forecasting: meter reading
Project Title: Meter Readings from a Railway Station (part 2)
NAME: ASWATHY GUNADEEP
EMAIL: aswathygunadeep@gmail.com
COLLEGE / COMPANY: NATIONAL INSTITUTE OF TECHNOLOGY KARNATAKA
setwd("C:/Users/user/Desktop/tarsha systems summer internship/datasets")
met1.df <- read.csv(paste("1.csv", sep=""))
sub.df <- subset(met1.df[,c(1,5,9,13,20,24,25,26,27,28,29,36,37,38,39,40)])
attach(sub.df)Forecasting future 3 results We use forecast function to predict possible next 3 values. We 1st convert whatever numeric vector values are present in our dataset into an R time series object.
library(forecast)
myts <- ts(sub.df)
forecast(myts, 3)## W.Total
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 4365.869 1770.950 6960.788 397.2834 8334.455
## 10482 4365.869 1698.642 7033.097 286.6965 8445.042
## 10483 4365.869 1628.242 7103.496 179.0296 8552.709
##
## VAr.Total
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 -1141.739 -2472.715 189.2370 -3177.291 893.8131
## 10482 -1141.739 -2517.629 234.1510 -3245.981 962.5032
## 10483 -1141.739 -2561.123 277.6445 -3312.499 1029.0208
##
## P.F
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 0.1060602 -0.2430591 0.4551795 -0.4278717 0.6399921
## 10482 0.1060602 -0.2575750 0.4696955 -0.4500719 0.6621923
## 10483 0.1060602 -0.2715333 0.4836538 -0.4714193 0.6835397
##
## VA.Total
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 5365.4 3232.608 7498.193 2103.576 8627.225
## 10482 5365.4 3195.945 7534.856 2047.505 8683.296
## 10483 5365.4 3159.892 7570.909 1992.366 8738.435
##
## Amps.Ave.
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 7.936767 4.651888 11.22165 2.912977 12.96056
## 10482 7.936767 4.601398 11.27214 2.835759 13.03778
## 10483 7.936767 4.551660 11.32187 2.759693 13.11384
##
## Frequency
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 49.98045 49.34948 50.61141 49.01547 50.94543
## 10482 49.98045 49.34948 50.61141 49.01546 50.94543
## 10483 49.98045 49.34948 50.61141 49.01546 50.94543
##
## Wh.Rec.
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 11700000 11691561 11708439 11687094 11712906
## 10482 11700000 11684735 11715265 11676654 11723346
## 10483 11700000 11676845 11723155 11664588 11735412
##
## VAh.Rec.
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 15403297 15383782 15422812 15373451 15433143
## 10482 15404767 15383400 15426133 15372089 15437444
## 10483 15406236 15383165 15429307 15370952 15441520
##
## VArh.I.Rec.
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 528997.5 528937.9 529057.2 528906.3 529088.7
## 10482 529312.6 529202.1 529423.2 529143.5 529481.7
## 10483 529621.4 529453.9 529789.0 529365.2 529877.7
##
## VArh.C.Rec.
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 -8630275 -8639493 -8621058 -8644372 -8616178
## 10482 -8630882 -8640153 -8621612 -8645060 -8616704
## 10483 -8631489 -8640814 -8622164 -8645750 -8617228
##
## Neutral.Current
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 0.3230546 -0.4748936 1.121003 -0.8973019 1.543411
## 10482 0.3230546 -0.5419039 1.188013 -0.9997852 1.645894
## 10483 0.3230546 -0.6040834 1.250193 -1.0948806 1.740990
##
## Rising.Demand
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 4783.708 4081.888 5485.527 3710.367 5857.048
## 10482 4793.128 3887.345 5698.912 3407.852 6178.405
## 10483 4800.673 3722.367 5878.979 3151.547 6449.800
##
## Maximum.Demand
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 8790.703 8686.287 8895.119 8631.012 8950.394
## 10482 8790.703 8685.485 8895.921 8629.786 8951.620
## 10483 8790.703 8684.689 8896.717 8628.569 8952.837
##
## RPM
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 1499.413 1480.484 1518.342 1470.464 1528.363
## 10482 1499.413 1480.484 1518.342 1470.464 1528.363
## 10483 1499.413 1480.484 1518.342 1470.464 1528.363
##
## Load.Hours.Received
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 3049055482 2407024932 3691086032 2067154488 4030956475
## 10482 3049055482 2148095545 3950015418 1671156165 4426954799
## 10483 3049055482 1948485453 4149625510 1365878873 4732232090
##
## No.Of.Intrruptions
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 5112300 5098993 5125606 5091949 5132650
## 10482 5112729 5095059 5130399 5085705 5139753
## 10483 5113158 5092002 5134314 5080803 5145513plot(forecast(myts, 3))
Exponential models to forecast results:
Both the HoltWinters() function and the ets() function in the forecast package, can be used to fit exponential models.
Let us try for a single variable, to predict total power and average current.
- Using ets() function for automated forecasting:
myts1 <- ts(sub.df$W.Total)
fit <- ets(myts1)
accuracy(fit)## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.04446492 2024.826 1297.163 -Inf Inf 0.8568332 -0.02051748forecast(fit, 5)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 4365.869 1770.950 6960.788 397.28336 8334.455
## 10482 4365.869 1698.642 7033.097 286.69653 8445.042
## 10483 4365.869 1628.242 7103.496 179.02961 8552.709
## 10484 4365.869 1559.608 7172.130 74.06283 8657.675
## 10485 4365.869 1492.613 7239.126 -28.39729 8760.136plot(forecast(fit, 5))
- Using HoltWinters() function to fit exponential models
par(mfrow=c(1,1))
myts2 <- ts(sub.df$Amps.Ave.)
fit1 <- HoltWinters(myts2, beta=FALSE, gamma=FALSE)
forecast(fit1, 3)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 10481 7.936228 4.650865 11.22159 2.911698 12.96076
## 10482 7.936228 4.600239 11.27222 2.834273 13.03818
## 10483 7.936228 4.550370 11.32209 2.758006 13.11445plot(forecast(fit1, 3))
Multiple linear regression(1)
fit2 <- lm(sub.df$W.Total ~ ., data=sub.df)
summary(fit2)##
## Call:
## lm(formula = sub.df$W.Total ~ ., data = sub.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9484.5 -88.2 -0.2 82.5 1004.7
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.899e+01 2.403e+02 -0.245 0.80612
## VAr.Total 5.838e-01 3.964e-03 147.274 < 2e-16 ***
## P.F 1.613e+03 1.407e+01 114.633 < 2e-16 ***
## VA.Total 1.052e+00 1.637e-02 64.271 < 2e-16 ***
## Amps.Ave. -5.228e+01 1.098e+01 -4.762 1.95e-06 ***
## Frequency 3.771e+04 2.247e+05 0.168 0.86674
## Wh.Rec. 1.379e-04 8.971e-05 1.537 0.12439
## VAh.Rec. 3.901e-05 1.197e-04 0.326 0.74444
## VArh.I.Rec. -5.339e-04 1.333e-04 -4.005 6.25e-05 ***
## VArh.C.Rec. 2.776e-04 1.069e-04 2.597 0.00942 **
## Neutral.Current 3.251e+01 2.813e+00 11.557 < 2e-16 ***
## Rising.Demand 1.568e-01 2.176e-03 72.047 < 2e-16 ***
## Maximum.Demand 2.978e-02 1.016e-02 2.931 0.00338 **
## RPM -1.258e+03 7.491e+03 -0.168 0.86665
## Load.Hours.Received -5.201e-09 1.815e-09 -2.866 0.00417 **
## No.Of.Intrruptions 5.486e-05 1.044e-05 5.255 1.51e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 230 on 10464 degrees of freedom
## Multiple R-squared: 0.9899, Adjusted R-squared: 0.9899
## F-statistic: 6.843e+04 on 15 and 10464 DF, p-value: < 2.2e-16The variables having 3 stars near the column having p values of the estimates, these stars show that the p-values of these estimates are statistically significant.Therefore, the affecting variables in this case are VAr.Total(total reactive power), P.F(power factor),VA.Total(total apparent power),Amps.Ave(average current), VArh.I.Rec.(Recative Inductive Energgy Received), Neutral.Current, Rising.Demand, No.Of.Intrruptions. The multiple R-squared value and the low residual standard error suggests that this is a pretty good model in determining total active power.
Multiple linear regression(2)
fit2 <- lm(sub.df$VAr.Total ~ ., data=sub.df)
summary(fit2)##
## Call:
## lm(formula = sub.df$VAr.Total ~ ., data = sub.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1550.0 -102.8 -21.8 58.8 13487.6
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.430e+02 3.381e+02 1.310 0.190109
## W.Total 1.156e+00 7.846e-03 147.274 < 2e-16 ***
## P.F -2.916e+03 8.479e+00 -343.941 < 2e-16 ***
## VA.Total -1.854e+00 2.028e-02 -91.439 < 2e-16 ***
## Amps.Ave. 5.395e+02 1.454e+01 37.117 < 2e-16 ***
## Frequency -2.677e+05 3.162e+05 -0.847 0.397249
## Wh.Rec. -5.652e-04 1.261e-04 -4.481 7.49e-06 ***
## VAh.Rec. 1.143e-04 1.683e-04 0.679 0.497020
## VArh.I.Rec. 1.122e-03 1.874e-04 5.989 2.18e-09 ***
## VArh.C.Rec. -5.795e-04 1.504e-04 -3.854 0.000117 ***
## Neutral.Current -6.855e+01 3.927e+00 -17.458 < 2e-16 ***
## Rising.Demand -8.349e-02 3.655e-03 -22.844 < 2e-16 ***
## Maximum.Demand -1.018e-01 1.427e-02 -7.135 1.04e-12 ***
## RPM 8.923e+03 1.054e+04 0.847 0.397231
## Load.Hours.Received 6.630e-09 2.553e-09 2.596 0.009431 **
## No.Of.Intrruptions -6.139e-05 1.469e-05 -4.178 2.96e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 323.6 on 10464 degrees of freedom
## Multiple R-squared: 0.9666, Adjusted R-squared: 0.9666
## F-statistic: 2.021e+04 on 15 and 10464 DF, p-value: < 2.2e-16The affecting variables in this case are W.Total(total active power), P.F(power factor),VA.Total(total apparent power),Amps.Ave(average current), Wh.Rec.(ActiveEnergy Received),VArh.I.Rec.(Recative Inductive Energgy Received), VArh.C.Rec(Recative Capacitive Energgy Received),Maximum.Demand, Neutral.Current, Rising.Demand, No.Of.Intrruptions. The multiple R-squared value and the residual standard error suggests that this model could be used, but not suggested, in determining total reactive power.
Multiple linear regression(3)
fit3 <- lm(sub.df$VA.Total ~ ., data=sub.df)
summary(fit3)##
## Call:
## lm(formula = sub.df$VA.Total ~ ., data = sub.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -903.7 -51.6 0.1 51.3 3837.0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.035e+02 1.215e+02 -0.851 0.394569
## W.Total 2.690e-01 4.185e-03 64.271 < 2e-16 ***
## VAr.Total -2.395e-01 2.619e-03 -91.439 < 2e-16 ***
## P.F -6.740e+02 8.416e+00 -80.081 < 2e-16 ***
## Amps.Ave. 4.918e+02 2.788e+00 176.391 < 2e-16 ***
## Frequency 2.752e+04 1.136e+05 0.242 0.808607
## Wh.Rec. -1.724e-04 4.533e-05 -3.803 0.000144 ***
## VAh.Rec. -3.271e-05 6.050e-05 -0.541 0.588803
## VArh.I.Rec. 5.059e-04 6.728e-05 7.519 5.99e-14 ***
## VArh.C.Rec. -2.847e-04 5.400e-05 -5.272 1.38e-07 ***
## Neutral.Current 3.626e+00 1.431e+00 2.534 0.011299 *
## Rising.Demand -3.615e-03 1.345e-03 -2.687 0.007213 **
## Maximum.Demand -1.762e-02 5.137e-03 -3.429 0.000608 ***
## RPM -9.172e+02 3.788e+03 -0.242 0.808671
## Load.Hours.Received 4.512e-10 9.179e-10 0.492 0.623013
## No.Of.Intrruptions -1.949e-05 5.282e-06 -3.691 0.000225 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 116.3 on 10464 degrees of freedom
## Multiple R-squared: 0.9957, Adjusted R-squared: 0.9957
## F-statistic: 1.632e+05 on 15 and 10464 DF, p-value: < 2.2e-16The affecting variables in this case are W.Total(total active power), VAr.Total(total reactive power), P.F(power factor),VA.Total(total apparent power),Amps.Ave(average current), Wh.Rec.(ActiveEnergy Received),VArh.I.Rec.(Recative Inductive Energgy Received), VArh.C.Rec(Recative Capacitive Energgy Received),Maximum.Demand, No.Of.Intrruptions. The multiple R-squared value and the low residual standard error suggests that this is a pretty good model in determining total apparent power.
Multiple linear regression(4)
fit4<- lm(sub.df$Amps.Ave. ~ ., data=sub.df)
summary(fit4)##
## Call:
## lm(formula = sub.df$Amps.Ave. ~ ., data = sub.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.1688 -0.1165 0.0047 0.1092 2.5197
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.100e-01 2.138e-01 0.982 0.325970
## W.Total -4.136e-05 8.686e-06 -4.762 1.95e-06 ***
## VAr.Total 2.156e-04 5.810e-06 37.117 < 2e-16 ***
## P.F 6.427e-01 1.772e-02 36.264 < 2e-16 ***
## VA.Total 1.522e-03 8.627e-06 176.391 < 2e-16 ***
## Frequency -6.242e+01 1.999e+02 -0.312 0.754847
## Wh.Rec. 2.993e-07 7.975e-08 3.752 0.000176 ***
## VAh.Rec. 5.522e-08 1.064e-07 0.519 0.603851
## VArh.I.Rec. -8.151e-07 1.184e-07 -6.884 6.17e-12 ***
## VArh.C.Rec. 4.785e-07 9.501e-08 5.037 4.81e-07 ***
## Neutral.Current -1.401e-02 2.515e-03 -5.572 2.58e-08 ***
## Rising.Demand -7.229e-05 2.259e-06 -31.998 < 2e-16 ***
## Maximum.Demand 2.723e-05 9.037e-06 3.013 0.002592 **
## RPM 2.080e+00 6.663e+00 0.312 0.754865
## Load.Hours.Received 1.169e-12 1.615e-12 0.724 0.469060
## No.Of.Intrruptions 1.541e-08 9.296e-09 1.658 0.097321 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2046 on 10464 degrees of freedom
## Multiple R-squared: 0.9943, Adjusted R-squared: 0.9943
## F-statistic: 1.219e+05 on 15 and 10464 DF, p-value: < 2.2e-16The affecting variables in this case are W.Total(total active power), VAr.Total(total reactive power), P.F(power factor),VA.Total(total apparent power), Wh.Rec.(ActiveEnergy Received),VArh.I.Rec.(Recative Inductive Energgy Received), VArh.C.Rec(Recative Capacitive Energgy Received),Neutral.Current,Rising.Demand. The multiple R-squared value and the very less residual standard error suggests that this is a very good model in determining average current.