Aalborg Universitet. Published in: I E E E Journal of Photovoltaics. DOI (link to publication from Publisher): /JPHOTOV.2012.

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1 Aalborg Universitet A New Tehnique for Traking the Global Maximum ower oint of V Arrays Operating Under artial-shading Conditions Koutroulis, Eftihios ; Blaabjerg, Frede ublished in: I E E E Journal of hotovoltais DOI (link to publiation from ublisher): 0.09/JHOTOV ubliation date: 202 Doument Version Early version, also known as pre-print Link to publiation from Aalborg University Citation for published version (AA): Koutroulis, E., & Blaabjerg, F. (202). A New Tehnique for Traking the Global Maximum ower oint of V Arrays Operating Under artial-shading Conditions. I E E E Journal of hotovoltais, 2(2), DOI: 0.09/JHOTOV General rights Copyright and moral rights for the publiations made aessible in the publi portal are retained by the authors and/or other opyright owners and it is a ondition of aessing publiations that users reognise and abide by the legal requirements assoiated with these rights.? Users may download and print one opy of any publiation from the publi portal for the purpose of private study or researh.? You may not further distribute the material or use it for any profit-making ativity or ommerial gain? You may freely distribute the URL identifying the publiation in the publi portal? Take down poliy If you believe that this doument breahes opyright please ontat us at vbn@aub.aau.dk providing details, and we will remove aess to the work immediately and investigate your laim. Downloaded from vbn.aau.dk on: august 5, 208

2 A New Tehnique for Traking the Global Maximum ower oint of V Arrays Operating under artial Shading Conditions Eftihios Koutroulis, Member, IEEE, and Frede Blaabjerg, Fellow, IEEE Abstrat The power-voltage harateristi of hotovoltai (V) arrays operating under partial shading onditions exhibits multiple loal Maximum ower oints (Ms). In this paper, a new method for traking the global M is presented, whih is based on ontrolling a DC/DC onverter onneted at the V array output, suh that it behaves as a onstant input-power load. The proposed method has the advantage that it an be applied in either stand-alone or grid-onneted V systems omprising V arrays with unknown eletrial harateristis and does not require knowledge about the V modules onfiguration within the V array. The experimental results verify that the proposed global M method guarantees onvergene to the global maximum power point under any partial shading onditions. Compared to past-proposed methods, the global MT proess is aomplished after muh less V array power perturbation steps. Index Terms DC-DC power onverters, Maximum power point traking, Miroontrollers, hotovoltai systems. I I. INTRODUCTION n typial hotovoltai (V) installations, V arrays are formed by onneting multiple V modules in various onfigurations (i.e. series, parallel, series-parallel et.) []. A bypass diode [2] or bypass swith [3] is onneted in parallel with eah V module for proteting the solar ells against effiieny degradation and hot-spot failure effets. Under uniform solar irradiation onditions among the individual V modules, the power-voltage harateristi of the V array exhibits a unique operating point where the V generated power is maximized (Maximum ower oint, M). Many Maximum ower oint Traking (MT) methods have been developed in the past in order to operate the V array at the M point [4], enabling the maximization of the V energy prodution under the ontinuously hanging solar irradiation and ambient temperature onditions. However, in the ase that one or more of the V modules omprising the V array are shaded (e.g. due to dust, shading from surrounding buildings, trees or poles, non-uniform solar irradiation inidene on ontoured flexible V arrays [5] in portable and building integrated V appliations et.), then the power-voltage harateristi of the V array exhibits multiple loal maxima and only one of them orresponds to the global maximum power point. Examples of the power-voltage (-V) harateristis of a V array operating under uniform and non-uniform solar irradiation onditions are depited in Fig.. The V array output power at the global M is lower than the sum of the maximum available power levels that the individual V modules are able to provide [6]. As analyzed in [7], under pratial operating onditions the loation and magnitude of the loal and global Ms depend on the stohastially varying shading pattern area and geometry as well as the onfiguration of the V modules within the V array. The onnetion of V ells and modules in parallel, proposed in [8] in order to avoid the effet of partial shading, is appliable only in low-power V systems (e.g. for portable appliations). Using the distributed MT (DMT) tehnique, a DC/DC power onverter with MT ontroller is inorporated at eah V module of the V array [6, 9], thus inreasing the total available M power of the V array. However, the entire V array is usually onneted to a entral power eletroni onverter in order to redue the V system ost and implementation omplexity []. Under partial shading onditions, the onventional MT tehniques fail to guarantee suessful traking of the global M [0], resulting in signifiant redution of both the generated power and the V energy prodution system reliability []. Aording to measurements performed under real operating onditions of V systems, the power loss due to the MT algorithm onvergene to a loal (instead of the global) M may be up to 70% []. In the 000 rooftop V systems program implemented in Germany, it has been reorded that the operation of the 4% of the installed V systems had been affeted by shading, with energy losses of E. Koutroulis is with the Department of Eletroni & Computer Engineering, Tehnial University of Crete, Chania, GR-7300, Greee ( efkout@eletronis.tu.gr). F. Blaabjerg is with the Department of Energy Tehnology, Aalborg University, Aalborg, DK-9220, Denmark ( fbl@et.aau.dk). Fig.. Examples of the power-voltage harateristis of a V array omposed of idential series-onneted V modules with bypass diodes for different irradiations.

3 2 the order of 0% [2]. The reonfiguration of the onnetions between the individual V modules omprising the V array, using a matrix of power swithes, has been proposed in [3]. The target of this reonfiguration is to form the parallel-onneted strings omprising the V array suh that they onsist of V modules operating under similar solar irradiation onditions. Using this method both the V energy prodution system omplexity and ost are signifiantly inreased. The appliation of the global MT algorithm proposed in [4] requires the haraterization of the V soure after eah partial shading topology has been established. In [5], the equations for the alulation of the loal Ms of partially shaded multi-rystalline silion V modules are provided. In [6], the global M is traked by sanning the -V urve based on information of the V modules open-iruit voltage and their onfiguration on the V array. The global MT methods presented in [7] and [8] are based on the measurements of the V array open-iruit voltage and solar irradiation or short-iruit urrent, respetively. The sequential extremum seeking ontrol algorithm and the Inremental Condutane-based MT method with step-size variation are applied in [9] and [20], respetively. A ommon drawbak of these methods is that they require knowledge of the eletrial harateristis of the V modules and/or their onfiguration within the V array. Thus, they are not really appliable for the development of ommerial V power proessing interfaes, where both the V array onfiguration and the V modules eletrial harateristis applied by the end-user are generally unknown. Additionally, the auray of the alulations is affeted by the V modules eletrial parameters deviation due to aging. The use of speialized sensors (e.g. for the measurement of solar irradiation) inreases the V system ost, while on the other hand during the measurement of the V array open-iruit voltage or short-iruit urrent the V energy prodution is suspended. In [2], a radial basis funtion and a three layered feedforward neural network are used to trak the global M, having the disadvantage that the MT ontrol system implementation omplexity is highly inreased. Additionally, onsiderable omputational efforts are required during the neural network training in order to ensure that the global MT proess will be performed reliable and aurate under any shading onditions. The MT algorithm based on a Fibonai sequene [22] does not guarantee onvergene to the global maximum power point. The artile Swarm Optimization (SO) [23], Geneti Algorithms (GAs) [24] and Differential Evolution (DE) [25] global MT approahes and the stohasti algorithm based on the haos searh theory, whih is presented in [26], exhibit signifiant algorithmi omplexity, whih inreases the implementation ost of the global MT ontrol system. The detetion of loal Ms using a periodi san sequene of the -V urve is frequently employed in ommerially available V power onditioning devies [27]. Due to the long time required for the ompletion of this proess, the V Fig. 2. The operating priniples of global MT methods. energy prodution is redued. A global MT sheme based on the DIviding RECTangles (DIRECT) optimization algorithm is proposed in [28], having the advantage of avoiding the omputation of the -V funtion gradient. However, it is not guaranteed that under any partial shading onditions the onvergene to the global maximum power point will be ahieved in fewer steps than an exhaustive searh proedure sanning the entire -V urve. The algorithmi omplexity and traking ineffiieny of the methods desribed above arise beause these methods are based on searhing for the global M by iteratively ontrolling the operating voltage of the V array load aording to the orresponding MT algorithm. As illustrated in Fig. 2, the resulting operating point of the V array lies on the intersetion of the V array and load powervoltage harateristis (e.g. points A and A 2 ). Thus, the past-proposed algorithms are unable to guarantee the disrimination between loal and global Ms, unless the V array output power is measured at a large number of operating points, spread over the entire voltage range of the V array. In this paper, a new method for traking the global maximum power point of V arrays operating under partial shading onditions, in either stand-alone or grid-onneted V systems, is presented. The V array is onneted to a DC/DC power onverter, whih is ontrolled by a miroontrollerbased ontrol unit. Initially, the power onverter is ontrolled to operate as an adjustable onstant input-power load. With referene to the power-voltage harateristis depited in Fig. 2, starting from the V array open-iruit ondition (point B ), the DC/DC onverter is ontrolled to draw a suessively higher amount of power. Hene, the V array operating point is progressively moved towards higher output power levels (points B, B 2, B 3, B 4 and B 5 ). It is observed that using this proess, the proposed algorithm avoids getting trapped in the loal M (point B l in Fig. 2) and suessfully detets the existene of the V array operating points B 4 and B 5, whih provide higher output power ompared to the loal M, without performing a V-urve sanning proedure over a wide voltage range. This proess is ontinued until onvergene to point B 6 is deteted, where the V array output power inrement is inhibited. This ondition indiates that the previous V array operating point (i.e. B 5 in Fig. 2) provides the maximum possible V array output power, thus orresponding to the global M. Then, the DC/DC onverter is ontrolled suh that the V array output voltage is regulated

4 3 to the global M point ( B 5 ) deteted in the previous phase of the algorithm. The experimental results presented in this paper verify that using this method enables the suessful detetion of the global M irrespetively of the number of loal Ms exhibited by the V array power-voltage harateristi and their loation relative to the global M. The global MT detetion proedure desribed above is exeuted periodially (e.g. every -5 min). Then, the erturb and Observe (&O) MT proess is applied in order to ontinuously trak the short-term variations of the previously deteted global M. Aording to [27], the iterative appliation of a V-urve san sequene with a 5 min san interval, results in a less than 0.06% maximum energy loss on un-shaded arrays. As it will be demonstrated in the experimental results, the proposed global MT proess is less time-onsuming than the V-urve sanning method. Thus, the periodi exeution of the proposed global MT proess does not result in signifiant energy loss in the ase that the V array is atually un-shaded. The &O MT algorithm has been seleted beause of its implementation simpliity, flexibility and robustness [29]. However, any of the past-proposed MT algorithms [4] an also be applied in order to onform with speifi V system design speifiations. Compared to the past-proposed global MT tehniques, the method presented in this paper has the advantage that it does not require knowledge of the eletrial harateristis of the V modules and their onfiguration within the V array. In the following setions of this paper the proposed global MT system is first analyzed in details and then validated by experimental results. II. THE ROOSED GLOBAL MT SYSTEM A detailed diagram of the proposed global MT system is depited in Fig. 3. Depending on the V system appliation domain, a Buk-type DC/DC power onverter is used to interfae the V array output power to either a battery bank or a DC/AC inverter onneted to the eletri grid [30, 3]. Both of these alternative types of DC/DC onverter load are represented in Fig. 3 by the voltage soure V o. The indutane of the able onneting the V array to the DC/DC onverter, Fig. 3. A detailed blok diagram of the proposed global MT system. Fig. 4. The prinipal waveforms of the proposed global MT system. L in, is onsidered for stability analysis purposes, as disussed below. The indutor, L, and the input and output filter apaitor values, C in and C, respetively, are alulated as desribed in [32] suh that the DC/DC onverter operates in ontinuous ondution mode and, simultaneously, the input and output voltage ripple fators are redued to an aeptable limit. The V array voltage is measured using an operational amplifier-based differential amplifier and the DC/DC onverter input urrent is measured with a Hall-effet-based urrent sensor. The proposed global MT proedure is performed in three onseutive phases; the onstant inputpower, V array voltage regulation and &O stage, respetively. In order to exeute these proesses, the DC/DC power onverter is ontrolled using either the WM # or the WM #2 ontrol signals depited in Fig. 3, whih are produed as analyzed in the following. A. DC/DC onverter onstant input-power mode In this setion, the DC/DC onverter operation and ontrol, suh that it behaves as an adjustable onstant input-power load, is presented. The operation of the DC/DC onverter in this operating mode onstitutes the basis for the detetion of the V array global M, aording to the proposed global MT ontrol algorithm. The input-output voltage relationship of a Buk-type DC/DC onverter is the following: ton V o = D V = V () Ts where V and V o (V) are the DC/DC onverter input and output voltage levels, respetively, D is the onverter duty yle ( 0 D ), T s is the swithing period and t on is the ON time of the power MOSFET WM ontrol signal. The WM # ontrol signal, depited in Fig. 3, is produed by omparing the instantaneous value of the DC/DC onverter input urrent, i(t) in with the ontrol signal V(t) generated by the ontrol unit. The orresponding waveforms are plotted in Fig. 4. The average value of i in (t) is equal to the V array DC output urrent, I (A) and it is given by: 2 ton V -Vo V -Vo ton I = I + t dt= It on + T 0 s L Ts Ts L 2 (2) Sine i in(t on )=V (t ), the value of I in (2) is alulated on

5 4 using (), as follows: V -Vo Vo I + t = I + T -t =V (t )= I L L Vo I =V (t on )- Ts -ton L on s on on 2 Combining (2) and (3), the DC/DC onverter average input power, (W), is alulated using the following equation: VT Vt = VI = V (t on )Vo - + 2L 2L 2 2 o s o on In the proposed method, the values of V(t) and (3) (4) V are Vo seleted suh that V(t)=V - t, thus resulting in: 2L 2 VT o s =VVo - (5) 2L where V is a DC ontrol signal of adjustable amplitude, produed by the ontrol unit aording to the global MT algorithm analyzed in the next setion. The DC/DC onverter output voltage, V o, depends on either the slowly-hanging battery state of harge (in standalone appliations) or the eletri-grid voltage (in gridonneted V systems) and remains approximately onstant during the onseutive steps of the global MT proess. Sine the values of T s and L are also onstant, it is onluded from () and (5) that for V V o the DC/DC onverter input power an be regulated to the desired level by adjusting the amplitude of the V ontrol signal (onstant input-power mode of operation). The urrent-voltage harateristis of the V array and DC/DC onverter operating under partial-shading and onstant-input-power onditions, respetively, are depited in Fig. 5. The points of intersetion (i.e. points A, B, C et. in Fig. 5) define the equilibrium operating points of the interonneted V array-dc/dc onverter system. ratially the able indutane, L in, is negligible. Thus, aording to the stability analysis presented in [33], whih has been performed for a V array onneted to a onstant-power load (e.g. a swithing power onverter with regulated output voltage) in a spaeraft power proessing system, the points A, C, E and F in Fig. 5 are stable, while points B and D are unstable. The points A, C, E and F in Fig. 5 orrespond to the points B- B 6 and B l of the -V urve depited in Fig. 2. In the proposed method, the global M is traked by ontrolling the DC/DC suh that it behaves as a onstant input-power load and simultaneously the V array operates at the stable operating points A, C, E and F, aording to the algorithm analyzed next. B. The Global Maximum ower oint Traking Algorithm A flow-hart of the proposed global MT ontrol algorithm is shown in Fig. 6. Initially, the global MT proess is performed in order to detet the position of the global maximum power point of the V array. During that phase of the proposed algorithm, the power onverter ontrol method is set suh that the power onverter operates as an adjustable onstant input-power load, as analyzed in the previous setion. The power drawn by the DC/DC onverter (i.e. the V array output power) is iteratively inreased by appropriately adjusting the amplitude of the V ontrol signal output by the D/A onverter, as follows: V ( k ) =V ( k ) +ΔV (6) where V ( k ), V ( k ) are the V signal values at steps k and k-, respetively [initially V(0)=0] and ΔV is the onstant perturbation applied. Inreasing the value of ΔV in (6) results in a redution of the time required to detet the V array global M, but also to redue the ability of the algorithm to disriminate loal and global Ms of similar power levels. At eah step, the V array operating voltage is measured and stored in the miroontroller memory. This proess is repeated until the operating point of the interonneted V array- DC/DC onverter system moves to point B 6 depited in Fig. 2, where the V array output power inrement is inhibited. This ondition indiates that the V array output power measured during the previous step of the algorithm orresponds to the global M. Then, the DC/DC onverter duty yle is iteratively redued until the V array output voltage is regulated to the global M. Only the V array output voltage is measured in order to perform this proess. Fig. 5. The urrent-voltage harateristis of the V array and the DC/DC onverter operating under partial shading and onstant input power onditions, respetively. Fig. 6. Flow-hart of the proposed global MT ontrol algorithm.

6 5 The proedure presented above is applied periodially (e.g. - 5 min) for deteting the position of the global M of the V array. Then, the &O MT algorithm is exeuted in order to maintain operation at the previously deteted global M during the short-term variations of solar irradiation and ambient temperature onditions. During the &O MT proess, the DC/DC onverter average input power is alulated by measuring the V array output voltage and urrent. The resulting value is ompared with the input power measured during the previous iteration of the algorithm. Aording to the result of the omparison, the duty yle of the WM #2 DC/DC onverter WM ontrol signal, depited in Fig. 3, is modified as follows: D k = D k-+δdk (7) ΔD =C sign ΔD sign( - ) where k k -,k,k - ΔD k is the duty yle hange at step k,,k and,k - are the V array output power levels at steps k and k-, respetively, C is a onstant determining the speed and auray of onvergene to the M point and the funtion sign(x) is defined as: sign(x)=, if x 0 (8) sign(x)= -, if x < 0 The duty yle is hanged ontinuously aording to the &O algorithm, resulting in steady-state operation around the global M. A method for the optimal seletion of the parameter C in (7) is desribed in [29]. III. EXERIMENTAL RESULTS A laboratory-prototype global MT system operating aording to the proposed methodology has been developed and tested under outdoor onditions. The ontrol unit of the proposed global MT system, whih is illustrated in Fig. 3, has been built around the Atmel AVR ATMEGA8535 miroontroller, whih features a 0-bit, 8-hannel, A/D onverter and on-hip 8-bit WM outputs. The swithing frequeny of the WM #2 ontrol signal has been set to 3.25 khz. The V array whih has been used onsists of three V modules onneted in series with a bypass diode in parallel with eah module. The M power and voltage ratings of eah V module under Standard Test Conditions (STC) are 5 W and 7.82 V, respetively. For performane validation purposes, the Buk-type power onverter output has been onneted to a 2 V / 7 Ah lead-aid battery. Also, the V modules omprising the V array were installed at different tilt angles suh that they reeive unequal amounts of solar irradiation. Thus, the resulting power-voltage harateristi of the V array exhibits both loal and global Ms. Initially, the V modules were installed suh that the global M is loated at a higher voltage ompared to the loal Ms (test ase #). The orresponding power-voltage harateristi of the V array was experimentally measured using a V-urve san proess and it is plotted in Fig. 7(a). Then, the proposed global MT method was applied. The experimentally measured operating points of the V array during the exeution of the proposed global MT proess (i.e. points - 2 ) are also indiated in Fig. 7(a). The minimum possible operating voltage of the V array is V, sine a disharged battery has been onneted at the DC/DC onverter output terminals. The global M detetion proess was initiated, setting the V array in an open-iruit operating ondition (point ). By progressively inreasing the value of the ontrol signal V, the DC/DC onverter was ontrolled suh that it draws an inreasing amount of power, thus ausing the suessive movement of the V array operating points in the trajetory At point 6 the next inrement of the DC/DC onverter input power moved the V array operating point at 7 ( V, 3.03 W). The resulting redution of the V array output power was sensed by the miroontroller-based ontrol unit, provoking the DC/DC onverter operation in the voltage regulation mode. Thus, the DC/DC onverter WM ontrol signal duty yle was iteratively redued until the V array operating point was restored at point 2 (52.9 V, 7.44 W), where the highest V output power was measured during the previous phase of the algorithm, through the trajetory Then, the exeution of the &O MT algorithm was initiated, resulting in a ontinuous osillation of the V array operating point around the previously deteted global M (i.e. point 2 ). During the &O MT proess, the maximum deviation of the V array operating power from the global M has been experimentally measured to be equal to 0.43 %. In order to validate that the proposed global MT method is equally effiient, irrespetively of the relative position of the loal and global Ms, the V modules were also installed (a) (b) Fig. 7. The experimentally measured power-voltage harateristi of the V array and the V array operating points during the operation of the proposed global MT system, in ase that the global M is loated at: (a) higher voltage (test ase #) and (b) lower voltage (test ase #2), ompared to the loal Ms.

7 6 suh that the global M is loated at a lower voltage ompared to the loal Ms (test ase #2). The resulting power-voltage harateristi of the V array was experimentally measured using a V-urve san proess and it is illustrated in Fig. 7(b). Then, the proposed global MT algorithm was exeuted. The experimentally measured operating points of the V array during the exeution of the proposed global MT proess (i.e. points - 8 ) are also depited in Fig. 7(b). During the global M detetion phase of the proposed algorithm, the V array operating point is ontinuously displaed, following the sequene In the test ase presented in Fig. 7(b), the global M is loated at the minimum possible operating voltage of the V array (i.e. V). Thus, at ( V, 7.45 W) the next inrement of the V ontrol signal 7 TABLE I EXERIMENTALLY MEASURED NUMBER OF V ARRAY OWER ERTURBATION STES REQUIRED TO DERIVE THE GLOBAL M roposed algorithm V-urve san artile Swarm Optimization (SO) does not alter the V array operating onditions, indiating that the resulting point, 8 ( V, 7.45 W), is the global M. During the voltage-regulation mode initiated next, the V array operating point was held at the global M point deteted at the previous step (i.e. point 8 ). Then, the &O MT proess was performed in order to trak the short-term variations of the global M. Due to the osillations inherent in the &O MT proess, the maximum deviation of the V array operating power from the global M in this test ase has been experimentally measured to be equal to 0.08%. In both of the test ases analyzed above, the proposed global MT algorithm suessfully avoided getting trapped in loal optima and ahieved onvergene to the global maximum power point of the V array. The miroontrollerbased ontrol unit of the laboratory-prototype global MT system was also programmed for traking the V array global M in the two test ases desribed above aording to the V-urve san sequene [27], artile Swarm Optimization (SO) [23] and Differential Evolution (DE) [25] methods. Only the WM #2 ontrol signal (Fig. 3) has been used for that purpose. In the V-urve san sequene algorithm, the duty-yle perturbation step has been set equal to that of the proposed algorithm [parameter C in (7)]. The values of the parameters affeting the operation of the SO and DE algorithms (e.g. number of agents in the SO method, termination riterion et.) have been set as desribed in [23] and [25], respetively. All algorithms suessfully deteted the position of the global M. The experimentally measured numbers of the V array power perturbation steps required by eah algorithm in order to derive the global M are given in Table I. It is observed that ompared to past-proposed Differential Evolution (DE) Test ase # Test ase # methods, using the algorithm presented will result in a muh faster onvergene to the global M. IV. CONCLUSION The detetion of global M is indispensable in order to maximize the V system energy prodution in the ase of V array partial shading. In this paper, a new method has been presented for traking the global M of V arrays in either stand-alone or grid-onneted V systems, whih is based on ontrolling the DC/DC power onverter onneted at the V array output suh that it behaves as a onstant input-power load. Compared to the past-proposed global MT tehniques, the method proposed in this paper has the advantage that it an be applied in V arrays with unknown eletrial harateristis and does not require knowledge of the V modules onfiguration within the V array. The experimental results verify that the proposed method guarantees onvergene to the global M under any partial shading onditions. Additionally, the global MT proess is aomplished with signifiantly less V array power perturbation steps than those obtained using past-proposed tehniques. The proposed method an easily be inorporated into any existing MT ontrol system in both high nominalpower-rating V systems and low-power energy harvesting appliations. ACKNOWLEDGMENT Dr. E. Koutroulis thanks his former graduate student Mr. Y. Kalogiannakis for his ontribution during the laboratoryprototype onstrution and experimental measurements. REFERENCES [] H. Ghoddami and A. Yazdani, A Single-Stage Three-hase hotovoltai System With Enhaned Maximum ower oint Traking Capability and Inreased ower Rating, IEEE Transations on ower Delivery, Vol. 26, No. 2, pp , April 20. [2] S. Dongaonkar, M.A. Alam, Y. Karthik, S. Mahapatra, Dapeng Wang and M. Frei, Identifiation, haraterization, and impliations of shadow degradation in thin film solar ells, in 20 IEEE International Reliability hysis Symposium (IRS), pp. 5E.4.-5E.4.5, 20. [3] G. 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