The process of converting renewable energy into power is generally complex, as many external factors play a role in how that energy is harvested and utilized. Typically, conditions are analyzed to try to maximize the harvested energy. For example, a solar panel, implemented using a photovoltaic (PV) array(s) can collect more energy when positioned perpendicularly to the sun on a cloudless day. As environmental conditions (e.g., cloud coverage, temperature, angle of irradiation of the sun with the solar panel, etc.) change, power extraction efficiently also changes.
Additionally, power efficiency provided by solar panels generally also varies as load conditions change. Accordingly, in order to properly extract the energy from solar panels in accordance with load conditions, maximum power point tracking procedures may be utilized. The maximum power point tracking (MPPT) procedures may determine the supply and demand of the PV array(s) and the load (e.g., appliances, machines, battery), and may be used to identify the optimal or near optimal voltage/current of the PV array at which power extraction may be maximized (or nearly maximized).
Rapid shifts in insolation conditions (e.g., changing cloud coverage, drop in temperature, changing angle of the sun with respect to the solar panels) may affect MPPT results, possibly causing erroneous MPPT results.
Disclosed herein are systems, methods and other implementations that provide efficient realization of maximum power point (MPP) determination that can be achieved in rapidly changing insolation conditions (e.g., environmental conditions, such as cloud coverage, temperature, position of the sun in the sky, etc.)
Thus, in some embodiments, a method for power tracking is disclosed. The method includes measuring a plurality of samples of power produced by a photovoltaic (PV) array over a first interval of time, determining, based on the measured plurality of samples of the power of the PV array, a non-linear predictive model of a behavior of the power produced by the PV array, and performing a first adjustment of the PV array's voltage at a second time instant subsequent to an end of the first interval of time. The method further includes measuring at a third time instant another sample of the power of the PV array with the adjusted voltage, and determining a power difference between the power of the PV array with the adjusted voltage at the third time instant and a computed power level of the PV array at the third time instant determined from the non-linear predictive model.
Embodiments of the method may include at least some of the features described in the present disclosure, including one or more of the following features.
The method may further include performing another adjustment of the voltage of the PV array based on the determined power difference between the power of the PV array with the adjusted voltage at the third time instant and the computed power level of the PV array at the third time instant determined from the non-linear predictive model.
Performing the other adjustment of the voltage of the PV array may include increasing the voltage of the PV array in response to a determination that the power difference is greater than ε when the first adjustment of the voltage of the PV array was a voltage increase, wherein ε is a pre-determined value smaller than power produced by the PV array.
Performing the other adjustment of the voltage of the PV array may include decreasing the voltage of the PV array in response to a determination that the power difference is less than ε when the first adjustment of the voltage of the PV array was a voltage increase, wherein ε is a pre-determined value smaller than power produced by the PV array.
Determining the non-linear predictive model of the behavior of the power produced by the PV array may include deriving the non-linear predictive model using one or more of, for example, interpolation polynomials, a least square technique, and/or trigonometric interpolation.
Measuring the plurality of samples of the power of the PV array over the first interval of time may include measuring the plurality of samples at irregular time periods during the first interval of time.
The non-linear predictive model of the behavior of the power of the PV array may include a non-linear predictive model of the behavior of the power of the PV array resulting from insolation changes.
The insolation changes may include one or more of, for example, a temperature change, a cloud cover change, and/or a sun position change.
In some embodiments, a system is disclosed. The system includes one or more photovoltaic (PV) arrays configured to convert solar irradiation into current, a sampling subsystem to measure one or more samples of power produced by the one or more PV arrays, and a controller. The controller is configured to determine, based on a plurality of samples of the power of the one or more PV array measured over a first time interval, a non-linear predictive model of a behavior of the power produced by the one or more PV arrays, cause a first adjustment of the one or more PV arrays' voltage at a second time instant subsequent to an end of the first interval of time, and determine a power difference between another sample of the power of the one or more PV arrays with the adjusted voltage measured at a third time instant and a computed power level of the one or more PV arrays at the third time instant determined from the non-linear predictive model.
Embodiments of the system may include at least some of the features described in the present disclosure, including at least some of the features described above in relation to the method, as well as one or more of the following features.
The controller may further be configured to cause another adjustment of the voltage of the one or more PV arrays based on the determined power difference between the power of the one or more PV arrays with the adjusted voltage at the third time instant and the computed power level of the one or more PV arrays at the third time instant determined from the non-linear predictive model.
The controller configured to cause the other adjustment of the voltage of the one or more PV arrays may be configured to cause an increase of the voltage of the one or more PV arrays in response to a determination that the power difference is greater than ε when the first adjustment of the voltage of the one or more PV arrays was a voltage increase, wherein ε is a pre-determined value smaller than power produced by the one or more PV arrays.
The controller configured to cause the other adjustment of the voltage of the one or more PV arrays may be configured to cause a decrease of the voltage of the PV array in response to a determination that the power difference is less than ε when the first adjustment of the voltage of the one or more PV arrays was a voltage increase, wherein ε is a pre-determined value smaller than power produced by the one or more PV arrays.
The controller configured to determine the non-linear predictive model of the behavior of the power produced by the one or more PV arrays may be configured to derive the non-linear predictive model using one or more of: interpolation polynomials, a least square technique, and trigonometric interpolation.
The controller may include one or more processors.
The sampling subsystem configured to measure the one or more samples of the power produced by the one or more PV arrays may be configured to measure the plurality of samples at irregular time periods during the first interval of time.
In some embodiments, a method for power tracking is disclosed. The method includes measuring a plurality of samples of power produced by a photovoltaic (PV) array over a first interval of time, determining, based on the measured plurality of samples of the power of the PV array, a non-linear predictive model of a behavior of the power produced by the PV array, and performing a first adjustment of the PV array's current at a second time instant subsequent to an end of the first interval of time. The method further includes measuring at a third time instant another sample of the power of the PV array with the adjusted current, and determining a power difference between the power of the PV array with the adjusted current at the third time instant and a computed power level of the PV array at the third time instant determined from the non-linear predictive model.
Embodiments of the method may include at least some of the features described in the present disclosure, including at least some of the features described above in relation to the first method and the system, as well as one or more of the following features.
The method may further include performing another adjustment of the current of the PV array based on the determined power difference between the power of the PV array with the adjusted current at the third time instant and the computed power level of the PV array at the third time instant determined from the non-linear predictive model.
In some embodiments, a method for power tracking is disclosed. The method includes measuring a plurality of samples of power produced by a photovoltaic (PV) array over a first interval of time, and determining, based on the measured plurality of samples of the power of the PV array, a linear predictive model of a behavior of the power produced by the PV array, the linear predictive model derived using a least square technique. The method further includes performing a first adjustment of the PV array's voltage at a second time instant subsequent to an end of the first interval of time, measuring at a third time instant another sample of the power of the PV array with the adjusted voltage, and determining a power difference between the power of the PV array with the adjusted voltage at the third time instant and a computed power level of the PV array at the third time instant determined from the linear predictive model derived using the least square technique.
Embodiments of the method may include at least some of the features described in the present disclosure, including at least some of the features described above in relation to the methods and the system.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly or conventionally understood. As used herein, the articles “a” and “an” refer to one or to more than one (i.e., to at least one) of the grammatical object of the article. By way of example, “an element” means one element or more than one element. “About” and/or “approximately” as used herein when referring to a measurable value such as an amount, a temporal duration, and the like, is meant to encompass variations of ±20% or ±10%, ±5%, or +0.1% from the specified value, as such variations are appropriate to in the context of the systems, devices, methods, and other implementations described herein.
As used herein, including in the claims, “and” as used in a list of items prefaced by “at least one of” or “one or more of” indicates that any combination of the listed items may be used. For example, a list of “at least one of A, B, and C” includes any of the combinations A or B or C or AB or AC or BC and/or ABC (i.e., A and B and C). Furthermore, to the extent more than one occurrence or use of the items A, B, or C is possible, multiple uses of A, B, and/or C may form part of the contemplated combinations. For example, a list of “at least one of A, B, and C” may also include AA, AAB, AAA, BB, etc.
Other and further objects, features, aspects, and advantages of the present disclosure will become better understood with the following detailed description of the accompanying drawings.
Like reference symbols in the various drawings indicate like elements.
Disclosed herein are techniques, systems, methods, devices, and other implementations, for estimating a maximum power point of a photovoltaic (PV) array. For example, in some embodiments, a solar power system includes a device that converts an electrical direct current produced in a PV array into an alternating current. The alternating current is then provided as an input into a computer-based system, which is configured, among other things, to track the MPP to enable efficiently harvesting power from the PV array. The computer-based system may further include a clock that is utilized to time intervals of the signal sampling period, intervals of the perturb cycle period, a perturb point, and an observe point. The alternating current is sampled at intervals, which are less than the interval of the perturb cycle, in order to generate a predictive model of power behavior of the array from which a trajectory of the predicted behavior of the PV array is generated. When the actual voltage of the array is perturbed, the difference between the actual power of the PV array and the predicted power at a subsequent time instant is determined. The MPP can be properly tracked in dynamic insolation conditions by allowing the direction of the next perturbation cycle to be correctly chosen based on the determined power difference. Other system implementations are possible.
In some embodiments, methods, systems, and other implementations are provided, including a method for power tracking that includes measuring a plurality of samples of power produced by a photovoltaic (PV) array over a first interval of time, determining, based on the measured plurality of samples of the power of the PV array, a non-linear predictive model of a behavior of the power produced by the PV array, and performing a first adjustment of the PV array's voltage at a second time instant subsequent to an end of the first interval of time. The method further includes measuring another sample of the power of the PV array with the adjusted voltage, and determining a power difference between the power of the PV array with the adjusted voltage at a third time instant and a computed power level of the PV array at the third time instant determined from the non-linear predictive model.
With reference to
Solar power may be measured in insolation, which is the amount of power (kilowatt hours) collected over a known surface area (square meters) and over a given time period (day). The insolation changes with changes to environmental conditions, such as temperature, cloud cover and position of the sun, and thus, the power produced by the PV modules fluctuates (generally in a non-linear manner) when changes to the environment in which the PV array 103 is deployed occur. In some embodiments, the PV array 103 may be mounted on a moveable support 105, which can be adjusted to position the planar surface of the array at an angle with the sun that seeks to maximize the radiation received from the sun.
In order to extract energy from the solar panels according to the load demand, in some embodiments, techniques and procedures to identify optimal, or near optimal, operating points of the PV array are performed. For example, as load and environmental conditions affecting performance of the PV array change, the optimal voltage or current of the PV array varies. However, because PV arrays are generally configured to operate at a constant operating point (e.g., at a constant voltage), fluctuating load and/or environmental conditions may render operation of the PV array, configured to operate at a set voltage or current, as non-optimal. Accordingly, in some implementations, as load and environmental conditions change, the operating points of the PV array may be adjusted so as to identify the optimal (or near optimal) operating point for the PV array for the present load and/or environmental conditions.
In some embodiments, techniques/procedures such as a maximum power point tracking (MPPT) procedure may be utilized. The MPPT procedure is configured to determine, based on the supply and demand of the PV array and the load, an optimal voltage (when the PV array is configured to operate with a constant voltage and a variable current that varies with changing environmental and/or load conditions), and/or the optimal current (when the PV array is configured to operate with a constant current and a variable voltage level that varies with changing environmental and/or load conditions) to enable optimal, e.g., maximum or near maximum, power to be provided by the PV array. For example, and with reference to
When a PV array is not operating at optimal or near optimal conditions, e.g., when the derivative dP/dV of the power vs. voltage curve is non-zero, a procedure, such as the Maximum Power Point Tracking (MPPT) method, may be implemented to iteratively adjust the voltage level of the PV array until optimal or near optimal power delivery by the PV array for the given load and/or environmental conditions is established.
For example, in some embodiments, an MPPT-based procedure may be implemented as a “perturb and observe” (P&O)-based procedure, in which the voltage of the PV array is periodically perturbed (e.g., the voltage produced by the PV array is adjusted), and the change in the current, and thus in the power, provided by the PV array as a result of the change in voltage, is observed. The difference between the observed power value and an earlier power value can thus provide a value representative of dP/dV. This procedure can be described according to the following equation:
P
PV(T)−PPV(0)=x (1)
where, PPV is the observed power of the photovoltaic array, T is the period of the perturb interval (in this example), and x is the difference in power over one period (T). If the change in the current (or power) is zero, i.e., x=0, the MPP is being realized. However, if the change in the power is such that the power increased or decreased, the MPP has shifted in accordance with the observed change. For example, if dP/dV>0, it can be concluded that the perturbation caused the array's operating power to move towards MPP, whereas if dP/dV<0, it can be concluded that the perturbation caused the array's operating power to move away from the MPP.
Accordingly, to implement MPPT procedures, the system 100 depicted in
MPPT Procedures implemented in accordance with, for example, Equation 1 above, measure the power (e.g., multiplying the array's voltage by the array's current) at one time instant (e.g., when the system was perturbed by, for example, causing the voltage of the array to increase or decrease), and at a subsequent time instant, T (the time period between the time instants should be sufficiently long to enable the power behavior of the array to settle down).
The computed power difference according to Equation 1 does not indicate what contributed to the power measured at the subsequent time instant. Particularly, if during the period of measurement environmental and load conditions were unchanged, then it can be assumed that the power measured at time instant T resulted substantially from the adjustment made to the voltage of the PV array. However, if there were changes to the environmental conditions in which the PV array is operating (temperature, cloud coverage, sun brightness, etc.) then these environmental changes may have contributed, at least to some extent, to the measured change in the power supplied by the PV array (for the purpose of explanation, it will be assumed that load conditions are not changed during the PV array power measurement period). It is therefore difficult to determine if the “power delta” sign, based on which the direction of tracking is determined, was in response to either the voltage perturbation, insolation changes, or both. Accordingly, under these circumstances, a computation of power difference in accordance with Equation 1 may provide a value that would not be an accurate indication of whether further adjustments to the voltage of the PV array are necessary, and/or in what direction (e.g., voltage increase, voltage decrease) the adjustment should be made. Consequently, power optimization procedures, such as the MPPT procedure, may be tracking in the wrong direction.
Therefore, in some embodiments, power optimization procedures for PV arrays that take into account the effect/contribution of insolation changes may be implemented. Particularly, in some implementations, computation of the power difference may be performed in accordance with a model that incorporates the effect/contribution of insolation changes to changes in the power supplied/produced by a PV array. With reference to
As further shown in
P
PV(T)−PPV
where T is a time instant, subsequent to the end of the sampling period and to the time instant when the PV array was perturbed, when the power supplied by the PV array is sampled. The difference between the actual power supplied by PV array (such actual power being affected by, for example, the perturbation and insolation changes) and the power level predicted using the mathematical model modeling the power behavior of the PV array as a result of insolation changes, provides a value representative of effect of perturbation on the power supplied by the PV array. The resultant value will therefore provide a more accurate indication of dP/dV, and will thus provide a more accurate and reliable tracking of the power behavior of the PV array so as to more quickly achieve an optimal, or near optimal, voltage level (or current level, in situations where the PV array has a near constant current and fluctuating voltage).
As will be described in greater details below, in some implementations, the model derived to predict the power behavior of the PV array as a result of insolation changes (at least for short term prediction) may be a non-linear model, e.g., high order models such as, for example, second and/or third order models. Use of non-linear models provide a more accurate and robust representation (e.g., as compared to representations provided, for example, by linear models) of a rate of change (in this case, the PV array's power rate of change), and therefore may enable more accurate tracking of the PV array's MPP. Additionally, use of a non-linear model enables non-constant sampling (i.e., using varying sampling intervals in which the sampling intervals between successive samples are not necessarily the same) to obtain the samples that are used to derive the non-linear representation corresponding to the samples. In some embodiments, and as will be described below in greater detail, derivation of non-linear predictive models to represent the behavior of PV array power resulting from insolation changes (or resulting from other factors) may be based on one or more of, for example, interpolation polynomials, a least square technique, and/or trigonometric interpolation.
With reference to
Based on the measured plurality of samples of the power level of the PV array, a non-linear predictive model of a behavior of the power produced by the PV array may be determined 320. As noted, in some embodiments, a non-linear model based on interpolation polynomials may be derived. Various forms may be used to represent interpolating polynomials. For example, an interpolating polynomial function may be represented as a linear combination of orthogonal polynomials. In some implementations, an interpolating polynomial may be represented as combination of Lagrangian polynomials. Particularly, a combination of Lagrangian polynomials may be represented as:
L(x)n/j=0Σyjlj(t) (3)
In order to determine the number of samples from a given set of, for example, n+1 data points at the intervals nTs at which the signal is sampled, the data points can be represented as xj=jTs and yj=Ppv(jTs), where j=0 . . . n. It is to be noted that although in this particular example the sampling interval is substantially constant, a non-constant (irregular) sampling interval may be used instead. Utilizing the aforementioned representation in equation (3), the polynomials can be expanded as the following mathematical function:
l
j(t)=(0≦i≦n,i≠j)Π(t−xi)/(xj−xi)=(t−x0)/(xj−x0) . . . (t−xj−1)/(xj−xj−1)·(t−xj+1)/(xj−xj+1) (4)
When the system is running on a clocked time interval, it is assumed that the time interval at which the signal is sampled is a unity time interval, e.g., Ts=1, 2, 3, etc. Equation (4) can then be reduced to:
l
j(t)=(0≦i≦n,i≠j)Π(t−i)/(j−i)=(t−0)/(j−0) . . . (t−(j−1)/(j−1)·(t−(j+1)/(j−(j+1) (5)
Equation (5) can thus be utilized to compute the sampled signal power at any number of intervals “n” to collect data points which predict the trajectory of the PV power signal. The integration of the Equation (5) provides the predictive PV power signal function Ppv
P
pv
model((n+1)Ts)|(n−i)=L(n+1)=y0l0(n+1)+y1l1(n+1) . . . y(n)(n+1)l(n)(n+1) (6)
In Equation (6), each l(n) can be derived from equation (5), with each selection of “n” producing “n+1” data points.
As an example, consider a situation where n=2. In this case, there are 3 sampling points, giving rise to the following expressions:
l
0(t)=(t−1)/(0−1)·(t−2)/(0−2)=(t−1)(t−2)/2
l(t)=(t−0)/(1−0)·(t−2)/(1−2)=−t(t−2)
l
2(t)=(t−0)/(2−0)·(t−1)/(2−1)=t(t−1)/2
P
PV
model(t)=y0l0(t)+y1l1(t)+y2l2(t)
With the above expression for PPV
Therefore, PPV
P(k)−PPV
Substituting the expression for the 2nd order Lagrangian PPV
P(k)−[P(k−1)−3P(k−⅔)+3P(k−⅓)], where the samples are a discretized distance of ⅓ from each other.
Accordingly:
dP(k)=P(k)−P(k−1)+3P(k−⅔)−3P(k−⅓)
Thus, to obtain output value 620, corresponding to dP(k), the implementation 600 includes a summing operator 610 that adds the sample 602, corresponding to P(k), to the negative of the preceding sample 604 (corresponding to P(k−⅓) that was amplified by an amplifier 612 with a gain of 3. The resultant sum of the summing operation at 610 is added, using the summing operator 616, to a resultant amplified valued of the sample 606, corresponding to P(k−⅔). The sample 606 is amplified using an amplifier 614 that also has a gain of 3. Finally, the result of the summing operator 616 is added to the negative of the sample 608, corresponding to P(k−1). It is to be noted that the implementation of
As another example, consider the situation where n=3. In this case, there are 4 sampling points, giving rise to the following expressions:
l
0(t)=(t−1)/(0−1)−(t−2)/(0−2)·(t−3)/(0−3)=(t−1)(t−2)(t−3)/(−6)
l
1(t)=(t−0)/(1−0)−(t−2)/(1−2)·(t−3)/(1−3)=t(t−2)(t−3)/2
l
2(t)=(t−0)/(2−0)−(t−1)/(2−1)·(t−3)/(2−3)=t(t−1)(t−3)/(−2)
l
3(t)=(t−0)/(3−0)−(t−1)/(3−1)·(t−2)/(3−2)=t(t−1)(t−2)/6
With above expressions, PPV
Therefore, the predicted power level at 4Ts, as computed based on the above derived expression, is:
P
PV
model(4Ts)=−PPV(0)+4PPV(Ts)−6PPV(2Ts)+4PPV(3Ts)
In some embodiments, derivation of another type of non-linear predictive model to represent the power behavior due to, for example, insolation changes, may be based on the Least Square Method. Using this technique, the resulting signal model is generally a polynomial function with a function order of in where m<n+1. The parameter in may be selected based on the desired modeling accuracy. The implementation of the least square method to facilitate derivation of a model based on the samples collected can be, in some embodiments, in the form of recursive calculations.
Derivation of a predictive model based on a least squares procedure may be implemented as follows. Given a set of n+1 data points, i.e., (x0,y0), . . . , (xn,yn), where xj=jTs and yj=PPV(jTs), and where j=0 n, the objective is to determine coefficients of the following polynomial:
P
PV
model(t)=y(t)=a0+a1t+a2t2+ . . . +amtm,
such that the criterion function φ is minimized, where, for example, φ may be:
φ=Σi=0n[yi−(a0+a1xi+a2xi2+ . . . +amxim)]2
The coefficients a0 . . . am are obtained as a solution of the following system of linear equations:
As an example, consider the situation where n=2, in which case there are 3 data sets, namely, (x0,y0), (x1,y1), and (x2,y2). Let Ts=1, in which case x0=0, x1=1, and x2=2. In this example, m=1, which means that in this case, when a statistical procedure, such as the least square procedure, is used to derive the predictive model, the predictive model may be represented as a first order (linear) function. Thus, PVpv
PV
pv
model
=a
0
+a
1
t
where a0 and a1 are obtained from:
3a0+a1(x0+x1+x2)=y0+y1+y2.
a
0(x0+x1+x2)+a1(x02+x12+x22)=x0y0+x1y1+x2y2
When substituting the values of x0=0, x1=1, and x2=2, the following set of equations are obtained:
3a0+3a1=y0+y1+y2; and
3a0+5a1=y1+2y2
and a0 and a1 can be determined to be:
a
1=(y2−y0)/2, and a0=⅚y0+⅓y1−⅙y2
PVpv
PV
pv
model=(y2−y0)t/2+⅚y0+⅓y1−⅙y2
Thus, at the time t=(n+1)Ts|n=2,Ts=1=3, PVpv
In yet another example, in some embodiments, derivation of another type of non-linear predictive model to represent the power behavior due to, for example, insolation changes, may be based on trigonometric interpolation. This derivation technique is suitable, for example, in situations where the model is to be represented as a periodic function. Consider, for example, the use of trigonometric interpolation for n+1 data points, namely (x0,y0), . . . , (xn,yn). A function F(x) may be represented as follows:
As an example, consider the situation where n=3. In this case, there are 4 sampling points which, for the purpose of illustration, are sampled at xj=jTs, where j=0, 1, 2, 3. With four (4) sample points, the predictive model, PPV
P
PV
model(t)=F(t)=y0[sin ½(t−1)sin ½(t−2)sin ½(t−3)]/[sin ½(0−1)sin ½(0−2)sin ½(0−3)]+y1[sin ½(t−0)sin ½(t−2)sin ½(t−3)]/[sin ½(1−0)sin ½(1−2)sin ½(1−3)]+y2[sin ½(t−0)sin ½(t−1)sin ½(t−3)]/[sin ½(2−0)sin ½(2−1)sin ½(2−3)]+y3[sin ½(t−0)sin ½(t−1)sin ½(t−2)]/[sin ½(3−0)sin ½(3−1)sin ½(3−2)]
For ease of illustration, in the above model derivation examples, the sampling points were assumed to be taken at equal duration intervals. However, as noted, derivations to obtain predictive model representations for the power behavior may be performed with sample points taken at non-constant (e.g., irregular) intervals. Additionally, although three different derivation techniques were illustrated, other techniques/procedures to determine non-linear predictive model to represent the power behavior of the PV array may be used in addition to or instead of the any of the above illustrated techniques/procedures.
Turning back to
At a third time instant T, where T>T1, another sample of the power of the PV array with an adjusted electrical attribute (e.g., adjusted voltage, in the example of
Having obtained the other sample, a power difference is determined 350 between the power of the PV array with the adjusted voltage at the third time instant and a computed power level of the PV array at the third time instant determined from using the non-linear predictive model. Thus, in some implementations, a determination is made of PPV(T)−PPV
The determined power difference may be utilized to track the MPP of the PV array and control the output of the PV array in relation to the load. For example, the determined power difference can be utilized to determine the next direction of perturbation (e.g., adjustment of an attribute of the PV array, be it the voltage or current) based on the sign of a result of the power difference, and to use the resultant sign (positive “+”, or negative “−”) to control the direction of the perturbation during the next cycle. Thus, in some embodiments, the procedures implemented to track the maximum power point of a PV array may include performing another adjustment of the voltage of the PV array based on the determined power difference between the power of the PV array with the adjusted voltage at the third time instant and the computed power level of the PV array at the third time instant as determined from the non-linear predictive model.
For example, in response to a determination that the power difference is greater than ε, where ε is a pre-determined value that is generally smaller than the power level of the PV array with the adjusted voltage (ε may be equal to 0 in some embodiments), if the preceding adjustment of the voltage (or another electrical attribute) of the PV array was a voltage increase then the next voltage adjustment for the PV array would be to increase the voltage. Particularly, if the computed power difference is determined to be greater than ε (e.g., greater than 0), this may indicate that the power is being tracked in the right direction. Therefore, if the previous adjustment was to increase the voltage, then the next adjustment should also be a voltage increase (e.g., by some pre-determined amount, by an amount that is based on, for example, the present voltage or power level, etc.) If the previous adjustment was a voltage decrease, then the next adjustment should also be a voltage decrease.
Conversely, if it is determined that the power difference is less than ε, and the preceding adjustment of the PV array was a voltage increase, then the next adjustment of the PV array's electrical attribute(s) may be to decrease the voltage. Particularly, because a computed power difference that is less than ε (e.g., less than 0) may indicate that the maximum power point is being tracked in the wrong direction (i.e., moving away from the maximum power point), if the previous adjustment was to increase the voltage of the PV array, then the voltage may have to be decreased on the next adjustment so as to reverse to tracking direction. Similarly, if it is determined that the power difference is less than ε, and the previous adjustment was a voltage decrease, then the next adjustment may be a voltage increase.
In some embodiments, the process of adjusting the electrical attribute(s) of the PV array may be repeated until, for example, an absolute value of the determined power difference is less than some pre-determined value, indicating that the PV array may have substantially or approximately reached its maximum power point.
While the implementations discussed above refer to the perturb and observe technique, similar implementations may also be realized in relation to other types of tracking techniques, including, for example, the incremental conductance procedure, the constant voltage procedure, etc. For example, in implementations based on incremental conductance procedure, the incremental conductance dI/dV is determined so as to compute the sign of dP/dV. With this procedure, the system is determined to have reached its MPP when dI/dV=−i/v. If the system has not reached its MPP yet, the system continues to be perturbed.
With reference to
The example system 400 also includes a Perturb Direction Computation module 430 which maintains a perturbation history (e.g., previous perturbation direction). The module determines, based on the power difference dP(kT) and the previous perturbation direction, what the next perturbation direction should be. For example if the previous PV voltage perturbation was in a positive direction (direction(k−1)>0) and the power difference (also referred to as “power increment”) is positive (i.e., dP(k)>0) then the next perturbation will be in a positive direction too. However if the power difference is negative (i.e., dP(k)<0) than the perturbation direction at t=kT should have the opposite sign to the direction in t=(k−1)T.
As further shown in
If direction(k)>0 than: Vref(k)=Vref(k−1)+Vperturbe step
If direction(k)<0 than: Vref(k)=Vref(k−1)−Vperturbe step
where Vperturbe step represents a perturbation step voltage, which may be a pre-determined step voltage, or may be an adjustable dynamically derived value. In some embodiments, Vref(k) may also be compared to an associated minimum and maximum limits and clipped to those limiting values. The minimum and maximum limits may be based on the PV generator, Inverter, and/or power converter specifications. The computed Vref(k) is provided to an inverter module configured, among other things, to adjust the current of the PV generator such that the PV voltage converges to the reference voltage level.
Performing the tracking and control procedures described herein may be facilitated, in some implementations, by a processor-based computing system which, for example, may be used to implement, at least partly, the controller 120 of
The processor-based device 510 is configured to facilitate, for example, the implementation of the tracking procedure, including facilitating measurement of sample points of the power output generated using a PV array, determining a non-linear predictive model representative of the power behavior of the PV array system resulting from such factors as insolation changes, determining whether power tracking is proceeding in the right direction, etc. The storage device 514 may thus include a computer program product that when executed on the processor-based device 510 causes the processor-based device to perform operations to facilitate the implementation of the above-described procedures. The processor-based device may further include peripheral devices to enable input/output functionality. Such peripheral devices may include, for example, a CD-ROM drive and/or flash drive, a network connection (implemented using, for example, a USB port, a wireless transceiver, etc.), for downloading related content to the connected system. Such peripheral devices may also be used for downloading software containing computer instructions to enable general operation of the respective system/device. Alternatively and/or additionally, in some embodiments, special purpose logic circuitry, e.g., an FPGA (field programmable gate array), a DSP processor, or an ASIC (application-specific integrated circuit) may be used in the implementation of the system 500. For example, in some implementations, a DSP processor may be used to implement the non-linear predictive model used to compute the predicted power behavior of the PV array due to, for example, insolation changes (or some other factor). An example of such an implementation is illustrated in
Computer programs (also known as programs, software, software applications or code) include machine instructions for a programmable processor, and may be implemented in a high-level procedural and/or object-oriented programming language, and/or in assembly/machine language. As used herein, the term “machine-readable medium” refers to any non-transitory computer program product, apparatus and/or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide machine instructions and/or data to a programmable processor, including a non-transitory machine-readable medium that receives machine instructions as a machine-readable signal.
Although solar energy is discussed in relation to the above implementations, the system, methods and all other implementations discussed above can also be used and applied in relation to other types of generators and for other forms of energy, such as energy harvested in wind generators and water pumps.
While particular embodiments have been disclosed herein in detail, this has been done by way of example for purposes of illustration only, and is not intended to be limiting with respect to the scope of the appended claims, which follow. In particular, it is contemplated that various substitutions, alterations, and modifications may be made without departing from the spirit and scope of the invention as defined by the claims. Other aspects, advantages, and modifications are considered to be within the scope of the following claims. The claims presented are representative of the embodiments and features disclosed herein. Other unclaimed embodiments and features are also contemplated. Accordingly, other embodiments are within the scope of the following claims.
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/US2012/025739 | 2/17/2012 | WO | 00 | 8/15/2014 |