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Abstractev

Levelized Full System Costs of Electricity

Different electricity generating technologies are often compared using the Levelized Costs

errof Electricity (LCOE), which summarize different ratios of fixed to variable costs into asingle cost metric. They have been criticized for ignoring the effects of intermittency andnon-dispatchability. This paper introduces the Levelized Full System Costs of Electricity(LFSCOE), a novel cost evaluation metric that compares the costs of serving the entirepemarket using just one source plus storage. Like LCOE, and in contrast to alternatives suchas System LCOE, LFSCOE condense the cost for each technology into one number per
market. The paper calculates LFSCOE for several technologies using data from two different
markets. It then discusses some refinements, including the LFSCOE-95 metric that requireoteach technology to supply only 95% of total demand.
Keywords: Intermittent renewables, Levelized Costs of Electricity (LCOE), System LCOE,

Pr

ep

rin

tn

Power Generation Economics, Electricity

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1

Introduction

The lifetime costs of an investment are key measures for decision-making. This is true for invest-

ment decisions in electricity markets as well, where the most popular measure to compare different
technologies for generating electricity are the Levelized Costs of Electricity (LCOE). To calculate

the LCOE, the expected lifetime generation of an electricity generating plant and the expectedev

costs to generate the lifetime electricity are calculated. After dividing total costs by total genera-tion, the final number (usually in USD/MWh) is derived. Input assumptions like capacity costs,
maintenance, marginal operating costs, or average capacity factor, which is particularly relevanterr

for renewable sources of electricity, are crucial for the calculation and vary by study.1 For example,
Lazard (2019) estimates the LCOE of coal between 66 and 152 USD/MWh and onshore between
28 and 54 USD/MWh, whereas EIA LCOE (2020) derives LCOE for coal at of USD/MWh andpe

LCOE for wind 40 USD/MW. Many recent studies indicate that the LCOE are the lowest foronshore wind and utility-scale solar using photovoltaic cells (hereafter referred to as “solar PV” or“solar”), findings frequently cited by proponents of a fast transition towards renewable electricity.
Nevertheless, if it is the cheapest source while not emitting CO2, why are countries still investingotheavily in new gas and coal power plants? Is it just because coal generation may employ more
people in politically sensitive regions of the country, or are there financial reasons not reflected intn

the LCOE?

Critiques of LCOE are not scarce. Joskow (2011) is one of the first to point out that LCOE ignore
the costs associated with intermittency. It is easy to see the fundamental misunderstanding inrin

LCOE: The LCOE describe the costs of generating electricity. However, the function of supply
in electricity markets is not to generate electricity but to provide a specified amount of electricity
to a specific place at a particular time. The locational aspect adds significant additional costs toep

renewables that are generally less flexible about where they can be sited than fossil fuel plants.
As a result, a larger grid is required to transport the electricity from, e.g., hydropower plants tothe demand in urban areas. These transmission costs are partly taken care of in some LCOE

Prestimates when a transmission cost adder is included in the LCOE. But the timing aspect turns
out to be even more crucial and the focus of this paper. Many renewables (like wind and solar)
1

I abbreviate the term “electricity plants that use renewable sources of energy” by “renewables”.

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are intermittent and non-dispatchable (hereafter referred to just as “intermittent” unless further
specified), and some that are not intermittent (like run-of-river-hydro) are often not fully dispatch-able.2 As long as the share of intermittent generation is low, sufficient dispatchable generation

capacity will usually be available to step in and replace missing intermittent generation output.
Economically, the fact that intermittent generation has no obligation to meet the demand can beev

seen as a hidden subsidy. One can even go one step further and argue that intermittent generation

is of zero value if it cannot be made available to consumers who demand a steady electricity flow.
To do that, however, supply and demand on the network must always be in balance. In effect,err

the ability to schedule other generators to continuously maintain that balance is necessary to givevalue to renewable output. The dispatchable generators thus raise the value of renewable generation, but the subsidy is “hidden” because the latter does not have to pay for it. Once the shareof intermittent generation increases to a certain level (and dispatchable capacity is shut down),peefforts have to be taken to maintain system reliability. But who should be responsible for thesecosts? How can the cost of integrating renewables into the system (which increases significantlywith their market share) be included in the evaluation of their cost?
Ueckerdt et al. (2013) address the cost of integrating renewables into a network by introducing

ot

the “System LCOE”. The System LCOE of an intermittent source are defined as the sum of the(marginal) generation costs (the LCOE) and the (marginal) integration costs, where integrationtn

costs can be split up into balancing costs, grid costs, and profile costs - see Section 2 for further
information of System LCOE. Unlike conventional LCOE, the System LCOE of renewable sourcesrinof electricity depend highly on their market share. If the share of wind (resp. solar) generation
increases, the generation costs (i.e., the LCOE) remain constant, while the integration costs increase significantly. In their calculation, the System LCOE for wind in Germany increase from 60

ep

EUR/MWh to almost 100 EUR/MWh if the share increases from 0% to 40%.
The System LCOE seem to be state of the art and reasonably accurate (see Reichenberg (2017)

for further refinement), but are apparently too complicated and “not catchy” enough to be used
Note that intermittency implies non-dispatchability, but not vice versa. Intermittency means that the capacityPr2

factor is subject to external influences and varies in a short time. In contrast, a source of electricity is nondispatchable if the operator cannot easily control its output.

2
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by a non-academic audience.3 However, there is a high necessity of a cost measure that includes

the costs of intermittency and is accessible to a broader audience. Since climate change and theaccompanying transition of the electricity market became a crucial topic in public debates andpolitics, the LCOE have become the most popular measure to evaluate investment decisions andmarket developments in electricity generation. As politicians and policymakers fail to understandev

the limitations and flaws of this measure and spread the idea that solar PV and wind are thecheapest sources of electricity, there is a need for a cost measure that addresses the limitations of
LCOE yet remains accessible to a broader audience by being catchy and straightforward.

errThis paper introduces a novel method to evaluate the costs of electricity that is catchy andincludes the costs of intermittency: The Levelized Full System Costs of Electricity (LFSCOE).
The LFSCOE are defined as the costs of providing electricity by a given generation technology,
assuming that a particular market has to be supplied solely by this source of electricity pluspestorage.4 Methodologically, the LFSCOE for intermittent or baseload technologies are the opposite
extreme of the LCOE. While the latter implicitly assume that a respective source has no obligation
to balance the market and meet the demand (and thus demand patterns and intermittency can beignored), LFSCOE assume that this source has maximal balancing and supply obligations. Thisot

paper shows that in both Germany and the region of the Electricity Reliability Council of Texas(ERCOT), the LFSCOE of wind and solar PV are higher than the most expensive dispatchabletn

technology examined in this paper.5 Simulating the effect of decreasing storage costs, we observethat although the LFSCOE for wind and solar drop significantly, even a storage cost reduction3

rinof 90% is insufficient not make wind or solar PV competitive on an LFSCOE basis.6 Allowing
It is worth noting that the calculation of LCOEs is by no means simple. The appendix to the Annual Outlook

of Energy requires more than 100 pages to introduce the terminology and describe the calculation process, see EIA

epModel Documentation (2020).
4
While storage is necessary for intermittent sources of generation, storage can also allow conventional dispatchable technologies to meet system load at lower costs, for example, by smoothing demand fluctuations and allowing
plants to operate at higher capacity factors.
5
Though the ERCOT market does not span all of Texas, ERCOT and Texas are used interchangeably in thisPrpaper.
6
Note that a decrease in storage costs is to some degree equivalent to an increase in the storage factor (i.e., theamount of MWh stored per MW installed). Some technologies (like solid-state batteries) cannot increase this factor,
while others (like flow batteries) can. This matter is briefly discussed, but a thorough analysis of an adjustable

3
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for losses in the charging and discharging process, it is interesting to see the small magnitude of
economic effects of even significant storage losses in such a system. Last, we extend the LFSCOE to
LFSCOE-95, which assume that only 95% of the system must be supplied by a certain technology
plus storage. While the LFSCOE-95 are only slightly lower than the LFSCOE for dispatchable

technologies, they are about 50% lower for intermittent sources, which challenges the economic

evsanity of 100% intermittent renewable targets.7

This paper is structured as follows: Section 2 introduces the method for calculating LFSCOE
and concludes with the cost evaluations for the markets in ERCOT/Texas and Germany. Sectionerr

3 examines different changes in the model assumptions (such as storage losses), follows up with ananalysis of significant decreases in storage costs, and concludes with introducing the LFSCOE-95.
Section 4 discusses potential model extensions and concludes.

peLiterature To my knowledge, the cost measure and evaluation methodology introduced in thispaper are new. However, studies have been conducted that address the cost of intermittent
renewables or baseload technologies when they are responsible for meeting the market demand.
Becker et al. (2014) examine the requirements of a fully renewable system in the U.S., whereasotHartley (2017) those of a wind-only market in Texas. Denholm et al. (2012) combine renewables
and nuclear with storage. For the market in Germany, Sinn (2017) discusses economic challengestn

by pointing out the large curtailment and storage requirements in a wind & solar market inGermany (using existing storage in Norway), while Zerrahn et al. (2018) conclude that electricalstorage would rather not limit the transition to renewable energy. It is important to note thatrin

the motivation of this paper is to introduce a novel methodology of calculating costs and then use
this methodology to examine some relevant counterfactuals. Given the simplifying assumptions,the numbers should not be seen as definitive.

ep

storage factor’s economic consequences is not part of this paper.
7
Decarbonization of electricity markets is often just defined as an emission reduction of at least 80%, circum-Prventing the challenge to decarbonize the last few percents - see Jenkins et al. (2018).

4This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4028640

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2

Levelized Full System Costs of Electricity

This section first introduces the concept of the Levelized Full System Costs of Electricity andcompares 5 dispatchable technologies with wind, utility scale solar PV (called “solar” from nowon), and an optimal combination of wind and solar.

ev

Assumptions A technology y has overnight capacity costs ccy , fixed operation and maintenancecosts (O&M) omcy , and variable (or constant marginal) costs vcy . Dispatchable technologies
have ramping times of rampupy and rampdowny , in percentage/hour relative to their currenterrgeneration (as depict in table 1). Note that all modern technologies can technically ramp-up
and ramp-down within an hour, making the ramping times redundant for the analysis which
only considers deterministic hourly demand (see below). However, frequent fast ramp-ups andramp-downs are not advisable and sometimes not permitted (for example for old nuclear plantspe- however, the costs in Table 1 are for new advanced plants). As a result of this, the ramping
values are set to rampupy = 150% and rampdowny = 50%, meaning that the utility can change
their output by ±50% per hour. This implicitly increases the costs for dispatchable generators,

otbut not by much as the demand fluctuations of consecutive hours are almost always within ±50%.
It is worth noting that the model only considers deterministic hourly demand and ignores any use

tn

of certain technologies outside the wholesale generation market (e.g. a natural gas combustion
turbine, which, unlike nuclear power plants, can also be used in the short-term balancing market).
In period t, intermittent and non-dispatchable generators have an hourly generation intensity ofrin

Rent ∈ [0, 1]. This value is nothing else than the maximal capacity factor in hour t of the renewable
plant - when the sun is shining or the wind is blowing, this value will be high (and close to 1), butduring the night, the intensity Rent will be equal to 0 for solar PV. The hourly demand is denoted

ep

with Dt for t = 1, ..., H (e.g. H = 8760 if the entire year is consider). Both intensity and demand
are assumed to be perfectly forecasted and are deterministic, i.e. possible demand response isignored. Following the calculations from EIA Assumptions (2020), the costs are averaged overPr

an investment period of 30 years, where the investment occurs in the first two years (thus, theovernight capacity costs are split evenly between year 1 and year 2) and the generation goes from

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Table 1: Cost Assumptions
Overnight
Capital Costs

O&M Costs

Variable Costs

ramp-up/down[USD/kW][USD/kW/year][USD/MWh][% per hour]

Biomass

4,401

125.2

28

150%/50%

Coal (USC)

3,661

40

25

Natural Gas CC

1,079

14

18

Natural Gas CT

710

7

Nuclear

6,317

121

Solar

1,331

15.2

Wind

1,319

26.2

Storage

1,383

24.7

150%/50%
150%/50%ev

Technology

150%/50%

8.4

150%/50%

0

-

0

-

0∗

-

er
r

28

Table 1: Main data source is EIA Costs (2020). The fixed costs include overnight capacity costs and fixed O&M. Wind fixed costs
are for on-shore wind. The variable costs include O& M and fuel costs, but do not include any carbon taxes or reserve payments forpeenvironmental purposes.

∗ Unlike for the generators, the variable costs for storage include all costs but purchasing the input fuel (which is electricity). As thesepurchasing costs are just transferred to the generators, they can be ignored if we evaluate the cost of the “generator + storage” system.

year 3 through year 30.8 The cost of capital is fixed at 6.7% (and thus the annual discount factorot

is β = 1/(1+0.067)) and the model implicitly assumes the same demand and hourly wind and solar
capacity factor profile in each of these years.9 The variable costs for storage are zero and there aretn

no losses in the storage process (the no-storage-losses assumption is relaxed in section 3). Storage
can store ρsf = 3 MWh per installed MW of generating capacity, which is equivalent to current
residential solid-state battery storage solutions. A moderate increase in the storage factor, whichrin

is discussed in section 3, is equivalent to decreasing the storage costs. For simplicity, no minimal
storage level or security backup is required (i.e. Ssecurity = 0 MWh), but demand has to be met at all
times. In practice, if a market is supplied solely by an intermittent source, it will be very unlikely

epthat no security storage is required as a backup. Furthermore, required security storage will also
depend on the average hourly demand, its variability and price elasticity, installed storage as well
8

Note that these investment periods seem to be quite generous for solar PV and wind, and too short for nuclear

Prand coal. On the other side, the construction period is generous for nuclear and coal, and too long for solar.
9
EIA Assumption (2020) calculates weighted average costs of capital for every year. As they are almost constant,using constant discount factor is a reasonable simplification.

6
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as installed generation capacity, and will vary between markets. Ignoring the security backup in
my model simplifies the analysis significantly and allows for maximal comparability.

Calculating the optimal installed capacity Let x ∈ RH+1 be the independent variable forthe stored electricity in MWh (i.e. x[t] is the storage level at the beginning of hour t), andgen ∈ RH the independent variable for the dispatchable generation in each period (i.e. gen[t] isev

the generation in period t).10 In the optimization problem, denote the installed capacity by rp(for intermittent “renewable power”) and dp (for “dispatchable power”), and the installed storageerrby sp (for “storage power”). Installed capacities, storage levels, and generation will be chosen tominimize total system costs conditional on meeting demand in every period. For any technology
y, the net present value of all non-variable costs (i.e fixed costs) ispe30
ccy ccy+β + ∑ β u−1 omcy ).
f cy = (22
u=3With this notation (and further explanations of each line below), intermittent sources of generation
with intensity Rent at period t solve the optimization problem
min rp ⋅ f cRen + sp ⋅ f cStorageotrp,sp,xs.t. 0 ≤ x[t + 1] ≤ x[t] + Rent ⋅ rp − Dt

(D.1)

−sp ≤ x[t + 1] − x[t] ≤ sp f or all t,

(S.1)

tn

f or all t,

Ssecurity ≤ x[t] ≤ sp ⋅ ρsf

f or all t,

10

(S.3)

rin

x[1] ≤ x[H + 1],(S.2)

To enhance readability, the elements of vectors that are independent variables are denoted with brackets [t]and the elements of vectors which are parameters are denoted with lower case t-s.

ep

It is worth noting that electricity storage does not store electricity itself, but converts it do a different form ofenergy (e.g. pumped hydro plants convert electric energy into kinetic energy). However, to enhance readability,Pr

we will use the term “storing electricity”.

7
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30

min

dp,sp,gen,x

dp ⋅ f cy + sp ⋅ f cstorage + ∑ β u−1
u=3s.t. 0 ≤ x[t + 1] ≤ x[t] + gen[t] − Dt

8760 H⋅ ∑ vcy ⋅ gen[t]H t=1

f or all t,−sp ≤ x[t + 1] − x[t] ≤ sp f or all t,
Ssecurity ≤ x[t] ≤ sp ⋅ ρsf

(D.2)
(S.1)
(S.2)

ev

f or all t,

x[1] ≤ x[H + 1],
gen[t] ≤ dp f or all t,

gen[t + 1] − gen[t]≤ rampupy
gen[t]err−rampdowny ≤iewedwhereas conventional sources y solve

f or all t,

(S.3)
(G.1)
(G.2)

The objective function calculates the total costs to meet the demand. For intermittent renewables,
this is just the costs of installing the capacity, for dispatchable sources, it also includes an additionalpeterm to account for the variable costs. Note that to calculate the net present value of these costs,
dispatchable generators are implicitly assumed to have the same generation for every year. If H issmaller than 8760, the hourly costs are extrapolated accordingly to account for an entire year.11

ot

Constraints (D.1) and (D.2) ensure that the demand Dt is met at any period t (and allows for freecurtailment/disposal of electricity if necessary), while (S.1) ensures that the storage is charged andtn

dispatched according to the technical maximum (which is the maximal installed power in GW).
Constraint (S.2) ensures that the storage level is technically feasible and larger than the security
storage. With a storage factor of ρsf = 3, we observe that the right hand side of (S.2) ensures thatrin(S.1) is never binding for intermittent technologies. In these systems, bp will be so high to ensurethat (S.2) is fulfilled so that (S.1) becomes redundant. Once the storage factor increases, however,(S.1) becomes binding at one point. Constraint (S.3) ensures that technologies are compared on
If H = 8760, there are 17523 independent variables. To reduce the computational burden in the counterfactual

ep

11

analysis, the optimization problem is only solved for half the year, i.e. H = 4380. To ensure that the solution is atleast theoretically feasible for the entire year, the condition
(X.1)

Pr

maxcapx ⋅ dp + sp ≥ max(Dt ).

is added. This ensures that the maximal annual demand can be met with the proposed solution. For intermittent
sources, the program can always be optimized over 8760 hours, which is particularly important as these costs are
driven by periods with low hourly capacity factor and seasonal properties.

8
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a level playing field by always requiring energy in storage to return to the same starting level atthe end of each simulation. Inequalities (G.1) and (G.2) restrict the generation to the maximal
capacity and the hourly change in generation to the respective ramp-up and ramp-down rate.

A solution to the optimization problem above (i.e. the optimal rp (or dp), sp, gen, and x) fory, GEN y , X y ).12 This is then the optimal installed capacity
technology y is denoted by (I y , Istorageyfor generation I y and storage Istorage
along with the hourly generation GEN y and hourly storageev

level X y . Not that the generation vector GEN y is an H × 1 dimensional vector for dispatchable
technologies (and equal to 0 for intermittent sources), whereas the storage level vector X is of sizeerr

H + 1 × 1 (and potentially equal to 0 if no storage is used).

Definition LFSCOE After solving the optimal installed capacity, generation, and storage levely(I y , Istorage, GEN y , X y ), define the LFSCOE of a dispatchable source as30

pe

LF SCOEy =y⋅ f cstorage + ∑ β u−1 ⋅ vcy ⋅I y ⋅ f cy + Istorageu=330∑ β u−1 ⋅u=38760 Hy∑ GENtH t=18760 H⋅ ∑ DtH t=1ot

and the LFSCOE of an intermittent source as

30

∑

u=3

tn

LF SCOERen =Ren
I Ren ⋅ f cRen + Istorage⋅ f cstorage

β u−1

8760

.

∑ Dt

t=1

The numerator is nothing else than the total cost of the system (and thus equal to the objectivefunction above). The denominator averages these total costs. The crucial element of the LFSCOE

rin

is the fact that costs are not averaged over the (discounted) lifetime generation but over the(discounted) lifetime demand that they and their associated storage support. For dispatchable

ep

sources, the lifetime generation is equal to (or at least close to) the lifetime demand as variablegeneration costs that are larger than 0 penalize producing excess output and as there are no storage
losses. By contrast, the next section shows that for intermittent generators, lifetime generationPris significantly higher than lifetime demand of the system, hereby causing a large amount of
overproduction and curtailed electricity. The Levelized Costs of Electricity account for some, but
not all, of the curtailment by adjusting the capacity factor and averaging over the total generation.
12

Existence and uniqueness of this solution are discussed in Appendix A.2.

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Ueckerdt et al. (2013) solves this issue by including overproduction in their cost estimation, but
as they limit their analysis to a 40% share of renewables, the overproduction is still relatively
small (see below a comparison between the LFSCOE and the results of Ueckerdt et al. (2013)).

Note that the LFSCOE are defined for one specific data set (e.g. one year for one region). If moredata on hourly demand and hourly capacity factors for a certain region is available (e.g. data forev

different years, see below) and this data cannot be incorporated into a joint optimization process,the LFSCOE are calculated separately and (with slight abuse of notation) redefined as the meanerrof each year (see calculation below).

Calculating the LFSCOE Starting with real market data for hourly demand, wind capacity
factor, and solar capacity factor from 2010/2011-2017 for Germany and 2012/2013-2019 for Texas,
the costs per MWh for each technology and year are calculated by solving the minimizationpe

problem as described above.13 We then define the LFSCOE of a technology as the mean of thecosts per MWh from each of the 8 years. Allowing also for a wind & solar mix, Table 2 and Figure
1 display the LFSCOE for each technology and market as well as the interval of the costs for eachotyear (note the different scale of the x-axis).

ep

rin

tn

Figure 1: LFSCOE Mean and Max/Min intervals in the German (left) and ERCOT market

Figure 1 displays the mean and the max/min intervals for every technology (as in Table 2).

Pr

Several interesting observations can be made. First, neither wind nor solar nor the wind & solar

13

As the installed capacity of solar was very low in 2010 in Germany and 2012 in Texas, the data does not seemtrustworthy. Thus the year 2010 in Germany and 2012 in Texas are excluded in the analysis of solar and the wind
& solar mix. For all other technologies, all 8 years are considered.

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Table 2: Levelized Full System Costs of Electricity

Germany

Texas

Technology

LFSCOE (Mean)[Min,Max]

LFSCOE (Mean)[Min,Max]

Biomass

104[100,109]

117[112,126]

Coal

78

[76,82]90

Natural Gas CC

35[34,36]40

Natural Gas CT

39[38,39]

Nuclear106[101,113]

Solar

1548

[1185,2058]

Wind

504

Wind&Solar

454[86,96]ev[38,41][40,42]

122[115,132]

413[341,579]

er
r

42

[438,552]

291[229,369][319,498]

225[178,358]

Table 2: Mean, Minimum, and Maximum in USD/MWh of the derived LFSCOE values. LFSCOE for Germany and Texas, using costpeassumptions as in Table 1 and a discounting factor of β = 1/(1 + 0.065).

mix seem economically competitive to the dispatchable sources on a LFSCOE basis. Even the
LFSCOE value of the wind & solar mix in Texas, which is the most competitive of the renewableot

technology installations considered, is almost twice as high as the LFSCOE value of the mostexpensive dispatchable technology.14 These differences stem from the storage requirement andlow capacity factors for wind and solar, see Appendix A.4. Second, while the LFSCOE for thetnconventional sources are slightly lower in Germany than in Texas, the LFSCOE for wind andespecially solar are much higher in Germany (e.g. 1548 USD/MWh for solar in Germany vs.

rin

413 USD/MWh for solar in Texas). The higher LFSCOE for dispatchable sources in the Texas
market can be explained by the seasonal variance in demand. In Texas, the peak demand in themonth with the highest demand is 67% higher than in the month with the lowest peak demand.

ep

This percentage is only 12% in Germany, which results in a higher overall capacity factor for
dispatchable technologies in Germany than in Texas (see Appendix A.1). The significantly higher
LFSCOE for wind and solar in Germany compared to Texas stem from the higher overall capacityPrfactor (0.35 vs. 0.20 for wind, and 0.23 vs. 0.11 for solar) and the fact that the high demand
14This is independent of the discount factor, which rather benefits technologies with higher upfront costs - seeAppendix A.3 for LFSCOE without discounting.

11
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periods in Texas (during summer days) are correlated with the high capacity factors for solar,
while the slightly higher demand in winter in Germany comes along with significantly lower solar

generation. This correlation explains the fact that the effective capacity factor (i.e. the average
dispatched electricity per hour) for solar is almost six times larger in Texas than in Germany -see Appendix A.3. Third, the variation between years of LFSCOEs for dispatchable sources are

ev

much lower than for wind and solar. This does not come as a surprise as dispatchable sources

depend only on one variable vector (demand) whereas wind and solar also depend on their own
hourly capacity factor and are particularly impacted by periods with low hourly capacity factor. Iferrconsumers are risk averse, this higher variance can come with additional costs as they are willingto pay a premium for capacity that is only used in the worst case scenarios.
Comparison with Levelized Costs of Electricity Using similar assumptions on costs as inpeTable 1, EIA LCOE (2020) derives the Levelized Costs of Electricity. As mentioned above, thiscalculation is by no means simple, and is described in detail in EIA Model Documentation (2020).
Table 3 summarizes their analysis and compares it with the LFSCOE derived above.
LCOE and LFSCOE are relatively similar for all intermediate-load technologies (Biomass, Coal,ot

and Natural Gas CC), which is a sign that the capacity factor assumed for the LCOE (and thus
the lifetime generation) is similar to the average capacity factor if only one of those technologytn(plus storage) is responsible for meeting the market demand. Natural Gas CT, seen as a peakload generator under LCOE assumptions, has significantly lower LFSCOE as its capacity factor
increases from 30% to almost 70% in Germany, while the capacity factor for nuclear, being therinhighest under LCOE assumptions (90%), drops to just under 80%.
The most striking difference can be seen for the intermittent technologies solar and wind. While the
LCOE assume no responsibility in meeting the demand and focus solely on the costs of generation,

ep

the LFSCOE assume full responsibility of meeting the demand. This responsibility comes at avery high price, making the LFSCOE for intermittent renewables up to 40 times higher than the

Pr

LCOE.

Comparison with System Levelized Costs of Electricity Ueckerdt et al. (2013) developed
the System LCOE to address the inability of LCOE to reflect the cost of intermittency. System
12This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4028640

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Table 3: Comparison of LCOE and LFSCOE

LFSCOELCOE

Texas[USD/MWh][USD/MWh][USD/MWh]

Biomass

95

104

117

Coal (USC)

76

78

90

Natural Gas CC

38

35

Natural Gas CT

67

39

Nuclear82

106

Solar PV

36

Wind

40

ev

Germany

40
42

122

er
r

Technology

1548

413

504

291

Table 3 displays the LCOE for onshore wind, while the LCOE for offshore wind are 122 USD/MWh. The data on the hourly windcapacity factor does not distinguish between on-shore and off-shore wind, thus the LFSCOE implicitly assume an on-shore/off-shorepe

mix as currently deployed in the market in the given year. The highest share of off-shore capacity in the data was in Germany in 2018,
which was ∼ 5GW offshore of the total ∼ 55GW installed capacity. The LCOE also include transmission costs (ranging between 1.1
USD/MWh for nuclear to 3.6 USD/MWh for solar), which are not part of the LFSCOEs (but can be added as a mark-up to the fixed
costs).

ot

LCOE are the sum of generation costs and integration costs for a renewable source. Integration
costs are split up into overproduction costs, full-load-hour reduction costs, and backup costs (plustngrid costs and balancing costs, but they are ignored in parts of the paper and in my analysis aswell).15 The System LCOE are a very accurate way of calculating the cost of renewables, but
their precision makes them less “catchy”, as they depend on the share of the renewable genera-rintion. Figure 3 shows the System LCOE for wind and solar in Germany, taken from Ueckerdt etal. (2013).

It is important to note that as the paper was published in 2013, the LCOEs (60 EUR/MWh forep

wind and 120 EUR/MWh for solar) are outdated as they dropped significantly since. It is interest15

Ueckerdt. et al (2013) define balancing costs of VRE (i.e. renewables) as follows: “Balancing costs occur

because VRE supply is uncertain. Day-ahead forecast errors and short-term variability of VRE cause intra-dayPradjustments of dispatchable power plants and require operating reserves that respond within minutes to seconds.”(page 65). The LFSCOE model assumes deterministic demand and capacity factors while the shortest time interval
is one hour. Thus, although storage is required to balance supply and demand, “balancing costs” as defined by
Ueckerdt et al. (2013) are ignored in the LFSCOE model.

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Figure 2: Graphs are taken from Ueckerdt et al. (2013), page 72, Figure 10.

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Figure 2: System LCOE for Wind (left) and Solar (right) in Germany.

ing to see that both LCOE and LFSCOE can be found in a complete System LCOE study: LCOE
are similar to System LCOE with renewables supplying a 0% share of final electricity, whereas

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LFSCOE are conceptually equivalent to System LCOE with renewables supplying a 100% shareof electricity. Indeed, if the LCOE values are adjusted to current LCOE estimations (which are
40 USD/MWh for wind and 34 USD/MWh for solar) and integration costs are extrapolated, theSystem LCOE ought to approach the direction of the LFSCOE as calculated in this paper. If theotintegration costs are extrapolated in Figure 2 in a linear fashion, the System LCOE will end up
substantially below the LFSCOE for Germany presented in Table 4 - but if an exponential growthtnof integration costs is assumed, the System LFSCOE actually reach the magnitude of LFSCOE
values as calculated above.

A key observation from the System LCOE analysis in Figure 2 is the increasing cost of over-rin

production as the share of renewables increases. The analysis of the effective capacity factors inAppendix A.3 shows that LFSCOE supports this observation: In a system with solely intermittent
generation, overproduction occurs on a large scale. However, the analysis of the effect of storage

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losses in the next section shows an advantage of overproduction. It turns out that even significant
losses in the storage process do not increase the LFSCOE by much, as the additional demand insome periods (due to storage losses) is more than compensated by the overproduction in otherPr

periods without having to invest more in expensive storage.

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Limitations of the LFSCOE As noted above, the LFSCOE can be seen as an opposite ex-treme of the LCOE and thus share similar limitation. LFSCOE are dependent on the locationand demand patterns, and should thus be presented as intervals if derived for a global context.

Furthermore, they do not internalize externalities and regulatory market conditions. Unlike LFSCOE, they include the cost of intermittency, but are much more dependent to outliers in demandCounterfactuals and Model Extensions

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3

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and renewable capacity factors.16

Counterfactual: Impact of falling storage costs Using the initial model as described above,
LFSCOE can be determined if the costs for storage decrease significantly.

tn

ot

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Figure 3: LFSCOE with decreasing capacity costs for storage.

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Figure 3: Development of LFSCOE if storage costs decrease significantly for the market in Germany (left) and Texas (right).

Figure 3 supports the intuition: Technologies that require large storage facilities (like wind andsolar) benefit from a significant decrease in storage costs, whereas the effect on the LFSCOE forep

dispatchable technologies (like nuclear and natural gas) is barely noticeable. A reduction in costsof storage capacity by even 95% would still not make the LFSCOE of wind, solar, or wind & solar
competitive to the dispatchable generation in Germany, but would at least in Texas move themPrbelow the LFSCOE of nuclear and biomass.
16

It is worth noting that the the combination of demand and capacity factors during the Texas Freeze 2021 did

not constitute an outlier for the LFSCOE calculations.

15
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It is important to note that the dispatch constraint (B.1) is never binding for the renewables,

meaning that a drop in storage costs can also be achieved by an increase in the storage factor.
While a decrease of costs per MW installed capacity by 75% seems unrealistic any time soon (seeSchmidt et al. (2019)), an increase in capacity factor by a factor of 4 (to 12 M W /M W h) canbe achieved more easily with storage technologies like flow batteries (which, however, have higher

ev

capacity costs at the moment).

Model Adjustment: Including storage losses and depreciation Next, the no-storage-errlosses assumption is relaxed. To simplify, there are three fundamentally different losses that
occur during a storage process: Losses can occur when the storage is charged with the generated
electricity (“Charging loss”), when it is dispatched (“discharging loss”) or while storage is idle but
charged to a certain point (“storage depreciation”) - see Appendix A.6 for further information.

peFigure 4 illustrates the effect of charging losses (left) and discharging losses (right) for the LFSCOE
with German market data, assuming that there are no other storage losses (e.g., no storage
depreciation).

ep

rin

tn

ot

Figure 4: LFSCOE with charging and discharging losses.

Figure 4: Note that the LFSCOE with charging losses of 40% are lower for wind and wind & solar than those with discharging lossesof 20% (522 vs. 565 for wind and 461 vs. 501 for wind & solar). For solar, LFSCOE with charging losses of 40% are higher than for
LFSCOE with discharging losses of 20% (1752 vs. 1656), but those with charging losses of 30% are lower (1627 USD/MWh).

Pr

The most striking observation is the low cost impact of storage losses, especially charging losses,
in the wind and the wind & solar system. This stems from the substantial overproduction under
the optimal capacity installation. Without storage losses, the abundant electricity is curtailed;
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with losses, it is just lost in the storage process. Given the different scale of the x-axis, one can saythat discharging losses, though very small for wind and wind & solar, are roughly twice as costly
as charging losses. Results for Texas (displayed in Appendix A.6) support these observations.

Model Adjustment: LFSCOE-95 Immediate critiques of LFSCOE address the unrealistic

assumption that an electricity market will rely on only one source of electricity (unless it is hydro,evwhich is basically the only source of domestic power generation for some countries with very
favorable geography like Paraguay or Albania). In addition, research on a complete reliance onerrintermittent renewables points out the significant cost reduction that could be achieved if thesystem would allow dispatchable technologies to back up renewables by supplying a small shareof demand (see for example Jenkins et al. (2018)). This thought experiment is included byintroducing the LFSCOE-95, the Levelized Full System Costs of Electricity if only 95% of thepemarket has to be supplied by this respective source of electricity. To calculate the LFSCOE-95,
assume that a generator is available that can generate electricity at the lowest costs available
for intermediate-load generation (i.e. mc95 = 18 U SD/M W h) but is restricted to only 5% of thedemand. After calculating the total costs associated to each considered technology (plus storage),ot

the LFSCOE-95 are then calculated by averaging not over the total system demand (which is
jointly supplied by the respective technology and the low-cost supply) but only over the totaltndemand that is supplied by the respective source of electricity (which is at least 95% of the total
electricity). This means that the low-cost generation is basically treated as an adjustment of thedemand curve (i.e. it reduces up to 5% of total demand at a price of mc95 = 18 U SD/M W h, but

rin

can choose in which period it reduced the demand).
Table 4 displays the mean LFSCOE-95 for the data on Germany and Texas and compares it with
the LFSCOE-100, while Figure 5 displays mean and intervals for the LFSCOE-95.

ep

There are a few things worth mentioning: First, for dispatchable generation, the LFSCOE-95
are lower than LFSCOE as the residual demand curve for the generator is flattened by the freePrgeneration, which increases the average capacity factor. The flattened seasonal demand curve also
reduces the difference in LFSCOEs between Texas and Germany. An additional consequence of theflattened demand curve is that the variance between years almost diminishes. For intermittent
sources, all effects observed for the dispatchable technologies are more extreme. Going from
17
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Table 4: Levelized Full System Costs of Electricity

Germany
LFSCOE-100

LFSCOE-95

LFSCOE-100

LFSCOE-95[USD/MWh][USD/MWh][USD/MWh][USD/MWh]

Biomass

104

90

117

95

Coal (USC)

78

67

90

Natural Gas CC

35

31

Natural Gas CT

39

36

Nuclear

106

90

Solar

1548

Wind

504

Wind & Solar

454

ev

72

40

32

42

37

122

96

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Technology

Texas

849

413

177

279

291

131

220

225

97

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Table 4 - LFSCOE-95: For computational reasons, storage is not an option for dispatchable technologies anymore. Given that only at
most 2% of electricity was dispatched from storage (see Table 3), this restriction does not distort the results.

LFSCOE-100 to LFSCOE-95, i.e. reducing the load responsibility of wind or solar from 100% to95%, reduces the costs by roughly 50%. However, the LFSCOE-95 for wind and solar in Germanyot

are still significantly higher than the LFSCOE-100 for all dispatchable sources, but especially thewind & solar mix in Texas appears to be as competitive as all non-natural-gas thermal generationtn

on a LFSCOE-95 basis. In any case, the LFSCOE-95 show that having dispatchable generation
to support the intermittent renewables reduces the total system costs significantly and should be4

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considered when planning the energy transition.

Conclusion

ep

Intermittency of generation makes the cost comparison between different generation technologies
much more difficult. While being a good measure to evaluate the cost to generate electricity, thePrmost popular cost measure, the Levelized Costs of Electricity, fails to include the costs associatedwith meeting the demand and providing usable electricity. On the other hand, the System Levelized Costs of Electricity by Ueckerdt et al. (2013) include the cost of integration and balancing,
but do not seem to be simple enough to make it to a broader audience. Using the radical but
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Figure 5: LFSCOE95 Mean and Variance in the German (left) and ERCOT market

straightforward assumption that each source of generation has to meet the demand over a given
year (with the help of storage), the Levelized Full System Costs of Electricity introduced in thispaper are the first cost measure to condense the cost of providing electricity to one number perpemarket and technology. With LFSCOE being much higher than the LCOE for wind and solar,
it becomes evident that LCOE are far from being an accurate measure to include the cost ofintermittency.

ot

Analyzing different sources of generation sources shows that the LFSCOE are much higher forwind and solar than for conventional and dispatchable fuels, which stems from the large require-tnment for storage to overcome wind and solar’s intermittency. However, even if these storage costs
drop by 90%, renewables are still not competitive on an LFSCOE basis.
Introducing the LFSCOE-95, which assume that up to 5% of the annual demand can be suppliedrin

by a very inexpensive dispatchable source of electricity, we show that reducing the responsibilityof intermittent renewables to supply only 95% of the demand will cut the system costs in half.
This observation is supported by existing literature criticizing any 100% emission-free approaches

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by pointing out the enormous costs of supplying the last 5%.
The cost evaluation concept in this paper can be refined in different ways. First, the evaluation of
LFSCOE can be refined by including transmission costs, capacity limits, or locational differencesPrin capacity factors. Second, using data from other parts of the world, LFSCOE for other markets
can be evaluated. Third, LFSCOE-95 can be relaxed further to LFSCOE-90 or any reasonable
demand reduction. Any extension, however, should find a balance between increasing accuracy

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while staying simple to address a broader audience.

References

Battery University. (2018). “What does Elevated Self-discharge Do?”. seeev

https://batteryuniversity.com/learn/article/elevating self discharge.

Becker, Gary S. (1965). “A theory of the allocation of time.” The Economic Journal, 75, 493-517.

United States Census Bureau. (2019). “American Community Survey - Home Heating Fuel”.

er
r



see https://www.census.gov/acs/www/about/why-we-ask-each-question/heating/

Cleanenergywire. (2020). Data on German sources of heating, see:https://www.cleanenergywire.org/factsheets/heating-40-million-homes-hurdles-phasing-out-fossil-pefuels-german-basements

Denholm, Paul, Jeffrey C. King, Charles F. Kutcher, Paul P.H. Wilson. (2012). “Decarbonizing
the Electricity Sector: Combining Renewable and Nuclear Energy using Thermal Storage.”

Hartley, Peter. (2017). “The Cost of Displacing Fossil Fuels: Some Evidence from Texas.” Rice

tn



ot

Energy Policy, 44: 301-311.

University, Working Paper.
Ibrahim, H., A. Ilinca, and J. Perron. (2008). “Energy Storage Systems - Characteristics andrinComparison.” Renewable and Sustainable Energy Reviews, 12: 1221-1250.
Jenkins, Jesse D., Max Luke, and Samuel Thernstrom. (2018). “Getting to Zero Carbon

ep

Emissions in the Electric Power Sector.” Joule, 2: 2498-2510.


Joskow, Paul. (2011). “Comparing the Costs of Intermittent and Dispatchable Electricity

Pr

Generating Technologies.” American Economic Review: Papers & Proceedings, 100:3: 238-241.

Lazard. (2019). “Lazard’s Levelized Costs Of Energy Analysis - Version 13.0”.

20This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4028640

iew
ed



Reichenberg, Lina, Frederik Hedenus, Mikael Odenberger, Filip Johnsson. (2017). “The Marginal
System LCOE of Variable Renewables - Evaluating High Penetration Levels of Wind and Solarin Europe.” Energy, 152: 914-924.



Schmidt, Oliver, Sylvain Melchior, Adam Hawkes, Lain Staffel. (2019). “Projecting the Future

Sinn, Hans-Werner. (2017). “Buffering Volatility: A Study on the Limits of Germany’s Energy
Revolution.” European Economic Review, 99: 130-150.

Ueckerdt, Falko, Lion Hirth, Gunnar Luderer, Ottmar Edenhofer. (2013). “System LCOE:

er
r



ev

Levelized Cost of Electricity Storage Technologies.” Joule, 3: 81-100.

What are the costs of variable renewables?”. Energy, 63: 61-75.


United States Census Bureau. (2019). “American Community Survey - Home Heating Fuel”.

pesee https://www.census.gov/acs/www/about/why-we-ask-each-question/heating/United States Energy Information Administration. (2009). “Household Energy Use in Texas”.
EIA’s 2009 Residential Energy Consumption Survey. Cited as “EIA Texas (2009)”.
United States Energy Information Administration. (2020). “Levelized Costs and LevelizedotLCOE (2020)”.
tn

Avoided Cost of New Generation Resources”. Annual Energy Outlook 2020. Cited as “EIA

United States Energy Information Administration. (2020). “The Electricity Market Module ofrin

the National Energy Modeling System: Model Documentation 2020”. Annual Energy Outlook
2020. Cited as “EIA Model Documentation (2020)”.


United States Energy Information Administration. (2020). “Cost and Performance Character-ep

istics of New Generation Technologies”. Annual Energy Outlook 2020. Cited as “EIA Costs(2020)”.

Zerrahn, Alexander, Wolf-Peter Schill, Claudia Kemfert. (2018). “On the Economics of Electri-Pr

cal Storage for Variable Renewable Energy Sources.” European Economic Review, 108: 259-279.

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Appendix A

A.1 Comparison of demand patterns in Germany and Texas Figure 6 displays the aver-age daily peak and minimal demand for Germany and ERCOT/Texas, where years are normalized

so that each year starts with a Monday. The comparison shows that the seasonal demand variation in Germany is relatively small compared to Texas. This does not come as a surprise as air

ev

conditioning accounts for a large share of residential electricity consumption in Texas, whereas it
is rarely utilized in Germany. However, heating is more important in Germany than in Texas, butwhile around 60% of the housing units in Texas use electricity for heating (see United States Cen-errsus Bureau (2019)), the main source of heating in Germany is natural gas (48.2% of households)
and oil (25.6% of households).17 Once heating gets electrified on a large scale, there should be alarger difference between the electricity demand in summer and in winter in Germany (unless air

peconditioning becomes popular in Germany as well).

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tn

ot

Figure 6: Average Minimal and Peak Demand in Germany (left) and the ERCOT market.

Figure 6 displays the average daily minimal and maximal demand in Germany and Texas over 8 years. The days are adjusted for

ep

weekdays, thus the first day of a year is always a Monday.

17

For Germany, see Cleanenergywire (2020); for Texas, see EIA Texas (2009). In 2009, households in Texas

use 18% of their total energy for cooling, almost exclusively by electric air conditioning units - which is very highcompared to the U.S. average of 6%. While the data shows that households in Texas use 22% of the energy forPrspace heating (compared to 41% in the U.S.).

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A.2 Existence and uniqueness of solution Existence of a solution is easily proved as theset of constraints is clearly convex and non-empty. In fact, any capacity installation that is large
enough can meet the constraints.

Uniqueness is more ambiguous: The solutions to both the intermittent and the dispatchable
problem are not necessarily unique. In fact, without losses in the storage process, the optimizationev

problems for both intermittent and dispatchable sources have an infinite number of solutions as
the storage can be charged at any time (unless there is no storage capacity in the optimal system,as for natural gas CT). Adding a bonus of  > 0 for keeping electricity in storage, which can beerrjustified as storage secures against unanticipated supply shortages, ensures the uniqueness of x foryevery investment tuple (I y , Istorage) of renewable sources. While uniqueness of the independent

variables can still not be ensured, the value of the objective function is unique, which is sufficientpefor the purpose of this paper.

A.3 Storage Characteristics Table 3 displays characteristics of the storage in the system. It is
not surprising that intermittent renewables require significantly more storage than the dispatchable
technologies, out of which those with low capacity costs like natural gas CC and CT barely useotstorage at all. Furthermore, as the hourly capacity factor for solar is equal to 0 in almost half ofthe periods (at night), it is not surprising that almost half of the electricity in the market solelytnsupplied by solar is dispatched from storage. The most surprising observation is probably thelength of storage cycles, which are not longer than 334 hours (i.e. about 14 days) in Texas and903 hours (i.e. about 38 days) in Germany. The main reason for the short storage cycles is therinsubstantial overproduction, which is apparently cheaper than investing in more storage. Relaxing
some model assumption like perfect forecastability would certainly increase the length of storage
cycles, but it raises the question whether seasonal storage is required if it stays expensive (at leastep

in Texas).

A.4 Counterfactual: No discounting Generation technologies with low capital costs butPrhigher variable costs benefit from a lower discounting factor (i.e. a higher cost of capital) comparedto those with higher capital costs and lower variable costs. As a thought experiment, Table 6
displays the LFSCOE (mean and min-max interval) without discounting of the future (i.e. a cost
23

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Table 5: Storage details on calculating the LFSCOE

Germany

Texas

Storage
Capacity

StoragedispatchMax
storage
cycle

Generation
Capacity

[GW]

[GW]

[%]

[hours][GW]

Biomass

76

14

0.1%

94

53

Coal

79

5

0.05%

64

Natural Gas CC

83

0.3

0%

15

Natural Gas CT

84

0.2

0%

6

Nuclear

73

31

0.5%

Solar

3709

2078

48.3%

Wind

1027

1030

9.2%

Wind&Solar

916

948

6.2%

Storage
Capacity

StoragedispatchMax
storage
cycle

[GW]

[%]

[hours]

33

1.9%

94

ev

Generation
Capacity

13

0.7%

64

69

0.3

0.0%

15

69

0

0.0%

6

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58

146

52

34

2.0%

146

909

438

792

49.6%

332

664

517

276

3.5%

128

669

368

262

1.5%

117

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Technology

Table 5 depicts the average storage capacity, generation capacity, storage dispatch (i.e. percentage of electricity coming from storage)
and the longest storing cycle. In Germany, both NGCC and NGCT use storage in only one of the 8 years. Their average dispatchedelectricity is not equal to 0 (apart from NGCT in Texas), but on average lower than 0.1%. Note that the average hourly demand is 58
GWh in Germany and 40 GWh in Texas.

otof capital of 0 %).

tn

A.5 Effective Capacity Factor Define the “effective” capacity factor as the average dispatchedelectricity per hour. This capacity factor is capped by the “technical” capacity factor, which isthe (maximal) generation of a source of electricity. The average technical capacity factor in therindata for wind (solar) is 35% (23%) in Texas and 18% (11%) in Germany. Table 8 displays theaverage effective capacity factor for each technology and the interval ranging from the minimal
to the maximal capacity factor for each year. As net dispatch from storage is not permitted andep

there are no losses in the storage process, this can be calculated by dividing the average hourly
demand by the installed capacity. Some observations can be made: First, the capacity factors for
dispatchable sources in Texas are lower than in Germany, which stems from the higher seasonalPrvariance of the demand. This means that capacity needs to be provided in Texas which only
becomes relevant for a few month in the summer. A direct implication of the lower capacity
factors are the higher LFSCOE values of dispatchable generation technologies in Texas compared
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Table 6: Levelized Full System Costs of Electricity without discounting

Germany
Technology

LFSCOE

Texas[min,max] Conf.Int.

[USD/MWh]

LFSCOE[USD/MWh][min,max] Conf.Int.

Biomass

71[69,74]78[75,82]

Coal

52[50,53]

57

NGCC

26

[26,27]

NGCT

33[33,34]

Nuclear60[58,64]

Solar

734

[564,965]

188[155,266]

Wind

247

[214,276]

146[117,174]

W+S

221

[160,240]

111[88,169]ev[55,60][28,29]35[34,35]

68[65,73]

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Table 6: Levelized Full System Costs of Electricity without discounting (i.e. with a cost of capital of 0%).

to Germany. Second, the effective capacity factors for wind and solar are significantly lower
than the technical capacity factor, implying that a large share of electricity gets curtailed. Anotinteresting observation is that though the technical capacity factors for solar are just twice as highin Texas than in Germany (23% vs. 11 %), the effective capacity factor is almost six times highertn

in Texas than in Germany. This means that not only solar do generators generate less in Germany,
they also sell significantly less electricity in a single-source market, making the investment evenrinless profitable.

A.6 Storage losses Next, the no-storage-losses assumption is relaxed. To simplify, there arethree fundamentally different losses that occur during a storage process (see Ibrahim et al. (2008)

ep

for a detailed description of storage technologies, and Schmidt et al. (2019) for current round-trip
efficiency estimations). First, losses can occur when the storage is charged with the generated
electricity. Let α1 ∈ (0, 1] be the share of electricity that reaches the storage facility in a charging

Pr

process (and thus 1 − α1 the share that is lost in the process), meaning that α1 = 1 would beequivalent to no losses in the charging process. For many storage technologies, this is the main
location for losses. Especially, turning water into hydrogen (so called Power-to-Gas) requires a25This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4028640

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Table 7: Average Annual Effective Capacity factor

Germany
Technology

Texas

LCOE
LFSCOE[min,max]

LFSCOE83%76.0%[72.0%,81.2%]

76.0%

Coal

85%

73.7%

[68.8%,81.2%]

68.9%

NGCC

87%

69.9%

[65.5%,73.8%]

58.2%

NGCT

30%

69.6%

[65.5%,73.5%]

Nuclear

90%

79.9%

[74.6%,84.8%]

Solar

29%

1.5%

[1.2%,2.0%]

Wind

40%

5.9%

Wind & Solar

–

6.5%

[70.9%,80.6%][61.0%,73.5%][55.9%,64.8%]

ev

Biomass[min,max][55.6%,64.4%]

76.9%[70.9%,81.8%]

10.4%[5.0%,12.9%]

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58.1%

[3.7%,7.5%]

7.8%[6.5%,9.6%][4.5%,7.7%]

10.9%[9.0%,12.4%]

Table 7: Capacity factors for LCOE taken from EIA LCOE (2020), where the table displays the capacity factors for onshore wind.

pe

The capacity factor for Wind & Solar is derived by dividing the the sum of the demand by the sum of the installed capacity.

significant amount of energy that cannot be fully recaptured, which is structurally nothing elsethan charging losses. Second, stored electricity can depreciate over time - this loss is denoted withotγ ∈ (0, 1]. Storage depreciation (or self-discharge) can have many different reasons: For hydrogen,it can occur due to leaks, for pumped hydro, it occurs due to evaporation (but might be offset
in part through rainfall and runoff), and for solid state batteries, it occurs due to an unwantedtnchemical reaction. Third, losses can occur when the stored electricity is dispatched back to thegrid - denote the share of electricity that reaches the grid by α2 ∈ (0, 1], i.e. the share of losses
is 1 − α2 . It is easy to see that “round-trip efficiency”, the most common term to describe therinefficiency of storage, is nothing else than α1 ⋅ α2 , and varies between 0.4 for Power-to-Gas and 0.88
for the flywheel as depict in Table 5. Unfortunately, the technologies with the highest round-trip

ep

efficiency sometimes come along with the highest depreciation (i.e. the lowest γ). In a context
where it is desirable to store the energy for different length of time, it will be optimal to have aPrdiversified storage portfolio.

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Table 8: Storage losses by technology
Round-trip
efficiency

Self-discharge[%][%/day]Pumped Hydro

78%

0%

Flywheel

88%

480%

Lithium-Ion

86%

0%

Vanadium redox-flow

73%

Hydrogen40%

ev

Technology

0%

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1%

Table 8 displays round-trip efficiency and self-discharge of selected storage technologies, taken from the accompanying documents ofSchmidt et al. (2019) (Table S4). The technology input parameters are from 2015 and the self-discharge is at an optimal charging
level. A self-discharge level of 480%/day could be reinterpreted to 20%/hour which can then be interpreted at γ = 0.8 if discharging
occurs at a fixed non-linear rate (which is, however, not the case for the flywheel).

peGiven the notations above, the system of equations for intermittent technologies changes tomin rp ⋅ f cRen + sp ⋅ f cstoragerp,sps.t. x[t + 1] − γx[t] ≤ (Rent ⋅ rp − Dt )α1 ,(D.1+)

1,
α2(D.1-)otx[t + 1] − γx[t] ≤ (Rent ⋅ rp − Dt )tn

−sp ≤ x[t + 1] − γ ⋅ x[t] ≤ sp,

Ssecurity ≤ x[t + 1] ≤ sp ⋅ ρsf ,x[1] ≤ x[H + 1].

(B.1)
(B.2)
(B.3)

rin

Constraints (D.1+) and (D.1−) ensure that demand is met at any time: (D.1+) has to hold in
periods where storage is charged (i.e. with an abundance of electricity), whereas (D.1−) corre-

ep

sponds to periods where electricity is generated by discharging storage.18 Note that the system
above only captures exponential storage depreciation γ. However, technologies like lithium-ion
batteries self-discharge at other than an exponential rate over time. In that case, the percentage

Prloss depends on both the time and the battery state/charging level, where 5% of the load depreciates within a day (if the battery was fully charged) and then just up to another 5% within
18

Note that by replacing the left hand side of (S.1) with max(Dt − Rent ⋅ rp) ≤ sp, which can be replaced by

α2 (Dz − Rz ) ⋅ rp ≤ sp at z = argmaxt Dt /Rent , H − 1 conditions can be removed from the optimization problem.

27
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4028640

iew
ed

the next month - see Battery University (2018). Given that storage cycles tend to be short, thelong-term depreciation can be ignored in the analysis, while the short-term storage depreciation

can be interpreted as a charging and discharging loss. As a result, γ will be fixed at 1 and thefocus will lay on charging and discharging losses.

Figure 8 depicts the effect of the LFSCOE values in Texas if charging and discharging costs areev

introduced. The observations of the LFSCOE in Germany hold here as well.

pe

er
r

Figure 7: LFSCOE with charging and discharging losses in Texas.

Figure 7 displays the LFSCOE in Texas with charging losses and discharging losses. Note that for every technology, the LFSCOE

Pr

ep

rin

tn

ot

with charging losses of 40% are always lower than those with 20% discharging losses.

28
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4028640