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fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2016.2544842, IEEE
Transactions on Power Electronics

Efficiency Improvement of Non-Uniformly-Aged

PV Arrays
Yihua Hu, Senior Member IEEE, Jiangfeng Zhang, Jiande Wu, Member, IEEE, Wenping Cao, Senior
Member, IEEE, Gui Yun Tian, Senior Member, IEEE, James L. Kirtley, Life Fellow, IEEE

Abstract—The utilization of solar energy by photovoltaic (PV) (PVs), solar energy.

systems have received much research and development (R&D)
attention across the globe. In the past decades, a large number of I. INTRODUCTION
PV array have been installed. Since the installed PV arrays often
operate in harsh environments, non-uniform aging can occur and Solar energy utilization has received much attention across
impact adversely on the performance of PV systems, especially in the globe over the last decades [1]-[6]. Currently, photovoltaic
the middle and late periods of their service life. Due to the high (PV) power devices are gaining in popularity in the global
cost of replacing aged PV modules by new modules, it is appealing renewable energy market, primarily owing to the reducing
to improve energy efficiency of aged PV systems. For this purpose, manufacture costs of PV panels and continuous improvement
this paper presents a PV module reconfiguration strategy to in power conversion technologies [7]-[8]. In practice, high
achieve the maximum power generation from non-uniformly aged energy conversion efficiency and long effective service time
PV arrays without significant investment. The proposed can help reducing capital and operating costs and thus are
reconfiguration strategy is based on the cell-unit structure of PV
modules, the operating voltage limit of gird-connected converter,
highly desired.
and the resulted bucket-effect of the maximum short circuit With the improvement of materials technologies,
current. The objectives are to analyze all the potential monocrystalline silicon and multicrystalline silicon now can be
reorganization options of the PV modules, find the maximum economically produced in large quantities. However, their
power point and express it in a proposition. This proposition is energy conversion efficiency from solar to electricity is still
further developed into a novel implementable algorithm to low. Typical efficiency for monocrystalline silicon solar cells is
calculate the maximum power generation and the corresponding around 20% while it is 18% for multicrystalline silicon solar
reconfiguration of the PV modules. The immediate benefits from cells [9]. On the power electronics side, high-performance
this reconfiguration are the increased total power output and switching devices (e.g. silicon carbon (SiC), super junction
maximum power point voltage information for global maximum
power point tracking (MPPT). A PV array simulation model is
MOSFETs) and new converter topologies (e.g. multi-level
used to illustrate the proposed method under three different cases. DC-AC and resonant DC-DC converters) can improve energy
Furthermore, an experimental rig is built to verify the conversion efficiency [10]-[12]. This part of energy conversion
effectiveness of the proposed method. The proposed method will efficiency can reach as high as 95% [12]. However, these
open an effective approach for condition-based maintenance of figures are typically for nominal and healthy operation of PV
emerging aging PV arrays. cells while in reality they are subject to various faults and aging
conditions, which reduce the lifetime of the PV cells and their
Index Terms—Maximum power tracking, non-uniform aging, operational efficiency. For these faulted or aged PV systems, an
offline reconfiguration, output characteristics, photovoltaics easy approach to improve energy efficiency is to replace aged
PV modules by brand new ones. However, this is not
Manuscript received May 13, 2015; revised October 11, 2015 and January economically acceptable to most of the PV system owners. This
31, 2016; accepted March 16, 2016.
Copyright © 2010 IEEE. Personal use of this material is permitted. However,
paper aims to propose a reconfiguration strategy for faulted or
permission to use this material for any other purposes must be obtained from aged PV systems so that the maximum power generation can be
the IEEE by sending a request to pubs-permissions@ieee.org. improved by simply rearranging the positions of the PV
Y. Hu is with the Department of Electrical Engineering and Electronic, modules. This reconfiguration strategy is derived from the
University of Liverpool, Liverpool, U.K. bucket effect of the maximum short circuit current of PV
J. Zhang is with the Department of Electronic and Electrical Engineering,
University of Strathclyde, Glasgow, UK.
strings, therefore, the basic structure and working principles of
J. Wu is with the College of Electrical Engineering, Zhejiang University, a PV system need to be introduced.
Hangzhou 310027, China (e-mail: eewjd@zju.edu.cn). There are four levels of components to form a PV system.
W. Cao is with the School of Electronics, Electrical Engineering and
Namely, PV cell-unit, PV module, PV string and PV array, as
Computer Science, Aston University, Birmingham, U.K.
G. Y. Tian is with the School of Electrical and Electronic Engineering, illustrated in Fig. 1. In order to restrict hotspots in the PV
Newcastle University, Newcastle upon Tyne, NE1 7RU, U.K., and also with module, a bypass diode is connected in parallel with PV cells;
the School of Automation Engineering, University of Electronic Science and such a structure is named a cell-unit (including m PV cells). In
Technology of China, Chengdu 610051, China. the PV system considered, assume that n cell-units are
J. L. Kirtley, Jr. is with the Department of Electrical Engineering and connected in series to form a PV module to raise the output
Computer Science, School of Engineering, Massachusetts Institute of
Technology, Cambridge, MA 02139 USA.
voltage, and s PV modules are connected in series to construct a
PV string. A number of PV strings are connected with diodes

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2016.2544842, IEEE
Transactions on Power Electronics

and then in parallel to become a PV array. The diodes can stop to calculate optimal solutions quickly enough, which increases
the current flow between strings, which is harmful. system costs. Paper [34] proposes a diffusion charge
redistribution method to achieve the maximum power. By
taking advantage of the intrinsic diffusion capacitance of the
solar cells, the number of power devices used is reduced to
simplify the system. Nonetheless, the majority of PV arrays are
not equipped with online reconfiguration equipment due to the
high cost.
So far the PV fault diagnosis and online reconfiguration
technology are still under development. In the middle and late
lifetime of the PV arrays, aging, especially non-uniform aging,
is a severe phenomenon that significantly decreases PV system
efficiency [35]-[37]. In the literature, a cost effective technique
to improve the energy efficiency of the aged PV arrays is still
lacking. This paper attempts to fill the gap by developing an
offline reconfiguration strategy for the “middle-aged and
elderly” PV arrays so as to maximize the solar power
generation.
The paper is organized as follows. Section II introduces
mathematical modeling of non-uniform aging PV array.
Section III illustrates the detection of aging PV. According to
aging information, section IV introduces the optimal PV
module reconfiguration algorithm. Section V illustrates the
proposed method by analytical study. Section VI presents
simulation and experimental results to verify the proposed
method, followed by a short conclusion in Section VII.

Fig. 1 Componential structure of the PV array. II. MATHEMATICAL MODELING

A new fault tolerance topology is developed to improve the
In order to increase the PV device’s effective service time, system performance that also can improve SRM driving system
fault diagnosis and remedial measures are two important fault tolerance ability.
approaches. Since PV panels often operate in outdoor harsh Non-uniform aging is a common problem in PVs which can
environments, potential hazards from dust, bird-dropping, be caused by lasting dust, shading, or water corrosion over a
partial shading and cell aging will affect the power generation long period of time [13][14]. Usually, there are many reasons
performance [13]-[15]. Therefore, detection techniques such as to cause aging differences. Due to the harsh operating
thermal cameras [16]-[21], earth-capacitance measurement environments, hail or stone can break the glass of some PV
(ECM) [22], time-domain reflectomery (TDR) [23], and modules. New modules are usually needed to replace broken
voltage/current sensors are widely applied to identify the modules so that the aging difference between new and old
irregularity of PV cells. Upon a fault, a non-uniform modules is high. Modules in the same locations can also suffer
temperature distribution can build up on the PV array and a differently from aging influences depending on the relative
thermal camera can help to locate the faulty PV module. The positions they are in. The modules at front and sides may be
ECM can locate the disconnection of any PV modules and the subjected to worse conditions such as duct and abrasion.
TDR can estimate the degradation of PV arrays. Nonetheless, Furthermore, modules in the same batch can also have aging
both ECM and TDR are expensive and only be employed as differences due to product quality variations. This is
offline fault diagnosis tools [22][23]. References [24] and [25] particularly true when they work towards the end of their
propose a PV array fault detection method by comparing service life. This paper addresses these aging differences and
simulated and measured output powers of PV arrays based on attempts to increase their overall output and lifetime expansion
the environment data. Paper [26] analyzes the dynamic of PV array by offline reconfiguration.
current-voltage characteristics to achieve fault diagnosis. In
paper [27], machine learning techniques are employed for PV A. Model of Healthy PV Cells
fault detection by measuring PV array voltage, current, The electrical characteristics of PVs are influenced by both
irradiance and temperature. temperature and illumination. The electrical model of the PV
After a fault is diagnosed, certain remedial measures need to cell is expressed by [2].
take place. In-situ reconfiguration is an effective solution ε ⋅V (1)
I= I L − I o [exp( ) − 1]
[28]-[34]. But this can only work if a large number of relays are Tm
used and the state of health (SoH) information of every PV
q (2)
module is available all the time. These two conditions cause ε=
higher system costs and also make the system controls Ns ⋅ K ⋅ A
complicated. In-situ reconfiguration also needs powerful CPUs

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Transactions on Power Electronics

G (3) Dbypass
IL = [I Lref +ki (Tm - Tref )]
Gref Cells
1 2 3 m
i3
unit
Tm 3 q ⋅ E BG 1 1 (4) i12 im
I o =I oref ( ) exp[ ( - )] Isc1

Current
Tref N s ⋅ A ⋅ K Tref Tm Iscm
Isc3 Range 3
where I is the PV module output current, IL is the photon current,
q is the quantity of electric charge, A is the diode characteristic Isc2 Range 2
factor, K is the Boltzmann constant, Io is the saturated current, Range 1
Tm is the PV module temperature, G is the irradiance, V is the Voltage
output voltage, Gref is the reference irradiance level (1000 Fig. 2 Non-uniformly aged cells in the cell-unit.
W/m²), ILref, Ioref are the reference values for IL and Io. ki is the
current-temperature coefficient provided by the PV
manufacturer. Tref is the reference temperature, Ns is the number
of series-connected cells, Tm is the PV module temperature. ε is
a constant depending on q, Ns, K, A, and is calculated by the
following equation:
I sc _ ref ε ⋅V mpp _ ref (5)
= I sc _ ref − I mpp _ ref [exp( ) − 1] Fig. 3 Equivalent circuit for the cell-unit in range 2.
ε ⋅V oc _ ref Tref
exp( ) −1
Tref As i12 increases, Vcu decreases to zero. The current switches
from Range 2 to Range 3. In Range 3, the cell-unit is bypassed
where Impp_ref, Isc_ref, Vmpp_ref and Voc_ref are the maximum power
by a diode, and the corresponding terminal voltage is -0.5 V (i.e.
point (MPP) current, short-circuit current, MPP voltage and
diode voltage drop). In Ranges 1 and 2, the current passing the
open-circuit voltage at a reference condition defined by the
cell-unit is i12, = im, where im is the PV module current. In
relevant standard.
Range 3, the current passing the bypass diode is i3, which is
B. Terminal Characteristics of Aged Cells equal to im.
When a PV cell is subject to aging, a direct indication is its From the analysis of Range 1-3, it can be found that the
lower output power than normal. Due to the p-n junction non-uniform aging of PV cells limits the power generation
characteristics of the PV cell, its open-circuit voltage only capacity of cell-units. This is termed the “bucket effect”.
changes slightly while the short-circuit current changes C. Model of Non-Uniformly Aged Cells
dramatically. According to references [38][39], the degradation
A PV array can age differently at the cell-unit, module and
of short-circuit current is about 10%, while the degradation
string levels.
open-circuit voltage is 2% in average after one year operation,
For a cell-unit with m series-connected PV cells, the
which means the short circuit has a dominated influence. From
relationship between the output current icu and the terminal
[36], the short current has close change rate with power loss.
output voltage Vcu depends on the PV’s operating points. To
Reference [40] also gives the conclusion that short current has
facilitate discussion on the three ranges, it is assumed that the
dominated influence while the open circuit voltage with
magnitude of the short-circuit currents for m cells is
negligible change after a 1.5 year aging experiment. Therefore,
in this paper, we take use of the short-circuit current to evaluate Isci1≤ Isci2 …≤ Iscim (8)
the aging condition of PV cells; and use the same open circuit Define icell as the actual current passing the PV cells. When
voltage to approximate aging conditions of PV cells. the current icell starts to increase from 0 to Isci1, all the cells
Fig. 2 presents a cell unit with m non-uniformly aged PV generate electricity. When icell exceeds Isci1 but less than Isci2 ,
cells, where Isc1, Isc2, Isc3 … Iscm are the short-circuit current for cell i1 cannot generate electricity: it is either bypassed or turned
cells 1, 2, 3 … m, respectively. There are three ranges in the into a resistor because of the bucket effect. As a result, the
current-voltage output characteristics. In Range 1, the relationship of icu and Vcu is summarized as follows.
maximum current is the minimum of all cells current (Isc1, Isc2, 1) If icell≤Isci1, the unit-cell operates in Range 1.
Isc3… Iscm) and all the cells generate electricity. Range 2 is a icu= icell≤Isci1 (9)
transitional interval. Its equivalent circuit is presented in Fig. 3 Vcu=mVcell (10)
and its terminal output voltage is given in Eq. (6). Due to a Where Vcell is equal to the voltage of every cell.
voltage drop on Re, the output voltage of the cell-unit is lower 2) If icell>Isci1, the cell-unit operates in Range 3.
than a healthy cell-unit. Vcu=-0.5V (11)
m −1 icell=0 (12)
∑V1
cell _ i − i12 ⋅ Re =
Vcu (6) icu=idiode (13)

where Vcell is the output voltage of the PV cell, Re is the where idiode is the bypass current flowing through the diode.
equivalent resistance of aged PV cell, and Vcu is the output The PV cells can work in Range 2 if there exists an integer
voltage of the cell-unit. k<m satisfying the conditions:
Iscik<icell≤Iscik+1

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Transactions on Power Electronics

k III. DETECTION OF PV AGING

( m − k )Vcell − icell ∑Rej ≥ 0 (14)
j =1 Aged modules have two typical characteristics: abnormal
When the cell-unit operates in Range 2, icu = icell and temperature and terminal electricity characteristics [3].
k
Accordingly, the detection of PV aging relies on the effective
( m − k )Vcell − icell ∑Rej
Vcu = (15) identification of one of the two characteristics.
j =1
A. Thermal Cameras
where Rej is the equivalent resistance of the jth cell.
Usually, Ranges 1 and 3 are the steady-state operational When the PV array is operational, a part of effective solar
conditions while Range 2 is a short transitional range between energy on the PV panel is transferred into electricity while the
the two and can often be ignored. rest is transferred into heat. Assume that the temperature
A PV string consists of s PV modules, with the terminal difference between PV cells and cover glass is neglected; cell
voltage Vstring and current istring. Let the terminal voltage, current temperature is uniform in a healthy module; and there is no
and maximum current from the kth PV module be Vmodule,k, thermal propagation across PV cells. Then the energy balance
max can be established as [5]:
imodule,k, and imodule ,?k , respectively. The following relationship
S =V ⋅ I +H pv Am (Tm - Ta ) (21)
can be established.
istring = imodule ,1 = imodule ,2 = … = imodule ,?s (16) S =G ⋅ Am (22)
where S is the effective solar absorbed flux, Ta is the ambient
=Vstring Vmodule ,1 + Vmodule ,2 +…+ Vmodule , s (17)
temperature, Hpv is an overall heat exchange coefficient in
Similarly, the bucket effect indicates that the maximum relation to the total surface area of the module, Am is the PV
max
current in the PV string is limited by the minimum imodule ,?k of module area.
Eqs. (1) and (21) form a parameter-based model with key
those non-bypassed modules. That is, istring ≤ imodule max
,?k , 1 ≤ k ≤ s ,
parameters I, V, Tm, S, Hpv and Ta. Fig. 4 illustrates a
and the kth module is not bypassed. multi-physical link of the PV array in the parameter-based
In practice, the cell-units within a PV module may be aged model, where E represents the electrical output power of the PV
differently and thus have different maximum short-circuit cell. The electrical model is mainly influenced by effective
currents. This case is called the “general non-uniform aging” in solar energy S and module temperature Tm, as illustrated in Eqs.
the paper. A simpler case for non-uniformly aged PV modules (3) and (22). The thermal characteristic is mainly influenced by
is that all cell-units in the same PV module are aged uniformly electrical power and effective solar energy, as shown in Eq.
so that the whole PV module can be characterized with a single (21). The temperature Tm and the total effective solar energy S
maximum short-circuit current of any cell-unit. This is termed are linked by the electro-thermal characteristics. For a given S,
the simplified non-uniform aging in this paper. the module temperature depends on the electrical power of the
A PV array consists of p parallel-connected PV strings; its PV module. The parameters Tm, I and V can be retrieved using
terminal voltage and current are denoted by Varray and iarray, thermography, current, and voltage sensors, respectively.
respectively. Let the terminal voltage and current for the jth PV S
string be Vstring,j and istring,j, respectively. Therefore: Ta
Hpv I
iarray=istring,1+istring,2+…+istring,p (18)
Varray = Vstring,1 = Vstring,2 = …=Vstring,p (19) Temperature Eq.(21)
Eqn.(3)

The power output from the PV array is the sum of strings, character Eq.(1)
Tm E =I ⋅ V
and is also limited by the bucket effect. That is, the maximum
power output from the simplified non-uniform aging PV array Electrical
p character
can be written as ∑min{P
j =1
max
j ,k : 1 ≤ k ≤ s ,and the (j, k)th Eq.(1)
and V
Eq.(21)

module is un-bypassed}, where Pjmax is the maximum power Fig. 4 Energy conversion within the PV array [3].
,k

output from the un-bypassed PV module at the position(j,k) When operating in Range 1, all the cells contribute to
(kth module in the jth string) of the PV array. Define imodule,j,k as electricity generation and it is impossible to distinguish an aged
the maximum short-circuit current in the (j,k) module; and q as module from the PV string. When operating at range 3, the most
the number of PV modules which generate electricity in the jth aged cells cannot generate electricity at the string current
string. Thus, (s-q) PV modules are bypassed by diodes in the working point so that a short circuit occurs at the cell-unit by its
th string. Then the maximum power Pjmax ,k is calculated as bypass diode. Therefore, At Range 3, the aged cell-unit is
, k = qVmodule i j
Pjmax q
(20) open-circuited and there is no solar energy transferred into
electricity. This leads to a higher temperature in the aged
where Vmodule is the MPP voltage supplied by a PV module, and cell-unit than the healthy ones. By changing the working points
i qj is the qth largest short-circuit current within the set { imodule,j,1, of PV array, all aged cell-units can be located from their
imodule,j,2,…, imodule,j,s}. For a normal PV module consisting of 3 thermal images.
cell-units, Vmodule=3Vcu, and Vcu is the MPP voltage a PV
cell-unit can provide.

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Transactions on Power Electronics

B. Time Domain Reflectomery (TDR) ,

TDR is another aging detection method. In TDR, a signal is where are determined by:
injected into the transmission line, and the signal will be = ( β1 + β 2 + β 3 +…+ β ( p −1) + β p )Vmodule (24)
P1max
distorted when mismatch occurs [22, 23]. Like a radar, the TDR
method analyzes the input signal and output signal, as shown in P=
2
max
2 ( β 2 + β 4 + β 6 +…+ β 2( p −1) + β 2 p ) Vmodule
Fig.5; the aging condition can be estimated according to the (25)
signal degradation. Note that illumination can influence the
impedance of PV cell; therefore, TDR can only be used in the
night. −1 =
Psmax ( s − 1) ( β s −1 + β 2( s −1) + β3( s −1) +…+ β( p −1)( s −1) + β p( s −1) )Vmodule
(26)
s
max
(
P= s β s + β 2 s + β 3 s +…+ β ( p −1) s + β ps Vmodule.
(27)
)
Consider a 2×3 PV array for example. This array has two
PV array
strings and each string has 3 PV modules (p=2, s=3). The
module maximum short-circuit currents are 0.9 pu, 0.8 pu, 0.2
Transition pu; 0.4 pu, 0.5 pu, 0.7 pu, respectively. If each string has only
Reflect signal
signal one operational module, the maximum powers from the first
Signal processing
and second strings are 0.9Vmodule and 0.7 Vmodule , respectively.
And fault diagnosis
The total power output is 1.6 Vmodule If each string has two
Input signal operational modules, the maximum power is (0.8+0.8) Vmodule
Fig. 5 Theory of TDR. =1.6 Vmodule from the first string and (0.5+0.5) Vmodule =1 Vmodule
Both of the thermal camera and TDR equipment can be used from the second string due to the bucket effect. The total power
temporarily to obtain the aging information of PV array. This is output is 2.6 Vmodule If all modules are operational, the
to say, there is no need to permanently install the maximum power is (0.2+0.2+0.2) Vmodule =0.6 Vmodule for the
reconfiguration equipment while temporary renting will be first string, and (0.4+0.4+0.4) Vmodule =1.2 Vmodule for the second
sufficient to obtain the PV aging information. This saves string. The total maximum power output is 1.8 Vmodule . From
hardware investment. this analysis, the maximum possible power generation is equal
to the max{1.6 Vmodule ,2.6 Vmodule ,1.8 Vmodule }=2.6 Vmodule Now
IV. OPTIMAL PV MODULE CONFIGURATION re-arrange these maximum short-circuit currents as follows:
In addition to three-phase 12/8 SRM driving systems, β1 = 0.9 > β 2 = 0.8 > β 3 = 0.7 > β 4 = 0.5 > β 5 = 0.4 > β 6 = 0.2
four-phase 8-slot/6-pole (8/6) SRM driving systems are also The power generation of the rearranged PV modules can be
widely used. The proposed fault tolerance also can be used in maximized when there are 1, 2 or 3 modules generating
four phase 8/6 SRM. electricity in each string (α is unknown).
After an aged module is detected, a remedial measure can If α =1, there is one module generating electricity in a
be employed to rearrange the faulted PV modules, prior to the string, then the rearrangement (0.9 pu, 0.7 pu, 0.4 pu; 0.8 pu,
replacement of the faulted modules which increases capital 0.5 pu, 0.2 pu) can ensure the maximum power generation. The
costs. corresponding maximum power is from the first
A. Theoretical Analysis string and from the second string, thus the total
From Eq. (20), it is noted that the maximum power output of power output is ( . This
a PV array depends on the maximum short-circuit current of explains Eq. (24).
each PV modules. Therefore, it is possible to rearrange aged PV If α =2, there are two modules generating electricity in
modules in a PV array in order to maximize the power output. each string, the rearrangement (0.9 pu, 0.8 pu, 0.4 pu; 0.7 pu,
Now, reorganizing all the maximum short circuit current values 0.5 pu, 0.2 pu) will produce the maximum power. The
from the highest to the lowest: maximum power is calculated by
β1 > β 2 > … > β ps (23) for the first string and
where β1 is the highest current and β ps the lowest from for the second string.
maximum short circuit currents The total power is
This explains Eq. (25).
If α =3, all the three modules in a string generate electricity,
When the PV array power generation is maximal, the number and the rearrangement (0.9 pu, 0.8 pu, 0.7 pu; 0.5 pu, 0.4 pu, 0.2
of working PV modules should be equal to that of un-bypassed pu) will generate the maximum power. The maximum power is
modules in all strings. This number (denoted by α) may vary
calculated by (
between 1 and s. Thus the output voltage of the PV string
for the first string and
equalizes this number multiplied by Vmodule .
Proposition: The maximum power output from a simplified ( . The total
non-uniform aging PV array is maximum power is 3( β 3 + β 6 )Vmodule =2.7 Vmodule . This explains

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Transactions on Power Electronics

Eq. (27). Clearly, this maximum power is greater than that for unoccupied places to accommodate PV modules. Therefore,
the unarranged arrays (2.6 Vmodule ). there are (ps-ps*) remaining places in these p strings.
Now the general proposition can be proved by applying This algorithm can be illustrated by the following flow
mathematical induction to α. The proof for α=1 is easy and now chart.
consider the case to deduce the statement for α=2 from α=1,
while the general proof is omitted as it is a simple repetition of
this proof for α=2. In fact, for α = 2 , we can assume the
maximum short-circuit currents of the two un-bypassed PV
modules in the -th string are γ 11 and γ 21 , l =1,2,…p. Without
loss of generality, we can further assume
that γ 11 > γ 21 > γ 12 > γ 22 > … > γ 1p > γ 2p . Then the maximum
power generated, denoted by P2max , is
P=
2
max
2 ( γ 21 + γ 22 + γ 23 +…+ γ 2p )Vmodule (28)
By definition of β1, β2,…, and βps in (23), β 2 is the second
largest maximum short-circuit current within these ps modules.
while γ 21 is not the largest PV module maximum short-circuit
current as there is γ 11 which is greater than γ 21 . Therefore,
β 2 ≥ γ 21 Similar reasoning deduces that β 4 ≥ γ 22 ,?
… β 2 p ≥ γ 2p ,
Fig. 6 Flow chart of the PV module reconfiguration strategy.
P=
2
max
(
2 β 2 + β 4 + β 6 +…+ β 2( p − 1) + )
? β 2 p Vmodule ≥ (γ 1
2 + γ 22 + γ 23 +…+ γ 2p )Vmodule .
Then, P2max is the maximum possible power output for α = 2 . V. ANALYTICAL STUDIES

B. PV Module Rearrangement Algorithm A. Simplified Non-Uniform Aging Cases

Assume the maximum short-circuit currents of all the PV A 2×2 PV array is employed in case studies where the
modules are given by {imodule,j,k:j=1,…,p; k=1,…,s}, and it is maximum short-circuit current of each PV module is given in
re-arranged from the highest to lowest as in Eq. (23) through per unit (pu). The specifications of the PV modules are
four steps. tabulated in Table I. The healthy PV module has the maximum
Step 1: short current, which is marked as 1 pu. The PV array aging
Calculate P1max , P2max , P3max , … , Psmax from Eq. (25). condition can be expressed as 1 pu, 0.5 pu; 0.2 pu, 0.1pu to
represent the conditions from healthy to aged. When PV array
Step 2. connected as (1 pu, 0.1 pu; 0.5 pu, 0.2 pu), their output curve is
Find the maximum from { P1max , P2max , P3max , … , Psmax } and shown in Fig. 7.
TABLE I SPECIFICATIONS OF THE PV MODULE
define the maximum as Psmax * where s* is an integer from
{1,2,3,…,s} so that
Psmax
* =max{ P 1
max
, P2
max
, P3
max
, … , P s
max
}.This implies that each
PV string has s* non-bypassed modules (generating electricity)
when the maximum power output of the PV array is achieved.
Step 3.
Rearrange the PV modules as follows:
3.1) Group the modules with maximum short-circuit currents β1,
β2,…βs* in the first PV string.
3.2) Group the modules with maximum short-circuit currents
βs*+1, βs*+2,…, β2s* in the second PV string.
3.3) Group the modules with maximum short-circuit currents
β2s*+1, β2s*+2,…, β3s* in the third PV string which is different to
3.1 and 3.2.
3.4) Repeat the above procedure to place modules with
maximum short-circuit currents
( β 3 s*+1 , β 3 s*+2 ,…, β 4 s* ), ( β 4 s*+1 , β 4 s*+2 ,…, β 5 s* ),…,( β ( p −1) s*+1 ,
β ( p −1) s*+2 ,…, β ps* ), and ensure that each of these
( β js*+1 , β js*+2 , …, β ( j +1) s* ), 3 ≤ j ≤ p − 1 , must occupy a
different string.
3.4) Place the remaining (ps-ps*) PV modules arbitrarily in the
remaining places of the p strings. Note that each string has (s-s*)

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Fig. 8 Output characteristics with two arrangement options (case 1).

The second case is for the 2×2 PV array with the aging
parameters of (1 pu, 0.3 pu; 0.5 pu, 0.4 pu). The output power is
obtained by simulation and presented in Fig. 9.

Fig. 7 The output characteristics without the rearrangement (1 pu, 0.1 pu; 0.5 pu,
0.2 pu).
Following Step 1 of the reconfiguration algorithm, p=s=2
these the maximum short-circuit currents can be re-ordered as:
β1=1>β2=0.5>β3=0.2>β4=0.1. Therefore, the maximum power
output is max{(1+0.5)Vmodule(pu), 2(0.5+0.1) Vmodule(pu)} =1.5 Fig. 9 Output characteristics without the rearrangement (1 pu, 0.3 pu; 0.5 pu,
Vmodule(pu). This maximum power is achieved by choosing only 0.4 pu).
one module from each string for electricity generation, i.e., *
=1. The existing sequence of the in Fig. 7, PV modules in this From Step 1 of the reconfiguration algorithm, p=s=2, these
PV can generate this maximum power. Therefore, there is no maximum short-circuit currents can be re-ordered as:
need for rearrangement. β1 =1> β 2 =0.5> β 3 =0.4> β 4 =0.3. The maximum power is
Note that there are only three options for rearrangement: (1 given by Psmax =max{(1+0.5)Vmodule(pu),
*
pu, 0.1 pu; 0.5 pu, 0.2 pu), (1 pu, 0.5 pu; 0.1 pu, 0.2 pu) and (1
2(0.5+0.3)Vmodule(pu)}=1.6Vmodule(pu). That is, s*=2 and all the
pu, 0.2 pu; 0.1 pu, 0.5 pu) where the notation (a, b; c, d)
modules must generate electricity. From Step 3.1, the two
indicates that the two modules (a and b) with the maximum
modules with maximum short-circuit currents β1 =1 and
short-circuit currents are placed in one string, and the other two
modules (c and d) are in another string. These are simulated in β 2 =0.5 are placed in one string while the other two modules
Fig. 10(a) and (b). It is clear that the arrangements (1 pu, 0.1 pu; with β 3 =0.4 and β 4 =0.3 are in another string. Therefore, the
0.5 pu, 0.2 pu) and (1 pu, 0.2 pu; 0.1 pu, 0.5 pu) provide the maximum power output can be achieved by the arrangement
identical maximum power (224 W) while the arrangement (1 pu, option (1 pu, 0.5 pu; 0.4 pu, 0.3 pu).
0.5 pu; 0.1 pu, 0.2 pu) has the maximum power of 207 W. The Similar to case 1, there are three possible options in case 2: (1
arrangement (1 pu, 0.2 pu; 0.1 pu, 0.5 pu) has also the pu, 0.3 pu; 0.5 pu, 0.4 pu), (1 pu, 0.4 pu; 0.5 pu, 0.3 pu), and (1
maximum power 1.5puVmodule. Obviously, the output powers in pu, 0.5 pu; 0.4 pu, 0.3 pu). It can be seen from Figs. 9 and 10
Fig. 7 and Fig. 8(b) are both 224 W, suggesting a good that the maximum power output from the three rearrangements
agreement between the analytical and simulation results. are 238 W, 244 W, and 273 W, respectively. Therefore, the
re-arranged PV array can gain 35 W more power than the
original PV array configuration.
From the two case studies, the proposed rearrangement
strategy can effectively improve the output power of
non-uniformly aged PV arrays. Furthermore, in the process of
the rearrangement, the MPP voltage area can be located which
assists in the online maximum power point tracking (MPPT).
Taking case 1 for example, the global MPP is located in the
MPP area of one module. In case 2, the global MPP is located in
the MPP area of two modules while the exact global MPP
voltage is determined by the module temperature.
(a) Option (1 pu, 0.5 pu; 0.1 pu, 0.2 pu)

(b) Option (1 pu, 0.2 pu; 0.1 pu, 0.5 pu) (a) Option (1 pu, 0.4 pu; 0.5 pu, 0.3 pu).

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cell-units in a PV module are put in a pair of parentheses. For

instance, the option (0.9 pu, 0.8 pu, 0.7 pu) indicates the
maximum short-circuit currents of the 3 cell-units in the first
PV module.
Assuming the output voltage to be fixed at α Vcu , α=1, 2, …,
9. In this case, the maximum power output can be calculated by
rating the maximum power output of all possible α. By doing so,
the maximum power is found to be 10.5pu Vcu at α=7.
Table III illustrates alternative PV module rearrangements
for the maximum power output out of possible 280 options. The
global maximum power is 12 Vcu (pu) when the voltage is 8 Vcu .
Compared to the original maximum power (10.5 Vcu (pu)), this
(b) Option (1 pu, 0.5 pu; 0.4 pu, 0.3 pu)
Fig. 10 Output characteristics with two arrangement options (case 2). arrangement has improved by 12.5% in power output.
B. General Non-Uniform Aging Cases C. Optimal PV Rearrangement under Converter Input Voltage
Limit
For general non-uniform aging modules, it is very difficult to
obtain any results similar to the obtained proposition. Consider Due to the limitation of inverter operations while PV arrays
a PV array with 3 cell-units in each PV module. The are connected to the grid, the minimum bus voltage of a single
phase inverter should be higher than 311V (220V/50Hz); and
total number of possible arrangements of the PV modules is
the minimum bus voltage of three phase inverter should be
, which is a higher than 538V (380V/50Hz). The corresponding PV array
huge number when or is big. For example, when p=5, s=10, operation points must be higher than the minimum bus voltage
this number equals 4.0279 × 1029 . Therefore, it is very difficult in a single stage converter. Therefore, the working voltage limit
to calculate the maximum power for all the possible PV module is introduced to the PV module reconfiguration strategy. The
arrangements for large p or s by enumerative search. Proposition and algorithm in Section IV.B can be revised as
Algorithms from combinatorial optimization (e.g. branch and follows to cater for this voltage limit. In fact, assume that a
bound methods) can be applied to search for the optimal converter input voltage limit requires the input voltage to be
maximal power when the number of possible rearrangements is θ Vmodule at least. Then it is straightforward that the maximum
huge. possible power output is: max{ Pi max : s ≥ i ≥ θ }.
Table II presents an example of a 3×3 array with the general And the searching algorithm in Section IV.B only needs to
non-uniform aging PV array with 3 cell-units in each PV search for those Pi max with i ≥ θ .
module. For this PV array, there are (93 )(36 )(33 ) /3! =280 possible
rearrangement options. Assume the PV modules are arranged
as in Table II where the maximum short-circuit currents of 3
TABLE II THE 3×3 ARRAY BEFORE REARRANGEMENT
Column (module)
Row [0.9 pu, 0.8 pu, 0.7 pu] [0.9 pu, 0.9 pu, 0.6 pu] [0.8pu, 0.5pu, 0.4pu]
(string) [0.7 pu, 0.6 pu, 0.6 pu] [0.9 pu, 0.5 pu, 0.4 pu] [0.6 pu, 0.4 pu, 0.3 pu]
[0.8 pu, 0.7 pu, 0.5 pu] [0.9 pu, 0.5 pu, 0.4 pu] [0.7 pu, 0.6 pu, 0.3 pu]
TABLE III THE 3×3 ARRAY AFTER REARRANGEMENT
Column (module)
Row [0.9 pu, 0.8 pu, 0.7 pu] [0.8 pu, 0.7 pu, 0.5 pu] [0.9 pu, 0.5 pu, 0.4 pu]
(string) [0.9 pu, 0.9 pu, 0.6 pu] [0.7 pu, 0.6 pu, 0.6 pu] [0.7 pu, 0.6 pu, 0.3 pu]
[0.8 pu, 0.5 pu, 0.4 pu] [0.9 pu, 0.5 pu, 0.4 pu] [0.6 pu, 0.4 pu, 0.3 pu]

A PV array model is built in Matlab. The per-unit maximum

VI. IMPLEMENTATION AND EXPERIMENTAL VALIDATION short-circuit current for each PV module in the 5×10 PV array
In order to validate the proposed strategy, a 9 kW array (p=5, s=10) is tabulated in Table IV. The corresponding output
under a non-uniform aging condition is used for simulation and characteristics are calculated and presented in Fig. 11. Without
experimental tests. Three cases representing PV array without a rearrangement, the maximum output power is 4587 W.
rearrangement, rearrangement without considering working In this PV array, there are α modules generating electricity in
voltage limit and rearrangement with considering working each string, while the rest (10-α) modules are bypassed by
voltage limit are investigated below. diodes. α is between 1 and 10. It suffices to calculate the
maximum power for each α and then find the greatest power
A. Simulation from the 10 calculations. Firstly, let us sort the maximum
Case 1:

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short-circuit currents for PV strings from largest to smallest, as short-circuit currents of 0.4 pu, 0.4 pu, 0.4 pu, 0.4 pu and 0.3 pu.
in Table V. Since each string has only one unoccupied place, the 5 modules
can be arbitrarily placed to fill the gap, as instructed in Step 3.5.
The remaining modules in each of the 5 strings is bypassed and
become idle; they are not in operation. The bucket effect
determines that all first 9 PV modules in each string with higher
maximum short circuit currents are operational to generate
power.

Fig. 11 Output characteristics of the 5×10 array without the rearrangement

(case 1).
For α=1, the maximum power is given by
Vmodule*(0.9+0.9+0.8+0.9+0.9) pu =4.4 Vmodule (pu) (29)
For α=2, the maximum power is
Vmodule *2*(0.9+0.9+0.8+0.8+0.9) pu =8.6 Vmodule (pu) (30)
Similarly, for α=3,4,…,10, the maximum powers are calculated
as: 12.3 Vmodule (pu), 15.6 Vmodule (pu), 19.5 Vmodule (pu), 22.8
Vmodule (pu), 25.9 Vmodule (pu), 26.4 Vmodule (pu), 24.3 Vmodule (pu), Fig. 12 Output characteristics of the 5×10 array with the rearrangement (case
20 Vmodule (pu). Therefore, the maximum power output is 26.4 1).
pu Vmodule when there are 7 PV modules in each PV string Case 2:
generating electricity. For a middle aged PV array, some modules are broken in the
Now consider the optimal PV module rearrangement. The array; usually, the faulty modules are replaced by new modules.
maximum short-circuit currents are re-organized from the In this scenario, the typical 5×10 PV array is presented in
highest to lowest as follows: Table VII, in which there are new modules with high
0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.8 pu 0.8 pu; performance scattered in the array. Due to the non-uniform of
0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu; aging, the corresponding output characteristics are calculated
0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.7 pu 0.7 pu; and presented in Fig. 13; the maximum output power is 1661W.
0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.6 pu;
0.6 pu 0.6 pu 0.5 pu 0.5 pu 0.5 pu 0.4 pu 0.4 pu 0.4 pu 0.4 pu 0.3 pu.
According to Eq. (23), β1=0.9, β2=0.9,…, β50=0.3.
Following Steps 1 and 2 in the reconfiguration algorithm, the
maximum power is now calculated by:
Vmodule *max{4.5pu, 8.8pu, 12.6pu, 16.8pu, 20.5 pu, 24pu, 28
pu, 30.4, 32.4, 32}=32.4 Vmodule (pu). This corresponds to the
case that the output voltage is 9 Vmodule , s*=9. There are 9 PV
modules in each string which generate electricity. Given that
the original maximum power output is only 26.4 Vmodule (pu),
this re-arranged PV array can generate 32.4 Vmodule (pu). This is
because those six modules are brought back to the generation
side by the reorganization (see Table VI). The corresponding
output characteristics are illustrated in Fig. 12. As can be seen Fig. 13 Output characteristics of the 5×10 array without the rearrangement
(case 2).
that the maximum output power is 5242 W with the
rearrangement, which is 655 W more than that without the
rearrangement (4587 W). Obviously, its energy efficiency is
improved by increasing 14.28% power generation.
Table VI is constructed by the rearrangement algorithm as
follows. From Step 3.1, 9 modules with the maximum
short-circuit currents (0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu
0.9 pu 0.9 pu 0.8 pu) are grouped in the first string. From Step
3.2, further 9 modules with the current of (0.8 pu 0.8 pu 0.8 pu
0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu) are placed in the
second string. When j = 2, 3, 4, 27, their respective modules are
put in the third, fourth and fifth strings following Step 3.4. Now,
45 PV modules are reorganized in the PV array, leaving 5 Fig. 14 Output characteristics of the 5×10 array with the rearrangement (case
modules un-sorted. These 5 modules have the maximum 2).

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Following a similar procedure as the previous example, the generating electricity in each PV string, and the corresponding
maximum power output equals 10 Vmodule , which is achieved I-V curves are presented in Fig. 14.
when all the 50 modules are activated to generate electricity.
Now consider the optimal rearrangement. From the algorithm
in Section IV-B, it is easy to find that the maximum power is
11.4 Vmodule (pu), which can be achieved by allowing 6 modules
TABLE IV THE 5×10 PV ARRAY WITHOUT REARRANGEMENT IN CASE 1
Column (module)
0.8 pu 0.8 pu 0.3 pu 0.6 pu 0.8 pu 0.9 pu 0.8 pu 0.9 pu 0.6 pu 0.9 pu
Row 0.8 pu 0.8 pu 0.4 pu 0.7 pu 0.9 pu 0.7 pu 0.8 pu 0.8 pu 0.8 pu 0.9 pu
(string) 0.8 pu 0.8 pu 0.8 pu 0.7 pu 0.6 pu 0.5 pu 0.5 pu 0.7 pu 0.7 pu 0.7 pu
0.8 pu 0.8 pu 0.7 pu 0.7 pu 0.9 pu 0.4 pu 0.4 pu 0.7 pu 0.8 pu 0.8 pu
0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.7 pu 0.7 pu 0.9 pu 0.5 pu 0.4 pu 0.9 pu
TABLE V REARRANGED STRINGS IN CASE 1
Column (module)
0.9 pu 0.9 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.6 pu 0.6 pu 0.3 pu
Row
0.9 pu 0.9 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.7 pu 0.7 pu 0.4 pu
(string)
0.8 pu 0.8 pu 0.8 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.6 pu 0.5 pu 0.5 pu
0.9 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.7 pu 0.7 pu 0.7 pu 0.4 pu 0.4 pu
0.9 pu 0.9 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.7 pu 0.7 pu 0.5 pu 0.4 pu
TABLE VI REARRANGEMENT OF THE 5×10 ARRAY IN CASE 1
Column (module)
0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.9 pu 0.8 pu 0.4 pu
Row 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.4 pu
(string) 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.8 pu 0.4 pu
0.8 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.7 pu 0.4 pu
0.7 pu 0.7 pu 0.7 pu 0.6 pu 0.6 pu 0.6 pu 0.5 pu 0.5 pu 0.5 pu 0.3 pu
TABLE VII THE 5×10 PV ARRAY WITHOUT REARRANGEMENT FOR CASE 2
Column (module)
1 pu 0.7 pu 1 pu 0.2 pu 0.3 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu
Row 1 pu 0.2 pu 0.2 pu 0.3 pu 0.4 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu
(string) 1 pu 0.3 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu
0.2 pu 0.2 pu 1 pu 0.3 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu
0.3pu 1 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu
TABLE VIII THE 5×10 PV ARRAY WITH REARRANGEMENT IN CASE 2
Column (module)
1 pu 1 pu 1 pu 1 pu 1 pu 1 pu 0.7 pu 0.4 pu 0.3 pu 0.3 pu
Row 0.3 pu 0.3 pu 0.3 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu
(string) 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu
0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu
0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu 0.2 pu

in Table IX and Fig. 15 before and after the rearrangement. For

B. Experimental Tests
the PV array without the reconfiguration presented in Fig. 15(a),
In the experiment, a 1620 W 3×3 array is employed to verify its maximum output power is 520 W, shown in Fig. 15(b). After
the proposed technique based on the availability. The PV applying the proposed strategy to the PV array, the PV array is
module parameters are identical to those in Table I. The aging rearranged (by swapping PV21 and PV32 positions), as shown
condition is realized by covering the two modules (PV21 and in Fig. 15(c). Experimental results show that the maximum
PV31) with plastic membrane. The test results are given in Fig. output power in the rearranged array is 590 W, illustrated in Fig.
15. The array output characteristics are obtained and presented 15(d), which increases 13.5%. Furthermore, because of this

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rearrangement, the global MPP shifts from a two-module MPP Table X presents a comparison of the proposed
area to a three-module MPP area, which can be directly used for reconfiguration strategy and existing online reconfiguration
the online global MPPT. strategies in the literature [27][32][33][41]. For condition
monitoring, the online reconfiguration methods require
TABLE IX COMPARISON OF PERFORMANCE BEFORE AND AFTER THE continuous monitoring that increases the system cost and
REARRANGEMENT computational burden while the proposed method only needs
periodic monitoring (e.g. during maintenance). For PV cell
reconfiguration, existing online reconfigurations strategies
need a large number of relays (e.g. high costs and high-end
controllers). For example, for a 10×10 array, in order to have a
complete flexible reconfiguration, a relay between any two
modules is needed, which is (1002 ) =100 × 99 / 2 =4950 . In case
any one of 4950 relays is faulted or malfunctions, conventional
online reconfiguration would not be realized and the PV array
output power would decrease dramatically. More importantly,
the number of relays used by existing online reconfiguration
methods increases exponentially with the PV array size,
limiting their widespread in real applications. On the contrary,
the proposed offline reconfiguration algorithm is simpler, more
cost-effective and more practical to implement, and it can be
applied to any array sizes without significant investment in
(a) PV array without the rearrangement hardware.

VII. CONCLUSION
Non-uniform aging of PV modules is a common
phenomenon in the PV power plants since they often operate a
long time in harsh environmental conditions. The non-uniform
aging decreases the PV array maximum output power and can
damage the PV modules if left untreated. Without rearranging
non-uniformly aged PV arrays, typical online global-MPPT
schemes can only track a compromised maximum rather than
its potential maximum power.
This paper has presented a new PV array reconfiguration
strategy to maximize the power generation of
(b) Output characteristics without the arrangement
non-uniformly-aged PV arrays without replacing aged PV
modules. It is found that the bucket effect is the key factor
affecting the operating mechanisms of PV arrays under
non-uniform aging conditions. The cell-unit structure of PV
module is investigated to study the aging characteristics of PV
modules. The mathematical models for non-uniformly aged PV
arrays are built. An optimized reconfiguration algorithm is
developed to take the full use of aged PV array for maximum
power output. The proposed strategy has been tested by
simulated on three cases and validated by experiments on a
1620-W PV array.
(c) PV array with the rearrangement
While the existing online reconfiguration methods may
provide online reconfiguration in real time for small PV arrays
but require large amount of relays, auxiliary power supply and
high-end controllers. As PV cell aging is a slow process, the
feature of online measurement in real time may not be useful to
justify the exponential increase in material and computational
costs. In contrast, the proposed offline method only needs
inexpensive equipment to perform periodic inspections of PV
cells (during maintenance). Therefore, the developed technique
can significantly improve energy efficiency and cost efficiency
of PV systems of any size. It opens one effective approach for
condition based maintenance in conjunction with in-situ smart
(d) Output characteristics with the arrangement monitoring [17, 21], which is important for large scale aged PV
Fig. 15 Experimental results for the 3×3 array. arrays.

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TABLE X COMPARISON OF THE PROPOSED RECONFIGURATION WITH ONLINE RECONFIGURATION

Item Online reconfiguration Proposed reconfiguration
[27][32][33] [41]
Hardware for Reconfiguration Number of relays needed for a p×s Manual work, no hardware investment
array is:
ps ( ps − 1)
( ps2 ) =
2
Hardware for Sensor (a) PV module conditions (e.g. current (a) No sensors installed on site
and voltage) should be monitored on (b) The PV module’s healthy
site conditions can be monitored by
(b) Powerful controllers are needed for thermal camera when the PV array
online sensor signal collection and needs to be maintained. The thermal
processing camera can be rented for short time
usage.
Auxiliary facilities (a) Power supply for sensors Not needed
(b) Power supply for relays
(c) Signal transmitters
Software (a)Do not consider cell-unit structure (a) Consider cell-unit structure of PV
(Algorithm differences) yet modules
(b) Need strong controller to support (b) Offline computing, no need for
online computing high performance controllers
Recommended PV array size Small scale PV arrays Large and small scale PV arrays

Recommended application scenarios Small-scale array regularly affected by Efficiency improvement for
shadows non-uniform aging PV arrays
[12] W. Li, W. Li, X. Xiang, Y. Hu, X. He, “High step-up interleaved converter
with built-in transformer voltage multiplier cells for sustainable energy
ACKNOWLEDGEMENT applications,” IEEE Trans. Power Electron., vol. 29, no. 6, pp. 2829-2836,
This work has partially funded by FP7 HEMOW and Marie Jun. 2014.
Curie International Outgoing Fellowship with MIT, EC, [13] S. Djordjevic, D. Parlevliet, P. Jennings, “Detectable faults on recently
2015-2016 to Prof. Wen-Ping Cao. installed solar modules in Western Australia,” Renewable Energy, vol. 67,
pp. 215-221, 2014.
[14] E. L. Meyer, E. Ernest van Dyk, “Assessing the reliability and degradation
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Transactions on Power Electronics

[27] Y. Zhao, R. Ball, J. Mosesian, J. F. de Palma, and B. Lehman,

“Graph-based semi-supervised learning for fault detection and Jiangfeng Zhang obtained his BSc and PhD in computing
classification in solar photovoltaic arrays,” IEEE Trans. Power Electron., mathematics and applied software from Xi'an Jiaotong
vol. 30, no. 5, pp. 2848- 2858, Feb. 2016. University, China, in July 1995 and December 1999,
[28] D. Nguyen，B. Lehman. “An adaptive solar photovoltaic array using respectively. He is a senior lecturer at the Department of
model-based reconfiguration algorithm,” IEEE Trans. Ind. Electron., vol. Electronic and Electrical Engineering, University of
55, no. 7, pp. 2644-2654, Jul. 2008. Strathclyde. He is also a member of the IFAC TC6.3
[29] P. J. Storey, P. R. Wilson, and D. Bagnall, “Improved optimization (Power and Energy Systems). His research interests
strategy for irradiance equalization in dynamic photovoltaic arrays,” IEEE include optimization modelling and control of energy
Trans. Power Electron., vol. 28, no. 6, pp. 2946-2956, Jun. 2013. systems, with a focus on energy efficiency and demand
[30] Z. M. Salameh, F. Dagher, “The effect of side management.
electrical array reconfiguration on the performance of a PV-powered
volumetric water pump,” IEEE Trans. Energy Conversion, vol. 5, no. 4, Jiande Wu was born in Zhejiang, China, in 1973.He
pp. 653-658, Dec. 1990. received the B.Sc. degree from the Department of
[31] Y. Wang, X. Lin, Y. Kim, N. Chang, and M. Pedram, “Architecture and Electrical Engineering, Zhejiang University,
control algorithms for combating partial shading in photovoltaic systems,” Hangzhou, China, and the M.Sc. degree in power
IEEE Trans. Computer-Aided Design Integr. Circuits Syst., vol. 33, no. 6, electronics from the College of Electrical Engineering,
pp. 917-929, Jun. 2014. Zhejiang University, in 1994 and 1997, respectively. In
[32] G. Velasco-Quesada, F. Guinjoan-Gispert, R. Pique-Lopez, M. 2012, he received the Ph.D. degree from the same
RomanLumbreras, and A. Conesa-Roca, “Electrical PV array university. Since 1997, he has been a faculty member
reconfiguration strategy for energy extraction improvement in at Zhejiang University, where he is currently an
grid-connected PV systems,” IEEE Trans. Ind. Electron., vol. 56, no. 11, associate professor. From Oct. 2013 to Oct. 2014, he was an academic visitor at
pp. 4319-4331, Nov. 2009. the University of Strathclyde, Glasgow, U.K. His research interests include
[33] J. Storey, P. R. Wilson, and D. Bagnall, “The optimized-string dynamic applications of power electronics and network communication.
photovoltaic array,” IEEE Trans. Power Electron., vol. 29, no. 4, pp.
1768-1776, Apr. 2014. Wenping Cao (M’05-SM’11) received the B.Eng in
[34] A. H. Chang, A. T. Avestruz, and S. B. Leeb, “Capacitor-less photovoltaic electrical engineering from Beijing Jiaotong University,
cell-level power balancing using diffusion charge redistribution,” IEEE Beijing, China, in 1991, and the Ph.D. degree in
Trans. Power Electron., vol. 30, no. 2, pp. 537-546, Feb. 2015. electrical machines and drives from the University of
[35] A. Ndiaye, C. M.F. Kebe, A. Charki, P. A. Ndiaye, V. Sambou, A. Kobi, Nottingham, Nottingham, U.K., in 2004.
“Degradation evaluation of crystalline-silicon photovoltaic modules after He is currently a Chair Professor of Electrical Power
a few operation years in a tropical environment,” Solar Energy, vol. 103, Engineering with Aston University, Birmingham, U.K.,
pp. 70-77, Feb. 2014. and also a Marie Curie Fellow with Massachusetts
[36] C. R. Osterwald, A. Anderberg, S. Rummel, L. Ottoson, “Degradation Institute of Technology, Cambridge, MA, U.S.A. His
analysis of weathered crystalline-silicon PV modules,” 29th IEEE research interests include fault analysis and condition
Photovoltaic Specialists Conference, New Orleans, Louisiana, 2002. monitoring of electric machines and power electronics.
[37] L. Cristaldi, M. Faifer, M. Rossi, S. Toscani, M. Catelani, L. Ciani, M.
Lazzaroni, “Simplified method for evaluating the effects of dust and Gui Yun Tian (M’01–SM’03) received the B.Sc. degree
aging on photovoltaic panels,” Measurement, vol. 54, pp. 207-214, Aug. in metrology and instrumentation and the M.Sc. degree in
2014. precision engineering from the University of Sichuan,
[38] N. Ababacar M. F. Cheikh A. Kébé, Pape Ndiaye, C. Abdérafi, K. Chengdu, China, in 1985 and 1988, respectively, and the
Abdessamad, S. Vincent, “A novel method for investigating photovoltaic Ph.D. degree from the University of Derby, Derby, U.K.,
module degradation,” Energy Procedia, vol. 36 pp. 1222-1231, 2011. in 1998. He was a Lecturer, Senior Lecturer, Reader,
[39] M. A. Munoz, M. C. Alonso-Garcia, Nieves Vela, F. Chenlo, “Early Professor, and the Head of the Group of Systems
degradation of silicon PV modules and guaranty conditions,” Solar Energy, Engineering, University of Huddersfield, Huddersfield,
vol. 85, pp. 2264–2274, 2011. U.K., from 2000 to 2006, Since 2007, he has been based
[40] D. Chianese, N Cereghetti, S. Rezzonico, and G. Travaglini, “18 types of at Newcastle University, Newcastle upon Tyne, U.K., where he has been the
PV modules under the lens,” Proc.16th Euro. PV Sol. Energy Conf., Chair Professor in sensor technologies. Currently, he is also with the School of
Glasgow, Scotland, 2000. Automation Engineering, University of Electronic Science and Technology of
[41] G. Petrone, G. Spagnuolo, B. Lehman, Y.Zhao, C.A.R. Paja, China, Chengdu, China. He has coordinated several research projects from the
and M. L. Gutierrez, “Control of photovoltaic arrays: dynamical Engineering and Physical Sciences Research Council, Royal Academy of
reconfiguration for fighting mismatched conditions and meeting load Engineering and FP7, on top of this he also has good collaboration with leading
requests, ” IEEE Industrial Electronics Magazine, vol. 9, No. 1 Mar. 2015, industrial companies, such as Airbus, Rolls Royce, BP, nPower, and TWI.
pp. 62-76.
James L. Kirtley, Jr. (LF’91) received the Ph.D.
degree from the Massachusetts Institute of Technology
Yihua Hu (SM’15, M’13) received the B.S. degree in (MIT), Cambridge, MA, USA, in 1971.
electrical motor drives in 2003, and the Ph.D. degree in He is a Professor of electrical engineering with the
power electronics and drives in 2011, both from China Department of Electrical Engineering and Computer
University of Mining and Technology, Jiangsu, China. Science, School of Engineering, MIT. His research
Between 2011 and 2013, he was with the College of interests include electric machinery and electric power
Electrical Engineering, Zhejiang University as a systems.
Postdoctoral Fellow. Between November 2012 and Prof. Kirtley served as the Editor-in-Chief of the
February 2013, he was an academic visiting scholar with IEEE TRANSACTIONS ON ENERGY CONVERSION from 1998 to 2006
the School of Electrical and Electronic Engineering, and continues to serve as an Editor for the journal, and he is a member of the
Newcastle University, Newcastle upon Tyne, UK. Editorial Board of Electric Power Components and Systems. He was the
Between 2013 and 2015, he worked as a Research Associate at the power recipient of the IEEE Third Millennium Medal in 2000 and the Nikola Tesla
electronics and motor drive group, the University of Strathclyde. Currently, he Prize in 2002. He was elected to the U.S. National Academy of Engineering in
is a Lecturer at the Department of Electrical Engineering and Electronics, 2007.
University of Liverpool (UoL). He has published more than 35 peer reviewed
technical papers in leading journals. His research interests include PV
generation system, power electronics converters & control, and electrical motor
drives.

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