Regression model for heat consumption monitoring and forecasting

Transcription

1 E3S Web of Conferences 39, (018) Regresson model for heat consumpton montorng and forecastng Tatyana Dobrovolskaya 1*, and Valery Stennkov 1 1 Melentev Energy Systems Insttute of Sberan Branch of the Russan Academy of Scences (ESI SB RAS), Ppelne Energy Systems Department, 130, Lermontov str., Irkutsk, Russa, Abstract. Heat supply s socally and economcally mportant n our country. In ths regard, hgh-qualty montorng and plannng of the development of heat supply systems are a strategc vector of scentfc research. Ths paper s focused on the studes demonstratng how to choose a methodologcal approach to descrbe changes n heat consumpton n the retrospectve. The change n heat consumpton s descrbed usng multple regresson models. In the frst part of the paper, the parameters for the regresson model are determned and a statstcal analyss of the obtaned model s performed. In the second part of the paper, to elmnate the multcollnearty of the regresson equaton, the number of dependent varables n the model s reduced. A statstcal analyss of the new regresson model and the exponental regresson model are carred out. The heat consumpton values obtaned usng these models are compared wth the statstcal data. The conclusons about the qualty of the obtaned regresson models are made. In the thrd part of the artcle, we make a forecast of heat consumpton n the medum term by usng a lnear regresson model and an exponental model. 1 Introducton Ths paper s a contnuaton of the research on heat consumpton montorng and forecastng [1]. It s devoted to the generalzaton and analyss of data on energy consumpton and economc ndces, whch are represented by tme seres. The studes were carred out to determne the closeness and nature of the relatonshp between the selected ndces and the type of heat consumpton dependence on the selected varables. An analyss of the lterature dealng wth the predcton of energy consumpton [,3] ndcates that the energy consumpton s most often calculated usng specfc ndcators for plannng. However, the average heat consumpton n resdental buldngs often does not reflect the real pcture, as t does not take nto account the clmatc features of the regon, the actual state of buldng envelopes, quanttatve and qualtatve characterstcs of energysavng measures. In ndustry, the forecast s based on ndcators of energy ntensty of varous ndustres, that are adopted based on the foregn experence. In ths case, t s qute dffcult to draw analoges due to sgnfcant dfferences n economc development and technologcal potental of the countres. The researchers from other countres often present * Correspondng author: makarova@sem.rk.ru The Authors, publshed by EDP Scences. Ths s an open access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense 4.0 (

2 E3S Web of Conferences 39, (018) the studes on the use of regresson models to analyse the current state and predct the levels of energy consumpton [4-10]. They make an emphass on the forecasts of electrcty consumpton for a short perod of tme (some hours or days). Ths paper presents a research nto a methodologcal approach to descrbe a change n heat consumpton for a retrospectve-calculated perod. The coeffcents of the multple regresson model of heat consumpton are determned. A comparson of lnear and nonlnear regresson models of the heat consumpton s performed. The research was conducted at the hghest herarchcal level. The total heat consumpton of the country was taken as the research object. Multple regresson models of heat consumpton.1 Determnaton of varables for regresson model A regresson analyss s one of the most wdely used statstcal tools to descrbe the varatons n a dependent varable (annual heat consumpton) wth ndependent varables used as nputs for the functons. The man goal of the regresson analyss s to fnd an approprate mathematcal model and determne the best coeffcents of the model from the gven data. The major objectve of the study was to dentfy the nput parameters for the models that would descrbe the heat consumpton n the best way. In the frst stage, we selected the parameters for the multple regresson model. A specfc feature of regresson models s the need to have prospectve estmates of regresson equatons (ndependent varables). Consequently, t s much more dffcult to choose the parameters as ndependent varables n the regresson equaton. The most authortatve forecasts of socal and economc ndcators are forecasts of soco-economc development, made by the Mnstry of Economc Development of the Russan Federaton. The research focused on the followng ndcators: nstalled electrc capacty of power plants (N, 10 6 kw), electrcty consumpton (W, 10 9 kw h), heat consumpton (Q, 10 6 Gcal), populaton (P, 10 6 people), nvestments n electrc power ndustry (ncludng dstrct heatng) (I, 10 9 RUB), gross domestc product (GDP) (GDP, 10 9 RUB), tme nterval (T, year). The consdered ndcators are represented by tme seres from 1990 to 014 [11, 1]. An ntal analyss of the system of the consdered ndcators s to dentfy strong relatonshp between the ndcators n the sample. Correlaton analyss allows us to determne f t s necessary to nclude the ndcators n the multple regresson model. The correlaton coeffcent s a mathematcal measure of correlaton between two values. We use a lnear correlaton coeffcent (Pearson correlaton coeffcent) [13, 14], because the ndcators are represented by absolute values. Table 1 demonstrates lnear correlaton coeffcents of selected ndcators. Table 1. Matrx of correlaton coeffcents of the consdered ndcators from 1990 to 014. Indcator T N W Q P I GDP T 1 N 0, W 0,4079 0, Q -0,98-0,65-0, P -0,858-0,538-0,3786 0, I 0,8818 0,8946 0,4088-0,7454-0,606 1 GDP 0,987 0,8698 0,454-0,895-0,854 0,8905 1

3 E3S Web of Conferences 39, (018) The object of our research s heat consumpton, therefore we can draw conclusons about the exstence of relatonshp between heat consumpton for the populaton, GDP and tme (the values of the tme perod). Along wth the data of the study, the autocorrelaton coeffcents of the consdered ndcators are calculated. Varous methods are used to reduce the autocorrelaton. The methods am to exclude the man development trends n the ntal data,.e. lnear trends. In ths paper, tme s ntroduced n the multple regresson equaton as an ndependent varable [15]. Lnear one-parameter regresson models of the selected ndcators were consdered earler n [1]. Further n the paper, we wll consder n more detal the dependence of heat consumpton on the selected ndcators, by usng a multple lnear regresson.. A multple lnear regresson model of heat consumpton A lnear regresson equaton n a general form can be wrtten as follows: Y 0 1X1 X mx m (1) where X vector of ndependent (explanatory) varables, B vector of parameter coeffcents (to be determned), random error (devaton), Y dependent (explaned) varable, m the number of explanatory varables, n the number of observatons. In order to unquely solve the problem of fndng the regresson equaton coeffcents, the nequalty n m 1 should be met. To estmate a multple lnear regresson, the statstcal relablty requres that the number of observatons be at least three tmes greater than the number of ndcators to be estmated [13-15]. In our case, n ths connecton, further calculatons are amed at fndng the regresson coeffcents. Equaton (1) n the case of lnear multparameter regresson of heat consumpton can be wrtten as: y b b1 x1 bx b3x3 b4 x4 b5 x5 b6 x6 e 0 () where y values of the explaned varable (heat consumpton); x values of explanatory varables ; b coeffcents of the consdered lnear multparameter regresson; e values of devatons of sample values of the explanatory varable from the values obtaned from the regresson equaton. The most common method of estmatng the coeffcents of the multparameter lnear regresson equaton s the least-squares method (LSM) [13-16]. The essence of the method conssts n mnmzng the sum of squares of devatons of the observed values of the dependent varable from ts values obtaned from the regresson equaton. Based on our requrement, the standard error should be mnmal, whch can also be wrtten n the followng form: n 1 n y yˆ ) ( ) mn 1 (. (3) Then the equaton of multple regresson for descrpton of a change n heat consumpton wll have the followng form: Q 3093,67 50,31 T 10,47 N 0,775 W 4,46 P 0,199 I 0, 048 GDP e mod. A statstcal analyss was made to estmate the statstcal error, the statstcal sgnfcance of regresson coeffcents and the overall qualty of the model. The statstcal error of the model n the retrospectve perod was about 1%. The coeffcents of the multple lnear regresson model are statstcally sgnfcant. The overall qualty of the 3

4 E3S Web of Conferences 39, (018) model s evaluated by determnaton coeffcent R. For the consdered multple regresson equaton, the determnaton coeffcent s The closer ths rato to 1, the closer the regresson equaton descrbes the behavour of the dependent varable Y. The determnaton coeffcent, however, can be qute hgh n the presence of concdng trends n the varables under consderaton, and as a consequence a hgh degree of multcollnearty of the varables. The man method to elmnate multcollnearty of the regresson model s the method of excludng varables. Further work wth the obtaned regresson model wll be amed at excludng correlated varables. The studes have ndcated that the change n heat consumpton s best descrbed by the regresson model wth two varables (GDP and tme), whch can be wrtten n the followng form: mod1 1 Q a0 a1t agdp e. (4) We calculated the values of the regresson coeffcents a of equaton (4) n accordance wth the LSM, and ths equaton has the followng form: mod1 1 Q 1971, ,887 T 0,0197 GDP. A statstcal analyss of the heat consumpton model (4) was performed. Statstcal error of the regresson equaton s or 4.1%. The regresson equaton coeffcents are statstcally sgnfcant. The determnaton coeffcent of the equaton s Based on the calculatons, we can conclude that the obtaned regresson equaton explans 87.7% of varaton n the dependent varable (heat consumpton)..3 A non-lnear regresson model of heat consumpton Changes n the heat consumpton can also be descrbed by an exponental equaton. The varables (regressors) as well as n the prevous model, wll be represented by tme and GDP ndcators. For ths study, however, we wll not use the absolute values of heat consumpton and GDP, but the base growth rates of these ndcators. The values of the ndcators n the fnal year are chosen as the base value n, due to the fact that logarthm wll be made exactly accordng to the basc growth of heat consumpton. The general equaton of exponental dependence of heat consumpton has the followng form: mod c0 c1 T c GDP Q e, (5) Q GDP where Q the basc growth of heat consumpton, 1,,.. n ; GDP the Qn GDPn basc growth of GDP, 1,,.. n ; c 0, c1, c the regresson equaton coeffcents. The LSM s used to calculate the values of the coeffcents of equaton (5). The equaton of heat consumpton dependng on tme and GDP wll be as follows: mod ln Q 0,463 0,0315 T 0,4681 GDP ln. A statstcal analyss was performed for ths model of heat consumpton. Based on the calculaton results we estmated the statstcal errors and the statstcal sgnfcance of the regresson equaton coeffcents. The determnaton coeffcent R was These calculatons are correct for the logarthm of the basc heat consumpton growth. Further, after reducton to exponental functon and multplcaton by value of heat consumpton n base year, the estmated determnaton coeffcent was

5 E3S Web of Conferences 39, (018) 3 Case study: heat consumpton montorng and forecastng The consdered regresson models qute well descrbe the change n heat consumpton n the retrospectve perod. These regresson models can be used to make a short-term forecast of heat consumpton. In accordance wth [17, 18], the forecast of GDP change was adopted and heat consumpton levels were calculated usng the obtaned regresson models. Two optons of the GDP change forecast were approved, and nterval estmates of heat consumpton for a prospectve perod were obtaned. The length of the forecast perod covered by the regresson model depends drectly on the retrospectve perod for whch the model s derved. It s assumed that the forecast perod should not exceed 1/3 of the retrospectve perod. Accordng to ths crcumstance, the heat consumpton forecast s made untl 00. Fgure 1 presents the results of the heat consumpton calculaton n accordance wth the two optons of economc development. Fg. 1. The use of a multple lnear regresson model and non-lnear regresson model for heat consumpton montorng and forecastng 4 Conclusons The studes have demonstrated that n accordance wth the economc development forecast [17, 18] based on the multple lnear regresson model, a decrease n heat consumpton by 00 may be 9.% n the frst opton of economc development or t can ncrease by 5.6% n the second opton compared to 014. Accordng to the exponental model used to predct heat consumpton, t can decrease by 00 to 7.1% n the frst opton or ncrease by 3.4% n the second opton compared to 014. The change range of heat consumpton, accordng to the exponental model, has narrower boundares, whch allows us to more accurately determne the possble level of heat consumpton. The dscrepancy between the projected values of heat consumpton at the level of 00, usng lnear and nonlnear regresson models, s no more than % ( Gcal). Thus, we can conclude that the obtaned regresson models can be used for montorng and medum-term forecastng of heat consumpton. In the future, we plan to contnue the research n ths area. Our plan s to 5

6 E3S Web of Conferences 39, (018) expand the models wth the explanatory varables, and descrbe the structure of heat consumpton, usng regresson models. The research was performed at Melentev Energy Systems Insttute SB RAS n the framework of scentfc projects III АААА-А and III АААА-А of the Fundamental Research Program of SB RAS. References 1. T.V. Dobrovolskaya. Montorng of heat consumpton levels usng regresson models. System research n power engneerng. Proceedngs of young scentsts of ISEM SB RAS. Vol (015). A.M. Mastepanov. A fuel and energy complex of Russa at the turn of the century: state, problems and prospects. 793 (010) 3. A.S. Nekrasov. An analyss and forecasts of the fuel and energy sector development. Selected works. 59 (013) 4. Mng Meng, Dongxao Nu. Annual electrcty consumpton analyss and forecastng of Chna based on few observatons methods. Energy converson an management, 5, (011) 5. N. Fumo, M.A. Rafe Bswas. Regresson analyss for predcton of resdental energy consumpton. Renewable and sustanable energy revews. 47, (015) 6. S. Smeekes, E. Wjler. Macroeconomc forecastng usng penalzed regresson methods. Internatonal journal of forecastng. 34, (018) 7. T. Catalna, V. Iordache, B. Caracaleanu. Multple regresson model for fast predcton of the heatng energy demand. Energy and buldngs. 57, (013) 8. Tngtng Fang, Rsto Lahdelma. Evaluaton of a multple lnear regresson model and SARIMA model n forecastng heat demand for dstrct heatng system. Appled Energy. 179, (016) 9. G.J. Tsekouras, E.N. Dalynas, N.D. Hatzargyrou, S. Kavatza. A non-lnear multvarable regresson model for mdterm energy forecastng of power systems. Electrc power systems research. 77, (007) 10. V.Banco, O. Manca, S. Nardn. Electrcty consumpton forecastng n Italy usng lnear regresson models. Energy. 34, (009) 11. Russan statstcal yearbook (013) 1. Federal state statstcs servce ( 13. E. Ferster, B. Renz. Methods of correlaton and regresson analyss. 30 (1983) 14. S.A. Borodch. Econometrcs: study gude. 408 (001) 15. G.A. Ivashchenko, G.S. Kldshev, R.A. Shmolova. Statstcal study of the man trends of development and nterrelaton n the ranks of dynamcs. 168 (1985) 16. S.V. Solodusha. Typcal problems of the basc course of econometrcs. 4 (007) 17. Energetcs of Russa: a vew to the future (Substantatng materals to the Energy strategy of Russa to 030). 616 (010) 18. The energy strategy of Russa to 030 ( 6