1 Introduction

A country’s energy needs are an important indicator of its economic development. Electricity consumption has been identified as one of the most important factors for the well-being of society and a critical determinant of a country’s progress [4]. As risk factors, increasing population demand combined with a country’s energy base tied to a single or few energy sources are vulnerabilities that threaten economic growth.

The main sources of electrical energy in the world are hydro, biomass, wind, solar, natural gas, oil derivatives, nuclear and coal [6]. The demand for diversification of energy sources, the concern for sustainability and the reduction of costs have led several branches of science in the search for greater efficiency of electrical energy generation systems using renewable sources. Among the main sources of renewable energy, solar energy has become increasingly important, especially in countries with tropical climates. According to a report by [6], in Brazil, the photovoltaic solar energy generation has evolved from 3,287 MW in 2020 to 4,632 MW in 2021.

[15] assert that solar energy is the largest source of energy available on Earth, which is a renewable and inexhaustible source of energy. Also, according to the authors, the growing demand and research in this field will make solar energy become a significant part of the world’s energy matrix in the future.

[1] explain that since the beginning of the 21st century, the traditional concept of centralized energy generation has been open to research and application of distributed generation (DG) or decentralized. A distributed system is mainly composed of small generator units connected directly to the consumer load and/or distribution grids, using mainly renewable energy sources such as photovoltaic [17]. In this system, each consumer can produce electricity and then connect to the distribution grid. In this way, the residential consumer can consume and also supply excess electricity to the local distribution center.

There are several advantages in the use of DG, among which the reduction of the electricity tariff paid by consumers to concessionaires stands out, since there is autonomy for the consumer to also produce energy. However, for [17], the study of which strategies could be used to increase the reduction of electrical energy consumption by concessionaires and consequently the use of DG to reduce the energy bill is still incipient.

When dealing with the management of photovoltaic systems, among the alternatives for a more efficient management, focusing on a higher quality and more economically viable energy distribution, computational intelligence (CI) has emerged as a promising option, since it seeks methods that possess or enhance the intelligent capacity of humans to solve problems, acquire and represent knowledge, in addition to recognizing patterns [11].

This article used as a reference the research by [17]. The idea at this first moment is to improve and update this work through adjustments in the fuzzy algorithm, mainly by improving the parameters of the linguistic variables, proposing other models for the system and adapting the configuration of photovoltaic technology to the present day.

In this sense, this research proposes to develop an intelligent photovoltaic system, using Fuzzy Logic as CI technique for decision-making about the best time to use or not to use the energy produced by DG, in a scenario where generators have an energy storage system coupled to them, with the aim of reducing the price of the energy bill for the final consumer. For this purpose, an environment with a different type of tariff modality is simulated, where the amount paid by the consumer depends on the time at which the energy is consumed, defined as a white tariff.

Finally, in addition to comparing the developed system with a previous work, the performance of a simple photovoltaic solar energy system (developed without any intelligent technique) is also simulated in order to compare it with the system developed through fuzzy logic.

The paper is presented as following: Sect. 2 proposes to present the literature review that supported this research. Section 3 describes the features of the proposed system, presenting the tariff modality used and the components of the photovoltaic system. Section 4 presents in detail the development of the fuzzy system. Section 5 describes the simulation created, explaining the database used, the specificities of the photovoltaic system components and how the fuzzy system is modeled. Section 6 describes the development of the research and presents the results obtained. Finally, Sect. 7 presents the conclusion about this research.

2 Literature Review

The application of artificial intelligence techniques in photovoltaic electrical systems is currently presented in a very frequent and promising way. There are several works that present fuzzy logic as an alternative to manage and optimize the distribution of energy in photovoltaic systems.

[12] presents an algorithm based on fuzzy logic to manage energy storage in a battery and also the energy demanded by consumers at the University of Naresuan, Thailand, in order to reduce the electricity bill. The main idea of the algorithm is to allow an intelligent switching between absorbing energy during periods of high solar irradiation and discharging energy to the load during times of high consumption. The fuzzy algorithm proved to be successful, as it reduced the annual energy bill by 17.58%.

The work by [5] addresses power management to improve network performance and generate smooth transitions between different power balance modes. This work presents a fuzzy system developed to provide a dynamic flow of energy from the grid, based on the network price, in order to decrease the energy rate and increase the useful life of the storage device. Experimental results were obtained which proved to be satisfactory.

Another relevant work found is the article by [14], which deals with energy management to maintain a balance between different energy sources, storage units and loads. In this article, fuzzy logic was used in order to maintain the balance between these two objectives. From the results exposed in this work, it was observed that this system demonstrated viability to be used as a solution to the problem.

[3] publishes a work in which an energy management system based on fuzzy logic is presented, where the objective is to smooth the profile of an electrothermal microgrid connected to the residential network. The proposed case study designs an energy management system to reduce the impact on the electrical grid when renewable energy sources are incorporated into pre-existing appliances connected to the grid. The simulation results used real data measured over a year and showed that the proposed management system design achieves a reduction of 11.4% of the maximum power absorbed from the network.

The publication by [10] proposes a residential smart microgrid topology linked to the distribution grid using fuzzy logic, which integrates a photovoltaic system, a fuel cell and a battery bank. To validate the functioning of the proposed energy management unit, a prototype of the system was developed and experimental tests were carried out. The management system was tested for three different residential load scenarios, both connected to the grid and isolated. The distribution and analysis of the energy cost provided for each management scenario showed the benefits of using this type of intelligent system for the consumer and for the utility.

[19] developed a coordinated control scheme of a battery energy storage system and DG units for a microgrid, based on fuzzy logic. The coordinated control scheme aims to mitigate the fluctuation of active power at the point of common coupling of the microgrid when it is connected to the grid and also to keep the frequency of the microgrid within the defined range for operation when it is isolated. In the control scheme, the SoC of the battery energy storage system is used as input for the coordinated control based on fuzzy logic. The results of the case study were satisfactory and showed that the proposed coordinated control scheme is capable of mitigating the fluctuation of active power at the common coupling point for grid-connected control and performing efficient frequency control for isolated operation.

3 Features of the Proposed System

In addition to the use of a DG system, this research prioritized the use of the white hourly tariff modality. According to [2], the white tariff is characterized as consisting of differentiated tariffs for energy consumption depending on the time of day. This modality is divided into three tariff types: peak tariff, intermediate tariff, and off-peak tariff.

The days of the week and times stipulated for tariff posts are defined and implemented by each electricity company distributor in Brazil, provided that they are previously approved and ratified by ANEEL [2]. Equatorial Energia is one of the energy distributors present in Brazil that have made available the white tariff modality for all consumer units, since January 1st, 2020. The values of each tariff are also defined by the energy distributors. At Equatorial Energia, for example, the values and periods of tariff posts must be approved by ANEEL in each periodic tariff review, which must occur every four years [7]. The schedules and values of the tariff stations defined for the State of Pará – Brazil since the year 2019 are specified in the items below:

  1. 1.

    peak time (from 6 pm to 8:59 pm): R$ 1.39;

  2. 2.

    intermediate time (from 4 pm to 5:59 pm and from 9 pm to 9:59 pm): R$ 0.87;

  3. 3.

    off-peak time (from 10 pm to 3:59 pm): R$ 0.49.

The benefits of using the white tariff can then be realized above all to consumers who consume very little between 4 pm and 10 pm, that is, during peak and intermediate time. The white tariff is a modality that, depending on the consumption profile and the habits of use of electric energy, presents itself as an interesting alternative for the residential consumer.

Another important issue for the system configuration of this application is the use of an integrated storage system connected to a hybrid photovoltaic system (both on-grid and off-grid). The presence of the battery in a photovoltaic production system is intended to accommodate the excess energy production of the residence. In this way, the extra energy can be used in case of power outages of the photovoltaic panel and/or the electrical network and to balance the load inserted in the grid [17]. In the context of the white tariff modality, it is possible to charge the battery when energy from the grid is cheap and to use it when energy is expensive. In this way, the use of the battery reduces the billed consumption of the consumer unit, especially during peak hours.

As a way of exemplifying this section, Fig. 1 presents the system components and the architecture proposed in this article for the residential photovoltaic installation.

Fig. 1.
figure 1

System components and architecture of residential photovoltaic installation [8]

Full size image

4 Development of the Fuzzy Algorithm

[18] defines a fuzzy system as a particular type of knowledge-based system where the knowledge base is built from a set of fuzzy rules. In this type of system, inputs are given in natural language, which, after going through the fuzzy inference process, are converted into a numerical format that is easy to manipulate. The steps for building a fuzzy system are described in Fig. 2.

Fig. 2.
figure 2

Steps for implementing a fuzzy system

Full size image

The fuzzy system developed in this research consists of 3 different fuzzy algorithms, one algorithm for each price range of the white tariff, as detailed previously. The fuzzy system is composed of 2 input variables (El and SoC) and an output variable (Eb). El represents the energy in kWh, that is, it is the value resulting from the subtraction of the energy produced by the DG (Eg) and the energy consumed by the consumer load (Ec). Thus, if El is positive, then there is more production than consumption, but if El is negative, then production is not enough to supply the demand for electricity.

SoC is the state of charge of electricity stored in the battery. If El is positive, it is possible to recharge the battery using the surplus electricity produced. If El is negative, the battery can be used to supply the energy demand.

Eb represents how much energy will be injected or utilized from the battery, that is, it represents the decision whether the battery will be charged or discharged. So, if Eb is positive, then energy can be inserted into the storage device. If Eb is negative, then the battery can be used by the customer load. However, these decisions will always depend on the time of day, El and SoC.

Table 1 presents the meaning of the linguistic sets of each variable.

Table 1. Definition of linguistic sets
Full size table

Table 2 shows the rule bases defined for each tariff configuration. For each rule created, two conclusions will be specified, based on the association of predefined inputs and outputs. Note that depending on the grid energy price, the rule will have a certain behavior, resulting in an output with a different value. For example, if there is low consumption surplus (El = NS) and if the battery is half full (SoC = ZE), then 3 situations can result:

  1. 1.

    Cheap energy: then there is no interaction with the battery (Eb = ZE);

  2. 2.

    Intermediate energy: then there is a small energy discharge in the battery (Eb = NS);

  3. 3.

    Expensive energy: then there is a big energy discharge in the battery (Eb = NB).

Each configuration has a set of 25 rules, for a total base of 75 rules.

Table 2. Rule base map for off-peak time (a), intermediate time (b) and peak time (c)
Full size table

The membership functions used to represent the linguistic sets were the triangular and trapezoidal forms. The maximum and minimum limits of the input variables (El and SoC) were determined based on the dataset values, for El the minimum limit was set at −6 kW and the maximum limit 4 kW, while for the SoC it was agreed the value in percentage limits of the energy contained in the battery ranging from 0 to 100%. Regarding the output variable (Eb), the limits followed the ±6 kW battery charge flow. The following graphs show the membership functions of the input and output variables, with their respective linguistic sets (Fig. 3).

Fig. 3.
figure 3

Membership function of the output variable El (a), SoC (b) and Eb (c)

Full size image

In addition, the fuzzy system uses the Mamdani inference method [18] and the defuzzification step is performed using the centroid method [18].

It is important to emphasize that the form used for the membership functions (triangular and trapezoidal) and the values used for the linguistic variables were defined empirically, based on a series of tests and adaptations, with the aim of finding the best configuration for the fuzzy system in question. In the same way, the configurations of the inference and defuzzification method were also defined both based on the used literature and based on system tests.

5 Simulation Specification

This paper improves the fuzzy system presented in [17] by changing the boundaries of the linguistic variables.

For the simulation of the system, real data on residential energy consumption and photovoltaic production over a period of one year were used. The public databases used were obtained from the Research Group in Knowledge Engineering and Decision Support (GECAD) at the Laboratory of Intelligent Electrical Systems (LASIE), located in Portugal at the Institute of Engineering - Polytecnica do Porto (ISEP /IPP) [9].

Data on residential consumption cover the period from December 2011 to March 2013, with a 15 min interval between one measurement and another. About photovoltaic production data, these include the months from January to December 2013, with an interval of 5 min between measurements. The measurement intervals were standardized in 5 min for residential consumption and photovoltaic production.

The simulation also adapted the composition of the photovoltaic electrical system to 13 photovoltaic panels, each one with a capacity of 340 W of power. Thus, the power of the installed system resulted in 4.42 kW. The residence has a maximum power demand of 6.8 kW and it is connected to a hybrid photovoltaic system, coupled to a LiFePO4 battery with a capacity of 13.5 kWh.

As a way of comparison, the system simulations were reproduced both for modeling considering a simple photovoltaic system, and for a photovoltaic system using fuzzy modeling. Both models are based on time of day, net energy and state of charge in the battery.

The simple photovoltaic system has a predetermined decision behavior, where, for this case, it follows the following procedures:

  • Excess energy only charges the battery during the day. If the battery is full, the surplus is sent to the electrical distribution grid;

  • The residence only uses energy from the distribution grid if the battery has a limit of 25% of the total;

  • The residence only uses the energy stored in the battery during the hours from 4 pm to 10 pm, that is, when energy is generally more expensive in the white tariff mode.

Decision making in the fuzzy system behaves in a more complex way, but the idea is to make a more specific and intelligent assessment for each situation and moment, considering the white tariff modality:

  • If the time of day is within the time range of the least expensive electricity rate, the system is more likely to store energy in the battery, depending on the state of charge;

  • For intermediate electricity cost, the fuzzy system tends to use the battery moderately;

  • When the cost of electricity is expensive, the system will try to use as much battery power as possible.

Equations (1) and (2) represent the punctual and annual electrical consumption Pc of the residence, respectively. When grid power Pgrid is a positive value, it means that there was surplus energy produced by DG, so this extra energy must be transferred to the distribution grid. When Pgrid is a negative value, it means that there is not enough energy in the residence, so the electrical grid must be used to supply this shortage. To arrive at the annual value of the residence’s energy bill B(total), Eqs. (3) and (4) are used, where Ts is the time period used (5 min) and the value of the fee f(t) depends on the tariff value at that moment.

$$ {\text{P}}_{c(n)} \, = \,{\text{P}}_{{{\text{grid}}(n{)}}} \, * \,T_{s} \,\,\,\,\,({\text{if}}\,\,P_{{{\text{grid}}}} \, < \,0) $$
(1)
$$ {\text{P}}_{{{\text{c}}({\text{total}})}} \, = \,\Sigma {\text{P}}_{c(n)} $$
(2)
$$ {\text{B}}_{\left( n \right)} \, = \,P_{{{\text{grid}}}} \, * \,T_{s} \, * \,{\text{fee}}_{\left( t \right)} \,\,\,\,({\text{if}}\,\,P_{rede} \, < \,0) $$
(3)
$$ {\text{B}}_{{({\text{t}}otal)}} \, = \,\Sigma {\text{B}}_{(n)} $$
(4)

For the development of the system, the Python programming language was used because it is known as a very intuitive syntax language and with a vast number of libraries and documentation available. For the implementation of fuzzy logic system in Python, the scikit-fuzzy library [16] was used. To analyze and manipulate data in a simpler way, the pandas library [13] was used. The graphical visualization of data in Python utilized was matplotlib library [13].

6 Research Results and Discussion

The total annual production of the photovoltaic system is 4426.37 kW, while the total annual residential consumption is 6801.28 kW. After developing the system and obtaining the results of the simulations, the resulting situations are observed and compared.

At first, the DG system without the fuzzy logic (commercially used by companies) consumes 4711.80 kW from the electrical distribution grid, which reduces the use of the electricity from the company by 30.72%, resulting in an annual invoice value of R$ 3312.20.

The second moment, which consists of adapting [17]’s research to current technologies, to the new data analysis and Python programming language, showed that the proposal consumes 3892.28 kW from the electrical distribution grid, with an annual cost of R$ 2590.25. Relative to the electricity distribution company’s annual residential consumption, the reduction was 42.77%.

Finally, the simulation for the DG system using the fuzzy logic proposed in this paper resulted in a grid consumption of 3708.32 kW and an annual cost of R$ 2399.10, that is, a reduction of 45.48% compared to the annual consumption from the company. These data are better analyzed and compared in Table 3.

Table 3. Comparison of simulation results
Full size table

The results presented are in line with the objective of this research. In Table 5, it is observed that there was a reduction in the total energy consumed by the electrical distribution grid, compared to the results obtained in the previous work. As a result of this reduction, the annual energy bill was reduced by R$ 191.15.

The simulation showed that the fuzzy system identifies the period in which there is greater energy production by the photovoltaic system and uses the battery more intensively, depending on the time of day, in order to use less the distribution grid. In contrast to the simple system that follows a linear pattern of energy storage in the battery. Figure 4 shows the behavior of the battery state of charge over a year, both for the simple system and for the fuzzy system.

Fig. 4.
figure 4

SoC of the battery on simple (a) and fuzzy (b) systems over one year

Full size image

It is observed that the fuzzy system requests less power from the distribution grid over time and injects power into it more uniformly. Positive values indicate injection of photovoltaic power into the grid and negative values indicate power consumption from the distribution grid throughout the residence. Figure 5 presents the behavior of the simple system and the fuzzy system in relation to the injection or consumption of power in the distribution grid.

Fig. 5.
figure 5

Grid power flow on simple (a) and fuzzy (b) systems over one year

Full size image

7 Conclusion

The main purpose of this article was to improve the use of photovoltaic energy in the context of white tariff in Brazil by using fuzzy systems. The proposed method was improved from previous work and the final setup could reduce the electricity bill for the residential consumer.

In order to adjust the system parameters, some limits of the input linguistic variables were modified. In the simulation, a battery sized in a more adjusted way and with a more current technology was also used to obtain a better cost benefit for a residence. A recent configuration of photovoltaic panels was used, with more efficient electrical power and better solar absorption technology. The modifications were satisfactory for the improvement in the results, allowing the continuation of the development of this research.

The results obtained brought a reduction of 14.05% in the energy consumed from the electrical distribution grid, when comparing the simple DG system developed without the use of IC with the proposed fuzzy system. This means a 31.73% reduction in the annual energy bill.

This work contributes to the CI area and to the academic community based on the expansion and progression of fuzzy logic studies applied to photovoltaic systems, with the aim of demonstrating the importance of these two subjects for improving decision-making and management of photovoltaic solar energy. In addition, the study and application of an intelligent system in a scenario that simulates the real world allows, among other contributions, the development of more innovative products for the energy market and products with better cost-benefits for the final consumer.

For future work, we intend to apply the proposed fuzzy systems for different energy production and consumption patterns from different cities of different Brazilian regions. We intend to verify if the proposal can be applied independently of the local, or if it requires small (or large) adjustments for better performance. It is also intended the study and application of other techniques of computational intelligence in order to compare with fuzzy logic.