1、 Nunzio Cotrufo is a PhD student and Radu Zmeureanu is a professor in the Department of Building, Civil and Environmental Engineering, Concordia University, Montral, Qubec, Canada. Lorenzo Natale is a visiting student from the INSA, Strasbourg, France. Virtual Outdoor Air Flow Meter for the Ongoing
2、Commissioning of HVAC Systems: Lessons from a Case Study Building Nunzio Cotrufo Lorenzo Natale Radu Zmeureanu, Eng, PhD Member ASHRAE ABSTRACT The use of trend data from Building Energy Management Systems (BEMS) is a cost-effective solution to provide the necessary data for ongoing commissioning. T
3、his paper presents the use of three different virtual air flow meters, along with trend data, recorded every 15 minutes for the estimation of the outdoor air flow rate brought in the air-handling units. A virtual flow meter estimates the value of a physical variable in the heating, ventilating and a
4、ir-conditioning system where a physical sensor does not exist. For this purpose, a mathematical model is used along with measurements from available sensors in the system. In this study, the results are presented as the ratio of the outdoor air flow rate to the supply air flow rate. Three mathematic
5、al models are applied to the mixing box to calculate : (a) a simplified energy balance equation along with air temperature measurements, (b) the air mass, water mass and energy balance equations along with measurements of air temperature and relative humidity, and (c) the energy balance equation alo
6、ng with measurements of air temperature and relative humidity. The uncertainty propagation due to measurement errors is also estimated. The case study building is a new research center of a university in Montreal. The paper presents results from April 7 to May 12, 2014. For each mathematical model a
7、 regression model is developed to be used by the virtual flow meter. The regression models based on a and b give good estimates with R2 = 0.97, with the verification data set; while the regression model based on c has low performance with R2 = 0.19. Due to the error propagation through the detailed
8、equations, the uncertainty of estimates is much higher in the second and third case. The regression model based on a is the best candidate for the virtual air flow meter. INTRODUCTION The implementation of ongoing commissioning of HVAC systems is essential to guarantee high levels of energy performa
9、nce and human comfort in buildings. Although many manufacturers provide embedded sensors in equipment, those sensors are often not sufficient or adequate for the purpose of ongoing commissioning. Additional sensors might be needed at additional cost (Li et al. 2011). The use of virtual sensors can b
10、e an effective way to avoid new physical sensors installation. Yu et al. (2011) listed a few disadvantages in using physical air flow meters: they are fragile, their implementation and maintenance are expensive, and it is not always possible to install a physical air flow meter in an air-handling un
11、it (AHU) because of its compact structure. Nassif et al. (2003) developed a model for outdoor air flow rate prediction in AHUs. They concluded that a minimum temperature difference of a few degrees is required between the outdoor, mixed and return air temperatures to reduce the uncertainty of estima
12、tes of the outdoor air flow rate. Lee and Dexter (2005) presented a fuzzy sensor for the measurement of mixed air temperature in AHUs, which accounts for the influence of sensor bias error and location in the airstream. Zhao et al. (2012) developed a virtual condenser fouling sensor for chillers usi
13、ng the already imbedded sensors. Song et al. (2012) proposed a virtual water flow rate meter, and presented a method to estimate the virtual sensor uncertainty coming from the propagation of errors of two directly measured variables (pump differential pressure and pump speed) and the fitting error o
14、f pump electric input curve. Yang et al. (2014) developed a virtual outdoor air flow sensor for HVAC control by using measurements of damper opening and pressure drop through the damper and through the overall system. McDonald et al. (2014) developed a virtual chilled water flow meter, by considerin
15、g several scenarios of available number of sensors, and BEMS trend data. Zmeureanu and Vanderbrooke (2015) used, for the calculation of air flow rate, only those BEMS measurements for which the air temperature difference between the outdoor, mixed and return air temperatures are greater than the mea
16、surement uncertainty. The above studies proved that virtual sensors could be used for the air and water flow measurements, and therefore for the ongoing commissioning of existing HVAC systems. However, the uncertainty and error propagation are issues to be considered in the virtual sensors developme
17、nt. The present study aims to investigate the feasibility and effectiveness of three different regression models, to be used as virtual air flow sensor models, to predict the outdoor air flow rate in an AHU in the absence of such a physical sensor. The result is presented as the ratio of the outdoor
18、 air flow rate to the supply air flow rate: (1) where: oa is the outdoor air flow rate, and sa is the supply air flow rate. Regression models are trained using measurements over four weeks from April 7 to May 5, 2014, and validated with measurements of seven days, from May 6 to 12, 2014. As a direct
19、 measurement of is not available, the verification of regression models is performed by comparing (i) the calculated mixed air temperature, which was obtained from the predicted , and (ii) the measured mixed air temperature. CASE STUDY BUILDING The air side HVAC system, installed in a university bui
20、lding in Montral, is composed of two AHUs installed in parallel and equipped each with mixing box, humidifier, heating and cooling coils, two variable speed supply fans and two return fans (Figure 1). Mixing and exhaust dampers allow for the variation of amount of recirculated air while the outdoor
21、intake dampers are always open. When the mixing dampers are fully open, 100% of return air is recirculated. There is a heat recovery loop between the return and outdoor air streams. For the analysis period, the average supply and return air temperature is 14.8C (56.6F) and 23.3C (73.9F) respectively
22、, while the outdoor air temperature varies between -7.0C (19.4F) and 29.8C (85.6F). A separate exhaust system serves the laboratory ventilation hoods and washrooms. Air temperature and relative humidity are measured in several places in the AHUs every 15 minutes by the BEMS, along with the supply an
23、d return air flow rates. No recalibration of sensors has been implemented before analysis. Data from the BEMS were first pre-processed. Measurements taken when the recovery loop was working are excluded from the data set, in order to use only the outdoor air temperature that enters directly the mixi
24、ng box, since the preheated or precooled air is not measured after the heat recovery coil. However, if the air temperature after the preheating/precooling coil is measured, or estimated from the measurements on the glycol loop of heat recovery, then the preheating/precooling air temperature can be u
25、sed instead of outside air temperature. Figure 1 Schematic of the HVAC air side system and installed sensors for air temperature (T), relative humidity (RH) and air flow rate (M). METHODOLOGY Three different mathematical models for are proposed. a) Temperature Based . This model uses only the sensib
26、le energy balance equation that is applied to the mixing box, using only the dry-bulb air temperature measurements (Equation 2): (2) where: Tma is the average mixed air temperature of two sensors, Toa is the outdoor air temperature, and Trca is the average recirculated air temperature of two sensors
27、. Since the return air temperature (Tra) is measured before the return fans, Trca was calculated as Tra + 1.8C (+ 3.2F), as measured by Zibin (2014). A polynomial second order regression model was developed based on the regressor term Tma Toa to predict t (Table 2). An empirical trial shows that the
28、 term Tma Toa is the highest correlated with ratio t, compared to other candidate regressors: Tma, Toa, Tma - Trca, Toa - Trca. Thus, the adopted regression model is intended as a black box data-driven model. b) Three Balance Equations Based . This model uses the energy balance equation (3), the wat
29、er mass balance equation (4) and the air mass balance equation (5). (3) (4) (5) where: hma is the enthalpy of the air at mixing condition; hoa is the outdoor air enthalpy; hrca is the recirculated air enthalpy; xrca is the humidity ratio, and rca is the mass flow rate of the recirculated air. The sy
30、stem of three equations has three unknowns: the outdoor air flow rate, the recirculated air flow rate, and the mixed air humidity ratio. Solving the system of equations, is obtained as follows: (6) where: Cp,a is the dry air specific heat at constant pressure; Cp,v is the water vapor specific heat a
31、t constant pressure; hfg is the water heat of vaporization. Similarly to the previous method, a regression model is developed in terms of Tma Toa (Table 2). c) Energy Balance Based . The air humidity ratio after the mixing box (which is unknown, as an air humidity sensor after the mixing box is not
32、installed, see Figure 1) is assumed to be equal to the supply air humidity ratio, and then the mixed air enthalpy is calculated by using the measured mixed air temperature. This assumption is valid under the following two conditions: 1. There is no humidification, as indicated by the humidifier valv
33、e modulation equal to 0%. 2. No condensation occurs between mixing and supply points. The second condition is imposed by considering the saturation degree of air at the cooling coil. Measurements for which the saturation degree was close to 100% have been excluded from the dataset as well as measure
34、ments taken when the air was humidified. As for the previous method (b), the outdoor and recirculated air enthalpy and humidity ratio are evaluated by using the measured air temperature and relative humidity. The d is thus given by: (7) Mixed air temperature has been derived from d, similarly to the
35、 verification strategy, and compared to mixed air temperature measurements. Derived Tma showed to overestimate Tma measurements, with an average temperature difference of 3.05C. At this step an iterative process was used to find the that gives the best fit for the d calculated by equation 7. For def
36、ferent , Tma has been derived from d and compared to Tma measured. The d variation resulting in the highest R2 index between derived and measured Tma has been selected. The optimized d (d*) is given by equation 7 plus = 0.20. For approach c, a multivariate regression model is developed using four re
37、gressors (outdoor air relative humidity, RHoa; mixed air temperature, Tma; outdoor air enthalpy, hoa; and return air enthalpy, hra), which resulted in the highest Pearsons coefficients of correlation. Table 2 shows the three models trained with a four-week data set (April 7 May 5). For model c no be
38、tter prediction capabilities is given by non-linear models, thus, a multivariate linear model is preferred. Those regression models use T in degree Celsius, RH in percentage, and h in kilojoule per kilogram. Table 2 Regression Model Formulations models Formulation Model a: t t = 1.004 - 0.071( Tma T
39、oa) - 0.002( Tma Toa)2 Model b: es es = 1.002 - 0.079( Tma Toa) - 0.002( Tma Toa)2 Model c: d d = 1.598 0.001 RHoa 0.055 Tma + 0.0155 hoa 0.009 hra The regression models are developed for the training period, and then applied to the validation data set (May 6-12). The idea is to develop prediction m
40、odels which need a reduced number of input variables (sensors). Short-term measurements for model development could also be used to collect data and calculate the ratio with equations 2, 6 and 7. Once the models are developed, only two air temperature measurements are needed for models a and b, to i
41、mplement the virtual air flow sensor; in the case of model c, three air temperatures (Tma, Toa and Tra) and two relative humidity measurements (RHoa and RHra) are needed. The advantage of reducing the number of sensors is greater for models b and c. For model a, the number of sensors is reduced only
42、 from three to two sensors. Verification As a direct measurement of is not available, the effectiveness of regression models is verified by comparing the mixed air temperature predicted by using from those models with the directly measured mixed air temperature. The mixed air temperature has been de
43、rived from as follows: (8) where: hma is the enthalpy of the mixed air enthalpy, derived from calculated value along with equation 3; xma is the mixed air humidity ratio, derived from calculated values along with equation 4. Uncertainty Analysis Measurements are always affected by a degree of uncert
44、ainty, due to two components: the fixed (bias) component and the random component (ASHRAE 2005). The overall uncertainty Ux of a measurement x is given by: (9) where: Bx is the bias (fixed) measure error, given by manufacturer documentation; Sx is the standard deviation; t is the critical t-value at
45、 a 95% confidence level, t = 1.645; n is the sample size. As the sample size is n = 2688, and the maximum n is equal to 120 in t-tables (Reddy, 2011), the case of infinite number of points sample is considered. Table 3 resumes the input values to evaluate measurement uncertainty for: supply and retu
46、rn air volume flow rate (Vsa , Vra), outdoor, return, mixed and supply air temperature (Toa , Tra , Tma , Tsa); and outdoor, supply and return air relative humidity (RHsa , RHra). The uncertainty propagation from direct measured variables and derived parameters has been estimated independently for b
47、oth the components and then combined (ASHRAE 2005), and presented in Table 4. Table 3. Component Values of Measurement Uncertainty Vsa , Vra Toa Tra , Tma , Tsa RHsa , RHra Bias (B) 10% (*) 0.3C 0.6C 3%(*) Standard deviation (S) 32 L/s 0.1C 0.08C 18%(*) (*) percentage on the full range of variation
48、countable by the sensor. RESULTS Table 4 presents the mean and standard deviation values of obtained with the three models along with uncertainty values. The results obtained through the models b and c show high uncertainties, due to the errors propagation. In the case of model c, considering that t
49、akes values between 0 and 1, the uncertainty is more than 10 times greater than the range of variation of ; hence this model is not useful for practical purposes. Table 4. Ratio : Mean Value, Standard Deviation and Uncertainty Mathematical model Mean value - Std - Bias error - Random error - Overall uncertainty - Model a: t 0.71 0.18 0.09 0.004 0.09 Model b: es 0.71 0.18 0.95 0.090 0.96 Model c: d 0.76 0.09 10.0 10.0 10.0 Regression Models: Development and Verificatio
