A New Proposal for the Use of Cooling Degree Hours for the Energy Simulation of Residential Buildings in Mexico

Abstract

The thermal energy simulation of residential buildings involves estimating electricity consumption from both household appliances and air conditioning systems, whose use is influenced by the ambient temperatures of each municipality. However, existing mathematical simulation models face limitations in accurately reproducing electricity consumption patterns in homes across different climate types. This study proposes an enhanced CDH method, developed through a new function aimed at improving the accuracy of residential cooling demand estimation by incorporating behavioral and climatic variability. The function introduces the use of adaptive comfort temperature thresholds specific to each climate type and a time-selective activation mechanism that calculates cooling demand only during the hours when ambient temperature exceeds the adaptive threshold. These activation periods are determined analytically using a Fourier-based temperature model. A representative sample of 35 municipalities in Mexico was selected, covering different climate types and domestic electricity rates. The construction characteristics and average energy use habits of typical dwellings were defined using national housing and energy data to support the simulations. The results show that integrating adaptive thresholds into the CDH equations reduces the simulation error to below 10% when compared to actual residential electricity consumption. The proposed model is applicable across all Mexican municipalities, regardless of climate variability.

1. Introduction

The residential sector is one of the largest energy consumers globally [1], accounting for nearly one third of the world’s final energy consumption and 26% of CO₂ emissions associated with energy use [2,3]. In Mexico, this sector represents 26.3% of the final consumption of the Sistema Eléctrico Nacional (SEN) [National Electrical System], and it is estimated that in 2038 this indicator will be 25.6% [4]. This high energy consumption in the country is commonly attributed to the use of inefficient equipment or poor operational practices [5]. However, the most significant factors influencing energy use are changes in ambient temperature and the increased reliance on air conditioning systems [6,7,8]. This is especially evident in densely populated urban areas experiencing extreme hot climates, where the urban heat island effect exacerbates cooling needs [9], making air conditioning essential for maintaining indoor comfort [3,10,11,12,13].

In Mexico, the climatic diversity ranges from arid zones to temperate, warm, and humid regions [14], leading to variations in residential energy consumption patterns from one location to another [10]. To mitigate the increase in residential electricity consumption driven by the use of household appliances, the country has implemented policies and programs aimed at enhancing energy efficiency [7], including financing, subsidies for equipment and materials, and regulations to ensure compliance with the minimum performance requirements. These measures also include standards for equipment, improvements to building thermal envelopes, and initiatives for the installation of renewable energy sources to significantly reduce electricity consumption [15,16,17,18,19].

Understanding the energy behavior of residential buildings implies taking into consideration the local climate, since it determines the need for heating or cooling or both systems during different seasons of the year [20,21]. According to Coskun et al. [6], methods for analyzing building energy consumption in relation to climate are categorized into three groups: single measurement methods, simplified multiple measurement methods, and detailed multiple measurement methods. The latter, by performing hour-by-hour calculations and simulating heat transfer, as well as the behavior of heating and cooling systems, provide the most accurate results. However, they require hourly weather data and demand a significant amount of time for calculations.

Other methods used to evaluate the impact of climatic conditions on energy consumption include building energy simulation (BES), Degree Days (DD), and Operating Temperature (OT) [13]. The BES method emerged from the need for computational tools to analyze energy systems in buildings [22], enabling the prediction and management of energy consumption in dwellings through dynamic simulations [23,24,25]. Although building energy simulations have gradually replaced simplified methods such as DD and DH (degree hours), the latter remain widely used due to their accessibility and lower complexity [6,9,26].

The DD and DH methods have proven to be effective in evaluating the climatic influence on building heating and cooling requirements [27,28]. However, the DH method, unlike the DD method, takes into account both temperature deviations and the duration of these variations throughout the day, making it a more accurate model for evaluating hourly ambient temperature and the energy requirements of air conditioning systems throughout the year [29,30,31,32].

Recent studies have proposed alternative approaches; for example, a study in Antalya, Turkey, suggests using exergy in the calculation of DH to assess thermodynamic performance in air conditioning systems. This approach considers additional factors such as ambient temperature, solar radiation, and the thermal properties of surfaces, providing a more comprehensive assessment of the climatic impact on energy use, overcoming the limitations of traditional methods.

In Mexico, the DH method was validated by Pérez-Tello et al. [21], who correlated the method with historical records of outdoor ambient temperature and electricity consumption, using a Fourier function expressed in Equation (1), where T(t) represents the ambient temperature for hour t of the day (Equation (2)), with parameters adjusted specifically for each municipality evaluated ($\mathsf{\mu }$, A, and B).

$$\mathrm{T}\left(\mathrm{t}\right)=\text{<}\mathsf{\mu }\text{>}+\mathrm{Acos}\left({\displaystyle \frac{2\mathsf{\pi }\mathrm{t}}{24}}\right)+\mathrm{Bsin}\left({\displaystyle \frac{2\mathsf{\pi }\mathrm{t}}{24}}\right); \mathrm{t}=1, 2, 3\text{…}24$$

(1)

where T(t) represents the dimensionless hourly outdoor temperature for a particular day defined in Equation (2), T_max and T_min are the recorded maximum and minimum temperature, and T(t) is the calculated value of temperature for time t.

$$\mathrm{T}\left(\mathrm{t}\right)={\displaystyle \frac{{\mathrm{T}}_{\max }-\mathrm{T}\left(\mathrm{t}\right)}{{\mathrm{T}}_{\max }-{\mathrm{T}}_{\min }}}$$

(2)

<μ>, A, and B are the mean value and the two coefficients of correlation given by the following:

$$〈\mathsf{\mu }〉={\displaystyle \frac{1}{24}}{\displaystyle {\sum }_{\mathrm{t}-1}^{24}}\mathsf{\mu }\left(\mathrm{t}\right)$$

(3)

$$\mathsf{\mu }\left(\mathrm{t}\right)={\displaystyle \frac{1}{\mathrm{N}}}{\sum }_{\mathrm{n}-1}^{\mathrm{N}}\mathrm{Tn}\left(\mathrm{t}\right), \mathrm{n}=1,2, \text{…}\mathrm{Ndays}$$

(4)

$$\mathrm{A}={\displaystyle \frac{2}{24}}{\sum }_{\mathrm{t}-1}^{24}\left[\mathsf{\mu }\left(\mathrm{t}\right)-〈\mathsf{\mu }〉\right]\cos 〈{\displaystyle \frac{2\mathsf{\pi }\mathrm{t}}{24}}〉$$

(5)

$$\mathrm{B}={\displaystyle \frac{2}{24}}{\sum }_{\mathrm{t}-1}^{24}\left[\mathsf{\mu }\left(\mathrm{t}\right)-〈\mathsf{\mu }〉\right]\sin 〈{\displaystyle \frac{2\mathsf{\pi }\mathrm{t}}{24}}〉$$

(6)

The Fourier-type model simplifies the calculation of DH by allowing the integration to be performed only once, using the previously obtained model and substituting the appropriate values of 〈μ〉, A, and B for the location of interest, thus avoiding the need to integrate data each time. Hence, the DH is then defined in Equation (7), where T₀ is the reference temperature, and T is the outdoor temperature.

$$\mathrm{DH}={\int }_{{\mathrm{T}}_0}^{\mathrm{T}}{\int }_0^{24}\mathrm{T}\left(\mathrm{t}\right)\mathrm{dtdT}$$

(7)

By substituting Equations (1)–(3) and integrating, Equation (4) is obtained.

$$\mathrm{DH}=24\left[{(\mathrm{T}}_{\max }-{\mathrm{T}}_0)-\text{<}\mathsf{\mu }\text{>}({\mathrm{T}}_{\max }-{\mathrm{T}}_{\min })\right]$$

(8)

This DH method has been applied in several projects focused on energy savings and efficient use [21,33,34,35], establishing a methodology for determining and characterizing the energy performance of the residential sector in certain regions of Mexico, particularly those with a hot–dry climate. However, traditional models, including those based on this formulation, accumulate Cooling Degree Hours whenever ambient temperature exceeds a fixed threshold, without considering the actual time window during which air conditioning systems are realistically in use. This continuous accumulation approach can lead to overestimations of cooling demand, particularly in climates with strong daily temperature fluctuations or where occupants adapt their cooling behavior based on varying comfort needs.

To overcome this limitation, the present study proposes an enhanced Cooling Degree Hours (CDH) formulation which introduces the integration of climate-specific adaptive temperature thresholds, derived from international and national comfort studies, and the introduction of a selective time-based activation model, which calculates CDH only during the actual period when ambient temperature exceeds the adaptive threshold. This is conducted analytically by solving for the intersection points between the temperature curve and the adaptive threshold, thus defining a daily operational window for AC use.

This enables us to simulate cooling demand with greater behavioral realism and climatic sensitivity. In doing so, this study addresses the weaknesses of both fixed-threshold DH models and overly complex BES tools, offering a robust and scalable alternative for modeling residential electricity use in diverse Mexican municipalities.

The present study aims to develop and validate an enhanced Cooling Degree Hours (CDH) model that improves the accuracy of residential cooling demand simulation across different climate zones in Mexico. This model integrates adaptive comfort temperature thresholds and time-selective activation periods for the air conditioning systems enabling a more realistic representation of climate variability and occupant behavior.

2. Materials and Methods

This section describes in detail the activities, equations, and criteria used in the development of this study. Based on census data, the construction characteristics of a typical Mexican dwelling are defined, and using functions from the Cooling Degree Hours (CDH) model, the energy performance of selected municipalities is compared. This method is applied through a thermal load simulation tool developed in Microsoft Excel by the Institute of Engineering at the Autonomous University of Baja California [Engineering Institute of the Autonomous University of Baja California] [21], aimed at simulating and analyzing the thermal energy aspects of housing under local climate conditions.

2.1. Data

To establish representative consumption profiles for residential buildings in a given locality, the municipalities of Mexico with more than 50,000 inhabitants were identified using data from INEGI (2020), which classifies them as urban areas. The selection of these municipalities focuses on areas where variations in climate conditions are expected to have a greater impact on energy consumption. According to the INEGI there are four great climates over the Mexican territory identified (see Figure 1). Arid conditions are predominant in the northern region, dry tropic in the west, temperate conditions are presented in the center, and humid tropic in the southeast part [14].

The climate data for the different municipalities were compiled from historical records from the database of the National Renewable Energy Laboratory (NREL) of the United States, as well as national records of the monthly total number of domestic consumers and energy consumption, which were obtained from the Sistema de Información Energética platform (SIE) [Energy Information System] which belongs to the Secretaría de Energía (SENER) [Secretariat of Energy] of Mexico [33], with the intent to update the information in the energy simulator and classify every municipality by rate type.

2.2. Sample Size

Determining the sample size constitutes the first step to ensure the statistical validity of this study’s results. The equation (9) proposed by Hernandez Sampieri [34] for finite populations was applied. This method ensures statistical validity by considering confidence level, margin of error, and the estimated population proportion. The equation is as follows:

$$\mathrm{n}={\displaystyle \frac{\mathrm{N}{\mathrm{Z}}^2\mathrm{p}(1-\mathrm{p})}{{\mathrm{Z}}^2\mathrm{p}(1-\mathrm{p})+(\text{∆}-{\mathrm{p}}^2\left)\right(\mathrm{N}-1)}}$$

(9)

where n is the required sample size, N is the size of the finite population (445 municipalities in Mexico classified as urban by INEGI, each with a population over 50,000 inhabitants), Z is the desired confidence level (1.645 for 90%), p is the estimated proportion of municipalities of interest (0.143, corresponding to the presence of the seven residential electricity rates currently in effect in the country) and Δ is the accepted margin of error (0.10 or 10%). The 90% confidence level was selected as a balance between statistical rigor and the practical constraints of data availability and modeling resources. These parameters ensured that the sample would adequately capture the diversity of climatic and regulatory conditions affecting electricity consumption in Mexico.

Under these criteria, a minimum representative sample of 31 municipalities was obtained. However, to ensure balanced representation across all electricity rate zones, the sample was extended to 35 municipalities, selecting 5 per rate type. This stratified sampling approach strengthens the geographic and regulatory diversity of the analysis, allowing for more robust simulation comparisons across different climate and electricity pricing contexts (see

Table 1. A list of municipalities per electric rate with a population of at least a hundred thousand or more inhabitants in 2020 (INEGI, 2020).

Municipality	Rate	Population	Municipality	Rate	Population
Aguascalientes, Ags.	1	948,990	Cadereyta Jiménez, N.L.	1C	122,337
Cuauhtémoc, Chih.	1	180,638	Monterrey, N.L.	1C	1,142,994
Durango, Dgo.	1	688,697	Victoria, Tamps.	1D	349,688
Morelia, Mich.	1	849,053	Navolato, Sin.	1D	149,122
San Miguel de Allende, Gto.	1	174,615	Mazatlán, Sin.	1D	501,441
Hidalgo del Parral, Chih.	1A	116,662	Mérida, Yuc.	1D	995,129
Cuautla, Mor.	1A	187,118	Matamoros, Tamps.	1D	541,979
Rioverde, S.L.P.	1A	97,943	Macuspana, Tab.	1E	158,601
Matehuala, S.L.P.	1A	102,199	Acuña, Coah.	1E	163,058
San Andrés Tuxtla, Ver.	1A	162,428	Navojoa, Son.	1E	164,387
Puerto Vallarta, Jal.	1B	291,839	Río Bravo, Tamps.	1E	132,484
Villa de Alvarez, Col.	1B	149,762	Guasave, Sin.	1E	289,370
Chihuahua, Chih.	1B	937,674	Nuevo Laredo, Tamps.	1F	425,058
Colima, Col.	1B	157,048	Ahome, Sin.	1F	459,310
Tuxtla Gutiérrez, Chis.	1B	604,147	Hermosillo, Son.	1F	936,263
San Nicolás de los Garza, N.L.	1C	412,199	Cájeme, Son.	1F	436,484
Juárez, Chih.	1C	1,512,450	Mexicali, B.C.	1F	1049,792
San Luis Río Colorado, Son.	1C	199,021

).

2.3. Characteristics of Average Mexican Home

The construction characteristics of the average Mexican dwelling were defined using data from two major nationwide sources, the 2020 Population and Housing Census (CPV) and the 2020 National Housing Survey (ENVI) [35], both conducted by the National Institute of Statistics and Geography (INEGI). These surveys involved in-person visits to households across Mexico’s nearly two million square kilometers, collecting updated and representative information on housing materials, household size, and living conditions. According to the 2020 census, 92% of homes have walls made of brick, block, or concrete, and 79% feature slab or concrete roofs. Most dwellings fall within a construction area of 56–100 m², have two rooms (42%), and are over 11 years old (75%). Additionally, only 1.5% of homes report any form of thermal insulation. These findings support the selection of representative typologies for energy simulation, including one-story, 60 m² homes with brick and concrete envelopes, which match the dominant construction patterns found in air-conditioned homes nationwide (see

Table 2. Physical characteristics of average Mexican home.

Characteristics	Mexican Home
Total air-conditioned surface	60 m2
Wall material	15 cm thick concrete block, with interior and exterior finish
Roof material	10 cm thick concrete slab, with interior finish and exterior reflective paint
Window area	4.7 m2
Door area	4 m2
Longitude	North and south walls 7.7 m, east and west walls 10 m
Height	2.8 m
Lighting power	190 W
Air conditioner equipment	Mini Split
EER	10
Thermostat temperature	23 °C (73.4 °F)
Inhabitant occupancy	3 persons, 24 h/day

).

The compiled information about the presence and usage of appliances at the household on a national level was obtained from the National Survey on Energy Consumption in Private Dwellings [Encuesta Nacional sobre Consumo de Energéticos en Viviendas Particulares] (ENCEVI) 2018 [11], which shows that the television is the most used device at home. For lighting, the most commonly used technology at the time of the survey (energy-efficient fluorescent lamps) was considered. The operating times of household appliances were determined based on the most representative usage distribution patterns. In certain cases, the survey identified the specific technology most frequently used for a given appliance (e.g., LCD televisions), along with typical hourly usage profiles differentiated by climatic region.

Table 3. Common residential appliances and average daily use in Mexico.

Appliance	Rated Power (W)	Daily Usage (h/day)	Factor Use
Refrigerator (small, new)	128	24	0.3
Television	105	2	1
Pedestal Fan	65	5	0.45
Radio	40	2	0.4
Iron	1000	36 min (when used)	0.06
Washing Machine	400	3 (when used)	0.05

summarizes the main household appliances and their average daily operating times for a typical Mexican household.

To define the baseline electricity consumption for residential dwellings, a daily load of 3.14 kWh/day was estimated, which corresponds to an annual total of 1146 kWh/year for general appliances. This value was derived from a detailed calculation using the rated power, usage time, and realistic usage factors for common household devices such as refrigerators, televisions, radios, irons, washing machines, and lighting systems (Table 3). These estimates are based on national-level data from INEGI, CONUEE, and ENCEVI [36,37,38]. An additional 0.146 kWh/day from a pedestal fan was included only for the warm season months (May to October, 184 days), contributing 27 kWh/year. This results in a total base electricity consumption of 1174 kWh/year, which was used as the default value for all pre-cooling simulations.

The thermal load simulator is updated with the necessary information for each municipality (climate data and coefficients m, A, and B), and the characteristics of the typical home reported in Table 2 and Table 3 are logged. Using the thermal load simulator that has been validated for more than 35 years according to Suástegui Macías (2014) [39], the energy behavior of the home is reproduced, applying the transfer function method proposed by the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE), as well as the DH criteria to determine the cooling capacity, heat removal rate, and electrical consumption of a conditioned enclosure.

This study was conducted on a typical house in Mexico; however, it is necessary to point out that Function 2 can be used in any type of building that requires the use of air conditioning equipment for cooling. Only the maximum and minimum daily temperatures and the coefficients (μ, A, and B) for the location where it is used are required.

2.4. Simulation

In order to accurately reproduce the thermal energy behavior of a typical home in the different municipalities of Mexico, the coefficients μ, A, and B corresponding to each municipality were incorporated into the thermal load simulator, together with the construction characteristics of the building and the air conditioning system. In addition, the average daily hours of air conditioning use, lighting power, and other internal loads were included to reflect realistic household energy patterns.

To determine the activation threshold of the air conditioning system, an adaptive temperature parameter was introduced into the simulator, based on comfort ranges reported in international studies on occupants’ thermal response, including Indraganti (2010), Yang et al. (2020), Hwang et al. (2009), Fang et al. (2021), Song et al. (2018), and Kim et al. (2017) [40,41,42,43,44,45], as well as national studies like Sánchez-Montes (2025) and Oropeza-Pérez et al. (2017) [46,47]. These sources provided comfort temperature ranges according to climate type, which served as the initial reference for warm, dry, and temperate climates in Mexico.

Drawing from this information, adaptation temperature ranges were defined for warm, dry, and temperate climates in Mexico. Using these values, iterative energy simulations were carried out for each location, adjusting the adaptive temperatures to evaluate their impact on energy consumption and comparing the results with actual electricity consumption records. In each simulation, the adaptive temperature was defined according to the climate type, determining the moment when air conditioning is activated in the DH cooling calculation.

Finally, values were selected that were within the comfort ranges identified in the international studies for each climate type and that also resulted in thermal energy simulations that best matched the actual electricity consumption of each location, minimizing the margin of error in the annual energy consumption estimates. As a result, adaptive temperatures were determined to be 32 °C for warm climates, 29.2 °C for dry climates, and 32.9 °C for temperate climates. This improved the accuracy of the simulations by considering occupants’ ability to tolerate higher temperatures before resorting to air conditioning.

To define the adaptive temperature threshold (T_adap) for each climate zone, a combination of international and national comfort studies was used. Specifically, the temperature ranges reported in studies conducted both in Mexico and in countries with similar climates or the same Köppen–García classification were considered. These ranges were used as the initial reference for each zone. The final values were then locally calibrated for each municipality by comparing simulated energy demand with actual residential electricity consumption and adjusting the thresholds to minimize the error between them. This approach allowed for context-specific calibration while remaining grounded in scientifically validated comfort ranges.

Table 4. Adaptive temperature thresholds (T_adap) by climate zone.

Climate Zone	City	Tadap (°C)	Source
A. Arid	Cuautla, San Andrés Tuxtla, Puerto Vallarta, Villa de Alvarez, Colima, Tuxtla Gutiérrez, Mérida y Macuspana	32 °C, 35 °C, 29.5 °C, 24.7 °C, 20.4 °C	[40,46,48].
B. Dry	Aguascalientes, Cuauhtemoc, Hidalgo del Parral, Rioverde, Matehuala, Chihuahua, San Nicolas de los Garza, Juárez, Monterrey, Navolato, Mazatlan, Acuña, Navojoa, Guasave, Nuevo Laredo, Ahome, Hermosillo, Cájeme, Mexicali, San Luis Rio Colorado	26 y 32.45 °C, 23.8 to 34.2 °C, 30.2 °C.	[27,41,48]
C. Temperate	Durango, Morelia, San Miguel de Allende, Cadereyta Jiménez, Victoria, Matamoros, Rio Bravo	35 °C, 27.3 to 33.1 °C, 24 to 37.5 °C	[42,43,45].
All	All	Under 33.5 °C	ANSI/ASHRAE 55-2010

lists the adaptive temperatures used, the corresponding climate classifications, the supporting references, and an indication of whether the threshold was directly adopted or adjusted (localized). This classification enabled the simulator to align the activation of cooling systems with regional thermal tolerance while retaining the flexibility to implement dynamic thresholds in future research or climate change scenarios.

Although the adaptive thresholds defined in this study were initially based on comfort ranges from both international and national research, comprehensive field studies covering the full diversity of Mexican climates and housing types remain limited. This represents an important gap that future research should address to further validate and refine the proposed adaptive temperature thresholds.

Additionally, energy simulations were performed using OpenStudio 3.9.0 (OS) software, incorporating the same typical home characteristics defined in Section 2.3 and Section 2.4. A 3D model of the typical Mexican home was created using SketchUp and imported into OpenStudio for simulation. The HVAC control settings in OS were established with a fixed cooling setpoint of 23 °C, consistent with the thermostat temperature reported in national housing statistics, rather than the adaptive thresholds used in the DH cooling calculations. Occupancy and equipment usage schedules were defined based on representative daily usage patterns reported in the National Survey on Energy Consumption in Private Dwellings (ENCEVI) 2018 and the National Housing Survey (ENVI) 2020, ensuring realistic hourly internal loads consistent with average household behavior in Mexico. The same weather files used for the Function 2 simulations were applied in OS, and the simulation period was uniformly set from May to October across all locations, corresponding to the months of the highest cooling demand in Mexican climates. These assumptions ensured consistent building and usage inputs for both simulation approaches, enabling a direct comparison of energy consumption estimates.

The calculated Assembly U-Factor was approximately 2.49 W/m²·K for the exterior walls and 3.36 W/m²·K for the roof, closely matching the U-values of 2.58 W/m²·K and 3.28 W/m²·K, respectively, used in the thermal load simulator. These consistent thermal properties ensured comparability between the Open Studio and thermal load simulations, allowing for a direct assessment of discrepancies based solely on calculation methodologies. A 3D model of the typical home generated with SketchUp and imported into OS is shown in Figure 2.

2.5. Proposal of New Function for Simulation

To improve the accuracy of cooling energy demand estimation across diverse climate zones, this study proposes an enhanced formulation of CDH that incorporates an adaptive temperature threshold. While the traditional model assumes that cooling demand arises whenever the daily outdoor temperature exceeds a reference temperature, the proposed function (referred to as Function 2) enhances realism by accounting for the actual operating hours of air conditioning systems. This function builds upon the original CDH methodology to better reproduce electricity consumption patterns across Mexican municipalities. It integrates a climate-specific adaptive comfort threshold and calculates the total number of CDH within a 24-h period between two specific time points at which the ambient temperature crosses the adaptive threshold.

The proposed function builds upon the original Fourier-based model introduced in the Introduction (Equation (1)) to represent hourly variations in outdoor temperature. To determine when cooling is required, an adaptive temperature threshold is incorporated as Equation (10):

$$\mathrm{C}={\displaystyle \frac{{\mathrm{T}}_{\max }-\mathrm{T}\left(\mathrm{t}\right)}{{\mathrm{T}}_{\max }-{\mathrm{T}}_{\min }}}$$

(10)

The intersection points between the ambient temperature function T(t) and the adaptive threshold C determine the hours of the air conditioning system’s activation and deactivation. These time points, t₁ and t₂, are obtained analytically by solving the condition T(t) = C, representing the intersection between the ambient temperature curve and the adaptive threshold, leading to Equations (11) and (12):

$${\mathrm{t}}_2=24{\displaystyle \frac{{\tan }^{-1}\left(\frac{-\mathrm{B}+\sqrt{({\mathrm{B}}^2+{\mathrm{A}}^2-{\left(\mathsf{\mu }-\mathrm{C}\right)}^2}}{\mathsf{\mu }-\mathrm{A}-\mathrm{C}}\right)}{\mathsf{\pi }}}$$

(11)

$${\mathrm{t}}_1=24{\displaystyle \frac{{ \tan }^{-1}\left(\frac{-\mathrm{B}-\sqrt{({\mathrm{B}}^2+{\mathrm{A}}^2-{\left(\mathsf{\mu }-\mathrm{C}\right)}^2}}{\mathsf{\mu }-\mathrm{A}-\mathrm{C}}\right)}{\mathsf{\pi }}}$$

(12)

To compute the CDH only during the effective cooling period, Function 2 (Equation (13)) is defined as the definite integral of the temperature function over the interval [t₁,t₂]:

Function 2:

$${\mathrm{DH}}_{\mathrm{Cooling}}={\int }_{{\mathrm{t}}_1}^{{\mathrm{t}}_2}\mathrm{T}\left(\mathrm{t}\right)\mathrm{dt}$$

(13)

Substituting Equation (1) into the integral and solving analytically yields the following:

$${\mathrm{DH}}_{\mathrm{Cooling}}=\left[\left({\mathrm{T}}_{\max }-{\mathrm{T}}_0\right)-\mathsf{\mu }\left({\mathrm{T}}_{\max }-{\mathrm{T}}_{\min }\right)\right]\left({\mathrm{t}}_2-{\mathrm{t}}_1\right)+{\displaystyle \frac{12({\mathrm{T}}_{\max }-{\mathrm{T}}_{\min })}{\mathsf{\pi }}}\left[\mathrm{A}\left(\mathrm{sen}\left({\displaystyle \frac{2\mathsf{\pi }{\mathrm{t}}_2}{24}}\right)-\mathrm{sen}\left({\displaystyle \frac{2\mathsf{\pi }{\mathrm{t}}_1}{24}}\right)\right)+\mathrm{B}\left(\cos \left({\displaystyle \frac{2\mathsf{\pi }{\mathrm{t}}_1}{24}}\right)-\cos \left({\displaystyle \frac{2\mathsf{\pi }{\mathrm{t}}_2}{24}}\right)\right)\right]$$

(14)

The term under the square root in the expressions for t1 and t2, (B² + A² − (μ − C)², must be non-negative to ensure real solutions. This requirement imposes the condition ${\left(\mathsf{\mu }-\mathrm{C}\right)}^2\le ({\mathrm{B}}^2+{\mathrm{A}}^2)$, which guarantees that the adaptive threshold is within the range of the daily thermal oscillation. If this condition is not met, it means that the ambient temperature never exceeded the threshold, and thus no cooling was needed, resulting in CDH = 0 for that day.

Data from 10 June 2019, from the city of Mexicali, was used as a reference to represent the behavior of each function in Figure 3. The graph with the area under the blue curve represents the original, unmodified function, and Function 2 is illustrated in green. A 24 h day is considered as the time period, where T_max is the maximum ambient temperature, T_adap represents the adaptive temperature threshold, T_min the minimum ambient temperature, and T_ref the thermostat reference temperature.

In most cases, T_amb exceeds T_adap only once a day, resulting in a continuous integration interval. However, on certain days of the year and in some locations, T_amb fluctuates in such a way that it crosses T_adap more than once in a single day, leading to three intersection points: a first crossing where T_amb rises and exceeds T_adap for the first time, initiating integration; a second crossing where T_amb temporarily drops below T_adap, interrupting the CDH calculation; and a third crossing where T_amb rises again and exceeds T_adap, restarting integration until it finally drops below the threshold. This behavior splits the integration into two shorter intervals, reducing the total CDH calculated compared to the original equation, which does not consider these intersections. This occurs mainly in locations where T_amb fluctuates near T_adap, rather than remaining consistently above this threshold throughout the day, causing it to rise and fall several times. As a result, Function 2 tends to estimate a lower value of CDH in these cases.

As an example, Figure 4 shows the variation in the CDH throughout the year for the city of Monterrey, calculated with the original methodology and the newly proposed function. It can be observed that during the warmer months, CDH increases significantly, indicating a higher cooling demand during that period. It can also be observed that Function 2 yields a lower number of CDH compared to the original function, due to the differences in how each function responds to the climatic conditions described earlier.

Usage factors for air conditioning were proposed for each type of electricity rate, which were iteratively adjusted in the simulations of the electricity consumption of a typical home, using the two previously described functions to calculate CDH for the different municipalities. This process made it possible to identify the usage factor that best replicated the average electricity consumption per household in each municipality, selecting the most representative value as a reference for each rate.

Subsequently, the correlation between the proposed factors and the average minimum summer temperature associated with each rate was analyzed, accepting those with a correlation higher than 90%. It is worth mentioning that, in Mexico, domestic electricity rates, determined by the Comisión Federal de Electricidad (CFE) [Federal Electricity Commission], are classified based on consumption levels and the average temperature of the region, in types 1, 1A, 1B, 1C, 1D, 1E, and 1F, that correspond to zones with different ranges of minimum summer temperature [48]. This classification directly affects the consumption thresholds and the cost per kilowatt-hour (kWh), influencing air-conditioned usage patterns in households [49].

Once the data were captured, simulations were conducted for each municipality, considering only those results where the difference from the 2019 annual electricity consumption records, obtained from a residential user database, remained within a ±10% margin. This criterion ensures the reliability and reproducibility of the results when compared with measured electricity consumption values while also testing the sensitivity of the design variables to reduce the number of unnecessary simulations.

3. Results

From the climatological data reported on the NREL website in 2019 of each municipality selected, the coefficients used in the thermal energy simulator were calculated (

Table 5. Simulation coefficients by municipality.

Municipality	A	B	m	Municipality	A	B	m
Aguascalientes, Ags.	0.30	0.38	0.53	Monterrey, N.L.	0.34	0.35	0.52
Cuauhtémoc, Chih.	0.37	0.30	0.51	Victoria, Tamps.	0.41	0.28	0.55
Durango, Dgo.	0.30	0.36	0.52	Navolato, Sin.	0.39	0.29	0.56
Morelia, Mich.	0.34	0.34	0.55	Mazatlán, Sin.	0.44	0.21	0.56
San Miguel de Allende, Gto.	0.34	0.35	0.55	Mérida, Yuc.	0.33	0.32	0.55
Hidalgo del Parral, Chih.	0.40	0.26	0.51	Matamoros, Tamps.	0.44	0.21	0.58
Cuautla, Mor.	0.33	0.34	0.53	Macuspana, Tab.	0.37	0.28	0.55
Rioverde, S.L.P.	0.36	0.34	0.57	Acuña, Coah.	0.25	0.41	0.51
Matehuala, S.L.P.	0.34	0.37	0.55	Navojoa, Son.	0.37	0.31	0.55
San Andrés Tuxtla, Ver.	0.37	0.30	0.56	Rio Bravo, Tamps.	0.36	0.33	0.57
Puerto Vallarta, Jal.	0.34	0.33	0.59	Guasave, Sin.	0.37	0.31	0.55
Villa de Alvarez, Col.	0.37	0.32	0.59	Nuevo Laredo, Tamps.	0.28	0.40	0.53
Chihuahua, Chih.	0.36	0.32	0.50	Ahome, Sin.	0.40	0.28	0.54
Colima, Col.	0.37	0.31	0.59	Hermosillo, Son.	0.34	0.36	0.53
Tuxtla Gutiérrez, Chis.	0.38	0.26	0.57	Cájeme, Son.	0.37	0.33	0.54
San Nicolás de los Garza, N.L.	0.38	0.32	0.52	Mexicali, B.C.	0.40	0.29	0.52
Juárez, Chih.	0.33	0.35	0.48	San Luis Río Colorado, Son.	0.29	0.39	0.52
Cadereyta Jiménez, N.L.	0.34	0.35	0.52

), as well as CDH by substituting the variables of the three applied functions. The results show constant coefficients by municipality and different CDH when applying each function.

Once the simulation coefficients were logged, the thermal energy profiles were obtained by adjusting the value of AC use per electric rate for each municipality. The values proposed as AC use factors per each electric rate are shown in

Table 6. AC use factor (regarding electric rate).

Rate	Proposed AC Use Factor
1	0.00
1A	0.04
1B	0.14
1C	0.34
1D	0.49
1E	0.54
1F	0.82

. These are used for the simulations of the electricity consumption of the average home depending on the rate of each municipality.

To ensure the representativeness of the proposed usage factors in Table 6, they were iteratively adjusted during simulations to match the average electricity consumption per household in each municipality. Only factors with a correlation above 90% with the average minimum summer temperature were accepted, ensuring both statistical validity and behavioral realism. This approach aligns with the structure of CFE’s temperature-based electricity rates, reinforcing the reliability of the selected factors.

The correlation obtained by comparing the value of those AC use factors with the minimum average temperature in the summer per rate was 0.98, as shown in Figure 5, which is considered very strong [50,51].

To evaluate the accuracy and applicability of different modeling approaches, a comparative analysis was conducted between the CDH-based model and the dynamic simulation results obtained using OpenStudio (OS) with EnergyPlus. Both models used the same construction and operational characteristics of the typical Mexican home described in Table 2. However, key differences in simulation structure and assumptions led to variation in the estimated energy consumption across locations.

The CDH-based models rely on empirical equations that incorporate ambient temperature profiles and, in the case of Function 2, adaptive temperature thresholds and time-selective activation. Open Studio, by contrast, performs detailed hourly simulations that include heat transfer through the envelope, internal gains, and thermostat-based control logic. This high-resolution approach tends to overestimate cooling energy use, especially in temperate climates where real users may delay AC use or tolerate higher temperatures before activation.

Figure 6 presents the results for 35 municipalities, comparing actual electricity consumption with the values simulated by each model. The results show that Function 2 consistently achieves the lowest deviation from real values, outperforming both Function 1 and OpenStudio across all climate types. This improvement is particularly evident in warm regions, where user behavior and thermal adaptation play a key role in cooling demand.

This comparison highlights the strengths of each method. The CDH-based model, with its lower data requirements and regional calibration, is suitable for large-scale assessments and policy scenarios. Open Studio offers more detailed thermal behavior modeling but may require further refinement or behavioral inputs to align with real consumption patterns. In future work, hybrid modeling strategies could be explored, combining empirical and dynamic approaches to enhance accuracy while retaining scalability.

In contrast, Function 1 tends to underestimate consumption due to the use of fixed temperature thresholds, while Open Studio generally overestimates it due to its assumption of immediate AC activation once indoor conditions exceed the thermostat setpoint. The clear divergence between these two approaches demonstrates the value of incorporating both climatic and behavioral adaptation, as achieved in Function 2.

The simulation results show higher electricity consumption in the municipalities with rate 1F (Figure 6), due to their extreme climate. It is important to note that the simulation consumption profile used in Function 3 represents a significant improvement in the accuracy of the predictions in comparison with Function 1 (original function previously reported).

By comparing the simulated energy consumption with the real electricity consumption values for the analyzed locations, it was found that the Open Studio (OS) software tends to overestimate electricity consumption in most cases. In contrast, the function based on the CDH method shows a notable improvement over the original function, which exhibits significant deviations from the real values, but the adjustments made in Function 2 enhanced its accuracy, making it the best match to the measured consumption in most municipalities.

Although only one final simulation result is presented per municipality, each result derives from a prior iterative process in which simulations were performed per location. In each case, the air conditioning usage factor was adjusted in small increments, and the resulting annual electricity consumption was computed using both Function 1 and Function 2. The configuration that minimized the percentage error between simulated and actual consumption was selected as the most statistically accurate scenario for each locality. This methodology ensures that the final results are reliable and derived from a robust parameter optimization experiment.

In the energy simulations of the typical home for the 35 municipalities, the calculated energy consumptions were compared with the annual electricity consumption records per user in each locality. Factors such as the maximum and minimum hourly temperatures, heat transfer coefficients, and air conditioning usage patterns can increase or decrease electricity consumption. The results obtained using Function 2 showed a margin of error within the range of ±10%, improving the accuracy compared to both the original function and OS software, as illustrated in Figure 7. This confirms that Function 2 most accurately reproduces the energy performance of homes in Mexico.

Furthermore, the close agreement between the calculated U-Factors in Open Studio (2.49 W/m²·K for exterior walls and 3.36 W/m²·K for the roof) and the U-values used in the thermal load simulator (2.58 W/m²·K and 3.28 W/m²·K, respectively) confirms the consistency of the thermal properties defined across both modeling approaches. The 3D model of the typical home, created using SketchUp and simulated in OS, ensured an accurate representation of building geometry and construction details. This alignment supports the validity of the comparative analysis, indicating that any discrepancies in energy consumption estimates between the models are primarily attributable to differences in calculation methodologies rather than inconsistencies in the definition of the building envelope.

The standard deviation of the annual electricity consumption obtained from the energy simulations for each method evaluated was calculated, showing that Function 2 achieved the best performance with a value of 6.2%, compared to 19% for the original function and 105% for OS software, as shown in

Table 7. Comparative statistical calculations of error percentages.

Statistical Method	Original Function	Function 2	Open Studio
Standard deviation	19%	6%	105%
Average percentage of errors	13%	0.2%	177%
Correlation coefficient	0.93	0.99	0.66
R2 coefficient	0.87	0.98	0.43

. Likewise, the correlation coefficients support this trend, with values of 0.99 for Function 2, 0.93 for the original function, and 0.66 for OS. Similarly, the coefficients of determination (R²) confirm the superiority of Function 2 with a coefficient of 0.98, compared to the values of 0.87 and 0.43 for the original function and OS, respectively.

4. Discussion

The proposed function for calculating CDH improves the ability to reproduce household electricity consumption in Mexico by 10%, on average, compared to the original function reported in previous studies. This improvement is achieved by incorporating the adaptive temperature threshold as a key variable in the thermal energy calculations for municipalities with different climate types. Along with thermostat temperatures, this threshold determines the performance of air conditioning equipment. The simulation results indicate that the adaptability conditions in municipalities with dry climate occur approximately 3 °C below those for municipalities with temperate and warm climate.

The electricity consumption profiles of the average home in each municipality were evaluated through thermal energy simulations, using the proposed CDH functions, assigning a value of the hours of AC use per electricity rate for each municipality. A strong correlation was found between the AC usage factors and the minimum average summer temperature assigned per electricity rate, resulting in a progressive increase in usage factors aligned with the alphabetical order of the rates. This proposal of AC use factors per electric rate, combined with data from national censuses and official reports on the characteristics of the average Mexican home, enabled the generation of simulated electricity consumption profiles that closely match actual billing records for each municipality.

The simulation results demonstrate that Function 2 shows better performance in reproducing electricity consumption, as it determines the CDH only when the hourly room temperature exceeds the adaptive temperature threshold between two specific moments in time per day. These results support the improvement in Function 2 with regard to the original one, offering a more precise and reliable tool for the estimation of thermal energy profiles in different municipalities in Mexico, with potential applications in the evaluation of the performance of energy efficiency actions in the domestic sector. When using Function 2 to determine electricity consumption projections for the domestic sector in Mexico, it is recommended that the effect of climate change be incorporated into the hourly temperatures for the coming years, since over long periods of time, the calculated results may have significant variations due to the energy requirements of the AC equipment.

Although the proposed model shows strong performance in simulating residential cooling demand, some limitations must be acknowledged. The approach relies on municipal-level average data, which may not capture intra-city variability in construction quality or occupant behavior. While the adaptive thresholds were primarily informed by international comfort studies and research from countries with similar climates, this study also incorporated localized research conducted in Mexico, such as the works by Sánchez-Montes [46] and Oropeza-Pérez et al. [47], which provided comfort ranges for warm and dry climates based on measurements in Mexican dwellings. These localized references were then calibrated by comparing simulated energy demand with actual electricity consumption records in each municipality, enhancing regional relevance. Nevertheless, comprehensive field studies across the full range of Mexican climates and housing types remain limited, representing a current gap that future research should address to further improve the accuracy and applicability of the proposed model.

5. Conclusions

This study proposed and validated an enhanced Cooling Degree Hours (CDH) method for improving the estimation of residential cooling demand across Mexico’s diverse climatic regions. Unlike traditional CDH models, Function 2 incorporates adaptive comfort temperature thresholds and time-selective activation periods based on Fourier-modeled temperature profiles. This innovation allows for a more realistic representation of cooling behavior in homes, especially in regions where occupant adaptation plays a significant role.

The model was applied to a representative sample of 35 municipalities, selected using a stratified method to ensure the coverage of all domestic electricity tariffs and climate types in Mexico. The simulation results showed that Function 2 consistently outperformed the original CDH function (Function 1) and approximated real electricity consumption with greater accuracy, achieving a percentage error below 10% in most cases.

Compared to dynamic simulation tools such as Open Studio, Function 2 offers a favorable balance between accuracy and simplicity, making it suitable for large-scale assessments and energy policy planning. The model’s scalability and low computational cost support its application to broader regional or national analyses without the intensive data and processing requirements of dynamic modeling.

Although the proposed model was developed for a typical 60 m² single-story dwelling representative of average housing conditions in Mexico, its direct application to multi-family or multi-story buildings would require adjustments to parameters such as occupancy density, internal loads, and construction assemblies to accurately reflect the thermal and energy behavior of these building types.

Future research may explore hybrid approaches that integrate adaptive CDH models with dynamic simulation tools to capture both behavioral adaptation and detailed building physics, enhancing the precision and relevance of residential energy forecasts under climate change scenarios.