IMPACT OF NEW DANISH HOURLY BASED NET METERING ON THE ACCEPTABLE SOLAR PV
SYSTEM COST
Dr. Søren Bækhøj Kjær, Christian H. Benz, Abraham Gonlazez
sbk@danfoss.com, benz@danfoss.com, abraham.gonlazez@danfoss.com
Danfoss Solar Inverters
Jyllandsgade 28, 6400 Sønderborg, DENMARK, +45 7488 1300, www.danfoss.com/solar
ABSTRACT: The purpose of this paper is to investigate the relationship between: the size of solar PV systems; their
orientations; yearly energy consumption in households; and the acceptable break-even cost of the solar PV systems.
By acceptable break-even cost, we think of the cost for a solar PV system, which will keep the solar PV business
continuing when supported by hourly net-metering. Measured, hourly electricity consumption from 46 households is
compared with the electricity generation from 16 different solar PV systems, with nominal power from 2 kW to 6
kW. A questioner with 122 respondents reveals that approximately 30% of the population will accept a 10 year
payback period. A 2 kW PV system can in this way cost between 4000 – 5700 €, all inclusive, when the payback
period must be equal to 10 years. A 6 kW PV system can in the same way cost between 9900 – 14 000 €. Operational
cost, discount rate and yearly degeneration of the solar PV system is omitted thus the results is an absolute maximum.
Keywords: Cost reduction; Economic Analysis; Financing; Modelling; PV Market; Sizing; Sociological; Strategy;
1
INTRODUCTION
The economics of solar PV systems are still depended
on extended feed in tariffs (FIT) given by different
political support programs, like the German EEG [1]. As
the cost of solar PV systems decreases the dependency on
the FIT also becomes less vital for investment in solar
PV. This decrease of independence is vital for the future
of solar PV, since the FITs are being reduced all the time.
Take Denmark as an example, yearly net-metering
was applied in years 2005-2012 [2] with some minor
corrects underway. This caused the Danish solar PV
marked to boom in years 2011 and 2012, with a total of
+400 MW being installed, see figure 1 [3].
Figure 1: Installed solar PV capacity in Denamrk over the
last 2½ years. Left axis is number of solar PV systems
and right axis is accumulated solar PV capacity. Courtesy
of EnergiNet.dk [3].
The reason for the large interest in solar PV was that
the electricity retail price in Denmark is around 0.290
€/kWh including taxes and VAT (1 € = 7.45 DKK), of
which the 0.168 € is taxes and VAT and the remaining
0.122 € is the real cost of the electricity, distribution and
Public Service Obligations (PSO) [4], [5]. The yearly
energy production would amount to some 400 000 000
kWh, thus the Government would lose around 65 million
€ a year in taxes and VAT.
Thus, a new law was imposed November 2012 [6]
and again in June 2013, changing yearly net-metering to
hourly net-metering. The new law involves a yearly cap
of 20 MW and maximum 6 kW per solar PV system.
Electricity produced and consumed inside the premises
within the hour do not have to be accounted for, while
electricity not consumed within the hour of production
must be sold for 0.174 €/kWh and bought back at a later
time for the normal retail price (around 0.290 €/kWh as
stated before). This is effective for the first 10 years and
after that, the selling price will be reduced to market price
(currently ~0.054 €/kWh, increases ~4%/a) [2], [6].
Solar PV systems outside this law are still required
to apply hourly net-metering with a selling price of 0.081
€/kWh the first 10 years and hereafter the market price in
the remaining years but without any cap of installed
capacity. This includes commercial solar PV systems,
e.g. free-field on top of parking lots, etc.
The amount of self-consumption (with-in the hour of
generation) of the solar PV generated electricity is
therefore having a great impact on the economics of the
solar PV system. In this paper we estimate the acceptable
break-even cost for different system sizes, when taking
spatial orientation, yearly energy consumption and
generation on an hourly basis into consideration.
Section 2 deals with the applied methods, results are
presented in section 3 and finally a conclusion is given in
section 4.
2
METHOD
2.1 Consumption data and solar PV generation data
The hourly energy consumption for year 2011, in
total 8760 hours, for 46 private households is applied.
This is only possible since SmartMeters are already
rolled out in the area of Sydjylland by the DSO
(distribution system operator) SE.dk. Households with
electrical heating, heat-pumps or already installed solar
PV systems during 2011 are omitted, in order not to
affect the results. The hourly consumption for a random
selected household is shown in figure 2.
Sixteen different spatial orientations for the solar PV
systems are applied, see figure 3 and table I. The data is
generated with the PVsyst software [7] for the town of
Brædstrup, Denmark. The hourly output power for one
particular day is shown in figure 4.
8760
𝑦
𝐸𝑋
ℎ𝑜𝑢𝑟𝑙𝑦
= ∑ 𝐸𝑋
ℎ𝑜𝑢𝑟=1
The self-consumption ratio is computed as:
𝑦
%𝑆𝐶 = 100%
𝐸𝑆𝐶
𝑦
𝐸𝑝𝑟𝑜𝑑
Figure 2: Hourly consumption over seven days. Each
series corresponds to one day.
Figure 3: Orientation and numbering of the 16
investigated solar PV systems.
Table I: Overview of the 16 solar PV types.
Case
Inc.
Dir.
Specific energy [kWh/kW]
1
2
3
4
5
6
7
8
9
10
11
12
13
30°
30°
30°
30°
30°
45°
45°
45°
45°
45°
30°
45°
30°
90° East
45° East
0°
45° West
90° West
90° East
45° East
0°
45° West
90° West
½ East +
½ West
½ East +
½ South
½ West +
½ South
½ East +
½ South
½ West +
½ South
820
930
980
930
810
770
920
970
910
760
810
770
900
14
15
16
45°
Figure 4: Output power from the 16 solar PV systems on
a clear-sky day. Upper show systems 1–10 and the lower
show systems 11–16.
890
2.3 Acceptable Break-Even Cost
The acceptable break-even cost for a solar PV
system, CPV, is evaluated by computing the net present
value (NPV) [8] for the two cases, with and without the
solar PV system (all quantities being positive)
870
870
𝑁
2.2 Modelling self-consumption
The consumption data and solar PV production data
is processed according to the following equations:
ℎ𝑜𝑢𝑟𝑙𝑦
ℎ𝑜𝑢𝑟𝑙𝑦
ℎ𝑜𝑢𝑟𝑙𝑦
𝐸𝑆𝐶
= 𝑚𝑖𝑛(𝐸𝑝𝑟𝑜𝑑 ; 𝐸𝑐𝑜𝑛𝑠 )
ℎ𝑜𝑢𝑟𝑙𝑦
𝐸𝑠𝑒𝑙𝑙
ℎ𝑜𝑢𝑟𝑙𝑦
𝐸𝑏𝑢𝑦
=
ℎ𝑜𝑢𝑟𝑙𝑦
= 𝐸𝑝𝑟𝑜𝑑
−
ℎ𝑜𝑢𝑟𝑙𝑦
𝐸𝑝𝑟𝑜𝑑 ;
𝑡=1
𝑦
𝑦
𝑦
𝐸𝑠𝑒𝑙𝑙,𝑡 ∙ 𝐶𝑠𝑒𝑙𝑙,𝑡 − 𝐸𝑏𝑢𝑦,𝑡 ∙ 𝐶𝑏𝑢𝑦,𝑡 + 𝐸𝑆𝐶,𝑡 ∙ 𝐶𝑏𝑢𝑦,𝑡
(1 + 𝑟)𝑡
𝑁
>∑
𝑡=1
ℎ𝑜𝑢𝑟𝑙𝑦
− 𝐸𝑆𝐶
ℎ𝑜𝑢𝑟𝑙𝑦
𝑚𝑎𝑥(𝐸𝑐𝑜𝑛𝑠
−𝐶𝑃𝑉 + ∑
𝑦
−𝐸𝑏𝑢𝑦,𝑡 ∙ 𝐶𝑏𝑢𝑦,𝑡
(1 + 𝑟)𝑡
which can be rearranged to
0)
where ESC is the amount of energy consumed within the
hour of generation, Eprod is the hourly energy production
from the solar PV system, Econs is the total hourly energy
consumption in the household, Esell is the surplus energy
sold to the utility and Ebuy is the energy bought from the
utility to cover the residual demand.
The yearly self-consumed, sold and bought energy is
computed according to
𝑁
𝐶𝑃𝑉 = ∑
𝑡=1
𝑦
𝑦
𝐸𝑠𝑒𝑙𝑙,𝑡 ∙ 𝐶𝑠𝑒𝑙𝑙,𝑡 + 𝐸𝑆𝐶,𝑡 ∙ 𝐶𝑏𝑢𝑦,𝑡
(1 + 𝑟)𝑡
where N is the total number of periods, e.g. acceptable
payback period in years and r is the discount rate, e.g. 6%
per year, Csell and Cbuy is the selling and buying costs,
respectively. Most private owners are pleased not using
the NPV approach, in which case the acceptable breakeven cost can be further reduced to
𝑁
𝑦
𝑦
𝐶𝑃𝑉 = ∑ 𝐸𝑠𝑒𝑙𝑙,𝑡 ∙ 𝐶𝑠𝑒𝑙𝑙,𝑡 + 𝐸𝑆𝐶,𝑡 ∙ 𝐶𝑏𝑢𝑦,𝑡
𝑡=0
which again can be simplified to
𝑦
𝑦
𝑚𝑒𝑎𝑛
𝐶𝑃𝑉 = [𝐸𝑠𝑒𝑙𝑙 ∙ 𝐶𝑠𝑒𝑙𝑙 + 𝐸𝑆𝐶 ∙ 𝐶𝑏𝑢𝑦
]∙𝑁
under the assumption that there are no yearly
degeneration or operational cost and by using a mean
energy cost, Cbyemean.
A survey among 122 private persons where
conducted to get an idea about the acceptable payback
period for a residential solar PV system, see table II.
Table II: Response from survey.
First reason to invest in a
solar PV system
Number
of
respondents
Acceptable payback
period [Y]
Good investment
89
7-8
Secure future expenses
16
8
To be “Green”
17
10
Figure 6: Correlation between yearly consumption and
self-consumption for the 46 users with a 3 kW solar PV
system case 3.
The acceptable break-even cost for the 16 cases are
plotted in figure 5 for a 10 years payback period, a selling
price of 0.174 €/kWh. The mean cost of buying
electricity over 10 years is set 0.338 €/kWh, since the
Danish electricity price is increasing with approximate
3.25% per year [9].
Figure 7: Plot of residuals between the measured and
modelled self-consumption.
The residual between the measured values and the
model, see figure 7, is computed as:
𝑦
𝑟𝑒𝑠 = %𝑆𝐶 − (𝑎 ∙ 𝐸𝑐𝑜𝑛𝑠 + 𝑏)
Figure 5: Acceptable break-even cost for the 16 cases
with a self-consumption between 30% and 50%.
Based on the preliminary results above, one can
conclude that it is important to increase both the specific
yield of the solar PV system but also the selfconsumption, in order to increase the acceptable breakeven cost to a level where solar PV systems also can be
purchased.
which has a zero mean. Assuming that the residuals are
following a normal distribution, the 95% confidence
interval of the residuals is given as [10]
𝑆
𝐶𝐼 = ±1.96 ∙
√𝑛
where S2 is the sample variance of the residuals and n is
the number of samples. The confidence interval is now
added to the model for self-consumption to get a range of
the probable values
𝑦
%𝑆𝐶𝑚𝑜𝑑𝑒𝑙 = 𝑎 ∙ 𝐸𝑐𝑜𝑛𝑠 + 𝑏 ± 1.96 ∙
3
2.4 Statistical Model
The correlation between self-consumption and yearly
energy consumption for a specific size of solar PV
system and the 46 households is depicted in figure 6 and
given as
𝑦
%𝑆𝐶𝑚𝑜𝑑𝑒𝑙 = 𝑎 ∙ 𝐸𝑐𝑜𝑛𝑠 + 𝑏
where the coefficients can be determined by regression:
𝑦
𝑎=
𝑐𝑜𝑣(%𝑆𝐶, 𝐸𝑐𝑜𝑛𝑠 )
𝑦
𝑣𝑎𝑟(𝐸𝑐𝑜𝑛𝑠 )
𝑦
𝑏 = 𝑚𝑒𝑎𝑛(%𝑆𝐶) − 𝑎 ∙ 𝑚𝑒𝑎𝑛(𝐸𝑐𝑜𝑛𝑠 )
𝑆
√𝑛
RESULTS
The first results presented in figure 8 shows the
relationship between nominal PV power and yearly
energy consumption for the 46 households included in
the survey, in order to obtain a self-consumption around
40%. The minimum values are for systems pointing
direct south (cases 3 and 8) and the maximum values are
for cases 5, 10-12. Besides, the graph also shows that
there is a clear linear connection between the size and
consumption.
The computed parameters for cases 3 and 11 are
shown in table III and IV and used to plot figure 9. Figure
9 shows the anticipated self-consumption for a household
with yearly energy consumption of 4000 kWh and for
nominal solar PV power between 2.0 and 6.0 kW.
Table V: Break-even costs for case 3.
Consumption \ Ppv
2000 kWh
3000 kWh
4000 kWh
5000 kWh
6000 kWh
7000 kWh
2 kW
€ 4.600
€ 4.800
€ 5.000
€ 5.300
€ 5.500
€ 5.700
3 kW
€ 6.400
€ 6.700
€ 7.000
€ 7.300
€ 7.700
€ 8.000
4 kW
€ 8.200
€ 8.600
€ 8.900
€ 9.300
€ 9.700
€ 10.100
5 kW
€ 9.900
€ 10.400
€ 10.800
€ 11.200
€ 11.600
€ 12.100
6 kW
€ 11.700
€ 12.100
€ 12.600
€ 13.100
€ 13.500
€ 14.000
5 kW
€ 8.500
€ 8.900
€ 9.300
€ 9.700
€ 10.100
€ 10.500
6 kW
€ 9.900
€ 10.400
€ 10.800
€ 11.300
€ 11.700
€ 12.200
Table VI: Break-even points for case 11.
Figure 8: Minimum and maximum size of PV systems in
order to achieve a self-consumption of 40%.
Table III: Parameters for case 3.
Nominal PV power [kW]
2.0
3.0
4.0
5.0
6.0
a * 1000
7.3
6.6
5.9
5.3
4.8
b
21
13
9.2
6.9
5.3
n
46
46
46
46
46
4.4
3.4
2.7
2.3
2.0
1.3
1.0
0.8
0.7
0.6
S
1.96 ∙
𝑆
√𝑛
4.0
5.0
6.0
a * 1000
7.5
7.2
6.7
6.2
5.7
b
28
18
12
9.0
6.9
n
46
46
46
46
46
5.5
4.2
3.4
2.8
2.4
1.6
1.2
1.0
0.8
0.7
1.96 ∙
𝑆
2 kW
€ 4.000
€ 4.200
€ 4.400
€ 4.600
€ 4.800
€ 5.000
3 kW
€ 5.500
€ 5.800
€ 6.100
€ 6.400
€ 6.700
€ 7.000
4 kW
€ 7.000
€ 7.300
€ 7.700
€ 8.100
€ 8.400
€ 8.800
Figure 10: Anticipated self-consumption (▲) and breakeven costs (excl. VAT) for 10 years (■) and 8 years (♦)
payback periods, respectively.
Table IV: Parameters for case 11.
Nominal PV power [kW]
2.0 3.0
S
Consumption \ Ppv
2000 kWh
3000 kWh
4000 kWh
5000 kWh
6000 kWh
7000 kWh
√𝑛
Figure 10 show the specific results for a medium
commercial energy consumer, with a year consumption
of approximately 300 000 kWh and a case 3 system. The
amount of self-consumption is >99% for solar PV
systems below 45 kW, after which it decreases toward
40% for a solar PV system which can cover the total
yearly consumption. The break-even costs are calculated
on the following assumptions: NPV algorithm with 6%
discount rate. Selling cost year 1-10: 0.081 €/kWh after
which it increases with 4.75% per year. Buying cost
0.215 €/kWh, which increases with 3.25% per year.
4
Figure 9: Anticipated self-consumption for a typical
household with yearly consumption of 4000 kWh and a
solar PV system type 3 or 11.
The acceptable break-even costs are given in tables V
and VI. They show that a household consuming 2000
kWh electricity per year with a perfect oriented roof can
accept up to 4600 € for a solar PV system with 2 kW
nominal PV power and still keep a simple payback period
of 10 years. If the orientation of the roof is less optimal,
they should not pay more than 4000 € for the same solar
PV system.
CONCLUSION
This paper focus on the acceptable break-even cost
for residential solar PV systems in Denmark, but the
method can also be applied in other areas with hourly or
instantaneous net-metering.
Hourly consumption data from 46 private households
is compared with the energy generation data from 16
different solar PV systems. The output of the comparison
is used to develop a linear regression model and a
statistical model of the residuals. These models are used
to predict the self-consumption for a given size of solar
PV system and yearly energy consumption for the
household. The energy production from the solar PV
system and the self-consumption is then used to calculate
the break-even cost for a payback period of 10 years.
A 2 kW PV system can cost 4000 – 5700 €, all
inclusive, when the payback period must be equal to 10
years. A 6 kW PV system can in the same way cost 9900
– 14 000 €.
A concrete example from a medium-sized
commercial energy consumer, shows that the break-even
cost can be in the range 800 – 1400 €/kW and still be a
good investment with 8 year payback period.
ACKNOWLEDGEMENT
We would like to thanks our colleagues, which allowed
us to use their personal electricity usage data.
Also Per Jørgensen and Karsten Wind, former SYD
ENERGI now SE.dk, for extracting the electricity usage
data from the SE database.
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