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    • 专利摘要:
    Modeling method of photovoltaic generators and follower of the maximum power point of a photovoltaic generator. Modeling method of photovoltaic generators for continuous localization throughout the day of the maximum power point (mpp) of a photovoltaic generator. The method measures the irradiance (g) on the photovoltaic generator that can be a panel, group of them or a complete installation. Follower of the maximum power point (mppt) of a photovoltaic generator, based on the resistance of its maximum power point (rmpp) and in the modeling method. (Machine-translation by Google Translate, not legally binding)
    公开号:ES2586977A1
    申请号:ES201530352
    申请日:2015-03-18
    公开日:2016-10-19
    发明作者:Juan Manuel ENRIQUE GÓMEZ；José Manuel Andújar Márquez
    申请人:Universidad de Huelva；
    IPC主号:
    专利说明:

    METHOD OF MODELING PHOTOVOLTAIC GENERATORS AND FOLLOW-UP OF THE MAXIMUM POWER POINT OF A PHOTOVOLTAIC GENERATOR Field of the Invention
    The present invention relates to a method and modeling system for photovoltaic generators - in English PhotVoltaic Generator (PVG) -. State of the art
    Many followers of the maximum power point are known - in English Maximum Power Point Tracker (MPPTs) -, a review of the main ones can be found at: -Enrique J.M., Andújar J.M., Martínez M.A. (2010). A Reliable, Fast and Low Cost Maximum Power Point Tracker for Photovoltaic Applications. Solar Energy Vol. 84. No.
    1. Pag. 79-89.-Hohm D. P., Ropp M. E. (2002). Comparative Study of Maximum Power Point TrackingAlgorithms Progress in Photovoltaics: Research and applications, November 2002.
    Generally, the followers of the maximum power point (MPPTs) that use models estimate the voltage at the maximum power point - in English Maximum Power Point Voltage (VMPP) - or the current at the maximum power point - in English Maximum Power Point Current (IMPP) - of the characteristic curve of the photovoltaic generator (PVG). For this they need a precise measurement of the solar irradiance (G) on the panel and the temperature (T) on the surface of each panel. In addition to the above, a good electrical model of the photovoltaic generator (PVG) is required. However, having a precise model of a photovoltaic generator (PVG) is not easy, since the panels that comprise it have parameters that can vary significantly between them, even if they belong to the same production line. On the other hand, the cost of measuring the temperature in each panel of an installation (think that an installation can contain tens, hundreds or thousands of panels) is, most of the time, economically and even technically unfeasible. The technical input problems are the following two: i) Due to the strong correlation of the fundamental variables of a generator
    Photovoltaic (PVG) (current, voltage, and therefore power) with solar radiation on
    the panel (measured as solar radiation perpendicular to the panel surface or


    irradiance (G); at the latitude of the invention at 35 ° of inclination over the horizontal, that is, G35 °) and its temperature (T), the maximum power point - in English Maximum Power Point (MPP) - of a photovoltaic panel is varying from continuous form during the day depending on the irradiance (G) and temperature (T) (see curves of Figures 1A, 1B obtained by simulation: characteristic curves of a typical photovoltaic generator (PVG) at constant temperature (T) and irradiance (G) variable –Figure 1A-e irradiance (G) constant and temperature (T) variable –Figure 1B). Of course, in the actual operation of the panel outside, variations in temperature (T) and irradiance (G) cannot be isolated as in Figures 1A and 1B, since temperature (T) and irradiance (G) vary to At the same time and in a different way.
    ii) In addition to the above, when a load (consumer element) is directly connected to a photovoltaic generator (PVG), the operating point of the photovoltaic generator (PVG) is given by the electrical characteristics of said load (its characteristic IV ), which means that the operating point of the photovoltaic generator (PVG) does not generally coincide with its maximum power point (MPP) (Figures 2A and 2B).
    The two previous problems –i) the point of maximum power (MPP) varies continuously and ii) the direct connection of a load does not place the photovoltaic generator (PVG) at its point of maximum power (MPP) -originate that an installation Photovoltaic where the load is connected directly to the photovoltaic generator (PVG) should be oversized, since not working most of the time (maybe never) at its maximum power point (MPP) and, therefore, not having an optimal performance at Throughout the day, its size should be larger (and therefore more expensive) than is necessary if it works permanently at its maximum power point (MPP). Description of the invention
    The invention relates to a method and a system for modeling photovoltaic generators (PVGs) as defined in the independent claims. The dependent claims define preferred embodiments of the invention. Regarding the state of the art, the invention proposes a simpler, more precise and economical method for the continuous location throughout the day of the point of maximum power (MPP) of a photovoltaic generator (PVG) connected to a load. It is based on the direct estimate of the maximum power point resistance (RMPP). This method


    it avoids the technically expensive and expensive process of having to measure the temperature of each panel of the photovoltaic generator (PVG), so that only a measure of the irradiance (G) is required. If the extension of the photovoltaic generator (PVG) were so large that it could be the case that it had panels with shadows (due to clouds for example) and others not, more than one point of irradiance measurement (G) would be necessary. In addition to the above, the invention includes a system based on the method that calculates directly and with great precision the duty cycle (δMPP) that the DC / DC converter has to continuously have, which conveniently locates the photovoltaic generator (PVG ) at its maximum power point (MPP) (Figures 3A and 3B). This system allows the photovoltaic generator (PVG) to "always see" the resistance of the maximum power point (RMPP) and, therefore, that its operating point is always located at its maximum power point (MPP). The invention has a new and different approach from what is known from the state of the art, since it demonstrates that the resistance of the maximum power point (RMPP) has no significant temperature dependencies, at least in the usual operating range. This transcendental result allows the photovoltaic generator (PVG) to be modeled at its maximum power point (MPP) only in terms of irradiance (G). Therefore the method and system of the invention only need to have irradiance measurements (G) to develop a precise maximum power point follower (MPPT). The invention represents a new, simple, precise and economical method, as well as a system, for the modeling of photovoltaic generators (PVGs) of all kinds, so that with a suitable electronic system, they can work at their maximum power point (MPP ), that is, the one in which the maximum possible energy is extracted from the photovoltaic generator (PVG) and, therefore, that in which the maximum performance is obtained. At the point of maximum power (MPP), the photovoltaic generator (PVG) works at maximum power (PMPP = VMPP * IMPP). The PVG can be an individual panel, a panel connection (array) or a complete photovoltaic field. The invention also includes the design and implementation of an electronic system that, from the developed models, allows any photovoltaic generator (PVG) to work permanently at its maximum power point (MPP). Photovoltaic generators (PVGs) have a serious restriction for their best performance, and it is their strong dependence on solar irradiance (G) and temperature in the


    surface of its panels (T). This makes the main variables that give the operation of the panel (current, voltage, and of course power) depend with the highest correlation of the incident solar irradiance (G) and the surface temperature (T). From here it is easily intuited that without adequate control, the current, voltage and power of a photovoltaic generator (PVG) is continuously changing throughout the day, subject to atmospheric conditions and, therefore, far away from the most of the time of its ideal values (IMPP, VMPP and PMPP respectively), that is, those corresponding to the point of maximum power (MPP). The method of the invention proposes the modeling of the photovoltaic generator (PVG) at its maximum power point (MPP) by its resistance at said point, maximum power point resistance (RMPP), which will be given from the voltage and Maximum power point current (MPP), that is: RMPP = VMPP / IMPP. The method of the invention is based on the fact demonstrated in the invention that the resistance of the maximum power point (RMPP) does not show significant dependencies with the panel temperature, at least in the usual range of use of the panel. This result allows the photovoltaic generator (PVG) to be modeled at its maximum power point (MPP) only in terms of the incident solar irradiance (G), thus obviating the temperature of its panels (T). In the invention the implementation of the modeling method is developed. The invention also relates to different models that allow to accurately estimate the resistance of the maximum power point (RMPP) of the photovoltaic generator (PVG). The maximum power point resistance (RMPP) models obtained allow an immediate industrial application: a new maximum power point follower (MPPT) based on the resistance of said maximum power point (RMPP), also object of this invention. This is achieved by controlling the duty cycle (δ) of a continuous / continuous converter (DC / DC converter) so that it places the photovoltaic generator (PVG) at its maximum power point (MPP) directly and continuously along of the whole day, which allows the photovoltaic generator (PVG) to transfer to the load connected to it the maximum possible energy during the entire daily period of operation, that is, that the maximum performance of the photovoltaic generator (PVG) is achieved.
    Description of the figures
    Figures 1A and 1B show characteristic curves of a photovoltaic generator (PVG)


    typical at constant temperature (T) and variable irradiance (G) -Figure 1A-e constant irradiance (G) and variable temperature (T) -Figure 1B-obtained by simulation. Figures 2A and 2B represent the connection of a load (consumer element) directly to a photovoltaic generator (PVG), where it can be seen that the operating point of the photovoltaic generator (PVG) is given by the electrical characteristics of said load ( its characteristic IV), which means that the operating point of the photovoltaic generator (PVG) does not generally coincide with its maximum power point (MPP). Figures 3A and 3B represent the connection of a load (consumer element) to the photovoltaic generator (PVG) by means of a DC / DC converter (2). Figure 4 represents the control system (3) that measures the irradiance (G) and the temperature (T) in the photovoltaic generator (PVG) as well as its I-V curve. The I-V curve is obtained by scanning the duty cycle (δ) of a continuous / continuous converter (DC / DC converter) (2). The system assembled in Figure 4 serves to obtain experimental data that allows to demonstrate in the invention that the maximum power point resistance (RMPP) does not show significant dependencies with the panel temperature, at least in the usual range of the panel. Figure 5 shows the behavior of a panel of a photovoltaic generator (PVG) against irradiance at 35º (G35º) and the surface temperature (T) during a typical day. Figure 5 is obtained with the system of Figure 4. Figure 6 shows the daily temperature path (T) versus irradiance at 35 ° (G35 °) on the same day as Figure 5. Note the hysteresis cycle or Difference between round-trip roads throughout the day. Figure 7 shows the daily evolution of the maximum power point power (PMPP) for the same day of Figure 5. Figure 7 is obtained with the system of Figure 4. Figure 8 represents the daily power path of the maximum power point (PMPP) with respect to G35º. Note the hysteresis cycle or difference between round-trip roads throughout the day. Figure 9 shows the daily trajectory of the maximum power point resistance (RMPP) for the same day as in Figure 5. Note its symmetry with respect to the central time of the day. Figure 7 is obtained with the system of Figure 4. Figure 10 represents the daily path of the maximum power point resistance (RMPP) with respect to G35 °. Note that there is no hysteresis or difference cycle


    between the round trips throughout the day.Figure 11 represents a real installation where the invention can be included.The numerical references of the elements of the invention are indicated below:Photovoltaic generator (PVG)Rear panel (1)DC / DC converter (2)Control system (3)Load Resistance (RL)Horizontal Pyranometer (20)Pyranometer with the inclination of the panels (30) Detailed description of the invention
    Some important aspects of the invention are:
    (i) A method of modeling the photovoltaic generator (PVG) at its maximum power point (MPP) through the resistance of the maximum power point (RMPP) using only solar irradiance (G) measurements.
    (ii) The implementation of the method to obtain models of the installation on which the method is applied.
    (iii) The models obtained.
    (iv) The modeling method of the duty cycle (δ) of the DC / DC converter (2) to continuously and permanently position the photovoltaic generator (PVG) at its maximum power point (MPP).
    (v) The system that based on the method and models is able to position the photovoltaic generator (PVG) permanently at its point of maximum power (MPP) throughout the day (full operating range).
    (TO) In the description of the method of the invention that follows, it can be seen that the resistance of the maximum power point (RMPP) does not depend on the temperature (T) of the panel. A first approach to the problem can be seen in the simulation of Figures 1A and 1B. Figure 1A shows the change of the maximum power point resistance (RMPP) with the irradiance (G) keeping the temperature (T) constant and Figure 1B the change of the maximum power point resistance (RMPP) with the temperature (T) keeping the irradiance (G) constant. Note in Figure 1A that the change in


    Maximum power point resistance (RMPP) is very pronounced, however in Figure 1B it can be seen that the maximum power point resistance (RMPP) varies during the day just 0.5 Ohm. This, although by simulation, gives an idea since the resistance of the maximum power point (RMPP) is very sensitive to irradiance (G) and very little to temperature (T). This evidence is also demonstrated in a practical way, and also in a conventional photovoltaic installation, where it is not possible to isolate the variation in temperature (T) with respect to irradiance (G) and vice versa. The adaptation of Figure 3B to Figure 4 allows to obtain the curve IV of a photovoltaic generator (PVG) as well as other curves such as that of Figure 5, where the behavior of a panel of a photovoltaic generator (PVG) is shown. during a typical day. Note that the path of irradiance (G) during the day is practically symmetrical with respect to noon, however the temperature path (T) does not. This means that if the trajectory of any variable of interest of the photovoltaic generator (PVG) (IMPP, VMPP, RMPP, etc.) is represented with respect to the irradiance
    (G) during a day and this trajectory has a marked symmetric character with respect to the noon, this variable will be strongly influenced by the irradiance (G), that is, strongly correlated with the irradiance (G). This means that the trajectory of the variable of interest during the day travels the same way back and forth during the day, leaving and arriving at the same point or, what is the same, the path from the beginning of the day until noon is the same as midday until the day falls. Figure 5 shows the behavior of the temperature (T) of the panel against the daily radiation at 35 ° (G35 °) on the same day used to obtain Figure 5. Note the high degree of hysteresis of the temperature path (T ), that is, the temperature path (T) does not start and returns along the same path. This suggests that although the temperature (T) depends a lot on the irradiance (G), it also depends on other meteorological variables (wind speed, ambient temperature, humidity, etc.). This experimental measure allows us to infer that if the daily trajectory of a variable with respect to irradiance (G) shows hysteresis, this variable will have strong temperature dependencies (T). The area covered by the hysteresis trajectory will give an idea of the degree of dependence. Figure 7 shows the daily evolution of the maximum power point power (PMPP) for the same day as Figure 5. Note the symmetry of the trajectory with respect to noon, which demonstrates a high correlation with irradiance (G). For the same day


    The daily path of the power at the point of maximum power (PMPP) with respect to G35º is drawn in Figure 8. Note the hysteresis cycle, which demonstrates the dependence of the power at the maximum power point (PMPP) on the temperature (T). Therefore, this method demonstrates the dependence of the maximum power point power (PMPP) (and therefore the current at the maximum power point (IMPP) and the voltage at the point at the maximum power point (VMPP ), PMPP = VMPP * IMPP), and consequently the maximum power point (MPP), hence it does not stop changing during the day with temperature (T) and irradiance (G). Therefore, and there was the difficulty until the present invention, any model-based algorithm for maximum power point tracking (MPP) by direct estimation of the maximum power point voltage (VMPP) and the current at the point Maximum power (IMPP) - or power at the maximum power point (PMPP) -, requires measurements of irradiance (G) and temperature (T). Since this invention solves the above by measuring only the irradiance (G), the question to be solved would be whether this is possible. Figure 9 shows the daily trajectory of the maximum power point resistance (RMPP) for the same day of Figure 5. Note its marked symmetric character with respect to the central time of the day, which demonstrates a very high correlation with irradiance (G). Figure 10 shows for the same day the path of resistance of the maximum power point (RMPP) against G35º. Note that there is no hysteresis cycle, which means that the resistance of the maximum power point (RMPP) has no significant dependence on temperature (T). This experimental result confirms what was already observed by simulation in Figure 1. The conclusion is clear: A method for monitoring the maximum power point (MPP) based on the maximum power point resistance (RMPP) does not require measurements Of temperature
    (T) and could be carried out with irradiance measurements (G) only. To formalize this result mathematically, equation (1) is written,
    Vh (,) h () · f () h (
    GT GT G)
    MPP V VG VG
    = ≈ == hG). (one)
    RMPP = (
    Ih (,) h () · f () h (
    GT GTG)
    MPP I IG IG
    where it is considered that the dependencies of the voltage at the maximum power point (VMPP) and the current at the maximum power point (IMPP) with the irradiance (G) and the temperature (T) are separable, and that the voltage at the maximum power point (VMPP)


    and the current at the point at the maximum power point (IMPP) varies in the same way with the temperature (T). With the data obtained through the analysis and experimentation performed, different resistance models of the maximum power point (RMPP) can be developed, the
    5 which are described below. For the adjustment of the models (search of thevalues of its parameters) known techniques can be used, such as "minimumssquares ”for example. For this, measures of selected days are used (such asexample day is provided in the invention which has given rise to Figures 5 to 10).Similarly, if you want to test the quality of the models made, they should be used
    10 other days different from the employees for the adjustment of the models. To assess the quality of these, you can use error measures such as: "Mean square error or RMSE", "Average absolute error or MAE", "Normalized average absolute error or NMAE" and "Systematic error or BIAS". The expressions of the errors are given in equations (2) to (6).
    1 N 2
    RMSE =
    (and - yˆ). (2)
    ∑ ii
    N
    i = 1
    1 N
    MAE = y - yˆ
    ∑ ii. (3)
    N
    i = 1
    yi - yˆ i
    1 N
    NMAE =
    . (4)
    ∑
    N
    i = 1
    yi
    yi - yˆ i
    100 N
    NMAE% =
    . (5)
    ∑
    N
    i = 1
    yi
    1 N
    BIAS = ∑ (yi - yˆ i). (6)
    N
    i = 1
    15 In them "yi" are the measured values of the variable, and "y ^ i" are those estimated by the model.
    Exponential modelThe exponential model and its parameters are in equations (7), (8), (9) and (10).


    G
    -
    C (7)
    R (Ω) = A + Be 1.
    MPP - E xp Dec 11
    A1 = 3,029 ± 0.028 (Ω), (8) B 68.1 ± 0.4 (Ω, (9)
    1 =)
    ⎛ W ⎞
    C = 139.4 ± 0.7. (10)
    1 ⎜ 2 ⎟
    ⎝ m ⎠
    Hyperbolic modelThe hyperbolic model and its parameters are given in equations (11), (12) and (13).
    R (Ω
    MPP - Hyp) = A2 + (11)
    G A2 = - 1.814 ± 0.027 (Ω), (12) ⎛ ΩW ⎞
    B2 = 3891 ± 92 ⎟. (13)
    ⎜
    ⎝ m ⎠
    Order 2 polynomial modelThis model and its parameters are given in equations (14), (15), (16) and (17).
    BC3
    )
    + 2, (14)
    RMPP - Pol 2 (Ω = A3 +
    GG A3 = - 2.38 ± 0.04 (Ω), (15) ⎛ ΩW ⎞
    B3 = 4297 ± 24 ⎜ 2 ⎟, (16) ⎝ m ⎠
    ⎛⎞ 2 ⎛ ΩW2 ⎞
    C3 = ⎝⎜ −409 ± 23 10 ⎟ ⎝⎜ m4 ⎟. (17) ⎠⎠
    Polynomial model of order 3


    This model and its parameters are given in equations (18), (19), (20), (21) and (22).
    B C D
    + 4
    + 4,
    R (Ω) = A +
    MPP - Pol 3 4 23 (18)
    GG G
    A4 = - 0.87 ± 0.05 (Ω), (19)
    ⎛ ⎞⎛ ΩW ⎞
    B = 284 ± 410, ⎝ ⎠⎝ m ⎠
    4 ⎜ ⎟⎜ 2 ⎟ (20)
    ⎛⎞ 3 ⎛ ΩW2 ⎞
    C = 272 ± 9 10, (21)
    4 ⎜ ⎟⎜ 4 ⎟
    ⎝ ⎠⎝ m ⎠
    ⎛⎞ 5 ⎛ ΩW3 ⎞
    D4 = ⎜ −167 ± 4 10 ⎜⎟. (22)
    ⎟ 6
    ⎝ ⎠⎝ m ⎠
    Weighted model This model is a mixture of exponential and hyperbolic models. The weighting factor "x" between one model and another is adjustable between 0 and 1. The model equation is shown in (23).
    R () = xR (Ω + (1− x)
    Ω ·) R (Ω). (2. 3)
    MPP −Pond MPP −ExpDec MPP −Hyp
    Offset + exponential + hyperbolic modelThis model and its parameters are given in equations (24), (25), (26), (27) and (28).
    G
    - D
    R (Ω) = A + Be C5 + 5. (24)
    MPP −OEH 55
    G
    At 0.29 ± 0.06 (Ω, (25)
    5 =)
    B5 = 30.0 ± 0.9 (Ω), (26)


    ⎛ W ⎞
    C = 142.3 ± 1.1 ⎝ m ⎠
    5 ⎜ 2 ⎟, (27)
    ⎛ ⎞⎛ ΩW ⎞
    D = 216 ± 5 10. (28)
    5 ⎜ ⎟⎜ 2 ⎟
    ⎝ ⎠⎝ m ⎠
    (B) The invention also relates to a maximum power point follower (MPPT) based on the resistance of said point, that is, the maximum power point resistance (RMPP)
    5 As seen in Figure 3A, the system designed in the invention locates thePhotovoltaic generator (PVG) at its maximum power point (MPP). At this point, theresistance that "sees" the photovoltaic generator (PVG) is obviously the resistance of themaximum power point (RMPP). The δMPP duty cycle (whose design is alsoobject of the invention) of the DC / DC converter (2) allows to locate the photovoltaic generator
    10 (PVG) at its maximum power point (MPP) directly and continuously throughout the day. The maximum power point resistance (RMPP) is related to it according to equation (29).
    R = f (δ, R). (29)
    MPP MPP L
    The function f of this equation is invertible, which can be written from (29) equation (30).
    −1 −1
    δ = ((hG),
    f R, R) = f (R), (30)
    MPP MPP L L
    In it h (G) represents any of the models presented in the invention that estimate the resistance of the maximum power point (RMPP). From the article Enrique J. M., Durán E., Sidrach M., Andújar J. M. (2007). Theoretical Assessment of the Maximum Power Point Tracking Efficiency of Photovoltaic Facilities With Different Converter Topologies. Solar Energy, 81 (1), pp. 31-38, 2007, it follows that
    20 equation (29) can be written as in (31).
    R = R (1 − δ) 2. (31)
    MPP L MPP
    However, this equation is in ideal conditions. However, the studies
    carried out in the invention demonstrate that from the measured resistance values 13


    of the maximum power point (RMPP), equation (31) should be written as in (32),
    R = R + R (1 − δ) 2. (32)
    MPP off L MPP
    where Roff is a non-zero value at the origin (offset) due to the non-idealities of the DC / DC converter (2), which is easily calculable and will generally have a different value (although always small) depending on the DC / DC converter (2) used in the
    5 assembly of Figure 3B.From the equation (32) the duty cycle value (δMPP) of theconverter of Figure 3B that locates directly and permanently throughout the day atPhotovoltaic generator (PVG) at its maximum power point (MPP). This is indicated inthe equation (33).
    R - RR - R
    MPP off MPP off δ MPP = 1−
    = 1−
    RL V0 (33) I0
    ,
    In it, the necessary value of the maximum power point resistance (RMPP) can be obtained by any of the models developed in the invention. The modeling method as well as the MPP tracking method are new, so it is not easy to compare them with the state of the art. However, with respect to the main advantages of the invention, the following may be mentioned:
    15 -Modeling errors: the method of the invention allows obtaining as much precision as required. It does not set lower or upper limits of error. -Speed: Unlike other MPP search methods, the method of the invention places the PVG in its MPP virtually instantaneously. -Direct location with Precision: Unlike other 20 MPP positioning methods, the methodology developed in this invention positions the PVG in its MPP directly, that is, without oscillations around it.
    - Other advantages are: it is not necessary to isolate (disconnect) the installation to locate your MPP (as other methods require). In addition, the methodology developed can be combined with other known MPP tracking techniques.
    As described above, a first aspect of the invention relates to a method of modeling photovoltaic generators for continuous location throughout the day of the maximum power point (MPP) of a photovoltaic generator (PVG). The method:


    1a) comprises measuring an irradiance (G) on a photovoltaic panel;
    1b) excludes measuring a temperature (T) on the photovoltaic panel.
    According to other features of the invention the method comprises:
    2) calculate a duty cycle (δMPP) of a DC / DC converter (2) to locate the
    5 photovoltaic generator at the point of maximum power (MPP) direct and
    continuously throughout the day.
    3) generate a maximum power point resistance model (RMPP)
    selected from:
    3a) an exponential model; 10 3b) a hyperbolic model;
    3c) a polynomial model of order 2;
    3d) a polynomial model of order 3;
    3e) a weighted model;
    3f) an Offset + exponential + hyperbolic model; 15 3g) a model derived from the irradiance measurement (G) and the calculation of the cycle of
    work (δMPP) of a DC / DC converter (2).
    The exponential model is defined by:
    G
    R Ω) A + 1 - C1.
    MPP - E xp Dec (= 1 Be
    A1 = 3,029 ± 0.028 (Ω),
    B 68.1 ± 0.4 (Ω,
    1 =)
    ⎛ W ⎞
    C = 139.4 ± 0.7.
    1 ⎜ 2 ⎟
    ⎝ m ⎠
    The hyperbolic model is defined by:
    R (Ω) = A +
    MPP - Hyp 2
    G
    A2 = - 1.814 ± 0.027 (Ω),


    ⎛ ΩW ⎞
    B = 3891 ± 9.
    2 ⎜⎟
    ⎝ m2 ⎠
    The polynomial model of order 2 is defined by:
    BC
    + 3,
    R (Ω) = A +
    MPP - Pol 23 2
    GG
    A3 = - 2.38 ± 0.04 (Ω),
    ⎛ ΩW ⎞
    B = 4297 ± 24,
    3 ⎜⎟
    ⎝ m2 ⎠
    ⎛⎞ 2 ⎛ ΩW2 ⎞
    C = −409 ± 2310.
    3 ⎜ ⎟⎜⎟
    ⎝ ⎠⎝ m4 ⎠
    The polynomial model of order 3 is defined by:
    BC 4 D4
    R (Ω) = A +
    ++,
    MPP - Pol 34 23
    GG G
    A4 = - 0.87 ± 0.05 (Ω),
    ⎛ ⎞⎛ ΩW ⎞
    B = 284 ± 410,
    4 ⎜ ⎟⎜ 2 ⎟
    ⎝ ⎠⎝ m ⎠
    ⎛⎞ 3 ⎛ ΩW2 ⎞
    C = 272 ± 910,
    4 ⎜ ⎟⎜ 4 ⎟
    ⎝ ⎠⎝ m ⎠
    ⎛⎞ 5 ⎛ ΩW3 ⎞
    D = −167 ± 410.
    4 ⎜ ⎟⎜ 6 ⎟
    ⎝ ⎠⎝ m ⎠
    The weighted model is defined by: a weighting factor "x" between an exponential model and an adjustable hyperbolic model between 0 and 1; Y
    R () = xR (Ω + (1− x)
    Ω ·) R (Ω).
    MPP −Pond MPP −ExpDec MPP −Hyp


    The Offset + exponential + hyperbolic model is defined by:
    G
    R (Ω) = A + Be - C5 + D5.
    MPP −OEH 5 5
    G A5 = 0.29 ± 0.06 (Ω), B5 = 30.0 ± 0.9 (Ω), ⎛ W ⎞
    C = 142.3 ± 1.1
    ,
    5 ⎜ 2 ⎟
    ⎝ m ⎠
    ⎛⎞
    D = 216 ± 5 10
    5 ⎜⎟
    ⎝⎠
    The duty cycle (δMPP) is calculated by:
    R - RR - R
    MPP off MPP off δ MPP = 1−
    = 1−
    RL V0 I0
    ,
    Where:
    ⎛ ΩW ⎞
    .
    ⎜ 2 ⎟
    ⎝ m ⎠
    5 Roff is a non-zero value at source (offset) due to non-idealities of the DC / DC converter (2). RL is the resistance of the load connected to the converter. V0 is the supply voltage of the load connected to the converter. I0 is the current consumed by the load connected to the converter.
    A second aspect of the invention relates to a maximum power point follower (MPPT) of a photovoltaic generator (PVG), based on its resistance in said (RMPP) and in the method described above, where the follower comprises a converter DC / DC (2) configured to locate the operating point of the photovoltaic generator at its maximum power point (MPP).
    15 According to other additional features, the DC / DC converter (2) is configured to be connected in parallel between the photovoltaic generator and the load to be supplied. To obtain the experimental results that demonstrate the modeling method,


    You have used a real installation as shown in Figure 11, located at a latitude: 37 °. The installation has 6 panels of 94 Wp each, oriented to the south with an inclination angle of 35º on the horizontal. Of the 6 panels available, only one of them has been used to demonstrate the invention, since it is not necessary to use more power.
    5 Therefore, for the experimental demonstration, the PVG is a 94 Wp panel. Thus, the photovoltaic generator (PVG) of Figure 4 is the first panel shown in Figure 11. The temperature of the panel (T in Figure 4) is measured according to norm, that is, at its rear (1) in Figure 11. It should be noted that the maximum power point tracking system (MPPT) developed in this invention does not require measurement
    10 panel temperature (T). However, the measurement is necessary to experimentally demonstrate the methodology developed, that is, to obtain Figures 5 and 6. The irradiance is measured for two angles of inclination (see Figure 4): in the horizontal plane (G0º) and in the of inclination of the panels (G35º). This is done to have a comparison of radiation in both planes; however, for the invention which
    15 uses is G35º. Both irradiance measurements are made with precision pyranometers, a horizontal pyranometer (20) and a pyranometer with the inclination of the panels (30) in Figure 11.

    权利要求:
    Claims (11)
    [1]
    1. Modeling method of photovoltaic generators for continuous location throughout the day of a point of maximum power (MPP) of a photovoltaic generator (PVG)
    5 characterized in that: 1a) comprises measuring an irradiance (G) on a panelphotovoltaic;1b) excludes measuring a temperature (T) on the photovoltaic panel.
    [2]
    2. Photovoltaic generator modeling method according to claim 1
    10 characterized in that it comprises calculating a duty cycle (δMPP) of a DC / DC converter (2) to locate the photovoltaic generator at the point of maximum power (MPP) directly and continuously throughout the day.
    [3]
    3. Modeling method of photovoltaic generators according to any of the
    Claims 1-2 characterized in that it comprises generating a maximum power point resistance model (RMPP) selected from: 3a) an exponential model; 3b) a hyperbolic model; 3c) a polynomial model of order 2;
    20 3d) a polynomial model of order 3; 3e) a weighted model; 3f) an Offset + exponential + hyperbolic model; 3g) a model derived from the irradiance measurement (G) and the calculation of the cycle of
    work (δMPP) of a DC / DC converter (2).
    [4]
    4. Photovoltaic generator modeling method according to claim 3 characterized in that the exponential model is defined by:
    G
    -
    R (Ω) = A + Be C1.
    MPP - E xp Dec 11
    A1 = 3,029 ± 0.028 (Ω),

    B1 = 68.1 ± 0.4 (Ω), ⎛ W ⎞
    C1 = 139.4 ± 0.7 ⎜.
    ⎟
    ⎝ m2 ⎠
    [5]
    5. Photovoltaic generator modeling method according to claim 3 characterized in that the hyperbolic model is defined by:
    R (Ω) = A +
    MPP - Hyp 2
    G A2 = - 1.814 ± 0.027 (Ω), ⎛ ΩW ⎞
    B2 = 3891 ± 92 ⎟.
    ⎜
    ⎝ m ⎠
    Method of modeling photovoltaic generators according to claim 3 characterized in that the polynomial model of order 2 is defined by:
    BC3
    R (= + 2,
    MPP - Pol 2 Ω) A3 +
    GG A3 = - 2.38 ± 0.04 (Ω), ⎛ ΩW ⎞
    B3 = 4297 ± 24 ⎜ 2,
    ⎟
    ⎝ m ⎠ ⎛⎞ 2 ⎛ ΩW2 ⎞
    C = −409 ± 2310.
    3 ⎜ ⎟⎜ 4 ⎟
    ⎝ ⎝ m
    ⎠⎠
    [7]
    7. Photovoltaic generator modeling method according to claim 3 characterized in that the polynomial model of order 3 is defined by:

    BC 4 D4
    ++,
    RMPP - Pol 3 (Ω) = A4 + 23
    GG G
    A4 = - 0.87 ± 0.05 (Ω),
    ⎛ ⎞⎛ ΩW ⎞
    B4 = ⎜ 284 ± 4 10 ⎜ 2,
    ⎟⎟
    ⎝ ⎠⎝ m ⎠
    ⎛⎞ 3 ⎛ ΩW2 ⎞
    C = 272 ± 910,
    4 ⎜ ⎟⎜ 4 ⎟
    ⎝ ⎠⎝ m ⎠
    ⎛ ⎞⎛ ΩW3 ⎞
    D4 = ⎜ −167 ± 4 10 ⎟ 5 ⎜ 6 ⎟. ⎝ ⎠⎝ m ⎠
    [8]
    8. Photovoltaic generator modeling method according to claims 4 and 5 characterized in that the weighted model is defined by:
    a weighting factor "x" between an exponential model and an adjustable hyperbolic model between 0 and 1; Y
    R () = xR (Ω + (1− x)
    Ω ·) R (Ω).
    MPP −Pond MPP −ExpDec MPP −Hyp
    [9]
    9. Photovoltaic generator modeling method according to claim 3 characterized in that the Offset + exponential + hyperbolic model is defined by:
    G
    - D
    R (Ω) = A + Be C5 + 5.
    MPP −OEH 55
    G
    At 0.29 ± 0.06 (Ω,
    5 =)
    B5 = 30.0 ± 0.9 (Ω),

    ⎛ W ⎞
    C = 142.3 ± 1.1
    ,
    5 ⎜ 2 ⎟
    ⎝ m ⎠
    ⎛ ⎞⎛ ΩW ⎞
    D = 216 ± 510.
    5 ⎜ ⎟⎜⎟
    ⎝ ⎠⎝ m2 ⎠
    [10]
    10. Photovoltaic generator modeling method according to any of claims 2-9 characterized in that the duty cycle (δMPP) is calculated by:
    R - RR - R
    MPP off MPP off
    δ MPP = 1−RL = 1− 0
    V I0
    ,
    Where:Roff is a non-zero value at source (offset) due to non-idealities of the DC / DC converter(2);RL is the resistance of the load connected to the converter;
    10 V0 is the supply voltage of the load connected to the converter; I0 is the current consumed by the load connected to the converter.
    [11]
    11. Follower of the maximum power point (MPPT) of a photovoltaic generator (PVG), based on the resistance of its maximum power point (RMPP) and the method of
    Any one of claims 1-10 characterized in that: 11a) comprises a DC / DC converter (2) configured to place the operating point of the photovoltaic generator at the maximum power point (MPP).
    [12]
    12. Follower of the maximum power point (MPPT) of a photovoltaic generator according to
    20 claim 11 characterized in that the DC / DC converter (2) is configured to be connected in parallel between the photovoltaic generator and the load to be fed.

    FIG. 1A FIG. 1 B
    FIG. 2A FIG. 2B
    FIG. 3A FIG. 3B

    Irradiance G 35º (W / m)
    FIG. 4
    fifty
    07:12 09:36 12:00 14:24 16:48 19:12
    Local time
    FIG. 5
    G 35º (W / m 2)
    FIG. 6
    Temperature T (ºC)
    P (W) P (W)
    MPP MPP
    70 60 50 40 30 20 10 0
    07:12 09:36 12:00 14:24 16:48 19:12 Local time
    FIG. 7

    G35º (W / m 2)
    FIG. 8

    R
    MPP
    R (Ω) R (Ω)
    MPP MPP
    07:12 09:36 12:00 14:24 16:48 19:12 Local time
    FIG. 9
    R
    MPP
    G35º (W)
    FIG. 10

    FIG. eleven
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    同族专利:
    公开号 | 公开日
    WO2016146872A1|2016-09-22|
    ES2586977B1|2017-05-22|
    引用文献:
    公开号 | 申请日 | 公开日 | 申请人 | 专利标题
    CN108180108A|2017-12-15|2018-06-19|南京工程学院|A kind of MPPT wireless sensor wind collecting methods based on resistance emulation|WO2005069096A1|2004-01-12|2005-07-28|Koninklijke Philips Electronics, N.V.|Solar power source with maximum power-point tracking|
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