Energy Consumption Prediction Model of the Residential Sector. Abstract. 1. Introduction

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1 Energy Consumption Prediction Model of the Residential Sector Patrícia Branquinho, Instituto Superior Técnico, Universidade de Lisboa Abstract Nowadays, the buildings sector is responsible for about 40% of the overall energy consumption in Europe, and it represents a key sector to implement different saving measures at an international level. A common way of reducing energy spending is through the adoption of smart meters, which allows recording and controlling the expenses regularly. This article aims to explore two methodologies of consumption forecast, one based on statistical models for dwellings with smart meters, and the second based on the simplification of physical models for dwellings without this type of equipment. Initially, the correlation between the climatic and socioeconomic variables was analysed through a statistical model, relating them to the energy consumption using linear regressions, in order to find an explanatory relation to consumption over two years. It was also found that socioeconomic variables have an impact on electricity consumption in the residential sector, explaining about 11% of it. It was thus possible to obtain a prediction model (baseline), per house, for the electricity consumption. The second methodology can predict the consumption based on the characteristics of the dwelling, yielding two equations for each neighbourhood, the respective heating and cooling requirements, which vary if the house has air conditioner or radiators. It is possible to conclude that, despite the estimated energy requirements being higher that the measurements with smart meters, the model can achieve an approximation of energy requirements per degree day. Keywords: Electricity consumption; residential sector; statistic model; baseline; 1. Introduction In Europe, the buildings sector is responsible for about 40% of the overall energy consumption, the biggest sector of final consumers, and for 36% of CO2 emissions [1]. The residential sector is estimated to represent, alone, 25% (in 2011) of the final energy consumption at the EU [2]. However, over 50% of this consumption can be reduced through energy efficiency measures, which may reach an annual reduction of 400 million tons of CO2, representing, almost all of the EU commitment under the Kyoto Protocol [3]. Thus, prediction of energy consumption gains an increased importance, in order to improve energy use and lower spending, therefore increasing energy efficiency [4]. To address this situation, the Member States have been promoting a set of measures to encourage the improvement of energy performance and comfort conditions in buildings, from which emerge Directives 2002/91/EU e 2009/72/CE, created to improve the energy efficiency of buildings and to introduce measures that optimize electricity consumption, including the adoption of smart meters, respectively. Regarding the need to create models of energy prediction, the scope of this study relates to the development of a methodology for prediction of monthly consumption. The proposed objective seeks an approximate forecast of electricity consumption in the residential sector for two types of dwellings. In homes where there is access to regular reporting of electricity consumption, due to smart meters, it is possible to develop a statistical prediction model - baseline - with information from various climatic and socioeconomic variables, easily accessible, which correlates these variables with the consumption of electricity. In homes where there is no information on the consumption of electricity, from the socioeconomic and climatic characteristics of the houses and data from energy certificates, using a physical model it will be possible to foresee which should be approximately the variation of consumption in the winter and summer seasons, depending on the needs of the parish. 1

2 The energy consumption of buildings has become a pertinent issue at international level, and different energy saving measures are being discussed in many countries [3]. In this context, the Directive 2009/72/EU appears in order to promote the energy efficiency in the Member States. The regulatory authority strongly recommends that electric companies optimize electricity consumption by providing energy management services, developing innovative pricing formulas assessment, or introducing smart meters or smart grids where appropriate. Smart meters are then considered important, in the sense that they provide the possibility of monitoring data in real time, which enables the user to meet their consumption patterns, recognize changes, and allow the user, at any time, to know if he is consuming more or less than he should. 2. Description of the case study In the first case, for the purpose of data analysis, were used electricity consumption values coming from 33 houses, by the smart meters. This data was collected during 2 years, 2012 and 2013, and presented monthly. It comes from the Smart GALP Project, which had as aim to study the savings from the use of a smart metering system, for multiple users. This way, of the 71 houses for which measurements were made, the dwellings whose measurements showed many flaws (mainly gaps in the recording process) were excluded, having then been selected the ones with measurements that had less than 15% of failures. Initially, the impact of climate variables was studied, in order to determine how the degree days calculated hourly, daily, weekly and monthly, the average temperature and the apparent temperature correlate with the electricity consumption in the residential sector. Subsequently, the variable that best explained the consumption, from among those listed above, was tested with another climatic variable, the natural light, along with two other variables not accounted for in the present energy forecasts. These were of socioeconomic nature, the price índex and the confidence index. The second method, for dwellings without smart meters, were considered average values by parish, withdrawn from energy certificates, in order to obtain the prediction model. There were obtained the heating and cooling needs through a simplified model, and subsequently was possible to compare the cooling needs with those calculated by the model used in RCCTE. 3. Method of statistic model for dwellings with smart meters The baseline was developed from a multivariable linear regression, based on the different variables already presented. Initially, the impact of the temperature and degree days was analysed, house by house, in order to conclude which variable best justifies consumption. The variables used for the heating analysis are: Hourly based degree days Daily based degree days Weekly based degree days Monthly based degree days Average temperature Aparent temperature Table 1 Variables simbology Simbology HDDh HDDd HDDw HDDm Tm Ta The climatic variable that best justifies the consumption was then tested along with a second climatic variable, natural light (NL), and socioeconomic variables: price index (PI) and confidence index (CI). This multivariable linear regression was performed using the Excel spreadsheet, with a data analysis function. Through it, it s possible to obtain the R square as well as the baseline equation, allowing to conclude on the existence of correlation between the data of each house, and analysing the improvement over the relation obtained before. 2

3 In the next chapter, it s mainly discussed, from the results presented, the root mean square error, which is a measure of the difference between the values predicted by the model and the values actually observed. This way, it is possible to conclude about the variation on the error, and observe its decrease while the correlation improves with certain variables Restrictions During the analysis, some restrictions were introduced in order to ensure the consistency of the obtained models. In particular, the following were introduced: Address: excluding residents outside, where temperature varies differently causing a different pattern of consumption. Central Heating: excluding from the analysis houses with central heating. This allows to measure the impact of the electricity in meeting the heating needs. 15% of data fails: a selection was made of the houses where less than 15% of the data in the smart meter was missing, thus reducing the influence of erroneous data (e.g. houses where there was verified that several days didn t present any consumption) and therefore improving the correlation. 4. Results for dwellings with smart meters In order to analyse the impact of socioeconomic variables, it was necessary to study first which of the climatic variables correlates best with the electricity consumption. There were made tests using the data from all the houses, with the aim of finding the root mean square error for each one: Root Mean Square Error (KWh/month) All the houses Table 2 Root mean square error by variable Houses from without central heating 15% data missing 15% from 15% without central heating HDDh 83,15 80,01 86,34 84,56 77,83 97,54 HDDd 83,37 79,98 86,31 83,59 75,04 93,66 HDDs 83,60 80,42 86,96 84,11 76,47 95,78 HDDm 86,96 82,66 89,20 90,99 80,44 101,07 Tm 91,64 88,35 96,32 97,43 87,25 110,87 Ta 93,72 89,84 98,00 100,93 88,80 112,96 From the table above, it is suggested that the daily heating degree days have a better correlation ie, have lower root mean square error. However, for the case studied without any restriction, ie, for all the houses, the smallest error is presented for hourly degree days. This error, 83,15 kwh/month, is yet very close to the error presented for the daily degree days, and since that adding restrictions will increase the study precision, the trend is to be the daily degree days that best justifies the electricity consumption, so this was the chosen variable to continue the study of socioeconomic variables impact. It should be noted that this high value is due to the fact that 33 houses with a big variety of consumptions have been considered, and that the consumption range varied from [0-200] kwh/month to [0-1500] kwh/month. This dispersion of the values makes the average root mean square error increase considerably, being however still useful to compare the impact of the variables on the consumption. For the hourly, daily and weekly degree days cases, in 7 of the 33 analysed cases the variables justify above 60% the electricity consumption behaviour, ie, the R square is above 60% which indicates a strong correlation. 3

4 Root Mean Square Error (kwh/month) 4.1. Identification of socioeconomic variables In the socioeconomic variables analysis, it was necessary to study how each one has impact on the linear regression, in order to examine its evolution and which best explains the consumption. This way, the following relations will be analysed: 1 DDAd 2 NL + DDAd 3 DDAd + PI 4 DDAd + PI + NL 5 DDAd + CI 6 DDAd + CI + NL 7 DDAd + PI + CI + NL All the houses Average Standart Deviation Table 3 Root Mean Square Error per correlation Houses from without central heating 15% data missing 15% from 15% without central heating Average Average Average Average Average 1 83,37 75,67 79,98 86,31 83,59 75,04 93, ,47 74,07 76,82 82,84 81,07 71,67 89,4 3 78,46 70,46 74,95 80,72 77,42 69,26 86, ,48 68,91 71,63 77,06 74,87 65,76 82, ,04 71,78 76,86 83,05 78,43 70,52 87,7 6 76,03 69,81 73,55 79,56 75,73 67,19 83, ,79 66,29 69,15 74,66 71,46 62,6 77,99 Regarding the results presented in the table above, it is possible to conclude that within the two socioeconomic variables, the one with the best results concerning the decrease of the error is the price index. However, the socioeconomic variables studied together present the lowest average value of the root mean square error. These variables can be tested together even though they are both are representative of the socioeconomic situation as they vary in different ways and at different range, making their joint analysis valid. Based on the standard deviation presented, it s possible to conclude that, since it has the same magnitude of the root mean square, there is some dispersion of values. This is justified as explained above, due to the fact that the consumption values vary in different ranges. It is possible to conclude that the consumption prediction equation is given by: (1) where corresponds to electricity consumption of dwelling I, the constant C obtained by linear regression is the interception with the y-axis, the greek constants correspond to the coefficients obtained by linear regression for each house, and HDDd, PI, CI, and NL correspond to the climatic and socioeconomic variables. Each house has an energy signature, behaviour patterns and different equipment, which cause the consumptions and their patterns to vary differently. Apart from analysing the difference between the root mean square errors, it is possible to directly analyse the impact of the price index. The improvement of the error will be analysed, ie, the decrease of the error of the correlations 4, 6, and 7 compared to the correlation 2. 4

5 Table 4 Improvement registered by the indexes All the houses Houses from without central heating 15% data missing 15% from 15% without central heating Improvement PI (%) 6,51 7,44 7,40 7,75 9,82 10,26 Improvement CI (%) 5,58 5,10 5,14 5,84 5,80 6,65 Improvement PI + CI (%) 11,19 11,47 11,63 12,01 13,88 15,49 It can be seen that the price and confidence indexes together bring an improvement to the regression of about 11,2% when considering all the houses, and 15,5% when restricted to households with less than 15% of data missing without central heating. Concerning the comparison between the indexes, it is noticeable that the price index improved the correlation to 10%, while the confidence index only explains up to about 7% of the electricity consumption. It is relevant to identify that the relative error of the correlation 7 corresponds to an average of 16,3% while the 2 nd correlation, which serves as comparison, is 18,1%. It is also possible to analyse at an R square level, how much the socioeconomic variables have improved the correlation with the electricity consumption. Table 5 Increase of the R square registed by the socioeconomic variables HDDd + NL HDDd + NL + PI + CI R Square Households % Households % [0-30] % 23 69, ,3 [31-60] % 3 9, ,4 [61-100] % 7 21,2 9 27,3 The table above confirms the evolution of the R square after adding variables to the regression. It is possible to verify that 9 of the 33 households show a strong correlation with the electricity consumption after adding socioeconomic variables, ie, the electricity consumption is well justified by the variables, resulting in 27% of strong correlation cases. It s also remarkable the increase of cases with reasonable correlation, which means that although there is still a part of the consumption which cannot be explained, the improvement is clear, increasing from 9% of the houses to 42%. 5. Physical principles model for households without smart meters 5.1. Simplified model In order to calculate the heating and cooling needs by household, was implemented a method based on the thesis [7] and in the article [8], to which some changes were made. This model was applied to all parishes of, based on data taken from households energy certificates for the 24 parishes. From the data obtained, were considered and analysed the following variables: the floor area, height, infiltration rate, percentage of glazing area and U value for the wall, floor and ceiling, and glazed. For each parish was obtained the average value for every variable, except in the case of the percentage of the glazing area and the U value of the floor and ceiling, with the purpose of obtaining the energy needs per household. Regarding the methodology used, it s calculated first: (2) (3) (4) 5

6 The length and width are calculated taking into account the perimeter as minimum (minimum wall area), ie, the used length is equal to the width. This gives minimum values for energy needs. With these parameters, it is possible to calculate the heat loss coefficient: (5) where I is the infiltration rate, V is the volume of the household, A the exposed area, U is the U value and corresponds to the percentage of glazing area. This equation defines completely the heat loss of a household, and it only remains to insert the external climatic variables, presented by the degree days. The total heat demand of a dwelling is given by: where DD are degree days. In conclusion, from this methodology are obtained two important values for analysis: total heating needs per heating degree day, and total cooling needs per cooling degree day Comparison of the model with the model from RCCTE RCCTE Regulamento das Características de Comportamento Térmico dos Edíficios describes all the requirements to meet the thermal conditions without excessive energy consumption. It also describes the method to calculate the heating and cooling needs for a house, which is similar to the process described above but with some significant differences. While calculating the heating needs by the model from RCCTE requires much information that is difficult to obtain, the cooling needs consider a simplified model, that can be used to compare with the adopted methodology. Thus, the cooling needs are given by: where corresponds to total gross earnings, is the earnings utilization factor and the useful area of the floor. The total gross earnings are calculated by summing several plots related to loads that result from the household earnings, from which were removed portions of the earnings through the glazing areas and internal loads due to occupancy. This method is defined in [9]. (6) (7) 6. Results for households without smart meters Following the analysis of the energy certificates, the annual daily degree day value was obtained for the year of 2013, corresponding to 634,5 for heating degree days and to 77,0 for cooling degree days. They were obtained for a base temperature of 15,5ºC for heating, and 25ºC for cooling. Through the calculations presented before, it is possible to present the values of the heating loss coefficient per household and the total heating and cooling needs per household per parish: Table 6 Heating loss coefficient and total heating and cooling needs per parish Parish Heating Loss Coefficient Q (W/C) for a household Total heating needs for a household (kwh/year) Total cooling needs for a household (kwh/year) Belém 905, , ,04 São Vicente 519, ,06 960,01 From the full table it can be concluded that the heating and cooling needs of a dwelling are, on average, kwh/year and 1272 kwh/year respectively, being higher in the parishes that have older houses, with higher heating loss coefficients, and with predominance of single glazing instead of 6

7 double. However, these values are clearly higher than the consumption recorded by smart meters, in which was found that the dwellings of, on average, have a consumption of 4427,7 kwh/year. This means that the consumption does not satisfy the heating needs. This conclusion is expected because in Portugal there are still many households that are not heated in winter or cooled in summer, especially in the centre and south of the country, where the climate is quite moderate. It is also noted that the energy consumption measured by the smart meters account for all kinds of consumption, including lighting and equipment, while in the table above are shown just heating and cooling needs. This difference between measured and estimated is further increased Comparative analysis of the heating needs between the models According to the data from the Smart GALP project it is possible to see which houses have air conditioning and which have electric radiators. It is therefore possible to observe the curve of consumption of each and determine when there is an increase of electricity consumption from the mid season to the winter, trying to take into account the part that corresponds to heating. In this case study was considered a COP of 3 for the air conditioning. In contrast, the radiators have a lower efficiency associated that is considered approximately 1. It was subtracted to the winter consumption the mid season consumption from the houses that have air conditioning or radiators, in order to realize which part is consumed due to heating. Thus, the following table is presented with the values of the consumption due to heating per month: Table 6 Energy variation for the winter months Energy variation for the winter months (kwh/month) Household AC Radiator Contrary to what would be expected, the houses with air conditioning have higher spending than the houses with radiator. This can be explained by the fact that households with air conditioning tend to turn it on longer to heat a larger area of the house as opposed to what happens with the radiator. From these results, considering that the monthly consumption values due to heating may last for 3 winter months, the consumption that is obtained is between 450 and 3000 kwh/year. These values, multiplied by the COP, result in a heat production between 1350 and 9000 kwh/year. 7

8 Regarding houses with radiators, there were obtained, for the 3 winter months, consumptions between 150 and 900 kwh/year. This value, much lower than the observed in the houses with air conditioning, is justified previously. Comparing these values with the estimated annual needs of kwh/year, it is possible to conclude that the requirements fall short of being satisfied, in accordance with what was estimated Comparative analysis of the cooling needs between the models As in the previous analysis, it was made a selection of the households whose consumption showed patterns visible in summer. Table 7 Energy variation for the summer months AC Energy variation for the summer months (kwh/month) For some of the dwellings in which previously stood out the consumption in the winter months, in the case of the summer months this consumption remained lower and more stable, camouflaging the use of air conditioning for cooling. In this analysis only two intakes were considered, for approximately 3 months in summer, ranging from 150 to 750 kwh/year. These values multiplied by the COP, result in a cooling production between 450 and 2250 kwh/year. The average cooling needs of 1272 kwh/year can be satisfied, since the value obtained for estimated needs is within the measured ones. Using the method from RCCTE, it was possible to obtain the total cooling needs per parish. These are presented in the table below, the highest and the lower values, and the corresponding cooling needs calculated by the simplified method: Table 8 Cooling needs Parish N vc (kwh/year) N cooling through the simplified method (kwh/year) Santo António 914, ,67 Santa Clara 529, ,76 Following the calculation of these needs values from the energy certificates were used, such as the heat loss coefficient from the walls, the wall area of the household, the infiltration rate, the average floor area and the height, by parish. However, some values are recommended by RCCTE according to the characteristics of the dwelling, such as: matches zone V2 S = 23ºC = 20ºC I r = 820 kwh/m 3, considering the horizontal value h e = 25 W/m 2 ºC = 0,5, for the average situation = 1190 = 2,6, for the average situation Based on the full table it can be concluded that the cooling needs of a household are, on average, 720 kwh/year, lower than the value recorded by the method previously developed. The parishes with higher cooling needs do not correspond to those previously obtained. This difference can be explained by the method of RCCTE not considering the percentage of the area of glazing or 8

9 the coefficient of heat transfer, as well as the coefficient of heat loss of the ceiling and floor on the calculation, which can change the final result. The results obtained by the two models are close, being obtained 1272 kwh/year for the simplified model, and 720 kwh/year for the one suggested by the RCCTE. However, considering that for many of the houses with air conditioning the increase in the consumption was not very visible during the summer months, the values obtained by the second model reflect lower estimated cooling needs and consequently the equation to be used will take into account the RCCTE model Prediction model of consumption per parish To complete the aim of obtaining the equations for the calculation of the energy needs of a house per parish, it was possible to obtain the equations that indicate how much the consumption increases in kwh per degree day. Then, the methodology for predicting heating consumption is: (8) and for cooling, where refers to the obtained results of the RCCTE model: in which the consumption variation is equal to a constant or which varies by parish, dividing by the efficiency, corresponding to 3 if it has air conditioning and 1 for dwellings with radiators (for the heating needs case), multiplying by the heating or cooling degree day, as desired. The and constants, which account all the features of the aforementioned household characteristics, being in this table just 7 parishes for demonstration purposes: Table 9 Heating and cooling coefficients Parishes [kwh/degree days] [kwh/degree days] Ajuda 13,74 8,84 Alcântara 16,02 9,52 Alvalade 18,45 9,82 Areeiro 18,96 11,41 Santo António 19,04 11,88 São Domingos de Benfica 18,01 9,21 São Vicente 12,46 9,14 Although these values were shown to predict the heating and cooling needs higher than what is actually consumed, they can still predict within the same order of magnitude in the case of the cooling needs, and an approximate estimative in the case of the heating needs. (9) 7. Conclusions Given the increasing need for higher energy efficiency, emphasized by the fact that the residential sector represents 40% of total energy consumption at European level, numerous suggestions for action are emerging driven by directives such as 2009/72/CE and 2002/91/EU. The prediction of energy becomes so relevant and important to implement because it allows consumers to register and control spending and thus understand their consumption pattern. 9

10 Two methods were developed for predicting electrical consumption for both houses with smart meters and for houses without this kind of devices. Throughout the article, the two methodologies mentioned above were studied by choosing easy access variables, ie, allowing that based on socioeconomic and climatic variables, or just by parish, one can predict the electricity consumption in the residential sector on a monthly basis. It was possible to obtain the prediction model of electricity consumption, primarily through a statistical model, the baseline. This model accounts for the price index and the confidence index as socioeconomic variables, and daily degree day and natural light as climatic variables. From this analysis was possible to acknowledge that socioeconomic variables introduce significant improvement which can mean that the state of the economy affects the consumption. The relative error associated that the correlation obtained, on average, is 16%, in which are reflected the behaviour of the inhabitants and other variables still to consider, concluding that the behavioural variable continues to have a major impact on the electricity consumption. This error indicates that, though climatic and socioeconomic variables are explanatory of the consumption, there is always a significant margin to explain. The often unpredictable changes in consumption make it difficult to create more accurate predictions, sometimes causing the baseline to act as a filter, rather than follow more abrupt changes. The models obtained by the second method estimate the heating and cooling needs above the actual consumption obtained by smart meters. However, the comparison with these devices could only be made for a number of houses (14 for heating and 2 for cooling), so it results that this model can predict only the order of magnitude. It is relevant to mention that this whole process is interconnected with some degree of uncertainty, which may contribute to the high amount of energy needs, given that some of the variables, especially the percentage of glazing area and the U value for floor and ceiling were considered average values at a country level. Although both models have an associated degree of uncertainty, and though the second model only enables the prediction of the order of magnitude of the consumption, the article presented demonstrates that it is possible to meet the target and get the prediction models of consumption based on variables of easy access, both of which allows the consumer to verify if he is consuming higher ou lower than he should, and thus promote the control of spending and boost energy efficiency in the residential sector. 8. References [1] European Comission [On-line], Data available: [2] Eurostat [On-line], Data available: [3] ADENE Agência para a energia [On-line], Data available: [4] H. Zhao and F. Magoulès, A review on the prediction of building energy consumption, Renew. Sustain. Energy Rev., vol. 16, no. 6, pp , Aug [5] European Parlament, DIRECTIVA 2002/91/CE DO PARLAMENTO EUROPEU E DO CONSELHO de 16 of December de 2002, no. 11, pp , [6] European Comission, Directiva 2009/72/CE do Parlamento Europeu e do Conselho de 13 de Julho de 2009 que estabelece regras comuns para o mercado interno da electricidade, vol. 2008, [7] A. S. Stavropoulos, Spatial analysis of heating and cooling energy needs in Alexis Serra Stavropoulos Dissertation to obtain Master s degree on Mechanical Engineering, [8] A. Durmayaz, M. Kadoǧlu, and Z. En, An application of the degree-hours method to estimate the residential heating energy requirement and fuel consumption in Istanbul, Energy, vol. 25, pp , [9] Decreto-Lei n o 80/2006, pp ,