, see Appendix A, Figure A.2.
C.4 Excluding the financial crisis
The findings of Figure C.2 suggest that regression results from Table 5 might be driven by the time horizon of the financial crisis. To test whether the results from Table 5 hold true when ignoring this time horizon, I exclude the crisis from the data sample. If it was true that results are time-varying and driven by the economic distress during the crisis, then the exclusion of this particular time will lead to different findings.
I repeat the regression of Equation (6) but only consider times outside the financial crisis. In particular, I run the same regression specification as before but exclude the time horizon from December 2007 until June 2009.30 Table C.3 shows the results.
Table C.3: Price vs. production excluding the financial crisis The table shows the regression results of pi,t =α+βGW hi,t+γpi,t−1+κT W ht+P11
j=1µjMj,t+i,t as specified in Equation (6). I subset the data sample with respect to capacity levels and run the regression excluding times of the financial crisis from December 2007 until June 2009 as defined by the US Business Cycle Expansions and Contractions by the National Bureau of Economic Research. The dependent variable is the relevant area log-price in DK1 or DK2, depending on where the individual turbine locates. Produc-tion estimates of turbine i at time t are standardized through Equation (1) and documented in GWh. I adjust for lagged electricity log-prices through γ and aggregated electricity consumption through κ with the explanatory variable measured in TWh. Furthermore, I account for seasonality in prices, production outputs and consumption estimates through monthly time fixed effects. Standard errors are clustered by time and documented the brackets below the estimates.
Dependent variable:
pt
Total 0-0.5MW 0.5-1MW 1-2MW 2-3MW 3+MW
(1) (2) (3) (4) (5) (6)
β: Turbine Prod. GW ht −0.507∗∗∗ −0.426∗∗∗ −0.737∗∗∗ −0.374∗∗∗ −0.275∗∗ −0.291∗∗
(0.102) (0.087) (0.152) (0.074) (0.112) (0.123) γ: El. Pricept−1 0.754∗∗∗ 0.746∗∗∗ 0.761∗∗∗ 0.763∗∗∗ 0.741∗∗∗ 0.733∗∗∗
(0.053) (0.053) (0.052) (0.057) (0.068) (0.083) κ: El. ConsumptionT W ht 0.044∗∗∗ 0.047∗∗∗ 0.042∗∗∗ 0.044∗∗∗ 0.072∗∗∗ 0.090∗∗∗
(0.008) (0.008) (0.007) (0.008) (0.010) (0.017)
Constantα 0.064 −0.003 0.133 0.014 −0.408∗∗ −0.714∗∗
(0.223) (0.223) (0.223) (0.227) (0.201) (0.346)
Month fixed effects? Yes Yes Yes Yes Yes Yes
Observations 517,340 128,236 329,983 32,390 17,400 9,331
Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
30This time span is commonly referred to as the horizon of the crisis, see US Business Cycle Expansions and Contractions by the National Bureau of Economic Research.
It still holds true that the largest capacity brackets of 2-3MW and 3+MW are least correlated to electricity prices and therefore depict ’the best’ option for investors under the assumption of constant costs to scale and exclusively considering correlations.
Furthermore, I run the linear regression with interaction effects between the financial crisis and production outputs, see Table C.4. Except for the the 2-3MW capacity level, I find no significant interaction effects between the crisis and production outputs.
The results of Table C.4 indicate that the financial crisis does not necessarily play a significant (although numbers are negative) role in the empirical findings of the main analysis. Absolute correlations seem to be relatively constant even when adjusting for the crisis. This is important for investors to consider when allocating capital to wind energy investments or potentially other renewable energy sources. Contrary to what the previous appendix section may suggest, it seems as if correlations between wind energy production and electricity prices are mostly stable throughout crises and could therefore depict a hedge in economic downturns.
Table C.4: Electricity prices, production, and the financial crisis
The table shows the regression results ofpi,t =α+βGW hi,t+ωN BERt+γpi,t−1+κT W ht+υ(N BERt× GW hi,t) +P11
j=1µjMj,t+i,t. Specifically, I subset the data sample with respect to capacity levels. The dependent variable is the relevant electricity log-price in area DK1 or DK2, depending on where the indi-vidual turbine locates. Production estimates of turbine iat timet are standardized through Equation (1) and documented in GWh. I control for lagged electricity prices (γ) as well as electricity consumption (κ) with the explanatory variable measured in TWh. The interaction term ofN BERtandGW hi,t depicts the correlation of production with electricity prices during the financial crisis as defined by the US Business Cycle Expansions and Contractions by the National Bureau of Economic Research, where N BERt is a dummy variable that is 1 during the crisis and 0 otherwise. Furthermore, I account for seasonality in price, production outputs and consumption estimates through monthly time fixed effects. Column 6 does not doc-ument estimates for the financial crisis and the interaction term because data is available only thereafter.
Standard errors are clustered by time and documented in the brackets below the estimates.
Dependent variable:
pt
Total 0-0.5MW 0.5-1MW 1-2MW 2-3MW 3+MW
(1) (2) (3) (4) (5) (6)
β: Turbine ProductionGW h −0.441∗∗∗ −0.376∗∗∗ −0.638∗∗∗ −0.323∗∗∗ −0.262∗∗ −0.291∗∗
(0.096) (0.082) (0.141) (0.070) (0.109) (0.123)
ω: Financial CrisisN BER 0.027 0.014 0.019 0.042 0.030
(0.052) (0.043) (0.062) (0.053) (0.051)
γ: El. Pricept−1 0.765∗∗∗ 0.755∗∗∗ 0.774∗∗∗ 0.773∗∗∗ 0.744∗∗∗ 0.733∗∗∗
(0.056) (0.056) (0.055) (0.059) (0.068) (0.083) κ: El. Consumption T W h 0.044∗∗∗ 0.047∗∗∗ 0.041∗∗∗ 0.044∗∗∗ 0.070∗∗∗ 0.090∗∗∗
(0.008) (0.008) (0.007) (0.008) (0.010) (0.017) υ: T. Production ×F. Crisis −0.021 0.082 0.038 −0.130 −0.388∗
(0.266) (0.186) (0.328) (0.266) (0.213)
Constantα 0.022 −0.040 0.082 −0.020 −0.404∗∗ −0.714∗∗
(0.230) (0.226) (0.232) (0.233) (0.202) (0.346)
Month fixed effects? Yes Yes Yes Yes Yes Yes
Observations 585,064 145,896 375,707 36,367 17,763 9,331
Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
C.5 Cash flows
In this appendix section, I show what the distribution of cash flows according toCt=M W ht×Pt and under different capacity levels. This implicitly assumes that the correlation between power prices and production is zero within months, so that investors capture the electricity price as denoted by the average price of a given month.
Figure C.3: Cash flows
I calculate cash-flows according toCt = M W ht×Pt for every turbine in the sample. Cash flows are in EUR. Production units ofM W htwere adjusted by capacity levels according to Equation (1). Distributions therefore depict average monthly cash-flows from electricity production for every MW in capacity. The vertical solid line is the mean. The dotted line depicts the median.
Total
0 5000 15000 25000
0500010000150002000025000
0−0.5MW
0 5000 15000 25000
0500010000150002000025000
0.5−1MW
0 5000 15000 25000
0500100015002000
1−2MW
0 5000 15000 25000
050100150200
2−3MW
Cash Flows per Month
0 5000 15000 25000
01020304050
3+MW
0 5000 15000 25000
0510152025
D High-Frequency Data
This appendix section graphically presents the relationship between wind speeds and power pro-duction by both a small and a large turbine. The data stems from a private investor in renewable energy.
Figure D.1: High-frequency turbine outputs and wind speeds
This plot shows high-frequency production outputs over wind speeds for an arbitrary small and large turbine each. The data was provided by a private investor in renewable energy. Specifically, the data depicts 10-minute production and output level data, which I aggregate to hourly estimates. I plot a randomly chosen subset of 20,000 observations each for both the small and the large turbine sample. The reason for only showing only a subset of the entire sample is to ensure visibility of the plot. Small turbines are those with a capacity of less than 0.75MW, and vice versa.
0 5 10 15 20 25
0.00.20.40.60.81.01.2
Wind Speed in m/s
MWh
Small turbine Large turbine