Preprint: Koami Soulemane Hayibo and Joshua M.Pearce. A review of the value of solar methodology with a case study of
the U.S. VOS. Renewable and Sustainable Energy Reviews 137, 2021, 110599. https://doi.org/10.1016/j.rser.2020.110599
A Review of the Value of Solar Methodology with a Case Study of the U.S. VOS
Koami Soulemane Hayibo1, Joshua M. Pearce2,3,*
1. Department of Electrical & Computer Engineering, Michigan Technological University, Houghton,
2. Department of Materials Science & Engineering, Michigan Technological University, Houghton, MI,
3. Visiting Professor of Photovoltaics and Nanoengineering, School of Electrical Engineering, Aalto
Distributed generation with solar photovoltaic (PV) technology is economically competitive if net
metered in the U.S. Yet there is evidence that net metering is misrepresenting the true value of
distributed solar generation so that the value of solar (VOS) is becoming the preferred method for
evaluating economics of grid-tied PV. VOS calculations are challenging and there is widespread
disagreement in the literature on the methods and data needed. To overcome these limitations, this
study reviews past VOS studies to develop a generalized model that considers realistic future avoided
costs and liabilities. The approach used here is bottom-up modeling where the final VOS for a utility
system is calculated. The avoided costs considered are: plant O&M fixed and variable; fuel; generation
capacity, reserve capacity, transmission capacity, distribution capacity, and environmental and health
liability. The VOS represents the sum of these avoided costs. Each sub-component of the VOS has a
sensitivity analysis run on the core variables and these sensitivities are applied for the total VOS. The
results show that grid-tied utility customers are being grossly under-compensated in most of the U.S. as
the value of solar eclipses the net metering rate as well as two-tiered rates. It can be concluded that
substantial future work is needed for regulatory reform to ensure that grid-tied solar PV owners are not
unjustly subsidizing U.S. electric utilities.
Distributed generation solar photovoltaic (PV) economically competitive if net metered in U.S.
Value of solar (VOS) is becoming preferred method for evaluating economics of grid-tied PV.
Here review VOS calculations, inputs and sensitivity analysis on all core variables
Results: VOS eclipses the net metering rate as well as two-tiered rates in US
Regulatory reform needed: solar PV owners are unjustly subsidizing electric utilities
Keywords: utility policy; photovoltaic; distributed generation; value of solar; net metering; economics
BBurner tip fuel price [$/MMBtu]
CDDistribution capacity [MW]
CGUtility generation capacity [p.u.]
CHHealth cost of natural gas [$/kWh]
CPV PV capacity for year ‘n’ [kW]
CTTransmission capacity [p.u.]
DUtility Discount rate
DEEnvironmental discount rate
DHHeat rate degradation rate
DPV Degradation rate of PV
EEnvironmental cost [$/MMBtu]
FUtility discount factor
FEEnvironmental discount factor
hNumber of hours in the analysis period
HCHeat rate of combined cycle gas turbine [Btu/kWh]
HCT Heat rate of peaker combustion turbine [Btu/kWh]
HnHeat rate for year n [Btu/kWh]
HPHeat rate of the plant [Btu/kWh]
HSSolar heat rate [Btu/kWh]
iNumber of years in analysis period
ICInstallation cost of combined cycle gas turbine [$/kW]
IDInvestment on distribution capacity per year without PV [$]
IDP Investment on distribution capacity per year with PV [$]
IPInstallation cost of peaker combustion turbine [$/kW]
MReserve capacity margin
nnth year of analysis period
OOutput of the PV [kWh]
PL1 1st year load capacity [kW]
PL10 10th year load capacity [kW]
QDistribution cost [$/kW]
SPV fleet shape [kW]
SCSolar capacity cost [$/kW]
UCUtility cost [$]
UFUtility fixed operation and maintenance cost [$/kW]
UPUtility price [$/kWh]
UTUtility transmission capacity cost [$/kW]
UVUtility variables operation and maintenance cost [$/kWh]
VOS Value of solar [$/kWh]
V1: Avoided operation and maintenance fixed cost [$]
V2: Avoided operation and maintenance variable cost [$]
V3: Avoided fuel cost [$]
V4: Avoided generation capacity cost [$]
V5: Avoided reserve Capacity cost [$]
V6: Avoided transmission capacity cost [$]
V7: Avoided distribution cost [$]
V8: Avoided environmental cost [$]
V9: Avoided health liability [$]
Solar photovoltaic (PV) technologies have had a rapid industrial learning curve [1-4], which has
resulted in continuous cost reductions and improved economics [5,6]. This constant cost reduction
pressure has resulted in a spot price of polysilicon Chinese-manufactured PV modules of only
US$0.18/W as of April 2020 . There are several technical improvements, which are both already
available and slated to drive the costs further down such as black silicon [8-10]. The International
Renewable Energy Agency (IRENA) can thus confidently predict that PV prices will fall by another
60% in the next decade . However, even at current prices, any scale of PV provides a levelized cost
of electricity (LCOE)  lower than the net metered cost of grid electricity  and this will only
improve with storage costs declining [14-18]. Specifically, PV already provides a lower levelized cost
of electricity [12,19,20] than coal-fired electricity [13,21,22]. In addition, PV technology can be
inherently distributed (e.g. each electricity consumer produces some or all of their electricity on site
thus becoming ‘prosumers’). Distributed generation with PV has several technical advantages,
including improved reliability, reduced transmission losses [23,24], enhanced voltage profile, reduced
transmission and distribution losses , transmission and distribution infrastructures deferment, and
enhanced power quality . As PV prices decline, prices of conventional fossil fuel-based electricity
production are increasing due to aging infrastructure [27-29], increased regulations (in some
jurisdictions) [30-33], fossil fuel scarcity [34-36], and pollution costs [37-41]. Thus, PV represents a
threat to conventional utility business models  and there is evidence that some utilities are
manipulating rates to discourage distributed generation with solar , while others are embracing it
such as Austin Texas or the state of Minnesota . Rates structures vary widely throughout the U.S.
[45-48] and there has been significant effort to determine the actual value of solar (VOS) electricity.
This shift towards VOS is fueled by criticisms of its predecessor , net metering, that is
misrepresenting the true value of distributed solar generation [50-52]. VOS is more representative of
the electricity cost because under a Value of Solar Tariff (VOST) scheme, the utility purchases part of,
or the whole net solar photovoltaic electricity generation from its customers, therefore dissociating the
VOST from the electricity retail price [51,53]. Performing a complete VOS calculation, however, is
challenging. One of the main challenges is data availability and accuracy [54,55]. Three data challenges
have been identified by  that are: 1) the time granularity of the solar irradiation data, 2) the origin
of the data, modeled versus measured, and 3) the data measurement accuracy. Other challenges faced
by utilities while assessing the VOS are which components to include in the calculations, and what
calculations method to assess the value of each components . The possible components across the
literature that are suggested to be included in a VOS as avoided costs and solar benefits are: energy
production costs (operation and maintenance) [45-47,57-63], electricity generation capacity costs
[45-47,50,57-63], transmission capacity costs [45-47,50,57-61,63], distribution capacity costs [45-
47,50,57-63], fuel costs [45-47,50,57,60-63], environmental costs [45,47,57,58,60-63], ancillary
including voltage control benefits [47,57-59,63], solar integration costs , market price
reduction benefits [47,60], economic development value or job creation [46,47,57,60,61], health
liability costs [57,60,64], and value of increased security [47,57]. A guidebook has been developed
by the United States’ Interstate Renewable Energy Council (IREC) for the calculation of several of the
VOS components . These methods have been further developed by the U.S. National Renewable
Energy Laboratory (NREL) . NREL has provided more detailed calculation methods than the
guidebook from the IREC with a different level of accuracy. The methods with a higher level of
accuracy are more complicated to implement and require a higher level of data granularity. A
qualitative study on VOS performed in 2014 suggested the inclusion of all relevant components in a
VOS studies . The calculation of the VOS can be done annually, as in the case of Austin Energy
[50,53], or can be fixed for a selected period, as per the case of Minnesota state’s VOS (25 years)
[45,53]. There are recently an increasing number of studies looking into externality-based components
of VOS especially environmental costs and health liability costs [65-67]. This is because a country
with high solar PV penetration rate provides a healthy population according to a German study . An
estimated average of 1,424 lives could be saved each summer in the Eastern United States, and $13.1
billion in terms of health savings if the total electricity generation capacity in the Eastern United States
included 17% of solar PV . For the entire U.S. if coal-fired electricity were replaced with solar
generation, roughly 52,000 premature American deaths would be prevented from reduced air pollution
alone . Not surprisingly, the latest report from North Carolina Clean Energy Technology Center
found out that there are policy changes on VOS across the United States with 46 states, in addition of
DC considering making significant changes in their solar policies and might be transitioning to a VOS
model in coming years .
This indicates VOS is the way of the future for grid integrated PV, but how exactly should solar be
valued on the modern grid? In this study the VOS literature is reviewed, and a generalized model is
developed taking realistic future avoided costs and liabilities into account from the literature. The
approach used here is a bottom-up modeling where the final value of solar to a utility system is
calculated. This model factors in the existing parameters, that have been identified in VOS studies in
different U.S. jurisdictions. The approach starts from the existing formula to calculate the levelized cost
of electricity from solar PV technology  and updates the formula by adding the avoided and
opportunity costs and the effect of different externalities. The costs considered in the study are: avoided
plant operation and maintenance (O&M) fixed cost; avoided O&M variable cost; avoided fuel cost;
avoided generation capacity cost, avoided reserve capacity cost, avoided transmission capacity cost,
avoided distribution capacity cost, avoided environmental cost, and the avoided health liability cost.
The value of solar represents the sum of these costs. Each sub-component of the VOS has a sensitivity
analysis run on the core variables and these sensitivities are applied for the total VOS. These
sensitivities are limited by the best available data on the variables in the literature and future work is
needed to quantify the secondary costs that would lead to an even higher VOS. The conservative results
developed here are presented and discussed in the context of aligning policy and regulations with
appropriate compensation for PV-asset owners and electric utility customers.
2.1. Avoided Plant O&M – Fixed Cost (V1):
The use of solar energy results in a displacement of energy production from conventional energy
sources. The avoided cost of plant operation and maintenance (V1) [$] depends on the energy saved by
using solar PV for electricity generation instead of conventional energy generation processes. Equation
(1) describes the calculation of the capacity of solar PV (CPV) [kW] throughout the lifetime of the solar
PV system. During the first year of operation, the installed solar PV system is considered to not have
suffered any degradation. Therefore, the capacity has a value of one. The degradation of the installed
solar PV system is expressed by the degradation rate of PV (DPV) and for a marginal year (n), the
marginal capacity of the installed PV system for that year would be:
( 1 )
The fixed O&M cost is directly linked to the need for new conventional electricity generation plants. If
the construction of new conventional generators in the location of interest can be avoided, there is no
need to include the fixed O&M in the valuation of solar for this location. To calculate the value of the
fixed O&M (V1), the value of the utility cost (UC) [$] needs to be known first. The utility cost depends
on four parameters, the capacity of solar PV (CPV) mentioned above, the utility capacity (CG) [p.u.], the
utility fixed O&M cost (UF) [$/kW], and the utility discount factor (F). To calculate this utility cost,
first the ratio of the capacity of solar to the utility capacity is calculated. This ratio is then multiplied by
the utility fixed O&M cost. A discount is applied to the result by multiplying it by the utility discount
factor . The discount factor (F) depends on the year and can be calculated by using the discount
rate (D). The discount factor for year (n) is :
( 2 )
The discount rate used in the formula describes the uncertainty and the fluctuation of the value of
money in time. The value of the discount rate differs when considered from a utility point of view or a
societal point of view and can highly impact the utility cost. While considering the economics of solar
PV systems,  has suggested the use of a discount rate lower than the value used by the utility.
( 2 )
The avoided plant O&M fixed cost (V1) is then calculated by summing the utility cost for all the years
included in the analysis period.
( 3 )
2.2. Avoided Plant O&M – Variable Cost (V2):
The utility cost for the avoided variable O&M cost (V2) [$] is calculated by multiplying the utility
variable O&M cost (UV) [$/kWh] by the energy saved by using solar PV systems or the output of the
solar PV system (O) [kWh], and the result is discounted by the discount factor (F).
( 4 )
The avoided variable O&M (V2) cost is the sum of the utility cost over the analysis period:
V2=∑ U C0
( 5 )
2.3. Avoided Fuel Cost (V3)
Additionally, the calculation of the utility price (UP) [$/kWh] require the knowledge of the equivalent
heat rate of a marginal solar. According to , the heat rate [Btu/kWh] describes how much fuel-
energy, on average, a generator uses in order to produce 1kWh of electricity. It is typically used in the
energy calculation of thermal-based plants and is therefore misleading for the calculation of solar
energy production. Since the method evaluates the avoided cost from thermal-based plants, however, it
is applied to solar PV generation. The heat rate (HS) [Btu/kWh] of solar PV or displaced fuel heat rate
during the first marginal year is calculated as:
( 6 )
In the equation above, the heat rate (Hp) [Btu/kWh] represent the real value of the utility plant’s heat
rate during the operation hours of the solar PV systems over the analysis period and the parameter (S)
[kW] describes the PV fleet shape that is the hourly PV fleet shape production over the hours (h) in the
After the heat rate for the first year has been calculated, the heat rate for the succeeding years in the
analysis period can be calculated by the following equation :
( 7 )
The primary use of heat rates is the assessment of the thermal conversion efficiency of fuel into
electricity by conventional power plants. As a result, it is natural to deduce that the rate at which the
heat rate (DH) decreases corresponds to the efficiency lost rate of the power plant .
The utility price (UP) depends on the heat rates and can be calculated once the heat rate is known as:
( 8 )
Another parameter to account for is the burner tip price (B)[$/MMBtu]. The burner tip price describes
the cost of burning fuel to create heat in any fuel-burning equipment .
The avoided fuel cost (V3) [$] is calculated in a similar way as the value of the fixed O&M. First, the
utility cost is calculated by multiplying the value of the per unit PV output (O) by the utility price (UP).
The result is then discounted by the discount factor. The discount factor used in the case of the avoided
fuel cost depends on the treasury yield . The avoided fuel cost is obtained by summing up the
utility cost over the analysis period.
( 9 )
( 10 )
2.4. Avoided Generation Capacity Cost (V4):
The installation of solar systems reduces the generation of electricity from new plants. This is
represented by the avoided capacity cost. To calculate the avoided generation capacity cost, the solar
capacity cost (SC) [$/kW] needs to be known. Two variables are essential to evaluate the solar capacity
cost, the cost of peaker combustion turbine (IP) [$/kW] and the installed capital cost (IC) [$/kW]. The
cost of peaker combustion turbine (IP) is the cost associated with the operation of a turbine that function
only when the electricity demand is at its highest. The installed capital cost (IC) describes the cost of
combined cycle gas turbine updated by the cost based on the heat rate. The solar capacity can be
calculated as follows :
HCT [Btu/kWh] and HC [Btu/kWh] are respectively the heat rate of the peaker combustion turbine, and
the combined cycle gas turbine. After the calculation of the solar capacity cost (SC), the utility cost can
be obtained by first, multiplying the ratio of solar PV capacity (CPV) and utility generation capacity (CG)
by the value of solar capacity cost (SC). Then, the result is discounted by the discount factor (F) to
obtain the final value of the utility cost. And as in the previous cases the value of avoided generation
capacity is the sum of the utility cost overs the analysis period.
( 12 )
( 13 )
2.5. Avoided Reserve Capacity Cost (V5):
The calculation of the avoided reserve capacity cost (V4) [$] follows the same pattern as the avoided
cost of generation capacity. But in this case, the effective solar capacity, that is the ratio of the solar PV
capacity (CPV) and utility generation capacity (CG) is multiply by the solar capacity cost, then the result
is multiplied by the reserve capacity margin (M) to obtain the utility costs. After that, the utility cost is
discounted as previously described by the discount factor (F). Then, the avoided reserve capacity is
calculated by adding up the utility cost over the analysis period .
( 14 )
V5=∑ U C0
( 15 )
2.6. Avoided Transmission Capacity Cost (V6):
The avoided transmission capacity cost (V6) [$] calculation is also performed similarly to the avoided
generation capacity cost. This cost describes the losses that are avoided when electricity does not have
to be transported on long distance because of installed solar systems. It is calculated by first multiply-
ing the utility transmission capacity cost (UT) [$/kW] by the solar PV capacity (CPV). The result is then
divided by the transmission capacity (CT) [p.u.] and the discount factor (F) is applied to obtain the util-
ity cost for a marginal year. The avoided transmission cost is calculated by the sum, over the years in
the analysis period, of the corresponding utility costs .
( 16 )
( 17 )
2.7. Avoided Distribution Capacity Cost (V7):
The two major variables that influence the avoided distribution capacity cost (V7) [$] are the peak
growth rate (K) and the system wide costs. The system wide costs account for several financial aspects
of a distribution plant, among which, overhead lines and devices, underground cables, line
transformers, leased property, streetlights, poles, towers etc. .
All the deferrable system wide costs throughout a year have been summed up and the result divided by
the yearly peak load increase in kW over a total period of a decade to obtain the distribution cost per
growth of demand.
The ratio of the 10th year peak load (PL10) [kW] and the 1st year peak load (PL1) [kW] are used in the
calculation of the growth rate (K) of demand. The expression of the growth rate (K) is as follows
( 18 )
The distribution capital cost (Q) [$/kW] is utility owned data and depends on the utility, and the growth
rate (K) that can be obtained by using the previous formula. An escalation factor is necessary to
evaluate the distribution cost for deferral consecutive years .
After obtaining the distribution cost (Q) from the utility and growth rate (K) calculated, the distribution
capacity (CD) [kW] can be calculated from the growth rate. The result is then multiplied by the
distribution cost and discounted by the discount factor (F) to get the discounted cost for a particular
year. The discounted cost for the analysis period can in turn be used to calculate the investment during
each year (ID) [$] of the analysis period .
( 19 )
When there is no other generation system than solar PV that comprised the installed capacity, the
investment per year (IDP) [$] in terms of deferred distribution can be calculated from the investment
(in terms of deferred distribution) ( 20 )
After obtaining the yearly investment without PV (ID) and the yearly investment in terms of deferred
distribution (IDP), the utility cost can be obtained by dividing the difference between the yearly
investment without PV and the yearly investment with PV by the distribution capacity (CD). This utility
cost can be called the deferred cost per kW of solar. This deferred cost per kW of solar is discounted by
the discount factor (F), multiplied by the solar PV capacity, and summed up over the analysis period to
obtain the avoided distribution capacity cost.
( 21 )
( 22 )
2.8. Avoided Environmental Cost (V8):
The three major pollutants that are considered in the calculation of the avoided environmental cost (V8)
[$] are: greenhouse gases (GHGs), pollutants sulfur dioxide, nitrogen oxide, and hazardous particulates
The two parameters that influences the cost linked to CO2 and other greenhouse gasses’ emission are
the social cost of CO2 and the gas emission factor . With these two variables, the cost of avoided
CO2 can be calculated in dollars and then the real value linked to this cost is obtained by converting the
previously calculated value in current value of dollars. This is done by multiplying the externality cost
of CO2 by the consumer price index (CPI) . The obtained result is then multiplied by the general es-
calation rate for the following years . The cost of CO2 for every year is obtained by multiplying the
previous value by pounds of CO2 per kWh. The same logic is applied to the other pollutants to calculate
the related costs and the cost related to all three categories of pollutant are added up to get the environ-
mental cost (E) [$/MMBtu].
By multiplying the environmental cost by the solar heat rate (HS), the utility cost (UC) is obtained. An
environmental discount factor (FE) is applied to the utility factor. The environmental discount factor
(FE) is defined as follows :
( 23 )
Here, DE is the environmental discount rate taken from the Social Cost of Carbon report .
( 24 )
( 25 )
2.9. Avoided health liability cost (V9):
The use of solar PV systems prevents part of the emissions of pollutants from getting into the air. This
can in turn result in great health benefits. The harmful pollutants that greatly impact human health are
NOx and SO2. These two chemicals react with other compounds when they are released in the air to
form a heavy and harmful product that is called particulate matter PM2.5, [84-86]. Particulate matter
PM2.5, can cause diseases such as lung cancer and cardiopulmonary diseases . It is difficult to
evaluate the cost related to the avoided health liabilities and the saved lives. Several works have
investigated the calculation of the cost of human health related to electricity production through fossil
fuels [88-91]. Nevertheless, the most relevant approach is the work of  because the methods
accounts for changes of the cost at a regional and plant level. This has been made possible because of
data collected by EPA on the emission level of facilities through the Clean Air Markets Program. The
result obtained by  is conservative as it does not include environmental impacts over the long term
(e.g. climate change) [66,68,69,92]. The calculation of the cost of health liability by  depends on
the quantity of pollutants emitted [tons/year] during a year, the cost of a unit mass of emission for each
pollutant in [$/tons], and the annual gross load [kWh/year].
The health cost of energy produced by fossil fuel sources (CH) [$/kWh] obtained by  are used to
calculate the utility cost. The utility cost (UC) is the product of the health cost by the PV systems output
(O), that is discounted by the environmental discount factor (FE).
( 26 )
The avoided health liability cost (V9) [$] is then calculated by:
( 27 )
2.10. Value of solar (VOS)
There are three different ways to represent the value of solar. It can be expressed either as the annual
cost [$] over the analysis period or the lifetime of the installed solar photovoltaic system, or as the cost
per unit of solar PV power installed [$/kW], or finally as the cost of generated electricity by the solar
system [$/kWh] . The most commonly used metric to express the VOS is the cost of electricity
generated by the solar system [$/kWh] because it is user friendly and is the same metric used by utili-
ties on electricity bills . To calculate the levelized value of VOS per kilowatt-hour of electricity
produced, the sum of the value of all the avoided cost is calculated and then divided by the total amount
of energy produced (O) during the analysis period discounted by the discount factor (F).
( 28 )
V1: Avoided O&M fixed cost
V2: Avoided O&M variable cost
V2: Avoided fuel cost
V4: Avoided generation capacity cost
V5: Avoided reserve capacity cost
V6: Avoided transmission capacity cost
V7: Avoided distribution cost
V8: Avoided environmental cost
V9: Avoided health liability cost
O: Output of the solar PV system
F: Utility discount factor
The calculation of VOS requires several parameters that come from different sources. Some parameters
are location dependent, while other parameters are state dependent, and there are parameters that are
utility dependent. Many of these parameters can also change from one year to another. As a result, there
are wide differences in the calculation of VOS across the literature . The utility-related parameters
that can change from one VOS calculation to another are the number of years in the analysis period (i),
the utility discount rate (D), the utility degradation rate, the utility O&M fixed, and variable costs, the
O&M cost escalation rate, the hourly heat rate (HP), the heat rate degradation rate (DH), the reserve ca-
pacity margin (M), the transmission capacity cost (UT), the peak load of year 1 (PL1) and year 10
(PL10), the distribution cost (Q), the distribution cost escalation factor (GD), and the distribution capac-
ity (CD). Parameters such as the cost of peaker combustion turbine (IP), the cost of combine cycle gas
turbine (IC), the heat rate of peaker combustion turbine (HCT), and the heat rate of combine cycle gas
turbine (HC) can be either obtained from the utility or from the U.S. Energy Information Agency. The
solar PV fleet (S) can also be obtained from the utility or by simulation using the open source Solar
Advisory Model (SAM) (https://github.com/NREL/SAM ) . Other variables that can affect the
VOS but are not controlled by the utility are the PV degradation rate (DPV), the environmental discount
factor (FE), the environmental cost of conventional energy, the health cost of conventional energy, and
the cost of natural gas on the energy market. Table 1 summarizes high and low estimates of the values
for the variables that are required to perform a VOS calculation and the VOS component they are used
Table 1. Assumptions used for required variables for a VOS calculation
Source VOS components
Degradation rate of PV
1  0.5 [57,93,
Distribution capacity (CD)
429000  237000  Avoided distribution cost
Distribution cost (Q) [$/
1104  678  Avoided distribution cost
Environment discount rate
2.5  5  Avoided environmental cost
Environmental Cost (E)
[$/metric tons of CO2]
[62-89]  [12-23]  Avoided environmental cost
Health cost of natural gas
0.025  0.025  Avoided health liability cost
Heat rate degradation rate
0.2  0.05  Avoided fuel cost (V3)
Heat rate of combined cy-
cle gas (HC) [Btu/kWh]
7627  Avoided generation capac-
ity cost (V4)
Avoided reserve capacity
Heat rate of peaker com-
bustion turbine (HCT)
11138  Avoided generation capac-
ity cost (V4)
Avoided reserve capacity
Installation capital cost of
combined cycle gas tur-
bine (IC) [$/kW]
896  Avoided generation capac-
ity cost (V4)
Avoided reserve capacity
Installation cost of peaker
combustion turbine (IP) [$/
1496  Avoided generation capac-
ity cost (V4)
Avoided reserve capacity
Load Growth Rate (K)
1.17  -0.94  Avoided distribution capac-
ity cost (V7)
Number of years in analy-
30  25 PV in-
Reserve capacity margin
36  13  Avoided reserve capacity
Solar Heat Rate (HS) [Btu/
8000  Avoided fuel cost (V3)
Avoided generation capac-
ity cost (V4)
Avoided reserve capacity
cost (UT) [$/kW]
130.535  17.895  Avoided transmission capac-
Utility Discount rate (D)
9  2.18  Avoided plants O&M fixed
Avoided plants O&M vari-
Avoided generation capac-
ity cost (V4)
Avoided reserve capacity
Avoided transmission ca-
pacity cost (V6)
Avoided distribution capac-
ity cost (V7)
Utility fixed O&M cost
18.86  7.44  Avoided O&M fixed cost
Utility variable O&M cost
0.01153  0.00216  Avoided O&M variable cost
3.1. Number of years in analysis period
The number of years in the analysis period varies and can be as low as 20 years, and as high as 30 years
or more [12,57]. The typical warranty provided by solar panels manufacturer is 25 years. As a result, it
is reasonable to set the lowest value of the analysis period to 25 years. Also, solar modules have proved
to continue to reliably deliver energy 30 years after the installation of the system , therefore, 30
years has been set as the higher value of the analysis period in this study. Keyes et al. have pointed out
that utility planning is often over shorter time periods (e.g. 10-20 years) . However, economic deci-
sions should be made over the entire life of the physical project not an arbitrary cutoff date  and
there are existing methods to estimate the load growth on the utility side as it is usually done for con-
ventional energy generators .
3.2. PV system degradation rate
The degradation rate of PV panels overtime depends on the location of operation as well as climate
conditions (temperature, wind speed, dust, etc.). A statistical study conducted by the National Renew-
able Energy Laboratory  has found the value of the PV system degradation rate to be comprised be-
tween 0.5% and 1%. These two values are the boundaries that will be used as low and high values for
the sensitivity analysis on the PV system degradation rate.
3.3. Utility discount rate
The discount rate is used to assess the change in money value overtime. This value can change
depending not only on the location, but also, on the utility. A discount rate value as high as 9% can be
used or a value as low as the inflation rate might be used. The discount rate used by utilities are usually
in the high values, but the social discount rate is closer to the inflation rate . As a result, 9% will be
considered as the high-end value of the discount rate while the current inflation rate of 2.18% will be
considered for the lowest value. It is important to note that the value of the inflation rate changes with
time and if this value is chosen as the discount rate it should be updated regularly for new calculations
of the VOS. Also, the value of the inflation rate can be subjected to ongoing events. The value of the
inflation rate of 2.18% was chosen at a date before the coronavirus outbreak in the United States that is
ongoing. The outbreak has brought the inflation rate to as low as 0.25%. This value will not be used to
run a sensitivity analysis because of the special conditions in which it occurred.
3.4. Environmental cost
The environmental cost associated with electricity production through conventional energy sources
depends on the cost associated with the pollution from carbon dioxide (CO2), carbon monoxide (CO),
nitrogen oxide (NOx), and hazardous particulates (PM). The environmental cost of carbon dioxide
dominates the cost of the other components. Different estimates of the CO2 cost are given by the EPA
. The cost of CO, NOx, and PM depends on state laws. The lowest value and highest value used for
the cost of CO, NOx, and PM were chosen from the state of Minnesota . It has been hypothesized
that if conventional energy sources are being used to produce electricity in the future, the effects on
environment are going to worsen (e.g. lower quality fuel, higher embodied energies, etc.), therefore the
environmental cost will be expected to increase. This will be investigated by raising the environmental
cost while analyzing the sensitivity of VOS to the environmental cost. This will show the trend of the
impact of the environmental cost on the VOS and in the future, the values will need to be updated
because the environmental cost is likely to exceed the maximum used value in this study.
3.5. Health liability cost
The health liability cost is a new calculated VOS component introduced by this study. This component
has been mentioned by several studies but was not incorporated in the calculation due to lack of data
for the evaluation [57,66,67,104]. The health and mortality impacts of coal in particular are so severe
an ethical case can be made for the industries elimination . For example, Burney estimated that
26,610 American lives were saved between 2005 and 2016 by a conversion of coal-fired units to
natural gas in the U.S. . More lives as well as non-lethal health impacts would be avoided with a
greater transition from coal to solar . The values used here were obtained from the study of 
that found the value of health impact cost of natural gas to be $0.025/kWh. As previously hypothesized,
the use of fossil fuel energy sources in the future will increase the emissions, and the cost of health care
has been escalating faster than inflation  thus increasing the cost of derived health liability.
Several increase rates will be investigated. Although it should be pointed out the approach taken here
was extremely conservative as the potential for climate/greenhouse gas emission liability [107,108]
was left for future work as discussed below.
3.6. Other parameters
The other parameters are utility related and in case of absence of utility data, generic values from the
U.S. government agencies is used as indicated in Table 1 and run through realistic percent increases or
decreases to determine their effect on the VOS components.
3.7. Sensitivity Analysis
A sensitivity analysis has been run on each of the nine VOS components as well as on the VOS. For
each component, the sensitivity has been analyzed for some of its parameters wherever data was
available. The evaluation of the variability of the VOS components has been performed for each
parameter. The sensitivity of a component to one of its parameters is determined by maintaining an
average value of the other parameters and varying the studied parameter from its lowest value to its
highest value. The different values that are obtained for the VOS component are then plotted to show
its variation according to the parameter studied. A correlation study between the different parameters
has not been conducted because there was no evident relationship between these parameters. Most of
the parameters are set by the utilities and is often not disclosed openly. An interaction study between
the parameters and how their interaction affects the VOS components would be interesting for future
studies where utility data are available.
A similar process has been used for the sensitivity analysis of the main VOS. The main VOS’s
variability has been studied according to the nine VOS components. For each component for which the
sensitivity of the VOS is analyzed, average values of the other components are maintained while the
studied component’s value is varied from its lowest value to its highest value.
4. Results and Discussion
The simulation results are plotted first for each VOS components. For each component, sensitivities on
the different input variables have been investigated. Then the sensitivity of the overall VOS to each of
the VOS components has been analyzed.
4.1. Avoided O&M fixed cost (V1)
Figure 1 shows the results for the avoided O&M fixed cost (V1). The sensitivity has been plotted for
five parameters: the utility O&M fixed cost, the utility O&M cost escalation, the PV degradation rate,
the utility discount rate, and the utility degradation rate. According to the results, the avoided O&M
cost is highly sensitive to the utility O&M fixed cost and O&M cost escalation. When the utility O&M
fixed cost increases, the avoided O&M cost increases accordingly and an increase in the O&M
escalation rate obviously increases the avoided O&M cost because it increases the utility fixed O&M
cost over the analysis period. V1 is also sensitive to the utility discount rate and decreases when the
discount rate increases. This means that using a discount rate close to the social discount rate while
conducting a VOS study will increase the avoided O&M cost while using a higher discount rate will
lower the cost. this is in accordance with the recommendation of  that is the use of a discount rate
lower than that of the utility in a distributed solar generation economic calculation. Also, the avoided
O&M fixed cost is not very sensitive to the utility degradation rate or the PV degradation rate.
Nevertheless, its value is slightly reduced when the PV degradation rate increases.
Figure 1. Sensitivity of avoided O&M fixed cost (V1) in terms of LCOE (¢/kWh) to its parameters
in percent change.
4.2. Avoided O&M variable cost (V2)
The parameters for which the avoided O&M variable cost’s (V2) sensitivity has been studied are: the
utility O&M variable cost, the utility O&M cost escalation, the PV degradation rate, and the utility
discount rate. The sensitivity of the avoided O&M to its parameters are plotted in Figure 2. Figure 2
shows a similar variation trend of V2 as compared to the case of the avoided fixed O&M cost. It is
highly sensitive to the utility variable O&M cost, and the O&M cost escalation. The avoided variable
O&M cost increases when the variable O&M, or the O&M cost escalation rate is increased but
decreases with the increase of the discount rate, and the PV degradation rate.
Figure 2. Sensitivity of avoided O&M variable cost (V2) in terms of LCOE (¢/kWh) to its
parameters in percent change.
4.3. Avoided fuel cost (V3)
In the case of the avoided fuel cost (V3), the variable considered for the sensitivity analysis are the heat
rate degradation rate, the natural gas price fluctuation rate and the PV degradation rate. While the
avoided fuel cost has shown to be not very dependent on the heat rate degradation rate or the PV
degradation rate, this value changes very quickly with a change in the natural gas price as in Figure 3.
This is an important factor that should be carefully considered while conducting a VOS study because
the price of natural gas is not fixed and varies according to several parameters that are not controlled by
the utility such as, the economy, the weather, market supply and demand [109,110]. The equivalent
heat rate degradation rate expresses the degradation of the utility plant’s efficiency over the analysis
period and when the efficiency decreases, there is a slight decrease in the avoided fuel cost. Another
value for which the avoided fuel’s sensitivity could have been studied is the equivalent heat rate for
solar, which was not analyzed in detail here because of the lack of utility data. This is left for future
Figure 3. Sensitivity of avoided fuel cost (V3) in terms of LCOE (¢/kWh) to its parameters in
4.4. Avoided generation capacity cost (V4)
The sensitivity of the avoided generation capacity cost (V4) has been plotted in Figure 4 for the
discount rate, the utility degradation, and the PV degradation rate. The V4 VOS component does not
have a high variability to the PV degradation rate even though it shows a decreasing trend with the
increase of PV degradation. But it reacts sharply to the utility degradation rate. This is because the
generation capacity of the utility is highly impacted by the utility degradation. Also, as previously
observed, when the discount rate grows far from the social discount rate, the avoided generation
capacity cost decreases.
Figure 4. Sensitivity of avoided generation capacity cost (V4) in terms of LCOE (¢/kWh) to its
parameters in percent change.
4.5. Avoided reserve capacity cost (V5)
The avoided reserve capacity cost (V5) expresses the reserve component of the generation capacity;
therefore, it can have a value of zero when there is no reserve capacity planned by the utility as shown
in Figure 5. V5 is highly sensitive to the reserve margin and the result shows that the more generation
capacity is reserved, the more the avoided generation capacity cost increases. On the other hand, the
avoided reserve capacity cost is not very sensitive to the discount rate compared to its sensitivity to the
other parameters. V5’s value goes up when the utility degradation rate increases and goes down when
the PV degradation rate increases.
Figure 5. Sensitivity of avoided reserve capacity cost (V5) in terms of LCOE (¢/kWh) to its
parameters in percent change.
4.6. Avoided transmission capacity cost (V6)
Three parameters have been analyzed in the sensitivity study of V6: the discount rate, the transmission
capacity cost, and the PV degradation rate. The parameter it is the most sensitive to is the transmission
capacity cost. Obviously, when the transmission is low cost in a location, the avoided cost associated
will be low. The results shown in Figure 6 make it clear that the avoided transmission capacity cost
does not change with the PV degradation rate or the discount rate. This is because the utility
transmission capacity has been assumed to be constant over the analysis period, and the transmission
capacity degradation rate has not been considered because utility data on this parameter was not
Figure 6. Sensitivity of avoided transmission capacity cost (V6) in terms of LCOE (¢/kWh) to its
parameters in percent change.
4.7. Avoided distribution capacity cost (V7)
The avoided distribution capacity cost (V7) is one of the most complicated VOS components to
evaluate. As shown in Figure 7, its sensitivity has been studied for six variables: the load growth rate,
the distribution capacity, the distribution capacity cost, the utility discount rate, the distribution cost
escalation, and the PV degradation rate. But it depends on more than six parameters. The growth rate,
for example is calculated from utility data, mainly, the load for the past ten years of operation [45,111].
Here, the sensitivity has been analyzed on the growth rate directly to be as widely applicable as
possible. Another parameter is the number of deferred years that is also a utility owned data.
The avoided distribution capacity cost naturally increases with the distribution capital cost. Figure 7
shows that the avoided distribution capacity cost does not fluctuate with the distribution capacity at all,
but it is highly sensitive to the discount rate, the distribution cost, and the distribution cost escalation
rate. It can even shift to a negative value when the discount rate is too low. This shows that choosing
the discount during a VOS study must be a trade-off between the social discount rate and the utility
discount rate. It is interesting to note that the avoided distribution capacity cost goes down when the
distribution cost escalation in increasing. A possible explanation for this observation is that when a
utility has enough distribution capacity, it will purchase less power from solar PV systems owners,
therefore the price goes down. The same reasoning can be used to explain the decreases of the cost
when the load growth goes up. Finally, V7 shows a slight decrease with the increase of the PV
Figure 7. Sensitivity of avoided distribution capacity cost (V7) in terms of LCOE (¢/kWh) to its
parameters in percent change.
4.8. Avoided environmental cost (V8)
The second most complicated component of the VOS calculation is the avoided environmental cost
(V8). The sensitivity has been analyzed for the three environmental discount rate scenarios provided by
the EPA . For each scenario, a sensitivity analysis has been conducted on the environmental cost
increase rate. V8 will increase when the chosen environmental discount rate is low but overall, each of
the three EPA scenarios show an increase when the environmental cost increase rate goes up as seen in
Figure 8. This is useful to see how the avoided environmental costs might change in the future.
Environmental externalities are volatile and changing quickly . If it is assumed that in the future,
the environmental impact of conventional energy production technologies will increase, then the costs
of the environmental externalities will increase as well . On the other hand, an increase in
distributed renewable energy generation could lead to a decrease or stabilization of the avoided
Figure 8. Sensitivity of avoided environmental cost (V8) in terms of LCOE (¢/kWh) to its
parameters in percent change.
4.9. Avoided health liability cost (V9)
The avoided health liability cost, V9, depends on three values, the health cost increase rate, the
environmental discount rate, and the PV degradation. This cost does not fluctuate with the PV
degradation rate but is very sensitive to the other two parameters. The environmental discount rate used
here is the same as the environmental discount rate used in the evaluation of the avoided environmental
cost’s sensitivity study. As a result, the avoided health liability cost decreases when the environmental
discount rate goes up as is the case for the avoided environmental cost.
Figure 9. Sensitivity of avoided health liability cost (V9) in terms of LCOE (¢/kWh) to its
parameters in percent change.
After the sensitivity analysis of each VOS component, the main VOS value has been studied to find out
how the impact of different components compare to one another and which components have more
variability. Figure 10 shows that the VOS is, in decreasing order, sensitive to the avoided
environmental cost (V8), avoided health liability cost (V9), avoided transmission capacity cost (V6),
avoided fuel cost (V3), avoided distribution capacity cost (V7), avoided O&M variable cost (V2),
avoided reserve capacity cost (V5), avoided O&M fixed cost (V1), and avoided generation capacity cost
Figure 10. Sensitivity of VOS LCOE (¢/kWh) to all the components in this study, in percent
The contribution of each VOS component to the overall VOS depends on the case. The lowest VOS
value calculated with the assumptions used in this study in term of LCOE is 9.37¢/kWh while the
highest value calculated is 50.65¢/kWh. This variation observed in the VOS value comes from the fact
that the parameters values considered from this study are chosen to have the lowest and the highest
value of a VOS. The values of calculated VOS using utility data are highly likely to be located within
this interval. It is also clear based on the values shown in Figure 10, that the VOS exceeds the net
metering rates (when they are even available as shown in Table 2) in the U.S. Thus, it can be concluded
that even when grid-tied solar owners are provided with a full net metered rate for electricity fed back
onto the grid they are effectively subsidizing the electric utility/other customers.
For the low VOS value case shown in Figure 11, the avoided distribution cost (V7), and the avoided
reserve capacity cost (V5) has no contribution in the VOS value. The avoided generation capacity cost
(V4) and the avoided health liability cost (V9) represent most of the VOS value followed by the avoided
environmental cost (V8) and avoided fuel cost (V3).
Figure 11. Contribution of each VOS component to the overall VOS LCOE – Low Cost Scenario.
The contribution of the avoided environmental (V8) cost increases with the VOS value as it becomes
the largest contributor to the overall value followed by the health liability (V9) cost as shown in Figure
12 representing a middle VOS value. The avoided generation capacity cost’s (V4) is reduced as well as
the contribution of the avoided fuel cost (V3).
Figure 12. Contribution of each VOS component to the overall VOS LCOE – Middle Cost
Figure 13 represents the contribution of each of the VOS components to the overall value in the case of
the highest obtained value in the scope of this study. The avoided environmental cost (V8), avoided
health liability cost (V9), and avoided transmission capacity cost (V6) represent 69% of the total cost.
Figure 13. Contribution of each VOS component to the overall VOS LCOE – High Cost Scenario.
The evolution of the cost percentage contribution of each VOS throughout Figure 11, Figure 12, and
Figure 13 shows the level of uncertainty of the VOS in respect to the corresponding component.
The lowest and highest LCOE VOS values obtained from the assumptions made in this study are
respectively 9.37¢/kWh and 50.65¢/kWh. The existing VOS studies results fall into this interval. The
sample calculation made by  for Minnesota is 13.5¢/kWh while  calculated a VOS of
10.7¢/kWh for Austin Energy. These values are in the lower spectrum of the result of this study
because of the considerations made. They incorporate less VOS components than the present study, and
this study focuses on sensitivity, therefore higher values of parameters have been considered. Other
results summarized by  have found the VOS to be 33.7¢/kWh in Maine, between 25.6 and
31.8¢/kWh in New Jersey and Pennsylvania , and 19.4¢/kWh in Washington DC. In general, the
VOS is much higher than the net metering costs as even the highest costs observed at the residential
level pay [50,62,112]. The residential net metering rates are also the highest as compared to
commercial and industrial rates so the latter two are even more unjustly compensated for installing
solar. Overall, this indicates that utilities are under-compensating customers with grid-connected PV
systems if they are only paying net metering rates, as displayed in Table 2. Table 2 shows a comparison
between VOS rates and net metering rates in the U.S. states mentioned above, wherever data is
available. As only a tiny fraction of utilities (3%) are paying full net metering rates anyway , there
is a need for regulators to ensure that solar customers are being adequately compensated for the value
of solar electricity they are sharing with the grid . Substantial future work is needed to ensure that
solar PV owners are not subsidizing non-solar electricity customers.
Table 2. Comparison of VOS rates and net metering rates for some U.S. States
State VOS Net Metering
Austin (Texas) 10.7¢/kWh Approximately 4 – 5¢/kWh
(1.2 – 1.6$/kWh) 
Maine 33.7¢/kWh 12.16 – 14.66¢/kWh 
New Jersey 25.6 – 28¢/kWh
Pennsylvania 28.2 – 31.8¢/kWh Minimum value of (4¢/kWh) 
5. Future Work
This study has covered a vast number of existing VOS components, but some components were not
included in this study due to the lack of a reliable evaluation methodology. These components include
the economic development cost, the avoided fuel hedge cost, and the avoided voltage regulation cost.
These represent opportunities for future work once the evaluation methodologies have been developed.
Also, there are some parameters sensitivities that would provide insights with multiple utility data sets.
These parameters include the analysis period, the hourly solar heat rate and solar PV fleet, and the 10-
years load profile. Future studies can focus on incorporating the sensitivities of these parameters into
the model or can use the foundation of this model to build on new VOS studies according to a specific
location and available data from utilities. Another limitation to this study is that it does not include the
effect of the load match factor, and loss saving factor.
As the results show the environmental and health costs can dwarf the technical costs and thereby
determine the VOS. There are also second order effects that can be used to obtain a more accurate VOS
values. For example, the negative impact of pollution from conventional fossil fuel electricity
generation on crop yields  as well as PV production could also be considered in future work to
give a more accurate V8. In addition, as greater percentages of PV are applied to the grid the avoided
costs will change and there is a need for a dynamic VOS akin to dynamic carbon life-cycle analyses
needed for real energy economics . This complexity will be further enhanced by the introduction
of PV and storage systems  as it will depend on size  and power flow management and
Perhaps the most urgent need for future work is accurate estimations of the value of avoided GHG
liability costs because the magnitude of the potential liability [107,108] could overwhelm other
subcomponents of the VOS. This is because as the realities of climate change have become more
established, a method gaining traction to account for the negative externalities is climate litigation
[107,108,121-131]. For utility VOS analysis this is particularly complex as it is difficult to know where
to draw the box around environmental costs. As some studies have concluded there is liability for past
emissions as well as for harm done in other nations . Liability for disastrous events is also
challenging to predict . Combining both other nations and disaster creates liability potential that
could become enormous with prioritization given to victims that are losing their land, culture, and lives
due to climate change . Tort-based lawsuits are already possible from a legal point of view ,
but there are other legal methods that could be used to reduce climate change such as public nuisance
laws . Some authors have argued a ‘polluters pay principle’ for carbon emissions . Other
studies have concluded that emitters such as conventional fossil fuel power plant operators should be
forced to buy long term insurance in order to cover their share of climate change costs for minimizing
risks in case of insolvencies . Determining what such insurance premiums should be is another
area of substantial future work. Determining what the greenhouse gas liability costs are for
conventional electricity generators (as well as potential avoided insurance costs) that can be avoided
with PV is extremely challenging. These estimates will become easier with time as climate change
impact studies become more granular thereby assigning specific costs to specific amounts of emissions.
In addition, realizing these climate liability costs in courtrooms will become more likely. As Krane
points out it is clear that as the negative impacts of climate change grow more pronounced, the fossil-
fuel based electricity industry faces a future that will be less accepting of current practices and that will
increase economic (and maybe even industry existential) risks . Avoiding these risks has real
value, which should be included in the VOS in the future.
This study demonstrated a detailed method for valuing the incorporation of solar PV-generated
electricity into the grid and analyzed the sensitivity of each VOS component to its input parameters,
and the overall sensitivity of the VOS to the each of its components. Several components have been
found to be sensitive to the utility discount rate, namely the avoided O&M fixed cost; avoided O&M
variable cost; avoided generation capacity cost, and the avoided distribution capacity cost. Except for
the avoided distribution capacity, the other components’ value decreases with the increase of the utility
discount rate. The distribution capacity is more sensitive to the discount rate than the other
components. It increases with the discount rate and can be negative if the discount rate is very low. This
has shown the necessity of carefully choosing the discount rate for VOS studies. Most of the VOS
values do not have a high variability to the solar PV degradation rate even though its increase slightly
reduces the value of each component, and the overall VOS. The environmental cost and the health
liability cost are sensitive to the cost increase rate that can be tied to the emissions impact of the
conventional energy sources. These two costs are likely to increase in the future with the worsening of
the emission of fossil fuel sources and more information about its effects, which increases potential
emissions liability for utilities. Finally, specific case studies could provide additional sensitivities on
the few areas of the VOS that were not evaluated in this paper to create better VOS models. Overall the
results of this study indicate that grid-tied utility customers are being grossly undercompensated in
most of the U.S. as the value of solar eclipses the net metering rate. The implications of this sensitivity
analysis demand a reevaluation of the compensation for U.S. PV prosumers as the VOS is much higher
than net metering or any lesser compensation schemes. Substantial future work is needed for regulatory
reform to ensure that solar owners are not unjustly subsidizing U.S. electric utilities. In addition, future
work can obtain an even more accurate (and higher) value of VOS by evaluating economic
development costs, the avoided fuel hedge costs, the avoided voltage regulation costs, secondary health
and environmental effects such as increased crop yields from PV-reduced pollution, and accurate
estimations of the value of avoided GHG liability costs or avoided GHG emissions liability insurance.
This research was supported by the Richard Witte Endowment.
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