Adaptive Distributed MPPT Algorithm for
Photovoltaic Systems
F. Scarpetta, M. Liserre, and R. A. Mastromauro
Department of Electrical and Electronic Engineering
Politecnico di Bari, Italy
[email protected], [email protected], [email protected]
Abstract - Fast change of the irradiance conditions entails
failure of the maximum power point tracking (MPPT) algorithm
in a photovoltaic system (PVS). In this paper it is proposed the
combination of a modified Perturb and Observe (P&O)
distributed MPPT and an adaptive algorithm. The MPPT has
been tested in case of hard mismatch conditions through
simulation showing high performance in terms of efficiency.
I. INTRODUCTION
Partial shading, and consequently mismatch, among photovoltaic (PV) modules represents one of the main causes of PVS mlssmg power production [1-2], [4]. Since mismatching leads to a MPPT efficiency decrement, the integration of the MPPT inside each PV panel is the frontier of this technology. There are several MPPT methods, which require different implementations depending on PVS
topology: single-stage or double-stage. In case of a doublestage conversion system the MPPT technique is used to control the DC/DC converter (the parallel connection of the MPPT can allow higher efficiency [9]), while in case of single-stage conversion system the MPPT is included in the DC/ AC converter control. A distributed MPPT (DMPPT) can be performed by means of a DC/DC converter inside each PV panel [10-12] or on the DC/AC converter unit integrated in each PV panel. It allows an improvement of the PVS power efficiency. Among the various MPPT techniques, the Perturb and Observe algorithm is one of the best compromises between implementation simplicity and reliability [8]. Otherwise, in case of rapid irradiance changing conditions, the P&O algorithm may result unstable. Many solutions, such as the Estimate-Perturb-Observe method [4], the dP-P&O
method [2] and the adaptive algorithm [ I], can be found in literature trying to improve the tracking performance. The application is on the PVS DC/AC converter. In this paper the dP-P&O MPPT is applied to the control of the DC/DC converter in case of distributed MPPT. By combining this MPPT with an adaptive algorithm, it is possible to obtain a fast response and a high efficiency also in case of rapid change of irradiance conditions. The behavior of a PVS where the panels are working under different level of shading is simulated in this paper and a performance comparison among traditional P&O, adaptive P&O and the adaptive dP-
P&O MPPT for fast changes of irradiance conditions is operated. In particular in Section IT the effects of mismatch on the PVS performance are analyzed; a brief introduction of DMPPT is reported in Section TIT; suggestions about the possible modification of the traditional P&O are detailed in Section IV; finally, the proposed adaptive dP-P&O MPPT for fast changes of irradiance conditions is described in Section V. The PVS model and the comparison results are shown, respectively, in Section VI and in Section VIT.
IT. THE MISMATCH EFFECT
PV panels are usually equipped with one or more bypass diodes (Fig. I ). Although the bypass diodes allow higher currents by adding a path in the circuit, they alter the power curve shape in case of irradiance mismatch. Fig.2 shows how
the mismatch irradiation affects the P-V curve shape of the PVS. Assuming the operating point located on the maximum peak, the power extraction is not optimal because happens that the shadowed panel needs a lower current to work in its maximum point thus reducing the power from the irradiated panel (Fig. 3). The reduction of power is higher (up to � 60%) in case of hard mismatch.
lilli/ t v�
Fig. I. PVS with panels connected in series and equipped with bypass diodes.
Voltage [Vj Fig. 2. Mismatch effect on the power-voltage curve of a PV array
connected in a 2x I matrix.
978-1-4673-2421-2/12/$31.00 ©2012 IEEE 5708
(I) " o "-
Voltage [VI Voltage [VI
Fig. 3. Power extracted from the irradiated (left) and shadowed (right) panel.
m. DISTRIBUTED MPPT
Tf the PVS is connected directly to an inverter with MPPT function included (Fig. 1) or in case a centralized DC/DC converter is used, the MPPT will not extract the maximum power under mismatch conditions due to the reasons shown before. The MPPT algorithm fails to track the right maximum power point due to the presence of relative peaks. Tn order to improve power extraction a distributed topology, with a boost converter for each panel and with its own MPPT algorithm, should be adopted [10] (Fig. 4). The main effect provided by the addition of a boost converter for each panel is the external P-V curve smoothing, hence there is just a sole maximum power point. Furthermore, assuming to work in this point, the power extracted from each panel is the maximum possible (Fig. 5).
10 20
Fig. 4. PVS with DMPPT.
30 40 50 60 Voltage [Vj
70 80
Fig. 5. P-V curve smoothing provided by the distributed DCIDC converters.
TV. P&O MPPT IMPROVEMENTS
The P&O method is based on the following criterion: the duty cycle of the boost DC/DC converter is perturbed and, as
long as the power drawn from the system increases, the direction of perturbation does not change. It results:
D(k+2)=D(k+l)+a, P(k+2»P(k+l),D(k+l»D(k) (1) D(k + 2) = D(k + 1) -a, P(k + 2) > P(k + 1), D(k + 1) < D(k)
where D is the duty cycle, a is the increment/decrement step and P the measured power. Otherwise, if the power drawn decreases, the sign of perturbation changes:
D(k+2)=D(k+l)+a, P(k+2) <P(k+l),D(k+l)<D(k) (2) D(k + 2) = D(k + 1) -a, P(k+ 2) < P(k + 1), D(k + 1) > D(k)
A. Adaptive MPPT algorithm
Since the P&O method needs a good compromise between dynamic response and steady-state performance, the incremental step of the duty cycle can be automatically adjusted. Tn [1] the tuning of the step is controlled as follows:
a(k)=M� a(k -1)
(3)
where ark) is the step of duty cycle at time k. The incremental step depends upon the historic value of step ark-i), the measure of the power variation LJP = P(k)-P(k-i) and the gain M. By choosing the right value of M and limiting the variation range of the step, it can be obtained the best performance, with the highest value of the increment when the working point is far from the target, and the lowest one In steady-state conditions.
B. Fast trackingfor irradiance changing conditions
It is known that the P&O methods may fail to track the optimal point by choosing the wrong direction during rapidly changing irradian ce, especially on cloudy days. Tn [2] it is proposed a solution, called "dP-P&O" method, which determines the right direction by adding a measurement (Px)
taken in the middle of the MPPT sampling period (Fig. 6). The application which can be found in literature is in case of PVS DC / AC power conversion stage. The following assumptions are considered:
1) The effect of perturbation on power curve is over when Px is taken;
:v " o "-
t kT kH T/2
Time [sl (k+1)T
Fig. 6. The dP-P&O method principle.
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2) The variation of environmental phenomena (irradiance, temperature) is constant during a sample time.
The power variation dP is evaluated as the difference between the change due to the perturbation of the duty cycle plus the environmental variations (dP]) and the variation due only to environmental conditions (dP2):
In the example shown in Fig. 6, the irradiance (and consequently, the power) increment does not affect the value of dP, which is negative. The advantage of this method is the possibility, in case of rapidly irradiance changing conditions, to switch rapidly between two control modes as illustrated in the next Section.
V. ADAPTIVE dP-P&O MPPT FOR FAST CHANGE TRRADIANCE CONDITIONS
An adaptive fast changing dP-P&O algorithm is implemented in this paper in case of application to a DC/DC distributed MPPT: as long as dP2<dP+Thr (where Thr is a fixed threshold) the traditional P&O MPPT method is used, since the environmental changing conditions are negligible, in this case the sign of perturbation is chosen equal to that of dP2• Tn case of high irradiance variations, the MPP impedance tends to lower values thus the duty cycle must increase (positive slope) in order to follow the new target and vice versa. Tn the example shown in Fig. 7, the tracking point moves from ' l' to '2' along a low-irradiation power curve: in
case of sudden irradiance increasing, this point shifts from '2' to '3' on the right side of the new, high-irradiation power curve, hence the correct tracking direction changes.
Combining the advantages of an adaptive algorithm with the dP-P&O, it is possible to pursue the MPP tracking despite environmental variations, for example during cloudy days. Tn Fig. 8 the complete flowchart of the proposed algorithm is illustrated. Voltage and current of the panel are sampled at TI2 seconds with respect to MPPT algorithm, sampled at T seconds, in order to take the additional sample (Px) during a period. The slope defines the tracking direction: if the environmental variations are predominant IdP21> IdPI
+ Thr, the slope sign of duty cycle is maintained.
� :u ;: 0 0..
225
200 P-V curve variation with 175 irradiance increasing 150
125
100
75
50
15 20 25 30 40
Voltage [Vj Fig. 7. Effect of sudden irradiance increasing on the MPP tracking
direction.
The automatic tuning of the increment/decrement step a takes place independently.
1. PVS DC POWER STAGE MODEL
The operation of the PVS shown in Fig.9 has been emulated testing both the traditional P&O and the proposed modified adaptive dP-P&O algorithm in order to compare the efficiency performances. The PVS is directly connected to a DC load of � (12 0), hence the DC/AC power stage IS
avoided in the model. The boost DC/DC converter used for testing is a
Synchronous boost with two power mosfets Ixys® n-channel, Coilcraft® inductor of IOOIlH (DC Resistance 32mO, Panasonic® electrolytic input capacitor of 120llF (internal resistance of 45mO), output capacitor of 220llF (resistance 30mO).
Fig. 8. Flowchart of the adaptive dP-P&O MPPT for fast changes of irradiance conditions.
Fig. 9. Operation of the PVS connected to a DC load.
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The commutation deadband time between the mosfets has been set at � (123 ns), taking into account the delay and rise/fall time of the transistors. The switching frequency is 40 kHz. An "average" model of the DC/DC converter has been used for simulation (Fig.lO) in order to reduce the high computational burden due to the high switching frequency, hence, for this purpose the power mosfets have been replaced by a current and a voltage controlled sources.
inductor Vcp=Vac*D(1-D) p
Fig. 10. Average model of the Synchronous Boost DCIDC converter.
The node a (active), p (passive) and c (common) of the circuit of Fig.1 0 are related to each other by the controlled sources; D indicates the duty cycle (amount of power transmitted to the output port); Req takes into account all the dissipative effects of capacitor, inductor and switches and it depends on duty cycle value.
The solar panel considered for simulations is one 220W Solsonica610 with 60 cells in series and 3 bypass diodes. The output current T of the panel, as known, is ("one diode
model"): [ q(V+TR,) ) V + TR T = T - T e nKT _ \ ____ S
ph 0 R p
(5)
Tph is the photocurrent (which depends on irradiation and temperature [5-6]); To is the reverse saturation current and it depends on temperature and n (ideality factor) [7]. The parameters characterization of R" Rp and n, proposed in [3], is based on a iterative method which gives the following results: R, = � (0.390), Rp = � (25330), n = � (1.18), To stc (reverse
saturation current in standard condition) = � (9.11 e-9 A).
IT. STMULATTON RESULTS
The dynamic response of the PVS shown in Fig.9 is firstly compared to a traditional, centralized MPPT algorithm performed into the inverter as shown in Fig.l. The assumption is that both the panels are fully irradiated (1000 W/m2) and they are at the same temperature (25°C). The impedance (at the inverter input) is set at 2 0.
When a mismatch condition, as shown in Fig.2 happens, the inverter fails the MPP tracking, matching the first relative maximum (about � 200 W) without reach the absolute maximum (Fig. I I ).
220 � Power Oi ;;: 0
a.
a Lf) x S <lI u c rn
"0 <lI Q. � 7 8
Voltage [V]
Fig. 11. Power / Impedance versus Voltage of a Centralized MPPT algorithm.
100 F========�==::::::::::-;;;;;::::::::--1 90
'* 70 � 60 u � 50
·u tE 40 w 30
20 100.'------,OCC.2,------="0.4.,-------,,0"=".6--...,OCC.8,--------'
Duty Cycle [%]
Fig. 12. EtlIciency versus Duty cycle of the synchronous Boost DCIDC converter.
With a distributed topology (Fig.9) it is possible to match the absolute maximum starting from the same conditions. Simulation results highlight that it is possible to extract all the available power (220 W from each panel, as reported in the panel datasheet) with duty cycle equal to just 19%. In Fig.12 the efficiency of the synchronous DC/DC converter is shown for different values of its output impedance: when it operates with duty cycle equal to 19% the losses are about � 3%.
Fig. 13 shows the extracted power and the duty cycle in case of DMPPT P&O algorithm: at 1.3 seconds, one of the two panel results shaded at � 800 W/m2, then the P&O
algorithm continues to work independently following the new MPP � 400W which is double in comparison with the traditional centralized MPPT. What it happens can be described by means of the power-voltage curve (Fig. 14).
When both panels are fully irradiated, the load parabola intersects the power curve in the linear part (' I ' ). If one panel is shaded, the new working point jumps on a temporary dashed curve ('2 ' ) at � 19% of duty cycle and finally reaches the new steady state ('3 ' ): in both conditions the power curves present only one peak.
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� Oi ;;: 0 a.
� ClJ
U >-u .2:-::J 0
250
200 Panels fully irradiated at lOOOW/m'
150 Power recovery when one panel is shaded (800W/m')
100 04 0.6 0.8 1.2 14 1.6 1.8 2.2
Time [sl a)
30
04 06 08 12 14 16 18 22
Time [sl b)
Figs. 13. DMPPT P&O algorithm performance in case of 20% mismatch: a) power; b) DCIDC converter duty cycle.
Oi ;;: o a.
500
Voltage [VI
Fig. 14. Power-Voltage curve in case of 20% mismatch.
Respect to the traditional P&O MPPT, the adaptive P&O
algorithm has the advantage to speed up the MPP tracking when the working point is far from the target. However, in case of fast irradiance variations, a larger step of the duty cycle may cause tracking failure. Considering a hard mismatch case by choosing very different irradiance signals for the two panels, as shown in Fig. 15, it can be seen that the adaptive algorithm can choose the wrong direction leading to power losses (Fig. 16).
The proposed adaptive dP-P&O MPPT algorithm for fast
changes of the irradiance conditions, shown in Fig. 8, is tested under the following assumptions: the step 'a' is limited in the range 0.01 - 0.05; the constant parameter M is chosen equal to 5-5 in order to compensate the power variation. It results that the efficiency can reach � 99.7%, while in case of the adaptive P&O the efficiency is � 98.2%, (Fig. 17) allowing an optimal and fast MPP tracking in comparison with the previous cases.
Oi ;;: o a.
� Oi ;;: 0 a.
�
: " : : . ··;� ···················· ;i
·····················+ ······ ............... ; ........................... , ....................... ;:................ I
Time [sl
Fig. 15. Trradiance signal profile chosen for the two panels.
400
350
300
Extracted power
250 0 3 4 5
Time [sl
Fig. 16. PVS maximum power versus extracted power in case of adaptive P&O (sample time 30ms).
400
6
Oi 350 ;;: o a.
300 power
250 o 4 6
Time [sl Fig. 17. Power extracted with the adaptive dP-P&O MPPT algorithm
for fast changes of the irradiance variations (sample time 30ms).
Finally, it is considered a traditional P&O DMPPT working with a half sample time: 15 ms in despite of 30 ms. The aim is to demonstrate how the choice of a higher sample frequency is irrelevant and the system keeps to follow wrong tracking direction during rapid variations of irradiance. Fig. 18 shows the irradiance profile chosen for this test: one of the two panels is constantly irradiated until 3s, when shadows cover the panel and causes an abrupt decrement.
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Oi ;;: o a.
- - �
.. ...
U�
"' us
... ...
o_�� PAAEl2(SHADOWJ
� ::/
/ / /'" / / v /
.. / / "' V ; /
,
'. , , ,
Time [s]
Fig. 18. Irradiance signal profile chosen for the two panels.
50
°0L-----�----�2------�3 ------4�---- �5�----� 6
Fig. 19. PVS maximum power versus extracted power in case of adaptive, high frequency P&O (sample time 15ms).
°0�----�----�2�----�3------�4------�5----�6
Fig. 20. Improved tracking of power with the adaptive dP-P&O algorithm (sample time 30ms).
The MPP tracking of the adaptive, high frequency algorithm without dP-P&O is shown in Fig.19: as it is expected, the sudden irradiance variations shift the operating point back and forth around the MPP (as seen in Fig. 7).
Tn the same mismatch conditions but with an higher sample time (30ms), the dP-P&O algorithm has been enabled in the boost dc/dc converters: it has been demonstrated that the tracking performances are better than in the previous case and the efficiency is around 99% (Fig. 20). This result is possible since, even if the duty cycle step width is high, the algorithm allows the tracking of the right direction ensuring a fast and accurate power recover.
.
Ill. CONCLUSIONS
In mismatch condition the use of a DMPPT algorithm allows better performance in comparison to a traditional MPPT applied to a centralized DC/DC converter topology. In this scenario the choice of an adaptive P&O MPPT can represent, respect to the well-known P&O, a good compromise between speed accuracy and power losses during the steady-state operation. However, it is verified that, the use of the adaptive P&O can fail the MPP tracking in case of hard mismatch with irradiance sudden variations.
Differently, an adaptive dP-P&O algorithm applied to the DC/DC converters in case of DMMT is proposed in this paper; it allows to switch between two control modes: a simple P&O MPPT in case of very limited environmental conditions variations, or redefining the tracking direction in case of fast and high variations. It is demonstrated that the adaptive dP-P&O improves efficiency in case of hard mismatch, which is around � 99%, despite the MPPT sample time.
REFERENCES
[I] w. Xiao, W.G. Dunford, "A modified adaptive Hill Climbing MPPT method for photovoltaic power systems," 351h annual IEEE power electronics specialist conference, pp. 1957-1958,2004. [2] D. Sera, R. Teodorescu, "Optimized maximum power point tracker for fast-changing environmental conditions," IEEE Trans. Ind. Electronics, vol. 55, Issue 7, 2008, pp. 2629-2637. [3] M.G. Villalva, 1.R. Gazoli, E.R. Filho, "Comprehensive approach to modeling and simulation of photovoltaic arrays," IEEE Trans. Power Electronics, vol. 24, no. 5,2009. [4] C. Liu, B. Wu, R. Cheung, "Advanced algorithm for MPPT control of photovoltaic systems," Canadian Solar Buildings Conference, Montreal,
2004. [5] D. Sera, R. Teodorescu, P. Rodriguez, "PV panel model based on datasheet values," Proc. IEEE Int. Symp. Ind. Electron. (ISIE 2007), pp. 2392-2396. [6] A Driesse, S. Harrison, P. Jain, "Evalutating the effectiveness of maximum power point tracking methods in photovoltaic power systems using array performance models," Proc. IEEE Power Electron. Spec. Conf (PESC 2007), pp. 145-151. [7] W. De Soto, S.A Klein, W.A Beckman, "Improvement and validation of a model for photovoltaic array performance," Solar Energy, vol. 80, no. I, , 2006, pp. 78-88. [8] R. A Mastromauro, M. Liserre, A Dell' Aquila, "Control Issues in Single-Stage photovoltaic Systems: MPPT, Current and Voltage Controf', Trans. Ind. Informatics, forthcoming issue. [9] R. Gules, 1. De Pellegrin Pacheco, RL. Hey, 1. Imhotl; "A Maximum Power Point Tracking System With Parallel Connection for PV Stand-Alone
Applications," IEEE Trans. Ind. Electron., vo1.55, no.7, pp.2674-2683, July 2008. [10] N. Femia, G. Lisi, G. Petrone, G. Spagnuolo, M. Vitelli, "Distributed Maximum Power Point Tracking of Photovoltaic Arrays: Novel Approach and System Analysis," IEEE Trans. Ind. Electron., vo1.55, no.7, pp.2610-2621, July 2008. [II] G. Petrone, G. Spagnuolo, M. Vitelli, "A Multivariable Perturb-andObserve Maximum Power Point Tracking Technique Applied to a SingleStage Photovoltaic Inverter ," IEEE Trans. Ind. Electron., vol. 58, no. I, pp. 76 - 84, Jan 2011. [12] Wu Wenkai, N. Pongratananukul, Qiu Weihong, K. Rustom, T. Kasparis, 1. Batarseh, "DSP-based multiple peak power tracking for expandable power system," Eighteenth Annual IEEE Applied Power Electronics Conference and Exposition, APEC '03, Miami Beach, Florida, USA, 9-13 Feb. 2003, vol. I , pp. 525- 530.
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