Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
- A system dynamics approach! -
Amin Al Y aquob
Graduate School of Policy and Management
Doshisha University
Kyoto, Japan
kbj1052@ mail3.doshisha.ac.jp
Kaoru Y amaguchi
Japan Futures Research Center
Awaji, Japan
director@ muratopia.org
Abstract
This paper discusses the feed in tariff policy for the rooftop photovoltaic market in
Germany. It attempts to explain the fluctuation pattern of the PV deployments occurred
between 2011 and 2014. The study aims to figure out the basic system structure behind this
phenomenon, and suggest a way to reduce the fluctuations and stabilize the PV market
growth. System dynamics method is used to build a simulation model as an alternative to
optimization method used in earlier research. The simulation model successfully replicates
the historical behavior. The model results were then analyzed to enhance feed in tariff
policy design to have a dynamic and real-time feed in tariff policy instead of stepped and
discontinuous one. The study concludes that dynamic price adjustments can significantly
improve the stability of the market growth. Dynamic price adjustment can provide more
cost-effective policy and provide reliable market projections for policy makers.
1 This paper was presented at the International System Dynamics Conference, Boston, MA, USA. July 2015
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
1. Introduction
Feed in tariff is one of the successful renewable energy policies that contributed to accelerating the diffusing
renewable energy around the world. It has been implemented in more than one hundred countries and states
(Couture et al. 2010). The policy also has been successful in reducing the technology cost, increase the
technological efficiency and innovation in its related industries (Campoccia et al. 2014). Feed-In Tariff (FIT)
policy drives market growth by providing developers long-term purchase agreements with fixed tariffs for
the sale of electricity generated from renewable energy (RE) sources (Menanteau, Finon, and Lamy 2003).
The policy contract usually lasts between 10 to 25 years (contract period is also referred as feed in tariff
term). For each renewable energy technology, the tariff price differs and is determined by different factors,
like technology cost, efficiency level, technology manufacturing maturity stage, in addition to the size and
location of its power plant. As cost declines and technology efficiency increases, the feed in tariff prices is
adjusted accordingly at the end of the feed in tariff qualifying period to guide the market development as
intended. The reduction rates of feed in tariffs are called degression rates and are determined by the authority
in charge of the policy (Klein 2012).
Germany is one of the leading countries that implemented the feed in tariff policy to boost renewable energy
development. The solar photovoltaic market in Germany has been mainly driven by the feed in tariff policy
since the year 2000. The German government introduced capacity corridor to guide the supply development
to be within 2.5 and 3.5 Giga-watt (GW) per a year (Duetche Bank 2012). Nevertheless, the deployment
quantities in the years of 2010 and 2011 have exceeded 7.5 GW. Such unexpected market response requires
urgent policy intervention because the cost implication may increase the budget in the magnitude of billion
of dollars (Chowdhury, Sumita, and Islam 2012; Frondel, Schmidt, and Vance 2014).
Impact of FIT on PV Market Growth in Germany
—— Free Standing FIT
Lo Roof mounted FIT
BIPV FIT
60 g
0% mame Annual Capacities MW
200
8,000 , 80
|
|
|
Figure 1: Impact of FIT on PV market growth in Germany
Source: (J acobs 2012)
As the feed in tariff policy budget is paid by the electricity consumers and or taxpayers. An unexpected
increase in renewable energy supply can result in the sudden increments in the electricity prices or taxes
2
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
(Frondel, Ritter, and Schmidt 2008). The fact that feed in tariff policy is a long-term contract creates a policy
trap for governments and create a long-term burden on the public. Therefore Missing the right time to adjust
the feed in tariff prices results in substantiative increase policy cost (Nemet 2009; Jacobs 2012). The feed in
tariff policy must be adjusted dynamically and efficiently.
Rooftop PV market in Germany constitutes around 30% of the total PV installations in Germany. Thanks to
high levels of feed in tariff, the cost of rooftop PV systems in Germany has witnessed a continuous decline.
However, the pattern of rooftop PV follows a cyclic pattern with spikes before price adjustments. This pattern
appears as project developers observe the declining cost and wait for the best time to install their projects, or
they rush to install more projects at the end of the qualifying period (Grau 2014).
Unlike large-scale photovoltaic projects, small-scale projects have a shorter development time and hence
respond quickly to policy changes. The rush to install behaviour is explained by three observations: 1)
deployments increases with profit levels proportionally, 2) profit expectations decrease over time and 3)
deployment accelerates right before the tariff price adjustment deadlines to benefit from high tariff prices,
creating a rush to install effect (Grau 2014). According to the estimates, a rooftop PV installation project has
a construction time between 15 to 3 weeks and an average of 7 weeks.
Historical Cost, Profit and Feed in Tauiff Price
0.5, eur/kwh
5,000 euro/kw
—
0.25 euro/kwh
2,500 euro/kw
0 euro/kw
2009-01-01 2009-11-12 2010-09-23 2011-08-04 2012-06-14 2013-04-25 2014-03-06
Dale
Historical Feed in Tariff Price : Base. ————____________._ewrokwh
Historical Profit : Base euro/kw
Historical PV System Cost : Base. ——————— aunokw
Figure 2: Feed in tariff is adjusted to cope with declining PV system cost
Development of Residential PV Installations in Germany
0.5. eum/kwh
400,000 kw/week
3,000 euro/kw
0.25. euro/kwh
200,000 kw/week
1,500 euro/kw
0 euro/kewh oT
2009-01-01 2010-02-25 2011-04-21 20120614 2013-08-08 2014-10-02
Date
Historical Feed in Tariff Price : Base. ————————_——— euro/kwh
Historical Installations : Base. —————______________—_ kwiweek
Historical Profit : Base euro/kw
Figure 3: Weekly deployment levels of photovoltaic projects in German
3
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
2. (Grau, 2014) Model
A regression model was used to estimate the deployment based on profit level. The model is enhanced to
model the rush to install effect using an optimization technique, where developers will decrease the
construction time to the minimum possible to ensure the highest level of profitability. Although the results
obtained from the optimization model replicate historical patterns fairly well, the model has a shortcoming
that it does not incorporate developers’ expectations of cost and price adjustments and the delay time needed
to form these expectations. Therefore, the model assumes perfect decision making for the PV developers. As
explained by (Sterman 2000) optimization techniques considers perfect outcomes and ignores the operational
processes in the decision making, as well as imperfections and the effect of bounded rationality.
In (Grau 2014) model the installation rate is calculated using the following:
Vera =O * Tea —€
Where, Y;+q is the installation quantity, 744 is the profit, and @ and c are parameters. The net profit is
given by:
Te+a = Vera — Pe
Where, v;,q is the present value, and p, is the average system cost. The present value is then formulated as:
n
— ah i)
Yy=fpeh Xe +i)
Where, f;, is the feed in tariff price at time t, and h is the average operational hours per a year, i is the interest
rate andj is the feed in tariff term. The feed in tariff price data is given in the figure, facility operational
hours is estimated with 900 kilo watt hour (kWh) per kilo watt kW system per a year. The interest rate is
assumed to be fixed at 3.5%, and the feed in tariff term for residential roof top photovoltaic projects is 20
years.
Grau Simulation vs Historical Data
400,000
300,000
= 200,000
&
99,600
2009-01-01 2009-11-12 2010-09-23 2011-08-04 2012-06-14 2013-04-25 2014-03-06
Date
Historical Installations : Base
Thilo Grau Simulation : Base
Figure 4: Comparison of (Grau, 2014) simulation and weekly historical installation of rooftop PV in Germany
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
3. System Dynamics Approach
The causal loop diagram shown in the figure below explains the growth of the deployment. As the first
observation suggests, the level of profitability gained by the investors and developers mainly influences the
deployment of PV projects. The economies of the scale of PV installations helps in reducing the overall cost
of PV projects and consequently the increase the profit levels, as illustrated in the reinforcing loop R1. The
project cost in turn reduces the generation cost (known as the Levelized Cost of Electricity Generation or
LCOE) and consequently the feed in tariff price. The tariff rate is adjusted discretely (or stepped fashion)
after a certain delay, called qualifying period. The price adjustment is determined by the generation cost and
predefined internal rate of return (IRR2). The price adjustment loop B1 helps to correct the incentive level to
make sure that the deployment levels as intended by the policymakers.
Nevertheless, the delay in systems usually creates fluctuations (Sterman 2000). Given the market growth
loop, we can assume that the cost will have a declining trend (with some fluctuation resulted from market
forces), and this allows more profit gains for the investors and developers. Consequently, the period before
the price adjustment (usually price reduction) will provide the highest level of profitability. The profit to
supply relationship developed by (Grau 2014) can be used to represent the inflow of a stock for intended
projects. These projects, however, are realized depending on the construction time or project completion
time decided by the developers. This allows us to explore the developers’ decision in more details.
Expected Feed in Tai
Price (Continuous) Frequency to adjust
qualifying period
+ \
a Expected Revenue \
R2
Rush Install \ ‘A
Ra A! me
Feed in Tariff Price “\ Profit vere deadline
te)
(Discret
Expect
caemtnn Cos . ot for wh
| mance a
Reveme
Bybced Cos
Ye bY 2
——- v nstaltions
ee
Sete 27
Figure 5: Model causal loop diagram
2 The IRR percentage in this model is estimated from historical data.
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
The project completion time is defined using the following relationship. Throughout the qualifying period,
the project completion time is assumed to be the average, 7 weeks, however, as the remaining period before
the price adjustment deadline becomes less than 7 weeks, the completion time is adjusted to be the maximum
possible as shown in the figure below. The policy term or the qualified period can be used to set a timeframe
for projects. That is the duration of a policy term (as shown in figure 6), provides an indicator or a deadline
for project developers. Hence the variable “remaining time before the deadline” is devised to estimate how
project developers plan their project schedules. When the remaining time before the deadline is less than 7
weeks, project completion can range between 7 and the minimum of 3 weeks using the relationship defined
in figure 7. This relationship, however, is not sufficient to explain the non-linear behavior of weekly
installations. The rush to install effect discussed above can be modeled using the developer expectation of
cost and project profitability. Unlike fixed or discrete feed in tariff price schedules, estimation of continuous
feed in tariff prices can provide an updated indicator of the likelihood of price changes.
FIT Policy Tem Remaining time before deadline
60 60
# 20 Hb it 4 30
a 0
2009-01-01 2011-01-06 2013-01-10 2009-01-01 2011-01-06 2013-01-10
Date Date
FIT Policy Term : Base. ——————— Remaining time before deadline : sim1
Figure 6: Designing the remaining time before the deadline
Project Completion Time
8
6
4
iz
0
0 1 2 3 4
Project Completion Time
Remaining time before deadline
Figure 7: Project completion time
The likelihood indicator influences the developers to speed their project construction if profits are expected
to decline in the future, vice versa. The likelihood can be represented as follow:
Les
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
Where L is the likelihood indicator, 7 is the project profit, and zis the expected profit. Using the likelihood
indicator, the developers form their expectations from the trend of profits as shown in loop R2 in the causal
loop diagram.
Likelihood of "Rush to Install" Effect
Multiplier effect
0 0.2 0.4 0.6 0.8 1
Profit/Expected Profit
Figure 8: Rush to install effect
As the pattern shows, the developers’ decision-making is influenced by time. Therefore, the probability
multiplier impact is marginal except at the 3“ quarter of the qualifying period. For this reason, a corrective
non-linear relationship is necessary. The following relationship in the figure below shows the impact of
remaining time before the price adjustment on the probability multiplier. This relationship is formulated as
follow:
e=L(R)
Where ¢ is the effect of remaining time on the decision for project deployment, R is the ratio of remaining
time. R is defined as:
tr
“ap
Where tp is remaining time befoe the qualified period deadline, and qp is the qualified period duration.
R
Effect of Remaining Time on Decision Making
1.2
Multiplier Effect
°
0.5 0.6 0.7 08 0.9 1
Figure 9: Effect of remaining time to complete projects
The interaction between these variables is explained in the stock flow diagram below. Note that the stock for
the simulated installations of PV project is disaggregated into three stocks, since its pattern matches a second
order material delay. The stock called “Installation before Connection” refers to the PV installations installed
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
by the project developers before they are connected to the electric grid. This stock will be used to analyzing
the PV installations pattern.
=F eed in Tarif stated net
- Price
FIT Policy
Project Cycle «——" "Term
Time
P
Fitphice RR
(Condruoes)
; Nomatzaton
pid —PEstimated —_efectable con
4 supply
Remaining ine to ~ Ny
rojectdiaton ‘Remaining time -«-—-Deadiine
ore before deadline '
NEE A
fe ee
conic x NF A
bat d accelerated Re ~
yp deployment —
Remaining time
‘fect
Likelihood effect Time effect table
table function function
Figure 10: Stock flow diagram
4. Model Results
Using the incremental developers expectation about cost and profit to form their decision-making process,
the model succeeded in replicating not only historical data but also the historical pattern and the logic behind
it. This provides an alternative method to the optimization technique used by (Grau 2014). The figure below
shows the expected profit which is developed from the parallel structure introduced in loop R2 and how it
influences the likelihood for the rush to install effect. The simulated result of installations is shown in figure
12.
Developer Expectations Likelihood for" Rush to Install"
3,000 euro/kw 400,000 kw/week
4 dmni 4 dmal
1,500 euro/kkw
2 dml 200,000 kw/week
0 eurokw aaniae |
0 aml
0 kw/week A f ee
2009-01-01 2010-09-23 2012-06-14 2014-03-06 Odml |“ V we
Date 2009-01-01 2010-06-10 2011-11-17 2013-04-25 2014-10-02
Expected Profit : Base umikw
Profit: Base euro/kw Historical Installations : Base, ———____________— ew/week
Probebility for developers to nish: Base. ———— dnl “Likelihood for "Rush to Insta mn
Figure 11: Project developer expectations and the likelihood of accelerated deployment
Using the understanding developed in the basic structure, the simulation results could replicate the
installation pattern.
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
Simulation Result
400,000
& 200,000
0
2009-01-01 2010-02-25 2011-04-21 2012-06-14 2013-08-08 2014-10-02
Date
Installations before Connection : sim!
Historical Installations : sim1
Figure 12: Model results
4.1 Discrete Feed in Tariff Policy
The PV system cost is a contributing variable to the design of feed in tariff policy. In order to see the impact
of PV system cost changes, the changes have to be tested against responsive feed in tariff policy. Since the
historical feed in tariff price data will not provide accurate results, the discrete model of the feed in tariff
price adjustments is developed for this purpose. Due to the complexity of the feed in tariff pricing policy, a
simpler model has been devised to testing purpose. The discrete model offers relatively accurate trend to the
historical data.
Discrete Feed in Tariff vs Historical Feed in Taniff
05
i 0.25
0
2009-01-01 2010-02-25 2011-04-21 2012-06-14 2013-08-08 2014-10-02
"Feed in tariff " : Base
Historical Feed in Tariff Price : Base
Figure 13: Feed in tariff comparison
4.2 Testing and Analysis for the Discrete (Stepped) Model
The model was tested using partial tests to verify its intended rationality. Specifically, the model was tested
to examine its response to unexpected changes in system cost. This will be modeled using STEP function for
the period between the 70" and 130 week. The results show reasonable behavior; the expected profits
increases when the cost increase and vice versa. This is because the R2 loop of developer expectation
dominates in the systems, in which the feed in tariff prices are adjusted accordingly to create a profitable
margin. Moreover, the developer expectations are derived from an exponential averaging of PV systems cost.
9
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
Also, the model was tested against extreme values. Testing the model with large values of unexpected cost
increases may lead to negative profits and consequently negative installation quantities. However, a
normalization relationship is introduced to correct this issue. The simulation of the discrete policy provided
excellent results similar to the historical pattern. However, to have an efficient policy the pattern has to be
more stable against fluctuations.
Impact of Unexpected Cost Change
0.5 eurofkwh
300,000 kw
0.25 eurofkwh
150,000 kw
0 eum/kwh
0 kw
2009-01-01 2010-06-10 2011-11-17 2013-04-25 2014-10-02
“Feed in tai pre (Disree)*
"Fed in y
Installation bere Connection
Installation bere Connection
ceurojlewh
euro/lewh
kw
kw
sim 1 unexpected cost increase
sim:
sim1 unexpected cost inerease
simi
Figure 14: Impact of Unexpected Cost Change
4.3 Continuous (Smooth) Feed in Tariff Policy
The continuous feed in tariff policy assumes no deadlines for price adjustments. Similar to electricity prices,
the tariff prices can determined depending on the updated cost of PV systems. This allows the policy to
remove a critical delay that causes the fluctuations of PV deployment. Moreover, based on this assumption,
as there are no deadlines, the majority of projects will have a completion time around the average of 7 weeks,
and there will be no need to shrink this period. Consequently, there will be no effect of remaining time
before the deadline, which is a major non-linearity in the discrete model that reinforces the deployment rate.
Installation - Two Policies Installation - Two Policies
300,000
g
i 0.25
2 150,000
0
2009-01-01 2011-01-06 2013-01-10
Date
“Fead in tariff price (Continuous)" : Base
“Fead in tariff price (Discrete)" : Bese. ———————
Figure 15
2009-01-01 2011-04-21 2013-08-08
Date
Installation before Connection : Discrete Policy
Installation before Connection : Continuous Policy
: Impact of two policies
10
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
The results show that the continuous policy is more robust and stable to change. The following figure shows
a STEP test of the cost increase of 50% between the 70" and 130" weeks. The developer expectation in the
case of continuous price adjustments stabilizes. The probability to rush becomes marginal as the model
eliminate the effect of remaining time.
Uexpected Cost Change Uexpected Cost Change
300,000 2
2 150,000 E42
04 06
2009-01-01, 2010-09-23 2012-06-14, 2014-03-06 2009-01-01 2010-06-10 2011-11-17 2013-04-25 2014-10-02
Date Dele
Installation before Connection : Continuous Policy Unexpected Cost Increase [anno develope tonic Commas Paki ees Coat mass
Installation before Connection : Discrete Policy Unexpected Cost Increase — Likelihood for developers to rush : Discrete Policy Unexpected Cost Increase
Figure 16: Unexpected cost change on PV installations
4.4 Comparison of Continuous and Discrete Policy
When comparing the results of the two policies, it is clear that the continuous policy can reduce substantive
policy costs. The policy budget to be realized by the end of the 2015 policy term (i.e. after 20 years) will in
the year of 2035. Discrete feed in tariff policy can introduce faster share of solar energy with the fluctuating
pattern as the growth is highly motivated by profit and unpredictable market conditions. Whereas continuous
policy offer slower but more reliable pattern, that prioritize cost efficiency rather than the speed of renewable
energy deployment. According to the model results, the discrete policy can achieve an operating capacity of
10 GW by October 2014 at a policy budget of around 5 trillion euros, while the continuous policy achieves
7 GW at the same period with a half the budget.
Operating Capacity Policy Budget by by 2035
20M 5e+012
2 10M DeeTITT $ 25et012
0 0
2009-01-01 2011-04-21 2013-08-08 2009-01-01 2011-04-21 2013-08-08
Date Date
Installations : Discrete Policy. Policy Budget : Continuous Policy, ————————
Installations : Continuous Policy. —————————— Policy Budget : Discrete Policy, —————————
Figure 17: Policy budget comparison
iL
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
5. Summary and Conclusion
The paper discussed the influence of feed in tariff policy on the development of rooftop PV in Germany.
Feedback loop analysis was used to identify issues incorporated in the discrete based feed in tariff policy.
We found that time delays and nonlinearities were a major cause for the cyclic fluctuations development
trend of PV deployments. The system dynamics model developed in this paper was capable of generating
historical pattem and allowed discrete and continuous policy comparison. The model showed how
continuous price adjustments could improve market growth while maintaining the policy budget under
control.
Acknowledgement
This research was funded by King Abdullah Al Saud Scholarship from the Ministry of Education in Saudi
Arabia’. We would like to thank all of those who provided their feedback and comments to improve this
study. Special thanks to Professor Y utaka Takahashi from Senshu University and all the reviews from the
System Dynamics community, for their invaluable comments and guidance.
3 The sponsor of this research does not influence the research results and is not accountable for its
outcome.
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Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
Appendix A
Comparison between our model and Grau model against historical data.
Comparison Enor Margin
200,000
Pog
é
-200,000
2009-01-01 2010-02-25 2011-04-21 2012-06-14 2013-08-08 2014-10-02
Date
Grau model error margin : Base
Our model error margin : Base
Figure 18: Simulation comparison showing the error margin between Grau and our models
13
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
6. Appendix B
System Dynamics Model Documentation
"1 - increase in cost"=
step(1, 0)+step(0.5, Time of change)-step(0.5, Time of change2)
Units: dmnli
"2- decrease in cost"=
step(1, 0)-step(0.2,Time of change)+step(0.2,Time of change2)
Units: dni
"3. Variable change"=
smooth3(random uniform(0,1,1),16)
Units: dmni
Alternating=
if then else(modulo(Time, FIT Policy Term)=0,pulse(Time, 0.1),0)
Units: dni
Anuity=
Units: dni
Averaging time=
2
Units: week
Change=
if then else(Switch for response to cost change=0, 1,
if then else(Switch for response to cost change=1,"1 - increase in cost",
if then else(S witch for response to cost change: '2- decrease in cost",
"3- Variable change")))
Units: dmnl
Switch for testing the system response to chnage in cost. 0: no
change, 1: step increase, 2: step decrease, 3: varibale change
using random parameter.
Connected and Operating Installations=INTEG (
connection,
0
Units: kw
connection=
Installation before Connection/per week
Units: kw/week
Deadline=
FIT Policy Term
Units: week
difference=
“Feed in tariff price (Discrete)"-"F eed in tariff price (Continuous)"
Units: euro/kwh
effect df{
{(0,0)-(1,1)],(0,0),(1,1))
Units: dmnl
Estimated cost=
14
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
param c*exp(param Connected and Operating Installations)
Units: euro/kw
Estimated electricity generation per kw system per a year=
Annual operation time in hours*kw kwh
Units: kwh/kw
Estimated net electricity generation per kw system=
Annual operation time in hours*Facility life time in years*kw kwh
Units: kwh/kw
Annual operation time in hours*16*kw kwh
Estimated net revenue=
Feed in tariff price*Estimated electricity generation per kw system per a year
*Anuity
Units: euro/kw
if then else(Time<260,900*20*F IT price, 900*20*F eed in tariff
box*(1-anuity))
Estimated Supply=
(param a*(P rofit)-param b)
Units: kw/week
-399998x + 861573 954684*exp(-0.714*(P roject cost/Quantity of
approved projects)) param a*LN(Profit NPV)-param b supply
rel(P rofit NPV) if then else(switch three=0, (param a*Historical
Profit)-param b, (param a*P rofit NPV)-param b)
Expected cost=
smooth(PV System cost, Averaging time)
Units: euro/kw
Expected FIT=
Expected generation cost(1HRR)
Units: euro/kwh
Expected generation cost=
((Expected cost+operation cost)/Estimated net electricity generation per kw system
)
Units: euro/kwh
Expected Installation=INTEG (
Expected Installation Rate-Installation rate,
initial capacity)
Units: kw
Expected Installation Rate=
Estimated Supply*Normalization
Units: kwiweek
Expected P rofit=
Expected Revenue-E xpected cost
Units: euro/kw
DELAY 3(Expected Revenue-Expected cost, 6)
Expected Revenue=
Estimated electricity generation per kw system per a year*€ xpected FIT*Anuity
Units: euro/kw
Feed in Tariff Degression Rate=
difference*Alternating/TIME STEP
Units: euro/kwh/week
15
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
(difference)*Alternating*16/per week
Feed in tariff price=
if then else(Feed in tariff switch=0,"F eed in Tariff Price (Historical )"
if then else(Feed in tariff switch=1, "Feed in tariff price (Discrete)",
"Feed in tariff price (Continuous)"))
Units: dmnl
“Feed in tariff price (Continuous)"=
Generation cost+(Generation cost*IRR)
Units: euro/kwh
if then else(Time<260, Historical Feed in Tariff Price,
Generation cost+(Generation cost*IRR))
"Feed in tariff price (Discrete)"=INTEG (
-Feed in Tariff Degression Rate,
“Feed in tariff price (Continuous)")
Units: euro/kwh
“Feed in Tariff Price (Historical )"=
fit historical dt(Time)
Units: euro/kwh
Feed in tariff switch=
1
Units: *tundefined* [1,2,1]
0 for historicla 1 for discrete 2 for continuous
FIT Policy Term=
if then else(Time<S2, 52,
if then else(Time<75, 26,
if then else(Time<104, 13,
if then else(Time<156, 26,
if then else(Time<178, 13,4)))))
Units: week [4,52,4]
if then else(Time<24, 12, if then else(Time<60,6, 3))
Generation cost=
((PV System cost+operation cost)/Esti net electricity ion per kw system
)
Units: euro/kwh
if then else(Time<261, Historical costestimated net electricity
generation per kw system, (Project cost+operation
cost)/estimated net electricity generation per kw system)
Historical Installations=
Historical Installation dt(Time)
Units: kw/week
initial capacity=
1
Units: kw
Installation before Connection=INTEG (
Installation rate-connection,
Units: kw
Installation rate=
(Expected Installation/project durattion)*Likelihood effect
16
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
Units: kw/week
IRR=
0.075
Units: dmnl
Initial IR R*(1-(Installation/G oal))
Likelihood effect=
Likelihood effect table function(Likelihood for developers to rush)*Time effect
Units: dmnl
Likelihood effect table function(
((0,0)-(1,2)],(0,0),(1,1.5))
Units: dmnl
Likelihood for developers to rush=
Profit xpected P rofit
Units: dni
Normalization=
effect df(Estimated Supply)
Units: dmnl
operation cost=
PV System costtoperation cost percentage
Units: euro/kw
operation cost percentage=
0.525
Units: dmnl
param a=
if then else(Time<52, 50, 50)
Units: (kw*kw)/(euro*week)
param b=
890
Units: kw/week
if then else(Time<=52, 37250,890)
param c=
3813.9
Units: dmnl
Units: dmnl
per week=
Units: week
Policy Budget=INTEG (
Connected and Operating Installations*€ stimated net revenue,
0)
Units: euro
Profit=
Estimated net revenue-PV System cost
Units: euro/kw
if then else(Time<261, estimated net revenue-Historical cost, )
17
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
Project Cycle Time=
if then else(modulo(Time, FIT Policy Term)=0,0, modulo(Time, FIT Policy Term
)
Units: week
project durattion=
if then else(Feed in tariff switch
(Remaining time before deadline)
Units: week
7, Remaining time to project duration relationship
PV System cost=
if then else( Switch System Cost=0, "PV System Cost (Historical)"*Change,
Estimated cost)
Units: euro/kw
The system cost can be either set to historical cost to validate
the model against the historical data using (Parameter
a*exp(P arameter b'Installations))*C hange or to setita
regression model to allow a feedback loop.
“PV System Cost (Historical)"=
Historical Cost Data(Time)
Units: euro/kw
Ratio of remaining time=
1-(Remaining time before deadline/Deadline)
Units: dmni
Remaining time before deadline=
(Deadline-P roject Cycle Time)
Units: week
Remaining time to project duration relationship(
{(0,0)-(20,10)},(0,3),(4,7))
Units: week
Switch for response to cost change=
0
Units: dmni (0,4,1]
Switch System Cost=
0
Units: dmni (0,1,1]
0: Historical Cost 1: Estimated Cost using a regression model
Thilo Grau Simulation=
Thilo Grau Model Simulation dt(Time)
Units: kw/week
Time effect=
if then else(Feed in tariff switch=2, 1, Time effect df(Ratio of remaining time
)
Units: dmnl
Time effect df(
{(0.5,0)-(1,1)],(0.5,0.25),(0.75,0.5),(1,1))
Units: dmnl
Time of change=
75
Units: week
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Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
Time of change2=
120
Units: week
TIME STEP =0.0625
Units: week [0,?]
The time step for the simulation.
19
Al Yaquob and Yamaguchi, (2015). Dynamic Feed in Tariff Price Adjustments for the Rooftop PV Market in Germany
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