Open AccessArticle

Multi-Objective Optimization of Building Ventilation Systems Using Model Predictive Control: Integrating Air Quality, Energy Cost, and Environmental Impact

Andreas Hyrup Andersen

and

Muhyiddine Jradi

Center for Energy Informatics, The Mærsk Mc-Kinney Møller Institute, University of Southern Denmark, 5230 Odense, Denmark

Author to whom correspondence should be addressed.

Appl. Sci. 2025, 15(1), 451; https://doi.org/10.3390/app15010451

Submission received: 4 December 2024 / Revised: 27 December 2024 / Accepted: 30 December 2024 / Published: 6 January 2025

(This article belongs to the Special Issue Digital Twin and IoT)

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Figure 1
Component overview for typical HVAC system (left) and the considered ventilation system (right). "> Figure 2
Components connections, and step simulation order for a model with one ventilation system servicing two building spaces. "> Figure 3
Relations between measured flow rate and power consumption (left), and flow rate and specific power consumption (right) for the supply fan in “ventilation system 1”. The measurements span all of 2022 with a 1 min resolution (525,600 data points) so a low opacity is used for each point in the graphs. "> Figure 4
Flow vs. specific power consumption for the supply fan in “ventilation system 1”. The data points are separated in three color groups according to graph coordinates. Color groups 1 and 2 indicate two clearly separated “belts” following slightly different flow rate and specific power correlations. Color group 3 contains the rest of the data points. "> Figure 5
Selected data points of measured flow rate against measured power consumption alongside fitted fan power function for the supply fan in “ventilation system 1” (left) and the exhaust fan in “ventilation system 1” (right). "> Figure 6
Simulated and measured values for CO2 concentration (left) and ventilation damper position (right) in the building space “Ø22-511-2” (139 m2 teaching room) during a workweek in 2018. "> Figure 7
Relative weightings of each objective in the multi-objective optimization performed in the four simulated scenarios using MPC. "> Figure 8
Electricity prices and CO2 emission factors for the one-week simulation period used in MPC simulation. "> Figure 9
Operation of Ø22-511-2 (139 m2 teaching space) with the “Balanced” MPC controller for one week (Wednesday–Tuesday). "> Figure 10
Electricity consumption, cost and CO2 emission from electricity consumption for VEN1 during one week with rule-base control. Note that cost and CO2 emission are measured per step (600 s). "> Figure 11
KPI (indoor air pollution), electricity cost and CO2 emission from electricity consumption for the case study building (four systems, 73 spaces) with rule-based control (Baseline) and each of the four tested MPC strategies for a one-week simulation period. ">

Versions Notes

Abstract

This paper presents a flexible heating, ventilation and air conditioning (HVAC) modeling framework developed for building digital twin implementation. The framework is showcased for the modeling and simulation of four ventilation systems in a 8500 m² university building. The developed model includes multiple objective model predictive control (MPC) with three objectives: electricity cost, indoor air quality and CO₂ emission attributed to electricity consumption. A control strategy comparison is conducted between several MPC solutions with different objective weightings and a rule-based control strategy, which emulates the current system control. A novel approach for air quality evaluation is proposed and used for the MPC modeling and strategy comparison in this study. In this comparison, a “balanced” MPC strategy reduces energy costs by 18% compared to rule-based control while also providing significantly better air quality. An economic strategy achieves 24% savings with some air quality reduction, while an air-quality-focused strategy provides nearly “perfect” air quality with 11% savings. Finally, an environmental strategy shows the potential for prioritizing CO₂ emissions over electricity costs. In this way, the strategy comparison illustrates the potential of MPC for the efficient operation and flexible objective prioritization according to stakeholder interests.

Keywords:

MPC; HVAC; ventilation; building; simulation; system control; multi-objective optimization; component-based modelling

1. Introduction

1.1. Background

As of June 2024, 107 countries, accountable for about 82% of global greenhouse gas emissions, had adopted pledges to achieve net-zero emissions [1]. Decarbonization of the building sector is a crucial component in achieving contemporary climate goals, as around 18.9% of current greenhouse gas emissions are attributed to energy use in buildings (2021) [2]. According to the Buildings Performance Institute Europe (BPIE), 97% of buildings in Europe are not energy efficient (2022) and the rate of energy renovation needs to drastically increase to reach climate neutrality by 2050 [3]. The need for smarter, more flexible and overall more energy efficient buildings calls for innovative approaches to improve building energy performance and enhance the operational efficiency, especially in the existing building stock.

One promising area of development is the use of building digital twins, which presents a more holistic approach to building energy modeling. The digital twin concept includes three elements: a physical system, a virtual representation and a connecting data flow [4]. For building digital twins, a virtual building representation is used to emulate the behavior of chosen aspects of its physical counterpart, such as thermal development, air pollution, system operation and/or noise propagation. The digital twin functions as a multipurpose tool which, depending on its scope, may be used to monitor, evaluate, predict, optimize, and manage a building with automated continuous commissioning and operational strategy planning. The complexity and scope of building digital twins can vary greatly depending on their application. Some approaches, such as the framework proposed by Yoon [5], aim to provide a combined platform for handling a multitude of data types during the entire building life cycle including both design phases and operation/commissioning. Other approaches are more limited in their scope focusing exclusively on certain building aspects and phases, such as facilitating structural load calculations for building design and retrofitting, or supporting operation and commissioning of selected building energy systems.

For effective widespread application in the current building stock, it is crucial that a digital twin framework enables a (mostly) automated setup of the virtual representation, ideally based on existing building documentation files such as building information modeling (BIM) files. It should also possess flexible modeling capabilities to be applicable across multiple building types and ensure optimal usage of the available building data. In this regard, a component-based modeling approach is advantageous, as it allows for flexible systems compositions and selection from several component models depending on available component specifications and measurements. A flexible building digital twin framework should incorporate fully and/or partially data-driven energy models as these are more easily scalable between buildings and typically provide better modeling accuracy than physics-based approaches [6].

In recent years, the use of digital twin approaches for both design and optimization in building energy simulation has accelerated [7]. The complexity, scope and application of building digital twin solutions vary greatly, but a majority of the literature consider modern buildings and rely heavily on existing building information, such as in the approach presented by Zaballos et al., where an existing building information model (BIM) is used as a backbone for campus building modeling [8]. Many of the proposed approaches rely on EnergyPlus or similar energy modeling software [9].

The use of model predictive control (MPC) for building operation optimization has been widely suggested and explored within the heating, ventilation and air conditioning (HVAC) modeling literature [10] and it is often found to be the optimal control approach in control strategy comparisons [6]. MPC is most commonly applied for temperature control focused on energy consumption/cost and thermal comfort. In some approaches, including a study by Široký et al. [11], the MPC optimizes energy consumption with predefined temperature constraints for thermal comfort. In other cases, including a study by Ascione et al. [12], a multi-objective MPC is used and thermal comfort is calculated using a thermal comfort parameter such as “predicted mean vote” (PMV). MPC has also been proposed for many other HVAC control purposes such as response improvement, peak load shifting and fluctuation reduction [13].

Within the HVAC modeling literature, air-quality-related comfort is not considered nearly as often as thermal comfort, and only a few MPC approaches include air quality objectives. On example is a study by Mossolly et al. [14], where a CO₂ threshold is set to indicate “permissible concentration” and a hyperbolic tangent function is defined around the threshold to define a scoring range (“The lower the better” approach), which is then used as the MPC objective. In this paper, a simpler penalty calculation proportional to CO₂ concentration is proposed for air quality evaluation, and its performance for MPC application is tested and discussed.

1.2. Paper Contribution

In this paper, a HVAC modeling framework, developed as part of a building digital twin framework, is showcased for simulation of ventilation system in a university campus building. The created building model is tested with different control strategies to demonstrate the framework’s potential for operational strategy testing and planning. Most of the examined control strategies incorporate multi-objective optimization with MPC and compare ventilation system operation with different weightings of the objectives: energy cost, indoor air quality and CO₂ emissions attributed to energy consumption.

This study introduces a novel HVAC modeling framework developed within the context of building digital twins, offering significant advancements over existing research in the field of building energy systems. By incorporating a multi-objective model predictive control (MPC) framework, it addresses the limitations of single-objective optimization approaches often found in the literature. The study demonstrates how the integration of energy cost, indoor air quality, and CO₂ emissions into the optimization process provides a holistic strategy for building performance management. Through scenario-based comparisons, the framework showcases the superiority of MPC over rule-based control, achieving a notable 18% energy reduction while significantly improving air quality, a dual benefit that aligns with and extends the findings of previous studies.

A key innovation of this study is the introduction of a novel air quality metric to evaluate ventilation system performance. This metric addresses the lack of standardized approaches for assessing indoor air quality in terms of CO₂ thresholds, offering a practical and meaningful tool for system comparison and optimization. Furthermore, the study embeds the HVAC modeling framework within a building digital twin environment, bridging the gap between traditional static building models and dynamic operational realities. This integration enhances the framework’s relevance for real-time simulations and predictive analytics, opening new avenues for proactive building management. The proposed framework adds value through its rapid and automated model setup process. By leveraging a combination of documented parameters, historical data, and literature-based estimates, the framework supports the quick and efficient deployment of system models, making it scalable for diverse building types and applications. Despite minor discrepancies during validation, the model’s ability to closely replicate actual system behavior ensures its reliability for operational planning. Moreover, the customizable objective prioritization within the MPC framework allows stakeholders to tailor operational strategies to specific goals, e.g., cost reduction, carbon footprint minimization, or enhancing occupant comfort.

The potential impact of this framework is significant, particularly in terms of energy efficiency and sustainability. With 18% energy savings demonstrated in this study, the framework contributes to achieving global sustainability goals while reducing operational costs. Its scalability and robustness further enhance its practical value, with the possibility of generalizing the approach to various building systems. Additionally, the integration of this framework into digital twin systems positions it as a critical enabler for smart building management, facilitating real-time optimization, fault detection, and adaptive control. Overall, this study offers a comprehensive and innovative solution for HVAC system modeling and optimization. Its integration of multi-objective MPC and digital twin technologies establishes a strong foundation for advancing building energy systems. The practical implications of this work extend beyond academic research to scalable, real-world applications, reinforcing its significance in the transition toward smarter, more sustainable building operations.

2. Materials and Methods

2.1. Ventilation System Model

The developed modeling framework is component-based and intended for flexible use in modeling and simulation of building HVAC systems. For this study, the framework is used to create a ventilation system model which is used for the comparison of different control strategies in a case study building. The model incorporates both physics-based and data-driven modeling techniques and is therefore a gray box (hybrid) approach.

The focus of this study is exclusively ventilation for air quality, so the developed model is reduced to only include ventilation system components. Figure 1 illustrates a typical component structure in HVAC systems and the components included in the reduced model used for this study.

The ventilation system is modeled as a quasi-steady-state system, where only the concentration of CO₂ in building spaces is treated as a continuous development during simulation steps. Other system attributes are considered constant within each time step, but variable between steps.

For each time step, the model simulates the process for every system component in a logical order determined by component connections. For example, the component connections and resulting simulation order for a single ventilation system servicing two building spaces is illustrated by Figure 2.

The component model used for each component type is based on well-established component models presented in the literature and validated in previous studies. The applied fan model for both supply and exhaust fans replicates the “Variable Speed Fan Model” from EnergyPlus [15] except flow rates are used in place of mass flow rates. It describes the correlation between flow rate and power consumption through three equations:

F_{f l o w} = \frac{Q_{f a n}}{Q_{f a n, m a x}}

(1)

F_{p l} = c_{1} + c_{2} F_{f l o w} + c_{3} F_{f l o w}^{2} + c_{4} F_{f l o w}^{3} + c_{5} F_{f l o w}^{4}

(2)

{\dot{W}}_{f a n} = F_{p l} {\dot{W}}_{f a n, m a x}

(3)

Using the current flow rate

Q_{f a n}

and nominal flow rate

Q_{f a n, m a x}

a flow fraction

F_{f l o w}

is determined in Equation (1). A part load factor

F_{p l}

is calculated using power coefficients

c_{1} - c_{5}

in Equation (2), where

c_{1} + c_{2} + c_{3} + c_{4} + c_{5} = 1

. The fan’s power consumption

{\dot{W}}_{f a n}

is then calculated in Equation (3) using the fan’s nominal power consumption

{\dot{W}}_{f a n, m a x}

A simple linear model is used for both supply and exhaust dampers to describe the relation between opening degree and flow rate. It is based on the pressure-independent damper component from Modelica Buildings Library [16]. The flow rate

Q_{d}

through the damper is calculated as the product of the nominal flow rate

Q_{d, m a x}

and the opening fraction

y \in [0, 1]

as described by Equation (4).

Q_{d} = y Q_{d, m a x}

(4)

In this study, the air quality evaluation and ventilation control is purely based on indoor concentration of CO₂. The purpose of the building space component is therefore to simulate the development of CO₂ in a designated volume

V_{s}

. The applied model is based on the principal of mass balance in a similar manner to the approach presented by Macarulla et al. [17]. The time-dependent change in building space CO₂ concentration

C_{s}

is described by the ordinary differential equation (ODE):

\frac{d C_{s}}{d t} = \frac{Q_{v e n} (C_{v e n} - C_{s}) + G_{s}}{V_{s}}

(5)

where

Q_{v e n}

is the ventilation flow rate,

C_{v e n}

is the CO₂ concentration in air delivered from ventilation and

G_{s}

is CO₂ generation within the space. The ventilation flow rate includes both forced and natural ventilation. Equation (5) relies on the assumptions that exhaust ventilation flow from a building space matches the supply ventilation flow to the space, and that CO₂ concentration in the exhausted air is equal to the average CO₂ concentration in the space. For application in the time discrete model, Equation (5) is transformed to a time-dependent function. It is an ODE of the type

\frac{d y}{d t} = b - a y

with the general solution

y = \frac{b + c e^{- a t}}{a}

. In this case,

a = \frac{Q_{v e n}}{V_{s}}

and

b = \frac{Q_{v e n} C_{v e n} + G_{s}}{V_{s}}

, so the time-dependent CO₂ development is given by Equation (6), where the constant c can be determined using initial values at the start of the time step.

C_{s} = \frac{\frac{Q_{v e n} C_{v e n} + G_{s}}{V_{s}} + c e^{- \frac{Q_{v e n}}{V_{s}} t}}{\frac{Q_{v e n}}{V_{s}}}

(6)

The CO₂ generation in a building space is calculated as follows:

G_{s} = K_{g e n} P_{s}

(7)

where

P_{s}

in the number of occupants and

K_{g e n}

is the CO₂ generation per occupant. For this study,

K_{g e n}

= 15 L/h is assumed, since this was found to be the average human generation during office activities in an experiment by Yang et al. [18].

The CO₂ sensors are assumed to accurately measure the concentration of CO₂ in their respective space. The output signal of the sensor model is thus equal to the actual CO₂ concentration in the space.

For each building space, a CO₂ controller is used to regulate the opening position of ventilation dampers. One of two models are used for the CO₂ controller components depending on the desired type of control. The simplest is a rule-based model, where one of several rules is chosen based on CO₂ concentration and the corresponding opening degree is used for the dampers. The other model utilizes model predictive control (MPC) to optimize damper control within a chosen prediction horizon. The optimization is multi-objective with the following objective function:

O b j = M i n \sum_{i = 1}^{N} w_{1} C o s t_{i} + w_{2} A i r K P I_{i} + w_{3} E m i s s i o n_{i}

(8)

where

C o s t

is the electricity cost,

A i r K P I

is a Key Performance Indicator (KPI) for indoor air quality (lower is better) and

E m i s s i o n

is the CO₂ emission attributed to the consumed electricity. Each objective has an adjustable weighting (

w_{1}

w_{2}

and

w_{3}

) and are evaluated for each simulation time step i within the prediction horizon. For every step, the optimization is constrained by the component equations presented in this section as well as fan flow limits (

0 \leq Q_{f a n} \leq Q_{f a n, m a x}

The developed model needs an input for occupancy in each space at each time step of a simulation. Additionally, predictions for occupancy, electricity price and CO₂ emission from electricity consumption are needed to use the MPC model for the CO₂ controller.

2.2. Air Quality Evaluation

The ability to evaluate and compare indoor air quality based on CO₂ concentration is essential for this study. For this purpose, a KPI is introduced to quantitatively represent the estimated level of discomfort attributed to imperfect air quality. The KPI for a building space between two points in time,

t_{0}

and

t_{1}

, is described by Equation (9), where P is the number of occupants,

C_{S}

is the space CO₂ concentration and

C_{T}

is a chosen CO₂ concentration threshold.

A i r K P I = \int_{t_{0}}^{t_{1}} P (t) \cdot M a x (0, C_{S} (t) - C_{T}) d t

(9)

Consequently, CO₂ levels below the threshold are attributed no discomfort and the KPI value scales linearly with number of occupants and with CO₂ concentration above the threshold.

CO₂ concentration is generally considered the most adequate indicator for indoor air quality [19] but while a number of studies have explored correlation between indoor CO₂ concentrations and discomfort/cognitive function, there is no consensus regarding an ideal concentration threshold for good air quality. In the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) standard 62-1989 [20], a limit of 1000 ppm CO₂ was recommended to “satisfy comfort (odor) criteria”. This has since become a widely used baseline for acceptable air quality; however, studies suggest that further lowering the CO₂ concentration is advisable. According to Alberts [21] “concentrations of CO₂ as low as 700 to 800 ppm are often associated with complaints of poor air quality by occupants” and a study by Allen et al. [22] indicated a noticeable difference in test subjects performance between average concentrations of 486–609 ppm and average concentrations of 726–761 ppm. In this study, a CO₂ threshold of

C_{T}

= 700 ppm is used for the KPI calculations.

2.3. Case Study

To evaluate the model performance and test different modes of control, a case study is conducted. The building considered is a modern and highly energy efficient teaching and office building located at the Odense Campus of the University of Southern Denmark. Finished in 2015, the building consists of three floors and a basement with a total area of around 8500 m². It contains 21 teaching rooms, eight study zones and a number of smaller spaces including personal offices, meetings rooms, toilets, copy rooms and tea kitchens. The teaching and office building has four separate ventilation systems, which each service a building quadrant. It is commonly used for building energy studies and is further described by M. Jradi et al. [23]. From the building schematics, a total of 73 ventilated building spaces are identified and included in the model.

Occupancy measurements are only available for a few building spaces with poor data quality, so except for the model validation, the simulations utilize generated occupancy schedules based on space type, space size, time of day, category of day (weekday, holiday, etc.) and an element of randomness. The applied occupancy generation method is included in the model framework as a general occupancy estimation tool, which can be scaled to other buildings and space types.

Currently, the ventilation damper openings in the teaching and office building are documented to be controlled with a four step rule-based strategy dependent on space CO₂ concentration:

\begin{matrix} C_{S} < 600 ppm : & 0 % opening \\ 600 ppm \leq C_{S} < 750 ppm : & 45 % opening \\ 750 ppm \leq C_{S} < 900 ppm : & 70 % opening \\ 900 ppm \leq C_{S} : & 100 % opening \end{matrix}

These rules will also be used for the rule-based CO₂ controller model in this study to replicate the actual operation of the building.

Both the supply and exhaust fan in all of the building’s four ventilation systems have the same technical specifications according to the building documentation:

Q_{f a n, m a x}

= 35,000 m³/h and

W_{f a n, m a x}

= 8667.4 W. The fan constants

c_{1} - c_{5}

are not documented, but are instead estimated using operational data from 2022. This parameter estimation in conducted using data from “ventilation system 1” (VEN1) and the determined fan constants are assumed to apply for all four ventilation systems. Figure 3 illustrates the relation between the measured flow rate and power consumption as well as flow rate and specific power consumption (i.e., power-to-flow-ratio) for the supply fan in 2022.

While not evident from Figure 3, data analysis shows that both the supply and exhaust fan in VEN1 are completely turned off with no power consumption 21.7% of the time (typically during night). To correctly model these instances, it is chosen that

c_{1} = 0

(i.e., no power consumption for

Q_{f a n}

= 0) for all fans. Close inspection of Figure 3 reveals that for

Q_{f a n}

> 1.2 m³/h, the data point forms two separate “belts” with a clear relation between flow rate and power consumption. Additionally, it is noted that for low flow rates (around 0.25 to 0.6 m³/h) there is seemingly little correlation between flow rate and power usage. In Figure 4, the data points are grouped based on flow rate and specific power consumption to highlight the different identified operation areas. With larger graph sizes, the clear separation between “Group 1” and “Group 2” is more evident.

Data analysis shows that over 99% of the data points in “Group 1” (Figure 4) are measurements from before 17 June 2022 00:00:00 and over 99% of the data points in “Group 2” are measurements from after this time. A similar change around the same time point is observed for the exhaust fan in VEN1. Clearly some change to the system occurred around this time, which resulted in slightly lower measured fan power consumption for comparable flow rates. Since the simulated periods in this study are more recent than 2022, the data from “Group 1” is not used for parameter estimation. “Group 3” contains a large cluster of data points in the low flow rate region 0.25 to 0.6 m³/h, which mostly corresponds to morning and evening operation with low ventilation demands. These data show no clear correlation between fan flow rate and specific energy consumption. Instead, it seems that the specific energy consumption for the supply fan fluctuates between ∼1150 and ∼2500 J/m³ independently of flow rate. Since the mechanics of this low flow rate region are unknown and fit poorly with a fixed power-to-flow rate relation, data points from “Group 3” are not used for parameter estimation. The supply fan constants are thus chosen to minimize the sum of the squared residuals from the data points in “Group 2” resulting in the function illustrated in Figure 5 (left). The exhaust fan constants are determined in a similar manner resulting in the function shown in Figure 5 (right).

The CO₂ concentration in ventilated air is assumed to be a constant

C_{v e n}

= 400 ppm (typical outdoor concentration). All building spaces are assumed to have a constant natural ventilation rate of 0.05

h^{- 1}

(room volumes per hour). This estimate is based on findings in the literature including [24,25]. The teaching and office building is connected to the Danish electricity grid in the pricing area “DK1”, so the simulations use historical electricity prices (DKK/MWh) [26] and CO₂ emission factors (g/kWh) [27] for this area.

The MPC optimization is formulated in the “GEKKO” Python library [28] and set to use the “IPOPT” solver which applies an interior-point method for the convex non-linear optimization. Due to computational limitations, some concessions were made for the simulations using MPC. Firstly, the prediction horizon was limited to 12 steps, and three combinations of time resolution and time horizon were benchmarked: 10 min/2 h, 20 min/4 h and 30 min/6 h. Of these, the 4 h optimization horizon with 20 min steps performed best and is used. The MPC still creates a new prediction every simulation time step (10 min) and applies the predicted optimal current position to the damper. Secondly, the MPC simulations will only include two building spaces. Thirdly, the MPC simulations will only cover a one-week period from the 6 March 00:00:00 (Wednesday) to the 12 March 23:50:00 (Tuesday) with 10 min time steps. Additionally the simulations have a 24 h warm-up period (5 March 00:00:00–23:50:00) to ensure realistic initial conditions.

With rule-based control, a simulation is performed for the same one-week period, but also for a one-year period from 1 July 2023 to 30 June 2024, again with 10 min time steps and initial warm-up. To compare performance of MPC and rule-based control, the MPC scenarios are “scaled up” through some assumptions. For the two rooms simulated with MPC, the ratio between combined total flow with a particular MPC controller and with rule-based control is calculated. The combined damper “schedule” (% of flow total at each step) for the two rooms with MPC is then applied to all rooms while preserving the ratio between the total flow of the MPC schedule and the total flow with rule-based control for each room. For the one-year period comparison, it is assumed that the ratio between cost, KPI and emission between each scenario is the same as for the one-week simulations.

3. Results

To validate the performance of the developed model, it is first used to simulate the operation of two spaces (Ø22-508-1 and Ø22-511-2) from the 9–13 April 2018, where measurements for occupancy and CO₂ concentration are available for comparison. For this validation, the CO₂ generation per (measured) occupant is estimated to be

K_{g e n}

= 10 L/h based data from a prior week. The models predicted CO₂ development and damper position for Ø22-511-2 is compared to measurements in Figure 6. From this comparison, it seems the model replicates real operation fairly well, although it appears that the actual system keeps the damper ∼20% open for some time after the CO₂ concentration falls below 600 ppm and consequently has significantly lower CO₂ concentration at night than predicted.

Five scenarios are explored for the operation of ventilation in the teaching and office building: one with the rule-based control (“Baseline”) and four using MPC with different objective weights (“Balanced”, “Air quality”, “Economic” and “Environmental”). Relative weighting in the scenarios is illustrated by Figure 7. The different MPC strategies in the scenarios are designed to represent different objective priorities:

Balanced: Aims to improve both air quality and cost compared to the baseline.
Air quality: Focus on achieving optimal air quality without excessive electricity consumption.
Economic: Focus on cost reduction while preserving acceptable air quality.
Environmental: Focus on CO₂ emission reduction while preserving acceptable air quality.

At equal weighting the KPI-cost relation is: 1000 ppm·h·person = 0.81 DKK, i.e., raising the CO₂ concentration by 1000 ppm above the threshold in one hour for one person produces the same penalty as increasing the electricity cost by 0.81 DKK. The emission–cost relation at equal weighting is 4.49

{kg}_{C O_{2}}

= 1 DKK, since the average electricity price (January–June 2024) in DKK is 4.49 times the average CO₂ emission in kg. The electricity prices and CO₂ emission factors for the simulated period are shown in Figure 8.

The MPC controllers are not provided with perfect occupancy predictions, as this would be unrealistic for a real application. Since the optimization often keeps CO₂ levels just below the concentration threshold, a larger than expected number of occupants will often lead to peaks significantly above the threshold even if the controller is prioritizing air quality. To counter this, the MPC optimization uses a 50 ppm lower threshold in the “Air quality” scenario and a 25 ppm lower threshold in the “Balanced” scenario.

Figure 9 shows the operation in building space Ø22-511-2 in the “Balanced” MPC scenario. The few hours with fully opened damper on the 9th and 10th of March are due to negative electricity prices. Figure 10 illustrates the performance of ventilation system 1 with rule-base control.

For the simulated week in the spring of 2024, the performance of each scenario are compared in Figure 11 and Table 1. Table 2 compares scenario performances for a one-year period between 1 July 2023 and 30 June 2024.

4. Discussion

The model framework allowed for a quick and highly automatic setup of the ventilation system model for the teaching and office building with component models chosen to best utilize the available data. The process showcases the incorporation of both documented parameter values from building descriptions, parameter estimation based on historical operation data and parameter estimation based on experiments in the literature.

The model validation showed that model predictions matched the actual system behavior with reasonable accuracy. Some of the deviation between model predictions and measurements seems to be caused by discrepancy between the expected and actual control strategy. To model the building-specific system more accurately, a better understanding of the systems reaction times/delays and the use of a 20% opening strategy is required.

The strategy comparison unsurprisingly shows that MPC is significantly more energy efficient than rule-based control for ventilation system operation. While providing significantly better air quality, the “Balanced” MPC controller managed to reduce energy consumption by 18%. This result is comparable to similar studies of MPC implementation in HVAC building systems, which typically show savings in the range of 10–30% compared to baseline control [10]. With a more cost-focused approach, the “Economic” MPC strategy managed to reduce energy consumption by 24% compared to the baseline, but provided notably worse air quality. On the other hand, the “Air quality” MPC strategy provided almost perfect air quality according to the KPI evaluation while still reducing electricity usage by 11%. The “Environmental” MPC strategy showed some potential for prioritizing CO₂ emission with a 4% emission reduction compared to the “Economic” strategy, but the CO₂ factor (emission from electricity use) is closely correlated to the electricity price as seen in Figure 8. In this way, the four explored combinations for relative MPC weightings produce significantly differing system control strategies, which each optimize according to their different prioritization in system performance metrics. This demonstrates the ease and effectiveness of objective weighting customization with a MPC strategy, which allows for flexible prioritization of performance metrics according to stakeholder interests.

The developed MPC is quite computationally demanding despite significant efforts to reduce optimization complexity and improve solver performance. This seems to be a common concern for MPC application in HVAC, due to the non-linearity and complexity of HVAC systems.

One interesting observation is that the developed MPC handles the KPI threshold poorly with imperfect information. The applied solution is to lower the optimizations KPI threshold a bit in scenarios where air quality is prioritized, but a better (and more computationally demanding) approach would be robust optimization, where several potential future occupancy schedules are explored at each time step and the optimal solution accounts for all potential futures and their likelihoods.

The KPI representing air-quality-related discomfort was established for this study, since no standard methods for measuring this metric were found in the literature. It functioned well for scenario comparison, but puts a large emphasis on the arbitrarily chosen CO₂ threshold, especially when air quality is valued highly. The challenge is such that the effect of CO₂ on human comfort and cognitive ability is not well documented for low CO₂ concentrations. Based on the study by Allen et al. [22], it seems more reasonable to view any reduction of CO₂ contraction as advantageous and thus use a threshold of

C_{T}

= 0 ppm. This approach would also be more appropriate for MPC optimization. Moreover, the approach of relying solely on CO₂ concentration for air quality evaluation is suboptimal and more elaborate considerations of airborne particulate matter, organic gases and inorganic gases should be incorporated in models for systems where these are measured. In such cases, the air quality evaluation method could be based on the thresholds proposed by the “WELL Building Standard” [29], which is an international “healthy building” certification program with widespread usage.

The developed model provides realistic and practical results, effectively capturing the key dynamics of the ventilation system. While some estimates and assumptions are incorporated, these align with common practices in system modeling to balance complexity and computational efficiency. For instance, the estimated fan constants for the VEN1 exhaust fan produce a power curve that aligns reasonably with measured data, demonstrating the model’s capability to approximate system behavior effectively.

To further enhance the robustness and accuracy of the ventilation modeling approach, exploring and benchmarking additional models for each component type could be a valuable future direction. Furthermore, incorporating data-driven parameter estimation techniques for factors such as air infiltration and occupant CO₂ generation could strengthen the reliability of the predictions. Leveraging advanced methods like artificial neural networks for occupancy prediction, provided sufficient training data are available, holds promise for improving predictive accuracy and operational efficiency.

5. Conclusions

This study presents a flexible HVAC modeling framework intended for building digital twin implementation and demonstrated its application for modeling of a building ventilation system. The developed ventilation system model incorporates both data-driven and physics-based methods and includes multiple approaches to ventilation control. The ventilation model is used to simulate the operation of a teaching and office building with different control strategies and compare their performance in regard to air quality, energy cost and environmental impact. A novel approach for air quality evaluation is proposed and used for the MPC modeling and control strategy comparison.

In the control strategy comparison, it is found that MPC performs significantly better than the current rule-based control scheme for all performance parameters. A balanced MPC approach, which prioritizes both operation cost and air quality, can reduce ventilation system energy cost by 18% while providing significantly better air quality. With a more economic focus, the MPC achieves a 24% cost reduction at some expense to the air quality, and with an air quality focus, the MPC delivers almost perfect air quality (according to the proposed evaluation method), while still providing an 11% cost reduction compared to the current operation strategy. It is also shown that with an environmental focus, the MPC can reduce the CO₂ emissions attributed to the ventilation system energy consumption. In this way, the strategy comparison illustrates the potential of MPC for efficient operation and flexible objective prioritization according to stakeholder interests. It also showcases one of the potential applications of the developed framework for building operation optimization.

This study presents the first case application of the developed framework, so testing and comparison of different component models was limited by the data available for the case study building. Additionally, the model validation is imperfect due to missing knowledge of some system operation details and poor data quality. Moreover, the MPC development and implementation was limited due to computational constraints and software issues.

For future work, exploring advanced optimization strategies, such as robust or stochastic optimization, to address imperfect information and dynamic uncertainties, including varying occupancy patterns, could enhance the reliability and adaptability of model predictive control (MPC) in HVAC applications. Simultaneously, benchmarking multiple component models for various system types, such as fans, air infiltration dynamics, and occupant CO₂ generation, would improve the generalizability and accuracy of ventilation system models across diverse building scenarios. Additionally, leveraging artificial neural networks or other AI models for predicting occupancy patterns based on historical and real-time data could significantly refine the precision of the proposed MPC solution.

Author Contributions

Conceptualization, A.H.A. and M.J.; methodology, A.H.A.; software, A.H.A.; validation, A.H.A.; formal analysis, A.H.A.; investigation, A.H.A.; resources, A.H.A. and M.J.; data curation, A.H.A.; writing—original draft preparation, A.H.A.; writing—review and editing, A.H.A. and M.J.; visualization, A.H.A.; supervision, M.J.; project administration, A.H.A. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The Python model and data used for the presented simulations are available on the repository: https://github.com/AHyrup/VentilationSystemModel (accessed on 31 December 2024).

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:

HVAC	Heating, Ventilation, and Air Conditioning
CO₂	Carbon dioxide
MPC	Model predictive control
PMV	predicted mean vote
ODE	Ordinary differential equation
KPI	Key Performance Indicator
ASHRAE	American Society of Heating, Refrigerating and Air-Conditioning
VEN3	Ventilation system 3 (in the case study building)
VEN1	Ventilation system 1 (in the case study building)

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Figure 1. Component overview for typical HVAC system (left) and the considered ventilation system (right).

Figure 2. Components connections, and step simulation order for a model with one ventilation system servicing two building spaces.

Figure 3. Relations between measured flow rate and power consumption (left), and flow rate and specific power consumption (right) for the supply fan in “ventilation system 1”. The measurements span all of 2022 with a 1 min resolution (525,600 data points) so a low opacity is used for each point in the graphs.

Figure 4. Flow vs. specific power consumption for the supply fan in “ventilation system 1”. The data points are separated in three color groups according to graph coordinates. Color groups 1 and 2 indicate two clearly separated “belts” following slightly different flow rate and specific power correlations. Color group 3 contains the rest of the data points.

Figure 5. Selected data points of measured flow rate against measured power consumption alongside fitted fan power function for the supply fan in “ventilation system 1” (left) and the exhaust fan in “ventilation system 1” (right).

Figure 6. Simulated and measured values for CO₂ concentration (left) and ventilation damper position (right) in the building space “Ø22-511-2” (139 m² teaching room) during a workweek in 2018.

Figure 7. Relative weightings of each objective in the multi-objective optimization performed in the four simulated scenarios using MPC.

Figure 8. Electricity prices and CO₂ emission factors for the one-week simulation period used in MPC simulation.

Figure 9. Operation of Ø22-511-2 (139 m² teaching space) with the “Balanced” MPC controller for one week (Wednesday–Tuesday).

Figure 10. Electricity consumption, cost and CO₂ emission from electricity consumption for VEN1 during one week with rule-base control. Note that cost and CO₂ emission are measured per step (600 s).

Figure 11. KPI (indoor air pollution), electricity cost and CO₂ emission from electricity consumption for the case study building (four systems, 73 spaces) with rule-based control (Baseline) and each of the four tested MPC strategies for a one-week simulation period.

Table 1. Performance comparison between the five scenarios for a one-week simulation period. KPI values are divided by 10⁶ for better visual comparison.

	Baseline	Balanced	Air Quality	Economic	Environmental
KPI [ppm·s·occupants/10⁶]	557	235	57	1011	980
Cost [DKK]	383	314	339	292	305
CO₂ Emission [kg]	127	114	120	106	102

Table 2. Performance comparison between the five scenarios for a one-year simulation period. KPI values are divided by 10⁶ for better visual comparison.

	Baseline	Balanced	Air Quality	Economic	Environmental
KPI [ppm·s·occupants/10⁶]	17,013	7172	1727	30,855	29,912
Cost [DKK]	15,190	12,469	13,471	11,595	12,100
CO₂ Emission [kg]	3106	2784	2945	2586	2492

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Andersen, A.H.; Jradi, M. Multi-Objective Optimization of Building Ventilation Systems Using Model Predictive Control: Integrating Air Quality, Energy Cost, and Environmental Impact. Appl. Sci. 2025, 15, 451. https://doi.org/10.3390/app15010451

AMA Style

Andersen AH, Jradi M. Multi-Objective Optimization of Building Ventilation Systems Using Model Predictive Control: Integrating Air Quality, Energy Cost, and Environmental Impact. Applied Sciences. 2025; 15(1):451. https://doi.org/10.3390/app15010451

Chicago/Turabian Style

Andersen, Andreas Hyrup, and Muhyiddine Jradi. 2025. "Multi-Objective Optimization of Building Ventilation Systems Using Model Predictive Control: Integrating Air Quality, Energy Cost, and Environmental Impact" Applied Sciences 15, no. 1: 451. https://doi.org/10.3390/app15010451

APA Style

Andersen, A. H., & Jradi, M. (2025). Multi-Objective Optimization of Building Ventilation Systems Using Model Predictive Control: Integrating Air Quality, Energy Cost, and Environmental Impact. Applied Sciences, 15(1), 451. https://doi.org/10.3390/app15010451

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Multi-Objective Optimization of Building Ventilation Systems Using Model Predictive Control: Integrating Air Quality, Energy Cost, and Environmental Impact

Abstract

1. Introduction

1.1. Background

1.2. Paper Contribution

2. Materials and Methods

2.1. Ventilation System Model

2.2. Air Quality Evaluation

2.3. Case Study

3. Results

4. Discussion

5. Conclusions

Author Contributions

Funding

Institutional Review Board Statement

Informed Consent Statement

Data Availability Statement

Conflicts of Interest

Abbreviations

References

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