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Energetic complementarity has been studied in recent years and can be an important tool for managers to decide on the design and operation of hybrid systems based on renewable energy resources. Complementarity is an ability presented by two or more energy resources to complement each other over time. Complementarity can be verified in one place or at different places. This second case can be termed as spatial complementarity and is more complex than the complementarity in the same place, requiring a specific approach for its quantification This paper discusses concepts related to energetic complementarity and presents the basis for a method to evaluate energetic time- complementarity across space, applying the concepts presented to the northern coast of the state of Rio Grande do Sul, the southernmost state of Brazil.

Energetic complementarity, as considered in this work, is a capacity presented by two energy resources to complement each other (completely or partially) in time and-or space. Beluco et al. [

This concept was designed to initially assess energetic complementarity in one place. However, complementarity can be verified between power plants located in the same location (or near each other), but also between power plants located far from each other. This second case extends the applicability of the concept of energetic complementarity and requires a method to express this spatial complementarity with maps.

This paper presents the basis for a method that allows quantifying complementarity throughout space and presents its application to a region in the State of Rio Grande do Sul. This paper also discusses some limitations of this method and next steps to be followed to improve the understanding of spatial complementarity. This paper clearly establishes basic concepts for the future layout of spatial complementarity maps.

Beluco et al. [_{t} is the partial energetic complementarity in time, where maximum and minimum availability of hydraulic energy occur, respectively, on Julian day number D h and d h (likewise D s and d s refer to the same days regarding solar energy). Note that if the differences | D − d | equal 180, then κ t = | d h − d s | / 180 , so that κ t = 1 if the maxima are 180 days apart, and κ t = 0 if the maxima coincide.

κ t = | d h − d s | | D h − d h | | D s − d s | (1)

On this work, spatial complementarity will be evaluated from the calculation of this temporal index, with the difference that the index will be calculated with resource data at different locations and no longer with data from two sources in the same place, as estimated by Beluco et al. [

So, for clarity of concepts, in this paper the complementarity calculated in only one place applying the index proposed by ref. [

This section will initially present a graphical method for evaluating spatial complementarity and will then describe some examples designed to demonstrate its applicability.

The proposed method for evaluating spatial complementarity in a given region consists of the following four steps: [

The study of spatial complementarity requires the establishment of a region to be studied and its modeling with a network of cells. In this paper, a network of hexagonal cells will be adopted, as they allow a better coverage of the surface. Each cell in this network will be assigned power generation information resulting from the added effect of all power plants in its area of influence. This step will be better understood in the next section, when a real case is analyzed.

The size and arrangement of the cells can be established according to the nature of the available energy resources or characteristics of the region to be studied. Once the data associated with the generating units of the study region are known, temporal complementarity can be determined with the application of Equation (1).

Just for simplicity, the examples described in this section throughout the next figures will consider the case where the differences shown below in Equation (1) are equal to 6. Thus, the months corresponding to the availability minima can be directly applied to upper part of this equation, leading to the evaluation of complementarity in time.

In this network, there are plants only in the central cell, which appears marked with a specific color, and there are indications of the months of the year in which maximum and minimum energy availability occurs. In the case of only one plant, the corresponding months of the energy resources available for this

plant will be indicated. In case this cell contains more than one plant, the months of maximum and minimum energy availability corresponding to the joint effect of the plants of that cell should be indicated.

A trivial situation, considering the determination of complementarity index, would be obtained by comparing two such networks, mounted to a region in which the compared plants were both located in the central cell. It would be equivalent to the calculation already known for the temporal complementarity in just one place. Results for such a case can lead to complementarity maps such as those presented by Beluco et al. [

The central cell of the left network indicates that the maximum availability occurs in January (month 1, from 1 to 12) while the minimum in the month of July (month 7). The cells on the right network indicate that maximum availability occurs in July while the minimum occurs in January. As the months of minimum availability of hydropower and wind energy are in this case with a difference of six months, these two energy resources present a complete complementarity and the index results equal to 1.

This result should be presented as a function of distance and a very appropri-

ate form for this presentation is shown in

If there were power plants in matching cells, complementarity between these cells could be considered to compose maps of complementarity, as discussed above. As power plants do not appear in matched cells in

In the sequence, some other basic cases, for a better understanding, will be presented and discussed.

The situation in

wind turbines in which there is a set of turbines in the central cell and other sets distributed in cells in the periphery of the analyzed region. These cells have the same maximum and minimum energy availability distributions of the previous cases. The comparisons will become more complex as there are more cells in the network on the left, as already appears in the next case.

the trivial case discussed above. The other bar corresponds to the comparison of the central cell of the network on the left with the cells on the periphery of the network on the right. As the lags correspond in these cases to six months, the values of complementarity correspond to the complete complementarity.

The cases above, shown in

of the presented method, and may be circumvented possibly with complementarity digrams that do not show only the maximum values at each distence.

This process for evaluating the spatial complementarity allows assessment of how power plants located in a given region may present complementary. Before this paper, this would be possible only peer-to-peer and now an evaluation is possible comparing plants at different sites. The survey of full complementarity can be an important tool for planning and management of energy resources.

One limitation is that spatial complementarities across different distances are represented in the same diagram. Another limitation is that different comple-

mentarities in the same distance will be shaded by the criterion adopted to define what complementarity will be in this position. In this paper, the graphs were assembled considering the maximum values in each distance, but average values of complementarity could also be adopted.

The region of the north coast of the state of Rio Grande do Sul, in the extreme south of Brazil, will be used for an example of application. This region can be viewed on Google Maps [

located respectively Osório I [

The analysis undertaken in this paper considers only the months in which the minimum energy availability occurs in the power plants located in these two

figures; analyzes considering energy and amplitude complementarity components will be undertaken following the research work. It is necessary to express in the two dimensions of a map a much larger amount of information and this paper constitutes a first step in the description of spatial complementarity.

Some cells appear in these figures containing several plants, while others contain few or no plants at all. A prior evaluation of the complementarity components will enable assessing whether the hexagonal cell network has been well established. The purpose of the analysis to be undertaken may induce the choice of a network with smaller cells. The dimensions of the cell network to be adopted should be related to the expected results.

The establishment of the network cells may influence the results of the energetic complementarity assessment, if complementary plants appear in the same cell. This internal complementarity to a cell cannot be identified in the data collection that will result in the evaluation of complementarity. An analysis considering the largest power plants should be undertaken and of course the analysis of a region with many power plants may require large computational processing capacities.

This paper discussed some issues related to energetic complemetarity and presented bases for a methodology allowing the determination of time complementarity through space. The proposal basically suggests the determination of the complementarity in time between different positions and their expression through a chart of complementarity as a function of distance. This paper also presented an application of the proposed methodology to the north coast of the State of Rio Grande do Sul, in southern Brazil.

The method has some limitations. One of them, spatial complementarity in several directions is presented in only one diagram, with superimposition of complementarity values for different directions in only one value. Another limitation, for a same distance, even in different positions, should be adopted only one value of complementarity; in principle, in this article, the maximum value was considered, but an average value could be considered.

This work was developed as a part of research activities on water resources management and renewable energy at the Instituto de Pesquisas Hidráulicas (IPH), Universidade Federal do Rio Grande do Sul (UFRGS). The authors acknowledge the support received by the institution. The second author acknowledges the financial support received from CNPq for his research work (proc. n. 309021/2014-6.).

Risso, A. and Beluco, A. (2017) Bases for a Methodology Assessing Time Complementarity in Space. Energy and Power Engineering, 9, 527-540. https://doi.org/10.4236/epe.2017.99037