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Impact of climate change on hydropower productionwithin the La Plata BasinHeinz Dieter Filla, Miriam Rita Moro Mineb, Cristovao Vicente Scapulatempo Fernandesc &Marcelo Rodrigues Bessad

a Professor, Department of Hydraulic and Sanitation, Federal University of Paraná,Curitiba, Brazil. Email:b Professor, Department of Hydraulic and Sanitation, Federal University of Paraná,Curitiba, Brazil. Email:c Professor, Department of Hydraulic and Sanitation, Federal University of Paraná,Curitiba, Brazil.d Professor, Department of Hydraulic and Sanitation, Federal University of Paraná,Curitiba, Brazil. Email:Accepted author version posted online: 15 Nov 2013.Published online: 28 Feb 2014.

To cite this article: Heinz Dieter Fill, Miriam Rita Moro Mine, Cristovao Vicente Scapulatempo Fernandes & MarceloRodrigues Bessa (2013) Impact of climate change on hydropower production within the La Plata Basin, InternationalJournal of River Basin Management, 11:4, 449-462, DOI: 10.1080/15715124.2013.865638

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Research paper

Impact of climate change on hydropower production within the La Plata Basin

HEINZ DIETER FILL, Professor, Department of Hydraulic and Sanitation, Federal University of Parana, Curitiba,Brazil. Email: heinzfill@yahoo.com

MIRIAM RITA MORO MINE, Professor, Department of Hydraulic and Sanitation, Federal University of Parana,Curitiba, Brazil. Email: mrmine.dhs@ufpr.br

CRISTOVAO VICENTE SCAPULATEMPO FERNANDES, Professor, Department of Hydraulic and Sanitation,Federal University of Parana, Curitiba, Brazil. Email: cris.dhs@ufpr.br (author for correspondence)

MARCELO RODRIGUES BESSA, Professor, Department of Hydraulic and Sanitation, Federal University ofParana, Curitiba, Brazil. Email: bessa@lactec.org.br

ABSTRACTThis paper aims to estimate the variation of the combined dependable energy output of the set of major hydropower plants within the Brazilian part of theLa Plata Basin due to possible climate changes during the twenty-first century. It uses and compares the predictions of two regional climate models,namely PROMES [Castro, M., Fernandez, C., and Gaertner, M.A., 1993. Description of a mesoscale atmospheric numerical model. In: J.I. Dıaz and J.L.Lions, eds. Mathematics, climate and environment. Rech. Math. Appl. Ser. Mason, 230–253; Gallardo, A., Galvan, C., and Mermejo, R., 2012.PROMES-MOSLEF: An atmosphere-ocean coupled regional model. Coupling and preliminary results over the Mediterranean basin. 4th HYMEXWorkshop 2 2010] and RCA models [Rummukainem, M., 2010. State-of-the-art with regional climate models. WIREs Climate Change, 1, 82–96].Rainfall and temperature predictions are converted into streamflow at key gauge stations using Variable Infiltration Capacity Model [Liang, X., Let-tenmaier, D.P., Wood, E.F., and Burges, E.F., 1994. A simple hydrologically based model of land surface water and energy fluxes for general circulationmodels. Journal of Geophysical Research, 99, n. D7, 14,451–14,428]. The evaluation of the dependable energy output used the natural energy hydro-graph method engineering consultants (Canambra Engineering Consultants, 1969. Power study of South Brazil. 13 v. Appendice XVII Final Report. Riode Janeiro: Canambra Engineering Consultants), combined with the Monte Carlo simulation of synthetic series of natural energy. The main contributionof this paper is the consolidation of a methodology that provides estimates of the system’s dependable energy as a function of the return period for bothobserved and future predicted streamflows. As a conclusion, a reduction of the dependable energy output of the hydropower plants within the La PlataBasin could be expected during the twenty-first century

Keywords: Climate change; stochastic processes; hydropower production; stationarity; risk assessment; natural energy hydrograph

1 Introduction

Hydropower as well as being often the cheapest alternative

of electric energy production depends on the availability of

streamflows. Its capability is always linked to a probability

of failure and depends upon the statistical characteristics of the

watershed hydrology. Hence, if these characteristics change, the

dependable energy output of a hydroelectric system also will

change.

Considering only one reservoir associated with one power

plant, the problem of determining the maximum power output

is traditionally solved considering a series of inflows and the

maximum storage capacity, subject to two important restrictions,

namely: (1) the continuity equation for storage and (2) storage at

all-time non-negative and less or equal to the maximum storage

volume.

The optimal solution of this problem is called firm yield

(Loucks et al. 2005) and considering a hydroelectric power

plant case, it is defined as primary or firm energy. This

problem may also be solved by simulation, varying the release

flow by trial and error until the condition of minimum storage

equal to zero is reached. Considering a system with more than

one power plant, the problem becomes complex because the

non-linear operational rules of distinct reservoirs require for

Received 28 February 2013. Accepted 3 October 2013.

ISSN 1571-5124 print/ISSN 1814-2060 onlinehttp://dx.doi.org/10.1080/15715124.2013.865638http://www.tandfonline.com

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Intl. J. River Basin Management Vol. 11, No. 4 (December 2013), pp. 449–462

# 2014 International Association for Hydro-Environment Engineering and Research

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defining the optimal solution stochastic dynamic programming

strategies (Grygier and Stedinger, 2008). In the case of many

reservoirs, the so-called ‘curse of dimensionality’ precludes in

practice the direct solution of the optimization problem.

This paper presents an original method for this evaluation and

its application to the variation of the combined dependable

energy output of the hydropower plants located within the

Brazilian part of the La Plata Basin. The natural energy hydro-

graph (NEH) method avoids these problems and allows with

reasonable accuracy the estimation of firm energy even for

large interconnected hydrosystems (Fill, 1980).

An important question that arises in the planning of the future

expansion of an electric power system with hydropower plants is

to assess how climate changes due to global warming effects will

influence this planning. In this context, the quantitative evalu-

ation of the system’s dependable energy output, under different

climate scenarios, is necessary for its realistic future expansion

planning.

In the context of climate change analysis, effort is added to pre-

dicting the climate change impacts by proposing adaptation strat-

egies for land-use, agriculture, rural development, hydropower

production, river transportation, water resources and ecological

systems in wetlands (Fernandes et al. 2011). In a more comprehen-

sive hydrological approach, addressing issues of crucial impor-

tance such as the flood risks, river navigation (problems induced

by sediment transport), hydropower production and ecological

systems in wetlands are demanding research attention, especially

for proposing feasible adaptation strategies. This paper presents an

evaluation of the combined dependable energy output of the

hydropower plants located within the Brazilian part of the La

Plata Basin, addressing the impact of future climate changes on

the energy output and allowing contributions to adjust planning

strategies of the agencies responsible for the expansion and oper-

ation of the Brazilian electric power system.

2 Methods and case study area

In order to establish the basis for the method herein developed to

assess the change in the energy output for a series of hydroplants

within the La Plata Basin, a simulation approach combined

with Climate Models Scenarios is proposed, which includes:

(i) generation of precipitation/temperature scenarios; (ii) the rain-

fall-runoff model; (iii) the NEH method; (iv) generation of

streamflows for climate change scenarios; (v) generation of syn-

thetic energy inflows series; and (vi) the Monte Carlo simulation

of these series. Figure 1 highlights the methodological approach

herein developed and represents the computational effort devel-

oped to achieve the goals of this research.

2.1 The relevance of the case study area

The area analysed in this paper comprises the watersheds of

both Parana and Uruguay rivers upstream of the international

border. In the case of the Parana River, the Itaipu plant at the

Brazil–Paraguay border is also included. This area comprises

about 50% of the total generation capability of Brazil.

The study area includes 68 major hydroelectric power plants

(installed capacity above 30 MW) with a combined capacity of

53.421 MW and drainage area of roughly 880.000 km2.

Natural streamflows at the power plant sites were estimated

from nine key hydrometric stations located at the main sub-

basins of the study area. These key stations are given in

Table 1 and their location is shown in Figure 2. The main charac-

teristics of the 68 hydropower plants of the analysed system are

given in Table 2, which includes average discharge of each plant,

Figure 1 Synthesis of the methodology developed.

Table 1 Characteristics of the key streamflow stations.

Sub-basin Station

Drainage

area (km2)

Mean flow

(1931–2005)

(m3/s) l/(s.km2)

1 Alto Paranaıba Emborcacao 29,100 486 16.7

2 Baixo

Paranaıba

Sao Simao 171,000 2396 14.0

3 Alto Grande Furnas 52,100 924 17.7

4 Baixo Grande Agua Vermelha 139,000 2089 15.0

5 Tiete Nova

Avanhandava

62,700 747 11.9

6 Paranapanema Capivara 84,700 1077 12.7

7 Iguacu Salto Osorio 45,800 1034 22.6

8 Uruguai Ita 44,100 1043 23.6

9 Parana increm. Itaipu 824,000 10,130 12.3

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usable storage volume, installed capacity productivity and

drainage area.

In this context, the plant productivity is defined as the average

generation per unit discharge and it is given by

K = gH h

1000(MW/m3/s), (1)

where g ¼ 9.81 m/s2; �H is the average net head (m); and h is the

plant efficiency.

The natural discharge is computed by linear combination (Eq.

2) of natural flows measured at key streamflow station within the

sub-basin (Table 2)

QUS(t) = aQ1(t) + bQ2(t) (m3/s), (2)

where Q1(t) and Q2(t) are the streamflows at the key stations, a

and b are the transfer coefficients and QUS(t) is the discharge at

the powerplant (Fill, 1980). Additionally, operations of thermal

plants as well as small run of river hydroplants were not con-

sidered in the analysis. Also the effects of interconnection with

hydropower plants outside the La Plata Basin were not included

in this study.

2.2 The NEH method

The NEH method herein presented is an improvement of the

solution developed by Canambra Engineering Consultants

(1969) for the evaluation of the firm energy output of a fully

integrated hydroelectric system. The main improvement is

related to the regional integration of hydroplants located in

different river basins that imposes a number of questions that

cannot be solved by merely combining basin results. For

example: (i) Does the critical streamflow period for the same

system as a whole coincide with the critical period for the

basin? (ii) Is the basin storage under or overdeveloped in

relation to the system requirements? (iii) To what extent can

electrical integration compensate for the lack of hydraulic regu-

lation? In such a context, critical streamflow period is defined

as the hydrologic period during which the design storage in

the system or river basin is entirely depleted in order to

supply primary energy.

The NEH method provides a simplified approach to hydro-

power regulation and to study the operation of pooled resources.

In order to understand the concept of this method, it should be

recognized that the operation of a power system must be directed

towards regulation of the energy production rather than regu-

lation of river flows. Although the two types of regulation

usually go together, there are many exceptions conceivable in

large systems. Hence the evaluation of a group of resources

Figure 2 Case study and the location of the key streamflow stations.

Impact of climate change on hydropower production 451

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Table 2 Characteristics of hydropower plants system.

Vuse Qus Pot Prod. Transf. Coef. Drain. area

PPN Cod Power plant Sub-basin Gauge 1 Gauge 2 106 m3 m3/s MW MW/m3/s a b km2

1 1 Camargos Grande Furnas – 672 132 46 0.171 0.1429 0 6279

2 2 Itutinga Grande Furnas – 0 132 232 0.227 0.1429 0 6302

3 211 Funil Grande Grande Furnas – 0 304 180 0.338 0.329 0 15,770

4 6 Furnas Grande Furnas – 17,217 924 1312 0.726 1 0 52,138

5 7 M. de Moraes Grande Furnas A. Vermelha 2500 1032 478 0.314 0.9073 0.0927 59,730

6 8 Estreito Grande Furnas A. Vermelha 0 1057 1104 0.546 0.8858 0.1142 61,252

7 9 Jaguara Grande Furnas A. Vermelha 0 1067 424 0.385 0.8773 0.1227 61,871

8 10 Igarapava Grande Furnas A. Vermelha 0 1097 210 0.146 0.8515 0.1485 63,693

9 11 Volta Grande Grande Furnas A. Vermelha 0 1163 380 0.232 0.7948 0.2052 67,691

10 12 Porto Colombia Grande Furnas A. Vermelha 0 1322 328 0.189 0.6584 0.3416 77,427

11 14 Caconde Grande Furnas A. Vermelha 504 54 80.4 0.777 –0.0464 0.0464 2588

12 15 E. da Cunha Grande Furnas A. Vermelha 0 88 109 0.745 –0.0755 0.0755 4392

13 16 A. S. Oliveira Grande Furnas A. Vermelha 0 89 32 0.198 –0.0764 0.0764 4471

14 17 Marimbondo Grande Furnas A. Vermelha 5260 1847 1488 0.476 0.2077 0.7923 118,515

15 18 A. Vermelha Grande Furnas A. Vermelha 5169 2089 1396 0.429 0 1 139,437

16 71 Santa Clara Iguacu S. Osorio – 262 101 120 0.748 0.0977 0 3912

17 72 Fundao Iguacu S. Osorio – 0 106 120 0.811 0.1025 0 4096

18 74 Foz do Areia Iguacu S. Osorio – 3805 645 1676 1.016 0.6238 0 30,127

19 76 Segredo Iguacu S.Osorio – 388 744 1260 0.940 0.7195 0 34,346

20 77 Salto Santiago Iguacu S. Osorio – 4113 987 1420 0.804 0.9545 0 43,852

21 78 Salto Osorio Iguacu S. Osorio – 0 1034 1078 0.612 1 0 45,769

22 222 Salto Caxias Iguacu S. Osorio – 0 1328 1240 0.567 1.2843 0 56,977

23 34 Ilha Solteira Parana S. Simao + A. Verm. Itaipu 12,828 5285 3444 0.322 0.8583 0.1417 377,197

24 245 Jupia Parana S. Simao + A. Verm. Itaipu 0 6399 1551 0.187 0.6609 0.3391 476,797

25 246 Porto Primavera Parana S. Simao + A. Verm. Itaipu 5600 7197 1540 0.155 0.5196 0.4804 571,855

26 266 Itaipu Parana S. Simao + A. Verm. Itaipu 0 10,130 14,000 1.021 0 1 823,555

27 241 Salto Rio Verdinho Parana Emborcacao S. Simao 0 197 93 0.350 –0.1031 0.1031 11,894

28 294 Salto Parana Emborcacao S. Simao 0 181 108 0.393 –0.0948 0.0948 10,924

29 99 Espora Parana Emborcacao S. Simao 138 62 32.1 0.376 –0.0325 0.0325 3757

30 251 Serra do Facao Paranaıba Emborcacao S. Simao 3447 179 213 0.575 0.3683 0 10,639

31 24 Emborcacao Paranaıba Emborcacao S. Simao 13,056 486 1192 1.007 1 0 29,050

32 25 Nova Ponte Paranaıba Emborcacao S. Simao 10,380 299 510 0.866 –0.1565 0.1565 15,480

33 206 Miranda Paranaıba Emborcacao S. Simao 146 348 408 0.558 –0.1822 0.1822 18,124

34 207 Capim Branco I Paranaıba Emborcacao S. Simao 1 355 240 0.494 –0.1859 0.1859 18,471

35 28 Capim Branco II Paranaıba Emborcacao S. Simao 1 371 210 0.393 –0.1942 0.1942 19,285

36 205 Corumba IV Paranaıba Emborcacao S. Simao 687.8 133 127 0.560 –0.0696 0.0696 6938

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37 23 Corumba III Paranaıba Emborcacao S. Simao 263 165 93.6 0.328 –0.0864 0.0864 8808

38 209 Corumba I Paranaıba Emborcacao S. Simao 1030 457 375 0.543 –0.2393 0.2393 27,604

39 31 Itumbiara Paranaıba Emborcacao S. Simao 12454 1560 2280 0.614 0.4377 0.5623 94,728

40 32 Cach. Dourada Paranaıba Emborcacao S. Simao 0 1637 658 0.268 0.3974 0.6026 99,775

41 33 Sao Simao Paranaıba Emborcacao S.Simao 5540 2396 1710 0.562 0 1 171,474

42 247 Cacu Paranaıba Emborcacao S. Simao 34.5 195 65.1 0.222 –0.1021 0.1021 15,715

43 248 Barra dos Coqueiros Parana Emborcacao S. Simao 47.84 204 90 0.287 –0.1068 0.1068 12,567

44 47 A. A. Laydner Paranapanema Capivara – 3165 222 97.8 0.259 0.2061 0 17,891

45 48 Piraju Paranapanema Capivara – 0 227 80 0.224 0.2108 0 18,336

46 49 Chavantes Paranapanema Capivara – 3041 340 414 0.583 0.3157 0 27,769

47 249 Ourinhos Paranapanema Capivara – 0 344 44.1 0.093 0.3194 0 28,160

48 50 L. N. Garcez Paranapanema Capivara – 0 453 72 0.145 0.4206 0 38,719

49 51 Canoas II Paranapanema Capivara – 0 461 69.9 0.126 0.428 0 39,531

50 52 Canoas I Paranapanema Capivara – 0 479 82.5 0.146 0.4448 0 41,276

51 61 Capivara Paranapanema Capivara – 5724 1077 640 0.351 1 0 84,715

52 62 Taquarucu Paranapanema Capivara – 0 1139 554 0.216 1.0576 0 88,707

53 63 Rosana Paranapanema Capivara – 0 1281 372 0.150 1.1894 0 100,799

54 237 Barra Bonita Tiete N. Avanhandava - 2566 437 140 0.148 0.585 0 33,156

55 238 A. S. Lima Tiete N. Avanhandava – 0 487 144 0.182 0.6519 0 36,708

56 239 Ibitinga Tiete N. Avanhandava – 0 582 131 0.174 0.7791 0 44,923

57 240 Promissao Tiete N. Avanhandava – 2128 700 264 0.176 0.9371 0 58,106

58 242 Nova Avanhandava Tiete N. Avanhandava – 0 747 347 0.244 1 0 62,727

60 318 Henry Borden Tiete N. Avanhandava – 0 39 888 5.693 0.0522 0 –

61 215 Barra Grande Uruguai Ita – 2302 293 690 1.244 0.2809 0 11,902

62 216 Campos Novos Uruguai Ita – 157 304 880 1.511 0.2915 0 14,454

63 217 Machadinho Uruguai Ita – 1057 739 1140 0.840 0.7085 0 31,956

64 92 Ita Uruguai Ita – 0 1043 1450 0.888 1 0 44,118

65 93 Passo Fundo Uruguai Ita – 1404 56 226 2.119 0.0537 0 2200

66 220 Monjolinho Uruguai Ita – 0 97 67 0.534 0.093 0 3821

67 286 Quebra-Queixo Uruguai Ita – 26 77 120 0.966 0.0738 0 2628

68 94 Foz do Chapeco Uruguai Ita – 1 1255 855 0.439 1.2033 0 53089

Notes: PPN, Powerplant Number. Plant number 59 has been omitted from the table, because of aggregation programme input.

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deals basically with two components: (i) unregulated river flows

and (ii) the regulating ability of a number of reservoirs.

The desired end result, regulation of energy output, can be

studied by stating both components in terms of energy: (i) unre-

gulated river flows can be converted for every plant site into

unregulated or so-called natural energy and (ii) the natural

energy at the site is the product of the natural flow, the potential

head and a constant.

The conversions for the power study are based on average

monthly flows and the result is a NEH for all the plants.

Summing of the monthly energy values for all the plants in the

system yields the system NEH.

EN(t) =∑

Qi(t)Ki(t) (avg MW), (3)

where Qi(t) is the natural discharge of plant i (Eq. 2), Ki(t) is the

plant productivity natural discharge of plant i (Eq. 1) and P is the

set of plants of the system.

The usable reservoir volumes can be expressed in terms of

energy by computing the generation possible with the stored

water when passed through all the downstream developed

head. The total for the system forms the energy storage pool

which is available to regulate the NEH to the system load

demand (maximum energy storage).

Amax =∑

i[R

Vi

2628

( )[∑

j[JiKj] (MW month), (4)

where Vi is the usable storage capacity of reservoir i in 106 m3, Kj

is the productivity of plant j (MW/m3/s), R is the set of reservoirs

in the electrical system and Ji is the set of plants downstream of

reservoir i.

Thus, the system analysis becomes analogous to a regulation

study for a single river with one reservoir and one hydropower

plant. The assumption of full hydraulic and electrical integration

is implied by the method. A brief review of these assumptions

follows below:

(i) To convert natural flow into natural energy an average head

must be chosen, i.e. the difference between average head-

water and average tailwater elevation. An average tailwater

level can be reasonably well estimated. However, in the

case of a plant with storage, the average headwater level

depends on the function of the reservoir in the system.

For reservoirs in the upper portion of the drainage area,

which are usually emptied first, the average level may cor-

respond to 50% volume drawdown; reservoirs farther

downstream may seldom empty and then the average

value lies fairly close to normal maximum water level.

The average hydraulic heads used in the present study

were estimated on the basis of a critical period operation

for historical series. It can be stated that on average or

higher water conditions, the average elevations are prob-

ably higher, but so are the tailwater levels.

(ii) Natural flows must be corrected for reservoir evaporation

losses. This can be done before the conversion to natural

energy or afterwards as a reduction of energy capability.

(iii) It is implied that all stored and natural energy is usable, i.e.

no spill occurs. This condition is seldom fully realized, but

is very close to the actual situation in a well-developed

hydrosystem when operated in low water years. A run-of-

river plant without upstream storage may have regular

spill, but this quantity is predictable and can be removed

from the NEH before the start of the system regulation

study.

(iv) The available natural energy is compared with the load

demand to decide on filling or drawdown from the energy

pool. The distribution of storage changes over the individ-

ual reservoirs and possible restrictions on their operation

(minimum releases, rule curves, etc.) are ignored. The

NEH method assumes that the system operation is flexible

enough to utilize all available storage in some manner for

the generation of primary energy.

(v) An obvious restriction on the filling of a reservoir storage is

the natural inflow. If a surplus of a natural energy originates

mainly below the controllable stretch of a river, it cannot be

added to the energy in storage. To take into account this

limitation, the portion of the natural energy that is control-

lable by reservoirs can be computed separately and com-

pared with the natural energy surplus during filling

periods to see whether it governs the operation of the

storage.

Finally, the NEH method is an interesting approach to study

hydropower systems wherein the regulation is aimed primarily

at power production and therefore the reservoir operation is not

subject to complex operating rules and the restrictions of

multi-purpose developments. In several cases, the solution has

been compared with results of detailed regulation studies and

found to be in good agreement (Canambra Engineering Consult-

ants, 1969, Fill, 1980, Gomide, 1986).

2.3 Climate change scenarios

Streamflow data for various climate scenarios were obtained

using regional circulation models (RCM) to generate precipi-

tation and temperature series and transforming these series into

streamflow series using a rainfall-runoff model. The RCM

models use the outputs of general circulation models (GCM)

and downscaling these to a scale compatible with the hydrologic

characteristics of the watershed.

In this research, two RCM models were used, namely the

PROMES model (Castro et al. 1993, Garrido et al. 2009,

Gallardo et al. 2012), developed by the University of Castilla

– La Mancha, and the RCA model from the Rossby Centre in

Sweden (Rummukainen 2010). The hydrologic rainfall-runoff

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model used was the Variable Infiltration Capacity (VIC) model

(Liang et al. 1994). The precipitation output of the RCM was cor-

rected for bias by the distribution method proposed by Saurral

and Barros (2009).

These models provide on the average reasonable results for

the south and the southeastern regions of Brazil and continuous

series of monthly streamflows for the key gauging stations were

obtained for the 1991–2098 period. However, because

Figure 3 Stationary analysis of natural energy.

Impact of climate change on hydropower production 455

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hydrological years (May–April) have been used in the analysis,

only the period from 1991 to 1997 was available.

The 1991–2097 period was divided into three sub-periods,

namely (1) 1991–2005 defined as ‘present’ used for comparison

with observed flows, (2) 2021–2070 called ‘near future’ and (3)

2071–2097 called ‘far future’. For each of these sub-periods, the

dependable power output of the system has been analysed. Each

sub-period has been considered as stationary for simulation

purposes.

Figure 3 shows the annual average natural energy of the

system for PROMES and RCA generated flows (Fill et al.

2012). For annual averages, the hydrologic year that lasts from

May to April of the next year has been used, due to the seasonal

characteristics of streamflows and characteristics of the Brazilian

portion of the La Plata Basin.

It can be seen from Figure 3 that the assumption of stationarity

within each sub-period seems reasonable, at least for this study,

where considerable uncertainty about the future scenarios is

present.

Each combination of a sub-period with a RCM model (or

observed flows) result in one natural energy series. These

series were denoted as basic series and their mean and standard

deviations are given in Table 3.

2.4 Synthetic energy series generation

For each basic series assumed stationary, the system’s natural

energy has been computed as explained in Section 2.2 and

their statistical parameters computed. The statistics computed

were mean, standard deviation, skew coefficient and autocorrela-

tion coefficient of mean annual flow. Based upon these statistics,

1000 synthetic series of mean annual natural energy were

generated by a first-order autoregressive (Markov) model with

a three parameter log-normal marginal distribution (Loucks

et al. 2005).

Then the mean annual energy was disaggregated into monthly

energy series by hydrologic scenarios (Fill et al. 2012). Hence,

1000 series of mean monthly natural energy were obtained for

each sub-period and for both RCM models. For the 1991–

2005 sub-period also synthetic natural energy series computed

from observed flows were considered. Thus seven cases were

analysed (three sub-periods times and two RCM model plus

observed flows). Each synthetic series has a length equal to the

Figure 4 Comparison of observed vs. PROMES generated flows 1991–2005 Itaipu station.

Table 3 Average and standard deviation of basic series of natural

energies – hydrologic years (avg MW).

Cases Mean

Standard deviation

Coefficient of

variation

Annual Monthly Annual Monthly

Observed

1991–2005

36,200 4690 13,400 0130 0371

PROMES

1991–2005

34,300 10,070 24,400 0293 0709

RCA 1991–2005 32,100 5040 18,800 0157 0587

PROMES

2021–2070

35,700 11,650 30,800 0326 0861

RCA 2021–2070 42,600 16,830 42,500 0395 0998

PROMES

2071–2097

38,000 13,360 33,800 0351 0889

RCA 2071–2097 38,600 14,060 32,800 0364 0849

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length of the corresponding basic series. Details of the synthetic

energy generation are shown in Appendix 1.

2.5 System simulation

Using the synthetic series generated for each case, the system

was simulated in order to compute the firm energy for each

series, ordering these (EF(1) ≤ EF(2) ≤ EF(n)) and attributing

toEF(i) the risk of failure, for a horizon of N years

rN = i

S + 1, (5)

where S is the number of synthetic series (S = 1000) and N is the

length of the synthetic series in years. From the risk rN , the so-

called return period is computed as (Fill et al. 2012).

Tr =1

1 − (1 − rN )1/N . (6)

The return period is defined as the expected value of the

time interval between successive failures of the system. For a

stationary system it will be constant and equal to the reciprocal

value of the conditional probability of failure within a year

given that there have been no failure in previous years

(CEHPAR 1991).

The use of the concept of return period to assess the reliability

of a system has the advantage of allowing comparison between

simulations with different durations (planning horizon). Consid-

ering that the risk of failure depends on the planning horizon and

increases monotonically with that horizon, comparisons of rN are

only meaningful for simulations with same duration. The specific

algorithm for the system simulation is presented in the appendix.

3 Results

Streamflow series for three different periods, namely 1991–

2005, 2021–2070 and 2071–2097, were generated by both

PROMES and RCA models using the VIC hydrologic model

for rainfall-runoff transformation for each of the nine key

gauging stations. Also the observed flows for the 1991–2005

period were collected for comparison.

Figure 5 Comparison of observed vs. RCA generated flows 1991–2005 Itaipu station.

Figure 6 Observed and generated monthly average flow 1991–2005Itaipu station.

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Figures 4 and 5 show the comparison of generated and

observed flows for the Itaipu station for PROMES and RCA

models, respectively (Fill et al. 2012). On the average, generated

flows represent 84% for RCA and 85% for PROMES of

observed flows. However, on a monthly basis, observed and gen-

erated flows diverge considerably. It is believed that this happens

Table 4 Comparison of time averaged flows at Itaipu station (1991–2005).

Month Observed, m3/s PROMES, m3/s RCA, m3/s Difference PROMES, % Difference RCA, %

January 16,100 13,300 14,100 –17.4 –12.4

February 19,100 19,600 14,900 +2.6 –22.0

March 16,500 18,100 17,000 +9.7 +3.0

April 13,700 16,300 11,400 +19.0 –16.8

May 11,400 11,600 7840 +1.8 –31.2

June 10,400 7980 8440 –23.3 –18.8

July 8720 7290 7240 –16.4 –17.0

August 7150 5060 7770 –29.2 +8.7

September 7780 5530 6610 –28.9 –15.0

October 9560 6540 9020 –31.6 –5.6

November 9520 7430 8620 –22.0 –9.4

December 12,400 8400 10,500 –32.3 –15.3

Average 11,860 10,510 10,290 –11.4 –13.2

Figure 7 Comparison of dependable energy obtained from observed and generated streamflow series – 1991–2005.

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because the bias correction scheme does not preserve the time

structure of precipitation and/or temperature values. The Itaipu

station, shown as an example, represents well the average behav-

iour of the basin since it is located at the most downstream

location of the Parana River.

For the other key gauging stations, the comparison of

observed and generated streamflows presented by Fill et al.(2012) shows similar behaviour with a good agreement on the

average for stations within the southeastern region (Furnas,

AguaVermelha, Emborcacao and Sao Simao) and poorer

results for the southern region (S. Osorio and Ita). However,

monthly streamflows show the same erratic behaviour at all

gauges (Fill et al. 2012).

Figure 6 shows average (1991–2005) streamflows for each

month for the same Itaipu station for observed PROMES and

RCA generated flows. Table 4 gives the corresponding numerical

figures and the departure of each model from observed values,

including the long-term averages.

It can be observed that the PROMES model provides higher

than observed values during February–April (wet season) and

lower than observed values for the reminder of the year. The

RCA model shows lower than observed flows during almost

the entire year (with exception of March and August), following

better the mean seasonal pattern than the PROMES model and

fitting generally better the observed values.

Considering the long-term average, both models underestimate

the mean observed flows by 11.4% for the PROMES model and

13.2% for the RCA model. The largest departures from observed

average values are at December for the PROMES model

(–32.3%) and at May for the RCA model (–31.2%).

For the analysis of the system’s dependable energy output, the

generated and observed streamflows at the key gauging stations

were transferred to the hydropowerplant sites, the flows were

transformed into energy inflows multiplying them by each is

plant productivity and finally these were added to get the

system’s aggregate natural energy. Using the statistical properties

of the system’s natural energy series, 1000 synthetic series were

generated for each basic series.

The representativeness of the synthetic series has been veri-

fied by comparing the sample distribution of mean and standard

Figure 8 Comparison of future dependable energy obtained from PROMES and RCA models – 2021–2070.

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deviation with the corresponding values of the basic series from

which they are derived. This comparison has been satisfactory

for all seven cases (Fill et al. 2012). These synthetic series

were then simulated and the dependable energy output as a func-

tion of the return period was obtained for each of the seven cases

(basic series).

Figures 7–9 show the results of the simulations, with the

dependable energy as a function of the return period. Table 5

gives the dependable energy output for selected return periods.

Table 6 gives the variation of the dependable energy from

present until the far future.

The 40-year return period corresponds approximately to

50% risk of failure over a planning horizon of 27.5 years and

is near the reliability of the Brazilian interconnected system

(CEHPAR 1991). A 10- or 20-year return period would be a

very risky situation (unless thermal backup plants are available)

and for a 100-year return period the system would be very

reliable.

Figure 9 Comparison of future dependable energy obtained from PROMES and RCA models – 2071–2097.

Table 5 Dependable energy for selected return periods (avg MW).

Tr (year)

Observed PROMES RCA

91–05 91–05 21–70 71–97 91–05 21–70 71–97

10 35,800 30,000 28,000 28,900 31,000 32,000 31,000

20 34,700 28,400 26,200 26,800 29,600 29,600 28,600

40 33,800 26,900 24,700 25,100 28,100 27,800 26,900

100 32,900 25,500 23,100 23,500 26,900 26,100 25,100

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Figures 7–9 show also, just for completeness, the success

probability for each energy output over the period analysed (15

years for present, 50 years for near future and 27 years for the

far future). As already mentioned, these figures are not compar-

able because the period considered was not the same.

It can be seen from graphs of Figures 7–9 as well as from

Table 5 that considering the PROMES model there was a

reduction followed by a slight increase for the dependable

energy. This behaviour has not been observed for the RCA

model.

Also, there is a considerable disagreement between the

dependable energy obtained for observed and generated stream-

flows for the 1991–2005 period (20.4% for PROMES and

16.9% for RCA for a 40 years return period). This may be

explained by the large differences in the mean and more impor-

tant in the standard deviation of the generated flows (see Table 3).

However, it is believed that comparing generated values of

present and future for the same RCM model, the relative vari-

ation of the dependable energy will be a reasonable estimate of

the energy capability variation in the future.

So it can be assumed that a reduction of this capability would

occur over the twenty-first century; however, care should be

taken with numerical values. This study shows reduction less

than 10%, but considering the absolute value between 1000

and 2000 avg MW this would imply in the additional construc-

tion of two or three large plants to compensate for the effects

of climate changes over the twenty-first century.

4 Conclusions

From the analysis outlined in this paper, besides the considerable

uncertainty on numerical results, several important conclusions

may be obtained. First of all, climate models (GCM and RCM)

at the present stage of development, when used in combination

with rainfall-runoff models, to generate river flows, still lack a

lot of ability to reproduce measured flows at gauging stations.

Even mean streamflows for each month show considerable

departure from observed values (up to 30%) changing thus the

average seasonal pattern. Differences between observed and gen-

erated long-term average flows are reasonable (, 15%);

however, for particular monthly flows errors of more than

100% are common. Because of their poor accuracy the use of

these models for the quantitative assessment on the future

streamflows is questionable and so is the exact evaluation of

energy capabilities in the future. However, climate models may

be used to define at least future trends in runoff and thus in the

dependable energy of hydroelectric systems. Accepted this

ability to reproduce qualitatively future trends it may be con-

cluded that throughout the twenty-first century a reduction of

the dependable energy output of hydropower plants within the

La Plata Basin should be expected. However, in order to assess

the numerical value of this reduction, the performance of

climate models including the bias correction of their output

should be improved. Thus, it is recommended to spend consider-

able efforts in order to improve GCM and RCM models aiming at

results on watershed scale and evaluating their performance by

comparison with surface measured data.

Acknowledgements

The authors like to acknowledge the effort and hard work of the

undergraduate and graduate students from UFPR that helped to

consolidate all the ideas herein included, during the development

of this project.

References

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Table 6 Variation of dependable energy within the twenty-first

century.

Tr (year)

△E (PROMES) △E (RCA)

Avg MW % Avg MW %

10 1100 3.67 0 0

20 1600 5.63 1000 3.38

40 1800 6.69 1200 4.27

100 2000 7.84 1800 6.69

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Appendix 1

A1 Generation of synthetic natural energy series

The generation of synthetic natural energy series has been per-

formed in two steps: (i) generation of mean annual series and

(ii) disaggregation into monthly natural energy series.

(i) Generation of mean annual series

X (0) = 0.

For t, 1,2 , . . . , N

X (t) = r(t − 1) +�������1 − r2

√Z(t),

EN(t) = e[X (t)(s+m)] + EN0,

where EN (t) is the natural energy at year t, EN0 is the lower

bound of EN (t), m is the mean of Ln EN t( ) − EN0( ), s is the stan-

dard deviation of Ln EN t( ) − EN0( ), r is the autocorrelation coef-

ficient of Ln EN t( ) − EN0( ), Z(t) is the independent standard

normal random numbers and N is the number of years.

(ii) Disaggregation into monthly natural energies

N vectors of coefficients: C j,t −EN(t, j)

EN(t)for j ¼ 1, 2, . . . , N

and t ¼ 1, 2, . . . , N are obtained from the basic monthly

series. Where EN(j, t) is the natural energy of the year t, month

j. and EN(t) is the average annual energy of the year t. After

generation of EN(t) above one vector is randomly selected and

the mean annual value is multiplied by coefficients of that vector.

A2 Simulation and dependable energy

Once the S synthetic series of natural energy were obtained, the

dependable energy as a function of the failure risk is obtained by

the following algorithm:

(1) Conversion of monthly energy matrices into vectors

t = (t − 1)∗12 + j with t= 1, 2, ..., 12 N ,

EN(t) = EN(j, t).

(2) System simulation

s = 0,

s = s + 1,

A(0) = Amax,

G = Go = EN(t),

t = 0,

t = t+ 1,

m = 0,

A(t) = min (Amax, A(t− 1) − G + EN(t)),

IF(A(tF − Amax) = m else= m = m + 1,

If (A(tF , 0)) ≈ (G = G0 + A(t)); go to2,

If (t = 12N ) ≈ (G = EF(S)); go to 1,

If (s = S) stop).

(3) Computation of risk and dependable energy

For s = 1, 2, . . . , S

SORT EF(s)[EF(1) ≤ EF(2) ≤ ......],

RISK = s/(S + 1),

TR = 1/[1 − (1 − RISK)1/N ].

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