1、OR-05-3-2 Optimal Control Strategies for Heated Radiant Floor Systems Pyeongchan Ihm, PhD ABSTRACT In this pape6 a transient numerical model for a radiant floor panel is integrated into a whole-building simulation program and utilized to evaluate various control strategies. Both conventional and opt
2、imal control strutegiesfor hot-water radiant floor systems applied to residential buildings are considered in this paper: The optimal controls are developed to maintain an acceptable thermal comfort levelfor occupants and to reduce heating energy cost. It isfound that the optimal controls have the p
3、otential to save up to 30% ofheating energy use compared to conventional controls. However, theperfor- mance ofoptimal control strategies depends on several design and operating conditions. INTRODUCTION Radiant floor panel heating systems are widely used in several European and Asian countries. They
4、 consist of embed- ded hot water coils in floor slabs ofresidential and commercial buildings to provide space heating. Recently, radiant systems have received renewed interest in the US due to their inherent advantages compared to conventional all-air heating systems including low-noise, potential e
5、nergy savings, uniform temperature distribution within spaces, and superior thermal comfort (ASHRAE 2000). Control strategies of radiant floor heating systems on slab-on-grade foundation are more challenging than those utilized to operate conventional hot air heating systems. Due to the inherent the
6、rmal inertia of the concrete slab and the ground, the control of a radiant floor heating system can be difficult. Previous investigations have studied control strate- gies for radiant floor heating panels to maintain space temper- ature using mostly one of two methods-temperature or heat Moncef Krar
7、ti, PhD, PE Member ASHRAE f ux modulation techniques. Temperature-modulation control sets the supply water temperature to be proportional to either outdoor temperature or to the difference between a desired setpoint and room air temperatures. Flux-modulation control attempts to ensure that a slab de
8、livers heat to the space at a rate per unit area proportional to the difference between the room air temperature and the slab surface temperature. The heat flux provided to the slab is proportional to the difference between the supply and return water temperatures. Using the concept of flux-modulati
9、on control developed by MacCluer (1989a, 1989b), Leigh (1991) and Leigh and MacCluer (1 994) evaluated the performance of flux-modula- tion controls through experimental testing using two identical thermal test cells with embedded piping radiant floor heating systems. The experimental analysis concl
10、uded that flux- modulation control has a more immediate response to sudden change in indoor thermal loads than temperature-modulation controls. Athienitis and Chen (1993) investigated the control performance of electric radiant floor heating systems utilizing the thermal storage capacity of solid co
11、ncrete block walls above a radiant floor in a full-scale outdoor test room to improve indoor thermal comfort and to reduce energy consumption as well as peak heating loads. Four control strat- egies were evaluated through computer simulation: conven- tional odoff control with constant setpoint, prop
12、ortional control with constant thermostat setpoint, proportional control with night setback using step changes in the setpoint profile, and proportional control with thermostat setback using ramp changes in setpoint profile. The results concluded that propor- tional control results in improved perfo
13、rmance of the system with thermal storage compared to odoff control. In addition, Pyeongchan Ihm is an assistant professor on the Faculty of Architectural Design and Engineering, Dong-A University, Busan, South Korea. Moncef Krarti is a professor in the Department of Civil, Environmental, and Archit
14、ectural Engineering, University of Colorado, Boulder, Colo. 02005 ASHRAE. 535 simple thermostat setpoint with night setback can save energy but often leads to a significant increase in peak heating load during cold days. Cho and Zaheer-uddin (I 997) performed an experimental study of embedded piping
15、 radiant floor heating systems in a facility with two identical rooms. Four control strategies are tested in the facility: conventional on-off control of the hot water pump based on feedback signal from room air temper- ature, proportional-integral control that modulates the two- way valve with room
16、 air temperature as a feedback signal, on- off control based on slab temperature, and on-off control with feedback signal from either room air temperature or the slab temperature. According to their experiments, Cho and Zaheer- uddin found that the proportional-integral control maintains room air te
17、mperature nearly at the desired thermostat setpoint, while the on-off control causes large indoor temperature fluc- tuations. More recently, Zaheer-uddin and Cho (2002) proposed two control strategies for embedded hot-water radi- ant floor heating systems. The control strategies include multi- stage
18、 on-off control and an augmented constant gain control using a simple dynamic model. All of the studies reported in the literature do not consider minimization of heating energy consumption for the radiant floor systems. Therefore, there is a need to explore and possi- bly develop control strategies
19、 to both improve indoor thermal comfort and save heating energy costs. In this paper, several control strategies are evaluated including conventional and optimal controls. Optimal control strategies are developed not only to maintain acceptable ther- mal comfort level for occupants but also to reduc
20、e heating energy cost. Using a numerical solution for radiant floor heat- ing systems integrated within a whole-building simulation program, optimal control strategies are evaluated and compared against conventional controls to both maintain the thermal comfort level of the occupants and reduce heat
21、ing energy cost. NUMERICAL MODEL Figure 1 shows a model for a radiant slab-on-grade floor. The slab-on-grade floor is heated either with electric wires or with hot water pipes. To analyze the performance of the radi- ant floor under various operating conditions, the temperature field within the slab
22、 and the ground is first determined. The unsteady-state temperature field within passive building elements (except the heated floor slab) and ground medium is subject to the time-dependent heat conduction equation with- out heat generation. The temperature distribution within the heated floor slab s
23、ubject to the heat conduction equation with heat generation is modified, adding the term of Q and presented as follows: _ I a I I Hot water pipe Concrete slab Insulaton Outdoor T. -=- - Gravel fill Foundation wall Grouna Water table T“ Figure 1 Two-dimensional model for ground-coupled heat transfer
24、for a typical hot water radiant floor heating system. 536 ASHRAE Transactions: Symposia 16 8 m Figure 3 Floor plan of one-story ranch house. Figure 2 Simplified heatedfloor embedded hot water pipe for the two-dimensional heat conduction problem. Using a control volume approach and pure implicit fini
25、te difference technique (Pantankar 1980), the heat conduction equation represented by Equations 1 and 2 can be solved. The implicit method was chosen since it is suitable for long-term analysis of a large two-dimensional domain. Indeed, the implicit method has the important advantage of being uncon-
26、 ditionally stable. That is, the solution remains stable for all space and time increments. The space-time domain (x, y, t) is subdivided into a rectangular grid system with variable space and time increments. Variable space increments are used with very fine grid in the region near the heat source,
27、 slab, and soil surface. Figure 2 describes typical control volumes for the heated floor model: a control volume with a heat source and another with no heat source (such as ground medium), which includes continuous hot water pipe and two control volumes for general and heat source nodal points. In F
28、igure 2, LP. presents the parallel length of each pipe that goes through one heat source node. Additionally, PH, PH-1, and PH+1 indicate heat source nodes. A more detailed description of the solution for Equations 1 and 2 and associated boundary conditions as well as the vali- dation of the solution
29、 against experimental data are provided by Ihm and Krarti (2004a). The integration of the developed model within a whole-building simulation program is described in Ihm and Krarti (2004b). PARAMETRIC ANALYSIS Building Description The ground-coupled heat transfer model for radiant floor heating syste
30、ms outlined in the previous section is implemented within a detailed building energy simulation program and is used to evaluate several control strategies for a typical residential building. Specifically, a one-story single-family ranch house is considered in the analysis conducted for this paper. A
31、 floor plan for a ranch house model is shown in Figure 3. In the analysis, three persons are assumed to occupy the house (i.e., one person per room) from 7 p.m. to 8 a.m. Within the occupied period, the internal heat gain is set to be 10.7 W/m2 (1 .O W/ft2). The exterior walls of the house are made
32、up of wood frame construction with R- 19 insulation. The roofhas R-30 insulation. The floor consists of 10 cm (4 in.) heavyweight concrete with 2.5 cm (1 in.) dense uniform insulation above the ground medium. Windows are double panes made up of 9.5 mm (3/8 in.) clear glass. For all the analyses carr
33、ied out in this paper, the maximum hot water flow rate is set to 0.1 kgis (13.2 lbdmin) with a constant hot water temperature of 40C (104F). Thermal comfort with the house is assessed using Fangers predicted mean vote or PMV indicators (Fanger 1970). Conventional Control Strategies In this section,
34、three conventional control strategies are investigated. All three control strategies utilize the propor- tional operation scheme but different control variables: mean air temperature (MAT), mean radiant temperature (MRT), and operative temperature (OT). The throttling range for all three control sch
35、emes is set to 51 “C (Il 3F) for fair comparison of their performance. The outdoor conditions are extracted from the TMY weather data for January 2 1 in Denver, CO. The aver- age outdoor temperature for January 21 is -12.2“C (10F). Figure 4 presents the total heating energy use and the number of hou
36、rs when thermal comfort levels exceed the acceptable range (Le., -0.5 i PMV i +0.5) for the three conventional controls. As shown in Figure4, total heating energy use is generally proportional to the increasing setpoint temperature for all three control strategies. Depending on the control strategy,
37、 lower setpoint temperature can save some heating energy use at the expense of a deterioration in the indoor thermal comfort. To further evaluate the performance of control strategies, the setpoint temperatures are selected based on both achieving low energy use and satisfying building thermal comfo
38、rt. Therefore, the setpoint temperatures are chosen as 20C (68F) for MAT-based control, 24C (75.2“F) for MRT-based ASHRAE Transactions: Symposia 537 -_ Figure 4a Performance of MAT-based proportional control. 16 14 2 O +Heat Energy +Hours over thermal comfort limit 1 Figure 46 Performance of MRT-bas
39、ed proportional control. 538 ASHRAE Transactions: Symposia Figure 4c Performance of OT-based proportional control. control, and 22C (71.6“F) for OT-based control for further analysis. Figure 5 shows hourly variations of both indoor mean air temperature and PMV index for the three control strategies.
40、 The MAT-based control scheme maintains the lowest indoor air temperature throughout the day. This result is due to the fact that the MAT-based control has the lowest hot-water heated slab surface temperature among all control strategies, resulting in low PMV values as shown in Figure 5. Table 1 sum
41、marizes the total heating energy use and cost for the three control strategies during January 21 in Denver, CO. The temperature setpoint for each control strategy is selected so indoor thermal comfort is maintained throughout the occupied period. The results of T indicate that MAT-based control prov
42、ides a small savings in heating energy and cost, and that MRT-based control uses more heating energy among the three controls to meet thermal comfort of occupants. OPTIMAL CONTROL STRATEGIES Optimal Control An optimization process consists of finding the values of selected control variables to minim
43、ize an objective function with some imposed constraints. Unlike optimal controls of HVAC systems and plants, which are modeled assuming steady-state conditions, radiant floor heating systems affect both the building heating/cooling loads as well as the perfor- mance of HVAC systems. Due to the dynam
44、ic characteristics of the radiant floor systems, optimal controls could be more appropriate than other conventional controls for reducing energy consumption while maintaining building thermal comfort. The controlled variable to optimize building energy use is selected as time-varying indoor air setp
45、oint temperature during one day to minimize the total daily operating cost, taking into account the constraint of maintaining indoor space temperatures within a range defined by upper and lower temperature limits. During the optimization process, the objective function is constrained by the conditio
46、n that thermal comfort has to be maintained during the occupied hours within acceptable levels. That is, the space indoor temperature should be kept within predefined indoor setpoint temperature limits. Simmonds (1 993) used optimal controls to demonstrate that additional energy savings could be ach
47、ieved by an HVAC system if the control is based on maintaining Fangers predicted-mean-vote (PMV) index rather than the dry-bulb temperature within a thermal comfort range. In general, a PMV value within 0.5 is acceptable for thermal comfort according to ASHRAE (2001). Thus, desired PMV values can be
48、 used as constraints of the objective function to keep proper indoor thermal comfort conditions during the occupied period using the following condition: (3) -0.5 I PMV 5 +0.5 Thus, the optimal control seeks to minimize the total energy use of radiant floor heating systems for any 24-hour period as
49、a function of the building thermal characteristics, ASHRAE Transactions: Symposia 539 t Control Strategies MAT MRT 0.4 X 0.3 .a 4 Temperature Total Heating Setpoint Energy Use 20C (68F) 24C (75.2“F) 73.7 MJ (69.8 MBtu) 74.7 MJ (70.8 MBtu) 0.2 j, 0.1 O -0.1 -0.2 -0.3 5.4 II il II I1111lllIIlIIIIII I ,IIIIII L,cn.IcIt5.5 O (322 i 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Hair of dayhour -B-MAT:MATconErol -6-MAT:MRTcontrd . . Q MATCYconlrol +PMV:MATcontrol -PMV:MRTcontrol O PMV:OTcaitd Figure 5 MAT and PMV variations for all three conventional
