ANALYSIS
OF ECONOMIC VIABILITY WITH THE USE OF MONTE CARLO SIMULATION FOR
MICROGENERATION OF PHOTOVOLTAIC ENERGY
José Antonio de Miranda Lammoglia
Universidade Federal Fluminense, Brazil
E-mail: jalammoglia@gmail.com
Nilson Brandalise
Universidade Federal Fluminense, Brazil
E-mail: nilson_01@yahoo.com.br
Submission: 18/09/2018
Revision: 08/11/2018
Accept: 28/11/2018
ABSTRACT
A series of
public policies are being adopted worldwide to seek greater participation of
renewable energy sources in the energy matrix. Brazil is a country that has a
predominantly renewable energy source, with hydroelectric energy being
responsible for the largest portion, but with enormous potential to be
exploited for solar energy. The objective of this study was to carry out an
analysis of the economic viability of a photovoltaic matrix in the distributed
microgeneration model from the residential consumer perspective. Through the
Monte Carlo simulation, 10.000 iterations were performed and the NPV was
calculated in each of them, then counted to recover the corresponding output
probability distribution and verified the NPV probability to be greater than
zero. The developed method has proved to be a reliable tool to support decision
making and can be applied to several scenarios. The scenario adopted for the
design of the photovoltaic system presented a 95.2% probability of returning
with an NPV above zero and this makes it economically feasible. The main
contribution of this paper is the replicability of the methodology used for other
economic analysis studies.
Keywords: photovoltaic; microgeneration;
economic viability; Monte Carlo simulation
1. INTRODUCTION
A
series of public policies are being adopted worldwide to seek greater
participation of renewable energy sources in the energy matrix. In the context
of sustainability, photovoltaic energy plays a crucial role given its
availability in abundance on the earth's surface.
Brazil
is a country that has a predominantly renewable energy source, with
hydroelectric energy accounting for the largest share, or 64.5% of all
electricity generation. On the other hand, there is still an enormous potential
for renewable sources of energy, especially solar energy (0,0%) (MINISTÉRIO DE MINAS E ENERGIA, 2017). Solar energy
is a source of clean energy with potential to be exploited in the country even
higher than countries that are currently leaders in using that source.
The
nature of the problem is: Is photovoltaic energy generation economically
attractive today?
The
objective of this work is to analyze the economic viability of a photovoltaic
matrix in the distributed microgeneration model, and as specific objectives to
raise the necessary criteria in the development of a grid tie photovoltaic
project and its evaluation by economic tools that aid in decision making by
determining viability from the perspective of the residential consumer.
The
work presents justification as: Although the Brazilian energy matrix is
predominantly hydraulic, costs for the generation, transmission and
distribution of energy are not negligible, given the continental dimensions
that Brazil has. In contrast to the increase in the cost of hydroelectric
power, the cost of photovoltaic energy is expected to fall due to economies of
scale and efficiency gains.
This
work has the following organization: first part consists of the bibliographical
research; data collect; market research of photovoltaic panels, accessories and
equipment; project development; cost calculations for project implementation;
calculation of project amortization, and feasibility analysis of the project
through Monte Carlo simulation.
2. LITERATURE REVIEW
2.1.
Operation
of a Photovoltaic Cell
A photovoltaic system
directly converts sunlight into electricity. The basic device of this system is
the photovoltaic cell. The cells may be pooled to form panels or matrices. A
panel is formed by a set of cells connected to obtain large voltages and / or
output currents. A photovoltaic array can be a panel or a set of panels
connected in series or parallel to form large photovoltaic systems. The voltage
and current available at the terminals of a photovoltaic device can directly
feed small loads, such as lighting systems and DC motors. More sophisticated applications
require electronic converters to process the electricity of the photovoltaic
device. These converters can be used to regulate the voltage and current in the
load, to control the flow of energy in grid tied systems and, mainly, to trace
the maximum power point of the device (VILLALVA; GAZOLI; FILHO, 2009).
A photovoltaic cell is
basically a semiconductor diode whose p-n junction is exposed to light.
Photovoltaic cells are made from various types of semiconductors using
different manufacturing processes. Monocrystalline and polycrystalline silicon
cells are the only ones found on a commercial scale today. The silicon cells
are composed of a thin layer of Si connected to the electrical terminals. One
side of the Si layer is doped to form the p-n junction. A thin metal grid is
placed on the surface of the semiconductor facing the Sun. Figure 1 illustrates
the physical structure of a photovoltaic cell. The photovoltaic phenomenon can
be described as the absorption of solar radiation, the generation and transport
of free transporters at the p-n junction and the collection of these electric
charges at the terminals of the device (VILLALVA; GAZOLI; FILHO, 2009).
Figure 1: Physical structure of a photovoltaic cell
Source:
Villalva, Gazoli and Filho (2009)
2.2.
Characterization
of Photovoltaic Systems
Photovoltaic systems can be
characterized in five main groups (FERREIRA et al., 2018):
2.2.1. Grid
Tie
The grid tie photovoltaic system,
usually installed in roofs and residential buildings, consists of a
photovoltaic panel that converts solar energy into electricity (direct current)
in which the presence of an inverter is required, which converts direct current
in alternating current with voltage and frequency compatible with the standards
of the electrical network to which the system is connected. The main advantages
of this type of system are the high productivity, the absence of bank of
battery and automatic shutdown in case of power shortage of the network, avoiding
the phenomena of the isolation (ZOMER; URBANETZ; RÜTHER, 2011).
The normative resolution No. 482 of
ANEEL - National Agency of Electric Energy, is the main document that regulates
the operation of grid-connected photovoltaic systems in Brazil. The resolution
defined the main rules for the operation of the so-called distributed micro and
minigeration, a model in which small users can produce their own electricity in
an integrated way to the distribution network of the concessionaires.
The resolution
also defined the "energy compensation" system. This system allows the
consumer to have deducted from the electricity bill the value of the amount of
energy produced by the photovoltaic system. Each unit of energy that is
produced by the photovoltaic system translates into an economy of the same
amount that the utility would charge to provide the consumer.
If the consumer
produces more than one month of consumption, for example, the utilities will
provide a credit for the extra energy produced. If the consumer has an interest
in producing all the energy that he consumes, he will pay in the monthly
invoice only the other expenses, almost all fixed, such as the "cost of
availability", known as "minimum fee", eventual tariff flags and
contribution to public lighting . Credits on energy that exceeded the
consumption are valid for 60 months and can be used when the consumption is
greater than the generation of energy, as in times of less insolation.
2.2.2. Isolated
Isolated or independent photovoltaic
systems are installed in areas with difficult access to the electricity grid,
generally rural areas. In this case, photovoltaic energy is the only source of
electricity and some storage is needed, as in batteries.
2.2.3. Hybrid
Hybrid photovoltaic power generation
works in conjunction with others, such as wind turbines or diesel. They are
considered more complex, such systems require a control capable of integrating
different forms of power generation. These systems can be connected to the
network, alone or have the network support.
2.2.4. Solar
Power Plants
These systems also connected to the
grid, produce a lot of electricity in a single point. The size of the plant
varies from hundreds of kilowatts and megawatts.
2.2.5. Applied
in Consumer Goods
Photovoltaic cells can also be
applied to a variety of electrical equipment such as clocks, calculators, toys,
battery chargers or solar covers to charge electric cars, irrigation systems,
signposting on highways, lampposts or public telephones, among others.
2.3.
Investment
Analysis Techniques
2.3.1. NPV -
Net Present Value
It's a sophisticated capital
budgeting technique. It is calculated by subtracting the initial investment
from the present value of the cash inflows project, which are discounted at the
cost rate of company's capital (GITMAN., 2013).
|
|
(1) |
Where:
- present value of cash receipts;
- initial investment;
- discount rate (equal to cost of company
capital);
- discount time of each cash inflow;
- discount time from last cash flow.
2.3.2. IRR -
Internal Rate of Return
It is the discount rate that equates
the NPV of an investment opportunity to zero (this is because the present value
of the cash inflows equals the initial investment). It is the compound annual
rate of return that the company will obtain, if it applies resources to a
project and receives the expected cash inflows (GITMAN., 2013).
|
|
(2) |
Where:
- present value of cash receipts;
- initial investment;
- discount time of each cash inflow;
- discount time from last cash flow.
2.4.
Monte
Carlo Simulation
In the construction of the first
atomic bomb, the Monte Carlo simulation method originated during World War II
throughout the research in the Los Alamos laboratory. It was proposed by Von
Neumann and Ulam for the solution of mathematical problems that were not viable
through analytical treatment. Initially, it was intended for the evaluation of
multiple integrals for the study of neutron diffusion. Then it was found that
it could be applied to other more complex mathematical problems of a
deterministic nature. The name Monte Carlo was adopted by the fact of the
presence of randomness remember games of chance in allusion to the famous
casino of Monaco founded in 1862, besides reasons of secrecy (BRANDALISE; CARDOSO, 2010).
Monte Carlo simulation is a
probabilistic approach that allows uncertainty to be considered when
calculating the expected value, that is, to assess what can happen and how it
is likely to occur. Using probabilistic distributions for the main input
parameters involved in the analysis, it is possible to retrieve the resulting
value as a probability distribution, from which uncertainty information can be
derived using common statistical methods. Each Monte Carlo iteration consists
of sampling at random values from the given input distributions and computing
the corresponding result (PILLOT; DE SIQUEIRA; DIAS, 2018).
Another definition for Monte Carlo
simulation is the random generation of numbers by means of algorithms using
probability distribution functions to obtain specific results on the process or
object being studied. It can be used in problem solving in several areas of
science. The main idea of the Monte Carlo simulation is that the extensive
repetition of a random sampling process allows a sufficiently large and random
sample space to be obtained for statistical inference.
This
random sampling is essential to simulate mathematically modeled real systems,
and also applies this statistical methodology to the concept of measurement
variability and uncertainty because it allows the generated results to vary
within a range determined by the algorithm as if they were random error
fluctuations. The algorithms used in Monte Carlo methods are simple and have
the ability to reduce the complexity of mathematically modeled systems (ROMERO; LOURENÇO, 2017).
2.5.
Criteria
for Decision Making
For the aid in the decision making
of investments in photovoltaic projects, it is necessary to have a clear image
of the criteria in the elaboration of the cash flow (DONG; XU; LIN, 2017):
2.5.1. a)
Local Insolation Conditions
The performance of the photovoltaic
module is highly dependent on the availability of solar radiation and
temperature of photovoltaic cells. This factor determines whether the
investment will be effective or not and will directly affect the daily
generation capacity, but this depends on the nature and can not be changed at
will. In this context, investments are mainly made in areas with good solar condition.
2.5.2. Real
Available Area
The amount of solar panels depends
on the actual area available, whether it is on a roof or an open area and
directly influences the daily generation capacity of the system. A high wall at
the edges of the roof, surrounding buildings and etc. can reduce the available
area. Given this situation, the site must be accurately evaluated, based on the
amount of solar panels required, in the condition of local sunlight and
suitable installation angle.
2.5.3. Local
Electricity Price
This factor has a direct impact on
the output value. The price is determined by generation, transmission and
distribution costs by region.
2.5.4. Interest
Rate on Loans
Financial support is needed for
almost all investment projects. To this end, some financial institutions have
established specific departments to finance photovoltaic projects.
2.5.5. Installation
Cost
This factor represents the largest
proportion of investment, there is cost of design, cost of equipment, cost of
labor and administrative cost. This factor is inversely proportional to the
scale effect, that is, the larger the project scale, the lower the installation
cost will be, when calculated with the installed capacity per Watt. The
increased production of photovoltaic products in recent years has reduced the
cost of the equipment considerably.
2.5.6. Cost
of Operation and Maintenance
This factor is included in the
annual operating expense of power generation to cover periodic maintenance,
surface cleaning of photovoltaic panels and other maintenance costs.
2.5.7. Tax
Subsidy
It is a component to promote the
development of distributed photovoltaic systems and considerable source of
revenue. Different local subsidy policies, such as subsidies based on
generation capacity and difference between retail and national electricity
tariffs to encourage local investments under the circumstance of solar
radiation under different conditions. These subsidies are an important way for
investors to recover costs very soon, to control capital risk and shorten the
payback period.
2.5.8. Taxes
One of the major barriers related to
Resolution 482/2012 was related to the collection of ICMS under the
"Electric Energy Compensation System." The ICMS - Tax on Circulation
of Goods and Services in turn is a State tax applicable to electric energy (OLIVEIRA, 2016).
Law 13.169, in its art. 8, reduced
to zero the rates of the Contribution to the Social Integration Program (PIS)
and the Program for the Formation of Civil Servants' Equity (PASEP) and the
Contribution for Social Security Financing - COFINS incident on the energy
injected into the network by the micro and minigerators. Then the Finance
Policy Council (ConFaz) issued a new agreement (16/2015) and authorized some
states to charge ICMS only on the difference between the energy consumed and
the energy injected into the network by the consumers.
2.5.9. Degradation
of Photovoltaic Modules
One of the most important features
of photovoltaic modules is their long life cycle, which can reach 30 years.
However, recent work has proven that photovoltaic modules can suffer
significant degradation before that time (BASTIDAS-RODRIGUEZ et al., 2017) and factors such
as hot and humid climate considerably increase the degradation of photovoltaic
modules (HUANG; WANG, 2018).
3. METHODOLOGY AND METHODS
For this study, the system was
designed with no restricted area available for an average monthly energy demand
of 350 kWh, located in the city of Volta Redonda, in the interior of the state
of Rio de Janeiro (Latitude - 22.523055 ° South and Longitude - 44.104166 °
West), where the minimum solar radiation at full sun is 4,32 hours per day and
occurs in the month of July. The minimum solar radiation is used to scale the
entire system so that it can guarantee the total energy supply of the residence
and was obtained through the program SunData v 3.0 in June 2018.
The system works
connected to the network, as it does not exist difficulties in the supply of
energy by the concessionaire. The surplus energy generated in other months of
the year and radiation in the hours without full sun are used as safety margin
for efficiency losses due to degradation of the solar panels and the generation
of credits through the energy compensation system, guaranteed by Normative
Resolution No. 482 of ANEEL. The equation used to size the number of solar
panels follows below:
(3)
Where:
- number of solar panels
- monthly energy demand
- maximum panel power
- hours of full sun
- wire efficiency
- system efficiency
This system eliminates the need for
a battery bank for energy storage, providing a lower initial and periodic investment
need since the batteries have a shorter life span than panels and need to be
changed a few times during the life of the project. The sizing proposed in this
study presents an initial investment, and this value varies with an increase of
up to 25% for the simulation, respectively the minimum and maximum values, R $
16.852,00 and R $ 21.065,00.
The energy supply is made by Light
Serviços de Eletricidade SA, which has three possible tariffs divided as
follows: green flag, yellow flag and red flag, which can be practiced depending
on the period of the year, the condition of the reservoirs of hydroelectric
power plants, consumption profile and etc. and are used in this study for the
simulation. As the system is located in the state of Rio de Janeiro and it is
part of the CONFAZ agreement (16/2015) and is supported by Law No. 13.169, in
addition to the project being designed to be self-sufficient and to operate in
the energy compensation system , the collection of ICMS, PIS / Pasep and COFINS
is zero.
In this study a discount rate of 10%
per year was used considering that the capital is its own. The minimum shelf
life of panels of 12 years, maximum of 20 years and the most probable of 18
years due to environmental conditions. The annual degradation of the modules is
already considered in the design of the system because it generates surplus
energy to compensate for these losses during the life cycle of the equipment.
Analyzes and calculations were
performed using Microsoft Office Excel software, as their use facilitates
calculations and random numbers are guaranteed for randomness, independence,
that the value is uniformly distributed and non-repetition of sequences.
For the Monte Carlo simulation, we
considered 10.000 iterations, resulting in so many results. Each NPV value was
calculated and then counted to retrieve the corresponding output probability
distribution. That is, after the 10.000 iterations the probability of the NPV
was verified to be greater than zero.
4. RESULTS
In order to meet the
monthly demand of 350 kWh, the minimum monthly amount of radiation hours in the
full sun, which occurs in July in the city of Volta Redonda-RJ, was used as can
be seen in Table 1.
Table 1:
Daily amount of hours in full sun in Volta Redonda-RJ
|
Month |
Full Sun
(hours/day) |
|
January |
5,08 |
|
February |
5,66 |
|
March |
5,03 |
|
April |
4,9 |
|
May |
4,41 |
|
June |
4,37 |
|
July |
4,32 |
|
August |
5,13 |
|
September |
4,84 |
|
October |
4,84 |
|
November |
4,60 |
|
December |
5,07 |
Source:
SunData v 3.0 (2018)
To meet the required
power demand with the availability of defined solar radiation of 4.32 hours per
day, the amount of solar panels can be seen in the calculations below, and the
required calculated investment can be seen in the details shown in Table 2.
=
Table 2:
Breakdown of Investment
|
Itens |
Amount |
Unit
Value (R$) |
Total
(R$) |
Participation
in Total Cost (%) |
|
Solar Panel 330 Wp |
9 |
689,00 |
6.201,00 |
36,80% |
|
Installation service |
1 |
3.000,00 |
3.000,00 |
17,80% |
|
Grid-Tie Inverter |
1 |
4.149,00 |
4.149,00 |
24,62% |
|
String Box |
1 |
752,00 |
752,00 |
4,46% |
|
Support for modules |
9 |
250,00 |
2.250,00 |
13,35% |
|
Miscellaneous (wiring and etc.) |
1 |
500,00 |
500,00 |
2,97% |
|
Total System Cost |
|
|
16.852,00 |
100% |
Source:
Prepared by the authors (2018)
The parameters raised
and used in the Monte Carlo simulation are presented in Table 3.
Table 3:
Parameters for simulation
|
Parameters |
Minimum |
More
probable |
Maximum |
|
Useful Life (years) |
12 |
18 |
20 |
|
Discount rate |
10,00% |
12,00% |
22,36% |
|
Total System Cost (R$) |
16.852,00 |
- |
21.065,00 |
|
Consumption (kWh / month) |
350,00 |
- |
384,91 |
|
Fixed cost (R$ / month) |
30,00 |
40,00 |
50,00 |
|
Electric tariff (R$ / kWh) |
0,91321 |
0,92860 |
0,96035 |
Source: Prepared by the authors (2018)
With the parameters
raised, it was possible to calculate the NPV of the project and, after 10.000
iterations, an average of R$ 6.175,73 was calculated, median of R$ 6.199,60 and
standard deviation of R$ 3.716,48. The values of NPVs found were normally
distributed according to the graph shown in Figure 2.
Figure
2 - Distribution of the NPV's
Source: Prepared by the
authors (2018).
After all the results,
the probability of 95.2% of the NPV was verified to be greater than zero.
5. CONCLUSION
Investment in a
photovoltaic solar energy system is a safe investment, regulated by ANEEL
itself. The equipment has a service life of up to 30 years and almost requires
no maintenance. Brazil is one of the countries with the highest solar radiation
in the world. Whenever there is sun, the system will produce electricity.
Photovoltaic systems
connected to the grid are an environmentally correct way to produce electricity
and an intelligent form of investment. The amount invested in the acquisition
of a system connected to the grid becomes an immediate economy in the electricity
bill.
In practice, many
residential users become energy providers for the network during the day, when
there is no one at home or consumption is too low, and become consumers at
night, when consumption increases and there is no generation. The account of
the users of the systems connected to the network is also a little different,
besides informing the energy consumed, it informs the energy produced during
the month.
Gains from the light
bill economy are even more evident to the residential consumer, who pays a
higher average tariff than commercial and industrial consumers.
Thus, the greater the
price of energy that the concessionaire charges the consumer, the greater the
value it will give as credit for the sale of energy produced by the consumer.
Therefore, in addition to reducing the energy bill, the system connected to the
network is a safe way to protect against increases in tariffs and energy bills.
These increases in energy tariffs occur annually because of inflation, changes
in the climate, such as droughts, and other political and economic factors -
that consumers who have a system connected to the network need not worry.
The results obtained in
this study show that the dimensioned photovoltaic system has a 95.2%
probability of returning with an NPV above zero and this makes it economically
feasible.
The methodology used in
this article can be replicated to other economic viability analyzes, where the
objective is to verify the probability of returning with positive NPV values.
As a suggestion of
future work, it is possible to include in this article a multicriteria tool
that takes into account besides the NPV, a IRR and payback.
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