ÍNDICE PRESUPUESTO
CAPÍTULO 02: CUADROS DE PROTECCIÓN
A single-floor office with an overall area of 555 m2, located in Montreal, Canada, is assumed,
and its simplified RC-network thermal model is developed. The choice of the office building and RC-network model is in accordance with the objectives of this research. Alternatively, the proposed methods can be applied to other buildings, by developing their thermal models. In order to validate the developed model, the simulated annual energy consumption is compared with the simulations of eQuest and TRANSYS software; less than 5% difference is observed between the compared values (see App. A). For building energy performance simulation, typical meteorological year weather data of Montreal is used. Montreal has a warm and humid summer, a very cold winter, and is located in climate zone 6 in ASHRAE climate zones map [96]. The office has five zones: north, east, central, south, and west. In all the zones except central zone, the wall with a connection to the outside has a window-wall ratio of 0.4. The ceiling heights, in all the zones, are equal to 3 meters. In each zone, there could be up to ten office workers. Fig. 4 shows the plan of the office, and the thermal model of one of the zones.
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Fig. 4: Simulated office (left), RC-network thermal model of east zone (right)
Each node represents an area with similar environmental parameters (e.g. temperature, lighting, and air velocity), such as a single zone, or one of the layers of the walls. Heat is transferred between the nodes by convection, conduction, or radiation. Resistances express conduction and convection from one zone to the other, or from outside through the wall, while capacitances represent thermal storage. For each zone, a specific set of energy balance equations is derived, from various types of energy exchanges processes, including (1) solar gain through windows, (2) internal heat gain from occupants, systems, and equipment, (3) infiltration, (4) heat exchange between the zones, (5) the effect of thermal storage of external walls, (6) the influence of blinds position on the conductive heat transfer of the windows, (7) artificial lighting, and (8) heating and cooling systems. For each zone of the office (i), the governing equation, representing energy balances, are in the form of:
𝜌𝑉𝑖 𝑐𝑝 𝜕𝑇𝑖 𝜕𝑡 = ∑ ℎ𝑐 𝑖−𝑗𝐴𝑠𝑗 (𝑇𝑠𝑗− 𝑇𝑖) 𝑛 𝑗=1 + ∑ 𝑚̇𝑖−𝑘 𝑐𝑝 (𝑇𝑘− 𝑇𝑖) 𝑚 𝑘=1 + 𝑞𝑖𝑛 (3.1)
The term 𝜌𝑉𝑖 𝑐𝑝represents the thermal capacitance of the fluid (air) inside the zone, in which 𝜌 is the density of air (kg/m3), Vi is the volume of the zone (m3), c
p is the specific heat of air (J/kg.K), and Ti is the temperature of the zone (K). Forward difference scheme is applied to the partial derivative, over some finite time interval (an hour), in hourly building energy performance
42 simulation: 𝜕𝑇𝑖
𝜕𝑡 =
𝑇𝑖𝑡+∆𝑡−𝑇𝑖𝑡
∆𝑡 . During the energy performance simulation, 𝑇𝑖
𝑡+∆𝑡 is the inside
temperature of the zone, calculated during that hour, ∆𝑡 is equal to one hour, and 𝑇𝑖𝑡 is the inside
temperature of that zone, calculated in the previous hour.
The term ℎ𝑐 𝑖−𝑗𝐴𝑠𝑗 (𝑇𝑠𝑗− 𝑇𝑖) in the governing equation expresses the convective heat transfer rate
(W) between the zone (i) and the surrounded surfaces (j). Tsj is the surface temperature, Asj is the contact area of the zone with the surface (m2), and h
c-i-j is the heat transfer coefficient (W/m2.K). Here, surfaces’ hc-i-j are replaced by U-values (thermal transmittance, including inside and outside film coefficients, W/m2.K), stated in Table 1.The term ∑ 𝑚̇
𝑖−𝑘 𝑐𝑝 (𝑇𝑘− 𝑇𝑖) 𝑚
𝑘=1 describes the rate of
energy exchange (W) due to the fluid flow between the zone and other zones, or between the zone and outdoor. In this equation, 𝑚̇𝑖−𝑘 is the pressure/temperature driven mass flow rate (kg/s) between
the two volumes, cp is the specific heat of air, transferred from another zone or from the outdoor, and Tk is one of the other zone’s temperature or outdoor temperature. 𝑞𝑖𝑛 represents the heat
generated in the zone from occupants and appliances, or from artificial lighting, or heating/cooling system. There could be specific relations between variables that shape nonlinear constraints of the optimization problem, and should be respected while solving the problem. In this model, there are nonlinear constraints, based on the effect of thermal storage of external walls, and also the influence of blind position on the conductive heat transfer of windows. It is assumed that the simulated office is on the middle floor of a high-rise office building. Accordingly, all the ceilings and floors are adiabatic. Values of parameters, used in the thermal model, are stated in Table 1.
Table 1: Building parameters
Parameter Value Parameter Value
Chiller COP 3.5 Exterior Wall Specific Heat (kJ/kg .K) 42
Electrical Heater Efficiency (n) 1 Exterior Wall Outdoor Surface Convection Heat Coefficient (W/m2.K) 34
Open Shade Window U-Value (W/m2.K) 2.3 Exterior Wall Indoor Surface Convection
Heat Coefficient (W/m2.K) 8.5 Close Shade Window U-Value (W/m2.K) 1.4 Interior Wall U-Value (W/m2.K) 1.5
Fluorescent Lamp Efficacy (lumens/W) 70 Fan Energy Consumption (W per m3/s of air) 1760
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3.1.2 Automated Control System
In each zone, four environmental parameters of artificial lighting, natural illumination, indoor temperature, and ventilation rate are automatically controlled, on an hourly basis. It is assumed that the office is occupied during weekdays from 9 am to 5 pm. Each zone is equipped with a Variable Air Volume (VAV) system that provides heating, cooling, and air ventilation. During the unoccupied hours, energy management and integrated control of the zones are based on the SOOP of energy consumption costs. The objective function of the SOOP method is only comprised of an energy costs term. For each zone, total energy consumption (Etotal) in an hour is the sum of energy
consumption of artificial lighting, chiller, boiler, and fan:
Etotal = Elighting+ Ecooling + Eheating + Efan (3.2)
The energy costs term in the objective function of the SOOP method, is the product of electricity or gas prices and the associated hourly energy consumption. Fixed rates of 8 cents per kWh and 20 cents per m3are assumed as electricity and gas prices in Montreal. For each hour of simulation,
the energy costs term, in the objective function is in the form of:
𝐸𝑛𝑒𝑟𝑔𝑦 𝑐𝑜𝑠𝑡𝑠 = [𝐸𝑙𝑒𝑐𝑃𝑟𝑖𝑐𝑒 . ∑ 𝐸𝑧𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 5 𝑧=1 + 𝐺𝑎𝑠𝑃𝑟𝑖𝑐𝑒 . ∑ 𝐸𝑧𝑔𝑎𝑠 5 𝑧=1 ] (3.3)
In which, E is the energy consumption in kWh; z is the number of the zone; ElecPrice and GasPriceare electricity and gas prices.
During the occupied hours, the proposed MOOP method automatically controls the indoor environmental conditions of the zones. In the objective function of the MOOP method, besides the energy costs term, an occupants’ productivity term is introduced. The occupants’ productivity term considers the overall productivity of occupants, with respect to indoor environmental conditions. Considering each occupant’s comfort preference, the proposed method manages the indoor environment to simultaneously optimize energy costs and occupants’ overall productivity.
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Table 2: Building schedule
Schedule Occupied Unoccupied
Minimum Indoor Illuminance (lux) [4] (always ≤ 2500 lux) 750 50
Occupancy Heat Generation (W/m2) 12.6 1.6
Equipment Heat Generation (W/m2) 10.7 3
Cooling Set-Point (°C) - 26.6
Heating Set-Point (°C) - 18.3
Minimum Conditioned Outdoor Air
Flow Rate (m3/s per m2) [16] + 0.0003 (infiltration) 0.0007 (only infiltration) 0.0003