# Long-Term Solar Photovoltaics Penetration in Single- and Two-Family Houses in Switzerland

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of the Agent-Based Model Implemented in This Study

^{®}register [47], by using open data for Switzerland [48] (see also Figure A2 in Appendix A). The Sinus-Milieus

^{®}is a scientific model to classify people according to life and ways of living and contextualize them with the socioeconomic status indicated by education, age, profession, and income. We then map the social classification categories of Sinus-Milieus

^{®}to the different types of adopters based on [49] (an adopter is an agent that adopts the technology, i.e., a single- or two-family house that invests in rooftop solar PV). Table 1 presents the mapping of the internal Sinus IDs used in the model to the actual Sinus-Milieus

^{®}categories, together with the mapping of the categories to the different types of adopters.

^{®}socioeconomic categories from 2005 [50] to 2016 [51] to approximate changes in the social and lifestyle preferences until 2050. Figure 5 presents the classification of agents into the different Sinus-Milieus

^{®}categories over time.

#### 2.1.1. Creating the Synthetic Population of the Agents

^{®}, the SolStis solar PV project database [54] and the Swiss Centre of Expertise in the Social Sciences (FORS) database of social and economic indicators [55]. The multi-dimensional dataset is created by applying Monte Carlo sampling to the fitted one-dimensional PDFs [56], following the methodology described in [57]. The same methodology for creating synthetic populations has been applied to other ABMs, such as in [58] for travel behavior and in [59] for the Multi-Agent Tranport Simulation model (MATSIM) [60]. In [61,62], it was shown that a synthetic population created by synthetic micro-data using Monte Carlo sampling is statistically equivalent to the real population.

^{®}category, annual electricity consumption, and usable rooftop area are random variables. The probability density functions of the random variables of income, age, and usable rooftop area are different per Canton. However, the probability density functions of annual electricity consumption and Sinus-Milieus

^{®}category do not depend on the agent’s Canton (mainly due to the lack of data at the time of the study). The income also affects the discount rate of the agent, reflecting different time preferences, access to capital, and risk stances, thus higher incomes are associated with lower discount rates. In this context, the discount rate of the individuals is also a random variable. The fitted PDFs of the random variables and their key quartiles are presented in Table A4, Table A5, Table A6 and Table A7.

^{®}category (88%—estimated from [51]), as well as between income and electricity consumption (60%, estimated from [65,66,67]).

^{®}categories (see Table A1), similar to the approach followed in [40]. Also, there is a 60% probability that an agent establish a link with another agent from the same location, following a similar methodology as in [35]. Because the population of agents is dynamic, also the total number of agent’s links is dynamic too and depends on agent’s Sinus-Milieus

^{®}category (see Table A2 and Table A3). Because the social network is established before the simulation, we avoid static (and perfect foresight) link structures by introducing some “noise”; every year there is a probability that an agent breaks an existing link and connects with another agent (see Table A3), following [40]. This mimics to some extent the real-world dynamics in human relationships.

#### 2.1.2. Modeling the Decision of an Agent to Invest

^{®}categories, reflecting different preferences of the different socioeconomic classes. These weights influence the slope of the adoption curve for each Sinus-Milieus

^{®}category [40]. When the total utility exceeds a threshold, then the agent invests in a solar PV system. The decision threshold is common across all Sinus-Milieus

^{®}categories and influences the adoption curve of the whole market segment of single- and two-family houses [40]. Each partial utility is a sigmoid function, the use of which is common in many theoretical and empirical studies including technology diffusion (for example, in [30,70,71]). A detailed discussion about the strengths and weaknesses of the S-curves is given in [72].

_{2}emissions avoided by the lifetime operation of the panel are less than the amount of CO

_{2}emitted during the construction of the panel [3]. With this approximation, no additional assumptions regarding the future electricity mix in Switzerland are necessary, which are beyond the scope of this analysis. In [74] it has been shown that the environmental benefits can be one of the most influential factors in the decision to invest in a solar PV system, but the responsiveness of the agents in the CO

_{2}emission savings declines as more emissions are avoided. The environmental utility is directly related to the injunctive social norm, which refers to the behavior commonly approved or disapproved of by a person’s reference group [75], i.e., investing in a solar PV technology is good for the mitigation of the climate change. In addition, because the definition of the environmental utility relates to the cumulative installations of the solar PV panels, it can also be interpreted as the level of awareness and knowledge of the potential adopter regarding the solar PV technology. In this context, the shape of the utility implies declining responsiveness of the agents as more knowledge about the solar PV technology is accumulated over time, e.g., via increased installations, marketing or advertising [76]. Hence, through the environmental utility, behavioral drivers are represented, such as the injunctive social norm and the awareness/knowledge about the technology (i.e., through campaigns).

^{®}category [40].

#### 2.1.3. Performing a Simulation

#### 2.1.4. Model Calibration and Validation

**λ**, contains the partial utility weights and the decision threshold. The second vector,

**θ**, contains the parameters corresponding to the “tipping points” of the partial utilities. We initialize k = 1..K vectors

**θ**, with different “tipping points” for the partial utilities, in such a way that the obtained functional forms of the partial utilities are very different for every k (maximum distance of two functions). For each k we use the vector of “tipping points”

_{k}**θ**to estimate, via maximum likelihood, a vector of weights

_{k}**λ**that minimizes the training error regarding the rate of adoption and the cumulative installed capacity of solar PV throughout 2009–2014. Then, we choose that model k, i.e., those vectors

_{k}**θ**and

_{k}**λ**, which produces the minimum error in the validation data set of the period of 2015–2017. For initializing the weights of the social network utility, we based on the evidence from the Swiss literature [14], as well as studies for other countries (see also [12,13]): one solar PV panel in a neighborhood increases the installation rate by 0.8–1% three months later.

_{k}#### 2.2. Scenario Definitions

_{2}Act that implements the Paris Agreement [79] (the Act is still under discussion in the Swiss parliament). Building efficiency and emission standards are not included in the Reference scenario and its variants. The inclusion of these standards would have a significant impact on the results and would dim the effect of the socioeconomic and technical drivers that are of the focus. Table 2 presents an overview of the main assumptions of the Reference scenario.

## 3. Results

#### 3.1. Reference Scenario

^{®}category 10) and the early adopters (Sinus-Milieus

^{®}categories 8 and 9). Main characteristics of the innovators are their willingness to take risks, their financial liquidity, and their high social status. Early adopters also have high social status and financial liquidity, but they are more discrete in adoption choices than the innovators. Finally, the early majority (Sinus-Milieus

^{®}categories 5 to 7) adopts innovations after a varying degree of time, which is longer than the innovators and early adopters. The behavior of the model regarding the participation of the different socioeconomic classes in the solar PV diffusion process is consistent with the literature (see for example [49]).

#### 3.2. Variants

## 4. Discussion

## 5. Conclusions and Policy Implications

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A1.**Expected annual electricity production from 1 KWp rooftop solar PV system in each Canton in kWh/yr. (own illustration based on [45]).

^{®}that groups the population to life and ways of living and contextualize them with the socioeconomic status indicated by education, profession, and income are given in Figure A2.

**Figure A2.**The Sinus-Milieus

^{®}in Switzerland for 2016. The bubbles represent the percentage of the population belonging to a particular socioeconomic group (own translation to English from the original figure in German provided by the Sinus-Milieus

^{®}Institute).

^{®}category. There are higher probabilities of an agent to establish links with agents from the same Sinus-Milieus

^{®}category. The probabilities are adapted from [40] based on the Sinus-Milieus

^{®}of Switzerland (Figure A2). For example, an agent of Sinus-Milieus

^{®}category 1 (Traditionals) has 65% probability of establishing a link with an agent belonging to the same category and 12% to establish a link with an agent from category 2 (Consumer-Materialists).

**Table A1.**Probability of an agent to connect with another agent according to the Sinus-Milieus

^{®}category.

Sinus ID | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

1 | 65 | 12 | 4 | 10 | 8 | 1 | 0 | 0 | 0 | 0 |

2 | 12 | 60 | 8 | 5 | 14 | 0 | 0 | 0 | 1 | 0 |

3 | 4 | 8 | 60 | 0 | 10 | 9 | 6 | 0 | 1 | 2 |

4 | 10 | 5 | 0 | 55 | 12 | 3 | 0 | 8 | 6 | 1 |

5 | 8 | 14 | 10 | 12 | 40 | 5 | 0 | 1 | 6 | 4 |

6 | 1 | 0 | 9 | 3 | 5 | 40 | 15 | 13 | 8 | 6 |

7 | 0 | 0 | 6 | 0 | 0 | 15 | 60 | 4 | 5 | 10 |

8 | 0 | 0 | 0 | 8 | 1 | 13 | 4 | 50 | 16 | 8 |

9 | 0 | 1 | 1 | 6 | 6 | 8 | 5 | 16 | 45 | 12 |

10 | 0 | 0 | 2 | 1 | 4 | 6 | 10 | 8 | 12 | 57 |

^{®}category is shown Table A2. They are based on [40], and they have been adapted to the Swiss Sinus-Milieus

^{®}.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|

# links | 6 | 10 | 9 | 8 | 8 | 7 | 7 | 7 | 7 | 6 |

^{®}category and are given in Table A3.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|

% | 0.25 | 0.25 | 1 | 0.75 | 0.5 | 1 | 1 | 0.5 | 0.5 | 1 |

**Table A4.**One-dimensional probability density functions used in the model, together with their data sources and method of future adjustment.

Random Variable | Probability Density Function | Future Adjustment To 2050 |
---|---|---|

Income | Gamma distribution is different per Canton, fitted from [67] | Its mean increases at an annual rate of 0.6%, based on the annual GDP per capita growth rate in Swiss Energy Strategy [44] |

Age | Discrete distribution; its values are the age ranges 20–29, 30–39, 40–49, 50–65; the probability of its value reflects the population age structure in each Canton [85] | The share of ages 20–39 decreases by 0.33% p.a., while the share of ages 40–65 increases by 0.67% p.a. following the assumptions in the Swiss Energy Strategy scenarios [44,86] |

Sinus-Milieus^{®} category | Discrete distribution; its values correspond to the ten categories of Sinus-Milieus^{®}; the probabilities reflect the share of the population in each category; same in all Cantons | The social structure follows the trends of the Sinus-Milieus^{®} structural changes observed during recent decades. |

Annual electricity consumption | Gamma distribution; fitted on data from [66]; same in all Cantons | Its mean is reduced on average by 1% p.a. based on the per capita electricity consumption in the “NEP” scenario of the Swiss Energy Strategy ^{1} [44] |

Usable rooftop area | Lognormal distribution; fitted on usable rooftop area data from 160 solar PV installations [54]; different for each Canton | Remains constant over time ^{2}; however, the area required for 1 kWp solar PV declines from 7.2 m^{2}/kWp in 2013 to 4 m^{2}/kWp by 2050 due to efficiency improvements [3] |

^{1}The NEP scenario is consistent with the near-term climate targets of the Swiss commitments in the Paris Agreement.

^{2}Time dynamics are implicitly introduced via the correlation of the distribution with the distribution of income.

^{®}category is given.

Canton | Canton Name | Annual Personal Income in Kchf (Gamma Distribution) | Age in Years Discrete Distribution Probabilities Per Age Group | |||||
---|---|---|---|---|---|---|---|---|

25% | 50% | 75% | 20–29 | 30–39 | 40–49 | 50–65 | ||

ZH | Zürich | 42.45 | 64.40 | 96.42 | 20% | 25% | 25% | 29% |

BE | Bern | 38.62 | 55.09 | 80.41 | 20% | 21% | 25% | 34% |

LU | Lucerne | 38.65 | 55.81 | 82.70 | 22% | 22% | 25% | 31% |

UR | Uri | 37.45 | 53.80 | 75.77 | 21% | 20% | 25% | 34% |

SZ | Schwyz | 40.49 | 61.36 | 100.11 | 19% | 21% | 26% | 33% |

OW | Obwalden | 37.45 | 54.93 | 82.18 | 21% | 20% | 25% | 34% |

NW | Nidwalden | 40.31 | 60.53 | 91.73 | 19% | 20% | 25% | 35% |

GL | Glarus | 36.04 | 52.45 | 76.87 | 21% | 20% | 23% | 35% |

ZG | Zug | 45.92 | 71.24 | 111.54 | 18% | 23% | 27% | 32% |

FR | Fribourg | 38.89 | 58.02 | 85.33 | 22% | 22% | 26% | 30% |

SO | Solothurn | 40.29 | 58.16 | 84.94 | 20% | 20% | 25% | 35% |

BS | Basel-Stadt | 38.77 | 57.75 | 87.81 | 21% | 25% | 23% | 31% |

BL | Basel-Landschaft | 44.95 | 66.50 | 96.36 | 19% | 20% | 26% | 35% |

SH | Schaffhausen | 38.74 | 55.89 | 80.55 | 21% | 21% | 24% | 35% |

AR | Appenzell Ausserrhoden | 36.85 | 54.07 | 81.40 | 20% | 19% | 25% | 36% |

AI | Appenzell Innerrhoden | 36.85 | 54.07 | 81.40 | 23% | 20% | 24% | 32% |

SG | St. Gallen | 37.45 | 54.27 | 79.35 | 23% | 21% | 24% | 32% |

GR | Graubünden | 38.08 | 55.78 | 82.94 | 21% | 20% | 25% | 34% |

AG | Aargau | 41.68 | 61.88 | 90.00 | 20% | 22% | 25% | 33% |

TG | Thurgau | 38.13 | 56.60 | 83.94 | 21% | 20% | 25% | 33% |

TI | Ticino | 34.99 | 53.04 | 81.02 | 18% | 21% | 28% | 34% |

VD | Vaud | 40.52 | 62.45 | 96.58 | 22% | 23% | 25% | 30% |

VS | Valais | 35.93 | 54.13 | 79.77 | 22% | 21% | 25% | 33% |

NE | Neuchâtel | 37.45 | 56.58 | 84.24 | 21% | 22% | 26% | 31% |

GE | Geneva | 41.40 | 66.36 | 100.12 | 21% | 25% | 25% | 29% |

JU | Jura | 34.26 | 50.90 | 75.89 | 21% | 19% | 25% | 35% |

**Table A6.**Probability density functions of the random variables identifying an agent, common to all Cantons.

Annual Electricity Consumption kWh (Gamma Distribution Quartiles) | Usable Rooftop Area (Lognormal Distribution Quartiles) | ||||
---|---|---|---|---|---|

25% | 50% | 75% | 25% | 50% | 75% |

4081 | 5200 | 6652 | 18.86 | 24.00 | 33.33 |

Discrete Distribution Probabilities per Sinus-Milieus^{®} Category | |||||||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

9 | 8 | 9 | 16 | 15 | 6 | 7 | 8 | 12 | 10 |

^{®}category (88%), income and rooftop area (85%), income and annual electricity consumption (60%).

## Appendix B

Index | Description |
---|---|

$t,tt$ | Periods ($t=2009\dots 2050$) |

$i,j$ | Agent ($i=1\dots 1200000)$ |

$u$ | Partial utility $u=f,e,i,s$ (f = financial, e = environmental, i = income, s = social network) |

$v$ | PV capacities available $pv=1\dots 30$ kW |

$c$ | Canton, $c=1\dots 26$ |

$s,ss$ | Sinus-Milieus^{®} category $s=1\dots 10$ |

$r$ | Support policy, capital subsidy or feed-in tariff ($r=sub,fit)$ |

Parameter | Description |
---|---|

${e}_{it}$ | Entry year $t$ of agent $i$ in the simulation (1 = agent $i$ enters in year $t$) |

${\overline{e}}_{it}$ | Existence of agent $i$ in year $t$ (1 = agent $i$ exists in year $t$) |

${\overline{c}}_{ic}$ | Existence of agent $i$ in Canton $c$ (1 = agent $i$ is located in Canton $c$) |

${\overline{s}}_{is}$ | Participation of agent $i$ in Sinus-Milieus^{®} category $s$ (1 = agent $i$ belongs in Sinus-Milieus^{®} $s$) |

${l}_{v}$ | Economic lifetime of solar PV system $v$ (years) |

${a}_{vt}$ | Square meters needed for installing the solar PV system $v$ in year $t$ (sqm) |

${\widehat{c}}_{v}$ | Capacity of solar PV system $v$ |

${x}_{vt}$ | Investment cost of the solar PV system $v$ in year $t$ (CHF) |

${\overline{x}}_{vt}$ | Fixed O&M cost of the solar PV system $v$ in year $t$ (CHF/yr.) |

${d}_{v}^{0}$ | Degradation rate of solar PV system at the end of the first year of its operation (%) |

${d}_{v}$ | Annual degradation rate of the solar PV system $v$ after the first year of its operation (%) |

${k}_{t}$ | Number of years that the feed-in tariff is received if investing in a solar PV system in year $t$ |

${z}_{rvt}$ | Level of policy support type $r$ received by the solar PV system $v$ if installed in year $t$ (CHF if $r=sub$, CHF/kWh if $r=fit$) |

${w}_{ust}$ | Calibration weights for the partial utility $u$ of Sinus-Milieus^{®} category $s$ in year $t$ |

${\mu}_{ut}$ | Shape parameter of the partial utility $u$ in year $t$ |

${\beta}_{ut}$ | Tipping-point parameter of the partial utility $u$ in year $t$ |

${\xi}_{s}$ | Decision threshold per sinus category $s$ |

${y}_{it}$ | Income of agent $i$ in year $t$ (kCHF) |

${g}_{it}$ | Grid connection costs of agent $i$ in year $t$ (CHF/kWp) |

${n}_{it}$ | Annual electricity consumption of agent $i$ in year $t$ (CHF/kWh) |

${m}_{it}$ | Production cost of electricity in the location of agent $i$ and year $t$ (CHF/kWh) |

${p}_{it}$ | Electricity price paid by agent $i$ in year $t$ (CHF/kWh) |

${\overline{i}}_{i}$ | Discount rate of agent $i$ (%) |

${q}_{i}$ | Expected annual electricity production of agent $i$ from 1 kWp solar PV system (kWh) |

${\overline{a}}_{i}$ | Usable rooftop area of agent $i$ for installing a solar PV system (sqm) |

Variable | Description |
---|---|

${\omega}_{it}$ | Agents that have installed a solar PV system in year t (1 = agent $i$h installs solar PV in year $t$) |

${\lambda}_{ijt}$ | Communication link between agents $i$ and $j$ in year $t$ (1 = link exists) |

${\overline{\lambda}}_{it}$ | Total links of agent $i$ in year $t$ |

${\lambda}_{i}^{max}$ | Maximum links that an agent $i$ can have with other agents |

${\tilde{\lambda}}_{it}$ | Number of communication links of $i$ with agents installed a solar PV system in year $t$ |

${\rho}_{ri}$ | Support policy chosen by agent (1 = agent $i$ chooses support policy $r$) |

${\varpi}_{it}$ | Total utility of agent $i$ in year $t$ [0,1] |

${\psi}_{uit}$ | Partial utility $u$ of agent $i$ in year $t$ [0,1] |

${\iota}_{it}$ | Installed capacity of solar PV system adopted by agent $i$ (kWp) |

${\phi}_{it}$ | Investment expenditure of agent in year $t$ (CHF) |

${\eta}_{rit}$ | Net Present Value of the cash flow of agent $i$ in period $t$ for support policy $r$ (CHF) |

${\pi}_{it}$ | Best net present value of the cash flow of agent $i$ in period $t$ (CHF) |

${\delta}_{it}$ | Discounted payback period of agent $i$ in year $t$ |

${\epsilon}_{it}$ | Electricity production from the installed solar PV system of agent $i$ in year $t$ (kWh) |

${\tau}_{i}$ | Share of electricity from solar PV which is consumed on-site (%) |

Decision algorithm:For each year $t$: For each agent $i$ with ${\overline{e}}_{it}>0$ and ${\omega}_{it}=0$: call: Break existing links and create new ones with probability ${\phi}_{is}$ ${\tilde{\lambda}}_{it}={\displaystyle \sum}_{j}{\lambda}_{ijt}{\omega}_{jt}$ ${\overline{\lambda}}_{it}={\displaystyle \sum}_{j}{\lambda}_{ijt}$ For each $v$ such that ${a}_{vt}\le {\overline{a}}_{i}$: ${\epsilon}_{it}={\displaystyle \sum}_{tt=1}^{tt=t+{l}_{v}}{\widehat{c}}_{v}{q}_{i}{\left(1-{d}_{o}\right)}^{1\times \left(tt=2\right)}{\left(1-d\right)}^{tt\times (tt>2)}$ $\underset{{\tau}_{i}}{\mathrm{max}}{\eta}_{"\mathrm{fit}"it}=-{x}_{vt}-{g}_{it}{\widehat{c}}_{v}+{\displaystyle \sum}_{tt=1}^{tt=t+{l}_{v}}\left(\frac{-{\overline{x}}_{vt}{\widehat{c}}_{v}-\left({n}_{it}-{\tau}_{i}{\epsilon}_{it}\right){p}_{itt}+{\epsilon}_{it}\left(1-{\tau}_{i}\right)\left\{{z}_{"\mathrm{fit}"vt}\times \left(tt\le k\left(t\right)\right)+{m}_{itt}\left(ttk\left(t\right)\right)\right\}}{{\left(1+{\overline{i}}_{i}\right)}^{tt}}\right)$ $\underset{{\tau}_{i}}{\mathrm{max}}{\eta}_{"\mathrm{sub}"it}=-{x}_{vt}+{z}_{"\mathrm{sub}"vt}-{g}_{it}{\widehat{c}}_{v}+{\displaystyle \sum}_{tt=1}^{tt=t+{l}_{v}}\left(\frac{-{\overline{x}}_{vt}{\widehat{c}}_{v}-\left({n}_{it}-{\tau}_{i}{\epsilon}_{it}\right){p}_{itt}+{\epsilon}_{it}\left(1-{\tau}_{i}\right){m}_{itt}}{{\left(1+{\overline{i}}_{i}\right)}^{tt}}\right)$ s.t $0\le {\tau}_{i}\le 1$ ${\pi}_{it}=\mathrm{max}\left({\eta}_{"\mathrm{fit}"it},{\eta}_{"\mathrm{sub}"it}\right)$ ${\delta}_{it}:=\{ttsuchthat{\pi}_{itt}=0)$ Next $v$ ${\psi}_{"\mathrm{f}"it}=\frac{\mathrm{exp}\left(-{\delta}_{it}+{\beta}_{"\mathrm{f}"t})/{\mu}_{"\mathrm{f}"t}\right)}{1+\mathrm{exp}\left(-{\delta}_{it}+{\beta}_{"\mathrm{f}"t})/{\mu}_{"\mathrm{f}"t}\right)}$, ${\psi}_{"\mathrm{e}"it}=\frac{\mathrm{exp}\left({\epsilon}_{it}-{\beta}_{"\mathrm{e}"t})/{\mu}_{"\mathrm{e}"t}\right)}{1+\mathrm{exp}\left({\epsilon}_{it}-{\beta}_{"\mathrm{e}"t})/{\mu}_{"\mathrm{e}"t}\right)}$, ${\psi}_{"\mathrm{i}"it}=\frac{\mathrm{exp}\left({y}_{it}-{\beta}_{"\mathrm{i}"t})/{\mu}_{"\mathrm{i}"t}\right)}{1+\mathrm{exp}\left({y}_{it}-{\beta}_{"\mathrm{i}"t})/{\mu}_{"\mathrm{i}"t}\right)}$, ${\psi}_{"\mathrm{s}"it}=\frac{\mathrm{exp}\left({\tilde{\lambda}}_{it}-{\beta}_{"\mathrm{s}"t}{\overline{\lambda}}_{it})/{\mu}_{"\mathrm{s}"t}\right)}{1+\mathrm{exp}\left({\tilde{\lambda}}_{it}-{\beta}_{"\mathrm{s}"t}{\overline{\lambda}}_{it})/{\mu}_{"\mathrm{s}"t}\right)}$ ${\varpi}_{it}={\displaystyle \sum}_{u,s}{\overline{s}}_{is}{w}_{ust}{\psi}_{uit}$ ${\omega}_{it}=1\times \left({\varpi}_{it}>{\displaystyle \sum}_{s}\left({\overline{s}}_{is}{\xi}_{s}\right)\right)$ Next $i$ Next $t$ |

Partial Utility | Shape Parameter μ | Tipping Point Parameter β | Comment |
---|---|---|---|

Financial | 2.7 | 13 | The parameter $\beta $ corresponds to the middle of the lifetime of solar PV systems |

Environmental | 50 | 650 | The parameter $\mu $ equals to the 1/13 of the lifetime electricity production of a 7 kWp reference system; the parameter $\beta $ equals to the lifetime production of a 7 kWp reference system |

Income | 10000 | Calculated during the simulation | The parameter $\beta $ is calculated in each simulation step as the average income of all agents existing in year $t$ |

Social Network | 2.8 | 0.5 | The parameter $\beta $ implies that the tipping point of 50% is reached when half of the links of the agent is with adopters |

^{®}categories.

**Table A12.**Calibrated weights of each partial utility and decision threshold per Sinus-Milieus

^{®}category.

Sinus-Milieus^{®} Category | Weight Financial Utility | Weight Environmental Utility | Weight Income Utility | Weight Social Network Utility |
---|---|---|---|---|

1 | 0.2576 | 0.2633 | 0.1924 | 0.2868 |

2 | 0.2319 | 0.2705 | 0.2180 | 0.2796 |

3 | 0.2422 | 0.2656 | 0.2218 | 0.2704 |

4 | 0.2642 | 0.2762 | 0.1929 | 0.2667 |

5 | 0.2520 | 0.2699 | 0.2045 | 0.2735 |

6 | 0.2515 | 0.2711 | 0.2085 | 0.2689 |

7 | 0.2537 | 0.2720 | 0.2053 | 0.2690 |

8 | 0.1750 | 0.2492 | 0.2326 | 0.3433 |

9 | 0.1737 | 0.2477 | 0.2337 | 0.3449 |

10 | 0.1746 | 0.2460 | 0.2304 | 0.3490 |

**Figure A5.**Comparison of the model results and actual statistics during the calibration and validation period of 2010–2017, regarding annual adopters (

**left**) and annual installed capacity (

**right**); the year of 2009 is not shown here, because it represents the initial conditions to start the simulation (i.e., both the adopters and the installed capacities are exogenously given to the model).

^{®}categories is about 0.23 (see also Table A12), it turns out that the short-term sensitivity of the decision mechanism to intense policy changes is about 5%.

**Figure A6.**Estimated elasticity of the financial partial utility to the policy intensity. The table on the left (

**a**) presents the estimated output, while the figure on the right (

**b**) presents the actual, fitted, and residual plots. A tipping point is visible, in which an abrupt change in the financial utility takes place when the policy intensity exceeds a threshold (the threshold depends on the investment costs and electricity prices).

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**Figure 3.**Annual sales (right axis), the cumulative installed capacity of solar PV in single- and two-family houses and comparison with the total cumulative installed capacity of solar PV (left axis) in Switzerland (own illustration based on [6]).

**Figure 5.**Population of agents (i.e., evolution of single- and two-family houses in Switzerland) per Sinus-Milieus

^{®}category; for a mapping to the IDs reported in the figure to the Sinus-Milieus

^{®}category, please see Table 1.

**Figure 6.**Annual rate of adoption (

**a**), cumulative adopters (

**b**), cumulative capacity (

**c**) and average installed capacity per adopter (

**d**) in the “Reference” scenario.

**Figure 7.**Cumulative adopters (

**a**) and annual adopters (

**b**) per Sinus-Milieus

^{®}category; for a mapping to the IDs reported in the figure to the Sinus-Milieus

^{®}category, please see Table 1.

**Figure 8.**Share of the partial utilities in the total utility function of agents that invested in a solar PV system (average across all adopters).

**Figure 9.**Geographical distribution of adopters; (

**a**) number of adopters per Canton; (

**b**) the percentage of adopters in total agents.

**Figure 10.**Overview of the installed solar PV capacity in single-family houses by 2050 (MW), according to different policy schemes, electricity price levels, specific investment cost, and discount rates, compared to the “Reference” scenario (dotted line).

**Table 1.**Mapping of IDs used in the model to Sinus-Milieus

^{®}category and classification of Sinus-Milieus

^{®}categories to the different types of adopters.

Model ID | Sinus-Milieus^{®} Category | Classification to Adopter Type |
---|---|---|

1 | Traditional | Late Majority, Laggards |

2 | Consumer-Materialists | Late Majority |

3 | Sensation-Oriented | Late Majority |

4 | Established | Late Majority, Early Majority |

5 | Modern Mainstreams | Early Majority |

6 | Adaptive Navigators | Early Majority |

7 | Cosmopolitan | Early Majority, Early Adopters |

8 | Liberal Intellectuals | Early Adopters |

9 | Social Ecologicals | Early Adopters |

10 | Performers | Early Adopters, Innovators |

Assumption | 2035 | 2050 | Source/Comment |
---|---|---|---|

Average household size | 2.01 | 1.97 | Assumption in the Swiss Energy Strategy scenarios [44] |

Electricity consumption per capita | –13% from 2000 levels | –18% from 2000 levels | Targets from the “Neue Energiepolitik” (NEP) scenario of the Swiss Energy Strategy [2,44] |

Average electricity price (Rp./kWh) | 32.1 | 33.6 | Estimations from the NEP scenario; the prices vary per Canton based on [80] |

Solar PV investment cost (CHF/kWp) | 1500–2600 | 1300–2000 | Overnight investment costs for sizes 1 –30 kWp from [3] |

Average discount rate (%) | 5.5 | 5.5 | Discount rates are from the NEP scenario and vary with agents’ income |

Feed-in tariff | - | - | Phase out from 2022 [2] |

Capital subsidy | - | - | Phase out from 2030 [2] |

Surcharge (Rp./kWh) | 2.3 | 2.3 | For the promotion of renewable electricity [2] |

Building efficiency or emission standards | Not included | Not included | Inclusion of building standards, which are part of the Swiss energy strategy and the revised CO_{2} Act, would have influenced the results of this study |

Building self-energy supply standards | Not included | Not included | |

Market configuration | Average cost | Average cost | Excess electricity can be sold at the average production cost of a utility |

Sensitivity Focus on | Variant Name | Variant Definition (Regarding the Reference Scenario) |
---|---|---|

Solar PV learning rates | High Cost | +20% investment cost in 2030 |

Low Cost | –20% investment cost in 2030 | |

Policy support schemes | Stronger Policy | +10 years continuation of the policy support |

Weaker Policy | –5 years in policy support (earlier phase-out) | |

Electricity price | Higher Price | +10% electricity prices until 2050 |

Lower Price | –10% electricity prices until 2050 | |

Cost of capital | High DRate | 12.5% discount rate on average across all agents |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Panos, E.; Margelou, S. Long-Term Solar Photovoltaics Penetration in Single- and Two-Family Houses in Switzerland. *Energies* **2019**, *12*, 2460.
https://doi.org/10.3390/en12132460

**AMA Style**

Panos E, Margelou S. Long-Term Solar Photovoltaics Penetration in Single- and Two-Family Houses in Switzerland. *Energies*. 2019; 12(13):2460.
https://doi.org/10.3390/en12132460

**Chicago/Turabian Style**

Panos, Evangelos, and Stavroula Margelou. 2019. "Long-Term Solar Photovoltaics Penetration in Single- and Two-Family Houses in Switzerland" *Energies* 12, no. 13: 2460.
https://doi.org/10.3390/en12132460