Influência da não estacionariedade nas curvas de regularização de reservatórios de usinas hidrelétricas

Degraf, Henrique; Detzel, Daniel Henrique Marco

Henrique Degraf

Universidade Federal do Paraná, Curitiba, PR, Brasil

https://orcid.org/0000-0002-8257-8564

Daniel Henrique Marco Detzel

Universidade Federal do Paraná, Curitiba, PR, Brasil

https://orcid.org/0000-0003-2841-6502

E-mails: degraf.henrique@gmail.com (HD), detzel@ufpr.br (DHMD)

Authors contributions

Henrique Degraf: Responsible by the streamflow data download from ONS portal, programming the codes used for the article, image formatting, text review.

Daniel Henrique Marco Detzel: Responsible by the streamflow data download from ONS portal, for the article, text review.

Editor-in-Chief: Adilson Pinheiro

Associated Editor: Carlos Henrique Ribeiro Lima

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Figure 1
Workflow of the proposed methodology. The procedure is applied individually for each considered time series.

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Figure 2
SIN’s subsystems and HPPs location. The four studied HPPs are highlighted.

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Figure 3
Autocorrelation (left panel) and partial autocorrelation (right panel) functions for the ENAs of SIN’s subsystems (a) Southeast/Central-west, (b) South, (c) Northeast, and (d) North.

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Figure 2
SIN’s subsystems and HPPs location. The four studied HPPs are highlighted.

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Figure 3
Autocorrelation (left panel) and partial autocorrelation (right panel) functions for the ENAs of SIN’s subsystems (a) Southeast/Central-west, (b) South, (c) Northeast, and (d) North.

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Figure 4
S-Y-R relationships for each EER: (a) Southeast/Central-West, (b) South, (c) Northeast, and (d) North. The blue and green curves were obtained with the historical series. The shades indicate the different reliability bands for the S-Y-R curves.

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Figure 5
S-Y-R relationships for each HPP: (a) Ilha Solteira, (b) Foz do Areia, (c) Sobradinho, and (d) Tucuruí. On the left panel, the reliability levels were obtained with the model estimated with the historical dataset censured at the opening dates of the HPPs. On the right panel, they were calculated using all the available data.

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Table 1
HPPs main information.

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Table 2
P-values of the normality test applied to the SIN EERs and studied HPPs. Bold p-values indicate null hypothesis rejection at a 0.05 significance level. For the non-normal series, logarithmic transformation was applied and submitted to the same test for normality confirmation.

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Table 3
AIC and BIC for AR(1) and ARMA(1,1) models fitted to ENAs and HPPs time series. The best model is the one that results in the minimum value of each criterion (in bold).

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Table 4
P-values for normality, homoscedasticity, and independence tests applied to the residuals obtained from the fitted AR(1) for all series. No rejections were found for a 0.05 significance level.

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Table 5
P-values of the nonstationarity tests applied to the SIN EERs. Bold p-values indicate null hypothesis rejection at a 0.05 significance level. The signs in Mann-Kendall test results suggest increasing (

+

) or decreasing (

-

) trends.

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Table 6
P-values of the nonstationarity tests applied to the studied HPPs. Bold p-values indicate null hypothesis rejection at a 0.05 significance level. The signs in Mann-Kendall test results suggest increasing (

+

) or decreasing (

-

) trends.

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Table 7
ENAs synthetic series validation. Results for the South and Northeast subsystems are also shown for the original nonstationary series, for comparison.

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Table 8
HPPs synthetic series validation. Results for Foz do Areia and Sobradinho are also shown for the original nonstationary series, for comparison.

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HPP	Basin	Opening date	Operator	Generation capacity (MW)	Useful storage capacity (hm³)
Ilha Solteira	Paraná	1973	CESP	3444	12828
Foz do Areia	Iguazu	1981	COPEL	1676	3805
Sobradinho	São Francisco	1979	CHESF	1050	28669
Tucuruí	Tocantins	1984	ELETRONORTE	8730	11293

ENA/HPP	Original Series	Log-transformed series
Southeast/Central-west	0.13	-
South	< 0.01	0.06
Northeast	< 0.01	0.76
North	0.57	-
Foz do Areia	0.02	0.14
Ilha Solteira	< 0.01	0.08
Sobradinho	0.02	0.79
Tucuruí	0.02	0.98

ENA/HPP	AR(1)		ARMA(1,1)
ENA/HPP	AIC	BIC	AIC	BIC
Southeast/Central-west	-245.80	-245.43	-246.32	-243.60
South	1554.32	1554.68	1556.43	1559.15
Northeast	-154.74	-154.37	-160.85	-158.13
North	1488.66	1489.02	1490.71	1493.43
Foz do Areia	590.54	590.22	592.81	594.16
Ilha Solteira	641.97	641.43	644.16	645.07
Sobradinho	-85.84	-86.21	-83.91	-82.66
Tucuruí	-96.12	-96.37	-95.11	-93.62

ENA/HPP (residuals)	Normality	Homoscedasticity	Independence
Southeast/Central-west	0.67	0.21	0.76
South	0.09	0.81	0.53
Northeast	0.86	0.29	0.23
North	0.09	0.37	0.56
Foz do Areia	0.48	0.43	0.20
Ilha Solteira	0.63	0.14	0.54
Sobradinho	0.10	0.82	0.78
Tucuruí	0.49	0.26	0.70

EER	Prewhitening	Mann-Kendall		Pettitt
EER	Prewhitening	p-value	Trend sign	p-value	Breakpoint (year)
Southeast/Central-west	Yes	0.33	$+$	0.09	1970
South	Yes	0.01	$+$	0.03	1970
Northeast	Yes	0.03	$-$	0.02	1991
North	No	0.29	$-$	0.55	1997

HPP	Prewhitening	Mann-Kendall		Pettitt
HPP	Prewhitening	p-value	Trend sign	p-value	Breakpoint (year)
Ilha Solteira	Yes	0.47	$+$	0.32	1971
Foz do Areia	Yes	0.04	$+$	0.06	1968
Sobradinho	Yes	0.04	$-$	0.04	1992
Tucuruí	Yes	0.73	$-$	0.72	1976

Series	M (m³/s)	SD (m³/s)	CV	SK	min (m³/s)	max (m³/s)	AC1	LD (years)	MD (m³/s)
	Southeast/Central-west
Historical	41900	7183	0.17	0.44	28240	77520	0.38	9	54940
Synthetic	41820	6810	0.16	0.44	27710	61650	0.36	8.6	54710
	South
Historical (original)	9185	3249	0.35	0.82	3148	21720	0.24	7	17850
Historical (stationary)	10380	3356	0.32	0.52	4299	21720	0.11	8	16960
Synthetic	10360	3328	0.32	-0.01	2121	18590	0.10	6.3	20030
	Northeast
Historical (original)	7795	2578	0.33	0.72	2525	15130	0.53	11	36380
Historical (stationary)	5928	1666	0.28	0.57	2525	10140	0.41	8	16290
Synthetic	5910	1672	0.28	0.77	2889	11320	0.41	9.8	14370
	North
Historical	12360	2358	0.19	0.17	5838	18660	0.19	8	16520
Synthetic	12360	2329	0.19	-0.02	6888	17760	0.16	6	13630

Series	M (m³/s)	SD (m³/s)	CV	SK	min (m³/s)	max (m³/s)	AC1	LD (years)	MD (m³/s)
	Ilha Solteira
Historical	5214	1184	0.23	0.98	2803	10680	0.42	9	9783
Synthetic	5202	1165	0.22	0.61	2949	8796	0.37	9.1	9523
	Foz do Areia
Historical (original)	659	243	0.37	0.83	249	1528	0.24	5	513
Historical (stationary)	731	252	0.34	0.66	259	1528	0.14	5	1073
Synthetic	731	269	0.36	1.01	284	1680	0.11	7.6	1565
	Sobradinho
Historical (original)	2531	840	0.33	0.73	796	4952	0.54	8	6127
Historical (stationary)	1942	555	0.28	0.58	796	3448	0.43	8	5466
Synthetic	1936	557	0.28	0.78	935	3744	0.43	10	4897
	Tucuruí
Historical	10990	2957	0.27	0.74	6070	18880	0.34	7	24590
Synthetic	10980	2880	0.26	0.67	5858	19350	0.36	8.3	20670

sgn [z_{j} - z_{i}] = \{\begin{matrix} 1, if (z_{j} - z_{i}) > 0 \\ 0, if (z_{j} - z_{i}) = 0 \\ - 1, if (z_{j} - z_{i}) < 0 \end{matrix}

z = \{\begin{matrix} \frac{M K - 1}{\sqrt{V A R [M K]}}, if M K > 0 \\ 0, if M K = 0 \\ \frac{M K + 1}{\sqrt{V A R [M K]}}, if M K < 0 \end{matrix}

[1] E-mails: degraf.henrique@gmail.com (HD), detzel@ufpr.br (DHMD)

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Influência da não estacionariedade nas curvas de regularização de reservatórios de usinas hidrelétricas

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