212 2 ( 4 252 ) No.2 in 212 (Total No.252 Vol.4) doi 1.3969/j.issn.1673-7237.212.2.16 STANDARD & TESTING 1 2 2 (1. 2184 2. 2184) CensusX12 ARMA ARMA TU111.19 A 1673-7237(212)2-55-5 Time Series Analysis Method and Its Application in Energy Consumption Forecast of an Actual Office Building ZHOU Rui-jin 1, PAN Yi-qun 2, HUANG Zhi-zhong 2 (1.College of Mechanical Engineering, Tongji University, Shanghai 2184, China; 2. Sino-German College of Applied Sciences, Tongji University, Shanghai 2184, China) Abstract: Based on time series analysis method, it establishes a forecast model of building energy consumption to forecast the monthly energy consumption of an office building in Shanghai. CensusX12 method is used to do seasonal adjustment, ARMA model is established and the seasonal factor is processed with accumulated temperature. The forecast results show that time series analysis method is applicable for building energy consumption forecast. Key w ords: time series; building energy consumption forecast; ARMA Model 1 (forward modeling) 2 (data-driven modeling) e- Quest EnergyPlus DeST 1 [1] 4 1 2 3 4 1.1 [2] {X t } [3] S.Sp. Pappas [4] ARMA 211-11-7 211-11-17 55
[5] [5] CensusX12 φ i θ i X t (S t ) (TC t ) (I t X t =S t +TC t +I t (1) X12 [5] Eviews X t ARMA S t SA t + l SA t SA t + l =φ 1 SA t + l -1 +φ 2 SA t + l -2 + +φ n SA t + l -n +a t + l -θ 1 SA t =TC t +I t (2) a t + l -1 -θ 2 a t + l -2 - -θ m a t + l -m (4) SA t 1.3 X t S t [6] ADF 1.2 Pearson r XY n Σ(X i -X )(Y i -Y ) ARMA i = 1 r XY = (5) n n Σ(X t SA t 姨 i -X ) 2 Σ(Y i = 1 姨 i -Y ) 2 i = 1 (SA t -1 SA t -2 ) (a t -1 a t -2 ) (ARMA Auto Regressive S t =f (T t ) Moving Average model) ARMA(n m)(n m SA t -φ 1 SA t -1 -φ 2 SA t -2 - -φ n SA t - n =a t -θ 1 a t -1 -θ 2 a t -2 - - θ m a t -m (3) φ i (i =1 2 n) θ i (i =1 2 ) 21 12 Box-Jenkins T 21 i =a 1 T 29 i +a 2 T 28 i +a 3 T 27 i (i =1 2 12) (6) a 1 +a 2 +a 3 =1 29 28 27 ( 1) [6] 1 Box-Jenkins a 1 =.5 a 2 =.35 a 3 =.15 Tab.1 Box-Jenkins Model Identification Method T 21 i =.5T 29 i +.35T 28 i +.15T 27 i (i =1 2 12) (7) (7) S 21 i =f (T 21 i )=f (.5T 29 i +.35T 28 i +.15T 27 i ) (8) ( ) AR(n) MA(m) ARMA(n m) 1.4 F SA t ARMA AIC S t (A-Information Criterion ) BIC T t (Schwarz ) X12 X t =SA t +S t 56
2 3 2 27 1 ~29 12 21 1 1 ~12 77 m 2 8% -1-2 2.1 27 1 ~29 12 36 1 1 ( 1) Electricity/kW h 8 1 8 6 1 A 27~29 4 Fig.1 Sequence diagram of monthly electricity consumption from 27 to 2 29 of office building A in Shanghai -2 1 Eviews X12 2 2(a) -6 X12 Electricity_SA t 2(b) Electricity_S t 2(c) 2(d) Electricity_TC t 2 2(d) Electricity_I t Electricity_SA/kW h 1 5 1 4 1 3 1 2 1 1 1 2(a) 9 1 2 1 16 1 12 1 8 1 4 1 96 2(b) 2(c) -4 A Electricity_S/kW h Electricity_TC/kW h Electricity_I/kW h 1 12 1 8 1 6 1 4 1 2 A A A A 27~29 ( ) Fig.2 Seasonal adjustment structure of monthly electricity consumption from 27 to 29 of office building A in Shanghai (Additive Model) SA t (Unit Root Test) 2 t -4.52 82 1% 5% 1% 3-3.632 9-2.948 44-2.612 874 t SA t 57
2 Electricity_SA t Tab.2 Unit root test result of Electricity_SA t Series t P. 4 P.5 ADF -4.53.1 Q 5 1% level -3.633 P.5 5% level -2.948 95% 1% level -2.613 Electricity_SA t 2.2 Electricity_SA t + l =1 115 839+1.572 447Electricity_ Electricity_SA t (ACF) SA t +l-1 -.661 732Electricity_SA t +l-2 +a t +l +2.314 653a t +l-1 - (PACF) 3 1.988 224a t + l -2 +.598 69a t + l -3 ARMA(n m) (9) n 2 m 3 3 Electricity_SA t Fig.3 Correlation function results of Electricity_SA t Series ARMA(2 2) ARMA(2 3) ARMA(3 2) ARMA(3 3) ARMA(2 4) ARMA(3 AIC ARMA(2 3) 4 5 ARMA(2 3) Fig.5 Autocorrelation function results of ARMA (2, 3) Model Residual Series 21 12 4) 6 21 BIC 1 ~12 Electricity_SA t 95% 6 Electricity_SA t 1 24 1 2 1 16 1 12 1 8 1 4 1 4 Fig.4 Model regression results 96 21M1 21M4 21M7 21M1 6 Electricity_SA t 95% Fig.6 Forecast value of Electricity_SA t with 95% Confidence Interval 2.3 27 ~29 36 ( 7) 3.865 844 58
Temp/ 1 9 8 7 6 5 4 3 2 1 7 Fig.7 Monthly accumulated temperature series of Shanghai 3 A 8 A Tab.3 Correlation coefficient of monthly energy consumption seasonal factor series of office building A and monthly accumulated temperature series of Shanghai Temp Electricity_S T t 1..865 844 Electricity_S.865 844 1. SPSS 2.7% Electricity_S 1 6 Temp 1 2 (Quadratic) R 2.848 F 8 92.34 4 4 A 4 Tab.4 Quadratic function regression coefficients of monthly energy consumption seasonal factor series of office building A and monthly 21M1 21M4 21M7 21M1 accumulated temperature series of Shanghai 9 A t Sig. T t -432.323-2.113.42 T t 2.873 4.636. C -81 535.858-1.73.93 Electricity t =Electricity_SA t +Electricity_S t (11) 12 8 4-4 -8-12 Fig.8 Regression result of monthly energy consumption seasonal factor series of office building A and monthly accumulated temperature series of Shanghai 9-16.48% 18.2% /kw h Residual Actual Fitted 3 2 1-1 -2 Fig.9 Forecast value and actual value of monthly electricity consumption of office building A in Shanghai 3 8 Actual Cen- Electricity_S Fitted Residual susx12 ARMA S t T t S t =.873T t2-432.323t t -81 535.858 (1) 2.4 3 (7) 21 (8) S t 21 (1) (2) X t =SA t +S t ( 62 ) 59
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