Evaluating the Economic Feasibility for utilizing PV Power Optimizers in Large-scale PV Plants for The Cases of Soiling, Mismatching, and Degradation

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Master Level Thesis

European Solar Engineering School

No. 252, Sept. 2018

Evaluating the Economic

Feasibility for utilizing PV Power

Optimizers in Large-scale PV

Plants for The Cases of Soiling,

Mismatching, and Degradation

Master thesis 30 credits, 2018 Solar Energy Engineering

Author: MHD Mouaz Alhamwi Supervisors: Désirée Kroner Examiner: Ewa Wäckelgård Course Code: EG4001 Examination date: 2018-09-17

Dalarna University Solar Energy

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Abstract

The solar PV modules are influenced by a variety of loss mechanisms by which the energy yield is affected. A PV system is the sum of individual PV modules which should ideally operate similarly, however, inhomogeneous soiling, mismatching, and degradation, which are the main focus in this study, lead to dissimilarities in PV modules operating behavior and thus, lead to losses which will be assessed intensively in terms of energy yield.

The dissimilarities in PV modules are referred to the ambient conditions or the PV modules characteristics which result in different modules’ maximum power point (MPP) and thus, different currents generated by each PV modules which cause the mismatching. However, the weakest PV module current governs the string current, and the weakest string voltage governs the voltage.

Power optimizers are electronic devices connected to the PV modules which adjust the voltages of the PV modules in order to obtain the same current as the weakest module and thus, extract the modules’ MPP. Hence, the overall performance of the PV plant is enhanced. On the other hand, the power optimizers add additional cost to the plant’s investment cost and thus, the extra energy yield achieved by utilizing the power optimizers must be sufficient to compensate the additional cost of the power optimizers. This is assessed by designing three systems, a reference system with SMA inverters, a system utilizes Tigo power optimizers and SMA inverters, and a system utilizes SolarEdge power optimizers and inverters. The study considers four different locations which are Borlänge, Madrid, Abu Dhabi, and New Delhi.

An Excel model is created and validated to emulate the inhomogeneous soiling and to evaluate the economic feasibility of the power optimizers. The model’s inputs are obtained from PVsyst and the precipitation data is obtained from Meteoblue and SMHI database. The economic model is based on the relation between Levelized Cost of Electricity (LCOE) which will be used to derive the discount rate. Graphs representing the discounted payback period as a function of the feed-in tariff for different discount rates is created in order to obtain the discounted payback period.

The amount of extra energy yielded by the Tigo and the SolarEdge systems is dependent on the soiling accumulated on the PV modules. Relative to the reference system, 6.5 % annual energy gain by the systems utilizing the power optimizers in soiling conditions, up to 2.1 % in the degradation conditions, and up to 9.7 % annual energy gain at 10 % mismatching rate. The extra energy yield is dependent on the location, however, the Tigo and the SolarEdge systems have yielded more energy than the reference system in all cases except one case when the mismatch losses is set to zero.

The precipitation pattern is very influential, and a scare precipitation leads to a reduction in the energy yield, in this case, the Tigo and the SolarEdge systems overall performance is enhanced and the extra energy gain becomes greater.

The Tigo system yield slightly more energy than the SolarEdge system in most cases, however, during the plant’s lifetime, the SolarEdge system could become more efficient than the Tigo system which is referred to the system’s sizing ratio. The degradation of the system or the soiling accumulation decreases the irradiation and thus, a slightly oversized PV array become suitable and deliver an optimal power to the inverters.

The SolarEdge system is feasible in all scenarios in terms of LCOE and discounted payback period, although its slightly lower performance relative to the Tigo system, this is referred to its low initial cost in comparison to the other systems. The Tigo system is mostly infeasible

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to its relatively high initial cost. However, feed-in tariffs higher than 20 € cent / kWh make all systems payback within less than 10 years.

The results have overall uncertainty within ± 6.5 % including PVsyst, Excel model, and the precipitation uncertainties. The uncertainty in the degradation and the mismatching calculations is limited to PVsyst uncertainty which is ± 5 %. The uncertainties in LCOE in the location of New Delhi, since it is the worst-case scenario, are 5.1 % and 4 % for the reference and the systems utilizing power optimizers, respectively.

Consequently, accommodating the uncertainties to the benefits gained by utilizing power optimizers indicates that the energy gain would oscillate in the range of 6 % - 6.9 % for the soiling calculations, 2 % - 2.2 % for the degradation simulations, and 9.2 % - 10.2 % for the mismatching simulations at 10 % mismatchrate.

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Acknowledgment

I would like to thank everybody who supported me during this work for their outstanding support including my family, my friends, and my supervisor Desiree Kroner.

I would like to sincerely thank my past teachers who provided every possible support and advice, who have provided me with the adequate knowledge for the completion of this work. I would like to thank PVsyst, SMHI, and Meteoblue team for providing me with the simulation software and the precipitation data required for this study and their support during this work.

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Abbreviations

Abbreviation Description

ANN Artificial neural network

ARC Anti-reflective coating

FLC Fuzzy logic controller

HC Hill climbing

Isc Short circuit current

IAM Incident angle modifier

IC Incremental conductance

LCOE Levelized cost of electricity

LID Light induced degradation

MPP Maximum power point

MPPT Maximum power point tracking

NAED Net annual energy yield

P&O Perturb and observe

PV Photovoltaic

PVSyst Photovoltaic system simulation software

STC Standard test conditions

Td Discounted payback period

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Nomenclature

Symbol Description Unit

𝜷_𝑽_𝒐𝒄 PV module’s voltage temperature coefficient %/ºC

𝝈 Standard deviation

𝝁 Mean soiling value %

𝑩 Annual benefits €

𝑪_𝒊𝒏𝒗 The inverter cost €

𝑪𝟎 Capital cost €

𝑪𝑶𝑴 Cost of operation and maintenance €

𝒅 Discount rate

I Current A

LCOE Levelized cost of electricity €/kWh

𝑵𝒎𝒐𝒅_𝒎𝒂𝒙 Maximum number of PV modules connected to one _inverter Module

𝑵_{𝒎𝒐𝒅,𝒔} Number of modules employed in each string

𝑵𝒑𝒗 Number of modules utilized in the system Module

𝑵_{𝒔𝒕𝒓𝒊𝒏𝒈} Maximum number of PV modules connected in series Module

𝑵_𝒊𝒏𝒗 Number of inverters needed Inverter

𝒏 The plant lifetime Years

𝑵𝑨𝑬𝑫 Net Annual Energy Yield kWh

P Power W

𝑷𝒊𝒏𝒗 Inverter rated power W

𝑷_𝒑𝒗 PV modules peak power W

𝑷_𝒊𝒏𝒗_𝒎𝒂𝒙 Inverter maximum input W

𝑷_{𝒑𝒍𝒂𝒏𝒕} PV plant targeted power kW

𝑷𝑹 Present value €

𝑷(𝒙) Probability function %

𝑺_𝒎𝒂𝒙 Maximum soiling %

𝑺_𝒎𝒊𝒏 Minimum soiling %

𝑺_𝒙 Maximum soiling in day x %

𝑺𝑻 Soiling saturation period Days

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𝑻_𝒔𝒕𝒄 Temperature at standard test conditions º

𝑼𝒔 Soiling calculations combined uncertainty %

𝑼_{𝑷𝑽𝒔𝒚𝒔𝒕} PVsyst uncertainty %

𝑼_{𝒎𝒐𝒅𝒆𝒍} Excel model uncertainty %

𝑼_𝒑𝒓𝒆 Precipitation uncertainty %

V Voltage V

𝑽𝒎𝒂𝒙 Maximum inverter input voltage V

𝑽_𝒐𝒄 Module open circuit voltage V

𝑽_𝒐𝒄_𝒎𝒂𝒙 Maximum open circuit voltage at worst case scenario V 𝑽_𝒊𝒏𝒗_𝒎𝒂𝒙 Maximum inverter voltage at worst case scenario V

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1 Introduction

Photovoltaic (PV) installations have been dramatically increased through the past years [1]. However, PV plants’ energy output is inextricably dependent on a modules’ electrical characteristics; which in turn are dependent on several factors such as electrical mismatching, modules’ degradation, and soiling [2].

The major influence of the previous factors can be observed on the current-voltage (I-V) and Power-Voltage (P-V) curves of modules where different maximum power point (MPP) will occur for each module, thereby different voltages and currents at MPP for each module will be observed. Consequently, for a string which consists of a number of modules in series, the string’s voltage would not be a major issue since the total string’s voltage is the sum of individual modules’ voltages; however, the weakest module with the lowest current will determine the total string’s current and thus, the string’s output power. [3].

In order to extract the maximum power from each string, a uniform current should be utilized in all modules in the string (and even for the cells which compose the module). Therefore, power optimizers are used to track the maximum power point of PV modules in order to extract the maximum energy. This is done by applying adjustments to the electrical characteristics of PV modules (voltage and current). [3],[4].

The employment of power optimizers in a modular level facilitates the tracking of MPP by compelling the module to operate at a voltage level corresponding to the global MPP. The energy gained by employing power optimizers is dependent on the tracking techniques and strategies which would define the efficiency of a power optimizer. [4], [5].

Utility-scale plants utilize a large number of modules which significantly increase the losses, mainly due to mismatching and non-uniform conditions due to the number of strings in parallel, whereas a negligible loss in power is observed in small-scale plants [6]. Consequently, the usage of power optimizers could be beneficial in such cases since many manufacturers claim up to 30 % extra energy yield when utilizing their power optimizers. In addition to various features like online monitoring and troubleshooting problems occurring at a modular level, together with 25 years warranty which corresponds to a PV modules warranty. [2]

PV plants operating under ideal conditions do not require additional investment in power optimizers, however, in practice, the plants are exposed to several operating conditions which decrease the energy yield. Based on that, utilizing power optimizers in PV plants become an interest.

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Aims

Due to a lack in literature studies regarding the level at which PV power optimizers become feasible in relation to a PV system losses, this thesis aims to investigate the feasibility of utilizing power optimizers in utility-scale PV plants regarding modules degradation, soiling, and mismatching, which are important factors in defining a plant’s energy yield which could be enhanced by utilizing power optimizers.

Several simulations with different scenarios will be carried out in order to define the extra energy gained by utilizing power optimizers as a percentage of the energy yield which would occur under ordinary operating conditions.

The extra cost occurred by utilizing the optimizers will be taken into account, and a breakeven point will be defined at which investing in power optimizers would be financially viable. The cost analysis will be based in different locations which correspond to different operating conditions and its corresponding losses.

Method

In order to obtain reliable results, a set of sequenced tasks will be undertaken. The following methodology steps will be performed to acquire results and achieve the desired aforementioned aims in the previous section.

 A comprehensive literature study on PV modules’ degradation rate, mismatching, and dust accumulation. This will give an overview of the mentioned phenomena. it will define the reasons behind a drop in PV output energy.

 The literature study will provide an approximate value of losses for each phenomenon for different projects in different locations.

 Utility-scale PV systems will be proposed and properly designed in this study with boundary conditions which will be defined in chapter 3 of this study. The proposed PV system will be simulated using PVsyst software. The simulation will take place in two phases. Phase one, the system will be simulated without utilizing power optimizers. The second phase will simulate the system with utilizing the power optimizers.

 The simulations will be carried out for different locations and climates in order to observe the impact of degradation, soiling, and mismatching on the proposed system.

 The initial values of PV modules’ degradation, mismatching, and soiling will be defined as the base case. This will be estimated based on values from the literature study performed in 2.1.3.

 A sensitivity analysis will be performed in order to assess the influence of soiling distribution, precipitation, and short circuit current and open circuit voltage dispersion on the system performance in terms of energy yield.

 The feed-in tariff differs for each country. Hence, cost analysis will be carried out in order to define the economic feasibility of utilizing power optimizers. The analysis will be based on the levelized cost of electricity as a function of the discount rate. Moreover, the systems’ discounted payback period as a function of the feed-in tariff and the discount rate.

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 The simulations results will be exported to Excel spreadsheet in order to gather different simulations’ result in one graph and carry out a comparison of different scenarios and economic analysis.

The discussion and conclusion sections will be based on the results acquired by performing the aforementioned method steps. Consequently, the level of degradation, mismatching, and soiling rates relative to the system’s LCOE which make the usage of power optimizers cost effective will be assessed.

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2 Previous work

Several factors affect a PV modules’ performance and lead to a decrease in the energy yield. These factors should be considered in order to estimate the approximate energy yield of a PV plant. Therefore, this study will consider the effect of degradation, soiling, and mismatching on large-scale PV plants and the benefits of utilizing power optimizers.

Degradation of PV modules

PV module degradation could be defined as the decay in a module’s and components’ properties which would influence the system’s performance. A degraded system would keep performing non-optimally until reaching a threshold where the degradation effect becomes problematic.[7]

PV modules are exposed to degradation throughout their lifetime. The degradation of individual cells and the degradation of a PV system limit the theoretical lifetime of a single cell which is 165 years. This degradation is referred to the aging of the modules, however, an early degradation could occur due to design failures or an emerging failure when modules are in operation [8].

The degradation mechanism could lead to system failure and its associated financial troubles. This raised the importance of comprehending the degradation phenomenon. The degradation could be assessed in labs by emulating outdoor conditions, however, an outdoor tests are more effective to assess the system’s degradation since the system would be dynamically monitored and therefore, the results could be applied to other similar PV plants.[9]

In [8], Munoz et.al have summarized the main defects in PV modules which cause degradations as follow:

 Discoloration.

 Delamination.

 Bubbles.

 Glass breakages and cracks in the cells.

 Defects in the anti-reflective coating (ACR).

 Hot spots.

2.1.1. Discoloration

Discoloration generally results in degradation in PV modules where the modules color become yellow or brown in worst cases. It is referred to the degradation of the adhesive material between the PV cells and the glass or the ethylene vinyl acetate EVA which decrease the amount of light transmitted to the PV cells, thus a drop in the energy produced by the cells. Ultraviolet radiation combined with high temperatures (more than 50 °C) is the main reason behind this type of degradation. [7], [8]

Discolorations are often visible and could be observed, however, it is not common that discoloration leads to a failure, yet it is considered as a degradation since a drop in the generated power occurs. Maximum loss observed due to discolorations were less than 5 % over a modules’ lifetime and it was observed to be roughly linear over the same period [10]. Discoloration could be observed in different areas within each module and in non-neighboring spots. This is referred to the nonuniform distribution or different characteristics of the utilized EVA. However, this could be problematic when the EVA becomes detached from the cells which cause water molecules penetration into the module. [7], [8].

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2.1.2. Delamination

Delamination is the detachment of PV module layers which increase light reflection and thus, the cells would absorb less light. All PV modules must pass the International Electrotechnical Commission IEC tests in order to be deployed, however, delamination might appear later during a plant’s lifetime. [7], [8].

Delamination is more likely to occur in hot and humid climates where moisture can penetrate the adhesive materials and lead to degradation. The usage of cheap materials aggregates this problem. However, a silicone gel lamination has been tested as a replacement of traditional EVA in PV modules, it resulted in lower materials’ corrosion and a better performance. [7], [11].

2.1.3. Bubbles

Bubbles are similar to the delamination phenomenon except that the loss of the EVA adhesive material occurs in a small area which is usually a result of gasses released and trapped in the module [7].

The bubbles complicate the modules’ heat dissipation which reduces the modules’ lifespan although, at the start of this problem, the module’s performance could be barely affected. The bubbles might not be visible to the naked eye. They could be formed on the module’s backside which results in high module’s temperature, and/or on the front side which causes a reduction of light absorbed by the solar cells. [7], [8].

2.1.4. Glass breakages and cracks in the cells

Glass breakage which mostly occurs during installation and transportation has an effect on modules’ degradation. This degradation might not have a severe effect on the performance, but it increases the probability of other degradation factors such as discoloration, corrosion, and delamination.[7]

Decreasing the thickness of silicon wafers utilized in PV modules has considerable financial interests, however, thinner silicon wafers are more fragile and could lead to cracks in the cells which can decrease the energy output. Micro-cracks usually occur during cells manufacturing and might not be visible to the naked eye, they could occur on both sides of cells and would be aggravated in outdoor working conditions. It is worthy to mention that cracks are generally difficult to observe without using optical methods like Electroluminescence imaging. [8], [11].

2.1.5. Defects in the anti-reflective coating (ARC)

In order to improve the radiation absorption, an ARC is utilized to trap light and increase the overall performance. However, ARC characteristics might change during the module’s lifetime which could lead to lower light transmittance especially in the visible range (600 - 700 nm) due to ARC discoloration and thus, decreases the performance. [8], [11]. 2.1.6. Hot spots

A hot spot in a PV module is an area with a high-temperature which could be caused by different failures. Shadowing of a cell will result in reverse operation mode which makes a PV cell consume energy and create a hot spot. Moreover, an interconnection failure between adjacent or cracked cells will develop hot spots. The hot spots affect the cells’ characteristics like wafer resistance and p-n junction deformity, thus, a power loss which is correlated to the module’s fill factor.

Moreover, several factors contribute to the degradation rate of a PV module. This rate would decrease the total energy yielded by a PV plant, but it does not necessarily lead to a failure.

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Jordan et. al have found that the average degradation rate is about 0.8 %/year and most data available have demonstrated degradation rate less than 1 %/year. [9]

Finally, multicrystalline silicon modules have the lowest degradation rate over other silicon-based modules. Nevertheless, uncertainties in the measurements, the balance of system, location dependent and other factors might be problematic in defining the accurate degradation rate. Hence, for long-term warranty, a degradation rate of maximum 0.5 % is required in addition to a proper plant’s commissioning to increase plants long-term reliability. [9].

Soiling

The accumulation of dust on PV modules might instigate a severe effect on the performance of a PV plant. A major problem that occurs with dust accumulation, is the transmittance decrement of the useful irradiation. This implies less irradiation absorbed by the solar cells and therefore less energy yielded. [12].

The soiling factor is intrinsically related to the climate where a PV plant is installed. Harsh climates where large-scale PV plants are usually installed could have a considerable effect on a PV plant’s performance. These climates which have abundance of solar radiation are usually deserts and arid areas such as the Arabian Gulf region. This indicates that a PV plant will be exposed to different environmental factors, most importantly sand and dust in desert regions, in addition to high ambient temperatures and high relative humidity. These extreme conditions would aggregate the dust accumulation and lower the system efficiency. [13] Soiling effect in small-scale PV systems does not have big attention, although the system performance is influenced by the dust accumulation. However, such systems which are usually installed in the cities are not exposed to extreme conditions such as the large-scale systems in arid areas. Yet, cities often have polluted air which contains particles, these particles could be accumulated on the modules and decrease the overall efficiency of the system.[12]

Moreover, many other factors could decrease the irradiation transmittance and thus decrease the energy yield. In comparison to dust, a serious problem could occur by bird’s droppings on PV modules since these droppings in many cases are stuck to the PV modules and not washed away by rainfalls. Furthermore, chemicals from industries and the growth of lichen and moss have an effect on the plant’s performance. Moreover, exhaust fumes produced by vehicles and chimneys in both large scale and residential PV systems could accumulate on the PV modules and result in lower PV plant’s performance. [14]

Soiling effect has different factors which should be considered when estimating the losses. These factors differ for each plant and location and could be shortly summarized as follow [12]:

 The soiling effect has a saturation point where the energy output of a PV plant would not be further affected, i.e. the transmittance would be no longer affected.

 The tilt angle of the PV array, where lower tilt angles seem to be more influenced by the dust accumulation.

 The particle size, where smaller particles aggregate the performance more than the larger one.

The saturation time is tilt and climate dependent and could not be observed with 0° tilt angle. This situation is yet much aggregated if the panels are not exposed to rainfalls. In [12] which was conducted in Belgium, the reduction of the transmittance of glass samples was remarkably observed even at day 58 during the spring season due to the high concentration of small airborne pollen particles, this decrement in transmittance was considerable because the glass samples were shielded from rainfalls. On the other hand, the same experiment was

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conducted and with samples exposed to ambient, and a saturation point occurred after five weeks (approximately 35 days) of exposure to the ambient and rain falls.

In [13], dust accumulation on the PV panels commenced a degradation in the power output. The PV modules were located in Doha and were, for five months, exposed to the dusty ambient without rainfalls and high relative humidity, this harsh environment caused 30 % drop in the total energy output. On the other hand, cleaning the modules increased the short circuit current by approximately 33 %.

To investigate the effect of particle size on the transmittance, an artificial contamination of different dust particles was conducted, the particles were white sand, clay, and cement with the size of approximately 250 µm, 68 µm, and 10 µm, respectively. The results showed a severe drop in transmittance at artificial contamination of 60 g/ m2_{, the transmittance was}

dropped to approximately 85 %, 52 %, and 33 %, for white sand, clay, and cement, respectively. [12]

The latter experiment results could be handy to estimate the soiling effect on the PV modules. The drop in transmittance for white sand could be derived from dusty climates such as gulf area and desert. Furthermore, 68 µm particle size corresponding to the size of airborne pollen (approximately 60 µm) which had an effect of 3 % to 4 % drop in transmittance in the spring season in Belgium [12].

It is worth mentioning that the first rainfall might make the modules dirtier due to unclean raindrops which collect airborne particles, however, the following rainfalls would have cleaner droplets and the cleaning effect would occur. Moreover, cleaning the modules on annual basis does not have a big influence on the performance of PV plant especially in harsh climates such as Gulf region; hence, cleaning intervals should be adjusted depending on a threshold of the acceptable reduction in energy yield. [12], [13]

Mismatching

A PV module is composed of several solar cells which ideally should have similar properties. However, in practice, the solar cells’ properties could differ which lead to mismatching between the cells. The mismatching in solar cells occurs due to the difference in the photocurrent, the shunt resistance, and the series resistance of the solar cells. Generally speaking, mismatching leads to a loss in power and thus the total PV module’s power is less than the sum of individual PV cells’ power; this loss is caused by optical losses and electrical losses such as interconnection ribbons and wiring etc. [3]

The optical losses could be reduced by utilizing anti-reflective coating and adjusting the space between the solar cells in order to maximize absorption and minimize the reflectance of the radiation. On the other hand, the electrical properties could be enhanced by minimizing the resistance of the interconnections, ribbons, and the contact resistance. New technologies to attach the solar cells such as conductive adhesive under low temperature would enhance the conductivity of the ribbons and enhance the module’s performance. However, an adequate number of solder points decreases the contact resistance and improves the electrical performance. [3]

The shunt and the series resistance define the electrical losses of a solar cell where the lower series resistance and the higher shunt resistance exhibit a better solar cell performance. However, the value of solar cells’ shunt and series resistances are not identical, therefore, different currents and voltages will be produced under illumination of solar cells. On a modular level, different voltages generated by the solar cells does not lead to mismatching due to the fact that the total voltage of a PV module is the sum of the voltages generated by each individual solar cell. On the other hand, the solar cell which has the lowest current

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current of the weakest cell, therefore, the extra current will be dissipated and mismatching losses will occur. [3].

In order to diminish mismatching losses in individual modules, a categorizing process is being utilized in PV cells manufactures. Based on short-circuit current and maximum power of a PV cell, electric characteristics are derived and therefore, cells composing a PV module have roughly same properties with allowable defined tolerance. The testing of cells is performed under standard test conditions (STC) and a mismatching tolerance should be provided in modules’ datasheet. [15]

Mixing cells with different electrical characteristics will lead to mismatching. On the other hand, cells with different characteristics within a minor deviation tolerance from the average value do not lead to power loss. Consequently, at a manufacturing level, sorting procedures to classify the solar cells based on standard deviation coefficient should be applied to avoid power loss. [15]

Mismatching in PV plants is caused by scattering of the electrical properties of PV cells and the heterogeneous illumination on the PV modules. The electrical properties scattering could be referred to a variety of factors such as degradation, hot spots etc. whereas the heterogeneous illumination could be caused by different tilt angles, soiling, birds dropping, shading etc. [16]

A common problem in PV plants is the mismatching in the modules’ I-V curve in a PV array which indicates that the global maximum power point (MPP) is not the same as the MPP for the individual modules and thus, mismatching losses arise. This problem could be partially solved by utilizing string inverters with several maximum power point tracking (MPPT) or by utilizing module-integrated inverters which increase the yield by 30 % but at the expense of investment cost. [6]

Lorente et.al in [6] demonstrated that in small-scale PV systems with a number of modules up to 40 modules, the mismatching losses are negligible and are not a big concern. On the other hand, large-scale PV plants are more complex, and the mismatching effect is influential.

Large-scale PV plants have an enormous number of PV modules forming series and parallel strings. However, even with modules with the same PV modules’ manufacturer and the same peak power, the electric characteristics would differ causing string mismatching. Yet, mismatching gets more sophisticated since adjusting MPP for each string will alter the string’s voltage, then the lowest string’s voltage will determine the MPP operating voltage. This issue gets more complex and the mismatching losses will be higher in case of a low number of MPP trackers in a system such as utilizing a central inverter with a limited amount of MPPTs for a large number of strings. [6]

Generally, a modules’ mismatch at STC is given by the manufactures. However, STC conditions don’t occur frequently and thus, defining the mismatching losses under different illumination levels was conducted by Pavan et.al [17]. The outcomes of the study demonstrated that modules’ mismatching could considerably alter under different illumination levels. Mismatching losses could also have a negative effect, relative to the initial value at STC in the datasheet, below certain irradiation value which was for this study 200 W/m2_{. Some authors suggested a range of mismatching losses for multi-crystalline}

modules as 0.4 % - 2.4 %, nevertheless, a proper ordering of modules can diminish the losses to 0.1 %. [17]

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Power optimizers

As mentioned earlier, degradation, soiling, and mismatching may initiate a considerable energy loss in PV plants, especially for large-scale PV plants, thus, the energy yield would be decreased which would have an unfavorable economic impact.

Inverters utilized in PV plants have MPPT efficiency which will be affected by current decoupling between PV modules. Current decoupling would change the I-V curve characteristics of a system and this lead to energy loss. In order to increase the system’s performance, MPP should be dynamically tracked since it is deemed crucial in PV systems and thus, DC-DC converters, known as power optimizers, could be utilized to track the modules’ MPP and allow the system as a whole to operate at the system’s global MPP voltage. [2], [5]

PV modules have bypass diodes which allow the current to pass through in case of the inoperative cell and thus, prevent the cell from behaving as a load instead of a generator. The diodes are essential in PV modules and a set of PV cells has one bypass diode. The diodes create steps in the I-V curve and multiple optimal points in the P-V curve, which in turns allow the determination of current and a voltage corresponding to MPP.

Moreover, if the cell does not produce any current, then the diode is forward biased and there will be no need for MPPT since the current passing through the module would not be limited by the affected cell. On the other hand, if a cell is partially damaged and generates low current, then the bypass diode will be reversed biased, thus, the modules’ current will be limited to the weakest cell current, and the need for MPPT become an interest. [2], [4] Extracting the maximum power of a PV system requires an efficient MPPT strategy which dynamically adjusts the duty cycle of the DC-DC converter in order to achieve the maximum power. An efficient MPPT should fulfill the following: [4]

 High accuracy and tracking speed of MPPT for rapid determination of the real MPP.

 The ability to obtain the real MPP out of several local points.

 Effectiveness in various operating conditions of PV systems.

 The ability to track the MPP at the sudden alterations and diminish the oscillations around the MPP.

 Simplicity.

Achieving the aforementioned properties of MPPT is done using different techniques. Those techniques are sorted into classic and modern techniques. The following is a brief description of the techniques utilized in power optimizers.

2.4.1. The conventional MPPT techniques

 Perturb and observe P&O: the main principle of this technique is to perturb the

voltage and observe the change in power. Once the power is decreased the voltage is decreased, otherwise, the voltage is increased. The main drawbacks are oscillations around the MPP and the faulty determination of the direction towards the MPP. The oscillation is dependent on the voltage step size in each individual perturbation of the voltage which is fixed in the conventional P&O technique. However, new methods were utilized to minimize the oscillations by starting the perturbation at an initial value of 10 % of the open circuit voltage (Voc) as a first step and applying half

the voltage of the former step as the subsequent perturbation. This approach increases the MPPT efficiency and leads to faster convergence to the MPP. [4], [5]

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 Incremental conductance IC: this method is based on applying a perturbation to

the voltage and detect changes in the current. The following equations describe the method mathematically: 𝑑𝑃 𝑑𝑉= 𝑑(𝑉𝐼) 𝑑𝑉 = 𝑉 𝑑𝐼 𝑑𝑉+ 𝐼 = 0 Equation 2.1

Where P is the power, V is the voltage, and I is the current. This implies that:

𝑑𝐼 𝑑𝑉= −

𝐼 𝑉

Equation 2.2

Hence, when the derivative of the current with respect to the voltage is greater than −_𝑉𝐼 , the module operates at the left of the P-V curve and thus, the voltage should be increased, otherwise, the voltage is decreased until Equation 2.2 is encountered. Determining the direction towards the MPP is solved in IC. However, ideally the, oscillations are eliminated when the real MPP is achieved. Yet, oscillations around the MPP occur due to environmental and electrical factors which alter a module’s MPP constantly. However, different methods could be deployed in order to decrease the oscillations error. [2], [4]

 Hill climbing HC: Same principle as P&O is employed in HC method except that

HC perturbs the duty cycle of the DC-DC converter by adjusting the pulse width modulation (PWM) of the MOSFET transistor. However, oscillations around MPP are still a major issue and thus, a modified algorithm which controls the perturbation step size was adapted to increase the efficiency and diminish the oscillations. [2], [4]

 Other methods: in addition to the abovementioned methods, several other

methods and algorithms were suggested such as the fractional open circuit voltage (Voc)/short circuit current (Isc), current sweep etc. [4]

Generally speaking, the main factors affecting the efficiency of the MPPT are the accuracy of defining the global MPP and the tracking speed. The perturbation step size is a major factor in defining the efficiency of the MPPT which will affect both the oscillations and the speed of tracking. Additionally, the DC-DC converter has switching losses which will increase for reaching higher tracking speed, still 90 % DC-DC converter efficiency is achievable. Yet, conventional methods like P&O and IC are the main algorithms employed in the commercial power optimizers due to its simplicity and cost in comparison to the modern methods. [2], [4], [5]

2.4.2. The modern MPPT techniques

Although the conventional methods simplicity and its easiness to be employed to the power optimizers, the performance is yet manipulated under certain conditions such as steady irradiation condition and the rapid change of the environmental conditions. Hence, various methods were suggested and tested to evolve the optimizers’ performance. [5]

 Artificial neural network ANN: this technique is based on a learning algorithm

which works similarly to a brain neuron. Three layers are implemented in this technique which are inputs, output, and a hidden layer/s. Variety of parameters are used as inputs to the algorithm (PV parameters, environmental parameters, shading pattern …etc.) and the output could be voltage or DC-DC cycle adjustment. The hidden layers are for pattern recognition (e.g. defining the perturbation step based on the environmental alteration), which increases the tracking efficiency but at the expense of the tracking speed due to the calculations time. Moreover, ANN should

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be system dependent, and reliable data should be provided as an input for efficient pattern recognition. It is worth mentioning that ANN could be implemented to P&O and IC techniques. [4], [5]

 Fuzzy logic controller FLC: the concept of fuzzy logic is based on a known

Boolean logic which has in its concept true, false, and in between. This algorithm compares the fuzzified inputs to a set of deduction rules to get a final fuzzy result which is interpreted to an analog output signal. The inputs to FLC are errors and change in errors which are calculated from the environmental conditions. This technique is quite complex since defining fuzzy rules and functions require a well-known knowledge of the system behavior. However, FLC can track the MPP faster than ANN, also combining FLC with P&O and HC facilitate the elimination of oscillations around MPP by adjusting suitable perturbation step size. [4], [5]

 Metaheuristic-based technique: different approaches are implemented in this

technique such as particle swarm optimization, artificial bee colony, and several other techniques. Those techniques are sophisticated and use its own intelligent algorithm to find the optimum path for defining the MPP, and all other parameters would be able to adapt to the new path as well. These methods are capable eliminating the oscillations around MPP, capable to define the optimum MPP out of multiple local optima which would occur in cases like shading, and those techniques are effective even with unclear mathematical model between objectives and decision variables. [4]

Generally speaking, metaheuristic-based methods are the most efficient way to reach the MPP. They have high tracking speed, no oscillations around MPP, and system independent which make them the best techniques to be implemented into power optimizers. However, defining an appropriate algorithm for each system and compare the performance of different algorithms still need to be evaluated. Yet, those techniques are costly and its implementation to the optimizers is still tricky and challenging. [4]

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3 Methodology and calculations procedures

In this chapter, a detailed description of the systems, the design, and the system’s parameters will be discussed. The simulations will be performed in four different locations which are: Borlänge, Madrid, Abu Dhabi, and New Delhi.

The system parameters were defined in order to obtain a proper input to PVsyst which is the software used in this study.

System description

This study considers large-scale solar power plants which indicates a solar power of the magnitude of 1 MW and upwards, accordingly, the system was designed to be approximately 1 MWpower plant.

The objective of the design was to evaluate the financial viability of employing power optimizers in large-scale PV power plants. This was done by simulating large-scale solar power plants using PVsyst and estimating the energy gained, when the optimizers are employed, in comparison to a reference system in which the optimizers are not employed. The proposed reference system consists of 290 W Luxor PV modules and 25 kW SMA inverters, therefore, the further systems utilizing power optimizers would be compared to the reference system. The systems in which utilizing power optimizers would test two different brands which are Tigo and SolarEdge optimizers. The system employing Tigo optimizers will employ SMA inverters whereas the system employing SolarEdge optimizers will employ SolarEdge inverters since SolarEdge optimizers work only with SolarEdge inverters. However, in any case, the total peak power installed (i.e. the number of modules) would remain constant in all systems.

The following sections describe the system components and system design. 3.1.1. PV modules

The solar modules utilized in the system are manufactured by a German company called Luxor. The chosen modules’ model is LX290P (monocrystalline), Table 3.1 shows the main module’s parameters and the module’s datasheet is attached in Appendix A

Table 3.1 Luxor modules main parameters

Rated power Pmpp 290 W

Rated current Impp 9.04 A

Rated voltage Vmpp 32.17 V

Efficiency at STC* _17.88 _%

Voltage temperature coefficient -0.30 %/ºC

Current temperature coefficient 0.05 %/ºC

Power temperature coefficient -0.41 %/ºC

* STC is the standard test conditions which are: irradiance 1000 W/m2_{| module temperature 25 ºC |}

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3.1.2. Inverters

Two types of inverters were employed in the simulations which are SMA Sunny tripower 25000TL with 25 kW rated power, and SolarEdge SE25K with 25 kW rated power. The aim of this study is to demonstrate the benefits of using power optimizers in PV systems and therefore, two types of optimizers were employed in the system which are SolarEdge and Tigo optimizers. However, Solar Edge system has a special architecture and cannot be employed without SolarEdge inverters, on the other hand, Tigo optimizers cannot be employed with SolarEdge inverters either. Hence, two different inverters were employed in the simulations. Table 3.2 shows the main parameters for both inverters employed in this study and the inverters datasheets are attached in Appendix B.

Table 3.2 Inverters main parameters obtained from the manufacturers’ datasheet [18], [19]

SolarEdge SMA Units

Input DC voltage 750 Nominal MPP voltage 600 V

Maximum DC voltage 900 Maximum DC voltage 1000 V

Maximum input current 37 Maximum current per _MPP 32.7 A

Maximum input DC power 33.8 Nominal input DC power 25.6 kW

Maximum output AC

power 25

Maximum output AC

power 25 kW

Maximum efficiency 98.16 Maximum efficiency 98.3 %

Output voltage 400 Output voltage 420 V

3.1.3. Power optimizers

This study will test the performance of two power optimizers which are Tigo and SolarEdge. The system will employ one optimizer for a pair of PV modules and the optimizers were sized accordingly. Since the PV module peak power is 290 W, the closest optimizer’s power which is included in PVsyst database was taken. Therefore, SolarEdge P600 and Tigo TS4-R-O-duo optimizers were employed in the system and have rated power as 600 W and 700 W, respectively. Table 3.3 and Table 3.4 show the power optimizers’ main parameters and the optimizers datasheets are attached in Appendix C.

Table 3.3 SolarEdge power optimizers main parameters [20]

SolarEdge Unit

Maximum power @ STC 600 W

Minimum MPP voltage 12.5 V

Maximum MPP voltage 80 V

Maximum PV voltage 96 V

Maximum input current 10.3 A

Maximum output current 15 A

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Table 3.4 Tigo power optimizers main parameters [21]

Tigo Unit

Maximum power @ STC 700 W

Total PV voltage @ STC 75 V

Maximum input current 12 A

Maximum efficiency (No boost) 99.6 %

3.1.4. System sizing

The systems were designed based on the aforementioned system components at STC conditions which are: irradiance 1000 W/m2_{, the temperature at 25 ºC, and air mass ratio}

(AM) = 1.5.

The reference system:

SMA inverters with a nominal power of 25 kW were employed in the system and thus, defining the maximum number of modules connected to the inverter was as following:

𝑁_{𝑚𝑜𝑑,𝑚𝑎𝑥} = 𝑃𝑖𝑛𝑣 𝑃_𝑝𝑣 =

25000

290 = 86 [𝑚𝑜𝑑𝑢𝑙𝑒] Equation 3.1

Where 𝑁_{𝑚𝑜𝑑,𝑚𝑎𝑥} is the maximum number of PV modules in which can be connected in series, 𝑃𝑖𝑛𝑣 is the inverter’s rated power, and 𝑃𝑝𝑣 is the PV module’s peak power.

In order to define the number of modules connected to each inverter, the sizing ratio could be considered which is the ratio of the rated inverter power to the PV modules peak power. An oversizing for the PV field is acceptable in most cases, sizing ratio up to 1.5 and 1.2 for northern Europe and southern Europe, respectively, is accepted. Therefore, 1.02 sizing ratio is acceptable for the system design and thus, 88 modules were employed in the system. [22] The maximum inverter power would therefore be:

𝑃_𝑖𝑛𝑣_𝑚𝑎𝑥 = 𝑁_𝑝𝑣∙ 𝑃_𝑝𝑣 = 88 × 290 = 25520 [𝑊] Equation 3.2

Where 𝑃𝑖𝑛𝑣𝑚𝑎𝑥 is the inverter maximum input, and 𝑁𝑝𝑣 is the number of PV modules

utilized in the system.

The maximum modules’ accumulated power at STC conditions is yet lower than the inverter maximum DC input power which is 25.6 kW. This implies that the chance of energy loss due to inverter’s power cut-off is eliminated.

The next step is to define the maximum number of modules connected in series in order to avoid exceeding the maximum input voltage of the inverter which is 1000 V as follows:

𝑁_{𝑠𝑡𝑟𝑖𝑛𝑔} =𝑉𝑚𝑎𝑥 𝑉𝑜𝑐

=1000

38.4 = 26 [𝑚𝑜𝑑𝑢𝑙𝑒] Equation 3.3

Where 𝑁𝑠𝑡𝑟𝑖𝑛𝑔 is the maximum number of modules which could be connected in series,

𝑉𝑚𝑎𝑥 is the maximum inverter’s input voltage, and 𝑉𝑜𝑐 is the PV module’s open circuit

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SMA inverter employed in the reference case has two maximum power point tracking (MPPT) inputs, the MPPTs are balanced and thus, the power distribution on each MPPT should ideally be the same. Therefore, 88 modules were distributed on two MPPTs resulting in 44 modules were connected to each MPPT.

Since we cannot connect more than 26 modules in series based on Equation 3.3, the 44 modules were thus distributed into two parallel strings of 22 modules each. Calculations for the string’s maximum voltage and the voltage at MPP, both at STC conditions, would result in 844.8 V and 692 V, respectively, which are within the inverter’s limits.

After defining the input power for each inverter, the next step is to define the number of inverters needed to obtain 1 MW PV plant as follows:

𝑁_𝑖𝑛𝑣 = 𝑃𝑝𝑙𝑎𝑛𝑡 𝑃_𝑖𝑛𝑣_𝑚𝑎𝑥 =

1000

25.52 ≅ 39 [𝑖𝑛𝑣𝑒𝑟𝑡𝑒𝑟] Equation 3.4

Where 𝑁𝑖𝑛𝑣 is the number of inverters needed in the PV plant, and 𝑃𝑝𝑙𝑎𝑛𝑡 is the PV plant’s

targeted power in kW.

Hence, the maximum installed power would be 995 kW.

The number of modules needed to form the PV plant would be: 39 × 88 = 3432 [𝑀𝑜𝑑𝑢𝑙𝑒]

And the total number of strings would be: 39 × 4 = 156 [𝑠𝑡𝑟𝑖𝑛𝑔]

Finally, the inverters must be protected against overvoltage, this occurs at worst case scenario when the ambient temperature is very low together with solar irradiation, in this case, the modules will produce higher voltages than their 𝑉𝑜𝑐 due to the voltage temperature

coefficient. Luxor modules have voltage temperature coefficient of -0.3 %/ºC. the worst-case scenario in this study would be the case of Borlänge, Sweden, where the ambient temperature could reach -30 ºC in extreme cases. Therefore, the maximum voltage at -30 ºC should be calculated and must be less than the inverter’s maximum input voltage.

𝑉_𝑜𝑐_𝑚𝑎𝑥 = 𝑉_𝑜𝑐− (𝛽_𝑉_𝑜𝑐∙ 𝑉_𝑜𝑐 ∙ (𝑇_𝑆𝑇𝐶− 𝑇₁)) Equation 3.5

𝑉_𝑜𝑐_{max (−30)} = 38.4 − (− 0.3

100× 38.4 × (25 − (−30))) 𝑉_𝑜𝑐_{max (−30)} = 45 [𝑉]

Where 𝑉𝑜𝑐_{max (−30)} is the maximum open circuit voltage at worst-case temperature, 𝑉𝑜𝑐 is the

open circuit voltage at STC conditions, 𝛽𝑉_𝑜𝑐 is the PV module’s voltage temperature

coefficient taken adopted from Table 3.1, 𝑇_𝑆𝑇𝐶 is the temperature at STC which is 25 ºC, and 𝑇1 is the lowest temperature reached at the worst-case scenario.

Hence, the string maximum voltage at -30 ºC would be:

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Where 𝑉𝑖𝑛𝑣_max(−30) is the maximum inverter voltage at -30 ºC, 𝑁𝑚𝑜𝑑,𝑠 is the number of

modules employed in each string in the system. The maximum voltage obtained in a worst-case scenario is 990 V which is less than the maximum inverter input voltage and thus, the system is protected against overvoltage.

At this point, the reference system was designed and ready to be simulated in PVsyst.

The system with the employment of Tigo power optimizers:

This system has the same configurations as the reference system except that it employs one power optimizer for each two PV modules which indicates employing 11 power optimizers in each string with a total of 1716 optimizers in the system.

The PV modules’ maximum voltage and current (45 V, 9.8 A) must not exceed the maximum input voltage and current of the power optimizer which is 90 V and 12 A which were met in the system design. The I/V curves for the PV modules and the optimizer are illustrated in Figure 3.1.

Figure 3.1 Tigo optimizer input limits taken from PVsyst

The system with the employment of SolarEdge power optimizers: System C

The system in which SolarEdge power optimizers are employed is slightly different than the system with Tigo optimizers and the reference system although all systems have the same peak power. SolarEdge optimizers can only be employed with SolarEdge inverters which work at fixed input voltage (i.e. the power optimizers adjust the total string’s voltage to meet the inverter fixed input voltage) which is 750 V for the inverters employed in this study. Furthermore, the inverters cannot be employed without the optimizers. For this reason, SolarEdge has a special design explained in PVsyst manual. [23]

The system was designed based on SolarEdge architecture model in PVsyst to attain 995 kW PV power plant which is necessary since the systems will be compared and thus, identical nominal power is required.

The system configuration employed 13 power optimizers in series (i.e. 26 modules in series) with a total of 1716 power optimizers in the whole system, and therefore the number of strings became 132 in order to obtain 995 kW peak power. Every four strings were connected to one inverter and therefore the total number of inverters needed became 33 inverters.

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The input characteristics for SolarEdge power optimizers employed in the system are shown in Figure 3.2 below.

Figure 3.2 SolarEdge optimizer input limits taken from PVsyst

It is worth mentioning that SolarEdge architecture design tool employs a larger number of modules in each string. The larger number of modules in each string the larger input power to the inverter. However, the inverter will cut-off when the input exceeds its highest limit and therefore, a power loss could occur, depending on the location, in SolarEdge system since the PV plant is slightly oversized based on SolarEdge architecture.

It is exceptional that the PV plant works at STC conditions since the operating cells’ temperature is usually higher than 25 ºC. The cells usually operate at 55 ºC which implies that an irradiation of 1120 W/m2_{should be obtained to reach the same energy yield}

as STC conditions, this situation is very seldom to occur [24]. However, the amount of loss in energy is not only dependent on the irradiation rather dependent on the clear sky conditions also. Intense irradiation together with an extraordinary clear sky, the scattered irradiation will be less and therefore, the incident irradiation on a plane perpendicular to the irradiation will be higher. This situation occurs episodically and not in all sites, however, in such cases, the inverter will cut-off and will give 25 kW AC maximum output.

Meteorological data and main design perspective inputs

The meteorological data utilized in the simulations were taken from Meteonorm 7.1 which is directly imported by PVsyst. PVsyst runs its simulations with one-hour time step which indicates that an hourly data should be provided. Usually, an hourly data is not provided, but rather than daily or monthly values. Thus, PVsyst includes Meteonorm 7.1 algorithms which generate synthetic hourly data based on monthly values. The algorithms employed in PVsyst is sophisticated and consider different factors, such as local conditions and clear sky models, in order to reach a reliable data. [23]

The synthetic hourly data generate the irradiance (both global horizontal and diffused irradiation), temperature, and wind velocity. However, these values are within acceptable accuracy since Meteonorm has become an effective tool for appraising the solar radiation. [25]

The synthetic hourly data is generated from monthly data which are averaged over a certain number of years, (1990 - 2010) for Borlänge, (1991 - 2010) for Madrid, (1992 - 2004) for Abu Dhabi, and (2001 - 2010) for New Delhi.

The software allows choosing either Hay model or Perez model in order to define the transposition model. The simulations will be run with Perez model which usually give between 0 % - 2 % higher annual energy yield than Hay’s model. [23]

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The system is assumed to be installed in an open area, the system’s vicinity would be grass, concrete, or soil which would be a realistic assumption and thus, The albedo values would swing between 0.15 - 0.35 except in the case of snow which could reach up to 0.82 [23]. Nonetheless, acquiring accurate albedo values require onsite measurements. On the other hand, albedo values have an insignificant effect on the system except for vertically installed modules which are not an interest in this study. Therefore, the albedo values will be preserved as PVsyst default values which are 0.2 for all months and all locations except 0.7 for the months of January, February, and March in the location of Borlänge, this is due to the fact that the albedo for snow is relatively high and reach up to 0.82 and thus, might have a larger effect on the system than the other ground types. [23]

The lowest ambient temperature which defines the system’s highest absolute voltage were taken as -30 ºC which is suitable for the location of Borlänge. Based on this temperature, the system’s highest voltage did not exceed the inverter’s maximum voltage as shown in Equation 3.5. However, this temperature is a design aspect to ensure that the highest absolute voltage will not exceed the maximum inverter input voltage in a worst-case scenario. PVsyst simulates based on the synthetic temperature data which is generated by Meteonorm 7.1 algorithm for each geographical location and the simulations might not utilize the temperature of -30 ºC. Thus, maintaining this value for the rest of the locations doesn’t interfere with the simulations and the associated energy yield. Therefore, - 30 ºC is kept as the lowest temperature for the rest of the locations.

Wind velocity is difficult to estimate, and it is intrinsically dependent on the spatial obstacles in the vicinity of a PV plant; however, the wind velocity does not have severe effects on solar systems and an accurate wind velocity data is not a big interest for solar power plants. Nevertheless, PVsyst uses Meteonorm Dll to generate hourly data based on monthly average data and this generated data is adequate as an input for solar power plants calculations. [23], [26]

System input parameters

In this chapter, systems’ parameters will be defined. The constant losses which will be utilized in all simulations will be defined, in addition to the soiling, mismatching, and degradation values which will be varied in the simulations.

All methods employed in the soiling, precipitation, mismatching, degradation, and economic models’ calculations will be comprehensively described.

3.3.1. System orientation and tilt angles

In order to obtain the highest annual energy yield, the modules must have an optimum azimuth and tilt angle which differs depending on the latitude. However, the system is assumed facing south, so the azimuth angle is 0º which is always the optimum azimuth’s angle for systems located in the northern hemisphere.

The tilt angle is trickier and more dependent on the location’s latitude; therefore, a batch simulation was executed to define the optimum tilt angle which gives the highest annual energy yield. Since this study is considering four different locations, the batch simulation, therefore, was executed for each location separately and the optimum tilt angles were optimized for each system accordingly.

3.3.2. Constant system losses input

PVsyst is an advanced tool which allows the users to choose between a variety of inputs. The detailed losses feature in PVsyst allows different types of losses to be included in the simulations. The system losses which were assumed constant in all performed simulations are described as following:

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The thermal parameter:

The system was assumed to be free mounted with air circulation. This parameter defines the thermal loss factor due to the thermal convection, this intrinsically defines the solar cells’ operating temperature which has a considerable effect on the system efficiency and thus, the annual energy yield. The default value for thermal loss coefficient for free mounted modules was chosen which to be 29 W/(m2_{K) as a constant loss factor.}

The ohmic losses:

The ohmic losses are a quadratic function with the current. The strings’ current is dependent on the irradiation which oscillates during the day, therefore, the ohmic losses are assessed at each simulation step in PVsyst (i.e. each hour). However, PVsyst allows a detailed computation of ohmic losses. Those losses in practice would significantly affect the system’s performance and cause a considerable energy loss. However, defining an accurate value requires acknowledgment of the system layout and dimensions, the components location in the field, and AC cabling which are out of the scope of this study. Therefore, the wiring was assumed to be properly designed with minimum losses and thus, the default value chosen was 1.5 % loss fraction at STC conditions.

Light-induced degradation (LID) and module quality:

LID is a physical phenomenon which is a degradation in the performance that occurs at the first hours of modules’ exposure to the irradiation. It is very difficult to estimate due to its dependency on the quality of the silicon wafers which were used in manufacturing the modules. However, the default value chosen was 2 % which is the PVsyst default value. [23] The module quality is linked to the modules’ tolerance which is positive for most newly manufactured modules. This means that the modules generate more energy than their peak power (in this study the modules’ tolerance is in the range of 0 - +2.2 %). PVsyst assumes one-quarter of the modules’ tolerance as default module quality (-0.6 in this study and the minus sign indicates an overproduction), and this default value was chosen.

Incidence Angle Modifier (IAM), Auxiliaries, and Unavailability:

The IAM is an optical property which affects the irradiation reaching each individual solar cell; it is dependent on the radiation’s incident angle on the surface. However, PVsyst uses different approaches in calculating the IAM ratio depending on the modules’ front surface, thus, ASHRAE model was chosen with its default values. [24]

Moreover, PVsyst allows defining auxiliary losses (such as night loss) and unavailability of the system (such as system shutdowns for maintenance) in its calculation. However, those values were neglected and kept as zeros.

Shading:

The software allows detailed calculation for shading and a 3-D model could be performed as well, however, the shading losses was out of the scope of this study and therefore they were neglected.

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3.3.3. Soiling, Mismatching, and Degradation losses

The study aims to assess the effect of soiling, mismatching, and degradation on PV systems, thus, those parameters were altered in each simulation.

Soiling:

Dust and snow cause the soiling effect and worsen the system performance. The accumulated soiling on the top of PV modules diminishes the irradiation absorbed by the solar cells which, depending on the dirtiness, could dramatically decrease the energy yield. PVsyst assumes a ratio of soiling accumulation on the PV modules and therefore, PVsyst decreases the irradiation penetration with the same ratio and then calculates the energy output accordingly. [27]

In practice, the soiling is not always homogeneous over each PV module and over the strings as well, this would lead to current mismatching and hotspots, and thus, significantly affecting the energy yield [28].

Since PVsyst does not have the possibility to identify the soiling distribution over the modules or the strings rather than identifying a monthly soiling percentage and the associated reduction in the absorbed irradiation [27]. Therefore, to overcome this difficulty, a PV array comprises of two PV modules and an inverter was designed in PVsyst to allow obtaining the current and the voltage values of each pair of modules and export them to an Excel sheet for analyzing afterward. The soiling ratio was altered from 1 % up to 40 % depending on the location. More details will be found later in 3.4.2.

Mismatching:

The software has a tool to calculate in details the mismatch losses depending on the system configuration. The calculations show the importance of the current mismatch since the lowest current in a string govern the total string’s current and thus, depending on the current relative difference between modules, a considerable loss of energy could occur.

The voltage relative difference in a string could be initiated by the wiring losses, temperature difference …etc. It has less influence than the current since the total voltage is the sum of all modules’ voltages. In the case of parallel strings, the lowest voltage is dominant, and the more strings in parallel the more voltage mismatch losses.

In this study, the mismatching losses, represented in PVsyst as power loss at MPP, will be altered in order to evaluate the energy loss. The alterations will range from 0 % to 10 % for the reference system as a worst-case scenario which could occur in cases such as birds dropping. The Tigo and SolarEdge systems do not have mismatch losses since power optimizers are employed. More details will be found in

Degradation:

Modules’ degradation in PVsyst is represented by the aging section in detailed losses. Basic curve provided by the modules’ manufactured is included in PVsyst, however, modifications are permissible. Degradation tolerance usually specified by the manufacturers in phases, this includes all types of degradations mentioned above in 2.1. For Luxor modules utilized in the system, the degradation factor is specified as 91 %, 84 %, and 80 % after 10, 20, and 25 years, respectively. Any degradation beyond these values would be considered as a fault and should be covered by the modules’ warranty.

A degradation of 20 % for 25 years corresponds to 0.8 % average yearly degradation excludind LID losses, however, modules’ degradation rate could tolerate in different climates [29]. Additionally, PV modules don’t altogether degrade at the same rate which leads to mismatch losses.