Using Multiple Regression Analysis to Develop Electricity Consumption Indicators for Public Schools

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1 Using Mutipe Regression Anaysis to Deveop Eectricity Consumption Indicators for Pubic Schoos CorJitz NO&I, Lund Institute of Technoogy, Sweden Jurek Pyrko, Lund Institute of Technoogy, Sweden ABSTRACT This paper deas with probems of using Mutipe Linear Regression (MLR) to deveop Eectricity Consumption Indicators (ECIs) for Swedish schoo buidings. Annua, monthy, daiy, houry, and peak ECIs are deveoped from whoe buiding houry oad data measured during one year. 26 schoos with a tota annua eectricity consumption of 17.5 GWh and a tota foor area of m2 are anaysed in this study. A schoos are mainy heated by district heating athough some of them use eectrica heating to a minor extent. By using the MLR approach, it is possibe to introduce variabes accounting for factors that can expain the eectricity consumption in schoo buidings. Such factors are sports centre and kitchen activities. This procedure eiminates the need of severa subgroups, ike schoos with or without kitchens. The methodoogy is easy to use for simiar studies and provides important information about factors affecting the eectricity consumption in schoos. Introduction Knowedge of various consumers eectricity consumption patterns and eectricity consumption indicators is required for (a) deveoping toos for energy auditors, (b) identifying operationa and maintenance probems (Lyberg 1987). The number of Swedish studies on eectricity consumption in commercia and pubic buidings is very imited. The Swedish eectric utiity Vattenfa carried out in 1991 the most extensive study of Swedish commercia and pubic buidings hitherto, where schoos were incuded in a category caed Education (Vattenfa 1992). Ony the annua eectricity consumption (both for entire buiding and for end-uses) was studied; the oad aspect was not considered. The average annua EC1 for the Education category was estimated to 53 kwh/m2yr. The first Swedish oad shape study on commercia and pubic buidings was carried out in This study presents typica oad shapes for approximatey 40 different types of buidings, ranging from one-famiy houses to commercia and industria buidings (SEF 1991). The oad shapes are presented in non-dimensiona terms (reated to annua eectricity consumption). Partiay, this study aso deas with ECIs and the average annua EC1 is determined to 42.8 kwh/m2yr. Another oad shape study on commercia and pubic buidings presents non-dimensiona oad shapes (reated to annua eectricity consumption) for six categories of Swedish commercia buidings and was carried out at the Lund Institute of Technoogy in 1996 (Nor&n 1997). Severa oad shape studies have been performed in Norway by EFI, however these studies focus on buidings using eectric resistance heating. The resuts are aso presented as reative oad shapes in some cases (Livik & Rismark 1990; Feiberg & Livik 1993; Livik 1987). Many studies have been carried out in the USA by the Lawrence Berkeey Nationa Laboratory and severa other research groups (Akbari et a. 1989, 1991). Using Mutipe Regression Anaysis to Deveop Eectricity Consumption Indicators

2 Background Traditionay, ECIs are cacuated as mean vaues and standard deviations. The deviations are often high, making it very difficut to determine what is a norma consumption. Many different kinds of features are mixed within the same category. The schoo category covers a kinds of schoos, from sma schoos with no mechanica ventiation up to arge schoos with a mechanica ventiation and arge kitchens. In a pre-study during 1996, 44 schoos were audited and the annua ECIs were anaysed. High variations were observed (22-12 kwh/mz*yr) but different instaations and activities can expain some of them. The mean EC1 was 61 kwh/m2*yr with an associated standard deviation of 22 kwh/m2*yr, and it is difficut to draw any concusions based on these figures with such high deviations. A coarse cassification can be done according to Tabe 1. Tabe 1. Resuts from Pre-study on Eectricity Consumption in Schoo Buidings 1 Sma schoos (<o00 m*) with no mechanica ventiation kwh/m*yr ( Schoos with ony mechanica exhaust air ventiation kwh/m*yr 1 Schoos with mechanica suppy and exhaust air ventiation. With or without sports centre, no kitchen Schoos with mechanica suppy and exhaust air ventiation. With or without sports centre, with kitchen Schoos with suspected operationa probems kwh/m*yr kwh/m*.yr >OO kwh/m*yr Another probem with traditiona ECIs is that they in most cases are based on annua figures which are insufficient for identification of operationa and maintenance probems. A rough estimation can be made but there is no possibiity to identify time periods with suspicious consumption profies. Another disadvantage with annua ECIs is that they do not provide any information about the factors affecting the eectricity consumption. Methodoogy The methodoogy can be described in the foowing three steps: Determination of features possibe to incude in the study, audits and inquiries and anaysis of measured oad data. The number of features incuded in the study was imited by the number of objects where one-hour measurements of the eectricity consumption are performed. 26 schoos with a tota foor area of m* and a tota annua eectricity consumption of 17.5 GWh were incuded. Anaysis of Measured Data At first, the measured data were checked for measurement errors by dividing data into three subgroups depending on day-type. Three day-types were identified: the measured Standard schoodays (172 days) Weekends and major hoidays (113 days) Weekdays during off-schoo periods, ike summer and Christmas (80 days) Nor&z and Pyrko

3 Hypothesis. The specific eectricity consumption (W/m*., kwh/m2) is presumed to be a function of the parameters isted beow. Severa other parameters can be important but these are discussed ater. Compared to other schoos, schoos with a arge kitchen show a higher specific eectrica demand during at east parts of the day. The demand eve depends on the ratio between the number of meas cooked daiy and the foor area of the schoo. Compared to other schoos, schoos with a arge sports centre show a higher specific eectrica demand at east during parts of the day, especiay during the evening. The demand eve depends on the ratio between the sports centre area and the foor area of the schoo. Compared to other schoos, secondary schoos show a higher specific eectrica demand at east during parts of the day. Compared to other schoos, schoos with a high popuation density (high ratio persons/m*) show a higher specific eectrica demand during at east parts of the day. Initia anaysis work. The first step was to make an initia anaysis in order to remove the parameters that showed no correation with the eectricity consumption. Athough some parameters seemed to have a significant infuence on the eectricity consumption in this initia anaysis, some of them were found to be non-significant during certain time periods. Another reason for excuding a parameter was high or unreasonabe variations from hour to hour, as occurred with the Sports centre parameter during daytime (6 a.m. - 3 p.m. on standard schoodays) and the Popuation density parameter (a hours during a days). The regression coefficient varied greaty and quite often the sign changed from hour to hour indicating that the parameter did not provide any information about actua operating conditions during these hours. It was considered correct not to incude the parameters in the anaysis during these time periods. Houry eectricity consumption. The houry eectricity consumption was anaysed by introducing factors that according to the hypothesis are affecting the eectricity consumption. The Houry Eectricity Consumption Indicator, HECI, was defined as: HECI = A, + K,.A, + K2.A, + D,.A3 -t T-A, 0%. 1) Where: K, K2 D3 = Number of meas cooked daiy in the kitchen (-/m*) = Reationship between sports centre area and foor area = Dummy variabe (DV), 1 for secondary schoos, otherwise 0 = Daiy mean outdoor temperature ( C> = Regression coefficients The regression was carried out for each of the hours -24 during the three different daytypes, totay 72 regressions. Data from a the 26 schoo.s were used in every regression. This means that the number of data points in each regression equaed the number of days for the specific day-type mutipied by 26, e.g. 26*172=4472 data points for the standard weekday case, 26*113=2938 data points for the weekend/hoiday case and 26*80=2080 data points for the off-schoo period. The reationship can be written with matrices: Y=XA where the vector Y contains the measured oad data normaised by the buiding foor area. The vector Y is then of the dimension 4472x1 in the standard weekday case. The X matrix contains the parameters iste,d above (1, K,, K,, D, and T), e.g. X is of the Using Mutipe Regression Anaysis to LPeveop Eectricity Consumption Indicators

4 dimension 4472x5 for the standard weekday case. The vector A contains the unknown regression coefficients (&-A,) which wi be estimated and is of the dimension 5x 1. Daiy, monthy and annua specific eectricity consumption. Daiy, monthy and annua ECIs were computed as sums of the houry ECIs, using the number of different day-types for monthy and annua eectricity consumption. Anaysis of the annua specific peak eectrica demand. The three highest demands for each schoo were used as response variabes. The reason for not choosing ony the annua peak demand for each object was that ony one year of oad data was avaiabe, there was a possibiity that the peak demand was caused by specia circumstances and is not representative of a schoo buiding. The Peak Eectricity Consumption Indicator, PECI, was defined as: PECI = A, + K,.A, + 2) Where: K, = Number of meas cooked daiy in the kitchen = DV, 1 for secondary schoos, otherwise 0 Z-A,, A3 = Regression coefficients (-/m*) If this reationship is written as Y=XA, then the vector Y contains the measured peak demands and is of dimension 78x1. The X matrix contains the parameters isted above (1, K, and DJ and is of dimension 78x3. The vector A is of dimension 3x1 and contains the unknown regression coefficients (A,,-A, and AJ which wi be estimated. Load factor. The oad factor, LF, was defined as: LF= Annua eectricity consumption (kwh) Annua peak eectrica dernand (kw).8760 (h) Statistica anaysis. The anaysis was performed on computer, using the software MINITAB. When using the ordinary east squares approach, a potentia probem is muticoinearity, e.g. when the correation among the independent variabes is high. A rue of thumb is that muticoinearity becomes a potentia probem when the partia correation between <any two independent variabes is higher than the partia correation between any of the independent variabes and the response variabe (Draper & Smith 1981). The highest correation exists between the Sports centre and the Type of schoo variabe and if the rue of thumb shoud be foowed, muticoinearity coud be a probem during hour 16, since it was the ony period that both variabes were used in the anaysis. It was considered to have a minor effect on the resuts and was not investigated any further but the potentia effects of muticoinearity must aways be taken into consideration. Resuts The resuts are shown in Tabe 2 to Tabe 6. NS denotes non-significance or that the resuts from the regression do not foow the hypothesis, i.e., that variabe is not incuded in the regression anaysis during these time periods. The resuts are aso shown in Figure 1 and Figure 2. The foowing assumptions were used when presenting the oad shapes graphicay: North and Pyrko

5 The ratio between number of meas cooked daiy and gross foor area is 0.2 for the Primary schoo with kitchen oad shape. The ratio between sports centre area and gross foor area is 0.10 for the Primary schoo with sports centre oad shape. Tabe 2. Resuts for Standard Weekday Houry Eectricity Consumption Hour 1 A,, W/m 1 A, W/(-/mz) 1 A, W/(m /m ) 1 A3 W/m2 1 A, W/m*. C R2 % NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS 20.0 NS NS 20.3 NS NS 20.0 NS NS 11.7 NS NS NS NS NS NS NS Figure 1. Load Shapes for Different Types of Schoo Buidings, Weekdays Using Mutipe Regression Anaysis to Deveop Eectricity Consumption Indicators

6 Tabe 3. Resuts for Weekend and Hoiday Houry Eectricity Consumption Hour T A, W/m Weekends A A W/m. C R2 % T Hoidavs K W/m A 4 W/m2. C R* % : f : : I I : I I : : : : :! : : : : : I : I HCMr Figure 2. Load Shapes for Schoo Buiding, Weekends and Hoidays Tabe 4. Resuts for the Annua Peak Demand & W/m2 A, W/(-/m ) zqzq Nor& and Pyrko

7 If the vaues in Tabe 2 are compared to the resuts in Tabe 4, it can be noticed that the major difference is the kitchen parameter where the highest houry EC1 is 21.5 W/(-/m*) but 33.7 W/(-/m*) for the peak demand ECI, an increase of 50%. This is an actua condition in the schoos with kitchens: the peak demand is substantiay higher compared to other demands during the year and high day-today demand variations exist in the schoos with kitchens, compared to the schoos without kitchens. The annua peak demand in secondary schoos was found to be higher than in primary schoos and this depends on the vocationa activities in many of the secondary schoos. ~~1 Tabe 5. Resuts for Daiy Eectricity Consumption SWd = Standard Weekdays; We = Weekends; Hd := Hoidays In order to cacuate an annua eectricity consumption, one must know the number of different day-types and the temperature profie for the year. If the figures from 1996 are used, this eads to the resuts in Tabe 6. Tabe Monthy and Annua Eectricity Consumption Month A, kwhm2* A, kwh/(-/m2) A, kwh/(m2/m2) A3 kwhjmz January February March Apri May June Juy August September October November December Tota Annua eectricity consumption is ony sighty affected by the different factors but for the case with schoos with kitchens it must be noticed that the kitchen parameter ony accounts for the kitchen equipment. The kitchen aso incudes severa other eectrica demanding equipment, such as ighting and ventiation. This part of the kitchen eectricity consumption is incuded in the A,,-term. The anaysis of the oad factor showed a noticeabe difference between schoos with and without kitchens; the resuts are shown for a 26 schoos in Figure 3. Six of the nine schoos with kitchens have a LF ower than 0.3 and among these there are four schoos with arge kitchens and two sma schoos (~6000 m*) aso equipped with a kitchen. One schoo has a sighty higher LF (0.3). The remaining two, which are quite arge schoos (>O 000 m*) and ony cook food for the individua schoo, have LF 0.34 and 0.36 respectivey. Using Mutipe Regression Anaysis to Deveop Eectricity Consumption Indicators

8 Figure 3. Resuts for the Load Factor (LF) for a 26 schoos This is an expected observation since the schoos with arge kitchens were found to have substantia higher peak eectrica demands compared to other schoos. Among the schoos with LF ower than 0.35, four of the six secondary schoos were found and these observations were aso expected since the annua peak demand was found to be higher in secondary schoos when compared to primary schoos. It is aso noticeabe that a but four schoos have LF ower than 0.4, whie these four show LF between This was further examined for one of the schoos and it was found that the ventiation system operated 24 hours a day, causing a high annua eectricity consumption. Discussion on Reasons for Deviations The poorest resuts were found at night (hrs 23-06) and some important reasons were identified. In some schoos, as much as 50% (100% in one case) of the ventiation system is in operation at night for different reasons, whie other schoos shut off the ventiation system at night. In some schoos the haway ighting is eft on at night to prevent burgary. Schoos with arge kitchens were at first presumed to show a higher consumption at night due to the refrigeration equipment running day and night, but this coud not be identified with the proposed method. During weekends and hoidays no correation between the described parameters (except for outdoor temperature) and the eectricity consumption was found and the resuts were very poor during these day-types; many activities take pace, not ony sports centre activities. During eary morning hours (hrs 06-OS), staff and pupis arrive at different times in different schoos, causing eary morning deviations. During hours 09-14, the highest deviations were found in schoos with kitchens, since cooking power varies with the food prepared. Substantia day-to-day variations were aso observed in some of the secondary schoos. The major factor may be varying eectricity demand. Afternoon and evening deviations were highest for schoos equipped with sports centres, which may or may not be open at night. Another important source of deviations is the fact that a schoos are not efficienty operated and this aso affects the resut to some extent; in this study three schoos with suspicious consumption patterns were found. This does not mean that the remaining 23 schoos are efficienty operated Nor-h and Pyrko

9 Verification Measurements from a schoo buiding ocated in the south of Sweden were used to verity the resuts. This 10,630 m* primary schoo hods approximatey 800 pupis and 100 members of staff and is equipped with 1164 m* sports centre. District heating is used for heating and hot water, and approximatey 1100 meas are cooked every day. This gives the foowing parameters in Eq. 1 and 2: K,=O. 10, K,=O. 11 and D,=O, the daiy outdoor temperature varies between 0.3 C and 2.8 C during the four days. The schoo was buit in 1967 and was retrofitted in the end of 1996 (finished / -96) when the od ventiation system was repaced. Houry measurements were carried out after the retrofitting in December 1996 and these data were used for verification. Figure 4 shows the measured demand compared to the demand that was cacuated using the ECIs from this study Tuesday 0. -mmr.a.=$! D!2 c ;; k-z Hour Wednesday.-rnrnboa,=~ 2 k z ;; R Hour A g 15. ] o- 5-* Measured Friday o-::::! I::: ::: I ::::: :::+ -mmr.cn~m 7 2 $ n & 2 Hour Figure 4. Measured Load Shapes and ECIs for Tuesday Friday The night-time demand is approximatey W/m* higher than predicted by the ECIs but monthy eectricity consumption data show a substantiay ower consumption during off-peak hours after / Before / 1997, the monthy off-peak consumption was MWh/month but is now reduced to MWh/month and this indicates an inefficient night-time and weekend consumption before the retrofitting. The tota monthy consumption during hours is aso reduced after /-1997, but not as much as the consumption during off-peak hours, indicating that the day-time consumption aso was somewhat inefficient before the retrofitting. Why this reduction did not occur immediatey after the retrofitting is not competey known; but the most probabe cause is that the tina adjustments of the ventiation system was done during Christmas 1996, and therefore, the eectricity consumption just after the retrofitting was amost unaffected. Off-peak hours are defined as 10 p.m. - 6 a.m. during weekdays and a hours during the weekend Using Mutipe Regression Anaysis to Deveop Eectricity Conwmption Indicators

10 The peak demand did not change after the retrofitting. Measured peak demand is 25.8 W/m* and the peak EC1 gives 25.0 W/m*. Measured annua eectricity consumption before the retrofitting was 70.6 kwh/m* and the ECIs gave 68 kwh/m*. This was surprising since the houry ECIs indicated high consumption, but this schoo is amost entirey cosed during summer hoidays and this is the most important singe reason for the simiarities between the annua ECIs and the differences between the houry ECIs. It was more difficut to verify the other parameters but for the case with the kitchen parameter there are oad data from a buiding which contains a schoo kitchen. The mean annua oad shape is shown together with the kitchen parameter in Figure 5. Athough the measurements not ony incude cooking equipment, some observations regarding the characteristics of the oad shapes can be made: Highest daiy demands occurs around 8 a.m. and 9 a.m. Between 9 a.m. and 11 a.m. the demand decreases rapidy. At 11 a.m. there is a temporariy dip foowed by a sight increase at 12 a.m. After 12 a.m. the demand decreases rapidy.,,,, -9. I II I HOW Figure 5. Measured Load Shape from a Schoo Buiding with Kitchen, Compared to Resuts from this Study No major concusions shoud be drawn except that the kitchen parameter has the same characteristics as a measured oad shape from a schoo kitchen. There are major differences between 4 p.m. and 7 a.m. but it is important to remember that the measured oad shape aso incudes indoor ighting, ventiation, pumps and other equipment. The reason for not using the measured data in the anaysis is that the measured data are not representative for the whoe schoo, the buiding is a part of this schoo but cooking is the main activity. Comparisons to Other Studies The resuts from this study are compared to the resuts from three other studies, two Swedish studies (Not-en 1997; SEF 1991) and one American study (Akbari et a. 1991). There are some differences between the three studies: two of them present non-dimensiona oad shapes and in order to compare these shapes with the resuts from this study,and the LBL report, one must use an annua consumption figure. To compare the resuts with this study, some other parameters must aso be chosen. The foowing parameters were used: Primary schoo without kitchen, annua eectricity consumption 64 kwh/m* Annua mean temperature +8 C. The four oad shapes are highy correated and the differences are sma, see Figure 6. No sports centre was considered when using the resuts from this study but LBL reports that some evening activities take pace and these were reported to be evening casses or maintenance; this is the major reason for the evening differences. No major concusion shoud be drawn athough the oad shapes are very simiar Nor& and Pyrko

11 2 -Nor& 1696 A ~~ :::: I:: I I:: :::::: ::::: -,,,,,,,o~=,, :! L (0 r E m E :: ij M 0 f HOW Figure 6. Resuts from this Study Compared to Resuts from Three Other Studies Discussion and Concusions It is important to remember that the chosen regression parameters are indicators for common activities in schoo buidings, and were not chosen to provide the best data fit. The concusion is that these parameters are important factors when anaysing the eectricity consumption in schoo buidings and the different indicator variabes are definitey usefu for the anaysis. Athough the Rz-vaue is ow during many hour:;, the proposed anaysis method is appicabe for simiar studies, at east for schoo buidings. The method is untested in other buiding types. One reason for ow Rz-vaues is that many parameters are not easiy quantifiabe, ike human behaviour and different day-to-day schedues. The methodoogy is a step away from the previous Swedish oad shape studies that presented reative oad shapes and the data materia in this study is much greater than in the two previous Swedish studies. Some concusions regarding schoo buiding eecnicity consumption can be drawn: Annua eectricity consumption is ony sighty affected by the studied factors but sti these have high infuence on the daiy oad shape. Night-time demand is very different from schoo to schoo depending on the choice of operating strategy. The schoo kitchen has a dominant infuence on the annua peak demand. Weekend and hoiday ECIs are very difficut to estimate, but again, this is mainy due to different operating strategies. Data for verification were ony avaiabe from one schoo and the measured oad shapes were correated to the presented ECIs. The ECIs indicated that the consumption was high, which was proved to be correct when studying the consumption data for The kitchen parameter was compared to measured data from a schoo buiding with kitchen activity as a main activity and the characteristics of the two oad shapes were simiar. Comparisons with the resuts from other studies showed simiarities and the oad shapes from the four different studies were highy correated. The oad demand was found to be temperature dependent athough oad data from district heated schoos are anaysed and it shoud be remembered that the schoos use district heating as the main heating system. Eectricity is used for some minor heating appications, such as: resistive heating in parts of the buidings, eectrica heaters in the venti.ating system and eectrica cois to keep the drain pipes free from ice. This is the major reason for the temperature dependence. Using Mutipe Regression Anaysis to Deveop Eectricity Consumption Indicators

12 Severa appications for the deveoped ECIs exist. Exampes incude: Comparisons with measured data in order to evaaate the eectricity consumption in a specific buiding. Estimation of oad shapes if measurements are not avaiabe. Estimation of annua peak demands. Acknowedgements This study was carried out with financia support from the Swedish Counci for Buiding Research, grant No and the Swedish Eectrica IJtiities R & D Company - Eforsk, grant No. 4014, to the Lund Institute of Technoogy, Dept. of Heat and Power Engineering, Div. of Energy Economics and Panning, Sweden. References Akbari, H., Eto, J., Turie, I., Heinemeier, K., Lebot, E., Nordman, B., and Rainer, L Integrated Estimation of Commercia Sector End-Use Load Shapes and Energy Use Intensities. LBL , Lawrence Berkeey Nationa Laboratory, USA. Akbari, H., Rainer, L., and Eto, J Integrated Estjmation of Commercia Sector End-Use Load Shapes and Energy Use Intensities, Phase II. Fina Report. LBL-30401, Lawrence Berkeey Nationa Laboratory, USA. Svenska Everksfoereningen (SEF) Beastningsberaekning med typkurvor. Stockhom, (In Swedish). Draper, Norman, R. and Smith, Harry Appied reqgres.sion anaysis. New York, John Wiey & Sons, 2nd ed. Feiberg, Nicoai and Livik, Kaus Energy and oad structure at various categories of endusers. EFI TR 4074, Trondheim. Livik, Kaus Main Findings of Load Research in Norway between EFI TR 3411, Trondheim. Vattenfa Lokaerna och energihushaaningen. Vaeingby, (In Swedish). Lyberg, M.E (Ed) Source Book for Energy Auditors voume 1. Internationa Energy Stockhom, Agency, Nor&, Co&z Typica oad shapes for six categories of Swedish commercia buidings. Dept. of Heat and Power Engineering, Report LUTMDN/TMVK SE. Lund. Rismark, Oe and Livik, Kaus Beastningskurver for bygg med forskjeige oppvarmingssystemer. EFI TR 3726, Trondheim (In Norwegian) Nor& and Pyrko