Electronic copy available at: http://ssrn.com/abstract=2495278 Robustness of Renewable Energy Support Schemes Facing Uncertainty and Regulatory Ambiguity Ingmar Ritzenhofen a,* , John R. Birge b , Stefan Spinler a a WHU – Otto Beisheim School of Management; Kuehne Foundation Endowed Chair in Logistics Management; Burgplatz 2, 56179 Vallendar, Germany b University of Chicago Booth School of Business; Jerry W. and Carol Lee Levin Professor of Operations Management; 5807 South Woodlawn Avenue, Chicago, IL 60637, United States Abstract Renewable portfolio standards, feed-in-tariffs, and market premia are widely used policy instru- ments to promote investments in renewable energy sources. Regulators continuously evaluate these instruments along the main electricity policy objectives of affordability, reliability, and sustainabil- ity. We develop a quantitative approach to assess these policies and their robustness to exogenous changes along these dimensions using a long-term dynamic capacity investment model. We compare their robustness in the light of uncertain renewable feed-in and ambiguous future regulation. We implement the robustness analysis employing different risk measures and find that renewable port- folio standards deliver most robust results, while feed-in-tariffs achieve target renewable buildup rates at least cost. Keywords: Renewable portfolio standards, Feed-in-tariffs, Power generation, Scenario reduction JEL: Q4, Q2, L9, L5 1. The Role of Renewable Energy Support Schemes Installations of renewable energy sources (RES) for electricity generation continue their growth path with investment of 214 Billion USD globally in 2013, equivalent to capacity additions of 80 GW (REN21, 2014). This investment boom is fueled by different RES support schemes (RESSS) such as renewable portfolio standards (RPS) and feed-in-tariffs (FIT) including market premia (MP) (Couture et al., 2010), which have been adopted by 79 and 98 countries, states, and provinces, respectively (REN21, 2014). In recent years, researchers have focused on assessing the effectiveness of these policy tools in driving RES investment (e.g., Mormann (2012)). However, ongoing public * Corresponding author. Tel.: +49 261 6509 434 Email addresses: [email protected](Ingmar Ritzenhofen), [email protected](John R. Birge), [email protected](Stefan Spinler)
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Electronic copy available at: http://ssrn.com/abstract=2495278
Robustness of Renewable Energy Support Schemes Facing Uncertainty andRegulatory Ambiguity
Ingmar Ritzenhofena,∗, John R. Birgeb, Stefan Spinlera
aWHU – Otto Beisheim School of Management; Kuehne Foundation Endowed Chair in Logistics Management;Burgplatz 2, 56179 Vallendar, Germany
bUniversity of Chicago Booth School of Business; Jerry W. and Carol Lee Levin Professor of OperationsManagement; 5807 South Woodlawn Avenue, Chicago, IL 60637, United States
Abstract
Renewable portfolio standards, feed-in-tariffs, and market premia are widely used policy instru-
ments to promote investments in renewable energy sources. Regulators continuously evaluate these
instruments along the main electricity policy objectives of affordability, reliability, and sustainabil-
ity. We develop a quantitative approach to assess these policies and their robustness to exogenous
changes along these dimensions using a long-term dynamic capacity investment model. We compare
their robustness in the light of uncertain renewable feed-in and ambiguous future regulation. We
implement the robustness analysis employing different risk measures and find that renewable port-
folio standards deliver most robust results, while feed-in-tariffs achieve target renewable buildup
rates at least cost.
Keywords: Renewable portfolio standards, Feed-in-tariffs, Power generation, Scenario reduction
JEL: Q4, Q2, L9, L5
1. The Role of Renewable Energy Support Schemes
Installations of renewable energy sources (RES) for electricity generation continue their growth
path with investment of 214 Billion USD globally in 2013, equivalent to capacity additions of 80 GW
(REN21, 2014). This investment boom is fueled by different RES support schemes (RESSS) such
as renewable portfolio standards (RPS) and feed-in-tariffs (FIT) including market premia (MP)
(Couture et al., 2010), which have been adopted by 79 and 98 countries, states, and provinces,
respectively (REN21, 2014). In recent years, researchers have focused on assessing the effectiveness
of these policy tools in driving RES investment (e.g., Mormann (2012)). However, ongoing public
geothermal, and 81% for biomass. RES, excluding geothermal, hydro, and nuclear, feature a CO2
intensity ιi of zero. For geothermal, ιi amounts to 0.054 t/MWh and to 0.374 t/MWh for OCGT
and CCGT (EIA, 2013b; Air Resources Board, 2013). The initially installed generation capacity
and its age structure are based on CEC (2013). We derive parameters for the demand function from
CAISO (2014) and a short-term price-sensitivity of demand βt of 0.1 USD/(MWh)2 in line with a
survey provided by Lijesen (2007). In line with Kettunen et al. (2011), we assume heterogeneous
investors with symmetrically distributed discrete discount rates d with a share φ1 = 10% of investors
applying d1 = 6%, φ2 = 20% use d2 = 8%, φ3 = 40% require d3 = 10%, φ4 = 20% take d4 = 12%, and
φ5 = 10% have d5 = 14%. All investors use a risk-free rate drf of 3% for revenues from MP and FIT
given their isolation from market risk. Together, all investors can build up to 2 GW of capacity of
each technology per year except nuclear and hydro. This is consistent with empirical evidence, as
maximum annual capacity additions amounted to 3.4 GW for OCGT and CCGT combined and 1
GW for each RES technology in the period 2002 to 2012 (CEC, 2013). Only a share φinv of this is
invested, if only some investors obtain NPVs and VaRs beyond Θi and ΘV aRi .
For the uncertain capacity factor multiplier. χi ∼ N(υi, σ2i ), we assume υi = 1 ∀ i = 1, ..., rint, σi
for wind of 14.8%, and 10.6% for solar consistent with the literature (NREL, 2014; Dean, 2010).
We base these estimates on data from CEC (2013) for 2001 to 2012 and fit the capacity factor
distributions. Q-Q plots for wind and solar indicate a reasonable fit to normal distributions.
Based on the Akaike information criterion (AIC) and Chi-square statistics the normal distribution
outperforms alternative distributions for solar. For wind, the normal distribution ranks sixth (out
of 18 distributions tested) according to the AIC with only a 10% lower AIC value than the best-
18
fit distribution, and ranks second according to the Chi-square statistics. We initially generate
S = 100 scenarios to reflect the uncertain capacity factor realizations and use a target cardinality
of S = 10. RES support rates for MP and FIT are calibrated so that they induce similar levels of
RES electricity production and CO2 emissions for comparability with the RPS.
For regulatory ambiguity,. we assume that two states of the ITC exist – either it is in place or
abolished. Potential abolition times are ambiguous and investors can only define the set of possible
abolition times but not their probability distribution. E.g., it can be argued that the ITC will
expire within the next 20 years. Thus, the number of scenarios amounts to 20 and is sufficiently
small in light of 10-20 iterations per run and 100 runs per RESSS, so that no scenario generation
and reduction techniques are needed. RES support rates from the uncertainty case are maintained
for comparability.
6. RPS as most Robust Support Scheme
As described in Ritzenhofen et al. (2014) in more detail, all three RESSS increase RES instal-
lations and RES electricity generation in a deterministic setting. FIT and MP can deliver these
results at lower cost given the lower risk exposure of investors benefiting from the certainty of FIT
and MP payments, while RPS provide the lowest electricity price volatility and deliver consistent
results for varying market conditions, which lead to substantial under- or over-investment under
FIT and MP schemes. Based on these deterministic results, we expect RPS schemes to exhibit a
greater robustness vis-a-vis uncertain and ambiguous input parameters compared to MP and FIT
schemes, while the latter are likely to deliver target RES buildups at lower cost.
6.1. Robustness against Uncertainty
For all three RESSS, we report average results and their distribution based on 100 runs per
scheme under RES capacity factor uncertainty. In Table 2 we show key results across policy di-
mensions for the deterministic case, the uncertain RES capacity factor case, and the regulatory
ambiguity case. For all RESSS, total cost only changes by less than 3% between the deterministic
case and the uncertain case. Equation 15 increases RES capacity under RPS, which we match
through calibration of MP and FIT rates. This and the adjustment of decision rules in Equation
10 increase cost. On the other hand, additional RES capacity reduces the need for costly and po-
19
Dimension Scheme Unit Deterministic Uncertain RES Policycase capacity factors ambiguity
Total cost RPS Billion USD 371/− 359/1% 373/3%Total cost MP Billion USD 346/− 341/1% 352/2%Total cost FIT Billion USD 307/− 316/1% 330/3%Electricity prices RPS USD/MWh 61/− 60/1% 60/1%Electricity prices MP USD/MWh 60/− 60/2% 61/2%Electricity prices FIT USD/MWh 57/− 56/7% 59/7%Electricity price volatility RPS % 11/− 17/12% 14/17%Electricity price volatility MP % 12/− 15/29% 11/44%Electricity price volatility FIT % 34/− 36/52% 25/80%CO2 emissions RPS Million t 576/− 573/1% 570/1%CO2 emissions MP Million t 565/− 581/3% 604/4%CO2 emissions FIT Million t 580/− 578/5% 608/8%RES generation RPS TWh 88/− 90/8% 90/7%RES generation MP TWh 90/− 94/10% 80/16%RES generation FIT TWh 89/− 87/14% 68/26%
Table 2: Key results across policy dimensions (averages / relative standard deviation)
tentially idle conventional capacity for meeting RAR requirements and decreases electricity market
prices. Therefore, the overall effect is mixed and depends on the precise calibration of the model.
We now compare RESSS performance under uncertainty as illustrated in Figure 1 in the Box-
and-Whisker-Plot. The boxes illustrate the second and third quartile of results and the whiskers
show maximum and minimum values. Three results become immediately apparent: first, total cost
under the RPS scheme are higher than under MP and FIT based on median values, 5% VaR, and
5% CVaR. We report both risk metrics for consistency with measures reported earlier and since
only CVaR ensures coherence for these market outcomes, which are non-normally distributed as
opposed to the normally distributed NPV results. Second, RPS is the most robust scheme across all
policy dimensions with the smallest ranges for quartiles and whiskers. Third, variability of results
is partly skewed in particular for electricity prices and their volatility under FIT.
Robustness of RPS compared to MP and FIT can be explained by the functionality of the REC
and electricity market. The REC market ensures that a pre-determined amount of RES electricity
is produced for all capacity factor realizations. For example, increases in RES electricity production
from existing plants given high capacity factors lower the rate of new RES investment and thereby
reduce REC prices (see Equation 7). At the same time, electricity prices drop given their convexity
in capacity factors, thereby decreasing price expectations for new investment and thus increasing
REC bids for new generation (see Equation 8). On the other hand, new investment under MP
20
Total cost of electricity*
Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**
%
CO2 emissions*Million t
Dimension RPS MP FIT
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD
300350400
305070
0%100%200%
400500600700
2060100140
362/362 349/349 322/324
Figure 1: Aggregate results for RPS, FIT, and MP under capacity factor uncertainty
and FIT is triggered by the threshold rules in Equation 10 and therefore changes easily. As shown
in Section 3.7, revenues of RES producers are isolated from the electricity market under a FIT
regime, as all RES electricity generated is dispatched into the market. This exacerbates the effect
of convex prices and is reflected in the asymmetric distributions of average electricity prices and
their volatility. While the range is narrow for RPS, electricity prices are skewed towards the low
end and their volatility towards the high end under MP and in particular under FIT, reflecting
how increasing intermittent RES supply depresses prices and increases volatility. In Figure 2, we
illustrate the trade-offs faced by regulators when designing RES policies. For example, if regulators
aim to achieve a CO2 target at least equal to the results under the RPS scheme, they could increase
FIT rates to boost RES generation and thereby ensure that even under non-favorable capacity factor
realizations the target is met. While total cost do not increase substantially, electricity prices drop
and their volatility rises sharply compared to the initial FIT calibration.
6.2. Robustness against Ambiguity
We account for regulatory ambiguity by investigating the possible abolition of ITCs within the
next 20 years. For such settings, probability distributions are usually unknown and only ranges
of results are reported. For comparability, we combine the results for the ambiguous case into
one average value and a standard deviation assuming equal weighting of all scenarios. Without
21
Total cost of electricity*Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**%
CO2 emissions*Million t
Dimension RPS FIT FIT+2% FIT+4% FIT+6%
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD and Million t of CO2, respectively
FIT+8%
300350400450
3040506070
0%100%200%
400500600700
2060100140
362/362 322/324 322/323 322/324 323/326320/321
583/584 622/632 597/608 580/591 576/584604/615
Figure 2: Effect of moderately increasing FIT support rate
additional information on ITC abolition times, this uniform probability distribution provides for an
unbiased initial guess and therefore a valid starting point for a this analysis. We observe that total
cost increases across schemes compared to the uncertain case driven by the potential abolition of
the ITC otherwise reducing net investments (see Table 2). This cost increase is most pronounced in
the VaR/CVaR, which rises from 362/362 to 387/387 Billion USD for RPS, from 349/349 to 360/361
for MP, and from 322/324 to 347/351 for FIT. These mean values and risk criteria highlight that
before the abolition of ITCs, the impact of regulatory ambiguity on investment decisions and thereby
electricity markets is small and only affects expected electricity prices. The impact amplifies with
earlier ITC policy changes and two counteracting effects emerge: the lost ITC reduces incentives for
RES investment, while these are increased by higher electricity prices in later periods. Compared
to the uncertainty case, RES investment drops under MP and FIT as profitability thresholds are
no longer met given the higher net upfront investment, which is partly compensated by higher
electricity prices under MP. However, for the RPS scheme with its exogenously set quota total RES
generation remains constant and part of the increase in cost from the ITC abolition is compensated
by a shift to wind power, which is not affected by ITC regulation. The RPS scheme continues to be
most robust followed by MP and FIT as similar dynamics apply as for the uncertainty case. This
illustrates that our methodology can be applied equally to uncertain and ambiguous settings and
that robustness performance of RESSS is similar under both settings.
22
6.3. Policy Implications
These results suggest that there is not a single “best” RESSS. For policy makers this implies
that the choice of a RESSS has to be matched carefully to specific policy objectives. On the one
hand, MP and FIT schemes have the potential to induce RES investment at lower cost. On the
other hand, RPS lead to lower electricity market price volatility and are more robust in light of
uncertain or ambiguous parameters such as RES capacity factors or regulatory changes. Further-
more, uncertainty not only increases performance variability along all policy dimensions but market
outcomes are also skewed as shown for electricity prices and their volatility. Consequently, pol-
icy makers should consciously make the trade-offs between these respective benefits and pitfalls.
Furthermore, our results indicate that policy makers should not only consider a single policy in
isolation but account for interactions between multiple policies – e.g. between the ITC and the
RPS – and potential changes to these inducing regulatory ambiguity.
7. Conclusions and Directions for Future Research
In this work, we develop a quantitative approach to investigate the structural impact of RESSS
on electricity markets under uncertainty and ambiguity. We measure performance and robustness
of RESSS along key policy dimensions. Moreover, we introduce appropriate risk measures and
use scenario reduction techniques to facilitate the implementation of the stochastic variables. This
approach can be extended to different electricity markets, to assess alternative electricity market
policies, or to account for alternative sources of uncertainty or ambiguity. In a numerical case
study, we show that for the CA electricity market RPS deliver more robust results along all policy
dimensions compared to a hypothetical MP or FIT and explain that this might come at higher cost.
While this novel approach provides for broad insights into the dynamics of electricity markets and
related policies such as RESSS, further research is needed to investigate the impact of more flexible
MP and FIT designs and to apply this framework to further markets, which is beyond the scope
of this paper. Additionally, further research is needed to investigate the impact of alternative risk
measures, other potential sources of uncertainty and ambiguity as well as to investigate different
ways investors learn how to deal with the uncertainty and ambiguity factors.
23
Acknowledgements
The authors would like to thank the University of Chicago Booth School of Business and the
Energy Policy Institute at Chicago (EPIC) for facilitating this collaboration. Moreover, the au-
thors gratefully acknowledge the valuable input from multiple members of the two above-mentioned
institutions.
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Appendix A. Scenario Reduction
Following an approach suggested by Heitsch and Romisch (2009) and Growe-Kuska et al. (2003),we reduce the number of scenarios as follows. Let χi ∀ i = 1, ..., rint be the stochastic variables withtheir realizations over time χui,tTt=1 ∀ i = 1, ..., rint jointly forming the scenarios χz ∀ z = 1, ..., S
with S being the number of scenarios. The probability of each scenario z is $z with ∑Sz=1$z = 1and Ωz being the probability distributions of the stochastic variables χi. We use the Kantorovichdistance DK (Growe-Kuska et al., 2003) to successively combine the most similar scenarios. Wereduce the number of scenarios S by the cardinality #Z of the index set of deleted scenarios Z tothe new number of target scenarios S. For a pre-specified Z ⊂ 1, ..., S, the Kantorovich distanceis defined as
DK(Ω,Ω′) = ∑z1∈Z
$z minz2∉Z
ct(χz1 , χ′z2) with ct(χz1 , χ′z2) ∶=T
∑t=1
∑rinti=1 ∣χz1i,t − χ
′z2i,t ∣
(1 + d)t (A.1)
with χz1 with χz1z1∉Z having minimal distances to χz2i . We discount with the risk-free rate drf
to attribute greater importance to early periods and reflect NPV-driven investor behavior. Wecompute the probability $z2
update of preserved scenarios χz2 with z2 ∉ Z as
$z2update =$
z2 + ∑z1∈J
$z1 . (A.2)
Therefore, we can formulate the “optimal reduction problem” (Growe-Kuska et al., 2003, p.2)as
min
⎧⎪⎪⎨⎪⎪⎩∑z1∈Z
$z minz2∉Z
ct(χz1 , χz2) ∶ Z ⊂ 1, ..., S,#Z = S − S⎫⎪⎪⎬⎪⎪⎭. (A.3)
Appendix B. Model Verification
In these parts of the Appendix, we show how we verify and validate the model at hand. Forthis purpose, we build on well-established approaches of Gass (1983) and Sargent (2012).
We continuously verify the model and attempt to ensure that the model “runs as intended”(Gass, 1983, p.609). This is done as follows. First, we develop a modular model structure asillustrated by Figure B.3 with each box and the computations for each decision rule being a separatemodule. Second, we test these modules separately, i.e. use simplified and stylized input datato verify whether each the relationships between inputs and outputs for each module behave asexpected.
In addition, we conduct further tests of the correctness of the model mechanization as part ofthe sensitivity analyses described in Section Appendix C.
Appendix C. Model Validation
Following Gass (1983), we then test the technical, operational, and dynamic validity of themodel in order to “establish how closely the model mirrors the perceived reality” of the electricitymarkets analyzed.
For the validation we build on the different philosophy of science methods – rationalism, em-piricism, and positive economics – as suggested in (Sargent, 2012, p.17). We validate the setup,
28
Repeat Ttimes for ititerations
Cost-optimal conventional generation portfolio1
Electricity prices
Updated generation portfolio
Electricitymarket
Stoppingafter con-vergence
Initial forecast Actual iterations
REC pricesREC market
Investor decisionson capacity
Investors decisions include Plant retirements at end of useful life Divestitures given lacking profitability
based on initial forecast/prior iteration New investments given positive expected
NPV based on initial forecast/prior iteration
100 repetitions with randomly drawn capacity factor scenarios
Figure B.3: Structural setup of dynamic capacity investment model
structure, and logic of the model to address rationalism. Empiricism requires us validate our as-sumptions and all model results against real data (where available). By validating outcomes we alsoaddress positive economics, which are only concerned with correct model results. We use variousvalidation techniques suggested by Gass (1983) and Sargent (2012), which we summarize in TablesC.3 and C.4. Details on these validation items are provided in the following Sections.
29
Type of technical validation Aspects Description
– Model validation Objectives of model – Modeling objectives explicitly outlined in Sections 1 and 2– Assessment of affordability, security of supply, sustainabilityof electricity supply, and robustness under RESSS
Appropriateness of structure – Choice of model motivated by literature review (see Section 2) and modelingobjectives– Documentation of structure illustrated in Figure B.3
Structural limitations – Limitations and assumptions discussed in Sections 3, 4, and 7– Further limitations (only implicitly mentioned via assumptions): Abstractionfrom transmission constraints given spatial aggregation of our analysis; no modelingof reserve or balancing power markets given their limited size; no incorporationof other exogenous shocks like economic crises beyond those explicitly modeled
Documentation of model – Extensive documentation in Sections 3 and 4 and in Ritzenhofen et al. (2014)– Logical/mathem. validation Model logic – Clear model logic and structure (see Figure B.3)
– Clear reflection electricity market (see Figure C.4)Critical points – Critical assumptions highlighted: rational and profit-oriented behavior;
heterogeneous investors attributing no risk to MP and FIT payments; constructionof representative plants per technology; constant climatic conditions, i.e. stationaryuncertainty factor distributions
Replication of results – Ability to replicate results in multiple model runs (deviationof average total cost of < 0.5% between sample runs)– Model available upon request
– Data validation Input data documentation – Extensive input data documentation in this work and in Ritzenhofen et al. (2014)Empirical data comparison – Use of data from industry reports and actual market outcomes
Table C.3: Technical model validity
30
Type of operational validation Aspects Description
– Results validation Face validity – Discussion of results with researchers, policy makers,and practitioners from utilities, RES project developers,and equipment manufacturers
Hypothesis tests – Formulation and comparison to hypotheses (e.g., see Section 6)Operational graphics – Monitoring of results through detailed non-aggregated output
graphs (see Section Appendix E)– Experimental validation Sensitivity analysis – Sensitivity analyses in Ritzenhofen et al. (2014)
– Additional sensitivity analyses on keyparameters (see Figure 2 and Section Appendix D)
– Comparative validation Comparison to other studies – RPS case with similar results as in otherstudies such as CPUC (2013); first, mainly addition of wind power,then increasingly solar power; reduction in geothermal and biomassover time– No direct comparison available for FIT and MP as alternativestudies for CA mostly model the existing RPS scheme– Electricity price progression in line with EIA (2014a)
– Policy impact validation Comparison against public debate – Similar discussions in journals and magazineslike The Economist (2013, 2014) elaborating onthe various challenges of electricity markets– Key aspects of this work such as market integration explicitlyhighlighted in recent electricity market reforms forexample in Germany (Agora Energiewende, 2014)
Table C.4: Operational model validity
31
1 Renewable energy certificates; 2 Utilities, transmission and distribution operators or others depending on local regulation; 3 Households, industry, and others; sometimes these are also the obliged entities depending on regulation
Regulator
Renewable generators
Electricity market REC1 market
Conventional generators
E $
E
$
REC $
REC$E $
RECData
RECQuota
E $ $
Retailers / obliged entities2
Electricity consumers3
Market Endogenous player Exogenous player
Regulator (ex ante announcement of
all annual quotas)
Renewable generators
(annual invest & hourly dispatch per plant &
technology)
Electricity market (hourly dispatch)
REC1 market (annual clearance)
Conventional generators
(annual invest & hourly dispatch per plant &
technology)
Retailers / obliged entities2
(hourly aggregate demand curve)
Electricity consumers3
(not simulated explicitly)
Figure C.4: Reflection of electricity market in model
Appendix D. Sensitivity analyses
32
Total cost of electricity*
Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**
%
CO2 emissions*Million t
Dimension RPS MP FIT
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD
300350400
305070
0%100%200%
400500600700
2060100140
365/365 349/349 326/328
Figure D.5: Results with standard deviation for capacity factors increased by 5 percentage points
Total cost of electricity*
Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**
%
CO2 emissions*Million t
Dimension RPS MP FIT
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD
300350400
305070
0%100%200%
400500600700
2060100140
363/364 349/350 323/325
Figure D.6: Results with 50 instead of 100 runs – set of runs 1
33
Total cost of electricity*
Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**
%
CO2 emissions*Million t
Dimension RPS MP FIT
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD
300350400
305070
0%100%200%
400500600700
2060100140
362/362 346/346 322/324
Figure D.7: Results with 50 instead of 100 runs – set of runs 2
Total cost of electricity*
Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**
%
CO2 emissions*Million t
Dimension RPS MP FIT
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD
300350400
305070
0%100%200%
400500600700
2060100140
363/363 348/349 320/322
Figure D.8: Results with 75 instead of 100 runs – set of runs 1
34
Total cost of electricity*
Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**
%
CO2 emissions*Million t
Dimension RPS MP FIT
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD
300350400
305070
0%100%200%
400500600700
2060100140
362/362 347/348 321/323
Figure D.9: Results with 75 instead of 100 runs – set of runs 2
Total cost of electricity*
Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**
%
CO2 emissions*Million t
Dimension RPS MP FIT
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD
300350400
305070
0%100%200%
400500600700
2060100140
362/362 348/349 322/324
Figure D.10: Results with 100 runs for result replication – set of runs 1
35
Total cost of electricity*
Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**
%
CO2 emissions*Million t
Dimension RPS MP FIT
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD
300350400
305070
0%100%200%
400500600700
2060100140
363/363 348/349 320/322
Figure D.11: Results with 100 runs for result replication – set of runs 2
Total cost of electricity*
Billion USD
Electricity prices**USD/MWh
RES gene-ration year 20TWh
Electricity price volatility**
%
CO2 emissions*Million t
Dimension RPS MP FIT
* Sum over 20 years; ** Average over 20 years VaR/CVaR in Billion USD
300350400
305070
0%100%200%
400500600700
2060100140
362/363 342/344 323/325
Figure D.12: Results with 20 remaining scenarios instead of 10
36
0
50
100
150
200
0 5 10 15 20U
SD/M
Wh
Iteration
Average electricity price
RPS MP FIT
020406080
100
0 5 10 15 20
GW
Iteration
Average installed total capacity
RPS MP FIT
Figure E.13: Electricity price behavior for sample run under RES capacity factor uncertainty
Hydro Nuclear CCGT OCGTBiomass Geothermal Wind onshore Solar PV
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
GW
RPS
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
GW
MP
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20G
W
FIT
Figure E.14: Installed capacity for sample run under RES capacity factor uncertainty
Appendix E. Operational Graphics
37
Hydro Nuclear CCGT OCGTBiomass Geothermal Wind onshore Solar PV
0
50
100
150
200
250
1 3 5 7 9 11 13 15 17 19
TW
h
RPS
0
50
100
150
200
250
1 3 5 7 9 11 13 15 17 19
TW
h
MP
0
50
100
150
200
250
1 3 5 7 9 11 13 15 17 19
TW
h
FIT
Figure E.15: Electricity generation for sample run under RES capacity factor uncertainty
98%
99%
100%
101%
102%
0 2 4 6 8 10 12 14 16 18 20
Fullfillment of RAR
RPS MP FIT
Figure E.16: RAR fulfillment for sample run under RES capacity factor uncertainty
0
50
100
150
200
0 5 10 15 20
USD
/MW
h
Iteration
Average electricity price
RPS MP FIT
020406080
100
0 5 10 15 20
GW
Iteration
Average installed total capacity
RPS MP FIT
Figure E.17: Convergence of results for sample run under RES capacity factor uncertainty