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Energy Procedía 6 (2011) 513-521

MEDGREEN 2011-LB

Optimization of energy management of a photovoltaic system by the fuzzy logic technique

F. Chekired*, A. Mahrane, M. Chikh, Z. Smara

Unité de développement des équipements solaires (UDES), route nationale N°11, BP386, Bou Ismail, 42415, Tipaza, Algerie.

Abstract

The efficiency of a photovoltaic system depends mainly on its energy management which takes in charge the storage and the distribution of the energy produced by the photovoltaic system in order to feed the load and to avoid any shortage of energy.

Our project concerns the energy management of a Stand Alone Photovoltaic System. This is done by elaborating an algorithmbased on the fuzzy logic technique which allows us to optimize the management of the storage system, ensuring a longer battery life, and the energy distribution available from the photovoltaic array and the batteries. It appears from the first results obtained that the fuzzy logic control maintains the battery voltage almost stable at the end phase of charge.

Key words: Stand-Alone Photovoltaic Systems (SAPVS), Energy Management, Battery, Fuzzy Logic, Fuzzy Controller.

1. Introduction

Climate change and oil shortage have prompted the ever-growing awareness about the need to use non pollutant energy. This favourable economic background conducted to an impressive growth rate of the photovoltaic industry in the last decade and it is expected to continue in the upcoming years. In this context, the number of PV installations increases year after year. As the initial cost is high, the users need to be ensured that the PV system installed will be reliable and energetically efficient [1]. The mastering of the performance of a Stand Alone Photovoltaic System (SAPVS) is done through the control and management of the energy of the system. The energy management of a PV system must both allow to:

■ Produce a maximum power from the photovoltaic generator,

■ Protect the battery against overcharge and deep discharge.

■ Satisfy the energy needs of the user by avoiding energy shortage.

* Corresponding author. Tel.:+213777248599; fax: +213240133. E-mail address: chekiredfathya@yahoo.fr

1876-6102 © 2011 Published by Elsevier Ltd. doi:10.1016/j.egypro.2011.05.059

We aim by our study to design and implement an energy management algorithm for SAPVS. After the modelization of the storage stage, we introduce a new technique, namely fuzzy logic which we use to design a fuzzy controller for batteries. That will allow us to optimize the management of the storage system ensuring a longer battery life and minimizing the potential malfunction of the elements constituting the photovoltaic system.

2. Energy management for Stand Alone Photovoltaic System (SAPVS)

A SAPVS consists of a photovoltaic generator composed of one or more solar panels, a set of batteries for electric energy storage, one or more DC-DC converters to provide the appropriate supply voltages for the batteries and continuous loads and a DC-AC converter for powering other AC devices [2], [3].

Fig. 1 A Stand Alone Photovoltaic System configuration

Due to the non-availability of permanent solar energy, for various reasons: weather, time of day, season etc..., the use of batteries as buffer of energy is required to guarantee continuous supply energy. In order to avoid any energy shortage and ensure a longer battery life, an energy management strategy is essential in a SAPVS.

3. Energy storage for SAPVS

3.1. Electrical model of battery

For the storage stage of photovoltaic system, both types of electrochemical storage battery as lead-acid (Pb acid) and nickel-cadmium (Ni-Cd) batteries are commonly used. Thanks to their sturdiness and stability, the lead-acid batteries are the most used in PV installations [4].

In order to study the operation of the battery, we have used a battery model shown on the figure 2 which is mainly based on:

■ The relation between the state of charge (SOC) and the charging current (IB) [4, 5].

■ The variation of the voltage (VB) according to the current and the state of charge (SOC) [4].

■ The variation of the capacity (CB) versus the current [4].

The models used for each stage of the battery model (figure 2) are described by the following mathe matical equations:

The capacitor model:

CB (t) =jt.0 la (t)dt + CBa (1)

CB (t) is the capacitor of the battery in (Ah) at a time t, CB i the initial capacitor of the battery in (Ah). Where:

Ic (t) = IB (t) - IGAZ (t)

Ic is the current of the capacitor, IB the current of the battery (A) and IoAS is the gasification current of the battery (A).

The gasification current model:

(t ) = Cl0

[Cv (Vele (t )-2.23)+Cr (TB (t )—20)]

C10 is the battery capacity at the rate of ten hours of discharge (Ah), Iq0 the standard gasification current (A), CV the voltage coefficient (V), VELE the battery element voltage (V). TC : temperature Coefficient (K). TB : Battery temperature (K).

The State of Charge (SOC) model:

The state of charge of a battery (SOC) is described by the mathematical equation:

■x100%

SOC(t ) = CB-(t )

The voltage model:

The charging voltage of the battery is described by the following equation:

VB (t) = EB (t) - Ro c x Ic (t)

EB is the internal voltage of the battery [6, 7], Ro, C is the internal resistance of charging phase

The discharging voltage of the battery expression is:

Vb (t) = Eb (t) - R

RO, D is the internal resistance of discharging phase [6, 7]. 3. 2. Simulation of the proposed model

Fig. 2 (a) Block diagram of the battery model [6], (b) Battery model under Simulink -Matlab environment.

Using the mathematical expressions related to each stage of the battery model, we have built the battery simulator in the Matlab-Simulink environment. This battery simulator allows us to study the charging and the discharging state of the Lead-acid battery used for storage in the case treated depending on the variation of the different parameters as the current, the voltage and the SOC of the battery. We have investigated the behaviour of the battery in two situations 'the state charge' and 'the discharge state' for a given fixed values of the battery current and for a constant temperature to 25o C.

In the case of the 'charge status ', the battery current takes the positive values of 0.5, 3, 5 and 9A, the case of 'discharge status ', the battery current takes the negative values of -0.5, -3, -5 and -9A. The temperature is fixed to 25OC in both cases.

The figure. 3. (a) and figure 3. (b) show the influence of the current battery value on the battery SOC.

0 . 0 ID

Time (s)

Ü 0 CO

V liB = - 0.5

¡A /B = - 3 A

/liB = - 5 A]

^IB = - 9 A

Time (S)

Fig. 3 (a) The battery SOC behaviour during the charging state; (b) The battery SOC behaviour during the discharging state.

We notice that the higher is the current for charging the battery the smaller is the time of charging. Thus, for a current of 9A the battery is charging in 20s while it takes 195s for a current of 0.5 A. We obtain for the 'discharge status' similar curves for the SOC of the battery than those we got for the 'charge status' case except that these curves decrease with time. It should be noted that the depth of discharge was set to 70% as shown as the figure. 3. (b)

4. Battery Fuzzy Controller

4.1. Introduction to the Fuzzy Logic technique

Several techniques are available for the implementation of the energy management algorithm [1]. Among them we have chosen the fuzzy logic technique which has low power dissipation, an optimized cost, is reliable and stable.

Fuzzy systems (FS) are based on fuzzy set theory and associated techniques pioneered by Lotfi Zadeh [9]. It is a non-linear control method, which attempts to apply the expert knowledge of an experienced user to the design of a fuzzy-based controller. Generally, as shown in figure 4, the Fuzzy Logic Controller (FLC) is composed by four main components:

a) The fuzzifier that maps crisp values into input fuzzy sets to activate rules.

b) The rules which define the controller behavior by using a set of IF-THEN statements.

c) The inference engine which maps input fuzzy sets into output fuzzy sets by applying the rules.

d) The defuzzifier that maps output fuzzy values into crisp values.

Real Uitput

Fig. 4 Fuzzy inference system

The rules describing the FLC operation are expressed as linguistic variables represented by fuzzy sets. The controller output is obtained by applying an inference mechanism [9, 10].

4. 2. Designing methodology of a battery Fuzzy controller

As the storage stage of the SAPV, in other words the battery, is one of the most sensitive block of the PV system, we have focused, as a first step, by elaborating an energy management for a SAPVS, on the energy storage management and battery controller. We propose 'an intelligent battery controller' based on a fuzzy algorithm.

The fuzzy controller which uses the Mamdani's FLC approach [11, 12, 13] has two fuzzy inputs and two fuzzy outputs (fig. 5). The two inputs are the voltage battery VB and the change of the battery voltage AVB, which are defined by:

AVfi (n) =VB (n) - VB (n - 1) (7)

Where:

n is the sampling time, and VB (n) is the instantaneous corresponding voltage. The output variables are the control signal of the switch K1 located between the photovoltaic generator and the battery and the control signal of the switch K2 located between the battery and the load (Fig. 1).

After applying the rules, which corresponds to the fuzzification step, the method of the center of gravity is used forthe defuzzication in order to find the actual values of Kj and K/> [11, 12, 13].

3 _t F ni i [flea [Ion Inferences Defmzificark'n

'b-► H Rnl&s -V

Data bas (Ie.50C.VB)

Fig. 5 Diagram of fuzzy controller for battery.

To improve this fuzzy algorithm, we will insert in one hand VR the required voltage for connecting the load while the battery is charging, on the other hand, VF the overcharging voltage for disconnecting the PV array while the battery is discharging to the load.

The battery voltage VB varies between 10.7 V and 14 V. The linguistic variables considered are: BUD for battery under-discharged, BD battery discharged BIC battery in charge, BC battery charged and BOC battery over-charged. The variation of the battery voltage AVB varies in the range of -50V to +50V. The linguistic variables associated to AVB are: NC for negative change, ZC for zero change and PC for positive change. The range of the K1output variable is (0 to 4) and its linguistic variables are chosen as K1 Off , K1 Off temporary, K1On and K1 On temporary. The range of the K2 output variable is (0 to 4) and its linguistic variables are identical to those of signal K1.

The battery voltage is always fluctuating. As the lead-acid batteries are very sensitive to the time of the load it is necessary to charge them with a current corresponding to a voltage VB which is between two thresholds: the maximum threshold (the gasification voltage) and the minimum threshold (the sulphating voltage). In our work, we used a battery of 12 V [6].

Figures 6 and 7 show the membership functions of the two inputs VB, AVB and the two outputs K1, K2 for the battery fuzzy controller.

if 11 i < b H it!- -.1 4 :, .: i 'i ■ b

rprtmrtlrt" MKittfcTfLr^-

Fig. 6 (a) Membership functions of input variable VB; (b) Membership functions of input variable A VB.

Fig. 7 (a) Membership functions of output variable K1; (b) Membership functions of output variable K2.

Table 1 shows the rule table of fuzzy controller where the inputs of the matrix are fuzzy sets of voltage (VB) and the change of the voltage (AVB). The output of this rules table is the state of two switches K1 and K2.

Table.1. Fuzzy inference of fuzzy controller inputs /outputs.

AVB VB BDD BD BIC BC BOC

NC K1 On On On On_temp Off

K2 Off Off_temp On On On

ZC K1 On On On On Off

K2 Off Off On On On

PC K1 K2 On Off On Off_temp On On Off_temp On Off On

In order to understand how to use this table, we give the following example: If we assume that the battery is deeply discharged (BDD) and the change of voltage is negative (NC) then the switch K1 will be off and K2 On.

5. Simulation and results

5. 1. Implementation of the battery fuzzy controller in a Stand Alone Photovoltaic System

For a given photovoltaic system, taking into account the conditions of the irradiance, the temperature and the SOC of the battery, the FLC orders the opening or the closing of both switches K1 and K2 such that to ensure an optimal management and distribution of the energy available from the photovoltaic field and the battery. Figure. 8 presents the implementation of the algorithm translated in table.1 under Matlab/ Simu link.

Fig. 8 Simulink block of the battery fuzzy controller.

5. 2. Simulation oof the battery fuzzy controller

Figure 9 represents the states of both switches Ki and K2 after applying the battery fuzzy controller,

Signal K2

Fig. 9 States of the switches K1 and K2 controlled by the fuzzy controller.

The figure 9 is a dynamical representation of the states of the K1 and K2 switches in response to the variations of VR and A VR according to the inference rules previously established and managed by the FLC in order to better regulate the battery voltage. The opening and closing of these switches controls the link between the generator and the battery and the link between the battery and the load.

j ¡

/ T=®t

_ _ l_l _ _ i_ i

! T=25CÍ°

0 S 10 15

30 35 30 35 40 45 60

Time (s)

15 20 25 30 35

Time (s)

Fig. 10 (a) Variation of the battery voltage not controlled; (b) Variation of the battery voltage set by the fuzzy

algorithm.

In order to evaluate the FLC performance, we have simulated, in a first stage, the energy management of a SAPVS which uses the on/off technique for the management. As it is shown on the figure 10(a), the range of the battery voltage variation is between 12V and 14 V.

The figure 10(b) shows the result obtained by inserting the FLC. The voltage delivered to the load at the end phase of charge is comprised in a narrow range situated between 11.7V and 12.5 V. As expected the FLC allows avoiding the successive overloads and deep discharge of the battery and then prevents any malfunction of the PV system.

6. Conclusion

We have presented in this paper the first version of a photovoltaic energy management system based on Fuzzy Logic Control technique. This technique allows us to manage with accuracy the switching mode of K1 and K2 which respectively control the battery charging mode and the feeding of the load. The transition time between the charging and discharging mode using this technique is very short comparing to the other techniques used in this field.

The next step of our work, concerns the use of other battery models which take into account several parameters like the efficiency of the battery, the State of Charge of the battery linked to the battery voltage.

7. Acknowledgement

We would like to thank Mr S. Elmetnani (UDES) for his valuable advices on the writings of this article

8. References

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