3.1. Sensitivity Analysis of Variables
PMV calculations are performed on four types of objective data, air temperature, MRT, relative humidity (RH), and air velocity, and two types of subjective data, CLO and MET. However, these variables do not have an equal influence on the PMV. This section describes the sensitivity analysis conducted to determine the effect of these six variables on the PMV in the subject residence.
Hawila et al. [26
] investigated the impact of PMV-based thermal comfort control during the heating period in a highly glazed room. According to the study, the energy consumption in a comfort-controlled space was highly sensitive to occupant-related parameters (metabolic rate and clothing level) and the mean radiant temperature compared to other parameters such as the relative humidity. Zhang et al. [11
] used the PMV index to optimize the control of thermal comfort and energy saving by monitoring the thermal sensation online. The study concluded that the PMV model has limitations in terms of its practical application. More precisely, selected PMV variables are difficult to monitor accurately and continuously owing to the limitations of experimental facilities. Therefore, providing accurate data to TCC sensors is the first step to ensure accuracy and reliability.
The accuracy of the data input into the controller is critical for developing the TCC for a Kuwaiti residential house. In addition, optimization of the TCC development necessitates identifying which data should be collected more accurately for this purpose. This was achieved by conducting a global sensitivity analysis using ASHRAE standard 55 [27
] coded in Python and using Latin hypercube sampling (LHS). The PMV sensitivity index was calculated using the standardized rank regression coefficient (SRRC). SRRCs can be estimated from a regression analysis, which is standardized to the variances of dependent and independent variables are 1. The sensitivity index makes it easy to interpret quantitative measurements of the influence of input parameters on model outputs (Figure 7
). The sensitivity index indicates the degree of influence of the six variables on the PMV, and the sign (+ or −) of the sensitivity index indicates the correlation between the variable and the PMV index. Separate sensitivity analyses were conducted for when the PMV was greater than or less than zero. The analyses were divided in this way because the sign of the correlation for each factor switches when PMV = 0. If the sensitivity analysis were conducted for all PMV values, the resulting sensitivity of each factor would be inaccurate.
The results of the sensitivity analyses showed that air temperature had the greatest influence on the PMV when PMV > 0, followed by MRT, MET, and air velocity in descending order. This result indicates that air temperature is the most important factor when setting the target temperature during the summer. However, when PMV < 0, MET had the greatest influence on PMV, followed in decreasing order by the air temperature, CLO value, and MRT. This result indicates that MET is the most important factor when setting the target temperature during the winter. Since houses in Kuwait are not heated, it is pointless to focus on PMV values less than zero. Therefore, accurate calculation of the AC setpoint temperature by the TCC in Kuwaiti residential houses requires accurate real-time data on the air temperature, MRT, MET, and air velocity.
On the other hand, two significant matters need to be taken into consideration when installing the TCC, namely the application of a sensor and the installation location for measurements of the four objective variables. It is preferable to install the TCC units on the same wall as existing thermostats in a residential house. Therefore, it is necessary to compare the MRT and airflow measurements along the wall with those in the center of the room among the four objective items. The position of the sensor should be defined more clearly if the difference in the MRT and air velocity in the PMV results is large between measurements along the wall and in the center of the room.
The characteristics of black bulb thermometers used to measure the MRT and air velocity sensors must be considered. The temperature and humidity sensors are robust and well understood, and, therefore, their use in the TCC was not expected to cause significant problems. However, the black bulb thermometers and air velocity sensors may be difficult to physically incorporate into the unit and may cause it to become prohibitively expensive. The sensitivity analysis in this study determined that the MRT and air velocity affect the PMV calculations. However, the air velocity sensors detect lower air speeds when they are installed on walls than when they are in the center of rooms. Furthermore, the problems associated with the size and installation location of the black bulb thermometers for measuring the MRT also have to be solved.
Consequently, it is necessary to analyze the effect of MRT and air velocity in detail when calculating the optimal temperature using PMV. In this regard, sensors were installed in the center of a cooling zone during August in a residential building in Kuwait (the residential house in Table 1
). The data showed that the average indoor air temperature was 18.8 °C, the average MRT was 18.6 °C, the average RH was 54.6%, and the average air velocity was 0.09 m/s. The difference between the actual indoor air temperature as measured at the center of the cooling zone and the MRT was only 0.2 °C (Figure 8
The following scenarios were analyzed to determine whether the black bulb thermometer and air velocity sensor should be included in the TCC. Based on the data measurements for the month of August, the PMV calculation of the following two scenarios were compared to basecase, the calculated PMV from the measured data.
Scenario (1) indoor air velocity = 0.09 m/s (the constant average value in August).
Scenario (2) indoor air temperature = MRT.
The optimal target temperature was determined by recursively calculating the PMV for each scenario using ASHRAE standard 55 coded in Python. Figure 5
shows the correlation between the two scenarios and the basecase. The larger the degree of scattering, the larger the error of the calculated PMV is when a scenario is applied. The figure shows that Scenario 2 has less impact on the actual PMV calculation than Scenario 1. The results also showed that the PMV for Scenario 1 had an average difference of 0.4 and the average PMV for Scenario 2 was 0.1 (Figure 9
). Given these results, the optimal setpoint temperature differed by 4 °C for Scenario 1 and 1 °C for Scenario 2 (Figure 10
The distribution of the PMV values and target temperatures of the base case (Measured) and two scenarios were analyzed (Figure 11
). The PMV values were distributed between −2 and −0.2 in all the scenarios but had the highest frequency between −1.7 and −0.4. The optimal setpoint temperature had the highest frequency between 24 °C and 25 °C. It was found that the occupants’ thermal comfort was predicted to be at a higher temperature when Scenario 1 and Scenario 2 were applied as compared to the base case. This showed that the frequency of the PMV index in both scenarios is higher at −0.8 and −0.7 in Figure 11
, such that the frequency of the optimal set temperature also has a lower temperature distribution at 24 °C. The difference in the frequency of the two scenarios showed that Scenario 1 is predicted to be warmer than Scenario 2. This result indicates that an indoor air velocity of 0.09 m/s had a greater influence on the PMV and target temperature calculations than when the indoor air temperature was equal to the MRT. Therefore, to maintain the optimal PMV, the optimal setpoint temperature was lower in Scenario 1 than in Scenario 2.
Next, the hourly PMV distribution was analyzed for the month of August by controlling the indoor temperature by using the two scenarios. Here, it should be noted that the PMV is always 0 when the temperature is optimally controlled, and thus the PMV range shown in Figure 12
is an error because of the assumptions on which the two scenarios are based. If the indoor setting temperature is controlled by these two scenarios and the PMV is in the thermal comfort range, the two scenarios do not have a significant effect on the indoor thermal comfort. As shown in Figure 12
, the daily PMV of both scenarios is in the range of −0.5 to 0.5. Therefore, even if the PMV is controlled by the optimal setpoint temperature by using the two scenarios, the influence of these two scenarios is within the thermal comfort range. In other words, occupants would feel comfortable regardless of whether the temperature was controlled as in either scenario.
3.2. Development of Controller and Composition
The thermal comfort-based controller-version 1 (TCC-V1) was developed based on the results of the sensitivity analysis and the thermal comfort range analysis for each scenario in Section 3.2
. At constant indoor air velocity of an average value and for an MRT value equal to that of the indoor air temperature, the PMV range was acceptable. Therefore, based on the results of the scenario analysis, the ability to measure the air velocity and the MRT were not considered when the TCC-V1 was designed. As such, the TCC-V1 was neither equipped with a black bulb thermometer nor an air velocity sensor for the present study.
The TCC-V1 we developed contained a controller, a communications unit, a monitoring device, and sensors. Their respective functions are as follows (Figure 13
Controller: the core of the TCC-V1. The controller computes the PMV index and the target temperature in real time based on data collected by the sensors.
Communication device: enables communication between the controller and the AC unit.
Monitoring device: confirms controller computational results by sending data to the controller. Although this function can be performed by the controller, the monitoring device acts as a data backup.
Sensors: measure temperature, humidity and whether the room is occupied and then sends the data to the controller.
Most Kuwait houses use traditional on/off controllers. The control sensor usually takes the form of an on/off thermostat and humidistat. On/off control is a simple and inexpensive way but is not accurate and quality [22
In this study, the PMV index was obtained from the ASHRAE standard 55 [28
] and a feedback method was used for temperature control in the TCC-V1 control. Feedback temperature control is an operation method that corrects the control amount to match the target temperature by returning the output signal to its input signal. The control method used in this study controlled the value of a variable by varying the target temperature with time to ensure that PMV = 0.
Operation of the TCC-V1 involved data communication between its individual devices (Figure 14
). The controller acted as the brain of the TCC-V1 by computing the PMV in real time based on data collected by the sensors. In this study, PMV was computed based on the temperature, humidity, MRT, air velocity, cloth value of people (CLO), and metabolic rate of people (MET). The target temperature was set such that PMV = 0, which is achieved by iterative calculation using the ASHRAE standard 55 and then transmitted to the AC unit. This process was continually repeated while the system was being operated. If the target temperature were to be adjusted manually, this value was sent to the controller and set as the target temperature. However, manual control was not tested in this study.