Characteristics of Domestic Hot Water Consumption Profiles in Multi-Family Buildings for Energy Modeling Purposes

Abstract

This paper presents a domestic hot water (DHW) consumption model for multi-family residential buildings that captures demand variability across monthly, daily, and hourly timescales. The model enables both the disaggregation of annual consumption for dynamic simulations and the generation of synthetic yet realistic DHW load profiles when detailed measurements are unavailable. It is developed from a dataset of 42 buildings containing 1376 apartments. The analysis identifies seasonal, weekly, and hourly usage patterns, reflecting the influence of apartment layout, building size, and user behavior under Polish climatic and cultural conditions. The proposed model reproduces seasonal deviations of up to 23%, with average daily demand falling to 77% of the annual mean in August and rising above the yearly average during winter months. It also captures weekly variability, with weekend consumption exceeding weekday levels by more than 16%. On working days, the hourly profile exhibits a clear dual-peak structure, with approximately 18% of daily demand occurring in the morning and up to 45% in the evening, whereas weekends show a flatter distribution without pronounced peaks. These results provide a robust basis for more accurate demand representation in energy modeling, system design, and optimization under local conditions.

1. Introduction

Under the growing energy and environmental requirements, domestic hot water (DHW) consumption in multi-family buildings is becoming a key element of energy optimization. The energy required to meet DHW demand accounts for approximately 17% of total household energy consumption in Poland [1,2] and around 15% in residential buildings across the European Union [3]. These values apply to existing buildings. In new constructions, characterized by low energy demand for space heating, the share of energy allocated to DHW preparation is significantly higher and may exceed 50% [4,5,6]. This has a considerable impact on system design and the choice of heat sources, particularly heat pumps and solar systems. Their optimal operation requires accurate DHW profiles that reflect local usage conditions. The importance of using real measurement data to improve the accuracy of DHW and thermal power demand forecasts was demonstrated by Rzeźnik et al. [7], who compared measured and predicted values in multi-family buildings and found significant discrepancies.

The first step toward developing such profiles is the accurate estimation of average daily domestic hot water (DHW) consumption, which serves as the starting point for subsequent modeling across different time scales. The literature presents different approaches to estimating this value, typically based on either the number of occupants or the usable floor area of the dwellings.

In Poland, the approach based on unit domestic hot water (DHW) consumption per capita was used in the first version of the regulation on the methodology for determining the energy performance of buildings, where it was set at 48 L per person [8]. However, Jaszewska and Szaflik [9] reported, based on a 13-year dataset, that the actual average water consumption was as low as 40.2 L per person per day. This decline was mainly attributed to the widespread introduction of individual water metering in residential buildings as well as the changes in user behavior, particularly the growing preference for showers over bathtubs. Rubina et al. [10] found an average DHW consumption of 43.3 L per person per day in 46 German apartments, with the associated energy demand for water heating estimated at 1.71 kWh per person per day, confirming levels comparable to those observed in Poland. A comprehensive overview of unit daily DHW consumption in various countries and operating conditions can be found in Chmielewska [6] and Ratajczak et al. [11].

In energy analyses, domestic hot water (DHW) consumption is often assumed to scale linearly with the number of users of the installation, and this approach is commonly adopted in technical regulations and calculation methods. However, numerous studies have shown a clear decline in per capita water consumption as household size increases. George et al. [12] reported that DHW use per person significantly decreases in multi-person households, attributing this effect to shared activities such as laundry and cleaning, as well as more efficient use of sanitary appliances. Similar findings were presented by Evarts and Swan [13], who analyzed data from over 1500 apartments and demonstrated that per capita consumption in single-person households was considerably higher than in multi-person households. Conversely, Parker [14] observed that DHW consumption per person tends to rise with the number of occupants, but the increase is nonlinear, as each additional person contributes progressively less to total use. Hendron [15] also described a comparable nonlinear effect, emphasizing the differential impact of children and additional household members on water use patterns, particularly in the context of personal hygiene.

Due to the difficulties in accurately determining the actual number of users of DHW systems in multi-family buildings, alternative methods for estimating hot water consumption have been increasingly proposed. These methods are based not on occupancy but on the floor area of the apartment or building. In Poland, this approach has been adopted in the currently binding regulation on the methodology for calculating the energy performance of buildings [16], which assumes a linear relationship between DHW demand and usable floor area. Unfortunately, this solution oversimplifies the estimation process, as it fails to account for important social and demographic factors. Sborz et al. [17] emphasized that floor area alone is not a sufficient predictor of DHW demand, as it does not reflect the diversity of household types, their structure, or the lifestyle of the occupants. Therefore, a simple linear relationship may lead to significant estimation errors and should be applied with caution in energy analyses. A more advanced approach has been implemented in the SAP 10.2 procedure [18], currently in force in the United Kingdom, where the effective number of occupants is determined using an exponential function of the usable floor area. This formulation better captures the nonlinear nature of the relationship and aligns with empirical findings indicating a decreasing per capita DHW consumption with increasing building size.

To more accurately reflect the demand for domestic hot water (DHW) in energy analyses and simulations of heat source performance, it is essential to account for the temporal variability of consumption. For this reason, the literature increasingly includes models describing seasonal, weekly, and daily DHW consumption profiles based on real measurements. The seasonal variability of DHW consumption is well documented in the literature and is mainly associated with the influence of outdoor air temperature and the temperature of the supply water. George et al. [12], using data from a large sample of Canadian residential buildings, reported a noticeable decrease in DHW demand during the summer, attributed to both higher ambient temperatures and changes in user behavior. Ahmed et al. [19] confirmed a similar trend in a study of 182 dwellings in Finland, where average water consumption in summer was 40 L per person per day compared to 46 L per person per day in winter. Meyer [20], however, observed a different seasonal pattern in South Africa, where consumption increased during the summer, driven by local climatic conditions and distinct water use behaviors. Meireles et al. [21] demonstrated a clear relationship between outdoor temperature and the share of hot water in total consumption, showing that this share systematically decreases as air temperature rises. These findings highlight the need to consider local climatic and cultural conditions in seasonal analyses, energy demand modeling, and the design of DHW systems.

In addition to seasonality, weekly variability is also a significant factor shaping domestic hot water (DHW) consumption patterns, as clearly identified in numerous studies. George et al. [12], showed that the lowest DHW consumption was recorded on Fridays, while the highest occurred on Sundays. This effect was attributed to residents spending more time at home on non-working days. Lomet et al. [22], based on research conducted in France, also confirmed the existence of such weekly patterns. In one of the analyzed buildings, a noticeable increase in DHW consumption was observed on Wednesdays, which the authors linked to a school-free day. In contrast, Ahmed et al. [19], analyzing data from 182 dwellings in Finland, reported a systematic decrease in weekend consumption of about 0.5–2.5 L per person per day. In Polish conditions, Szaflik [23] demonstrated that the highest daily DHW consumption occurred on Saturdays and Sundays, likely reflecting differences in lifestyle and the greater presence of residents at home during those days.

In the context of accurately modeling energy demand for DHW preparation, hourly consumption profiles developed from measured data in real buildings are gaining growing importance. These profiles enable realistic representation of short-term consumption variability, which is crucial for evaluating the performance of heat sources, sizing storage capacities, and optimizing system control strategies.

The literature emphasizes that the shape of the hourly consumption profile is significantly influenced by climatic conditions, local customs, and residents’ daily routines. Fuentes et al. [24] identified clear differences between the hourly hot water consumption patterns in Scandinavian and Southern European countries. In northern regions, morning demand peaks dominate, whereas in southern countries, DHW usage is concentrated mainly in the evening. These differences were attributed to variations in daily schedules and hygiene habits. It is worth noting that the morning peak commonly reported in many studies may not accurately reflect real usage patterns in Poland, where the distribution of DHW consumption may be more uniform throughout the day or shifted toward the evening hours.

The most commonly used hourly domestic hot water (DHW) consumption profiles in energy simulations are those developed through research initiatives such as IEA Annex 42 [25] and IEA Task 26 [26], as well as profiles established in technical standards such as EN 15316-3-1 [27]. These profiles form the basis of numerous analyses performed with tools like TRNSYS, EnergyPlus, TAS, or IES VE. EN 15316-3-1 [27] defines DHW profiles for various types of users, including a three-person household, with a pronounced morning peak (7:00–9:00) and reduced evening consumption. However, the absence of seasonal and weekly variation limits its accuracy in localized analyses. The profile from IEA Annex 42 [25], based on data from several countries (including Germany, Switzerland, and the USA), distinguishes between weekdays and weekends and features a distinct morning peak, though it was not calibrated for Polish conditions. The IEA Task 26 [26] profile has a high temporal resolution (on a minute scale) and accounts for both seasonality and weekly variation. The evening peak often exceeds the morning one, and overall consumption is higher on weekends. This model offers high flexibility but must be applied cautiously in different climatic and cultural contexts. Finally, Hendron [15], in the Building America Benchmark model developed by NREL, introduced detailed end-use breakdowns and differentiation between days of the week. However, due to its U.S. origin, its use in Europe requires careful adjustment to local conditions.

A comparison and overview of various hourly domestic hot water (DHW) profiles and their structures was presented in detail by Mazzoni et al. [28], who emphasized that the choice of an appropriate profile significantly affects the outcomes of energy simulations, particularly in the context of storage tank sizing, heat source operation optimization, and energy storage analysis. The authors also highlighted that the lack of a profile based on country-specific data can lead to substantial design errors, reinforcing the need for regional calibration of models or the development of dedicated national measurement databases. As demonstrated by Rzeźnik et al. [7], the analysis of real measurement data from residential buildings not only enables the reconstruction of actual DHW consumption profiles but also allows for the assessment of user comfort and thermal losses in the system—factors often neglected in theoretical models. Furthermore, De Simone et al. [29] proposed a classification of five daily DHW consumption profile types, based on data from 127 single-family houses in Germany. These profiles differed in the number and distribution of demand peaks, reflecting varying usage patterns related to household size and residents’ daily routines. Additionally, Marszal-Pomianowska et al. [30] showed that domestic hot water draw-off profiles differ between weekdays and weekends. Weekdays typically exhibit a single, pronounced morning peak, while weekends are characterized by two milder peaks—one in the morning and another in the evening—reflecting changes in daily routines and occupancy patterns.

In the context of renewable energy systems, such as heat pumps powered by photovoltaic (PV) installations, the importance of local DHW consumption data was also emphasized by Pater [31]. The study demonstrated that increasing energy self-consumption is possible when demand profiles are aligned with PV generation characteristics. During the design phase of heat sources—especially solar systems—it is crucial to consider the seasonal mismatch between DHW demand and solar energy availability. As shown by Sborz et al. [32], despite high solar radiation in summer, DHW demand drops significantly, which may lead to system oversizing if local and seasonal consumption patterns are not properly considered in system design. Furthermore, Maltais and Gosselin [33] showed that DHW demand can be effectively predicted even with limited access to measurement data. Their study applied neural networks to forecast consumption in systems of various sizes—from individual dwellings to entire multi-family buildings. The results demonstrated that prediction accuracy increases with the level of data aggregation, and larger systems exhibit greater stability in outcomes. This approach confirms the usefulness of data-driven methods in energy analysis and control optimization of DHW systems, even under limited high-resolution data availability.

It should be noted that none of the above-described profiles were developed using measurement data from buildings located in Poland. This raises justified concerns about their direct applicability to national analyses. Differences in lifestyle, household structure, and system configurations may result in discrepancies between actual and modeled domestic hot water (DHW) demand. Hourly profiles represent a key component of any detailed energy analysis, especially in the context of heat source sizing, storage tank energy storage system design, as well as the optimization of equipment operation under dynamic conditions. Therefore, this study proposes a method for generating DHW demand profiles based on data collected in Polish residential buildings. The primary objective is to develop a time-resolved model of DHW consumption in multi-family buildings in Poland, grounded in extensive measurements and suitable for practical applications in energy modeling and system design.

2. Materials and Methods

The objective of this study was to develop and validate a model describing the variability of domestic hot water (DHW) consumption in multi-family residential buildings across three temporal scales: monthly, daily, and hourly. The proposed concept for constructing DHW consumption profiles is intended for both statistical analyses and practical engineering applications, including energy audits, computer simulations, and the design of domestic hot water systems.

To ensure flexibility and applicability model at different levels of detail, a stepwise structure based on the introduction of correction factors was adopted. This approach enables the transition from average daily consumption to a detailed hourly profile. As a result, the model can be applied both in the absence of measurement data and when only aggregated information is available (e.g., annual DHW consumption).

The model development process consisted of four key stages:

• Estimation of the average daily DHW consumption, based on the building’s structure—specifically, the number of apartments by room count and their usable floor area.
• Incorporation of seasonal variations in demand, by applying monthly correction factors reflecting the influence of climatic conditions and vacation periods on hot water consumption.
• Introduction of weekly variability, by distinguishing three types of days (Mondays, weekdays from Tuesday to Friday, and weekends), for which distinct usage patterns of the water system were observed.
• Development of hourly consumption profiles, separately for weekdays and weekends, based on the relative distribution of demand across the hours of the day.

Measurement Data

The foundation of the developed model was a dataset comprising measurements collected from 42 multi-family residential buildings located in Wrocław and Zawidów, Poland, encompassing a total of 1376 apartments. These two cities differ significantly in size and urban structure, which allowed the dataset to capture varied usage conditions and provide a basis for developing a more universally applicable national model. Each apartment was equipped with an individual water meter recording both hot and cold water consumption. The permissible measurement error of the devices was ±3%. Most meters were equipped with impulse transmitters for remote reading, which ensured high continuity and accuracy of the data. The dataset covers the period from 2012 to 2017, although the time range varied depending on the modeling stage and data availability in individual buildings. The average hot water temperature in all analyzed buildings was set at 55 °C.

Different data subsets were used at various stages of the model development process, as detailed below:

• The model of average daily DHW consumption was developed based on data from 16 buildings located in Wrocław (773 apartments). Additionally, data on apartment structure—including the number of rooms and usable floor area—along with annual hot water consumption for 626 apartments, were obtained from housing managers. The measurement period spanned two years.
• Seasonal variation analysis was carried out using monthly data from 30 buildings (818 apartments). The measurement period covered four years.
• Daily profiles for specific days of the week (weekdays/weekends) and hourly DHW consumption profiles were derived from measurements conducted in boiler rooms of three multi-family buildings. The recording period lasted five years.

The model was developed using a training dataset comprising 90% of the total data. The remaining 10%, originating from different measurement years and from buildings not included in the training phase, was used for independent validation and error assessment of the model predictions.

3. Results and Discussion

To develop a realistic model of domestic hot water (DHW) consumption in multi-family residential buildings, a comprehensive analysis of measurement data was conducted. The main objective was to identify key temporal patterns in DHW usage and to assess the extent to which factors such as season, day of the week, and daily routines affect the intensity and distribution of demand.

The dataset comprised DHW consumption records at three temporal resolutions: monthly, daily, and hourly. This allowed for the identification of both seasonal fluctuations and recurring daily patterns reflecting typical occupant behavior. Particular emphasis was placed on the analysis of hourly data, given its critical relevance for dynamic simulations of heat source operation and for the design of systems based on low-temperature and renewable energy technologies.

The following section summarizes the principal findings from the data analysis and presents selected figures illustrating the relationship between DHW consumption and time dependent variables. These results provide the foundation for the subsequent development of time-resolved DHW consumption models discussed later in the paper.

3.1. Monthly Time-Step Data Analysis

For each building, monthly deviations of daily hot water consumption from the annual average were calculated. This resulted in dimensionless values of the average monthly DHW consumption index in the analyzed multi-family buildings, as shown in Figure 1. The highest consumption values were observed during the winter months (January to March), while the lowest occurred in the summer (July to August). The observed seasonal variation may be attributed to both differences in usage patterns (e.g., higher occupancy rates during colder months) and the physical characteristics of DHW systems. Lower cold water temperatures in winter increase the proportion of hot water in the mixed water drawn at outlets, thereby raising the measured DHW consumption. Additionally, during the heating season, users tend to prefer higher water temperatures, further contributing to the increased share of hot water in overall water usage.

Differences between individual months reached up to several percentage points in relation to the annual average, highlighting the necessity of including seasonality in predictive models of DHW demand. The average consumption pattern throughout the year remains relatively stable from September to December, which provides a basis for defining monthly correction factors in simulation-based modeling. Statistical analysis confirmed the significance of the observed differences. The Kruskal–Wallis test showed that monthly DHW consumption values differed significantly. Statistically significant differences were found, for example, between the winter months (January to March) and the late summer to autumn period (July to October).

3.2. Daily Time-Step Data Analysis

For each building, daily domestic hot water (DHW) consumption was calculated and normalized relative to the average daily value obtained by dividing the total weekly consumption by seven. This approach yielded dimensionless indicators representing the distribution of average daily DHW use in the analyzed multi-family buildings, which are illustrated in Figure 2. The data were visualized using box plots, enabling the assessment of both the spread and the central tendency of consumption for each day of the week.

Moderate differences in DHW consumption intensity between weekdays were observed. On average, the lowest consumption occurred on Mondays, while significantly higher usage was recorded on Saturdays and Sundays. This pattern may be explained by increased occupancy during weekends, as well as hygiene-related activities performed more frequently on non-working days (e.g., cleaning). The observed variation in the data range (non-outlier range) also suggests greater heterogeneity in user behavior on weekends. This may be relevant not only for analyzing average demand but also for assessing peak load conditions within DHW systems.

To statistically evaluate the significance of daily consumption differences between weekdays, an analysis of variance (ANOVA) was performed. Prior to that, the necessary assumptions were verified, including distribution normality (Shapiro–Wilk test) and homogeneity of variance (Brown–Forsythe and Levene tests). The results confirmed statistically significant differences in average DHW consumption across specific days. A post hoc Tukey test further revealed significantly higher weekend consumption compared to weekdays, as well as notable differences between Monday and Wednesday and Thursday.

3.3. Hourly Time-Step Data Analysis

To provide a detailed characterization of domestic hot water (DHW) usage throughout the day, an analysis was conducted using measurement data from a selected complex of multi-family buildings. For each day, hourly hot water consumption was determined and normalized by dividing the total daily consumption by 24. This approach yielded dimensionless values representing the relative hourly share of the total daily DHW usage, enabling comparisons of usage patterns regardless of absolute consumption levels.

Figure 3 presents the hourly DHW consumption profile for a selected weekday (Wednesday) over the analyzed period. The plot shows the median, interquartile range, and non-outlier values, offering insight into the typical daily rhythm as well as variability across observations. A clear bimodal profile is evident, with higher consumption observed during the morning hours (6:00–9:00) and in the evening (19:00–24:00). During the daytime hours (10:00–16:00), usage declines, typical working-day behavior of residents. It is also worth noting the greater variability in evening consumption, which may indicate differences in user habits related to return times and evening activities.

The raw data plotted on the graph reveal the presence of outliers, which can be linked to atypical days such as Christmas Eve, New Year’s Eve (31 December), and New Year’s Day. These days are characterized by altered household activity patterns, resulting in reduced DHW consumption or a shift in peak hours. For example, New Year’s Day shows a delayed morning peak, while Christmas Eve is marked by low evening consumption. These phenomena confirm the rationale for excluding such days as unrepresentative when modeling hourly demand profiles.

Figure 4 presents the average hourly profiles of domestic hot water (DHW) usage share, differentiated by individual weekdays. The line connecting hourly values in the chart should be interpreted as a trend line, indicating the overall consumption pattern and the timing of peaks. It facilitates the comparison of profiles between weekdays. It does not represent intermediate measurements but serves as a visual aid for illustrating typical user behavior. A clearly bimodal consumption pattern is observed across all days, with a morning peak between 7:00 and 8:00 and an evening peak between 20:00 and 23:00. The profiles from Monday to Thursday exhibit strong similarity, whereas Friday shows a noticeable reduction in evening consumption intensity.

The lower consumption share between 20:00 and 23:00 on Fridays may be attributed to shifts in user behavior related to the approaching weekend. This hypothesis is supported by statistical analysis—ANOVA combined with Tukey’s post hoc test confirmed statistically significant differences during selected hours. Notable differences were found between Friday and other weekdays, including at 22:00, as well as between Friday and Tuesday at 20:00, and between Friday, Tuesday, and Thursday at 21:00. Additionally, statistically significant differences were identified in the morning hours, such as at 8:00 between Friday and Monday.

Figure 5 presents the averaged hourly profiles of domestic hot water (DHW) consumption for Saturdays and Sundays. As in Figure 4, the connecting line is to be interpreted as a trend line rather than an interpolation of intermediate data points. Compared to weekdays, a noticeable shift in the timing of peak demand is observed. Morning usage begins to rise around 8:00, reaching a maximum between 9:00 and 11:00. The evening peak occurs between 20:00 and 23:00 and displays a more extended distribution than on weekdays.

Weekend profiles are more symmetrical and exhibit smoother transitions, reflecting the more flexible daily routines of residents. Data analysis reveals distinct differences between Saturday and Sunday. Evening DHW consumption on Saturdays is significantly lower than on Sundays, particularly between 20:00 and 23:00, as well as during the morning (8:00–9:00) and early afternoon (16:00–17:00).

The statistical analysis confirmed the significance of these differences. Tukey’s post hoc test showed that the differences between Saturday and Sunday during selected hours are statistically significant (p < 0.05). These findings suggest that, in certain modeling applications, it may be beneficial to treat Saturday and Sunday separately—especially in the context of hourly DHW demand modeling.

Figure 6 presents the average hourly profile of domestic hot water (DHW) consumption in a multi-family residential building, broken down by month. As in Figure 4, the connecting line is to be interpreted as a trend line rather than an interpolation of intermediate data points.

The analyzed distribution exhibits a characteristic dual-peak structure, typical for residential buildings, with a morning maximum generally occurring between 7:00 and 8:00 and an evening peak between 20:00 and 23:00. This shape remains relatively stable throughout the year; however, certain statistically significant differences between months were identified.

During the winter period (December to February), a decrease in morning consumption and a shift of the evening peak to earlier hours (around 20:00) was found. In contrast, during the summer months (July to August), the evening peak was delayed to approximately 21:00, which may be attributed to later daily routines of residents in warmer periods. Overall, the winter period also displayed a greater share of evening consumption in the daily structure, which may be linked to longer time spent at home and lower cold water temperatures. Despite these variations, the hourly profile was generally consistent, justifying the use of averaged values in the subsequent modeling stages.

The analysis of hourly data, including the breakdown by both days of the week and months of the year, revealed distinct differences in daily domestic hot water (DHW) consumption patterns. Notably, shifts in peak hours and variability in consumption intensity were observed between weekdays and weekends. Nevertheless, profiles for consecutive weekdays (Monday to Thursday) were characterized by strong consistency, with statistically significant differences primarily found on Friday evenings, reflecting the end of the working week rather than a fundamentally different daily routine. In contrast, although Saturdays and Sundays differed, both showed shifted activity patterns and greater flexibility in daily consumption, which justified their treatment as a separate group.

From the perspective of modeling and calibration of the hourly profile, further segmentation of the week (e.g., assigning each day a separate profile) would increase the complexity of the model without a proportional improvement in accuracy. Moreover, the use of an excessive number of profiles raises the risk of overfitting to historical data, thereby reducing the predictive capability of the model under changing user behavior.

Therefore, the model adopts two representative hourly profiles—one for weekdays and another for weekends—as a compromise between precision and simplicity. This approach is also supported by relevant literature, where such a division is commonly applied to describe typical consumption patterns in residential buildings. Averaging within these two groups allows the capture of the main behavioral trends of users while maintaining clarity and broad applicability of the hourly profile.

4. Model Development

Based on a detailed analysis of measurement data, a domestic hot water (DHW) consumption model was developed to reflect actual demand across multiple temporal resolutions. The model follows a hierarchical structure, progressively increasing time resolution and improving the accuracy of real consumption pattern representation.

In the first step, an average daily DHW consumption model was formulated for a multi-family building, taking into account the number and structure of individual dwellings. Subsequently, correction factors were applied to reflect seasonal, weekly, and daily variability. These coefficients enabled the transformation of daily values into more detailed monthly, weekly, and hourly profiles.

The proposed approach enables not only a realistic representation of DHW consumption variability, but also guarantees consistency between models developed at different temporal scales. The following sections present a detailed discussion of each stage of the model development process.

4.1. Average Daily Domestic Hot Water Consumption Model

To estimate the baseline demand for domestic hot water (DHW) in multi-family buildings, a model for predicting average daily consumption was developed. This represents the first stage in the hierarchical structure for representing DHW usage and serves as the foundation for subsequent transformations at monthly, daily, and hourly resolutions.

The model takes into account both the total annual DHW consumption and the geometric characteristics of the dwellings, particularly their usable floor area and the number of rooms. The latter serves as a proxy for the number of occupants and the intensity of hot water usage. In [6], two variants of the average daily DHW consumption estimation model were proposed, both developed using multiple regression analysis and described in detail in [34].

Model 1 ($\overline{V_d}$)—is based on the number of one-room apartments ($n_1$), two-room ($n_2$), three-room ($n_3$), and four-room units ($n_4$), as defined by Equation (1). It enables a quick estimation of DHW demand using widely available data on apartment layout, without requiring detailed information on dwelling floor area.

$$\overline{V_d}={0.063·n}_1+{0.084·n}_2+0.106·\left(n_3+n_4\right)+0.015, {\mathrm{m}}^3/\mathrm{d}\mathrm{a}\mathrm{y}$$

(1)

Model 2 ($\overline{V_d})$ considers both the number of apartments and their usable floor area, categorized by the number of rooms. This approach enables a more accurate representation of the influence of spatial characteristics on DHW consumption, which may be particularly important in atypical buildings such as modern apartment complexes, where relatively few rooms are often associated with a large total area. This average daily consumption model is defined by Equation (2), where $A_1$ is the total floor area of one-room apartments, $A_2$ is the total floor area of two-room apartments, $A_3$ is the total floor area of three-room apartments, and $A_4$ is the total floor area of four-room apartments.

$$\overline{V_d}={0.0021·A}_1+{0.0018·A}_2+{0.0017·A}_3+{0.0011·A}_4+0.011, {\mathrm{m}}^3/\mathrm{d}\mathrm{a}\mathrm{y}$$

(2)

Both models were calibrated using multiple linear regression and achieved a high level of statistical fit. The average estimation error for Model 1 was 10%, whereas Model 2 achieved a lower error of approximately 8%, confirming its superior predictive accuracy within the analyzed sample.

Ultimately, Model 1 was selected for further analysis due to its simplicity, lower input data requirements, and ease of application in engineering practice. This model is particularly useful during preliminary design stages, where detailed information on apartment geometry is often unavailable. Model 2, on the other hand, is recommended when more comprehensive building documentation is available and when the goal is to obtain a more precise estimation of DHW demand, especially in buildings with atypical apartment structures.

In Poland, most of the existing national regulations relate domestic hot water (DHW) consumption to the number of occupants, which is difficult to determine precisely in multi-family buildings. Only the regulation on the methodology for preparing energy performance certificates [16] adopts a linear dependence of DHW consumption on apartment floor area. To assess the effectiveness of this approach, the same dataset used for validating the proposed models was applied, enabling a direct comparison. However, the analysis revealed that this regulation-based method is subject to significant error, with an average deviation of up to 20%. The error is smaller in buildings with a balanced distribution of one-, two-, three-, and four-room apartments, but it increases considerably in more heterogeneous structures, particularly where one-room or four-room apartments are absent. In such cases, discrepancies reach as high as 50%, meaning that predictions based on Polish regulations may result in substantial overestimation or underestimation of actual demand. An additional limitation is that the regulation-based model refers to the heated floor area of the building, which also includes common spaces. This does not necessarily correspond to a higher number of occupants and may therefore lead to misestimations. Compared with this approach, the proposed models demonstrate lower error levels and better capacity to reflect the diverse structure of multi-family buildings, confirming their greater suitability for predicting DHW demand.

4.2. Monthly Model of Domestic Hot Water Consumption

To describe the seasonal variability of domestic hot water (DHW) demand in multifamily buildings, a monthly model for estimating DHW consumption was developed. This model captures the natural changes in user behavior throughout the year, which are influenced by both climatic and behavioral factors. The monthly DHW consumption in buildings $\left(V_{m_i}\right)$ was determined according to Equation (3), where $d_{m_i}$ is the number of days in month i, and $s_{m_i}$ is the monthly correction factor.

$$V_{m_i}=s_{m_i}·\overline{V_d}·d_{m_i},$$

(3)

As part of the study [6], two approaches were proposed for modeling the correction factor $s_{m_i}$, which represents the monthly deviations in domestic hot water (DHW) consumption. These approaches were described in detail in publication [35].

Model 1$\left(s_{m_i}\right)$—based on multiple regression, incorporates the influence of average monthly outdoor temperatures and the share of vacation days on domestic hot water (DHW) consumption. Although this model achieved a high coefficient of determination, its practical application requires access to current meteorological data and school holiday calendars, which may not always be readily available. The final form of the model is presented in Equation (4), where $T_{\mathrm{a}\mathrm{v}\mathrm{g},\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}}$ denotes the annual average outdoor air temperature, $T_{\mathrm{a}\mathrm{v}\mathrm{g},m_i}$ represents the average monthly temperature, $d_{{vac,m}_i}$ is the number of school vacation days in a given month, and $d_{m_i}$ refers to the number of days in the month.

$$s_{m_i}=0.363·\left(1+0.2·{\displaystyle \frac{T_{\mathrm{a}\mathrm{v}\mathrm{g},\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}}-T_{\mathrm{a}\mathrm{v}\mathrm{g},m_i}}{T_{\mathrm{a}\mathrm{v}\mathrm{g},\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}}}}\right)-0.184·{\displaystyle \frac{d_{{vac,m}_i}}{d_{m_i}}}+0.671,$$

(4)

Model 2 $\left(s_{m_i}\right)$—a simplified approach based solely on the assignment of domestic hot water (DHW) consumption to specific months of the year, without considering any external variables. The values of monthly correction factors were directly derived from empirical measurements, with the sample extended using the bootstrap resampling method. This technique involves repeated random sampling with replacement from the available dataset, allowing the reconstruction of the full distribution of DHW consumption variability without the need for time-consuming and costly collection of new measurement data.

Due to its ease of implementation and independence from additional input data, Model 2, based on correction factors assigned to individual months, was selected for further analysis and recommendations. The values of these correction factors are presented in

Table 1. Monthly correction factor $s_{m_i}$ for domestic hot water (DHW).

Month	1	2	3	4	5	6	7	8	9	10	11	12
$s_{m_i}$	1.10	1.09	1.11	1.07	1.01	0.92	0.88	0.77	0.93	1.00	1.04	1.07

. This approach enables straightforward adaptation of the model in energy simulations and optimization analyses without the need to collect supplementary information.

The obtained correction factors confirm the distinct seasonality of domestic hot water (DHW) consumption, with increased demand during the winter months (January to March and November to December) and a significant decrease during the summer holiday period (July and August). The lowest values were observed in August, when the consumption dropped to 77 percent of the average. This pattern is consistent with typical user behavior, such as vacation-related absences that reduce the number of residents. The highest DHW consumption was recorded in January and March, corresponding to the lowest cold water temperatures, which are influenced by the characteristics of the water supply system. The mean estimation error of the model was 5.5%. The assumption of a constant monthly domestic hot water (DHW) consumption, without accounting for seasonal variations, leads to a significant deterioration in the accuracy of results. The analysis showed that under such an assumption, the average estimation error increases to approximately 13%. This indicates that neglecting seasonal fluctuations may introduce systematic deviations in the calculations. The findings demonstrate that the application of a simple indicator-based correction model provides a high level of estimation accuracy while maintaining minimal requirements in terms of input data availability.

4.3. Daily Domestic Hot Water Consumption Model

As part of the analysis of daily domestic hot water (DHW) consumption, a model was developed to account for variations in usage depending on the day of the week. The daily variability model $V_{d_{j,i}}$ is based on deviations in water use on specific days of the week relative to the average daily monthly consumption $\overline{V_d}$, and is described by Equation (5), where $s_{d_j}$ and $s_{m_i}$ are correction factors reflecting the influence of the day of the week and the month, respectively.

$$V_{d_{j,i}}={s_{d_j}·s}_{m_i}·\overline{V_d},$$

(5)

To determine the correction factor $s_{d_j}$, which accounts for daily variations in DHW consumption depending on the day of the week, the results of the statistical analysis presented in the earlier section of the article were used. This analysis demonstrated that domestic hot water usage differs significantly between individual days of the week, with particularly low values observed on Mondays and the highest consumption occurring during weekends. Based on these findings, three distinct groups of days with differing consumption patterns were identified: Mondays, weekdays from Tuesday to Friday, and weekends.

The proposed correction factors $s_{d_j}$, presented in

Table 2. Daily correction factors $s_{d_j}$ for domestic hot water consumption by day of the week.

Day of the Week	Monday	Tuesday–Friday	Saturday–Sunday
$s_{d_j}$	0.83	0.96	1.16

, capture these variations and enable scaling of daily DHW consumption relative to the annual average value. This approach balances simplicity with accuracy while facilitating practical implementation in engineering applications.

The correction factor values assigned to these groups are presented in Table 2. They reflect the observed differences and allow for scaling daily domestic hot water (DHW) consumption relative to the annual average value. The proposed division of the week into three day-type groups—Monday, Tuesday to Friday, and Saturday to Sunday—is based both on the observed structure of daily domestic hot water (DHW) consumption and on the results of statistical testing.

This simplified classification helps minimize the risk of overfitting the model to historical data and facilitates its implementation in energy simulation tools.

In particular, the lower consumption observed on Mondays may be related to reduced occupancy of dwellings after the weekend or limited hygienic activities. In contrast, higher consumption on Saturdays and Sundays reflects increased time spent at home, more intensive use of bathrooms, and household tasks such as laundry or cleaning.

This formulation of the model provides a foundation for further decomposition of daily consumption values into hourly profiles, while ensuring consistency with the earlier modeling stages.

4.4. Hourly Model of Domestic Hot Water Consumption

To accurately represent the consumption profile of domestic hot water (DHW) in multi-family residential buildings, an hourly model was developed based on metered data recorded at one-hour intervals.

The hourly variability model $V_{h_{n,j,i}}$, was derived from deviations in consumption observed at specific hours of the day relative to the average daily consumption $V_{d_{j,i}}$, and is defined by the following Equation (6) where $s_{h_n}$ is the hourly correction factor.

$$V_{h_{n,j,i}}=s_{h_n}·V_{d_{j,i}},$$

(6)

The hourly correction coefficients $s_{h_n}$, presented in

Table 3. Hourly correction factors $s_{h_n}$ for domestic hot water consumption.

Hour	Working Days	Weekends
1	0.027	0.030
2	0.009	0.014
3	0.004	0.006
4	0.003	0.004
5	0.005	0.004
6	0.027	0.004
7	0.083	0.011
8	0.068	0.030
9	0.047	0.058
10	0.040	0.073
11	0.033	0.076
12	0.029	0.062
13	0.025	0.051
14	0.023	0.045
15	0.024	0.041
16	0.025	0.037
17	0.031	0.035
18	0.038	0.036
19	0.054	0.050
20	0.084	0.077
21	0.086	0.075
22	0.089	0.066
23	0.086	0.067
24	0.059	0.050

, indicate the share of DHW consumption assigned to each hour of the day, differentiated for weekdays and weekends. These values, derived from the analysis of measurement data, capture the typical daily activity patterns of occupants in multi-family residential buildings.

The distribution of the hourly correction coefficients reveals the characteristic dual-peak pattern of domestic hot water (DHW) consumption. On weekdays, distinct morning (approximately 6:00–7:00) and evening (approximately 19:00–22:00) peaks are observed. During weekends, these peaks shift in time. The morning peak typically occurs between 9:00 and 11:00, while the evening peak appears slightly earlier than on weekdays. The weekend consumption profile is also characterized by a smoother shape and more uniform distribution throughout the day, reflecting the less structured daily routines typically observed on Saturdays and Sundays.

In the EN 15316-3-1 standard [27], the recommended European profile based on energy use for domestic hot water (DHW) preparation (for a family with showers) allocates about 28% of daily consumption to the morning hours, while the evening peak is concentrated within a short time period. In Polish conditions, a clear shift of activity toward the evening is observed: in the developed measurement-based profile, the morning accounts for about 18% of daily consumption, whereas the evening reaches approximately 45%, aligning with the schedule of a typical working day. Due to the climate, relatively few people take morning baths, and water use during this time is mainly associated with meal preparation and basic hygiene activities. The application of standardized profiles therefore leads to an underestimation of evening loads and does not account for differences between weekdays and weekends or the influence of household size and apartment floor area. Despite these limitations, this standard is widely used in hourly simulations of heating system operation, including heat pumps, which makes its comparison with measurement data particularly important. Similar assumptions—with a predominance of morning consumption—are also adopted in popular simulation tools (TRNSYS, EnergyPlus, IDA ICE, DesignBuilder), which fail to accurately reflect the Polish context.

4.5. Structure of the Domestic Hot Water Consumption Model

The final structure of the domestic hot water (DHW) consumption model is presented in Figure 7 in the form of a block diagram. The graphical representation of subsequent calculation steps illustrates the relationships between different levels of temporal resolution—starting from the average daily consumption value, through monthly and daily corrections, up to the final reconstruction of the hourly consumption profile.

The diagram also shows the correction coefficients assigned to each stage (Table 1, Table 2 and Table 3), which allow the model to account for seasonality as well as weekly and daily variability, all within a single, coherent framework. This approach facilitates the implementation of the model in computational tools, while also providing a clear understanding of the logic behind the estimation of DHW demand in multi-family residential buildings.

The hierarchical structure of the proposed model makes it adaptable to diverse climatic and cultural conditions. Correction factors at each stage are explicitly linked to user habits, standard workday patterns, and other behavioral determinants. This design enables the redefinition of annual average DHW consumption as the primary input parameter, which can then be modified using reduction factors calibrated to local conditions. Consequently, the model is expected to perform well in regions with climatic conditions and usage patterns similar to those in Poland, while remaining transferable to other contexts through calibration based on local seasonal, daily, and hourly patterns.

Beyond its methodological contribution, the model has practical implications for the integration of renewable energy systems. The pronounced evening peak in DHW demand identified in Polish conditions may limit direct synchronization with photovoltaic generation, which typically peaks at midday. This underlines the importance of thermal storage, enabling surplus solar energy to be stored during the day and used to meet evening demand. The model also provides a robust basis for optimizing heat pump operation, as the structure of hourly demand profiles supports the design of load-shifting strategies that align electricity consumption with periods of lower grid demand or greater renewable availability. In district heating systems, capturing seasonal and daily variability is equally important, as it allows operators to forecast peak loads and evaluate the benefits of demand-side management strategies. Overall, the proposed framework facilitates the development of more flexible, resilient, and efficient energy systems by better aligning DHW demand with renewable supply profiles.

5. Conclusions

The developed model of domestic hot water (DHW) consumption in multi-family buildings provides a comprehensive tool for reproducing demand variability at different time scales—from monthly, through daily, down to hourly resolution. This model can be used both to estimate DHW consumption based on information about the building structure and to disaggregate aggregated values such as annual or monthly water consumption into finer time intervals. Therefore, it finds application in energy simulations, heat source analysis, system design, as well as in optimization and predictive tasks.

The modeling process is based on a hierarchical approach, in which each subsequent step refines the previous one while maintaining consistency with the input data and ensuring the scalability of the solution. The first stage involves determining the average daily DHW consumption in the building, depending on the number and type of apartments (i.e., the number of one-, two-, three- and four-room flats). This formula enables a quick estimation of design demand in situations where no measurement data are available and may also serve as a reference point for further analysis. It is particularly useful in energy simulations, where time-specific consumption data are required as model input.

The next step of the model accounts for seasonal variability in DHW demand by introducing monthly correction factors. Monthly consumption profiles reflect natural changes in user demand throughout the year due to both climatic conditions and shifts in resident activity. In this work, a simplified model was applied, assigning specific correction values to each month based on an analysis of measured data. This approach allows for an accurate disaggregation of average annual consumption into monthly values without relying on up-to-date meteorological data or school calendars. The resulting monthly model can be used, for instance, to break down annual or quarterly billing data, making it suitable for seasonal simulations and heating system planning.

The third modeling step addresses daily variability depending on the day of the week. Statistical analysis of measurement data showed significant differences between Mondays, weekdays from Tuesday to Friday, and weekends. Based on these findings, three distinct groups of days were identified, each assigned a dedicated correction factor. This classification represents a compromise between accuracy and implementation simplicity. It captures the main weekly trends without the risk of overfitting the model to historical data. Higher consumption during weekends is associated with greater occupancy and more intensive use of sanitary facilities, while lower demand on Mondays may result from residents being absent after weekend travel or from shifted hygiene routines. Incorporating this level of detail allows the model to reflect weekly cyclicality more accurately and strengthens its reliability in demand-side management analyses.

The final step involves the development of an hourly model, which introduces correction factors reflecting intra-day variability in DHW usage. These coefficients were determined separately for weekdays and weekends, based on measurement data recorded at an hourly time step. The model captures typical user activity patterns, including morning, afternoon, and evening peaks, and enables precise modeling of instantaneous demand. This level of resolution is essential for the design of systems with thermal buffers, the selection of dynamically responsive heat sources (e.g., heat pumps), and the analysis of distribution system heat losses.

All model stages were developed based on multi-year measurement data, which ensures their high representativeness and statistical reliability. Moreover, the use of correction factors at each modeling phase enables easy adaptation of the model to varying levels of data availability—from rough estimates to actual meter readings. As a result, the model can be used not only for design and simulation purposes but also for monitoring and optimizing the performance of real DHW systems in multi-family residential buildings.

Future research should extend this study by exploring DHW consumption variability across different residential and non-residential building types and climatic conditions. Another promising direction is the use of data-driven and machine learning methods to improve modeling accuracy and support real-time prediction. Expanding the measurement base with long-term, high-resolution data would also allow for a deeper understanding of occupant behavior and its impact on DHW demand.