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A PRINCIPAL COMPONENT ANALYSIS-BASED APPROACH FOR THE ONGOING COMMISSIONING OF CENTRIFUGAL CHILLERS N. Cotrufo; R. Zmeureanu Department of Building, Civil and Environmental Engineering, Centre for Zero
A PRINCIPAL COMPONENT ANALYSIS-BASED APPROACH FOR THE ONGOING COMMISSIONING OF CENTRIFUGAL CHILLERS N. Cotrufo; R. Zmeureanu Department of Building, Civil and Environmental Engineering, Centre for Zero Energy Building Studies, Concordia University, 1455 de Maisonneuve West, Montréal, Québec, Canada H3G 1M8 ABSTRACT Ongoing commissioning (OCx) of HVAC systems aims to continuously monitor and analyse the building systems operation to detect faults and performance degradation in terms of operation costs, energy use and demand as well as quality of indoor environment. A huge amount of relevant operation data are collected and stored by the Building Automated System (BAS). Hence the extraction of information through data mining is a challenging aspect. Anomaly detection, clustering, classification and regression analysis are examples of data mining techniques. Regression techniques are probably the most used to identify relationships between measured data, and between indices of performance and data. Artificial Neural Network (ANN) models and Support Vector Method (SVM) are other examples of statistical learning techniques. This paper presents the use of Principal Component Analysis (PCA) for the OCx of chillers in a large cooling plant. PCA allows to drastically reduce the number of variables, preserving most of the information included in the original data set. A PCA based commissioning approach has been applied in this study to highlight changes in chiller operation level through the years, detect unexpected measurement values and address commissioning effort to solve them. Measurements have been collected by the BAS from two centrifugal chillers, of 3165 kw (900 tons) cooling capacity each, over six cooling seasons (May to September, from 2009 to 2014). The Principal Components (PCs) visualization have allowed to identify different operation patterns, supporting clustering and classification techniques implementation. The effectiveness of PC visualization is due to the PCA capability to reduce the number of variables to be used as regressors, and to represent, in a 2-D PCbased space, a data set made of several inter-correlated variables. Visualization techniques are considered very important to increase awareness and knowledge of building operators about equipment operation. Keywords: Principal Component Analysis, Ongoing Commissioning, HVAC systems INTRODUCTION The use of Principal Component Analysis (PCA) for OCx of HVAC systems was not exploited enough in the recent past. PCA based detection and diagnosis methods have been developed for AHUs and AHU sensor faults, Wang and Xiao [1] and Li and Wen [2]. In [3] a PCA based linear regression model has been developed to predict electricity consumption in an office building. All the above cited studies highlight the PCA capability to reduce large number of variables to few new components while maintaining most of the information. In this paper, PCA is applied to the BAS trend data from a cooling plant to identify patterns, implement OCx and visualize variations in chiller operation performance over the years. METHOD PCA transformation, applied to a data set X of j inter-correlated variables and i observations, produces a new set F of j independent variables, the Principal Components (PCs), which contains the same original data set information. F elements (f i,j ), named scores, are the CISBAT September 9-11, Lausanne, Switzerland 407 coordinates of the original data along the PCs, and are given by linear combination (1) of the x i,j Original Variables (OVs) with the coefficient matrix Q, made of q j,j elements [4]. Q is evaluated by PCA transformation. f i,j = x i,1 q 1,j + x i,2 q 2,j + + x i,j-1 q j-1,j + x i,j q j,j (1) Dealing with variables of different units and range of variation, some sort of data normalization is needed [5]. Here, given a data set X = [i x j], of i observations and j variables, normalization goes through the average column values (m j ), and the j columns standard deviations (σ j ): zx i = x i m i σ i (2) Variables reduction results from the distribution of explained variance along the PCs (figure 1). The first 2-3 PCs account together for the most of the original data set variance. Chiller #2 operation data from 2010 to 2014 have been compared against a 2009 data based threshold. Data sets have been normalized (3), and projected into a 2-D PCs based space (4), with reference to 2009 data PCA transformation: zx 2010 = X 2010 mx i,2009 σx i,2009 (3) F 2010 = zx 2010 x Q 2009 (4) where: zx 2010 is the 2010 normalized data set; X 2010 is the original 2010 data set; mx i,2009 is the 2009 data set mean value vector; σx i,2009 is the 2009 data set standard deviation vector; F 2010 is the 2010 matrix of scores; Q 2009 is the 2009 matrix of PCA coefficients. An elliptical threshold condition has been formulated (5), based on the Gaussian approximation of scores distribution along PCs. Hence, around 95% of scores is expected to be within the interval [-2 σ pc ; 2 σ pc ] around the mean value. y b 2 (1 x2 a 2) ; a = 2 σ pc1 ; b = 2 σ pc2 (5) RESULTS This study focuses on a cooling plant installed in a University Campus in Montreal, QC. It consists of two centrifugal chillers (CH-1 and CH-2) of 3165 kw (900 tons) cooling capacity each. When one chiller is not sufficient to match the thermal load, the second one starts, working simultaneously with the first chiller. Chilled water is circulated by constant speed pumps of around 86.5 L/s [6]. The BAS collected measurements each 15 minutes. Data set includes 9,408 measurements per cooling season, over 14 weeks, for four different operation modes: a) both the chillers (CH-1 and CH-2) work at the same time; b) only CH-1 works; c) only CH-2 works; d) no chiller. We considered nine variables at plant level: chilled water flow rate from the central plant, ṁ chw ; difference of return supply chilled water temperature, ΔT CP ; electrical power input to CH-1 and CH-2, E CH-1 and E CH-2 ; water temperature difference CH 1 at the evaporator of CH-1 and CH-2, ΔT CHW and ΔT CH 2 CHW ; water temperature difference at CH 1 the condenser of CH-1 and CH-2, ΔT CND and ΔT CH 2 CND ; outdoor air temperature, T OA. A preliminary PCA based analysis has been conducted at plant level. Coefficient matrix Q with the projection coefficients for the first two PCs are given in (6). Equation (7) gives an example of i score calculation for PC # CISBAT September 9-11, Lausanne, Switzerland (6) f i,1 = x i, x i, x i,j-1 (-0.196) + x i,j (7) Figure 1 shows the cumulative original data set variance explained by PCs. The first two PCs account together for about 93% of the original data set information. Figure 2 shows the scores from 2009 data set represented in a 2-D PCs based space. It is worth to notice that PCA distinguishes different operation modes through well-defined point clouds, which can be useful to identify normal operation modes and detect abnormal situations. The case of CH-2 working alone have been considered for a PCA-based analysis. A threshold condition, developed based on 2009 data set, has been applied to data over six cooling seasons to highlight changes in CH-2 operation level. A separate five OVs list has been considered for chiller analysis: electrical power input, E CH-2 [kw]; outdoor air temperature, T OA [ºC]; CH 2 CH 2 difference of water temperature across the evaporator and condenser, ΔT CHW and ΔT CND [ºC]; chilled water flow rate, ṁ chw [L/s] (table 1). Figure 1: Cumulative variance explained by PCs, cooling plant data set from summer Figure 2: Cooling plant 2009 data set scores plotted in a 2-D PC based space. E CH-2 [kw] T OA [ C] ΔT CHW [ C] ΔT CND [ C] ṁ chw [L/s] Range of variation Mean value Standard deviation Table 1. Selected original variables of summer 2009 for the PCA of chiller CH-2 PC #1 and PC #2 together account for about 92% of information in the original CH-2 data set. In Figure 3 are represented the OV axes in a 2-D PC based space, given plotting the first two column of the coefficient matrix data scores for PC #1 and #2 are represented in Figure CISBAT September 9-11, Lausanne, Switzerland 409 4. Any interpretation of scores distribution should be based on OV axes orientation. Assuming a Gaussian distribution of scores along PC axes, around 95% of scores are expected to be within the range [-2 σ; 2 σ]. For PC #1, 97% of the scores is in the range [- 2 σ 1 ; 2 σ 1 ] while, for PC #2, 98% of the scores is within the range [-2 σ 2 ; 2 σ 2 ]. Figure 5 shows results from applying 2009 threshold condition to following cooling season data sets. Results are given in terms of percentage of data points per year, which comply with 2009 threshold. Over six years, the percentage of data points within the threshold decreases from 93.3% (2009) to 83.7% (2014). The annual mean values of the PC #1 and PC #2 through the years (Figure 6) moved from the origin, which could indicate the change of annual mean operation data. Figure 3. CH-2 OV axes projected on a 2-D principal component based space. Figure data sample plotted against the threshold in a 2-D PCs based space. Figure 5. Percentage of data points per year which comply with the 2009 based threshold condition. Figure 6. Variation of annual mean values of PC #1 and #2, 2009 to DISCUSSION The threshold condition can give information about quantitative aspects in operation changes. The trend of percentage of outliers per year highlights that some change in operation occurred (figure 5), although it is not necessary to be considered as degradation. We name this phase detection. Otherwise, in order to understand the causes of operation changes, we have to deal with the OV axes orientation (figure 3). The more a point is located far from the zero- 410 CISBAT September 9-11, Lausanne, Switzerland value of the j-variable axis, the more an unexpected j-variable value characterizes that point. For each outliers, the distance from the zero-value of each variable axis has been evaluated. Table 2 gives, for 2014 scores, the statistics of the most influential OV per outlier. Variables Count [-] Percent [%] 1 Electrical power input Outdoor air temperature Difference of water temperature across the evaporator Difference of water temperature across the condenser Chilled water flow rate after the two chillers Table 2. Frequency of the most influential original variables of 2014 data set Over 639 outliers have been detected for 2014 data set. According to table 2, the outdoor air temperature and the chilled water flow rate are the outliers most influential OVs. The outdoor air temperature is accountable for 97.2% of the outliers, while the remaining 2.8% are due to the chilled water flow rate. In this case, the commissioning efforts focus on those two OVs variables. A detailed investigation revealed that the outdoor air temperature measurements had fast and abnormal temperature variation within one time step (15 minutes). That was due to two elements: the difference in outdoor air temperature between 2009 and 2014, and the need for re-calibration and re-location of the air temperature sensor. PCA showed to be effective in the detection of abnormal values. Figure data set in a 2-D PC based space against the reference threshold. The axis of chilled water flow rate is showed. Figure modified data set in a 2-D PC based space against the reference threshold. The axis of chilled water flow rate is showed. The expected chilled water flow rate, for only one chiller works, is around 86.5 L/s. Several times during the summer of 2014, some isolated, unexpected values, have been recorded (figure 7). A test is simulated by excluding the unexpected chilled flow rate measurements from the data set. PCA applied to modified data set shows that ṁ chw is not anymore responsible for any of the remaining outliers (figure 8). Again, the PCA based approach correctly detected abnormal values and addressed efforts in the right direction. CISBAT September 9-11, Lausanne, Switzerland 411 CONCLUSION PCA has been used to study a cooling plant and its changes in performance through six consecutively summer seasons. A threshold definition has been given based on 2009 reference data set, and changes in the equipment performance have been highlighted in terms of outliers from the threshold, which is intended as representative of proper chiller operation. The proposed approach proved to effectively capture the variation in percentage of points which comply with the threshold condition, from 93.3 % in 2009 to 83.7 % in The chiller s performance seems to change, although the change is not qualified as a system degradation. Also, the proposed method allowed to identify the influential OVs for outliers in 2014, effectively addressing efforts to identify faults in chiller operation. The possibility to reduce to two principal components a bigger number of original variables allows to display 2-D representations of the equipment performance. This would increase building operator s awareness and knowledge in HVAC system operation. ACKNOWLEDGEMENT The authors acknowledge the support from the NSERC Smart Net Zero Energy Buildings Network and from the Faculty of Engineering and Computer Science, Concordia University, Montreal Canada. REFERENCES 1. Wang, S., & Xiao, F.: Detection and diagnosis of AHU sensor faults using principal component analysis method. Energy Conversion and Management, 45(17), , 2004; 2. Li, S., & Wen, J.: A model-based fault detection and diagnostic methodology based on PCA method and wavelet transform. Energy and Buildings, 68, 63-71, 2014; 3. Lam, J. C., Wan, K. K., Cheung, K., & Yang, L.: Principal component analysis of electricity use in office buildings. Energy and Buildings, 40(5), , 2008; 4. Abdi, H., & Williams, L. J.: Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics, 2(4), , 2010; 5. Reddy, T. A.: Applied data analysis and modeling for energy engineers and scientists Springer Science & Business Media, 2011; 6. Monfet, D.: New Ongoing Commissioning Approach of Central Plants: Methodology and Case Study, PhD Thesis, Concordia University, Montreal, QC, CISBAT September 9-11, Lausanne, Switzerland
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