Method and system for dynamic state estimation of a photovoltaic system based on solar irradiance variations

Abstract

The application discloses a photovoltaic system dynamic state estimation method and system based on solar irradiance variation, considers the randomness of solar irradiance as unknown input of DSE, and combines the same into the unscented Kalman filter algorithm in the form of unbiased minimum variance, so that the state estimation of the photovoltaic system is realized. The method can estimate the dynamic state of the photovoltaic system in time and accurately, solves the problem that the estimation precision is influenced by the illumination fluctuation, and better describes the operation state of the power system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of dynamic state estimation of power systems, and mainly relates to a photovoltaic system dynamic state estimation method and system based on solar irradiance variation. BACKGROUND

[0002] In recent years, the global photovoltaic industry has rapidly expanded due to its environmental characteristics. However, due to the significant influence of external climatic factors on photovoltaic systems, it exhibits obvious volatility and randomness. These fluctuations in turn cause problems for power systems, such as reduced power quality and misoperation of relay protection. In addition, numerous power electronic equipment devices have fundamentally changed the dynamic response of power systems, which undoubtedly leads to an increase in the complexity of power system operation and control. Therefore, it is necessary to estimate the dynamic state of the photovoltaic system in a timely and accurate manner in order to better describe the operating state of the power system.

[0003] Dynamic state estimation (DSE) has the ability to track real-time states, and many studies have focused on developing tools for DSE in power systems and applying them to traditional synchronous generators. However, when it comes to state estimation of photovoltaic systems, most existing work adopts static estimation or overly simplified dynamic models. In addition, previous work has not taken into account the volatility of solar irradiance, which poses a threat to the accuracy of the estimation. SUMMARY

[0004] The present application proposes a photovoltaic system dynamic state estimation method and system based on solar irradiance variation, which takes the randomness of solar irradiance as an unknown input of DSE and combines it into the unscented Kalman filter algorithm in the form of unbiased minimum variance, to realize the state estimation of the photovoltaic system. The method of the present application can estimate the dynamic state of the photovoltaic system in a timely and accurate manner, solving the problem of estimation accuracy affected by light fluctuation and better describing the operating state of the power system.

[0005] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is: a photovoltaic system dynamic state estimation method based on solar irradiance variation, which takes the randomness of solar irradiance as an unknown input of DSE and combines it into the unscented Kalman filter algorithm in the form of unbiased minimum variance, to realize the state estimation of the photovoltaic system.

[0006] As an improvement of the present application, the photovoltaic system dynamic state estimation method based on solar irradiance variation comprises the following steps:

[0007] S1: Establish a dynamic state estimation model of photovoltaic system, the model includes nonlinear photovoltaic system process equation and measurement equation; the process equation describes the dynamic behavior of the photovoltaic system, and the measurement equation is used to associate the measurement value of the system with the state prediction value, specifically:

[0008] x k =f(x k-1 ,u k )+G k d k +w k

[0009] z k =h(x k ,u k )+v k

[0010] Wherein, and are photovoltaic state variables and measurement variables respectively, and are known input and unknown input respectively, f(·) and h(·) are nonlinear functions, w k and v k are process noise and measurement noise with mean 0 respectively, G k is a known matrix representing the influence of unknown input on state variable;

[0011] S2: Construct an unscented Kalman filter algorithm based on unbiased minimum variance, which is an extension of the traditional unscented Kalman filter algorithm, and the target is to optimize the state estimation process in an unbiased and minimum variance manner, combined with the above dynamic state estimation model, more accurate and reliable estimation results are provided;

[0012] S3: Establish the expression of the influence of unknown input light on photovoltaic state variable, the expression is derived according to the partial derivative of state variable to light when the unknown input is derived from light change, the relationship between light and photovoltaic system state variable is established, and the expression of G k is obtained, which further improves the photovoltaic dynamic state estimation model.

[0013] As an improvement of the application, in the step S1, the photovoltaic state estimation model depends on the process equation and measurement equation provided by the photovoltaic model. The two-stage model of the photovoltaic system adopted is composed of photovoltaic array, boost converter, inverter and filter, and its differential algebraic equation is as follows:

[0014] Differential equation:

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Algebraic equation:

[0026] D = k p (u pv -u m )+k i D1

[0027]

[0028] u dc i dc = u id i d +u iq i q

[0029] u rd = u sd +L f i q -[k ip (i dref -i d )+k ii u rd1 ]

[0030] u rq = u sq -L f i d -[k ip (i qref -i q )+k ii u rq1 ]

[0031] i dref = k op (u dcref -u dc)+k oi i dref1

[0032] i qref =k op (q dcref -q)+k oi i qref1

[0033] where D1, u rd1 , u rq1 , i dref1 and i qref1 are intermediate states, i pv and u pv are the output current and voltage of the photovoltaic array, u oc , i sc , u m and i m are the open-circuit voltage, short-circuit current, maximum power voltage and maximum power current of the photovoltaic module in actual conditions, C1 and C2 are coefficients, C pv , L dc and C dc are the array capacitance, inductance and capacitance of the boost converter, D is the duty cycle of the switch, i L is the inductance current of the boost converter, i dc and u dc are the output current and voltage of the boost converter, k p and k i are the proportional and integral control gains of the controller, u id and u iq are the d-axis and q-axis components of the inverter output voltage, u rd and u rq are the d-axis and q-axis components of the modulation wave, U tri is the peak value of the carrier, u dcref and q dcref are the DC side reference voltage and output side reference reactive power, k op and k oi are the proportional and integral control gains of the outer loop controller, k ip and k ii are the proportional and integral control gains of the inner loop controller, q is the actual output reactive power of the photovoltaic system, i d and i q are the d-axis and q-axis components of the photovoltaic system actual output current, i dref and i qref are the d-axis and q-axis components of the output reference current, u sd and u sq are the d-axis and q-axis components of the grid voltage, L fis the filter inductance and ω is the grid angular frequency.

[0034] As another improvement of the application, the open circuit voltage u oc , short circuit current i sc , maximum power voltage u m and maximum power current i m of the photovoltaic module in the actual situation are respectively:

[0035]

[0036]

[0037]

[0038]

[0039] where S and T are the light radiation intensity and temperature respectively, u' oc , i' sc , u' m and i' m are the corresponding measured values provided by the manufacturer under standard test conditions.

[0040] As yet another improvement of the application, the step S2 specifically comprises the following steps:

[0041] S21: Given the state estimation value at time k-1 The nonlinearity of the system is handled by using unscented transformation The weight of each point is w i = 1 / 2n, i = 1, …, 2n; the sigma points are propagated through the nonlinear function to obtain the updated sigma points

[0042]

[0043]

[0044] At this time, the expression of the predicted mean value of the state vector and the predicted covariance matrix are:

[0045]

[0046]

[0047] Based on the updated sigma points, the expression of the predicted measurement vector is:

[0048]

[0049]

[0050] Error update covariance matrix and cross covariance matrix The calculation formula is:

[0051]

[0052]

[0053] Wherein The covariance matrix is respectively And

[0054] S22: The nonlinear measurement equation is statistically linearized, and the expression is:

[0055]

[0056] Wherein ε k Indicates that the error has a mean of zero, and the expression of the covariance matrix is

[0057] S23: Based on the minimum unbiased variance estimation standard, the expression of unknown input State vector And covariance matrix Is:

[0058]

[0059] In the expression of the above unknown input, state vector and covariance matrix, the specific calculation formula of part of the matrix is:

[0060]

[0061] As a further improvement of the present application, the step S3 specifically comprises the following steps:

[0062] S31, based on the nonlinear system process model and the photovoltaic model, the partial derivative of the above state variable with respect to the unknown input light is calculated, and the expression of the influence of light on the photovoltaic state variable, i.e. G k The expression is:

[0063] For state variables u rd1 ,u rq1 ,i d ,i q ,i dref1 ,i qref1 There is no explicit expression about solar irradiance, then about state variable x = [u pvi L u dc D1,u rd1 u rq1 i d i q i dref1 i qref1 ] T G in the state estimation model above k The specific form can be written as:

[0064] G k =[G1,G2,G3,G4,0,0,0,0,0,0] T

[0065] Wherein, G1, G2, G3, G4 are state variables u pv i L u dc D1 is the partial derivative of light, which describes the influence of light on photovoltaic state variables.

[0066] S32, considering the relationship between parameters and light, further obtained:

[0067]

[0068]

[0069]

[0070] Wherein

[0071]

[0072] In order to achieve the above purpose, the technical scheme adopted by the present application is: a photovoltaic system dynamic state estimation system based on solar irradiance variation, comprising a computer program, the computer program is executed by the processor to realize the steps of the method as described above.

[0073] Compared with the prior art, the present application has the beneficial effects: the present application proposes a photovoltaic system dynamic state estimation method and system considering solar irradiance variation in view of the era background of large-scale photovoltaic access to power grid.

[0074] In the aspect of photovoltaic model selection, the existing DSE work in the field of photovoltaic is based on simplified photovoltaic model, and these models only pay attention to photovoltaic power generation. The present application firstly studies DSE in a detailed two-stage photovoltaic model, wherein the photovoltaic array, boost converter, inverter and filter are all included, which is conducive to better describing dynamic characteristics and inferring the operating conditions of photovoltaic system.

[0075] In terms of algorithms, the dynamic state estimation method provided by the technology takes photovoltaics as unknown input, deduces the relationship between photovoltaic parameters and solar irradiance, obtains an expression reflecting the influence of light fluctuation on state variables, which allows us to develop DSE based on unbiased minimum variance under unknown input. Even in the case of severe changes in solar irradiance, the state of photovoltaics can be accurately and reliably estimated, solving the problem of the influence of light fluctuation on estimation accuracy and better describing the operating state of the power system. BRIEF DESCRIPTION OF DRAWINGS

[0076] Figure 1 is a flowchart of the photovoltaic system dynamic state estimation method based on solar irradiance changes according to the present application;

[0077] Figure 2 is a schematic diagram of the power system connected with photovoltaics in embodiment 1 and embodiment 2 of the present application;

[0078] Figure 3 is a schematic diagram of the solar irradiance fluctuation in embodiment 1 of the present application;

[0079] Figure 4 is the verification result of embodiment 1 of the present application;

[0080] Figure 5 is a schematic diagram of the solar irradiance fluctuation in embodiment 2 of the present application;

[0081] Figure 6 is the verification result of embodiment 2 of the present application. DETAILED DESCRIPTION

[0082] The present application will be further illustrated below in conjunction with the drawings and specific embodiments, and it should be understood that the following specific embodiments are only used to illustrate the present application and not to limit the scope of the present application.

[0083] Embodiment 1

[0084] This embodiment is applied to a New England 33-bus 1-generator system connected with photovoltaics. The power generation system connected with photovoltaics is shown in Figure 2 , wherein four two-stage photovoltaics are connected to nodes 8, 13, 28 and 32, and the photovoltaic components are initially under standard test conditions, i.e. solar irradiance is 1000 W / (m2), component temperature is 25℃, and spectrum is AM1.5G. Disturbance is applied by setting load shedding at the 4th second of simulation. The total simulation time is set to 10 seconds.

[0085] The photovoltaic system dynamic state estimation method based on solar irradiance changes, as shown in Figure 1 , comprises the following steps:

[0086] S1: Establish a dynamic state estimation model of the photovoltaic system, which includes a nonlinear photovoltaic system process equation and a measurement equation. The process equation describes the dynamic behavior of the photovoltaic system, and the measurement equation relates the measurement value of the system to the state prediction value, specifically:

[0087] x k =f(x k-1 ,u k )+G k d k +w k

[0088] z k =h(x k ,u k )+v k

[0089] wherein, and are photovoltaic state variables and measurement variables, respectively, and are known inputs and unknown inputs, respectively, f(·) and h(·) are nonlinear functions, w k and v k are process noise and measurement noise with mean 0, and the covariance matrices are and G k is a known matrix representing the influence of unknown inputs on state variables;

[0090] S11: The photovoltaic state estimation model relies on the process equation and the measurement equation provided by the photovoltaic model. The two-stage model of the photovoltaic system adopted is composed of four parts: photovoltaic array, boost converter, inverter and filter, and its differential algebraic equation is as follows:

[0091] Differential equation:

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] Algebraic equation:

[0103] D = k p (u pv -u m )+k i D1

[0104]

[0105] u dc i dc = u id i d +u iq i q

[0106] u rd = u sd +L f i q -[k ip (i dref -i d )+k ii u rd1 ]

[0107] u rq = u sq -L f i d -[k ip (i qref -i q )+k ii u rq1 ]

[0108] i dref = k op (u dcref -u dc )+k oi i dref1

[0109] i qref = k op (q dcref -q)+k oi i qref1

[0110] where D1, u rd1 , u rq1 , i dref1 and i qref1 are intermediate states, i pv and u pvare the output current and output voltage of the photovoltaic array, respectively, u oc sc m m are the open-circuit voltage, short-circuit current, maximum power voltage and maximum power current of the photovoltaic module in actual conditions, C1 and C2 are coefficients, C pv dc dc are the array capacitance, inductance and capacitance of the boost converter, respectively, D is the duty cycle of the switch, i L is the inductance current of the boost converter, i dc and u dc are the output current and output voltage of the boost converter, respectively, k p and k i are the proportional and integral control gains of the controller, respectively, u id and u iq are the d-axis and q-axis components of the inverter output voltage, respectively, u rd and u rq are the d-axis and q-axis components of the modulation wave, respectively, U tri is the peak value of the carrier, u dcref and q dcref are the DC side reference voltage and output side reference reactive power, respectively, k op and k oi are the proportional and integral control gains of the outer loop controller, respectively, k ip and k ii are the proportional and integral control gains of the inner loop controller, respectively, q is the actual output reactive power of the photovoltaic system, i d and i q are the d-axis and q-axis components of the photovoltaic system actual output current, respectively, i dref and i qref are the d-axis and q-axis components of the output reference current, respectively, u sd and u sq are the d-axis and q-axis components of the grid voltage, respectively, L f is the filter inductance, and ω is the grid angular frequency.

[0111] S12: the open-circuit voltage u oc , short-circuit current i sc , maximum power voltage u m and maximum power current i m of the photovoltaic module in actual conditions are respectively:

[0112]

[0113]

[0114] ​​​​​

[0115]

[0116] where S and T are the light radiation intensity (W / m2) and temperature (°C) respectively, u' and i' are the corresponding measured values provided by the manufacturer under standard test conditions. oc , i’ sc , u' m and i' m are the corresponding measured values provided by the manufacturer under standard test conditions.

[0117] S2: Construct an unscented Kalman filter algorithm based on unbiased minimum variance, which is an extension of the traditional unscented Kalman filter algorithm, and its goal is to optimize the state estimation process in an unbiased and minimum variance manner, combined with the above dynamic state estimation model, to provide more accurate and reliable estimation results;

[0118] S21: Given the state estimation value at time k-1 The nonlinearity of the system is processed by unscented transformation, and 2n sigma points are selected The weight of each point is w i =1 / 2n, i=1,…,2n. The sigma points are propagated through the nonlinear function to obtain the updated sigma points

[0119]

[0120] At this time, the predicted mean value of the state vector is and the expression of the predicted covariance matrix

[0121]

[0122] Based on the updated sigma points, the expression of the predicted measurement vector

[0123]

[0124]

[0125]

[0126] The error update covariance matrix and the cross covariance matrix The calculation formula is:

[0127]

[0128]

[0129] where​​

[0130] S22: statistically linearize the nonlinear measurement equation, expressed as:

[0131]

[0132] wherein ε k represents an error with a mean of zero, and the expression of the covariance matrix thereof is

[0133] S23: based on the minimum unbiased variance estimation standard, derive the expression of the unknown input state vector and covariance matrix :

[0134]

[0135] As another improvement of the present application, in the expression of the unknown input, state vector and covariance matrix formed by the step S23, the specific calculation formula of part of the matrix is:

[0136]

[0137] S3: establish the expression of the influence of the unknown input light on the photovoltaic state variable, and according to the partial derivative of the state variable to the light derived from the photovoltaic model, the relationship between the light and the photovoltaic system state variable is established, that is, the expression of G k is obtained, which further perfects the photovoltaic dynamic state estimation model;

[0138] S31: based on the nonlinear system process model and the photovoltaic model, calculate the partial derivative of the above state variable to the unknown input light, and establish the expression of the influence of the light on the photovoltaic state variable, that is, G k :

[0139] For state variables u rd1 ,i rq1 ,i d ,i q ,i dref1 ,i qref1 , there is no explicit expression about the solar irradiance, and then about the state variable x = [u pv ,i L ,u dc ,D1,u rd1 ,u rq1 ,i d ,i q ,i dref1 ,i qref1 ]T G k The specific form can be written as:

[0140] G k = [G1, G2, G3, G4, 0, 0, 0, 0, 0, 0] T

[0141] Wherein, G1, G2, G3, G4 are state variables u pv ,i L ,u dc D1 is the partial derivative of light, which describes the influence of light on photovoltaic state variables.

[0142] S32: Considering the relationship between parameters and light, further obtained:

[0143]

[0144]

[0145]

[0146] Wherein:

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153] According to the solar irradiance fluctuation model based on stochastic differential equation in the embodiment, the change of solar irradiance is simulated as an example scene, and the proposed dynamic state estimation method is simulated and verified.

[0154] The stochastic differential equation is:

[0155] dξ t = μ(ξ t , t)dt + σ(ξ t , t)dW t

[0156] Wherein ξ t is a random excitation, W t represents a standard Wiener process, and μ(·) and σ(·) represent drift and diffusion terms respectively.

[0157] The beta distribution simulating the light irradiation is a solar irradiance fluctuation model:

[0158]

[0159]

[0160] The simulated beta distribution probability density function is:

[0161]

[0162] Where a and b are shape parameters, and B(a, b) is a function ensuring that the integral of the probability density function is 1.

[0163] Set a = 4, b = 1, select a light fluctuation scenario, and verify the estimation performance of the proposed method under this light scenario.

[0164] The selected solar irradiance fluctuation scenario in this simulation verification is shown in Figure 3 . Figure 4 The simulation results of the photovoltaic state variables obtained by the method proposed in the application are shown in Figure 4 It can be seen that the results of the method are very similar to the true values, and therefore, the proposed method can quickly and accurately track the dynamic changes of the photovoltaic system under the condition of solar irradiance change.

[0165] Example 2

[0166] This embodiment is also applicable to the New England 33-bus 1-generator system connected to photovoltaics as shown in Figure 2 . Among them, four two-stage photovoltaics are connected to nodes 8, 13, 28 and 32, and the photovoltaic components are initially under standard test conditions, i.e. solar irradiance is 1000 W / (m2), component temperature is 25℃, and spectrum is AM1.5G. Disturbance is applied by setting load shedding at the 4th second of simulation. At the same time, in addition to the proposed method, the UKF algorithm is also used to estimate the state variables of the photovoltaic to make a comparison. The total simulation time is set to 10 seconds.

[0167] According to the steps of the application, the dynamic state estimation of the photovoltaic system is performed, and the light fluctuation scenario is set as shown in Figure 5 . Figure 6The simulation results of the photovoltaic state variables obtained by the two methods are shown, and it can be seen that the estimation results obtained by the proposed method are almost the same as the estimation results of the true state, while the results given by the UKF method have a large deviation from the true value, especially when the solar irradiance fluctuates sharply, because the parameters related to the solar irradiance have a non-negligible mutation, so they can no longer be regarded as constant parameters, resulting in a high deviation of the estimation results of the UKF. In contrast, the proposed method takes the solar irradiance as an unknown input, and then estimates the dynamic state of the photovoltaic system and the unknown input together, ensuring that a relatively accurate estimation result can be obtained, verifying the estimation performance of the proposed algorithm.

[0168] In summary, the photovoltaic system dynamic state estimation method based on solar irradiance variation provided in the present application provides support for mastering the real-time operation state of the new power system, and includes the following steps: S1, establishing a photovoltaic system dynamic state estimation model; S2, constructing an unscented Kalman filter algorithm (UKF-UMV) based on unbiased minimum variance;

[0169] S3, establishing an expression of the influence of unknown input light on photovoltaic state variables. The present application fully considers the volatility and randomness of the photovoltaic system caused by external factors such as light, takes the light volatility as an unknown input, and estimates the dynamic state of the photovoltaic system, so as to accurately estimate the dynamic state of the photovoltaic system in time, and solves the problem of light volatility affecting the estimation accuracy, so as to better describe the operation state of the power system.

[0170] It should be noted that the above content only illustrates the technical idea of the present application, and cannot limit the protection scope of the present application. For ordinary skilled persons in the technical field, a number of improvements and refinements can be made without departing from the principles of the present application, and these improvements and refinements all fall within the protection scope of the claims of the present application.

Claims

1. A method for dynamic state estimation of a photovoltaic system based on changes in solar irradiance, characterized in that: The randomness of solar irradiance is treated as an unknown input to the DSE (Digital State Estimation) algorithm, and it is incorporated into the unscented Kalman filter algorithm in the form of unbiased minimum variance to achieve state estimation of the photovoltaic system. This includes the following steps: S1: Establish a dynamic state estimation model for the photovoltaic system. The model is based on a two-stage photovoltaic system model, which consists of four main parts: a photovoltaic array, a boost converter, an inverter, and a filter. Its differential-algebraic equations are shown below: Differential equations: ； Algebraic equations: ； in, , , , and It is an intermediate state. and These are the output current and output voltage of the photovoltaic array, respectively. , , and These are the open-circuit voltage, short-circuit current, maximum power voltage, and maximum power current of the photovoltaic module under actual conditions. and Both are coefficients. , and These are the array capacitors, the inductor and capacitor of the boost converter, respectively. It is the duty cycle of the switch. It is the inductor current of the boost converter. and These are the output current and output voltage of the boost converter, respectively. and These are the proportional and integral control gains of the controller. and These are the d-axis and q-axis components of the inverter output voltage, respectively. and These are the d-axis and q-axis components of the modulated wave, respectively. It is the peak value of the carrier wave. and These are the DC-side reference voltage and the output-side reference reactive power, respectively. and These are the proportional and integral control gains of the outer loop controller, respectively. and These are the proportional and integral control gains of the inner loop controller. It is the actual reactive power output of the photovoltaic system. and These are the d-axis and q-axis components of the actual output current of the photovoltaic system. and These are the d-axis and q-axis components of the output reference current. and These are the d-axis and q-axis components of the grid voltage. It is the filter inductor. It is the angular frequency of the power grid; The process equations and measurement equations for the nonlinear photovoltaic system are established as follows: ； in, and These are photovoltaic state variables and measurement variables, respectively. and These are known input and unknown input, respectively. and It is a nonlinear function. and These are process noise and measurement noise, each with a mean of 0. It is a known matrix representing the effect of unknown inputs on state variables, with subscripts... Indicates the first At that moment; S2: Construct an unscented Kalman filter algorithm based on unbiased minimum variance. The algorithm optimizes the state estimation process by using unbiased and minimum variance methods. S3: Establish an expression for the influence of unknown input illumination on photovoltaic state variables. The expression is derived from the photovoltaic model to obtain the partial derivatives of the state variables with respect to illumination. The relationship between illumination and photovoltaic system state variables is established to realize dynamic state estimation of the photovoltaic system. S31. Based on the nonlinear system process model and the photovoltaic model, calculate the partial derivatives of the above state variables with respect to the unknown input illumination, and establish the influence of illumination on the photovoltaic state variables. The expression: Regarding state variables In the above state estimation model The specific form is as follows: ； in, These are state variables. Partial derivative with respect to illumination; S32. Considering the relationship between parameters and illumination, we further obtain: ； in: ； ； ； ； ； ； in, It is an intermediate state. It is the output voltage of the photovoltaic array. This refers to the short-circuit current of the photovoltaic module under actual conditions. For coefficients, , and These are the array capacitors, the inductor and capacitor of the boost converter, respectively. It is the duty cycle of the switch. It is the inductor current of the boost converter. It is the output voltage of the boost converter. For temperature, , , and This represents the corresponding measured value under standard test conditions.

2. The method for dynamic state estimation of a photovoltaic system based on changes in solar irradiance as described in claim 1, characterized in that: The open-circuit voltage of the photovoltaic module Short-circuit current Maximum power voltage and maximum power current They are respectively: ； ； ； ； in, and These are light radiation intensity and temperature, respectively. , , and The corresponding measurement values ​​provided by the manufacturer under standard test conditions.

3. A dynamic state estimation system for a photovoltaic system based on changes in solar irradiance, comprising a computer program, characterized in that: When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-2 above.

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