Highlighting the Probabilistic Behavior of Occupants’ Preferences in Energy Consumption by Integrating a Thermal Comfort Controller in a Tropical Climate
Abstract
:1. Introduction
2. Materials and Methods
2.1. Description of the Case Study
- Passive: Only natural ventilation through windows (either (1) open or (2) closed) was considered.
- Active: (3) Windows closed and air conditioning equipment turned on are considered.
2.2. Parametric and Sensibility Analysis
2.3. Simplified Thermal Model
2.4. Parametric Optimization
2.5. Simulation Case Selection and Controller Implementation
- Probabilistic scenario, developed by Kim et al. [44] in a study carried out in Australia, where the probability of executing an action with respect to a random number is evaluated, using Equations (5) and (6):
- Deterministic scenario: It considers a window opening and air conditioning hours obtained from a survey conducted by De León [45] in 33 Panamanian residences.
- Combined model #1: Deterministic and probabilistic scenarios are integrated, giving priority to the probabilistic method.
- Combined model #2: Deterministic and probabilistic scenarios are integrated, giving priority to the deterministic method.
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
T | Temperature | %WWR | Window to Wall Ratio |
PMV | Predicted mean vote | RC | Resistance–Capacitance |
ePMV | Extension of the PMV | 4R3C | Four resistance three capacitance thermal model |
BEM | Building Energy Modeling | 5R3C | Five resistance three capacitance thermal model |
IoT | Internet of Things | R1 | Windows resistance |
nZEB | Nearly zero energy building | R2 | External Ceilings and Walls resistance |
PI | Proportional Integrative | R3 | Internal Ceilings and Walls resistance |
BR1 | Bedroom 1 | R4 | Floor resistance |
BR2 | Bedroom 2 | R5 | Air Conditioning resistance |
CR | Control Room | GSol | Solar Gains |
LR | Living Room | Tout | Outside Temperature |
BES | Building Energy System | Tpp | Wall and Celling Temperature |
U | Heat Transfer coefficient | Tia | Indoor air Temperature |
HRmax | Maximum Relative Humidity | Tfloor | Floor Temperature |
HRmin | Minimum Relative Humidity | C1 | Air Capacitance |
ASHRAE | American Society of Heating, Refrigeration and Air-Conditioning Engineers | C2 | Ceilings and Walls capacitance |
p | p value | C3 | Floor capacitance |
met | Metabolic Rate | Tset | Air conditioning set point temperature |
clo | Clothing Insulation | AC | Air Conditioning |
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Step | Procedure |
---|---|
1 | Determination of the case study |
2 | Parametric and Sensibility Analysis to identify relevant variables |
3 | Formulation of thermal model that describes the case study (thermal resistance/capacitance model) |
4 | Simulation of the case performance to obtain the case’s thermal behavior |
5 | Parametric optimization by means of gray-box tools, training, and validation of the parameters |
6 | Determination of occupant decision-making scenarios |
7 | Determination of proportional and integrative values for each scenario |
8 | Integration of thermal model, occupant decision controller, and PMV calculation |
Elements | Value | U (W/m2K) |
---|---|---|
Concrete block’s Base thickness | 150 mm | 2.533 |
Concrete block’s wall thickness | 100 mm | 1.241 |
Concrete block’s roof thickness | 280 mm | 0.719 |
Concrete block’s ground thickness | 100 mm | 3.316 |
Infiltration rate | 0.70 ach | - |
Description | Value | U (W/m2K) |
---|---|---|
Wall to Window ratio | 30% | 3.779 |
Window Height | 1.50 m | |
Window spacing | 5 m | |
Window sill’s height | 0.80 m | |
Blinds | No blinds | |
Openess percentage | 50% |
Month | Tmax (°C) Hour | Tmin (°C) Hour | HRmax (%) Hour | HRmin (%) Hour | Wind Speed (m/s) | Wind Direction (°) |
---|---|---|---|---|---|---|
January 3 | 35 15:00 | 23.9 6:00 | 94 5:00 | 44 15:00 | 0.43 | 126 |
February 20 | 34.6 15:00 | 22.2 6:00 | 93 6:00 | 40 15:00 | 2.77 | 85.77 |
March 17 | 35.6 15:00 | 24.9 6:00 | 73 6:00 | 36 16:00 | 2.3 | 49 |
April 11 | 35.3 15:00 | 24.8 6:00 | 82 24:00 | 44 16:00 | 1.75 | 87 |
May 20 | 34.8 15:00 | 24.5 6:00 | 90 6:00 | 53 16:00 | 0.87 | 83.3 |
June 23 | 32.8 15:00 | 23.4 6:00 | 94 6:00 | 58 15:00 | 0.45 | 108.25 |
July 21 | 35.5 16:00 | 24.3 6:00 | 97 4:00 | 49 16:00 | 0.3 | 89.3 |
August 19 | 34.7 15:00 | 24.1 6:00 | 95 5:00 | 52 15:00 | 3.9 | 188 |
September 1 | 32.5 15:00 | 23 6:00 | 98 24:00 | 60 15:00 | 2.1 | 83 |
October 20 | 32.5 15:00 | 23 6:00 | 96 6:00 | 62 14:00 | 2.33 | 90.67 |
November 11 | 32.9 15:00 | 23.7 6:00 | 94 5:00 | 61 13:00 | 2.55 | 80 |
December 16 | 34.3 15:00 | 24.6 6:00 | 94 7:00 | 50 16:00 | 4.2 | 34.5 |
Passive Case: Closed Windows | |||||||
---|---|---|---|---|---|---|---|
JAN TO APRIL | MAY TO AUGUST | SEPT TO DEC | |||||
Parameters | (K/W) | 5.69 × 10−3 | 6.09 × 10−3 | 7.26 × 10−3 | 7.25 × 10−3 | 5.35 × 10−3 | 6.93 × 10−3 |
(K/W) | 4.47 × 10−4 | 6.67 × 10−4 | 1.27 × 10−3 | 8.69 × 10−4 | 6.76 × 10−4 | 1.68 × 10−3 | |
(K/W) | 95 | 100 | 100 | 100 | 63 | 100 | |
(K/W) | 8.11 | 5.81 | 6.15 | 5.44 | 11.12 | 6.76 | |
(J/K) | 5.50 × 105 | 1.89 × 106 | 2.94 × 106 | 2.34 × 106 | 3.14 × 106 | 3.84 × 106 | |
(J/K) | 5.98 × 106 | 4.66 × 106 | 2.63 × 106 | 3.82 × 106 | 3.75 × 106 | 2.28 × 106 | |
(J/K) | 9.60 × 105 | 2.48 × 105 | 1.39 × 106 | 5.37 × 105 | 1.10 × 106 | 6.50 × 103 | |
Training | Fit (1/3 of the data) | 80.73% | 84.09% | 85.60% | 87.99% | 79.55% | 82.70% |
Error (°C) | 0.44 | 0.30 | 0.26 | 0.18 | 0.50 | 0.36 | |
365 Days Validation | Fit (all data) | 68.09% | 67.84% | 80.12% | 77.34% | 70.87% | 72.73% |
Error (°C) | 1.15 | 1.01 | 0.62 | 0.66 | 1.49 | 0.76 |
Passive Case: Windows Opened at 50% | |||||||
---|---|---|---|---|---|---|---|
JAN TO APRIL | MAY TO AUGUST | SEPT TO DEC | |||||
Parameters | (K/W) | 5.66 × 10−4 | 3.50 × 10−4 | 1.20 × 10−3 | 6.12 × 10−4 | 9.65 × 10−4 | 6.12 × 10−4 |
(K/W) | 8.69 × 10−4 | 1.27 × 10−3 | 8.69 × 10−4 | 1.27× 10−3 | 8.69 × 10−4 | 1.27× 10−3 | |
(K/W) | 100 | 100 | 100 | 100 | 100 | 100 | |
(K/W) | 5.44 | 6.15 | 5.44 | 6.15 | 5.44 | 6.15 | |
(J/K) | 2.34 × 106 | 2.94 × 106 | 2.34 × 106 | 2.94 × 106 | 2.34 × 106 | 2.94 × 106 | |
(J/K) | 3.82 × 106 | 2.63 × 106 | 3.82 × 106 | 2.63 × 106 | 3.82 × 106 | 2.63 × 106 | |
(J/K) | 5.37 × 105 | 1.39 × 106 | 5.37 × 105 | 1.39 × 106 | 5.37 × 105 | 1.39 × 106 | |
Training | Fit (1/3 of the data) | 85.56% | 85.37% | 81.27% | 82.10% | 82.12% | 82.12% |
Error (°C) | 0.21 | 0.21 | 0.25 | 0.22 | 0.22 | 0.22 | |
365 Days Validation | Fit (all data) | 76.27% | 76.91% | 70.67% | 76.01% | 73.08% | 76.01% |
Error (°C) | 0.69 | 0.84 | 0.59 | 0.66 | 0.56 | 0.66 |
AIR CONDITIONING ON (ACTIVE CASE) | |||
---|---|---|---|
JANUARY 4TH 10 a.m.–12 p.m. | |||
Parameters | (K/W) | 7.26 × 10−3 | 7.25 × 10−3 |
(K/W) | 1.27 × 10−3 | 8.69 × 10−4 | |
(K/W) | 100 | 100 | |
(K/W) | 6.15 | 5.44 | |
(K/W) | 100 | 100 | |
(J/K) | 2.94 × 106 | 2.34 × 106 | |
(J/K) | 2.63 × 106 | 3.82 × 106 | |
(J/K) | 1.39 × 106 | 5.37 × 105 | |
Training | Fit | 84.22% | 87.78% |
Cost | 0.1576 | 0.0945 |
Parameter | R4C3: Passive, Closed Windows | R4C3: Passive, Open Windows (50%) | R5C3: Active, AC ON, Closed Windows |
---|---|---|---|
(K/W) | 7.25 × 10−3 | 1.20 × 10−3 | 7.25 × 10−3 |
(K/W) | 8.69 × 10−4 | 8.69 × 10−4 | 8.69 × 10−4 |
(K/W) | 100 | 100 | 100 |
(K/W) | 5.44 | 5.44 | 5.44 |
(K/W) | - | - | 100 |
(J/K) | 2.34 × 106 | 2.34 × 106 | 2.34 × 106 |
(J/K) | 3.82 × 106 | 3.82 × 106 | 3.82 × 106 |
(J/K) | 5.37 × 105 | 5.37 × 105 | 5.37 × 105 |
Controller Based on Scenario | P | I |
---|---|---|
Probabilistic scenario | 50 | −1.40 × 10−3 |
Deterministic scenario | 50 | −6.88 × 10−4 |
Combined model #1 | 50 | −1.40 × 10−3 |
Combined model #2 | 50 | −1.05 × 10−4 |
Month | Probabilistic Method’s Control System | Deterministic Method’s Control System | Combined Model #1′s Control System | Combined Model #2′s Control System |
---|---|---|---|---|
AC Energy Consumption (kWh) | ||||
January | 219.7 | 155.2 | 319.4 | 209.8 |
February | 207.8 | 153.0 | 330.5 | 200.9 |
March | 259.7 | 175.5 | 375.3 | 235.8 |
April | 243.3 | 169.6 | 356.9 | 226.0 |
May | 190.6 | 155.4 | 298.4 | 203.6 |
June | 141.8 | 128.7 | 222.3 | 178.1 |
July | 176.8 | 169.9 | 299.7 | 189.9 |
August | 162.0 | 152.8 | 285.5 | 176.6 |
September | 142.5 | 122.4 | 246.3 | 167.9 |
October | 125.5 | 135.9 | 221.9 | 183.4 |
November | 121.7 | 111.9 | 174.2 | 156.4 |
December | 193.5 | 144.2 | 316.3 | 201.8 |
Annual | 2185.2 | 1774.7 | 3446.8 | 2330.6 |
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Aversa, A.; Ballestero, L.; Chen Austin, M. Highlighting the Probabilistic Behavior of Occupants’ Preferences in Energy Consumption by Integrating a Thermal Comfort Controller in a Tropical Climate. Sustainability 2022, 14, 9591. https://doi.org/10.3390/su14159591
Aversa A, Ballestero L, Chen Austin M. Highlighting the Probabilistic Behavior of Occupants’ Preferences in Energy Consumption by Integrating a Thermal Comfort Controller in a Tropical Climate. Sustainability. 2022; 14(15):9591. https://doi.org/10.3390/su14159591
Chicago/Turabian StyleAversa, Alejandra, Luis Ballestero, and Miguel Chen Austin. 2022. "Highlighting the Probabilistic Behavior of Occupants’ Preferences in Energy Consumption by Integrating a Thermal Comfort Controller in a Tropical Climate" Sustainability 14, no. 15: 9591. https://doi.org/10.3390/su14159591