Maximum Partially Shaded Conditions
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 4, APRIL 2008
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Maximum Power Point Tracking Scheme for PV Systems Operating Under Partially Shaded Conditions
Hiren Patel and Vivek Agarwal, Senior Member, IEEE
Abstract—Current–voltage and power–voltage characteristics of large photovoltaic (PV) arrays under partially shaded conditions are characterized by multiple steps and peaks. This makes the tracking of the actual maximum power point (MPP) [global peak (GP)] a difficult task. In addition, most of the existing schemes are unable to extract maximum power from the PV array under these conditions. This paper proposes a novel algorithm to track the global power peak under partially shaded conditions. The formulation of the algorithm is based on several critical observations made out of an extensive study of the PV characteristics and the behavior of the global and local peaks under partially shaded conditions. The proposed algorithm works in conjunction with a dc–dc converter to track the GP. In order to accelerate the tracking speed, a feedforward control scheme for operating the dc–dc converter is also proposed, which uses the reference voltage information from the tracking algorithm to shift the operation toward the MPP. The tracking time with this controller is about one-tenth as compared to a conventional controller. All the observations and conclusions, including simulation and experimental results, are presented. Index Terms—Global peak (GP), maximum power point tracking (MPPT), partial shading, power–voltage (P –V ) characteristics.
I. I NTRODUCTION HE ever-increasing demand for low-cost energy and growing concern about environmental issues has generated enormous interest in the utilization of nonconventional energy sources such as the solar energy. The freely and abundantly available solar energy can be easily converted into electrical energy using photovoltaic (PV) cells. A PV source has the advantage of low maintenance cost, absence of moving/rotating parts, and pollution-free energy conversion process. However, a major drawback of the PV source is its ineffectiveness during the nights or low insolation periods or during partially shaded conditions. High initial capital cost has been another deterrent in the popularity of PV systems [1]. These drawbacks notwithstanding, the PV systems have emerged as one of the most popular alternatives to conventional energy, thanks to the
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Manuscript received May 16, 2007; revised December 5, 2007. H. Patel is with the Department of Electrical Engineering, Sarvajanik College of Engineering and Technology, Surat 395001, India. V. Agarwal is with the Department of Electrical Engineering, Indian Institute of Technology Bombay (IITB), Mumbai 400076, India (e-mail: agarwal@ ee.iitb.ac.in). Digital Object Identifier 10.1109/TIE.2008.917118
advancement in technology and favorable government policies in several countries. A major challenge in the use of PV is posed by its nonlinear current–voltage (I –V ) characteristics, which result in a unique maximum power point (MPP) on its power–voltage (P –V ) curve. The matter is further complicated due to the dependence of these characteristics on solar insolation and temperature. As these parameters vary continuously, MPP also varies. Considering the high initial capital cost of a PV source and its low energy conversion efficiency, it is imperative to operate the PV source at MPP so that maximum power can be extracted. In general, a PV source is operated in conjunction with a dc–dc power converter, whose duty cycle is modulated in order to track the instantaneous MPP of the PV source. Several tracking schemes have been proposed [2]–[12]. Among the popular tracking schemes are the perturb and observe (P&O) or hill climbing [4], [5], incremental conductance [8], shortcircuit current [2], open-circuit voltage [7], and ripple correlation approaches [6]. Some modified techniques have also been proposed, with the objective of minimizing the hardware or improving the performance [7], [9]–[12]. The tracking schemes mentioned above are effective and time tested under uniform solar insolation, where the P –V curve of a PV module exhibits only one MPP for a given temperature and insolation. Bruendlinger et al. have tested various commercially available inverters in partially shaded conditions and have found that the power loss due to shading can be as high as 70% [13]. Under partially shaded conditions, when the entire array does not receive uniform insolation, the P –V characteristics get more complex, displaying multiple peaks [only one of which is the global peak (GP); the rest are local peaks] [14]. An analytical model, based on Lambert function and its properties, has been presented [15]. It is capable of simulating the presence of multiple peaks under various conditions like different insolation and temperature levels, shading patterns, mismatch, etc. The computational time and the memory needed by this model is less. The presence of multiple peaks reduces the effectiveness of the existing MPP tracking (MPPT) schemes, which assume a single peak power point on the P –V characteristic. The occurrence of partially shaded conditions being quite common (e.g., due to clouds, trees, etc.), there is a need to develop special MPPT schemes that can track the GP under these conditions. The other option is to use intelligent PV modules [16] or alternating current modules.
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Fig. 1. Terminology used for the various components of a partially shaded PV array. (a) PV module. (b) Series assembly with two subassemblies. (c) Group. (d) Array with three groups.
Some researchers [17]–[19] have worked on GP tracking schemes for PV arrays operating under nonuniform insolation conditions. Miyatake et al. [17] have reported an MPPT scheme that uses Fibonacci sequence to track the GP under partially shaded conditions. However, the method does not guarantee GP tracking under all conditions. Kobayashi et al. [18] have proposed a two-stage method to track the GP. In the first stage, the operating point moves into the vicinity of the GP on the load line Rpm = Vpm /Ipm , and in the second stage, it converges to the actual GP. Vpm and Ipm are approximately equal to 80% and 90% of the open-circuit voltage VOC and short-circuit current ISC of the PV array, respectively. However, in this method, if the GP lies on the left side of the load line (Rpm ), i.e., Rpm > Ractual (where Ractual = Vactual /Iactual ), the operating point is temporarily shifted to 90% of VOC , thereby missing the GP. Solodovnik et al. [19] have suggested a statespace-based approach to search the GP. This method is fast and accurate but is system specific, is complex, and requires more sensors. This paper proposes a novel method that is capable of tracking the GP under partially shaded conditions. Based on an extensive study of partially shaded PV arrays, Section II describes certain critical observations on the I –V and P –V curves of partially shaded arrays. Section III describes the proposed algorithm to track the GP, while Section IV deals with the novel scheme used to achieve a quick response of the dc–dc converter to track the MPP. Sections V and VI present the simulation and experimental results, respectively. The main conclusions are summarized in Section VII. II. C RITICAL O BSERVATIONS U NDER P ARTIALLY S HADED C ONDITIONS Using a simulation model developed in the MATLAB/ SIMULINK software [20], the authors have conducted a comprehensive study of the I –V and P –V characteristics of the partially shaded PV array. This model uses a special terminology to describe the partially shaded array, as depicted in Fig. 1. The terminology helps in simplifying the complex shading pattern of the large PV array and, hence, to study the characteristics of the large partially shaded PV array. A PV module [Fig. 1(a)] is considered to be shaded if three or more of its cells are receiving lower than normal insolation. Series-connected PV modules, receiving similar insolation,
form a “subassembly” [Fig. 1(b)]. Several series-connected subassemblies, each with a different level of insolation, form a “series assembly” [Fig. 1(b)]. A “group” is made up of several similar series assemblies (having identical P –V characteristics) connected in parallel [Fig. 1(c)]. Various parallel-connected groups, with different shading patterns constitute a PV array [Fig. 1(d)]. Fig. 2 shows the P –V curves, obtained using the developed model, for a PV array having 900 modules (10 in series × 90 in parallel) with a complex shading pattern (having several groups). Fig. 2(a) describes the shading pattern on the array, while Fig. 2(b)–(d) shows the P –V curves for the array at different insolation levels. Fig. 2(e) shows the characteristic equation on which the PV cell is modeled. For further discussion, the simpler example of the shaded PV array shown in Fig. 1(d), having only three distinct groups, is considered. Fig. 3 shows the P –V curves corresponding to this array. The P –V curves (C1 , C2 , and C3 ) for one series assembly each from groups 1–3 are shown in Fig. 3(a). Fig. 3(b) shows the P –V curves (D1 , D2 and D3 ) for the entire groups 1–3 obtained by scaling the curves C1 , C2 , and C3 on the current axis. It is observed that the peaks PS1 , PS2 , and PS3 occur at V1 = 65 V, V2 = 114 V, and V3 = 163 V, respectively. It is important to note that since four modules are unshaded in each series assembly of group 1, the peak PS1 occurs nearly at voltage V1 = 4 × 16.3 = 65 V, where 16.3 V is 80% of the open-circuit voltage of the module (VOC_module ) considered. A similar reasoning can be applied to PS2 and PS3 , which occur at nearly V2 (= 7 × 16.3 = 114 V) and V3 (= 10 × 16.3 = 163 V), respectively. The position of peaks PS1 , PS2 , and PS3 govern the position of the peaks PG1 through PG3 [Fig. 3(b)] and, hence, of PAmax1 through PAmax3 on the P –V curve of the entire array [Fig. 3(c)]. Hence, the peaks PAmax1 , PAmax2 , and PAmax3 occur nearly at the voltages V1 , V2 , and V3 , respectively. A significant outcome of this observation is that the array power peaks are displaced from each other by an integral multiple of 80% of VOC_module (n × 0.8 × VOC_module ), where “n” is an integer. As the minimum integral difference in the number of shaded modules between the series assemblies of two groups is one, the minimum possible displacement between two consecutive peaks is 0.8 × VOC_module . In Figs. 1(d) and 2(a), the number of shaded modules in the series assemblies decreases as one moves from the first series assembly to the last one (i.e., from left to right). Furthermore,
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Fig. 2. P –V curves for the PV array under partially shaded conditions. (a) Sample PV array with insolation of 1000 W/m2 (G = 1, where G is the solar insolation in kilowatts per square meter) on the unshaded modules and lower insolation on shaded modules. (b) Shaded modules with 100 W/m2 (G = 0.1 kW/m2 ). (c) Shaded modules with 300 W/m2 (G = 0.3 kW/m2 ). (d) Shaded modules with 600 W/m2 (G = 0.6 kW/m2 ). Characteristics under uniform insolation are also given in (b). (e) Characteristic equation on which the model is built.
Fig. 3. (a) C1 , C2 , and C3 represent P –V curves for series assembly, corresponding to groups 1, 2, and 3, respectively. (b) D1 , D2 , and D3 represent P –V curves for groups 1, 2 and 3, respectively. (c) Resultant P –V curve for the entire array.
only two levels of insolation were considered. Fig. 4 illustrates a more complex case, where a PV array with an arbitrary shading pattern and more than two levels of insolation are considered. The array size is the same as that in Fig. 2(a). Using the terminology defined in Fig. 1, the array in Fig. 4(a) can be divided into seven groups. The integers at the bottom of the array represent the “groups” formed in the array due to nonuniform insolation. Fig. 4(b) shows the P –V characteristic for the random shading pattern shown in Fig. 4(a). Some of the critical observations made from an extensive study of the PV curves of the partially shaded arrays Figs. 2–4 are listed as follows. 1) I –V curves under partially shaded conditions have multiple steps, while the P –V curves are characterized by multiple peaks.
2) In addition to insolation and temperature, the magnitude of GP, and the voltage at which it occurs are also dependent on the shading pattern and array configuration. 3) Fig. 2(b) shows that the GP may lie on the left side of the load line. 4) The peaks on the P –V curve occur nearly at multiples of 80% of VOC_module (Fig. 3). 5) The minimum displacement between successive peaks is nearly 80% of VOC_module (Fig. 3). 6) Extensive study of P –V curves, as well as practical data, have revealed that when the P –V curve is traversed from either side, the magnitude of the peaks increases. After reaching the GP, the magnitude of the subsequent peaks (if they are present) continuously decreases (Figs. 2 –4).
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Fig. 4. (a) PV array (of size 10 × 90) with a random shading pattern. The array is scaled down such that each series assembly represents three similar series assemblies connected in parallel. (b) Resultant P –V curve for the entire array.
III. A LGORITHM FOR THE P ROPOSED MPPT S CHEME Fig. 5 shows the flowchart of the proposed algorithm to track the GP under partially shaded conditions. The execution of the algorithm always starts with reference voltage (Vref ) value set equal to 85% of VOC (block 1) as shown in the “Main Program” in Fig. 5. Until any disturbance (or timer interrupt) occurs, it maintains the operation at the GP by continuously implementing the hill climbing [3] or the P&O method (blocks 2 and 3). When any sudden disturbance (like partial shading) or timer interrupt occur, the “Main Program” identifies the requirement for tracking the GP (blocks 4–6) and calls the “GP track subroutine” (block 7a). “GP track subroutine” tracks the new GP and, then, once again, pass on the control to the “Main Program,” which maintains the operation at this new GP. “GP track subroutine” is also called periodically at a 25-s interval when the timer generates an interrupt (block 7b). In addition to this, the scheme can also be easily modified to have the feature of GP tracking when the user wants to initiate it. The user may be the supervisor of a large PV array who realizes that PV array is partially shaded but does not know the exact operating point where the MPP occurs. To understand the algorithm, assume that a GP had just been reached when a sudden insolation change shifts the operating point to the vicinity of one of the local peaks (e.g., point D [Fig. 2(c)]). This local peak (point D) is tracked by the P&O method (block 2). Whether MPP is reached or not, is checked by determining the sign of the power in two subsequent perturbations (block 3). When the first local peak (point D) is tracked, the algorithm stores the current information about PV array’s output power and output voltage as Pmax _last and Vm_last , respectively. The algorithm then sets the flag (flag = 1) for checking the GP on the left side of point D (block 4). The sudden change in the insolation level (∆G) or shading leads to a variation in power (= ∆P ). If ∆P is greater than a certain critical power variation (= ∆Pcrit ), then GP tracking starts (blocks 5 and 6). To determine ∆P , array’s output power at two different time instants, 0.01 s apart, is considered. It is reported that the sudden variations in insolation are small in magnitude (smaller than G = 0.027 kW/m2 ) and occur within 1 s [21]. Based on this, ∆Pcrit can be fine tuned, depending upon the PV system and its environment (can be certain percentage of the array’s output power capacity or set corresponding to
change in the output power of an array for desired ∆G, where ∆G < 0.027 kW/m2 ). If any of the aforementioned condition for GP tracking occurs, the “GP track subroutine” starts, scanning the P –V curve for other peaks. This is done by applying a disturbance ∆Vlarge , which should be less than the minimum possible displacement between the two successive peaks (observation 5, block 8). To ensure that no peak is missed during the tracking, ∆Vlarge can be considered as 60%–70% of VOC_module . The lower the value is, the higher the time required to track the GP but the lower the risk of missing the GP will be. The initial disturbance is toward the left side (toward point E), which is indicated by “flag = 1” (block 10). If a uniform insolation condition does not exist (block 9) and if any of the limits (blocks 11 and 12), discussed later, is not reached, the slope dP/dV is measured at the new operating point (block 14). If the slope is positive, the disturbance is continued in the same direction (blocks 15 and 16) until “Vmin ,” the lowest voltage below which the GP is not likely to occur (block 12), is reached. However, if the slope dP/dV is negative, it indicates that there is another peak (point E) in the vicinity, and hence, the conventional MPP technique is applied to track this peak (point E, block 17). If the power corresponding to this peak is less than the previous one, the initial operating point (i.e., the previous largest peak observed during the tracking, point D) is restored, and the disturbance is now applied in the other direction (blocks 18, 20, and 21). The right side movement is indicated by “flag = −1” (block 21). If the power at the new peak is more than the previous one, then Pmax _last and Vm_last are updated (block 19), this peak is considered as the likely candidate for the GP, and the disturbance on the left side on P –V curve is continued until a smaller peak or Vmin is reached (block 12). Now, the disturbance is applied toward the right side, and a similar process is carried out (block 13). The slope dP/dV is measured after every large disturbance, and if it is positive, it indicates a local peak in the vicinity. This peak is tracked, and if its magnitude is greater than Pmax_last , the disturbance is continued on the right side. However, during this process, if any smaller peak (point A) is observed, the operation is restored at the point (point B) which it has stored as the MPP during this tracking. The operation is even restored at point B, if Vmax is reached, where Vmax is equal to 85% of VOC_module (block 11). The algorithm continues to track the peak until it comes to the very first peak that is generating less power than the peak it observed last. Hence, this algorithm does not have to scan the entire P –V curve. If only one peak exists on the P –V curve, as is the case during uniform insolation, the algorithm may scan the entire range. To avoid this, after the application of each large disturbance (∆Vlarge ), oscillations in the power are measured. It has been observed that in case of uniform insolation, as soon as the operating point shifts close to ISC (i.e., away from MPP), the application of a large disturbance in Vref results in large oscillations in the array power. Hence, in such a case, if the oscillations are greater than a certain tolerable power variation (∆Ptol : 4%–5% of array capacity), the controller immediately restores the operation to the GP (block 9).
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Fig. 5.
Flowchart for the proposed MPPT control.
IV. D UTY C YCLE C OMPUTATION FOR DC–DC C ONVERTER C ONTROL Fig. 6(a) shows the circuit schematic of a boost-type dc–dc power converter whose duty cycle is modulated as per the algorithm used for electrical tracking of the MPP. In a conventional controller working with the P&O method, duty cycle (D∗ ) is generated as follows [22]: D∗ = 1 − (Vref /Vo ) (1)
Fig. 6. (a) Circuit schematic for boost converter used for tracking MPP. (b) Proposed control scheme for the dc–dc converter. (LB = 5 mH, Cp = 2000 µH, Cf = 1000 µH, and Lf = 0.1 mH).
where Vref is the reference voltage obtained using the MPPT algorithm described in Section III, and Vo is the output voltage of the dc–dc converter. It is observed that such a controller is slow to respond. The proposed controller overcomes this drawback. Here, the control signal for dc–dc converter is obtained in a feedforward manner, as shown in Fig. 6(b). The controller is fast to respond and can quickly track the MPP. The principle involved in this controller can be mathematically explained as under. If ∆D is the perturbation in the actual
duty cycle D, then D + ∆D = 1 − (Vpv + ∆Vpv )/(Vo + ∆Vo ) (2)
where Vpv is the PV array voltage, while ∆Vpv and ∆Vo are changes in PV array and output voltages of the dc–dc converter, respectively.
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Fig. 7. P –V characteristic for the array of Fig. 1(d), with solar insolation of 1000 W/m2 .
If ∆Vo
Vo , then (2) leads to (3) as follows: ∆D = −∆Vpv /Vo . (3)
This additional disturbance ∆D, when subtracted from the actual duty cycle D, amplifies the disturbance toward the MPP, and therefore, the MPP is attained quickly. The above mathematical analysis is explained with the help of Fig. 7, which shows the P –V curve of the array represented by Fig. 1(d). Point A indicates the initial operating point for which the PV array output voltage is Vin . To reach the MPP, the conventional controller sets the reference voltage Vref by giving a perturbation (here, reduction in the operating voltage) in such a way that the movement is toward the MPP. Vref is then used to calculate the new duty cycle D∗ . As Vref < Vin , the new duty cycle, D∗ = 1 − (Vref /Vo ), increases. As a result, the same output voltage Vo can be obtained by having a smaller PV array voltage. Thus, the operating point moves toward the MPP. In the proposed controller, an additional disturbance ∆D = k × (Vref − Vin ) is introduced in the duty cycle computation, where “k ” is a positive constant. At Vref < Vin , ∆D is negative. The duty cycle for the next switching cycle is determined by two terms, namely 1) 1 − (Vref /Vo ) and 2) ∆D, as given in the following: D∗ = 1 − Vref /Vo − ∆D. (4)
Fig. 8. Comparison of the performance of the conventional controller with the one shown in Fig. 6(b).
dotted box in Fig. 8(a). It shows that at t = 3.5 s, when the array regains the original (uniform) insolation condition, the conventional controller reduces the reference voltage slowly, and hence, the array output voltage and power also change slowly. Unlike this, the additional disturbance ∆D in the proposed controller quickly regains the new equilibrium point where the maximum power is obtained (corresponding to Vpv = 162 V). The time taken to reach MPP is less than one-tenth of that taken by the conventional controller. V. S IMULATION R ESULTS This section presents the simulation results with the proposed algorithm. Fig. 9 shows the performance with uniform insolation (G = 1 kW/m2 ) and also during the partially shaded conditions (G = 1 kW/m2 on modules receiving full insolation and G = 0.3 kW/m2 on shaded modules [Fig. 2(c)]). Until t = 9 s, uniform insolation occurs. At t = 0 s, the algorithm starts scanning the P –V curve on the left side and does not detect any peak until the third disturbance, where the power oscillations are very high. Hence, the system restores the operation to the last peak tracked. Then, it scans the curve on the right side of the last peak point. With the second perturbation, the operating point reaches Vmax . Hence, the last peak point (GP in this case) is quickly restored. Fig. 10 shows the zoomed view of Fig. 9 for the time interval 9.5–12.5 s. It shows how the algorithm tracks the GP when the sudden insolation variation or shading occurs. At t = 9 s, a partially shaded condition, represented by Fig. 2(c), exists. Due to the sudden insolation variation, the system operating point
Similar to a conventional controller, the first term’s effect is an increase in the duty cycle for the next switching cycle. In addition, as ∆D is negative, the second term also increases the duty cycle. Hence, for the same output voltage Vo , the decrease in PV array voltage is much more than the previous case, which restores the MPP much faster than the conventional method. The effectiveness of this controller to rapidly track the MPP is demonstrated using Fig. 8. Proportional controller gain k and sampling time are considered as 0.5 and 1 ms, respectively. The array considered for this purpose is the one represented by Fig. 1(d). The insolation level in the time range 0–2 s and for times greater than 3.5 s is 1 kW/m2 , and during these intervals, the entire array receives uniform insolation. For the period between 2 and 3.5 s, a sudden change in environmental conditions occurs, which causes the partial shading of the array. The insolation level on the shaded module is 0.1 kW/m2 . Fig. 8(a) shows the variation of the reference and PV array voltages for the conventional and proposed controllers. Fig. 8(b) shows the zoomed view of the area bounded by the
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Fig. 9. Response of the boost dc–dc converter in delivering the peak power to the load. (a) Reference voltage set by the controller. (b) PV array’s output voltage. (c) PV array’s output current. (d) PV array’s output power.
Fig. 10. Zoomed view of Fig. 9(a) and (d). (a) GP tracking due to the sudden insolation change at t = 9 s. Points A through C correspond to the points marked A through C on the P –V curve of Fig. 2(c). (b) Zoomed view of (a) over the time range 11.394–11.408 s. It shows that as soon as the controller detects the existence of peak power point (which may be local or GP) in the vicinity, the P&O method is initiated, and the peak power point is tracked.
shifts to point D, which, in fact, is a local maximum. As seen in Fig. 10, the controller immediately starts searching for the GP by giving initial disturbance on the left side of the operating
point. It reaches the minimum reference voltage limit with the two disturbances, and hence, the operation is restored at point D. Now, the disturbance is applied in the other direction. With the first disturbance, it comes in the vicinity of point C and determines that the slope (dP/dV ) is positive. The P&O method is then applied to track the peak. As this peak is greater than the peak point D, the controller updates its peak power point information, and point C is now treated as the reference point for the next disturbance. With another disturbance, the operating point shifts close to B. The controller tracks this peak and determines that it is larger than peak C. Similarly, with two more disturbances (from peak B), the point A is reached, which is smaller than B, and hence, the controller immediately restores the operation at point B, which is the GP. At t = 25 s, when the timer interrupt initiates the GP tracking, the controller immediately detects smaller peaks on either side of point B. Hence, it can quickly restore the operation to the GP. The scanning required would be less if the system was initially trapped (due to insolation variation at t = 9 s) at point C or B or A instead of D. The periodicity of the timer interrupt for the case shown in Fig. 10 is considered as 25 s, while that for the case represented by Table I is 5 min. However, in a real environment, the probability of occurrence of large sudden variations (15%–120% change of the rated capacity of array occurring within 0–5 s) is very less (of the order of 10−7 [21]). Hence, the period after which timer interrupt occurs should be more and should be appropriately set, depending upon the place (i.e., city/country) and the analysis of the past years’ weather data. A more practical case is simulated here (Table I and Figs. 11 and 12), considering gradually changing environmental conditions.
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TABLE I INSOLATION CONDITIONS FOR THE CASE REPRESENTED BY Figs. 11 AND 12
TABLE II COMPARISON OF THE PROPOSED ALGORITHM
Fig. 11. Change in the PV characteristic of the array during the gradual occurrence of partial shading. G = 0.87 kW/m2 for unshaded modules and Gn for shaded modules. Array and shading pattern are the same as that of Fig. 2(a).
Fig. 13.
Partially shaded PV array used in the experimental setup.
Fig. 12. Performance of the proposed algorithm under gradually varying shading conditions. As seen, the GP tracking period is very small (pointed by arrow), and hence, power lost due to periodic tracking is negligible.
Fig. 14. (a) P –V and (b) I –V characteristics obtained with the experimental setup.
Fig. 12 shows comparison of the variation in power when operating with the proposed algorithm and conventional MPP method like P&O under the conditions represented by Table I. The path traversed for conventional method is ABCDEDCBA, while that for the proposed method is ABCDEF GCBA. The timer interrupts lead to different path traversals, ultimately leading to extraction of more power. Table II shows the comparison of the power tracked and the array utilization for the proposed algorithm and the conventional methods. VI. E XPERIMENTAL R ESULTS The PV array, considered for the experimental setup is shown in Fig. 13. It comprises three series assemblies each with six series-connected PV modules, each having a rating of PMAX =
38 W, IMPP = 2.29 A, VMPP = 16.6 V, ISC = 2.55 A, and VOC = 21.5 V at an insolation level of 1000 W/m2 and a temperature of 25 ◦ C. Out of three series assemblies of the array, the first two are artificially shaded with the partially transparent gelatin paper. In the first series assembly, two modules are shaded, while in the second series assembly, three modules are shaded. Fig. 14 shows the characteristics of the PV array for the measurements recorded at 4:00 P. M . on March 26, 2007. The characteristics are obtained by varying the load resistance in discrete steps. The maximum power obtained, corresponding to the GP, is 223 W, while the power corresponding to local peaks are P1 = 167 W and P2 = 194 W, respectively. The current and voltage at the GP are 2.67 A and 83.3 V, respectively. The values recorded for VOC and ISC are 109 V and 4.44 A, respectively. As six modules are connected in series
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Fig. 15. Experimental observations. (a) Tracking of GP by varying the duty cycle of the dc–dc converter. (b) PV array’s output voltage, current, and power along with the reference duty cycle (D∗ ) of the dc–dc converter.
in each series assembly, VOC_module is 18.1 V (= 108.7/6). Voltages V1 and V2 recorded at the local peak points are 42 and 56.7 V, respectively. Thus, V2 and V1 occur at about “n × 0.8 × VOC_module ,” where n (the number of unshaded modules in a series assembly in that group) is equal to 4 for the first series assembly and 3 for the second. This implies that the displacement between these peaks (P1 and P2 ) is about 0.8 × VOC_module , which is in accordance with observation 4 listed at the end of Section II. Fig. 15 shows the results obtained at 3:40 P. M . on the same day. As the insolation is somewhat higher at this time, the current and, hence, the power obtained are higher than those obtained at 4:00 P. M . Fig. 15(a) shows the I –V characteristics obtained by varying the duty ratio of a dc–dc boost converter. The curve is obtained in the XY mode by using the persistent feature of Tektronix’s TDS2014 digital storage oscilloscope. The converter is designed for a power capacity of 500 W. On the basis of the algorithm and control strategy discussed in Sections III and IV, respectively, the duty cycle of the converter is calculated and controlled with ATMEL’s 89S52 microcontroller. Fig. 15(a) shows that although the power level is higher, the nature of the characteristic has not changed from that represented in Fig. 14(b). Fig. 15(b) shows the GP tracking with the proposed algorithm. The maximum power obtained at GP under these conditions is 233 W. The current and voltage at the GP are 2.85 A and 82 V, respectively.
2) It is observed that the peaks follow a specific trend in which the power at a peak point continues to increase until it reaches the GP, and afterward, it continuously decreases. The proposed method is based on this observation, and hence, it does not require the scanning of the entire P –V curve. This results in a lower tracking time. 3) The scheme is also effective under uniform insolation conditions. 4) An additional supervisory control can easily be incorporated in the algorithm by using an external interrupt of the microcontroller. This can assist the supervisor of a large PV array to initiate GP tracking whenever required. 5) The interval at which the GP tracking is repeated can be set by simply adjusting the timer count appropriately. Thus, the user can set the different periodic checking intervals under different weather conditions or seasons. 6) The proposed feedforward control scheme, with an additional disturbance, makes the response of the controller much faster—nearly ten times. Simulation and experimental results have been presented to demonstrate the proposed MPPT algorithm and the control scheme of the dc–dc converter. R EFERENCES
[1] J. H. R. Enslin, M. S. Wolf, D. B. Snyman, and W. Swiegers, “Integrated photovoltaic maximum power point tracking converter,” IEEE Trans. Ind. Electron., vol. 44, no. 6, pp. 769–773, Dec. 1997. [2] T. Noguchi, S. Togashi, and R. Nakamoto, “Short-current pulse-based maximum-power-point tracking method for multiple photovoltaic and converter module system,” IEEE Trans. Ind. Electron., vol. 49, no. 1, pp. 217–223, Feb. 2002. [3] V. Salas, E. Olias, A. Barrado, and A. Lazaro, “Review of the maximum power point tracking algorithms for stand-alone photovoltaic systems,” Sol. Energy Mater. Sol. Cells, vol. 90, no. 11, pp. 1555–1578, Jul. 2006. [4] C. Hua, J. Lin, and C. Chen, “Implementation of a DSP-controlled photovoltaic system with peak power tracking,” IEEE Trans. Ind. Electron., vol. 45, no. 1, pp. 99–107, Feb. 1998. [5] N. Fernia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Optimization of perturb and observe maximum power point tracking method,” IEEE Trans. Power Electron., vol. 20, no. 4, pp. 963–973, Jul. 2005. [6] T. Esram, J. W. Kimball, P. T. Krein, P. L. Chapman, and P. Midya, “Dynamic maximum power point tracking of photovoltaic arrays using ripple correlation control,” IEEE Trans. Power Electron., vol. 21, no. 5, pp. 1282–1291, Sep. 2006. [7] C. Dorofte, U. Borup, and F. Blaabjerg, “A combined two-method MPPT control scheme for grid-connected photovoltaic systems,” in Proc. Eur. Conf. Power Electron. Appl., Sep. 11–14, 2005, pp. 1–10. [8] K. H. Hussein and I. Muta, “Maximum photovoltaic power tracking: An algorithm for rapidly changing atmospheric conditions,” Proc. Inst. Electr. Eng.—Generation, Transmission Distribution, vol. 142, no. 1, pp. 59–64, Jan. 1995. [9] D. Sera, T. Kerekes, R. Teodorescu, and F. Blaabjerg, “Improved MPPT method for rapidly changing environmental conditions,” in Proc. IEEE Int. Ind. Electron. Symp., Jul. 2006, vol. 2, pp. 1420–1425. [10] N. Kasa, T. Iida, and H. Iwamoto, “Maximum power point tracking with capacitor identifier for photovoltaic power system,” Proc. Inst. Electr. Eng.—Electr. Power Appl., vol. 147, no. 6, pp. 497–502, Nov. 2000. [11] N. Kasa, T. Iida, and L. Chen, “Flyback inverter controlled by sensorless current MPPT for photovoltaic power system,” IEEE Trans. Ind. Electron., vol. 52, no. 4, pp. 1145–1152, Aug. 2005. [12] M. Veerachary, T. Senjyu, and K. Uezato, “Maximum power point tracking control of IDB converter supplied PV system,” Proc. Inst. Electr. Eng.—Electr. Power Appl., vol. 148, no. 6, pp. 494–502, Nov. 2001. [13] R. Bruendlinger, B. Bletterie, M. Milde, and H. Oldenkamp, “Maximum power point tracking performance under partially shaded PV array
VII. C ONCLUSION The P –V characteristics of a PV array get more complex under partially shaded conditions and bear multiple peaks. The location of the GP on the P –V characteristics is not fixed and is dependent on various parameters like insolation, temperature, and array configuration. Based on a comprehensive study of the I –V and P –V characteristics of a partially shaded array, several critical observations, which are useful for GP tracking, have been made, and an algorithm for tracking the GP has been presented. The salient features of the method are given as follows. 1) The method is simple, yet effective, to track the GP in case of partially shaded conditions and can be implemented by an inexpensive low-end microcontroller.
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[14] [15]
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[22]
conditions,” in Proc. 21st EUPVSEC, Dresden, Germany, Sept. 2006, pp. 2157–2160. W. Xiao, N. Ozog, and W. G. Dunford, “Topology study of photovoltaic interface for maximum power point tracking,” IEEE Trans. Ind. Electron., vol. 54, no. 3, pp. 1696–1704, Jun. 2007. G. Petrone, G. Spagnuolo, and M. Vitelli, “Analytical model of mismatched photovoltaic fields by means of Lambert W-function,” Sol. Energy Mater. Sol. Cells, vol. 91, no. 18, pp. 1652–1657, Nov. 2007. E. Roman, R. Alonso, P. Ibanez, S. Elorduizapatarietxe, and D. Goitia, “Intelligent PV module for grid-connected PV systems,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1066–1073, Jun. 2006. M. Miyatake, T. Inada, I. Hiratsuka, H. Zhao, H. Otsuka, and M. Nakano, “Control characteristics of a Fibonacci-search-based maximum power point tracker when a photovoltaic array is partially shaded,” in Proc. IEEE IPEMC, 2004, vol. 2, pp. 816–821. K. Kobayashi, I. Takano, and Y. Sawada, “A study of a two stage maximum power point tracking control of a photovoltaic system under partially shaded insolation conditions,” Sol. Energy Mater. Sol. Cells, vol. 90, no. 18/19, pp. 2975–2988, Nov. 2006. E. V. Solodovnik, S. Liu, and R. A. Dougal, “Power controller design for maximum power tracking in solar installations,” IEEE Trans. Power Electron., vol. 19, no. 5, pp. 1295–1304, Sep. 2004. G. Walker, “Evaluating MPPT converter topologies using a MATLAB PV model,” J. Elect. Electron. Eng., Australia, IE Aust., vol. 21, no. 1, pp. 49–56, 2001. B. Bletterie and R. Bruendlinger, “Quantifying dynamic MPPT performance under realistic conditions—First test results: The way forward,” in Proc. 21st Eur. Photovoltaic Solar Energy Conf. Exhib., Dresden, Germany, Sep. 2006, pp. 2347–2351. H. Patel and V. Agarwal, “PV based distributed generation with compensation feature under unbalanced and non-linear load conditions for a 3-φ, 4 wire system,” in Proc. IEEE Int. Conf. Ind. Technol., Mumbai, India, Dec. 2006, pp. 322–327.
Hiren Patel received the B.E. degree in electrical engineering from South Gujarat University, Surat, India, in 1996, and the M.Tech. degree in energy systems in 2003 from the Indian Institute of Technology, Bombay (IITB), Mumbai, India, where he is currently working toward the Ph.D. degree in electrical engineering. He is an Assistant Professor with the Department of Electrical Engineering, Sarvajanik College of Engineering and Technology, Surat. His research interests include computer-aided simulation techniques, distributed generation, and renewable energy, particularly energy extraction from photovoltaic arrays.
Vivek Agarwal (S’92–M’95–SM’01) received the bachelor’s degree in physics from Delhi University, Delhi, India, the M.E. degree in electrical engineering from the Indian Institute of Science, Bangalore, India, and the Ph.D. degree from the University of Victoria, BC, Canada. He was briefly with Statpower Technologies, Burnaby, Canada, as a Research Engineer. In 1995, he joined the Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India, where he is currently a Professor. He works on modeling and simulation of new power converter configurations, intelligent and hybrid control of power electronic systems, power quality issues, EMI/EMC issues, and conditioning of energy from nonconventional sources. His main field of interest is power electronics. Dr. Agarwal is a Fellow of the Institution of Electronics and Telecommunication Engineers and a Life Member of the Indian Society for Technical Education.
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Maximum Power Point Tracking Scheme for PV Systems Operating Under Partially Shaded Conditions
Hiren Patel and Vivek Agarwal, Senior Member, IEEE
Abstract—Current–voltage and power–voltage characteristics of large photovoltaic (PV) arrays under partially shaded conditions are characterized by multiple steps and peaks. This makes the tracking of the actual maximum power point (MPP) [global peak (GP)] a difficult task. In addition, most of the existing schemes are unable to extract maximum power from the PV array under these conditions. This paper proposes a novel algorithm to track the global power peak under partially shaded conditions. The formulation of the algorithm is based on several critical observations made out of an extensive study of the PV characteristics and the behavior of the global and local peaks under partially shaded conditions. The proposed algorithm works in conjunction with a dc–dc converter to track the GP. In order to accelerate the tracking speed, a feedforward control scheme for operating the dc–dc converter is also proposed, which uses the reference voltage information from the tracking algorithm to shift the operation toward the MPP. The tracking time with this controller is about one-tenth as compared to a conventional controller. All the observations and conclusions, including simulation and experimental results, are presented. Index Terms—Global peak (GP), maximum power point tracking (MPPT), partial shading, power–voltage (P –V ) characteristics.
I. I NTRODUCTION HE ever-increasing demand for low-cost energy and growing concern about environmental issues has generated enormous interest in the utilization of nonconventional energy sources such as the solar energy. The freely and abundantly available solar energy can be easily converted into electrical energy using photovoltaic (PV) cells. A PV source has the advantage of low maintenance cost, absence of moving/rotating parts, and pollution-free energy conversion process. However, a major drawback of the PV source is its ineffectiveness during the nights or low insolation periods or during partially shaded conditions. High initial capital cost has been another deterrent in the popularity of PV systems [1]. These drawbacks notwithstanding, the PV systems have emerged as one of the most popular alternatives to conventional energy, thanks to the
T
Manuscript received May 16, 2007; revised December 5, 2007. H. Patel is with the Department of Electrical Engineering, Sarvajanik College of Engineering and Technology, Surat 395001, India. V. Agarwal is with the Department of Electrical Engineering, Indian Institute of Technology Bombay (IITB), Mumbai 400076, India (e-mail: agarwal@ ee.iitb.ac.in). Digital Object Identifier 10.1109/TIE.2008.917118
advancement in technology and favorable government policies in several countries. A major challenge in the use of PV is posed by its nonlinear current–voltage (I –V ) characteristics, which result in a unique maximum power point (MPP) on its power–voltage (P –V ) curve. The matter is further complicated due to the dependence of these characteristics on solar insolation and temperature. As these parameters vary continuously, MPP also varies. Considering the high initial capital cost of a PV source and its low energy conversion efficiency, it is imperative to operate the PV source at MPP so that maximum power can be extracted. In general, a PV source is operated in conjunction with a dc–dc power converter, whose duty cycle is modulated in order to track the instantaneous MPP of the PV source. Several tracking schemes have been proposed [2]–[12]. Among the popular tracking schemes are the perturb and observe (P&O) or hill climbing [4], [5], incremental conductance [8], shortcircuit current [2], open-circuit voltage [7], and ripple correlation approaches [6]. Some modified techniques have also been proposed, with the objective of minimizing the hardware or improving the performance [7], [9]–[12]. The tracking schemes mentioned above are effective and time tested under uniform solar insolation, where the P –V curve of a PV module exhibits only one MPP for a given temperature and insolation. Bruendlinger et al. have tested various commercially available inverters in partially shaded conditions and have found that the power loss due to shading can be as high as 70% [13]. Under partially shaded conditions, when the entire array does not receive uniform insolation, the P –V characteristics get more complex, displaying multiple peaks [only one of which is the global peak (GP); the rest are local peaks] [14]. An analytical model, based on Lambert function and its properties, has been presented [15]. It is capable of simulating the presence of multiple peaks under various conditions like different insolation and temperature levels, shading patterns, mismatch, etc. The computational time and the memory needed by this model is less. The presence of multiple peaks reduces the effectiveness of the existing MPP tracking (MPPT) schemes, which assume a single peak power point on the P –V characteristic. The occurrence of partially shaded conditions being quite common (e.g., due to clouds, trees, etc.), there is a need to develop special MPPT schemes that can track the GP under these conditions. The other option is to use intelligent PV modules [16] or alternating current modules.
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Fig. 1. Terminology used for the various components of a partially shaded PV array. (a) PV module. (b) Series assembly with two subassemblies. (c) Group. (d) Array with three groups.
Some researchers [17]–[19] have worked on GP tracking schemes for PV arrays operating under nonuniform insolation conditions. Miyatake et al. [17] have reported an MPPT scheme that uses Fibonacci sequence to track the GP under partially shaded conditions. However, the method does not guarantee GP tracking under all conditions. Kobayashi et al. [18] have proposed a two-stage method to track the GP. In the first stage, the operating point moves into the vicinity of the GP on the load line Rpm = Vpm /Ipm , and in the second stage, it converges to the actual GP. Vpm and Ipm are approximately equal to 80% and 90% of the open-circuit voltage VOC and short-circuit current ISC of the PV array, respectively. However, in this method, if the GP lies on the left side of the load line (Rpm ), i.e., Rpm > Ractual (where Ractual = Vactual /Iactual ), the operating point is temporarily shifted to 90% of VOC , thereby missing the GP. Solodovnik et al. [19] have suggested a statespace-based approach to search the GP. This method is fast and accurate but is system specific, is complex, and requires more sensors. This paper proposes a novel method that is capable of tracking the GP under partially shaded conditions. Based on an extensive study of partially shaded PV arrays, Section II describes certain critical observations on the I –V and P –V curves of partially shaded arrays. Section III describes the proposed algorithm to track the GP, while Section IV deals with the novel scheme used to achieve a quick response of the dc–dc converter to track the MPP. Sections V and VI present the simulation and experimental results, respectively. The main conclusions are summarized in Section VII. II. C RITICAL O BSERVATIONS U NDER P ARTIALLY S HADED C ONDITIONS Using a simulation model developed in the MATLAB/ SIMULINK software [20], the authors have conducted a comprehensive study of the I –V and P –V characteristics of the partially shaded PV array. This model uses a special terminology to describe the partially shaded array, as depicted in Fig. 1. The terminology helps in simplifying the complex shading pattern of the large PV array and, hence, to study the characteristics of the large partially shaded PV array. A PV module [Fig. 1(a)] is considered to be shaded if three or more of its cells are receiving lower than normal insolation. Series-connected PV modules, receiving similar insolation,
form a “subassembly” [Fig. 1(b)]. Several series-connected subassemblies, each with a different level of insolation, form a “series assembly” [Fig. 1(b)]. A “group” is made up of several similar series assemblies (having identical P –V characteristics) connected in parallel [Fig. 1(c)]. Various parallel-connected groups, with different shading patterns constitute a PV array [Fig. 1(d)]. Fig. 2 shows the P –V curves, obtained using the developed model, for a PV array having 900 modules (10 in series × 90 in parallel) with a complex shading pattern (having several groups). Fig. 2(a) describes the shading pattern on the array, while Fig. 2(b)–(d) shows the P –V curves for the array at different insolation levels. Fig. 2(e) shows the characteristic equation on which the PV cell is modeled. For further discussion, the simpler example of the shaded PV array shown in Fig. 1(d), having only three distinct groups, is considered. Fig. 3 shows the P –V curves corresponding to this array. The P –V curves (C1 , C2 , and C3 ) for one series assembly each from groups 1–3 are shown in Fig. 3(a). Fig. 3(b) shows the P –V curves (D1 , D2 and D3 ) for the entire groups 1–3 obtained by scaling the curves C1 , C2 , and C3 on the current axis. It is observed that the peaks PS1 , PS2 , and PS3 occur at V1 = 65 V, V2 = 114 V, and V3 = 163 V, respectively. It is important to note that since four modules are unshaded in each series assembly of group 1, the peak PS1 occurs nearly at voltage V1 = 4 × 16.3 = 65 V, where 16.3 V is 80% of the open-circuit voltage of the module (VOC_module ) considered. A similar reasoning can be applied to PS2 and PS3 , which occur at nearly V2 (= 7 × 16.3 = 114 V) and V3 (= 10 × 16.3 = 163 V), respectively. The position of peaks PS1 , PS2 , and PS3 govern the position of the peaks PG1 through PG3 [Fig. 3(b)] and, hence, of PAmax1 through PAmax3 on the P –V curve of the entire array [Fig. 3(c)]. Hence, the peaks PAmax1 , PAmax2 , and PAmax3 occur nearly at the voltages V1 , V2 , and V3 , respectively. A significant outcome of this observation is that the array power peaks are displaced from each other by an integral multiple of 80% of VOC_module (n × 0.8 × VOC_module ), where “n” is an integer. As the minimum integral difference in the number of shaded modules between the series assemblies of two groups is one, the minimum possible displacement between two consecutive peaks is 0.8 × VOC_module . In Figs. 1(d) and 2(a), the number of shaded modules in the series assemblies decreases as one moves from the first series assembly to the last one (i.e., from left to right). Furthermore,
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Fig. 2. P –V curves for the PV array under partially shaded conditions. (a) Sample PV array with insolation of 1000 W/m2 (G = 1, where G is the solar insolation in kilowatts per square meter) on the unshaded modules and lower insolation on shaded modules. (b) Shaded modules with 100 W/m2 (G = 0.1 kW/m2 ). (c) Shaded modules with 300 W/m2 (G = 0.3 kW/m2 ). (d) Shaded modules with 600 W/m2 (G = 0.6 kW/m2 ). Characteristics under uniform insolation are also given in (b). (e) Characteristic equation on which the model is built.
Fig. 3. (a) C1 , C2 , and C3 represent P –V curves for series assembly, corresponding to groups 1, 2, and 3, respectively. (b) D1 , D2 , and D3 represent P –V curves for groups 1, 2 and 3, respectively. (c) Resultant P –V curve for the entire array.
only two levels of insolation were considered. Fig. 4 illustrates a more complex case, where a PV array with an arbitrary shading pattern and more than two levels of insolation are considered. The array size is the same as that in Fig. 2(a). Using the terminology defined in Fig. 1, the array in Fig. 4(a) can be divided into seven groups. The integers at the bottom of the array represent the “groups” formed in the array due to nonuniform insolation. Fig. 4(b) shows the P –V characteristic for the random shading pattern shown in Fig. 4(a). Some of the critical observations made from an extensive study of the PV curves of the partially shaded arrays Figs. 2–4 are listed as follows. 1) I –V curves under partially shaded conditions have multiple steps, while the P –V curves are characterized by multiple peaks.
2) In addition to insolation and temperature, the magnitude of GP, and the voltage at which it occurs are also dependent on the shading pattern and array configuration. 3) Fig. 2(b) shows that the GP may lie on the left side of the load line. 4) The peaks on the P –V curve occur nearly at multiples of 80% of VOC_module (Fig. 3). 5) The minimum displacement between successive peaks is nearly 80% of VOC_module (Fig. 3). 6) Extensive study of P –V curves, as well as practical data, have revealed that when the P –V curve is traversed from either side, the magnitude of the peaks increases. After reaching the GP, the magnitude of the subsequent peaks (if they are present) continuously decreases (Figs. 2 –4).
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Fig. 4. (a) PV array (of size 10 × 90) with a random shading pattern. The array is scaled down such that each series assembly represents three similar series assemblies connected in parallel. (b) Resultant P –V curve for the entire array.
III. A LGORITHM FOR THE P ROPOSED MPPT S CHEME Fig. 5 shows the flowchart of the proposed algorithm to track the GP under partially shaded conditions. The execution of the algorithm always starts with reference voltage (Vref ) value set equal to 85% of VOC (block 1) as shown in the “Main Program” in Fig. 5. Until any disturbance (or timer interrupt) occurs, it maintains the operation at the GP by continuously implementing the hill climbing [3] or the P&O method (blocks 2 and 3). When any sudden disturbance (like partial shading) or timer interrupt occur, the “Main Program” identifies the requirement for tracking the GP (blocks 4–6) and calls the “GP track subroutine” (block 7a). “GP track subroutine” tracks the new GP and, then, once again, pass on the control to the “Main Program,” which maintains the operation at this new GP. “GP track subroutine” is also called periodically at a 25-s interval when the timer generates an interrupt (block 7b). In addition to this, the scheme can also be easily modified to have the feature of GP tracking when the user wants to initiate it. The user may be the supervisor of a large PV array who realizes that PV array is partially shaded but does not know the exact operating point where the MPP occurs. To understand the algorithm, assume that a GP had just been reached when a sudden insolation change shifts the operating point to the vicinity of one of the local peaks (e.g., point D [Fig. 2(c)]). This local peak (point D) is tracked by the P&O method (block 2). Whether MPP is reached or not, is checked by determining the sign of the power in two subsequent perturbations (block 3). When the first local peak (point D) is tracked, the algorithm stores the current information about PV array’s output power and output voltage as Pmax _last and Vm_last , respectively. The algorithm then sets the flag (flag = 1) for checking the GP on the left side of point D (block 4). The sudden change in the insolation level (∆G) or shading leads to a variation in power (= ∆P ). If ∆P is greater than a certain critical power variation (= ∆Pcrit ), then GP tracking starts (blocks 5 and 6). To determine ∆P , array’s output power at two different time instants, 0.01 s apart, is considered. It is reported that the sudden variations in insolation are small in magnitude (smaller than G = 0.027 kW/m2 ) and occur within 1 s [21]. Based on this, ∆Pcrit can be fine tuned, depending upon the PV system and its environment (can be certain percentage of the array’s output power capacity or set corresponding to
change in the output power of an array for desired ∆G, where ∆G < 0.027 kW/m2 ). If any of the aforementioned condition for GP tracking occurs, the “GP track subroutine” starts, scanning the P –V curve for other peaks. This is done by applying a disturbance ∆Vlarge , which should be less than the minimum possible displacement between the two successive peaks (observation 5, block 8). To ensure that no peak is missed during the tracking, ∆Vlarge can be considered as 60%–70% of VOC_module . The lower the value is, the higher the time required to track the GP but the lower the risk of missing the GP will be. The initial disturbance is toward the left side (toward point E), which is indicated by “flag = 1” (block 10). If a uniform insolation condition does not exist (block 9) and if any of the limits (blocks 11 and 12), discussed later, is not reached, the slope dP/dV is measured at the new operating point (block 14). If the slope is positive, the disturbance is continued in the same direction (blocks 15 and 16) until “Vmin ,” the lowest voltage below which the GP is not likely to occur (block 12), is reached. However, if the slope dP/dV is negative, it indicates that there is another peak (point E) in the vicinity, and hence, the conventional MPP technique is applied to track this peak (point E, block 17). If the power corresponding to this peak is less than the previous one, the initial operating point (i.e., the previous largest peak observed during the tracking, point D) is restored, and the disturbance is now applied in the other direction (blocks 18, 20, and 21). The right side movement is indicated by “flag = −1” (block 21). If the power at the new peak is more than the previous one, then Pmax _last and Vm_last are updated (block 19), this peak is considered as the likely candidate for the GP, and the disturbance on the left side on P –V curve is continued until a smaller peak or Vmin is reached (block 12). Now, the disturbance is applied toward the right side, and a similar process is carried out (block 13). The slope dP/dV is measured after every large disturbance, and if it is positive, it indicates a local peak in the vicinity. This peak is tracked, and if its magnitude is greater than Pmax_last , the disturbance is continued on the right side. However, during this process, if any smaller peak (point A) is observed, the operation is restored at the point (point B) which it has stored as the MPP during this tracking. The operation is even restored at point B, if Vmax is reached, where Vmax is equal to 85% of VOC_module (block 11). The algorithm continues to track the peak until it comes to the very first peak that is generating less power than the peak it observed last. Hence, this algorithm does not have to scan the entire P –V curve. If only one peak exists on the P –V curve, as is the case during uniform insolation, the algorithm may scan the entire range. To avoid this, after the application of each large disturbance (∆Vlarge ), oscillations in the power are measured. It has been observed that in case of uniform insolation, as soon as the operating point shifts close to ISC (i.e., away from MPP), the application of a large disturbance in Vref results in large oscillations in the array power. Hence, in such a case, if the oscillations are greater than a certain tolerable power variation (∆Ptol : 4%–5% of array capacity), the controller immediately restores the operation to the GP (block 9).
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Fig. 5.
Flowchart for the proposed MPPT control.
IV. D UTY C YCLE C OMPUTATION FOR DC–DC C ONVERTER C ONTROL Fig. 6(a) shows the circuit schematic of a boost-type dc–dc power converter whose duty cycle is modulated as per the algorithm used for electrical tracking of the MPP. In a conventional controller working with the P&O method, duty cycle (D∗ ) is generated as follows [22]: D∗ = 1 − (Vref /Vo ) (1)
Fig. 6. (a) Circuit schematic for boost converter used for tracking MPP. (b) Proposed control scheme for the dc–dc converter. (LB = 5 mH, Cp = 2000 µH, Cf = 1000 µH, and Lf = 0.1 mH).
where Vref is the reference voltage obtained using the MPPT algorithm described in Section III, and Vo is the output voltage of the dc–dc converter. It is observed that such a controller is slow to respond. The proposed controller overcomes this drawback. Here, the control signal for dc–dc converter is obtained in a feedforward manner, as shown in Fig. 6(b). The controller is fast to respond and can quickly track the MPP. The principle involved in this controller can be mathematically explained as under. If ∆D is the perturbation in the actual
duty cycle D, then D + ∆D = 1 − (Vpv + ∆Vpv )/(Vo + ∆Vo ) (2)
where Vpv is the PV array voltage, while ∆Vpv and ∆Vo are changes in PV array and output voltages of the dc–dc converter, respectively.
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Fig. 7. P –V characteristic for the array of Fig. 1(d), with solar insolation of 1000 W/m2 .
If ∆Vo
Vo , then (2) leads to (3) as follows: ∆D = −∆Vpv /Vo . (3)
This additional disturbance ∆D, when subtracted from the actual duty cycle D, amplifies the disturbance toward the MPP, and therefore, the MPP is attained quickly. The above mathematical analysis is explained with the help of Fig. 7, which shows the P –V curve of the array represented by Fig. 1(d). Point A indicates the initial operating point for which the PV array output voltage is Vin . To reach the MPP, the conventional controller sets the reference voltage Vref by giving a perturbation (here, reduction in the operating voltage) in such a way that the movement is toward the MPP. Vref is then used to calculate the new duty cycle D∗ . As Vref < Vin , the new duty cycle, D∗ = 1 − (Vref /Vo ), increases. As a result, the same output voltage Vo can be obtained by having a smaller PV array voltage. Thus, the operating point moves toward the MPP. In the proposed controller, an additional disturbance ∆D = k × (Vref − Vin ) is introduced in the duty cycle computation, where “k ” is a positive constant. At Vref < Vin , ∆D is negative. The duty cycle for the next switching cycle is determined by two terms, namely 1) 1 − (Vref /Vo ) and 2) ∆D, as given in the following: D∗ = 1 − Vref /Vo − ∆D. (4)
Fig. 8. Comparison of the performance of the conventional controller with the one shown in Fig. 6(b).
dotted box in Fig. 8(a). It shows that at t = 3.5 s, when the array regains the original (uniform) insolation condition, the conventional controller reduces the reference voltage slowly, and hence, the array output voltage and power also change slowly. Unlike this, the additional disturbance ∆D in the proposed controller quickly regains the new equilibrium point where the maximum power is obtained (corresponding to Vpv = 162 V). The time taken to reach MPP is less than one-tenth of that taken by the conventional controller. V. S IMULATION R ESULTS This section presents the simulation results with the proposed algorithm. Fig. 9 shows the performance with uniform insolation (G = 1 kW/m2 ) and also during the partially shaded conditions (G = 1 kW/m2 on modules receiving full insolation and G = 0.3 kW/m2 on shaded modules [Fig. 2(c)]). Until t = 9 s, uniform insolation occurs. At t = 0 s, the algorithm starts scanning the P –V curve on the left side and does not detect any peak until the third disturbance, where the power oscillations are very high. Hence, the system restores the operation to the last peak tracked. Then, it scans the curve on the right side of the last peak point. With the second perturbation, the operating point reaches Vmax . Hence, the last peak point (GP in this case) is quickly restored. Fig. 10 shows the zoomed view of Fig. 9 for the time interval 9.5–12.5 s. It shows how the algorithm tracks the GP when the sudden insolation variation or shading occurs. At t = 9 s, a partially shaded condition, represented by Fig. 2(c), exists. Due to the sudden insolation variation, the system operating point
Similar to a conventional controller, the first term’s effect is an increase in the duty cycle for the next switching cycle. In addition, as ∆D is negative, the second term also increases the duty cycle. Hence, for the same output voltage Vo , the decrease in PV array voltage is much more than the previous case, which restores the MPP much faster than the conventional method. The effectiveness of this controller to rapidly track the MPP is demonstrated using Fig. 8. Proportional controller gain k and sampling time are considered as 0.5 and 1 ms, respectively. The array considered for this purpose is the one represented by Fig. 1(d). The insolation level in the time range 0–2 s and for times greater than 3.5 s is 1 kW/m2 , and during these intervals, the entire array receives uniform insolation. For the period between 2 and 3.5 s, a sudden change in environmental conditions occurs, which causes the partial shading of the array. The insolation level on the shaded module is 0.1 kW/m2 . Fig. 8(a) shows the variation of the reference and PV array voltages for the conventional and proposed controllers. Fig. 8(b) shows the zoomed view of the area bounded by the
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Fig. 9. Response of the boost dc–dc converter in delivering the peak power to the load. (a) Reference voltage set by the controller. (b) PV array’s output voltage. (c) PV array’s output current. (d) PV array’s output power.
Fig. 10. Zoomed view of Fig. 9(a) and (d). (a) GP tracking due to the sudden insolation change at t = 9 s. Points A through C correspond to the points marked A through C on the P –V curve of Fig. 2(c). (b) Zoomed view of (a) over the time range 11.394–11.408 s. It shows that as soon as the controller detects the existence of peak power point (which may be local or GP) in the vicinity, the P&O method is initiated, and the peak power point is tracked.
shifts to point D, which, in fact, is a local maximum. As seen in Fig. 10, the controller immediately starts searching for the GP by giving initial disturbance on the left side of the operating
point. It reaches the minimum reference voltage limit with the two disturbances, and hence, the operation is restored at point D. Now, the disturbance is applied in the other direction. With the first disturbance, it comes in the vicinity of point C and determines that the slope (dP/dV ) is positive. The P&O method is then applied to track the peak. As this peak is greater than the peak point D, the controller updates its peak power point information, and point C is now treated as the reference point for the next disturbance. With another disturbance, the operating point shifts close to B. The controller tracks this peak and determines that it is larger than peak C. Similarly, with two more disturbances (from peak B), the point A is reached, which is smaller than B, and hence, the controller immediately restores the operation at point B, which is the GP. At t = 25 s, when the timer interrupt initiates the GP tracking, the controller immediately detects smaller peaks on either side of point B. Hence, it can quickly restore the operation to the GP. The scanning required would be less if the system was initially trapped (due to insolation variation at t = 9 s) at point C or B or A instead of D. The periodicity of the timer interrupt for the case shown in Fig. 10 is considered as 25 s, while that for the case represented by Table I is 5 min. However, in a real environment, the probability of occurrence of large sudden variations (15%–120% change of the rated capacity of array occurring within 0–5 s) is very less (of the order of 10−7 [21]). Hence, the period after which timer interrupt occurs should be more and should be appropriately set, depending upon the place (i.e., city/country) and the analysis of the past years’ weather data. A more practical case is simulated here (Table I and Figs. 11 and 12), considering gradually changing environmental conditions.
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TABLE I INSOLATION CONDITIONS FOR THE CASE REPRESENTED BY Figs. 11 AND 12
TABLE II COMPARISON OF THE PROPOSED ALGORITHM
Fig. 11. Change in the PV characteristic of the array during the gradual occurrence of partial shading. G = 0.87 kW/m2 for unshaded modules and Gn for shaded modules. Array and shading pattern are the same as that of Fig. 2(a).
Fig. 13.
Partially shaded PV array used in the experimental setup.
Fig. 12. Performance of the proposed algorithm under gradually varying shading conditions. As seen, the GP tracking period is very small (pointed by arrow), and hence, power lost due to periodic tracking is negligible.
Fig. 14. (a) P –V and (b) I –V characteristics obtained with the experimental setup.
Fig. 12 shows comparison of the variation in power when operating with the proposed algorithm and conventional MPP method like P&O under the conditions represented by Table I. The path traversed for conventional method is ABCDEDCBA, while that for the proposed method is ABCDEF GCBA. The timer interrupts lead to different path traversals, ultimately leading to extraction of more power. Table II shows the comparison of the power tracked and the array utilization for the proposed algorithm and the conventional methods. VI. E XPERIMENTAL R ESULTS The PV array, considered for the experimental setup is shown in Fig. 13. It comprises three series assemblies each with six series-connected PV modules, each having a rating of PMAX =
38 W, IMPP = 2.29 A, VMPP = 16.6 V, ISC = 2.55 A, and VOC = 21.5 V at an insolation level of 1000 W/m2 and a temperature of 25 ◦ C. Out of three series assemblies of the array, the first two are artificially shaded with the partially transparent gelatin paper. In the first series assembly, two modules are shaded, while in the second series assembly, three modules are shaded. Fig. 14 shows the characteristics of the PV array for the measurements recorded at 4:00 P. M . on March 26, 2007. The characteristics are obtained by varying the load resistance in discrete steps. The maximum power obtained, corresponding to the GP, is 223 W, while the power corresponding to local peaks are P1 = 167 W and P2 = 194 W, respectively. The current and voltage at the GP are 2.67 A and 83.3 V, respectively. The values recorded for VOC and ISC are 109 V and 4.44 A, respectively. As six modules are connected in series
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Fig. 15. Experimental observations. (a) Tracking of GP by varying the duty cycle of the dc–dc converter. (b) PV array’s output voltage, current, and power along with the reference duty cycle (D∗ ) of the dc–dc converter.
in each series assembly, VOC_module is 18.1 V (= 108.7/6). Voltages V1 and V2 recorded at the local peak points are 42 and 56.7 V, respectively. Thus, V2 and V1 occur at about “n × 0.8 × VOC_module ,” where n (the number of unshaded modules in a series assembly in that group) is equal to 4 for the first series assembly and 3 for the second. This implies that the displacement between these peaks (P1 and P2 ) is about 0.8 × VOC_module , which is in accordance with observation 4 listed at the end of Section II. Fig. 15 shows the results obtained at 3:40 P. M . on the same day. As the insolation is somewhat higher at this time, the current and, hence, the power obtained are higher than those obtained at 4:00 P. M . Fig. 15(a) shows the I –V characteristics obtained by varying the duty ratio of a dc–dc boost converter. The curve is obtained in the XY mode by using the persistent feature of Tektronix’s TDS2014 digital storage oscilloscope. The converter is designed for a power capacity of 500 W. On the basis of the algorithm and control strategy discussed in Sections III and IV, respectively, the duty cycle of the converter is calculated and controlled with ATMEL’s 89S52 microcontroller. Fig. 15(a) shows that although the power level is higher, the nature of the characteristic has not changed from that represented in Fig. 14(b). Fig. 15(b) shows the GP tracking with the proposed algorithm. The maximum power obtained at GP under these conditions is 233 W. The current and voltage at the GP are 2.85 A and 82 V, respectively.
2) It is observed that the peaks follow a specific trend in which the power at a peak point continues to increase until it reaches the GP, and afterward, it continuously decreases. The proposed method is based on this observation, and hence, it does not require the scanning of the entire P –V curve. This results in a lower tracking time. 3) The scheme is also effective under uniform insolation conditions. 4) An additional supervisory control can easily be incorporated in the algorithm by using an external interrupt of the microcontroller. This can assist the supervisor of a large PV array to initiate GP tracking whenever required. 5) The interval at which the GP tracking is repeated can be set by simply adjusting the timer count appropriately. Thus, the user can set the different periodic checking intervals under different weather conditions or seasons. 6) The proposed feedforward control scheme, with an additional disturbance, makes the response of the controller much faster—nearly ten times. Simulation and experimental results have been presented to demonstrate the proposed MPPT algorithm and the control scheme of the dc–dc converter. R EFERENCES
[1] J. H. R. Enslin, M. S. Wolf, D. B. Snyman, and W. Swiegers, “Integrated photovoltaic maximum power point tracking converter,” IEEE Trans. Ind. Electron., vol. 44, no. 6, pp. 769–773, Dec. 1997. [2] T. Noguchi, S. Togashi, and R. Nakamoto, “Short-current pulse-based maximum-power-point tracking method for multiple photovoltaic and converter module system,” IEEE Trans. Ind. Electron., vol. 49, no. 1, pp. 217–223, Feb. 2002. [3] V. Salas, E. Olias, A. Barrado, and A. Lazaro, “Review of the maximum power point tracking algorithms for stand-alone photovoltaic systems,” Sol. Energy Mater. Sol. Cells, vol. 90, no. 11, pp. 1555–1578, Jul. 2006. [4] C. Hua, J. Lin, and C. Chen, “Implementation of a DSP-controlled photovoltaic system with peak power tracking,” IEEE Trans. Ind. Electron., vol. 45, no. 1, pp. 99–107, Feb. 1998. [5] N. Fernia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Optimization of perturb and observe maximum power point tracking method,” IEEE Trans. Power Electron., vol. 20, no. 4, pp. 963–973, Jul. 2005. [6] T. Esram, J. W. Kimball, P. T. Krein, P. L. Chapman, and P. Midya, “Dynamic maximum power point tracking of photovoltaic arrays using ripple correlation control,” IEEE Trans. Power Electron., vol. 21, no. 5, pp. 1282–1291, Sep. 2006. [7] C. Dorofte, U. Borup, and F. Blaabjerg, “A combined two-method MPPT control scheme for grid-connected photovoltaic systems,” in Proc. Eur. Conf. Power Electron. Appl., Sep. 11–14, 2005, pp. 1–10. [8] K. H. Hussein and I. Muta, “Maximum photovoltaic power tracking: An algorithm for rapidly changing atmospheric conditions,” Proc. Inst. Electr. Eng.—Generation, Transmission Distribution, vol. 142, no. 1, pp. 59–64, Jan. 1995. [9] D. Sera, T. Kerekes, R. Teodorescu, and F. Blaabjerg, “Improved MPPT method for rapidly changing environmental conditions,” in Proc. IEEE Int. Ind. Electron. Symp., Jul. 2006, vol. 2, pp. 1420–1425. [10] N. Kasa, T. Iida, and H. Iwamoto, “Maximum power point tracking with capacitor identifier for photovoltaic power system,” Proc. Inst. Electr. Eng.—Electr. Power Appl., vol. 147, no. 6, pp. 497–502, Nov. 2000. [11] N. Kasa, T. Iida, and L. Chen, “Flyback inverter controlled by sensorless current MPPT for photovoltaic power system,” IEEE Trans. Ind. Electron., vol. 52, no. 4, pp. 1145–1152, Aug. 2005. [12] M. Veerachary, T. Senjyu, and K. Uezato, “Maximum power point tracking control of IDB converter supplied PV system,” Proc. Inst. Electr. Eng.—Electr. Power Appl., vol. 148, no. 6, pp. 494–502, Nov. 2001. [13] R. Bruendlinger, B. Bletterie, M. Milde, and H. Oldenkamp, “Maximum power point tracking performance under partially shaded PV array
VII. C ONCLUSION The P –V characteristics of a PV array get more complex under partially shaded conditions and bear multiple peaks. The location of the GP on the P –V characteristics is not fixed and is dependent on various parameters like insolation, temperature, and array configuration. Based on a comprehensive study of the I –V and P –V characteristics of a partially shaded array, several critical observations, which are useful for GP tracking, have been made, and an algorithm for tracking the GP has been presented. The salient features of the method are given as follows. 1) The method is simple, yet effective, to track the GP in case of partially shaded conditions and can be implemented by an inexpensive low-end microcontroller.
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Hiren Patel received the B.E. degree in electrical engineering from South Gujarat University, Surat, India, in 1996, and the M.Tech. degree in energy systems in 2003 from the Indian Institute of Technology, Bombay (IITB), Mumbai, India, where he is currently working toward the Ph.D. degree in electrical engineering. He is an Assistant Professor with the Department of Electrical Engineering, Sarvajanik College of Engineering and Technology, Surat. His research interests include computer-aided simulation techniques, distributed generation, and renewable energy, particularly energy extraction from photovoltaic arrays.
Vivek Agarwal (S’92–M’95–SM’01) received the bachelor’s degree in physics from Delhi University, Delhi, India, the M.E. degree in electrical engineering from the Indian Institute of Science, Bangalore, India, and the Ph.D. degree from the University of Victoria, BC, Canada. He was briefly with Statpower Technologies, Burnaby, Canada, as a Research Engineer. In 1995, he joined the Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India, where he is currently a Professor. He works on modeling and simulation of new power converter configurations, intelligent and hybrid control of power electronic systems, power quality issues, EMI/EMC issues, and conditioning of energy from nonconventional sources. His main field of interest is power electronics. Dr. Agarwal is a Fellow of the Institution of Electronics and Telecommunication Engineers and a Life Member of the Indian Society for Technical Education.
