See discussions, stats, and author profiles for this publication at: https://www.researchgate.

net/publication/280568224

Estimation of PV Module Parameters from Datasheet Information Using

Optimization Techniques

Conference Paper · March 2015

DOI: 10.1109/ICIT.2015.7125507

CITATIONS READS

13 1,520

2 authors:

M. A. Awadallah B. Venkatesh
Ryerson University Ryerson University
61 PUBLICATIONS   1,382 CITATIONS    191 PUBLICATIONS   4,429 CITATIONS   

SEE PROFILE SEE PROFILE

Some of the authors of this publication are also working on these related projects:

Pole-mounted energy storage system for reliability enhancement of local distribution companies View project

Line-Wise Power Flow and Voltage Collapse View project

All content following this page was uploaded by M. A. Awadallah on 30 July 2015.

The user has requested enhancement of the downloaded file.

Estimation of PV Module Parameters from Datasheet
Information Using Optimization Techniques
Mohamed A. Awadallah Bala Venkatesh
Centre for Urban Energy Department of Electrical and Computer Engineering
Ryerson University Ryerson University
Toronto ON, Canada Toronto ON, Canada
awadalla@ryerson.ca bala@ryerson.ca

Abstract—The paper presents a technique for parameter methods are used to express the parameters in terms of known
estimation of photovoltaic (PV) modules from datasheet performance of the module under certain conditions [1]-[4].
information. The manufacturer normally provides open-circuit The performance could be obtained from the module ratings
voltage, short-circuit current, maximum power, and voltage at given in the datasheet [1], [2], or from direct measurement [3],
maximum power under the standard test conditions (STC). The [4]. Numerical iterative techniques may be required to extract
four datasheet values represent the targeted performance of the the parameters from given performance indices [1]; otherwise,
module. Parameter estimation is formulated as an optimization direct solution is possible upon some mathematical
problem solved by traditional nonlinear programming simplification assumptions [2]. Although most of the literature
techniques as well as global search algorithms. The objective is
work considers parameter estimation of the single-diode
to search a set of parameters that minimizes the error between
targeted and computed performance. The methodology is
equivalent circuit of PV cells, some publications are dedicated
successfully applied to single- and double-diode equivalent to the double-diode model as well [4].
circuits of PV modules. Evidently, the need to perform Fitting computed performance to measured performance
prototype lab testing, for the purpose of parameter estimation, is with minimal error is another technique to search a set of
eliminated. Results show that genetic algorithms (GA) parameters that best represent the PV module [5]-[7]. The
outperform other optimization techniques in obtaining the curve fitting methods vary between least square [5], voltage
equivalent circuit parameters of a commercially available PV fitting near open circuit and current fitting near short circuit
module.
[6], and auxiliary function fitting [7].
Index Terms—Genetic algorithms, simulated annealing, Optimization algorithms are exploited to estimate PV
nonlinear programming, parameter estimation, PV modules. module parameters by minimizing certain objective functions
[8]-[13]. In [8], the discrepancy between measured and
I. INTRODUCTION computed module current is used as an objective function to
Solar energy comes next to wind as the fastest developing be minimized by particle swarm optimization (PSO) and
renewable source. The light energy of sun is converted to DC genetic algorithms (GA). Statistical and cluster analyses are
electricity by photovoltaic (PV) cells. When the rays of sun used with PSO to fit measured performance to that computed
light hit the semiconductor material of PV cells, the electrons through the seven-parameter double-diode model of PV
gain energy allowing them to transfer from the valence band modules [9]. The difference between measured and computed
to conduction band. A PV cell typically generates about 2 W current is minimized via GA to extract PV module parameters
at 0.5 V; accordingly, cells are connected in series to form a [10]. In [11], an objective function based on the rate of change
PV module that produces higher voltage. The modules are of module current with respect to its voltage is minimized
then connected in different series and parallel configurations using bacterial foraging (BF), GA, and artificial immune
forming PV arrays in order to attain the desired level of systems (AIS). A similar objective function is minimized by
voltage and current. The operation and control of PV arrays differential evolution (DE) in [12]. Mean square error
require accurate mathematical modeling, where the estimation comparing computed current and that supplied by the
of module parameters becomes vital. manufacturer datasheet is minimized by DE to estimate the
single-diode model parameters [13].
The equivalent circuit parameters of many electrical
systems are usually extracted from the experimental results of This paper presents a methodology for estimating the
prototype laboratory testing. Nevertheless, some publications equivalent circuit parameters of PV modules from datasheet
in the literature consider parameter estimation of PV modules information. The manufacturer-supplied open-circuit voltage,
from the manufacturer datasheet information. Analytical short-circuit current, maximum power, and voltage at

This work was sponsored by the Centre for Urban Energy, Ryerson
University, Toronto ON, Canada.

978-1-4799-7800-7/15/$31.00 ©2015 IEEE 2777

maximum power under standard test conditions (STC) raise the level of output voltage and current, Fig. 1(b), the
represent the targeted performance. An optimization algorithm output current is expressed as
searches the parameter set which minimizes the relative
absolute error (RAE) between computed and targeted
 1 3 4
performance. The optimization problem is solved using three 0  6 8 95

= -
 − -.
 /  2 25
− 17 −
: + ;

 9
nonlinear programing algorithms implemented by the Matlab
function ‘fmincon’ as well as the global search techniques of
(4)
GA and simulated annealing (SA). The method is applied to
the single- and double-diode models of a market-available PV
module. Results show the effectiveness of proposed method
and superiority of GA to other techniques. The need to where Np and Ns are the number of cells in parallel and series,
perform prototype testing in order to estimate the parameters respectively.
is evidently eliminated. Complicated mathematical derivations
and obscuring approximating assumptions are also avoided.
The proposed methodology relies on performance
characteristics spanning the whole range of operation from
open circuit to short circuit. Unlike other literature work, the
objective function formulation is straightforward and requires
no mathematical derivations.
(a)
II. MODELING OF PV CELLS
A. Single-Diode Model
As shown in Fig. 1(a), a PV cell can be modeled with a
current source in parallel to a diode, a shunt resistance to
account for leakage current, and a series resistance to
represent losses related to load current. Accordingly, the cell
current is given as

    
   

 =
 −

  − 1 − (1)


where Ic is the cell current, A, Iph is the photocurrent, A, Ios is

(b)
the reverse saturation current of the diode, A, q is the electron
charge, C, A is the diode ideality factor, K is Boltzmann Fig. 1. Single-diode model of: (a) PV cell, and (b) PV array.
constant, J/oK, T is the cell temperature, oK, Vc is the cell
voltage, V, Rs is the series resistance, Ohm, and Rsh is the
shunt resistance, Ohm. The photocurrent depends on the solar Equations (1) through (3) describe the performance of a
irradiance and cell temperature, and is given as PV cell. The model correlates the output variables of the cell,
Vc and Ic, with the independent variables representing the
environmental conditions, λ and T, through physical constants

 =  
 +  ! − !" # (2) and system parameters. The Boltzmann constant (K), electron
charge (q), band gap energy of the semiconductor (Eg), and
reference temperature (Tr) are all constants. Whereas, series
where λ is the solar irradiance, kW/m2, In is the nominal short- resistance (Rs), shunt resistance (Rsh), diode ideality factor (A),
circuit current at 1000 W/m2 and 25 oC, ki is the short-circuit nominal short-circuit current (In), reverse saturation current at
current temperature coefficient, A/oK, and Tr is the reference reference temperature and irradiance (Ior), and short-circuit
temperature, oK. Meanwhile, the reverse saturation current of current temperature coefficient (ki) are parameters of the PV
the diode varies with temperature, and is given as cell. The numbers of cells in series and parallel are required to
compute the performance of a PV array using (4).
B. Double-Diode Model
'( * *
$ & ) + ,

 =
"
   %  (3) In the double-diode model of a PV cell, two diodes are in
$%
parallel with the photocurrent source as shown in Fig. 2. The
model is known to be more accurate than the single-diode
model, especially at low irradiance levels. One diode
where Ior is the reverse saturation current of the diode at
represents the diffusion current in the p–n junction, whereas
reference temperature and irradiance, A, Eg is the band gap
energy of the semiconductor material, J/C. When PV cells are the other takes the space-charge recombination effect into
connected in series and parallel forming a PV array in order to account. Both single- and double-diode models are widely

2778
 |GHI + GI |
accepted to represent the behavior of monocrystalline and ;CD = ∑JK8 (8)
polycrystalline semiconductor PV cells. The output I-V GI

characteristic equation of the double-diode model becomes where XCi is the ith computed index and XTi is the ith targeted
index. The short-circuit current temperature coefficient (ki)
=
   

 =
 −
 8 < >*?$ − 1@
and nominal short-circuit current at STC (In) are usually
supplied by the manufacturer through datasheet. Therefore,
=
    : + ;
 
−
 A < >B ?$ − 1@ −
the parameters to be estimated for the single-diode model are
;  the series resistance (Rs), shunt resistance (Rsh), diode ideality
(5) factor (A), and diode reverse saturation current at reference
temperature and irradiance (Ior). However, for the double-
The reverse saturation currents of the two diodes are expressed diode model, six parameters are to be estimated including Rs,
in terms of their values at reference irradiance and temperature Rsh, A1, A2, Ior1, and Ior2.
as
The RAE given in (8) is considered an objective function
'( * *
$ & ) + ,

 8 =
"8
  *  % 
to be minimized by optimization techniques. The optimization
(6)
$% problem is independently solved by the nonlinear
programming algorithms coded in the Matlab function
and
‘fmincon’ as well as the global search routines of GA and SA.
'( * *
$ & ) + ,

 A =
"A
  B
The objective function formulation of this work covers a wide
%  (7)
$% operating range and requires no prototype testing or
mathematical derivation, unlike other practices [8]-[13].
Equations (5), (2), (6), and (7) represent the mathematical
model based on the double-diode equivalent circuit. The IV. OPTIMIZATION TECHNIQUES
model parameters are series resistance (Rs), shunt resistance A. Nonlinear Programming Algorithms
(Rsh), ideality factors for both diodes (A1 and A2), nominal
short-circuit current (In), reverse saturation current at reference The Matlab function ‘fmincon’ enables the use of four
temperature and irradiance for both diodes (Ior1 and Ior2), and different nonlinear optimization algorithms [14]. The trust-
short-circuit current temperature coefficient (ki). It is obvious region algorithm is one of the most basic, yet powerful, search
that the second diode adds two parameters to the model. techniques of optimization. However, the algorithm requires
user-defined derivatives of the objective function, which is not
possible for the problem at hand. Accordingly, the trust-region
algorithm is not used with the present optimization problem.
The active-set algorithm solves the Karush-Kuhn-Tucker
(KKT) equations, which are necessary conditions for
optimality of constrained problems. The algorithm, therefore,
attempts to compute the Lagrange multipliers directly. It
Fig. 2. Double-diode model of a PV cell. assures superlinear convergence by accumulating second-
order information using a quasi-Newton updating procedure.
Active-set is, however, a medium-scale algorithm. The
Manufacturer datasheets normally supply the open-circuit sequential quadratic programming (SQP) algorithm is quite
voltage, short-circuit current, and maximum power point similar to active-set; however, some differences exist in favor
under STC (1000 W/m2 irradiance, 25 oC temperature, and 1.5 of SQP. The differences include strict feasibility with respect
air mass). Datasheets also provide temperature coefficients of to bounds, adaptive step size, fast convergence, efficient use
short-circuit current, open-circuit voltage, and maximum of memory, possibility of objective and constraint functions
power. combination, and second-order approximation of constraints.

III. PROBLEM STATEMENT The interior-point algorithm of nonlinear programming

solves a sequence of approximate minimization problems.
The objective of this research is to estimate the model Solution of an approximate problem incorporates either a
parameters of PV modules from datasheet information. The direct step or a conjugate gradient step using a trust region.
module characteristics supplied by the manufacturer at STC The optimization problem of this work is independently
are considered the targeted performance. A set of parameters solved using the active-set, SQP, and interior-point algorithms
which yields computed performance as close as possible to as coded by the Matlab function ‘fmincon’.
targeted performance is sought. The targeted performance
signifies four indices, i.e., the short-circuit current, open- B. Simulated Annealing
circuit voltage, maximum power, and voltage at maximum An optimization method that mimics the physical process
power, all at STC, as supplied by the manufacturer. The of heating, then slowly cooling down, a material to decrease
obtained parameter set has to minimize the relative absolute defects and minimize system energy is called simulated
error (RAE) that measures the discrepancy between computed annealing [15]. Annealing is the technique of closely
and targeted performance. The RAE is expressed as controlling the temperature when cooling the material to
ensure that it reaches an optimal state. The SA routine works
in such a way that a new point is randomly generated in the

2779
search space every iteration. The distance of the new point attributed GA with the ability to escape local optima, besides
from the current point, or the search extent, follows a the robustness of attaining global ones.
probability distribution with a scale proportional to
temperature. The algorithm accepts any new point that lowers V. RESULTS
the objective function. However, points that raise the objective The equivalent circuit parameters of a commercial PV
function could be accepted with certain probability in order to module are estimated via the proposed technique. The
help the routine escape local minima. The temperature is an datasheet information of the Solarex MSX60 PV module is
SA parameter which affects the distance of a trial point from given in Table I. The short-circuit current at STC (In) and
the current point as well as the probability of accepting a trial short-circuit current temperature coefficient (ki) are provided
point with higher objective function. An annealing schedule is by the manufacturer. Therefore, the single-diode model lacks
selected to systematically decrease the temperature and reduce four parameters (Rs, Rsh, A, and Ior), whereas the sought
the search extent as the algorithm proceeds in order to parameters of the double-diode model are six (Rs, Rsh, A1, A2,
converge to a minimum. Ior1, and Ior2). The target performance denotes the short-circuit
current, open-circuit voltage, maximum power, and voltage at
Temperature decreases gradually as the algorithm maximum power under STC (Isc, Voc, Pmax, and VMPP,
proceeds; it could be a function of the iteration number. The respectively) as supplied by the manufacturer. The nonlinear
slower the rate of temperature decrease, the better the chance optimization problem is solved in four- and six-dimension
to find an optimal solution, but the longer the convergence search spaces for the single- and double-diode models,
time. The annealing parameter is a proxy for the iteration respectively.
number. The algorithm can raise temperature by setting the
annealing parameter to a lower value than the current iteration. TABLE I. DATASHEET INFORMATION OF THE PV MODULE
Re-annealing raises the temperature after the algorithm
accepts a certain number of new points, and starts the search Short-circuit current at SCT 3.8 A
again at a higher temperature to escape local minima. Unlike
Open-circuit voltage at STC 21.1 V
other multi-agent optimization techniques, SA is a single-point
global search algorithm with lesser computational burden per Maximum output power at STC 60 W
iteration. Stopping criteria of the routine include stagnation of MPP Voltage at SCT 17.1 V
fitness function, reaching runtime limit, processing certain
number of iterations, obtaining a desired value of the objective SC current temperature coefficient (ki) 0.065 %/oC
function, evaluating the objective function for a pre-defined Number of cells in series 36
number of times, or a combination of such conditions.
C. Genetic Algorithms The objective function of (8) is independently minimized
The GA is a probabilistic random guided search technique using three nonlinear programming algorithms and two global
inspired by the Darwinian theory of evolution, which employs search techniques. The obtained parameters of the single- and
the “survival of the fittest” concept of natural biology [15]. double-diode models are given in Table II for different
One distinct feature of GA is that the routine starts searching optimization techniques. Due to the stochastic nature of SA
from a population of points, not a single point, with no need to and GA, both algorithms are run for 10 times on every case,
have information about the derivatives of the objective where the best results are reported in Table II. In terms of the
function. The algorithm codes prospective solutions of the objective function value at convergence, GA always yields the
problem as a population of individual chromosomes of best result. Meanwhile, the global search techniques generally
different genes. The population is randomly initialized and the reach a less value of the objective function than all nonlinear
individuals are evaluated based on the corresponding values of programming algorithms. In terms of the convergence time,
an objective fitness function. Fit individuals are nonlinear programming algorithms are distinctly faster.
probabilistically copied to the “mating pool”, while weak
individuals likely die as their probability of selection is small The quality of the estimated parameters is tested by
due to the poor fitness. The natural genetic processes of inserting each set into the corresponding model in order to
crossover and mutation are then imitated in order to mate compute the performance. Computed performance indices are
parents of the current generation, and produce the offspring of compared with targeted ones in Table III, and the percentage
the next generation. Based on Darwin’s theory, the population error is also given. It appears that the performance indices
evolves from one generation to the next as the best fitness computed via the parameters estimated by GA are the closest
improves. to targeted ones. In general, the global search techniques of
SA and GA converge to better solutions of the present
In spite of the remarkable robustness of GA in finding problem than nonlinear programming algorithms. Also, the
global optima, the slowness of operation could be a significant performance computed by the double-diode model is more
obstacle in some applications. However, GA has proven accurate than that of the single-diode model. The most
notable effectiveness in many types of optimization problems. challenging part for a parameter set is to attain the targeted
Coding of individual solutions has granted GA one more maximum power at the targeted voltage. Best result is
apparent plus, which is its adaptability to certain optimization obtained via single-diode model with parameters estimated by
problems that could not be solved by classical or even some GA. An experimental verification study of these results will be
other evolutionary techniques. The sequentially applied published in a subsequent paper.
genetic operations of selection, crossover, and mutation

2780
 TABLE II. ESTIMATED PARAMETERS OF THE PV MODULE

Single-diode model
Nonlinear programming algorithms Global search algorithms
Parameter
Active set SQP Interior point SA GA
Rs, Ω 0.5201 0.7677 0.571 0.2548 0.3379
Rsh, Ω 200 200 200 400.77 455.83
A 1.1393 1.1952 1.1737 1.2814 1.2732
Ior, A 6.53×10–9 1.02×10–8 1.022×10–8 7.6593×10–8 6.2178×10–8
Convergence time, sec 8.96 9.89 11.26 48.62 48.61
Objective Function 0.0158 0.0559 0.0243 0.0057 0.0011
Double-diode model
Rs, Ω 0.761 0.7677 0.4217 0.3905 0.3471
Rsh, Ω 200 200 199.69 322.36 430.86
A1 1.1808 1.1952 1.1437 1.1615 1.2506
A2 2.0002 2.0002 1.9982 1.6319 1.9858
Ior1, A 7.28×10–9 1.02×10–8 8.03×10–9 1.21×10–8 4.45×10–8
Ior2, A 2.32×10–6 1.02×10–8 8.97×10–9 5.88×10–8 4.98×10–9
Convergence time, sec 9.34 11.1 8.71 64.4 38.38
Objective Function 0.0531 0.0558 0.0072 0.0067 8.0530×10–4

TABLE III. SOLUTION COMPARISON BASED ON COMPUTED PERFORMANCE OF THE PV MODULE

Single-diode model
Nonlinear programming algorithms Global search algorithms
Performance Active set SQP Interior point SA GA
Targeted
Index (STC) Error, Error, Error, Error, Error,
Computed Computed Computed Computed Computed
% % % % %
Isc, A 3.8 3.7901 –0.26 3.7855 –0.38 3.7892 –0.28 3.7976 –0.06 3.7972 –0.07
Voc, V 21.1 21.2455 0.69 21.7939 3.29 21.4003 1.42 20.9933 –0.51 21.1065 0.03
Pmax, W 60 59.9999 –0.0002 60.265 0.44 59.9484 –0.09 59.9979 –0.004 59.9997 –0.001
VMPP, V 17.1 17.208 0.63 17.352 1.47 17.208 0.63 17.1 0 17.1 0
Double-diode model
Isc, A 3.8 3.7856 –0.38 3.7855 –0.38 3.792 –0.21 3.7954 –0.12 3.7969 –0.08
Voc, V 21.1 21.806 3.35 21.7935 3.29 21.1087 0.04 20.9899 –0.52 21.1031 0.01
Pmax, W 60 59.677 –0.54 60.2602 0.43 59.971 –0.05 60.0145 0.024 60.0098 0.016
VMPP, V 17.1 17.28 1.05 17.352 1.47 17.172 0.42 17.064 –0.21 17.1 0

[2] G. Farivar and B. Asaei, “A new approach for solar module

temperature estimation using simple diode model,” IEEE Trans. on
VI. CONCLUSIONS Energy Conversion, vol. 26, no. 4, December 2011, pp. 1118–1126.
[3] R. Chenni, M. Makhlouf, T. Kerbache, and A. Bouzid, “A detailed
The paper presents a methodology for estimating PV modeling method for photovoltaic cells,” Energy, vol. 32, 2007, pp.
module parameters based on optimization techniques. The task 1724–1730.
is formulated as a nonlinear optimization problem that [4] S. H. Chan, and J. C. H. Phang, “Analytical methods for the extraction
minimizes the discrepancy between computed and targeted of solar-cell single- and double-diode model parameters from I-V
performances. Computed performance is obtained characteristics,” IEEE Trans. on Electron Devices, vol. 34, no. 2,
February 1987, pp. 286–293.
independently through single- and double-diode models; [5] T. Ikegami, T. Maezono, F. Nakanishi, Y. Yamagata, and K. Ebihara,
whereas, targeted performance represent nominal outputs at “Estimation of equivalent circuit parameters of PV module and its
STC as reported in the datasheet. The problem is solved using application to optimal operation of PV system,” Solar Energy
different nonlinear optimization algorithms and global search Materials and Solar Cells, vol. 67, 2001, pp. 389–395.
techniques. The obtained sets of parameters are evaluated by [6] M. Haouari-Merbah, M. Belhamel, I. Tobias, and J. M. Ruiz,
“Extraction and analysis of solar cell parameters from the illuminated
comparing their computed performance to targeted current-voltage curve,” Solar Energy Materials and Solar Cells, vol.
performance. Although nonlinear optimization algorithms 87, 2005, pp. 225–233.
require lesser time for convergence, results of global search [7] M. Chegaar, G. Azzouzi, and P. Mialhe, “Simple parameter extraction
techniques are clearly more accurate. Best results are usually method for illuminated solar cells,” Solid-State Electronics, vol. 50,
obtained through GA. 2006, pp. 1234–1237.
[8] M. Ye, X. Wang, and Y. Xu, “Parameter extraction of solar cells using
REFERENCES particle swarm optimization,” Journal of Applied Physics, vol. 105,
094502, 2009.
[1] A. Chatterjee, A. Keyhani, and D. Kapoor, “Identification of [9] L. Sandrolini, M. Artioli, and U. Reggiani, “Numerical method for the
photovoltaic source models,” IEEE Trans. on Energy Conversion, vol. extraction of photovoltaic module double-diode model parameters
26, no. 3, September 2011, pp. 883–889. through cluster analysis,” Applied Energy, vol. 87, 2010, pp. 442–451.

2781
 [10] M. Zagrouba, A. Sellami, M. Bouaicha, and M. Ksouri, “Identification [13] W. T. da Costa, J. F. Fardin, D. S. L. Simonetti, and L. V. B. Neto,
of PV solar cells and modules parameters using the genetic “Identification of photovoltaic model parameters by differential
algorithms: Application to maximum power extraction,” Solar Energy, evolution,” In Proc. IEEE Int. Conference on Industrial Technology,
vol. 84, 2010, pp. 860–866. Vina del Mar, Chile, 14–17 March, 2010, pp. 931–936.
[11] N. Krishnakumar, R. Venugopalan, and N. Rajasekar, “Bacterial [14] Optimization Toolbox User’s Guide for MATLAB (R2014a),
foraging algorithm based parameter estimation of solar PV model,” In Mathworks, 2014.
Proc. Int. Conference on Microelectronics, Communication, and [15] Global Optimization Toolbox User’s Guide for MATLAB (R2014a),
Renewable Energy, Kanjirapally, Kerala, India, 4 – 6 June, 2013, pp. Mathworks, 2014.
1–6.
[12] K. Ishaque and Z. Salam, “An improved modeling method to
determine the model parameters of photovoltaic (PV) modules using
differential evolution (DE)” Solar Energy, vol. 85, 2011, pp. 2349–
2359.

2782

View publication stats

Powered by TCPDF (www.tcpdf.org)