APE, SR and MM

Obtaining the whole spectral distribution for every wavelength for every hour would require special instruments and as well as that, the treatment of a large amount of data would be needed. It would be useful to identify a certain spectral distribution with a single parameter instead. The most common ones that have been used in the literature are the Average photons energy (APE) and the AM. The APE measures the average energy of the photons belonging to a radiation with a certain spectral distribution:

𝐴𝑃𝐸 = ∫ 𝐸(𝜆)𝑑𝜆

∫ 𝛷 ( )

where 𝐸(𝜆) [𝑊 𝑚 𝑛𝑚 ] is the spectral irradiance, 𝛷 _{( )} [𝑚 𝑛𝑚 𝑠 − 1] is the spectral photon flux and a [nm] and b [nm] are the lower and upper limits of the waveband of the solar spectrum considered [49]. Several works examined the relationship of this parameter with astronomical and atmospheric characteristics. According to [50] and [51], the APE increases when the zenith angle decreases. When the zenith angle is large, the light crosses a longer fraction of the atmosphere and the Rayleigh scattering in the UV region, caused by aerosols and gases, is more important. The radiation will then be constituted more by photons with longer wavelength that carry a smaller amount of energy, thus reducing the average photons energy. On the other hand, [52] and [53] show how a higher content of water vapour in the atmosphere during cloudy days, results in a bigger APE value. Water vapour absorbs well the infrared region [54], making the spectrum blue shifted. Depending on which spectrum interval is considered, the APE value relative to the standard AM1.5 spectrum is 1.88eV or 1.58eV for the range 350-1050 nm and 350-1700 nm respectively [48].

21 The Spectral Response (SR) is a factor that measures how effectively a certain PV technology responds to the different wavelengths of an incoming radiation, it goes from 0 to 1 and it depends on the band gap of the module.

The panel will harvest more efficiently those wavelengths slightly higher than the one carrying exactly the amount of energy similar to the one of the band gap, it will then be less and less effective with shorter wavelength, since the energy of the photons will increase and the losses due to thermalization will be larger, whereas the longer wavelength will not be utilized and the spectral response will quickly go to zero. Technologies with a larger bandgap like a-Si and Cd-Te will have a SR curve shifted more on the left than the one with a smaller bandgap (c-Si and CIGS) as illustrated in Figure 19, where the SR curves of several PV technologies are shown. The SR could be seen as a series of efficiency values relative to each part of the spectrum and can be used to calculate the short circuit current, knowing the irradiation spectrum 𝐺 [47]:

𝐽 = 𝑆𝑅(𝜆) ∗ 𝐺 ∗ 𝑑𝜆

Figure 19 - Normalized spectral response data for single junction PV technologies. Data taken from measurements at Fraunhofer ISE [55]

The mismatch factor (MM) is a measure of the spectral gains or losses between the actual and the AM1.5 reference spectrum, according to the IEC 60904-7 standard [56]:

𝑀𝑀 =∫ 𝐸(𝜆)𝑆𝑅(𝜆)𝑑𝜆 ∫ 𝐸∗( )

∫ 𝐸∗( ) ∫ 𝐸(𝜆)𝑑𝜆

Where 𝑆𝑅(𝜆) is the spectral response of the PV device, 𝐸_{∗( )} (𝑊 ∗ 𝑀 ∗ 𝑛𝑚 ) is the spectral irradiance of the standard spectrum AM1.5, 𝜆 (nm) and 𝜆 (nm) are the lower and upper limits of the wavelength where the PV device is active, 𝜆 (nm) and 𝜆 (nm) are the lower and upper limits of the full spectrum (300-4000 nm). A MM value of 1.02 means that the PV module presents a spectral gain of 2%. The MM is a useful parameter that can quantify how much more or less the PV panel is harvesting a radiation with a particular spectral distribution, compared to a radiation with the same total power, calculated as the integral of the spectrum, but standard spectral distribution.

The spectral factor (SF) is an alternative index to the MM used in literature that quantifies in percentage how much the performance of a PV differs between an actual spectral distribution and the standard AM1.5-G.

22 2.3.3 Previous studies on the spectral effect

Many studies investigated the effect of a variable spectral distribution on the yield of different PV technologies.

Two studies, [57] and [58], measured the spectral distribution of the irradiation and the actual production of the PV modules in Lima and south-eastern Brazil respectively. In both cases, the annual APE is blue shifted with a small seasonality variation, due to the low latitude and high solar angles, and so low values of AM, throughout all year. They both conclude that mostly large bandgap technology benefit from higher APE values like a-Si, Cd-Te and Perovskite whereas, small bandgap modules like CIGS, are less affected by the spectral distribution and present an opposite trend as illustrated in Figure 20, where the mismatch factor of several PV technologies is plotted against the APE. Both papers also underline how important it is not to neglect spectral irradiance in low latitude sites, where the annual output variation can be up to 10 %, while, in mid-latitude sites, where the sun height changes significantly during the year, the seasonality tends to result in an overall small annual variation, since the effect in summer can be the opposite than the one in winter, partially cancelling each other.

Figure 20 - Monthly weighted MM vs monthly weighted APE for various PV technologies in Sao Paulo. Here 1.88eV is the APE of the AM1.5 standard spectrum. [58]

A similar study is conducted in India and it can be seen how the monthly variation of the APE value follows atmospheric and seasonal factors [48]. The autumn, characterised by low AM values and the monsoons and so cloudy weather, presents a high APE. Whereas in winter, where the AM becomes higher and the humidity lower, the APE goes down. Figure 21 illustrates the APE trend over the course of a year, in this study, 1.58 eV represents the average photons energy of the standard AM1.5 radiation.

Figure 21 - Monthly variation of average photon energy (APE) in India. [48]

The same work shows how the AM affect the useful fraction of radiation for some PV technologies with a large bandgap, a-Si included. The useful fraction is an alternative way to address the variation in performance due to

23 different spectral distributions. Figure 22 describes this relation, large bandgap technologies decrease their performance with higher AM values, which make the radiation more red.

Figure 22 - Relation between AM and normalized useful fraction (UF) for three PV technologies. [48]

Nofuentes et al [59] analyse the spectral gains for some PV technologies in two cities in Spain, considered as a good example of mid-latitude sunny locations, with no extreme weather conditions like storms and persistent cloudy sky. The summer is mostly blue-shifted while the winter has a red-rich spectrum, because of the AM. Figure 23 shows how large bandgap technologies, like amorphous silicon on the left-hand side, are more affected, increasing their output during the summer and decreasing it in the winter, while CIGS, on the right-hand side, presents a flatter curve. Besides, they are also characterized by an opposite trend, a-Si gains in summer and CIGS gains from the red-rich spectra in winter.

Figure 23 - Experimental and modelled values of the monthly spectral mismatch factor in Jaen for the modules considered: a-Si (left), CIGS (right)

Chantana et al [60], demonstrate how red-shifted spectra with an APE value below 1.88 eV result in spectral gains for small bandgap PV technologies, which have a SR curve more shifted on the right. The more the SR is on the right, the larger the gains for spectra richer in longer wavelengths regions. Figure 24 shows the SR on the left-hand side and the MM trends on the graph on the right-hand side, for several technologies considered in the experiment.

It can be noticed that there is a clear relation between the SR curve position respect to the wavelength region and the slope of the MM vs APE curves. As the SR peaks go from left to right, the slopes of the relation between MM and APE goes from higher positive values to larger negative ones.

24 Figure 24 - Relative spectral response of the different type PV modules and pyranometer (left). MM for the a-Si, perov, Cd-Te, CIS, BC, mc-Si, and HIT PV technologies as a function of APE. [53]

Dirnberger et al [61], perform a similar investigation for five different PV technologies in Freiburg, Germany, a mid-high latitude location with cloudy weather. The results are given in terms of monthly and annual average spectral impact in percentage for four different PV technologies, as can be seen in Table 1. Once again, a-Si, a large bandgap material, is the one showing higher annual average effect compared to the crystalline silicon and CIGS technologies. However, even if the overall annual average impact of small bandgap materials is only 1.1%

and 0.6% for c-Si and CIGS, it is important to notice that during winter months, their average gains reach values above 3 %. Figure 25, shows the spectral impact for the largest and smallest bandgap technology examined in the paper for a two years period, they have opposite seasonal trends and CIGS gains in the winter and stays the same during summer, since the winter season in Germany is characterized by low solar angles that shift the spectrum to the infra-red region.

Table 1 - Monthly spectral impact based on the monthly sums of irradiance of a reference year and the determined average monthly spectral impact [55]

FREIBURG

monthly spectral impact (%)

month a-Si c-Si high-eff c-Si CIGS

1 -2 1,9 2,4 2,6

2 -1,3 1 1,4 1,6

3 0,1 0,7 0,8 0,9

4 3,5 1,2 0,9 0,4

5 4,2 1,5 0,9 0,3

6 5,1 1,4 0,8 0

7 5,3 1,5 0,8 0

8 5,3 1,6 0,9 0,1

9 4,3 1,5 1 0,4

10 2,8 1,9 1,7 1,3

11 0,8 2,1 2,2 2,1

12 -2,2 2,4 3 3,3

Annual (%) 3,4 1,4 1,1 0,6

25 Figure 25 - Comparison of monthly spectral impact calculated from data as measured and with a calibration correction function, for a-Si, which was most affected, and CIGS, which was least affected. [62]

2.4 Optimal Tilt Angle

The optimum tilt angle is the slope that yields the highest amount of energy during a chosen time span, it is usually a function of the latitude and the day of the year. According to [63], during winter, the most harvesting slope is about (latitude + 15), whereas in summer, (latitude – 15). Ahmad and Tiwari [64] investigate the optimal tilt angle for a flat-plate collector in several locations around the world and found that the average optimum slope for the winter season at New Delhi is equal to the latitude +19 and for the summer is (latitude – 16); whereas, the best tilt angle for the whole year is equal to the latitude. Elminir et al [65] compute the best angle for a surface in Helwan, Egypt and performs an extensive research on previous similar works. The results are in line with what many other studies found, around (Latitude + 15) in winter and (latitude – 15) in summer, while the optimum angle throughout the year is approximately the same as the site’s latitude. Kern and Harris [66] found that the optimum value also depends on the climate and the demand characteristics. Jacobson and Jadhav [67], underline how two locations at the same latitude (Calgary, Canada and Beek, Netherlands) have a different optimal tilt (45 for the former ad 34 for the latter), mainly due to the fact that the European city has a greater cloudiness and aerosol pollution, resulting in a more significant diffuse radiation component, which is isotropic and can be better harvested with lower tilt angles. The same paper, gathers data from a large number of cities in the world and estimate a polynomial fit of optimal tilt as a function of the latitude, shown in Figure 26. In the graph, the red curve bends for higher latitudes, due to the cloudier conditions of Nordic locations.

26 Figure 26 - Estimated optimal tilt angles and 3-rd order polynomial fits through them of fixed-tilt solar collectors for countries in the northern hemisphere [67]

2.5 Dispatch strategy

In a hybrid Power System, elaborating a robust strategy to determine when and how each source is used is of extreme importance, in order to manage the system in a smart way, optimize the use of renewables, minimize the use of fossil-fuel and avoid waste of installed capacity and capital. Especially when variable sources like solar and wind belong to the picture, it is fundamental to plan in advance the behaviour that the system should follow in any given situations. A literature review on previous works that investigated into the dispatch strategies of Hybrid Power System was made to understand what is the state-of-the-art regarding this topic. Many works present their own optimized strategy for PV-diesel hybrid system [68] [69], microgrid [70] or Trigeneration Power Systems [71].

Soudan and Darya [72] go even beyond, developing a smart switching control among the components of a PV-Battery-Diesel system based on the day-ahead weather forecast, to pre-determine how much renewable energy will be available to decide whether to start-up the diesel generator or rely more on the storage. The main difference between the two is that the former requires some time to kick in, whereas batteries have a fast response. Therefore, when the PV is expected to produce a decent amount of power during the day, the batteries are used to quickly fill in the gaps if there will be any, instead of switch on and off the generator continuously. On the other hand, if a cloudy day is expected, the diesel generator is turned on and kept running for several hours to cover the load and recharge the battery too. This paper proposes three different algorithms based on what is the main priority for the developer. The first algorithm aims to minimize the number of hours when the DG is used, without any regards for the cycling frequency. The second minimizes the generator cycling, which is done by just keeping the DG running once it is started-up during night-time. The objective of the third is to use the battery in an optimal way.

It is interesting because it calculates the ability of the battery to be charged again by the PV before night-time and based on that it decides whether to discharge them or to use the DG to cover the load at a certain time. This algorithm is illustrated by the flowchart in Figure 27.

27 Figure 27 - Decision flowchart to make optimal use of the battery according to [73]

3 Methodology

In order to address the research objectives, the excel tool developed by Ericsson Energy System has been utilized as a reference. The hybrid pv-diesel power system and any effect of the topics addressed in the research will be developed, implemented and analysed with the model.

3.1 Model Development

During the thesis work, the Excel Tool was implemented and additional components of the system were added in the calculation, to make the model more similar to a real case and to increase the accuracy of the results obtained from it.

3.1.1 MPPT

An MPPT is used to extract the maximum possible amount of power from the PV array, by making it work at its maximum power point voltage and then converting it to the best voltage to get the maximum current into the battery bank. To size an MPPT, it is firstly needed to identify the battery nominal voltage 𝑉 and the PV array peak

28 power 𝑊 , from which the maximum current that the controller should be able to handle is found. Following the Ohm’s law:

𝐼 ≥𝑊

𝑉

After selecting an MPPT that can cover that amperage, it has to be checked that the voltage of maximum power point 𝑉 of the array lies within the operating voltage range that the MPPT can handle. In fact, an MPPT is characterized by un upper and lower voltage limits and if the PV output is beyond those safety values the controller might be damaged. Moreover, the open circuit voltage 𝑉 (which is usually higher than the 𝑉 ) has to be below the controller’s upper limit. Since the 𝑉 and 𝑉 vary with the cell temperature, it has to be verified that the adjusted values, related to the operating temperature of the cells, are within the safety range. Moreover, the current and voltage output of the array depends on the number of panels and whether they are connected in strings or in parallel.

Hence, a control on the voltage output of the PV system, depending on the disposition of the panels and the ambient temperature for every hour, was added to the Excel model, since it previously lacked of this information and was assuming a direct connection between the PV array and the batteries without any voltage requirements or power losses, which is not possible in a real case. The MPPT operating range is given by the supplier, as well as the variation of the PV performance according to the voltage output,Table 2. The MPPT can absorb a 12 A current and a voltage between 120 V and 425 V. In addition, the efficiency of the PV is maximum when the voltage output is between 200 V and 425 V, while it linearly decreases for voltages below 200 V by a factor of 0,5 %/V.

Table 2 - Voltage operaing range and maximum amperage of the MPPT Operating Limits

Table 3 - Variation of efficiency as a function of the input voltage from the PV array to the MPPT s48-2000e3 Performance Considerations

For every hour of the year, the model checks how many strings in parallel the controller can handle depending on the amperage limit.

𝑛 𝑜𝑓 𝑠𝑡𝑟𝑖𝑛𝑔𝑠 = 𝑅𝑜𝑢𝑛𝑑 𝐷𝑜𝑤𝑛 𝐼 𝐼

In this case, the 𝐼 = 12 𝐴 and the 𝐼 ~11 𝐴, so only one string can be connected to each MPPT.

29 Then it computes the voltage output of the PV array as a function of the number of panels connected in series in a single string and the ambient temperature gathered from the meteorological data source, it checks that it stays within the MPPT range and eventually, it calculates the temperature-related losses.

𝑉 _, = 𝑉 ∗ 1 − 𝛼 ∗ (𝑇 − 𝑇 ) ∗ 𝑁

with 𝑁 the number of panels in a string and 𝑇 the ambient temperature, since the open circuit voltage refers to the panel condition at cold start, the cell temperature is the same as the ambient one. For the maximum power point voltage, the cell is in operating conditions and its temperature is roughly 30 °C more than the ambient one.

𝑉 _, = 𝑉 ∗ [1 − 𝛼 ∗ (𝑇 − 𝑇 + 30)] ∗ 𝑁

The output current produced by the single string will be given by:

𝐼 = 𝐼 ∗ [1 − 𝛼 ∗ (𝑇 − 𝑇 + 30)]

The power actually delivered will be given by the multiplication of the voltage and current of the array. However, it cannot be higher than the MPPT nominal power

𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑 = min (𝑉 _, ∗ 𝐼 ∗ 𝑁 ; 𝑊 ∗ 𝑁 )

With 𝑁 the number of the strings in parallel and 𝑁 the number of MPPT.

Lastly, the temperature losses are calculated

𝑇 = 1 − min 1; 1 − 0,005 ∗ 200 − 𝑉 _, ; 𝑠. 𝑡. {𝑉 _, < 400 𝑉 ; 𝑉 _, > 120 𝑉}

In conclusion, with this additional sheet, the model is able to account for the power reduction related to the temperature, by adjusting the true value of the voltage and current of the maximum point for every hour, resulting in a lower or higher maximum deliverable power. Besides, the maximum power that can be transmitted by the MPPT is added as an upper limit.

3.1.2 Battery

The model allows the user to choose among three different configurations:

 Stand alone or pure solar

 Diesel generator backup

 Grid connected system

When a secondary power source is available, either genset or grid, the system is not allowed to bring the state of charge of the battery below 20 % in order to prolong their lifetime, as it is known that the higher the dept-of-discharge is, the less number of cycles the battery will be able to perform. The dept-of-dept-of-discharge is the complement of the state of charge [74].

Batteries manufacturer often suggest a maximum DOD, going beyond that will shorten battery life. Watanabe and Kinoshita [75] show how discharging completely the battery increases the rate of cell deterioration.

On the other hand, when a stand-alone (pure solar) mode is chosen, the option to fully discharge the batteries was

On the other hand, when a stand-alone (pure solar) mode is chosen, the option to fully discharge the batteries was