2013 American Control Conference (ACC) Washington, DC, USA, June 17-19, 2013
MPPT for Photovoltaic Conversion Systems Using Genetic Algorithm and Robust Control* M.
Dahmane, Student Member IEEE, J. Bosche, A. EI-Hajjaji and X. Pierre
Abstract- This paper proposes an algorithm of maximum
power point tracking (MPPT) applied for photovoltaic (PV) power generation systems.
The strategy of this algorithm
considers the value of short circuit current to generate the current at the maximum power. In this work, the current reference is generated by genetic algorithm
(GA).
In this way,
short-circuit current measurements are not necessary, thus overcoming the reduction in output that result.
A
robust
control law using Linear Matrix Inequality (LMI) tools is developed to track
the
current
reference at the optimum
operating point of the PV-panel, in the sense of the MPPT algorithm. The performances of the proposed approach are ensured in simulation, using real proliles of irradiance and temperature measured on platform.
I.
INTRODUCTION
The current global energy situation can be summarized simply: the offer was increasingly difficult to meet demand. This increased energy demand is justified on the one hand, by a considerable technological development with the emergence of a multitude of systems that depend on energy, and secondly, to demographic changes. Yet the emergence of some countries in Asia, Latin America or in Eastern Europe, but also a growing world population, suggest energy needs increasingly important. On the other hand, these energy requirements are largely met by fossil fuels that emit greenhouse gases, and whose reserves are largely weakened by decades. Energy is at the heart of all subjects of discussion, debate and political news. This is a critical situation humankind has ever faced, which can be seen as a challenge, that of providing for energy needs from clean energy sources. Photovoltaic energy is clean energy that can be converted into electricity. It designates the electricity produced by transformation of a party of solar irradiance with a photovoltaic cell. The electrical association of several cells forms a PV panel. The characteristic of PV panel is that the available maximum power is provided only in a single operating point given by a localized voltage and current known [11], called Maximum Power Point (MPP). The problem in this characteristic is that the position of the MPP is not fixed but it varies according to the irradiance, the temperature and load [12]. On the other hand, solar panels are not very efficient with only about 12-20% (according to the solar-cell's technology and operating conditions) efficiency in their ability to convert sunlight to electrical power. So, in order to maximize the power derived from the PV panel; it's *Resrach supported by European Regional Development Fund and "Ie conseil regional de Picardie". M. Dahmane, J. Bosche, A. EL Hajjaji and
X. Pierre are with University
of Picardie Jules Verne, and researchers in the MIS Laboratory, 33, rue Saint Leu, 80000 Amiens France (e-mail: given
[email protected]).
978-1-4799-0178-4/$31.00 ©2013 AACC
crucial to operate PV energy conversion systems near maximum power point to increase the output efficiency of PV. This requires a technique to search (track) the MPP called maximum power point tracking (MPPT) algorithm [11]. A number of MPPT techniques have been developed for PV systems [6], [8], [14], and for all conventional MPPT techniques the main problem is how to obtain optimal operating points (voltage and current) automatically at maximum PV output power under variable climatic conditions. Several MPPT techniques can be mentioned: (i) the perturbation and observation (P&O) algorithm [1]: this is the most widely used method in commercial PV panel because it is easy to implement. This algorithm runs periodically by perturbing the operating current point of the panel and observing the power variation. From the power current characteristic of the panel, then it is to increase the value of current when the power decreases. The MPP is achieved when the power variation is almost zero; (ii) the incremental conductance (INC) algorithm [2] is implemented by periodically checking the slope of the Power-tension curve of a PV panel. If the slope becomes zero or equal to a pre defined small value, the perturbation is stopped and the PV panel is forced to work at this operating point; (iii) open and short-circuit method [5]: this method assumes a constant ratio between the open-circuit voltage Vac and the voltage at the maximum power Vmp and between the short-circuit current Imp and the current at the maximum power Imp, respectively [13]. This method is interesting but requires knowing the value of Vmp (or Imp) in real-time. Indeed these values vary markedly depending on the irradiance and temperature; (iv) intelligent based methods as Fuzzy logic methods [3], [7], [8], [9], [10]; (v) artificial neural network [4]. In this paper, short-circuit current generator algorithm is considered. The particularity of this work is that Iscvalue is not measured but estimated using a genetic algorithm (GA). This overcomes the problems, in terms of reduction in output, caused by short-circuit current Iscmeasurements. The paper is structured as follows. In section II, the PV-module and the Boost converter are described. The development of the control tools is given in section III. The strategy of the reference current Imp generation through GA and the development of a robust control law using LMI techniques [15] and allowing the tracking of this current are presented in this section. Simulation illustrations with irradiation and temperature profiles are proposed in section IV whereas conclusion and future works are summarized in section V. The Kronecker product is denoted by 0. is the 2-norm of matrix M induced by the Euclidean vector-norm, i.e. the maximal singular value of M. Un is the Notations:
IIMllz
6595
identity matrix of order
{.
n. ({]) is a null matrix of suitable
Xl
dimension.
II. PV
The electrical equivalent circuit of PV-panel is usually represented by the single or the double diode model. In this work the PV panel is simply considered as a voltage generator vpv and a current ipv' The considered photovoltaic conversion chain is shown in figure 1.
I
I
:I
{:z
V,,, I �I --
�+-
PV·Panel
------
�
Consider XT = [iv v] E lRi as the state vector, A E lRi2x2 the stat matrix, B E lRi2X1 the input matrix, and, D E lRi2X1 an exogenous input matrix. The stat representation is such that: X=
Ax+B(x)u+J
( vpv
l vFW
)
VI I
u E [0, 1] is the control input corresponding to the duty cycle. Note that the input matrix depends on the state of the system.
-L �
-1--
----
(2)
1 . ( l-u ) x2 = ---- Xl - -- X2 R C2 C2
MODULE AND BOOST MODELING
Mathematical model
A.
R, (l-u) 1 --(vFW +x2)-LvpV LXI --L
=-
.-
Boost
Load
B.
Figure!. PV energy conversion system.
Where L and RL are the self-inductance and its resistance; C1 the input capacitance; VFw the tension of the forward diode and we consider the load as resistance R. Remark: considering the value of C1given in Table 1, it can be supposed that 1pv "" iL. (iL the current debited on the self-conductance L).
Polytopic realization
The model presented in (3) is nonlinear in the state. Indeed, it considers an input matrix lBl =B (Xl' x2) that depends on the state variables iL and v. In this part, the Linear Time Varying (LTV) model (3) is expressed on a polytopic form. In fact, the boost controller is designed to be robust to a certain range of state variables such as:
(4)
The expression of the current iL in term of voltage vpm current and temperature is given by equations (1):
The matrix lBl is then assumed to belong to a polytope of matrices 'B defined by:
Where 8
E 8,
the set of all barycentric coordinates:
(1) (6) _
VT-
kT
The extreme matrices B;, i= 1, ... , N are the vertices of
q
Where 1ph is the photo-generated current; 10 the dark saturation current; Rs the cell series resistance; Rp the cell shunt resistance; T the diode quality factor; q the electron charge (1.6xlO,19 C); k, the Boltzmann's constant (1.38xlO,23 11K) and T the ambient temperature in kelvin. The values of both 1sc and Vac are given by the PV module manufacturers in the datasheet [17]. According to Figure 1, the state model of the system is deduced from the well-known of laws of Kirchhoff. It leads to the following stat equations:
such
as
( )
'B
Bl=B ivE , B2=B iL, V , B3=B (�, 0 ,
andB4 =B (ivv) .
( )
The polytopic model of the all system (PV-boost converter-load) is then described by the matrix M such as: M= 00(8) =
;=N
;=N
;=1
;=1
L 8;00;= L [A; B; Jd = [A
III.
lBl
J ] (7)
THE CONTROL STRATEGY
The control strategy consists of two steps and is illustrated in Figure 2:
6596
•
From the weather conditions in terms of temperature of the panel surface's T and irradiance G, the "G.A." Block allows generating a reference current Ire!corresponding to the current at the maximum power Imp.
•
[�}
The "ROBUST CONTROL" block allows tracking the reference current Ire! by generating a control signal u for the Boost Converter.
G�
-R,
Uo -1
L 1-uo
L
C2
RC2
1
X
!B
A. The augmented model
In order to ensure a smooth tracking of the reference current, a new state variable is introduced. It corresponds to the integral of the tracking error E as shown in Figure3.
We define (
=
I E, with E
=
Ire! - iL
=
Xl ·
Ire! -
Ax + B(X)
.
�+ J (:;:)
_ Ire! ( -
(8)
Xl
It leads to the following augmented state-space model: -R,
-1
L
L
C2
RC2
-1
0
x
�
0
[;;; 1 vpw
VPV
Ire!
(10)
o
=
0 0 0
[X
�
--x2 +vpw
0
L
+
-1
u+
C2
L
0
0
0
0
AX + S(X)u +
0
-1
0
J(;�;)
XT
=
Iii
�
B ce)
'D
II!J.ull::;
H
E
"'"=1 B c e)
=
{z
IIwl12::; p*
(10) with
vpw
(11)
�
t ) B,B,
E
q
a
+ [3z[3T ZT
