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1 "Evaluation of Easily Accessible Parameters for Assessing the Performance and Economic Feasibility of Residential Photovoltaic Systems: An Analysis Using a Smart Meter Dataset of Households in Catalonia" Dimitrios Stasinos, Dimitrios Zafirakis University of West Attica - Department of Mechanical Engineering Abstract Evaluating residential photovoltaic (PV) energy systems typically requires detailed energy demand data, which is costly and time-consuming to collect. This study examines whether easily accessible parameters, specifically mean and peak annual electricity consumption from household bills, can predict key system indicators, including renewable energy penetration, selfconsumption, and relative annual rate of return. Using a sample of homes in Catalonia, the research aims to establish simple predictive relationships that reduce reliance on extensive data collection, enabling faster and more cost-effective assessment of PV system performance and economic feasibility. Results show that installations based on peak demand exhibit unstable patterns across households. In contrast, sizing installations based on mean annual hourly consumption provides a more consistent approach, as system behavior among homes is relatively similar. This method achieves good accuracy in predicting self-consumption, renewable energy penetration, and thus relative annual rate of return. Evaluation of the predictions shows only slight deviations in return rate for low-capacity installations. For higher capacities, greater than approximately five times the mean value, self-consumption and return rate are accurately predicted across different scenarios. This approach provides a simple, scalable solution for evaluating PV system feasibility, making it applicable and reliable for the majority of residential houses in similar environments. By reducing the need for complex data collection, it offers a faster, more accessible pathway to assess the economic and environmental benefits of PV energy systems. Keywords Sustainability, Green Energy, Decentralized Production, Renewable Energy, Photovoltaic (PV), Urban Energy, Urban Energy Communities, Positive Energy Districts 2 Contents Abstract....................................................................................................................................................................................................... 1 Table of figures .......................................................................................................................................................................................... 2 Introduction ................................................................................................................................................................................................ 3 Methodology .............................................................................................................................................................................................. 3 Data collection & process .................................................................................................................................................................... 3 i. Electricity demand data .................................................................................................................................................... 3 ii. Solar radiation and PV energy production data .............................................................................................................. 3 Technical system model and parameters............................................................................................................................................. 3 Techno-economic model ...................................................................................................................................................................... 4 Results ........................................................................................................................................................................................................ 5 Self-consumption and penetration patterns ......................................................................................................................................... 5 Techno-economic analysis ................................................................................................................................................................... 6 Predictions evaluation................................................................................................................................................................................ 8 Discussion .................................................................................................................................................................................................. 8 Conclusions ................................................................................................................................................................................................ 8 References .................................................................................................................................................................................................. 9 Table of figures Figure 1:House Data .................................................................................................................................................................................. 3 Figure 2: Cost per Installed Capacity vs Installed Capacity ................................................................................................................... 4 Figure 3: Electricity prices for household consumers - bi-annual data .................................................................................................. 4 Figure 4: Normalised Capacity vs Self Consumption and Penetration .................................................................................................. 5 Figure 5: Normalised Capacity vs Self Consumption across houses ..................................................................................................... 6 Figure 6: rARR vs Normalised Capacity for Different Export Prices .................................................................................................... 6 Figure 7: Heatmap of rARR Across Different Annual Demands (kWh) and Costs per Installed Capacity ........................................ 7 Figure 8: rARR vs Normalised Capacity for Different Export Prices Across houses........................................................................... 7 Figure 9: Forecasts Evaluation. Heatmap of rARR for a spectrum of Self Consumption Predictions across Normalised Installed Capacities ................................................................................................................................................................................................... 8 3 Introduction The increasing adoption of residential photovoltaic (PV) energy systems has prompted the need for effective investment assessments and system sizing to ensure optimal performance and economic feasibility. However, traditional methods of evaluating these systems often rely on the collection of detailed and costly energy demand datasets, which can be both timeconsuming and expensive for households and energy planners (Christopoulos et al., 2025; Granderson et al., 2011; Sarmas et al., 2022). In this context, the problem lies in the need to balance system capacity, self-consumption, and renewable energy penetration with the economic return on investment. Therefore, the need for more accessible and cost-effective methods to predict energy system performance is critical for accelerating the adoption of renewable energy solutions in residential areas. In this study, the main focus is to investigate the relationships between two parameters: the peak demand value, which plays a key role in investment assessment, and the mean annual consumption, which is the most easily obtainable parameter, as it can be directly derived from household electricity bills. Additionally, and on that note, the study examines the corresponding basic technical and economic parameters - such as the penetration of renewable energy, the self-consumption, and the annual rate of return across a spectrum of available possibilities - that influence investment decisions and outcomes in energy infrastructure. Many studies note the importance of peak demand because capacity decisions must ensure reliability at the highest load moments especially for not interconnected to the grid systems. For example, the OECD reports that ‘’peak demand’’ is used in the electricity sector because the generation and network capacity are dimensioned to meet the maximum load requirement, plus reserves, during a year.” (Impact of Smart Grid Technologies on Peak Load to 2050, 2011). As an alternative predictive parameter, mean annual consumption can serve as a easily accessible parameter , requiring minimal additional measurement effort (Stingl et al., 2018). The goal therefore is to ascertain whether those two parameters are accurate in the prediction of other important system parameters, and to identify the way they interact. The expected outcome is to establish predictive relationships in the researched environment, that can reduce reliance on costly extensive data collection. Methodology Data collection & process i. Electricity demand data The electricity demand data were obtained from a smart meter dataset of Spanish households (Granja et al., 2022; Quesada et al., 2024). Data cleansing was performed to retain only households with more than 80% non-missing values. In the Catalonia region, 14 households met this criterion. (Similar, but smaller dataset from Athens, Greece, can be found in (Athanasoulias et al., 2024)) Entity User ID Province House_01 08cae6bb461092126fcb53a73f9f249a48030403a0a04e859f186076b8a001bc Tarragona House_02 1357820753de0e3b4fc795ea1adf94846286d2021f98d4eefb3a88d9bb74119b Tarragona House_03 192dea045d18530b34b06861f7e2b733ccfede4003e85cad0e50351a8b137839 Tarragona House_04 4e49f574c91b3604c61b4b9c029c7e5f1680ae00a2c50ed15a8295838e268f18 Barcelona House_05 565ef6a18c4eb46593a55bea94dba29d82cd6b18b8fa882aa7696c98a6cd1cdf Tarragona House_06 5b62247cfa9daa055e8a7997c16e66c695656209f8fa208e8fd9969597627741 Barcelona House_07 601a42883edadc5b9b5fc505976f45f45b93dc1093c196afa23570c5ea110797 Barcelona House_08 67eca7e8d145082b7ed48887d0a7ba1a0d0d6dd7317d9b4fb87b35ce2ed28094 Barcelona House_09 75074e50d894675cf7660563aecaa51e157d631b9027b9d17b3b9b372c3eb1a4 Barcelona House_10 b071f2184be23a550f2fa3a78b9080909c439dfd637bcb97d11a70b8a6f87466 Barcelona House_11 b6b271f3daaa367f91d979456474d3086dfb78418795013319475bb88038757d Barcelona House_12 bf6cca750eb4de250334ab779b6ee572db9ae9e3f5dbe1ca721477115a497195 Tarragona House_13 e1ae794b59855a904af6162cb9b301855a4dfe4159620e820991cf55ecfba8b5 Tarragona House_14 f2d04fee1ed5131e4787b375fa3c8ed9bb7788ef808b05fc071b05a9ac6f9311 Barcelona ii. Solar radiation and PV energy production data The PV energy production data were extracted from(“Photovoltaic Geographical Information System (PVGIS) - The Joint Research Centre,” 2024). The analysis assumed an optimal panel slope and azimuth, 1 kWp crystalline silicon panels, and total system losses of 14% accounting for temperature effects, cabling, inverter inefficiencies, and other factors. Technical system model and parameters As a first step, for the 14 households, the patterns of self-consumption and penetration were evaluated with respect to mean annual hourly and peak electricity consumption, using electricity demand and PV production data from the year 2023. Selfconsumption refers to the percentage of electricity produced by the PV system that is directly consumed by the household, and it is a key technical parameter for assessing the system’s economic performance. Penetration refers to the ratio of PV-generated electricity to the household’s total energy consumption and is crucial for achieving the European renewable energy target of at least 42.5% by 2030 (“Renewable energy targets - European Commission,” n.d.). These parameters are flexible and can be influenced by other techniques, such as load shifting, which shifts electricity demand to periods of higher PV production, thereby increasing self-consumption (Christopoulos et al., 2023; Tzanes et al., 2024). In addition, the installed PV capacity for each household was determined as a ratio of either the mean annual demand or the peak annual demand. Hourly electricity production was calculated using PVGIS data for 1 kWp panels and scaled proportionally to the installed capacity. For each installation size, the hourly difference between household demand and PV production was computed. Yearly self-consumption and penetration were then derived from these hourly balances. Installed capacities values range from 0 Figure 1:House Data 4 up to 20 times the mean annual hourly demand, in steps of 0.2 and up to 2 times the peak annual demand, in steps of 0.1. The formulas for the technical parameters are listed below: • Normalised Capacity, Pnorm = Installed Capacity (kWp) / Mean Annual Hourly Demand (kW) • Normalised Capacity, Pnorm,NPV = Installed Capacity (kWp) / Peak Annual Hourly Demand (kW)} • Hourly Self Consumption (kWh)= {Hourly Production ,if Production ≤ Demand Demand ,if Production > Demand • Annual Self Consumption (kWh)= ∑Hourly Self Consumption 8760 n=0 • Self-Consumption Ratio = Annual Self Consumption (kWh) / Annual Production (kWh) • PV Penetration Ratio = Annual Self Consumption (kWh) / Annual Demand (kWh) Techno-economic model In this step, the energy system is evaluated using the relative Annual Rate of Return (rARR). While traditional Net Present Value (NPV) or Internal Rate of Return (IRR) analyses assess the profitability of an investment, they do not allow for direct comparisons across different scenarios. In our case, the goal is to evaluate the investment relative to the pre-investment electricity bill for each household, enabling meaningful comparisons and the extraction of general conclusions. The rARR calculation, in this study, does not account for interest rates on individual cash flows, simplifying the analysis while maintaining its comparative utility. The rARR represents the portion of the annual electricity bill that the investment effectively covers, after accounting for the initial cost of the installation. In addition, electricity pricing can either be fixed or it can follow market fluctuations, in this study only fixed pricing values are used for the evaluation. While energy prices are subject to uncertainty, the general trend indicates that export prices have decreased over time. During the early deployment of residential PV systems, export prices were significantly higher than they are today(Talavera et al., 2010). Conversely, import prices have followed a generally increasing trend over the same period. (“Check the price of electricity today,” n.d.; “Electricity price statistics,” n.d.; Czipf, 2025; Micheli et al., 2024).Also, installation costs are dependent on the scale of the system. For smaller installations, fixed costs, such as interconnection, cabling, and permits, can disproportionately increase the total installation cost, often leading to an exponential rise in the price per installed kWp, as illustrated in the graph below. • Annual Profit (€ ) = [ if Cost Post Installation (€ ) ≥ 0: Annual electricity Cost Pre Installation (€ ) -Annua Electricity Cost post Installation (€ ) , Demand (kWh) * Import Price(€/kWh) – [(Demand (kWh) - Self Consumption (kWh)) * import price (€/kWh) - (Production (kWh) – self Consumption (kWh)) * Export price (€/kWh) ], [if Cost Post Installation < 0: Annual Profit (€ ) = Annual Cost Pre Installation (€ )] • Yearly Normalised Initial Cost (€ / n) = Capacity (kW) * Cost per Installed Capacity (€ / kW) / Investment Lifespan (n) • Annual electricity Cost Pre Installation (€) = Demand (kWh) * Import price (€ / kWh) • Annual Electricity Cost Post Installation (€) = (Demand (kWh) - self-consumption(kWh) * import price (€/kWh) - (Production (kWh) – self consumption (kWh)) *export price (€/kWh) • Mean Hourly Demand: m = Demand (kWh) / 8760 (hours) & Capacity (kW) = Pnorm (kW) * m Figure 3: Electricity prices for household consumers - bi-annual data Figure 2: Cost per Installed Capacity vs Installed Capacity 5 The general formulas describing the techno-economic system are as follows: Parameters Symbol Spectrum Parameter type Import Price Cimp 0.15 -0.30 (€/kWh) Variable: 20 steps Export Price Cexp 0.00-0.10 (€/kWh) Variable: 20 steps Normalised Mean Annual Hourly Demand Pnorm 0-20 (ratio) Variable: intervals of 0.2 Production for Capacity 1kWp P0 894 (kWh/year) Constant for region Total Annual Demand D 500 ,2000 (kWh/year) Variable: 500 or 2000 Self-Consumption - Pnorm Trendlines A(Pnorm) Pnorm :0-20, (kWh) 3Trendlines relative Annual Return Rate ={ Annual Profit − Yearly Normalised Initial Cost Cost Pre Installation ,if Cost Post Installation ≥0 Cost Pre Installation − Yearly Normalised Initial Cost Cost Pre Installation ,if Cost Post Installation<0 rARR= { [D∗Cimp−[(D−A∗PnormmPo)Cimp−(PnormmPo−A∗MnormmPo)Cexp]] − PnormmCo n D∗Cimp ,if Cost Post ≥0 D∗Cimp − PnormmCo n D∗Cimp ,if Cost Post<0 Annual Cost Post Installation= [(D−A∗MnormmPo)Cimp−(MnormmPo−A∗MnormmPo)Cexp] The Self-Consumption formulas, A(Mnorm), are derived from the corresponding graph trendlines, and separated for low, mean and high values, Amean,low,high ,from (Figure 4)={ Self Consumption (Pnorm,mean)=0.856e−0.258Mnorm+0.143 Self Consumption (Pnorm,low)=0.630e−0.237Mnorm+0.116 Self Consumption (Pnorm,high)=0.964e−0.224Mnorm+0.143 Results Self-consumption and penetration patterns The following graphs illustrate the predicted patterns of self-consumption and renewable energy penetration in relation to the mean annual hourly demand and the peak hourly annual demand across different households. The graphs are providing insights into how varying household consumption patterns and installation strategy influence the parameters of residential photovoltaic (PV) systems. Figure 4: Normalised Capacity vs Self Consumption and Penetration 6 The strategy of sizing residential installations using peak demand falls short in estimating the critical parameters. Conversely, sizing based on mean demand demonstrates more accurate predictions of penetration and self-consumption. For small installations, prediction accuracy when using mean demand varies by approximately ±0.1 for self-consumption and ±0.05 for penetration. For larger installations—those exceeding five times the mean demand—predictions stabilize, with an accuracy of ±0.05 for both self-consumption and penetration across all cases. This approach represents a practical alternative to traditional techno-economic analyses, which typically require extensive metering data and time to forecast similar values. Given these promising results, the next step is to investigate whether the extremes of self-consumption can be correlated with other known parameters. The hypothesis is that high peaks, unstable demand patterns, or low mean demand could negatively influence energy system performance. In addition, the maximum penetration that can be achieved without battery storage is around 50% at max for maximum installation and from 20% to 40% for economically feasible systems. In the subsequent graph, the data is separated by household and color-coded according to either the peak-to-mean demand ratio (as a proxy for demand instability) or the absolute mean demand. As observed, no clear correlation between self-consumption and either the ratio or mean value emerges. These findings suggest that peak events over the year does not reliably represent the overall demand behavior of a household. Techno-economic analysis The same strategy is applied here, analyzing the behavior at the level of individual households. Low-demand houses tend to exhibit the poorest outcomes. This can be explained by the initial cost per unit of installed capacity, which is variable and decreases as the total system capacity increases, as shown in (Figure 2). This observation further reinforces the idea that energy communities, in addition to achieving better energy management and reducing excess energy production, can also benefit from cost reductions per unit of capacity due to economies of scale . In the following graph the rARR parameters is shown for different installation capacities, export prices. The “safe area” for export prices above 0.2 €/kWh is also identified, this area represents the range that remains relatively low risk for possible reductions in export prices.In addition it can be concluded that without a grid interconnection, and for installation cost equal to 1000 €/kWp , only small installations are feasible, particularly for households with an import price greater than 0.20–0.22 €/kWh (Figure 8). Also it can be derived that increasing installation capacity up to 10-14 times the mean demand can Figure 5: Normalised Capacity vs Self Consumption across houses Figure 6: rARR vs Normalised Capacity for Different Export Prices 7 be beneficial, if an export price of higher than 0.04 - 0.06 €/kWh is guaranteed.On the contrary, installations above 10-14 times the mean deamand are detrimental. For export prices of 0.1, 0.08 and 0.06 €/kWh the maximum influence of bill’s price reduction is observed, because the grid subtracts exported energy from the bill, once the bill reaches zero, additional exports no longer provide economic benefit in most cases. In (figure 7) it can be observed that all houses, across the different scenarios, appear to follow the same pattern, showing no significant differences. Peaks, lows, and steady regions remain consistent when normalized by the mean annual hourly consumption. In addition low-demand households seem to be more influenced by the initial fixed costs of the installation. The most influential parameter, besides import and export prices, is the initial cost per installed capacity. On that note, in (Fifure 8) the rARR is calculated for variable initial costs and different demands. In can also be derived that, a lower installation cost expands the feasible region, making the system more economically viable and beneficial across different installed capacities. On the other hand, for increasing installation costs the non-profitable region increases. Figure 7: rARR vs Normalised Capacity for Different Export Prices Across houses Figure 8: Heatmap of rARR Across Different Annual Demands (kWh) and Costs per Installed Capacity 8 Predictions evaluation The results for rARR (Figure 9), using the mean, low, and high-end of the self-consumption distribution across different installed capacities, show that as the system size increases, the potential error becomes very small. Specifically, as the installation capacity grows, the system's self-consumption decreases and stabilizes, leading to lower influence. The export price, on the other hand, becomes more influential and plays a more prominent role in the rARR calculation at higher installations capacities. To sum up, in larger installations, export prices contribute significantly to the economic feasibility, whereas self-consumption variations have a reduced impact. The forecasts can predict the rARR for different installation scenarios, however, in smaller installations the error margins can be quite larger than in bigger ones, around ±0.1. These errors often correspond to cases where lower import prices and export prices ranges are deemed feasible, although in reality, they might not be. If the installed capacity is below 14 times the mean demand and if the export prices are greater than 0.03 €/kWh the system is, in all cases, economically feasible and profitable. Finally, for systems with Pnorm values above 14, the risk becomes extremely high, indicating that over dimensioned systems (those larger than 14 times the mean) can lead to unpredictable and uncertain economic outcomes, even with extremely high export prices the system may not be profitable. Discussion While the analysis provides valuable insights, there are some limitations to consider. First, the economic model used in this study does not take into account interest rates. This factor can significantly impact the long-term return for a PV system. The data used in this study is also specific to the Catalonia region in Spain, which means that the results may not be directly applicable to other geographical areas. Different solar radiation, latitudes and climate conditions would likely influence energy production and system performance. For example, regions at higher latitudes with less solar radiation may experience lower PV output compared to the Catalonia region. Additionally, the study assumes a fixed PV orientation based on maximizing yearly production, dynamic systems that adjust their orientation could offer higher efficiency. Another limitation is the uncertainty in import/export energy prices over time. The model assumes a fixed price for both energy export and import prices, but they can also follow the market prices that fluctuate, which could affect the return rate. Conclusions This study investigates the use of easily accessible parameters, mean and peak annual electricity consumption, as predictors for evaluating the performance and economic feasibility of residential photovoltaic (PV) systems. By analyzing a dataset of Spanish households, the research explores whether simplified methods, such as using household electricity bills, can reduce the need for detailed energy consumption data, thus enabling faster and more cost-effective integration of PV systems. The key findings of this study are: 1. Impact of Sizing Strategies: Sizing PV installations based on peak demand yields unstable performance across households, while sizing based on mean annual demand provides consistent and accurate predictions of critical Figure 9: Forecasts Evaluation. Heatmap of rARR for a spectrum of Self Consumption Predictions across Normalised Installed Capacities 9 parameters and their patterns, such as self-consumption, renewable energy penetration, and the relative annual rate of return (rARR). This approach offers a simpler, more reliable and less data demanding method for assessing PV system performance. 2. Feasibility of Small vs. Large Systems: For small PV installations, prediction accuracy for self-consumption and renewable energy penetration, based on mean demand, varies with deviations of around ±0.05 for self-consumption and ±0.1 for penetration. However, for larger systems (those greater than five times the mean demand), these predictions stabilize, and the accuracy improves, with deviations falling to ±0.05 for penetration and almost 0 for selfconsumption. 3. Economic Feasibility: The rARR analysis shows that as system size increases, self-consumption becomes less important, while export price matters more. For systems sized between around 3 and 14 times the average energy demand, as long as the export price is above 0.03 €/kWh, the system remains economically viable. Larger systems may see diminishing returns due to reliance on export prices. 4. Role of Installation Costs: Low demand households are particularly sensitive to the initial fixed costs of PV installations. The initial cost per unit of installed capacity is a key determinant of economic feasibility. As the total system capacity increases, the relative cost per unit decreases, making larger systems more cost-effective. For relative installation costs above 1100€/kWp, the non-profitable region is significant, indicating that higher initial costs make the system less economically viable. 5. Insights for Energy Communities: Energy communities, which aggregate multiple residential installations could benefit from economies of scale. Larger installations, either individual or community-based, not only reduce the cost per installed kWp due to scaling, but also offer better energy management and higher profitability by reducing the grid exports and by increasing self-consumption (Stasinos et al., 2024). This finding highlights the potential advantages of cooperative energy systems for reducing costs and optimizing energy use at a community level. 6. General Applicability of the Method: The predictive relationships derived from this study, based on easily accessible parameters, are applicable to a wide range of residential scenarios in similar environments. The approach allows for quick, cost-effective evaluations of the economic viability of PV systems in various contexts, reducing the need for extensive data collection and making the adoption of renewable energy technologies more accessible. 7. PV Penetration: The maximum penetration that can be achieved without battery storage is around 50% for maximum installed capacity and around 20% to 40% for more economically feasible systems. In conclusion, this study demonstrates that mean annual electricity consumptions is effective, easily accessible parameters for predicting key system outcomes such as self-consumption, renewable energy penetration, and economic feasibility. These simplified methods offer a practical alternative to traditional techno-economic analyses, enabling faster and more cost-effective assessments of residential PV systems. References Athanasoulias, S., Guasselli, F., Doulamis, N., Doulamis, A., Ipiotis, N., Katsari, A., Stankovic, L., Stankovic, V., 2024. The Plegma dataset: domestic appliance-level and aggregate electricity demand with metadata from Greece. Scientific Data 11. https://doi.org/10.1038/s41597-024-03208-0 Check the price of electricity today [WWW Document], n.d. 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