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The notion of energetic complementarity can be a tool for energy resource managers to prioritize energy generation projects based on renewable resources in both interconnected and independent systems. As a tool in decision-making, it is important to know better the influence of energetic complementarity on the performance of hybrid systems especially with regard to energy shortages but also in relation to other parameters. In recent years, hydro PV hybrid systems have become a growing target of researchers and designers for the idea of installing photovoltaic modules on the water surface of reservoirs. Energetic complementarity has three components: time-complementarity, energy-amplitude and amplitude-complementarity. This paper is dedicated to the study of the influence of time-complementarity on the storage of energy through batteries in hydro PV hybrid systems. The method applied is in the literature and suggests the simulation of the system under study with the idealization of energy availabilities, to remove the effects of climatic variations and the characteristic intermittency of renewable resources. Simulations were performed with the well-known software Homer. The results provided the variations of the states of charge of the batteries as a function of different time-complementarities, indicating as expected better performances associated to higher time-complementarities. The results indicated that the cost of energy for a hybrid system with 28 batteries was equal to US$ 0.502 per kWh and that this cost increased as the time complementarity between energy resources moved away from the situation corresponding to full complementarity. The simulations also showed that the maintenance of the zero failure condition supplying the demands of the consumer loads requires that the load be reduced to 52% if the complementarity is reduced from the full complementarity to zero complementarity, with the cost of energy going from US$ 0.502 per kWh to US$ 0.796 per kWh. The results also allow a better understanding of the influence of time complementarity on the performance of hybrid systems.

The climatological and geomorphological characteristics of the Brazilian national territory form a scenario of great hydraulic availability, which is currently used by the electric energy sector for power generation. This energy production corresponds to approximately 64% of the domestic supply generated by the system. In contrast, photovoltaic solar energy has only a 0.01% share in this offer, despite the great potential available [

Some of the factors that hamper photovoltaic utilization are the seasonal variability of the resource availability and the intermittence caused by the limited daily sunshine time. As a technical solution to these factors, accumulation systems transfer energy from the period of high energy availability to the period of low or zero availability at the cost of increasing the total investment of the system to guarantee the supply of the consumer loads.

The use of two or more energy resources in the same energy system can contribute to its feasibility, with technical advantages in its performance. In addition, a hybrid system can also have improved feasibility if there is complementarity between exploited energy resources. Energetic complementarity can influence the design of generating equipment and storage devices, and can also be better exploited as a consequence of the available storage media.

Energetic complementarity has been discussed for many years, but it was the work of Beluco [

The influence of complementarity on the performance of energy generation systems can be determined with the application of the method proposed by Beluco [

Over the last few years, hydroelectric photovoltaic hybrid systems have focused increasing attention of researchers and designers with the idea of installing photovoltaic panels on the water surface of reservoirs. The works of Gisbert [

The notion of energetic complementarity is somewhat instinctive, but more in-depth work on the subject has been unleashed in the last ten years. Several works, as shown above, are dedicated to the identification of complementarity between different renewable energy resources and their expression through maps. Another work front should identify the influence of energetic complementarity on the performance of hybrid systems.

Among the most recent studies related to energetic complementarity, Monforti [

An et al. [

This article is inserted in the research process focused on the influences of energetic complementarity on the performance of hybrid systems, specifically with the application of the method proposed by Beluco [

This article has four sections besides this introduction. The next section discusses the method applied to understand the influence of time-complementarity on storage through batteries. The following section describes the hybrid system being studied and the simulations performed with Homer. The two subsequent sections respectively present the results and conclusions.

The influence of energetic complementarity in time on energy storage through batteries in hydro PV hybrid systems will be studied with the application of the method proposed by [

With ideal energy availability describing the available renewable energy resources, the hydro PV hybrid system under study will be simulated with the well-known software Homer. The system under study will be simulated for several different time complementarities between full complementarity and zero complementarity, as defined by Beluco et al. [

κ t = | d 1 − d 2 | | D 1 − d 1 | | D 2 − d 2 | (1)

In this equation, D is the number of the day (or month) in which the maximum energy availability occurs and d is the day (or month) in which the minimum value occurs. Subscript 1 indicates one of the energy resources while the number 2 indicates the other. The denominator assesses whether energy resources have a 180-day (or six-month) interval between maximum and minimum energy availability, which also affects the complementarity in time between the renewable energy resources considered.

The software Homer [

The simulation of the same hydro PV hybrid system with different energy availabilities, between full complementarity and zero complementarity, with availability data established by the Method of Beluco, will provide the performance of energy storage through batteries as a function of the different complementarities. The difference of the results of this work for results obtained with real data is that this will require larger banks of batteries for the same performance.

The study undertaken in this work was based on the hybrid system illustrated in

This system was simulated with idealized energy resources, as suggested by the Method of Beluco, simulating different values for the time-complementarity index.

The hydroelectric power plant has 2.22 kW of installed power and its construction cost was considered as being equal to US$ 1750 per kW, with a useful life of 25 years. The photovoltaic modules sums 17,532 kWp and its construction cost was considered as being equal to US$ 3000 per kWp, with a useful life of 12.5 years. The converter costs $900 per kW, with 90% efficiency both as an inverter and as a rectifier, with 100% capacity for both. The consumer load is constant and dimensioned to present consumption equal to the available energy in the situation of full complementarity, with 3.8 kW of permanent consumption and 91.2 kWh of daily consumption.

The batteries selected for the simulations of this work were the model 6FM200D [

Two sets of five complete simulations for five complementarity values were performed. In the first, a set of 1476 simulations for 87 values of sensibility, for each complete simulation, were performed. In the second set, 1476 simulations for 48 values of sensibility, for each complete simulation, were performed. The values of the optimization variables and the sensitivity inputs are shown respectively in

The results are presented and discussed in the next chapter.

The results for the system of

Clearly, battery charge variations occur between late night and early morning, until solar power is sufficient for energy storage. The minimum states of charge of batteries will be the lower the higher the contributions of solar energy. The

Optimization variables | Number of batteries^{a} | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | ||||||||||

16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | ||||||||||

24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | ||||||||||

32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | ||||||||||

Converter capacity [kW] | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.2 | ||||||||||

1.4 | 1.6 | 1.8 | 2.0 | 2.2 | 2.4 | 2.6 | |||||||||||

2.8 | 3.0 | 4.0 | 5.0 | 6.0 | |||||||||||||

Sensitivity inputs | AC load [kWh/d] | 91.200 | 86.640 | 95.760 | |||||||||||||

Maximum annual capacity shortage [%] | 0.0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 4.0 | |||||||||

5.0 | 6.0 | 7.0 | 8.0 | 9.0 | 10.0 | 11.0 | 12.0 | ||||||||||

13.0 | 14.0 | 15.0 | 16.0 | 17.0 | 18.0 | 19.0 | 20.0 | ||||||||||

21.0 | 22.0 | 23.0 | 23.0 | 25.0 | |||||||||||||

Optimization variables | Number of batteries^{a} | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | ||||||||||||

16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | ||||||||||||

24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | ||||||||||||

32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | ||||||||||||

Converter capacity [kW] | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | 1.2 | ||||||||||||

1.4 | 1.6 | 1.8 | 2.0 | 2.2 | 2.4 | 2.6 | |||||||||||||

2.8 | 3.0 | 4.0 | 5.0 | 6.0 | |||||||||||||||

Sensitivity inputs | AC load [kWh/d] | 90.288 | 89.376 | 88.464 | 87.552 | 86.640 | 85.728 | ||||||||||||

84.816 | 83.904 | 82.992 | 82.080 | 81.168 | 80.256 | ||||||||||||||

79.344 | 78.432 | 77.520 | 76.708 | 75.696 | 74.784 | ||||||||||||||

73.872 | 72.960 | 72.048 | 71.136 | 70.224 | 69;312 | ||||||||||||||

68.400 | 67.488 | 66.576 | 65.664 | 64.752 | 63.840 | ||||||||||||||

62.928 | 62.016 | 61.104 | 60.192 | 59.280 | 58.368 | ||||||||||||||

57.456 | 56.544 | 55.632 | 54.720 | 53.808 | 52.896 | ||||||||||||||

51.984 | 51.072 | 50.160 | 49.248 | 48.336 | 47.424 | ||||||||||||||

Maximum annual capacity shortage [%] | 0.0 | ||||||||||||||||||

daily variations in the state of charge of batteries will be lower as the higher the hydroelectric contributions.

These results reproduce some results presented by Beluco [

the state of charge of the batteries in this work occur because the bank of 28 batteries considered allows a total autonomy of only 10.6 hours.

The full complementarity of this system allows the batteries to reach their maximum SOC at the end of every day of the year. The discharge depths vary throughout the year and are smaller when the maximum water availability is verified. The greater variability of the solar energy causes that the greater discharge depths coincide with the minimum values of water availability.

From this point, two sets of results were obtained. The first (Figures 5-8) corresponds to the results with the energy availability (

Figures 5(a)-(d) respectively show the evolution of the results in

Throughout these figures, to the extent that the period of greatest sunshine migrates to the first semester, coinciding with the period of greater water availability, the oscillations of the states of charge of batteries become smaller and the states of charge approximate their maximum values. Likewise, in the second half of the year, there are greater fluctuations in the states of charge of batteries and a greater approximation of their minimum values.

It is interesting to observe how the pattern of the images in

displacements of the periods along the year with maximum states of charge and periods with minimum states of charge of the batteries respectively towards the first half and the second half of the year, as complementarity becomes zero.

This trend can be confirmed by the frequency histogram of the states of charge in

correspond to the maximum states of charge of batteries. The intermediate lags present intermediate values of frequencies, with growth of extreme values. For zero lag, that is, with zero complementarity, the most frequent states of charge are the maximum and minimum values of charge of batteries.

With regard to energy shortage, as can be expected,

The cost of energy as a function of time-complementarity, by the method with which the simulations were executed, presents a lesser adherence to reality. Even

so, the cost of energy is also shown in

with decreasing values, so that there are no failures in the energy supply to the consumer loads even with the complementarity being reduced.

complementarity approaches zero and the available resources approach the combination between

This paper studied the influence of time-complementarity on the performance of energy storage through batteries in hybrid hydroelectric photovoltaic systems. The study was based on simulations with the well-known software Homer and the application of the Method of Beluco to study hybrid systems based on complementary resources.

The simulations showed the evolution of the performance of batteries over a year for different values of complementarity. The results indicated that the cost of energy for a hybrid system with 28 batteries was equal to US$ 0.502 per kWh and that this cost increased as the complementarity moved away from the situation with complete complementarity.

The simulations also showed that the maintenance of the zero failure condition supplying the demands of the consumer loads requires that the consumer load be reduced to 52% if the complementarity is reduced from the full complementarity to zero complementarity, with the cost of energy going from US$ 0.502 per kWh to US$ 0.796 per kWh.

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

During Fo, F.A., Beluco, A., Rossini, E.G. and de Souza, J. (2018) Influence of Time Complementarity on Energy Storage through Batteries in Hydro PV Hybrid Energy System. Computational Water, Energy, and Environmental Engineering, 7, 142-159. https://doi.org/10.4236/cweee.2018.73010