NEURAL NETWORK SOLAR IRRADIANCE SENSOR
FIELD OF THE INVENTION
[0001] The present disclosure is related to photovoltaic (PV) array systems.
BACKGROUND
[0002] Solar irradiance plays a role in efficiency of photovoltaic power plants. However, devices for solar irradiance measurement, such as pyranometers and pyrheliometers, are often expensive and difficult to calibrate. As a result, such devices are often undesirable for use in photovoltaic power plants.
[0003] In order to reduce the need for specialized solar irradiance equipment, researchers have developed different algorithms to perform Maximum Power Point tracking (MPPT) in photovoltaic (PV) array systems. Some MPPT functions avoid a direct measurement of solar irradiance, and rely on a concave shape of the PV array power-voltage curve and search for the Maximum Power Point (MPP) through iterative processes, without knowledge of solar irradiance. Examples of these methods include perturb and observe (P&O) and incremental conductance algorithms, respectively. However, these methods may oscillate around the MPP and may respond poorly under rapidly changing irradiance.
[0004] Other approaches to perform MPPT functions include a prediction/estimation of the solar irradiance from equations which describe a PV array model and then use the predicted/estimated value to perform the MPPT function. However, in many deployments relatively precise solar irradiance sensing is necessary for optimal operation, and PV power plants often span over a relatively large geographical area which may result in non-uniform irradiance. Known as shading effect, this adversely affects the overall efficiency of the power extraction process when prediction/estimation techniques are implemented. More precise estimations/predictions may be obtained from (i) a modularization of a PV power plant into various segments using one power converter and a separate MPP tracking algorithm per segment, and (ii) a dynamic reconfiguration of the PV panels' interconnection with only one power converter.
SUMMARY OF THE INVENTION
[0005] Since a precise tracking of the irradiance at various locations through the power plant is desired and/or necessary in one or more of the examples above, low-cost irradiance sensors are highly desirable. One aspect of the present disclosure provides a novel approach for solar irradiance measurement based on neural networks, which may be used in photovoltaic power plants to sense solar irradiance and hence enhance efficiency. Although other low-cost irradiance sensors have been proposed, one advantage of the approach proposed herein lies in the simplicity of construction, leading to low cost, along with enhanced accuracy.
[0006] The foregoing has outlined rather broadly the features and technical advantages of examples according to the disclosure in order that the detailed description that follows may be better understood. Additional features and advantages will be described hereinafter. The conception and specific examples disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present disclosure. Such equivalent constructions do not depart from the spirit and scope of the appended claims. Features which are believed to be characteristic of the concepts disclosed herein, both as to their organization and method of operation, together with associated advantages will be better understood from the following description when considered in connection with the accompanying figures. Each of the figures is provided for the purpose of illustration and description only, and not as a definition of the limits of the claims. BRIEF DESCRIPTION OF THE DRAWINGS
[0007] A further understanding of the nature and advantages of the present invention may be realized by reference to the following drawings.
[0008] FIG. 1 is a graph depicting current versus voltage (I - V) relationships for various levels of irradiance on a photovoltaic cell, according to various aspects of the disclosure;
[0009] FIG. 2 is a graph depicting current versus voltage (I - V) relationships for various temperatures of a photovoltaic cell, according to various aspects of the disclosure;
[0010] FIG. 3 is a block diagram illustrating an irradiance sensing system, according to various aspects of the disclosure;
[0011] FIG. 4 is a block diagram illustrating a PV array circuit mathematical model, according to various aspects of the disclosure;
[0012] FIG. 5 is a graph depicting mean squared error for training exemplary neural networks, according to various aspects of the disclosure;
[0013] FIG. 6 is a block diagram illustrating a neural network according to various aspects of the disclosure;
[0014] FIG. 7 is a graph depicting measurements made using a sensor of the present disclosure and a commercially available irradiance sensor, according to various aspects of the disclosure;
[0015] FIG. 8 is another graph depicting measurements made using a sensor of the present disclosure and a commercially available irradiance sensor, according to various aspects of the disclosure;
[0016] FIG. 9 is a graph depicting solar irradiance and temperature measurements made using a sensor of the present disclosure and a commercially available irradiance sensor, according to various aspects of the disclosure; and [0017] FIG. 10 is another graph depicting solar irradiance and temperature measurements made using a sensor of the present disclosure and a commercially available irradiance sensor, according to various aspects of the disclosure.
DETAILED DESCRIPTION
[0018] Solar irradiance is a key parameter for maximum power point (MPP) tracking (MPPT) in photovoltaic (PV) power plants. This is because the operating point at which a PV array delivers its maximum power changes as a function of the solar irradiance and cell temperature. This is illustrated in FIGS. 1 and 2 through typical current-voltage (I - V) curves for a PV array. FIG. 1 shows typical 7 - V performance curves 100 for different irradiance values with G\ < G2 < G3 < G4 < G5, while FIG. 2 shows typical I - V performance curves 200 for different cell temperature values with T\ < 12 < 73 < T4 < T5.
[0019] Using ideas developed for both MPPT and solar irradiance estimation, a novel low-cost solar irradiance sensor is provided according to certain examples of the present disclosure. One approach comprises using one or a small number of PV cells together with a neural network (NN) algorithm appositely tailored for the solution of an inverse problem. In some examples, NNs are used to track the MPP without the knowledge of the solar irradiance. In various examples provided herein implementation of a NN approach is provided to sense the irradiance, which in turn can be also used to track the MPP.
[0020] One exemplary sensor is implemented through one or more of: a photovoltaic cell, a temperature sensor, and a low-cost microcontroller. The use of a microcontroller allows for a straightforward calibration and interfacing, via RS232, RS485, Ethernet, or any other communication device known in the art, with the rest of the PV power plant control system. Such communication may enable remote-control through an embedded web server. An initial estimate suggests the device proposed herein may cost less than 10% with respect to its commercially available counterparts, making it attractive for a large deployment in photovoltaic power plants. The use of a microcontroller allows for relatively easy calibration, updates, and enhancement by simply adding code libraries.
[0021] In one embodiment, referred to herein as accurate double, one or more NNs are implemented in the microcontroller(s) with the use of accurate double-precision mathematic library, C compilers and integrated development environment. Calibration of cell irradiance may be performed utilizing a PV cell model obtained, for example, from manufacturer datasheets. In other examples, calibration of cell irradiance may be performed utilizing a PV cell model obtained through laboratory measurements, which may reduce potential errors due to parasitic elements and/or inaccuracies on datasheets.
[0022] Turning now to FIG. 3, a block diagram illustrates a sensor 300 according to one embodiment of the disclosure. As seen, one, or a small number of PV cells 305 may be arranged in series and/or parallel, forming a small sensing PV panel 310. The sensing PV panel 310 may receive irradiance 311 (indicated as G), and may provide an output current in response to the received irradiance 311. The sensing PV panel 310 may be then electronically coupled to a known testing resistor ( ?test) 315, and a voltage 320 across the testing resistor 315 may be measured. Such an approach may inexpensively and easily measure and provide the voltage 320 across the cell terminals of the sensing PV panel 310 and may also be used to measure the cell temperature. In some examples, a separate temperature sensor 325 may provide a temperature measurement 330, and may be located on or adjacent to the PV panel 310. In certain examples, these voltage and temperature values are provided to a microcontroller 335. The microcontroller may compute a current value 345 according to the voltage 320 divided by the value of Rtest. Using the current value 345, voltage value 320, and temperature value 330, the microprocessor 335 may execute a properly trained NN algorithm 340 based on a PV cell model such as described above, which then computes the measured solar irradiance 350 (Gm) with great accuracy.
[0023] Such a sensor 300 may be located, for example, next to a power-producing PV panel or may even be integrated with a power producing PV panel. This features the advantage that the sensing PV panel 310 will "see" the same solar irradiance and temperature as that "seen" by the power-producing PV panel, leading to improved performance.
[0024] The NN training process and hence the performance of the sensor 300 relies on a knowledge of the PV array's 310 7 - V performance curves 100 and 200 for different irradiance and temperature values, such as those illustrated in FIGS. 1 and 2, respectively. Performance I - V curves 100 and 200 for PV cells can be obtained using their mathematical model along with standard information provided by manufacturer's datasheets, for example. Additionally or alternatively, operating points may be experimentally generated in the laboratory under controlled environmental conditions.
[0025] According to certain examples, illustrated in FIG. 4, a training-set may be generated using a PV array mathematical model 400, which may include a circuital model for a single PV cell and its generalization to a number of cells in series using a current source 405 representing the current generated at a particular irradiance G, an anti-parallel diode, a series resistance 415 and shunt resistance 420. One embodiment may also use a modified circuit which replaces the anti-parallel diode 410 by an external control current source 410 as illustrated in FIG. 4. One advantage of this model is that it allows for including an arbitrary number of cells connected in series and/or parallel into a single circuital representation including all details of each cell. The FIG. 4 model corresponds to a building block to generate performance I - V utilized to train the N 320 of FIG. 3, for example.
[0026] The output current of the PV cell of FIG. 4 may be expressed as / = Ilu - In0 - IP- In one embodiment, lm is the photo current or irradiance current 405, which may be generated when the cell is exposed to sunlight. Ι&0 may comprise the current flowing through the anti-parallel diode or external control current source 410, which may induce the non-linear characteristics of the PV cell. Ip may be a shunt current due to the shunt resistor 415 branch. Substituting relevant expressions for Tdio and 7P, in the above equation, the equation becomes: / = Im - I0[exv(q((V+IRS)/nkT)) - 1] - (V + IRS)/R?, where q = 1.602 x 10~19 C is the electron's electric charge, k = 1.3806503 x 1023 J/K is the Boltzmann constant, T is the temperature of the cell, Io is the diode saturation current or cell reverse saturation current, n is the ideality factor or the ideal constant of the diode, and Rs and ?p represent the series 420 and shunt 415 resistance, respectively. A voltage 425 across the anti-parallel diode or external control current source 410 may be provided and the output of the above equation may be determined at 430 and provided as an input to the external control current source 410 of FIG. 4 to generate performance / - V for the training sets.
[0027] This model can be generalized to an arbitrary number of cells connected in series, say Ns, and in parallel, say Np, to form a small array of Ns x Np cells. This may be needed to match voltage/current levels needed by the microcontroller. One such generalized model may take the form of / = rin - I'o[Qxp((q(V + IR's)/NsnkT)) - 1] - (V + IR 's)/R 'P. In such an embodiment, various "prime" values may be interpreted according to Table 1 : SUBSTITUTIONS FOR THE MODEL OF A PV ARRAY
TABLE 1
[0028] The I - V performance characteristic of a single PV cell and an array described by the equations above, the parameters l
m, I
0, Rp, R&, and n depend on the solar irradiance (G), the cell temperature (7), and certain reference parameters, namely G
ref, 7 , 7i
rr,
ref, o,ref, R?,ieu ¾ref and η
Ιβί , as described by: I
in =
- (E
g/kT)); R
? = ?
P,ref(G/G
ref); and R
$ = R
s_
iei; n = η
Ιβί.
[0029] may comprise the relative temperature coefficient of the short-circuit current, which may represent the rate of change of the short-circuit current with respect to temperature. Manufacturers may occasionally provide the absolute temperature coefficient of the short-circuit current,T , for a particular panel. The relationship between andT isT = a¾r,ref- Furthermore, Eg may comprise the bandgap energy for silicon in eV. Analytical expressions for Eg may be obtained through curve fitting from experimental measurements, for example, and may vary. One expression for Eg comprises Eg = (1 . 16 - 7.02 x 104 x (^/(T - 1 108)) x q. The I- V curves described above, in addition to the breakdown of the various constituent parameters described above provide a representation for the performance of a PV cell or array and may be used to train the NN. The reference parameters may be PV-cell specific and may be obtained based at least in part on information available on manufacturers' datasheets. [0030] Operating points making up the training-set can alternatively or additionally be generated in the laboratory under controlled environmental conditions. The sensing PV cell can be exposed to an adjustable controlled irradiance level and the PV cell loaded at various levels— for example through using a rheostat— followed by direct measurement of the PV array output voltage and current and cell temperature. This methodology may overcome inaccuracies stemming from: (i) parasitic elements existing on the circuital realization of the proposed sensor; (^differences between the PV array's datasheet and the actual PV array being used; and (Hi) tolerance of the testing resistor.
[0031] When using NNs for applications, the training process often requires a high level of accuracy and depends on the design of the various stages— size of hidden layer, size of training and validation sets, early stopping, etc.— for a specific problem. A well trained NN may adapt to data outside the training set which translates into finding suitable matrices of synaptic weights and bias vectors in terms of a nonlinear optimization problem. In one embodiment, the Levenberg-Marquardt algorithm may be used for the training process. Furthermore, to reduce computation cost and memory usage in the microcontroller, a NN configuration may be chosen with a lowest number of neurons possible. One adopted NN, illustrated in FIG. 6, has a feedforward architecture and is characterized by a three-layer structure 600 with: (i) three input neurons (with linear activation function) 605; (H) eight neurons 610 for the hidden layer with tansig activation function; and (Hi) one output neuron (with linear activation function) 615 for prediction of the measured irradiance, Gm.
[0032] In one embodiment, a suitable training-set may be constructed by using N different I - V curves depending on the irradiance using a constant temperature. Likewise, M different I - V curves may be obtained by varying the temperature at a constant irradiance. Thus, N x M training-set patterns may be created by simulating a PV cell model.
[0033] Additionally, the NN may be trained to return Gm from the operating point identified by the voltage (V ) and current (7) at the PV cell terminals and the temperature on the PV cell surface (7). The trio x = [V, I, J] may correspond to the NN's input vector, as illustrated in FIG. 6. Furthermore, in the PV cell model described by the equations above, a one to one relationship may exist between the operating points x and the single values of G. Yet further, in certain hardware implementations only V and T have to be measured. Indeed, direct measurement of I may be avoided through using a known testing resistor, Rtesh so the current I can be computed using Ohm's Law. In order to improve accuracy and make the various numerical processes more robust, the value of i?test may be selected so that most of the operating points lie around the elbow of the PV cell's I - V curves, thus benefiting from a greater range of values for all three variables [V, I, T\.
[0034] One training process may define maximum and minimum values for V, I, T and G, return the matrices of synaptic weights W\ andJ
2, and bias vectors B\ and B
2 for the first and second layer, respectively. The measured irradiance G
m may be computed through the following three- step procedure: (1) Normalization of the input data, according to the formulae: x
nj=( j - x™)/(i
maxj - χ™
1^) for j = 1, 2, 3 and where Xj corresponds to V, I and T for j =1, 2, and 3, respectively, x
maXj and x
1™^ are the maximum and minimum values of V, I and T, and x
nj is the normalized input value within the range [-1 1]; (2) Computation of the normalized irradiance: G
n = Wi x tansig(J l x x
n +
= (2/(1 + e
2A)) - 1; and (3) De-normalization of G
n in order to obtain the actual solar irradiance value G
m = (G
max - G
mm)G
n + G
mn. [0035] In one example, the circuit schematic of FIG. 3 may include a sensing PV array realized by a prepackaged eight-cell array manufactured by IXYS, part # KXOB22-01X8, rated at 3.4 V/3.8 mA at MPP under standard testing conditions. Using the specifications available on the manufacturer's datasheet, a complete mathematical model for the performance of the array may be built using the procedure outlined above.
[0036] In one example, a NN training set was implemented in a MATLAB® environment through ten different operating points at equidistant irradiance values from 100 to 1500 W/m2 and five different operating points at equidistant temperature values from 260 to 360 (K), which leads a training set size of 50 operating points [V, I, T\. Given the PV array characteristics, the resistance of the testing resistor was selected to be i?test = 921 Ω and was realized through a simple axial-lead resistor. This allowed operating points to be selected around the elbow of the PV array I - V curve. The goal for mean square error (MSE) on the training set was fixed equal to 8 x 103 and the learning process took around 2 minutes. FIG. 5 shows a graph 500 of the mean square error (MSE) during the NN training. After 4125 epochs the target value of 10~2 for MSE was reached.
[0037] According to certain examples, a PV array terminal voltage may be measured using an internal analog/digital (AD) converter embedded in the microcontroller (e.g., microcontroller 335 of FIG. 3). A temperature sensor, in on example, was realized using a one-wire sensor Maxim Integrated® model # DS18B20, and the microcontroller used for data processing was a PIC18F6627 manufactured by Microchip Technology Inc. This device belongs to the low- cost low-power PIC 18/8-bit family, featuring a 4 kB RAM memory and a 96 kB reprogrammable flash memory; 12 AD converters; and SPI, I2C, and RS232/RS485 interfaces. Of course, one of skill in the art will readily recognize that these components are merely exemplary, and that numerous other components may be utilized in other examples.
[0038] In some embodiments, the microcontroller may comprise an 8-bit microcontroller that may be configured to implement one or more accurate double-precision mathematic libraries which are available for the development of the firmware of microcontrollers. The NN algorithm described above may be adapted to run in the microcontroller, and may be coded in C language, in some embodiments. The C code may comprise a set of initializing functions and a main process. The latter may control the peripheral units, manage the communication protocol(s), acquires the input data, execute the implemented NN routine, and output the computed irradiance. The routines for control and communication processes may be developed by means of the MPLABTM X IDE and compiled through a compiler such as the Microchip C 18 compiler. This may restitute a HEX code file which may be downloaded into the microcontroller, such as via an Ethernet connection, for example. Furthermore, the microcontroller may be interfaced to a personal computer (or other computer) through a RS232/RS485 or an Ethernet cable. The aforementioned features of the microcontroller may allow for easy update, recalibration, or the inclusion of new customized features. The entire NN routine, in some embodiments, may occupy about 5904 bytes of program memory and 186 bytes of data memory.
[0039] Table II shows the cost of the main components for the hardware realization of one exemplary embodiment. The overall cost of all components is around USD $50, a small fraction of the cost of most commercially available irradiance sensors.
EXPERIMENTAL SETUP COMPONENTS AND COST
Component Off-the shelf part # Cost (USD $) PV cell KXOB22-01X8 5.8
Temperature Sensor DS18B20 4.5
Microcontroller PIC18F6627 11.0
Other components Connectors, case, etc. 10.0/30.0
Total Cost: 41.3/51.3
TABLE II
[0040] Several outdoor experiments were performed using the hardware prototype described above. The exemplary sensor was contrasted against a commercial sensor. The device available for comparison is a laser power sensor part # LM-10 HTD manufactured by Coherent, Inc. [0041] The PV cells utilized in exemplary sensors may correspond to a monocrystalline silicon cell pack, which may absorb light within the wavelength range of 0.3-1.1 μπι. On the other hand, the LM-10 HTD device may also comprise a thermopile-based sensor calibrated to measure irradiance within the spectrum 0.25-10.6 μπι. Due to the mismatch in the wavelength spectrum, monocrystalline silicon cell and thermopile-based sensors may not yield substantially similar readings. Therefore, experimental procedures were developed to quantify these differences through the definition of mismatch ratio (MR). In the case of irradiance measured by a sensor based on monocrystalline silicon cells (GPv) versus one based on a thermopile (GTp), the mismatch ratio (MR = Gpv/GTp) is 0.946. This correction was applied to the outdoor measurements in order to compare the sensor readings.
[0042] FIG. 7 shows data per comparison collected at a time of relatively constant irradiance around noon, while FIG. 8 shows data collected at a period of rapidly changing irradiance during dusk. The correlation among the readings is evident. Furthermore, Figs. 9 and 10 present the same data as those of Figs. 7 and 8, respectively resampled every 3 minutes and plotted using a linear fit. Temperature readings are also shown in the bottom plot in the figures. As the figures suggest, the irradiance readings in the LM-10 HTD sensor— designed for indoor laser power measurements in the absence of wind— are affected by fluctuations in the temperature due to the wind, while the NN sensor proposed herein is insensitive to these fluctuations.
[0043] As discussed herein, a novel low-cost NN-based solar irradiance sensor conceived to be utilized in large PV power plants for precise tracking of solar irradiance within the PV power plant layout is disclosed. A mathematical model as well as a practical realization of the sensor has been described and outdoor measurements have been used to validate the sensor. A feature of the approach proposed herein lies in the simplicity of construction along with increased accuracy, thanks to the use of the NN implemented in an embedded system through a microcontroller. Furthermore, the use a microcontroller allows for updates, enhancement, and customization by simply by adding code libraries. Moreover, it can be interfaced via RS232 or RS485 with other instruments or connected via Ethernet and remote controlled through its embedded web server. One advantage of the sensor is that it can be conveniently located next to a power-producing PV panel or even integrated with it. As a result, the sensing PV panel will "see" exactly the same solar irradiance and temperature as what is "seen" by the power- producing PV panel, leading to precise irradiance tracking which can in turn be used for improved MPPT performance.
[0044] With reference now to FIG. 11, a flowchart 1100 of operational steps for MPPT of a PV array is described. The operations of flowchart 1100 may be performed, for example, by microcontroller 335 of FIG. 3. As will be readily understood by one of skill in the art, numerous other alternatives may be implemented to perform operations similar to those of FIG. 11 to provide MPPT. In the example of FIG. 11, temperature information is received from a temperature sensor associated with at least one PV cell of an irradiance sensor, as indicated at block 1105. PV current information associated with the at least one PV cell is received at block 1110, and PV voltage information associated with the at least one PV cell is received at block 1115. At block 1120, an irradiance present at the PV cell is determined based on the PV current, PV voltage, and temperature. The PV array may then be controlled for MPPT based at least in part of the determined irradiance.
[0045] The detailed description set forth above in connection with the appended drawings describes exemplary embodiments and does not represent the only embodiments that may be implemented or that are within the scope of the claims. The term "exemplary" when used in this description means "serving as an example, instance, or illustration," and not "preferred" or "advantageous over other embodiments." The detailed description includes specific details for the purpose of providing an understanding of the described techniques. These techniques, however, may be practiced without these specific details. In some instances, well-known structures and devices are shown in block diagram form in order to avoid obscuring the concepts of the described embodiments.
[0046] The various illustrative blocks and modules described in connection with the disclosure herein may be implemented or performed with a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.
[0047] The functions described herein may be implemented in hardware, software executed by a processor, firmware, or any combination thereof. If implemented in software executed by a processor, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Other examples and implementations are within the scope and spirit of the disclosure and appended claims. For example, due to the nature of software, functions described above can be implemented using software executed by a processor, hardware, firmware, hardwiring, or combinations of any of these. Features implementing functions may also be physically located at various positions, including being distributed such that portions of functions are implemented at different physical locations. Also, as used herein, including in the claims, "or" as used in a list of items prefaced by "at least one of indicates a disjunctive list such that, for example, a list of "at least one of A, B, or C" means A or B or C or AB or AC or BC or ABC (i.e., A and B and C).
[0048] The previous description of the disclosure is provided to enable a person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the spirit or scope of the disclosure. Throughout this disclosure the term "example" or "exemplary" indicates an example or instance and does not imply or require any preference for the noted example. Thus, the disclosure is not to be limited to the examples and designs described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.