EP4639761A1

EP4639761A1 - Method for determining an efficiency coefficient of a photovoltaic system

Info

Publication number: EP4639761A1
Application number: EP23837198.3A
Authority: EP
Inventors: Maxime LEURENT; Domenico Di Domenico
Original assignee: TotalEnergies Onetech SAS
Current assignee: TotalEnergies Onetech SAS
Priority date: 2022-12-21
Filing date: 2023-12-19
Publication date: 2025-10-29
Also published as: WO2024133280A1

Abstract

This invention addresses a computer-implemented method for determining an efficiency coefficient of a photovoltaic system (2), characterized in that it comprises the following steps: - determining a peak power value of the photovoltaic system (2); - obtaining previous irradiance values associated with respective previous output power values and with respective times of at least one previous day; - determining efficiency coefficients values at respective times of a day, based on the peak power value, on the previous irradiance values, on the respective previous output power values and on the respective times of the at least one previous day.

Description

Description Title of the invention: Method for determining an efficiency coefficient of a photovoltaic system

[0001] The invention relates to the field of energy forecasting, more specifically to the field of solar energy forecasting.

[0002] In a photovoltaic power station, it is expected from the energy management system to forecast output power values to be provided by the station at different times of a day, in particular to meet contractual commitments.

[0003] It is known to determine an output power value of a photovoltaic system according to the following formula: P = c * kWc * GHI, wherein P is the output power value of the photovoltaic system, GHI is a global horizontal irradiance value received by the photovoltaic system, kWc is the peak power of the photovoltaic system, and c is an efficiency coefficient of the photovoltaic system taking into account the state of the photovoltaic system at a specific time, such as soiling of the photovoltaic cells, wear, occasional failures, unexpected shading.

[0004] Therefore, to forecast the power to be provided by the station at different times on a future day, existing methods use GHI forecast data, provided by other entities, to forecast the output power value of a specific time according to the mentioned formula and based on the GHI forecast value at this specific time, the peak power value and an estimated efficiency coefficient c.

[0005] However, it is difficult to estimate the efficiency coefficient c of the formula, as it changes over time within a single day and also in the long run, having a huge impact on the output power value.

[0006] As a result, using the formula without precisely knowing the efficiency coefficient c fails to precisely forecast the power to be provided.

[0007] It is also useful to monitor the evolution of this coefficient c for the maintenance of the photovoltaic system.

[0008] Document WO2017/035629 teaches a method and system for solar power forecasting, wherein the output power value of the photovoltaic system is not forecast based on the formula but based on an artificial intelligence model.

[0009] However, input data required to forecast the output power value, and training data required to generate the model, comprise types of data that are difficult or costly to retrieve, such as cloudiness, cloud types, cloud-shadow location, or satellite-based images for estimating obstructions data.

[0010] Furthermore, to be efficient, the artificial intelligence model needs lots of training data, for example a year of historical data. When a new phenomenon happens, such as sand rain, such a trained model will produce inaccurate output power values if it has not been trained to take into account such a phenomenon.

[0011] Finally, such an artificial intelligence model works as a black box and does not allow to determine an efficiency coefficient of a photovoltaic system and follow its evolution over time within a day and more.

[0012] A need therefore exists for a simple method to determine an efficiency coefficient of a photovoltaic system, before using this coefficient to forecast an output power value or to monitor the efficiency of the photovoltaic system over time.

[0013] According to one aspect of the invention, there is provided a computer- implemented method for determining an efficiency coefficient of a photovoltaic system, characterized in that it comprises the following steps:

- determining a peak power value of the photovoltaic system;

- obtaining previous irradiance values associated with respective previous output power values and with respective times of at least one previous day;

- determining efficiency coefficients values at respective times of a day, based on the peak power value, on the previous irradiance values, on the respective previous output power values and on the respective times of the at least one previous day.

[0014] Thus, the evolution of the efficiency coefficient over time is modelled based on previous output power values and their associated previous irradiance value at their respective times in a previous day. The efficiency coefficients values are then used either to accurately forecast an output power value or to monitor the state of the photovoltaic system over time.

[0015] Other optional characteristics are introduced thereafter and can be taken alone or in combination.

[0016] Preferably, the step of determining efficiency coefficients values comprises :

- determining, based on the peak power value, on the previous irradiance values, on the previous output power values and on the times of the at least one previous day, a function depending on time,

- determining, based on the function, the efficiency coefficients values at the respective times of a day.

[0017] Thus, the function allows to determine, for any time in a day, the value of the efficiency coefficient of the photovoltaic system. The input of the function is the time of the day for which the coefficient is to be determined. [0018] Advantageously, the step of determining the function comprises a step of determining, based on the peak power value, on the previous irradiance values, on the previous output power values and on the times of the at least one previous day, pairs of parameters of the function, each of the pairs having an efficiency coefficient value and a time value defining discrete efficiency coefficient values at specific times.

[0019] Thus, the function has pairs of parameters for which, in each pair, a coefficient value is associated with a time value. In other terms, a pair of parameter is a point having an efficiency coefficient value and a time value. Several pairs form several discrete efficiency coefficient values distributed over time. The function allows to determine the efficiency coefficient values at any time in a day based on these discrete values, in other terms based on these pairs of parameters and on the time of the day. Therefore, it is necessary to determine these parameters based, in particular, on the previous output power values and on the previous irradiance values.

[0020] Preferably, the step of determining the pairs of parameters of the function comprises a step of fitting the parameters based on the peak power value, on the previous irradiance values, on the previous output power values and on the times of the at least one previous day.

[0021] Thus, the pairs of parameters are fitted in order to find the pairs of parameters that allow the efficiency coefficient values to be as accurate as possible.

[0022] Advantageously, the step of fitting comprises a step of :

- determining theoretical output power values based the peak power value, on the previous irradiance values, and on pairs of parameters having efficiency coefficient values to be fitted and time values to be fitted,

- fitting the efficiency coefficient values and the time values of the pairs of parameters based on a deviation between previous output power values and theoretical output power values.

[0023] Thus, the step of fitting is based on a comparison between theoretical output power values, determined based on the parameters to be fitted, and real previous output power values, associated with the same respective previous times. Thus, in this option, the fitting step is not based on a comparison between previous coefficient values and theoretical coefficient values. Indeed, determining previous coefficient values would necessitate to divide an output power value by other values, for example by a small irradiance value, which could results in inaccurate efficiency coefficients values. It is therefore more accurate to compare theoretical output power values and previous output power values to fit the pairs of parameters.

[0024] Preferably, the step of determining, based on the function, the efficiency coefficients values at the respective times of the day, comprises a step of interpolating, to determine the efficiency coefficient values, based on the discrete eff efficiency coefficient values at specific times

[0025] Thus, the function comprises an interpolating step that allows to determine the efficiency coefficient values at any time in a day based on an interpolation between the discrete values, in other terms based on the pairs of parameters. In other terms, the pairs of parameters correspond to values of efficiency coefficients at some specific times of a day, and the efficiency coefficients values to be determined for other times are determined based on interpolations of these parameters.

[0026] Advantageously, the step of determining the pairs of parameters comprises a step of determining between two and fifty pairs of parameters, preferably between five and fifteen, respecting the following requirements:

- efficiency coefficient values of the pairs are between two predetermined values, the two predetermined values being preferably respectively zero and four;

- at least one of the pairs of parameters has a time value before a predetermined time of the day and at least another one of the pairs of parameters has a time value after a predetermined time of the day;

- the time value differences between each consecutive pair of parameters of the day are more than a predetermined duration, preferably ten minutes.

[0027] Thus, determining only a few pairs of parameters, in other terms a few efficiency coefficient values associated with time values, allows to simplify a model of the efficiency and to smooth a curve related to the evolution of the efficiency over time. The requirements allow to have the coefficient values of the parameters well distributed over the day and thus to take into account every main part of a day.

[0028] Advantageously, the step of obtaining the previous irradiance values associated with respective output power values comprises:

- retrieving previous irradiances values received by the photovoltaic system at respective times of the at least one previous day;

- retrieving previous output power values provided by the photovoltaic system at respective times of the same at least one previous day;

- associating each of these previous irradiance values to one of the previous output power values when:

- the time of the previous irradiance value and the time of the previous output power value are separated by less than a predetermined time value,

- the previous output power value is less than a predetermined maximal value, the maximal value corresponding to a power limit of an inverter of the photovoltaic system minus a tolerance value, - the previous irradiance value is greater than or equal to a predetermined minimum irradiance value, and

- the time of the previous output power value is separated from the time of a previous output power value equal to or greater than the maximal value by a predetermined time value.

[0029] Thus, in order to benefit only from relevant values, previous values that are likely to correspond to a maximal limit of the inverter are deleted, because the measured previous output power value, limited, does not correspond to the previous irradiance value associated with the same time, and values measured near after are also deleted even if they do not match a limit, because it is possible that the inverter needs time to resume its normal functioning after the end of a limitation.

[0030] Preferably, previous irradiance values associated with respective output power values and respective times are associated with times of a single solar day, and the step of determining efficiency coefficients values at respective times of a day comprises determining efficiency coefficients values at respective times of the single solar day

[0031] Advantageously, wherein the previous day being a first previous day, the method comprises, when predetermined requirements are not met, at least another step of obtaining previous output power values associated with previous irradiances values from at least another previous day preceding the first previous day, the previous irradiance values being associated with respective output power values of a same day, these associations from different previous day being associated with times of the single the solar, the predetermined requirements being:

- the number of obtained associations for the solar day is less than a predetermined minimal number, the minimal number being preferably one hundred, or

- no obtained association has a time before a predetermined morning time of the solar day, or

- no obtained association has a time after a predetermined afternoon time of the solar day, or

- two obtained associations are separated by a time greater than a maximal separation time, preferably two hours, without obtained association therebetween.

[0032] Thus, the associations obtained from a previous day are not relevant enough when there are not enough values, when the times of these associations are not distributed enough within the solar day or when a considerable part of the solar day does not contain any association. In these cases, it is decided to obtain output power values associated with irradiance values from a at least a second day before the first day. All the associations of output power values and irradiances values, retrieved on different previous days, are accumulated on a single solar day. It is then possible to have, for a specific time of the solar day, several associations of output power values and irradiance values. That makes it possible to determine the evolution of the efficiency coefficient within a day based on data from several and different previous days.

[0033] It is possible to add data from several previous weeks, but more than four weeks is not encouraged as seasonal changes have an impact on the efficiency coefficient.

[0034] In an embodiment, the irradiance values correspond to global horizontal irradiance (GHI) values or to plan of array (POA) values.

[0035] Global horizontal irradiance values are values which are simple to obtain, for example from another entity registering the global horizontal irradiance values received at locations and at different times. Indeed, plan of array values, to be determined directly, necessitate pyranometers in the plan of each panel, which is costly.

[0036] However, even without several pyranometers, POA values can be calculated according to the invention.

[0037] When the plan of array (POA) irradiance values are calculated, the plan of array irradiance (POA) values received by the photovoltaic system are retrieved by the following steps:

- retrieving previous global horizontal irradiance (GHI) values received by the photovoltaic systems associated with respective times of the at least one previous day; for each of the global horizontal irradiance values:

- determining the astronomical global irradiance value having the same time, based on a zenith angle of the Sun at the time;

- determining an attenuation coefficient value of the atmosphere based on the global horizontal irradiance value, on the astronomical global horizontal irradiance value and on an azimuth angle of the Sun at the time;

- determining a diffuse horizontal irradiance (DHI) value based on a relationship between the diffuse irradiance and the total irradiance, and based on the attenuation coefficient value;

- determining a direct normal irradiance (DNI) value based on the diffuse horizontal irradiance value (DHI), on the zenith angle of the Sun at the time and on the global horizontal irradiance (GHI) value;

- determining the projection value of the direct normal irradiance (DNI) value in the plan of array, based on the direct normal irradiance (DNI) value, on the tilt and azimuth angles of the photovoltaic system at the time and on the zenith and azimuth angle of the Sun at the time;

- determining the projection value of the diffuse horizontal irradiance (DHI) value on the plan of array, based on the diffuse horizontal irradiance value and on the tilt angle of the photovoltaic system at the time; - determining the plan of array (POA) irradiance value at the time based on the projection value of the direct normal irradiance value (DNI) and on the projection value of the diffuse horizontal irradiance value (DHI).

[0038] Plan of array irradiance values are more accurate than global horizontal irradiance values (GHI), as they take into account the orientation of the panels of the photovoltaic system. As diffuse and direct parts of the irradiance do not evolve in the same manner, it is important to calculate each of these parts in order to obtain the plan of array value.

[0039] It is also provided, according to another aspect of the invention, a computer- implemented method for forecasting a photovoltaic output power value to be provided by a photovoltaic system, comprising the following steps of:

- determining the peak power of the photovoltaic system;

- forecasting a value of irradiance to be received by the photovoltaic system at a time in a day;

- determining an efficiency coefficient value of the photovoltaic system at the time of the day;

- forecasting an output power value to be provided by the photovoltaic system at the time of the day based on the peak power, on the forecasted value of irradiance at the time and on the determined efficiency coefficient value at the time; characterized in that determining the efficiency coefficient value at the time is performed according to the described method for determining an efficiency coefficient value.

[0040] As the efficiency coefficient is determined according to the invention, the forecasting of the photovoltaic output power value at a specific time is accurate.

[0041] Advantageously, forecasting the output power value comprises the steps of:

- estimating theoretical output power values at respective theoretical times of a theoretical day, based on the theoretical efficiency coefficients, on the peak power value and on the previous irradiance values;

- determining fitted output power values at the respective theoretical times of the theoretical day, by fitting the theoretical output power values based on the previous output power values;

- forecasting the output power value based on one of the fitted power values.

[0042] Thus, first of all, theoretical output power values are determined based on the theoretical efficiency coefficient values, and then, a step of fitting is performed to improve the model to forecast output power values.

[0043] In an embodiment, the value of irradiance corresponds to a global horizontal irradiance (GHI) value or to a plan of array (POA) value. [0044] When not enough pyranometers allow to directly forecast POA values, the plan of array irradiance (POA) value to be received by the photovoltaic system is forecasted by the following steps:

- forecasting a global horizontal irradiance value to be received by the photovoltaic system at the time;

- determining the astronomical global horizontal irradiance value having the same time, based on a zenith angle of the Sun at the time;

- determining a diffuse horizontal irradiance value based on a relationship between the diffuse irradiance and the total irradiance, and based on the attenuation coefficient value;

- determining a direct normal irradiance value based on the diffuse horizontal irradiance value, on the zenith angle of the Sun at the time and on the global horizontal irradiance value;

- determining the projection value of the direct normal irradiance value in the plan of array, based on the direct normal irradiance value, on the tilt and azimuth angles of the photovoltaic system at the time and on the zenith and azimuth angle of the Sun at the time;

- determining the projection value of the diffuse horizontal irradiance value on the plan of array, based on the diffuse horizontal irradiance value and on the titlt angle of the photovoltaic system at the time;

- determining the plan of array irradiance value at the time based on the projection value of the direct normal irradiance value and on the projection value of the diffuse horizontal irradiance value.

[0045] Thus, plan of array (POA) irradiance values are more accurate than global horizontal irradiance values (GHI), as they take into account the orientation of the panels of the system.

[0046] It is also provided, according to another aspect of the invention, a data processing system comprising means for implementing the steps of the computer-implemented method for determining an efficiency coefficient of a photovoltaic system, described above, or the steps of the computer-implemented method for forecasting a photovoltaic output power value to be provided by a photovoltaic system, described above.

[0047] It is also provided, according to another aspect of the invention, a computer program comprising instructions which, when the program is executed by a computer, causes the computer to implement the steps of the computer-implemented method for determining an efficiency coefficient of a photovoltaic system, described above, or the steps of the computer- implemented method for forecasting a photovoltaic output power value to be provided by a photovoltaic system, described above.

[0048] It is also provided, according to another aspect of the invention, a computer- readable recording medium comprising instructions which, when executed by a computer, causes the computer to perform the steps of the computer-implemented method for determining an efficiency coefficient of a photovoltaic system, described above, or the steps of the computer-implemented method for forecasting a photovoltaic output power value to be provided by a photovoltaic system.

Brief description of figures

[0049] The invention will be better understood on reading the following description given solely by way of example and made with reference to the accompanying drawings in which:

[0050] [Fig. 1] is a schematic representation of a system implementing the invention ;

[0051] [Fig. 2] is a schematic representation of a solar panel of an embodiment of the invention ;

[0052] [Fig. 3] is a flowchart of a mode of implementation of the invention;

[0053] [Fig. 4] is a graph related to a mode of implementation of the invention;

[0054] [Fig. 5] is a graph related to a mode of implementation of the invention;

[0055] [Fig. 6] is a graph related to a mode of implementation of the invention;

[0056] [Fig. 7] is a flowchart of a mode of implementation of the invention;

[0057] [Fig. 8] is a graph related to results of a mode of implementation of the invention; [0058] [Fig. 9] is a graph related to results of a mode of implementation of the invention; [0059] [Fig. 10] is a flowchart of a mode of implementation of the invention.

[0060] [Fig. 11] is a flowchart of a mode of implementation of the invention.

Detailed description

[0061] Figure 1 illustrates an energy management system 1 , a photovoltaic system 2 and an electric grid 3. The energy management system 1 implements the methods of the invention that aims at determining an efficiency coefficient of the photovoltaic system 2 and at forecasting an output power value of the photovoltaic system 2 transmitted to the electric grid 3. This efficiency coefficient is a value representing the proportion of electrical power that the photovoltaic system 2 is capable of supplying in respect with a theoretical value depending on conditions at a specific moment in time. The efficiency coefficient value is thus a “power efficiency coefficient” or a "power proportionality coefficient". As it evolves over time, it can also be called a “time-dependent power efficiency coefficient” or a “time-dependent power proportionality coefficient”, or any combination of all of these terms.

[0062] The energy management system 1 comprises a database 11 that is able to register historical data that will be described. The system 1 also comprises a data processing system 12, having conventional computer means such as processors units, that is able to calculate an efficiency coefficient and a forecast output power value according to methods that will be described below. The system 1 also comprises a pyranometer 13 that is able to obtain irradiance values received by the photovoltaic system 2 and that will be further discussed below. The system 1 also comprises energy measuring means 14 that will not be described, to obtain the output power values of the photovoltaic system transmitted to the electric grid 3. The system 1 also comprises a computer-readable recording medium 15 including a computer program 16 comprising instructions which, when the program is executed by a computer, cause the computer to implement the steps of the methods that will be described. In the embodiments described thereafter, the program 16 is executed by the processing system 12 in collaboration with the database 11 , the pyranometer 13 and the energy measuring means 14 to implement the step of the methods by the energy management system 1.

[0063] The photovoltaic system 2 comprises several photovoltaic panels that are situated in a common geographical location but are positioned, inclined in different manners.

[0064] One of the panels 21 of the photovoltaic system 2 is schematically represented in figure 2. Are referenced tilt angle 0_t between the panel 21 and the horizontal plane 22, azimuth angle 0Arra_y between the panel 21 and the direction of the South 23, zenith angle 0_Z between the Sun S and the vertical plane, azimuth angle 0A between the Sun S and the South direction.

[0065] The photovoltaic system comprises several panels 21 , whose angles are different. Some of these panels are equipped with a tracker of the maximum light and are able to rotate in order to receive an optimal amount of irradiance at each time. Some other panels are stationary. The photovoltaic system 2 also comprises an inverter able to control the output power to be provided by the photovoltaic system 2 to the electric grid 3. The inverter is in particular constrained by power limitations at specific times that are provided by a photovoltaic system manager or by another entity.

[0066] However, the pyranometer 13 is a single measuring instrument common for all of the panels of the system 2 and is not able to rotate. It is able to determine a single value of global horizontal irradiance (GHI) received, at each measure, at the geographical location of the photovoltaic system 2.

[0067] To meet contractual requirements, in particular with the manager entity of the electric grid 3, it is expected from the energy system 1 to provide forecast output power values of the photovoltaic system 2 at different times of a future day.

[0068] The invention is based on the following formula: P = c * kWc * Irr, wherein P is the output power value of the photovoltaic system 2 at a specific time of the day, kWc is the peak power value of the photovoltaic system 2, which is a feature of the photovoltaic system 2 that can be known from the supplier of the system and that does not evolve over time, Irr is an irradiance value received by the photovoltaic system at the same specific time of the day, and c is an efficiency coefficient value of the photovoltaic system 2 that is unknown. In the following example, the efficiency coefficient deals with the efficiency of the whole system 2. Alternatively, it could deal with the efficiency of one panel 21 or even one photovoltaic cell provided that the peak power value, irradiance values and the output power values of the considered panel or cell can be retrieved.

[0069] As it will be described below, the irradiance value /rr is, in specific embodiments, a Global Horizontal Irradiance (GHI) value measured by the pyranometer 13, as described in reference to method 1000. Alternatively, /rr is a Plan Of Array (POA) value, more accurate. A POA value of one photovoltaic panel is directly available when a pyranometer is positioned in the plan of this panel. A POA value of the system 2 would necessitate pyranometers in the plan of each panels of the system 2, at any time. However, a POA value may also be determined, based on the GHI value, as described below in reference to method 2000.

[0070] Computer-Implemented method 1000, implemented by the energy management system 1 , aims at determining a efficiency coefficient CC,H (h) of the photovoltaic system, at any time h of a day, and will be described in reference to figure 3. An efficiency coefficient CC,H (h) corresponds to the state of the photovoltaic system 2 at a specific time h, depending on various factors such as soiling of the photovoltaic cells, wear, occasional failures, unexpected shading. It evolves over a day, for example due to specific shadings, and it also evolves over weeks, notably because of soiling. It is important to forecast it accurately for each time of a future day it in order to forecast an accurate output power value at this times of the day, but is also important to monitor its evolution over the long run.

[0071] Step 1010 is determining a peak power value kWc of the photovoltaic system 2. That value may be provided by the supplier of the photovoltaic system 2. It is a feature dependent on the characteristics of the panels of the photovoltaic system when they are made, that does not evolve over time.

[0072] Step 1020 is retrieving previous global horizontal irradiance (GHI) values received by the photovoltaic system 2 at respective times of a previous week. A GHI value corresponds to the total irradiance over an horizontal plane, at a specific geographical location. In our example, these values were registered by the pyranometer 13 and stored in the database 11 , wherein they are associated with a specific day and a specific time of the day they were registered.

[0073] The term “previous" aims at differentiating values that were measured, obtained or determined on a specific time, from forecast values to be predicted or constant values independent on the time. In this context, the term “previous" is equivalent to other terms having a same meaning such as “historical", “past’, “former¹’.

[0074] Step 1030 is retrieving previous output power values Pj provided by the photovoltaic system 2 to the electric grid 3 at respective times of the same previous week. These output power values were measured by the measuring means 14 and stored in the database 11 , wherein they are associated with a specific day and a specific time i the day at which they were measured.

[0075] Step 1040 is associating each retrieved irradiance value to one of the retrieved output power corresponding to the same time of the same day, in order to create associations of output power values, irradiances values, and their time of a day. Concretely, for one output power value and its time to be considered, the closest irradiance value from a time before is associated. This associating step is performed according to the following requirements:

[0076] - the time of the previous irradiance value on one hand, and the time of the previous output power value on the other hand, to be associated with each other, must be separated by less than a predetermined time value of thirty seconds. This predetermined time value can be changed by a user of the energy management system 1. This requirement ensures that the time of previous irradiance value and the time of the previous output value correspond approximately to the same time of the day.

[0077] - the previous output power value to be associated with the previous irradiance value is less than a maximal value, this maximal value corresponding to a power limit of the inverter of the photovoltaic system 2 minus a tolerance value. This tolerance value can match, for example, 0.1% of the maximal output power of the inverter of the photovoltaic system 2. This requirement ensures that, if the inverter was limited by a limitation order, the retrieved output power corresponding to the time of the limitation is not taken into account, as it does not correspond to the output power value that could have been emitted, without limitation, thanks to the irradiance value received at this time.

[0078] - the time of the previous output power value is separated from the time of a previous output power value equal to or greater than this maximal value by a predetermined time value of twenty seconds that can be changed by a user. This feature ensures that the previous output powers values having time near after an output power value corresponding to a limitation order of the inverter are also not taken into account, as the inverter takes time to resume its optimal functioning after the end of a limitation command.

[0079] - the previous irradiance value is greater than or equal to a predetermined minimum irradiance value, for example 10Watts/m². This feature ensures that weak irradiance values, which may not correspond to relevant output power values, are not taken into account.

[0080] At the end of this step 1040, the energy system 1 has obtained, for a week of previous days, associations between a day, a time i of the day, previous output power values Pi and irradiances power values I rn corresponding to this time of this previous day.

[0081] At step 1050, these associations, from different previous days, are associated with a same single solar day, depending on the solar time corresponding to their associated time of a day. In other terms, the day to which they were attached no longer counts, only the solar time within this day counts. Associations from different days are thus accumulated on a single solar day. Thus, as a result, at times within a single solar day are situated a plurality of associations, that is to say previous output power values associated with irradiances values. Figure 4 illustrates a solar day comprising 52064 points corresponding to 52064 associations from a week of previous days, accumulated over a single solar day. As they come from different days, one can find, for a same time of the solar day, a plurality of associations. On figure 4, only the previous output power value of the association is illustrated, depending on the time i of the solar day, but previous irradiance values, not illustrated, are also associated with each of these points.

[0082] From now, all the steps are performed from values situated on this single solar day.

[0083] Step 1060 is a verifying step to check whether the data accumulated from the previous week and reported on a single solar day are relevant enough. All of the following requirements must be checked:

[0084] - The number of obtained associations for the solar day is equal to or greater than a predetermined minimal number. The minimal number is preferably one hundred but can be changed by a user of the system 1.

[0085] - at least one obtained association has a time before a predetermined morning time of the solar day that can be, for example, 9am, and can be changed by a user.

[0086] - at least one obtained association has a time after a predetermined afternoon time of the solar day that can be, for example, 3pm and can be changed by a user.

[0087] - there are always two obtained associations separated by a time less than a maximal separation time, preferably two hours. This separated time can be changed by a user.

[0088] These features ensure that there are enough data covering the whole solar day.

[0089] If one of these requirements is not met, the method 1000 includes news steps 1020 to 1050 applied to another previous week preceding the previous week, in order to retrieve associations of previous irradiance values, previous output power values and their times based on two previous weeks instead of one. These associations are accumulated over the single solar day and the verifying step 1060 is performed again. If the requirement fails to be met, it is possible to further add other preceding weeks of data, in other terms it is possible to obtain previous associations from previous weeks of previous days, then to form data over the single solar day in the same manner, and to check whether the accumulated data over these previous weeks are relevant thanks to step 1060, until the requirements are met. However, it is best not to add another previous week after the data of four previous weeks were added. Indeed, over the course of long-term periods, the performances of the panels are affected by seasonal changes. Therefore, it is advantageous to base calculations on data from a short period of a year. [0090] Instead of applying steps 1020 to 1050 to another previous week of data, the system 1 can be configured to apply steps 1020 to 1050 to a different period of time, for example to another previous day of data. In that case, previous days of data are added until the requirements are met.

[0091] Starting from step 1070, a function CC.H, depending on any time h of a day, is to be determined. This function has ten pairs of parameters (Cj, Hj), wherein j=1..10, and wherein Cj is an efficiency coefficient value and Hj is a time value of a day associated with the Cj value. Thus, these pairs of parameters correspond to efficiency values distributed throughout the day. In other terms, these parameters define discrete efficiency coefficient values at specific times of the day. Function CC,H allows to determine an efficiency coefficient value CC,H (h) at any time h of a day, based on these discrete values, according to the following formula :

[0092] Thus, according to this formula, function CC,H comprises a step of interpolating, to determine the efficiency coefficients values CC,H (h) of any time h in a day, based on two of the discrete efficiency coefficient values Cj, these two discrete efficiency coefficients values Cj having time values Hj respectively before and after the respective times h of the day at which the efficiency coefficients values CC,H (h) are determined. This interpolation step can be performed, for example, thanks to the function interp from the library numpy of Python language.

[0093] The goal of step 1070 is thus to determine the best ten pairs of parameters (Cj, Hj).

[0094] First of all, the ten pairs of parameters (Cj, Hj) have to respect the following requirements:

[0095] - Efficiency coefficient values Cj of the pairs are between two zero and four. These predetermined values could be changed by a user.

[0096] - At least one of the pairs of parameters has a time value Hj before a morning time, for example 9 am, and another one of the pairs of parameters has a time value Hj after evening time, for example 6pm. These predetermined time values could be changed by a user.

[0097] - The time value differences between each consecutive pair of parameters of the day are more than ten minutes. This duration could be changed by a user.

[0098] To determine the best pairs of parameters (Cj, Hj), step 1070 is fitting these parameters to find the ten fitted pairs of parameters (Cj, Hj) that minimize the following deviation, for each of the 52064 previous values : wherein Pi = CC,H (h) * kWc * Irn, i being the times of the solar day respectively associated with the previous ouput power values Pj and with previous irradiance values Irn, and wherein Pj is a theoretical output power value at time i.

[0099] In other terms, step 1070 is determining theoretical output power values Pi based the peak power value kWc, on the previous irradiance values Irn, and on pairs of parameters (Cj,Hj) having parameters time values Hj to be fitted and parameters efficiency coefficient values Cj to be fitted. Step 1070 is then fitting these time values Hj and these efficiency coefficients values Cj of the pairs (Cj, Hj) of parameters based on the deviation between previous output power values Pj and theoretical output power values Pj.

[0100] This step of fitting these ten pairs of parameters (Cj, Hj), to find the fitted pairs, can be performed thanks to the function basinhopping, from library scipy of python language.

[0101] When the ten pairs of parameters (Cj, Hj) that allows to minimize this deviation have been found, these pairs are considered as the fitted pairs of parameters. These ten fitted pairs of parameters are stored into the database 11 . As already mentioned, these pairs of parameters define discrete efficiency coefficient values distributed at specific times of the day.

[0102] A step 1080, any efficiency coefficient value CC,H (h) of a day at a specific time h is interpolated based on these fitted pairs of parameters, that is to say based on these discrete values, according to function CC,H (h) and the formula above.

[0103] Thus, step 1080 results in a curve of efficiency coefficient values CC,H (h) depending on time h, that corresponds to the evolution of the efficiency of the photovoltaic system 2 over the time of a day. Figure 6 illustrates a curve 31 of the evolution of the efficiency coefficient CC,H (h) over a solar day, and the 52064 previous efficiency coefficients that were obtained and accumulated over the single solar day. This is the result of method 1000 for determining an efficiency coefficient of the photovoltaic system 2.

[0104] The number of pairs of parameters can be different from ten. Preferably, it is between five and fifteen to stay low while covering the whole solar day in a relevant manner, but this number could also be fifty, which remains well below the number of 52064 coefficients. Selecting such a low number of pairs of parameters at this step and with these rules allows to smooth the curve associated with CC,H (h) within a day. At the minimum, a number of two pairs of parameters is also possible, but it is advantageous to take into account most of the parts of a day thanks to more pairs of parameters.

[0105] This method 1000 allows to take into account, without intervening, the soiling of the panels and their evolution, as well as the shading that happens at specific times of the day. As it will be described later, it can then be used for determining the forecast output power value of the photovoltaic system 2 at specific times of a future day. [0106] Furthermore, when made on different periods of the year, for example when based on four previous weeks in February and then four previous weeks in March, it is possible to compare the evolution of the efficiency coefficient over a solar day in February and then over a solar day in March. In other terms it is possible to detect an evolution of the efficiency of the photovoltaic system over a long run. This evolution depends in particular on potential failures or wear of the system 2. Thus, monitoring the evolution of the efficiency coefficient over the long run may allow to decide on maintenance operations on the photovoltaic system 2.

[0107] In method 1000, the value of irradiance r was the global horizontal value (GHI).

[0108] Alternatively, the value of irradiance Irr is a plan of array (POA) value determined thanks to pyranometers situated in the plane of each photovoltaic panel. This POA value is more accurate than the GHI value. Indeed, the POA value addresses the total irradiance, not in a horizontal plane, but in the plan of the panels of the photovoltaic system 2, and takes into account the proportion between diffuse and direct irradiance.

[0109] However, it is costly to implement pyranometers in the plane of each photovoltaic panel.

[0110] Therefore, now we will describe a method 2000 of determining the efficiency coefficient, wherein the previous value of irradiance Irr is based on a plan of array (POA) value that is calculated based on a single GHI value for the system 2 and on other data that will be detailed.

[0111] Method 2000 is thus identical to method 1000, except that it comprises further steps to determine the previous POA value based on the corresponding provided previous GHI value.

[0112] Step 2010 is the same as step 1020 of retrieving previous global horizontal irradiance (GHI) values received by the photovoltaic systems associated with respective times of the at least one previous day.

[0113] The following steps are performed for each of these previous global horizontal irradiance values and in reference to figures 7, illustrating the flowchart, and figure 2 illustrating the various angles to be considered. It is important to note that they will be described in reference to one single photovoltaic panel of photovoltaic system 2, schematically represented in figure 2. The resulting previous POA values for each panels of the system 2 will be added.

[0114] Step 2020 is determining the astronomical global horizontal irradiance (AGHI) having the same time as the previous GHI value obtained by the pyranometer 13. The astronomical global horizontal irradiance (AGHI) value corresponds to the GHI value from which the effect of the atmosphere is removed, and depends on the location of the Sun. That AGHI value is based on the cosinus of the zenith angle 0z of the Sun at this time, multiplied by a constant to be determined by the skilled person. This constant corresponds to the irradiance outside the atmosphere on a plane perpendicular to the solar rays. The 0z value is determined thanks to geographical coordinates of the photovoltaic system 2 already known or provided by a global positioning system (GPS) for example, and by an astronomical formula known by the skilled person. Furthermore, advantageously, the precision of the 0z value is well improved thanks to the “equation of time". This correction takes into account the variations of the speed with which the Earth moves on its elliptical orbit around the Sun and the inclination of its axis with respect to the plane of the orbit. The equation of time implies a time difference which can go up to a maximum of 16 minutes 25 seconds. The way to implement this equation to improve the accuracy of 0z is known by the skilled person.

[0115] Step 2030 is determining an attenuation coefficient value k_t of the atmosphere based on the previous global horizontal irradiance value (GHI), on the astronomical global horizontal irradiance value (AGHI) and on an azimuth angle of the Sun (0A), still and always at the specific time of the previous GHI value time. Indeed, the average distance between Earth and Sun is about 150 million kilometers. Satellite measurements show that, at this distance, the Earth receives Sun radiation with an AGHI value of 1361 Watts/m², thus defined as the power that would receive a unit area that would be perpendicular to the radiation just above the Earth's atmosphere. Knowledge of the GHI value measured at each instant at a point on the Earth's surface and in the azimuth of the Sun, at this point and at this instant, allows the calculation of the atmosphere attenuation factor, defined as according to the following formula: k_t = GHI /AGHI * cos (0_A) .

[0116] Step 2040 is determining a previous diffuse horizontal irradiance (DHI) value based on a relationship between the diffuse irradiance (DHI) and the total horizontal irradiance (GHI), and based on the attenuation coefficient value (k_t). Diffuse irradiance differentiates from direct irradiance. The key difference between diffuse irradiance and direct irradiance is that direct irradiance is the solar radiation that passes directly through the atmosphere from the Sun without any scattering effect, whereas diffuse irradiance is the solar radiation that is scattered by the atmosphere and reaches the ground. Experimental data demonstrated a correlation between, on one hand, k_t and, on the other hand, the ratio between the diffuse horizontal irradiance (DHI) and global horizontal irradiance (GHI). Thus, DHI = f(k_t) * GHI, wherein, in this embodiment, is has been found through experimental data that f(k_t) has the following definitions:

- if 0 < _kt <= 0.32, f(kt) = 1.09 - 0.09* k_t,

- if k_t > 0.32, f(k_t) = 0.9511 - 0.1604 * (k_t - 0.1) + 4.388 * (k_t - 0.1)² - 16.638 * (k_t - 0.1)³ + 12.336 * (k_t - 0.1)⁴

- if k_t > 0.8, f(k_t) = 0.3256

[0117] Step 2050 is determining a previous direct normal irradiance (DNI) value based on the diffuse horizontal irradiance value (DHI), on the zenith angle 0_Z of the Sun at the time and on the global horizontal irradiance (GHI) value, according to the following formula: DNI =

(GHI—DHD

Direct normal irradiance is the direct irradiance of the Sun on a plane perpendicular cos (9z) to the rays of the Sun.

[0118] At the end of step 2050, the global horizontal irradiance (GHI) is decomposed into two parts: the direct normal irradiance DNI and the diffuse horizontal irradiance DHL

[0119] Step 2060 is determining the projection value of the direct normal irradiance (DNI 0t) value in the plan of the panel, based on the direct normal irradiance (DNI) value, on the tilt and azimuth angles of the photovoltaic system at the time and on the zenith and azimuth angle of the Sun at the time, according to the following formula: DNI_et = DNI * (cos 0z * cos Qt + sin 0z * sin 6t * cos(6 _Array — 0 )) .

[0120] Step 2070 is determining the projection value of the diffuse horizontal irradiance

(DH let) value on the plan of the panel, based on the diffuse horizontal irradiance value and on the tilt angle of the photovoltaic system at the time, according to the following formula:D/7/_et =

DHl*l+cos9t

. That DHIet value corresponds to the isotropic part of the projection value, in other

2 terms to the irradiance coming from the celestial vault and considered to be uniformly distributed.

[0121] Other parts of the projection value of the diffuse horizontal irradiance, such as the circumsolar part representing the refraction of rays in a zone surrounding the Sun, and the bright part of the horizon, are ignored in this calculation, but their values could be approximated by a skilled person from knowledge found in scientific literature.

[0122] Of course, steps 2060 and 2070 need the system 1 to know the different angles of the panels illustrated on figure 2. If the panels do not rotate over time, these angles are constant. If one or several rotate over time, the angles need to be measured by a tracker or calculated.

[0123] Step 2080 is determining the previous plan of array (POA) irradiance value at the time based on the projection value of the direct normal irradiance value (DNI0_t) and on the projection value of the diffuse horizontal irradiance value (DHI0_t), according to the following formula: POA = DNIQt + DHIQt.

[0124] It is worth noting that other phenomena could have been considered to determine the POA value, such as reflection, but their influence for determining the plan of array (POA) value is marginal compared to direct normal irradiance (DNI) and diffuse horizontal irradiance (DHI).

[0125] However, optionally, in case a panel of the system is a bifacial panel, it is advantageous to take into account the reflection to determine the POA for each face of this facial panel. Thus, in that case, the plan of array (POA) value for one face of the bifacial panel is determined according to the following formula: POA = DNI_et + DHI_et + RI_et, wherein RIQ = GH/*(l-cos(0t))

* psol, wherein pso is the albedo value that can be measured, known or retrieved by a skilled person.

[0126] The end of step 2080 is one previous POA value, corresponding to an accurate value of irradiance in the plan of one panel of the photovoltaic system 2, and associated with a specific solar time of the previous day at which this irradiance was received.

[0127] At step 2090, all the POA values of the panels of the system, associated with the same specific time, are added to each other. Thus, the POA value of the photovoltaic system 2 has been determined.

[0128] By performing these steps for each previous GHI value retrieved, all the corresponding previous plan of array values of the photovoltaic system 2 have been determined and associated with their respective time over the solar day.

[0129] The other steps of method 2000 are steps 1030 to 1090, wherein each previous irradiance value Irr is a POA value of the photovoltaic system. In other terms, at step 1040 each association attribute a previous output power value to a previous POA value and to its time, this previous POA value being calculated, thanks to steps 2010 to 2090, from the GHI value provided. It is important to note that one GHI value is obtained by the single pyranometer 13 of the photovoltaic system 2. However, at a specific time, each panel may have a different POA value, based on this same GHI value and on the respective different angles values of the panels.

[0130] Another method to obtain a POA value would be to place mobile pyranometers associated with each panel of the photovoltaic system 2 and configured to determine the irradiance received in the plane of the panel at each time of the day. It would be too expensive. Determining the POA based on one single value of GHI provided by the single pyranometer 13, and thanks to the angles of the panels, is cheaper and simpler to operate.

[0131] Figures 8 and 9 allow to compare the efficiency coefficient values determined from the previous GHI values (figure 8), in other terms according to method 1000, and the efficiency coefficient values determined from the previous POA values (figure 9), in other terms from method 2000. They also illustrates an ex post facto calculation of the efficiency coefficient c, based on real measured output power values and irradiance, in order to compare the models of method 1000 and 2000 to the true values of c. These graphs correspond to a day wherein a cloud prevents direct irradiance around 1.30 pm.

[0132] In figure 8, curve 32 related to the efficiency coefficients values correctly follows the values of the calculated c. However, this curve slightly decreases around 1.30pm, whereas the efficiency of the photovoltaic system should not depend on the irradiance. In figure 9, curve 33 also correctly follows the c values, and even stay constant at the time of the cloud, which shows that the efficiency does not depend on the irradiance. [0133] As a conclusion, although efficiency coefficients calculated according to method 1000 from GHI values provide good results, it is advantageous to use POA values from method 2000, in order to have efficiency coefficients more independent from the irradiance and thus more accurate, in particular when cloud events impact the direct irradiance.

[0134] Method 3000 is a method, implemented by the energy system 1 , for forecasting a photovoltaic output power value to be provided by a photovoltaic system 2. It will be described in reference with figure 10. This method is implemented in particular when the manager of the electric grid 3 asks the manager of the photovoltaic system 2 to forecast the output power values to be provided in a future day at different times of the day.

[0135] Step 3010 is determining the peak power kWc of the photovoltaic system 2. These features are known by the user or provided by the supplier of the photovoltaic system 2. These feature do not change over time.

[0136] Step 3020 is forecasting a value of irradiance to be received by the photovoltaic system at a time in a day. That forecast value of irradiance may be provided by an external weather data provider. In particular, this external weather data provide provides the Global Horizontal Irradiances (GHI) values to be received on the location of the photovoltaic system 2 at different times over the future day.

[0137] Step 3030 is determining the efficiency coefficients of the photovoltaic system 2. That step is performed according to method 1000 or method 2000. In our example described in reference with method 1000, that step is performed based on the 52064 associations between a previous output power value, an irradiance value, and their time, these 52064 associations being associated with a single solar day, as explained above.

[0138] Step 3040 is calculating the forecast output power value based on this efficiency coefficient, on the peak power value kWc and on the forecast irradiance value Irr.

[0139] By doing it for each instant hi of a future day, Step 3040 result in a curve related to the forecast output power values of the future day, based on the forecast irradiance value at each time of the day, on kWc and on the interpolated coefficients Cc,n(h), interpolated based on the fitted pairs of parameters (Cj, Hj).

[0140] Alternatively, instead of forecasting a GHI value at step 3020 of method 3000, a POA value is forecast. This forecast POA value is available if pyranometers are situated in each plan of each photovoltaic panel and thus allow to forecast the global POA value of system 2.

[0141] However, placing such a number of pyranometers is costly.

[0142] Therefore, method 4000, of figure 11 , is identical to method 3000, except on the fact that the forecast GHI value is used for determining a forecast POA value, in the exact same manner as, in method 2000, the “previous GHI value" was used to determine a “previous POA value". In other terms, in method 4000, the forecast GHI value, provided for example by a weather data supply entity, is used, as well as the various angles of the Sun and of the photovoltaic system 2, to determine a forecast POA value of the photovoltaic system 2 at a specific time of a day, according to steps 2020 to 2090.

[0143] The forecast POA of method 4000 value is then used in the same manner as the forecast GHI value in method 3000 for determining the output power value.

[0144] Method 4000 results, like method 3000, in a curve related to the forecast output power values of the future day, but based on the forecast POA value at each time of the day, on kWc and on the efficiency coefficients CC,H (h)at each time of the day.

[0145] It is worth noting that, as well as in method 3000, the efficiency coefficient CC,H (h) of method 4000 may be determined using method 1000, with previous GHI values, or using method 2000, with previous POA values. Naturally, the most accurate choices would be to use method 2000 for determining the coefficient Cc,n(h) of system 2, and method 4000, based on the coefficient CC,H (h) of method 2000, for determining a forecast output power value.

[0146] The invention is not limited to the embodiments presented and other embodiments will appear clearly to those skilled in the art.

[0147] In particular, it is possible to implement the described methods in relation with photovoltaic systems having different types, number and setting of panels, as the determination of the values are not dependent on the features of the panels.

[0148] The methods were described in relation with previous weeks of data, but they may be implemented in relation with a small amount of previous data, for example with only a single day of data. However, the accuracy of the methods is improved as previous data increases, until a point wherein seasonal change affect the accuracy, in particular until four weeks of previous data.

[0149] Although the methods are described in a sequential manner, it would appear to the skilled person that output power value or irradiance values that are just obtained at current time can directly be used, without waiting, as previous output power and irradiance values in the methods to determine the efficiency coefficient or forecast an output power value. In other terms, previous values can be used in real time.

Claims

[Claim 1] Computer-implemented method (1000, 2000) for determining an efficiency coefficient (CC.H (h)) of a photovoltaic system (2), characterized in that it comprises the following steps:

- determining (1010) a peak power value (kWc) of the photovoltaic system;

- obtaining (1020, 1030, 1040, 1050) previous irradiance values (Irn) associated with respective previous output power values (Pj) and with respective times (i) of at least one previous day;

- determining (1070, 1080) efficiency coefficients values CC,H (h) at respective times (h) of a day, based on the peak power value (kWc), on the previous irradiance values (Irn), on the respective previous output power values (Pj) and on the respective times (i) of the at least one previous day.

[Claim 2] Method (1000, 2000) according to the preceding claim, wherein the step of determining (1070, 1080) efficiency coefficients values comprises :

- determining (1070), based on the peak power value (kWc), on the previous irradiance values (Irn), on the previous output power values (Pj) and on the times (i) of the at least one previous day, a function (CC.H) depending on time (h),

- determining (1080), based on the function (CC.H), the efficiency coefficients values (CC.H (h)) at the respective times (h) of a day.

[Claim 3] Method (1000, 2000) according to the preceding claim, wherein the step of determining (1070) the function (CC.H) comprises a step of determining, based on the peak power value (kWc), on the previous irradiance values (Irn), on the previous output power values (Pj) and on the times (i) of the at least one previous day, pairs of parameters (Cj, Hj) of the function, each of the pairs (Cj, Hj) having an efficiency coefficient value (Cj) and a time value (Hj) defining discrete efficiency coefficients values at specific times.

[Claim 4] Method (1000, 2000) according to the preceding claim, wherein the step of determining (1070) the pairs of parameters (Cj, Hj) of the function comprises a step of fitting the parameters based on the peak power value (kWc), on the previous irradiance values (Irn), on the previous output power values (Pj) and on the times (i) of the at least one previous day.

[Claim 5] Method (1000, 2000) according to the preceding claim, wherein the step of fitting (1070) comprises a step of :

- determining theoretical output power values (Pi) based the peak power value (kWc), on the previous irradiance values (Irn), and on pairs of parameters (Cj, Hj) having efficiency coefficient values (Cj) to be fitted and time values (Hj) to be fitted,

- fitting the efficiency coefficient values (Cj) and the time values (Hj) of the pairs of parameters based on a deviation between previous output power values (Pj) and theoretical output power values (Pi).

[Claim 6] Method (1000, 2000) according to at least claim 3, wherein the step of determining (1080), based on the function (cC,H), the efficiency coefficients values (cC,H (h)) at the respective times (h) of the day, comprises a step of interpolating (1080), to determine the efficiency coefficients values (cC,H (h)), based on the discrete efficiency coefficients values at specific times.

[Claim 7] Method (1000, 2000) according to at least claim 3, wherein the step of determining the pairs of parameters (Cj, Hj) comprises a step of determining between two and fifty pairs of parameters (Cj, Hj), preferably between five and fifteen, respecting the following requirements:

- efficiency coefficient values (Cj) of the pairs are between two predetermined values, the two predetermined values being preferably respectively zero and four;

- at least one of the pairs of parameters has a time value (Hj) before a predetermined time of the day and at least another one of the pairs of parameters has a time (Hj) value after a predetermined time of the day;

- the time value differences between each consecutive pair of parameters (Cj, Hj) of the day are more than a predetermined duration, preferably ten minutes.

[Claim 8] Method (1000, 2000) according to any one of the preceding claims, wherein the step of obtaining the previous irradiance values (Irn) associated with respective output power values (Pj) comprises: - retrieving (1020) previous irradiances values (Irn) received by the photovoltaic system (2) at respective times of the at least one previous day;

- retrieving (1030) previous output power values (Pj) provided by the photovoltaic system (2) at respective times of the same at least one previous day;

- associating (1040) each of these previous irradiance values (Irn) to one of the previous output power values (Pj) when:

- the time of the previous irradiance value (Irri) and the time of the previous output power value (Pj) are separated by less than a predetermined time value,

- the previous output power value (Pj) is less than a maximal value, the maximal value corresponding to a power limit of an inverter of the photovoltaic system (2) minus a tolerance value,

- the previous irradiance value (Irn) is greater than or equal to a predetermined minimum irradiance value,

- the time of the previous output power value (Pj) is separated from the time of a previous output power value equal to or greater than the maximal value by a predetermined time value.

[Claim 9] Method (1000, 2000) according to any one of the preceding claims, wherein previous irradiance values (Irn) associated with respective output power values (Pj) and with respective times (i) are associated (1050) with times of a single solar day, wherein the step of determining efficiency coefficients values CC,H (h) at respective times (h) of a day comprises determining efficiency coefficients values at respective times of the single solar day.

[Claim 10] Method (1000, 2000) according to the preceding claim, wherein the previous day being a first previous day, the method comprises (1060), when predetermined requirements are not met, at least another step of obtaining previous output power values (Pj) associated with previous irradiances values (Irn) from at least another previous day preceding the first previous day, the previous irradiance values (Irn) being associated with respective output power values (Pj) of a same day, these associations from different previous day being associated with times (i) of the single the solar, the predetermined requirements being: - the number of obtained associations for the solar day is less than a predetermined minimal number, the minimal number being preferably one hundred, or

- two obtained associations are separated by a time greater than a maximal separation time, preferably two hours, without retrieved value therebetween.

[Claim 11] Method (1000, 2000) according to any one of the preceding claims, wherein the irradiance values correspond to global horizontal irradiance (GHI) values or to plan of array (POA) values.

[Claim 12] Method (2000) according to the preceding claim, wherein, the irradiance values correspond to plan of array (POA) irradiance values, the plan of array irradiance (POA) values received by the photovoltaic system (2) being retrieved by the following steps:

- retrieving (2010) previous global horizontal irradiance (GHI) values received by the photovoltaic systems associated with respective times of the at least one previous day; for each of the global horizontal irradiance values:

- determining (2020) the astronomical global horizontal irradiance (AGHI) value having the same time, based on a zenith angle (0_Z) of the Sun at the time;

- determining (2030) an attenuation coefficient (k_t) value of the atmosphere based on the global horizontal irradiance value, on the astronomical global horizontal irradiance (AGHI) value and on an azimuth angle (0A) of the Sun at the time;

- determining (2040) a diffuse horizontal irradiance (DHI) value based on a relationship between the diffuse irradiance and the total irradiance, and based on the attenuation coefficient value (k_t);

- determining (2050) a direct normal irradiance (DNI) value based on the diffuse horizontal irradiance value (DHI), on the zenith angle (0_Z) of the Sun at the time and on the global horizontal irradiance (GHI) value; - determining (2060) the projection value of the direct normal irradiance (DNIQt) value on the plan of array, based on the direct normal irradiance (DNI) value, on the tilt (0_t) and azimuth (0Arra_y) angles of the photovoltaic system (2) at the time and on the zenith (0_Z) and azimuth (0A) angle of the Sun at the time;

- determining (2070) the projection value (DHI0_t) of the diffuse horizontal irradiance (DHI) value on the plan of array, based on the diffuse horizontal irradiance value and on the titlt angle (0_t) of the photovoltaic system (2) at the time;

- determining (2080) the plan of array (POA) irradiance value at the time based on the projection value of the direct normal irradiance value (DNI0_t) and on the projection value of the diffuse horizontal irradiance value (DHI0t).

[Claim 13] Computer-implemented method (3000, 4000) for forecasting a photovoltaic output power value to be provided by a photovoltaic system (2), comprising the following steps of:

- determining (3010) the peak power (kWc) of the photovoltaic system;

- forecasting (3020) a value of irradiance to be received by the photovoltaic system at a time (h) in a day;

- determining (3030) an efficiency coefficient value (CC.H (h)) of the photovoltaic system at the time (h) of the day;

- forecasting (3040) an output power value to be provided by the photovoltaic system at the time (h) of the day based on the peak power (kWc), on the forecasted value of irradiance at the time and on the determined efficiency coefficient value (CC.H (h)) at the time (h); characterized in that determining the efficiency coefficient value (CC.H (h)) at the time (h) is performed according to any one of the preceding claims (1000, 2000).

[Claim 14] Method (3000, 4000) according to one of the preceding claims, wherein the value of irradiance corresponds to a global horizontal irradiance (GHI) value or to a plan of array (POA) value.

[Claim 15] Method (4000) according preceding claim, wherein the value of irradiance corresponds to a plan of array (POA) value, the plan of array irradiance (POA) value to be received by the photovoltaic system being forecasted by the following steps:

- forecasting a global horizontal irradiance value to be received by the photovoltaic system (2) at the time;

- determining the astronomical global horizontal irradiance (AGHI) value having the same time, based on a zenith angle (0_z)of the Sun at the time;

- determining an attenuation coefficient (k_t) value of the atmosphere based on the global horizontal irradiance (GHI) value, on the astronomical global horizontal irradiance (AGHI) value and on an azimuth angle (0_Z) of the Sun at the time;

- determining a diffuse horizontal irradiance (DHI) value based on a relationship between the diffuse irradiance and the total irradiance, and based on the attenuation coefficient value (k_t);

- determining a direct normal irradiance (DNI) value based on the diffuse horizontal irradiance value (DHI), on the zenith angle (0_Z) of the Sun at the time and on the global horizontal irradiance (GHI) value;

- determining the projection value of the direct normal irradiance (DNI0_t) value in the plan of array, based on the direct normal irradiance (DNI) value, on the tilt (0_t) and azimuth (0Arra_y) angles of the photovoltaic system at the time and on the zenith (0_Z) and azimuth (0A) angle of the Sun at the time;

- determining the projection value of the diffuse horizontal irradiance (DHI 0t) value on the plan of array, based on the diffuse horizontal irradiance value (DHI) and on the tilt angle (0_t) of the photovoltaic system (2) at the time;

- determining the plan of array (POA) irradiance value at the time based on the projection value of the direct normal irradiance value (DN I0_t) and on the projection value of the diffuse horizontal irradiance value (DH 10_t) .

[Claim 16] A data processing system (1) comprising means (12) for implementing the steps of the method (1000, 2000) of claim 1 to 12 or the steps of the method (3000, 4000) of claim 13 to 15.

[Claim 17] A computer program (16) comprising instructions which, when the program (16) is executed by a computer, cause the computer to implement the steps of the method (1000, 2000) of claim 1 to 12 or the steps of the method (3000, 4000) of claim 13 to 15. [Claim 18] A computer-readable recording medium (15) comprising instructions which, when executed by a computer, cause the computer to perform the steps of the method (1000, 2000) of claim 1 to 12 or the steps of the method (3000, 4000) of claim 12 to 15.