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# Optimization of photovoltaic (PV) integration on building envelope: a case study in France

Farzaneh Changizi, Martin Thebault, Christophe Ménézo

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## To cite this version:

Farzaneh Changizi, Martin Thebault, Christophe Ménézo. Optimization of photovoltaic (PV) integration on building envelope: a case study in France. Journal of Physics: Conference Series, 2025, 3140 (3), pp.032009. 10.1088/1742-6596/3140/3/032009. hal-05393255

HAL Id: hal-05393255

https://cnrs.hal.science/hal-05393255v1

Submitted on 3 Dec 2025

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# Optimization of photovoltaic (PV) integration on building envelope: a case study in France

To cite this article: F Changizi et al 2025 *J. Phys.: Conf. Ser.* **3140** 032009

View the [article online](#) for updates and enhancements.

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- *Optimization of photovoltaic (PV) integration on building envelope: a case study in France*
F Changizi, M Thebault and C Ménézo

<figure><img src="image_4.png" /></figure>
# Optimization of photovoltaic (PV) integration on building envelope: a case study in France

F Changizi¹, M Thebault¹ and C Ménézo¹

¹ University Savoie Mont Blanc, LOCIE, UMR CNRS 5271, Le Bourget-du-Lac, Cedex F 73376, France

E-mail: farzaneh.changizi@univ-smb.fr

**Abstract.** With the increasing integration of photovoltaic (PV) systems in residential buildings and their growing deployment in urban areas, it is essential to adopt a bottom-up approach and systematically examine the optimal placement of PV panels at the building scale. This study evaluates key building criteria and analyzes the correlation between energy production and consumption across different orientations. To determine the optimal placement of PV panels, a holistic approach is adopted, incorporating energy, economic, and environmental indicators such as load matching, net present value, payback period, levelized cost of energy, and annual carbon emissions. Additionally, a new flexibility factor, load-Match pricing, is utilized to assess the influence of electricity pricing on the load matching factor. Each indicator is first optimized as a single objective, followed by a multi-objective optimization approach to balance trade-offs between energy, economic, and environmental indicators. The results highlight that façades are more effective in enhancing load matching, whereas roofs offer greater economic benefits. Further insights of optimization process are discussed.

## Nomenclature

<table><tr><td>d</td><td>Discount rate</td><td>P<sub>r</sub></td><td>Retail price (€/kWh)</td></tr><tr><td>I<sub>0</sub></td><td>Initial investment (€)</td><td>P<sub>w</sub></td><td>Wholesale price (€/kWh)</td></tr><tr><td>L</td><td>Energy consumption (kWh)</td><td>S<sub>0</sub></td><td>Subsidies (€)</td></tr><tr><td>L<sub>p</sub></td><td>Electricity price (€/kWh)</td><td>T</td><td>System lifetime (years)</td></tr><tr><td>OM</td><td>Operation and maintenance costs (€)</td><td>t</td><td>Time step index</td></tr><tr><td>P</td><td>PV energy production (kWh)</td><td>μ<sub>grid</sub></td><td>Grid CO<sub>2</sub> emission rate (g/kWh)</td></tr><tr><td></td><td></td><td>μ<sub>PV</sub></td><td>PV CO<sub>2</sub> emission rate (g/kWh)</td></tr></table>

## 1. Introduction

Renewable energy accounts for only 6% of global final energy use in buildings but must rise to 18.1% by 2030 to meet net-zero goals [1]. Integrating photovoltaic (PV) systems into building envelopes is a key strategy to increase on-site clean energy and reduce grid dependence. While solar PV offers notable energy benefits, its intermittent generation—peaking at midday—often misaligns with residential demand, which is typically higher in the morning and evening, causing mismatches between production and consumption.

The Load Matching indicator (LM) reflects how well on-site PV generation aligns with building energy use. It is assessed using metrics such as self-consumption (SC), self-sufficiency (SS) [2], loss of load probability (LOLP), and on-site energy ratio (OER) [3]. Studies show that

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Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
using east and west façades, in addition to roofs, can improve LM by better aligning production with demand [2, 5], even though south-facing PVs generally yield the highest annual output [4].

Recent studies show that non-optimal PV placements can improve self-consumption and reduce system costs by better matching generation with demand [6]. In France, optimizing PV integration for self-consumption improved LM and net present value, though roofs were more profitable while façades offered better LM [7]. In Spain, façade-mounted PVs improved SC by 9%, reduced payback by over 2 years, and increased annual output by up to 59% [8], which aligns with the findings of Murithi et al. (2024), who also demonstrated the energy and economic benefits of façade-mounted PVs [9].

Studies have also considered flexibility indicators which account for electricity prices based on peak and off-peak periods to provide a more dynamic assessment of PV system performance and integration. These indicators evaluate the ability of the system to shift or align electricity generation with periods of high electricity demand or price. By incorporating time-of-use tariffs, such flexibility metrics help in quantifying the potential cost savings and grid-support capabilities of PV systems [2][10].

While previous studies have examined various indicators for optimal PV placement, the role of specific orientations—especially the underexplored north façade—remains insufficiently addressed. This study uses real consumption data and local energy-economic factors in France to assess optimal PV placement on building envelopes using five indicators: Load Match (LM), Net Present Value (NPV), Payback Period (PP), Levelized Cost of Energy (LCOE), and Annual Carbon Emissions (ACE). Additionally, a new indicator—Load-Match Pricing (LMP)—is introduced to capture the time-resolved economic value of PV generation by linking output to hourly wholesale electricity prices. This approach moves beyond flat-rate methods, emphasizing the real-time financial benefits of self-consumed solar energy. In the following the case study is presented and the optimization process is explained and discussed.

## 2. Material and Method

For this study, a residential building with a 10×10 meter footprint, 3-meter height, and a 30° pitched roof was considered. Shading was neglected in this study and assumed to be zero for all surfaces of the building envelope. Weather data for Lyon, taken from NSRDB with a 30-minute resolution, was processed using PVLIB to obtain the power output of one PV panel [12]. The PV module ‘Silevo_Triex_2014’, with an efficiency of 20%, and the inverter ‘SolarEdge_240V’, along with the ‘open_rack_glass’ configuration for temperature parameters, were used in the modeling with ‘ModelChain’. The power output of one PV module is shown in Figure 1. Energy consumption data (load) from EtudELECT [11], covering nearly one year in France with a 30-minute resolution, was processed based on an annual consumption rate of 68 kWh/m². It should be mentioned that 25 days of missing data from EtudELECT were not included in the simulation but were accounted for when calculating the building’s annual consumption. The load variation and monthly consumption in kWh are shown in Figure 1. In addition, the daily variation of consumption for a typical day in each season is shown in Figure 2.

The DC peak power output of the module under standard test conditions (STC) is 0.3 kWp. The lifetime of the PV system is considered 30 years, with a discount rate of 3%. The cost of implementing PV on the roof is assumed to be half that of the façade. The retail electricity price is 0.2 €/kWh, while the wholesale price is 0.13 €/kWh for total PV capacities below 9 kWp, and 0.07 €/kWh for capacities between 9 to 100 kWp, and no subsidies are applied for capacities greater than 100 kWp. Operations and maintenance costs are also considered at 1% of the initial investment which are used for economic indicators [13]. Wholesale electricity prices were used to calculate load match pricing [14]. The emission rate for PV is assumed to be constant across all time steps at 46 gCO₂/kWh, while grid CO₂ emission rates with hourly resolution are used for the environmental (ACE) indicator in the analysis [15][16].
<figure><img src="image_6.png" /><figcaption>Figure 1. Daily and monthly Load (left) and PV energy generation (right)</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 2. Daily load variation</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 3. Case-study with unfolded envelope</figcaption></figure>

As mentioned before, several objectives related to energy, economy, and the environment are defined. The PV production is expressed in Equation (1), where $X_i$, and $P_{PV,i}(t)$ represent the number, and power output of a PV panel. The overall optimization goal—minimizing the selected indicators—is presented in Equation (2). The specific formulations for each individual objective are detailed in Equations (3) to (8). First, each indicator is individually assessed through discrete mono-objective optimization using Genetic Algorithms (GA). Subsequently, the discrete NSGA-III algorithm is applied to explore the trade-offs and interactions among the multiple objectives. For both optimizations, the population size is set to 50, with a crossover rate of 0.8, mutation probability of 0.2, mutation rate of 0.5, and elitism of 0.5, over 100 iterations. This process is repeated 100 times for mono-objective optimization and 1000 times for multi-objective optimization. The optimal value among all runs is selected as the final result. For the representation of results, the unfolded (2D) view of the 3D building envelope is shown in Figure 3. Each surface is identified by the following subscripts: S (South), N (North), E (East), W (West), RS (South-facing Roof), and RN (North-facing Roof).

$$P(t) = \int_{1}^{T} \left( \sum_{i=0}^{5} X_i \cdot P_{PV,i}(t) \right) dt \qquad (1)$$

$$f(x) = [f_1(x) : \text{LM}, f_2(x) : \text{LMP}, f_3(x) : -\text{NPV}, f_4(x) : \text{PP}, f_5(x) : \text{LCOE}, f_6(x) : \text{ACE}] \quad (2)$$

$$f_1(x) = \int_{t=1}^{T} |L(t) - P(t)| dt \qquad (3)$$

$$f_2(x) = \int_{t=1}^{T} |L(t) - P(t)| \cdot L_p(t) dt \qquad (4)$$

$$f_3(x) = S_0 + \sum_{t=1}^{T} [\min(L(t), P(t)) \cdot P_r + \max(0, P(t) - L(t)) \cdot P_w] (1+d)^{-t} \qquad (5)$$

$$f_4(x) = \text{PP}, \text{ with } f_3(x, T = \text{PP}) = 0 \qquad (6)$$

$$f_5(x) = \frac{I_0 + \sum_{t=1}^{T} \frac{OM_t}{(1+d)^t}}{\sum_{t=1}^{T} \frac{P(t)}{(1+d)^t}} \qquad (7)$$
$$f_6(x) = \sum_{t=1}^{T} \mu_{\text{grid}} \cdot \max(0, L(t) - P(t)) + \mu_{\text{pv}} \sum_{t=1}^{T} P(t) \qquad (8)$$

### 3. Results

#### 3.1. Mono-objective optimizations

The results of the LM indicator indicate that implementing PV panels on façades provides a better match between the load and PV production compared to roof-mounted PV panels. As it is shown in Figure 4, the optimization results determined that PV placement on the façade is optimal, with no panels allocated to the roof. Also, LMP objective devote 4, and 3 PV panels for south and north façade respectively which offers a different design compared with load-maching indicator shown in Figure 5. The results show that LMP indicator shows 21% self-sufficiency and 82% self-consumption. The performance metrics related to these objectives are shown in Table 1. Moreover, the results of NPV, PP, and LCOE as economic objectives show that roof is

<figure><img src="image_9.png" /><figcaption>Figure 5. Optimal LMP</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 6. Optimal PP</figcaption></figure>

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more favorable for PV implementation. The NPV objective shows that 30 panels are installed, utilizing most of the area of the south-facing roof for PV implementation which is similar to PP optimal solution which is illustrated in Figure 6. However, by considering the LCOE indicator, the whole area of south-facing roof is devoted to PV implementation with 34 panels. Moreover, the optimization of ACE indicator determines 2, 2, 1, and 7 PV panels for the south, west, east façades and north-facing roof respectively. The findings show that the highest SC value for the LM objective, whereas this value decreases for economic objectives. Conversely, SS shows opposite trends for economic objectives (see Table 1). In Table 2 the value of optimal

<table><caption>Table 1. Performance Metrics.</caption><thead><tr><th rowspan="2">Metric</th><th rowspan="2">LM</th><th rowspan="2">LMP</th><th colspan="2">Objective</th><th rowspan="2">LCOE</th><th rowspan="2">ACE</th></tr><tr><th>NPV</th><th>PP</th></tr></thead><tbody><tr><td>SS</td><td>0.20</td><td>0.21</td><td>0.27</td><td>0.27</td><td>0.27</td><td>0.21</td></tr><tr><td>SC</td><td>0.87</td><td>0.82</td><td>0.16</td><td>0.16</td><td>0.14</td><td>0.56</td></tr><tr><td>LOLP</td><td>0.85</td><td>0.83</td><td>0.69</td><td>0.69</td><td>0.68</td><td>0.76</td></tr><tr><td>OER</td><td>0.23</td><td>0.25</td><td>1.73</td><td>1.73</td><td>1.96</td><td>0.38</td></tr></tbody></table>

values across other objectives are reported. The optimal LM value is 5277 kWh, while this value tend to increase by more than 2 times for NPV value. On the other hand, NPV value for the optimal solution is €44346, and it is where PV implementation is devoted for south-facing roof. Interestingly, when applying the optimal values of NPV objective to the LM, LMP, and ACE objectives, the resulting NPV values become negative due to the reliance on façades for energy generation. Notably, the LM, LMP, and ACE objectives result in invalid payback periods that
exceed the typical 30-year lifespan of a PV system. This is a critical insight, as it suggests that over the typical 30-year lifespan of a PV system, such a configuration fails to recoup the initial investment, leading to financial loss. It underscores that optimizing solely for energy-related objectives can lead to economically unfeasible outcomes, with investment recovery timelines far beyond the system's expected operational life.

<table><caption>**Table 2.** Optimal values across objective functions.</caption><thead><tr><th rowspan="2">Obj.</th><th rowspan="2">Func.</th><th colspan="6">Optimal Value of Obj.</th></tr><tr><th>LM</th><th>LMP</th><th>NPV</th><th>PP</th><th>LCOE</th><th>ACE</th></tr></thead><tbody><tr><td>LM</td><td>(kWh)</td><td><strong>5277</strong></td><td>5305</td><td>13875</td><td>13875</td><td>15298</td><td>5890</td></tr><tr><td>LMP</td><td>(kWh*€)</td><td>1711</td><td><strong>1707</strong></td><td>3156</td><td>3156</td><td>3409</td><td>1832</td></tr><tr><td>NPV</td><td>(€)</td><td>-6362</td><td>-5344</td><td><strong>44346</strong></td><td>44346</td><td>27358</td><td>-4623</td></tr><tr><td>PP</td><td>(y)</td><td>-</td><td>-</td><td>5</td><td><strong>5</strong></td><td>8</td><td>-</td></tr><tr><td>LCOE</td><td>(€/kWh)</td><td>0.32</td><td>0.29</td><td>0.04</td><td>0.04</td><td><strong>0.04</strong></td><td>0.32</td></tr><tr><td>ACE</td><td>(kg)</td><td>133</td><td>111</td><td>129</td><td>129</td><td>133</td><td><strong>110</strong></td></tr></tbody></table>

## 3.2. Multi-objective optimization

The variability in Table 2 highlights the importance of addressing energy, economic, and environmental objectives together. For example, LMP, PP, and ACE yield divergent outcomes, emphasising the value of multi-objective optimization. Using NSGA-III, these three objectives were optimized simultaneously. Results (Figure 7) indicate that placing six PV panels on the south-facing roof yields a globally optimal solution, achieving kWh*€1798 in LMP, an 8-year payback period, and 111 kg of annual carbon emissions. This setup also achieves 59% self-consumption, 21% self-sufficiency, 79% loss of load probability, and a 35% on-site energy ratio.

<figure><img src="image_13.png" /><figcaption>**Figure 7.** Results of multi-objective optimization</figcaption></figure>

## 4. Discussion and Conclusion

In this study, the optimal PV coverage for a one story residential house with the footprint of 100 m² and the total energy consumption of 6334 kWh is investigated. The aim is to identify optimal PV installation solutions based on multiple criteria, including energy indicators (e.g., load matching), economic indicators (e.g., net present value, payback period, and levelized cost of energy), and environmental indicators (annual carbon emissions). In addition to previous
studies that have used flexibility indicators based on peak and off-peak pricing [2][10], this study introduces LMP as a new flexibility indicator. LMP provides a time-resolved economic evaluation by linking PV generation to hourly electricity prices. These indicators are first optimized individually and then collectively used in multi-objective optimization.

The mono-objective optimization results show that the optimal solution for LMP involves placing PV panels with two panels on the east and one on the west which is similar to the configuration of LM optimal solution. However, they differ in the coverage of the south and north façades. The LMP results indicate that installing four PV panels on the south façade and three on the north façade offers an optimal solution when considering both energy production and market price dynamics. This approach is beneficial because it captures the real-time economic value of solar energy, enabling more informed decisions that enhance system flexibility and financial performance. Notably, the optimal placements for maximizing both LM and LMP were found primarily on the south and north façades. Previous studies often neglect the north façade due to its lower power production, yet this study demonstrates that the low but constant production of north façade significantly contributes to the optimal LM and LMP solution. The economic objectives (NPV, PP, and LCOE) consistently show that the roof is the most favorable surface for PV installation. Both NPV and PP results suggest installing 30 panels on the south-facing roof, while the LCOE objective supports fully covering the south-facing roof with 34 panels. The payback period is 5 years, and the LCOE is 0.04 €/kWh for the optimal solution.

The annual carbon emissions (ACE) indicator is employed to quantify the reduction in carbon emissions achievable through the use of PV systems. The optimization approach prioritizes PV utilization when its associated carbon emission is lower than those of the grid. Results from ACE optimization indicate that the installation of two PV panels on south façade, two and one PV panels on the west and east façades, and seven PV panels on north-facing roof represents the optimal solution under the given data conditions. This indicator is subsequently integrated into the multi-objective framework to evaluate trade-offs with other objectives.

The clear differences between energy and economic indicators emphasize the need for multi-objective optimization in PV strategies. Focusing solely on energy may overlook financial viability. Thus, multi-objective optimization was applied for load-match pricing (LMP), payback period (PP), and annual carbon emissions (ACE). Results show the optimal design uses six panels on the south-facing roof, achieving 59% self-consumption and 21% self-sufficiency. Rather than aiming for full building autonomy(self-sufficiency), this study focuses on uncovering relationships that inform optimal PV placement at the building scale. Such insights are valuable when scaling up to urban contexts, as they clarify interactions among energy, economic, and flexibility indicators. Building-scale optimization provides a solid foundation for designing distributed PV systems across multiple buildings, where factors like orientation and energy demand variability become more complex. This bottom-up knowledge supports more integrated planning at larger scales (e.g., district level) and enhances performance metrics. However, practical limitations of façade PV installations—such as visual impact, maintenance, shading, and structural constraints—are not fully considered here. Future research should incorporate these factors to develop more comprehensive optimization models for building and urban scales.

## Acknowledgments

This work has been funded as part of the FlexTASE project within the Priority Research Program and Equipment (PEPR) TASE (Advanced Technologies for Energy Systems), funded by France 2030 (grant number ANR 22-PETA-0009). This work has been supported by the French National Research Agency, through Investments for Future Program (ref. ANR-18-EURE-0016 – Solar Academy).
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