Multi-Variable Optimization of Building Thermal Design Using Genetic Algorithms
Abstract
:1. Introduction
2. Methods
2.1. Building Description
2.2. Design Variables
- Glazing type characterized by three parameters of the glazing, i.e., heat transfer coefficient (U), solar heat gain coefficient (SHGC) and visible transmittance (Tvis). The optimization was performed for four different types of glazing (Table 3). In the Table 4 the reference value (bold characters) and cost of the glass are shown.
- Windows area (glazing + frame) defined by the sixteen discrete value of windows size (Table 4). Depending on the size of the window the frame surface is automatically calculated for each window.
- External walls, ground floor and ceiling to the unheated attic defined by the thickness of polystyrene and mineral wool. Six options for all kinds of partition are considered.
- Air leakage level defined by infiltration change rate (four various values).
- Orientation defined by the azimuth angle between the north and the front of the house. Sixteen options for the orientation are considered (Table 4).
2.3. Economic Analysis
- Efficiency of heating system ηH = 0.78 [61],
- Efficiency of cooling system ηC = 3.79 [61],
- Price of energy from natural gas PH(gas) = 0.0394 €/kWh at 1 September 2017,
- Price of electrical energy PC(el.) = 0.1294 €/kWh at 1 September 2017,
- Investment costs (Table 4),
- Nominal interest rate i = 7% and inflation rate f = 2%. Accordingly, the real interest rate r = 4.9%,
- Escalation in energy price e = 2%,
- Lifespan N = 30 years.
2.4. Optimization Algorithm
- value encoding,
- self-adaptive rank-based roulette wheel selection with power scaling (k),
- self-adaptive uniform crossover with probability (Pc),
- self-adaptive mutation realized by adding some number (S) to or subtracting it from mutated gene with probability (Pm).
2.5. Model Validation
3. Results
3.1. Cases 1 and 2 (Optimization of Windows Area and Windows Area + Azimuth)
3.1.1. Building with Cooling
3.1.2. Building without Cooling
3.2. Cases 3 and 4 (Optimization of Insulations and Insulations + Azimuth)
3.3. Cases 5 and 6 (Optimization of Glazing Type, Windows Area and Insulations (5) + Azimuth(6))
3.3.1. Building with Cooling
3.3.2. Building without Cooling
3.4. Case 7 (All Variable)
3.5. Summary
4. Conclusions
- The cheapest way to reduce the energy consumption for heating and cooling is to locate windows on the southern side of the building. This applies especially to rooms with smaller internal gains.
- Selecting windows should not be based solely on the heat transfer coefficient (which is a widespread practice with investors). Solar optical properties of windows also significantly affect the cost of the energy consumption, especially in case without cooling system.
- The optimum glazing area for buildings with cooling is highly dependent on external walls insulation. The simulation results showed that the windows area varies from the minimum norm value to 130% of this value. In order to achieve minimum LCC in a building without cooling (WC), the windows area should be tens of percent larger than the requirements set out in the Standards.
- In case of limited investment costs optimization regarding only insulation of external partitions is more effective than optimization of windows only (due to LCC). In the analyzed building it is 5%.
- When determining the design parameters of a building in transitional climates, both cooling and heating costs should be considered. The optimization of a building from the heating point of view greatly reduces heating costs, however, the thermal comfort in summer deteriorates dramatically.
- One should make decisions about having or not having a cooling system installed prior to determining optimum qualities of a building. Without a cooling system, apart from life cycle cost, extra objective functions e.g., a thermal comfort index need to be employed.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Room | Weekdays | Weekends | ||
---|---|---|---|---|
Occupant | Equipment | Occupant | Equipment | |
Living room | 6 a.m. to 7 a.m. (4) * 4 p.m. to 6 p.m. (4) 6 p.m. to 10 p.m. (1) | 4 p.m. to 6 p.m. (cook.) 4 p.m. to 10 p.m. (TV) all day (fridge) | 8 a.m. to 11 a.m. (4) 1 p.m. to 4 p.m. (2) 4 p.m. to 6 p.m. (4) 6 p.m. to 10 p.m. (2) | 4 p.m. to 6 p.m. (cook.) 4 p.m. to 10 p.m. (TV) all day (fridge) |
Room 1 | 6 p.m. to 6 a.m. (1) | 6 p.m. to 10 p.m. (PC) | 8 p.m. to 8 a.m. (1) | 8 p.m. to 10 p.m. (PC) |
Room 2 | 6 p.m. to 10 p.m. (1) | 6 p.m. to 10 p.m. (PC) | - | - |
Room 3 | 10 p.m. to 6 a.m. (2) | - | 10 p.m. to 8 a.m. (2) | - |
Room 4 | 6 p.m. to 6 a.m. (1) | - | 8 p.m. to 8 a.m. (1) | - |
Parameters | Value |
---|---|
Number of Occupants | 4 |
Number of Heated Floors | 1 |
Area of Heated Floor | 150 m2 |
Floor-to-floor Height | 2.6 m |
External Wall Construction | Brick with polystyrene insulation, U = 0.22 W/m2·K |
Ceiling Construction | Ferroconcrete with mineral wool insulation, U = 0.18 W/m2·K |
Roof Construction | Covered with ceramic tiles and uninsulated |
Ground Floor Construction | Concrete with polystyrene insulation, U = 0.29 W/m2·K |
Windows Construction | Double glazed, PCV frame, Uwindow = 1.13 W/m2·K |
External Door Construction | Wood, U = 1.50 W/m2·K |
Opaque External Wall | 102.15 m2 |
Window Area | 23.25 m2 |
Ventilation | Natural |
Cooling System | Split system air conditioner (electricity) |
Heating System | Central heating with radiators (natural gas) |
Type of Glazing | Glazing Construction | Uglass, W/m2 K | Uframe *, W/m2 K | Uwindow **, W/m2 K | SHGC | Tvis |
---|---|---|---|---|---|---|
Glazing G10 | Planiclear 4 mm | 1 | 1.35 | 1.13 | 0.49 | 0.72 |
Argon 16 mm | ||||||
Planitherm ONE 4 mm | ||||||
Glazing G07 | Planitherm LUX 4 mm | 0.68 | 1.35 | 0.9 | 0.61 | 0.73 |
Argon 16 mm | ||||||
Planiclear 4mm | ||||||
Argon 16 mm | ||||||
Planitherm LUX 4 mm | ||||||
Glazing G06 | Planitherm XN 4 mm | 0.61 | 1.35 | 0.85 | 0.51 | 0.74 |
Argon 16 mm | ||||||
Planiclear 4 mm | ||||||
Argon 16 mm | ||||||
Planitherm XN 4 mm | ||||||
Glazing G05 | Planitherm XN 4 mm | 0.52 | 1.35 | 0.78 | 0.43 | 0.65 |
Argon 16 mm | ||||||
Planiclear 4 mm | ||||||
Argon 16 mm | ||||||
Planitherm ONE 4 mm |
Design Variable | Options | Cost * |
---|---|---|
Glazing Type for Window | G10 | 34.4 €/m2 |
G07 | 64.7 €/m2 | |
G06 | 53.5 €/m2 | |
G05 | 57.9 €/m2 | |
Windows area | Height: 1.5 m | 0 € for all options |
Width: 0 and 0.75 m–4.25 m with step 0.25 m | ||
Windows area for RB: 23.25 m2 | ||
Insulation | ||
Ground floor: polystyrene (λ = 0.031 W/mK) | 5, 6, 8, 10, 12, 15 cm (thickness) | 51.9 €/m3 |
External wall: polystyrene (λ = 0.031 W/mK) | 12, 15, 18, 20, 22, 25 cm (thickness) | 46.0 €/m3 |
Ceiling to unheated attic: mineral wool (λ = 0.038 W/mK) | 20, 22, 25, 28, 30, 35 cm (thickness) | 0.3 €/m2 for 1 cm of thickness |
Air infiltration level | 0.3, 0.5, 0.7, 1.0 h−1 | 0 € for all options |
Azimuth (orientation of the building relatively to the north) | 0–337.5 with step 22.5 | 0 € for all options |
Additionally included the costs of window frame and installation and cost of external wall construction. |
Case Study | Glazing Type | Windows Area | Insulation | Infiltration | Azimuth |
---|---|---|---|---|---|
1, 1WC | + | ||||
2, 2WC | + | + | |||
3, 3WC | + | ||||
4, 4WC | + | + | |||
5, 5WC | + | + | + | ||
6, 6WC | + | + | + | + | |
7, 7WC | + | + | + | + | + |
LCC, € | Heating Demand, kWh/m2 | Cooling Demand, kWh/m2 |
---|---|---|
11,236 | 69.2 | 7.7 |
10,416 | 69.0 | - |
Case | 1 | 1 | 1 | 1 | 1WC | |
---|---|---|---|---|---|---|
Type of Glazing | G10 | G07 | G06 | G05 | G07 | |
Window Area, m2 | W1 | 3.000 | 3.000 | 2.250 | 2.250 | 0 |
W2 | 0 | 0 | 1.125 | 1.125 | 6.375 | |
W3 | 6.375 | 6.375 | 6.375 | 6.375 | 6.375 | |
W4 | 2.250 | 2.250 | 4.125 | 4.125 | 5.625 | |
W5 | 3.375 | 3.375 | 3.375 | 3.375 | 4.125 | |
W6 | 0 | 0 | 0 | 0 | 0 | |
W7 | 3.375 | 3.375 | 3.375 | 3.375 | 4.125 | |
W8 | 4.125 | 4.125 | 6.375 | 6.375 | 6.375 | |
W9 | 0 | 0 | 0 | 0 | 0 | |
Sum of Windows Area, m2 | 22.50 | 22.50 | 27.00 | 27.00 | 33.00 | |
Sum of Glazing Area, m2 | 15.57 | 15.57 | 18.79 | 18.79 | 23.43 | |
LCC, € | 10,801 | 10,616 | 10,574 | 10,684 | 9034 | |
LCC Savings, % | 3.9 | 5.5 | 5.9 | 4.9 | 13.3 | |
Heating demand, kWh/m2 | 66.8 | 61.1 | 61.8 | 63.3 | 55.5 | |
Cooling demand, kWh/m2 | 7.5 | 9.5 | 9.1 | 7.0 | - | |
Total energy savings, % | 3.3 | 8.1 | 7.9 | 8.6 | 19.5 |
Case | 2 | 2 | 2 | 2 | 2WC | |
---|---|---|---|---|---|---|
Type of Glazing | G10 | G07 | G06 | G05 | G07 | |
Window area, m2 | W1 | 3.000 | 3.000 | 6.375 | 6.375 | 3.000 |
W2 | 0 | 0 | 0 | 0 | 0 | |
W3 | 6.375 | 6.375 | 3.000 | 3.000 | 6.375 | |
W4 | 2.250 | 2.250 | 2.250 | 2.250 | 5.625 | |
W5 | 3.375 | 3.375 | 5.625 | 5.625 | 5.625 | |
W6 | 0 | 0 | 0 | 0 | 0 | |
W7 | 3.375 | 3.375 | 4.125 | 4.125 | 4.875 | |
W8 | 4.125 | 4.125 | 0 | 0 | 6.375 | |
W9 | 0 | 0 | 4.125 | 4.125 | 5.625 | |
Building orientation, deg * | 337.5 | 337.5 | 247.5 | 247.5 | 292.5 | |
Sum of windows area, m2 | 22.50 | 22.50 | 25.50 | 25.50 | 37.50 | |
Sum of glazing area, m2 | 15.57 | 15.57 | 17.85 | 17.85 | 26.20 | |
LCC, € | 10,691 | 10,515 | 10,475 | 10,566 | 8800 | |
LCC savings, % | 4.9 | 6.4 | 6.8 | 6.0 | 15.5 | |
Heating demand, kWh/m2 | 65.7 | 59.9 | 61.0 | 62.6 | 52.8 | |
Cooling demand, kWh/m2 | 8.1 | 10.4 | 9.7 | 7.4 | – | |
Total energy savings, % | 4.0 | 8.6 | 8.1 | 9.0 | 23.4 |
Case | 3 | 4 | 3WC | 4WC | |
---|---|---|---|---|---|
Insulation, cm | IEW | 18 | 18 | 20 | 20 |
IGF | 12 | 12 | 15 | 15 | |
ICA | 28 | 28 | 30 | 30 | |
Building Orientation, deg * | - | 337.5 | - | 292.5 | |
LCC, € | 10,050 | 9989 | 8402 | 8240 | |
LCC Savings, % | 10.6 | 11.1 | 19.3 | 20.9 | |
Heating Demand, kWh/m2 | 48.8 | 48.1 | 44.9 | 43.8 | |
Cooling Demand, kWh/m2 | 14.5 | 14.9 | - | - | |
Total Energy Savings, % | 17.7 | 18.1 | 34.9 | 36.5 |
Case | 5 | 6 | 7 | 5WC | 6WC | 7WC | |
---|---|---|---|---|---|---|---|
Type of Glazing | G06 | G05 | G05 | G07 | G07 | G07 | |
Window Area, m2 | W1 | 0 | 0 | 0 | 0 | 3.000 | 3.000 |
W2 | 3.000 | 3.000 | 3.000 | 4.125 | 0 | 0 | |
W3 | 6.375 | 6.375 | 6.375 | 6.375 | 6.375 | 6.375 | |
W4 | 2.250 | 2.250 | 2.250 | 5.625 | 5.625 | 5.625 | |
W5 | 2.250 | 2.250 | 2.250 | 4.125 | 5.625 | 5.625 | |
W6 | 1.500 | 1.500 | 1.500 | 0 | 0 | 0 | |
W7 | 3.375 | 3.375 | 3.375 | 4.125 | 4.125 | 4.125 | |
W8 | 3.750 | 3.375 | 3.750 | 6.375 | 6.375 | 6.375 | |
W9 | 0 | 0 | 0 | 0 | 0 | 0 | |
Building Orientation, deg * | - | 337.5 | 337.5 | - | 315.0 | 292.5 | |
Insulation, cm | IEW | 18 | 18 | 18 | 18 | 18 | 18 |
IGF | 12 | 10 | 12 | 15 | 15 | 15 | |
ICA | 28 | 28 | 28 | 28 | 28 | 28 | |
Infiltration, h−1 | - | - | 0.3 | - | - | 0.3 | |
Sum of Windows Area, m2 | 22.50 | 22.50 | 22.13 | 30.75 | 31.13 | 31.13 | |
Sum of Glazing Area, m2 | 15.48 | 15.48 | 15.17 | 21.78 | 21.87 | 21.87 | |
LCC, € | 9417 | 9363 | 7390 | 7266 | 7110 | 5093 | |
LCC savings, % | 16.2 | 16.7 | 34.2 | 30.2 | 31.7 | 51.1 | |
Heating demand, kWh/m2 | 43.3 | 43.9 | 30.5 | 34.8 | 33.6 | 20.2 | |
Cooling demand, kWh/m2 | 14.0 | 11.9 | 13.9 | – | – | – | |
Total energy savings, % | 25.5 | 27.5 | 42.3 | 49.6 | 51.3 | 70.7 |
Case | RB | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
---|---|---|---|---|---|---|---|---|---|
Type of Glazing | G10 | G06 | G06 | G10 | G10 | G06 | G05 | G05 | |
Sum of windows area, m2 | 23.25 | 27.00 | 25.50 | 23.25 | 23.25 | 22.50 | 22.50 | 22.13 | |
South-facing windows, % | 32 | 63 | 54 | 32 | 32 | 53 | 55 | 56 | |
Building orientation, deg * | 0 | 0 | 247.5 | 0 | 337.5 | 0 | 337.5 | 337.5 | |
Insulation, cm | IEW | 12 | 12 | 12 | 18 | 18 | 18 | 18 | 18 |
IGF | 5 | 5 | 5 | 12 | 12 | 10 | 12 | 12 | |
ICA | 20 | 20 | 20 | 28 | 28 | 28 | 28 | 28 | |
Infiltration, h−1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.3 | |
LCC savings, € | 0 | 663 | 761 | 1187 | 1247 | 1820 | 1873 | 3846 | |
LCC savings, % | 0 | 5.9 | 6.8 | 10.6 | 11.1 | 16.2 | 16.7 | 34.2 |
© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Ferdyn-Grygierek, J.; Grygierek, K. Multi-Variable Optimization of Building Thermal Design Using Genetic Algorithms. Energies 2017, 10, 1570. https://doi.org/10.3390/en10101570
Ferdyn-Grygierek J, Grygierek K. Multi-Variable Optimization of Building Thermal Design Using Genetic Algorithms. Energies. 2017; 10(10):1570. https://doi.org/10.3390/en10101570
Chicago/Turabian StyleFerdyn-Grygierek, Joanna, and Krzysztof Grygierek. 2017. "Multi-Variable Optimization of Building Thermal Design Using Genetic Algorithms" Energies 10, no. 10: 1570. https://doi.org/10.3390/en10101570