about each solar panel, connected in series with other panels as part of a PV array, are collected by means of a distributed wireless sensor network. Simulation ...
Innovative Algorithm for True Maximum Detection Based on Individual PV Panel Sensor Network P. Guerriero*, G. Vallone**, V. d’Alessandro*, and S. Daliento* *Department of Electrical Engineering and Information Technology, University of Naples Federico II, via Claudio 21, 80125 Naples, Italy **IER s.r.l., Maddaloni, Italy II. THE ALGORITHM
Abstract— In this paper, an innovative MPPT algorithm is presented, which exploits actual operating parameters of each solar panel of a PV string to reach the true maximum position, even in case of local shading occurrence. Data about each solar panel, connected in series with other panels as part of a PV array, are collected by means of a distributed wireless sensor network. Simulation results demonstrate the robustness and reliability of the proposed algorithm in a wide range of temperatures and for several irradiance profiles. An extensive experimental campaign evidences the capability of the approach to accurately locate the maximum power point in a shorter time compared to traditional approaches. Index Terms—Mismatch, maximum power tracking (MPPT), photovoltaic (PV) string, shading.
The iMPPT algorithm is devised to estimate voltage and current corresponding to all L-MPPs in the I–V curve of a PV string from the knowledge of the actual short circuit current Isc and open circuit voltage Voc of the individual panels collected by a sensor network, and some additional information easily obtained from the panel datasheet. In particular, Isc and Voc are used to assess local irradiance and temperature. All panels with similar irradiance are clustered into groups, each of them corresponding to the occurrence of a local maximum. Finally, synthetic group parameters are determined to be used in L-MPPs identification. The shape of a panel I–V curve depends on irradiance and temperature. Synthetic parameters corresponding to standard conditions (1000 W/m2 AM 1.5 @ 25°C) are taken from the module datasheet, namely, short circuit current Isc,STC, open circuit voltage Voc,STC, and MPP voltage VMPP,STC and current IMPP,STC. The relations between the above currents (IMPP,STC, Isc,STC) and voltages (VMPP,STC, Voc,STC) can be written by defining two additional parameters kV,STC and kI,STC as follows: VMPP , STC kV , STC Voc , STC (1) I MPP ,STC kI ,STC I sc , STC
point
I. INTRODUCTION Maximum power point trackers (MPPTs) play an important role in photovoltaic (PV) power systems because they maximize the power output for a given set of operating conditions. Partial shading over PV arrays can be a serious hindrance to the proper functioning of an MPPT; it occurs mostly in domestic applications, often affected by architectural shading issues (e.g., TV antennas, trees, buildings). Considerable power loss might arise if a local MPP (L-MPP) is reached, which does not coincide with the absolute MPP. Therefore, the most popular algorithms embedded in commercial stringinverters provide an additional periodically-performed procedure to skip the unwanted L-MPPs and to force the operating point of the string close to the real MPP [1]. Unfortunately, algorithms based on a deterministic approach that exploits only low-granularity parameters such as short circuit current and open circuit voltage of the string may fail in estimating the position of the MPP. In order to tackle the above mentioned drawback, distributed approaches have been proposed, relying on individual panel energy converters, namely, dc-dc converters [2], [3] and micro-inverters [4]-[6]. In this paper, an alternative approach is proposed for string-inverters. The information-based MPPT algorithm, hereafter denoted as iMPPT, is structured in two stages: (i) the first estimates the MPP position by exploiting individual panels data collected by a wireless sensor network [7], [8]; (ii) the second, based on an optimized Perturb and Observe (P&O) algorithm [1], is devised to accurately reach the absolute MPP.
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In a similar fashion, the voltage and current at an MPP corresponding to arbitrary irradiance (G) and temperature (T) conditions can be expressed as VMPP kV (T , G ) Voc (2) I MPP k I (T , G ) I sc In (2), Voc and Isc are measured by wireless sensors (Section III), and coefficients kV and kI are given by kV T , G kV , STC P kV >TSTC T G @ (3) k I T , G k I , STC P kI >TSTC T G @ where parameters ȝkV and ȝkI depend upon temperature coefficients of Voc, Isc, and Pmax, and T is estimated thanks to the knowledge of Voc and G, in turn assessed from Isc. It is worth noting that (3) was empirically derived on the basis of an extensive experimental campaign conducted over wide ranges of irradiance and temperature. Let us now consider a PV string composed of two panels under sunny (high irradiance level) and shaded (low irradiance level) conditions, respectively. As shown in Fig. 1, the I–V curves of individual panels are
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As a consequence, in a PV string under uneven irradiance and temperature conditions, the position of the L-MPPs can be obtained by clustering the panels as function of the short circuit current levels and by determining for each group equivalent parameters kV_EQ and kI_EQ that account for the aforementioned effects.
characterized by different shapes, short circuit currents, and open circuit voltages (subscripts 1 and 2 designate the sunny and shaded modules, respectively). It can be observed that the string characteristic presents two regions resembling the individual panel curves. The proposed string model relies on the main idea that it is possible to identify the panel involved in the shape definition of each region and obtain L-MPP positions by exploiting the aforementioned parameters kV and kI. Unfortunately, the curve region including the MPP associated to the shaded panel is affected by the presence of the sunny panel. Fig. 2 shows how this region is modified by adding in series an increasing number of sunny panels, which results in a growing value of the LMPP current. On the other hand, the contribution of the sunny panel to the L-MPP position depends on the difference in terms of short circuit current with respect to the shaded panel. As shown in Fig. 3, the L-MPP voltage increases as the short circuit current ratio decreases.
10 Isc2
String current [A]
8 6 4 2 0 0.0
0.2
0.4
0.6
0.8
1.0
Normalized string voltage [V] 10
Current [A]
8 6
Fig. 3 Characteristics of the two-panel string by varying the short circuit current Isc2 of the shaded module, as determined by normalizing the string voltage to Voc. Filled triangles identify the L-MPPs induced by the shaded module.
string sunny panel shaded panel
Isc=Isc1 Isc2
The iMPPT algorithm is based on a simplified string model relying on the assumption that a current–voltage characteristic can be obtained by composing trapezoidal approximations of individual panel curves. This representation is carried out by intersecting a horizontal line, passing through the panel Isc and a second line containing the panel Voc and the MPP. The resulting characteristic has a trapezoidal shape, as shown in Fig. 4. Let us consider a partially shaded PV string composed of N equal panels under Q (Q N) different irradiance levels. The panels can be divided into M groups (M Q) corresponding to M short circuit current ranges so that each group gives rise to a local maximum in the power– voltage curve. Groups are sorted by short circuit current values in descending order.
4 2 0 0
Voc
Voc2 Voc1 10
20
30
40
50
Voltage [V]
60
70
80
Fig. 1. Current–voltage characteristic of a string comprising a sunny and a shaded module (solid line), along with the individual curves of the panels (dotted and dashed, respectively). The open circuit voltage Voc and short circuit current Isc associated to the string and to the modules are also identified.
Normalized current I/Isc2
1.0 0.8
Isc IMPP
0.6
2-panel string, partial shading sunny panel sunny panel, trapezoidal approximation
Number of sunny panels 0.4 0.2 0.0
String voltage [V] Fig. 2. Characteristics of a string including only one shaded module, as obtained by varying the number of series-connected sunny panels. In particular, the portion resembling the individual curve of the shaded module is represented by normalizing the current to the short circuit value Isc2 and translating the curves so that their open circuit voltages coincide. Filled triangles represent the L-MPPs induced by the shaded module.
VMPP Voc Fig. 4. Current–voltage characteristic of a two-panel string comprising a sunny and a shaded module (solid line), along with the sunny panel curve (dotted), and its trapezoidal approximation (dashed). VMPP, IMPP, Voc and Isc of the panel are also shown.
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The current value corresponding to the L-MPP of the m-th group is – by following the panel analogous (2) – obtained as I L MPP _ Gr ,m k I _ Gr ,m I sc _ Gr ,m , (4)
VL-MPP_Gr
where Isc_Gr,m is the lowest Isc of the modules belonging to the group; the equivalent group parameter kI_Gr,m is empirically evaluated as N P _ Gr , m
¦ i 1
k I _ Gr , m
I sc _ Gr ,m
¦N
P _ Gr , j
PL-MPP_Gr
Am
N P _ Gr , m Am
m 1
Am
k I ,i
I sc ,i
,
(5)
I sc _ Gr , j
where NP_Gr,m is the number of panels in the m-th group, Isc,i is the short circuit current of the i-th module in the mth group, NP_Gr,j is the number of modules of the j-th group among the m-1 ones (all characterized by higher Isc_Gr with respect to the m-th). Let us note that the first term at the numerator of the RHS of (5) takes into account the nonuniformity of short circuit currents of panels belonging to the group, while the second term Am accounts for the change in L-MPP position due to the m-1 groups, as depicted in Figs. 2 and 3. The voltage value corresponding to the L-MPP of the m-th group is obtained as the sum of the contributions of each group according to the following relation: M
VL MPP _ Gr ,m
¦ w 1
¦N
P _ G ,w
(11)
III. THE SYSTEM The system implementing the proposed algorithm is depicted in Fig. 5. A network controller (PV Unit) collects individual panel operating parameters (Isc, Voc) measured by the distributed sensor network (PV Monitor) [7], [8]. The algorithm is coded into a double-stage controller embedded in a test string-inverter. The first stage of the iMPPT controller receives panels data from the PV Unit and estimates the voltage (Vref,0) corresponding to the absolute MPP; the second stage, relying on an optimized Perturb and Observe (P&O) approach [1], is thus allowed to track the actual MPP through the Vref signal.
M
Voc _ Gr , w cwm D VD
VL-MPP_Gr T I L-MPP_Gr ,
where matrices C and C are defined according to (7), and IL-MPP_Gr is an M×M matrix whose m-th diagonal element is given by IL-MPP_Gr,m and the non-diagonal ones are zero. The maximum PL-MPP_Gr and the related VL-MPP_Gr values can be considered as absolute MPP power and voltage, respectively.
I sc _ Gr , j I sc _ Gr , m
j 1
ª Voc _ Gr ,1 º ª N P _ Gr ,1 º « » « » « . » « . » C «Voc _ Gr , w » D VD C « N P _ Gr ,w » (10) « » « » « . » « . » « » « » ¬Voc _ Gr , M ¼ ¬ N P _ Gr , M ¼
cwm ,(6)
w 1
the bypassed groups providing a negative voltage depending on the number (D) and the forward voltage (VD) of the bypass diodes of each panel; coefficients c wm and cwm are defined as cwm
kV _ EQ ,wm
cwm
1 ® ¯0
cwm
(7)
0
cwm z 0
kV_EQ,wm is the equivalent kV to be considered to calculate the contribution of the w-th group to the voltage of the m-th L-MPP, and can be expressed as
kV _ EQ , wm
Fig. 5. Structure of the system implementing the proposed algorithm.
I sc _ Gr , m kV _ Gr , w 1 1 I L-MPP_Gr,w > I sc_Gr,m ° ° I sc _ Gr ,w ® I L-MPP_Gr,w d I sc_Gr,m d I sc_Gr,w , (8) ° kV _ Gr , w °0 otherwise ¯
IV. NUMERICAL ANALYSIS The proposed algorithm was tested by performing an extensive set of simulations; in particular, 715 different irradiance profiles and 8 temperature values (from 10°C to 80°C) were considered. A calibrated PV cell model was used to build a string composed by 10 panels, each including 40 cells and equipped with 2 bypass diodes. The mean errors affecting the estimated power and voltage of the local maxima over the 715 irradiance profiles are shown in Fig. 6a and 6b, respectively. The results evidence the robustness of the algorithm with respect to irradiance and temperature variations, thus proving the effectiveness of the adopted temperature compensation method defined by (3). An inspection of the figures reveals that the mean error is
where kV_Gr,w is the kV of the w-th group obtained by means of linear interpolation of kV values according to the adopted trapezoidal approximation (see Fig. 4), and given by N P _ Gr , w
ª
¦ « k
kV _ Gr , w
i 1
¬
V ,i
1
I sc_Gr ,w
N P _ Gr , w
I sc ,i
º 1» ¼.
(9)
It is now straightforward to give a compact form to the computation of voltage and corresponding power values at the L-MPPs:
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lower than 4% and 3% for the local maxima power and the voltage, respectively. Moreover, the compensation reduces the dependence of the error on temperature and leads to an underestimate of power and voltage values, the latter being desirable from the perspective of a correct tracking.
acquisition while the inverter is involved in the MPPT procedure. PV string (generator)
A B Reference PV panel Trigger
Synchronization box
C
GPIB - IEEE 488 RS232 RS232 dc load
(a)
Inverter under test
Fig. 7. Test-bench block diagram: multimeters A and B are used as amperemeter and voltmeter, respectively; multimeter C performs an indirect irradiance monitoring thanks to a real-time short circuit measurement; a synchronization box controlled by a PC remote station handles the switching of the PV string between dc-load and inverter, and triggers the multimeters to simultaneously acquire data (blue line); three serial buses are employed: two RS232 (green lines) connect the PC remote station to the dc-load and the synchronization box, and an IEEE-488 (red) favors data transfer among station and multimeters.
VI. EXPERIMENTAL RESULTS (b)
Traditional MPPT algorithms embedded in stringinverters are based on a double-step procedure: (1) at system start-up, the MPP voltage is estimated through a “fractional voltage” approach according to the following relation [1]: (12) VMPP kV Voc string
Fig. 6. Simulation results: mean (over 715 irradiance profiles) error affecting the estimation of (a) power and (b) voltage at the local maxima with temperature-compensated parameters (blue bars) and with constant parameters (red).
V. THE TEST-BENCH
where Voc-string is the open circuit voltage measured at the inverter terminals, and kV is a parameter usually equal to 0.8-0.85, and independent of the number of seriesconnected modules, of their STC features, as well as of environmental conditions; (2) in the second step, several iterations of a P&O algorithm allow reaching the MPP. Subsequently, a voltage sweep around the nominal input voltage of the inverter is employed as step (1) instead of the “fractional voltage” approach. The algorithm is repeated every 10-15 mins. The test-bench was employed to perform a comparison in terms of static efficiency between the iMPPT algorithm and a traditional double-step MPPT. Both the MPPTs were implemented in the controller of a doublestage topology test string-inverter. The traditional MPPT was tested by intentionally obscuring the PV string so as to obtain P–V curves deeply impacted by partial shading, and showing local maxima at about 145 and 220 V (Fig. 8a). As expected, the preliminary MPP voltage estimation procedure drives the operating point of the string to a voltage equal to about 80% of Voc (kV§0.8). Afterward, due to the positive gradient mechanism, the operating point reaches a local maximum 30% lower than the true MPP; this highlights
In order to perform a complete analysis of the iMPPT in terms of MPPT efficiency, a fully custom test-bench (Fig. 7) was implemented [9], which handles the following main phases: (a) instrumentation configuration sequence, (b) I–V curve tracing sequence, and (c) PV generator operating point monitoring. Considering each step in detail: Instrumentation configuration sequence: first, the x PC remote station sets the parameters of multimeters for acquisition; I–V tracing sequence: subsequently, the PC remote x station (i) forces the synchronization board to switch the PV string to the electronic load, (ii) configures the load operating mode to “Constant Current” and sets the current ramp parameters, (iii) makes the board provide a trigger signal (an 8-second-long square wave with period amounting to 40 ms, which corresponds to 200 acquired points), (iv) manages data transfer from multimeters and, finally, forces again the synchronization board to switch back the PV string to the inverter; PV generator operating point monitoring: then, the x PC remote station (i) sets multimeter to continuous acquisition mode and (ii) manages a periodic data
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VII. CONCLUSION
that this algorithm does not operate correctly when the string is affected by severe partial shading. The iMPPT was applied in the same conditions (Fig. 8b). As expected, the proposed algorithm provides an accurate preliminary voltage reference (Vref,0) very close to the true maximum, and makes the second stage, relying on the positive gradient mechanism, drive the operating point of the string to the MPP. Fig. 8c shows the behavior of the instantaneous output power provided by the two approaches. This experiment plainly evidences that the iMPPT does not exhibit tracking failure in case of local maxima occurrence, thereby avoiding undesired power losses. 350
string power-voltage characteristic standard MPP tracking
300
String power [W]
Local information about the operation of each panel embedded in a string can significantly improve the overall efficiency of a PV system. In this paper, a novel MPPT algorithm – referred to as iMPPT – has been presented, which exploits the information provided by a sensor network applied to individual panels. A wide experimental campaign has been performed by using the proposed algorithm to control the first stage of a string inverter. Results demonstrate the capability of the approach to identify the true MPP, thus avoiding power losses due to tracking failures. Moreover, a faster convergence has been achieved with respect to a classic P&O algorithm. A simple test-bench has been used to compare a traditional double-stage algorithm and the proposed approach in terms of static MPPT efficiency under partial shading conditions. The system traces the evolution of the operating point of the inverter during the MPP tracking and periodically compares collected data to the traced I–V curves of the string. It has been found that the iMPPT exhibits a high MPPT efficiency even in partial shading condition, whereas the traditional MPPT is subject to a tracking failure leading to a reduction in the overall efficiency up to 30%. It can be concluded that the iMPPT represents a viable alternative to distributed energy conversion systems for string-inverter applications.
250 200 150 100 50
(a)
0 50
100
150
String voltage [V]
200
250
350 string power-voltage characteristic iMPP tracking
String power [W]
300
REFERENCES [1] T. Esram, and P. L. Chapman, “Comparison of photovoltaic array maximum power point tracking techniques,” IEEE Transactions on Energy Conversion, vol. 22, no. 2, pp. 439-449, 2007. [2] N. Femia, G. Lisi, G. Petrone, G. Spagnuolo, and M. Vitelli, “Distributed maximum power point tracking of photovoltaic arrays: novel approach and system analysis,” IEEE Transactions on Industrial Electronics, vol. 55, no. 7, pp. 2610-2621, 2008. [3] G. Graditi, G. Adinolfi, N. Femia, and M. Vitelli, “Comparative analysis of synchronous rectification boost and diode rectification boost converter for DMPPT applications,” in Proc. IEEE International Symposium on Industrial Electronics, 2011, pp. 1000-1005. [4] X. Cao and W. Zhang, “Grid-connected solar Microinverter reference design,” in Proc. International Conference on New Technology of Agricultural Engineering, 2011, pp. 239-243. [5] J. R. Gazoli, M. G. Villalva, T. G. Siqueira, and E. Ruppert, “Micro-inverter for integrated grid-tie PV module using resonant controller,” in Proc. IEEE Power and Energy Society General Meeting, 2012, pp. 1-8. [6] W. Bower, R. West, and A. Dickerson, “Innovative PV micro-inverter topology eliminates electrolytic capacitors for longer lifetime,” in Proc. 4th World Conference on Photovoltaic Energy Conversion, 2006, pp. 2038-2041. [7] M. Gargiulo, P. Guerriero, S. Daliento, A. Irace, V. d'Alessandro, M. Crisci, A. Smarrelli, and M. Smarrelli, “A novel wireless self-powered microcontroller-based monitoring circuit for photovoltaic panels in gridconnected systems,” in Proc. International Symposium on
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(b)
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Fig. 8. Trajectories of (a) traditional MPPT and (b) iMPPT under partial shading conditions. The string P–V curves (blue lines) traced just before the tracking action are reported to be used as reference. In (c) the string instantaneous power vs. time referring to both the iMPPT (red line) and the traditional MPPT (black) are compared.
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Power Electronics Electrical Drives Automation and Motion, 2010, pp. 164-168. [8] P. Guerriero, S. Daliento, V. d’Alessandro, L. Petrazzuoli, and G. Vallone, “Effective real-time performance monitoring and diagnostics of individual panels in PV plants,” submitted to IEEE International Conference on Clean Electrical Power, 2013 (accepted for presentation). [9] P. Guerriero, S. Daliento, V. d’Alessandro, and G. Vallone, “A simple test-bench to evaluate partial shading effects on the MPPT efficiency of a PV inverter,” submitted to IEEE International Conference on Clean Electrical Power, 2013 (accepted for presentation).
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