ELD analysis under tropical climate using wavelet and regression approaches for power management: Indonesia case study

Figures & data

Figure 1. Variation of ELD and temperature average: (a) the whole observed period, (b) January 2018.

Figure 2. ELD and solar radiation duration: a) the whole observed period, (b) January 2018.

Figure 3. Work flow for ELD analysis.

Figure 4. Phase difference circle.

Figure 5. Return series form for each data variable.

Figure 6. CWT spectrum of the ELD.

Figure 7. CWT spectrum for each weather variable: (a) temperature, (b) solar radiation exposure, (c) humidity, and (d) wind speed.

Figure 8. Wavelet coherence between ELD and temperature.

Notes: The thick black contour shows a 5% significance level against the red noise. Power is denoted by a color code that runs from blue (low power) to red (high power) for Figures 8 to 11.

Figure 9. Wavelet coherence between ELD and solar radiation.

Figure 10. Wavelet coherence between ELD and humidity.

Figure 11. Wavelet coherence between ELD and wind speed.

Table 1. Regression results for the whole period.

Variable	ELDwp model (Equation 6(6) $\begin{array}{rl}& EL{D}_{wp}={\delta }_0+{\delta }_{1}TEM+{\delta }_{2}SOL+{\delta }_{3}HUM+{\delta }_{4}WIN\\ & +u_t\end{array}$(6) )
	Coefficient	p-value	Standard error	Ranking
${\delta }_0$	273.7174	0.0995	166.0291
TEM	50.8053	0.0000	4.1148	1
SOL	4.1140	0.0000	0.8193	2
HUM	2.0144	0.0197	0.8623	3
WIN	4.9653	0.2031	3.8971	NS
AR(1)	0.8283	0.0000	0.0413
AR(2)	0.1309	0.0006	0.0380
Regression statistic
R^2	0.9148
Adj. R^2	0.9144
S.E. Reg.	85.8194
Prob. of FS	0.0000
AIC	11.7487
SC	11.7807
D-W Stat.	2.0531

Notes: NS is insignificant variable. Adj. R² value without insignificance variable (WIN) in the model is 0.9143.

Table 2. Regression results for the rainy season.

Variable	ELDrs model (Equaton 7(7) $\begin{array}{rl}& EL{D}_{rs}={\gamma }_0+{\gamma }_{1}TEM+{\gamma }_{2}SOL+{\gamma }_{3}HUM+{\gamma }_{4}WIN\\ & +u_t\end{array}$(7) )
	Coefficient	p-value	Standard error	Ranking
${\gamma }_0$	442.7343	0.1366	296.9836
TEM	50.9510	0.0000	6.3918	1
SOL	5.7848	0.0000	1.0721	2
HUM	−0.3250	0.8507	1.7261	NS
WIN	7.7789	0.0879	4.5497	NS
AR(1)	0.8303	0.0000	0.0557
AR(2)	0.1181	0.0177	0.0496
Regression statistic
R^2	0.8975
Adj. R^2	0.8964
S.E. Reg.	92.9570
Prob. of FS	0.0000
AIC	11.9149
SC	11.9366
D-W Stat.	2.0590

Notes: NS is an insignificant variable. Adj. R² value without insignificance variables (HUM and WIN) in the model is 0.8963.

Table 3. Regression results for the dry season.

Variable	ELDds model (Equation 8(8) $\begin{array}{rl}& EL{D}_{ds}={\lambda }_0+{\lambda }_{1}TEM+{\lambda }_{2}SOL+{\lambda }_{3}HUM+{\lambda }_{4}WIN\\ & +u_t\end{array}$(8) )
	Coefficient	p-value	Standard error	Ranking
${\lambda }_0$	587.0709	0.0074	218.3795
TEM	37.6183	0.0000	5.8843	1
SOL	1.8976	0.1280	1.2447	NS
HUM	2.8283	0.0047	0.9969	2
WIN	−1.1703	0.8937	8.7542	NS
AR(1)	0.8130	0.0000	0.0549
AR(2)	0.1524	0.0035	0.0519
Regression statistic
R^2	0.9249
Adj. R^2	0.9241
S.E. Reg.	81.9317
Prob. of FS	0.0000
AIC	11.6623
SC	11.7171
D-W Stat.	2.0366

Notes: NS is insignificant variable. Adj. R² value without insignificance variables (SOL and WIN) in the model is 0.9241.

Table 4. Typical weather parameters in the rainy season.

	TEM (°C)	SOL (hour)	HUM (%)	WIN (m/sec)
Maximum	33.20	11.00	95.00	8.00
Minimum	24.30	0.00	57.00	1.00
Daily data number	544	544	544	544

Table 5. Typical weather parameters in the dry season.

	TEM (°C)	SOL (hour)	HUM (%)	WIN (m/sec)
Maximum	30.60	11.00	93.00	3.10
Minimum	25.10	0.00	52.00	1.00
Daily data number	552	552	552	552

Figure 12. Histogram of daily temperature values: (a) rainy season, (b) dry season.

Figure 13. Histogram of daily humidity values: (a) rainy season, (b) dry season.

Data availability statement

Supporting data for this research are provided upon request to corresponding author.