A pilot study for a possible installation of Photovoltaic modules at The University of Havana: Bachelor's thesis in a field study in Havana, Cuba

IN

DEGREE PROJECT TECHNOLOGY,

FIRST CYCLE, 15 CREDITS

STOCKHOLM SWEDEN 2018 ,

A pilot study for a possible installation of Photovoltaic modules at The University of Havana

Bachelor’s thesis in a field study in Havana, Cuba CAROLINE ELIASSON

ELIN RAHMQVIST

Abstract

In 2014 the Cuban government announced that 24% of the country’s generated electricity will come from renewable energy sources by 2030. In Cuba the emissions have drastically risen over the past decade due to the increasing amount of electricity demand. Today most of the generated electricity is produced by burning oil. To achieve this goal before 2030 major investments in renewable energy will be required. There is also a big concern in Cuba about climate change, as Cuba’s geographical position is very vulnerable to drastic weather changes. This drive efforts towards a more sustainable society, in addition to the economic aspect of being independent of imported oil.

The objective of the study is to evaluate the economical, ecological and social profitability of PV systems in Cuba. The main purpose will consist of making economic and technical calculations using the software Matlab (version R2016a) for the installation of the PV system on the building most suitable at The University of Havana. The study will consider both a PV system with and without energy storage. The PV module that will be investigated in this study is the crystalline silicone cells, since this is the most common used in PV system in Cuba. This is to enable for the university to become partly or completely independent from the electricity generated by the government owned electricity company (UNE). It is important for the university to become independent from the national electricity grid due to the high number of power-cuts and since the electricity company in Cuba regulates how much electricity that can be consumed each month. The project will consider both economic, ecological and social aspects to find the best solution for the installation of PV system at The University of Havana.

The study showed that the most suitable building for a PV system installation is the building of Institute of Science and Technology of Materials. All three orientations examined in this study cover the electricity consumption during an average day and can work as a backup system. The result concluded that the most economical and optimized installation, taking into account the desired

function of the PV system for the building of IMRE is an incline angle of 20°, 270 number of installed PV modules and an orientation towards south if installing a PV system with energy storage. The excess electricity from the PV system has assumed to be used for recharging the battery or sold back to the grid for same price as the private PV companies sell electricity for, 0,06-0,07 USD/kWh. It was concluded that the cost of generated electricity from a PV system installed at The University of Havana is 5,5-32,5 % cheaper with battery and without battery the cost is 47,8-62,7 % cheaper than current price of generated electricity at 0,15-0,21 USD/kWh. The result from this study complements other studies done and validates that also smaller PV systems are economical profitable in Cuba. This study has shown that it is economic, ecological and social profitable to install a PV system at The University of Havana.

Resumen

Las emisiones de gases de invernaderos en Cuba han aumentado drásticamente en la última década, a causa de la creciente demanda del uso de la electricidad. En la actualidad la mayor parte de la

electricidad generada en el país se obtiene por la quema del petróleo. En el año 2014, el gobierno de Cuba se propuso la meta, de que un 24% de la electricidad generada en el país en el 2030, fuese obtenida a partir de las fuentes de energías renovables. Para cumplir este objetivo antes del año 2030, será imprescindible hacer grandes inversiones en nuevas tecnologías para el uso de las fuentes de energías renovables. En Cuba también existe una gran preocupación por el cambio climático debido a las vulnerabilidades de la isla frente a los fenómenos atmosféricos que afectan al país por su situación geográfica. Esto ha incrementado los esfuerzos para alcanzar un desarrollo socioeconómico sostenible y la independencia energética del país.

El objetivo de este estudio es evaluar la rentabilidad económica, ecológica y social de los sistemas fotovoltaicos (FV) en Cuba. Para lograr este fin se hacen cálculos económicos y técnicos utilizando el software Matlab versión R2016a para la instalación de los sistemas FV en los edificios de la Universidad de La Habana. El estudio considera ambos tipos de sistemas FV, con y sin almacenamiento de energía.

Los módulos FV que se investigan en este trabajo son los basados en celdas solares de silicio cristalino porque estas son las celdas más usadas en los sistemas FV de Cuba. Este proyecto contribuirá a que la universidad se independice parcial o completamente de la electricidad generada en el país. La independencia de la red eléctrica nacional es muy importante para la universidad por la gran cantidad de cortes eléctricos a causa de las regulaciones del consumo energético de cada mes. El proyecto considera los aspectos socioeconómicos y ecológicos para encontrar el sistema FV óptimo en la Universidad de La Habana.

El estudio demuestra que uno de las edificaciones que cumple con las condiciones óptimas para la instalación de un sistema fotovoltaico en la Universidad de La Habana es el edifico central del IMRE.

Los aspectos examinados en este estudio consideran el consumo energético promedio en el día y la

capacidad de respaldo del sistema FV. Teniendo en cuenta, las características de un sistema FV con

almacenamiento de energía en los edificios de IMRE, se concluyó que la instalación óptima y más

económica tiene un ángulo de inclinación de 20°, una cantidad de 270 módulos FV instalados y una

orientación hacia el sur. Los resultados indicaron que el costo de un sistema FV instalado en la

Universidad de La Habana es 5,5-32,5%, más económico con batería, y sin batería el costo es 47,8-

62,7% más económico que la electricidad generada actualmente. Estos resultados complementan otros

estudios realizados y demuestran que el uso de sistemas FV más pequeños son rentables

económicamente en Cuba. Este estudio ha demostrado que la instalación de un sistema FV en la

Universidad de La Habana es ecológica, económica y socialmente rentable.

Sammanfattning

År 2014 meddelade den kubanska regeringen att 24 % av landets elproduktion ska vid år 2030 komma från förnybara energikällor. På Kuba har utsläppen ökat drastiskt under det senaste decenniet på grund av den ökande efterfrågan på el. Idag produceras majoriteten av den genererade elen från olja och för att uppnå målet om en ökad mängd förnybara energikällor före år 2030 krävs stora investeringar. Det finns en stor oro på Kuba kring klimatförändringarna, på grund av att landets geografiska position är mycket sårbar för drastiska väderförändringar. Detta driver ansträngningarna mot ett mer hållbart samhälle, utöver den ekonomiska aspekten att vara oberoende av importerad olja.

Syftet med studien är att utvärdera PV-systemets ekonomiska, ekologiska och sociala lönsamhet på Kuba. Huvudsyftet kommer att bestå av att göra ekonomiska och tekniska beräkningar med

softwareprogrammet Matlab (version 2016a) för installation av PV-systemet på de byggnader som anses lämpligast att installera på. Studien kommer att utvärdera både ett PV-system med och utan energilagring. I denna studie är de kristallina silikoncellerna som tillämpas eftersom dessa är de mest förekommande på Kuba. Installation av ett PV system kommer kunna göra det möjligt för universitetet att bli helt eller delvis oberoende av den el som genereras av det statligt ägda elbolaget (UNE). Det är viktigt för universitetet att bli oberoende av det nationella elnätet på grund av det stora antalet

strömavbrott som existerar idag och eftersom Kubas elbolag reglerar hur mycket el som kan konsumeras varje månad. Projektet kommer att överväga både ekonomiskt, sociala och ekologiska aspekter för att finna den bästa lösningen för installation av ett PV-system vid Havannas Universitet.

Studien visade att den lämpligaste byggnaden för en installation av PV-system är på en av

byggnaderna som tillhör Institute of Science and Technology of Materials. Alla tre orienteringar för en installation som undersöktes i denna studie täcker elförbrukningen under en genomsnittlig dag och kan även fungera som ett backupsystem. Resultatet visade att den mest ekonomiska och optimala

installationen med hänsyn till PV-systemets önskvärda funktion för byggnaden, är en lutningsvinkel

på 20 °, en installation på 270 PV-moduler och med en orientering mot söder om PV-systemet

installeras med energilagring. Överskottselen från PV systemet har antagits att användas till att ladda

upp batterierna eller säljas tillbaka till nätet för samma pris som för privata solcellsföretag säljer för,

0,06–0,07 USD/kWh. Slutsatsen för kostnaden för genererad el från ett PV-system installerat vid

Havannas Universitet är att det blir 5,5–32,5% billigare med batteri och utan batteri är kostnaden

47,8–62,7% billigare än nuvarande elproduktion i landet, 0,15-0,21 USD/kWh. Resultatet av denna

studie kompletterar andra studier som gjorts och validerar att även mindre installation av PV-system är

ekonomiskt lönsamma på Kuba. Denna studie har visat att det är ekonomiskt, ekologiskt och socialt

lönsamt att installera ett PV-system vid Havannas Universitet.

Acknowledgement

This bachelor thesis has been conducted during the spring of 2018 as an exchange with The university of Havana and The Royal Institute of Technology (KTH). 10 weeks of the project have been spent in Havana at the Institute of Science and Technology of Materials. We hope that this work will be in use for the university and that the Cuban government can see the great economical, ecological and social potential in installing PV systems at The University of Havana.

First of all, we would like to thank René Díaz Suárez and Julio Cesar Rimada Herrera that are working at the Institute of Science and Technology of Materials. Without them this project would never have been possible, and we are forever grateful for all help, knowledge and patience they have given to us. It has been an honor to have the opportunity to come to Cuba and learn about the PVs, electricity market, country and the culture here. To Anabel Lam, the Deputy Director of Postgraduate and International Relations at the Institute of Science and Technology of Materials, we want to thank for making our stay in Cuba amazing and for helping us in all difficulties it means to live and enter into a new culture. Further thanks we want to direct to Dr. C Daniel Stolik for all great knowledge about the PVs and Cuban electricity market he has shared with us.

A great thanks to Fredrika Bremer Förbundets Stipendiestiftelse and The ÅForsk Foundation, without financial support from them the trip to Cuba would never have been possible. We would also like to thank Sandra Andersson from the Swedish Institute of Hydro and Meteorology (SMHI) for all the help in understanding the complexness in solar radiation and weather.

Finally, we would like to thank Lennart Söder, our tutor at KTH who has given us great inputs,

advices and ideas during the way in order to improve the project.

Table of Contents

1. INTRODUCTION ... - 1 -

1.1 B

ACKGROUND

... - 1 -

1.2 T

HE OBJECTIVE OF THE PROJECT

... - 2 -

1.3 D

ISCUSSION OF USED LITERATURE

... - 3 -

1.4 N

OMENCLATURE

... - 3 -

2. THE METHOD ... - 5 -

2.1 M

ETHOD FOR DETERMINE ACCURACY OF THE DESIGNED MODEL AND OUTPUT ENERGY

... - 5 -

2.2 I

NSTALLATION AND TECHNICAL CALCULATIONS

... - 5 -

2.3 E

CONOMIC CALCULATIONS

... - 7 -

2.4 M

ETHOD FOR SOCIAL AND ECOLOGICAL RESULTS

... - 7 -

3. THEORETICAL BACKGROUND ... - 9 -

3.1 S

OLAR RADIATION

... - 9 -

3.1.1 The sun’s position ... - 9 -

3.1.2 Conversion of solar radiation on the horizontal plane to an inclined surface... - 11 -

3.2 PV

CELLS

... - 12 -

3.2.1 Bypass diode ... - 13 -

3.3 PV

^SYSTEM

... - 14 -

3.3.1 The output from the PV system ... - 15 -

3.3.2 Battery ... - 15 -

3.3.3 Installation ... - 16 -

3.4 E

CONOMY

... - 18 -

3.4.1 Levelized Cost of Electricity ... - 18 -

3.4.2 Payback method ... - 19 -

3.5 C

^UBA

’

S ELECTRICAL MARKET

... - 20 -

4. RESULTS ... - 22 -

4.1 A

CCURACY OF DESIGNED MODEL TESTED IN

N

ORRKÖPING

, S

WEDEN

... - 22 -

4.2 T

ECHNICAL RESULTS

... - 24 -

4.2.1 The efficiency of PV cells and solar radiation ... - 24 -

4.2.2 Installation ... - 25 -

4.3. E

CONOMIC RESULTS

... - 28 -

4.3.1 Installation with orientation to south ... - 28 -

4.3.2 Installation with orientation to north-south ... - 29 -

4.3.3 Installation with orientation to east-west ... - 31 -

4.3.2 Summarize of different installation ... - 32 -

4.4 S

ENSITIVITY ANALYSIS

... - 33 -

4.5 E

COLOGICAL RESULTS

... - 35 -

4.6 S

OCIAL RESULTS

... - 37 -

5. DISCUSSION ... - 39 -

5.1 A

CCURACY OF DESIGNED MODEL

... - 39 -

5.2 D

ESIGNED MODEL AND INSTALLATION

... - 39 -

5.3 E

CONOMIC

... - 40 -

5.4 E

COLOGICAL AND SOCIAL

... - 42 -

5.5 F

UTURE

... - 42 -

6. CONCLUSION ... - 44 -

REFERENCES ... - 45 -

APPENDIX ... - 49 -

APPENDIX ... - 50 -

Table of Tables

Table 1. Comparison of annual output energy with different energy companies and designed Matlab version R2016a model. ... - 22 - Table 2. Calculated annual energy output for one or two PV modules with different inclined angles and scenarios. ... - 24 - Table 3. Scenario - orientation to the south. The table include the minimum spacing,

maximal number of PV modules and the total installed area for different inclined angles for the PV modules. ... - 26 - Table 4. Scenario - orientation to the north-south. The table include the minimum spacing, maximal number of PV modules and the total installed area for different inclined angles for the PV modules. ... - 27 - Table 5. Scenario - orientation to the east-west. The table include the minimum spacing, maximal number of PV modules and the total installed area for different inclined angles for the PV modules. ... - 27 - Table 6. Minimum effect for inverters [kW] and kWp for optimal number of PV modules for different inclined angles and orientations without battery. ... - 28 - Table 7. Minimum effect for inverters [kW], minimum energy capacity in battery [Ah]/[V]

and kWp for optimal number of PV modules with different inclined angles and orientations

with battery. ... - 28 -

Table 8. Scenario - Illustrate the lowest number of years for PB for different inclined angles

when the installation is without and with battery. ... - 29 -

Table 9. Scenario - Illustrate the lowest number of years for PB for different inclined

angles when the installation is without and with battery... - 30 -

Table 10. Scenario - Illustrate the lowest number of years for PB for different inclined

angles when the installation is without and with battery... - 31 -

Table 11. Summarize of result for different installation without battery. ... - 32 -

Table 12. Summarize of result for different installation with battery. ... - 32 -

Table 13. Comparison between CO2-e g/kWh emissions from PV plants and Oil plants. . - 37 -

Table 14. The affect from the PV system on social factors. ... - 38 -

1. Introduction

1.1 Background

Climate change is causing problems all around the globe, from natural disasters, long droughts, lack of water, starvation and an increasing number of climate refuges. In the world, 79 % of all primary energy used comes from fossil fuels, emitting a great number of carbon dioxide which causes the temperature in the atmosphere to increase (Beaton, et al., 2016). 40 % of the global emissions of carbon dioxide related to energy comes from electricity and heat production and this is due to the sector’s high dependency of fossil fuels (Ang & Su, 2016). The demand of electricity is constantly increasing, from 1990 to 2013 the electricity production increased by 94% in the world (Ang & Su, 2016). According to the World Energy Forum the fossil-based oil, coal and gas reserves will be exhausted in less than ten decades. The rapidly diminishing of natural resources and the high demand of conventional energy have forced countries and companies to look for alternate sources (Beaton, et al., 2016). Consequently, the need of new alternative energy forms and sustainable development is becoming increasingly important in the world.

In 2016 the United Nations implemented 17 Sustainable Development goals to meet the urgent global challenges by 2030. The aim is to develop a sustainable future; economically, socially and

ecologically and to achieve global justice between countries. The 17 goals include eliminating poverty, stimulating international cooperation and technological innovation and improving the environment and reducing climate change. To be able to meet UN's sustainable goal number 7,

“Ensure access to affordable, reliable, sustainable and modern energy for all” and number 13,

“Take urgent action to combat climate change and its impacts”, radical changes must be done in all countries’ electricity production and energy supply. The electricity production has to come from renewable and sustainable energy plants to ensure sustainability, affordable, reliable and modern energy for all. (United Nations, 2016)

One renewable and sustainable energy supply is photovoltaic (PV) cells where solar radiation is directly converted into electrical energy. The scientist Alexandre Edmond Becquerel discovered the photo-electric effect when performing electro-chemical experiments in the year 1839 (Mertens, 2014).

PV is the only energy supply which can produce electricity where it is consumed and has a low cost of operation and maintenance. PV cells are the fastest growing source of electricity in the last decade and the total installed capacity are approaching 200 GW in the world (Jordan, et al., 2016). The potential for PV cells in Cuba have great potential due to the high number of solar hours, 3000 hours of sunshine per year with approximately 5 kWh/m

²

per day (Hernández & Martel, n.d).

Cuba has a subtropical climate and the country is located in the Caribbean Sea and lies between 20°12´-23°17´N and longitudes -80°53´-84°57´W (Beatón, et al., 2012). Due to Cuba’s geographical position the country is vulnerable to climate changes and hurricanes. This drive efforts towards a more sustainable society and to secure the energy supply, in addition to the economic aspect of being independent of imported oil. The government is already making major investments in renewable energy, for example by financing different research projects (Beaton, et al., 2016).

The energy situation in Cuba has changed drastically during the past 50 years and the different energy strategies are usually divided into three periods. The first period begins in 1959 (Díaz Suárez, 2018) &

(Rimada Herrera, 2018b) and ends in 1991, the fall of the Soviet Union (Beatón, et al., 2012). During this period the country build the largest energy generation infrastructure and had a high consumption of oil and products imported from Soviet Union, which was highly subsidized (Kaisti, et al., 2015).

Nearly 90% of the fuel needs was imported from Soviet Union (Panfil, et al., 2017a). Before the

Cuban revolution in 1959 around 50% of the households where connected to the grid, and by 1989 this

number had increased to 95%. After the fall of the Soviet Union, 1991, all trade links to Cuba were cut

rapidly which caused a shock for the country and led to the GDP fell 35 % during 4 years (Kaisti, et

al., 2015). The second period which reaches between 1992 and 2003 a National Energy Source

Development Program was applied to reduce Cuba’s energy imports and increase the energy supply

from domestic energy resources. The third period between 2004 to present time has been influence by the large number of blackouts and the energy crisis 2004-2005 (Beatón, et al., 2012). In 2014 Cuba had a generating capacity of 6169 MW. During this period several hurricane related power cuts have happened, for example year 2004 left approximately 1 million people without electricity for 10 days (Panfil, et al., 2017a).

Cuba has done several changes in its energy policy to reduce its dependence on imported fossil fuels and to increase energy efficiency and the use of renewable energy (Beaton, et al., 2016). The

introduction of the Cuban Electricity Conservation Program, Energy Conservation Program of the Ministry of Education and The Energy Revolution have had good results in electrifying the country and helped change the way Cuba transforms and uses fuels technologies. The policy The Energy Revolution included several goals and two of them were; “Increased energy efficiency” and “Greater use of sustainable resources”. To reach the goal, “Increased energy efficiency”, millions of appliances have been replaced to more efficient alternatives in Cuban homes and the country has switched to compact fluorescent light bulbs which has reduced the annual electricity consumption by 3-4%

(Vazquez, et al., 2015) & (Beatón, et al., 2012).

The demand of electricity has increased with almost 60 % since 1995 and is still increasing (Oficina Nacional de Estadística e Información, 2015). Due to the increasing number of tourists, the energy demand increased by 16% from 2015 to 2016. The energy demand will continue to increase and put pressure on the already stressed electric grid (Panfil, et al., 2017a). Consequently, Cuba is in great need of more electricity and smart energy solutions. Today, the energy sector in Cuba distribute electricity to approximately 97% of the country (Beatón, et al., 2012). In 2014 the Cuban government announced that 24% of the country’s generated electricity will come from renewable energy sources by 2030 (Beaton, et al., 2016). Approximately 53% of Cuba’s energy is from imported fuels and to achieve this goal before 2030 major investments in renewable energy will be required (Beaton, et al., 2016).

The LUCES Laboratory is located at the Institute of Science and Technology of Materials (IMRE) at The University of Havana. LUCES is supposed to be a central laboratory for all Cuban universities and provide service for different national and international clients. The government of Cuba has invested in new equipment for the LUCES Laboratory and according to Dr. J.C Rimada Herrera this equipment has a value of 1.1 million US dollars. The problem for the university is the great number of power cuts (approximately one power cut per week lasting for 6-8 hours) at the national grid which can cause damage to the equipment if turned off suddenly (Díaz Suárez, 2018). This can increase costs due to interrupted and loss of tests done using the equipment and in worst case dangerous explosions. To prevent this from occurring an installation of electrical protection and backup is needed to ensure no sudden electrical failure. This can ensure safety while working in the laboratory for the staff and also reducing costs for repairing expensive equipment (Rimada Herrera, 2018a).

Another problematic aspect for the university and safety for staff and equipment is the regulation of electricity. Today the government owned electricity company Union Electrics (UNE) regulates how much electricity that can be consumed each month. If the limit is exceeded the consequences are that the power will be cut off which happens often in the hotter months. This leads to some of the facilities at the university must close for a couple of days (Rimada Herrera, 2018b). Therefore, The University of Havana wants to conduct a pilot study about a PV system to see if this could be a possible

alternative for them, in order to be partially or completely independent from the electricity produced by the government. The University of Havana also wants to receive state funding for the installation cost of the PV system and therefore this pilot study will be material for decision making of this matter.

This pilot study also aims to investigate ecological and social aspects of a possible installation of a PV system to reach the most sustainable solution for providing electricity to The University of Havana.

1.2 The objective of the project

at The University of Havana is economic, social and environmental profitable. The project will be a support for the government of Cuba in decision making for a possible installation of a

PV system. This is to enable for the university to become partly or completely

independent from the electricity generated by the UNE. The project aims to find the most sustainable solution for an installation of a PV backup system at The University of Havana.

To complete the purpose of this project, following questions will be answered:

•

Is it profitable to install a PV system at The University of Havana from an economic point of view for the government?

•

Which location or locations will be optimal for a PV system at The University of Havana?

•

What is the optimal number, incline angle and orientation of PV modules for an installation of a PV system at The University of Havana?

•

Do PV modules have a greater climate impact than the current production of electricity in Havana?

•

Are PV systems more sustainable from a social perspective compared to current power plants providing electricity for the Universidad de la Habana?

1.3 Discussion of used literature

The websites used for estimating cost of different components used in the PV system (such as inverters and the PV modules) can be questionable. There are many different websites with prices of PV components and using other websites would probably give a different result. The websites were chosen in discussion with people with high experience in the PV sector. Some of the prices are consider quite expensive in the PV sector but that was chosen with the purpose to apply the precautionary principle.

The people interviewed for this project are all working in the PV sector and their answers can therefore be biased. A try to have an interview with a person from UNE was made but was

unsuccessful. Therefore, the project was unable to receive information from other perspectives. Some of the literature used in the project are not published or peer reviewed. This can cause questionable values presented in this study. Due to lack of public information the literatures were not excluded in order to enable a completion of the study. To minimize the risk of error from these sources the information retrieved was confirmed from different parties.

1.4 Nomenclature

𝐴𝑖 = the ratio between the solar constant 𝐺𝑠𝑐 and the extraterrestrial radiation, 𝐺𝑜𝑛

𝐶𝐵= Cost for building permission

𝐶𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡 = Cost of the change of the equipment

𝐶𝑒= Total cost for equipment (world market prize), such as cables, inverter etc.

𝐶𝑓𝑢𝑒𝑙 = Cost of fuel [curency/kWh]

𝐶𝑖 = Cost for installation of the PV system at sight 𝐶𝑖𝑛= Yearly insurance cost

𝐶𝑙 = Cost for lightning protection at sight

𝐶𝑚𝑎𝑖𝑛𝑡𝑒𝑛𝑎𝑛𝑐𝑒 = Yearly maintenance cost per installed PV module 𝐶_{𝑝𝑙𝑎𝑛}= Total cost for planning of the project

𝐶𝑃𝑉= Cost for one PV module

𝐶𝑠ℎ𝑖𝑝= Total cost for foreign shipment of equipment including PV modules 𝐶𝑡= Cost for toll

𝐶𝑇 = Total cost of installation, investment

𝐶𝑡𝑟𝑎𝑛𝑠= Total cost for domestic transportation to given sight of installation 𝐶𝐼= Cash inflow

CO2-e = CO2 equivalent 𝐶𝑂= Cash outflow c-Si = crystalline silicon

D= the horizontal distance from the PV module and the object 𝐷𝑐 = Desired deep discharge of battery [%]

E = Diffuse radiation, the solar radiation after its direction has been changed by scattering by the atmosphere on a horizontal surface

𝐸 = The desired energy demand of the battery [kWh]

𝐸_{𝑒𝑛𝑒𝑟𝑔𝑦}= Total annual energy output generated by the PV system Ei,s = Diffuse radiation on a inclined surface

EU = European Union

𝐺𝑜𝑛 = The extraterrestrial radiation, the intensity of the solar radiation on top of the atmosphere.

𝐺𝑠𝑐 = The solar constant, 1367 W/m² H2SO4 = diluted sulphuric acid

I = Global radiation, the total solar radiation on a horizontal surface Ii,s = Global radiation on a inclined surface

INOCT = 800 W/m² of solar radiation 𝐾 = expense or income

𝐿 = Latitude, the angular location north or south of the equator according to WGS84 (World Geodetic System 1984) 𝐿𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 = Longitude of the location

𝐿𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑚𝑒𝑟𝑖𝑑𝑖𝑎𝑛 = Standard meridian for the local time zone LCOE = Levelized Cost of Electricity (LCOE)

MPPT = Maximum power point tracker 𝑁𝐶𝐹 = Net Cash Flow

NOCT = Nominal Operating Cell Temperature Pb = lead

PB = Pay-back PbO2 = lead dioxide PV = Photovoltaic

Rb = the ratio between the direct radiation on a horizontal plane and the direct radiation on a tilted surface S = Beam radiation, the direct solar radiation without being scattered by the atmosphere on a horizontal surface Si,s = Beam radiation on a inclined surface

SMHI = Sveriges Meterologiska och Hydrologiska Institut (The Meteorological and Hydrological Institute of Sweden) STC = Standard Test Conditions

Ta = ambient temperature

Ta,NOCT = The ambient temperature is set to 20°𝐶 and the wind speed is 1 m/s 𝑇𝑐,𝑁𝑂𝐶𝑇 = Depends on the PV cell, between 43°𝐶 and 48°𝐶

𝑇𝑙𝑖𝑓𝑒 = Economical lifespan 𝑇𝑃𝐵= Payback time

UNE = Union Electrics, Cuban government owned electricity company 𝑉 = The voltage [V]

WEEE = Waste Electrical and Electronic Equipment

Wp = Watt-Peak, describes the peak power of the module under optimal conditions 𝑑 = Yearly degradation rate of the efficiency of a PV module

h= is the height difference between the object and the PV module

h = The hour angle describes the rotation of the earth around its own axis in relation to the sun's movement over the sky 𝑖 = Year

𝑛 = Lifespan of PV module 𝑟 = Discount rate

t = local time, from 0-23 [h]

𝑡𝑙𝑜𝑐𝑎𝑙 𝑡𝑖𝑚𝑒 = The local time for the location in question 𝑥 = Number of PV modules

∅ = The elevation angle, the angle between the horizontal plane and the solar beam

𝜃 = The angle of incidence, the angle between the normal to the inclined surface (PV cells) and the solar beam 𝜃𝑧 = Solar zenith angle, the angle between the solar beam and the normal from the horizontal plane

𝛾_𝑠𝑢𝑛 = Azimuth angle of the sun, the projection of the sun’s position in the sky on the horizontal plane. The angle is oriented from south with positive direction towards west

𝛾𝑠𝑢𝑟𝑓 = Azimuth angle of the inclined surface. The angle is oriented from south with positive direction towards west 𝛿 = Declination angle, the angle between the sun’s radiation and the equatorial plane

𝛼 = the slope on the PV cell 𝜌𝑔 = albedo

2. The method

The main purpose will consist of making economic and technical calculations for the installation of the PV modules on the buildings most suitable at The University of Havana. The PV module that will be investigated in this study is the crystalline silicon cells, since this is the most common used in PV system in Cuba (Díaz Suárez, 2018). All calculations and optimizations will be done using the software Matlab version R2016a. The study is a quantitative study where the data used is collected through literature studies, measurements and continuous personal contact with several experienced persons at the university which work with the PV development in Cuba.

2.1 Method for determine accuracy of the designed model and output energy

Hourly weather data including solar radiation, altitude angle and solar azimuth angle was retrieved from SMHI (Andersson, 2018). The location of the measured solar radiation was at SMHI’s

headquarter located in Norrköping, Sweden. The available weather data was for the years 2007-2017.

The designed model was made in the software program Matlab version R2016a.

The energy output of the designed model was calculated with equation [3.3.1.2], the total solar

radiation on a tilted surface and the efficiency of a PV module was calculated with equations [3.1.1.1]- [3.1.1.8], [3.1.2.1]- [3.1.2.7] and [3.3.1.1]. A comparison between different energy companies’

calculated energy output with the designed model’s energy output was done to be able to determine the accuracy of the model.

To verify the accuracy of the designed model it was tested on a fictive house in Sweden located in Norrköping. The location of the house was chosen to a place close to where the measurements are conducted by SMHI to minimize the errors in the calculations. Only one orientation was examined (south), and the values used can be seen in appendix . The values were retrieved from Söder (2014) and Homer Energy program (2018).

A comparison between calculated angles and the angles measured by SMHI of the zenith angle and solar azimuth angle were also made to validate the equation [3.1.1.6] and [3.1.1.7]. To check the accuracy of measured and calculated values of the altitude angle ( ∅) and the solar azimuth angle ( 𝛾

𝑠𝑢𝑛

) a sun path chart was plotted over the year to enable a comparison with measured values from SMHI.

2.2 Installation and technical calculations

The possible roof for installation was chosen according to desired purpose of the PV system (backup for certain equipment in different laboratories) and in discussion with people at the university. Three installation scenarios with different inclined angles were simulated in Matlab:

- Scenario - An installation with all PV modules orientated towards south.

- Scenario - An installation with a pyramid shaped installation of PV modules (see section 3.3.3 for explanation and shown in figure 8) where 50% of the PV modules were oriented towards north and the rest towards south.

- Scenario - An installation with a pyramid shaped installation of PV modules (see section 3.3.3 for explanation and shown in figure 8) where 50% of the PV modules were directed towards east and the others to west.

To conclude the maximum installation area and the maximum number of PV modules for the three

scenarios, a shading analysis was conducted to decide the risk of shading on the investigated roof from

objects near the building. The distance was measured from every object in relationship to the building

investigated to compare to the result from the minimum distance (D

1

, D

2

, D

3

and D

4

) calculated with

equations [3.3.3.1a] and [3.3.3.1b]. A safety distance (for lightning protection equipment) from the

roof edge was decided to 1,8 meters and is explained in section 3.3.3. To calculate the minimum

spacing (d

min

) between the PV modules two types of shelf-shading were considered and calculated

using equations [3.3.3.2a] and [3.3.3.2b]. A minimum spacing was decided to 0,5 meters in order to enable maintenance of the PV modules.

A different location than Havana was chosen due to the lack of hourly weather data measured in Cuba.

Key West (USA) was chosen after discussion with the tutor and a comparison between the locations’

sun hours, average radiation per day and geographical location. The weather data including solar radiation, zenith angle and solar azimuth angle for Key West which was used for the equations was downloaded from the National Centers for Environmental Information (National Centers for Environmental Information, 2005) and the exact location is Key West International Airport (see appendix for geographical coordinates). Year 2000-2005 was chosen due to lack of temperature and solar radiation data for later years. Leap years were excluded in the calculations. A small number of hourly temperature values were interpolated using standard linear-interpolation. When the lack of values for temperature were more than five hours in a row, an average of the specific hour from different years was used in order to reach a nominal value. The weather data for Havana was collected from the Cuban meteorology center and the radiation data was given in kWh/m

²

for an average day per month (Pelaez, 2018).

The total daily electricity consumption was measured into three time spans; “Pico” (peak): 5 pm -10 pm, “Dia” (day): 5 am - 5 pm and “Madrugada” (early morning/night): 10 pm – 5 am. An average value for every hour in each time span was calculated. For the calculations with a backup system the data used for electricity consumption was modified with the assumption of one power-cut once a week with a time span of 8 hours during the “Dia” time span, these values were set to zero. For the

remaining four hours of the “Dia” time span a nominal value was calculated for the specific hours. The consumption data was modified to enable calculations for division of energy for every hour and to reach the desired function of the backup system.

The division of energy consumption from the national grid, PV system and battery were calculated for each hour and was matched with the modified consumption data, the calculations of the hourly energy output of the PV system and the battery capacity. When a power cut occurred in the consumption data (consumption data equaled zero) the energy production from the PV system was matched with an average hourly consumption. If the average hourly consumption was higher than the production from the PV system, the battery would match the remaining energy demand. This assumption was possible since the battery capacity was designed to match a power cut of 8 hours without support from the PV system. The battery capacity was calculated by using equation [3.3.2.1] and an average energy demand during the “Dia” time span was used since this is the highest energy consumption during one day at the Institute of Science and Technology of Materials. The energy for charging the battery was overlooked since the battery was concluded to be used for a small number of hours compared to the energy generated by the PV system and calculating a charge time for batteries is very complexed.

Type of battery was chosen by a literature study and discussion with experienced persons to meet the desired purpose. The capacity of the national grid and the charge capacity have been assumed to be sufficient for an installation of a PV system at The University of Havana.

The technical calculations consist of a combination of the efficiency of a PV module using equation

[3.3.1.1], the output of the PV system calculated with equation [3.3.1.2] and the total solar radiation on

a tilted surface (PV module) using the equations [3.1.1.1]- [3.1.1.8] and [3.1.2.1]- [3.1.2.7]. Technical

values were collected from a literature study and personal contacts and the average values were then

calculated and used in designed model, see appendix . The cooling effect on the PV modules from

the wind was excluded in the calculations due to rapid change of weather conditions in Cuba (Díaz

Suárez, 2018). An average albedo for Cuba was chosen to a fixed value (see section 3.1.2 and figure 4)

(Díaz Suárez, 2018). For the PV backup system bidirectional inverters and control systems were

included in the calculations in order to balance the system (Díaz Suárez, 2018). All technical

specifications and values used in calculations are summarized in appendix .

2.3 Economic calculations

The collection of data for the economical calculations consist of electricity consumption for the buildings, investigation about taxes, subsidizing and the electric price. The information about the electric market, taxes and regulations in Cuba were retrieved through dialogues with experienced people and a literature study. A precautionary principle was used in order to evaluate the worst-case- scenario when deciding the price for shipment by boat. Two different scenarios were investigated for the shipment, one from the London port and the other from the Shanghai port and three different volumes for the container were examine (20ft, 40 ft and 45 ft). The prices for the three volumes for the container differ depending on the maximum allowed value in the container, the maximum values used were 10 000 USD and 100 000 USD. An online shipment calculation from the World Freight Rates (2013) was used to calculate the shipment cost for the two scenarios with different containers and allowed maximum value, an average price was determined. The transportation cost from the seaport to the university was calculating by using Google Maps to estimate the distance, assuming one big truck was used for the transportation and calculating the petrol cost for this distance and truck. It was assumed that two persons was working for packing, unpacking and driving the truck.

Prices for equipment and material for the PV installation have been collected from a PV webstore (Europe Solar Store, 2018). For the materials inexistent on the website other nominal values were calculated using other websites, see appendix . The website was chosen after discussion with the engineer at the university. Appendix displays all assumed values.

Methods used to conclude the economical result were Levelized Cost of Electricity (LCOE) and the Payback method for the different scenarios for the PV modules. Equations for the methods were retrieved through a literature study. The calculations were made by using equations [3.4.1.1]- [3.4.1.6]

for LCOE and equations [3.4.2.1] and [3.4.2.2] for the PB method. The cost of generated electricity from UNE varies between 0,15-0,21 USD/kWh. In the PB calculations the highest electricity price (0,21 USD/kWh) from UNE was used. For the university the cost of electricity is subsidized to 90%

but was not taken into account in this study. The installation cost of the PV system will be financed by the government and since The University of Havana and UNE are state owned, the real generated cost of electricity will indirect affect the investment. Calculating with the subsidized cost will be irrelevant and redundant. For the PB method every value exceeding 26 years were normed to 26, since values above 26 years were irrelevant. Values used in the calculations for PB method and LCOE are displayed in appendix .

A sensitivity analysis was conducted to analyse the changes of economical profitability with changing prices and discount rate. The analyse was completed for the most economical profitable option. The value chosen to analyse in LCOE was the changing discount rate from 0-10%. An evaluation of the decrease in the prices of PV modules and lead-acid batteries were also made. The PB-method was analyzed in the sensitivity analysis where the future prediction of the oil price was examined for a future high price and a future low price of the oil. From U.S. Energy Information Administration (EIA, 2017a) & (EIA, 2017b) the prices were retrieved. Since Cuba buys subsidized oil from

Venezuela the future high and low price was calculated with a decrease and increase in percentage and added to the current variated price (0,15-0,21 USD/kWh). It was also examined how the PB time would be affected if the price for selling generated electricity changed. The variation in the values of LCOE and PB time per installed capacity, kW

p

were examined.

2.4 Method for social and ecological results

Life cycle assessments of PV modules have been done several times and since there are a great

number of studies done in the same subject the ecological impact was investigated through a literature

study of earlier life cycle assessments of the PV module. An evaluation on the recycling possibilities

of PV modules and the social impact of the PV system were carried out through a literature study. A

minor literature study of crude oil was also conducted in order to enable a comparison between the

two energy options. In the comparison it was assumed that all of the national generated electricity

comes from crude oil in order to limit the extent of the project. The social results were conducted

through a literature study and personal contact with experienced persons in the PV business.

3. Theoretical background

3.1 Solar radiation

When calculating the output energy from a PV system there are several important parameters to consider. One of the most important aspects is the solar radiation which consists of two parts: extra- terrestrial solar radiation (above the atmosphere) and global solar radiation (below the atmosphere at the surface) (Khatib & Elmenreich, 2016) . The amount of solar radiation from the sun reaching the earth surface varies over the day and the year, due to variations in the sun’s position in the sky relative to the geographic location and varying cloudiness. When the extra-terrestrial solar radiation beam reaches the atmosphere, many components of the solar beam are absorbed, diminished and scattered.

The solar radiation from the sun without being scattered by the atmosphere is often called direct solar radiation (S) and the solar radiation scattered by the atmosphere is referred to as the diffuse radiation (E). The sum of direct solar radiation and diffuse radiation (the total solar radiation on a horizontal surface) is referred to as global radiation, I (Beckman & Duffie, 2013). The position of the sun is a function of time and the geographic location of the observer and there are several angles to consider when constructing a model (SMHI, 2018).

3.1.1 The sun’s position

It takes almost one year (365,25 days to be precise) for the earth to travel around the sun in an almost perfect circle. The axis of the earth is tilted and because of this the height of the sun changes during the year. The declination angle ( 𝛿) gives the tilt of the earth compared to the sun and is given by equation [3.1.1.1], see figure 1. The declination angle varies depending on the season and is a function of the day of the year (n). (Beckman & Duffie, 2013)

𝛿 = 23,45°

₁₈₀^𝜋

sin (

₃₆₅^2𝜋

(284 + 𝑛)) [𝑅𝑎𝑑𝑖𝑎𝑛] [3.1.1.1]

Figure 1.The declination angle of the earth rotating around the sun (Elemenreich & Khatib, 2016).

The hour angle (h) explains the earth’s rotation (15° per hour) around its own axis relatively to the sun’s location. In the morning, the hour angle is negative and in the afternoon the angle is positive. To calculate the hour angle equation [3.1.1.2] is used. Where the local solar time ( 𝑡

_𝐿𝑆𝑇

) is defined as the time in which the sun at noon has reached its highest point of the day and is located exactly in the south (Mertens, 2014). The local solar time is determined with equation [3.1.1.3]. The parameter E is a correction of time in minutes and is calculated with equation [3.1.1.4]. Where the parameter B is calculated with equation [3.1.1.5] where n is the day of the year (Beckman & Duffie, 2013).

h = ( 𝑡

_𝐿𝑆𝑇

– 12) *15 [degrees] [3.1.1.2]

𝑡

_𝐿𝑆𝑇

= 4(𝐿

𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑚𝑒𝑟𝑖𝑑𝑖𝑎𝑛

− 𝐿

𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛

) + 𝑡

_{𝑙𝑜𝑐𝑎𝑙 𝑡𝑖𝑚𝑒}

+ 𝐸 [3.1.1.3]

𝐸 = 229,2 (0,000075 + 0,001868 cos 𝐵 − 0,032077 sin 𝐵 − 0,014615 cos 2𝐵 − 0,04089 sin 2𝐵

[3.1.1.4]

𝐵 = (𝑛 − 1)

³⁶⁰₃₆₅

[3.1.1.5]

Where,

𝐿

𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑚𝑒𝑟𝑖𝑑𝑖𝑎𝑛

= Standard meridian for the local time zone 𝐿

𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛

= Longitude of the location

𝑡

_{𝑙𝑜𝑐𝑎𝑙 𝑡𝑖𝑚𝑒}

= The local time for the location in question The hour angle (h), latitude (L), the solar zenith angle ( 𝜃

_𝑧

) and the declination angle (𝛿 ) is used in equation [3.1.1.7] to calculate the solar azimuth angle ( 𝛾

_𝑠𝑢𝑛

). 𝜃

_𝑧

is the angle between the normal to the horizontal plane and the solar beam, see figure 3. It is the complement to the altitude angle ( ∅), shown in figure 2. The solar zenith angle is calculated with equation

[3.1.1.6]. 𝛾

_𝑠𝑢𝑛

is the projection of the sun’s position in the sky on the horizontal plane. The solar azimuth angle is negative when the hour angle is negative and positive when the hour angle is positive. The solar azimuth angle can have values in the range of 180 ° to -180° and where south is 0 degrees and is orientated clockwise (see figure 2). (Beckman & Duffie, 2013)

𝜃

𝑧

= cos

⁻¹

(cos 𝐿 cos 𝛿 cos ℎ + sin 𝐿 sin 𝛿) [3.1.1.6]

𝛾

_𝑠𝑢𝑛

= 𝑠𝑖𝑔𝑛(ℎ) |cos

⁻¹

(

^{𝑐𝑜𝑠𝜃}_{𝑠𝑖𝑛𝜃}^{𝑧 𝑠𝑖𝑛𝐿−𝑠𝑖𝑛𝛿}

𝑧 𝑐𝑜𝑠𝐿

)| [3.1.1.7]

The angles explained with equations [3.1.1.1] and [3.1.1.2] are related to the angle of incidence (𝜃) between the normal (N) to the inclined surface and the direct solar radiation also known as altitude angle ( ∅), see figure 2 and 3. The relationship between the different angles is shown in equation [3.1.1.8] where 𝛼 is the inclined angle of the PV modules and 𝛾

𝑠𝑢𝑟𝑓

is the azimuth angle of the surface. When using equation [3.1.1.8] it is crucial to ensure that the sun is not blocked by the earth, the hour angle needs to be between sunrise and sunset (Beckman & Duffie, 2013).

cos 𝜃 = sin 𝛿 𝑠𝑖𝑛 𝐿 𝑐𝑜𝑠 𝛼 − 𝑠𝑖𝑛 𝛿 𝑐𝑜𝑠 𝐿 𝑠𝑖𝑛 𝛼 𝑐𝑜𝑠 𝛾

_{𝑠𝑢𝑟𝑓}

+ 𝑐𝑜𝑠 𝛿 cos 𝐿 cos 𝛼 cos ℎ +

cos 𝛿 sin 𝐿 sin 𝛼 cos 𝛾

_{𝑠𝑢𝑟𝑓}

cos ℎ + cos 𝛿 sin 𝛼 sin 𝛾

_{𝑠𝑢𝑟𝑓}

sin ℎ [3.1.1.8]

Figure 2. How the solar azimuth angle orientates around the sun clockwise, where south is 0 degree (Beckman &

Duffie, 2013).

Figure 3. How the different angles are related to the earth’s rotation around the sun and the PV module (Beckman & Duffie, 2013).

3.1.2 Conversion of solar radiation on the horizontal plane to an inclined surface Direct radiation measured on a horizontal surface can be converted to an inclined surface using equation [3.1.2.1]. 𝑅

𝑏

is the ratio between the direct radiation on a horizontal plane and the direct radiation on an inclined surface, which can be simplified by cosine of the angle of incidence and the solar zenith angle, as presented in equation [3.1.2.2]. 𝑅

_𝑏

is only defined when both 𝑐𝑜𝑠𝜃 > 0 and 𝑐𝑜𝑠𝜃

_𝑧

> 0, when the sun is above the horizontal. This method is suitable for most hours of the day, but the hours around sunrise and sunset the equation for 𝑅

_𝑏

can give unrepresentative values. To correct this value, it is often set to zero or as a negligible part of the total daily output. (Beckman &

Duffie, 2013)

𝑆

_𝑖,𝑠

= 𝑅

_𝑏

𝑆 [3.1.2.1]

𝑅

_𝑏

=

_{𝑐𝑜𝑠𝜃}^{𝑐𝑜𝑠𝜃}

𝑧

[3.1.2.2]

Diffuse radiation is more complexed to convert from a horizontal to a tilted surface than direct radiation. Therefore, a simplified model, called Hay and Davies model is used with the assumption that the diffuse radiation is isotropic (Beckman & Duffie, 2013). According to Beckman, et al. (1990), this simplified model is almost as accurate as the more complexed models. The conversion of diffuse radiation measured on a horizontal surface can be converted to a tilted surface using equation

[3.1.2.3]. 𝐴

_𝑖

is the ratio between the solar constant 𝐺

_𝑠𝑐

and the extraterrestrial radiation, 𝐺

_𝑜𝑛

shown in equation [3.1.2.4]. The solar constant is chosen to 1367 W/m

²

which has an uncertainty under 1%

according to The World Radiation Center. The extraterrestrial radiation varies due to the earth's elliptical orbit around the sun resulting in that the distance between the sun and earth varies

throughout the year. Equation [3.1.2.5] explains how to calculate the extraterrestrial radiation each day and has an error of ±0,01% . B is calculated according to equation [3.1.1.5] and n represents the nth day of the year (Beckman & Duffie, 2013).

𝐸𝑖,𝑠= 𝐸 [(1 − 𝐴𝑖) (^{1+𝑐𝑜𝑠𝛼}₂ ) + 𝐴𝑖𝑅𝑏] [3.1.2.3]

𝐴𝑖=_𝐺^𝐺𝑠𝑐

𝑜𝑛

[3.1.2.4]

𝐺𝑜𝑛= 𝐺𝑠𝑐(1,000110 + 0,034221 cos(𝐵) + 0,001280𝑠𝑖𝑛𝐵 + 0,000719𝑐𝑜𝑠2𝐵 + 0,000077𝑠𝑖𝑛2𝐵)

[3.1.2.5]

Reflected radiation is complex to calculate just like the diffuse radiation. Therefore, the same

assumption is made for reflected radiation that all radiation is isotropic. If this assumption is made,

equation [3.1.2.6] can be used to calculate the reflected radiation on a tilted surface, 𝐸

_{𝑅𝑖,𝑠}

(Beckman &

Duffie, 2013). The average albedo ( 𝜌

_𝑔

) varies depending on the latitude. Albedo is a measurement of a material’s ability to reflect radiation (NE Nationalencyklopedin AB, 2018). Figure 4 shows the

average value depending on the latitude (Climate Data Information, 2015).

𝐸

_{𝑅𝑖,𝑠}

=

^{𝐼𝜌𝑔(1−cos𝛼)}₂

[3.1.2.6]

Figure 4. Displays how the average albedo varies depending on the latitude (Climate Data Information, 2015).

Global radiation is the total solar radiation reaching a horizontal surface (SMHI, 2018). The sum of direct, diffuse and reflected radiation gives the total global radiation. The calculation for global radiation on a tilted surface is shown in equation [3.1.2.7] (Beckman & Duffie, 2013).

𝐼

_𝑖,𝑠

= 𝑆

_𝑖,𝑠

+ 𝐸

_𝑖,𝑠

+ 𝐸

_{𝑅𝑖,𝑠}

[3.1.2.7]

3.2 PV cells

The basic function of a PV cell is shown in figure 5, it is made up of crystalline structure which is dipped into different semiconductor material, creating two layers with a contact zone between them.

These two layers are called N and P and are treated with different substances which creates a shortage of free electrons on the P-layer and an excess of free electrons on the N-layer. This leads to that one of the semiconductor will have a positive polarity and the other, negative polarity. When solar radiation hits the surface of the cell some photons absorbed by the material will cause the electrons to move freely due to an increase in energy which will lead to a flow of electrons, an electric current. The electrical contact with the PV cell is made through a metal base on the bottom of the cell and by metal grids on the top of the cell. (Mir-Artigues & Río del, 2016)

Normally the cells are connected in series of 36, 48, 60 or 72 cells (Mertens, 2014). In Cuba the most

common number of cells in one PV module is 60 or 72 due to the standard in the national grid and

because of the climate and weather changes in Cuba. A PV module of 60 cells covers an average area

of 1 m x 1,6-1,7 m and 72 cells cover an average area of 1 m x 2 m, depending on the brand and type

(Díaz Suárez, 2018). After the cells are connected they are encapsulated with different materials such

as glass, aluminum, EVA (ethylene-vinyl acetate) and Tedlar (polyvinyl fluoride) in order to protect

the cells from weather and humidity (Mir-Artigues & Río del, 2016).

Figure 5. Basic description of a PV cell (Ulin, 2017).

There are many different types of PV cells. The most common PV cell used around the globe and in Cuba is crystalline silicon (c-Si) PV cell (Díaz Suárez, 2018) & (Mir-Artigues & Río del, 2016). The crystalline silicon cells are divided into two, monocrystalline and polycrystalline cells. The difference between mono- and polycrystalline cells is that mono is made of one single crystalline silicon and poly consist of a great number of silicon crystals. Monocrystalline cells have a higher efficiency but are more expensive due to the higher process cost, they have a maximum theoretical efficiency of approximately 30%. Polycrystalline cells have a maximum theoretical efficiency of approximately 26%. Once the PV cells are encapsulated to protect for environmental conditions their efficiency decrease. When the PV cells are installed the ambient temperature and the weather at the location will cause the efficiency to decrease even more (Mertens, 2014).

Other PV cells used commercially are Gallium arsenide cells and thin-film cells. Gallium arsenide cells have a very high efficiency but are very expensive due to high costs on the materials used and the manufacturing cost. Thin-film cells are the second most commonly used PV cell. The width of a thin- film cell is only around 3 μm and since the cells are so thin they require much less materials and energy than crystalline cells and are therefore usually cheaper. One problem is that their performance reduces strongly in the primary days of use, around 10-20% reduce in efficiency (Mir-Artigues & Río del, 2016).

The efficiency of a PV cell is affected by the temperature. This is because of the reduction of

operating voltage of the cell due to increased temperature. A PV cell loses some of its performance if the temperature is above 25℃. One-degree increase causes a loss of 0,45-0,5% energy generated by the PV cell. The performance of the PV cell is also depending on the degradation every year. Due to an outdoor exposure such as wind, sun, dirt and humidity the performance of a PV cell will decrease every year. How much the performance will decrease depends on the climate and type of PV cell. For crystalline silicon cells the degradation rate is around 0,75-0,8% per year from the initial maximum performance. (Mir-Artigues & Río del, 2016)

3.2.1 Bypass diode

Bypass diodes are used in PV modules to minimize the effects of shading and so-called hotspots.

Hotspots are extreme heating of a PV cell due to shading and caused by other PV cells in series connection with the shaded PV cell. Since PV cells normally are connected in series, the cell being shaded affects the current in all the other cells. Bypass diodes keeps the current at the desired level and minimizes the effect of shading. In a PV module only a few bypass diodes are connected to the

module, located in the module connection box which is placed at the back of the PV module.

Normally, one bypass diode is connected to 12, 18 or 24 cells. Therefore, PV modules are still affected

by shading but the effect is lower than it would be without bypass diodes. To connect one bypass

diode for every PV cell they would have to be encapsulate with the module. This makes it impossible

to replace the bypass diodes in case of a failure and it is hard to dissipate the heat created by the

bypass diodes in case of shading. A parallel connection of all PV cells would cause a very high current and thick cables would be needed to transport this current. Another problem would be that the voltage would be very low due to parallel connection which will be very hard to transform if connected to the grid. (Mertens, 2014)

3.3 PV system

There are different types of PV system depending on the desired performance of the system; stand- alone PV system, grid-connected PV system and grid-connected PV system with energy storage.

Stand-alone system consists of PV modules, loads and storage batteries. In this system it is very important that the batteries do not get overcharged since it can cause great damage to the batteries.

To avoid this problem high-voltage or power- shunting devices are used to cut of the current to the batteries when they are fully charged to avoid damage (Beckman & Duffie, 2013) . Grid-

connected PV system shown in figure 6, consist of one to several PV modules connected in parallel or series to the inverter and a connection to the grid

(Díaz Suárez, 2018). The inverter has a MPPT to maximize the output power from the PV module and converts the power from the PV module so the voltage is the required one to connect to the grid (Beckman & Duffie, 2013). The inverter is important because it converts direct current delivered by the PV modules into desired shape of alternating current and feeds it into the public grid (Mertens, 2014).

A grid-connected PV system with energy storage shown in figure 7, consist of the same components as the grid-connected PV system without energy storage but also has storage batteries and a more complex inverter, a bidirectional inverter. The system offers great advantage such as

uninterrupted power supply. The bidirectional inverter consists of an inverter, transformer and a control system synchronizing where the electricity should come from. The system also includes a measurement equipment measuring all values in the system, current, voltage etc. It works as a support to the inverter and signals to the inverter in case of a problem. If there is a power cut on the national grid the control system will immediately (in

less than 17 ms) take control of the network and connect the battery as energy source and the total system will not be affected of the power cut. The control system will also regulate when the battery should be charged and not, avoiding overcharging the battery. (Díaz Suárez, 2017)

Since PV systems are expensive it is very important to minimize the losses in the system. There are five parameters that explains the losses in a PV system (Mir-Artigues & Río del, 2016):

- Losses caused by weather and climate, which is explained in section 3.2.

- Losses from the installation and equipment in the PV system, such as inverters, losses from cables and shading. The losses vary depending on how the installation is made and what kind

Figure 6. Grid-connected PV system with an inverter (Díaz Suárez, 2018).

Figure 7. Grid-connected PV system with energy storage and inverters (Díaz Suárez, 2018).

losses of 4-5%. For cables, DC wires cause losses around 1,5% due to the resistances in the wires and AC wires around 2%.

- Losses due to lack of maintenance of the PV system. Dirt and feces from birds can cause a loss of 4% if the PV system is not maintained and cleaned properly.

- Losses due to unexpected events. This parameter is hard to take in consideration when calculating and estimating the efficiency and economic profitability of a PV system.

- Losses due to the degradation rate of the cells over the years, which is explained in section 3.2.

3.3.1 The output from the PV system

When calculating the efficiency of a PV module as in equation [3.3.1.1] it is typical to use values measured at a standard test conditions (STC), where the cell is tested at the temperature 𝑇

𝑐,𝑆𝑇𝐶

= 25°𝐶 and exposed to solar radiation of 1000 W/m

²

. The nominal operating cell temperature (NOCT) is the temperature of the cell when it is exposed to 800 W/m

²

of solar radiation (I

NOCT

), the ambient

temperature (T

a,NOCT

) is set to 20 °𝐶 and the wind speed is 1 m/s. Depending on the PV cell the 𝑇

_{𝑐,𝑁𝑂𝐶𝑇}

varies between 43 °𝐶 and 48°𝐶 (Díaz Suárez, 2017) & (Homer Energy, 2018). The values for the PV modules’s efficiency at STC (n

STC

) and the temperature coefficient (𝜇) depends on the PV cell and is given by the PV module manufacturer. T

a

is the ambient temperature (Beckman & Duffie, 2013).

𝜂

_𝑐

= 𝜂

_𝑆𝑇𝐶

[1 − 𝜇(𝑇

_𝑎

− 𝑇

_{𝑐,𝑆𝑇𝐶}

+ 𝐼

_𝑖,𝑠^{(𝑇𝑐,𝑁𝑂𝐶𝑇}_𝐼 ^{−𝑇𝑎,𝑁𝑂𝐶𝑇)}

𝑁𝑂𝐶𝑇

(1 − 𝜂

_𝑆𝑇𝐶

) [3.3.1.1]

The electricity production from the PV system depends on the solar radiation on the inclined surface ( 𝐼

_𝑖,𝑠

) , the area of the PV module (A), the number of PV modules (n) and the PV’s efficiency ( 𝜂

_𝑐

).

𝜂

𝑎𝑑𝑑

depends on the efficiency of the other parts in the system such as inverters. The output of the PV system is calculated with equation [3.3.1.2]. (Söder, 2014)

𝑃 = 𝑛𝐴 𝐼

_𝑖,𝑠

𝜂

_𝑐

𝜂

_𝑎𝑑𝑑

[3.3.1.2]

3.3.2 Battery

There are many different types of batteries that can be used in a PV system such as lead-acid batteries, nickel-iron batteries and lithium-ion batteries. Lithium-ion batteries have a high performance, they used to be very expensive but are now used more frequently on the market since the price is decreasing. Nickel-iron batteries have a very high life cycle, up to 50 years but has a low energy density and efficiency (Díaz Suárez, 2017). In PV systems the most frequently used is Lead-Acid battery. This is because of their low price which is of high importance since the life cycle of most batteries are under 10 years (Mertens, 2014).

The basic function of a battery is to store electrical energy by filling the battery with an electrolyte and having two different nodes consisting of different materials. These nodes create the negative node (anode) and the positive (cathode) when reacting with the electrolyte. By connecting them with a closed circuit a current of electrons is created, electricity. To charge the battery the circuit and the reactions work backwards instead (Burrow, et al., 2017). The life cycle of a battery is determined by the time until the battery works under 80% of its original nominal capacity. Frequent deep discharges (the region of withdrawn capacity of 80% or more) can result in extreme reduction of the life cycle of the battery and therefore precaution of these activities should always be made. The capacity of a battery depends on two variables, the temperature and the discharge current. At low temperatures the capacity of the battery is always lower (Mertens, 2014).

Lead-acid batteries consist of an electrolyte of H2SO4 (diluted sulphuric acid). The anode is made of

lead (Pb) and the cathode is made of lead dioxide (PbO

2

). In the electrolyte the actual storage of

energy occurs. When the battery is being charged the density of the electrolyte is increasing. There are

many different type of lead-acid batteries. The best choice for a more frequent and continuous use for

over 15-20 years are the reinforced plate batteries. There are two different kinds of these batteries,