1、Andreas K. Athienitis is a professor in the Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Quebec, Canada. Jos A. Candanedo and Amlie Allard are graduate students under Dr. Athienitiss supervision. Solar-Assisted Radiant Floor Heating in a Net-Zero Energ
2、y Residential Building Jos A. Candanedo Amlie Allard Andreas K. Athienitis, PhD, PE Student Member ASHRAE Student Member ASHRAE Member ASHRAE ABSTRACT This paper investigates predictive control strategies applied to radiant floor heating system in a net-zero energy solar home. Control operations are
3、 performed by adjusting variables such as the temperature set-point, the radiant floor heating systems heat delivery rate, and the solar gains transmitted through the fenestration (for instance, by changing the position of motorized shading devices). The mathematical models used for the implementati
4、on of control strategies are simplified linear transfer function models, based on thermal networks models. The use of transfer function models, which can also be obtained from system identification of building simulation output data, considerably facilitates the implementation of computationally dem
5、anding control strategies. Applications of Model Predictive Control (MPC), a set of algorithms that employ a model of the system to predict its response to future disturbances, are presented and discussed. MPC techniques -or alternative predictive control algorithms- are necessary to manage the coll
6、ection, storage and delivery of passive solar gains, and thus to regulate indoor temperatures and maintain comfortable indoor conditions for the occupants. INTRODUCTION This paper investigates the application of predictive control in an advanced solar home with a radiant floor heating (RFH) system,
7、through the implementation of a simplified transfer function model. Predictive control can be used to maintain a comfortable indoor environment by anticipating the buildings response to expected weather conditions. Passive solar heating offers significant possibilities for reducing space heating loa
8、ds in residential buildings, thus enabling the construction of net-zero energy houses. Despite this potential, poor passive solar design and/or inadequate control strategies may lead to overheating (Argiriou et al. 2000; Chiras 2002). This concern represents a potential obstacle for the widespread a
9、doption of this passive solar design. This paper examines an example of model predictive control (MPC) of an RFH system and of dynamic fenestration devices (e.g., a roller blind) based on simple transfer function model of a house. This strategy optimizes indoor temperature conditions while significa
10、ntly improving the energy performance. High mass RFH fits well with direct gain passive solar design since a floor with significant thermal mass (e.g. concrete) can be used as a thermal energy storage (TES) device for both the solar heat gains and the heat delivered by the HVAC system, especially wh
11、en the floor system piping is installed relatively deep into the floor slab. Predictive control can significantly contribute to maintaining comfortable conditions inside a solar house, particularly during the “shoulder seasons” (spring and fall) in which overhangs are not as effective in preventing
12、excessive solar heat gains. Traditional control strategies, such as ON/OFF or PID control, are reactive: actions are taken when the control variable diverges from the reference value. In contrast, predictive control could be described as proactive: actions are taken to maintain the desired set-point
13、 by using data on expected changes in the disturbance conditions. This characteristic of predictive control helps in managing the long time constants (in the order of hours or even days) associated with large thermal capacitances. LV-11-C009 2011 ASHRAE 712011. American Society of Heating, Refrigera
14、ting and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 117, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAES prior written permission.METHODOLOGY Case S
15、tudy The building model used for these simulations is roughly based on the kitchen/dining-room of the Alstonvale Net Zero House (ANZH), an advanced solar house which was under construction in Montral until recently (Candanedo and Athienitis 2010a). This house unfortunately suffered significant damag
16、e during a fire in May 2010. The ANZH house, whose re-construction is being planned, relied heavily on passive solar heating as a fundamental component of its design (Figure 1a). An RFH system was intended as the system for delivering auxiliary heating to the house spaces. In this study, a simplifie
17、d representation of the kichen/dining-room was used (Figure 1b). This simplified model, detached from the rest of the house, consists of a rectangular room (6.5 m 21.3 ft x 5.0 m 16.4 ft) with its narrowest wall facing due South. The south wall had a 5.5 m2(59.2 ft2) window, while the west wall had
18、a 2.5 m2(26.9 ft2) window. Table 1 provides other details. Figure 1. (a) The Alstonvale Net Zero House (kitchen/dining room within the frame); (b) an adapted model of the kitchen/dining room space. Table 1. Construction parameters of the finite difference model. Component Construction details / Comm
19、ents Approximate R-value Walls Brick/insulation/gypsum board. All four walls are exposed to the outdoor environment. 5.6 RSI (R-32) Floor Concrete slab, 2.5 in (6.3 cm) for the baseline case and 6 in (15 cm) for comparison. For the baseline case, heat is injected at 0.31 in (0.8 cm) from the bottom
20、and the lower surface is exposed to a basement maintained at 16C. 0.04 RSI (R-0.21), 2.5-in 0.09 RSI (R-0.50), 6-in Ceiling Insulation batt between wood studs covering 15% of the area. Gypsum board exposed to the room space. Other side exposed to a non-ventilated attic space. 8.0 RSI (R-45) Roof Woo
21、d shingles on shingle backer board. 0.36 RSI (R-2) Windows Triple-glazed, low-emissivity, argon-filled windows with a SHGC (at normal incidence angle) of 0.57. 1.08 RSI (R-6.1) Thermal Network Model Predictive or anticipatory control requires a model of the “plant” or system that is being controlled
22、. Several researchers have applied neural networks to create “black box” models that can be used for predictive control (Argiriou et al. 2000), including the case of hydronic radiant heating systems (Argiriou et al. 2004). Kummert et al. (2006) utilized a space-state model obtained from system ident
23、ification for predictive control. In the case under discussion, a customized finite-difference model of the building, based on a thermal network representation (Figure 2), was implemented as a MATLAB M-file (MATLAB 2008). This thermal network included four capacitances for the floor slab, one capaci
24、tance in each of the walls and one corresponding to the air node. The thermal network includes a resistance between the indoor air and outdoor air, which accounts for the heat loss through the windows and the infiltration (fixed at 0.1 air changes per hour). Convective phenomena are treated by fixed
25、 convective heat transfer coefficients. South72 ASHRAE TransactionsFigure 2. Thermal network model of the room shown in Figure 1b. Tois the exterior temperature, Tbthe basement temperature, Tsa_xare sol-air temperatures, and Sr the solar heat gains entering the room. The arrows represent thermal rad
26、iation exchanges between the internal surfaces Temperatures were calculated by applying a fully explicit finite difference scheme, in which the temperatures for a given time step only depend on temperatures of previous time steps. Equation 1 is used to calculate the temperature of a node i for the t
27、ime step p+1 for the case of nodes with a thermal capacitance: ,1 ,1nkp ipip ip sikkTTtTT QCR+=+ +(1) In the case of nodes without capacitance (e.g, surface nodes), the corresponding equation is given by: ,1,1,11SnkpkikipnkikTQRTR=+=+=(2) The heat source in the floor is considered as a uniform sourc
28、e (planar) at the depth at which the piping is located. Long-wave radiation exchange between the room internal surfaces is calculated by solving the radiosity matrix (Incropera and DeWitt 2002). Astronomical and geometric calculations are used to determine the solar altitude and azimuth angles for a
29、 given time, and thus the incidence angles on each surface. Solar gains are then calculated considering the impact of the incidence angle on direct transmittance. The diffuse transmittance is calculated as the direct transmittance at a 60 incidence angle. 2011 ASHRAE 73Simplified Transfer Function M
30、odel Building simulation tools and detailed thermal-network models can provide adequate representations of the buildings behavior. However, it has been found that simple models with relatively few thermal resistances and capacitances can adequately represent the systems behavior in the case of solar
31、 houses (Athienitis et al. 1990; Athienitis 1994; Fraise et al. 2002; Kmpf and Robinson 2007). A simpler, more manageable model facilites computationally demanding tasks, such as those associated with optimal control strategies, while offering insight into the systems behavior. An example of simple
32、model is a transfer function (TF) representation, which is based on assuming that the building behaves mainly as a linear system. Although phenomena such as radiation and convection are non-linear, conduction through the building envelope is predominantly linear. Moreover, temperature fluctuations i
33、nside the room under normal operating conditions will be kept near an operating point, which validates the linearization of the convection and radiation equations. Outdoor temperature, solar radiation and the heat delivered by the floor heating system are the main factors affecting the indoor temper
34、ature fluctuations. Since the superposition principle applies for a linear system each of these inputs can be analyzed independently (Candanedo and Athienitis 2010b); their global effect can be found by adding their individual impacts. Approximate transfer functions, either continuous or discrete, c
35、an be found between the indoor air temperature and each input by applying forcing functions and then using system identification techniques (Candanedo and Athienitis 2010b). This methodology was applied to the finite difference model presented above in order to develop a simplified TF model. In this
36、 case the selected inputs are the solar gains, the outdoor temperature and the heat output of the heating system (Figure 3a). Using solar gains as an input does not mean neglecting the effect of solar radiation on exterior walls: it only means that the radiation entering the room functions as a good
37、 indicator of the overall radiation conditions. As shown in Figure 3b, there is good agreement between the finite difference model and the transfer function model under free-floating conditions, with a maximum difference of about 2 C (3.6 F). Under normal conditions, in which temperature fluctuation
38、s are controlled, discrepancies are expected to be smaller. Figure 3. (a) Transfer function model for the room; (b) comparison between the output of the finite differencemodel and the transfer function model under free-floating conditions (i.e., no heat delivered by the floor heating system). Model
39、Predictive Control Implementation Control of radiant floor heating (RFH). A simple TF model facilitates the implementation of advanced control strategies. For example, with a TF model it is easier to apply features available in commercial software tools especially designed for testing advanced contr
40、ols. Model Predictive Control (MPC) is the name given to several optimization algorithms (Rossiter 2003) used to calculate optimal sequences of present and future values for the control variable(s), based on knowledge of the plant (i.e., a model) and expected disturbances (Chen 2001). Since an MPC a
41、lgorithm is anticipatory by definition, it is useful for managing systems with large time constants. For the case of a single output, the MPC algorithm calculates a sequence of values for the control variable in order to minimize the following quantity (Bemporad et al. 2010): 74 ASHRAE Transactions2
42、11() ( ) ( )Pnjj jijSk w r k i y k i= =+ (3) in which the S(k) is the weighted sum of square deviations at time step k, wjis a weighting factor for output j, rj(k+i) is the reference (i.e., desired value) at time step k + i and yj (k+i) is the expected output value at k + i. The TF model obtained fo
43、r the kitchen/dining room space was implemented in MATLAB/Simulink, and then used to test an MPC for the RFH system. Maximum and minimum values of the control variable (i.e., the heat delivered by the RFH system) and other constraints may be introduced. Figure 4 shows the temperature obtained with a
44、n MPC applied to the transfer function model of the baseline case (i.e. for the 2.5-in concrete slab) for a period of 100 days under Montral climate conditions. The expected solar gains and outdoor temperatures (obtained from the weather file) are used to calculate the heat output (constrained betwe
45、en 0 and 1500 W 0 and 5.118 kBTU/h ) of the radiant floor heating sytem. Since the HVAC system cannot provide cooling, the MPC does not maintain the air temperature at the desired set-point (21 C 69.8 F), but attempts to minimize the deviation. The air temperature rarely exceeds 26 C (78.8 F) and on
46、ly once goes beyond 30 C (86 F). Over a period of 4 months (Nov.-Feb.), the heat delivered by the RFH is 1524 kWh (5203.6 kBTU). Figure 4. Indoor temperature (Tin) and heat output with a TF model used in MPC. Maximum heat output = 1500 W(5.118kBTU/h). Control of Effective Blind Transmittance As Figu
47、re 4 illustrates, predictive control of a RFH system can improve thermal comfort conditions inside the room, but large heat solar gains might still produce overheating occasionally. Motorized roller blinds, venetian blinds, electrochromic windows and similar technologies can be used to reduce the so
48、lar heat gains entering the space by rejecting a portion of the heat gains. However, since solar gains can supply a large portion of the heating needs of the space, it is important not to reduce too much the effective transmittance of the “blinds1”. As in the case of radiant floor heating, the selec
49、tion of an optimum level of transmittance (corresponding, for instance, to a blind position) needs to consider the long-lasting impact of an action. This study shows that predictive control can be used to find the optimal (or near-optimal) combination of radiant heating output and effective blind transmittance based on current and expected weather conditions. In this investigation, the control of solar gains is carried out by taking two further steps with the model: (a) It is assumed tha
