Global MPPT Scheme for Photovoltaic String Inverters ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 7, JULY 2014

Global MPPT Scheme for Photovoltaic String Inverters Based on Restricted Voltage Window Search Algorithm Mutlu Boztepe, Member, IEEE, Francesc Guinjoan, Member, IEEE, Guillermo Velasco-Quesada, Member, IEEE, Santiago Silvestre, Senior Member, IEEE, Aissa Chouder, and Engin Karatepe, Member, IEEE

Abstract—String inverter photovoltaic (PV) systems with bypass diodes require improved global maximum power point tracking (GMPPT) algorithms to effectively reach the absolute maximum power operating point. Several GMPPT algorithms have been proposed to deal with this problem, but most of them require scanning wide voltage ranges of the PV array from nearly zero voltage to open-circuit voltage that increases the scanning time and, in turn, causes energy loss. This paper presents a novel GMPPT method which significantly restricts the voltage window search range and tracks the global power peak rapidly in all shading conditions. Simulation tests and experimental comparisons with another GMPPT algorithm are presented to highlight the features of the presented approach. Index Terms—Maximum power point (MPP) tracking (MPPT), partial shading, photovoltaic (PV) power systems, string inverters.

I. I NTRODUCTION

S

OLAR ENERGY is abundant, freely available, and promising renewable energy source and can be converted directly to electrical energy by photovoltaic (PV) modules. The PV system size ranges from a single PV module to a large power plant; however, the building-integrated PV (BIPV) systems have widespread adoption worldwide [1]. In most cases, the BIPV system is connected to the utility grid through a PV inverter which may have mainly two different topologies such as central and string. Nowadays, the string topology is the present technology for BIPV systems due to some limitations of the central inverter one, such as power losses in centralized maximum power point (MPP) tracking (MPPT), nonflexibility, and losses in string diodes [2]. All types of grid-connected PV inverters must have MPPT facility to extract maximum power from the PV modules, Manuscript received February 5, 2013; revised May 23, 2013; accepted July 23, 2013. Date of publication September 9, 2013; date of current version January 31, 2014. M. Boztepe and E. Karatepe are with the Department of Electrical and Electronics Engineering, Ege University, 35100 Izmir, Turkey (e-mail: [email protected]; [email protected]). F. Guinjoan and S. Silvestre are with the Departamento de Ingenieria Electrónica, Escuela Técnica Superior de Ingenieros de Telecomunicación de Barcelona, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain (e-mail: [email protected]; [email protected]). G. Velasco-Quesada is with the Departamento de Ingeniería Electrónica, Escuela Universitaria de Ingeniería Técnica Industrial de Barcelona, Universitat Politècnica de Catalunya, 08036 Barcelona, Spain (e-mail: guillermo. [email protected]). A. Chouder is with the Development Centre of Renewable Energies, Algiers 16340, Algeria (e-mail: [email protected]). Digital Object Identifier 10.1109/TIE.2013.2281163

since its output characteristic is nonlinear and depends on the temperature and solar irradiance. Conventional MPPT methods, which are well summarized in [3], can accurately track the MPP under uniform irradiance condition [4]. Among them, the perturbation and observation (P&O) and incremental conductance methods are the most popular ones, particularly for lowcost applications [5]. On the other hand, trees, clouds, near buildings, television aerials, chimneys, and other roof structures can create partial shading on the PV module surfaces, which affect the power–voltage characteristic drastically, and create multiple local peaks [6], [7]. In such a case, conventional MPPT schemes are not effective since they are designed for single peak and may converge to any local peak instead of the global one, causing significant reduction in system performance [8]. As an example, 41% of the installed PV systems in the German 1000 Roofs Programme were affected by shading, causing 10% energy loss [9]. It is reported in [10] that the power loss due to the improper MPPT may be as high as 70% according to the real measurements. Thus, in recent years, numerous studies worldwide have been performed to mitigate the power loss due to partial shading [11]. The total cross-tied connection of PV modules increases the immunity against partial shading [12], [13], but it is not applicable for string topology. On the other hand, several MPPT methods for nonuniform irradiance operation have been proposed in literature. Some of them are hardware based, such as the dynamic reconfiguration of PV modules according to the shading pattern [14], [15], a dc/dc converter in series with each string [16], distributed MPPT concept [17], [18], moduleintegrated dc/dc converters [19], [20], multilevel converters [21], parallel-connected MPPTs [22], and power electronics equalizers [23]. All of these methods require additional power circuitry which decreases the reliability and efficiency and increases both hardware complexity and system cost. However, some other MPPT methods are based on a search algorithm and can be realized by only modifying the control software in the present commercial power converters. These methods may be more preferable since they do not increase component count of the system. However, some of them are very complex to apply for commercial equipment, such as the Fibonacci search algorithm [24], [25], artificial neural network and fuzzy logic with polar controller [26], particle swarm optimization [27], [28], Bayesian fusion technique [29], differential evolution [30], sequential extremum seeking control [31], ant colony optimization [32], modified fuzzy-logic controller [33],

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BOZTEPE et al.: GLOBAL MPPT SCHEME FOR PHOTOVOLTAIC STRING INVERTERS BASED ON VWS ALGORITHM

and parametric search algorithm in [34]. Alternatively, less complex schemes are two-stage MPPT control algorithm [35], global peak (GP) search algorithm [36], dividing rectangle [37], and predetermined linear-function-based [38] search algorithms. In addition, Koutroulis and Blaabjerg [39] propose a global MPPT (GMPPT) search algorithm by employing constant-power operation. However, in order to detect small power differences between local peaks, the perturbed power levels should be very small, which, in turn, makes the algorithm slower. Moreover, it needs a constant-input-power dc/dc converter. All search algorithms use a wisely defined operating voltage range so as to ensure that none of the potentially global power peak is missed. However, most of them scan almost 80% of the entire P −V curve [11] that increases the scanning time significantly and therefore causes extra power loss. This drawback is particularly severe for PV systems having high open-circuit voltage. On the other hand, another important issue which is generally ignored is the power loss caused by the search algorithm under uniform irradiance condition. In this case, the P −V curves should be periodically checked to detect changes in operating conditions, such as partial shading. Checking methods based on the scanning of the overall P −V curve take long time and significantly increase the energy loss. In this concern, only few algorithms [35], [37] have dedicated methods to rapidly detect uniform irradiation operation. This paper presents a novel GMPPT algorithm, referred to as voltage window (VW) search (VWS), which restricts the voltage range to be scanned, thus improving the algorithm speed and performance, and can track GPs in all shading conditions. Moreover, the algorithm fixes the voltage range at its lowest value under uniform irradiance operation, thus reducing power losses in this case. The algorithm applies for a string inverter topology since it is the most widely used configuration in BIPV systems and exhibits better performances as regards power extraction than central inverters under nonuniform irradiance operation [2]. II. M AIN PARAMETERS OF GMPPT A LGORITHM The main parameters of the proposed GMPPT algorithm are the global voltage step, the power operating triangle (POT), and the VW. These parameters are addressed in the following sections, and the optimal values of some of them are investigated. In this concern, since the characteristics of the PV string with bypass diodes are substantially affected by nonuniform irradiance, the module-based PV model [40] is preferred in the simulations since it gives good accuracy in partial shaded conditions without increasing computational effort. In the modulebased model, the group of cells connected in parallel to one bypass diode is called as a “part” and modeled by using a single diode electrical equivalent circuit. In this concern, a current practice in crystalline solar cells is to connect two bypass diodes per module to prevent hotspot damages [41]. Accordingly, a typical PV module can be modeled by using two equivalent circuits (labeled part-A and part-B) and two bypass diodes, as shown in Fig. 1.

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Fig. 1. Representation of the module-based PV model.

Fig. 2. Distribution of the voltage difference between two adjacent local peaks as normalized to VocP at STC.

A. Definition and Choice of the Global Voltage Step The global voltage step parameter, noted as ΔVGSTEP , is defined as the fixed voltage increment imposed by the GMPPT algorithm to find the global maximum. The choice of this parameter value directly affects both the scanning time and the algorithm accuracy. However, the optimum value should be around the voltage difference between two adjacent local power peaks. For this reason, a set of simulations is carried out by using 1000 random irradiance values between 100 and 1000 W/m2 through MATLAB Simulink considering 2, 4, 6, 8, and 16 numbers of series-connected PV modules, with two bypass diodes each. The cell temperature Tc is estimated using normal operating cell temperature (NOCT) [42] as follows: Tc = Ta + (NOCT − 20)(G/800)

(1)

where Ta is the ambient temperature in degrees Celsius and G is the solar irradiance in watts per square meter. The NOCT and Ta are fixed to 45 ◦ C and 25 ◦ C, respectively. All PV modules are assumed to operate at the same cell temperature given by (1), where G is taken as the mean value of the random irradiances. The simulation results, shown in Fig. 2, are normalized to the open-circuit voltage of single part of a PV module, referred to as VocP , at standard test conditions (STCs) (1000 W/m2 , 25 ◦ C, and an air mass of 1.5). As it can be seen in Fig. 2, the voltage difference between two adjacent local power peaks varies in wide range starting from 0.5 VocP , but its value is located around 0.8 VocP in most of the cases.

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Fig. 3. Criteria for the choice of ΔVGSTEP .

Fig. 4.

To better illustrate the choice of ΔVGSTEP , Fig. 3 shows the power-versus-voltage (P −V ) curves corresponding to two different irradiance levels for the case of a series-connected PV array of six modules and the sampled values according to the value of ΔVGSTEP . As it will be detailed later, the algorithm operating principle takes the maximum value of the power samples and launches a conventional P&O algorithm. As it can be seen from Fig. 3, both ΔVGSTEP = 0.5 VocP and ΔVGSTEP = 1.0 VocP are suitable voltage steps to reach the global maximums B and D. On the contrary, ΔVGSTEP = 1.5 VocP misses the global maximum B since the P&O algorithm evolves toward point B . However, it has been observed from the simulations that ΔVGSTEP = 1.0 VocP may fail when two local peaks have nearly equal power values. If this is the case, the tracking efficiency slightly decreases according to power differences between the local peaks. Hence, the value of ΔVGSTEP can be selected between 0.5 VocP and 1.0 VocP by balancing the tradeoff between the tracking efficiency and convergence speed. On the other hand, the value of VocP can be obtained from the PV module datasheet dividing the rated open-circuit voltage of the PV module by the number of bypass diodes connected to it, e.g., it corresponds to the half of the open-circuit voltage for PV modules with two bypass diodes. Alternatively, a default VocP value, suitable for all PV array structures, can be determined from the minimum breakdown voltage of the solar cells. In a PV module, the number of solar cells bypassed by a diode is determined according to the breakdown voltage of the cells to prevent hot-spot damage. Since avalanche breakdown voltages range from 12 to 20 V for poly-Si cells and up to 30 V for mono-Si ones [41], a suitable conservative default value can be fixed at VocP = 11 V.

VOC and short-circuit current ISC , respectively, and they can be expressed as

B. POT and VW The POT is generally defined on the P −V curve by the x-axis and two straight lines, namely, constant voltage and constant current. For example, in Fig. 4, the constant voltage and current lines in STCs are fixed by the open-circuit voltage

Illustration of POT and VW.

p = ISC v

(2)

v = VOC

(3)

where p and v stand for PV power and PV voltage, respectively. As the irradiance is lower than 1000 W/m2 (the cell temperature is assumed constant), all operating points for the PV array should be inside of the POT even for nonuniform irradiation (also shown in Fig. 4). The VW is defined as [Vmin , Vmax ], which establishes the upper and lower limits of the voltage range to be scanned around the global MPP. The important benefit of the POT is to define the VW according to the power level. For example, in Fig. 4, the VW of point Q, whose power is PQ , corresponds to the voltage range between the intersection points of the constant-power line p = PQ with both (2) and (3), corresponding to points A and B, respectively. It means that operating points below the voltages of point A cannot have higher power than PQ . This property can be used to restrict the voltage range to be scanned by the GMPPT search algorithm and can speed up the GMPPT searching process remarkably, particularly in weak shading or uniform irradiance condition where the VW will get close to the its minimum value. C. Choice of the Upper Limit of the VW Narrowing the VW will improve the algorithm speed: Whereas the lower limit Vmin is adjusted with respect to the power, the upper limit Vmax (previously fixed to the v = VOC line) would correspond to the maximum possible voltage for global MPP. In this regard, this maximum voltage is investigated through MATLAB Simulink by using 2000 random irradiation values for each of the 20 PV modules connected in series in five different ranges. The cell temperature Tc is estimated by using (1), as detailed in Section II-A. Fig. 5 shows the simulation results for an ambient temperature of Ta = 0 ◦ C. It can be seen that the maximum possible global MPP voltage,


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Fig. 6. Illustration for POT update.

Fig. 5.

Global MPP voltage for 2000 random irradiance values at Ta = 0 ◦ C. TABLE I G LOBAL MPP VOLTAGE VARIATIONS

which is the closest one to the open-circuit voltage, never exceeds 0.887 VOC even under strong uniform irradiance conditions. For higher ambient temperatures than 0 ◦ C, this value reduces proportionally, as shown in Table I. Therefore, a VW upper limit for the VWS algorithm can be fixed at 0.9 VOC conservatively. On the other hand, the slope of the power–voltage curve toward the open-circuit voltage is negative and abrupt, meaning that the algorithm operation in this region would cause significant energy loss. Therefore, reducing the maximum voltage limit of VW to 0.9 VOC excludes most part of this region from the scope of the VW [Vmin , 0.9 VOC ], thus increasing the energy yield of the algorithm. It can be noted that, in practical applications, the maximum MPP operating voltage of the power converter should also be taken into account for the selection of Vmax . D. Discussion on the Algorithm Parameters The proposed algorithm uses the values of both ISC and VOC to define the first triangle POTSTC . Since these values vary significantly with irradiance and temperature, an evaluation of how these variations affect the algorithm operation results is mandatory. Fig. 6 shows a power–voltage curve at uniform solar irradiance of 600 W/m2 . The POTSTC , which does not closely cover the P −V curve, is also shown in the same figure. Let us assume that the PV array is operating at point Q. The minimum Vmin and maximum Vmax values of the VW can be determined using PQ and POTSTC , as explained previously. After measuring the current at Vmin , the algorithm finds point A, as detailed in Section III, and then, a new triangle POT1 can be drawn, as shown in Fig. 6. Unlike the POTSTC , the POT1 closely covers the P −V curve. Hence, the POTs are updated according to the current measurements of the P −V

curve, enabling the algorithm to be effective for all irradiance conditions. On the other hand, the algorithm could also determine the ISC and VOC values by simple measurements instead of using the datasheet values. For example, a tuning procedure can be initiated under moderate uniform irradiances in which the opencircuit voltage can be easily measured at no-load condition since the input port of the power stage usually includes a dc capacitive bus holding the input voltage. Similarly, the shortcircuit current can be measured by short-circuiting the PV cells, provided that the input port of the power stage can operate under short-circuit conditions. Otherwise, the measured current at minimum MPP voltage of the power converter can be taken as a good approximation of the short-circuit current. The measurement procedure can be performed only once during installation or repeated periodically, e.g., once a day, to get the most accurate values for the POT. III. A LGORITHM O PERATING P RINCIPLE The proposed algorithm flowchart is shown in Fig. 7(a) and consists of a local MPPT (LMPPT), a VWS algorithm, whose flowchart is shown in Fig. 7(b), and a decision block in charge of selecting one of these algorithms. While the VWS algorithm looks for an operating point around the global power peak of the power–voltage curve, the LMPPT algorithm takes the operating point from the VWS and finds the global power peak by using conventional techniques. For the present case, the well-known P&O method is chosen as LMPPT because of its simplicity and widespread use. The decision block includes a fixed timer and a suddenpower-change detector. The fixed timer triggers the VWS algorithm in fixed time intervals and ensures that the P −V curve is periodically scanned. The periodic scanning is in charge of detecting local power peak variations resulting from slowly varying atmospheric conditions since they are very difficult to detect by the sudden-power-change detector. However, each periodic scan of P −V curve also causes a certain amount of power loss. It is reported in [39] that a 15-min time interval reduces the unshaded power extraction to less than 0.06%. This is an ignorable power reduction, but the period is too long to

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Fig. 7. Flowcharts of (a) the proposed GMPPT algorithm and (b) VWS algorithm.

follow the GP fast enough. As presented in the next section, the proposed VWS algorithm exhibits a fast convergence to the GP under uniform irradiance condition, thus reducing the losses. On the other hand, in order to quickly react when sudden shading or irradiation change occurs, the power change is inspected by the algorithm via comparing the last two consecutive measurements through a ratio defined as ΔPpv /ΔVpv . If the ΔPpv /ΔVpv ratio at the measured point is higher than a certain threshold value (|ΔPpv /ΔVpv | > threshold), the VWS algorithm is triggered. This ratio can be expressed as follows [3]: ΔPpv /ΔVpv = Ipv + Vpv (ΔIpv /ΔVpv ).

(4)

The algorithm operation in front of sudden changes is illustrated in Fig. 8, where two P −V curves corresponding to higher (curve A) and lower (curve B) irradiances are depicted around the MPP. As shown in Fig. 8, ΔPpv /ΔVpv = 0 at MPP, and under no irradiance changes (i.e., remaining on curve A), the LMPPT algorithm works around the MPP; thus, ΔPpv /ΔVpv will be small in this region (see slope1). In contrast, any P −V curve changes (e.g., curve B) will result in larger ΔPpv /ΔVpv values (see slope2) than the one in normal operation (slope1). Hence, the irradiance changes can be detected by evaluating and comparing ΔPpv /ΔVpv with a threshold level. As it can be seen from (4), the slope of the P −V curve also depends on the operating current, i.e., the operating power. Therefore, in order to obtain a proper operation in all irradiance conditions, the threshold value is defined as a linear function of operating current Ipv , namely,

Fig. 8.

Illustration of the slopes for sudden-shading detection method.

ΔPpv /ΔVpv > kIpv , where k is a parameter adjusted by trial and error according to the desired power change sensitivity of the algorithm. Moreover, in order to prevent false triggering just after completing the VWS algorithm, where the ratio ΔPpv /ΔVpv can be very high temporarily, the decision block should be inhibited until the LMPPT reaches the steady state. A. VWS Algorithm Operation The VWS algorithm operation and its corresponding flowchart in Fig. 7(b) can be explained by referring the P −V


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Fig. 10. Simulink block scheme of the GMPPT system.

is worth to note that this procedure does not depend on the choice of the initial operating point Q and assumes that the power-to-voltage curve does not change during the searching process. IV. E VALUATION OF THE A LGORITHM O PERATION

Fig. 9.

VWS algorithm operating principle: Narrowing the VW.

curve shown in Fig. 9. The variable Pstore is used to retain the highest power measured during the searching process. Assuming an arbitrary starting operating point Q with a power value PQ (then, Pstore = PQ ), the first VW can be found from the POTSTC . Whereas the upper limit of the VW remains constant at Vmax = 0.9 VOC , the lower limit VminSTC can be found in (2) as VminSTC = Pstore /ISC . The search of the global maximum is therefore restricted to the VW of [VminSTC , Vmax ]. The power at point 1 P1 is then checked, and since P1 < Pstore , a new POT, labeled POT1 , is defined as shown in Fig. 9. The new VW is now [Vmin 1 , Vmax ], where Vmin 1 can be found similarly as before by using Vmin 1 = Pstore /I1 , where I1 is the current corresponding to point 1. Then, by using the voltage V1 of point 1, the algorithm computes the voltages defined as v = V1 + kΔVGSTEP ; k = 1, 2, . . . , and checks the minimum voltage falling inside the new VW (i.e., vmin ∈ [Vmin 1 , Vmax ]). The voltage of point 2 fulfills this condition, whereas points a, b, and c are skipped. After checking of point 2, since P2 < Pstore , a new POT, labeled POT2 , is described as shown in Fig. 9. Then, the VW is updated as [Vmin 2 , Vmax ], where Vmin 2 can be found using Vmin 2 = Pstore /I2 . Again, the algorithm computes the voltages defined as v = V2 + kΔVGSTEP ; k = 1, 2, . . . , and selects the minimum voltage inside the new VW. As it can be seen in Fig. 9, point 3 fulfills this condition, and the algorithm checks the power at this point P3 . Since P3 > Pstore , the value of P3 is stored and retained for further comparisons (Pstore = P3 ), and the algorithm checks the next voltage, i.e., V4 = V3 + ΔVGSTEP . Since, for point 4, P4 > Pstore , the value of Pstore is updated again (Pstore = P4 ), and the algorithm checks the next voltage V5 = V4 + ΔVGSTEP . Since, now, P5 < Pstore , a new POT, labeled POT5 , is defined. The new VW is now [Vmin 5 , Vmax ], where Vmin 5 can be found using Vmin 5 = Pstore /I5 . Then, the algorithm computes the voltages defined as v = V5 + kΔVGSTEP ; k = 1, 2, . . .. As it can be seen in Fig. 9, the remaining points (point d and more) are not inside the VW; thus, all are skipped, and the global searching process ends and sends to a conventional LMPPT algorithm the last retained value of Pstore = P4 and the corresponding voltage V4 as the new voltage reference. It

The operation of the proposed VWS algorithm under dynamic irradiation conditions is evaluated through the MATLAB Simulink scheme shown in Fig. 10, which includes the following: 1) the PV string formed by ten series-connected OST-80 PV modules with two bypass diodes per module; the module parameters are taken from [43]; 2) the proposed GMPPT algorithm, which gives at any time the voltage reference to the inverter; and 3) the inverter input port, which is modeled as an ideal controlled voltage source. This source is controlled by a proportional–integral voltage loop [44] in charge of fixing the PV string voltage at the reference voltage given by the GMPPT. The global irradiance is set to 900 W/m2 . For the nonuniform irradiance case, only two PV modules are shaded, and their irradiances are reduced to 400 W/m2 for a certain period of time. In order to make the simulations more distinguishable, the fixed timer trigger period of VWS algorithm and the time constant of the inverter input voltage control loop are selected as 0.25 s and 1 ms, respectively. The details of the algorithm operation are given in the following. A. Case 1: Transition From Uniform to Nonuniform Irradiation Fig. 11(a) shows the power-versus-voltage curves for the transition between uniform (dashed line) and nonuniform (solid line) irradiances. The curve of nonuniform irradiance is also shown in Fig. 11(b) to highlight the algorithm operation. The simulation of the power, voltage, and current of the string depicted in Fig. 11(c) considers that the uniform irradiance takes place during the interval 0 ≤ t < 0.025 s. At t = 0.025 s, the array is partially shaded and remains on this state until the simulation ends at t = 0.37 s. Assuming that the array operates at point Q in Fig. 11(a) during 0 ≤ t < 0.025 s, at t = 0.025 s, the operating point moves from Q to Q just after shading occurs since the array voltage is kept constant by the inverter. The large power difference between the two operating points is sensed by the decision block in Fig. 7(a), which triggers the VWS algorithm, as shown in Fig. 11(c). The VW is calculated through the POT in STC by using the power of the current operating point Q , and then, the voltage of point 1 is checked. The algorithm continuously increases the power until reaching point 8, which corresponds

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to the point of the highest power. In contrast, at point 9, the power is decreased, and then, a new VW [Vmin 9 − Vmax ] is defined. As it can be seen in Fig. 11(a), the subsequent perturbation points a, b, and c are out of the VW. Therefore, the voltage of point 8 is served as a new reference to the LMPPT algorithm which tracks the GP, as shown in Fig. 11(c). Since the array operating point remains on Q, after 0.25 s, the VWS algorithm is triggered by the fixed timer, as shown in Fig. 11(c). Referring to Fig. 11(b) and according to the power level PQ , the minimum voltage VminSTC is calculated, and point 1 is checked at first. Since its power is lower than PQ , a new VW is defined [Vmin 1 − Vmax ], and point a is skipped since it falls outside of the new VW. The VW is updated for points 2, 3, and 4 since their power is also lower than PQ . Again, points b, c, and d are ignored since they are outside of the VW. Accordingly, the algorithm decides that Q is the global power peak in only four steps. B. Case 2: Transition From Nonuniform to Uniform Irradiation

Fig. 11. Algorithm operation for uniform-to-nonuniform irradiance transition. (a) P −V curves for the transition from (dashed line) uniform to (solid line) nonuniform irradiance. (b) P −V curve during the nonuniform irradiance. (c) Power, voltage, and current of the string.

Fig. 12(a) shows the power-versus-voltage curves for the transition between nonuniform (dashed line) and uniform (solid line) irradiances. The P −V curve of uniform irradiance is also shown in Fig. 12(b) to highlight the algorithm operation. The simulation of the power, voltage, and current of the string depicted in Fig. 12(c) considers that the uniform irradiance takes place during the interval 0 ≤ t < 0.025 s. At t = 0.025 s, the array is partially shaded and remains on this state until the simulation ends at t = 0.4 s. Assuming that the array operates at point Q in Fig. 12(a) during 0 ≤ t < 0.025 s when shading is removed at t = 0.025 s, the operating point shifts from point Q to point Q due to the inverter constant voltage operation, as shown in Fig. 12(a) and (c). As for case 1, this power variation is detected by the decision block which launches the VWS algorithm at point Q . After checking point 1, a new VW is defined [Vmin 1 − Vmax ], and point a is skipped since it is outside of VW. The algorithm successively checks points 2, 3, and 4, continuously increasing the power until reaching point 5, which corresponds to the point of the highest power. Points b and c, whose voltages are higher than the upper voltage limit of the VW, are skipped. Finally, the voltage of point 5 is delivered as a new voltage reference for the LMPPT algorithm, which properly tracks the GP, as shown in Fig. 12(c). Since the array operating point remains on Q, the fixed timer launches the VWS algorithm at a fixed rate of 0.25 s, as shown in Fig. 12(c). As previously described in Section III and as shown in Fig. 12(b), the POT in STC is built to determine, from the power level PQ , the voltage of the first point to be tested VminSTC . It can be also noticed from Fig. 12(b) that only three perturbation points are required to check the VW since points a, b, and c are outside the VW and can be skipped. The power corresponding to these perturbation points is not higher than PQ ; therefore, the VWS algorithm does not change the operating point. It should be noted that the PV power slightly decreases during the VWS operation, thus improving the energy yield efficiency of the algorithm.


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Fig. 13. Experimental setup.

Fig. 14. Power–voltage curves programmed in the SAS.

V. E XPERIMENTAL R ESULTS

Fig. 12. Algorithm operation for nonuniform-to-uniform irradiance transition. (a) P −V curves for the transition from (dashed line) nonuniform to (solid line) uniform irradiance. (b) P −V curve during the uniform irradiance. (c) Power, voltage, and current of the PV string.

The performance of the VWS algorithm is experimentally evaluated and compared to the algorithm described in [36]. As shown in Fig. 13, the experiments were conducted on a test bench formed by a PC, a dc programmable load (HP 6060B), and three solar array simulators (SASs) (Agilent E4350B and E4360B). All these devices are controlled by a PC using MATLAB via a General Purpose Interface Bus. The programmable load operates in constant voltage mode and fixes the operating voltage of the SAS. The three SASs are series connected and form a PV array of an open-circuit voltage up to 60 V and a short-circuit current up to 5 A. The experimental behavior of both algorithms has been carried out by programming the SAS for three different irradiance patterns shown in Fig. 14, referred to as curves 1, 2, and 3, which exhibit one, two, and three power peaks, respectively. A fair comparison between both algorithms requires the equivalent parameters to be set at equal values. In this concern, both algorithms include a local P&O MPPT whose perturbation time interval and voltage step are equally set to 0.2 s and 0.4 V, respectively. In the same way, the fixed time trigger period is fixed to 28 s for both algorithms. For detection of sudden irradiance changes, the critical power variation for the algorithm in [36] is set to ΔPcrit = 15 W, whereas the VWS threshold

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TABLE II T RACKING E FFICIENCY AND P OWER C OMPARISON

Fig. 15. Experimentally measured tracking voltage, current, and power for the VWS algorithm.

algorithm in [36] fails due to the low magnitude of power change (i.e., ΔP < ΔPcrit ) and recovers the global search at t = 71 s, owing to the fixed time trigger. In contrast, the VWS algorithm uses the slope method described in Section III and successfully detects the irradiance change even for such small change. On the other hand, at t = 102 s, both algorithms are triggered by the fixed timer. It is clearly seen in Figs. 15 and 16 that the proposed algorithm achieves the global search very fast, with only two perturbations, whereas the algorithm in [36] takes longer time. For comparative quantification purposes, the total extracted energy E and the tracking efficiency ηT are computed for both algorithms from Figs. 15 and 16. These variables are defined as t2 E=

P dτ t1

t2

t2 ηT =

P dτ t1

Pmax dτ

(5)

t1

where t1 and t2 define the computing time interval, P is the extracted power, and Pmax is the maximum power of the PV array at any time. The results are shown in Table II and evidence a superior feature of the VWS algorithm even with the exception of time interval between 60 and 75 s, where the algorithm in [36] loses considerable energy due to the failure in the detection of irradiance change. Fig. 16. Experimentally measured tracking voltage, current, and power for the algorithm in [36].

VI. C ONCLUSION

constant is set to k = 1.9. The power, voltage, and current waveforms obtained from the test are shown in Figs. 15 and 16 for the VWS algorithm and the algorithm in [36], respectively. The curves applied to the SAS during the experiment are also depicted in the same figures. At t = 0 s, according to their operating principles, both algorithms start from nearly 0.8 Voc , and the 150-W GP of curve1 is tracked. At t = 15 s, curve 2 is applied, and both algorithms start a global search and find the global MPP. During the search phase, as can be seen in Figs. 15 and 16, whereas the VWS algorithm does not check voltages below 20 V, the algorithm in [36] goes down to the minimum MPP voltage defined as 5 V. In addition, it should be noted that the power variation during the searching phase in VWS is always higher than 50 W, thus resulting in more energy yield. Similar comparisons can be made for the other transitions. It is important to note that, at t = 60 s, curve 2 is replaced by curve 1 and the detection

This paper has presented a novel GMPPT algorithm, referred to as VWS for string-based PV systems to find the global power peak in any shading conditions. The proposed VWS algorithm has three important features which improve the searching performance: 1) relatively large voltage step, which is nearly equal to the half of the open-circuit voltage of a PV module; 2) the POT, which restricts the VW to be scanned with respect to the operating power; and 3) the capability to skip some perturbation steps by using the POT. By means of these features, the algorithm can complete the scanning of the whole P −V curve with only few perturbations, particularly at uniform irradiation and weak shading cases. Moreover, since the relationships leading to the desired VW around the global maximum power value are simple, the algorithm can be easily implemented into a low-cost microcontroller and can be included in the MPPT software of commercial PV string inverters. The authors believe that, if the number of series-connected PV modules is high, the benefits of the proposed algorithm increase significantly.


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Mutlu Boztepe (M’12) received the B.Sc. degree from Dokuz Eylül University, Izmir, Turkey, in 1991, and the M.Sc. and Ph.D. degrees from Ege University, Izmir, in 1995 and 2002, respectively. He is currently an Assistant Professor with the Department of Electrical and Electronics Engineering, Ege University. His research interests are power electronics, design and control of power converters, and grid integration of photovoltaic systems.

Santiago Silvestre (SM’13) received the M.S. and Ph.D. degrees in telecommunication engineering from the Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, in 1992 and 1996, respectively. He is currently an Associate Professor with the Departamento de Ingenieria Electrónica, Escuela Técnica Superior de Ingenieros de Telecomunicación de Barcelona, UPC. His research interests include modeling and simulation of PV systems, fault detection, and automatic supervisión of PV sytems.

Francesc Guinjoan (M’92) received the Ingeniero de Telecomunicación and the Doctor Ingeniero de Telecomunicación degrees from the Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, in 1984 and 1990, respectively, and the Docteur es Sciences degree from Université Paul Sabatier, Toulouse, France, in 1992. He is currently an Associate Professor with the Departamento de Ingenieria Electrónica, Escuela Técnica Superior de Ingenieros de Telecomunicación de Barcelona, UPC. He has coauthored more than 80 papers in international journals and conference proceedings. His research interests include power electronics modeling and control for renewable energy systems. Dr. Guinjoan was a Guest Coeditor of the Special Issue on “Smart Devices for Renewable Energy Systems” of the IEEE T RANSACTIONS ON I NDUS TRIAL E LECTRONICS in 2011.

Guillermo Velasco-Quesada (S’04–M’09) received the Ingeniero Técnico Industrial en Electricidad, the Ingeniero en Electrónica, and the Doctor en Ingeniería Electrónica degrees from the Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, in 1990, 2002, and 2008, respectively. He is currently an Associate Professor with the Departamento de Ingeniería Electrónica, Escuela Universitaria de Ingeniería Técnica Industrial de Barcelona, UPC. His main research interests include analysis, modeling and control of power systems for renewable energy applications, and grid-connected PV systems based on reconfigurable topologies.

Aissa Chouder received the Ingénieur in Electronics and Magister in Electronics degrees from Ferhat Abbas University, Sétif, Algeria, in 1991 and 1999, respectively, and the Ph.D. degree in electronic engineering from the Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, in 2010. He is currently a Senior Researcher with the Photovoltaic Laboratory, Development Centre of Renewable Energies, Algiers, Algeria. His research interests include power electronics modeling and control for renewable energy systems.

Engin Karatepe (M’08) received the B.Sc. degree from Gaziantep University, Gaziantep, Turkey, in 1995, and the M.Sc. and Ph.D. degrees from Ege University, Izmir, Turkey, in 2000 and 2006, respectively. He is currently an Associate Professor with the Department of Electrical and Electronics Engineering, Ege University, Izmir. His research interests include network integration of distributed power generation, power system analysis, and intelligent system applications to operation and control of renewable energy systems.