Wind energy assessment and mapping using terrain nonlinear autoregressive neural network (TNARX) and wind station data

Figures & data

Figure 1. Position of the existing station and target locations.

Figure 2. Process of EFFNN development.

Table 1. PDF and CDF models

PDF	Equation PDF and CDF	Equation	Remarks
Weibull	$p(v)=\frac{k}{c}{\left(\frac{v}{c}\right)}^{k-1}exp{\left\{-\left(\frac{v}{c}\right)\right\}}^k$	3	v > 0, k, c > 0, where c is the scale parameter measure in m/s and k is the shape parameter which has no unit
	$P(v)=\underset{0}{\overset{\infty }{\int }}p(v)dv=1-exp{\left\{-\left(\frac{v}{c}\right)\right\}}^k$	4
Rayleigh	$p(v)=\frac{2v}{c^2}exp-{\left[\frac{v}{c}\right]}^2$	5	Rayleigh is a special case of the Weibull function with k = 2
Gamma	$p(v)=\frac{v^{k-1}}{c\Gamma (k)}exp\left[-\frac{v}{c}\right]$	5	Where Ґ (v) is an incomplete Gamma function
	$P(v)=\frac{\Gamma {\left(\frac{v}{c}\right)}^k}{\Gamma \left(\alpha \right)}$	6
Lognormal	$p(v)=\frac{1}{vc\sqrt{2\pi }}exp\left[-\frac{1}{2}{\left(\frac{ln-c}{c}\right)}^2\right]$	7	Where Ø is the Laplace integral function.
	$P(v)=\varphi \left(\frac{lnv-k}{c}\right)$	8
Erlang	$p(v)=1-exp\left[-\frac{-v}{k}\right]\sum _{i=0}^{c-1}\frac{v^i}{k^{i}i}$	9	Where α is an integer, contrary to the Gamma
	$P(v)=\left[-{\left(\frac{c}{v-\gamma }\right)}^{\alpha }\right]$	10

Table 2. GOF models

GOF	Equation	Number
KS	$D=Max\left(D^{+},D^{-}\right),D^{+}=Max\left(\frac{1}{n}-F\left(\frac{1}{n}-F\left(x_i\right)\right)\right)$	11
	$D^{-}=Max\left(F(x_i)-\frac{i-1}{n}\right)$	12
AD	$A^2=-n-\frac{1}{n}\sum _{i=1}^N\left(2i-1\right)\left[lnF(x_i^{})+ln(F(x_{n+1+i}))\right]$	13
CS	$x^2=\sum _{i=1}^k\frac{{\left(O_i-E_i\right)}^2}{E_i},E_i=F(x_2)-F(x_1)$	14

Figure 3. A sample of wind speed map of Sarawak at 20 m.

Figure 4. Wind power based on exact and formulated model.

Figure 5. ANN training (a) Matu (b) Tatau.

Figure 6. Correlation between ANN and reference based on training data sets for (a) Matu and (b) Tatu.

Figure 7. Regression between ANN and reference based on whole training data sets for (a) Matu and (b) Tatu.

Figure 8. Comparison between predicted and observed monthly wind speed.

Table 3. Summary of the percentile of missing wind speed values

Items	Bintulu	Total
Number of observations	3,653	3,653
No of valid data points	3,640	3,640
Missing values	13	13
Percentage	0.36%	0.22%

Table 4. Effectiveness of methods based on station

Station	Methods	Prediction accuracy	Coefficient of determination (R ^2)	Mean absolute error (MAE)	Root mean square error (RMSE)
Miri	NB	0.67	0.59	3.42	8.78
	NF	0.63	0.54	3.89	8.04
	Li	0.89	0.81	2.19	7.66
	CS	0.93	0.86	2.05	4.65

Notes: NB: Newton Backward, NF: Newton Forward, Linear Interpolation, CS: Cubic Spline.

Figure 9. Variation of daily average wind speed for ten years (2006–2015).

Figure 10. Wind direction for ten years (2006–2015) at Bintulu, Matu, and Tatau.

Table 5. Wind speed (2006–2015) at 10–40 m heights in Sibu

	Wind speed (m/s)
Month	10 m	20 m	30 m	40 m
January	1.59	2.06	2.40	2.67
February	1.60	2.07	2.41	2.68
March	1.60	2.07	2.41	2.68
April	1.54	1.99	2.32	2.58
May	1.50	1.94	2.26	2.51
June	1.47	1.90	2.21	2.46
July	1.47	1.91	2.22	2.47
August	1.49	1.93	2.25	2.50
September	1.51	1.96	2.28	2.54
October	1.49	1.93	2.24	2.50
November	1.48	1.92	2.23	2.49
December	1.47	1.90	2.21	2.46
Annual	1.52	1.97	2.29	2.55

Table 6. Comparisons of monthly air densities at different heights (2006–2015) at Sibu

Month	ρ(h, r h ) kg/m^3
	10 m	20 m	30 m	40 m
January	1.158	1.157	1.156	1.155
February	1.162	1.161	1.160	1.159
March	1.163	1.162	1.161	1.160
April	1.162	1.161	1.160	1.159
May	1.162	1.161	1.160	1.159
June	1.162	1.161	1.160	1.159
July	1.162	1.161	1.160	1.159
August	1.162	1.161	1.160	1.159
September	1.162	1.161	1.160	1.159
October	1.162	1.161	1.160	1.159
November	1.162	1.161	1.160	1.159
December	1.162	1.161	1.160	1.159
Average	1.162	1.161	1.160	1.159

Table 7. GOF summary at Bintulu

S/No	Distribution	KS		AD		CS
		Statistic	Rank	Statistic	Rank	Statistic	Rank
1	Erlang	0.12431	4	62.064	4	525.45	4
2	Gamma	0.06992	1	15.922	1	229.9	2
3	Weibull	0.08156	3	16.644	3	230.03	3
4	Rayleigh (2P)	0.26491	5	370.42	5	2396.3	5
5	Lognormal	0.07412	2	16.013	2	229.9	1

Figure 11. Weibull model fitted wind power density.

Figure 12. Gamma model fitted wind power density.

Table 8. Comparisons of wind power density at predicted locations

Station	10–40 m Actual wind power density (W/m^2)		10–40 m Weibull wind power density (W/m^2)		10–40 m Gamma wind power density (W/m^2)
	Min	Max	Min	Max	Min	Max
Matu	2.37	12.77	2.80	15.80	2.47	13.56
Tatau	2.70	9.62	3.16	11.03	2.92	10.02

Table 9. Comparisons of wind energy density at predicted locations

Station	10–40 m Actual wind energy density (kWh/m^2/year)		10–40 m Weibull wind energy density (kWh/m^2/year)		10–40 m Gamma wind energy density (kWh/m^2/year)
	Min	Max	Min	Max	Min	Max
Matu	20.79	93.14	24.57	111.86	21.68	118.75
Tatau	23.68	84.22	27.69	96.64	26.10	87.81

Figure 13. Computed AEO at different elevation.