PV Sizing and Investment Support Tool for Household Installations: A Case Study for Croatia

Abstract

In the wake of the green energy transition, the European Union is using solar energy as its focal point. Different supporting development schemes aim to bring energy closer to the hands of the citizens. In various European countries, the integration of solar energy in households has made significant steps forward, but in Croatia, the process has been lagging, with just humble results of installed rooftop solar capacity being integrated in recent years. The uptake of this process is happening, and it is important to facilitate the process to make it more efficient. In this regard, there are two main aspects covered in this paper. The first deals with the problem by disseminating the statistics and findings of the online tool accessible to the public, which aims to widely promote the integration of solar using the provision of precise and on-the-spot information for all interested citizens. The second aspect deals with the simulation segment, aiming to provide deeper insights into the solar integration process and its legal and administrative framework based on the insights gathered from the PV sizing optimization tool expanded with additional multi-scenario simulation analysis.

1. Introduction

In recent years, the European Union has witnessed a remarkable surge in the adoption of solar photovoltaic (PV) systems driven by ambitious renewable energy targets and a growing awareness of the need to transition towards cleaner, more sustainable, and independent energy sources. Alongside this momentum, the concept of self-consumption has emerged as a key focus within the solar PV sector. Self-consumption refers to the utilization of locally generated solar energy for on-site consumption, thereby reducing reliance on the conventional grid and further promoting energy independence. As the European Union aims to accelerate the deployment of solar PV systems, understanding the drivers, challenges, and potential benefits of self-consumption becomes crucial for policymakers, industry stakeholders, and citizens turning into prosumers. This research article aims to delve into the specifics of self-consumption in the context of solar PV in Croatia, examining its current status, exploring regulatory frameworks, and assessing the economic and environmental implications within the broader energy landscape.

Since the legislation framework update, there has been a growing interest and clear economic incentive for end consumers to come together and engage in energy sharing. This trend has been particularly pronounced in the European Union, driven by the introduction of the legislative package “Clean Energy for all Europeans” [1] and the directives focusing on renewable energy communities (RECs) [2] and citizen energy communities (CECs) [3]. Broadly speaking, energy sharing among prosumers can be facilitated through bilateral agreements, community-based models, or a combination of both approaches. The authors in [4] considered household prosumers using wind and solar PV with battery systems according to the Portuguese legal framework. As stated in the paper, the current Portuguese legal context allows for electricity generation for the prosumer’s self-consumption, where the excess electricity injected into the LV grid is remunerated with 90% of the average monthly closing price of the Iberian Energy Market Operator (OMIE). The authors in [5], among other specifics, deal with the topic of self-consumption with energy surplus (up to 100 kW), according to the new regulation of renewable self-production in Spain. As stated in the mentioned paper, at the end of the billing period, which is one month, the excess energy is compensated in the prosumer’s invoice, where the invoice cannot be negative. The price at which the hourly excess energy is valued is either agreed upon between the supplier and the prosumer (if the supply contract with a free dealer is available) or is set as the average hourly price from the day-ahead and intraday markets (if the voluntary supply contract for the small consumer with a reference dealer is available) reduced by the balancing cost (lower price than the purchased energy). The authors in [6] expanded the research on self-consumption in Spain based on France, Germany, Italy, Great Britain, and Finland and described the technical specifics and differences. Furthermore, as stated in [7], the Italian legal framework implemented the prices for self-consumed electricity with the values of 100 EUR/MWh and 110 EUR/MWh for the collective self-consumption (CSC) and RECs, respectively. The incentive is contracted for 20 years, and the system output must not exceed 200 kW.

While the integration of renewable energy sources has been recognized as a driving measure of energy transition and alleviation of some of the energy crisis aspects, the whole context needs to be addressed more widely. This is specifically important when observing the motivation for and obstacles to household solar integration. The most important aspect is usually the household income [8], but the overall picture is more complex [9,10]. Also, to avoid potential rebound and negative effects [11], the whole legislation and support scheme needs to be thoughtfully set. Therefore, the value of research, such as the one presented in this paper, can be found in the provision of insights and guidelines for a better understanding of the different effects of pricing and incentive schemes.

Nevertheless, the simultaneous ambition of the EU to achieve complete climate neutrality by 2050 while reducing certain aspects of social inequalities, such as energy poverty, remains a high-priority objective formalized within its legislative framework, inherently promoting the low-carbon transition in the EU and its member states. A holistic approach to tackling this problem is shown in this paper, which highlights two contributions. The first is the overview of the problem via the dissemination of the statistics for the Croatian case and findings of the online simulation tool for the PV system sizing accessible to the public, which aims to widely promote solar integration using the provision of precise and on-the-spot information for all interested citizens. The second aspect deals with the simulation segment, aiming to provide deeper insights into the solar integration process and its legal and administrative framework based on the insights gathered from the optimization tool expanded with additional multi-scenario simulation analysis regarding different financial aspects.

The paper is structured as follows: Section 2 discusses the current status of PV solar development in Croatia via the visualization of different energy data; Section 3 describes the statistics from the dataset gathered from the PV optimization tool aimed at being used by the general public to support the solar integration process uptake; Section 4 provides further insight into the current options and legislation framework via the simulation results for different options and results analysis; Section 5 concludes the paper and provides possible future research directions.

2. Current Status of Energy Transition Process in Croatia—Households’ Point of View

The current status of overall energy usage in Croatia can be presented from two different perspectives.

From the total energy consumption and usage perspective, there is a significant reliance on biomass and fossil fuels, with approximately more than half of the total energy consumption being supplied from the sources listed in the table below (

Table 1. The sources of primary energy consumption in Croatia in 2021.

Fuel Energy Source by Types	Percentage of Total Energy Supply [%]
Fuel wood	33.2
Crude oil	12.0
Natural gas	12.3
Hydropower	29.8
Heat sources	0.3
Renewable energy sources	12.4

) [12]. It should be noted that in the energy statistics of Croatia, due to the inherited nature of our energy mix, nuclear energy is not listed. This is due to the fact that Croatia shares 50% of the nuclear power plant Krško (NPP Krško), which is located in the neighboring county of Slovenia. Therefore, Table 1 shows the energy resources in Croatia, while

Table 2. Electricity production shares of different energy sources in Croatia’s energy mix.

Year	Share in Electricity Production [%]
	Geothermal	Solar	Wind	DG *	Hydro	Exchange	Thermo	Nuclear
2018	0.0%	0.4%	7.2%	3.2%	40.7%	14.2%	19.1%	14.7%
2019	0.4%	0.4%	7.9%	4.2%	31.0%	18.4%	22.0%	14.9%
2020	0.4%	0.4%	9.8%	4.9%	31.7%	9.4%	25.3%	17.1%
2021	0.4%	0.4%	11.1%	5.2%	38.0%	23.4%	23.4%	14.6%
2022	0.3%	0.5%	12.5%	5.4%	28.9%	26.4%	26.4%	14.4%

* Distributed generation from renewable sources—biomass, biogas, and CHP.

shows the energy mix of the Croatian electricity sector, which includes the production of NPP Krško as well as the “local” Croatian power plants, hydro, thermal, and renewables.

From the other perspective, the electricity sector in Croatia is highly renewable primarily due to the fact that the system has a large share of hydropower in its energy mix. Out of a total of 5600 MW of the installed capacity, hydro represents 2126 MW, thermo represents 2019 MW, wind represents almost 980 MW, solar capacity represents 250 MW and the rest are other distributed generation sources. The total gross electricity consumption in recent years ranges around 18 TWh with peaks around 3000 MW. The Croatian transmission system operator (TSO) HOPS [13,14], distribution system operator (DSO) HEP-ODS [15,16], and the national utility company HEP Ltd., Zagreb, Croatia [17] data show that the total electricity consumption in Croatia was in a large share of renewable energy but also show very low success of solar integration since most of the RES production increase is due to wind integration (Table 2). The underlying conclusion that can be drawn in comparison to the total energy usage from Table 1 is that Croatia still significantly depends on non-renewable energy sources when observed from the total energy perspective. On the other hand, when observing only electricity production, the status is significantly more renewable due to the large hydropower fleet, but at the same time, Table 2 shows really low numbers for solar integration. This indicates that energy transition should increase and the process of wider solar integration should be implemented.

Despite the significant solar potential and high interest of developers [18], wider solar integration has not occurred in recent years due to multiple reasons. Some of the reasoning can be found in low electricity prices, which are among the lowest in the EU, and in legislative barriers, which are very severe in the Croatian legislation framework [19].

Adapting the data from [20], the installed capacity of photovoltaic power plants per capita in the EU countries shows that Croatia is many times less successful than countries with much fewer solar hours and less insolation potential (Figure 1). This encourages questioning of the current investment policies and incentives but also requires a wider perspective observation.

The presented data show great potential for further increasing renewable electricity usage and transitioning it to the transport and heating sectors. But this needs to be strengthened by the more inclusive position of individuals and households that strongly relate to the wider integration of solar energy in Croatia, highlighting household solar installations. Here, it is important to mention one difference that can be overlooked when observing the statistics and the data presented earlier. The main advantage of solar production close to consumption is precisely the provision of self-supply. When assessing the total power generated from solar energy, most of it is consumed in the same location, with only approximately 30% of this electricity being returned to the grid and observed in the total energy gross production, as shown in Table 2. These data can be found in the distribution system operator reports; for now, this includes all the solar power generation in Croatia [16] since, momentarily in mid-2023, there are no transmission-level solar power plants connected to the grid. Figure 2 shows the total distribution-level solar capacity. This is going to change in the coming years, but this specific process is not directly within the scope of this paper, which focuses on household-level solar energy. When observing the short-term horizon (up to 2026) or long-term horizon (up to 2050), the prediction can be found in different government strategic documents. The prediction of the growth rate for such a long-time horizon is a complex problem with a lot of value, but this paper tried to set the background of the current status and shows the statistics for 2022 by presenting all the information gathered in a single table. When providing the projections of other relevant institutions, such as the national strategic document of the Republic of Croatia with its accelerated energy transition scenario taken from the energy development strategy of the Republic of Croatia until 2030 with a view to 2050 [21] and Scenario SN as a climate neutral scenario from the report on climate neutral scenario of the Republic of Croatia NCEP [22], it can be seen that in 2030, around 1.5 GW of solar is anticipated to be in the system.

In the Croatian regulatory framework, the prosumers participate in two main financial models: net-metering (“samoopskrba” in Croatian language legislation) and net-billing (“krajnji kupac s vlastitom proizvodnjom” in Croatian language legislation). Net-metering represents a financial model under which the excess electricity exported to the power grid can be used later when the demand is higher than the on-site production. Prosumers in this model use the power grid as an export option for their excess production. The net-billing model, on the other hand, represents a model in which the two electricity costs, import and export, are separated. The prosumers then pay for the imported electricity and are remunerated at a lower export price for the exported electricity. More discussion on this is presented in Section 4 using simulation results, but for a wider understanding, it is also important to observe the current situation and some of the motivations and drivers for the changes pending in the Croatian market.

First, when observing the available data, there are some conclusions that can be drawn regarding the status of the development. The current number of installed solar summarizes the current status in mid-2023 as follows:

• The total number of PV solar power plants is 9170;
• The total power of all PV solar plants is 280 MW;
• From the total number, around 4100 installations (≈45%) are in the net-metering scheme with ≈25 MW capacity representing only ≈9% of the total power.

The data presented in the figures below (Figure 3 and Figure 4) were obtained from Croatian DSO and combined with OpenStreetMap settlement data [23] in QGIS, version 3.14 [24]. All solar installations, as mentioned before, are connected to the DSO network since no solar power is connected to the TSO network. Every user with a power generation system connected to a distribution network has attributes describing their energy sources (solar, wind, biogas, etc.), connection power, metering/billing type, connection voltage level, DSO area code, and postal code address. The postal code and area code were matched with settlement names that were previously associated with the DSO distribution area division to distinguish the places from different areas sharing the same identification. The presented data are the total PV generation capacities grouped for each settlement in Croatia. This is further divided into two aspects: the first covers all medium-voltage and low-voltage PV connections (Figure 3), whereas the second shows only the household-level low-voltage connection under the PV-generation net-metering model.

From the figures, it can be observed that despite the solar potential being greater in the coastal region, which will be represented by the Split data in the following sections, the realization of solar installations is not strictly dependent on this, and there are comparatively more household installations in the continental parts of Croatia. This also shows that personal motivation plays an important role in this process; hence, this stresses the importance of providing precise and easy-to-understand information to the general public even more. The same trend can be observed when all the solar installations are considered (Figure 3) since the continental regions show a greater density of solar installations on industrial customers who currently hold the majority of the total number of solar installations in Croatia. Also, as it can be seen, currently there are several larger solar power plants in operation with a capacity of 1 MW and greater, and they correspond with the larger yellow grouping circles (Figure 3). This trend is changing in the coming years, but this is a separate process since investing in several MW projects requires somewhat different prerequisites to be met compared to household solar. Nevertheless, both processes converge into a single goal of achieving an efficient green transition.

3. PV Sizing Optimization Tool—Statistics and Gathered Datasets

Although the research was performed under the METAR project [25], some further insights into the status and potential interest for further development of household solar can be observed.

What is significant for the future observation of differences and the expected number of installations of small rooftop solar power plants is the data obtained using the solar calculator [26], an online optimization tool made for the assessment and optimization of rooftop solar power plants with the maximization of self-consumption share under the net-metering model [27]. This tool intends to ease the decision-making process of rooftop solar installation.

The data include cleaned inputs of the unique and complete entries from different individuals and citizens of different Croatian regions. The total number of unique location dataset entries is 11,143 and includes the basic consumption data in high (hours 06 to 22) and low tariffs (hours 22 to 06), angle, and the orientation of the rooftop. For the self-consumption optimization process, location, consumption, and rooftop configuration are significant parameters, and their distribution is shown in the table below (

Table 3. Solar calculator significant input parameters for the observed dataset.

Parameter/ Indicator	Angle [°]	Orientation [North to South]	High-Tariff Annual Consumption [kWh]	Low-Tariff Annual Consumption [kWh]
count	11,143	11,143	11,143	11,143
mean	25.8	South—5915 entries out of 11,143	4547	2362
std	13.1	--	2588	2141
min	0	north	1500	500
max	75	south	10,000	10,000

). The data were gathered throughout the course of approximately 12 months from 2022 to 2023.

Furthermore, when inspecting the relevance of the data, a significant number of citizens completed the informative process and made an effort to input all the data required. It can be seen that despite the spread being noticeable, the majority of the houses have a good orientation towards the south with a favorable angle. The majority of entries, roughly 50% of the total entries, are related to the data of a home with a southern rooftop orientation with an approximate roof angle of 30 degrees, which represents good prerequisites for the installation (Figure 5).

Figure 6 shows an interesting socio-economic trend where citizens aiming to install solar in average households with an average annual consumption ranging from 6500 to 7000 kWh, whereas an average Croatian household uses 3500–4000 kWh annually. Basically, the average household consumption that is observed is higher than the average assumed household consumption in Croatia [28], which is around 4000 kWh, indicating that the people interested in solar investment are also using more energy on average, meaning that this additional solar production could have higher benefits from the energy perspective but will have smaller benefits regarding the energy poverty aspects in the first stages of rooftop solar proliferation. On a side note, this could lead to the conclusion that further work needs to be invested into providing an efficient framework for supporting the integration of solar for all members of the community.

The regional differences are again observable from the available solar resource, which benefits the coastal regions. This trend is visible through a number of higher power potential installations in these regions and lower output power in the continental regions (Figure 7). This figure shows that the average annual production of coastal regions is grouped “higher” in the area with larger annual productions circled for Split coastal area in comparison to continental Zagreb areas. For example, the Split coastal region, highlighted with orange shapes, shows an average tendency to have an installation in the “upper” regions of the 3D graph showing the average higher installed capacity. On the other hand, the continental Zagreb region highlighted in blue tends to have installed capacities grouped closer to the “middle” region of the plot.

4. Multiple Scenario Comparisons of Solar PV Financial Models for Households

This section presents the comparison between the solar PV financial models of different households, both current and possible future ones, from the perspective of the single prosumer. The main motivation is to examine the socio-economic and legal aspects, as well as the household solar potential and sustainability in the form of multiple scenario analysis. The main methodology for the online PV sizing tool, whose statistics have been presented in the previous section, is explained in [27]. The main limitations in the simulation analysis are the variabilities on the production and consumption side. These annual variabilities have been considered and analyzed in [27] and are out of scope for this paper. The methodology for the simulation analysis consists of expressing the electricity costs for all financial models (according to the Croatian legal framework) and calculating them for each possible scenario using the assumptions and parameters described in the following section. The electricity consumption dataset was obtained in cooperation with Croatian electricity suppliers and the solar PV production dataset was obtained from PVGIS [29]. The sensitivity analysis was conducted according to the following types:

• electricity consumption profiles with L1 normalized values shown in the figure below (Figure 8):

  ○

  higher during summer ≈+S;

  ○

  higher during winter ≈+W;

  ○

  approximately equal ≈E.

• tariff models:

  ○

  one-tariff (1T);

  ○

  two-tariff (2T), where the 2T model is divided into high-tariff (HT) and low-tariff (LT).

• geographical locations: Zagreb (ZG—northern/continental Croatia) or Split (ST—southern/coastal Croatia).

The variable input parameter is the total yearly electricity consumption ranging from 1000 kWh to 20,000 kWh with an increased step of 250 kWh, totaling 77 scenarios. The installed PV power ranges from 0.5 kW to 20 kW with an increased step of 0.25 kW, resulting in 79 scenarios. These 77 and 79 scenarios are simulated throughout the three types of the mentioned consumption profiles, two-tariff models, and two geographical locations, returning a total number of 72,996 scenarios that were put under three different production pricing financial models. The timestep used in the simulations is 1 h since this was the lowest available timestep provided by the PVGIS. The input data are presented in the table below (

Table 4. Input data parameters for the PV production simulations.

Description	Abbreviation	Value	Unit
Total electricity prices per tariffs	${\mathsf{\pi }}_{(\mathrm{z}=\mathrm{H}\mathrm{T})}^{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$, ${\mathsf{\pi }}_{(\mathrm{z}=\mathrm{L}\mathrm{T})}^{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}, {\mathsf{\pi }}_{(\mathrm{z}=1\mathrm{T})}^{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$	0.163, 0.087, 0.146	EUR/kWh
Electrical energy prices per tariffs	${\mathsf{\pi }}_{(\mathrm{z}=\mathrm{H}\mathrm{T})}^{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}$, ${\mathsf{\pi }}_{(\mathrm{z}=\mathrm{L}\mathrm{T})}^{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}, {\mathsf{\pi }}_{(\mathrm{z}=1\mathrm{T})}^{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}$	0.0748, 0.037, 0.070	EUR/kWh
Solar PV-specific investment costs	$\mathrm{P}{\mathrm{V}}^{{\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}}_{\mathrm{i}\mathrm{n}\mathrm{v}}}$	1350	EUR/kW
Solar PV lifetime	$\mathrm{P}{\mathrm{V}}^{\mathrm{l}\mathrm{i}\mathrm{f}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}$	30	years
Solar PV fixed orientation	-	South	-
Solar PV fixed incline angle	-	35	°
Solar PV system losses	-	10	%
(Lat, Lon) for Zagreb/Split	-	(45.816, 15.998)/(43.512, 16.440)	decimal °

).

There are three main solar PV financial models for households used in the previously mentioned scenarios. Two active models for the prosumers are the current version of the net-metering model and the net-billing model, henceforth referred to as NM (net-metering) and NB (net-billing) models. The remaining model is an updated version of the current net-metering model, henceforth referred to as the NM+ model. For these different financial models, the total costs associated with the installation and operation of household solar are simulated. All financial models are simulated in order to conduct a comparative analysis of various PV integration strategies.

The simulated household’s annual electricity costs before the installation of solar PV (${\mathrm{C}}^{{\mathrm{b}\mathrm{e}\mathrm{f}}_{\mathrm{a}\mathrm{n}\mathrm{n}}}$) are calculated as follows shown by Equation (1):

$${\mathrm{C}}^{{\mathrm{b}\mathrm{e}\mathrm{f}}_{\mathrm{a}\mathrm{n}\mathrm{n}}}={{\displaystyle \sum }}_{\mathrm{z}}{\sum }_{\mathrm{t}}{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}\times {\mathsf{\pi }}_{\left(\mathrm{z}\right)}^{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\times {\mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}\times ∆\mathrm{t}$$

(1)

where ${\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}$ represents the electricity consumption (kWh/h), $∆\mathrm{t}$ represents the timestep (1 h), ${\mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}$ represents the binary matrix for z throughout t, z represents the tariff type (1T, HT, and LT), and t is the timestep of the simulation. Binary matrix (${\mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}$) is expressed as visible in Equation (2) (Binary values of 1 are between 7 and 21 h during winter and 8 and 22 h during summer, and binary values of 0 are active for the remaining hours):

$${\mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}=\left\{\begin{array}{c}\mathrm{k}=2\mathrm{T} \left\{\begin{array}{c}\left[\mathrm{0,1}\right], \mathrm{i}\mathrm{f} \mathrm{z}=\mathrm{H}\mathrm{T}\\ 1-{\mathrm{X}}_{\left(\mathrm{z}=\mathrm{H}\mathrm{T},\mathrm{t}\right)}^{\mathrm{b}\mathrm{i}\mathrm{n}}, \mathrm{i}\mathrm{f} \mathrm{z}=\mathrm{L}\mathrm{T} \\ 0, \mathrm{i}\mathrm{f} \mathrm{z}=1\mathrm{T}\end{array}\right.\\ \mathrm{k}=1\mathrm{T} \left\{\begin{array}{c}0, \mathrm{i}\mathrm{f} \mathrm{z}=\mathrm{H}\mathrm{T} \\ 0, \mathrm{i}\mathrm{f} \mathrm{z}=\mathrm{L}\mathrm{T} \\ 1, \mathrm{i}\mathrm{f} \mathrm{z}=1\mathrm{T} \end{array}\right.\end{array}\right.$$

(2)

where k represents the tariff model (1T or 2T), of which only one is active per scenario. Solar PV investment costs (${\mathrm{C}}^{\mathrm{i}\mathrm{n}\mathrm{v}}$) are calculated as follows using Equation (3).

$${\mathrm{C}}^{\mathrm{i}\mathrm{n}\mathrm{v}}=\mathrm{P}{\mathrm{V}}^{\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}}\times \mathrm{P}{\mathrm{V}}^{{\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}}_{\mathrm{i}\mathrm{n}\mathrm{v}}}$$

(3)

where $\mathrm{P}{\mathrm{V}}^{\mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}}$ (kW) represents the nominal installed PV power. Annual costs (EUR/year) of the electricity after the installation of PV in a specific model (${\mathrm{C}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}^{\mathrm{a}\mathrm{n}\mathrm{n}}$) are expressed as the sum of monthly costs, if it is not specified otherwise:

$${\mathrm{C}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}^{\mathrm{a}\mathrm{n}\mathrm{n}}={\sum }_{\mathrm{m}}{\mathrm{C}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l},\mathrm{m}\right)}$$

(4)

Simple financial indicators, such as annual savings (${\mathrm{S}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}^{\mathrm{a}\mathrm{n}\mathrm{n}}$) in EUR/year, are represented by Equation (5), a simple payback period (${\mathrm{S}\mathrm{P}\mathrm{P}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}$) in years is represented by Equation (6), and a simple net-present value (${\mathrm{S}\mathrm{N}\mathrm{P}\mathrm{V}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}$) in EUR is represented by Equation (7).

$${\mathrm{S}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}^{\mathrm{a}\mathrm{n}\mathrm{n}}={\mathrm{C}}^{{\mathrm{b}\mathrm{e}\mathrm{f}}_{\mathrm{a}\mathrm{n}\mathrm{n}}}-{\mathrm{C}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}^{\mathrm{a}\mathrm{n}\mathrm{n}} [\mathrm{E}\mathrm{U}\mathrm{R}/\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}]$$

(5)

$${\mathrm{S}\mathrm{P}\mathrm{P}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}=\frac{{\mathrm{C}}^{\mathrm{i}\mathrm{n}\mathrm{v}}}{{\mathrm{S}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}^{\mathrm{a}\mathrm{n}\mathrm{n}}}[\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}]$$

(6)

$${\mathrm{S}\mathrm{N}\mathrm{P}\mathrm{V}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}={\mathrm{S}}_{\left(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\right)}^{\mathrm{a}\mathrm{n}\mathrm{n}}\times \mathrm{P}{\mathrm{V}}^{\mathrm{l}\mathrm{i}\mathrm{f}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}-{\mathrm{C}}^{\mathrm{i}\mathrm{n}\mathrm{v}} \left[\mathrm{E}\mathrm{U}\mathrm{R}\right]$$

(7)

In the above equations for the financial indicators, the model represents the observed financial model (NM, NB, and NM+).

4.1. Current Net-Metering Model (NM)

The current version of the net-metering model, as well as the technical specifics regarding the installation of the PV and connection to the grid, are described in [30], as mentioned in the introduction. The NM model represents the main solar PV financial model for the prosumers of the household category. According to the current regulations, if the prosumer in the previous year exported more electricity compared to the imported amount from the grid, which occurs if, for example, the solar PV is oversized, the financial model for the current year switches to the NB model, which is far less profitable. This condition where the exported electricity is greater than imported electricity on an annual basis is from here on referred to as the main annual condition.

Monthly electricity costs (EUR/month) after the installation of PV in the NM model are calculated using Equation (8):

$${\mathrm{C}}_{(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}=\mathrm{N}\mathrm{M},\mathrm{m})}=\left\{\begin{array}{c}{\displaystyle {\displaystyle \sum }_{\mathrm{z}}}\left({\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)} }^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}\left({\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}-{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}\right)\times ∆\mathrm{t}\times {\mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}\right)\times {\mathsf{\pi }}_{\left(\mathrm{z}\right)}^{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}, \mathrm{i}\mathrm{f} {\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)}}^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}\left({\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}-{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}\right)\times ∆\mathrm{t}\ge 0\\ {\displaystyle {\displaystyle \sum }_{\mathrm{z}}}\left({\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)} }^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}\left({\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}-{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}\right)\times ∆\mathrm{t}\times {\mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}\right)\times {0.8\times \mathsf{\pi }}_{\left(\mathrm{z}\right)}^{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}, \mathrm{e}\mathrm{l}\mathrm{s}\mathrm{e}\end{array}\right.$$

(8)

where ${\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}$ represents the electricity production from solar PV (kWh/h) and ${{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)}$ and ${{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}$ represent the start and end timesteps in a specific month m. In simple words, if the electricity consumption in a specific month is greater than an on-site generation, the prosumer pays only for the net consumed energy and, if there is a surplus in generation, the prosumer is remunerated for the net overgeneration according to the set prices under the NM model.

4.2. The Net-Billing Model (NB)

The net-billing model is also described in [30] and is currently the model to which the prosumer is switched if the main annual condition is true. NB model is currently also a solar PV financial model for the prosumers of the business category and not the household category. The business category prosumers do not have the option to participate in the NM model. NB model is implemented on a 15 min resolution; however, due to the limitations of obtaining the 15 min PV data, the NB model in this research is implemented on a 1 h resolution.

For an easier understanding of this model, some auxiliary variables are introduced, such as the hourly import (${\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{i}\mathrm{m}\mathrm{p}}$) and export (${\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{e}\mathrm{x}\mathrm{p}}$) of the electricity described by Equations (9) and (10), respectively.

$${\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{i}\mathrm{m}\mathrm{p}}=\left\{\begin{array}{c}\left({\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}-{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}\right)\times ∆\mathrm{t}, \mathrm{i}\mathrm{f} \left({\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}-{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}\right)\times ∆\mathrm{t}\ge 0\\ 0, \mathrm{e}\mathrm{l}\mathrm{s}\mathrm{e}\end{array}\right.$$

(9)

$${\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{e}\mathrm{x}\mathrm{p}}=\left\{\begin{array}{c}\left({\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}-{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}\right)\times ∆\mathrm{t}, \mathrm{i}\mathrm{f} \left({\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}-{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}\right)\times ∆\mathrm{t}<0\\ 0, \mathrm{e}\mathrm{l}\mathrm{s}\mathrm{e}\end{array}\right.$$

(10)

Monthly redemption price (${\mathsf{\pi }}_{(\mathrm{k},\mathrm{m})}^{\mathrm{e}\mathrm{x}\mathrm{p}}$) (EUR/month) for the exported electricity in a specific month and a specific tariff model is calculated using Equation (11):

$${\mathsf{\pi }}_{\left(\mathrm{m}\right)}^{\mathrm{e}\mathrm{x}\mathrm{p}}=\left\{\begin{array}{c}\frac{{{\displaystyle \sum }}_{\mathrm{z}}\left({\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)}}^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{i}\mathrm{m}\mathrm{p}}{\times \mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}\right)\times {\mathsf{\pi }}_{\left(\mathrm{z}\right)}^{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}}{{\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)}}^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{i}\mathrm{m}\mathrm{p}}}, \mathrm{i}\mathrm{f} {\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)}}^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{i}\mathrm{m}\mathrm{p}}{\ge \mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{e}\mathrm{x}\mathrm{p}}\\ \frac{{{\displaystyle \sum }}_{\mathrm{z}}\left({\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)}}^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{i}\mathrm{m}\mathrm{p}}{\times \mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}\right)\times {\mathsf{\pi }}_{\left(\mathrm{z}\right)}^{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}}{{\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)}}^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{e}\mathrm{x}\mathrm{p}}}, \mathrm{e}\mathrm{l}\mathrm{s}\mathrm{e}\end{array}\right.$$

(11)

As can be seen in Equations (9) and (10), the energy netting for the imported and exported electricity takes place on the 15 min interval, or as explained earlier on a 1 h basis in this research, as opposed to the NM model where the energy netting is performed monthly. In short, the prosumer pays the total price for all the imported electricity and is separately remunerated for all the exported electricity. Furthermore, the export price is variable over months and decreases (penalized) in months when there is more export than import (else condition in Equation (11)). Overall, by separating the electricity costs and penalizing the export price, this approach makes the NB model less profitable for the household prosumer than the NM model.

Monthly costs (EUR/month) of the electricity after the installation of PV in the NB model are calculated as using Equation (12):

$${\mathrm{C}}_{(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}=\mathrm{N}\mathrm{B},\mathrm{m})}=\left[{{\displaystyle \sum }}_{\mathrm{z}}\left({\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)}}^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{i}\mathrm{m}\mathrm{p}}{\times \mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}\right)\times {\mathsf{\pi }}_{\left(\mathrm{z}\right)}^{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\right]+\left({\sum }_{{{\mathrm{t}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}}_{\left(\mathrm{m}\right)}}^{{{\mathrm{t}}_{\mathrm{e}\mathrm{n}\mathrm{d}}}_{\left(\mathrm{m}\right)}}{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{e}\mathrm{x}\mathrm{p}}\right){\times \mathsf{\pi }}_{\left(\mathrm{m}\right)}^{\mathrm{e}\mathrm{x}\mathrm{p}}\times 0.9$$

(12)

where ${\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{e}\mathrm{x}\mathrm{p}}$ is negative, hence the export costs are negative.

4.3. Updated Net-Metering Model (NM+)

According to the suggestions stated in [31] for updating the Croatian Act on Renewable Energy Sources and High-efficiency Cogeneration [30], it can be concluded that the NM model will not be switched to the NB model if the main annual condition is true. However, the electricity excess at the end of the year will be taken into account as the main part of the update compared to the NM model. The NM+ is modeled using this approach if the main annual condition is false, and then the calculation is equal to the current NM model. However, if the main annual condition is true, the electricity costs are calculated as in the NM model for the entire year, but the electricity excess (total exported difference) at the end of the year is also considered and the excess energy price for the surplus production is corrected and reduced. Annual electricity costs in the NM+ model are formulated as shown in Equation (13):

$${\mathrm{C}}_{(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}=\mathrm{N}\mathrm{M}+)}^{\mathrm{a}\mathrm{n}\mathrm{n}}=\left\{\begin{array}{c}{\mathrm{C}}_{(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}=\mathrm{N}\mathrm{M})}^{\mathrm{a}\mathrm{n}\mathrm{n}}, \mathrm{i}\mathrm{f} {\sum }_{\mathrm{t}}\left({\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}-{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}\right)\times ∆\mathrm{t}\ge 0\\ {\mathrm{C}}_{(\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}=\mathrm{N}\mathrm{M})}^{\mathrm{a}\mathrm{n}\mathrm{n}}+{{\displaystyle \sum }}_{\mathrm{z}}\left({\sum }_{\mathrm{t}}\left({\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{P}\mathrm{V}}-{\mathrm{P}}_{\left(\mathrm{t}\right)}^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}\right){\times ∆\mathrm{t}\times \mathrm{X}}_{(\mathrm{z},\mathrm{t})}^{\mathrm{b}\mathrm{i}\mathrm{n}}\right)\times {\mathsf{\pi }}_{\left(\mathrm{z}\right)}^{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}\times {\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}, \mathrm{e}\mathrm{l}\mathrm{s}\mathrm{e}\end{array}\right.$$

(13)

where ${\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}$ represents the correction coefficient of the export price. This coefficient has been used in simulations with discrete values of 0.2, 0.4, 0.6, 0.8, and 1.

4.4. Results of the Simulations

A total number of 72,996 scenarios are simulated throughout the three described financial models (NM, NB, and NM+) for solar PV prosumers of the household category. These scenarios are represented by three types of consumption profiles, two-tariff models, and two geographical locations, thereby providing a very detailed analysis of how each factor affects the profitability of solar rooftop PV. The main financial indicators used in this research are SPP and SNPV represented in the 2D and 3D figures in the following subsection, as well as the matrix colormaps.

Figure 9 shows the comparison of SNPVs for different financial models and scenarios of Zagreb, 2T model, summer consumption profile, and annual consumption of 10,000 kWh. For the NM model, the optimal power is the one with the maximum SNPV, which is the boundary power, or the last PV power that results in the positive annual electricity difference not causing the switch to a less profitable NB model. For the scenario depicted in Figure 9, the optimal PV power size would be 7.75 kW, as shown with the black dotted vertical line, as the size for which maximum benefit is reached and the NM model is kept.

Figure 10 shows the comparison of SPPs for different financial models and the same scenario as in Figure 9. As can be seen, the NM model results in the lowest SPP values for different installed PV powers. The optimal PV power of 7.75 kW for the mentioned scenario results in an SPP of a little below eight years and an SNPV of a little above EUR 30,000. On the other hand, the same scenario for Split would result in the optimal PV power of 6.5 kW, SPP of 6.28 years, and SNPV of a little above EUR 33,000. Furthermore, the increase in ${\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}$ from 0 to 1 (in the NM+ model) results in an increase in the SPPs and a decrease in the SNPV values. NB model is generally the least profitable one; however, it is important to notice that high values of ${\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}$ result in high penalization of the oversized PVs and thus the NM+ model with high values of ${\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}$ can become even less profitable than the NB model.

Figure 11 shows the analysis of how the three consumption profiles and two-tariff models affect the SNPVs for the current financial models, NM and NB. The scenario is again shown for Zagreb with an annual consumption of 10,000 kWh.

Figure 12 shows the analysis of how the three consumption profiles and two-tariff models affect the SPPs for the current financial models (NM and NB). The scenario is also the same for Zagreb with an annual consumption of 10,000 kWh. Figure 11 and Figure 12 show that the 2T model and higher consumption during summer result in the highest SNPVs and lowest SPPs, both for NM and NB models. Also, as mentioned earlier, the differences between Zagreb and Split come from the better solar resource potential in the Split region as the Split region manifests shorter SPP and higher SNPV.

Since there is a noticeable number of scenarios simulated over multiple variable factors, important results are presented using 3D figures, as shown in Figure 13, Figure 14 and Figure 15. The main variable input parameters are annual electricity consumption (kWh) and installed PV power (kW), represented as horizontal axes, and the SNPV (EUR) and SPP (years) values, represented as the vertical axis. The black dots in Figure 13, Figure 14 and Figure 15 on the NM and NB planes represent the boundary PV powers, and the black half-plane in Figure 13 and Figure 14 underneath all SNPV planes represents the negative annual electricity difference (kWh). In short, from the perspective of the NM model, in Figure 13 and Figure 14, all the PV powers on the right of the black dots are undersized PVs, the black dots are optimal PVs, and all the PV powers on the left from the black dots and above the black half-plane are oversized PVs. In Figure 15, all the PV powers on the left of the black dots are undersized, and the power right from the black dots are oversized PVs. The black dots represent the optimal PV powers because they result in the highest SNPVs from the perspective of the NM model.

In Figure 14, it can be seen that the dispersion of the SNPVs between consumption profiles and the tariff models for both models (NM and NB) is the highest in the boundary scenario of the largest consumption (20,000 kWh/annually) and the largest PV installed (20 kW). The least dispersion of the results (between consumption profiles and tariff models) occurs in the three remaining boundary scenarios: lowest consumption and highest PV, highest consumption and lowest PV, and lowest consumption and lowest PV.

As seen in Figure 15, the NB model has the highest SPPs, especially after the optimal power. However, the high values of ${\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}$ result in high penalization of the oversized PVs, as stated before, thus making the NM+ model with high values of ${\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}$ even less profitable than the current NB model.

Furthermore, statistical analysis of the obtained results is presented using a colormap matrix, as shown in Figure 16 and Figure 17. More precisely, the mean, standard deviation (std), and median values of SNPV and SPP for Zagreb and Split are shown. These results span over all oversized PV powers that cause negative annual electricity differences, due to which the main annual condition is met.

4.5. Discussion of the Simulation Results

By analyzing the simulation results presented in the previous subsection, the following main conclusions can be drawn:

• NM model is the most profitable model among all the compared models (for smaller and greater capacities compared to the optimal PV powers);
• The two-tariff (2T) model is more profitable than the one-tariff (1T) model for all financial models in most of the consumption profile scenarios;
• The 1T model is more profitable than the 2T model only in the scenarios of 1T +S and 1T ≈E and only against the scenario 2T +W. This means that the one-tariff model is a good selection in cases where most consumption occurs during the day;
• The NM+ model is generally more profitable than the NB model; however, due to its penalizing nature, the NM+ model’s SNPVs start to slow down the increase as the installed PV power and ${\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}$ increase (for installed capacity greater than the optimal PV powers), to the point where the NM+ becomes less profitable than the NB model (for high values of ${\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}$);
• Both NB and NM+ models penalize the prosumers if they oversize their solar PV investment; this penalization in the NM+ model depends on the value of ${\kappa }^{\mathrm{e}\mathrm{x}\mathrm{p}}$, and in the NB model, it depends on the separation of the import and export costs, as well as the export price ${\mathsf{\pi }}_{\left(\mathrm{m}\right)}^{\mathrm{e}\mathrm{x}\mathrm{p}}$. These prices are variable and can lead to high penalization if the exported electricity in a specific month is much higher than the imported one;
• PV installations in Split are more profitable than the ones in Zagreb due to the higher solar insolation in this region, which manifests in better financial indicators;

  ○

  the optimal powers for Split in the NM model are lower, their SPPs are lower and result in higher SNPVs when compared to Zagreb;

• The optimal power for the NM model is suboptimal for the NB model; they are near the optimal value, but slightly higher power results in slightly higher SNPVs;
• It is important to correctly size the household PV in the current Croatian legislative framework.

5. Conclusions

This paper presents a PV sizing optimization and investment support tool for household installations with specific data showing a case study for Croatia. By tackling the PV sizing simulation analysis and processing the PV tool statistics, this paper addresses different socio-economic and technical aspects of wider sustainable solar integration. This provides a basis for more sustainable development of stronger citizen positions who, through the energy transition, become more independent and self-sufficient from the energy perspective. In the first segment of the paper, a general overview of the current situation was provided with the identification of some underlying problems identified and with the first step solution description via the development of the online PV sizing tool, colloquially called a solar calculator. The tool aims to raise the awareness and level of information citizens can obtain, and some of the results and statistics are presented. To further deepen the understanding of the solar integration process in households, a series of simulations were performed in order to assess the impact of different sizing decisions and different potential legislation decisions. The conclusion is that the net-metering model provides the most financial incentive but will not be available for long since it has some inherent drawbacks. Also, the alternative models that alter the current situation can still provide a good enough model for Croatian citizens to make the decision of investing in rooftop PV systems.

As a continuation of the research, a thorough revision of the current legislative frameworks of the EU countries will be conducted, and the impact of different incentives will be assessed via the simulation of the Croatian dataset. This might be of interest to policymakers and the public since it could further help in shaping the process of wider solar integration in Croatia.