Photovoltaic array maximum power point tracking using a fuzzy-sliding mode control.

Sellam, Mebrouk ; Hazzab, Abdeldjebar ; Bourahla, Mohamed 等

Introduction

With industrial development the problem of energy shortage is more and more aggravating. The photovoltaic (PV) systems are rapidly expanding and have increasing in electric power technology and regarded as the green energy of the new century control, sizing and management of stand-alone photovoltaic systems are based on static method and energy estimation allowing the simulation of PV system in average condition [1]. A solar panel is the fundamental energy conversion component of the PV systems. Its conversion efficiency depends on many extrinsic factors, such as insolation (incident solar radiation) levels, temperature, and load condition. In order to extract maximum power from the panel, a maximum-power-point tracker (MPPT), which is a dc/dc converter, is usually connected between the panel and the load. Various maximum-power-point (MPP) tracking methods such as power matching scheme [3], curve-fitting technique [4], perturb-and-observe method (PAOM) [5], and incremental-conductance technique (ICT) [6], Fuzzy Logic Control [7], sliding mode control [8] have been proposed.

In various nonlinear system control issues, fuzzy controller is recently a popular method to combine with sliding mode control method that can improve some disadvantages in this issue. Comparing with the classical control theory, the fuzzy control theory does not pay much attention to the stability of system, and the stability of the controlled system cannot be so guaranteed. In fact, the stability is observed based on following two assumptions: First, the input/output data and system parameters must be crisply known. Second, the system has to be known precisely. The fuzzy controller is weaker in stability because it lacks a strict mathematics model to demonstrate, although many researches show that it can be stabilized anyway [9]. Nevertheless, the concept of a sliding mode controller (SMC) can be employed to be a basis to ensure the stability of the controller.

In this paper the feature of a smooth control action of FLC has be used to overcome the disadvantages of the SMC systems. This is achieved by merging of the FLC with the variable structure of the SMC to form a Fuzzy Sliding Mode Controller (FSMC). In this hybrid control system, the strength of the sliding mode control lies in its ability to account for modeling imprecision and external disturbances while the FLC provides better damping and reduced chattering. The numerical simulation results of the proposed scheme have presented good performances compared to the adaptive sliding mode control.

Solar Array Mathematic Model

The equivalent circuit model of a solar cell consists of a current generator and a diode plus series and parallel resistance [2]. The mathematical equation expressing the output current of single cell is given as Eq. (1).

I = [I.sub.ph]-[I.sub.0][exp (e*(V+[R.sub.s]*I)/n.*A*[K.sub.B]*[T.sub.c])-1]- V+[R.sub.s]*I/[R.sub.sh]

Where [I.sub.ph]: photocurrent;

[I.sub.0] : saturation current;

Q: electron charge;

V: solar cell voltage;

[R.sub.s]: series cell resistance;

[R.sub.sh]: shunt cell resistance;

Principle of maximum power point tracking control [3]

The photovoltaic module operation depends strongly on the load characteristics, (Fig. 1 and 2) to which it are connected [5]. Indeed, for a load, with an internal resistance iR, the optimal adaptation occurs only at one particular operating point, called Maximum Power Point (MPP) and noted in our case max P.

Thus, when a direct connection is carried out between the source and the load, (Fig. 1), the output of the PV module is seldom maximum and the operating point is not optimal.

To overcome this problem, it is necessary to add an adaptation device, MPPT controller with a DC-DC converter, between the source and the load, (Fig. 3), [4, 5]. Furthermore the characteristics of a PV system vary with temperature and insolation [5]. So, the MPPT controller is also required to track the new modified maximum power point in its corresponding curve whenever temperature and/or insolation variation occurs.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Sliding Mode MPPT Controller

A Sliding Mode Controller is a Variable Structure Controller (VSC). Basically, a VSC includes several different continuous functions that map plant state to a control surface, and the switching among the functions is determined by plant state and is represented by a switching function [8, 9].

Without lost of generality, consider the design of a sliding mode controller for the following second order system:

[??] + [a.sub.i] [??] + [a.sub.2]x = b x u

We assume b > 0. u(t) is the input to the system. A possible choice of the structure of a sliding mode controller is [9]:

u = [u.sub.eq] + k x sign(s) (2)

Where [u.sub.eq] is called equivalent control which dictates the motion of the state trajectory along the sliding surface [9]; k is a constant, representing the maximum controller output required to overcome parameter uncertainties and disturbances. s is called the switching function because the control action switches its sign on the two sides of the switching surface s=o. For a second order system s is defined as [9, 10]:

s = [??] + [lambda]e (3)

where e = [x.sub.d] - x and [x.sub.d] is the desired state. [lambda] is a constant. sign(s) is the sign function, which is defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The control strategy guarantees that the system trajectories move toward and stay on the sliding surface s = 0 from any initial condition if the following condition is met:

s x [??] [less than or equal to] - [eta] (5)

where [eta] is a positive constant that guarantees the system trajectories hit the sliding surface in finite time [9].

Using a sign function often causes chattering in practice. One solution is to introduce a boundary layer around the switching surface [9, 10]:

u = [u.sub.s] + [u.sub.eq] (6)

where:

[u.sub.s] = k x sat (s/[xi]) (7)

where the constant factor [xi] defines the thickness of the boundary layer. sat (s/[xi]) is a saturation function that is defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

The characteristic of [u.sub.s] versus s/[xi] is shown in figure. 4.

[FIGURE 4 OMITTED]

Figure 3 shows the functional diagram of the simulated photovoltaic system. The DC-DC converter is the boost chopper of figure 4. The sliding mode MPPT controller is simulated under standard conditions with Temperature 27 [degrees]C and solar insolation 1000W/[m.sub.2]. The figure 6 shows the results of this test and prove the efficiency of the sliding mode MPPT controller to maintain continuously the panel power at its maximum value.

[FIGURE 5 OMITTED]

Fuzzy Sliding Mode MPPT Controller

The disadvantage of sliding mode controllers is that the discontinuous control signal produces chattering dynamics; chatter is aggravated by small time delays in the system. In order to eliminate the chattering phenomenon, different schemes have been proposed in the literature. However, this does not solve the problem completely. In this section, a fuzzy sliding surface is introduced to develop a sliding mode controller, where the function k x sat(s/[xi]) of all sliding mode controllers is replaced by a fuzzy system mechanism to reduce the chattering phenomenon. This approach shows that a particular fuzzy controller is an extension of an SMC with boundary layer [9].

Because the data manipulated in the fuzzy inference mechanism is based on fuzzy set theory, the associated fuzzy sets involved in the fuzzy control rules are defined as follows:

BN : Big Negative         Bigger
MN : Medium Negative      Big
ZE : Zero                 Medium
MP : Medium Positive      Small
BP : Big Positive         Smaller

Since only five fuzzy subsets, BN, MN, ZE, MP and BP, are defined for s, the fuzzy inference mechanism contains five rules for the fuzzy logic controller output. The resulting fuzzy inference rules for the output variable [u.sub.n] are as follows:

Rule 1: IF s is BN THEN [u.sub.n] is Bigger

Rule 2: IF s is MN THEN [u.sub.n] is Big

Rule 3: IF s is ZE THEN [u.sub.n] is Medium

Rule 4: IF s is MP THEN [u.sub.n] is Small

Rule 5: IF s is BP THEN [u.sub.n] is Smaller

The input and output membership functions are defined on Figure 6 and 7. Figure 8 shows the result of a defuzzified output [u.sub.n] for a fuzzy input s.

In this study, the triangular membership functions and center average defuzzification method are adopted, as they are computationally simple, intuitively plausible, and most frequently used in the literature.

The fuzzy sliding mode MPPT controller is simulated under the same conditions used with the sliding mode controller. The figure 9 shows the results of this test and prove the efficiency of the fuzzy sliding mode MPPT controller to maintain continuously the panel power at its maximum value very rapidly.

A comparison between the panel power controlled with a fuzzy sliding mode controller and that with the sliding mode controller under standard conditions: Temperature (27 [degrees]C) and solar insolation 1000W/[m.sub.2] IM by a SMC and a FSMC is presented in fig. 10. This comparison shows clearly that the fuzzy sliding mode controller gives good performances.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

Conclusion

In this paper we have presented a novel method for control of the PV system through the MPPT using fuzzy-sliding mode control. Designed system has succeeded to reduce the PV-array area and increase their output, obtained result indicates that the proposed method can successfully be used for control of MPPT for stand-alone PV system and give a minimum economic cost. It has been shown in the results of simulation that the proposed controller gives good performances compared to the sliding mode MPPT controller.

References

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Mebrouk Sellam *, Abdeldjebar Hazzab * and Mohamed Bourahla **

* L.P.D.S. Laboratory Universality of Bechar ** Laboratory of Power Electronics University of SC. Technologie Oran, Algeria selammabrouk@yahoo.fr, a_hazzab@yahoo.fr