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The Value of Lost Load (VoLL) in European
Electricity Markets: Uses, Methodologies, Future
Directions
Gregory P. Swinand1, Ashwini Natraj2, Anuj Singh3, Joseph McEnri4
1, 2, 3 LE Europe, 4 Fitzwilliam Place, Dublin, Ireland, 4MEPS Consulting, Dublin, Ireland
Abstract—This paper reviews the uses and estimation
methodologies for the Value of Lost Load (VoLL) in European
electricity markets. VoLL is defined by the Clean Energy Package
as a €/MWh estimate of the maximum electricity price that
customers are willing to pay (WTP) to avoid an outage. As
European energy markets continue to strive to improve
competition, quality, reliability and efficiency, while integrating
greater shares of renewable energy, estimating key market
parameters such as the VoLL becomes increasingly important.
Recent EU regulation is to be adopted requiring regulators and
Transmission System Operators to estimate and publish VoLL
based on a clear and transparent methodology.
The ‘correct’ method of VoLL estimation should depend on what
VoLL will be used for. Despite this, little has been done to
summarize the uses of VoLL. This paper fills that gap. Literature
review and review of regulations show many uses of VoLL,
including calculating reliability standards, back-stop pricing
when demand exceeds supply in energy, balancing, capacity
markets, and reserves markets. Different uses of VoLL suggest
different values even within a single use, such as setting reliability
standards and levels of investment; there are likely differences in
the ‘correct’ VoLL between TSO and DNO levels, as the drivers
of reliability and nature of lost load will be fundamentally
different.
The correct estimation method should depend on the use. The
existing literature shows a wide range of methods for estimating
VoLL, including surveys of WTP, Choice Experiments, and
production function techniques. These different approaches have
led to a wide range of estimated values and may have potential
biases. We review the estimates and potential biases of existing
methods. Studies show a range of VoLL estimates from €1,500 to
€22,940/MWh, while one MS uses a VoLL of circa €19,500 for
reliability but a VoLL of €3,500 for reserve-repricing. Other
studies have shown VoLL likely varies by numerous customer
characteristics, including time-of-day, season, customer type,
duration, and frequency.
Future directions are emerging for VoLL research and we
synthesize these with our findings. Market power and the use of
1
The number of hours of expected lost load in a year.
978-1-7281-1257-2/19/$31.00 ©2019 IEEE
price-cap-mitigation tools should be considered when estimating
VoLL and whether prices should be allowed to reach VoLL.
Customer demand-side participation interacts with VoLL
estimates used to set capacity prices (CP). Likely outage causes
and Loss of Load Expectation (LOLE) modelling will also have
real implications as the standard relation where
LOLE=CP/VoLL will not always hold. Finally, different VoLLs
and quality levels may have important fairness implications.
Index Terms—Electricity, Value-of-lost-load, Reliability,
Balancing, Economics
I. INTRODUCTION
II. HOW IS VOLL USED
A. Setting Reliability Standards
One of the most important uses of VoLL has been in setting
reliability standards. A reliability standard in terms of the loss
of load expectation (LOLE)
1
, the cost of new capacity or entry
(CONE), then an optimal condition implies a VoLL and (under
certain conditions) vice versa. This method was used in setting
the reliability standards in Great Britain (GB) when considering
a variety of reforms, including in anticipation of changes to
promote capacity market auctions [1]. To see the importance of
how VoLL is being used, consider the derivation of the standard
in GB. Starting with a net benefit equation:
NB(k)=REB-BC(k)-EC(k) ()
Where NB is the net benefit to consumers, k is a level of
capacity, REB is the benefit of reliable electricity, BC is the cost
of blackouts, and EC is the cost of electricity production. The
cost of blackouts BC(k)=EEUxVoLL, where EEU is expected
energy unserved. The optimal level of capacity is found by
differentiation and the first order conditions that NB’=0,
implying the incremental costs and benefits be equal:
dBC(k)/dk=-(dEC(k))/dk ()
The incremental cost of electricity with respect to capacity
k is the CONE; note the units are as the annualized competitive
per unit rental rate (e.g. €/MW/yr):
dBC(k)/dk =-(dEEU(k))/dk VoLL=-CONE ()
The incremental benefit of capacity is fewer hours of EEU,
and thus is the negative of Loss of Load Expectation, or, -
dEEU(k)/dk=LOLE, which is what sets the reliability standard
(typically expressed as an expected number of hours per year).
LOLE=CONE/VoLL ()
The DECC analysis [1] then goes on to consider their
reliability standard and empirical estimates of VoLL [2] and
CONE [3]. Note that the standard is a subject of policy whereas
the other values are empirical estimates.
Considering the use of VoLL in the reliability standard and
the analysis starts to shed light on some of the assumptions
about VoLL. For example, the VoLL figure used in the GB
reliability standard is the load-share-weighted-average of
VoLLs for domestic and SME customers in GB at winter peak.
Large industrial users are excluded as it was assumed they
could avail of either contracts for load shedding, or other
mitigation such as back-up generation. The rationale for these
assumptions now should be clear. Because the TSO or load-
shedding event cannot choose any particular customer, then the
weighted-average VoLL appears to be the most reasonable
figure; because the winter peak is the most important time of
potential disruption, then this is also the most reasonable
approach. Finally, the optimality condition requires that the
CONE is constant and the incremental benefit of reliability to
be decreasing (both of which seem reasonable assumptions).
Note that if market-based capacity pricing is used, including
DSM and all forms of capacity, then this assumption might be
unlikely to hold in the short run (in the long run, additional
capacity can be built).
Figure 1. Optimal reliability with costant cost of capacity and decreasing
marginal benefit of security
Given these rationales and assumptions, we can see that
using the same VoLL as in the reliability standard approach for
other electricity system reliability policies, may not be optimal.
For example, VoLL is being encouraged to be used in terms of
day-ahead market price caps or balancing market price caps.
Since these markets/production programs will vary through the
year, and the VoLL for summer and winter is likely to be quite
different, it would appear that an optimal VoLL policy for such
dynamic markets would reflect these seasonal dynamics.
Further, the LOLE and CONE for balancing might not be the
same as in the standard reliability setting. Indeed, we observe
that GB actually has a different and lower VoLL £6,000/MWh
(€6,818) for balancing market repricing purposes (which was
only recently raised from £3,000). Whether different LOLE
and CONE associated with balancing was indeed the rationale
for GB having two VoLLs (one for balancing and one for
setting the reliability standard), is difficult to know for sure, but
in this light two VoLLs might be optimal.
Moreover, the VoLL used in the reliability standard
approach is set with the assumptions of setting a single number
reliability standard, as a function of generation capacity, in
mind. A similar argument might be made if a single VoLL
number was used to set, e.g., a price floor or penalty value for
capacity auctions or non-provision penalties. (to our
knowledge) no particular consideration of transmission
capacity or distribution capacity, and their incremental costs,
was taken when choosing the VoLL for GB’s reliability
standard. However, consumers are most likely to experience
security of supply problems due to distribution-level problems,
and thus the consistency of such an approach with a single
VoLL used in other settings might be questioned. If, for
example, VoLL was being used to consider costs and benefits
of transmission or distribution assets, then it is quite possible
the values would more appropriately be related to different
periods or groups, and more than one VoLL might be most
appropriate depending on the setting.
Imagining different VoLLs for different purposes is not
novel. Ovaere et al [3] consider the possibility of different
VoLLs and different reliability levels in the context of
transmission investments. They make the point that the
‘correct’ value of VoLL should depend also on how electricity
curtailment is managed and that the curtailment technology
capability will impact the VoLL which should be applied (in
other words, how does curtailment actually occur and can
higher VoLL users be curtailed after lower VoLL users). The
main idea is that if curtailment is of one user type or geography
over another, then the VoLLs might reflect that (or
alternatively, curtailment could follow the VoLL estimates).
Further, curtailment often involves a cascade of actions before
rolling blackouts, such as controlled voltage reductions. In fact,
these considerations were studied in detail by London
Economics [2], but the application of the weighted-average
single VoLL was seen as mostly a policy decision (as was the
reliability standard choice at the time).
The study of VoLL in the context of distribution security of
supply was further undertaken by Electricity Northwest [4].
The ELNW study estimated VoLL based on different customer
groups and also for aspects of outage that Discos might control,
such as duration and time of year. The overall conclusion of
their report was their research provided “robust evidence that
the existing single ‘vanilla’ VoLL, applied to all customer
segments, fails to adequately reflect the significant variation
that exists in the financial and social impact of supply
interruptions across the full spectrum of customer types.”
While “fails” is perhaps an unnecessarily pejorative word, since
we have seen that the single VoLL approach was chosen for a
specific reason, the point that optimal use of VoLL might
involve using different VoLL for different customer types is
nonetheless important.
In the distribution context, note that the reliability standard
approach of DECC [1] can easily be adopted. Assume for
example, that there is an incremental annual unit level cost of
distribution assets, analogous to CONE (call it COD), and that
an EEU value can be estimated. This can sometimes be done
with Monte Carlo Simulations [24] and [25]. The EEU can be
simulated using probability distributions of faults and fault
durations derived from historical network data and applied to
various network configurations with the appropriate customer
load, considering time of day and seasonal factors, at the time
of the fault occurring. Monte Carlo simulations can be run for
different levels of component redundancy to estimate the
changes in the EEU and the distribution of EEU in the Monte
Carlo simulation. As the costs of additional network
redundancy (COD) are easily obtainable from historical project
cost information in the Distribution Network Operator (DNO),
these can be compared to the benefit of EEU priced using
VoLL. This allows for a direct cost-benefit analysis of specific
network locational redundancy or general distribution security
of supply requirements for a different probability of occurrence
levels. The quality of service benefits the network
reinforcement brings, is thus costed at the level of the
customers’ willingness-to-pay to avoid an outage. Use of
different VoLLs for different customer types and investments
cannot be ruled out, but we note this would required associating
specific investments and user groups with specific VoLLs,
although this has been done by [2] and [4].
Another important consideration when relating VoLL to
investment/reliability policy in distribution is whether the
second order conditions of the optimal policy condition will be
satisfied. A key difference between the reliability standard in
the market-wide generation capacity versus distribution
investments may be areas of scale and scope
economies/diseconomies as output expands for the Disco.
Thus, the capacity cost curve in Fig. 1 cannot be assumed flat,
although a long-run flat incremental cost curve might not be a
bad assumption. A further complication may be that decreasing
marginal benefit of security of supply may also not be a good
assumption. London Economics [2] and Electricity Northwest
[4] studies suggest nonlinearities with respect to duration. So
for example, one two-hour outage may not equal two one-hour
outages.
Finally, Electricity Northwest [4] makes the point that
different consumer groups very likely have different VoLLs.
Should this mean different investment levels or different
reliability standards for different customers or geographic
locations with the distribution network? Such policy would
raise many questions, such as what to do if demographics shift
or businesses move while investments are fixed, etc.
2
See for example, para 13 from Subject: SA.48648 (2017/NN) -
Belgium - Strategic Reserve
B. Setting Price Caps
III. ELECTRICITY PRICING AND THE ECONOMICS OF VOLL
Since VoLL is entering policy as a means of encouraging
economic efficiency in energy and balancing markets, it is
useful to discuss the economics of VoLL in the context of
supply and demand. It has been argued in a number of cases,
most notably recently in EC DG Comp approvals of State Aid
for strategic reserves, that allowing prices on energy or
balancing markets to rise to VoLL in times of scarcity is
desirable.
2
Figure 2. VoLL with Basic Linear Supply and Demand
Figure 3. VoLL with Horizontal/Vertical Linear Demand
Fig. 2 shows classic market linear supply and demand with
socially optimal price p* and quantity q* at price=marginal
cost (p=mc). The supply curve eventually becomes vertical as
q expands indicating limited industry capacity. If demand
shifts out to D’, the market price may rise to a price consistent
with the maximum willingness-to-pay in the standard
situation. Note that in the classic market, consumers may have
different willingness-to-pay and the maximum is the point
VoLL?
VoLL?
where q=0—will this be equal to VoLL as estimated from
various methods? The answer is not likely. The classic
demand curve is built with the notion that consumers all have
different WTP and as price rises lower WTP consumers are
priced out of the market. Our single weighted-average VoLL
does not seem consistent with this.
Alternatively, Fig. 3 shows a different assumption about the
shape of demand. Demand is vertical around (p*,q*), but
reaches a maximum (and minimum) and then is horizontal. In
this situation, consumers use the same quantity for a range of
prices. This might be more akin to what one might assume in
electricity market demand, although explicitness in these
assumptions is sometimes overlooked.
3
An important point is
allocative efficiency does not require p*=VoLL in the Fig. 3
situation (any price p* and above will give the optimal q*.
Moreover, the marginal (first order conditions) approach of the
relationship between VoLL, capacity cost, and LOLE is not
clear in this context.
In the case of energy and balancing markets (as opposed to
capacity markets), it cannot be assumed that the incremental
benefits of reliability are separable from the benefits of energy
consumption (as in the reliability standard derivation). In terms
of the incremental benefits of added energy to consumers, it is
useful to recall that price caps in the original electricity pool in
England & Wales were set at a maximum price (assumed
above any marginal cost) adjusted for LOLExVoLL.[5]. If
LOLE is changing through the year, then should price caps also
reflect this dynamic?
The argument made for setting energy market price caps at
VoLL is often the ‘missing money’ problem proposition. This
says a market failure exists because if prices cannot rise to
what people are willing to pay, then prices will not signal
demand/efficient investment. This argument may not always
be valid for policy. In general, a price cap at VoLL may or
may not incentivize sufficient investment to achieve a certain
reliability standard. To see this, suppose VoLL is €10/kWh,
the levelized cost of new generation of €8.99/kW and unit
variable costs are €1/kWh and the standard is no outages.
Suppose further that with probability one, in one hour of the
year, demand will exceed supply by 1kW, and demand will
exceed supply with probability zero in all other hours. If we set
the price cap at VoLL, let us assume an entrant anticipates this
and enters, and generates 1kWh and earns €10 and makes
0.01€ profit; the standard is met. If the cost of capacity
increases a small amount, the standard will not be achieved; if
it falls, the standard will be met but prices will be higher than
they otherwise could be. Setting the price cap at VoLL has
neither guaranteed a minimum cost or the standard being
met—these both depend on the relative size of VoLL to the
cost of capacity.
3
One can imagine downward sloping piecewise linear kinks in the
demand curve to allow for limited demand response.
IV. HOW IS VOLL CALCULATED
A. Methods of VoLL Estimation
The two most commonly used methods for estimating
VoLL are revealed preferences and stated preferences; the
former is arguably closer to actual consumer actions. This is
because the stated preference method is a representation of
what people say, while revealed preference models what
consumers actually do. Nonetheless, the caveats associated
with revealed preference methods restrict their use and general
suitability. The early research by Kroes and Sheldon (1988) [6]
highlight limitations associated with revealed preference
methods, which include difficulty in obtaining significant
variation in the revealed preference data and the inability to use
this approach to evaluate consumer demand under yet-to-exist
conditions. Similarly, stated preference methods also suffer
from certain limitations and one of the major issues is the
hypothetical bias that results from the diversion of responses
elicited for hypothetical formats from the responses elicited for
non-hypothetical formats (Huffman and McCluskey, 2017)
[7].
4
Within these two broad methodological techniques, there
are different ways for estimating VoLL. The revealed
preference method includes approaches such as case studies
and the production function approach. ACER [8] suggests that
case studies of previous supply outages can be treated like a
natural experiment, where estimates of the resulting costs to
the economy and consumers can potentially provide VoLL
estimates. However, events where such case-studies can be
carried out are rare, given the high level of supply security in
Europe. One such example where case-study was employed to
derive VoLL was the power shortage in Cyprus in 2011,
following an explosion that destroyed 60% of its power
generation. Zachariadis and Poullikkas (2012) [9] used this
case and applied the production function approach to estimate
a VoLL of €6.5/kWh. The production function approach
allows estimation of the impact of supply disruption on
different sectors of the economy which can be measured using
macro-economic data. The production function approach has
been used to estimate VoLL in different settings in the EU [10]
including an average VoLL of €8.7/kWh, Ireland [11] an
average VoLL of 12€/kWh in ROI, Germany [12] and average
VoLL of €11.04/kWh and €11.92 for the service sector and
household respectively, Spain [13] an average VoLL of €4.39
kWh, Portugal [14] an average VoLL of €5.12 kWh, and
Austria [15] an average VoLL of €17.1/kWh.
A major shortcoming of the production function method is
that it usually fails to account for production processes which
are batch versus continuous, the level of capacity utilisation in
the industry, and the level of criticality of electricity for the
production process. Thus, some industries may not suffer
much lost annual production from interruptions. Further,
industries with low criticality of electricity use, such as
construction or natural gas transport, will have low electricity
use but high value added, and thus ‘high’ estimates of VoLL
[1].
4
A more elaborate discussion of the pros and cons of these methods
is presented in Section IV.B.
The second method for calculating VoLL rests on the
stated-preference approach. This includes survey designs such
as Contingent Valuation Methods (CVM) and Choice
Experiments (CE) to arrive at the Willingness to Pay (WTP)
and Willingness to Accept (WTA) for a hypothetical supply
disruption, where estimates of WTP and WTA are normalised
using units of time to estimate VoLL [8]. WTP and WTA can
be estimated using open-ended CVMs; however, the National
Oceanic and Atmospheric Administration (NOAA) panel
headed by Arrow et al [16] proposed that the open-ended
responses to WTP or WTA are unlikely to provide reliable
valuations due to lack of realism and associated strategic bias.
Nonetheless, open-ended CVM has been used to estimate
VoLL by [17], Hartman et al, [18], and [19] for Italy, the USA
and Germany, respectively. The other approach for CVM is
designing a survey with a closed scenario for recording WTP
and WTA. Essentially, this means fixing monetary amounts
that may increase or fall in subsequent rounds of questions
depending on the survey response. One of the advantages of
this technique over open-ended CVMs is that the closed-form
may provide anchoring which is in contrast to the confusion
and challenge in answering an open-ended question. CVMs
using closed-ended questions have been used by [20] and [21]
in Norway and USA amongst others.
In addition to the CVM techniques, recent years have seen
a surge in studies using CE technique for deriving WTP and
WTA for estimating VoLL. CE presents respondents with two
choices that differ on some attributes where one of the options
is chosen. The key attributes in each of the options are changed
with each scenario presented in the survey such that CEs can
be used to estimate marginal WTP/WTA for different
attributes. Moreover, CEs are highly suited in circumstances
where there is a need to estimate trade-offs between different
attributes. The CE technique has been used in estimation of
VoLL by [2], [22], [19], and [23] amongst others.
B. Pros and Cons of Different Methods
Although revealed preference methods such as case studies
and the production function approach do not require
hypothetical setups, application of such methods lacks the
ability to estimate hypothetical outage costs, especially in
circumstances where the energy interruption is relatively
infrequent. Moreover, though there is advantage of deriving
robust estimates for VoLL for the whole economy or different
sectors using data under the production function approach, the
availability and quality of data remain as key limitations. With
these factors limiting the use and applicability of revealed
preference methods, the stated preference methods using CVM
and CE to estimate VoLL through WTP and WTA is a good
solution. The stated preference methods can be applied in
different situations for different consumer types and are not
dependent on occurrence of the actual scenario in question.
However, stated preference techniques are subject to strategic
bias, especially in open-ended CVM methods. Moreover, as
stated in [8], there is lack of consistency and possibility for
discrepancy between VoLL estimates derived from WTP and
WTA values. Further, the quality and results of stated
preference methods are highly dependent on the design of
surveys and overall surveying approach (questionnaire,
wording of questions and form of response). Lastly, stated
preference methods are time-intensive where requirement of a
large sample of consumers can incur higher cost.
V. FUTURE DIRECTIONS OF VOLL
Since we have argued that the setting of VoLL should
account for how it is to be used, the future directions of VoLL
in policy terms should account for both how VoLL will be used
and the dynamics of consumers’ demands for reliability in
energy. Three major future dynamics in electricity markets are
the advent of: demand-side participation/smart meters;
increased renewables/intermittent generation; and, increased
demand from storage including electric vehicles.
Demand-side participation may make the need to set price
caps at VoLL obsolete as customers will be able to actively
reduce consumption in day-ahead or perhaps near real-time and
thus reveal their true preference for interruption. In essence, the
willingness-to-pay for energy and reliability, or lack of it, will
ensure efficient reliability. This would further solve the
problems associated with changing VoLL by season, time of
day, and with the passage of time, as correct responses from
consumers will reflect their seasonal preferences.
Ever increasing shares of intermittent generation on the
system will likely increase the cost of reliability while
decreasing the average cost of energy. In theory, the marginal
cost of reliability in the long run might always be assumed to
be flat, as it might be assumed additional thermal generation
units can always be added. What interactions this has with
other aspects of reliability and the cost of ancillary services,
however, are difficult to predict. The obvious policy response
is to ensure payment streams for capacity or balancing and
ancillary services that are independent of energy prices, and that
energy price margins alone cannot be relied upon to give
sufficient reliability. How this might interact with the first
future event, i.e., smart meters and demand side participation is
an interesting concept. One might imagine large wind
generation days with low energy costs but high
reliability/balancing/ancillary services costs—can one imagine
consumers adjusting their willingness to pay for reliability
independently of energy prices via smart meters and DSM?
Finally, increasing penetration of storage technologies and
demand from electric vehicles, batteries and related
technologies may also impact the usefulness of VoLL or how
VoLL should be used. The advent of higher penetration of
these technologies may mean consumers’ marginal benefit
curve (Fig. 1) is no longer everywhere decreasing/convex. In
other words, small additions to reliability may be worth less as
consumers can store their own energy or shift demand. The
relationship between VoLL and CONE may become more
complex, and the value of capacity and cost benefit may be less
clear. What will be needed perhaps may be an overall
reliability, such that batteries have sufficient time to recharge.
VoLL might be a function of several parameters such as total
energy supplied over a longer period (than an hour for
example).
This paper has discussed the uses and methods and future
directions of VoLL. Different uses of VoLL may imply
different willingness to pay to avoid outages and thus different
VoLLs. Alternatively, curtailments and investments might be
shaped or chosen with different VoLLs of different users in
mind, if they can be identified. Estimating VoLL invariably
involves using methods with assumptions that will impact the
value of VoLL. Finally, the advent of future technologies such
as smart meters and DSM, intermittent renewables generation,
and storage and EVs may further interact and change the uses
and needs of VoLL estimation and how estimates fit into policy.
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