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The microeconomics of residential photovoltaics: Tariffs, network operation and maintenance, and ancillary services in distribution-level electricity markets
Solar Energy 140 (2016) 188–198
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Solar Energy journal homepage: www.elsevier.com/locate/solener
The microeconomics of residential photovoltaics: Tariffs, network operation and maintenance, and ancillary services in distribution-level electricity markets Riccardo Boero ⇑, Scott N. Backhaus, Brian K. Edwards Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA
a r t i c l e
i n f o
Article history: Received 14 July 2015 Received in revised form 25 October 2016 Accepted 3 November 2016 Available online 12 November 2016 Keywords: Residential photovoltaics Ancillary services Feed-in tariffs Net metering
a b s t r a c t We develop a microeconomic model of a distribution-level electricity market that takes explicit account of residential photovoltaics (PV) adoption. The model allows us to study the consequences of most tariffs on PV adoption and the consequences of increased residential PV adoption under the assumption of economic sustainability for electric utilities. We validate the model using U.S. data and extend it to consider different pricing schemes for operation and maintenance costs of the distribution network and for ancillary services. Results show that net metering promotes more environmental benefits and social welfare than other tariffs. However, if costs to operate the distribution network increase, net metering will amplify the unequal distribution of surplus among households. In conclusion, maintaining the economic sustainability of electric utilities under net metering may become extremely difficult unless the uneven distribution of surplus is legitimated by environmental benefits. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Recent reductions in the total cost of installing residential photovoltaic (PV) systems have increased global diffusion (Rigter and Vidican, 2010; Thiam, 2011; Lin and Wesseh, 2013; Chowdhury et al., 2014) of this renewable energy source. Changes in technology and markets have reduced both PV module production costs (Goodrich et al., 2012) and installation costs (Friedman et al., 2013). Further, public policies (Timilsina et al., 2012; Dong et al., 2014; Jimenez et al., 2016) in the form of rebates (Kwan, 2012) or tax credits (Burns and Kang, 2012) have encouraged an increasing number of households to adopt PV systems. There are concerns that high rates of residential PV adoption may impact electricity distribution networks. In particular, it has been noted that the diffusion of residential PV requires new and updated grid equipment (Eltawil and Zhao, 2010), and that it reduces utility revenues more than it reduces costs. These considAbbreviations: APS, Arizona Public Service; EIA, U.S. Energy Information Administration; FIT, feed-in tariff; JCP&L, Jersey Central Power & Light; NetM, net metering tariff; NetPS, net purchase and sale tariff; O&M, operation and maintenance; PG&E, Pacific Gas & Electric; PSE&G, Public Service Electric and Gas Company; SRP, Salt River Project; SCE, Southern California Edison; SDG&E, San Diego Gas & Electric; TEP, Tucson Electric Power. ⇑ Corresponding author. E-mail addresses: [email protected] (R. Boero), [email protected] (S.N. Backhaus), [email protected] (B.K. Edwards). http://dx.doi.org/10.1016/j.solener.2016.11.010 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.
erations introduce additional economic and financial challenges (Satchwell et al., 2014) for utilities. There are additional concerns that public polices vis a vis utility budget constraints can cause costs to be shifted between households. These issues and others suggest the need for a better understanding of how different tariff mechanisms affect PV adoption rates, social welfare, and the surplus distribution between households. Case studies so far have pointed out how policies (Burns and Kang, 2012; Chowdhury et al., 2014), social dynamics (Guo and Song, 2015), and economic incentives (Rigter and Vidican, 2010; Jimenez et al., 2016) contribute to PV adoption and to its emerging patterns (Guidolin and Mortarino, 2010; Kwan, 2012). Along empirical studies, models of innovation diffusion (Rao and Kishore, 2010; Popp et al., 2011; Hsu, 2012; Islam, 2014) have focused on processes of technology adoption. The analytical concerns mentioned above require a different modeling approach capable of concurrently representing the dispersed and individual-level decision-making typical of PV diffusion (Islam, 2014; Guo and Song, 2015), the system-level effects impacting the environment, households, social welfare, and electric utilities through tariffs and costs, and the complex feedback between those levels. We develop a microeconomic model of a distribution-level electricity market that extends the model presented in Yamamoto (2012). The model presented in this paper addresses household
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investment in PV and incorporates budget constraints on electric utilities. Incorporating utility budget constraints allows us to examine issues relating to how pricing mechanisms affect household incentives to adopt PV and how household PV penetration rates affect distribution utility profitability. This approach also allows us to examine how electricity surpluses are distributed between households. Finally, this approach also allows comparing the effects of different tariffs (Lesser and Su, 2008; Cory et al., 2009) on both household surplus and social welfare (Wand and Leuthold, 2011). After presenting the validation of the basic theoretical model using data observed in the United States under the net metering tariff, we extend it to investigate the challenges posed by increasing and additional costs due to PV adoption. We study the interaction between tariffs and schemes implemented to collect resources for the most common additional costs introduced by PV, which are for operating and maintaining the distribution network and ancillary services. We conclude with a brief discussion of the main results and limitations of our analysis and sketch possible future directions of research.
The third tariff we consider is the feed-in tariff (FIT). This tariff is based on readings from two separated household meters in households that have installed PV. One meter measures electricity consumption while the other measures electricity generation. Under FIT, the whole generation is sold to the electric utility at price p and the whole consumption is paid by households at price r. Finally, if zi is the amount of electricity household i generates with solar panels, we can use the parameter t to model the billing effect of different tariffs. Specifically, ðtÞzi indicates the amount of PV-generated energy sold by household i to the electric utility, and ð1 tÞzi represents the part of zi that is used to offset household consumption. Let qi represent the quantity of electricity consumed by household i. In Duke et al. (2005), empirical evidence suggests that the average generating power of residential solar panels is strictly P P lower than household needs ( N zi < N qi ). We assume this holds at the consumer level as well, zi < qi . Under FIT, t ¼ 1, and all PV-generated electricity is sold to the electric utility and none is used to offset consumption because generation and consumption are metered separately. Under NetPS, 0 < t < 0:5 because zi < qi . Under NetM, we have 0 < t < 0:5 as well, but in this case t will be lower than in NetPS because the billing period is longer. Table 1 summarizes the values of the t under each tariff scheme.
2. The basic model 2.2. Residential PV supply function We consider the presence of a finite number of households N. Each household installs residential PV if the investment is profitable. Households adopting residential PV determine the supply of PV-generated energy. Further, an electric utility EU sells electricity, provides the distribution network, buys PV-generated electricity, and buys electricity and ancillary services from utility-scale conventional and renewable energy generators. Households are consumers, but become producers if they install solar panels. The electric utility is an intermediary, selling electricity generated at the utility scale to all households and buying and selling power from PV-adopting households. The electric utility is also a service provider (distribution network maintenance, reliable and secure power flow, etc.). Exchanges between the electric utility and utility-scale power generators happen at a wholesale spot price c, which is determined by dynamics in the electricity market at the transmission level. Exchanges of power between the electric utility and households happen according to two regulated prices. The first, r, is the standard retail rate at which the household would purchase power from the utility. The second, p, is the price paid by the utility when buying residential PV energy from the household.
We assume that household demand for electricity is a constant qi , is exogenous, and is inelastic. 2.2.1. Household investment decision The household investment decision in PV is a simple binary decision, with investment occurring if household utility derived from investing exceeds household utility from not investing. Eq. (1) shows the household utility function ui for the investment in PV, where K i is the discounted cost of installing, operating, and maintaining solar panels for their expected lifetime,
ui ¼ K i þ pðtÞzi þ rð1 tÞzi :
Under FIT, r does not influence household utility because generated electricity is sold entirely to the electric utility at price p and no generated electricity is used to reduce demand qi . 2.2.2. Derivation of the supply function From Eq. (1) we know that each household has a reservation price pi , below which household investments in PV are not profitable,
pi ¼ 2.1. Tariffs We consider here three tariffs commonly found in contemporary electricity markets. The first one is net metering (NetM). It is based on the household-level compensation of generation and consumption over a rather long billing period, typically lasting between one month and one year. Under NetM, at the end of the billing period the accounting balance between consumption and generation is computed. If the household has generated more than it has consumed in the period, it sells the difference to the electric utility at price p. Otherwise, the household buys the excess of consumption from the electric utility at price r. The second tariff is net purchase and sale (NetPS). It is similar to net metering in that it is determined partly by the net difference consumed and generated. Under NetPS, the compensation is computed continuously using the shortest possible billing interval, typically every 15 min. Moreover, NetM would converge to NetPS if the billing period were to be shortened as much as possible.
ð1Þ
ki rð1 tÞzi 1 ki ¼ rð1 tÞ : t zi t i zi
ð2Þ
If we order the households from 1 to N according to an increasing reservation price, we obtain the supply function in Fig. 1. Further, defining Z as the sum of energy generated by houseP holds with residential PV (Z ¼ N zi ) and k as the average total cost P ki of a unit of residential PV generation capacity k ¼ PN z , we can N i
linearize the supply function,
p¼
1 ðk rð1 tÞÞZ: t
ð3Þ
Table 1 Definition of tariff parameters. Tariff
Acronym
Parameter Value
Net metering Net purchase and sale Feed-in tariff
NetM NetPS FIT
0 < tNetM < t NetPS 0 < tNetPS < 0:5 t FIT ¼ 1
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an incentive to keep a high volume of sales if it depends on those revenues. The total profit of an electric utility PEU depends on the net quantity of electricity purchased from transmission-level power generators at price c, and sold to customers at price r, and on the net quantity of PV electricity purchased by the electric utility from households at price p (instead of price c), i.e.,
PEU ¼ ðr cÞðQ ð1 tÞZÞ ðp cÞtZ;
P
ð4Þ
where Q is the total electricity demanded (Q ¼ N qi ). Regulations prevent electric utilities from having profits beyond the return on their capital costs, i.e., PEU ¼ 0, implying
p¼
Fig. 1. Derivation of the supply function from household investment decision.
ðr cÞðQ ð1 tÞZÞ þ c: tZ
ð5Þ
Eq. (5) suggests that retail prices r and p should be greater than c, i.e., c should be marked up at a level that depends on tariffs and level of PV adoption.
According to the supply function, the installation of residential PV increases with the payment for PV-generated energy p. A decrease in costs k, due to technological innovation or to subsidies from the government, increases the amount of PV-generated power Z. Our parameterization t of the tariffs also impacts the supply.
2.4. Feasible equilibria Feasible equilibria are pairs of p and r constrained by zero utility profits and parameterized by different levels of Z, costs c and tariffs t. These equilibria are found from Eqs. (3) and (5), i.e.,
2.3. The electric utility
8 Z kZ1 þ1 Þ Q ðc r > > > c ¼ QZ ðZ1Þð1tÞþ1 > < Z kZ1 þ1 Þ ; p Q ðc ¼ 1t kc Z ðZ1Þð1tÞþ1 ð1 tÞ Z > c > Q > > : Z–0
Because many utilities have adopted the so-called decoupling of sales and revenues, we assume that connection charges cover capital costs. This means that the utility collects revenues covering the capital cost by dividing this cost by the number of served households (cc ¼ CC ). Each household pays the same cc, and its utility is N negatively affected equally. However, this does not affect the customer reserve price or Z. The decoupling of sales and revenues by electric utilities is motivated by the fact that if electric utility profits and revenues are related to sales, a negative incentive emerges in energy conservation and in PV diffusion. The electric utility has
ð6Þ
p/c 0
0
2
100
4
r/c
200
6
300
8
and are plotted in Fig. 2. From Fig. 2 it is possible to analyze some important differences in the behavior of the system under different tariffs. For the FIT, because p ¼ kZ, the payment of PV-generated energy at price p is allowed only by large increases in r. In contrast, under NetM, we observe a modest increment of r and an initial
0
100
200
300
0
100
Z
300
NetM (t = 0.1)
NetPS (t = 0.49)
0
0
200
500
400
r/c
p/c
600
1000
800
1500
NetPS (t = 0.49)
1000
NetM (t = 0.1)
200
Z
0
100
200
Z FIT (t = 1)
300
0
100
200
Z FIT (t = 1)
Fig. 2. Feasible equilibria in r and p over Z under different tariffs t (k = 2, c = 0.5, Q = 400).
300
191
Pi qi
¼
rqi ¼ r: qi
ð7Þ
For households adopting PV (Eq. (8)), the surplus is affected both by r and p. The surplus increases by what is sold to the electric utility (at price p) and decreases by what is bought from the electric utility (at price r and computed as the difference between total consumption and compensation with zi ), i.e.,
Pi qi
¼p
tzi q ð1 tÞzi zi r i ¼ ðpt þ rð1 tÞÞ r: qi qi qi
ð8Þ
10 5 0 -5
surplus per unit of energy
15
Under NetM the difference between the surplus of adopting and non-adopting households is initially large, and it decreases as households adopt PV (Fig. 3, with zi =qi ¼ 0:8). Under FIT (Fig. 4), the surplus difference in favor of adopting households increases over the adoption rate. Further, the surplus of non-adopting households is very negatively affected by increasing levels of PV because, under this tariff, all resources needed to pay for PV-generated energy are paid in terms of increases in r. Under both tariffs the surplus of adopting households can be positive even if we do not include the utility derived from consum-
0
100
200
300
0 0
Households adopting PV
Fig. 3. Surplus per quantity of consumed energy under tariff NetM (t = 0.1, qzii ¼ 0:8, k = 2, c = 0.5).
100
200
300
Z Households non adopting PV
Households adopting PV
Fig. 4. Surplus per quantity of consumed energy under tariff FIT (t = 1, qzii ¼ 0:8, k = 2, c = 0.5).
ing electricity. Finally it is important to note that under NetM the cost implied by increasing levels of PV adoption is more equally shared between PV-adopting and non-adopting households than it is under FIT, and that, if we compare the surplus for nonadopting households under FIT and NetM, in absolute terms FIT implies much greater costs for non-adopting households. The model suggests that, given the values of exogenous parameters (e.g., k determined by technology), the electric utility has the power to determine the level of PV adoption Z by manipulating p and r. However, increases of Z are accompanied by changes in household surpluses. Policy measures such as tax credits subsidizing residential solar panels can be incorporated into our model as reductions in the costs of installing solar panels (given by k). From Eq. (6) we know that the result, under any tariff, is a decrease in r and p values for the same levels of adoption, and a shift of the intrinsic cost of PV adoption towards a broader tax base or future generations. 2.6. Social welfare maximization Because we know how household surpluses vary over PV adoption and we know the set of feasible equilibria determined jointly by PV supply and the budget constraint of the electric utility, it is possible to study the optimal solution where the electric utility or the regulatory agency modifies Z by means of r and p in order to maximize social welfare. The optimization problem is the maximization of the social welfare function W, which is composed by the surplus of all households and by the environmental benefit given by using a renewable energy source. The surplus of the electric utility is not included in social welfare because it is bounded to be null, and thus, on the contrary, it enters the set of optimization constraints. The surplus of all households is as in Eq. (8), but referred to the population-level variable Q and using Z as the measure of PV adoption. The environmental benefit of Z is represented by the parameter b, implicitly assumed to be positive (b > 0). The constraint to the maximization of the social welfare is represented by the intersection between the supply function and the electric utility budget constraint. The resulting problem is
maximize W ¼ ptZ þ rð1 tÞZ rQ þ bZ; Z
s:t: Eq: ð6Þ:
Z Households non adopting PV
-200
To support the argument that adopting PV affects more negatively non-adopting households under FIT, we analyze how surplus varies between PV-adopting and non-adopting households. We expect a positive difference in favor of PV-adopting households because the system has to reward adopting households for their investment if Z increases. In other words, it should provide households with enough revenue to cover the solar panel installation costs. Without considering the utility that households gain by consuming energy, which is constant under our assumption of inelastic demand, buying energy for consumption reduces household surplus and selling household energy to the electric utility increases household surplus. Thus, the surplus definition collapses to a measure of the average net cost of consumed energy. In the case of non-adopting households, the surplus computed over a single unit of consumed energy (Pi =qi ) is negative and equal to the price r, i.e.,
surplus per unit of energy
2.5. Household surplus
-400
sharp increase in p, followed by an asymptotic decrease of that price as Z increases. Because all customers pay r under both tariff schemes, our comparison suggests that PV adoption leads to more negative impacts on non-adopting households under FIT.
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ð9Þ
By substituting r and p of Eq. (6) in W, we obtain a social welfare measure that is dependent only on Z and that respects maximization constraints, i.e.,
R. Boero et al. / Solar Energy 140 (2016) 188–198
þ
ðct 3c bÞQZ þ 2cQ 2 ðt 1ÞZ 2 þ ð1 tÞZ Q
:
0
ððct þ k þ cÞQ þ ðc bÞt þ c þ bÞZ 2 ðt 1ÞZ 2 þ ð1 tÞZ Q
-1000
ðt 1ÞZ þ ð1 tÞZ Q
þ
ð10Þ
To study the maximization of social welfare, we need to differentiate the analysis by different values of t. First, if t < 0:5, which holds under both NetM and NetPS cases, there is no global equilibrium because social welfare can be increased by increasing PV generation Z. In fact, whatever the positive value of b, social welfare is determined by the fraction in Eq. (10) where Z 3 is the highest order in the numerator and Z 2 is high-
W
2
-3000
ðc þ bÞðt 1ÞZ 3
-4000
W¼
-2000
192
0
10
est order in the denominator. The coefficient of Z 2 is ðt 1Þ that is always negative because we are considering t < 0:5. The coefficient of Z 3 is ðc þ bÞðt 1Þ that is always negative as well because ðt 1Þ is negative and both c and b are positive. Under NetPS and NetM social welfare is maximized by the highest level of Z possible, but there can be points where, locally, the first derivative of W is null. Second, with the FIT, the welfare function is much simpler and we can compute the first and second derivatives of W, 2
W ¼ kZ þ ð2c þ bÞZ 2cQ; 0
W ¼ 2kZ þ 2c þ b;
ð11Þ
W 00 ¼ 2k: Because the second derivative of W is always negative because k > 0, to solve the maximization problem we impose W 0 ¼ 0 and we find the internal solution to the maximization of social welfare, Z_ ¼ ð2c þ bÞ=ð2kÞ. The equilibrium point can be interpreted as the one where the average environmental benefit b equals twice the total net cost of PV adoption, i.e., b ¼ 2ðkZ_ cÞ, that is the cost of installed solar panels kZ decreased by saving consumption from conventional utility-scale power sources c. The social equilibrium of PV adoption under FIT is very low unless the environmental benefit is particularly significant. Nevertheless, with the FIT the optimal level of PV adoption is increased by exogenous shocks incrementing prices of primary energy sources (c), technological shocks that improve the environmental benefits of PV (b), and technological shocks that decrease the costs to adopt PV (k). Public policies, such as tax credits that decrease the cost of installing solar panels (i.e., decreasing k), do not change the equilibrium solution because the social welfare function W should include also the cost of the policy. The social welfare function is plotted in Fig. 5 with the parameters used for previous graphs and with b ¼ 20. From the dynamic viewpoint, the figure suggests that because markets start from a situation where the adoption of residential PV is null, tariffs have similar impacts at the beginning, providing similar initial incentives to adoption because the marginal social benefit is comparable. However, beyond lower levels of Z there can be different dynamics under different tariffs, and the presence of stationary points (W 0 ¼ 0) presented in Table 2. Under FIT, we have the lowest level of local maximum of social welfare. That point is also the global maximum under that tariff. Under NetM and NetPS, there are local maximum points for higher values of Z, then, with Z increasing beyond them, there are decreases in social welfare until a local minimum, and finally an ever-increasing social welfare. It is evident that, if the dynamics starts from a very low value of Z, the system could stop in the local maximum but the numerical example shows that decreases in t, which represent increases in the length of the billing period,
20
30
40
50
Z NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
Fig. 5. Social welfare (k = 2, c = 0.5, Q = 400, b = 20).
Table 2 Local equilibria in the numerical example (k = 2, c = 0.5, Q = 400, b = 20). Tariff
Local maximum (Z)
Local minimum (Z)
9.09 6.52 5.25
16.05 33.00 N/A
NetM (t ¼ 0:1) NetPS (t ¼ 0:49) FIT (t ¼ 1)
generate higher values of the local maximum. Finally, very low values of t can transform the shape of the social welfare function in one monotonically increasing over Z. 3. Validation of the basic model The basic model comprises the supply function and the budget constraint of the electric utility. While the supply function depends on the daily decision making of hundreds or thousands of households, the utility budget constraint is influenced by prices that are governed by slower regulatory processes. Even though it is conceivable that the null profit hypothesis about electric utilities is not continuously supported due to the duration of the regulatory process and uncertainty in near-term forecasting of costs and revenues, it is possible to use an empirical model to test the validity of both components of the model. We use data for eight utilities in Arizona, California, and New Jersey, three of the most populous U.S. states. All utilities considered have adopted NetM. The database is organized as monthly values by each utility over the period 2001–2014. Appendix A provides details about the data. Prices are in U.S. $ per kW h of electricity. Total installation costs, including capital and installation costs net of rebates, are in $ 1000 per each kW of capacity. Z and Q are in monthly kW h. In the first equation derived from the supply function (Eq. (3)), the dependent variable is the cumulative PV adoption rate Z=Q observed by utility i at time t (measured as percentage),
Z ¼ b1 Q i;t
3 X ki;ty y¼1
3
3 X
þ b2
þ ai þ kt þ i;t :
3 X r i;ty
di;ty
y¼1
3
þ b3
y¼1
3
3 X pi;ty
þ b4
y¼1
3 ð12Þ
Explanatory variables are the average values of k; d; r and p observed in utility i’s service area in the three months preceding period t. Variable d presents the average number of days needed
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to obtain a rebate from the state. It can be thought of as an approximate measure of the bureaucratic ‘‘red tape” costs that should be added to k. We also use dummy variables to capture individual and timeinvariant effects at the level of the utility and its service area (a) and time-variant exogenous shocks affecting all areas equally (k), such as changes in interest rates and seasonal dynamics. The theoretical model (Eq. (3)) suggests that the dependent variable, PV adoption, should increase with increases of r and p, i.e., respectively, what could be saved and earned with PV, and with decreases of k and d, i.e., the cost of investing in PV. We consider two more equations (Eqs. (13) and (14)) representing the simultaneous determination of r and p in each time t by the electric utility and state regulatory agencies i,
P3 Z
P3
y¼1 pi;ty
r i;t ¼ b1
3 P3
þ b2
y¼1 c i;ty þ b5 3
þ b4
þ b4
y¼1 r i;ty
3 P3
þ b2
y¼1 c i;ty
3
i;ty
y¼1 Q
P3 þ b5
Z y¼1 pi;ty Q
i;ty
3
y¼1 c i;ty Q i
3
Coefficients (std. err.)
k d r p
0.002⁄⁄(0.001) 0.000⁄⁄(0.000) 0.113⁄(0.044) 0.448⁄⁄(0.054) Yes (Prob. > F: 0.000) Yes (Prob. > F: 0.000) 0.014⁄⁄(0.055) 0.937
Z/Q (Eq. (12))
a
k Constant R2 r (Eq. (13))
Z y¼1 r i;ty Q
k Constant R2 p (Eq. (14))
ð13Þ
r Z/Q r(Z/Q) c cQ
a
i;ty
k Constant R2
3
þ ai þ kt þ i;t :
p Z/Q p(Z/Q) c cQ
a
P3 þ b3
Independent var. and R2
i;ty
3 c Q i;ty i y¼1 þ ai þ kt þ i;t ; 3
P3
3
þ b3
Dependent var.
P3
P3 Z
P3 pi;t ¼ b1
y¼1 Q
Table 3 Estimation results.
ð14Þ
The explanatory variables are the other retail prices, p and r respectively; the level of PV adoption Z=Q ; the interaction term that measures possible combined effects of variation in the retail price and the level of adoption; and the wholesale price c in the service area of utility i during the three months preceding period t. We also use the interaction term that captures the potential joint effects of c and the amount of consumption Q, controlling for possible scale effects driven by the size of markets in service areas. Dummy variables a and k are added to capture individual and time-variant exogenous shocks in a manner similar to the treatment in Eq. (12). The theoretical model of the electric utility (Eq. (5)) suggests that r and p should increase with increases of expenditures to buy electricity at the transmission level (c). Further, due to the numerator in the right hand-side of Eq. (5), r should increase if pay to PV-adopting households pðZ=Q Þ increases, and p should decrease as utility revenues decrease due to PV adoption (i.e., when rðZ=Q Þ increases). The model in Eq. (5) does not suggest the direction of the relationship between r and p and between the prices and the level of adoption (Z=Q ). Further, the solution of the model in Eq. (6) and the top panels presented in Fig. 2 (i.e., the ones related to NetM) show that such relations may vary depending on the level of adoption. We use a Zellner’s seemingly unrelated regression SUR model (Zellner, 1962) to account for the contemporaneous correlation between error terms (results of the Breusch-Pagan indicates rejection of the null hypothesis of independence with p = 0.000). Table 3 presents the results of the conjoint estimation of the three equations over 387 observations, confirming what the theoretical model predicted. Households are more willing to install PV if installation costs decrease, including those related to ‘‘red tape”, and if energy prices increase. Similarly, in the equations representing the budget constraint of the electric utility, the largest coefficient in the determination of r is positively associated with the payment of electricity in excess to PV-adopting households (i.e., pðZ=Q Þ). At the same time, in determining p the most relevant component is the loss of revenues due to compensation of generation and consumption in PV-adopting households (i.e., rðZ=Q Þ). Further,
⁄ ⁄⁄
0.586⁄⁄(0.102) 0.325⁄⁄(0.104) 7.292⁄⁄(1.802) 0.536⁄⁄(0.187) 0.000⁄(0.000) yes (Prob. > F: 0.000) yes (Prob. > F: 0.000) 0.073⁄⁄(0.011) 0.934 0.188⁄⁄(0.041) 0.434⁄⁄(0.073) 1.718⁄⁄(0.620) 1.006⁄⁄(0.116) 0.000⁄⁄(0.000) yes (Prob. > F: 0.000) yes (Prob. > F: 0.000) 0.068⁄⁄(0.007) 0.897
Significant at the 0.05 levels. Significant at the 0.01 levels.
both r and p are positively related to the wholesale electricity price c; increases in this latter determine increases in retail prices. 4. Model extension: network charges We extend the basic model to investigate charges aimed at covering costs for the operation and maintenance of the distribution network by the electric utility, under the assumption that more costs of this kind could emerge because of the presence of residential PV. We consider three possible charging schemes used by the electric utility to charge those costs to customers in the electricity bill. In the first case, we assume that total costs for the O&M of the distribution network, called M, are paid by electric utility customers on a per household basis (the network charge is n ¼ M ). It N does not affect the electricity distribution market because M is constant and n is paid by each household equally and unresponsively to the adoption of PV. In the second charging scheme, network charges are paid as a surcharge over r, i.e., a surcharge over the electricity that is distributed to customers by the electric utility. The third scheme considers an equal surcharge over both the electricity sold by the electric utility to customers and the electricity bought by the electric utility from PV adopters. In this case, the network charge is applied both to r and p. We model these last two network charging schemes by modifying r and, eventually, p by means of the parameter m: when m ¼ 1, the gross network charge n is paid only on r; when m ¼ 0:5, half of n is paid equally on r and p. With the introduction of the parameter m, the network charge is defined as mn. 4.1. Charges Substituting constraint (5) of the basic model, the new budget constraint of the electric utility becomes
ðr mn cÞðQ ð1 tÞZÞ ðp þ ð1 mÞn cÞtZ ¼ 0 mnðQ ð1 tÞZÞ þ ð1 mÞntZ ¼ M
:
ð15Þ
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We first assume that r and p remain the prices paid and received by households for electricity, thus, their supply function does not change. Prices r and p can now be interpreted as net prices, computed considering network charges. If the gross standard electricity rate is r 0 , customers pay electricity at the net price r ¼ r0 þ mn. Similarly, if p0 is the gross price at which the electric utility buys from residential PV generators, these receive the net price p ¼ p0 ð1 mÞn. Second, we assume that the condition of null profits for the electric utility needs to be changed as in the first equation in (15). The price r obtained from selling electricity is reduced by the network charge, while the price paid to PV-generating customers p is increased to reflect that it would be higher if not subtracting the network charge. The second equation of the new budget constraint of the electric utility states that revenues from network charges are equal to the cost to cover M, which is the cost for operating and maintaining the distribution network. Solving (15) for p and n, we find
5. Model extension: ancillary services
where p is not dependent on n but it is decreased by a fraction of M, and n depends on the costs it has to cover M, on the electricity tariff t, on the network charging scheme m, and on PV adoption levels (Fig. 6, with M ¼ 10). Considering that the average network charge is computed as mn, its lowest level is set when the tariff is FIT (t ¼ 1) and the network charging scheme applies a surcharge on both r and p (m ¼ 0:5), because increases in Z allow reducing mn (right panel of Fig. 6). Under NetM network charges are higher than in NetPS and FIT, and increasing over Z.
We extend the model further to consider ancillary services that electric utilities have to buy or provide internally to guarantee reliable and secure energy provision. Ancillary services can be divided in two types: frequency regulation and spinning reserve. Frequency regulation services maintain frequency stability in normal operations and under normal variability of demand. When the demand varies significantly or when there is a significant disruption on the supply side, spinning reserve is activated. Because the amount of spinning reserve is usually computed as the capacity of the largest generator in the system, spinning reserve is not affected by the rate of residential PV adoption. On the contrary, utilities purchase frequency regulation services based on the need to offset frequency fluctuations under normal circumstances as determined by two components. First, frequency fluctuations are positively related to the amount of energy that is exchanged in the distribution network. This means that compensating for consumption and generation at the household level reduces fluctuations, and increasing PV adoption Z decreases the need for and the cost of frequency regulation. Second, frequency fluctuations are increased when residential PV adoption Z increases because of the uncertainty in generation. In fact, substituting power generated by conventional utilityscale generators with residential PV increases fluctuations because conventional generators are usually more secure and dispatchable, and at the same time energy yields from solar panels are intrinsically uncertain because of the weather. The key point is thus to investigate what happens to the electricity distribution market whether the first or the second component prevails.
4.2. Equilibria
5.1. Charges
Considering the price p definition derived above with the price p definition derived from the PV supply function in Eq. (3), feasible solutions of r in the electricity market are
We modify the electric utility budget function (Eq. (4)) to include the costs for frequency regulation. We introduce a service charge mf that depends on the charging scheme adopted. As with network O&M, m can take value 1 if the service charge is a surcharge over r; it takes value 0.5 if the surcharge is over both r and p. The new budget of the electric utility is
p ¼ ðrcÞðQð1tÞZÞM tZ M n ¼ ðtmÞZþmQ
;
ð16Þ
M Z k Z 1 þ cQ þ1 r ¼ ZQ c : c Q ðZ 1Þð1 tÞ þ 1
ð17Þ
8 < ðr mf cÞðQ ð1 tÞZÞ ðp þ ð1 mÞf cÞtZ ¼ 0 a : : mf ðQ ð1 tÞZÞ þ ð1 mÞftZ ¼ F QZ
Eq. (17) shows that r increases by a fraction of M under any tariff, while p decreases by a fraction of M that increases over Z under NetM and NetPS. Under FIT p is not affected by r and M, and it is p ¼ kZ. In summary, feasible equilibria for the system are not affected by charging schemes m. Similarly, optimal equilibria of the social welfare are not affected by network charges mn and network costs M.
.08
mn
.06
.08
In the second equation of (18), we describe the constraint on the revenues of the service charge and the cost for frequency regulation. We use the parameter a to model which component of frequency regulation prevails to determine an increasing or decreasing cost of fluctuations management over Z.
.06
0
.02
.04 0
.02
mn
ð18Þ
.04
(
0
100
200
300
0
100
Z NetM (t = 0.1) FIT (t = 1)
200
300
Z NetPS (t = 0.49)
NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
Fig. 6. Value of network charges mn under different tariffs t, and with charging scheme m = 1 on the left and m = 0.5 on the right (k = 2, c = 0.5, Q = 400, M = 10).
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R. Boero et al. / Solar Energy 140 (2016) 188–198
If a ¼ 0, the cost covered by service charges is constant and equal to F, and the analysis is the same as when considering the costs to operate and maintain the distribution network. If a ¼ 1, the total cost of frequency regulation proportionally increases with the PV adoption rate. If a ¼ 1, the opposite is true. When a ¼ 1; F represents the maximum cost of frequency regulation, reached in the limit situation where Z ¼ Q . When a ¼ 1; F represents the minimum cost of frequency regulation reached in the same limit situation of Z ¼ Q . The solutions of p and f for the electric utility budget constraints are tZ
> :f ¼ ð Þ ðtmÞZþmQ Z a Q
:
5.2. Equilibria Considering the p definition from the electric utility budget constraint in conjunction with the one derived in the PV supply function (Eq. (3)) allows us to represent feasible market equilibria as
ð19Þ
As expected, the amount of f is increased by Z if a ¼ 1 and decreased by Z otherwise. Price p behaves in the opposite way because it is decreased by a fraction of FðZ=Q Þ if a ¼ 1.
Z
c
F Z a Z 1 þ cQ þ1 Q
Z Q
ðZ 1Þð1 tÞ þ 1
ð20Þ
.008 .006
mf
0 0
100
200
300
0
100
200
Z NetM (t = 0.1) FIT (t = 1)
mf 100
200
NetPS (t = 0.49)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
NetPS (t = 0.49)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 0
300
Z
NetM (t = 0.1) FIT (t = 1)
mf
:
.01
k
.002
.004 0
.002
mf
.006
.008
.01
r Q ¼ c
.004
8 Z a > < p ¼ ðrcÞðQ ð1tÞZÞF ðQ Þ
Values of the average charge of frequency regulation mf are presented in Fig. 7 for different tariffs, F ¼ 10, and the other parameters with values identical to the ones used for preceding figures. As the figure shows and as expected, with any tariff and charging scheme, the charge required for frequency regulation increases over Z if the total cost of frequency regulation increases over Z. The opposite is valid otherwise. In all cases, the charge is more in NetM and less in FIT because of the possibility to offset production and consumption at the household level.
300
0
100
200
Z
300
Z
NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
W 0
10
20
30
40
50
-8000 -6000 -4000 -2000
W
-8000 -6000 -4000 -2000
0
0
Fig. 7. Value of frequency regulation charges mf under different tariffs t, charging scheme m = 1 on the left and m = 0.5 on the right, a = 1 on the top and a = 1 on the bottom (k = 2, c = 0.5, Q = 400, F = 10).
0
10
20
Z NetM (t = 0.1) FIT (t = 1)
30
40
50
Z NetPS (t = 0.49)
NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
Fig. 8. Social welfare W with frequency regulation charge a = +1 on the left and a = 1 on the right (k = 2, c = 0.5, Q = 400, b = 20, F = 10).
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Prices are not affected by frequency regulation charges and, under FIT, price p is not affected by frequency regulation costs. As discussed above regarding network charges, frequency regulation has no impact on the existence of social welfare optima. However, the absolute value of social welfare and the position of the eventual global optimum are modified (e.g., under FIT Z_ is higher if a ¼ 1 and lower if a ¼ 1). Further, as the right panel of Fig. 8 shows, when the cost of frequency regulation decreases over Z, the initial marginal social benefit of adopting PV is strong under any tariff.
6. Conclusions We have presented here a theoretical model that describes how different tariffs impact distribution-level electricity markets with diffusing residential PV. The model takes into account budget constraints of electric utilities, showing how a surplus advantage in favor of PV adoption can be created in the system. The surplus advantage is the only mechanism that could increase levels of residential PV unless exogenous shocks, such as those from technology, intervene. At the same time, the creation of such an advantage leads to a specular disadvantage for non-adopting households, while the inequality in surplus distribution makes problematic the management of consensus by regulatory agencies and the maximization of social welfare. In this context, the main result of our analysis is twofold. First, looking at the analysis of the basic model, the NetM tariff seems to be preferable for supporting increasing levels of PV adoption. Second, the same tariff looks much less preferable if increasing levels of PV adoption carry additional costs associated with the distribution network. As Figs. 3 and 4 show, NetM allows high levels of PV adoption with less burden on non-adopting households than in FIT. In FIT, because of the lack of energy compensation at the household level, resources to pay for PV-generated energy have to be raised by increasing the standard electricity rate, which strongly impacts the welfare of non-adopting households. At the same time, if PV adoption implies additional or increased costs in the system (e.g., network O&M, ancillary services), under NetM the collection of resources to cover such costs could amplify the inequality in surplus distribution between households. If charges are applied on a uniform per household basis, the gap in the surplus distribution does not change but non-adopting households must pay even more for investment decisions taken by others, although they enjoy environmental benefits equally. If, on the contrary, charges are applied on prices, under NetM the distribution of surplus becomes progressively more unequal because of the compensation of energy at the household level that reduces the turnover between utilities and PV-adopters. In fact, as Figs. 6 and 7 show, with NetM, charges always increase over Z, regardless of the adopted charging scheme. The only other solution for charging additional costs could be to differentiate per household charges by kind of household, similar to recently proposed policies that charge a monthly contribution per kW to newly installed residential PV (e.g., the ‘‘reliability charge” added to NetM in Arizona). However, this strategy presents several problematic issues that require further investigation. First, it introduces a further segmentation of households, dividing PVadopters in early and recent ones. Second, if successful, the welfare improvement goes largely to non-adopting households but also, partially, to early adopters. Third, if the tariff is determined dynamically to cover costs added by PV, the cost is entirely shifted from early PV-adopters to new ones. Fourth, the determination of the charge is complex and should consider both the elasticity of adoption on total installation costs and the elasticity of additional net-
work costs on levels of adoption. In the worst case scenario, the new charge would only stop the diffusion of residential PV leaving the uneven distribution of surplus as it is. In conclusion, our analysis supports the observed widening of the gap between retail electricity prices in European countries, which have adopted FIT, and in the Unites States, which has adopted NetM (Marcy and Metelitsa, 2014). The analysis also supports the observed high retail price of electricity in countries with high PV adoption and FIT (e.g., Germany - Lesser and Su, 2008). However, our analysis is limited by the assumption of complete inelasticity of energy consumption. The impact of different tariffs on household energy consumption remains largely unknown today but it could surely modify the comparative analysis of tariffs (Yamamoto, 2012).
Appendix A. Data collection and transformation Only a few data sources regarding residential PV installations are publicly available and they refer to state policies promoting its adoption by means of economic incentives (e.g., rebates on total installation costs). Data are made public for matters of accountability. We use detailed data for California, Arizona, and New Jersey. In particular, the state initiative Go Solar California (2014) provides records of PV installations in three California electric utilities: PG&E, SCE and SDG&E. The initiative Arizona Goes Solar (2014) provides data for all utilities in Arizona but, for the purpose of our analysis, we consider only APS, SRP and TEP. Similarly, the initiative New Jersey’s Clean Energy Program (2014) provides data for all utilities operating in New Jersey but we focus on the two largest ones, JCP&L and PSE&G. In summary, we consider eight utilities that cover most service areas and customers in the three states. Data are related to the rebate requests presented by households intending to install rooftop photovoltaics. We consider the date when the first request of reservation is presented (i.e., when the public rebate is requested) as the date in which the decision to install solar panels has been taken. We created the dataset in May 2014 and selected only residential installations completed at that time. The resulting dataset considers 125,517 installations in California, 37,473 in Arizona, 17,691 in New Jersey and it spans from 2001 to 2014. Because the data regarding New Jersey considers only the capacity of the installed modules but not the installation costs, we estimate the total costs of installations in that state by multiplying capacity by state-level annual average costs reported in Barbose et al. (2013). The dataset is transformed in monthly values by utility. Prices and costs are transformed in constant prices using the Consumer Price Index published by the U.S. Bureau of Labor Statistics. We compute k as the difference between the average total cost of installation of 1 kW of solar panels and the average rebate that has been obtained for the same capacity of generation. We also compute the number of days that has been required by state agencies to assign the rebate to requesting households. Furthermore, we need three more wholesale and retail prices to describe the market (i.e., c; r and p). The price c is estimated for each utility using wholesale electricity data provided by the Department of Energy’s Energy Information Agency (EIA). In particular, for utilities in New Jersey, we consider the average price at the PJM West Hub. For Arizona we consider average prices at Palo Verde. For PG&E we consider average prices at the Northern California hub (NP-15). For the two remaining utilities in California, we use average prices at the Southern California hub (SP-15).
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R. Boero et al. / Solar Energy 140 (2016) 188–198 Table A.1 Summary statistics. Variable Z/Q (in percentage) k (in 1000$ per kW) Num. of days c (in $ per kW h) r (in $ per kW h) p (in $ per kW h)
Minimum
Maximum
Mean
Standard deviation
0.048 3.078 20.500 0.022 0.051 0.024
11.162 8.496 677.000 0.137 0.170 0.093
3.010 5.453 161.213 0.047 0.105 0.050
2.459 1.202 73.128 0.018 0.032 0.017
Price r is computed as the bundled electricity rate valid in different periods. This information has been collected from utility and state regulator websites. Price p is collected in the same way. However, in New Jersey p is not published by utilities because it is defined as the average peak tariff at the wholesale level observed in the last 12 months. We thus estimate it as the average maximum daily price over the last 12 months at the PJM West hub. To complete the dataset, we include two other kinds of information provided by EIA. First, we include the monthly average electricity consumption by residential customers in each state, in 2012. Second, we include the number of residential customers (i.e., households) served by each utility in 2012. Knowing the average amount of consumption by residential customer and the number of households served, we compute a variable Q that is the total amount of monthly consumption by residential customers in each utility. We finally compute Z as the cumulated amount of installed PV capacity, and Z=Q that is the percentage of PV adoption. The data we use are synthesized in Table A.1, where summary statistics are presented for main variables and prices are constant at the level of April 2014. Appendix B. Notations Table B.1 summarizes and explains the symbols used in the basic model and in extensions.
Table B.1 Theoretical model notations. Symbol
Description
a
Parameter modeling variations of total ancillary services costs over Z Average environmental benefit derived from one unit of energy produced by residential PV Average price of one unit of energy generated at the utility-scale and transmission level Total capital costs and returns of the electric utility Total costs of ancillary services
b c CC a F QZ ki k
Net present value of total capital, installation and O&M costs of PV for household i P PN ki z N i
mf mn M N p
PEU Pi qi Q r t ui W zi Z
Service charge aimed at collecting revenues to cover F
a Z Q
Network charge aimed at collecting revenues to cover M Total cost to operate and maintain the distribution network Number of households Price paid by the electric utility for PV-generated energy in excess Total profit of the electric utility Total profit of household i Electricity demanded by household i P N qi Standard electricity rate for households Tariff parameter (see Table 1) Household i’s utility of installing solar panels Social welfare Total amount of energy generated with PV by household i P N zi
References Arizona Goes Solar, 2014.. Barbose, G.L., Darghouth, N., Weaver, S., Ryan, H.W., 2013. Tracking the Sun VI: An Historical Summary of the Installed Price of Photovoltaics in the United States from 1998 to 2012. Tech. Rep. Lawrence Berkeley National Laboratory. Burns, J.E., Kang, J.-S., 2012. Comparative economic analysis of supporting policies for residential solar (PV) in the United States: Solar Renewable Energy Credit (SREC) potential. Energy Policy 44 (0), 217–225. http://dx.doi.org/10.1016/j. enpol.2012.01.045. ISSN 0301-4215. Chowdhury, S., Sumita, U., Islam, A., Bedja, I., 2014. Importance of policy for energy system transformation: diffusion of PV technology in Japan and Germany. Energy Policy 68, 285–293. Cory, K.S., Couture, T., Kreycik, C., 2009. Feed-in Tariff Policy: Design, Implementation, and RPS Policy Interactions. National Renewable Energy Laboratory. Dong, G., Wiser, R., Rai, V., 2014. Incentive Pass-through for Residential Solar Systems in California. Tech. Rep. Lawrence Berkeley National Laboratory. Duke, R., Williams, R., Payne, A., 2005. Accelerating residential PV expansion: demand analysis for competitive electricity market. Energy Policy 33 (15), 1912–1929. Eltawil, M.A., Zhao, Z., 2010. Grid-connected photovoltaic power systems: technical and potential problems – a review. Renew. Sust. Energy Rev. 14 (1), 112–129. http://dx.doi.org/10.1016/j.rser.2009.07.015. ISSN 1364-0321. Friedman, B., Ardani, K., Feldman, D., Citron, R., Margolis, R., Zuboy, J., 2013. Benchmarking Non-Hardware Balance-of-System (Soft) Costs for U.S. Photovoltaic Systems, Using a Bottom-Up Approach and Installer Survey Second Edition. Tech. Rep. National Renewable Energy Laboratory. Goodrich, A., James, T., Woodhouse, M., 2012. Residential, Commercial, and UtilityScale Photovoltaic (PV) System Prices in the United States: Current Drivers and Cost-Reduction Opportunities. Tech. Rep. National Renewable Energy Laboratory. Go Solar California, 2014. . Popp, D., Hascic, I., Medhi, N., 2011. Technology and the diffusion of renewable energy. Energy Econ. 33 (4), 648–662. Rao, K.U., Kishore, V., 2010. A review of technology diffusion models with special reference to renewable energy technologies. Renew. Sust. Energy Rev. 14 (3), 1070–1078. Rigter, J., Vidican, G., 2010. Cost and optimal feed-in tariff for small scale photovoltaic systems in China. Energy Policy 38 (11), 6989–7000. Satchwell, A., Mills, A., Barbose, G., Wiser, R., Cappers, P., Darghouth, N., 2014. Financial Impacts of Net-Metered PV on Utilities and Ratepayers: A Scoping Study of Two Prototypical U.S. Utilities. Tech. Rep. Lawrence Berkeley National Laboratory.
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Thiam, D.R., 2011. An energy pricing scheme for the diffusion of decentralized renewable technology investment in developing countries. Energy Policy 39 (7), 4284–4297. Timilsina, G.R., Kurdgelashvili, L., Narbel, P.A., 2012. Solar energy: markets, economics and policies. Renew. Sust. Energy Rev. 16 (1), 449–465. Wand, R., Leuthold, F., 2011. Feed-in tariffs for photovoltaics: learning by doing in Germany? Appl. Energy 88 (12), 4387–4399.
Yamamoto, Y., 2012. Pricing electricity from residential photovoltaic systems: a comparison of feed-in tariffs, net metering, and net purchase and sale. Solar Energy 86 (9), 2678–2685. Zellner, A., 1962. An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J. Am. Stat. Assoc. 57, 348–368.
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Solar Energy journal homepage: www.elsevier.com/locate/solener
The microeconomics of residential photovoltaics: Tariffs, network operation and maintenance, and ancillary services in distribution-level electricity markets Riccardo Boero ⇑, Scott N. Backhaus, Brian K. Edwards Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA
a r t i c l e
i n f o
Article history: Received 14 July 2015 Received in revised form 25 October 2016 Accepted 3 November 2016 Available online 12 November 2016 Keywords: Residential photovoltaics Ancillary services Feed-in tariffs Net metering
a b s t r a c t We develop a microeconomic model of a distribution-level electricity market that takes explicit account of residential photovoltaics (PV) adoption. The model allows us to study the consequences of most tariffs on PV adoption and the consequences of increased residential PV adoption under the assumption of economic sustainability for electric utilities. We validate the model using U.S. data and extend it to consider different pricing schemes for operation and maintenance costs of the distribution network and for ancillary services. Results show that net metering promotes more environmental benefits and social welfare than other tariffs. However, if costs to operate the distribution network increase, net metering will amplify the unequal distribution of surplus among households. In conclusion, maintaining the economic sustainability of electric utilities under net metering may become extremely difficult unless the uneven distribution of surplus is legitimated by environmental benefits. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Recent reductions in the total cost of installing residential photovoltaic (PV) systems have increased global diffusion (Rigter and Vidican, 2010; Thiam, 2011; Lin and Wesseh, 2013; Chowdhury et al., 2014) of this renewable energy source. Changes in technology and markets have reduced both PV module production costs (Goodrich et al., 2012) and installation costs (Friedman et al., 2013). Further, public policies (Timilsina et al., 2012; Dong et al., 2014; Jimenez et al., 2016) in the form of rebates (Kwan, 2012) or tax credits (Burns and Kang, 2012) have encouraged an increasing number of households to adopt PV systems. There are concerns that high rates of residential PV adoption may impact electricity distribution networks. In particular, it has been noted that the diffusion of residential PV requires new and updated grid equipment (Eltawil and Zhao, 2010), and that it reduces utility revenues more than it reduces costs. These considAbbreviations: APS, Arizona Public Service; EIA, U.S. Energy Information Administration; FIT, feed-in tariff; JCP&L, Jersey Central Power & Light; NetM, net metering tariff; NetPS, net purchase and sale tariff; O&M, operation and maintenance; PG&E, Pacific Gas & Electric; PSE&G, Public Service Electric and Gas Company; SRP, Salt River Project; SCE, Southern California Edison; SDG&E, San Diego Gas & Electric; TEP, Tucson Electric Power. ⇑ Corresponding author. E-mail addresses: [email protected] (R. Boero), [email protected] (S.N. Backhaus), [email protected] (B.K. Edwards). http://dx.doi.org/10.1016/j.solener.2016.11.010 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.
erations introduce additional economic and financial challenges (Satchwell et al., 2014) for utilities. There are additional concerns that public polices vis a vis utility budget constraints can cause costs to be shifted between households. These issues and others suggest the need for a better understanding of how different tariff mechanisms affect PV adoption rates, social welfare, and the surplus distribution between households. Case studies so far have pointed out how policies (Burns and Kang, 2012; Chowdhury et al., 2014), social dynamics (Guo and Song, 2015), and economic incentives (Rigter and Vidican, 2010; Jimenez et al., 2016) contribute to PV adoption and to its emerging patterns (Guidolin and Mortarino, 2010; Kwan, 2012). Along empirical studies, models of innovation diffusion (Rao and Kishore, 2010; Popp et al., 2011; Hsu, 2012; Islam, 2014) have focused on processes of technology adoption. The analytical concerns mentioned above require a different modeling approach capable of concurrently representing the dispersed and individual-level decision-making typical of PV diffusion (Islam, 2014; Guo and Song, 2015), the system-level effects impacting the environment, households, social welfare, and electric utilities through tariffs and costs, and the complex feedback between those levels. We develop a microeconomic model of a distribution-level electricity market that extends the model presented in Yamamoto (2012). The model presented in this paper addresses household
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investment in PV and incorporates budget constraints on electric utilities. Incorporating utility budget constraints allows us to examine issues relating to how pricing mechanisms affect household incentives to adopt PV and how household PV penetration rates affect distribution utility profitability. This approach also allows us to examine how electricity surpluses are distributed between households. Finally, this approach also allows comparing the effects of different tariffs (Lesser and Su, 2008; Cory et al., 2009) on both household surplus and social welfare (Wand and Leuthold, 2011). After presenting the validation of the basic theoretical model using data observed in the United States under the net metering tariff, we extend it to investigate the challenges posed by increasing and additional costs due to PV adoption. We study the interaction between tariffs and schemes implemented to collect resources for the most common additional costs introduced by PV, which are for operating and maintaining the distribution network and ancillary services. We conclude with a brief discussion of the main results and limitations of our analysis and sketch possible future directions of research.
The third tariff we consider is the feed-in tariff (FIT). This tariff is based on readings from two separated household meters in households that have installed PV. One meter measures electricity consumption while the other measures electricity generation. Under FIT, the whole generation is sold to the electric utility at price p and the whole consumption is paid by households at price r. Finally, if zi is the amount of electricity household i generates with solar panels, we can use the parameter t to model the billing effect of different tariffs. Specifically, ðtÞzi indicates the amount of PV-generated energy sold by household i to the electric utility, and ð1 tÞzi represents the part of zi that is used to offset household consumption. Let qi represent the quantity of electricity consumed by household i. In Duke et al. (2005), empirical evidence suggests that the average generating power of residential solar panels is strictly P P lower than household needs ( N zi < N qi ). We assume this holds at the consumer level as well, zi < qi . Under FIT, t ¼ 1, and all PV-generated electricity is sold to the electric utility and none is used to offset consumption because generation and consumption are metered separately. Under NetPS, 0 < t < 0:5 because zi < qi . Under NetM, we have 0 < t < 0:5 as well, but in this case t will be lower than in NetPS because the billing period is longer. Table 1 summarizes the values of the t under each tariff scheme.
2. The basic model 2.2. Residential PV supply function We consider the presence of a finite number of households N. Each household installs residential PV if the investment is profitable. Households adopting residential PV determine the supply of PV-generated energy. Further, an electric utility EU sells electricity, provides the distribution network, buys PV-generated electricity, and buys electricity and ancillary services from utility-scale conventional and renewable energy generators. Households are consumers, but become producers if they install solar panels. The electric utility is an intermediary, selling electricity generated at the utility scale to all households and buying and selling power from PV-adopting households. The electric utility is also a service provider (distribution network maintenance, reliable and secure power flow, etc.). Exchanges between the electric utility and utility-scale power generators happen at a wholesale spot price c, which is determined by dynamics in the electricity market at the transmission level. Exchanges of power between the electric utility and households happen according to two regulated prices. The first, r, is the standard retail rate at which the household would purchase power from the utility. The second, p, is the price paid by the utility when buying residential PV energy from the household.
We assume that household demand for electricity is a constant qi , is exogenous, and is inelastic. 2.2.1. Household investment decision The household investment decision in PV is a simple binary decision, with investment occurring if household utility derived from investing exceeds household utility from not investing. Eq. (1) shows the household utility function ui for the investment in PV, where K i is the discounted cost of installing, operating, and maintaining solar panels for their expected lifetime,
ui ¼ K i þ pðtÞzi þ rð1 tÞzi :
Under FIT, r does not influence household utility because generated electricity is sold entirely to the electric utility at price p and no generated electricity is used to reduce demand qi . 2.2.2. Derivation of the supply function From Eq. (1) we know that each household has a reservation price pi , below which household investments in PV are not profitable,
pi ¼ 2.1. Tariffs We consider here three tariffs commonly found in contemporary electricity markets. The first one is net metering (NetM). It is based on the household-level compensation of generation and consumption over a rather long billing period, typically lasting between one month and one year. Under NetM, at the end of the billing period the accounting balance between consumption and generation is computed. If the household has generated more than it has consumed in the period, it sells the difference to the electric utility at price p. Otherwise, the household buys the excess of consumption from the electric utility at price r. The second tariff is net purchase and sale (NetPS). It is similar to net metering in that it is determined partly by the net difference consumed and generated. Under NetPS, the compensation is computed continuously using the shortest possible billing interval, typically every 15 min. Moreover, NetM would converge to NetPS if the billing period were to be shortened as much as possible.
ð1Þ
ki rð1 tÞzi 1 ki ¼ rð1 tÞ : t zi t i zi
ð2Þ
If we order the households from 1 to N according to an increasing reservation price, we obtain the supply function in Fig. 1. Further, defining Z as the sum of energy generated by houseP holds with residential PV (Z ¼ N zi ) and k as the average total cost P ki of a unit of residential PV generation capacity k ¼ PN z , we can N i
linearize the supply function,
p¼
1 ðk rð1 tÞÞZ: t
ð3Þ
Table 1 Definition of tariff parameters. Tariff
Acronym
Parameter Value
Net metering Net purchase and sale Feed-in tariff
NetM NetPS FIT
0 < tNetM < t NetPS 0 < tNetPS < 0:5 t FIT ¼ 1
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R. Boero et al. / Solar Energy 140 (2016) 188–198
an incentive to keep a high volume of sales if it depends on those revenues. The total profit of an electric utility PEU depends on the net quantity of electricity purchased from transmission-level power generators at price c, and sold to customers at price r, and on the net quantity of PV electricity purchased by the electric utility from households at price p (instead of price c), i.e.,
PEU ¼ ðr cÞðQ ð1 tÞZÞ ðp cÞtZ;
P
ð4Þ
where Q is the total electricity demanded (Q ¼ N qi ). Regulations prevent electric utilities from having profits beyond the return on their capital costs, i.e., PEU ¼ 0, implying
p¼
Fig. 1. Derivation of the supply function from household investment decision.
ðr cÞðQ ð1 tÞZÞ þ c: tZ
ð5Þ
Eq. (5) suggests that retail prices r and p should be greater than c, i.e., c should be marked up at a level that depends on tariffs and level of PV adoption.
According to the supply function, the installation of residential PV increases with the payment for PV-generated energy p. A decrease in costs k, due to technological innovation or to subsidies from the government, increases the amount of PV-generated power Z. Our parameterization t of the tariffs also impacts the supply.
2.4. Feasible equilibria Feasible equilibria are pairs of p and r constrained by zero utility profits and parameterized by different levels of Z, costs c and tariffs t. These equilibria are found from Eqs. (3) and (5), i.e.,
2.3. The electric utility
8 Z kZ1 þ1 Þ Q ðc r > > > c ¼ QZ ðZ1Þð1tÞþ1 > < Z kZ1 þ1 Þ ; p Q ðc ¼ 1t kc Z ðZ1Þð1tÞþ1 ð1 tÞ Z > c > Q > > : Z–0
Because many utilities have adopted the so-called decoupling of sales and revenues, we assume that connection charges cover capital costs. This means that the utility collects revenues covering the capital cost by dividing this cost by the number of served households (cc ¼ CC ). Each household pays the same cc, and its utility is N negatively affected equally. However, this does not affect the customer reserve price or Z. The decoupling of sales and revenues by electric utilities is motivated by the fact that if electric utility profits and revenues are related to sales, a negative incentive emerges in energy conservation and in PV diffusion. The electric utility has
ð6Þ
p/c 0
0
2
100
4
r/c
200
6
300
8
and are plotted in Fig. 2. From Fig. 2 it is possible to analyze some important differences in the behavior of the system under different tariffs. For the FIT, because p ¼ kZ, the payment of PV-generated energy at price p is allowed only by large increases in r. In contrast, under NetM, we observe a modest increment of r and an initial
0
100
200
300
0
100
Z
300
NetM (t = 0.1)
NetPS (t = 0.49)
0
0
200
500
400
r/c
p/c
600
1000
800
1500
NetPS (t = 0.49)
1000
NetM (t = 0.1)
200
Z
0
100
200
Z FIT (t = 1)
300
0
100
200
Z FIT (t = 1)
Fig. 2. Feasible equilibria in r and p over Z under different tariffs t (k = 2, c = 0.5, Q = 400).
300
191
Pi qi
¼
rqi ¼ r: qi
ð7Þ
For households adopting PV (Eq. (8)), the surplus is affected both by r and p. The surplus increases by what is sold to the electric utility (at price p) and decreases by what is bought from the electric utility (at price r and computed as the difference between total consumption and compensation with zi ), i.e.,
Pi qi
¼p
tzi q ð1 tÞzi zi r i ¼ ðpt þ rð1 tÞÞ r: qi qi qi
ð8Þ
10 5 0 -5
surplus per unit of energy
15
Under NetM the difference between the surplus of adopting and non-adopting households is initially large, and it decreases as households adopt PV (Fig. 3, with zi =qi ¼ 0:8). Under FIT (Fig. 4), the surplus difference in favor of adopting households increases over the adoption rate. Further, the surplus of non-adopting households is very negatively affected by increasing levels of PV because, under this tariff, all resources needed to pay for PV-generated energy are paid in terms of increases in r. Under both tariffs the surplus of adopting households can be positive even if we do not include the utility derived from consum-
0
100
200
300
0 0
Households adopting PV
Fig. 3. Surplus per quantity of consumed energy under tariff NetM (t = 0.1, qzii ¼ 0:8, k = 2, c = 0.5).
100
200
300
Z Households non adopting PV
Households adopting PV
Fig. 4. Surplus per quantity of consumed energy under tariff FIT (t = 1, qzii ¼ 0:8, k = 2, c = 0.5).
ing electricity. Finally it is important to note that under NetM the cost implied by increasing levels of PV adoption is more equally shared between PV-adopting and non-adopting households than it is under FIT, and that, if we compare the surplus for nonadopting households under FIT and NetM, in absolute terms FIT implies much greater costs for non-adopting households. The model suggests that, given the values of exogenous parameters (e.g., k determined by technology), the electric utility has the power to determine the level of PV adoption Z by manipulating p and r. However, increases of Z are accompanied by changes in household surpluses. Policy measures such as tax credits subsidizing residential solar panels can be incorporated into our model as reductions in the costs of installing solar panels (given by k). From Eq. (6) we know that the result, under any tariff, is a decrease in r and p values for the same levels of adoption, and a shift of the intrinsic cost of PV adoption towards a broader tax base or future generations. 2.6. Social welfare maximization Because we know how household surpluses vary over PV adoption and we know the set of feasible equilibria determined jointly by PV supply and the budget constraint of the electric utility, it is possible to study the optimal solution where the electric utility or the regulatory agency modifies Z by means of r and p in order to maximize social welfare. The optimization problem is the maximization of the social welfare function W, which is composed by the surplus of all households and by the environmental benefit given by using a renewable energy source. The surplus of the electric utility is not included in social welfare because it is bounded to be null, and thus, on the contrary, it enters the set of optimization constraints. The surplus of all households is as in Eq. (8), but referred to the population-level variable Q and using Z as the measure of PV adoption. The environmental benefit of Z is represented by the parameter b, implicitly assumed to be positive (b > 0). The constraint to the maximization of the social welfare is represented by the intersection between the supply function and the electric utility budget constraint. The resulting problem is
maximize W ¼ ptZ þ rð1 tÞZ rQ þ bZ; Z
s:t: Eq: ð6Þ:
Z Households non adopting PV
-200
To support the argument that adopting PV affects more negatively non-adopting households under FIT, we analyze how surplus varies between PV-adopting and non-adopting households. We expect a positive difference in favor of PV-adopting households because the system has to reward adopting households for their investment if Z increases. In other words, it should provide households with enough revenue to cover the solar panel installation costs. Without considering the utility that households gain by consuming energy, which is constant under our assumption of inelastic demand, buying energy for consumption reduces household surplus and selling household energy to the electric utility increases household surplus. Thus, the surplus definition collapses to a measure of the average net cost of consumed energy. In the case of non-adopting households, the surplus computed over a single unit of consumed energy (Pi =qi ) is negative and equal to the price r, i.e.,
surplus per unit of energy
2.5. Household surplus
-400
sharp increase in p, followed by an asymptotic decrease of that price as Z increases. Because all customers pay r under both tariff schemes, our comparison suggests that PV adoption leads to more negative impacts on non-adopting households under FIT.
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ð9Þ
By substituting r and p of Eq. (6) in W, we obtain a social welfare measure that is dependent only on Z and that respects maximization constraints, i.e.,
R. Boero et al. / Solar Energy 140 (2016) 188–198
þ
ðct 3c bÞQZ þ 2cQ 2 ðt 1ÞZ 2 þ ð1 tÞZ Q
:
0
ððct þ k þ cÞQ þ ðc bÞt þ c þ bÞZ 2 ðt 1ÞZ 2 þ ð1 tÞZ Q
-1000
ðt 1ÞZ þ ð1 tÞZ Q
þ
ð10Þ
To study the maximization of social welfare, we need to differentiate the analysis by different values of t. First, if t < 0:5, which holds under both NetM and NetPS cases, there is no global equilibrium because social welfare can be increased by increasing PV generation Z. In fact, whatever the positive value of b, social welfare is determined by the fraction in Eq. (10) where Z 3 is the highest order in the numerator and Z 2 is high-
W
2
-3000
ðc þ bÞðt 1ÞZ 3
-4000
W¼
-2000
192
0
10
est order in the denominator. The coefficient of Z 2 is ðt 1Þ that is always negative because we are considering t < 0:5. The coefficient of Z 3 is ðc þ bÞðt 1Þ that is always negative as well because ðt 1Þ is negative and both c and b are positive. Under NetPS and NetM social welfare is maximized by the highest level of Z possible, but there can be points where, locally, the first derivative of W is null. Second, with the FIT, the welfare function is much simpler and we can compute the first and second derivatives of W, 2
W ¼ kZ þ ð2c þ bÞZ 2cQ; 0
W ¼ 2kZ þ 2c þ b;
ð11Þ
W 00 ¼ 2k: Because the second derivative of W is always negative because k > 0, to solve the maximization problem we impose W 0 ¼ 0 and we find the internal solution to the maximization of social welfare, Z_ ¼ ð2c þ bÞ=ð2kÞ. The equilibrium point can be interpreted as the one where the average environmental benefit b equals twice the total net cost of PV adoption, i.e., b ¼ 2ðkZ_ cÞ, that is the cost of installed solar panels kZ decreased by saving consumption from conventional utility-scale power sources c. The social equilibrium of PV adoption under FIT is very low unless the environmental benefit is particularly significant. Nevertheless, with the FIT the optimal level of PV adoption is increased by exogenous shocks incrementing prices of primary energy sources (c), technological shocks that improve the environmental benefits of PV (b), and technological shocks that decrease the costs to adopt PV (k). Public policies, such as tax credits that decrease the cost of installing solar panels (i.e., decreasing k), do not change the equilibrium solution because the social welfare function W should include also the cost of the policy. The social welfare function is plotted in Fig. 5 with the parameters used for previous graphs and with b ¼ 20. From the dynamic viewpoint, the figure suggests that because markets start from a situation where the adoption of residential PV is null, tariffs have similar impacts at the beginning, providing similar initial incentives to adoption because the marginal social benefit is comparable. However, beyond lower levels of Z there can be different dynamics under different tariffs, and the presence of stationary points (W 0 ¼ 0) presented in Table 2. Under FIT, we have the lowest level of local maximum of social welfare. That point is also the global maximum under that tariff. Under NetM and NetPS, there are local maximum points for higher values of Z, then, with Z increasing beyond them, there are decreases in social welfare until a local minimum, and finally an ever-increasing social welfare. It is evident that, if the dynamics starts from a very low value of Z, the system could stop in the local maximum but the numerical example shows that decreases in t, which represent increases in the length of the billing period,
20
30
40
50
Z NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
Fig. 5. Social welfare (k = 2, c = 0.5, Q = 400, b = 20).
Table 2 Local equilibria in the numerical example (k = 2, c = 0.5, Q = 400, b = 20). Tariff
Local maximum (Z)
Local minimum (Z)
9.09 6.52 5.25
16.05 33.00 N/A
NetM (t ¼ 0:1) NetPS (t ¼ 0:49) FIT (t ¼ 1)
generate higher values of the local maximum. Finally, very low values of t can transform the shape of the social welfare function in one monotonically increasing over Z. 3. Validation of the basic model The basic model comprises the supply function and the budget constraint of the electric utility. While the supply function depends on the daily decision making of hundreds or thousands of households, the utility budget constraint is influenced by prices that are governed by slower regulatory processes. Even though it is conceivable that the null profit hypothesis about electric utilities is not continuously supported due to the duration of the regulatory process and uncertainty in near-term forecasting of costs and revenues, it is possible to use an empirical model to test the validity of both components of the model. We use data for eight utilities in Arizona, California, and New Jersey, three of the most populous U.S. states. All utilities considered have adopted NetM. The database is organized as monthly values by each utility over the period 2001–2014. Appendix A provides details about the data. Prices are in U.S. $ per kW h of electricity. Total installation costs, including capital and installation costs net of rebates, are in $ 1000 per each kW of capacity. Z and Q are in monthly kW h. In the first equation derived from the supply function (Eq. (3)), the dependent variable is the cumulative PV adoption rate Z=Q observed by utility i at time t (measured as percentage),
Z ¼ b1 Q i;t
3 X ki;ty y¼1
3
3 X
þ b2
þ ai þ kt þ i;t :
3 X r i;ty
di;ty
y¼1
3
þ b3
y¼1
3
3 X pi;ty
þ b4
y¼1
3 ð12Þ
Explanatory variables are the average values of k; d; r and p observed in utility i’s service area in the three months preceding period t. Variable d presents the average number of days needed
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to obtain a rebate from the state. It can be thought of as an approximate measure of the bureaucratic ‘‘red tape” costs that should be added to k. We also use dummy variables to capture individual and timeinvariant effects at the level of the utility and its service area (a) and time-variant exogenous shocks affecting all areas equally (k), such as changes in interest rates and seasonal dynamics. The theoretical model (Eq. (3)) suggests that the dependent variable, PV adoption, should increase with increases of r and p, i.e., respectively, what could be saved and earned with PV, and with decreases of k and d, i.e., the cost of investing in PV. We consider two more equations (Eqs. (13) and (14)) representing the simultaneous determination of r and p in each time t by the electric utility and state regulatory agencies i,
P3 Z
P3
y¼1 pi;ty
r i;t ¼ b1
3 P3
þ b2
y¼1 c i;ty þ b5 3
þ b4
þ b4
y¼1 r i;ty
3 P3
þ b2
y¼1 c i;ty
3
i;ty
y¼1 Q
P3 þ b5
Z y¼1 pi;ty Q
i;ty
3
y¼1 c i;ty Q i
3
Coefficients (std. err.)
k d r p
0.002⁄⁄(0.001) 0.000⁄⁄(0.000) 0.113⁄(0.044) 0.448⁄⁄(0.054) Yes (Prob. > F: 0.000) Yes (Prob. > F: 0.000) 0.014⁄⁄(0.055) 0.937
Z/Q (Eq. (12))
a
k Constant R2 r (Eq. (13))
Z y¼1 r i;ty Q
k Constant R2 p (Eq. (14))
ð13Þ
r Z/Q r(Z/Q) c cQ
a
i;ty
k Constant R2
3
þ ai þ kt þ i;t :
p Z/Q p(Z/Q) c cQ
a
P3 þ b3
Independent var. and R2
i;ty
3 c Q i;ty i y¼1 þ ai þ kt þ i;t ; 3
P3
3
þ b3
Dependent var.
P3
P3 Z
P3 pi;t ¼ b1
y¼1 Q
Table 3 Estimation results.
ð14Þ
The explanatory variables are the other retail prices, p and r respectively; the level of PV adoption Z=Q ; the interaction term that measures possible combined effects of variation in the retail price and the level of adoption; and the wholesale price c in the service area of utility i during the three months preceding period t. We also use the interaction term that captures the potential joint effects of c and the amount of consumption Q, controlling for possible scale effects driven by the size of markets in service areas. Dummy variables a and k are added to capture individual and time-variant exogenous shocks in a manner similar to the treatment in Eq. (12). The theoretical model of the electric utility (Eq. (5)) suggests that r and p should increase with increases of expenditures to buy electricity at the transmission level (c). Further, due to the numerator in the right hand-side of Eq. (5), r should increase if pay to PV-adopting households pðZ=Q Þ increases, and p should decrease as utility revenues decrease due to PV adoption (i.e., when rðZ=Q Þ increases). The model in Eq. (5) does not suggest the direction of the relationship between r and p and between the prices and the level of adoption (Z=Q ). Further, the solution of the model in Eq. (6) and the top panels presented in Fig. 2 (i.e., the ones related to NetM) show that such relations may vary depending on the level of adoption. We use a Zellner’s seemingly unrelated regression SUR model (Zellner, 1962) to account for the contemporaneous correlation between error terms (results of the Breusch-Pagan indicates rejection of the null hypothesis of independence with p = 0.000). Table 3 presents the results of the conjoint estimation of the three equations over 387 observations, confirming what the theoretical model predicted. Households are more willing to install PV if installation costs decrease, including those related to ‘‘red tape”, and if energy prices increase. Similarly, in the equations representing the budget constraint of the electric utility, the largest coefficient in the determination of r is positively associated with the payment of electricity in excess to PV-adopting households (i.e., pðZ=Q Þ). At the same time, in determining p the most relevant component is the loss of revenues due to compensation of generation and consumption in PV-adopting households (i.e., rðZ=Q Þ). Further,
⁄ ⁄⁄
0.586⁄⁄(0.102) 0.325⁄⁄(0.104) 7.292⁄⁄(1.802) 0.536⁄⁄(0.187) 0.000⁄(0.000) yes (Prob. > F: 0.000) yes (Prob. > F: 0.000) 0.073⁄⁄(0.011) 0.934 0.188⁄⁄(0.041) 0.434⁄⁄(0.073) 1.718⁄⁄(0.620) 1.006⁄⁄(0.116) 0.000⁄⁄(0.000) yes (Prob. > F: 0.000) yes (Prob. > F: 0.000) 0.068⁄⁄(0.007) 0.897
Significant at the 0.05 levels. Significant at the 0.01 levels.
both r and p are positively related to the wholesale electricity price c; increases in this latter determine increases in retail prices. 4. Model extension: network charges We extend the basic model to investigate charges aimed at covering costs for the operation and maintenance of the distribution network by the electric utility, under the assumption that more costs of this kind could emerge because of the presence of residential PV. We consider three possible charging schemes used by the electric utility to charge those costs to customers in the electricity bill. In the first case, we assume that total costs for the O&M of the distribution network, called M, are paid by electric utility customers on a per household basis (the network charge is n ¼ M ). It N does not affect the electricity distribution market because M is constant and n is paid by each household equally and unresponsively to the adoption of PV. In the second charging scheme, network charges are paid as a surcharge over r, i.e., a surcharge over the electricity that is distributed to customers by the electric utility. The third scheme considers an equal surcharge over both the electricity sold by the electric utility to customers and the electricity bought by the electric utility from PV adopters. In this case, the network charge is applied both to r and p. We model these last two network charging schemes by modifying r and, eventually, p by means of the parameter m: when m ¼ 1, the gross network charge n is paid only on r; when m ¼ 0:5, half of n is paid equally on r and p. With the introduction of the parameter m, the network charge is defined as mn. 4.1. Charges Substituting constraint (5) of the basic model, the new budget constraint of the electric utility becomes
ðr mn cÞðQ ð1 tÞZÞ ðp þ ð1 mÞn cÞtZ ¼ 0 mnðQ ð1 tÞZÞ þ ð1 mÞntZ ¼ M
:
ð15Þ
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We first assume that r and p remain the prices paid and received by households for electricity, thus, their supply function does not change. Prices r and p can now be interpreted as net prices, computed considering network charges. If the gross standard electricity rate is r 0 , customers pay electricity at the net price r ¼ r0 þ mn. Similarly, if p0 is the gross price at which the electric utility buys from residential PV generators, these receive the net price p ¼ p0 ð1 mÞn. Second, we assume that the condition of null profits for the electric utility needs to be changed as in the first equation in (15). The price r obtained from selling electricity is reduced by the network charge, while the price paid to PV-generating customers p is increased to reflect that it would be higher if not subtracting the network charge. The second equation of the new budget constraint of the electric utility states that revenues from network charges are equal to the cost to cover M, which is the cost for operating and maintaining the distribution network. Solving (15) for p and n, we find
5. Model extension: ancillary services
where p is not dependent on n but it is decreased by a fraction of M, and n depends on the costs it has to cover M, on the electricity tariff t, on the network charging scheme m, and on PV adoption levels (Fig. 6, with M ¼ 10). Considering that the average network charge is computed as mn, its lowest level is set when the tariff is FIT (t ¼ 1) and the network charging scheme applies a surcharge on both r and p (m ¼ 0:5), because increases in Z allow reducing mn (right panel of Fig. 6). Under NetM network charges are higher than in NetPS and FIT, and increasing over Z.
We extend the model further to consider ancillary services that electric utilities have to buy or provide internally to guarantee reliable and secure energy provision. Ancillary services can be divided in two types: frequency regulation and spinning reserve. Frequency regulation services maintain frequency stability in normal operations and under normal variability of demand. When the demand varies significantly or when there is a significant disruption on the supply side, spinning reserve is activated. Because the amount of spinning reserve is usually computed as the capacity of the largest generator in the system, spinning reserve is not affected by the rate of residential PV adoption. On the contrary, utilities purchase frequency regulation services based on the need to offset frequency fluctuations under normal circumstances as determined by two components. First, frequency fluctuations are positively related to the amount of energy that is exchanged in the distribution network. This means that compensating for consumption and generation at the household level reduces fluctuations, and increasing PV adoption Z decreases the need for and the cost of frequency regulation. Second, frequency fluctuations are increased when residential PV adoption Z increases because of the uncertainty in generation. In fact, substituting power generated by conventional utilityscale generators with residential PV increases fluctuations because conventional generators are usually more secure and dispatchable, and at the same time energy yields from solar panels are intrinsically uncertain because of the weather. The key point is thus to investigate what happens to the electricity distribution market whether the first or the second component prevails.
4.2. Equilibria
5.1. Charges
Considering the price p definition derived above with the price p definition derived from the PV supply function in Eq. (3), feasible solutions of r in the electricity market are
We modify the electric utility budget function (Eq. (4)) to include the costs for frequency regulation. We introduce a service charge mf that depends on the charging scheme adopted. As with network O&M, m can take value 1 if the service charge is a surcharge over r; it takes value 0.5 if the surcharge is over both r and p. The new budget of the electric utility is
p ¼ ðrcÞðQð1tÞZÞM tZ M n ¼ ðtmÞZþmQ
;
ð16Þ
M Z k Z 1 þ cQ þ1 r ¼ ZQ c : c Q ðZ 1Þð1 tÞ þ 1
ð17Þ
8 < ðr mf cÞðQ ð1 tÞZÞ ðp þ ð1 mÞf cÞtZ ¼ 0 a : : mf ðQ ð1 tÞZÞ þ ð1 mÞftZ ¼ F QZ
Eq. (17) shows that r increases by a fraction of M under any tariff, while p decreases by a fraction of M that increases over Z under NetM and NetPS. Under FIT p is not affected by r and M, and it is p ¼ kZ. In summary, feasible equilibria for the system are not affected by charging schemes m. Similarly, optimal equilibria of the social welfare are not affected by network charges mn and network costs M.
.08
mn
.06
.08
In the second equation of (18), we describe the constraint on the revenues of the service charge and the cost for frequency regulation. We use the parameter a to model which component of frequency regulation prevails to determine an increasing or decreasing cost of fluctuations management over Z.
.06
0
.02
.04 0
.02
mn
ð18Þ
.04
(
0
100
200
300
0
100
Z NetM (t = 0.1) FIT (t = 1)
200
300
Z NetPS (t = 0.49)
NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
Fig. 6. Value of network charges mn under different tariffs t, and with charging scheme m = 1 on the left and m = 0.5 on the right (k = 2, c = 0.5, Q = 400, M = 10).
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If a ¼ 0, the cost covered by service charges is constant and equal to F, and the analysis is the same as when considering the costs to operate and maintain the distribution network. If a ¼ 1, the total cost of frequency regulation proportionally increases with the PV adoption rate. If a ¼ 1, the opposite is true. When a ¼ 1; F represents the maximum cost of frequency regulation, reached in the limit situation where Z ¼ Q . When a ¼ 1; F represents the minimum cost of frequency regulation reached in the same limit situation of Z ¼ Q . The solutions of p and f for the electric utility budget constraints are tZ
> :f ¼ ð Þ ðtmÞZþmQ Z a Q
:
5.2. Equilibria Considering the p definition from the electric utility budget constraint in conjunction with the one derived in the PV supply function (Eq. (3)) allows us to represent feasible market equilibria as
ð19Þ
As expected, the amount of f is increased by Z if a ¼ 1 and decreased by Z otherwise. Price p behaves in the opposite way because it is decreased by a fraction of FðZ=Q Þ if a ¼ 1.
Z
c
F Z a Z 1 þ cQ þ1 Q
Z Q
ðZ 1Þð1 tÞ þ 1
ð20Þ
.008 .006
mf
0 0
100
200
300
0
100
200
Z NetM (t = 0.1) FIT (t = 1)
mf 100
200
NetPS (t = 0.49)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
NetPS (t = 0.49)
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 0
300
Z
NetM (t = 0.1) FIT (t = 1)
mf
:
.01
k
.002
.004 0
.002
mf
.006
.008
.01
r Q ¼ c
.004
8 Z a > < p ¼ ðrcÞðQ ð1tÞZÞF ðQ Þ
Values of the average charge of frequency regulation mf are presented in Fig. 7 for different tariffs, F ¼ 10, and the other parameters with values identical to the ones used for preceding figures. As the figure shows and as expected, with any tariff and charging scheme, the charge required for frequency regulation increases over Z if the total cost of frequency regulation increases over Z. The opposite is valid otherwise. In all cases, the charge is more in NetM and less in FIT because of the possibility to offset production and consumption at the household level.
300
0
100
200
Z
300
Z
NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
W 0
10
20
30
40
50
-8000 -6000 -4000 -2000
W
-8000 -6000 -4000 -2000
0
0
Fig. 7. Value of frequency regulation charges mf under different tariffs t, charging scheme m = 1 on the left and m = 0.5 on the right, a = 1 on the top and a = 1 on the bottom (k = 2, c = 0.5, Q = 400, F = 10).
0
10
20
Z NetM (t = 0.1) FIT (t = 1)
30
40
50
Z NetPS (t = 0.49)
NetM (t = 0.1) FIT (t = 1)
NetPS (t = 0.49)
Fig. 8. Social welfare W with frequency regulation charge a = +1 on the left and a = 1 on the right (k = 2, c = 0.5, Q = 400, b = 20, F = 10).
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Prices are not affected by frequency regulation charges and, under FIT, price p is not affected by frequency regulation costs. As discussed above regarding network charges, frequency regulation has no impact on the existence of social welfare optima. However, the absolute value of social welfare and the position of the eventual global optimum are modified (e.g., under FIT Z_ is higher if a ¼ 1 and lower if a ¼ 1). Further, as the right panel of Fig. 8 shows, when the cost of frequency regulation decreases over Z, the initial marginal social benefit of adopting PV is strong under any tariff.
6. Conclusions We have presented here a theoretical model that describes how different tariffs impact distribution-level electricity markets with diffusing residential PV. The model takes into account budget constraints of electric utilities, showing how a surplus advantage in favor of PV adoption can be created in the system. The surplus advantage is the only mechanism that could increase levels of residential PV unless exogenous shocks, such as those from technology, intervene. At the same time, the creation of such an advantage leads to a specular disadvantage for non-adopting households, while the inequality in surplus distribution makes problematic the management of consensus by regulatory agencies and the maximization of social welfare. In this context, the main result of our analysis is twofold. First, looking at the analysis of the basic model, the NetM tariff seems to be preferable for supporting increasing levels of PV adoption. Second, the same tariff looks much less preferable if increasing levels of PV adoption carry additional costs associated with the distribution network. As Figs. 3 and 4 show, NetM allows high levels of PV adoption with less burden on non-adopting households than in FIT. In FIT, because of the lack of energy compensation at the household level, resources to pay for PV-generated energy have to be raised by increasing the standard electricity rate, which strongly impacts the welfare of non-adopting households. At the same time, if PV adoption implies additional or increased costs in the system (e.g., network O&M, ancillary services), under NetM the collection of resources to cover such costs could amplify the inequality in surplus distribution between households. If charges are applied on a uniform per household basis, the gap in the surplus distribution does not change but non-adopting households must pay even more for investment decisions taken by others, although they enjoy environmental benefits equally. If, on the contrary, charges are applied on prices, under NetM the distribution of surplus becomes progressively more unequal because of the compensation of energy at the household level that reduces the turnover between utilities and PV-adopters. In fact, as Figs. 6 and 7 show, with NetM, charges always increase over Z, regardless of the adopted charging scheme. The only other solution for charging additional costs could be to differentiate per household charges by kind of household, similar to recently proposed policies that charge a monthly contribution per kW to newly installed residential PV (e.g., the ‘‘reliability charge” added to NetM in Arizona). However, this strategy presents several problematic issues that require further investigation. First, it introduces a further segmentation of households, dividing PVadopters in early and recent ones. Second, if successful, the welfare improvement goes largely to non-adopting households but also, partially, to early adopters. Third, if the tariff is determined dynamically to cover costs added by PV, the cost is entirely shifted from early PV-adopters to new ones. Fourth, the determination of the charge is complex and should consider both the elasticity of adoption on total installation costs and the elasticity of additional net-
work costs on levels of adoption. In the worst case scenario, the new charge would only stop the diffusion of residential PV leaving the uneven distribution of surplus as it is. In conclusion, our analysis supports the observed widening of the gap between retail electricity prices in European countries, which have adopted FIT, and in the Unites States, which has adopted NetM (Marcy and Metelitsa, 2014). The analysis also supports the observed high retail price of electricity in countries with high PV adoption and FIT (e.g., Germany - Lesser and Su, 2008). However, our analysis is limited by the assumption of complete inelasticity of energy consumption. The impact of different tariffs on household energy consumption remains largely unknown today but it could surely modify the comparative analysis of tariffs (Yamamoto, 2012).
Appendix A. Data collection and transformation Only a few data sources regarding residential PV installations are publicly available and they refer to state policies promoting its adoption by means of economic incentives (e.g., rebates on total installation costs). Data are made public for matters of accountability. We use detailed data for California, Arizona, and New Jersey. In particular, the state initiative Go Solar California (2014) provides records of PV installations in three California electric utilities: PG&E, SCE and SDG&E. The initiative Arizona Goes Solar (2014) provides data for all utilities in Arizona but, for the purpose of our analysis, we consider only APS, SRP and TEP. Similarly, the initiative New Jersey’s Clean Energy Program (2014) provides data for all utilities operating in New Jersey but we focus on the two largest ones, JCP&L and PSE&G. In summary, we consider eight utilities that cover most service areas and customers in the three states. Data are related to the rebate requests presented by households intending to install rooftop photovoltaics. We consider the date when the first request of reservation is presented (i.e., when the public rebate is requested) as the date in which the decision to install solar panels has been taken. We created the dataset in May 2014 and selected only residential installations completed at that time. The resulting dataset considers 125,517 installations in California, 37,473 in Arizona, 17,691 in New Jersey and it spans from 2001 to 2014. Because the data regarding New Jersey considers only the capacity of the installed modules but not the installation costs, we estimate the total costs of installations in that state by multiplying capacity by state-level annual average costs reported in Barbose et al. (2013). The dataset is transformed in monthly values by utility. Prices and costs are transformed in constant prices using the Consumer Price Index published by the U.S. Bureau of Labor Statistics. We compute k as the difference between the average total cost of installation of 1 kW of solar panels and the average rebate that has been obtained for the same capacity of generation. We also compute the number of days that has been required by state agencies to assign the rebate to requesting households. Furthermore, we need three more wholesale and retail prices to describe the market (i.e., c; r and p). The price c is estimated for each utility using wholesale electricity data provided by the Department of Energy’s Energy Information Agency (EIA). In particular, for utilities in New Jersey, we consider the average price at the PJM West Hub. For Arizona we consider average prices at Palo Verde. For PG&E we consider average prices at the Northern California hub (NP-15). For the two remaining utilities in California, we use average prices at the Southern California hub (SP-15).
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R. Boero et al. / Solar Energy 140 (2016) 188–198 Table A.1 Summary statistics. Variable Z/Q (in percentage) k (in 1000$ per kW) Num. of days c (in $ per kW h) r (in $ per kW h) p (in $ per kW h)
Minimum
Maximum
Mean
Standard deviation
0.048 3.078 20.500 0.022 0.051 0.024
11.162 8.496 677.000 0.137 0.170 0.093
3.010 5.453 161.213 0.047 0.105 0.050
2.459 1.202 73.128 0.018 0.032 0.017
Price r is computed as the bundled electricity rate valid in different periods. This information has been collected from utility and state regulator websites. Price p is collected in the same way. However, in New Jersey p is not published by utilities because it is defined as the average peak tariff at the wholesale level observed in the last 12 months. We thus estimate it as the average maximum daily price over the last 12 months at the PJM West hub. To complete the dataset, we include two other kinds of information provided by EIA. First, we include the monthly average electricity consumption by residential customers in each state, in 2012. Second, we include the number of residential customers (i.e., households) served by each utility in 2012. Knowing the average amount of consumption by residential customer and the number of households served, we compute a variable Q that is the total amount of monthly consumption by residential customers in each utility. We finally compute Z as the cumulated amount of installed PV capacity, and Z=Q that is the percentage of PV adoption. The data we use are synthesized in Table A.1, where summary statistics are presented for main variables and prices are constant at the level of April 2014. Appendix B. Notations Table B.1 summarizes and explains the symbols used in the basic model and in extensions.
Table B.1 Theoretical model notations. Symbol
Description
a
Parameter modeling variations of total ancillary services costs over Z Average environmental benefit derived from one unit of energy produced by residential PV Average price of one unit of energy generated at the utility-scale and transmission level Total capital costs and returns of the electric utility Total costs of ancillary services
b c CC a F QZ ki k
Net present value of total capital, installation and O&M costs of PV for household i P PN ki z N i
mf mn M N p
PEU Pi qi Q r t ui W zi Z
Service charge aimed at collecting revenues to cover F
a Z Q
Network charge aimed at collecting revenues to cover M Total cost to operate and maintain the distribution network Number of households Price paid by the electric utility for PV-generated energy in excess Total profit of the electric utility Total profit of household i Electricity demanded by household i P N qi Standard electricity rate for households Tariff parameter (see Table 1) Household i’s utility of installing solar panels Social welfare Total amount of energy generated with PV by household i P N zi
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