Techno-economic feasibility analysis of photovoltaic systems in remote areas for indigenous communities in the Colombian Guajira

Techno-economic feasibility analysis of photovoltaic systems in remote areas for indigenous communities in the Colombian Guajira

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx Contents lists available at ScienceDirect Renewable and Sustainable Energy Reviews journ...

662KB Sizes 2 Downloads 53 Views

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

Contents lists available at ScienceDirect

Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Techno-economic feasibility analysis of photovoltaic systems in remote areas for indigenous communities in the Colombian Guajira

A R T I C L E I N F O

A BS T RAC T

Keywords: Indigenous communities Photovoltaic systems Electricity generation costs Electricity network Remote areas Renewable energy Sustainability

Universal access to clean electricity can be achieved in harmony with measures aimed at reducing environmental burdens at a comparatively competitive investment cost. In this paper, we sized and conducted an economic analysis of three photovoltaic systems for installation in remote areas populated by indigenous communities. These alternative electricity access solutions were designed using a decision support framework that considers optimal system sizing, reliability and efficiency. The study considered three community size scenarios: small communities or Segment 1 (S1), medium communities or Segment 2 (S2) and large communities or Segment 3 (S3). Thanks to this information, we were able to estimate the energy demand within each scenario and design three optimized renewable energy systems. According to the results, the cost of energy was calculated as being COP $1,125, COP $1002 and COP $1159 per kWh for communities S1, S2 and S3, respectively. Scenario S2 is the cheapest option due to the lower average household income (COP $61.369 per month with respect to COP $81.975 and COP $86.460 for S1 and S3, respectively). Finally, the results clearly indicate that the cost per kWh could be as little as COP $450, COP $401 and COP $464 for segments S1, S2 and S3, respectively (values closer to the 2015 national average unit cost in kWh, which was COP $391 for the off-grid system), if the government were to subsidize up to 60% of the electricity supply cost. This shows that, under this assumption, the evaluated technology could be competitive alternative for meeting the energy needs of the target population.

1. Introduction The promotion of sustainable energy must be compatible with economic and social issues. In fact, universal access to clean electricity can be achieved in harmony with measures devised to contain emissions growth and, importantly, at a comparatively modest investment cost [1]. Currently, global society faces two major problems regarding electricity generation and delivery. The first is the more or less imminent depletion, depending on the source, of world fossil fuel (especially crude oil) reserves [2,3]. The second is evidence that fossil fuel combustion releases huge amounts of carbon dioxide (CO2 ) and other greenhouse gases into the atmosphere to the point that it has been identified as the main cause of climate change [4]. Therefore, there are ongoing attempts in many regions of the world to coordinate efforts to implement actions to replace fossil fuels with other renewable sources of energy in order to meet demand without causing huge environmental impacts [5]. Sikka et al. defined energy as the lifeblood of any society, and indigenous communities in remote regions are no exception. They claim that dependence on distant energy production systems should be avoided by means of a local energy supply, taking into account that such systems have significant problems, one being distribution [6]. There is a need to go beyond the economic and technical problems of energy supply and better analyze its sustainability dimensions. Renewable energy resources have enormous potential and can meet the present world energy demand. They can enhance diversity in energy supply markets, secure long-term sustainable energy supplies, and reduce local and global atmospheric emissions [7]. They can also provide commercially attractive options for meeting specific needs for energy services (particularly in developing countries and rural areas). Photovoltaics (PV) are one of the most promising renewable energy technologies. PV systems are popularly configured as: stand-alone, gridconnected, and hybrid systems. They are being rapidly deployed in both the developed and developing the world [8]. While the specific problems associated with electricity supply may seem peripheral to the far-reaching disadvantages faced by households in remote communities, evidence suggests the electricity accessibility and affordability is closely linked to housing, education, health and social welfare outcomes [9]. Thanks to the large share of hydroelectricity, Colombia has a very clean electricity generation mix, and energy consumption that is well below average international electricity consumption levels. Conventional power, generated by large hydroelectric plants and produced by thermoelectric generators burning coal, gas and other fossil fuels, accounts for 66% and 32% of national generation, respectively. The current capacity of renewable energy resources (2% of total electricity generation) is produced by photovoltaic solar systems, small hydroelectric stations and a wind park located in La Guajira in northern Colombia [10]. Thanks to its geospatial position, Colombia has the potential to generate energy from nonconventional, solar, wind, biomass, geothermal and solid waste resources [11,12]. From the viewpoint of legislation, Law 1715/2014, (the Renewable Energies Law [13]) promotes the development and use of non-conventional energy sources (especially renewable sources) in the national energy system, establishes the legal framework and mechanisms for the use of non-conventional energy sources, especially renewable sources, and provides tax incentives for the investment in such projects. http://dx.doi.org/10.1016/j.rser.2017.05.101 Received 18 April 2016Received in revised form 7 March 2017Accepted 18 May 2017 1364-0321/ © 2017 Elsevier Ltd. All rights reserved.

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

Colombia has managed to increase access to electricity in recent years. In Colombia, the National Interconnected System (NIS) connects 48% of the national territory and serves 97% of the population. Rural electrification and non-interconnected zones (NIZ) account for 52% of the country's surface area (17 departments and 1441 municipalities) and 625,000 people [14]. About 3,000,000 Colombian homes are located in remote areas, 83% of which have electricity. The Colombian Regulatory Commission for Energy and Gas (CREG) is the body responsible for establishing the cost of electricity for users of the NIS. Although rates can be determined for isolated areas [15,16], they will depend on the investment outlay at each place. More studies on solar energy are still needed to identify the different characteristics of the region and support the investment decisions [17,18]. CREG defines the regulatory system that should guarantee the long-term reliability of electricity supply in Colombia. These regulations establish the costs of electricity for the users of the NIS [19,20]. The use of renewable energy is spreading rapidly. This is highlighted by the fact that every year more renewable electricity capacity than the (net) capacity of all fossil fuels combined is added the world over. Likewise, the total number of countries with renewable energy policies increased once again in 2015 [21]. According to the REN21's 2016 Global Status Report, at least 173 countries had renewable energy targets, and an estimated 146 countries will report some kind of renewable energies at national, state or provincial level by the end of the year [21]. Currently, there are several papers concerning Colombia's options for adopting the renewable perspective to diversify the energy market and supply electricity to remote and/or isolated areas where about one million households do not have a reliable electricity service. One of the issues that these studies agree upon is the country's potential in regard to renewable energy resources [22–25]. There are now two important issues worth considering in order to address the economic concerns surrounding renewable energy in Colombia. On one hand, a national financing plan earmarking 32 billion dollars for renewable energy projects, the renovation and expansion of public lighting, indoor or outdoor lighting, co-generation and self-generation has been launched. In this respect, the Ministry of Mines and Energy, the Mining and Energy Planning Unit (UPME), the Financial Institution for Development FIDENTER and the Inter-American Development Bank (IDB) announced a special credit line for projects and investments with favorable terms [26]. On the other hand, the Ministry of Mines and Energy and the National Finance Development Institution signed an agreement in October 2016 to promote a program to integrate renewable energies (PER) into the Colombian electricity mix in order to leverage Colombia's massive potential in this respect [27]. In Colombia, there are several indigenous groups. These ethnic groups are native Colombians that inhabited Colombia even before the arrival of Europeans. The National Statistics Department puts Colombia's indigenous population at 1,500,000 or 3.4% of the national population. The Andes and La Guajira account for almost 80% of this population. The largest indigenous people in Colombia are the Wayuu in La Guajira. The Wayuu inhabit the arid La Guajira peninsula on the Venezuela-Colombia border and along the Caribbean Sea coast. In this region, only 45.1% of the dwellings located in rural areas have access to electricity [28–30]. In this case, distances and accessibility are the main problems for connection to the electricity network. This generates high electricity supply costs. Many indigenous communities in this area are located far away from power grids and have no way of accessing an electric power supply. Access to food and water is a major concern for these communities. Moreover, the insufficiency of food production and other kinds of welfare generation systems, such as water treatment, medicine storage or air conditioning, etc., puts the population at risk. Under these conditions, people are unable to pursue activities like arable and livestock farming, fisheries and other occupations. Therefore, it is difficult to achieve a sustainable economy. All these issues combined pose a major threat to the livelihood of the indigenous population. However, indigenous peoples have adapted to these adverse conditions and looked for solutions to improve their living conditions with the help of other communities. Currently, there is little chance of supplying indigenous communities with electricity from the national grid. The problems include long distances to connect the main power lines, plant maintenance problems, too small a number of users per community to encourage investment, and few social interest groups to push for improved conditions. Some remote areas do not have enough energy resources to generate electricity from conventional hydroelectric and thermal sources. Therefore, other solutions such as diesel generation have been adopted as the best option for solving their problems in the short term. However, the high cost of diesel generating plants and fuel transportation pushes the electricity price up too high for it to be eligible for government subsidies. In addition, diesel generators do not have a long life expectancy and require constant maintenance to ensure reliability. Renewable energies are emerging as a good solution primarily for the country to reduce the high costs of expensive plant. The country has sizeable renewable (solar and wind) resources [11,12,31]; and the La Guajira area, in particular, is one of the best sites [32]. Renewable energy offers many advantages [33]: it brings together a number of highly profitable innovative technological components that can be combined to build alternative energy systems as a comprehensive development proposal for meeting the energy needs of isolated areas. The current reduction in the cost of renewable energy is an important step forward towards supplying the country's remote communities with electricity. Although solar and wind energy are better options for reducing energy costs in remote areas [32], they must be implemented as part of a sustainable energy model. Photovoltaic solar energy systems are used widely to meet the electricity needs of the population [34]. These systems are known as autonomous photovoltaic systems (APS) and network-connected photovoltaic systems (NCPS), both designed to produce electricity on a large scale for users. APS can be designed to meet the specific demand of a population and sized according to system reliability [35]. Some methods are capable of sizing APS by applying simple mathematics; and others use computer software to evaluate technical and economic parameters throughout the project lifetime [36]. This type of technology has been applied in Peru, where a range of conditions have been taken into account to build a sustainable PV project for rural areas. The project accounts for technical conditions, such as good quality control of all PV system components (battery, charge controller, etc.), social conditions, and management conditions [37]. According to Manfred Horn, the Taquile Island project on Lake Titicaca has proved that there is a real possibility of achieving sustainable basic rural electrification using solar systems. Some achievements of the Peruvian project are: 1) APS beneficiaries are ultimately their owners, and this encourages proper maintenance, and 2) the project that won the tender included a strict quality control of equipment, installation, and after-sales service (training, monitoring, replacement of defective components, etc.). The program developed in the village of Carupana offered the population services that did not exist before the introduction of photovoltaic systems [38]. Today, APS are a cost-effective and durable electrification alternative for rural areas. In recent years, they have been adopted by many countries as a result of the positive results of their deployment in remote communities under the premise of contributing to sustainable development [39]. In some populations, APS have helped overcome extreme poverty by improving the population's quality of life (education, agriculture, communication and health). Furthermore, this solution has created conditions that promote competitiveness while mitigating climate change [38,40–42]. The definition of a renewable energy model for remote communities without an electricity supply is an important issue to be solved in advance of 2

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

Fig. 1. Steps for determining APSA.

Fig. 2. Lower, middle, and upper Guajira. Source: Google Maps [52]

project development or decision making and feasibility analyses. The model must be optimized taking into account the different types of housing, population characteristics, consumption habits, and other factors [43]. In this research, we designed autonomous photovoltaic system arrangements (APSA) capable of supplying indigenous communities with electricity. The feasibility test involved selecting and classifying the population by energy demand into three major consumer groups. We then conducted a technical feasibility study of the design of each of the photovoltaic system. The prices of the components required for the photovoltaic system arrangements were determined as part of the financial assessment of the system. A cost-effectiveness analysis was performed to determine the behavior of the APSA by combining and efficiently interconnecting the different components. We report energy production, average energy per household, initial investment, operating and maintenance costs, average monthly payment per household and other important analyses. The paper is structured as follows. Section 1 gives a brief introduction and reviews the literature focusing on studies of photovoltaic systems in remote areas and their application, the identification of the problems that have to be solved to analyze the applications, and the advantages and disadvantages of distributed generation. Section 2 clearly explains the research methodology applied in this research in order to calculate the different APSAs that represent the current state of renewable energy. Section 3 reports the results of the feasibility test and analysis, including the selection of power load, the designed systems and the economic analysis. Section 4 discusses the best technologies and outlines the policy

3

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

Table 1 Solar irradiance (kWh/m2/day). Source: SSE.NASA. [53] NASA surface meteorology and solar energy: RETScreen Data Month

Air temperature °C

Relative humidity %

Daily horizontal solar irradiance kWh/m2/d

Atmospheric pressure kPa

Wind speed m/s

Earth temperature °C

January February March April May June July August September October November December Annual Measured at (m)

27.2 26.8 27.0 27.6 28.1 28.1 27.3 27.0 26.8 27.0 27.6 27.8 27.4

66.1% 68.7% 72.1% 73.9% 75.0% 76.3% 77.7% 78.2% 78.0% 77.7% 71.7% 65.7% 73.4%

5.71 6.48 6.97 7.04 6.09 4.64 4.79 5.41 5.83 5.42 5.36 5.45 5.77

101.2 101.1 101.0 100.9 100.8 100.8 100.9 101.0 101.0 101.0 101.0 101.2 101.0

3.1 3.1 3.5 3.7 4.3 7.8 7.2 6.8 5.3 3.6 3.2 3.7 4.6 10.0

28.3 28.4 29.1 29.9 30.1 29.0 27.9 27.5 28.0 28.6 28.9 28.6 28.7 0.0

Table 2 Distribution of the sample. Municipality

Number of communities

Percentage

Uribía Manaure Maicao Riohacha Total

130 127 66 58 381

34% 33% 17% 15% 100%

Table 3 Cost of photovoltaic system components. Source: Green Energy Latin America (2015)

Unit

PV module

Inverter-charger, MPPT charge controller

255Ah/12 V AGM batteries

COL $2048 (COL $/W)

5 K MPPT: COL $3185.000

COL $1,100,000

Fig. 3. Hourly load demand for communities with a population of 50 (S1).

Fig. 4. Hourly load demand for communities with a population of 125 (S2).

4

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

Fig. 5. Hourly load demand for communities with a population of 200 (S3). Table 4 Technical specifications of photovoltaic systems. General information

Communities

Indigenous population System power (kW) Equipment 250 wp photovoltaic module GEMKS 5 K multifunctional equipment (MPPT) 255 Ah/12 V AGM battery PV module mounting structure Electricity meter for the energy supplied to households Electricity meter for total production Programmable electricity meter Electrical protection and cabinets

S1 9 Quantities 36 1 15 10 1 1 8 1

S2 20

S3 27

80 3 20 20 1 1 17 1

108 3 50 27 1 1 23 1

Table 5 Energy production of photovoltaic systems. Community systems

Power (kW)

No. of households

Annual production (kWh/year)

Monthly production (kWh/m)

Daily production (kWh/day)

Average energy consumption per household (kWh/day)

S1 S2 S3

9 20 27

8 17 23

15,987 35,527 47,962

1332 2961 3997

44.4 98.7 133.2

5.6 5.8 5.8

Table 6 Photovoltaic systems cost. Systems

Power (kW)

PV generator

Storage system

Converter

Initial investment

Annual operating cost ($/year)

Monthly operating cost ($/m)

S1 S2 S3

9 20 27

$50,470,704 $102,463,200 $128,911,936

$11,000,000 $22,000,000 $29,700,000

$9,555,000 $25,480,000 $28,665,000

$71,025,704 $149,943,200 $187,276,928

1,911,767 4,098,736 5,153,733

159,314 341,561 429,478

Table 7 Photovoltaic system sustainability. Systems

Power (kW)

No. of households

Population

Energy cost ($/kWh)

Monthly cost per family ($/m)

Annual production (kWh/year)

Annual cost per family ($/year)

S1 S2 S3

9,00 20,00 27,00

8,00 17,00 23,00

48,00 113,00 138,00

1.125,00 1.002,00 1.159,00

86.460,00 61.369,00 81.975,00

15.987,00 35.527,00 47.962,00

1.037.515,00 736.429,00 983.705,00

implications of their application for Wayuu communities. Section 5 presents the conclusions of the research. 2. Methodology used in the study The methodology used to determine the different solar energy resource arrangements for indigenous communities is based on designing a technically sound system. This implies the correct sizing of the system with respect to capacity, and an optimal design for better reliability and improved efficiency. The main objective of system design is to optimally improve the energy quality for a given load factor. Fig. 1 shows the methodology applied to determine the different photovoltaic system arrangements for indigenous communities. First we defined the local area in order to analyze affordable resources and energy demand. Second, we evaluated renewable sources to assess and select the resources available in the area. Finally, we designed an optimal power generation system. A software tool, called Hybrid Optimization Model for Electric Renewables (HOMER) [44], was used to size the systems. The result of the analysis is a list of feasible power supply systems, sorted 5

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

Fig. 6. Relationship between energy production and generation costs.

Table 8 Comparison of photovoltaic system sustainability. Systems

Power (Kw)

No. of households

Population

Energy cost (without subsidy)

Energy costa (60% subsidy)

Energy costa (NIS)

S1 S2 S3

9 20 27

8 17 23

48 113 138

$1125 $1002 $1159

$ 450 $ 401 $ 464

$ 390.6

a

Energy cost in $/kWh.

according to their net present value. 2.1. Software tool HOMER software, developed by the company Homer Energy, was used to simulate all the scenarios and design the APSA. This software facilitates calculations using information such as updated technology, costs, lifetime, installation cost, maintenance cost, and other variables. HOMER accounts for all possible combinations of a number of variables that are initially defined by the user. The optimal or best solution is selected based on the choice of one or more criteria, such as: a) percentage of unsupplied energy or unmet electric load; b) percentage of the electricity capacity not used or excess generation; c) break-even grid extension distance; d) levelized cost of energy (LCE); and d) total net present cost (NPC) [45]. Several institutions and scientists have used HOMER to design and analyze the implementation of renewable systems around the world, AlKaraghouli et al., addressed the electricity demand of rural areas in southern Iraq using HOMER software. They put forward a new photovoltaic solar system to meet the electricity needs of health clinics in the region. They suggested that the best system to satisfy a daily load of 31.6 kWh was composed of 6 kW PV modules, 80 batteries (225 Ah and 6 V), and a 3 kW inverter [46]. Adaramola et al., describes a study of northern Nigeria that examined the feasibility of a solar PV grid connected to the electricity generation system using HOMER energy optimization software. This study investigated the economic viability of implementing a combination of 80 kW solar PV and 100 kW from the region's grid. It was concluded that the cost of electricity could be significantly reduced [47]. Kusakana performed research analyzing the potential of using hydrokinetic-based hybrid systems for low-cost and sustainable electricity supply to isolated loads for rural areas of South Africa where water resource availability is adequate. He investigated different hybrid system configurations using HOMER software. The results from two case studies suggested that hybrid systems with hydrokinetic modules were the most economically feasible option [48]. Likewise, Shah et al., studied the technical feasibility of a combined system of PV+battery+CHP (combined heat and power) for three representative regions in the US, using the HOMER software. They concluded that the electricity generated by each component of the hybrid system was suitable for the residential load demand. The sensitivity analysis results showed that conservatively sized systems were technically viable in any continental American climate [49]. Other authors reported the use of HOMER to perform technical–economic feasibility studies on the construction of PV power plants. For instance, Mostafaeipour et al. describe the use of HOMER in 14 areas of Khuzestan province using a hybrid approach composed of data envelopment analysis (DEA), balanced scorecard (BSC) and game theory (GT) to rank the selected areas [50]. 3. Description of the study area La Guajira is a state in northeastern Colombia, covering about 21,000 km2. The Santa Marta mountain range constitutes a natural barrier between this state and the rest of the country. This region is divided into three areas known as Upper Guajira, Middle Guajira and Southern Guajira [51], as shown in Fig. 2. The Upper Guajira covers the northernmost area of the peninsula, is semi-arid and has scant vegetation, with an isolated low altitude mountain range: the Serranía de Macuira (865 m). The Middle Guajira has an arid, mostly flat and, in some areas, rolling landscape. Finally, the Southern Guajira covers the Montes de Oca and the Serranía del Perijá mountain ranges on the border with Venezuela and the valley formed with the Sierra Nevada de Santa Marta mountain range. La Guajira is home to Columbia's biggest opencast coal mine: Cerrejon. Another 6

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

important feature is the Manaure salt mine, salt being one of the region's main products. These are hard-to-access areas, where the provision of basic services for the population is very deficient, and sometimes unavailable. The Upper Guajira is an arid and desertic land bordering the Caribbean Sea and Venezuela. The Middle Guajira is located on the northern edge of the Santa Marta mountain range. Finally the Lower Guajira is located to the east of Santa Marta mountain range and the Rancheria river valleys. This is the area that is home to most of the population of La Guajira state. The Upper and Middle Guajira are inhabited by the Wayuu indigenous communities, which account for 95.27% of the total indigenous population in the region [29]. They have their own language “wayuunaiki”. The Koguis and Wiwa are two other indigenous peoples living in the Santa Marta mountain range.. 4. Local solar resources In the study area, experimental measurements indicate a global horizontal irradiance intensity of more than 5 kWh/m2/day. The average behavior for all the months of the year is shown in Table 1. Solar irradiance data have been estimated from satellite images at the geographical latitude and longitude coordinates 11.51°N / 72.348°E. The satellite images have a spectral resolution of 1° (approximately 100 km), and a monthly temporal resolution (averages over the 10 years). The highest irradiance is perceived in the month of April and the lowest in the month June. Other important data are air temperature values, which do not exceed 28 °C on an annual scale. 5. Definition of electrical demand It is vital to identify the difference between demand (kW) and consumption (kWh) in order to improve energy cost reduction options. Load demands were identified by conducting an energy consumption survey in several communities. Most Wayuu communities are located in the municipalities of Manaure, Uribía, Maicao and Riohacha. An estimated population of 219,646 indigenous people live in the Middle and Upper Guajira (indigenous population projections by Colombian National Department of Statistics (DANE) for 2012). The sample was determined taking into account the number of people per household in Colombia. This is 3.9 people per household in the country as a whole, whereas there are 5.1 people per household in La Guajira [54]. In this context, we divide a population of 219,646 living in the Middle and Upper Guajira (according to DANE) by 5.1, which yields an estimated total of 43,068 indigenous households in this area. The selected sample of the population was calculated using (1), where n is the sample, N is the total population, Z is the reliability level, P is the expected proportion, Q = 1-P, and e is the error.

n=

Z 2*P*Q*N e 2 (N − 1) + Z 2*P*Q

(1)

Considering that N=43068, Z=95%, P=0.5, Q=0.5, e=5%, by substitution, we have that n=380.77 or there are approximately 381 households. Table 2 shows the percentage of households in the selected sample by municipality with a view to studying consumption. According to the consumption survey, the population was divided according to consumption as shown below: 1. Populations of up to 50 (8 households) were considered small communities and they were classified in Segment 1 (S1), 2. Populations of up to 125 (17 households) were considered as medium-sized communities and were classified in Segment 2 (S2). 3. Populations of up to 150 (23 households) were considered as large communities and were classified in Segment 3 (S3). This classification is used to determine the design of the APSA for the Wayuu communities as reported below. The hourly demand curve was modeled to evaluate various changing options of energy demand and to find an optimal combination of energy resources. 6. Results and analysis 6.1. APSA design We determined the energy potential in the study area and the optimal inclination angle of PV modules. Then, we designed the PV system considering climate behavior. Furthermore, the batteries were sized to provide lower-cost reliability for three days of autonomy. Finally, we determined the regulatory system, inverters, and the wiring for each system. The photovoltaic power generator, PPV, was calculated using (2), where YPV is the power of a photovoltaic panel under standard conditions, FPV is the power reduction factor of a photovoltaic panel, Gt is the direct solar radiation incidence on a photovoltaic panel, and Gstc is solar radiation under standard conditions (1 kW/m2).

⎡G ⎤ PPV = YPV *FPV ⎢ t ⎥ ⎣ Gstc ⎦

(2)

6.2. Economic analysis In the light of the technical design, the financial information was gathered from data provided by the company Green Energy Latin America. Table 3 shows the cost of the photovoltaic system components needed for the APSA design. Although the system is independent, it is designed from the viewpoint of reliability. The system was sized with battery banks capable of storing energy to guarantee the overnight electricity supply. All calculations were made considering that the batteries have a five-year lifespan and the rest of the components have a 20-year lifespan. Annual operation and maintenance costs were accounted for as being 1.5% of the initial investment for each system [55]. 7

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

6.3. Levelized energy cost The levelized energy cost (LEC) is calculated by dividing the annualized cost of producing electricity (the total annualized cost minus the cost of serving the thermal load) by the total electrical load served [45], according to (3). The second term in the numerator is the annual cost of serving the thermal load, where Ethermal=0 in systems with no thermal load. Cann,tot is the total annual cost of the system [$/year], cboiler is the boiler marginal cost [$/kWh], Hthermal is the total thermal load served [kWh/year], Eprim,AC is the AC primary load served [kWh/year], Eprim,DC is the DC primary load served [kWh/year], Edef is the deferrable load served [kWh/year], and Egrid,sales is the total energy sales to the network [kWh/year].

LCE =

Cann, tot − cboiler Hthermal Eprim, AC + Eprim, DC + Edef + Egrid , sales

(3)

The total net present cost, CNPC [$], of each project was calculated using (4) [45]. Cann,tot is the total annual cost [$/year], CRF is a function returning the capital recovery factor, i is the annual real interest rate [%], and Rproj is the project lifetime [year].

CNPC =

Cann, tot CRF (i , Rproj )

(4)

6.4. Power demand Fig. 3 illustrates the hourly load demand for communities classified in Segment 1 with a population of 50. Consumption for "S1" has three maximum peaks during the day. The first peak, between 6.00 and 7.00 h, reaches 2 kW. The second peak, between 12.00 and 13.00 h, reaches 2.4 kW. The third peak, between 18.00 and 21.00 h, reaches 2.7 kW. Demand sometimes drops to a minimum of 0.7 kW. The energy consumed by this kind of communities is 33 kWh/day. Fig. 4 illustrates the hourly load demand for communities classified in Segment 2 with a population of 125. Consumption for "S2" has two maximum peaks during the day. The first peak, between 11.00 and 12.00 h, reaches 7.5 kW. The second peak, between 18.00 and 20.00 h, reaches 6 kW. Demand sometimes drops to a minimum of 1.5 kW. The energy consumed by this kind of communities is 71 kWh/day. Fig. 5 illustrates the hourly load demand for communities classified in Segment 3 with a population of 200. Consumption for "S3" has three maximum peaks during the day. The first peak, between 6.00 and 7.00 h, reaches 5.7 kW. The second peak, between 12.00 and 13.00 h, reaches 7.7 kW. The third peak, between 18.00 and 21.00 h, reaches 2 kW. Demand sometimes drops to a minimum of 0.7 kW. The energy consumed by this kind of community is 95 kWh/day. Figs. 3–5 illustrate the demand of the communities under study. They include a 20% increment over hourly consumption considered as safety margin. This is safeguard to assure a more robust system design. These three consumption levels were used to test the APSA design, considering system economics and reliability. Consumption behaves similarly for S1 and S3 during the day, although magnitudes are different. Consumption for S2 differs from the others, because it has two peaks at different hours. This suggests that the system should be configured differently for each community in order to optimize the generation capacity of each one. 6.5. APSA sizes Table 4 shows the system sizes including all the components for the three case studies: communities S1, S2, and S3. The results reported in Table 4 were yielded by multiple simulations in HOMER. During the simulations, the behavior of the variables was analyzed with a view to guaranteeing the quality of the system based on electricity supply continuity and economic sustainability. Finally, the most optimal APSA configuration for each of the communities was output for each system. This configuration guarantees 100% continuity of supply, using a MPPT system to manage production and a battery that stores power for two days of autonomy. Looking at Table 4, we find that the recommended system for the S1, S2 and S3 communities has, respectively, powers of 9 kW, 20 kW and 27 kW, plus a PV generator consisting of 36, 80 and 108 250 wp modules and a storage system consisting of 15, 20 and 50 255 Ah/12 V AGM batteries. It also includes data such as the number of MPPTs and the PV module mounting structure. In order to provide all the households within the study area with a reliable energy supply, we accounted for the installation of programmable bidirectional energy meters to supply each dwelling with a specified power threshold for a specified time. The aim was to promote a fair and equitable distribution among the population. 6.6. Energy production Table 5 shows the annual, monthly and daily production and the average energy produced by each APSA in units of energy. The average energy consumption per household is 5.6 kWh/day for S1 and 5.8 kWh/day for S2 and S3. According to this technical configuration, daily energy production is equitably distributed within each community, supplying all households with their respective share. For example, the daily output of the S1 system is, according to Table 4, 44.4 kWh. This is divided between eight dwellings (50 inhabitants) belonging to community S1, establishing that each household will have access to 5.6 kWh/day. Energy is distributed similarly in the S2 and S3 communities. 6.7. Component costs Table 6 shows the cost of each component used for the APSA. It accounts for the initial investment, and annual and monthly operating costs for each system. The PV generator cost includes the cost of other equipment (the module mounting structures, the household supply metering network, etc.). All the costs are directly proportional to the required increment in electric power. The aim is to distribute generation and maintenance costs among users (households). The main idea is for users to guarantee the economic 8

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

sustainability of the system through payments that will cover the operating and maintenance costs of the entire system. This also includes system salvage costs (costs of replacing damaged parts). This methodology involves a higher monthly payment from communities, but is, however, necessary to guarantee the long-term sustainability of the system (20 years). Table 7 and Fig. 6 illustrate the relationship between annual energy production and annual and monthly generation costs for the systems designed to supply each household with electricity. This analysis is based on two assumptions: on one hand, the government or a non-profit organization will provide the initial investment for system implementation, and, on the other hand, the indigenous communities will, in the future, set up community groups responsible for administering and operating this technology. However, this scheme requires a monthly payment to ensure the long-term sustainability of the system. The average monthly payments per household were calculated at COL $ 19,914, COL $ 20,092 and COL $ 18,673 for communities S1, S2 and S3, respectively. Although S3 supplies the most expensive energy of the three systems. There is not much difference between the costs of S1 and S3. S2 is the cheaper due to the lower average income per household. UPME Resolution 355/2004 established the subsistence consumption as the minimum amount of electricity used per month by a typical user to meet basic needs. Subsistence consumption was set at 173 kWh/month for areas under 1000 m above sea level and at 130 kWh/month for zones over 1000 m above sea level. As a subsistence consumption of 173 kWh/month is equivalent to 5.7 kWh/day per household, the systems designed for the Wayuu communities producing about 5.8 kWh/day assure that the population would be supplied with enough energy to meet their basic needs. The cost of energy is COL $1,125, COL $1002 and COL $1159 for S1, S2 and S3, respectively. These results are far removed from the national average unit cost of kWh for 2015, whose value was COL $391 for the NIS [49]. However, this price is regarded as low compared with the development of other photovoltaic systems. Moreover, the methodology for calculating the monthly payment per household is based on charging beneficiary households for the system operating and maintenance costs instead of the total cost per kWh of the amount of energy consumed. Furthermore, Colombian government Resolution 186 of December 30, 2010, modifies article 3 of Law 1117/2006 in relation to the application of subsidies to Strata 1 and 2 users of the electric power services. It establishes that Strata 1 and 2 users may receive subsidies of no more than 60% and 50%, respectively, of the cost of supplying the household with public electric power; however, it does not regulate the percentages of subsidies for the country's non-interconnected zones in which rural electrification programs are implemented. Even though there is no established percentage subsidy for non-interconnected areas, let us evaluate the sustainability of the design considering the possibility of the government subsidizing up to 60% of the electricity supply taking into account that the population of the area concerned is classed as Strata 1. Table 8 shows the results of this exercise, where the cost per kWh is significantly lower, dropping to levels of COL $450, COL $401 and COL $464 for segments S1, S2 and S3, respectively. These values are close to the unit cost per kWh for the NIS. This suggests that, under this assumption, the evaluated technology is a potentially competitive option for meeting the energy needs of the target population. 7. Conclusions This paper reported the sizing of three solar photovoltaic systems for Wayuu indigenous communities and their economic analysis. The systems meet the UPME requirement of maintaining system reliability at a low cost. The required investment for implementation is low compared with the cost of expanding the interconnected power system due to the long distances that it would have to cover to supply remote areas of Colombia's La Guajira region. All systems were optimized and customized to meet the technical specifications and natural conditions of the area and guarantee energy efficiency. La Guajira offers excellent weather conditions for implementing APSAs for the Wayuu communities. The results confirm that it is possible to enter into a direct two-way communication with the indigenous population to gather information on their real needs and raise their awareness of the advantages and benefits of an electric power service. Based on this information, we can discover the reality and context of the study population, estimate the energy demand of three population groups (S1, S2 and S3), and design three optimized renewable energy systems. The systems were optimized and tailored to each community type in order to efficiently meet the technical specifications and natural conditions of these areas of the Colombian La Guajira, and have the potential for adaptation to other regions. Similarly, this research helped to provide reliable key information for the design of the energy systems. This information was used as HOMER software input, applying a net present value of the investment required to deploy the three evaluated photovoltaic projects and considering the balance of operating and maintenance costs (including salvage cost. From the results of the economic analysis, we were able to evaluate the possibility of determining the operating and maintenance cost per household. The monthly payment per household ensures project sustainability, regardless of the local government support and commitment. In terms of energy, it was found once again that the La Guajira region offers excellent weather conditions for the implementation of APSAs. Consequently, it was possible to size systems that have the potential to supply each household with the energy needed to meet the minimum level of electricity defined in kWh by the UPME. Finally, the technical design and economic analysis of the three photovoltaic solar systems revealed that, thanks to the region's great potential, the initial investment and commissioning expenses may be low compared to the costs of expanding the national grid to bring electricity services to the areas in question. This is certainly a sound argument in favor of decision making to benefit the population within the study region. In future research, we intend to explore the possibility of the government covering the costs of the initial investment in the system which would be transferred to the population for administration. La Guajira has been the subject of many natural resources (wind and solar power) studies and is capable of generating electrical energy through the implementation of wind and photovoltaic systems [24,56–58]. One such study simulated seven scenarios for energy supply in the area known as Puerto Estrella - Uribia with a population of 800. The main objective of the study was to analyze the application of photovoltaic panels, wind turbines and diesel generators in a hybrid system. One of the key results of the study was the optimum sizing of the system (500 320 W photovoltaic panels, one 10 kW wind turbine, one 25 kW diesel generator and 250 batteries). This would require an initial capital of US $521,078, whereas the operating costs would be US $24,652 / year, the total net cost would be US $836,210 and the energy cost would be US $0.473 / kWh, equivalent to COL $1410. The conclusion was that, for the load scale considered in this study, electricity production by photovoltaic panels is more economically favorable than the use of wind turbines. However, it was found that wind turbines could be economically more competitive at larger production scales [57]. According to Table 8, the study argues that La Guajira has good solar radiation levels that could be exploited first to electrify isolated local populations and second to implement large-scale projects to inject electrical energy to the NIS. Moreover, bearing in mind that Colombia is working 9

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx

on a regulation aimed at encouraging the use of renewable technologies across the country, the above cost of energy prices for isolated communities will be much more favorable when it is introduced [59]. Based on the experiences of other countries like Mexico, which, like La Guajira, has good solar radiation data and where the state supports renewable energy initiatives, we find that the cost of PV energy is already favorable for self-consumption. In another words, PV energy is, according to the Grid Parity Monitor, competitive in the residential and commercial sector [60]. Bearing in mind the aim of implementing energy solutions for the indigenous communities of the Colombian La Guajira, beneficiaries, in this case isolated populations, are advised to form associations and strengthen social union in order to assure that they can guarantee, through nonprofit cooperatives, the management of the installed PV systems in the future. This could be an efficient way of defraying the costs of installed power, taking into account that the costs associated with the generation system will drop as the installed power increases. Acknowledgment We would like to thank the Universidad de la Guajira, Colombia (International agreement Nº 4734), for its financial support for conducting this research. References [1] United Nations. World Economic and Social Survey 2013; 2013. http://dx.doi.org/10.1016/j.compind.2010.10.001. [2] SENER. Perspectiva del Mercado de Petróleo Crudo 2010–2025. Ciudad de Mexico; 2011. [3] Ortiz Lopez A, Urrutia Milla D. Tendencias Mundiales En El Uso De La Electricidad En El Transporte (Tecnologías, Costos, Perspectivas). Opciones Para La Región Metropolitana; 2009:60. [4] SEMARNAT. Cambio climático: Ciencia, evidencia y acciones; 2010. [5] Mosquera J, Fernández S, Mosquera J. Análisis de emisiones de CO2 para diferentes combustibles en la población de taxis en Pereira y Dosquebradas. Sci Tech - Univ Tecnológica Pereira; 2010:XVI:141–6. [6] Sikka M, Thornton TF, Worl R. Sustainable biomass energy and Indigenous Cultural models of well-being in an Alaska forest ecosystem. Ecol Soc 2013;18. http://dx.doi.org/ 10.5751/ES-05763-180338. [7] Tiwari GN, Dubey S. Fundamentals of photovoltaic modules and their applications. Royal Society of Chemistry; 2010. [8] Ismail MS, Moghavvemi M, Mahlia TMI. Techno-economic analysis of an optimized photovoltaic and diesel generator hybrid power system for remote houses in a tropical climate. Energy Convers Manag 2013;69:163–73. http://dx.doi.org/10.1016/j.enconman.2013.02.005. [9] QCOSS. Empowering remote communities: Experiences of Aboriginal and Torres Strait Islander customers using electricity pre-payment meters in Queensland; 2014. [10] Devis-Morales A, Montoya-Sánchez RA, Osorio AF, Otero-Díaz LJ. Ocean thermal energy resources in Colombia. Renew Energy 2014;66:759–69. http://dx.doi.org/10.1016/ j.renene.2014.01.010. [11] BREG, ARE. The Colombia off-grid market in 12 pages, Players and Business Opportunities; 2014. [12] Quijano HR, Botero BS, Domínguez BJ. MODERGIS application: integrated simulation platform to promote and develop renewable sustainable energy plans, Colombian case study. Renew Sustain Energy Rev 2012;16:5176–87. http://dx.doi.org/10.1016/j.rser.2012.05.006. [13] El Congreso de Colombia. Ley 1715 de 2014. Colombia: UPME; 2014. [14] Procolombia. Electric Power in Colombia. Power Generation - 2015; 2015:23. [15] Comision de regulación de energía y Gas. Bases conceptuales para la regulación de la prestación del servicio en zonas no interconectadas; 2003:56. [16] Comisión de regulación de energía y gas (CREG). Marco regulatorio para la prestacion del servicio de energia electrica en las zonas no interconectadas; 2007:58. [17] Ramakumar R, Hughes WL. Renewable energy sources and rural development in developing countries. IEEE Trans Educ 1981;24:242–51. http://dx.doi.org/10.1109/ TE.1981.4321499. [18] Ruiz BJ, Rodríguez-Padilla V. Renewable energy sources in the Colombian energy policy, analysis and perspectives. Energy Policy 2006;34:3684–90. http://dx.doi.org/10.1016/ j.enpol.2005.08.007. [19] Comisión de regulación de energía y gas. Definición de la fórmula tarifaria de energía eléctrica, para el próximo periodo tarifario; 2007:16. [20] Comisión de Regulación de Energía y Gas. Resolución No. 119 DE2007; 2007:29. [21] REN 21. RENEWABLES 2016 GLOBAL STATUS REPORT. Paris, France; 2016. [22] Cuervo FI, Botero SB. Wind power reliability valuation in a Hydro-Dominated power market: the Colombian case. Renew Sustain Energy Rev 2016;57:1359–72. http://dx.doi.org/ 10.1016/j.rser.2015.12.159. [23] Gaona EE, Trujillo CL, Guacaneme JA. Rural microgrids and its potential application in Colombia. Renew Sustain Energy Rev 2015;51:125–37. http://dx.doi.org/10.1016/ j.rser.2015.04.176. [24] Hernandez JA, Velasco D, Trujillo CL. Analysis of the effect of the implementation of photovoltaic systems like option of distributed generation in Colombia. Renew Sustain Energy Rev 2011;15:2290–8. http://dx.doi.org/10.1016/j.rser.2011.02.003. [25] Osorio AF, Ortega S, Arango-Aramburo S. Assessment of the marine power potential in Colombia. Renew Sustain Energy Rev 2016;53:966–77. http://dx.doi.org/10.1016/ j.rser.2015.09.057. [26] Sopelia. Plataforma solar de América Latina. 6-04-2016; 2016:3. 〈http://www.energiasolar.lat/solar-colombia/〉. [Accessed 1 December 2016]. [27] Ministerio de Minas y Energía. Colombia avanza en la incorporación de energías renovables al sistema eléctrico. 20-10-2016; 2016:2. 〈https://www.minminas.gov.co/web/10180/ 1332?IdNoticia=23829018〉 [Accessed 7 November 2016]. [28] International Work Group for Indigenous Affairs. Colombia; 2016:120–8. 〈http://www.iwgia.org/regions/latin-america/colombia〉 [Accessed 2 November 2016]. [29] Sofiyanti N, Fitmawati DI, Roza AA. Stenochlaena Riauensis (Blechnaceae), A new fern species from riau, Indonesia. Bangladesh J Plant Taxon 2015;22:137–41. http:// dx.doi.org/10.1007/s13398-014-0173-7.2. [30] Sistema de informacion Eléctrico Colombiano (SIEL). Consultas Estadisticas; 2016. [31] IDEAM U. Atlas Interactivo - IDEAM n.d. 〈http://atlas.ideam.gov.co/presentacion/〉 [Accessed 9 January 2017]. [32] Hoogwijk M, de Vries B, Turkenburg W. Assessment of the global and regional geographical, technical and economic potential of onshore wind energy. Energy Econ 2004;26:889–919. http://dx.doi.org/10.1016/j.eneco.2004.04.016. [33] Observatorio europeo LEADER. Fuentes de energía renovables, fuentes de desarrollo sostenible. Cumbria; 1999. [34] Change IP on C. Summary for Policymakers. in: Intergovernmental Panel on Climate Change, editor. Clim. Chang. 2013 - Phys. Sci. Basis, Cambridge: Cambridge University Press; 2014, p. 1–30. http://dx.doi.org/10.1017/CBO9781107415324.004. [35] Aguilera J, Hontoria L. Dimensionado de sistemas fotovoltaicos autónomos. Fundam. Dimens. y Apl. la energía Sol. fotovoltaica, Madrid, España.: 2004, p. 1–26. [36] Borges R, Gina C, Sera S, Sera AS. Dimensionado mediante simulación de sistemas de energía solar fotovoltaica aplicados a la electrificación rural. Red Rev Científicas América Lat El Caribe, España Y Port; 2011:14:13–21. [37] Horn M. Tecnología fotovoltaica para una electrificación rural sostenible en países de desarrollo ; la experiencia del Perú. Guzlop Ed; 2012:1:35. [38] Ladino Peralta RE. La energía solar fotovoltaica como factor de desarrollo en zonas rurales de Colombia. Caso: vereda Carupana, municipio de Tauramena, departamento de Casanare. Pontificia Universidad Javeriana; 2011. [39] Colegio oficial de ingenieros Telecomunicación. Energia Solar Fotovoltaica. Madrid, España; 2002. [40] Instituto Interamericano de Cooperación para la Agricultura. Use of and access to renewable energies in rural territories; 2015:1:48. [41] Morales LRV, Zilles R. Utilización de la energía fotovoltaica en pequeñas actividades productivas en zonas rurales; 2010:11. [42] Bello C, Vera L Sistemas AB fotovoltaicos en escuelas rurales: el caso de la provincia de corrientes, Argentina. Univ Nac Del Nord n.d.:1–9. [43] Salehin S, Ferdaous MT, Chowdhury RM, Shithi SS, Rofi MSRB, Mohammed MA. Assessment of renewable energy systems combining techno-economic optimization with energy scenario analysis. Energy 2016;112:729–41. http://dx.doi.org/10.1016/j.energy.2016.06.110. [44] HOMER official webpage. HOMER - Hybrid Renewable and Distributed Generation System Design Software n.d. 〈http://www.homerenergy.com/〉 [Accessed 18 November 2016].

10

Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx [45] Homer Energy. HOMER Pro Version 3.6 User Manual; 2016:416. [46] Al-Karaghouli A, Kazmerski LL. Optimization and life-cycle cost of health clinic PV system for a rural area in southern Iraq using HOMER software. Sol Energy 2010;84:710–4. http://dx.doi.org/10.1016/j.solener.2010.01.024. [47] Adaramola MS. Viability of grid-connected solar PV energy system in Jos, Nigeria. Int J Electr Power Energy Syst 2014;61:64–9. http://dx.doi.org/10.1016/j.ijepes.2014.03.015. [48] Kusakana K. Techno-economic analysis of off-grid hydrokinetic-based hybrid energy systems for onshore/remote area in South Africa. Energy 2014;68:947–57. http://dx.doi.org/ 10.1016/j.energy.2014.01.100. [49] Shah KK, Mundada AS, Pearce JM. Performance of U.S. hybrid distributed energy systems: solar photovoltaic, battery and combined heat and power. Energy Convers Manag 2015;105:71–80. http://dx.doi.org/10.1016/j.enconman.2015.07.048. [50] Mostafaeipour A, Qolipour M, Mohammadi K. Evaluation of installing photovoltaic plants using a hybrid approach for Khuzestan province, Iran. Renew Sustain Energy Rev 2016;60:60–74. http://dx.doi.org/10.1016/j.rser.2016.01.105. [51] Puerta C. Roles y estrategias de los gobiernos indígenas en el sistema de salud colombiano. Rev Colomb Antropol 2004;40:85–121. [52] Google. Google Maps n.d. 〈https://www.google.es/maps〉 [Accessed 18 November 2016]. [53] NASA. Surface meteorology and Solar Energy n.d. 〈https://eosweb.larc.nasa.gov/sse/〉 [Accessed 18 November 2016]. [54] Dane. Metodología Censo General 2005. Bogotá D.C., Colombia; 2009. [55] Breyer C, Gerlach A, Mueller J, Beacker H, Milner A. Grid-parity analysis for EU and US regions and market segments - Dynamics of grid-parity and dependence on solar irradiance, local electricity prices and PV progress ratio. 24th Eur. Photovolt. Sol. Energy Conference, Hamburg, Germany; 2009. [56] Caspary G. Gauging the future competitiveness of renewable energy in Colombia. Energy Econ 2009;31:443–9. http://dx.doi.org/10.1016/j.eneco.2008.12.007. [57] Haghighat Mamaghani A, Avella Escandon SA, Najafi B, Shirazi A, Rinaldi F. Techno-economic feasibility of photovoltaic, wind, diesel and hybrid electrification systems for offgrid rural electrification in Colombia. Renew Energy 2016;97:293–305. http://dx.doi.org/10.1016/j.renene.2016.05.086. [58] Botero BS, Isaza CF, Valencia A. Evaluation of methodologies for remunerating wind power's reliability in Colombia. Renew Sustain Energy Rev 2010;14:2049–58. http:// dx.doi.org/10.1016/j.rser.2010.02.005. [59] Asociación Mexicana de Energía Solar Fotovoltaica (ASOLMEX). Costos de energía fotovoltáica; 2016:3. 〈http://www.asolmex.org/eng/costos.html〉 [Accessed 15 November 2016]. [60] Energias Renovables. El autoconsumo FV ya es competitivo en el sector residencial de México. 19 Junio 2015 2015. 〈http://www.energias-renovables.com/fotovoltaica/elautoconsumo-fv-ya-es-competitivo-en-20150619〉 [Accessed 15 November 2016].

Andrés Vides-Prado, Edgar Ojeda Camargo, Carlos Vides-Prado, Israel Herrera Orozco,, Faustino Chenlo, John E. Candelo, Agustín Barrios Sarmiento Department of Industrial Engineering, Universidad de la Guajira, Km 5 Vía a Maicao, PBX (5), 728 2729 Riohacha, Colombia Faculty of Industrial Engineering, Universidad de la Guajira, Km 5 Vía a Maicao, PBX (5), 728 2729 Riohacha, Colombia Department of Environmental Engineering, Universidad de la Guajira, Km 5 Vía a Maicao, PBX (5), 728 2729 Riohacha, Colombia Energy System Analysis Unit – Energy Department, CIEMAT, Av Complutense 40, 28040 Madrid, Spain Photovoltaic Solar Power Unit, CIEMAT, Av Complutense 40, 28040 Madrid, Spain Department of Electrical Energy and Automation, Universidad Nacional de Colombia – Sede Medellín, Carrera 80 No. 65 – 223, Medellín, Colombia Department of Mathematics, Universidad del Norte, Km 5 vía a Puerto, Barranquilla, Colombia E-mail address: [email protected]



Corresponding author.

11