An Occupancy-Weighted Energy Consumption and Thermal Comfort Control Model by Communication and Reallocation Algorithms

1. Introduction

Conventional Heating, Ventilation, and Air Conditioning (HVAC) control architectures operate independently on a per-building basis. However, they prequently fail to dynamically adapt to spatiotemporal variations in occupancy rate and transient thermal loads, leading to concurrent energy inefficiencies and suboptimal thermal comfort. Recent, several studies have investigated to establish a demand-side flexibility framework that optimizes building HVAC operations across multiple zones and structures through the indices of occupancy-weighted thermal comfort and energy efficiency. This study proposes a predictive, real-time control framework that continuously monitors and forecasts zone-level headcount and personal parameters such as metabolic rate and clothing insulation. The algorithm dynamically minimizes the discomfort across the system under peak power constraints. Beyond standard energy-saving protocols or single-building thermal comfort regulation, this work establishes a formal mathematical architecture for inter-building energy reallocation, weighted dynamically by human occupancy.

2. Literature Review

3. Research Method

3.1. Building Model

The U.S. Energy Information Administration's Commercial Buildings Energy Consumption Survey (CBECS) provides essential data for analyzing energy use across public, commercial, and residential sectors. This comprehensive resource establishes the Energy Use Intensity (EUI) benchmarks for fourteen major building classifications [22~24]. While CBECS categorizes standard building uses extensively, some unique or non-standard uses are grouped together, as seen in Table 1., which details building geometry and component specifications.

Table 1.

Building geometry and component specification

The foundation of this system is real-time sensing. The diagram begins by distinguishing between two rooms with highly disparate occupancy characteristics: Room A (Retail - Low Use/Occupancy) and Room B (Food Service - High Use/Occupancy). This distinction is a fundamental input, allowing the system to understand where users are concentrated. This difference dictates the initial priority for energy distribution. The the entire operation is the Central Communication and Optimization Module. This module connects directly to the principles of central optimization. The module uses its real-time understanding of occupancy and space purpose to establish a “load-based priority” for energy allocation. Fig. 1. visually confirms this by placing a literal neural network schematic inside the optimization loop. The ANN receives input data such as temperature setpoints and indoor temperature, and dynamically optimizes the supply signal to the local HVAC actuators. Occupancy-weighted discomfort modeling is where the core logic mentioned in my academic English revision is put into practice. The system uses a weighted discomfort cost function to generate optimal control signals that maximize social welfare. The central module senses that occupants in high-use food service are significantly larger than retail. The module recognizes that the priority for comfort is lower in this space. It sends a relaxed setpoint command, causing supply temperature to drift further from the local thermal neutral point. This intentionally allows a minor increase in perceived discomfort, but significantly decreases the energy burden in that zone. The optimization engine prioritizes the discomfort penalty in this highly-occupied space. It maintains an aggressive setpoint, causing the supply temperature signal to tightly track the neutral comfort temperature. This shift ensures high thermal comfort satisfaction for the larger number of users, consistent with the occupant-centric principles discussed in the literature. The diagram explicitly visualizes the novel inter-space energy transfer mechanism that I highlighted in my technical overview. The Dynamic Energy Reallocation labels with associated memory module architectures and arrow vectors confirm that the system goes beyond simply varying setpoints.

Fig. 1.

Schematic approach

A key feature is that the central module uses past experiences stored in the memory architectures to anticipate load shifts. The reduced energy consumption in the low-priority zone (Room A) is mathematically and physically “shifted” to satisfy the increased comfort prioritized in the high-priority zone (Room B). This dynamic reallocation proves that user-centric HVAC control can serve as a primary technical mechanism for demand-side flexibility in multi-building scenarios, exactly as specified in your research framework. Simply, this diagram is a holistic visual validation of the academic theories you are studying, explicitly demonstrating how occupancy detection, data-driven optimization, multi-zone control, and inter-building energy transfers converge into a unified, next-generation HVAC optimization system for sustainable built environments.

3.2. Occupancy-Based Control Model

In order to maintain real-time computational tractability, Fanger’s ISO 7730 PMV formulation is linearized around the thermal neutral point T_{comf, k} [25,26]. For building k at time step t, the neutral indoor temperature T_{comf, k} (t) is evaluated based on the average metabolic rate M_k (t) (met) and clothing insulation I_{cl, k} (t) (clo):

$\[ T_{comf,k}\left(t\right)=f\left(M_{k\left(t\right),}{I}_{cl,k}\left(t\right),v_k,R{H}_k\right) \]$

(Eq. 1)

$\[ PM{V}_{k\left(t\right)}\approx {\alpha }_k\cdot \left(T_{\text{in,k}}\left(t\right)-T_{\text{comf,k}}\left(t\right)\right) \]$

(Eq. 2)

where, “α_k” denotes the thermal sensitivity factor of zone k.

$\[ \begin{array}{c}{D}_{k\left(t\right)}=N_{k\left(t\right)}\cdot {\omega }_k\cdot {\left[PM{V}_{k\left(t\right)}\right]}^2\hfill \\ =N_k\left(t\right)\cdot {\omega }_k\cdot {\alpha }_k^2\cdot {\left(T_{\in \text{,k}}\left(\text{t}\right)-{\text{T}}_{\text{comf,k}}\left(\text{t}\right)\right)}^2\hfill \end{array} \]$

(Eq. 3)

where, “ω” is priority weighting factor accounting for room-use criticalities.

The thermal response of each building is modeled using a 1st-order Lumped Resistance-Capacitance formulation [27,28].

$\[ C_k\cdot \begin{array}{l}\frac{d{T}_{\text{in,k}}\left(\text{t}\right)}{dt}\hfill \\ =\frac{T_{\text{out}}\left(\text{t}\right)-T_{\text{in,k}}\left(\text{t}\right)}{R_k}+Q_{\text{int,k}}\left(\text{t}\right)+Q_{\text{system,k}}\left(\text{t}\right)\hfill \end{array} \]$

(Eq. 4)

$\[ P_{\text{system,k}}\left(\text{t}\right)=\frac{\left|{\text{Q}}_{\text{system,k}}\left(\text{t}\right)\right|}{\text{CO}{\text{P}}_{\text{k}}} \]$

(Eq. 5)

where, “C_k” is lumped thermal capacitance (J/K), “R_k” is equivalent thermal resistance of the building envelope (K/kW), “Q_{int, k} (t)” is internal heat gains from occupants and equipment, “Q_{hvac, k} (t)” is thermal energy supplied or extracted by the HVAC unit (kW), “P_{hvac, k} (t)” is determined via the Coefficient of Performance (COP_k).

To suppress sensor noise and forecast headcount over the control horizon H, a discrete state-space smoothing model is applied:

$\[ {\widehat{N}}_k\left(t+1\right)=\gamma \cdot {\text{N}}_{\text{occu,k }}\left(t\right)+\left(1-\gamma \right)\cdot \widehat{{\text{N}}_{\text{k}}}\left(\text{t}\right)+{\delta }_{\text{k}}\left(\text{t}\right) \]$

(Eq. 6)

where, “N_{measured, k} (t)” is raw real-time occupancy data from computer vision or access-control sensors, “γ” is smoothing coefficient (0<γ<1), “δ_k(t)” is categorical time-of-day trend correction term.

$\[ {\text{min}}_{{\text{T}}_{\in \left(\text{t}\right)}}\text{J}=\sum _{\tau =\text{t}}^{\text{t}+\text{H}-1}\left[\sum _{\text{k}=1}^{\text{M}}{\text{D}}_{\text{k}}\left(\tau \right)+{\text{λ}}_{\text{E}}\cdot \sum _{\text{k}=1}^{\text{M}}{\text{P}}_{\text{system},\text{k}}\left(\tau \right)\right] \]$

(Eq. 7)

Thermal System State Equations: Compliance with 1R1C differential continuous state transitions. Global Peak Power Capacity Limit, Safety Operational Bounds, Allowable PMV Bounds are fomulated below:

$\[ \sum _{k=1}^M{P}_{system,k}\left(\tau \right)\le P_{comm,\text{max}}\left(\tau \right) \]$

(Eq. 8)

$\[ \begin{array}{cc}{T}_{\text{min,k}}\le T_{\in ,\text{k}}\left(\tau \right)\le {\text{T}}_{\text{max,k}}\text{,}\hfill & \forall k\in \left[\mathrm{1,2},\dots M\right]\hfill \end{array} \]$

(Eq. 9)

$\[ PM{V}_{\text{min}}\le \text{PM}{\text{V}}_{\text{k}\left(\tau \right)}\le \text{PM}{\text{V}}_{\text{max}} \]$

(Eq. 10)

The flow diagram in Fig. 2. outlines a continuous loop designed to optimize multi-building HVAC controls, prioritizing human comfort based on real-time occupancy. The system gathers current environmental data (outdoor and indoor temperature/humidity for buildings A and B) and specific occupant profiles. Then, using statistically-derived trends, the system forecasts near-future occupancy (N_k). It then computes the baseline thermal comfort index (PMV) for each building. The third phase is the core logical step. It establishes two key functions:A “Discomfort Function” for each building, which is mathematically weighted based on the number of occupants (N). The more people in a space, the “heavier” the priority for comfort in that zone. A Total Power Constraint that ensures combined energy usage of both buildings stays under a set maximum cap. The primary goal is minimizing Total Social Discomfort across both structures. The algorithm calculates the optimal temperature setpoint vector needed to meet this goal. Crucially, as a sub-clause, if Building A is much less occupied than Building B (N_A ≪ N_B), it intentionally “relaxes” the Building A setpoint to save energy, which is then dynamically reallocated to prioritize thermal comfort in the more populated Building B. The newly calculated optimal setpoints are sent to each building's HVAC system. Building A enters an Energy Saving Mode based on its relaxed setpoint, while Building B enters a Thermal Comfort Priority Mode. After a specific control interval, the entire process loops back to Step 1.

Fig. 2.

Flow diagram of the communication and reallocation

4. Results and Discussion

The simulation framework like Fig. 3. evaluated the proposed central communication and energy reallocation engine using real-world outdoor air temperature data as the primary environmental input. As shown in Fig. 4., the outdoor temperature profile from May 1st to May 7th exhibited significant diurnal fluctuations, ranging from near 2℃ to peaks approaching 24℃. Before analyzing the thermal control responses to this weather data, the predictive capability of the ANN was validated. The Multilayer Perceptron (MLP) model, trained over 1,000 iterations using a scaled conjugate gradient backpropagation algorithm, achieved high statistical accuracy. Specifically, the model yielded a coefficient of determination (R²) of 0.99147 for the mass flow rate and 0.98911 for the supply air temperature, confirming its robustness for integration into the unified simulation framework.

Fig. 3.

Simulation process of the communication and reallocation

Fig. 4.

Outdoor air temperature of Incheon City in Korea

The operational differences between conventional HVAC control and the proposed occupant-centric model are clearly visualized through the indoor temperature graphs across the first week of May. Fig. 5. and Fig. 6. display the indoor air temperatures for Room A and Room B when controlled by the baseline model. The graphs illustrate that the conventional dead-band thermostat suffers from severe, high-frequency signal volatility, causing the temperature to oscillate constantly and erratically between 21.5℃ and 21.8℃. Furthermore, the baseline system fails to prevent sudden system overshoot during peak outdoor thermal loads. For example, around May 3rd and May 7th, both rooms experienced sharp indoor temperature spikes exceeding 22.5℃ and 23.0℃, directly mirroring the outdoor temperature peaks seen in Fig. 4.

Fig. 5.

Room A Indoor air temperature controlled by the baseline model

Fig. 6.

Room B Indoor air temperature controlled by the baseline model

Conversely, Fig. 7. (Room A) and Fig. 8. (Room B) demonstrate the indoor temperatures governed by the communication and reallocation model. The most immediate observation is the successful mitigation of the high-frequency control signal volatility; the temperature curves are smooth and maintain homeostasis without the erratic switching seen in the baseline.

Fig. 7.

Room A Indoor air temperature controlled by the communication and reallocation model

Fig. 8.

Room B Indoor air temperature controlled by the communication and reallocation model

The distinct curves in Fig. 7. and Fig. 8. validate the algorithm’s “load-based priority” logic. In Room A (the retail space with low occupancy), the system intentionally sends a relaxed setpoint command, allowing the temperature to drift smoothly upwards (peaking near 22.5℃ on May 7th) to decrease the energy burden in that zone. Meanwhile, in Room B (the high-occupancy food service space), the supply temperature tightly tracks the neutral comfort temperature, utilizing the energy saved from Room A to prevent overshoot and maximize thermal comfort satisfaction for the larger number of users.

The mathematical and physical shifting of energy consumption from the low-priority zone to the high-priority zone successfully resolved the trade-off between energy savings and thermal comfort. The quantitative improvements in energy use are detailed in Table 2. During the period, the baseline model's EUI was 39.87kWh/m² for Room A and 37.44kWh/m² for Room B, whereas the Communication and Reallocation (C+R) model reduced this to 38.52kWh/m² and 36.81kWh/m² representing a 3.39% and 1.68% increase in energy efficiency, respectively. On an annual scale, the proposed framework sustained an overall energy footprint reduction from 77.31kWh/m² to 75.33kWh/m², yielding a 2.56% efficiency improvement. Concurrently, the system massively improved ergonomic metrics. Table 3. details the thermal comfort tracking precision, measured via the Coefficient of Variation of the Root Mean Square Error (CvRMSE). The baseline CvRMSE of 0.27 was halved to 0.12 for Room A, and 0.22 to 0.11 for Room B by the C+R model, marking a substantial 55.56% and 50.00% improvement in thermal comfort, respectively. Totally, the C+R model improved the CvRMSE from 0.25 to 0.12, representing a 52.00% increase in sustained thermal comfort homeostasis.

Table 2.

Comparison of the total energy use

Table 3.

Comparison of the thermal comfort

4. Conclusion

This study investigated the effectiveness of an occupancy-weighted energy consumption and thermal comfort control model utilizing communication and reallocation algorithms. By dynamically shifting energy from low-priority, low-occupancy zones to high-priority, high-occupancy zones, the system successfully resolved the trade-off between energy savings and thermal comfort. Regarding the results, the key contributions can be summarized like below:

• 1) Occupancy Paradigm Shift: Moves away from static, floor-area-based energy distribution models by introducing a mathematically rigorous resource allocation scheme rooted in occupant-weighted social welfare.
• 2) Low Computational Overhead: Formulated as a quadratic programming problem, allowing real-time implementation on standard local building automation systems without complex deep-learning overhead.
• 3) Scalability via Distributed Architecture: Easily extends to large-scale multi-building complexes, where individual building controllers solve local sub-problems and the central server coordinates shared power capacity constraints.

However, this study has weaknesses. The system’s final validation was limited to simulation applications framework, relying on a simplified 1st-order Lumped Resistance-Capacitance formulation and a just one-week outdoor weather profile. Therefore, a follow-up study will be conducted focusing on the specific physical characteristics and operational mechanisms of the algorithm, as well as the expansion of the learning processes for handling huge control data.

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