3.1. Problem Statement
Environmental degradation caused by deforestation, gas emission, and environmental pollution has caused countries to rethink their electric systems. As a solution to the problems caused by the unsustainable exploration of fossil fuels, renewable energies have become the focus of attention of a broad range of agents. However, in Brazil, unlike other countries, the investment in photovoltaic solar energy was driven by different reasons, such the increase in the cost of energy produced in thermoelectric plants and the emission of greenhouse gases by burning of fossil fuels [39
Among other solutions, PSE shows up as a viable and necessary source of electrical energy. Given that it is located mostly in the intertropical region and has excellent potential for solar energy utilization throughout the year, the Brazilian solar radiation is higher than the European for almost its entire territory [41
]. Based on Renewable Energy Country Attractiveness Index [42
], Brazil is eighth in the raking of attractiveness when speaking of photovoltaic solar energy. In 2014, Brazil had its total installed to power up to 15 MW, and in 2015, the same number surpassed 32 MW. Statistics of the Mines and Energy Ministry [43
] indicated that by 2018 Brazil should be between the 20 countries with the most prominent generation of solar energy.
On the other hand, the high cost of acquisition of photovoltaic and their low conversion efficiency from solar irradiation to electrical energy are the main impediments to the large-scale diffusion of these systems [44
]. As a solution, the government can understand the dynamic of PSE development from other countries and propose policies that improve the use of solar energy in an urban environment [46
]. Given that the future of the PES depends on several issues, it needs to be planned and controlled. For this purpose, scenario planning is a fundamental tool [47
3.2. Model Development
In order to provide a quasi-quantitative model for scenario planning, regarding the studied problem of PSE development in Brazil, the FCM development process was conducted in six steps. Figure 1
offers a visual representation of these steps for better understanding of the procedure and for the convenience of the readers.
Step 1: Obtaining concepts from participants.
The first step deals with the determination of the most essential independent variables that define the examined problem and affect the dependent variable. Participants are asked to determine the concepts of the system but only the most important in order to avoid designing a system with a vast number of variables that would be difficult to study.
Step 2: Qualitative assignment of cause-effect relationships between concepts.
In the second step, participants are asked to assign values on the scale of 1–10 and to determine whether there is a positive or negative cause-effect relationship for the weighted interconnections among the depended and most significant variables that constitute the FCM model. Ten (10) denotes the highest strength and one (1) the lowest. The sign + (plus) denotes a positive influence, whereas the sign – (minus) denotes a negative influence that one node has to another.
Step 3: Weights Normalization (coding into an adjacency matrix).
Weights given to each link were then normalized between 0 and 1 (as described in Table 1
), considering positive and negative values for coding into the adjacency matrix [48
]. So, we substitute the qualitative values assigned by the stakeholders for expressing the degree of influence with the corresponding quantitative values, in order to define the weight matrix of each stakeholder, as presented in Table 1
. For example, the qualitative value 10 (that denotes the highest strength) is substituted by the quantitative weight value 1.
Step 4: Producing individual FCMs from each group.
In this step, every group of the participants was asked to construct an individual FCM by defining the primary variables and determining the weights values of all causal relationships. This process also includes the identification of the decision concept, which is a dependent variable for the problem under investigation. As we aim to analyze the Brazilian Solar Photovoltaic Energy Sector, the dependent variable was set to be the “Development of PSE in Brazil”. The procedure that was followed, is described below in detail, as the authors want to highlight the importance of all the steps taken for the success of this study.
Step 5: Groups Aggregation producing an Overall FCM.
In this step, all individually coded cognitive maps from the three groups were aggregated and an overall group FCM (Collective-FCM) was produced that includes all the concepts from all individual cognitive maps. This collective FCM represents the perception of all the stakeholders and is enriched with the knowledge of all stakeholders involved.
Step 6: Visualization of collective FCM.
After the aggregation process, that was based on the weighted average method, the Collective-FCM was analyzed using the FCMWizard software tool (version 1.0, E.I. Papageorgiou, Larissa, Greece). Since the tool includes modelling and visualization capabilities, a visual representation of the condensed FCM model was created by FCMWizard, which specifically illustrates the concepts and all the connections between them. The graphical representation of the collective FCM is presented in Section 4.1
, where an overview of the FCMWizard tool is presented.
Following the steps above, the authors carried out the project with the help of researchers of the University of São Paulo (USP) and University of Brasília (UNB) specialized in the solar photovoltaic energy. They along with other specialized stakeholders (such as specialists from the National Electric Energy Agency (government), the Brazilian Solar Energy Association (professionals)) were the primary sources of data and information for the development of this research.
Interviews were conducted individually or with pairs of specialists from the National Electric Energy Agency (government), the World Wildlife Fund (NGO), Brazilian Solar Energy Association (professionals), and researchers from the University of São Paulo and Brasília (specialists). A workshop was also carried out with a group of eight graduate students of the Institute of Energy and Environment of the University of São Paulo, IEE/USP, to consolidate the FCMs.
Specifically, a pretest was first carried out with a potential consumer with a business background, through an individual interview, during which the dynamics of FCMs and the proposed method were explained. The respondent had trouble defining the primary variables (concepts) and establishing the exact weights (from −1 to 1) of the causal relations. After proper guidance and following the contents of Table 1
, in the end, he managed to develop a potential FCM.
The second FCM was constructed after interviewing a specialist in SPE from the University of Brasília (UNB). He responded with great enthusiasm and a consensus was reached for 12 interrelated concepts, establishing at the same time the causal relations and respective weights.
In the next FCM, the proposed method was investigated with the help of a group of SPE specialists from IEE/USP. In a workshop with eight participants, the dynamics of FCMs and the proposed method were explained. These specialists identified 13 concepts and established their connections and weights. In this type of approach (workshop), the most prominent advantage came from the debate among the participants. Instead of creating individual FCMs, the authors suggested a collaborative process for scenario planning where the participants cooperated to produce a more productive and accurate knowledge in the form of a consolidated FCM. The weight value for each interconnection is calculated as the average of all values that each participant gave for the corresponding interconnection, taking into consideration Table 1
. However, the FCM achieved by the group of specialists from USP, presented in Figure 2
, was not a significant improvement regarding complexity and robustness in comparison with the others.
The FCMs elaborated from the information of the specialists, and stakeholders were integrated into a single FCM. Table 2
presents the list of the concepts contained in this collective FCM, with a short description of them. They identified 29 concepts in total and established the connections and weights among these concepts. Also, they determined the 10 most central concepts (concepts in bold in Table 2
) in terms of significance in the decision making process through scenario analysis. Moreover, the weights of the connections were equal to the average of the weights established by the specialists and stakeholders.
In this context, a 29-nodes FCM model was produced from the experts/stakeholders and its adjacency matrix (see Figure 3
) was created accordingly, including the causal relationships between the concepts and their weight.