Sample type by group and expected volatility characteristics.
\r\n\tIn this book, the different factors of liquefaction, the field methods and laboratory tests to identify a potentially liquefiable soil aim to be reviewed; in addition with history cases (ground behavior during the occurrence of an earthquake, state of stress, deformation, shear strength, flow, etc.).
\r\n\tA very important aspect of this topic is the presentation of the different constructive techniques used to ground improvement (vibrocompaction, dynamic compaction, jet grouting, chemical injection, replacement, etc.), placing special emphasis on those constructive methods used to solve problems on structures already located in areas of low relative density with liquefaction potential, where the installation of monitoring and control equipment is also required (tiltmeters, piezometers, topographic points, seismographs, pressure cells, etc.).
‘Distillation is the most widely used separation technique in the petroleum industry’ [1].
At present, petroleum remains the major source of energy resources, and for more than 100 years, it has been the main source of fuels used in alternative internal combustion engines in auto-motion as well, both for spark ignition engines (SIE1), traditionally known as petrol engines, and for compression ignition engines (CIE2), or diesel engines. Nevertheless, we must bear in mind that differences in the operation of spark ignition and compression ignition engines require very different types of fuels.
When we speak about petroleum-derived fossil fuels, used as automotive fuel, we must remember that in a given series of hydrocarbons the ignition temperature decreases as the molecular weight increases because the cracking of large molecules needs less activation energies [1], whereby:
The SIE require low boiling hydrocarbons, with a soft combustion temperature and a relatively high spontaneous ignition temperature.
In the CIE, hydrocarbons with low spontaneous ignition temperatures are preferable, whereby the compounds of low boiling points are unsuitable.
From the chemical composition viewpoint, petrol is a blend of hydrocarbons between C4 and C11, with boiling points between 25 and 210°C and in which we can find all types of hydrocarbons: paraffins, isoparaffins, olefins, aromatics, naphthenes, etc. They may also contain oxygenated compounds such as ethers (MTBE, ETBE, TAME3) and pure alcohols in variable proportions: minimum amounts of sulphur and nitrogen as well as additives (detergents, anti-knock, etc.).
From the chemical composition viewpoint, the diesel fuels are a blend of different components obtained from different refining processes, with a majority of hydrocarbons between C10 and C16, with boiling ranges between about 160 and 360°C, and low amounts of sulphur and nitrogen. Additives are also present in their formulations [2–4].
Petroleum is, even today, the source of energy most used worldwide, but it is not an inexhaustible source of energy; this fact, together with the need to protect the environment, has led to the search for new automotive fuels and for the modification of the characteristics of the existing ones. One of the paths chosen in recent years has been to include biofuels in the formulation of conventional automotive fuels given their great capacity for blend with petroleum-derived fuels [5].
Incorporating biofuels and/or bioethanol to petrol and biodiesel (FAME4) to diesel is a path to a more sustainable energy future and involves a great R&D effort since it is necessary to study how blending modifies fuel characteristics in the search for optimal behaviour in any automobile engine [6].
As a general rule, according to international specifications, petrol can be combined with bioethanol in a percentage not exceeding 10% by volume and diesel with biodiesel up to a maximum of 7% in volume without informing consumers about it. There are also specially designed vehicles that can support a mixture of petrol with 85% by volume of bioethanol (E85) and taxis or buses that use a mixture of diesel and biodiesel in a proportion of 70:30% by volume (B30) [7].
Now, any fuel which is in the market should guarantee that their use in an engine will provide the projected energy performance that it will satisfy any other capacity inherent to their use and it will perform to the environmental quality level required. In order to comply with these conditions, those fuels must comply with certain specifications, i.e. a set of physical and chemical characteristics with maximum or minimum specified values, obtained through test procedures or standards [8, 9], including their volatility.
With the aim of controlling engine performance and the formation of vapours which may form explosive mixtures with air or escape to the atmosphere as emissions (VOCs—volatile organic compounds), most of the specifications for petroleum distillate products, specially the main automotive engine fuels, limit the values of certain distillation characteristics (volatility).
A fuel distillation range provides decisive information about its composition, its use and its behaviour during storage.
Among the wide variety of features to consider when establishing the quality of a fuel used in auto-motion, volatility stands out as one of the most critical ones since it is a characteristic directly related to engine performance and pollutant emissions [2–4].
Petrol is a fuel which is a liquid state in the fuel tank and in the fuel injectors (or carburettor on older engines) and which is nebulized with air before being injected into the combustion chamber:
If the volatility of fuel is low, the petrol does not exist in the gas phase, and there will be difficulties with the starting up of the engine and the behaviour of the engines in cold regimes.
If the volatility is high, the petrol can be vaporized in the tank itself or in the pipelines (‘vapour lock’). As a consequence the injection rate is inadequate, and the engine drowns.
The volatility characteristics of a diesel have a great influence on the performance of diesel engines:
If the volatility is low, then high distillation end points are obtained, which are indicative of high combustion times and poor combustion of heavy hydrocarbons. This will lead to the formation of smoke, loss of power and increased fuel consumption.
If the volatility is high, then the fuel can cause incidents of ‘vapour lock’ in the lines.
Volatility is not a physical magnitude that can be measured directly; it is necessary to define methods of evaluating it. One universally used method to determine the volatility of a fuel is the distillation test [10, 11] that offers different information according to the type of fuel tested.
The distillation test measures the percentage of vaporized fuel as the temperature increases. The test result is a curve obtained under standardized conditions of temperature versus percentage of evaporated fuel (Figure 1) wherein the different sections of the curve allow us to interpret the different behaviours of the product:
At least 20% V/V fuel must be vaporized below 70°C to ensure good cold start capability. If this percentage is lower, then difficulties may occur at start-up; if it is too high, evaporation losses will occur in the fuel tank, and vapour bubbles may form in the intake manifold of the vehicle.
The temperature at which 50% V/V of fuel is vaporized is a critical parameter, since if it is too low it can cause the solidification of water vapour contained in the intake air resulting in formation of ice on elements forming the blend.
If the temperature at which 90% V/V of the fuel is vaporized is too high, then the fuel can remain in liquid form within the cylinder, displacing the lubricant and coming to cause oil dilution. Additionally, combustion may be hampered, causing irregular operation of the engine. Also, the presence of hydrocarbons of high boiling point in the petrol is decisive for the generation of polluting emissions.
Distillation curve of petrol.
The percentages of fuel evaporated at 70, 100 and 150°C are limited. Additionally, a limitation in the final boiling point of to 210°C is also implemented in the regulations, ensuring the complete combustion of hydrocarbons and the non-formation of deposits in the combustion chamber and spark plugs.
In a CIE, the volatility problems that may be present are notably different from those in SIE. In the regulations, there are no limitations in the light section of the curve but only for the end zone, where the fractionation of the components occurs.
The distillation test, in this case, measures the percentage of fuel which is recovered as the temperature increases. The test result is a curve obtained under standardized conditions of temperature versus percentage recovered (Figure 2). In these, fuel is important to note:
The temperature at which vaporization ends, since if this is very high, combustion of the less volatile components will be incomplete, fuel droplets may reach the cylinder walls and dilution of the lubricating oil may take place, thereby increasing wear and producing coke deposits in the combustion chamber and waste segments [3].
The end point of the fractionation of the components. This parameter is established so as 65% V/V must not have distilled before 250°C; 85% V/V should be distilled before 350°C,and 95% V/V before 360°C.
Distillation curve of diesel.
Figure 3 shows the distillation curves associated to both types of automotive fuels, petrol and diesel.
Comparison between distillation curves of petrol and diesel.
ISO 3405 International Standard has been adopted by the European Standard EN ISO 3405, and it received the rank of the National Standard, by publication in the national language of an identical text under the responsibility of a member of CEN (European Committee for Standardization): UNE-EN ISO 3405 (Spain), DIN-EN ISO 3405 (Germany), etc.
This procedure aims to establish the steps ‘for determining the distillation characteristics of light and middle distillates derived from petroleum having initial boiling points above 0°C and end points below approximately 400°C’.
There are standards similar to ISO 3405 developed by other agencies with the same objective, such as ASTM D86: Standard Test Method for Distillation of Petroleum Products and Liquid Fuels at Atmospheric Pressure, whose first version dates from 1978, or IP 123: Petroleum Products—Determination of Distillation Characteristics at Atmospheric Pressure.
The test samples are classified into ‘groups’ based on their composition and the characteristics of expected volatility. In the case of fuels for automotive engines, petrol with up to 10% V/V ethanol is included in Group 1 and diesels with up to 20% V/V biodiesel in Group 4 (Table 1). Belonging to a particular group defines the setup of the equipment to be used and the condenser temperature. Finally, it determines the operation conditions to be used in the process of distillation by ISO 3405 (Table 2).
Group 1 | Group 4 | |
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Type of sample | Petrol | Diesel |
Reid vapour pressure (kPa) | ≥65.5 | <65.5 |
Characteristics of expected volatility | ||
Initial distillation point, IDP (°C) | – | >100 |
Final boiling point, FBP (°C) | ≤250 | >250 |
Sample type by group and expected volatility characteristics.
Group 1 | Group 4 | |
---|---|---|
Temperature of condensador bath (°C) | 0–1 | 0–60 |
Temperature of medium around recovered receiving cylinder (°C) | 13–18 | ±3 of charge |
Time from the first heat to IBP (min) | 5–10 | 5–15 |
Time from IBP to 5% (V/V) recovered (s) | 60–100 | – |
Uniform average rate from 5% (V V) of recovered to 5 mL in the flask (mL/min) | 4–5 | 4–5 |
Time from 5 mL residue in the flask to FBP (min) | ≤5 | ≤5 |
Test conditions.
During the testing process, a 100 mL test portion is distilled under the specified conditions appropriate to the fuel group, and systematic observations of thermometer readings and volumes of condensate recovered are made.
The introduction of new formulations in automotive fuels made necessary the adaptation of the standard in effect at the time of their appearance (ISO 3405:2000), and, given the volatility characteristics of the new formulations, it was also necessary to validate the test method again based on new precision criteria.
The new version of the ISO 3405 standard (2011) establishes new criteria, based on the group to which it belongs the sample tested, to determine the validity of two results obtained under the same conditions by one operator using the same apparatus, in the same operating conditions, on the same day, on identical samples (repeatability, r) or obtained by different operators working in different laboratories on identical material test (reproducibility, R).
In the case of petrol and bioethanol blends (Group 1), these criteria are listed in Tables 3 and 4 and in the case of diesel and biodiesel blends (Group 4) in Tables 5 and 6.
2000 | Evaporated % (V/V) | 2011 | |
---|---|---|---|
Repeatability Group 1 | Repeatability Group 1 | Valid range (°C) | |
3.9 | IBP | 0.0295 (E + 51.19) | 20–70 |
r2 + 0.56 | 10 | 1.33 | 35–95 |
r2 | 50 | 0.74 | 65–220 |
r2 | 90 | 0.00755 (E + 59.77) | 110–245 |
4.4 | FBP | 3.33 | 135–260 |
Repeatability (Group 1).
r2 is a constant function of the slope, ∆C/∆V, at each distillation point, with values calculated from r2 = 0.673 (∆C/∆V) + 1.131.
E is the temperature at the percentage evaporated within the prescribed valid range.
2000 | Evaporated % (V/V) | 2011 | |
---|---|---|---|
Repeatability Group 4 | Repeatability Group 4 | Valid range (°C) | |
3.5 | IBP | 0.018 T | 145–220 |
1.42 (∆C/∆V) + 1.2 | 10 | 0.0094 T | 160–265 |
1.42 (∆C/∆V) + 1.2 | 50 | 0.94 | 170–295 |
1.08 (∆C/∆V) + 1.1 | 90 | 0.0041 T | 180–340 |
1.08 (∆C/∆V) + 1.1 | 95 | 0.01515 (T–140) | 260–340 |
3.5 | FBP | 2.2 | 195–365 |
Repeatability (Group 4).
Slope: ∆C/∆V
T is the temperature at the percentage recovered within the prescribed valid range.
2000 | Evaporated % (V/V) | 2011 | |
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Reproducibility Group 1 | Reproducibility Group 1 | Valid range (°C) | |
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Reproducibility (Group 1).
R2 is a constant function of the slope, ∆C/∆V, at each distillation point, with values calculated from R2 = 1.998 (∆C/∆V) + 2.617.
E is the temperature at the percentage evaporated within the prescribed valid range.
2000 | Evaporated % (V/V) | 2011 | |
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Reproducibility Group 4 | Reproducibility Group 4 | Valid range (°C) | |
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Reproducibility (Group 4).
Slope: ∆C/∆V
T is the temperature at the percentage recovered within the prescribed valid range.
Step 1.
A sample selection of automotive fuel (petrol, diesel) with and without blend of biofuel (bioethanol, biodiesel) for a field study is used. The variations in product volatility as a result of the presence of biofuel in its composition are checked.
Each sample is tested in duplicate by two operators.
Step 2.
The changes in criteria established for repeatability and reproducibility in Standard ISO 3405 are studied; certified reference materials are used.
Acetone: cleaning solvent.
Certified reference material (CRM).
Distillation flasks: flasks should have a capacity of 125 mL and be constructed of heat-resistant glass, according to the dimensions and tolerances given in Standard ISO 3405:2011.
Receiving cylinder: graduate cylinder of 100 mL capacity, with a mark at 100 mL and metal base.
Residue cylinder of 5 mL capacity.
Certified temperature-sensor pt100 to an accuracy of 0.01C.
Centring device, for centring the temperature sensor, adjusts the neck distillation flask, allows to centre the temperature sensor and prevents steam leaks.
Automated equipment for petroleum product distillation satisfies the requirements established in the Standard ISO 3405:2011; the maximum error tracking device level is 0.3 mL.
Clean the condenser tube, employing acetone. Dry thoroughly to remove any portion of acetone used for cleaning the device.
Check that the temperature probe is properly seated in the centring device. Check your state and proper cleaning.
Choose the support plate of the flask as the orifice diameter thereof according to the type of sample to be tested (Table 7).
Check that the value of atmospheric pressure recorded by the apparatus is coincident with that indicated by the recording barometer atmospheric pressure in the laboratory.
Group 1 | Group 4 | |
---|---|---|
Diameter of hole in flask-support board (mm) | 38 | 50 |
Temperature at start of test (°C) | ||
Flask and thermometer | 13–18 | ≤ambient |
Flask-support board and shield | ≤ambient | – |
Receiving cylinder and sample | 13–18 | 13 at ambient |
Preparation of apparatus.
Measure the test portion precisely to the 100 mL mark of the receiving cylinder, and then transfer it as completely as practical to the distillation flask, taking care that none of the liquid flows into the vapour tube. If irregular boiling (bumping) is expected, add a small volume of clean and dry boiling chips to the test portion.
Fit the flask vapour tube, provided with a silicone rubber stopper, tightly into the condenser tube. Adjust the distillation flask in a vertical position so that the vapour tube extends into the condenser tube for a distance of 25–50 mm. Raise and adjust the flask-support board to fit snugly against the bottom of the flask.
Fit the receiving cylinder with a drip deflector, through which the distillate is going to drip.
Place the receiving cylinder that was used to measure the test portion, without drying, into the bad under the lower end of the condenser tube so that the end of the condenser tube is centred in the receiving cylinder and extends therein for a distance of at least 25 mm.
After the choice of the method, which has been specifically developed to the distillation test according to Table 2 and the corresponding group, follow the steps indicated by the system software. Any distillation that does not meet above conditions must be repeated, as well as those in which the actual loss differs by more than 2 mL from the estimated value.
The data required for calculations is recorded in the range between the initial and the final boiling point, with an accuracy of 0.1 mL for all the readings on the receiving cylinder and with an accuracy of 0.1°C for all the readings on the temperature sensor.
Distillations carried out with automated instrument do not require manual calculation; the system software makes the appropriate calculations according to the corrective measures established by the Standard. However, it is certainly right to check the atmospheric pressure value does not differ by more than ±10 hPa from the value provided by the barometer in the laboratory.
Distillation test is carried out on 24 petrol samples with a bioethanol percentage that varies between 0.0 and 4.0% V/V, obtaining their corresponding distillation curves. Among these curves, we have selected seven for being analyzed and included in the present paper. Obtained results are shown in Figure 4.
Distillation curves: petrol and blends with bioethanol (0.0–4.0% V/V).
After studying the trend and as the different sections of the curve give the opportunity to interpret the different product performances, a particular observation of each section is developed, making a graphic comparison on the basis of an average value (Figures 5–7).
Initial section (IBP-E20). Distillation curves of petrol samples.
Middle section (E20-E70). Distillation curves of petrol samples.
Final section (E70-FBP). Distillation curves of petrol samples.
Distillation test is carried out on 24 diesel samples which contain a different biodiesel percentage (FAME), obtaining their corresponding distillation curves. Among these curves, we have selected seven for being analyzed and included in the present paper; six of them correspond to diesel samples with a usual biodiesel percentage, between 0.0 and 7.0% V/V. However, the other one corresponds to a diesel sample with a 30% V/V biodiesel percentage; this is outside the Standard scope. Obtained results are shown in Figure 8.
Distillation curves: diesel and blends with FAME (0.0–30.0% V/V).
As in the case of petrol samples, here we study the trend and the different sections of the distillation curve. However, in this case, the distillation curve will be divided for its study in two different sections: the first one comprises from the initial distillation point until 60% of the total volume is collected, whereas the second one comprises from this point to the final distillation point. A graphic comparison on the basis of an average value is also used here to illustrate the results, making a graphic comparison on the basis of an average value (Figures 9 and 10).
Initial section (IBP-R50). Distillation curves of diesel samples.
Final section (R65-FBP). Distillation curves of diesel samples.
In order to know and be able to check the quantitative change derived from the precision requirement set in the new edition of the Standard, which involves repeatability and reproducibility, two different certified reference materials are used; one of them matches with the petrol boiling range, whereas the other one matches with the diesel boiling range.
Two analysts are involved in the test process; each using a different distillation automated equipment, in the same laboratory, and maintaining the required operation conditions for the standardized calculation. Distillation test is carried out in duplicate, and their results are shown in Figures 11–14.
Quality control according to ISO 3405:2000; petrol-CRM.
Quality control ISO 3405:2011; petrol-CRM.
Quality control according to ISO 3405:2000; diesel-CRM.
Quality control according to ISO 3405:2011; diesel-CRM.
The fourth edition of ISO 3405 Standard came into force on 15 January 2011. This fourth edition cancelled and replaced the third edition, which had come into force on 1 March 2000. It is noteworthy that the text of this new edition is in line with the American Standard ASTM D86, widely used throughout the petroleum industry.
The fourth edition of ISO 3405 Standard introduces significant changes which are the result of the new formulations of automotive fuels and which are listed below:
The latest edition of the Standard is wider in scope. It has been modified in order to include the new fuel formulations, obtained from mixtures of biofuels and petrol (containing up to 10% V/V of ethanol) and diesel (containing up to 20% V/V of biodiesel). Additionally, it establishes a clear definition of ‘light distillates’ and ‘middle distillates’.
Petrol from direct distillation (the petroleum fraction obtained by distillation at atmospheric pressure) no longer has their own group (the former Group 0, since the latest edition of the Standard refers only to four distillation Groups 1, 2, 3 and 4), instead of the former five Groups 0, 1, 2, 3 and 4. Petrol and their mixtures with bioethanol belong to Group 1, while diesel and their mixtures with biodiesel belong to Group 4.
This Standard specifies an assay method, utilizing either manual or automated equipment. However, its latest edition sets the automated alternative as the reference method in the event of a dispute, unless otherwise agreed.
The latest edition of the Standard includes a specific point related to the test procedure utilizing automated equipment. Although the former edition allowed the use of this type of equipment, the procedure had not been defined so far. Nowadays, most distillation tests are carried out utilizing automated equipment. Once programmed, the procedure is performed in an autonomous way by the instrument, but programming them is not easy. It requires an absolute control and knowledge of the process as well as of the conditions required for each specific sample. The validity on the findings remains dependant on performing a validation study.
The latest edition of the Standard requires the establishment of new criteria for calculating repeatability and reproducibility.
The latest Standard specifies the percentages of distillate required at specific temperatures for petrol. Accordingly, the Standard includes a normative annex (Annex C) which provides values of reproducibility of petrol percent volume evaporated at 70, 100, 150 and 180°C. These reproducibility statements were estimated for the specification temperatures and percentages from the data collected in an inter-laboratory study:
E70 → R = 2.7% V/V.
E100 → R = 2.2% V/V.
E150 → R = 1.3% V/V.
E180 → R = 1.1% V/V.
As we set before, the petrol distillation curve study was developed through its analysis in three different sections. From the study of the two first sections (IBP-E20; E20-E70), we conclude that the evaporated percentage is higher in blends. So, in the range between 30 and 90°C, which comprises from IBP to the middle boiling point, the petrol volatility increases from bioethanol addition. In the final section, the sample distillation curves coincide to a great extent, and there are no any significant changes, as might be expected from the bioethanol boiling point.
For diesel blends, containing up to 7% V/V biodiesel, the study of the distillation curve indicates the recovered percentage has risen slightly in the first section, while we can observe a bigger variation in the last one, where the fractioning of the heavy components of the samples takes place; this is between R90 and R95.
Diesel blends, containing 30% V/V biodiesel, are outside the ISO 3405:2011 Standard scope. Distillation test has been carried out, considering them as part of Group 4 and, then, accordingly to the conditions established for that group.
Distillation curve for diesel blends, containing 30% V/V biodiesel, indicates clearly the volatility diminution from the own characteristics of the biodiesel: high boiling point and low volatility (Figure 15). As in this type of products, the volatility diminution is directly related to the viscosity; the use of this type of blends in the engines is intimately related to their operation and performance.
Diesel distillation curves, 0.0% V/V and 30.0% V/V FAME.
The latest edition of the Standard, ISO 3405:2011, establishes new repeatability and reproducibility criteria. This new criteria has reduced measure variations allowed in the whole range, affecting petrol (Group 1) and diesel (Group 4). Relatively small variations are allowed in the middle section of the distillation curve, whereas a more significant variation is allowed in the IBP and FBP determination, as shown in Figures 16 and 17.
The values of repeatability and reproducibility for the same petrol-CRM, according to ISO 3405:2011 and ISO 3405:2000.
The values of repeatability and reproducibility for the same diesel-CRM, according to ISO 3405:2011 and ISO 3405:2000.
The EU has promoted turning plants into fuel as a way to reduce carbon emissions from transport for the last 10 years. Today however, some say that biofuels have become part of the problem and actually have generated more CO2 than they saved, as the demand for crops needed to produce them has led to the destruction of forests. The EU now wants to limit the amount of fuel produced from food crops and shift to biofuels that are produced from non-food sources, such as waste.
The EU is committed to meeting 10% of its transport fuel needs from renewable sources, mostly biofuels, by 2020. But pressure is growing to change this policy by limiting the amount of food-based biofuels.
In response to these concerns, the European Parliament voted in favour of a compromise deal with the Council to limit the amount of fuel produced from food crops such as rapeseed and palm oil. The new legislation will enter into force in 2017 [12].
The future liquid automotive fuel formulations will remain dependant on distillation test as a powerful quality control tool. It provides useful information, which can be employed to establish optimal conditions of use in the appropriate engines, as well as to establish safe conditions for storage, transportation and delivery.
In 2011, the addition of up to 10% V/V bioethanol in petrol and up to 20% V/V of biodiesel in diesel, as a result of biofuel promotion, has prompted a careful review of the ISO 3405 Standard: Petroleum Products. Determination of Distillation Characteristics at Atmospheric Pressure.
Changes include:
The broadening of the scope to cover these new products
The adjustment of the calculations related to the method accuracy
Standard relating to test standardization, which establishes the procedure to determine the distillation characteristics of petroleum products at atmospheric pressure, remains open to future review and updating.
Renewable energy resources have become a promissory alternative to overcome the problems related to high pollution and limited sources of conventional energy. So, the analysis of energy resources and their economic feasibility is a concern topic for researchers around the world [1, 2, 3, 4]. In this context, photovoltaic power plants have become one of the most important renewable sources of energy that have rapidly spread in the last decade. However, the assessment of the solar resource is not a topic usually approached by engineers and researchers due to the complexity in the process of computing the data, being extensive when the global horizontal irradiation is processed to obtain the global tilde irradiation. Therefore, this book chapter provides a step-by-step methodology for computing the global irradiation over the plane of photovoltaic arrays.
The quality of solar resource data is critical for economic and technical assessment of solar power installation. Understanding uncertainty and managing weather-related risk are essential for successful planning and operating of solar electricity assets. High-quality solar resource and meteorological data can be obtained by two approaches: high-accuracy instruments installed at a meteorological station and complex solar meteorological models, which are validated using high-quality ground instruments [5].
The input information available for PV designers is usually restricted to the 12-monthly mean values of global horizontal irradiation (GHI) and average temperature, which characterize solar climate of locations. However, the global irradiation over the plane of the PV array is necessary to calculate the energy production of a photovoltaic system.
The assessment of radiation arriving on an inclined surface, using global horizontal data as input, raises two main problems; first, to separate the GHI into their direct and diffuse components (decomposition) and, second, from them, to estimate the radiation components falling on an inclined surface (transposition) [6]. To solve these problems, it is important to describe in detail parameters such as declination angle, solar hour angle, solar zenith, solar altitude, solar azimuth, angle of incidence, solar constant, extraterrestrial irradiance over the horizontal surface, clearness index, and diffuse fraction index [6, 7, 8].
As regards decomposition models, in Ref. [9], authors reviewed and compared four decomposition models for monthly average of horizontal daily irradiation: a linear relationship proposed by Page [10], two polynomial equations defined by the authors of Refs. [11, 12], and a local correlation proposed by Macagnan et al. [13]. The authors of Ref. [9] stand out for the Page decomposition model of Ref. [10] in combination with the Perez transposition model [13] as a good performance combination used for passing from global horizontal irradiation to effective in-plane irradiance when it is started from monthly average of daily irradiation values. After applying the decomposition models, direct, diffuse, and albedo components of irradiation can be obtained.
For obtaining radiation components falling on an inclined surface, geometric considerations can be taken into account [9]. In Ref. [9], eight transposition models were reviewed, obtaining the best results using the Perez model [13]. Similar results were obtained in Ref. [14], where four transposition models were compared and validated with two-year data measured at site, and Liu and Jordan isotropic sky model is used in this book chapter due to its simplicity of implementation and good results reported in Ref. [15].
This book chapter describes in detail a methodology to determine the global irradiation over the plane of photovoltaic arrays. The chapter is organized as follows: Section 2 contains the proposed methodology, Section 3 includes experimental results that include data processing, and Section 4 presents the conclusions.
The proposed methodology includes the data processing and also the definitions to understand it. Therefore, some basic definitions are presented below:
It is the angle between the equatorial plane and a straight line drawn between the center of the Earth and the center of the sun. It may be considered as approximately constant over the course of any day. It can be calculated using Eq. (1), where
It is the difference between noon and the selected moment of the day in terms of a 360° rotation in 24 h.
where
Solar zenith is the angle between the vertical and the incident solar beam, and it can also be described as the angle of incidence of beam radiation on a horizontal surface [6]. The complement of the zenith angle is called the solar altitude,
Eq. (7) can be used to find the sunrise angle (
In accordance with the sign convention,
It is the angle between the meridians of the locations and the sun. It can also be described as the angular displacement from noon to the projection of beam radiation on the horizontal plane. The solar azimuth is given by:
In the Northern Hemisphere, true solar is the reference of the system, and it is defined as positive toward the west, that is, in the evening, and negative toward the east, that is, in the morning [6]. In Figure 1, the solar zenith, solar altitude, and solar azimuth are described.
Position of the sun relative to a fixed point on the earth defining the solar azimuth (ψs), the solar zenith (θzs), and the solar altitude (γs).
Most practical applications require the position of the sun relative to an inclined plane to be determined. The angle of solar incidence between the sun’s rays and the normal to the surface is given by:
where
Definition of angles used as coordinates for an element of sky radiation to an inclined plane of tilt β and oriented to α.
It is the amount of solar radiation received at the top of the atmosphere on a normal plane at the mean Earth-sun distance [6]. A good approximation of this value is:
Extraterrestrial irradiance over the horizontal surface (
If Eq. (14) is integrated over the day, the following expression is obtained:
Hence, average daily extraterrestrial irradiation in a month over a surface is obtained by:
The value calculated in Eq. (16) is used to estimate the clearness index (
It is the relation between the solar radiation at the Earth’s surface and the extraterrestrial radiation over the horizontal plane. The clearness index
where
It is the relation between the diffuse radiation over the horizontal plane and the global radiation over the horizontal plane. This index is widely used on decomposition models to separate the global radiation into its direct and diffuse components.
The modeling process for calculating the effective in-plane hourly irradiation when starting from monthly average of horizontal daily irradiation and using monthly average daily irradiance profiles is shown in Figure 3 [9].
Calculation of daily irradiation on an inclined surface.
The daily irradiance profile can be defined in terms of irradiance divided by daily irradiation and on assuming that the profile of the extraterrestrial horizontal solar radiation translates directly into the profile of the diffuse component while an empirical correction is needed for global radiation [11]. The following equations describe the model to calculate the daily irradiance profile starting from daily average monthly values:
with
where
The diffuse component of the average daily irradiation,
The decomposition model proposed by Page consists of a linear equation that correlated the diffuse fraction index and the clearness index using data from locations situated between 40°N and 40°S, and it is given by:
Once the global horizontal irradiance is separated into direct and diffuse components and the daily irradiance profile is obtained, it is necessary to calculate the effective irradiance on the plane of the array. The irradiance over the plane with a tilt
where
The beam transposition factor is calculated straightforward from simple geometric considerations [9]:
Assuming isotropic albedo radiation, the corresponding transposition factor is given by:
where
The diffuse transposition factor depends on the assumption made for the sky radiance distribution. In Ref. [9], eight transposition models are reviewed, obtaining the best results using the Perez model. Similar results are obtained in Ref. [14], where four transposition models are compared and validated with two-year data measured at site, and the most accurate results were obtained by the Hay and Davies transposition model and the Perez transposition model. In this work, the Liu and Jordan isotropic sky model is used due to its simplicity of implementation and good results as reported in Ref. [15].
In the transposition model proposed by Liu and Jordan, the diffuse radiation is given by an isotropic component coming from the entire celestial hemisphere. The diffuse transposition factor is given by:
In summary, the global irradiation over the tilted plane is calculated by:
Santa Cruz del Islote in Colombia was used as a location for the case study. Data that consist on the monthly average daily global horizontal irradiance (
Location | Islote de Santa Cruz, Colombia | |
---|---|---|
Latitude | 9.79 | |
Longitude | −75.859167 | |
Time zone (GTM) | −5 | |
Tilt | 10 | Plane inclination |
Azimuth | 0 | Plane orientation (South = 0°; West 90°) |
GRF | 0.2 | Ground reflection factor (0–1) Default = 0.2 |
Month | Daily sum of global irradiation [Wh/m2] | Average diurnal (24-h) air temperature [°C] |
January | 5922.6 | 27.8 |
February | 6271.4 | 27.6 |
March | 6267.7 | 27.6 |
April | 5906.7 | 27.7 |
May | 5367.7 | 27.9 |
June | 5396.7 | 28.5 |
July | 5587.1 | 28.7 |
August | 5538.7 | 28.5 |
September | 5363.3 | 28.2 |
October | 5025.8 | 27.9 |
November | 4970.0 | 27.8 |
December | 5200.0 | 28.0 |
Average | 5568.1 | 28.0 |
Meteorological input parameters [16].
A MATLAB routine was used to compute the monthly global irradiance over the horizontal and over the plane. Results were also compared with the data that can be processed from Solargis, and Table 2 shows the results obtained. Comparison shows that the results are good enough for the purpose of this work.
Global horizontal irradiation (kWh/m2) Solargis | Global horizontal irradiation (kWh/m2) calculated | Dev (%) | Global tilted irradiation (kWh/m2) Solargis | Global tilted irradiation (kWh/m2) calculated | Dev (%) | |
---|---|---|---|---|---|---|
January | 183.6 | 182.0 | −0.88% | 201.9 | 198.6 | −1.65% |
February | 175.6 | 174.2 | −0.81% | 186.9 | 184.3 | −1.41% |
March | 194.3 | 193.0 | −0.68% | 198.5 | 196.2 | −1.14% |
April | 177.2 | 176.1 | −0.65% | 175 | 172.9 | −1.17% |
May | 166.4 | 165.2 | −0.70% | 160.1 | 158.8 | −0.83% |
June | 161.9 | 160.8 | −0.71% | 153.6 | 152.6 | −0.65% |
July | 173.2 | 172.0 | −0.69% | 165.3 | 163.9 | −0.84% |
August | 171.7 | 170.6 | −0.65% | 167.8 | 166.1 | −1.03% |
September | 160.9 | 159.8 | −0.70% | 162 | 160.1 | −1.17% |
October | 155.8 | 154.4 | −0.91% | 162.4 | 159.5 | −1.79% |
November | 149.1 | 147.7 | −0.96% | 160.5 | 157.1 | −2.13% |
December | 161.2 | 159.7 | −0.93% | 177.8 | 174.1 | −2.09% |
Year | 2030.9 | 2015.3 | −0.77% | 2071.8 | 2044.1 | −1.34% |
Global horizontal and tilted irradiations.
In Figure 4, it is shown the daily global profile on the horizontal and on the tilted plane for the first 4 days of the year calculated for the selected location. As expected, global tilde irradiation is higher than the global horizontal irradiation.
Daily global irradiation calculated for “Islote de Santa Cruz.”
This book chapter presented a methodology that describes in detail the data processing to obtain the global irradiation over the plane of photovoltaic arrays. The methodology includes definitions and equations necessary to perform the processing of the data. The following parameters were described and along with their equations: declination angle, solar hour angle, solar zenith, solar altitude, solar azimuth, angle of incidence, solar constant, extraterrestrial irradiance over the horizontal surface, clearness index, and diffuse fraction index.
The obtention of the global irradiance over a tilde plane requires decomposition models, which provide direct, diffuse, and albedo components of irradiation. This book chapter provides global horizontal irradiation to effective in-plane irradiance when it is started from monthly average of daily irradiation values.
This book chapter is extensive in the use of geometric considerations. This is due to the fact that input data are global horizontal irradiation and average temperature, while output data are the global irradiation over a tilde PV plane. Therefore, equations and schemes were provided for facilitating the explanation.
The authors gratefully acknowledge the financial support provided by the Colombia Scientific Program within the framework of the call “Ecosistema Científico” (Contract No. FP44842-218-2018). The authors also want to thank the “Programa de Sostenibilidad de la UdeA.”
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