Projection of the diffusion of photovoltaic systems in residential low voltage consumers

Projection of the diffusion of photovoltaic systems in residential low voltage consumers

Accepted Manuscript Projection of the diffusion of photovoltaic systems in residential low voltage consumers L.L.C. dos Santos, L.N. Canha, D.P. Berna...
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Accepted Manuscript Projection of the diffusion of photovoltaic systems in residential low voltage consumers L.L.C. dos Santos, L.N. Canha, D.P. Bernardon PII:

S0960-1481(17)30958-8

DOI:

10.1016/j.renene.2017.09.088

Reference:

RENE 9286

To appear in:

Renewable Energy

Received Date: 21 April 2017 Revised Date:

5 September 2017

Accepted Date: 29 September 2017

Please cite this article as: dos Santos LLC, Canha LN, Bernardon DP, Projection of the diffusion of photovoltaic systems in residential low voltage consumers, Renewable Energy (2017), doi: 10.1016/ j.renene.2017.09.088. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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ACCEPTED MANUSCRIPT

Projection of the Diffusion of Photovoltaic Systems in Residential Low Voltage Consumers

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L. L. C. dos Santos*, L. N. Canha, D. P. Bernardon

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Corresponding author. Tel.: +55 55 32208344, Fax: +55 55 32208030 E-mail address: [email protected] Abstract

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UFSM – Federal University of Santa Maria, RS, Brazil

With the advent of Distributed Generation (DG), the consumers start to play an active role in the electric system, where they are able to invest in a specific generation system, with solar energy, as the most promising source for residential consumers Low Voltage (LV). For system planning studies, the adoption of DG by residential consumers, introduces a factor of uncertainty, since the decision to adhere to DG relays on the subjective judgment of each individual. In this context, this work presents a new methodology for the projection of diffusion of photovoltaic systems in residential consumers of LV. The model was developed using the System Dynamic technique in conjunction with the Bass model to foresee the diffusion of photovoltaic systems in residential consumers throughout time. After the projection of these consumers, the Monte Carlo Method is used to determine the diffusion of Photovoltaic Systems throughout space. Finally, to evaluate the performance and the efficiency of the proposed method, different scenarios of diffusion projection were tested in the southern Brazil. The results demonstrate that the diffusion of Photovoltaic System depends on several factors, for example, the price of the panel’s installation, energy tariff, incentives for Photovoltaic systems purchase, adoption by other consumers.

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Keywords – Diffusion, Systems Dynamics Technique, Monte Carlo Method, Bass Model, Projection,

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Photovoltaic Systems.

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Nomenclature  – Income of 5 to 10 minimum salaries , , , ,  – Contributions in the decision-making  . – Adoption of PV systems by other consumers  ′ – Adopters of photovoltaic panels . – Autonomy  – Income of 10 to 20 minimum salaries . . – Business strategies  – Income higher than 20 salaries  – Total consumers  . – Complexity of the PV system  – Urban residences  – The cash flow DG – Distributed Generation . – Durability  – Rural residences  – Economic Aspect

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1. INTRODUCTION

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. . – Environmental concern . . – Environmental issues  – Owned residences . – Financing to buy the PV system – Apartment-type residences ! – House-type residences !. – Higher than 10 minimum salaries  – Radiation  – The discount rate  – Initial investment  . – Import duties .  – Incentive programs "#. $% – Lack of knowledge ". &. – Low rate incentive "%. – Lower than 10 minimum salaries LV – Low Voltage ' – Management aspect '. – Maintenance '#. – Marketing MCM – Monte Carlo Method ( – Net Present Value – Coefficient of innovation  – Potential adopters  – Political Aspect . %. – Public awareness of the population s – Photovoltaic systems * – Coefficient of imitation +, – Quality of the PV system - – Social aspect SD – System Dynamic Technique -. . – Service fees and microcredit -. – Subsidy policies  –Time  – Technical Aspect .. –Feed in tariffs .. '. – Tariff Models /# –Weak and neglected after-sales

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 – Energy of the PV system ACCEPTED MANUSCRIPT

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Many countries are betting on the installation of renewable sources to reduce the emission of

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greenhouse gases. In view of that there has been an increase in the use of Distributed Generation (DG) by

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consumers. These environmental issues are the consumers’ concerns, with become part of social aspects,

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as well as a governmental concern (political aspects), and the management aspects by companies that

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work with sales and installation of DG. One of the most promising sources for DG in Low Voltage (LV)

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MANUSCRIPT is the photovoltaic panels, mainly forACCEPTED residential consumers, because of its ease of installation.

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1.1. Motivation The dissemination of DG from renewable sources and Demand Response programs makes the

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system planning a challenge for the distribution system operators, since the traditional load growth

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projections, based on decentralized approaches, become impractical [1]. This is due to the stochastic

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nature of renewable energy sources and the load demand. Large-scale penetration of these resources into

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power systems can compromise network reliability, reduce power quality, increase power losses and

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voltage deviations [2, 3, 4, 5].

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Although there are already models that consider DG in planning studies, these approaches

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consider allocation and optimal design of DG and centralized control by the system operators [6, 7, 8, 9].

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One of the weaknesses about these proposed models is that they don’t explore adequately the

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uncertainties associated with LV consumer behavior, when it generates its own energy.

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When talking about LV’s consumers, it is not known where the generators will be inserted in the

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distribution network, for this, studies about the projection of the diffusion of the DG’s insertion in

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residential consumers of LV must be done. As well as the factors those lead you to the consumer's

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decision to join a photovoltaic system.

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1.2. Literature Review

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The knowledge about the scope on sources diffusion of the distributed generation is fundamental

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for the electrical systems’ operation and planning. The main challenge is estimate the use of these

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technologies in the LV’s consumers in terms of various aspects: socio-technical, economic, managerial

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and political [10], which contribute for the consumers’ decision-making.

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One of the alternatives to estimate the diffusion of photovoltaic systems is through consumer

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surveys. Several countries have been adopting this strategy with the use of questionnaires: The

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Netherlands [11], United Kingdom [12], Australia [13], India [14].

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According to researches, there are some barriers for the adoption of residential photovoltaic

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systems, for example, the convenience on the use of the electricity from the supply network, which is

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ACCEPTED directly offered by the energy distributor [12, 15],MANUSCRIPT the lack of familiarity with solar panels and their

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benefits [15, 11], the lack of information regarding photovoltaic panels [16, 11] and the need for

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maintenance [15]. Likewise, there are incentives for the adoption of photovoltaic systems, for instance, the

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independence from the energy distributor, the discussion with other adopters [11], the cost reduction, the

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environmental concern [5], [15], [17] and [11], the increase of electricity tariffs [13] and [5]. In [16]

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points out that the purchase of a photovoltaic system by other individuals is a motivating factor, as it

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helps to overcome uncertainties associated with the adoption of photovoltaic panels. In [11] and [18]

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argue that the adoptive public of photovoltaic systems consists predominantly of middle-aged men with

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income and educational level above average.

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This way, [19] and [15] explore the acceptance of the consumer in adhering to the photovoltaic

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systems. In [19] presents a theoretical model of consumer decision and [15] explores the role of consumer

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acceptance and models its effects by applying the fuzzy logic considering three parameters:

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environmental concern, the cost of solar panels and maintenance of the system. Some authors have a greater concern about economic issues. Authors in [20] evaluate the

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economic performance of solar panels in the coverage of residential and commercial buildings under the

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technological, economic and geographic factors. In [21] summarizes the last and the most important

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environmental and economic analysis of a grid-connected hybrid network consisted by renewable

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resources. In addition, [22] does a study to boost the new renewable technologies considering the parity

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of the network, under political and economic aspects. In [23] makes an analysis on a photovoltaic system

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connected to the network using the tariff parity model.

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In this sense, [24] questions the use of tariff parity exclusively, assuming that by reaching a level

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of cost-effectiveness is not enough to guarantee the insertion of a technology. As an example, the author

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mentions that the solar water heating systems have already reached tariff parity in many places but, none

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the less, they have not spread massively around the world.

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In [25] presents a comparative analysis of the main support mechanisms for promoting

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MANUSCRIPT photovoltaic systems in six EuropeanACCEPTED Union countries (France, Germany, Greece, Italy, Spain and United

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Kingdom), by using as factors: discounted cash flow (DCF), Pay-Back-period (PBP), the Net Present

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Value (NPV) and the Internal Rate of Return (IRR). Similarly [26] examines the differences among feed-

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in tariffs, net metering and buying and selling electric power using a simple microeconomic model. One of the recent works that make the modelling of the diffusion of photovoltaic systems is from

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[27], who has a less comprehensive view about the barriers that affect the adoption of photovoltaic

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systems by residential consumers. The author uses the System Dynamics technique together with the Bass

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model, where consumer diffusion is modelled only considering the time of return of investment.

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In particular, the implementation of photovoltaic systems in Brazil is an important alternative in

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the context of the Brazilian energy crisis, even [28] carried out an analysis of scenarios, perspectives and

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policies in the implementation for low-income consumers. And [29] concludes that without the economic

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viability of photovoltaic systems in Brazil, only a small number of businesses and private houses will

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invest in these systems due to a lack of profitability.

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As discussed above, although there are studies that deal with diffusion, most of them are limited in

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analysing the barriers for the diffusion of Photovoltaic Systems (PV systems), which indicates the need

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for a refinement about the model used, as well as the considered parameters. 1.3. Contributions

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The objective of this research work is to propose a global methodology for forecast the diffusion

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of photovoltaic systems for residential consumers of LV for the purposes of planning of the utility, using

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as a tool the System Dynamics Technique in conjunction with the Bass model, and the Monte Carlo

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Method (MCM). The uncertainties of the parameters are considered by simulating different scenarios and

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making sensitivity analysis.

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The main contributions of this research work are:

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(i)

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methodology to analyze the diffusion of PV Systems on two dimensions: throughout time and throughout space;

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definition of dynamic models for the representation of aspects: economic, managerial,

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identification of potential locations for the growth on the use of photovoltaic panels;

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method to define the range of insertion of DG by using the MCM;

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As case studies, several scenarios of implementation of photovoltaic systems in Brazil in LV

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consumers were researched and analysed.

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1.4. Structure of the Paper

For a better understanding, this work is organized as follows: the section 2 contextualizes the

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diffusion problem from the perspective of the diffusion of photovoltaic systems, the section 3 presents the

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methodology applied in order to obtain the diffusion of photovoltaic systems in residential consumers

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throughout time and throughout space. Section 4, presents a case study and the analyses on the results and

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the section 5 presents the final considerations of this research.

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2. DIFFUSION OF PHOTOVOLTAIC SYSTEMS

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The diffusion of photovoltaic systems in residential consumers of LV can be considered a

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diffusion of innovations problem. Gabriel Tarde, social psychologist, was a pioneer in the studies about

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diffusion of innovations, publishing the book "The Laws of Imitation" [30]. Tarde recognized the role of

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opinion leaders in the adoption (which he denominated imitation) or rejection of an innovation, but his

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ideas were not readily accepted [31].

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In [32] assert that diffusion is commonly used to describe the process by which individuals and

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companies in a society/economy adopt a new technology or replace an old technology by a new one.

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According to [31], diffusion is the process by which an innovation is communicated through certain

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channels throughout time among members of a social system. It is a special kind of communication, in

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which the messages are connected to new ideas.

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On the other hand, [33] defines the diffusion of innovation as being a process of penetration in the

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market of new products and services, being this process driven by social influences. These influences

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include all interdependencies among the consumers that affect various actors in the market with or

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without their explicit knowledge.

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is enormous, one of the first works was proposed by Everett Rogers [31], in the book “Diffusion of

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Innovations”, a classic published in 1961. For diffusion models applied to the sales of new products, there

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is [35], the main impetus underlying of these contributions is a new model of the product growth

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suggested by [36].

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ACCEPTED According to [34], the literature on diffusionMANUSCRIPT of new products and social and technical innovations

With these considerations, it is understood that the diffusion process is the path of adopting an

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innovation over time by individuals or organizations that are part of a social system. The

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Fig. 1 presents a model of stages in the decision process of an innovation.

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Fig. 1. Stage model in the decision process of an innovation. Source: [31].

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According to [31] the model of stages in the decision-making process of an innovation is

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composed by five steps. The first is the knowledge, that is when the individual is exposed to the existence

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and the gains of innovation, the understanding of how it works. The second step is the persuasion, it

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occurs when the individual takes a favourable or unfavourable attitude towards the innovation. The third

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step is the decision, when the individual engages in activities that lead to a choice to seize or reject the

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innovation. The implementation takes place when the individual puts the innovation into use. And finally,

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the confirmation that is when the individual aims at the strengthening of an already done innovation-

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decision, but he can reverse the previous decision if it is exposed to conflicting messages about

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innovation.

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The adoption of innovations, such as technologies of renewable energy, is a complex process with

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several interconnected factors. In [15], the author argues that mapping the diffusion process of renewable

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sources is not a trivial task because it involves many uncertainties due to technological, economic and

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social aspects. Research on the diffusion of photovoltaic systems exists since the 1980's, being [37] one of

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the precursors.

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In [31] states that one of the mechanisms that helps in the diffusion process of an innovation are

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ACCEPTED MANUSCRIPT the conditions of homophilia (identity of values and knowledge), and among the ones that hinder the

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process are those of heterophilia (differences of values and knowledge). The different conditions that

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separate people from different income are values and level of education. In Brazil the level of income

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correlated with level of education. According to [31] not all individuals in a social system adopt an innovation at the same time.

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Instead, they adopt in a sequence of time, and they can be classified into adoption categories based on

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when they start using a new idea.

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The Fig. 2 shows the normal frequency distribution divided into five categories of adoption: (1)

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innovators, (2) early adopters, (3) early majority, (4) late majority, and (5) laggards. It demonstrates the

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action data represented by an S-shaped curve (cumulative).

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Fig. 2. Innovation adoption curves. Source: [31].

Both curves, Fig. 2 are about the same data, the adoption of an innovation over time by the

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members of a social system. But the bell curve shows these data in terms of number of individuals who

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adopt an innovation each year, while the S-shaped curve shows these data on a cumulative basis [31].

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Based on the study of [31], Frank Bass in 1969 conceived the model of Bass diffusion [36], which

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is now a mathematical contribution to the theory of diffusion of innovations, able to generate a sigmoid

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curve of the market penetration rate along of time. The Bass model assumes that the potential consumers

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of an innovation are influenced by two processes: mass communication and interpersonal communication.

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.() * = + (() 1 − () 

(1)

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Where, f (t) is the probability of adoption at time, t, F(t) is the cumulative distribution, p is the

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innovation coefficient, which represents the external influence to the diffusion process, q is the coefficient

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of imitation, representing the internal influence to the diffusion process, m is the final potential market,

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that is the number of individuals who will adopt the technology with enough time of diffusion; and N (t)

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is the cumulative number of adopters.

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Related to equation (1), in theACCEPTED formulation ofMANUSCRIPT the Bass adoption rate f (t), two main parameters are

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used: p which is exogenous and represents the innovative portion of the population which is endogenous

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and represents the imitants. In the same way as the Rogers' theory, the Bass model assumes that the

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probability of adoption increases according to higher the prior adoption [35]. Therefore, to solve the problem of diffusion of innovations, in the context of photovoltaic

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systems, we chose the System Dynamics technique along with the Bass model. In [34] discusses that the

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Systems Dynamics is a methodology aimed at the study and management of complex systems with

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feedback, whick allows the connection of various aspects - technical, economic, social and managerial– in

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a coherent conceptual model.

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The System Dynamics technique was created throughout the 20th century by the professor Jay W.

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Forrester from Massachusetts Institute of Technology and first presented in his book Industrial Dynamics

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[38]. This technique has as its basic elements the feedbacks, flows, accumulation of flows (stocks) and

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delays. The mathematical description of a system dynamics model technique is done with the help of

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nonlinear ordinary differential equations [34].

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According to [34], one of the failures at the logistic models of diffusion of any innovation is a

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problem in relation to initialization, in logistics (and in the other simple growth models, including

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Richards and Weibull) zero is a balance, the model can not explain the origin of the initial adopters.

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In light of this, Frank Bass has developed a model for diffusion of innovations which overcomes

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the problem in relation to initialization, assuming that the potential adopters become aware of innovation

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through external sources of information whose magnitude and persuasion are constant over time.

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The Bass model was introduced as a tool for predict the sales of new products, the positive

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feedback is usually interpreted as word of mouth (imitation) and the external sources of awareness and

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adoption are interpreted as the effect of advertising (innovation). The Bass model of diffusion became one

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of the most popular models in the diffusion of new products, being widely used at marketing, strategy,

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technology management among other fields.

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The Fig. 3 shows the BassACCEPTED model in the MANUSCRIPT form of System Dynamics, which is composed by

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adoption rate, regulated by the parameters of innovation and imitation, whose function is to consume the

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stock of potential adopters and supply the adopters.

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In Fig. 3 the total adoption rate is the sum of adoptions resulting from word of mouth and external influences. Thus, the AR rate is given by equation (2).

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AR=Adoption from Advertising + Adoption from Word of Mouth Being:

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Adoption from Adversiting = aP

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The adoption from word of mouth is given by equation (4):

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(2)

The adoption rate is given by equation (5).

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AR = aP + CiPA/N

(4)

When an innovation is introduced, the adoptive population is zero, the only source of adoption

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will be the external influences such as advertising. Advertising will be greater at the beginning of the

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decision-making process and will gradually decrease as the potential adopters will exhaust.

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The System Dynamics model allows changing the structure of the system by modifying, for

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example, the parameters of innovation and imitation, or even by making structural changes, such as the

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addition of other loops and variables. In this way, the System Dynamics offers an interesting structure to

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combine the fundamental basis of the Bass model, considering the evolution of the diffusion in time and

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the aspects: social, technical, economic, political and management.

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According to [34] the diffusion of innovations often follows growth patterns, where positive

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feedbacks create exponential growth of a successful innovation, and the negative feedbacks limit the

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growth of innovation.

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ACCEPTED MANUSCRIPT For the estimation of DG comprehensiveness, the Monte Carlo Method was used to make a

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weighted raffle with the criteria based on consumers with DG from cities belonging to a specific region.

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3. METHODOLOGY FOR DIFFUSION OF PHOTOVOLTAIC SYSTEMS With the attendance to the growing demand and the environmental concern, the distributed

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generation based on photovoltaic systems has been gaining prominence in the recent years. The global PV

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systems market has grown rapidly over the past decade at a steadily increasing rate which will lead the

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PV systems as one of the major sources of power generation in the world [39]. It is expected that, in a

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near future, there will be an increase in the amount of PV systems installed in the residential consumers.

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That way, the main goals of this research reported in this document are to study, to model and to

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analyse the projection of the diffusion of photovoltaic systems in residential consumers. This diffusion is

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analysed in two dimensions: throughout time and throughout space. In the Fig. 4 we presents the

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proposed methodology architecture.

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Fig. 4. Proposed methodology architecture

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As shown in Fig. 4, the proposed methodology starts at identifying the barriers for the diffusion of

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PV Systems, which are described in the literature review. From that, the diffusion of PV Systems

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throughout time is modeled using the System Dynamics technique. This model determines the innovation

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adoption curve considering the five aspects proposed. Thereafter, the MCM is applied to determine the

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diffusion of PV Systems throughout space. It establishes which consumers will adopt the PV System and

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their respective number of photovoltaic panels for the whole region in study.

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3.1 DIFFUSION THROUGHOUT TIME USING SD

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The SD technique is used in conjunction with the Bass model. According to [40], constructing a

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model (SD) is an iterative, trial and error process. A template is usually built in steps. Increasing the

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complexity until it is able to replicate the observed behaviour of the system.

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In [40] describes an 8 steps ofACCEPTED an approach toMANUSCRIPT build and test a model, which are summarized in the diagram bellow, Fig. 5.

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Fig. 5. Architecture for the construction model of the SD. Source: [40].

The 8 steps, Fig. 5, will be presented throughout this study.

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In the first step, getting acquainted about the system is necessary in way to obtain more

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knowledge about the purpose of the model and clearly identifying the most important variables [40]. The processes of diffusion are targets of scientific researches because they are considered as

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complex phenomenon, which depend on several aspects. In this work, the model developed is divided in

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five aspects: economic, management, political, social and technical, as presented in Table 1.

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TABLE I ASPECTS CONSIDERED IN THE MODEL OF SYSTEM DYNAMICS

None of the studies found in the literature includes all the variables in a single model, as presented

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in the given Table I. In view of this, the model of prediction of insertion of photovoltaic systems in low

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voltage consumers was developed.

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In the second step, be specific about the dynamic problem, the expected dynamic behavior of the

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model is shown in Fig. 2, since it is the diffusion of an innovation. The steps 3 and 5 are, respectively, the constructions of the stock and flow diagrams and the

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estimates of parameter values. According to [40], the estimation of each parameter of the model must be

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done in an individualized way. Some parameters can be known with perfect accuracy (100%), others may

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have an accuracy of 10% and others may be totally unknown. The causal loop diagram will not be

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presented in this work, because we used the stock and flow diagram for the simulation of the model.

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In the model of prediction of insertion of photovoltaic systems, Fig. 6, is is formed by 5 aspects

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and the coefficients of innovation and imitation proposed by Frank Bass [36]. For the construction of this

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proposed model, we drove our studies based on literary revision, but in a more embracing systemic

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MANUSCRIPT vision. We encompassed a greater ACCEPTED number of aspects, while the other previously studies have only

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presented a few of them. Each of the aspects, as well as the coefficients of the Bass model, have a weight that varies from 0

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to 1, which leads to a positive influence on the rate of adoption (positive feedback), for example, if there

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is an increase in the aspects, not only the rate of adoption increases but also the number of adopters. The

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negative feedback is the potential of adopters of PV system since the number of adopters can not be

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greater than the total number of potential adopters, who are a portion of the total consumers. This all

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depends on the place of installation and the salary of the residence to be installed the photovoltaic system.

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Fig. 6. Submodel of the diffusion process of photovoltaic systems

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The variable of the adoption rate, equation 6, indicates a portion of the population that would be

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able to acquire a photovoltaic system, which increases the stock of PV system adopters and reduces the

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stock of potential adopters, considering the economic, management, political, social and technical aspects

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and the coefficients of innovation and imitation.

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   = ∗  + * ∗  ∗

 7  ∗ ( ∗  +  ∗ ' +  ∗  +  ∗ - +  ∗ ) 

(6)

Where p is the coefficient of innovation and q is the coefficient of imitation, PA are potential

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adopters, APV are the adopters of photovoltaic panels, CT is the total consumers, a, b, c, d, e are the

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contributions in the decision-making for each aspect considered, EA is the Economic Aspect, MA is the

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Management Aspect, PoA is the Political Aspect, SA is the Social Aspect and TA is Technical Aspect.

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In the following sections the general model, Fig. 6, will be detailed. An analyze will be done on

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each of the 5 aspects it is composed, and the interactions between the variables that constitute each one of

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these aspects will be determined.

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A. Economic Aspect

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The economic aspect has a greater degree of importance in the adopters of PV system, because

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when installing a photovoltaic system, the consumer is concerned about to the economic benefit. In this

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ACCEPTED respect, what is considered are the net present valueMANUSCRIPT of the photovoltaic system (panels and inverter) and

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the energy grid, the payback time, financing to buy the PV system, and political and technical aspects that

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make the installation of photovoltaic panels economically competitive. In the Fig. 7 is presented the

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model of the economic aspect. In order to calculate payback, if you use the installation price and the cash flow, the installation

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price depends on the price of the photovoltaic panel, the number of panels and the price of the inverter.

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The cash flow depends on the energy of the panel, which is calculated by the solar resources, the number

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of panels, the panel power used and the panel efficiency, the tariff and the operating cost of the system.

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The comparator compares the NPV grid and the NPV panel, considering 20 years. If the NPV grid

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is less than the NPV panel, the comparator is equal 0, otherwise, it is equal 1. For the NPV grid

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calculation the annual demand and the tariff are used. Also, for the NPV of the panels’ calculation, the

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installation price, network energy (total demand less panel energy), tariff and operating cost are used.

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Fig. 7. Model of the economic aspect

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By the analysis of Fig. 7 it is possible to notice that with the increase of adopters of PV system

375

there is a decrease in the price of photovoltaic systems, which will reduce the payback and the NPV of the

376

panel, that consequently, increases the economic aspects, which also increases the adoption rate.

EP

374

Simple payback does not take into account the interest rate, inflation or opportunity cost in the

378

period. However, by the ease calculation from the consumer’s point of view, it will be one of the options

379

in economic aspects, along with the net present value of the photovoltaic system and energy grid, and the

380

financing to buy the PV system, besides the political and technical aspects that influence economic

381

aspects. The equation 7 presents the adoption rate related to economic aspects.

AC C

377

 =   ∗ 0.3 + exp(−1.3863 ∗ #) + 0.2 ∗ . +0.15 ∗  + 0.1 ∗ 

(7)

15

382

MANUSCRIPT Where Comparator, makes aACCEPTED comparison between the values of NPV grid and NPV of the panel.

383

If NPV Panel higher than the NPV grid, then comparator is 1, otherwise, it is zero. The element payback

384

is the time of return of investment, Finan. is the financing to buy the PV system.

386

As presented in Fig. 7, the economic aspect depends on the net present values, which are calculated through equation 8, and payback which is calculated by equation 9. B

( = A CD

 (1 + )

# =

(8)

(9)

Where, DCF is the cash flow, t is the moment when the cash flow occurred, i is the discount rate, Ii is the initial investment.

389

B. Management Aspect

M AN U

388

SC

387

 

RI PT

385

390

The management aspect depends on marketing, business strategies and the weak and neglected

391

after-sales service provided by the companies that work with PV system, incentive programs and service

392

fees and microcredit. The Fig. 8 presents the model of the management aspect. On the other hand, the calculation of marketing and business strategies depends on companies that

394

work with PV system and potential of early adopters. The incentive programs and service fee and

395

microcredit rates can range from 0 to 1, being two inputs to the model. These 4 variables (marketing,

396

business strategies, incentive programs, service fee programs and microcredit) have positive feedback in

397

relation to the management aspect. If the variable increase the management aspect, potential adopters

398

will, consequently, increase. And the weak and neglected after-sales service of these companies, it will

399

depend on business strategies. If the business strategies are reduced, after-sales service decreases, which

400

diminishes the management aspect leading on an influence on the adoption rate.

AC C

EP

TE D

393

401 402

403

Fig. 8. Model of the management aspect

In Fig. 8 is shown that these companies that work with PV system, increase depending on the

16

404

ACCEPTED MANUSCRIPT adopters of PV system, influencing marketing and business strategies. In this view, a weak and neglected

405

after-sales service of photovoltaic systems can be reduced by business strategies. Incentive programs of

406

service fee and microcredit will directly influence the management aspects, which affect the adoption rate

407

of photovoltaic systems.

408

Equation 10 presents the adoption rate in relation to the management aspects.

RI PT

 = . .∗ 0.2 − /# ∗ 0.1 + '#.∗ 0.2 + . .∗ 0.25 + -. .∗ 0.25

(10)

Where Bus. str. means the business strategies practiced by the PV system companies, the Weak is

410

the weak and neglected after-sales service of the PV system, Mark. is the marketing practiced by the PV

411

system companies, the Incen. Prog. represents the incentive programs for the purchase of PV system; and

412

Ser. Fees are the service fees and microcredit for the purchase of PV system.

413

C. Political Aspect

M AN U

SC

409

414

The political aspect depends on environmental issues, feed-in tariffs, tariff models, low interest

415

rates policy and subsidy policies for the purchase of PV system and import taxes. In Fig. 9 is presented

416

the model of the political aspect.

Environmental issues can range from 0 to 1, depending on where the study will be done. The feed-

418

in tariffs, tariff models, low interest rate policies and subsidy policies depend on political stability that,

419

consequently, depends on economic stability. Related to the import tax, it depends on the economic

420

stability that depends on political stability, the adopters of PV system and the total consumers.

422

EP

AC C

421

TE D

417

Fig. 9. Model of the political aspect

423

In the above, Fig. 9, is preseted that with the increase of the adopters of PV system there is an

424

increase of economic stability, which increases political stability and influences in the political aspects.

425

By contrast, with a decrease of these adopters PV system, it diminishes the economic and political

426

stability, and by diminishing the political aspects, it influence on the adoption rate. In the Equation 11 is

427

shown the adoption rate by political aspects.

MANUSCRIPT  = .. '.∗ 0.1 + ". &.∗ACCEPTED 0.2 + -.∗ 0.2 + ..∗ 0.3 −  .∗ 0.2 + . .∗ 0.2

17 (11)

Where Tariff Mo. is the tariff models, the L. Rat. is a low rate incentive for the purchase of PV

429

system, Sub. shows the subsidy policies for the purchase of PV system, Tarif. means the feed in tariffs in

430

the installing of PV system and Imp. is the import duties of components of photovoltaic systems and Env.

431

Ins. refers to environmental issues.

432

D. Social Aspect

RI PT

428

The social aspect depends on many factors, such as the adoption of photovoltaic systems by other

434

consumers, the lack of knowledge of potential adopters in relation to photovoltaic panels, the

435

environmental concern from the population, public awareness and the autonomy of the energy distributor.

436

The Fig. 10 presents the model of the social aspect.

M AN U

SC

433

The adoption of PV system, by other consumers, will depend on whether the adopters are satisfied

438

with the product. The lack of knowledge depends directly on the education campaigns, increasing the

439

education campaigns if the lack of knowledge decreases. The environmental concern and public

440

awareness depend on the income related education and human development index (HDI). The autonomy

441

of the energy distributor will depend on the potential adopters, for example, a portion of potential

442

adopters who see the advantage, do not depend exclusively on electric energy distributor.

444

EP

443

TE D

437

Fig. 10. Model of the social aspect

In Fig. 10 it can be seen that, with the increase of the adopters of PV system increases the

446

adoption of PV system by other consumers, which consequently, increases the social aspect. Another fact

447

in this model is the lack of knowledge will depend on the potential adopters that can be solved by

448

education campaigns. The autonomy in relation to the supply from energy distributor will depend on the

449

potential adopters, which increases with the decrease of the potential adopters. The environmental

450

concern and the public awareness depend on schooling and education index.

451

AC C

445

Equation 12 presents the adoption rate in relation to social aspects.

- =  .∗ 0.25 + .∗ 0.15ACCEPTED + . %.∗MANUSCRIPT 0.2 − "#. $%.∗ 0.15 + . .∗ 0.25

18 (12)

Where Adop. represents adoption of PV system by other consumers, Auton. is autonomy in the

453

autonomy in relation to supply from energy distributor, Pub. Awar means the public awareness from the

454

population, Lack. Know. is the lack of knowledge regarding the photovoltaic panels and Env. Con. is

455

shown as the environmental concern.

456

E. Technical Aspect

RI PT

452

The technical aspect depends on the quality of the photovoltaic system, the energy of the panel,

458

durability, maintenance requirement and the complexity of the panels. Fig. 11 presents the model of the

459

technical aspect.

SC

457

The quality of the panels will depend on companies that work with PV system working with PV

461

system and adopter of PV system. The panel energy depends on efficiency, solar resources, number of

462

panels and the panel power. The durability of the photovoltaic system will increase over the years, but

463

new types of technologies are being used to deal with it. The maintenance demand will depend on the

464

total consumers and the adopters of PV system. The complexity of the panels will depend on the potential

465

of early adopters and the potential adopters, the more consumers adhere to this, the less complex will be

466

to next consumers.

468

TE D

EP

467

M AN U

460

Fig. 11. Model of the technical aspect

In Fig. 11, the companies that work with PV system increase according to the PV system adopters,

470

and this influences the quality of photovoltaic system, which interferes in the technical aspects, which

471

will influence the adoption rate that changes the adopters of PV system and consequently will changes the

472

potential of adopters that influence in the complexity of the PV system. Equation 13 presents the adoption

473

rate in relation to the economic aspects.

AC C

469

 = +, ∗ 0.35 +  ∗ 0.15 + .∗ 0.2 − '.∗ 0.2 −  .∗ 0.1 474

(13)

Where Quality is the quality of the PV system, Energy means the energy of the PV system, Durab.

19

475

represents the durability, Mainten. isACCEPTED regarded as theMANUSCRIPT concern of consumers on doing system maintenance

476

and Comp. is shown the complexity of the system.

478 479

F. Complete Model Fig. 12 presents the complete model, considering the five aspects and the coefficients of innovation and imitation, where can analyse how the variables interact with each other.

480 481

Fig. 12. Complete Model

RI PT

477

From the analysis of the Fig. 12, it can be seen that the potential adopters of the photovoltaic

483

systems will depend on a portion of the total consumers that are in residences that do not present any

484

difficulty for installation, and the greater possibility is found in households with income higher than ten

485

minimum salaries.

than 10 minimum salaries).   = ∗  + * ∗  ∗

489 490

 7  ∗ ( ∗  +  ∗ ' +  ∗  +  ∗ - +  ∗ ) "%.∗ 0.3 + !.∗ 0.7

(14)

Where Low. are the households with income lower than 10 minimum salaries and Hig. are households with income higher than 10 minimum salaries.

EP

488

M AN U

487

Equation 14 presents the adoption rate by considering the salary of the consumer (less and more

TE D

486

SC

482

According to the model presented in Fig. 12, the number of consumers with photovoltaic systems is estimated considering a horizon of 20 years.

492

3.2 DIFFUSION THROUGHOUT SPACE USING MCM

AC C

491

493

In item 3.1, a model for the diffusion of photovoltaic systems was proposed, where the number of

494

consumers who will accede to DG in each of the 20 years for a region of study was determined. After the

495

diffusion of consumers with DG throughout time, is made the diffusion of these consumers throughout

496

space, that is, the number of consumers from each one of the cities belonging to the study region is

497

determined.

20

498

ACCEPTED MANUSCRIPT Thus, the Monte Carlo Method is used to estimate the diffusion of photovoltaic panels in the area

499

of study. In this way, the weighted raffle was done based on the numbers of consumers who had the

500

photovoltaic panels obtained in the model of system dynamics for the cities belonging to the studied

501

region. The Fig. 13 presents the structure for a model construction of the MCM. To do that, in the first

503

step are defined the variables, which leads to a second moment, where the frequency distributions are

504

built. Later on, the incidence intervals of the random numbers, in each city, are defined based on the

505

frequency of distributions. After that, as a last step, the scenarios are simulated according to the random

506

numbers collected before.

SC

RI PT

502

M AN U

507 508

Fig. 13. Structure for a model construction of the MCM

In the diffusion model throughout space we considered some variables as input parameters. The

510

variables are: household income (5 to 10 minimum salaries, 10 to 20 minimum salaries and more than 20

511

minimum salaries), if it is urban or a rural residence, type of residence (house or apartment), occupancy

512

condition (own or rented). The collected data will be discretized to determine the frequency of occurrence

513

for each one of the participant cities in this investigation. In order to, the Equation 15 presents the

514

calculation to get the frequency of occurrence, which will be used in the installation of photovoltaic

515

panels in each city.

EP

TE D

509

AC C

 ∗ 0.1  ∗ 0.3  ∗ 0.6  ∗ 0.7  ∗ 0.3  ∗0 !  +  +  +  +  ∑D  ∑D  ∑D  ∑D  ∑D  ∑D  ∑D ∑D ! ∑D  *. F. = + + + + 5 5 5 5 5

(15)

516

Where A are households with income of 5 to 10 minimum salaries, B are households with income

517

of 10 to 20 minimum salaries and C are households with income higher than 20 minimum salaries, D is

518

the urban residences and E is the rural residences, F is the owned residences, G is the apartments, H is the

519

houses, I is the radiation.

520

The model works through generation of random numbers distributed within a range from 0 to 1.

21

521

ACCEPTED MANUSCRIPT Depending on the number drawn, one of the cities belonging to the region will be chosen according to its

522

frequency of occurrence. In a way to reduce the error, 1000 iterations are tested.

523

4. CASE STUDY AND RESULTS This item is intended to validate the proposed model for the projection of diffusion of photovoltaic

525

systems. The case study is done in the state of Rio Grande do Sul, a state located in the southern region of

526

Brazil, which is geographically divided in 7 mesoregions, as shown in Fig. 14. The investigation

527

considered a horizon of 20 years.

RI PT

524

SC

528

530 531 532

Fig. 14. Map of Rio Grande do Sul, Brazil. Source: [41].

M AN U

529

For the application model is used the base data. A. Base Data

The base data are the values used in the input variables from the complete model, Fig. 12. 1) Available Potential: For the calculation the solar photovoltaic potential of each mesoregion of RS,

534

Brazil, is taken into account the area of study, factor of use of the area with solar collectors, factor of

535

conversion from energy radiated to electric energy, and the daily solar radiation. The calculation is

536

based on [42], through equation 16.

EP

TE D

533

537

 ∗ H ∗ I ∗ & ∗ 0,27 ∗ 365 

(16)

AC C

=

538

Where E - Annual Energy, TWh/km²/year, A - Area of study, in km², FU - Factor of area

539

utilization with solar collectors, in relation to the total area, FU=0,0001, FC - Conversion factor of

540

radiated energy to electric energy, FC=0,15, R - Daily solar radiation, in MJ/m².day, F – Conversion

541

factor for TW equal to 1000.

542 543

Table II presents the solar photovoltaic generation energy

available annually from each

mesoregion in the state of RS, Brazil. This data is calculated by using the equation (16).

544 545 546

22

ACCEPTED MANUSCRIPT TABLE II ENERGY ANNUALLY AVAILABLE FOR SOLAR GENERATION IN EACH MESOREGION OF RS

By the analysis of Table II it is found that the most favorable region for the installation of

548

photovoltaic panels are mesoregion 5 followed by mesoregion 7. Therefore, the mesoregion 7 was chosen

549

because there is a high energy value and a smaller number of cities.

550

2) Resources Available: In order to generate the solar energy, an analysis about daily global solar

551

radiation is made by using the data available on the website of the National Aeronautics and Space

552

Administration (NASA). The Fig. 15 presents the daily global solar radiation in mesoregion 7, as it is

553

the mesoregion with the highest annual energy available, in Uruguaiana city.

SC

RI PT

547

M AN U

554 555

Fig. 15. Daily global solar radiation in mesoregion 7

556

3) DG Technology: with the daily global solar radiation data, Fig. 15, the photovoltaic module

560 561 562 563

TE D

559

4) Efficiency of the Panel: According to the manufacturer’s manual the KD245GH photovoltaic module has an efficiency of 14.8%, or 85.2% reduction factor. 5) Number of Panels: 6 photovoltaic panels were used per residence, because they had a lower NPV panel in relation to other amounts of panels.

EP

558

KD245GH 245W from the Kyocera manufacturer was chosen.

6) System Lifetime: According to the manufacturer’s data, the system lifetime was considered about 20 years (Photovoltaic module and inverter).

AC C

557

564

7) Installation Price: It was considered a price of US$ 2263.00 and a reduction of 1% per year.

565

8) Operating price: It was considered a price of US$ 22.63 per year.

566

9) Residence consumption: It was used a consumption range of up to 500 kWh/m. The Fig. 16 presents

567

the daily consumption of the residence analysed. The obtained data are from a distributor located in

568

the south of Brazil.

569

23

570

ACCEPTED MANUSCRIPT Fig. 16. Daily consumption of the residence

571

10) Electric energy tariff: it was used base on RGE Sul, the energy distributor in mesoregion 7, the price

572

is R$ 0,517539 kWh, plus 43% referring to the Tax on Circulation of Goods and Services (ICMS). 11) Financing: The financing value will be 0 (without financing) or 1 (with financing).

574

12) Incentive programs: They can vary from 0 to 1, being 0 without incentive programs.

575

13) Service fee and microcredit: They can vary from 0 to 1, being 0 without incentive programs.

576

14) More than 10 minimum salaries: According to the Brazilian Institute of Geography and Statistics

577

(IBGE) data only 7.11% of the residences in mesoregion 7 have an income of more than 10 minimum

578

salaries.

581 582 583 584

SC

M AN U

580

15) Less than 10 minimum salaries: The IBGE data estimates 92.89% of the residences belonging to mesoregion 7 have an income of less than 10 minimum salaries.

16) Durability: It varies from 0 to 1, with an increase of 0.02 per year, due to the technologies of photovoltaic systems development.

17) Installation Difficulty: It was considered 20% of the residences that had difficulties to install the photovoltaic panels.

TE D

579

RI PT

573

18) Coefficient of Innovation (p): The value considered was 0.015.

586

19) Coefficient of Imitation (q): The value considered was 0.9.

EP

585

In [43] analyzed the parameter estimates of 213 published applications of the Bass model and its

588

extensions. They authors report the average value of p = 0.03 and the average value of q = 0.38. In this

589

work, the values of p and q were defined through a sensitivity analysis, Fig. 5.

590

B. Case Study for Diffusion of photovoltaic systems throughout time

AC C

587

591

The next step of the SD technique, Fig. 5, runs the model to get the reference model (step 6).

592

For the case study of the diffusion of photovoltaic systems in mesoregion 7, was used the

593

complete model, presented in a Fig. 12. There are, in this mesoregion, about 233398 residential

594

consumers and 23517 rural consumers in the year 2015. By analyzing the last 10 years according to

24

595

ACCEPTED Foundation of Economics and Statistics (FEE) data,MANUSCRIPT the residential consumers have 1.65% annual growth,

596

but, on the other hand, the rural consumers have 2.6% annual growth. Of the total consumers, it was considered that 20% of the residences presented difficulties to

598

install the photovoltaic systems, and 92% had an income of less than 10 minimum salaries and 8% have

599

income of more than 10 minimum salaries. From this perspective, the potential adopters of mesoregion 7

600

is calculated. Thus, the potential adopters in year 1 are 62220 consumers, which represents 25% of total

601

consumers.

602

RI PT

597

For the simulation about each of the scenarios, the Vensim [44] software was used, which determines the estimative of new consumers with DG in a 20 years horizon.

604

C. Case Study for Diffusion of photovoltaic systems throughout space

M AN U

SC

603

The Fig. 17 presents the frequency of occurrence for each of the cities in mesoregion 7, equation

606

15, the accumulated frequency is presented in blue and amplitude in red. From the weighted raffle by

607

using the criteria of random numbers (from 0 to 1), the number of consumers, who will have the

608

photovoltaic systems installed in their houses, is determined.

610

Fig. 17. Frequency of occurrence for each cities

EP

609

TE D

605

From the analysis of Fig. 17, it is possible to assert that the cities with the highest tendency to

612

install photovoltaic panels is city 6 followed by city 16. It happnes because these cities have a larger

613

amplitude, that is, a higher frequency of occurrence (red).

614 615

AC C

611

Since the number of consumers with photovoltaic systems, in year 20, the diffusion of these consumers in each of these 19 cities is determined.

616

In step 7, Fig. 5, the conduct sensitivity analysis is made. After each test, the reference mode must

617

maintain a suitable behavior, achieving the robustness of the model. A model is called robust when it

618

generates the same general pattern despite the great uncertainty in parameter values [40].

619

In the last step of the model, it test the impact of policies. This step has the purpose of evaluating

25

620

ACCEPTED MANUSCRIPT the behavior of the system, which can varies the estimates of the parameters associated to the political

621

variables (the variables controlled by the designer).

622

•

623

In the first scenario, all aspects (economic, management, social, political and technical) were

624

considered equal to 1, coefficient of innovation equal 0.9 and imitation equal 0.015. In the Fig. 18 is

625

presented the curve of potential adopters.

RI PT

Scenario 1

626

Fig. 18. Adopters of PV system – scenario 1

SC

627

It can be seen from Fig. 18 that, when the five aspects are equal to 1, the PV system adopters

629

reach their maximum number in the year 16. From this year there are no new potential adopters that can

630

become adopters, so the quantity remains the same.

631 632

M AN U

628

From the number of consumers with DG in year 20 (62220), shown in Fig. 18, the diffusion of this consumers is determined, according to Fig. 19.

TE D

633 634

Fig. 19. Consumers with DG in scenario 1

Fig. 19 shows the number of consumers with photovoltaic panels in each of the cities from the

636

mesoregion 7. The city 2 has the lowest number of consumers with DG, only 813 consumers, and the city

637

6, with 9442 consumers, has the largest number.

AC C

EP

635

638 639 640

•

641

In the second scenario it was considered that there would be no incentives for the installation of

642

photovoltaic panels, that is, financing, incentive programs, service fee, microcredit, import tax, low

643

interest rate and subsidy, tariff models, feed in, education campaigns equal zero, current situation of

644

Brazil. In this way, the Fig. 20 presents the curve of the adopters of PV system in a 20 years horizon.

Scenario 2

ACCEPTED Fig. 20. Adopters of MANUSCRIPT PV system – scenario 2

645

26

646

By Fig. 20 analysis, there are 45980 consumers with photovoltaic panels in year 20, which

647

corresponds to 73% of potential adopters. As there is no incentive to buy them, the growth rate is lower if

648

compared to Scenario 1, where all incentives were equal to 1. The Fig. 21 shows the diffusion of 45980 PV system adopters in each city.

RI PT

649 650

Fig. 21. Consumers with DG in scenario 2

652

In scenario 2, Fig. 21, the number of consumers with DG in cities 2 and 6 is, respectively, 638 and 6957.

M AN U

653

SC

651

654

•

655

Considering the data from Scenario 2 and making a reduction of 50% in the electric energy tariff,

656

with ICMS, the number of consumers with DG (32660) has a reduction of 28% if compared to Scenario

657

2, as shown in Fig. 22.

TE D

Scenario 3

658 659

662

EP

661

The analysis of Fig. 22 shows that with a reduction in the price of the electric energy tariff charged by the concessionaires, the number of consumers with DG decreases if compared to Scenario 2.

AC C

660

Fig. 22. Adopters of PV system – scenario 3

The Fig. 23 shows the number of consumers in each of the cities.

663 664

Fig. 23. Consumers with DG in scenario 3

665

•

666

Considering the data from scenario 2 in price of photovoltaic systems from the year 5 to the year

667

10, and from year 11 to the year 14 financing for the purchase of photovoltaic systems and education

668

campaigns, Fig. 24 presents the curve of adopters of scenario 4.

Scenario 4

27

669

ACCEPTED MANUSCRIPT

670

Fig. 24. Adopters of PV system– scenario 4

In Fig. 24 can be observed that from year 5 to year 10 there was a smaller growth of DG adopters,

672

due to the fact that the system became more expensive. In a way to improve this result, in the years 11 to

673

14 education campaigns and financing for its purchase were done.

674 675

RI PT

671

In the year 20 the number of consumers with DG was of 46760. Then, in this yaer was taken as criteria the weighted raffle and the number of PV system adopters obtained in each city, Fig. 25.

SC

676

Fig. 25. Consumers with DG in scenario 4

•

M AN U

677

In the fifth scenario, incentives for the installation of photovoltaic systems (financing, incentive

681

programs, service fee, microcredit, import tax, low interest rate policy and subsidy, tariff models, feed in,

682

education campaigns, environmental issues) are considered. The PV system adopters are presented in Fig.

683

26.

685

Fig. 26. Adopters of PV system– scenario 5

EP

684

Scenario 5

TE D

678 679 680

From the Fig. 26 analysis is known that there are 60740 consumers with photovoltaic panels in the

687

year 20 and the number of consumers with DG has a higher penetration rate. It happens because in this

688

scenario the incentives were considered in all 20 years for their purchase.

689 690

AC C

686

By considering the number of consumers with DG in year 20, it was possible to determine the number of PV system adopters in each city, Fig. 27.

691 692

Fig. 27. Consumers with DG in scenario 5

28

ACCEPTED MANUSCRIPT With the number of consumers with DG obtained in each city, it is probable that the energy

693 694

distributor use this data as their planning purposes.

695

•

696

The Table III and the Fig. 28 presents the comparison among the 5 scenarios analysed, by considering the variables of the model in relation to the diffusion of PV system.

698 699

RI PT

697

Comparison among the scenarios

In the best scenario analyzed (scenario 1), when all aspects are equal to 1, it takes 16 years for all potential adopters become adopters of PV system.

In Scenario 2, even without incentives to install the PV system, the number of adopters in the year

701

20 is significant, since the price of the PV system tends to decrease and the tariff tends to increase over

702

the years and the adoption of PV system by other consumers have a positive influence on the adoption

703

rate.

M AN U

SC

700

704

The Scenario 3, no incentive is considered, but there was a reduction in the tariff. This reduction

705

makes the NPV grid become smaller than the NPV panel generates an increase in payback, economic

706

aspect, which reduces the adoption rate and consequently the adopters of PV system. In scenario 4, no incentive is considered, and between the periods from the year 5 to the year 10

708

there is an increase in the price of the PV system, which makes the adopters of PV system decrease. In

709

order to resolve this change in the year 11 to 14 there is financing for the purchase of the PV system,

710

which, again increases the adoption of PV system by consumers. Accorging to the Scenario 4 there are

711

more consumers using the PV system in the year 20 if compared to the Scenario 2.

AC C

EP

TE D

707

712

In the last scenario analyzed, incentives are considered for the installation of the PV system. With

713

those incentives, the adopters of PV system increase significantly, when compared to the scenario without

714

incentives (Scenario 2).

715 716 717 718

TABLE III COMPARISON AMONG THE SCENARIOS ANALYZED

ACCEPTED MANUSCRIPT Fig. 28. Comparison among the scenarios analyzed

719

29

720 Table III and the Fig. 28 show that the number of consumers with DG will increase when there is

722

some kind of incentive and will decrease when the tariff of the electric energy grid decreases, the price of

723

the photovoltaic system increases or if there are no incentives for the purchase of the PV system.

724

5. CONCLUSIONS

RI PT

721

The diffusion of photovoltaic panels in residential consumers is extremely important for planning

726

studies about electrical system, since the decision to adhere to this type of system depends on each

727

individual and not on the centralized decision of a government.

SC

725

In this way, the main contributions of this work are the use of the system dynamics technique in

729

conjunction with the Bass model to predict the diffusion of DG in residential consumers of LV

730

throughout time, where the quantity of consumers is determined by each year and considering the five

731

aspects: economic, management, political, social and technical and the coefficients of the Bass model (p e

732

q). These aspects and coefficients must have their parameters estimated, so that, the simulation can be

733

done, after sensitivity analysis and the policy test to determine if the behavior of the model is coherent.

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From the system dynamics technique is possible to relate and understand the systemic variables

735

that will boost the diffusion of photovoltaic sources in electric energy distribution systems throughout

736

time.

EP

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Allied to this, there is the Monte Carlo Method to determine the diffusion of these consumers

738

throughout time, where it is determined where the new photovoltaic panels will be inserted in the study

739

area, by considering the variables: household income, if the residence is rural or urban, type of domicile,

740

condition of occupation and radiation.

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Thus, a case study was carried out in southern Brazil, where the potential locations for the growth

742

of the photovoltaic panels were identified. The mesoregion 7 in the state of RS was chosen for the

743

projection of diffusion of photovoltaic systems, where 5 scenarios were considered. Also, simulations

30

744

MANUSCRIPT were carried out in these scenariosACCEPTED by considering the changes in the electric energy tariff, price of

745

photovoltaic systems, education campaigns and incentives for the purchase of PV system. The results collected in the 5 scenarios were satisfactory. They showed that the curves obtained

747

through time diffusion are in agreement with the diffusion curve of innovations proposed by Rogers,

748

where even with the change of parameters the model is robust. Then, it assumes that in the total of

749

population, only a few consumers have a greater tendency to install photovoltaic systems in their homes,

750

it was verified that until the year 20, most of these potential consumers will install them.

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The SD model shows that without any kind of financing and advertising incentives the adoption

752

rate of PV system gets lower and if there is a reduction of electric energy tariff from the electric power

753

distributor the adoption rate gets even lower.

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As the price of the photovoltaic system increases, the number of adopters of PV system decreases.

755

In this way, one alternative to increase the diffusion is through financing the PV system and education

756

campaigns showing to consumers the benefits on installing the PV system. Then, by considering the incentives for the installation of photovoltaic systems (financing,

758

incentive programs, service tax, microcredit, import tax, low interest subsidy policy, tariff models, feed

759

in, education campaigns and environmental issues), the adoption rate of PV system by consumers

760

becomes extremely high, making about 98% of potential adopters to become PV system adopters.

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Also, the diffusion throughout space presents a satisfactory behavior, since it depends on the

762

frequency of occurrence of each city and it is possible to define the growth or stagnation of the PV system

763

in each one of the cities belonging to the region of study.

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The proposed methodology can be used by the energy distributors in way to make a more exact

765

planning study in the electric systems, because the methodology takes into account the aspects related to

766

the consumer’s decision to adhere the photovoltaic systems, and these factors involve a lot of uncertainty.

767

6. AKNOWLEDGEMENTS

768

The authors would like to thank the technical and financial support of AES Sul Distribuidora

769

Gaúcha de Energia SA, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq),

31

770

ACCEPTED MANUSCRIPT Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS) and Coordenação de

771

Aperfeiçoamento de Pessoal de Nível Superior (CAPES).

772

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ACCEPTED MANUSCRIPT TABLE I ASPECTS CONSIDERED IN THE MODEL OF SYSTEM DYNAMICS Economic Aspects

Management Aspects

Political Aspects

Social Aspects

Technical Aspects

NPV panel

Business strategies

Political stability

Lack of knowledge

Quality of PV system

NPV grid

Marketing (publicity)

Economic stability

Public awareness

Complexity of PV system

Financing to buy the PV

Service fee and microcredit

Subsidy policies for the

Adoption of PV system by

Maintenance demand

purchase of PV system

other consumers Income-related education

Cost of innovation decreases

PV system after sale service

Low interest rate policies for

over time

weak and neglected

the purchase of PV system

Payback

Incentive programs

Companies that work with PV system

RI PT

system

Import tax

Environmental concern

Local solar radiation

Tariff

Feed-in tariffs

Education campaigns

Difficulty of installation

Salary of the consumer

Tariff models

Autonomy in relation to the

Energy Panel (efficiency,

supply from energy

power, solar resources)

distributor Environmental issues

Less than 10 minimum

Durability

SC

Installation price

salaries

Operating

More than 10 minimum

Number of Panels

M AN U

salaries

ICMS

TABLE II ENERGY ANNUALLY AVAILABLE FOR SOLAR GENERATION IN EACH MESOREGION OF RS Total area (km²)

Mesoregion 1 Mesoregion 2 Mesoregion 3 Mesoregion 4 Mesoregion 5 Mesoregion 6 Mesoregion 7 Total of RS

25594.689 17192.037 29734.982 25749.128 64930.583 42539.655 62861.157 268602.231

Daily global solar radiation (MJ/m².day) 15 14 14 14 15 14 15 14.42

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Regions

Annual global solar radiation (kWh/m²/year) 1520.79075 1419.4047 1419.4047 1419.4047 1520.79075 1419.4047 1520.79075 1462.85

Annual energy (TWh/km²/year) 0.58 0.36 0.63 0.54 1.48 0.90 1.43 6.18

ACCEPTED MANUSCRIPT TABLE III COMPARISON AMONG THE SCENARIOS ANALYZED Scenarios

Variables

Conclusion

Scenario 1

All aspects equal 1

In the year 16 the number of consumers with DG is 62220 100% of PV system adopters in relation to the potential adopters 17.46% of PV system adopters in

Scenario 2

Without incentives for the purchase of PV system

RI PT

relation to the total of consumers 45980 consumers in the year 20

73.90% of PV system adopters in relation to the potential adopters

12.90% of PV system adopters in

32660 consumers in the year 20

PV system and reduction of 50% in the

52.50% of PV sytem adopters in

electricity tariff

relation to the potential adopters

relation to the total of consumers 46760 consumers with DG in year 20

PV system, increase of the price of the

75.15% of PV system adopters in

photovoltaic system and financing for

relation to the potential adopters

their purchase

13.12% of PV system adopters in relation to the total of consumers

Considering incentives for the purchase

Year 20 there are 60740 consumers

of PV system

with DG

EP AC C

9.16% of PV system adopters in

Without incentives for the purchase of

TE D

Scenario 4

Scenario 5

Without incentives for the purchase of

M AN U

Scenario 3

SC

relation to the total of consumers

97.62% of PV system adopters in relation to the potential adopters 17.05% of PV system adopters in relation to the total of consumers

ACCEPTED MANUSCRIPT I. Knowledge

II. Persuasion

III. Decision

IV. Implementation

V. Confirmation

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Fig. 1. Stage model in the decision process of an innovation. Source: [31].

ACCEPTED MANUSCRIPT

+

Adoption rate

+

+

Less than 10 minimum salaries

-

Adopters of PV system

+ Social Aspect + + + Management + + Aspect + Q P

More than 10 minimum salaries

Environmetal concern HDI

Potential of early Adopters

Satisfied clients Adoption of PV system by other consumers

Public awareness

Income in related education

M AN U

Total consumers

+

+

Technical Aspect

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Fig. 10. Model of the social aspect

AC C

Education campaigns

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+

+ Potential Adopters

+

Economic Aspect

Political Aspect

Lack of knowledge

SC

+

Autonomy in relation to the supply from energy distributor

ACCEPTED MANUSCRIPT

Total consumers

-

Adoption rate +

+

+

+

+

Adopters of PV system

-

+

+

Q

Economic Aspect

P

Maintenance demand

Quality of PV system

Panel Energy

Solar resources + + Technical Aspect Number of Panel power panels + Durability

M AN U

Political Aspect

-

Efficiency

RI PT

Potential Adopters

Companies that work with PV system

Difficulty of installation

+

+

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Fig. 11. Model of the technical aspect

AC C

Complexity of PV system

SC

Social Aspect Management Aspect

Potential of early Adopters

ACCEPTED MANUSCRIPT Public awareness

Environmetal concern IDH

Social Aspect

Income in related education

Autonomy in relation to the supply from energy distributor Satisfied clients

Feed-in Tariffs

Difficulty of installation Less than 10 minimum salaries

Low interest rate policies for the purchase of PV system Net Metering

Total consumers

Adoption of PV system by other consumers

Import tax

Environme ntal issues

More than 10 minimum salaries