# On the Assessment of the Chilean Solar Thermal Regulation Using a Modular Simulation Model Coupled to a Multiobjective Optimization Algorithm

Jorge Contreras, Benjamin Kadoch, Fabián Bustos

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Jorge Contreras, Benjamin Kadoch, Fabián Bustos. On the Assessment of the Chilean Solar Thermal Regulation Using a Modular Simulation Model Coupled to a Multiobjective Optimization Algorithm. International Journal of Energy Research, 2024, 2024 (1), 10.1155/2024/7478549. doi:10.4707/432

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Research Article

# On the Assessment of the Chilean Solar Thermal Regulation Using a Modular Simulation Model Coupled to a Multiobjective Optimization Algorithm

Jorge Contreras ID,<fnref n="1" /> Benjamin Kadoch ID,<fnref n="2" /> and Fabián Bustos ID<fnref n="3" />

Correspondence should be addressed to Benjamin Kadoch; benjamin.kadoch@univ-amu.fr

Received 16 February 2024; Revised 20 June 2024; Accepted 24 June 2024

Academic Editor: Mohamed Louzazni

Copyright © 2024 Jorge Contreras et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In Chile, the solar thermal regulation DS331, which utilizes a global modeling approach, governs the deployment of solar thermal systems (STSs) across highly variable climatic zones. This regulation's one-size-fits-all approach often misrepresents the solar potential and economic feasibility in different regions. To address these limitations, we introduce a refined modular energy model that incorporates a 1D multinode stratification technique for hot water storage. This model is associated with a multiobjective optimization process using the NSGA-II algorithm, focusing on optimizing the solar collector area and storage volume to maximize solar fraction and life cycle savings (LCSs) across 20 major Chilean cities. Our results demonstrated that the optimized systems achieve solar fractions ranging from 0.92 to 1.00, significantly improving upon the current regulation's performance, particularly in southern regions where solar radiation is lower. Notably, the optimized configurations suggested a potential reduction in collector areas by up to 20% and storage volumes by up to 15% compared to those recommended by DS331, while still exceeding the legal requirements for the solar fraction. This optimization made it possible to increase LCS by ~25%–30% across various scenarios, indicating a substantial improvement in cost-effectiveness. Based on these findings, existing solar thermal regulations should be revised to take into account local climatic and consumption data. Such adjustments would ensure more accurate sizing of STS, enhanced economic viability, and greater incentive alignment for widespread adoption. This study underlines the critical role of detailed, location-specific energy modeling in shaping effective energy policies and advancing the deployment of renewable technologies in diverse environmental contexts.

## 1. Introduction

Chile's primary energy mix, similar to that of many developing countries, is heavily reliant on fossil fuels, accounting for nearly 80% of its total energy consumption despite the country's significant potential for harnessing solar energy [1]. With no domestic oil reserves, Chile must import virtually all its fossil fuel needs, making it highly vulnerable to international fuel price fluctuations and posing risks to its economic development [2]. On the other side, Chile has an enormous solar energy potential that could lead to a significant reduction in fossil fuel consumption and greenhouse gas emissions in the country's residential sector [3]. The energy needs of this sector to produce domestic hot water (DHW)

are currently satisfied by ~70% liquefied gas, 25% natural gas, and 5% from electricity, firewood, and other fuels, with minimal use of renewable energy [4]. Therefore, solar thermal energy could play a significant role to reduce the primary energy consumption, thus contributing to reach the sustainable development goals proposed by the Agenda 2030 [5].

In response to the growing interest in solar thermal energy and the national goal of energy independence, the Chilean Government Enacted Law 20,365 in 2009, offering tax incentives to construction companies implementing STS in new residential buildings [6]. This legislation requires STS to achieve a minimal annual solar fraction, defined as the ratio of annual energy supplied by the STS to the annual

<footnote n="1">¹EPROIC Ingeniería y Construcción Ltda, Viña del Mar, Chile</footnote>

<footnote n="2">²Aix-Marseille Université, CNRS, IUSTI, Marseille, France</footnote>

<footnote n="3">³Department of Geophysics, University of Chile, Avenue Blanco Encalada 2002, Santiago, Chile</footnote>
DHW energy demand, with a permissible verification tolerance of up to 15% [4]. Continuous regulation evaluation is then crucial for enhancing solar thermal energy deployment and ensuring long-term sustainability. While studies have compared Chilean regulations with international standards and assessed the impact of incentives, the effectiveness of these regulations in terms of solar modeling has yet to be thoroughly examined [4, 7].

The use of solar thermal energy for DHW and heating applications has been studied specifically for Chile in recent years by several researchers. The solar potential of roof housing in Valparaiso was estimated by Araya-Muñoz et al. [8] using aerial photography, topographic groundwork, and meteorological data. Escobar et al. [9] evaluated the potential of solar thermal systems (STSs) in Chile using measurements and satellite estimations, finding that solar fractions of up to 80% are achievable. The combined use of STS, heat pump, and conventional boiler was evaluated in [10] for commercial, in [11] for residential, and in [12] for mining applications. The effect of the hot water consumption profile on life-cycle savings (LCS) for a flat-plate solar water collector plant across the country was evaluated by Araya et al. [13] by using a genetic algorithm (GA).

In Brazil, the widespread use of electrical showerheads in the country contributes to a significant burden on the electricity sector, with high running energy costs and low return on investment [14]. Moreover, the technical and economic viability of low-cost domestic solar hot water systems (DSHWS) in low-income residential dwellings has been assessed, showing attractive results for utility-scale deployment [15]. It is worth noting that the potential for carbon dioxide reduction varies across different climatic zones, with solar water heating systems demonstrating low CO₂ emissions reduction in hot regions [16]. Additionally, studies have evaluated the impact of DSHWS on the cost of a hot shower in low-income dwellings, revealing significant savings and highlighting the distorted tariff model that only accounts for energy consumption per residential unit [17]. Furthermore, analyses have found that the south region of Brazil is identified as having the best sites for implementation, while the southeast region offers the greatest economic potential [18].

Similar research has been conducted in Mexico, where solar water heaters have the potential to save significant amounts of energy and reduce carbon emissions [19]. However, barriers related to building conditions, low income, and access to water need to be addressed to facilitate the widespread adoption of solar water heating systems [20]. Overall, these studies provide valuable insights into the technical, economic, and environmental aspects of solar water heating systems in low-income residential dwellings, highlighting their potential benefits and the challenges that need to be overcome.

Regrettably, the comparison of regulation effectiveness in terms of solar modeling has not been assessed. Availability of advanced techniques to model and optimize technical components of STSs with less computational cost for policy-making are available easiest than never before. The utilization of such techniques to optimize parameters should be addressed to provide more detailed tools to improve tax

utilization performance. One advanced approach could be multiobjective optimization techniques using evolutionary algorithms. This technique has proven to be an effective method to design and control for residential building applications [21, 22]. This approach has been utilized recently, for example, in [23], where the dominant parameters affecting the robustness of solar DHW system performance were identified through a parametric study. The problem of consumption profiles affecting the optimization process was addressed by Renaldi et al. [24], indicating that it is crucial for the sizing process of STSs. The combined utilization of multiobjective optimization with GA, along with more detailed solar thermal energy models that could consider the DHW consumption profile, could be a time-effective approach to evaluate solar thermal regulation with the aim of providing more reliable information to policy-makers and applicants for tax benefits.

The objective of this study is to assess the current Chilean solar thermal regulation by comparing its prescribed performance with optimized results from a validated modular simulation model. This research highlights the novelty of employing more sophisticated models to assess STSs, demonstrating the necessity for advanced methodologies that can capture nuanced performance differences under diverse climatic conditions.

The remainder of this paper is organized as follows: Section 2 describes the methodology, including the geographical conditions, system configurations, and energy models used in our simulations. Section 3 presents the results and discussion, highlighting the optimized STS parameters and their implications across different Chilean climates. Finally, Section 4 concludes the paper with a summary of our findings and recommendations for future research and policy considerations.

## 2. Methodology

### 2.1. *Geographical Conditions and Chilean Solar Climate Zones (CSCZs)*
Chile's geography is remarkably diverse, spanning 4,329 km in length and averaging 180 km in width. Positioned between latitudes 17° 30' S and 56° 30' S, it encompasses a total area of 756,096.4 km², including Pacific islands such as Easter Island. The population is ~17,373,831, with 40% residing in the Santiago Metropolitan area, 11% in the Concepción Region, and 10% in the Valparaíso Region [25]. Figure 1 displays the selected cities for this study alongside solar radiation data across the country. These cities are among Chile's most populous and host significant services and industries. The solar radiation data, representing average hourly solar radiation on an inclined plane at the city's latitude and average hourly ambient temperature, was obtained from the Ministry of Energy's Solar Energy Explorer [26].

Despite Chile's diverse geography and climate, the Chilean regulation [6] establishes only six CSCZs, as depicted in Figure 1, with specified minimum solar contribution requirements for each zone, as listed in Table 1.

### 2.2. *System Configuration*
The modular design of the STS used for providing DHW is depicted in Figure 2. This system consists of flat-plate solar collectors designed to convert solar radiation into usable thermal energy, a vertically oriented
<figure><img src="image_2.png" /><figcaption>FIGURE 1: Map of Chile showing solar radiation distribution [26] and the Chilean solar climate zones (CSCZs) as defined by Law 20,365 [6]. Solar radiation is illustrated on a plane inclined at the corresponding latitude.</figcaption></figure>

cylindrical storage tank for accumulating this energy, and an auxiliary heater to address any deficits in solar energy. These components are interconnected through insulated pipelines that facilitate the flow of a working fluid [27]. The storage tank's vertical arrangement enhances thermal stratification,

allowing for higher temperatures at the top and cooler temperatures at the bottom. Additionally, the auxiliary system includes a natural gas boiler that supplies the necessary energy to maintain operational temperatures whenever the STS's solar output is insufficient.
<table><caption>TABLE 1: Description of CSCZ according to global mean annual global solar radiation, mean annual daily global solar radiation and the minimum required solar contribution ($f_{min}$).</caption><thead><tr><th>SCZ</th><th>H' (kW·hr/m<sup>2</sup> year)</th><th>H (kW·hr/m<sup>2</sup>)</th><th>f<sub>min</sub> (%)</th></tr></thead><tbody><tr><td>A</td><td>≥ 1,948</td><td>H ≥ 5.34</td><td>75</td></tr><tr><td>B</td><td>1,701–1,948</td><td>4.66–5.34</td><td>66</td></tr><tr><td>C</td><td>1,454–1,701</td><td>3.98–4.66</td><td>57</td></tr><tr><td>D</td><td>1,208–1,454</td><td>3.31–3.98</td><td>48</td></tr><tr><td>E</td><td>961–1,208</td><td>2.63–3.31</td><td>39</td></tr><tr><td>F</td><td>&lt;961</td><td>&lt;2.63</td><td>30</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>FIGURE 2: Scheme of the solar thermal system utilized for simulations with the modules considered, taken from [13].</figcaption></figure>

The optimization model's assumptions include:

(1) Collector slope matching the city's latitude and orientation toward the north to maximize annual solar capture.

(2) Each collector has a 2.23 m² absorption area, 0.811 optical efficiency, and 3.653 W/m²·K overall loss factor [4].

(3) The useful energy provided by solar collectors is computed using the approach proposed by Hottel and Whillier [28].

(4) The cylindrical storage tank is modeled considering 1D stratification, where each node is assumed to be perfectly mixed [29].

(5) DHW outlet temperature is set at 45 °C as per Chinese standards [6].

(6) The storage tank volume to collector area ratio (l/m²) complies with [6]: $40 \le \frac{V}{A} \le 180$.

(7) Excludes losses beyond the STS itself.

2.3. *Energy Model.* Energy models for each subsystem were developed and implemented using MATLAB. Under steady-state conditions, the performance of a solar collector is analyzed using

an energy balance equation. This equation describes the useful energy output, $\dot{Q}_u$, of a flat-plate solar collector as the difference between the absorbed solar radiation and thermal losses, as formulated by Hottel and Whillier [28]:

$$ \dot{Q}_u = A_c F_r [I_T(\tau\alpha) - U_L(T_{in,c} - T_{amb})]^+ . \quad (1) $$

Empirically, the performance of a solar collector is assessed by exposing it to sunlight and measuring the temperature at the fluid's inlet and outlet alongside the flow rate. The useful thermal gain is calculated as follows [29]:

$$ \dot{Q}_u = \dot{m}_c c_p (T_{out,c} - T_{in,c}) . \quad (2) $$

The storage tank is modeled using a 1D multinode stratification approach [29]. Its cylindrical shape promotes stratification, enhancing the system's efficiency by facilitating the extraction of hot water from the top and the delivery of colder water to the bottom, thus optimizing the overall energy efficiency [2]. Figure 3(a) illustrates the divided volume of the tank into multiple nodes, each assumed to be perfectly mixed. The energy balance for each node is expressed by Equation (3):
<figure><img src="image_4.png" /><figcaption>FIGURE 3: Schematic diagram of the storage tank illustrating (a) the stratification methodology and (b) the energy balance at node j.</figcaption></figure>

$$m_{s,j}c_p \frac{dT_{s,j}}{dt} = U_s A_{s,j} (T_{s,j} - T_{amb}) + \frac{(k_f + \Delta k) A_{tr,j} (T_{s,j+1} - T_{s,j})}{\Delta x} + \frac{(k_f + \Delta k) A_{tr,j} (T_{s,j-1} - T_{s,j})}{\Delta x} + \dot{Q}_{up} + \dot{Q}_{down} + \dot{Q}_{one} + \dot{Q}_{end}, \quad (3)$$

where the terms are defined as follows:

$$\dot{Q}_{up} = (\dot{m}_l - \dot{m}_c)c_p(T_{s,j+1} - T_{s,j}), \quad \text{if } \dot{m}_c < \dot{m}_l, \quad (4)$$

$$\dot{Q}_{down} = (\dot{m}_c - \dot{m}_l)c_p(T_{s,j-1} - T_{s,j}), \quad \text{if } \dot{m}_c > \dot{m}_l, \quad (5)$$

$$\dot{Q}_{one} = \dot{m}_c c_p T_{out,c} - \dot{m}_l c_p T_{s,1}, \quad \text{if } j = 1, \quad (6)$$

$$\dot{Q}_{end} = \dot{m}_l c_p T_{sup} - \dot{m}_c c_p T_{s,N}, \quad \text{if } j = N, \quad (7)$$

and $\Delta k$ is a modification factor for conductivity, given by the following:

$$\Delta k = k_w \frac{A_{s,w}}{A_{s,fl}}. \quad (8)$$

Important relationships affecting storage tank simulations include the ratio between tank height (H) and tank diameter (d) ratio, typically between 1.5 and 3.5. In this study, this ratio is set as $H = 2.5d$ [30]. Additionally, the relationship between collector surface area and storage volume is critical due to significant temperature variability within the tank.

Finally, the auxiliary system, an existing natural gas boiler, supplements the STS when solar energy is insufficient. The heat provided by this system is calculated using Equation (9):

$$\dot{Q}_{aux} = \dot{m}_l c_p (T_{load} - T_{s,1})^+. \quad (9)$$

Thus, the overall system energy balance is maintained by accounting for all heat contributions and losses as expressed in Equation (10):

$$\dot{Q}_{load} = [\dot{Q}_{u} + \dot{Q}_{aux} - \dot{Q}_{loss}]^{+}. \quad (10)$$

This equation ensures that the required energy, $\dot{Q}_{load}$, primarily derived from the STS, is supplemented by the auxiliary system as needed to maintain optimal tank water temperature.

## 2.4. Hot Water Demand.
The study models a multifamily building's DHW demand following Chilean standards, which stipulate a water temperature of 45 °C and a daily consumption volume of 30 l/person. For the building in question, the total daily DHW requirement is 2,700 l. Given the significant variability in DHW consumption patterns across different regions due to a variety of factors, including climate, socioeconomic conditions, and lifestyle [31], this study employs six distinct daily hot water consumption profiles, as outlined by Araya et al. [13]. While current regulations assume a uniform consumption pattern similar to Profile 1, this research explores the implications of diverse usage profiles on the evaluation of tax benefits, providing a more nuanced understanding of DHW demand dynamics. The profiles are summarized in Table 2.

## 2.5. Financial Model and Economic Aspects.
This section presents the financial model, describing the detailed cost calculations and financial assumptions that are essential to determining the economic feasibility and benefits of adopting solar thermal energy.

The financial analysis of STSs under varying CSCZs and DHW consumption profiles is conducted using the life cycle saving (LCS) approach [29, 32]. This method evaluates the economic viability of STS by comparing the life cycle costs (LCC) of conventional energy systems and STS inclusive of auxiliary heating solutions. The LCC includes the initial investment, the replacement, and the annual operation and maintenance (O&M) expenses, in addition to the cost of auxiliary power when solar energy is insufficient. The calculation
<table><caption>TABLE 2: Daily hot water demand profiles used, adapted from [13].</caption><thead><tr><th>Thermal profile description</th><th>Profile</th></tr></thead><tbody><tr><td>Profile 1: uniform consumption throughout the day</td><td></td></tr><tr><td>Profile 2: uniform consumption between 8:00 and 16:00 hr</td><td></td></tr><tr><td>Profile 3: concentrated consumption, 90% between 13:00 and 15:00 hr and 10% at 16 hr</td><td></td></tr><tr><td>Profile 4: increasing consumption from 7:00 to 15:00 hr</td><td></td></tr><tr><td>Profile 5: based on ISO 9,459–3:2007 domestic thermal water use</td><td></td></tr><tr><td>Profile 6: incremental consumption peaking during hours of high solar radiation, then decreasing</td><td></td></tr></tbody></table>

of LCS is crucial for determining the cost-effectiveness of implementing STS compared to conventional energy systems. The LCS, representing the net savings of using STS compared to conventional systems, is a critical indicator for assessing the financial attractiveness of solar thermal solutions. It is defined as the difference between the LCC of conventional systems (LCC<sub>con</sub>) and that of STSs with auxiliary components (LCC<sub>sol</sub>) [29]:

$$LCS = LCC_{con} - LCC_{sol}. \qquad (11)$$

The present worth factor (PWF), as presented by Duffie and Beckman [29], is applied to discount future expenses to their present value, accounting for the project's lifespan (N), market discount rate ($r_i$), and inflation (r):

$$\text{PWF}(N, r_i, r) = \sum_{j=1}^{N} \frac{(1+r_i)^{j-1}}{(1+r)^j} = \begin{cases} \frac{1}{r-r_i} \left(1-\left(\frac{1+r_i}{1+r}\right)^N\right) & \text{if } r_i \neq r \\ \frac{N}{1+r_i} & \text{if } r_i = r \end{cases}. \qquad (12)$$

The LCC for conventional systems (LCC<sub>con</sub>) relies on the total demand ($Q_{load}$), fuel cost ($C_{fuel}$), and PWF:

$$LCC_{con} = Q_{load}C_{fuel}\text{PWF}(N, r_i, r). \qquad (13)$$

Conversely, the LCC for STS (LCC<sub>sol</sub>) incorporates initial investments, debt payments, and operational expenses,

including auxiliary system costs:

$$LCC_{sol} = C(1-f_d) + D \cdot \text{PWF}(N', r_i, r) + (C_{O&M} + C_{aux}) \cdot \text{PWF}(N, r_i, r), \qquad (14)$$

where C is the initial cost, D denotes annual debt payments, $C_{O&M}$ represents annual operation and maintenance costs,
<table><caption>TABLE 3: System costs and financial parameters.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>Energy costs</td><td></td><td></td></tr><tr><td>Electricity</td><td>0.13</td><td>USD/kW·hr</td></tr><tr><td>Gas (LPG)</td><td>1.3</td><td>USD/mJ</td></tr><tr><td>Investment costs</td><td></td><td></td></tr><tr><td>Solar collector</td><td>300.1</td><td>USD/m<sup>2</sup></td></tr><tr><td>Storage tank</td><td>2,000.4</td><td>USD/m<sup>3</sup></td></tr><tr><td>O&amp;M</td><td>5</td><td>% of investment cost</td></tr><tr><td>Financial parameters</td><td></td><td></td></tr><tr><td>Inflation rate</td><td>3</td><td>%</td></tr><tr><td>Discount rate</td><td>10</td><td>%</td></tr><tr><td>Project lifespan</td><td>20</td><td>Years</td></tr><tr><td>Leverage ratio</td><td>50</td><td>%</td></tr><tr><td>Interest rate on debt</td><td>10</td><td>%</td></tr><tr><td>Debt repayment period</td><td>10</td><td>Years</td></tr></tbody></table>

and $C_{aux}$ is the cost associated with the auxiliary system. The initial investment is defined as follows:

$$C = c_{fixed} + c_{c}A_{c} + c_{s}V_{s}, \quad (15)$$

where $c_{fixed}$ is the fixed cost, $c_c$ is the cost per solar collector area, $c_s$ is the cost per volume unit of the storage tank. The annual payments of initial investment debt are computed using the following:

$$D = \frac{f_d \cdot C(r_d(1 + r_d)^{N'})}{(1 + r_d)^{N'} - 1}, \quad (16)$$

where $f_d$ represents the leverage rate and $N'$ the debt evaluation period. The auxiliary system costs are expressed as a function of the auxiliary energy required ($Q_{aux}$) as follows:

$$C_{aux} = Q_{aux}C_{fuel}PWF(N, r_i, r). \quad (17)$$

The financial parameters, system costs, and assumptions used in this analysis are detailed in Table 3, and parameters are extracted from [33], providing a basis for evaluating the economic performance of STS in Chile.

## 2.6. Multicriteria Optimization.
Multicriteria optimization seeks to balance multiple objectives, recognizing that improvements in one area may lead to tradeoffs in another [34]. This study employs the NSGA-II GA [35] for its robustness in handling complex optimization problems with multiple objectives and constraints. Indeed, NSGA-II is an evolutionary algorithm that applies the principle of dominance-based selection to generate and maintain a set of the best compromises with respect to several objectives that may be contradictory. A major limitation is its inability to guarantee an exact solution for multiobjective optimization problems, instead providing a set of nondominated solutions that form a Pareto front.

<figure><img src="image_5.png" /><figcaption>FIGURE 4: Optimization of LCS and a solar fraction ($f$) using the NSGA-II algorithm for Arica, illustrated with hot water demand Profile 1.</figcaption></figure>

By simulating various configurations of collector area and storage volume across different CSCZs and consumption profiles, the algorithm is used to identify a set of Pareto-optimal solutions, each representing an optimal tradeoff between objectives such as maximizing solar fraction and minimizing system cost. The parameters of NSGA II [35] used in this study are the following. The percentages of mutation and crossing are 40% and 70%, respectively. Fifty individuals and 300 generations are considered, which corresponds to 15,000 evaluations per city and profile of demands.

## 2.7. Multicriteria Decision-Making.
The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method [36] guides the selection of the best solution from the Pareto-optimal set by identifying the option closest to the ideal solution, thereby facilitating decision-making among multiple criteria. This approach is particularly valuable in weighing the relative merits of system configurations to achieve both high efficiency and cost-effectiveness in STS deployment. For example, in Figure 4, the best solutions of the city of Arica with Profile 1 are at the extremities of the Pareto front for each objective function. By applying the TOPSIS methodology, the best decision is obtained for both criteria.

## 2.8. Optimization Procedure Summary.
This subsection provides an overview of the optimization process:

The objectives of this study are to maximize the solar fraction and the LCS which are related to energy and cost criteria, respectively. The dimension parameters considered for our optimization study are the surface of solar collectors $A_c$ and the volume of the storage tank $V_s$. The relationship between the volume of the storage tank and the installed surface of the solar thermal collectors is imposed by Chilean regulations:
<table><caption>TABLE 4: Synthesis of the optimization problem.</caption><thead><tr><th>Variables</th><th>Range</th><th>Objectives to be maximized</th></tr></thead><tbody><tr><td>Collector area A<sub>c</sub> (m<sup>2</sup>)</td><td>[2–200]</td><td>Solar fraction f</td></tr><tr><td>Storage tank volume V<sub>s</sub> (m<sup>3</sup>)</td><td>[1–20]</td><td>Life-cycle savings LCS (USD)</td></tr><tr><td colspan="3">Constraint</td></tr><tr><td colspan="3">40 ≤ 10<sup>3</sup> · V<sub>s</sub>/A<sub>c</sub> ≤ 180</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>FIGURE 5: Procedure chart.</figcaption></figure>

$$40 \leq \frac{V}{A} \leq 180. \qquad (18)$$

This criterion is taken into account in the NSGA II optimization algorithm by rejecting configurations that do not meet this condition. The optimization problem with objectives, parameters of variations, and constraints is summarized in Table 4.

Figure 5 shows a schematic diagram of the multiobjective optimization procedure used, whose main principles are as follows. After selecting the city and the DHW draw profile, an initial population is randomly selected from the parameter space subject to a constraint on the ratio of collector area and storage tank volume as defined in Table 4. Then the NSGA II optimization algorithm converges to a Pareto front built for Solar fraction and LCS to be maximized. This Pareto front is the set of nondominated solutions obtained from the parameter sets generated by crossover and mutation, and which respects the ratio constraint. Based on the Pareto front, a multiobjective decision technique, TOPSIS, is applied to define the best compromise, which then gives us the optimized parameters for the given city and DHW profile.

### 3. Results and Discussion

In this section, a critical assessment of the current solar thermal regulation in Chile (DS331) is conducted by comparing

this regulation with a detailed modular energy model coupled with a multiobjective optimization approach. First, in Section 3.1, the overall optimized results obtained using our procedure for different hot water demand profiles and for the different cities studied are examined. A comparison is then conducted with the Chilean standard in Section 3.2. Finally, the monthly dynamics of optimized results are investigated for different configurations (Section 3.3).

3.1. *Optimized Results.* The optimization results are investigated below. These results are obtained using the TOPSIS method applied to the Pareto front resulting from NSGA-II optimization for given cities and hot water demand profiles.

Figure 4 shows the Pareto front obtained from NSGA-II for the city of Arica and Profile 1 of the hot water demand. Similar results were obtained for every case studied. The nonlinear curve illustrates that the LCS and *f* evolutions are not similar. This is confirmed by the fact that the maxima of LCS and *f* are located opposite each other. Moreover, the ranges of LCS ∈ [5, 000, 22, 500] and *f* ∈ [0.92, 1] are not of the same order, which means that a small variation of *f* could generate a strong change in LCS. A plateau is also observed around *f* ≈ 1. This value could be approached by oversizing the system with a large surface of the solar collectors and a large volume of the water tank, which will be accompanied by a significant increase in the cost, so a decrease of LCS.
<figure><img src="image_7.png" /><figcaption>FIGURE 6: Optimized results for selected cities regarding surface area, storage volume, LCS, and solar fraction *f*, presented for the optimized area (m²) and volume (m³).</figcaption></figure>

From the Pareto Front, optimized collector area and hot water storage volume are selected using the TOPSIS decision-making technique, as illustrated by the “Best for *f*” in Figure 4 for Profile 1 in Arica. The distribution of optimized design parameters across the country, alongside LCS and *f* for the six consumption profiles, is illustrated in Figure 6. Geographical

influences are notable; southern cities, receiving less solar radiation, typically require larger collector areas to achieve higher solar fractions, while coastal cities, with frequent cloudy conditions, experience reduced average solar radiation. These results align with expectations, although the impact varies depending on the consumption profile and storage capacity.
For instance, Profile 3 (green) demonstrates a smaller collector area in the southern city of Puerto Williams (city 20) compared to cities like Temuco (city 13), Puerto Montt (city 15), and Castro (city 16), which are located further north. To enhance energy and financial outcomes, an increase in hot water storage volume is necessary for these cities, varying with the consumption profile. Conversely, under Profile 4 (red), cities 13 and 16 require less collector surface and storage volume compared to Puerto Williams (city 10). Comparatively, Puerto Montt (city 15) shows a smaller collector surface and storage volume than Puerto Williams. Such distinctions are critical for policy-making, suggesting the potential for tailored tax benefits based on CSCZs and consumption profiles in upcoming regulations.

Regarding hot water storage, its sensitivity to meteorological zones is less pronounced than that of collector surface area, but it is predominantly influenced by consumption profiles. For instance, in northern cities, Profiles 1 (blue) and 3 (green) necessitate larger storage volumes, whereas in southern cities, Profile 2 plays a more significant role in increasing storage capacity. All optimized systems exceed the solar fraction minimums set by current law, qualifying them for tax benefits.

This comparative evaluation underscores the need for a nuanced approach in the regulatory assessment of STSs. By integrating diverse consumption profiles and considering geographical variability, policymakers can refine solar thermal incentives to better reflect the operational realities of STS deployment across Chile's varied climatic landscape.

### 3.2. *Comparison Results*
This subsection of the study employs the optimized design parameters as inputs to evaluate the solar fraction ($f$) as defined by the current Chilean solar thermal regulation (DS331), accessible through the Solar Energy Explorer online platform provided by the Chilean Ministry of Energy [26]. A comparative analysis between the DS331 methodology and the modular simulation model augmented by a GA (referred to here as the GA method for brevity) is presented in Figure 7. This comparison employs scatter plots to illustrate the discrepancies in $f$ calculations under varied optimization scenarios: (a) TOPSIS, (b) maximum LCSs, and (c) maximum $f$.

In the comparative graphs of Figure 7, the y-axis represents $f$ as predicted by DS331, while the x-axis depicts the results derived from the GA model. The diagonal line ($y=x$) serves as a benchmark, indicating instances where DS331 predictions align with GA model outcomes. Notably, the analysis reveals that while predictions converge around higher solar fractions, particularly evident in the northern regions with abundant solar irradiance, significant discrepancies emerge as solar fractions diminish. This misalignment is pronounced in the results obtained for southern cities, where the DS331 method consistently underestimates $f$ compared to the GA model. The magnitude of this underestimation accentuates as one moves toward cities with lower solar irradiance.

To quantify the divergence between the two methodologies across all evaluated profiles, the root mean square error (RMSE) was calculated, revealing that solar fractions for

Profiles 1, 5, and 6 exhibit an RMSE of 0.15, with maximal disparities of 0.27, 0.26, and 0.25, respectively. Profiles 2 and 3 show slightly larger discrepancies, both with an RMSE of 0.17 and maximal differences reaching up to 0.33 and 0.27. Profile 4, representing the city of Valparaíso, showcases the greatest deviation with an RMSE of 0.21.

Interestingly, when focusing on results that optimized LCS within the Pareto front, the observed discrepancies align closely with those identified using the TOPSIS methodology. This consistency underscores the nuanced relationship between system sizing parameters and their impact on $f$ and LCS, particularly when assessed through the lens of the sophisticated GA model as opposed to the DS331 method. These results are consistent with those found in [31], confirming that (DHW) consumption profiles may play a really important role in establishing energy policies.

The ensuing analysis focuses on cities that represent the diverse climatic spectrum of Chile. A detailed examination over a year, utilizing the optimized parameters for six distinct water consumption profiles, reveals the disparity between the current regulatory framework and the advanced GA method (Figure 8). These analyses not only quantify the deviation between the two approaches but also offer insights into potential regulatory enhancements to better capture the solar fraction across varied climatic zones.

For the CSCZ A, in Figure 8, corresponding to the northern zone, which is the one with the highest solar radiation in the country, solar fractions between the GA model and DS331 methodology differ only slightly and even, in some situations, the most sophisticated model predicted lower solar fractions. This situation is completely different when the other CSCZ's, which are characterized by lower solar radiation, are analyzed. For example, the current regulation presents a lower solar fraction compared to the GA model for the city of Santiago. This is the capital and the most populated city of the country and consequently, where most market potential exists. Thus, it is necessary to consider evaluate deeper these results to avoid oversizing of STSs. It is important to mention that 27% of the evaluations were below the minimum required if they were evaluated according to the current actual regulation. Indeed, this is mainly due to the different consumption profiles that the current regulation does not consider. These differences are more remarkable in southern cities where under predictions of a solar fraction by the current methodology are greater. Profile 1 is the most comparable one due to a similar consumption profile between the two methods. In zones C and E, corresponding to the city of Talca and Castro, the current regulation will not allow the system for the tax benefit.

These findings underscore a critical observation: the methodology currently employed by the Chilean government for the allocation of solar thermal tax benefits consistently yields lower solar fractions, particularly for consumption profiles and solar climate zones with inherently lower solar irradiance. The study further identifies a pressing need for a more nuanced approach in regulatory assessment to avoid potential oversizing of STSs, which could inadvertently hinder their broader
<figure><img src="image_8.png" /><figcaption>FIGURE 7: Comparison of solar fraction (f) calculations between DS331 and the GA model under various optimization conditions: (a) TOPSIS, (b) maximum LCS, and (c) maximum f.</figcaption></figure>

implementation. In addition, the authors of [37] quantified the effects of climate change on the variation of climatic zones and heating energy consumption of residential buildings in southern Chile, unveiling the impossibility of using actual building norms in the future.

3.3. *Monthly Energy Dynamics*. For a deeper understanding of the results, monthly energy dynamics for both models are presented in this part.

Figures 7 and 8 highlight notable differences in the solar fractions derived from the proposed GA model and the DS331
<figure><img src="image_9.png" /><figcaption>FIGURE 8: Illustration of the monthly evolution of solar fraction across six representative cities in Chile, utilizing optimized parameters. The red dashed line denotes the minimum solar fraction requisite for tax benefit eligibility.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>FIGURE 9: Continued.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>FIGURE 9: Monthly dynamics of energy over a year for the cities of CSCZ A (a–e) using uniform consumption profile (Profile 1). Above each plot, the optimized A_c, V_s, LCS, and annual solar fraction results are given. The inclination of the solar collector is identical to the latitude of each city as recommended by the regulation [6].</figcaption></figure>

methods across various CSCZs, particularly under conditions of lower solar fractions. These differences are further explored by examining the annual energy dynamics of cities within CSCZ A, the northernmost zone known for its high solar energy resources. Here, uniform Profile 1 is employed for consistency with the DS331's standard consumption profile.

Figure 9 illustrates the monthly energy performance throughout the year for five selected cities in CSCZ A, where the available energy from solar radiation (E\_avail) is plotted using a dash-dot line. This indicator is calculated as follows:

$$E_{avail} = \left( \sum_{i=1}^{24} I_i \times A_c \right) \times n, \qquad (19)$$

where I is the average hourly solar radiation, A_c is the optimized collector area, and n is the number of days per month, allows for direct comparison between the GA model and DS331 outcomes. Notably, in Arica (Figure 9(a)), the detailed GA model forecasts lower solar fractions from May to November, with the greatest discrepancies in September. Conversely,
<figure><img src="image_12.png" /><figcaption>FIGURE 10: Continued.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>FIGURE 10: Comparison of results using uniform consumption profile (Profile 1) with GA method with DS331 regulation. The selected cities corresponds to the cities of CSCZ A (a–e). All simulations are performed using the same parameters for the solar area ($A_c = 34.7 \text{ m}^2$) and tank volume ($V_s = 3.59 \text{ m}^3$) corresponding to the average of optimized parameters for these cities in Figure 9. The inclination of the solar collector is identical to the latitude of each city as recommended by the regulation [6].</figcaption></figure>

in Copiapo (Figure 9(e)), located in the southern part of CSCZ A with less solar radiation, the GA model predicts higher solar fractions during the summer, a trend that reverses in winter, extending until November, where DS331 estimates higher fractions.

This analysis indicates that the optimized systems perform effectively even in areas with lesser solar resources, such as Copiapo. Cities, like Calama (Figure 9(d)) and Antofagasta, also show that the GA method generally yields higher solar fractions than the DS331 method throughout most of the year. These observations suggest that as solar radiation availability increases, both methodologies converge, reflecting closer results due to reaching the upper limit of a solar fraction where excess energy is not utilized. While a detailed mathematical analysis of these differences could provide deeper insights, it falls beyond this study's scope, which aims to critique current regulations and suggest updates for the DS331 based on empirical findings.

To further compare the two methodologies in relation to solar fraction, we analyzed the average optimized parameters for the five cities within CSCZ A, shown in Figure 9. Using these averages, a collector area of 34.7 m² and a water storage volume of 3.59 m³, new simulations were conducted across these cities. Figure 10 displays the results, which include the annual solar fraction and LCS obtained via the GA method. This comparative analysis reveals that solar fraction discrepancies between the two methodologies are generally smaller for northern cities than for southern ones within the same CSCZ. For instance, in Arica, DS331 typically predicts higher solar fractions than the GA method, whereas in Copiapó, the GA method predicts higher fractions. This

<table><caption>TABLE 5: Global yearly solar fractions and percentage of difference for CZCS A.</caption><thead><tr><td>City</td><td>DS331</td><td>GA</td><td>Percentage of difference</td></tr></thead><tbody><tr><td>Arica</td><td>0.98</td><td>0.92</td><td>6</td></tr><tr><td>Iquique</td><td>0.92</td><td>0.92</td><td>0</td></tr><tr><td>Antofagasta</td><td>0.94</td><td>0.98</td><td>-4</td></tr><tr><td>Calama</td><td>0.98</td><td>0.96</td><td>2</td></tr><tr><td>Copiapo</td><td>0.87</td><td>0.95</td><td>-9</td></tr></tbody></table>

trend demonstrates that DS331 tends to overestimate solar fractions in the north but underestimates them as one moves southward, as detailed in Table 5.

A comparative analysis was conducted for cities in southern Chile, where solar radiation is minimal, to evaluate the disparities between the DS331 and the GA method under low solar fractions. The cities studied, shown in Figure 11, include Puerto Montt and Coyhaique in CSCZ D, Castro and Puerto Natales in CSCZ E, and Punta Arenas and Puerto Williams in CSCZ F. For this analysis, uniform water consumption (Profile 1) and optimized parameters derived from the GA method were applied to each city and compared using the DS331 methodology. Unlike the northern cities, significant differences were noted in solar fraction results across all southern cities, especially during the winter months, as depicted in Figure 11. This marked divergence, particularly when solar radiation is low, underscores the challenge of adhering to regulatory solar fraction requirements. Such scenarios suggest that regulatory models might need to account for larger collector areas to meet these requirements in regions with lower
<figure><img src="image_14.png" /><figcaption>FIGURE 11: Continued.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>FIGURE 11: Monthly energy dynamics over a year for the southern cities (a–f) using uniform consumption profile (Profile 1). Above each plot also, the optimized $A_c$, $V_s$, LCS, and annual solar fraction results are given. The inclination of the solar collector is identical to the latitude of each city as recommended by the regulation [6].</figcaption></figure>

<table><caption>TABLE 6: Differences of annual average solar fraction for both methods for the cities of Figure 11.</caption><thead><tr><td>City</td><td>DS331</td><td>GA</td><td>Percentage of difference</td></tr></thead><tbody><tr><td>Puerto Montt</td><td>0.60</td><td>0.86</td><td>-43</td></tr><tr><td>Castro</td><td>0.56</td><td>0.89</td><td>-59</td></tr><tr><td>Coyhaique</td><td>0.63</td><td>0.85</td><td>-35</td></tr><tr><td>Puerto Natales</td><td>0.47</td><td>0.76</td><td>-61</td></tr><tr><td>Punta Arenas</td><td>0.55</td><td>0.80</td><td>-45</td></tr><tr><td>Puerto Williams</td><td>0.59</td><td>0.66</td><td>-11</td></tr></tbody></table>

solar availability. Detailed percentage differences in annual average solar fractions between the two methods are tabulated in Table 6.

In Figure 11, the collector area and water storage volume are standardized to 54.5 m² and 2.9 m³, respectively, representing average values derived from optimization across the six cities studied. Figure 12 compares these results using both the GA method and the DS331 approach with identical sizing parameters. It also displays the annual solar fraction and LCS results from the GA method. This comparison reveals that the GA method generally yields a smoother evolution of the solar fraction compared to the DS331 method.

Punta Arenas, with its considerable population and significant heating needs, presents substantial potential for the deployment of solar energy technologies, particularly when leveraged through well-applied tax benefits. Figure 13 illustrates the monthly energy dynamics for Punta Arenas, situated in CSCZ E, comparing results from the GA method and the standard DS331 under optimized parameters across various hot water consumption profiles. Although DS331

generally employs a uniform consumption profile, limiting precise comparative analysis, results consistently show that the GA method yields higher solar fractions than DS331, indicating that modular modeling with optimization can enhance solar fractions without necessitating larger collector surfaces. The disparity is most pronounced in June, the period of lowest energy availability and solar fraction. This comparison also reveals that methodologies converge as the solar fraction increases with greater energy availability. Notably, the highest annual solar fraction occurs under Profile 3, where 90% of consumption is concentrated between 13:00 and 15:00, with the remaining 10% at 16:00 (Figure 13(c)). Conversely, the most favorable LCSs are observed with Profile 4, requiring a collector area of 42.9 m² and a storage volume of 2.33 m³.

The enhanced LCS and improved solar fractions achieved through our optimization model not only demonstrate the potential for increased economic viability but also highlight the importance of accurate system sizing tailored to specific regional solar irradiance profiles. Our results suggest that
<figure><img src="image_16.png" /><figcaption>FIGURE 12: Continued.</figcaption></figure>
<figure><img src="image_17.png" /></figure>

FIGURE 12: Comparison of results using uniform consumption profile (Profile 1) with proposed model and with current regulation (DS331). The selected cities corresponds to the most southern cities of the country (a–f) where normally solar potential is neglected. All simulations are performed using the same parameters for the solar area ($A_c = 54.5 \text{ m}^2$) and tank volume ($V_s = 2.9 \text{ m}^3$) corresponding to the average of optimized parameters for these cities (Figure 11). The inclination of the solar collector is identical to the latitude of each city as recommended by the regulation [6].

<figure><img src="image_18.png" /></figure>

FIGURE 13: Continued.
<figure><img src="image_19.png" /><figcaption>FIGURE 13: Monthly dynamics of energy variables for each demand profile (a–f). City selected: Punta Arenas.</figcaption></figure>

proper configuration can lead to significant cost savings and optimized energy utilization, particularly in regions with lower solar irradiance.

**4. Conclusions and Policy Implications**

This investigation critically assesses the adequacy of the Chilean solar thermal regulation (DS331) across the diverse climatic zones of Chile. Through comprehensive simulations spanning the country, this study juxtaposes the DS331 model's outcomes with those derived from a refined modular simulation model. This advanced model leverages a 1D

multinode stratification approach for hot water storage, previously validated in [13]. The examination of the regulatory framework was conducted against six daily hot water consumption profiles and encompassed 20 major Chilean cities to fully represent the climatic diversity influencing STS's efficiency and the allocation of tax benefits. An evolutionary algorithm-driven optimization was integrated with the simulation model to identify the optimal configuration of collector area and storage volume that maximizes solar fraction and LCSS over a 20-year horizon. The use of a complex methodological approach was motivated by two reasons: to propose enhancements to the existing solar thermal regulations and to
illustrate the limits of using generalized models for key concepts such as tax incentives. The efficacy of an energy policy is fundamentally linked to the reliability of the methods employed for system evaluation and the precision in forecasting the energy yield of STS. The principal findings from this study are the following:

(1) The convergence of results from both methodologies is observed as the solar fractions approach unity, primarily in the northern regions of Chile, where solar irradiance is significantly higher.

(2) The divergence between methodologies intensifies at lower solar fractions, with the current regulation typically underestimating solar fractions compared to the modular simulation model for identical system configurations.

(3) The incorporation of diverse hot water consumption profiles reveals substantial discrepancies, underscoring the importance of considering varied usage patterns in the regulatory assessment.

**4.1. Implications for Policy and Regulation.** This study provides essential information for policy-makers striving to refine strategies to encourage the adoption of solar thermal technologies. Effective energy policy serves as a crucial lever for encouraging the market penetration of renewable energy solutions. However, regulatory models may overestimate system size and, consequently, investment costs, which could discourage STS deployment. The streamlined modular simulation model, augmented by a GA optimization technique, emerges as a cost-efficient and reliable methodology for estimating solar fractions. This approach, by yielding more accurate energy production forecasts, can significantly enhance the determination of tax benefits.

**4.2. Recommendations for Future Research.** To build upon the fundamental insights offered by this study, future research should extend the analysis to quantify the impact of STS deployment on CO₂ emissions reduction. Furthermore, the integration of other key economic indicators would provide a more holistic view of the benefits and costs associated with STS investment, which would better guide policy formulation and regulatory adjustments.

In conclusion, this study not only argues for a revision of current solar thermal regulations in Chile but also serves as a basis for future research aimed at improving the design and implementation of renewable energy systems worldwide. By addressing the outlined challenges and exploring suggested future research directions, this study can contribute to a better understanding and exploitation of the unique opportunities that solar thermal energy presents in the pursuit of sustainable and resilient energy solutions.

## Nomenclature

$A_c$: Collector area (m²)

$A_{s,fl}$: Cross-sectional area of the fluid (m²)

$A_{s,j}$: Surface area of jth node (m²)

$A_{s,w}$: Cross-sectional area of tank wall (m²)

$A_{tr,j}$: Cross-sectional area of jth node (m²)

ANN: Artificial neural networks

$c_p$: Specific heat (J/kg·°C)

$C$: Total cost of initial investment (USD)

$c_e$: Cost of collector per unit area (USD/m²)

$c_{fixed}$: Fixed cost (USD)

$C_{fuel}$: Cost of fuel (USD/J)

$C_{O&M}$: Annual cost in operation and maintenance (USD)

$c_g$: Cost of storage tank per unit volume (USD/m³)

$CSCZ_s$: Chilean solar climate zones

$d$: Diameter of storage tank (m)

$D$: Annual debt payment (USD)

$f$: Solar fraction

$f_d$: Leverage rate (%)

FPSWC: Flat-plate solar water collectors

GA: Genetic algorithm

$H$: Height of storage tank (m)

$I_T$: Global irradiation on an inclined surface (W/m²)

$k_f$: Water thermal conductivity (W/m·°C)

$k_w$: Tank wall thermal conductivity (W/m·°C)

LCC: Life-cycle cost (USD)

LCS: Life-cycle savings (USD)

$\dot{m}_c$: Mass flow rate from the collector (kg/s)

$\dot{m}_f$: Mass flow rate toward load (kg/s)

$\dot{m}_l'$: Hourly mass flow rate toward load (kg/hr)

$m_s$: Mass of water in storage tank (kg)

$N$: Evaluation period (years)

$n_{month}$: Number of the month

$N'$: Debt evaluation period (years)

No: Number of nodes of the storage tank

PWF: Present worth factor

$\dot{Q}_{aux}$: Rate of energy from auxiliary system (W)

$\dot{Q}_{down}$: Downward net energy rate between two adjacent storage tank nodes (W)

$\dot{Q}_{end}$: Energy rate from the difference between the inlet's mass flow from the net and the outlet's mass flow to the collector in the last node of the storage tank (W)

$\dot{Q}_{load}$: Rate of energy required by the load (W)

$\dot{Q}_{loss}$: Energy loss rate from the storage tank to the environment (W)

$\dot{Q}_{one}$: Energy rate from the difference between the inlet's mass flow from the collector and the outlet's mass flow to the load in the first node of the storage tank (W)

$\dot{Q}_{up}$: Upward net energy rate between two adjacent storage tank nodes (W)

$\dot{Q}_{u}$: Useful energy rate from the collector (W)

$Q$: Energy (J)

$r$: Discount rate (%)

$r_d$: Debt interest rate (%)

$r_e$: Fuel escalation rate (%)

$r_f$: Inflation rate (%)

$T_{amb}$: Ambient temperature (°C)

$T_{in,c}$: Collector inlet temperature (°C)

$T_{load}$: Required hot water charging temperature (°C)

$T_{max}$: Maximum monthly temperature (°C)
$T_{\text{out,c}}$: Outlet temperature from the collector (°C)

$T_{s,j}$: Storage tank temperature in jth node (°C)

TMY: Typical meteorological year

$T_{\text{min}}$: Minimum monthly temperature (°C)

$U_L$: Overall collector heat loss coefficient (W/m²·°C)

$U_s$: Overall heat loss coefficient of the storage tank (W/m²·°C)

$V_s$: Volume of storage tank (m³)

$\Delta x$: Length of storage tank node (m)

## Greek Symbols

φ: Utilizability

ρ: Density of water (kg/m³)

$\tau\alpha$: Transmittance-absorptance of the collector.

## Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## Additional Points

**Highlights.** Current Chilean solar regulation method is compared with a more detailed methodology. Current regulation and detailed method results are similar for high radiation zones. Comparison results are up to 61% difference for low solar radiation zones. Multiobjective optimization method to be used for solar energy policy is proposed.

## Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that might be perceived to impact the integrity of the research presented in this paper.

## Acknowledgments

The authors would like to acknowledge that the study was independently carried out without external financial assistance. Open access funding enabled and organized by COUPERIN CY23.

## References

[1] A. Ortega, R. Escobar, S. Colle, and S. L. de Abreu, "The state of solar energy resource assessment in Chile," *Renewable Energy*, vol. 35, no. 11, pp. 2514-2524, 2010.

[2] F. Bustos, A. Toledo, J. Contreras, and A. Fuentes, "Sensitivity analysis of a photovoltaic solar plant in Chile," *Renewable Energy*, vol. 87, pp. 145-153, 2016.

[3] A. Molina, M. Falvey, and R. Rondanelli, "A solar radiation database for Chile," *Scientific Reports*, vol. 7, no. 1, pp. 1-11, 2017.

[4] L. M. López-Ochoa, K. Verichev, J. Las-Heras-Casas, and M. Carpio, "Solar domestic hot water regulation in the Latin American residential sector with the implementation of the energy performance of buildings directive: the case of Chile," *Energy*, vol. 188, Article ID 115985, 2019.

[5] A. A. Adenle, "Assessment of solar energy technologies in Africa-opportunities and challenges in meeting the 2030 agenda and sustainable development goals," *Energy Policy*, vol. 137, Article ID 111180, 2020.

[6] Chilean Ministry of Finance, Chilean Ministry of Economy, "Development and reconstruction, chilean ministry of energy. consolidated supreme decree no. 331 (updated by supreme decree no. 33), through which the regulation of law no. 20365 is approved, which establishes tax exemptions for thermal solar systems [decreto supremo n° 331 consolidado (actualizado por decreto supremo n° 33), mediante el que se aprueba el reglamento de la ley n° 20365, que establece franquicia tributaria respecto de sistemas solares thermicos]. 2016 (in spanish)," 2014, https://sst.minenergia.cl/?wpdmpro=reglamento&wpdmdl=1641.

[7] A. Sánchez-Braza and M. D. P. Pablo-Romero, "Evaluation of property tax bonus to promote solar thermal systems in Andalusia (Spain)," *Energy Policy*, vol. 67, pp. 832-843, 2014.

[8] D. Araya-Muñoz, D. Carvajal, A. Sáez-Carreño, S. Bensaid, and E. Soto-Márquez, "Assessing the solar potential of roofs in Valparaíso (Chile)," *Energy and Buildings*, vol. 69, pp. 62-73, 2014.

[9] R. A. Escobar, C. Cortés, A. Pino et al., "Estimating the potential for solar energy utilization in Chile by satellite-derived data and ground station measurements," *Solar Energy*, vol. 121, pp. 139-151, 2015.

[10] F. Bustos, C. Lazo, J. Contreras, and A. Fuentes, "Analysis of a solar and aerothermal plant combined with a conventional system in an ESCO model in Chile," *Renewable and Sustainable Energy Reviews*, vol. 60, pp. 1156-1167, 2016.

[11] J. Vega and C. Cuevas, "Simulation study of a combined solar and heat pump system for heating and domestic hot water in a medium rise residential building at Concepción in Chile," *Applied Thermal Engineering*, vol. 141, pp. 565-578, 2018.

[12] G. Quiñones, C. Felbol, C. Valenzuela, J. M. Cardemil, and R. A. Escobar, "Analyzing the potential for solar thermal energy utilization in the Chilean copper mining industry," *Solar Energy*, vol. 197, pp. 292-310, 2020.

[13] R. Araya, F. Bustos, J. Contreras, and A. Fuentes, "Life-cycle savings for a flat-plate solar water collector plant in Chile," *Renewable Energy*, vol. 112, pp. 365-377, 2017.

[14] H. F. Naspolini, H. S. G. Militão, and R. Rüther, "The role and benefits of solar water heating in the energy demands of low-income dwellings in Brazil," *Energy Conversion and Management*, vol. 51, no. 12, pp. 2835-2845, 2010.

[15] H. F. Naspolini and R. Rüther, "Assessing the technical and economic viability of low-cost domestic solar hot water systems (DSHWS) in low-income residential dwellings in Brazil," *Renewable Energy*, vol. 48, pp. 92-99, 2012.

[16] V. M. T. Bessa and R. T. A. Prado, "Reduction of carbon dioxide emissions by solar water heating systems and passive technologies in social housing," *Energy Policy*, vol. 83, pp. 138-150, 2015.

[17] H. F. Naspolini and R. Rüther, "Impacts of domestic solar water heating (DSWH) systems on the cost of a hot shower in low-income dwellings in Brazil," *Renewable Energy*, vol. 111, pp. 124-130, 2017.

[18] T. Cruz, R. Schaeffer, A. F. P. Lucena, S. Melo, and R. Dutra, "Solar water heating technical-economic potential in the household sector in Brazil," *Renewable Energy*, vol. 146, pp. 1618-1639, 2020.

[19] J. A. Rosas-Flores, D. Rosas-Flores, and J. L. F. Zayas, "Potential energy saving in urban and rural households of Mexico by use of solar water heaters, using geographical information system,"
*Renewable and Sustainable Energy Reviews*, vol. 53, pp. 243-252, 2016.

[20] L. Salgado-Conrado and A. Lopez-Montelongo, "Barriers and solutions of solar water heaters in Mexican household," *Solar Energy*, vol. 188, pp. 831-838, 2019.

[21] A. Lapertot, M. Cuny, B. Kadoch, and O. Le Métayer, "Optimization of an earth-air heat exchanger combined with a heat recovery ventilation for residential building needs," *Energy and Buildings*, vol. 235, Article ID 110702, 2021.

[22] A. Rey and R. Zmeureanu, "Multi-objective optimization framework for the selection of configuration and equipment sizing of solar thermal combisystems," *Energy*, vol. 145, pp. 182-194, 2018.

[23] S. Launay, B. Kadoch, O. Le Métayer, and C. Parrado, "Analysis strategy for multi-criteria optimization: application to inter-seasonal solar heat storage for residential building needs," *Energy*, vol. 171, pp. 419-434, 2019.

[24] R. Renaldi, A. Kipprakis, and D. Friedrich, "An optimisation framework for thermal energy storage integration in a residential heat pump heating system," *Applied Energy*, vol. 186, Part 3, pp. 520-529, 2017.

[25] I. N. de Estadísticas, "Resultados censo," Accessed: 2021-03-03, 2017.

[26] Ministerio de Energía, "C. Explorador solar".

[27] A. Araújo and R. Silva, "Energy modeling of solar water heating systems with on-off control and thermally stratified storage using a fast computation algorithm," *Renewable Energy*, vol. 150, pp. 891-906, 2020.

[28] H. Hottel and A. Whillier, "Evaluation of Flat-Plate Solar Collector Performance," *Transactions Conference Use of Solar Energy*, vol. 3, 1955.

[29] J. A. Duffie and W. A. Beckman, *Solar Engineering of Thermal Processes*, John Wiley & Sons, 2013.

[30] I. M. R. Pérez, *Unsteady Laminar Convection in Cylindrical Domains: Numerical Studies and Application to Solar Water Storage Tanks*, Universitat Politècnica de Catalunya, 2007.

[31] A. Pérez-Fargallo, D. Bienvenido-Huertas, S. Contreras-Espinoza, and L. Marín-Restrepo, "Domestic hot water consumption prediction models suited for dwellings in central-southern parts of Chile," *Journal of Building Engineering*, vol. 49, Article ID 104024, 2022.

[32] S. Kalogirou, "Economic analysis of solar energy systems using spreadsheets," *Renewable Energy*, vol. 9, no. 1-4, pp. 1303-1307, 1996.

[33] S. A. Kalogirou, "Optimization of solar systems using artificial neural-networks and genetic algorithms," *Applied Energy*, vol. 77, no. 4, pp. 383-405, 2004.

[34] M. Ehrgott, *Multicriteria Optimization*, Springer-Verlag, Berlin, Heidelberg, 2005.

[35] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," *IEEE Transactions on Evolutionary Computation*, vol. 6, no. 2, pp. 182-197, 2002.

[36] G. H. Tzeng and J. J. Huang, *Multiple Attribute Decision Making: Methods and Applications*, CRC Press, Taylor and Francis Group, A Chapman & Hall Book, Boca Raton, 2011.

[37] K. Verichev, M. Zamorano, and M. Carpio, "Effects of climate change on variations in climatic zones and heating energy consumption of residential buildings in the southern Chile," *Energy and Buildings*, vol. 215, Article ID 109874, 2020.