If two or more renewable energy sources are available in the same region, their complementary can be advantageous in a hybrid power system. Three indices are defined in this work for assessing the complementarity of solar and wind resources for energy production. Based on existing data of solar radiation and wind speed, these complementarity indices were calculated and represented in the form of maps for the state of Rio Grande do Sul, in southern Brazil. The results found suggest that there are some areas of the state where the use of hybrid wind-solar power systems could be more effective than single photovoltaic or wind systems.
Operational inflexibility is one of the main problems with most renewable or low-carbon technologies for power generation. The power output of these energies usually depends on diurnal and seasonal patterns of the corresponding natural resources used for generating electricity. However, if two or more energy sources exist in the same region, and in significant quantities, this might well justify their complementary use in a hybrid power system.
Referring to energy sources, Beluco et al. [
The definition of a hybrid power system, for this paper, is similar to the one given by Lukuyu and Cardell [
There is an increasing interest in assessing complementarity between renewable energy resources. Over the last decade, many authors have worked and written about this subject. Examples of this are the papers by Notton et al. [
As stated by Hoicka and Rowlands [
The structure of this document is as follows: In Section 2, a definition of the complementarity indices applied and their equations are presented. Section 3 explains the data sources and methods used for estimating solar and wind energy availability, as well as the corresponding equations. In Section 4, the resulting complementarity maps are exhibited and discussed. Finally, the main conclusions from this work are presented on Section 5.
Representing complementarity through maps is thought to be beneficial, because maps are an adequate form of summarizing, comparing and displaying information in a manner that is easy to understand for most people. This could be useful in the planning stages or in the decision making process for implementing a small hybrid power system.
In order to explore the complementarity feature of solar and wind energy sources, it is important to know the resources availability regarding their amplitude (minimum and maximum values), average value and behavior along time. Complementarity between solar and wind energy sources can be quantified by means of suitable indices.
Three indices are defined in this work for assessing the complementarity of solar and wind resources for energy production. Their equations and definitions are described in the following subsections.
The Amplitude-related partial complementarity index ia, assesses the relationship between the values of the differences of the maxima to the minima of two energy resources availability functions. Based on the work of Beluco et al. [
(2)
It can be easily observed that if the differences δw and δs are equal, the index ia would be equal to 1. For this work, a scale factor of 10 will be used, in order to make ia equal to 10 when δw and δs are equal, and tending to 0 with the increase of their difference.
According to Beluco et al. [
Two complementarity components are included and combined in the Time- and Energy-related partial complementarity index iet. Beluco et al. [
Rio Grande do Sul is a subtropical state of Brazil, and because of that, is subject to four seasons a year. Based on that, the Time-related complementarity for this work will be considered between seasons (six different combinations). The Equations (3) and (4) are used for calculating iet: In these equations, Ew [
(3)
The 1 and 2 in the subscript indicate the two seasons under consideration (e.g. 1-spring and 2-fall). As it was the case for the partial complementarity index ia, a scale factor of 10 is applied to the index iet found. Therefore, if iet = 0, it means there is no complementarity, in time and energy, of solar and wind energy sources between these two seasons of the year. If iet > 0, it represents that there is some complementarity, in time and energy, between these two seasons of the year. When iet < 0, it will be assumed that no complementarity takes place. Finally, if iet = 10, it implies a maximum complementarity, both in time and energy, of solar and wind energy sources.
As explained by Beluco et al. [
Based on the range of values used in this work for ia and iet, it can be easily observed that the values of iT will be between 0 and 100, with 100 denoting an area with full energetic complementarity.
This section presents the data sources used for this paper, as well as the methods employed to process the information available on these, in order to calculate and produce the complementarity maps of solar and wind energy sources for Rio Grande do Sul.
Colors are used for representing numerical values of geographical features in maps. The digitization of these maps allows using the pixel information, given by the palette, for extracting data that can be combined with other sources for compiling new maps using GIS software.
A computer program was developed at the UFRGS Solar Energy Lab to perform the pixel color reading of the maps, by using the getpixel (x,y) function of Visual Basic.NET, which returns the numeric value corresponding to that of the pixel color, by comparing it to a reference palette.
For each nine pixels group was calculated the average of the numeric values associated to them, and then, this average substitutes each individual value.
The computer program starts reading the pixel at the second column of the second row, and continues reading from left to right, every other three pixels, until it finds a pixel with a color defined in the reference palette, and based on this, the average is calculated for this and the other eight surrounding pixels, continuing this process until the end of the row. After this, the reading restarts at the second pixel three rows below, always from left to right, following the same previous method until getting to the last row, according to what is shown in
When the computer program finds one or more pixels with a color not defined in the reference palette, these are not considered for calculating the corresponding nine pixel group average.
The images used as data sources for this paper, which analyzes complementarity in Rio Grande do Sul, are maps with the average wind speed at 50 meters height, surface roughness and solar radiation on a horizontal surface. It is required to transform wind speed from 50 m to 10 m high, in order to use small wind turbines, with lower towers. For a better estimation of available solar energy, a correction is made for calculating the solar radiation on a 45˚ sloped surface.
The information related to solar radiation on a horizontal surface for Rio Grande do Sul is taken from the work of Martinazzo [
The computer program explained on the previous subsection was used to extract the information, from these three types of maps, for the average day of the central month of each season.
The resulting images are maps with 254 rows (each encompassing 1'35" of latitude) and 251 columns (each encompassing 1'54" of longitude). The information stored on the cells of these maps can be used in the equations cited in this work.
Solar radiation data can be available at several different forms, and each one of these can be used for a multiplicity of purposes in the design and development of solar energy systems. Jakhrani et al. [
The method used in this work for estimating the solar energy availability (monthly incident solar radiation on a sloped surface) was the isotropic sky model described in Duffie and Beckman [
The value chosen for representing the solar energy availability was considered to be that of the average day of the central month of each season.
The declination δ was found from the approximate equation of Cooper [
The sunset hour angle ωS is determined by means of Equation (7).
Month | Average day | Declination (δ) | n |
---|---|---|---|
January | 17 | −20.9 | 17 |
February | 16 | −13.0 | 47 |
March | 16 | −2.4 | 75 |
April | 15 | 9.4 | 105 |
May | 15 | 18.8 | 135 |
June | 11 | 23.1 | 162 |
July | 17 | 21.2 | 198 |
August | 16 | 13.5 | 228 |
September | 15 | 2.2 | 258 |
October | 15 | −9.6 | 288 |
November | 14 | −18.9 | 318 |
December | 10 | −23.0 | 344 |
The monthly average daily extraterrestrial radiation Ho, is found using the average day for a particular month, because on that day, the Ho value is the closest to the average extraterrestrial radiation value of the month. With solar constant GSC equal to 1367 W/m² (adopted by the World Radiation Center), the equations given by Duffie and Beckman [
Irradiation distribution along the year presents a seasonal trend with daily overlapped fluctuations. For this reason, it is necessary to make this distribution independent of the season, by means of dividing the monthly average daily total radiation on a horizontal surface H by the monthly average daily extraterrestrial radiation Ho. This results in the monthly average clearness index Kt, which can be calculated with Equation (10).
On a cloudy day, the global radiation on horizontal surfaces received would indicate the diffuse radiation by means of an suitable index, Kd, correlated to Kt. The Equation (11) allows estimating the diffuse radiation fraction Kd:
For ωS ≤ 81.4˚ and 0.3 ≤ Kt ≤ 0.8, Duffie and Beckman [
The sunset hour angle on a sloped surface, ωSt, is initially found by means of computing the intermediate value ωS2, using the Equation (14).
Once the ωS2 value is available, this is compared with ωS. If ωS < ωS2, then ωSt = ωS2; else ωSt = ωS2.
The geometric factor Rb, which expresses ratio of the average daily beam radiation on the tilted surface to that on a horizontal surface for the corresponding month, can be used to estimate the daily radiation on a sloped surface. For the southern hemisphere, Duffie and Beckman [
With the features previously found, it is possible to estimate HT [MJ/m2], the monthly average daily radiation on the sloped surface. The expression for calculating HT, at the average day of the central month of each season, is available at Duffie and Beckman [
As mentioned before in a previous section, for this work, the information related to the monthly average daily radiation on a horizontal surface at Rio Grande do Sul can be obtained from Martinazzo [
Like almost every type of energy on the planet, energy coming from the wind is an indirect form of solar energy. The heating of the atmosphere, due to the absorption of solar radiation, combined with the earth’s rotation generates global and local wind patterns.
According to Leishman [
length parameter, z0, representing the effects of the terrain on the upstream boundary layer development. The logarithmic law equation for the time-aver- aged wind profile is shown in Equation (17), where V(h) [m/s] is the wind speed as a funciont of height above ground level h [m], Vref [m/s] is the reference wind speed, href [m] is the reference height and zo [m] is the roughness length.
Type of Terrain | Roughness length z0 (m) |
---|---|
Cities, forests | 0.7 |
Suburbs, wooded countryside | 0.3 |
Villages, countryside with trees and hedges | 0.1 |
Open farmland, few trees and buildings | 0.03 |
Flat grassy plains | 0.01 |
Flat desert, rough sea | 0.001 |
has the limitation of not considering temperature or atmospheric pressure, factors that also have influence on the wind speed.
For this work, wind speed at 10 m above ground level is estimated based on available wind speed data at 50 m and surface roughness information, derived from Camargo et al. [
The average power per disk areas wept out by the blades of the wind turbine, PW/A [W/m2], can be written as shown I Equation (17), where CP [
In this work, in order to estimate the average daily wind energy availability derived from the average wind speed at 10meters height, the following values were adopted for these parameters: CP equal to 100%, ηC equal to 100%, ke equal to 2.5 and ρair equal to 1.225 kg/m3.
The value of 100% assumed for CP and ηC are obviously not realistic (in fact, the maximum value of Cp is usually less than 50%), but this simplification was made for making the result independent of the wind turbine quality or type. The ke factor of 2.5, uniform for the whole State, was deemed the best fit for the analyzed region.
Based on the methods and equations described in this paper, the three indices defined in this work for assessing the complementarity of solar and wind resources for energy production were calculated, and the corresponding maps for Rio Grande do Sul were created. These maps are shown in
As previously described in this document, the total complementarity index, iT, is found by multiplying, together and overlaid,
This paper described the main equations, concepts and considerations used for producing complementarity maps of solar and wind energy sources over a region, including the transformation of usually available information, like solar radiation on horizontal surfaces and wind speed at 50 m above ground level, to solar radiation on sloped surfaces and wind speed at lower heights, in order to improve accuracy. Suitable indices for expressing this complementarity are also
explained.
The Rio Grande do Sul State, in southern Brazil, was used as case study to illustrate the methods explained in this work. The corresponding results showed that the greatest existing time- and energy-complementarity, between seasons, is the one for winter-summer. Similarly, the index used to depict this type of complementarity has its lowest values between summer-autumn and winter-spring.
The map showing the amplitude-related partial complementarity index, ia, exhibits values along the whole range of options for this index. The lowest values for this complementarity type are found at northern and western regions of the state.
Based on the map displaying the total complementarity index, it can be also concluded that there are regions, in Rio Grande do Sul, where the use of hybrid wind-solar power systems could be more effective than single photovoltaic or wind systems.
Complementarity maps can be used as a tool for a preliminary identification of regions with potential for installing hybrid power systems. Obviously, every important technical, economic and social criteria must be also included in the decision making process and when assessing the sites.
Pianezzola, G., Krenzinger, A. and Canales, F.A. (2017) Complementarity Maps of Wind and Solar Energy Resources for Rio Grande do Sul, Brazil. Energy and Power Engineering, 9, 489-504. https://doi.org/10.4236/epe.2017.99034