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16A MAXIMUM POWER POINT TRACKING FUZZY LOGIC CONTROLLER FOR PHOTOVOLTAIC PUMPING SYSTEM
A. El Jouni*, R. El Bachtiri**
* LESSI Laboratory, Department of Physics, Faculty of science, Sidi Mohamed Ben Abdellah University Dhar El Mehraz, BP: 1796, 30000 Fez-Atlas, Morocco. Phone: (+212) 62 58 45 08; E-mail: [email protected] ** REEPER Group, High School of Technology, Sidi Mohamed Ben Abdellah University BP: 2427 Fez Morocco Phone: (+ 212) 61 70 28 50; E-mail: [email protected]
Received: 14 Sept 2007; accepted: 19 Oct 2007
In this paper, the fuzzy controller is used to track the maximum power point (MPP) for a photovoltaic pumping system. For the best use, the photovoltaic (PV) panel must operate at its maximum power point (MPP). The PV panel efficiency, for given conditions, is maximal when its voltage equals a certain value that is optimal voltage which depends on irradiation, temperature and panel state. The pumping system considered in this paper consists of a photovoltaic generator (PVG) with a power electronic converter allowing maximum power point tracking (MPPT), the whole is feeding a DC motor coupling with a centrifugal pump. In the presence of the temperature and irradiation variations, the duty cycle of the converter, which is chosen as the controller law, is adjusted by using fuzzy logic controller (FLC) to track the MPP. The used FLC, incorporates expert knowledge, and doesn't depend on system mathematical model accurate. The effectiveness of the proposed approach is investigated by simulation at different operating conditions in Matlab/Simulink environment.
Keywords: photovoltaic pumping system, DC/DC converter, fuzzy logic controller, maximum power point tracking
Organization(s): Researcher student in laboratory of electronics, signal-systems and Information science (LESSI), Sidi Mohamed Ben Abdellah University (USMBA), Dhar El Mehraz, faculty of science, in Fez, Morocco.
Education: DESA degree (2002-2004) automatic and systems analysis, License degree (1991-1995) physics electronic. Experience: Since 2000 I'm teacher.
Main range of scientific interests: automatic and electrical engineering, renewable energy in power systems.
Publications: 2 papers in international scientific journals.
Abdeslam El Jouni
0.
Rachid El Bachtiri
Organization(s): Researcher teacher in Sidi Mohammed Ben Abdellah University (USMBA), Higher School of Technology (EST), in Fez, Morocco. Assisting Master (21/10/88), Ability Professor (22/01/97), Higher teaching Professor (22/01/01).
Education: Engineer (1983-1988), Mohammadia School of Engineers (EMI) Rabat, Morocco.
Doctor of Sciences Applied (January 1997), Catholic University of Louvain (1992-1997) at Louvain-
LaNeuve (Belgium), Faculty of Science Applied (FSA), Laboratory (LEI).
Experience: Lectures and Directed Work: Power Electronics and Electrical engineering. Person in charge for a team of research "team of research in electrical engineering, power electronics and renewable energies" (REEPER at the higher school of technology in Fez) belonging to the laboratory: "laboratory" (LESSI at the Faculty of Science in Fez).
Main range of scientific interests: electrical engineering, industrial electronics; resonance static conversion, effects of the harmonics, and their attenuation. Renewable energies; optimal use of the photovoltaic electrical power.
Publications: Papers in the power electronics and renewable energy field.
Introduction
It is well established that energy production and use based on consumption of fossil fuels can have deleterious environmental and human health impacts, including the potential of global warming of the earth through changes in the atmosphere's concentration of
carbon dioxide. The worldwide conventional energy sources are rapidly depleting. The increasing of the world energy demand, due to modern industrial society and population growth, is motivating a lot of investments in renewable energy source such as photovoltaic (PV) power, since it is clean, pollution-free and inexhaustible. One of the most popular applications of the photovoltaic
energy utilization is the water pumping system driven by electrical motors. A PV array is a non-linear power source. There is a unique point on the curve (PowerVoltage), called the maximum power point (MPP), at which the PV array produces maximum output power and its voltage equals a certain value that is the optimal voltage. As it is well known, the MPP of a PV power generation system depends on array temperature, solar irradiation, and PV cells ageing, so it is necessary to constantly track the MPP [1, 2, 3] of the solar array. A switch-mode power converter, called a maximum power point tracker, can be used to maintain the PV array's operating point at the MPP. The pumping system considered in this paper consists of a photovoltaic generator (PVG) with a power electronic converter allowing maximum power point tracking (MPPT), the whole is feeding a DC motor coupling with a centrifugal pump. Instead of maximizing the PV power, we will maximize the pump power, i.e. his rotation speed. For years, research has focused on various MPP control algorithms to track the maximum power of the PV array. These techniques include methods using neural networks [4, 5], perturbation and observation (P&O) methods [6, 7], incremental conductance [8], slide control method [1, 9] and computational methods. One of the computational methods which have demonstrated fine performances under different environmental operating conditions is the fuzzy based MPPT technique [3, 10, 11]. In recent years, fuzzy logic control has been widely used for industrial processes owing to their heuristic nature associated with simplicity and effectiveness for booth linear and nonlinear systems. However, in a number of cases, such as those, when parameter variations take place, or when disturbances are present, or when there is no simple mathematical model, fuzzy logic based control systems have shown superior performance to those obtained by conventional control algorithms. The main advantages of fuzzy logic controllers over the conventional controllers are: they do not need accurate mathematical model, they can work with imprecise inputs, they can handle nonlinearity and they are more robust than conventional nonlinear controllers. The aim of this paper is to present a fuzzy control of the duty cycle of the boost converter, that is considered as the control law of the system, to track the maximum rotation speed of the pump for different operating conditions. The paper is organized as follows: in section 2 mathematical model of the photovoltaic pumping system is given. In section 3, the structure configuration of the fuzzy logic controller applied of the system is presented. Section 4 presents the simulation results and a conclusion is given at the end of the paper.
Description of the photovoltaic pumping system
A photovoltaic water pumping system is mainly composed by a PV generator, a power electronic converter as a control organ, and an electrical motor usually coupled to a centrifugal pump. The schematic diagram of the proposed system is shown in Fig. 1. It
consists of a photovoltaic generator (PVG), a DC/DC boost converter and DC motor with a constant magnetic flux driving a centrifugal pump.
Sun
PVG-
Regulator
Fig. 1. General diagram of the photovoltaic pumping system Photovoltaic generator model
The solar cell is a non-linear power source, the output current and voltage depend on the irradiation level and temperature. The equivalent circuit of a PV module is shown in Fig. 2. The solar cell modules can only provide maximum power at specific voltage and current levels. So, for the PV array, there is a unique point on its P - Vp curve at which the power is maximum, and for optimum utilization, the equilibrium operating point of the PV array should coincide with this point.
Ip
Rs
i
Fig. 2. PV module equivalent circuit
The characteristic equation Vp - Ip of a PV module is given by the following equation:
Ip = Iph -10 (exp[ + RsIp)]-1)-(1)
with I0 = 10r - I0
' T *
exp
Kj
Rsh
_L -1
T T
V 7-1
À a Iph = [Iscr + Ki (T - Tr )]- and A = a
1000
NjKT
where Iph - photocurrent, I0 - cell reverse saturation current, I0r - cell saturation current at Tr, ISCR - short circuit current at 298.15 K and 1 kW/m2, KI - short circuit current temperature coefficient at ISCR, X - solar irradiation in W/m2, EGO - band gap for silicon, y -ideality factor, Tr - reference temperature, T - cell temperature, K - Boltzmann's constant and q - electron charge.
The PVG is composed of many strings of PV module in series, connected in parallel, in order to provide the desired values of input voltage and current of DC motor
system. This PVG exhibits a non-linear Ig characteristic given, by the following equation.
+ RgIg
Vg
Ig = Iphg -10(expU(( + RsgIg )]- l)- g + sg g , (2)
Rshg
where Vg - the PVG output voltage, Ig - the PVG output current, Ag = A/Ns - the PVG constant, Rsg = (N/Np) Rs -the PVG series resistance, Rshg = (N/Np), Rsh - the PVG parallel resistance, Iphg = NpIph - the photocurrent of the PVG, log = NpIo - the saturation current of the PVG, Ns -the number of PV connected in series and Np - the number of parallel paths. Both Ns and Np are designed carefully to have the amount of energy required by the motor pump. The variation of the output Vg - Pg characteristic of the PVG generator as function of irradiation and temperature is shown in Fig. 3 and Fig. 4 respectively, where Pg = = VgIg is the PVG power.
298.15 K
1. 0.8 KW/m2
2. 0 KW/m2
3. 1 KW/m2
45
50 15 25 35 PVG output voltage (V)
continuously the output characteristics of a PVG to the input characteristics of a DC motor. The power electronic converter is a boost chopper (Fig. 5) inserted between the PVG generator and the motor with a variable duty cycle a. The output voltage of the PVG is fed to the boost converter. It has to be adjusted to the optimum value by adjusting the duty ratio to the required value. The main function of the converter is to adjust the PVG output voltage to a value in which the PVG transfers maximum energy to the motor. The duty ratio of the boost converter is adjusted with the help of a fuzzy logic controller (FLC).
Fig. 3. Characteristic of the PVG with constant temperature and varying irradiation
From these figures, at any value of irradiation and temperature, there is only one point at which Pg is maximal. This point is called the MPP. Due to the relatively high cost of the PVGs, it recommended to operate at this MPP at all values of irradiation and temperature to increase the efficiency of the system.
0.9.KW/m2
1. 288.15 K
2. 298.15 K
3. 308.15 K
50 150 250 350 450
PVG output voltage (V)
Fig. 4. Characteristic of the PVG with constant irradiation and varying temperature
Power electronic converter
In order to improve the performance of a photovoltaic pumping system, a controlled DC-DC converter known as a maximum power point tracker is used to match
Fig. 5. Boost chopper
If the chopping frequency is sufficiently higher than the system characteristic frequencies, we can replace the converter with an equivalent continuous model. By considering the mean values of the electric quantities over a chopping period, the state equations of the converter are:
Im = (1 -aV - C
V dt
dIg
Vg = (1 -a)m + L0—f¡- + >0Ig + aRDSIg :
(3)
(4)
where L0 - the inductor of the converter, C0 - the output capacitor of the converter, r0 - the inductor equivalent resistance, and RDS - the MOSFET resistance ON. The inductor value, L0, required such the converter operates in the continuous conduction mode is calculated such that the peak inductor current at maximum input power does not exceed the power switch current rating. So
a
L0 is calculated as: L0 > Vg fj^ • The output capacitor value calculated to give the desired peak-to-peak output
voltage ripple is: C0 >
Ia
where fs - the switching
AVc fs
frequency, AI - the maximum input current ripple, AVC -the maximum output voltage ripple and am - the duty cycle at maximum converter input power.
Electrical motor modeling
We consider a DC motor with a constant magnetic flux and we neglect the magnetic reaction and the commutation phenomena. The choice of a DC motor for
International Scientific Journal for Alternative Energy and Ecology № 5 (61) 2008
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a PV powered system is economical because PV arrays supply DC power. Also, photovoltaic modules produce direct current, so using DC motors eliminates the need for AC/DC power converters. The mathematical relation that describes the dynamic model of a DC motor with constant magnetic flux can be expressed as follows:
Vm = RIm + L+ Ec (5)
dt
with Ec = Ke Q. The motor torque is:
Cm = KmIm . (6)
The parameters of the DC motor are: Ke - the back emf constant, Km - the torque constant, L - the armature inductance, R - the armature resistance and Q - the rotation speed.
Centrifugal pump model
For PV water pumping systems, two types of pumps are widely used: the volumetric pump and the centrifugal pump. It is found in the case of the centrifugal pumps, the operation takes place for longer periods even for low irradiation levels, and the load characteristic is in closer proximity to the PVG maximum power locus [12]. The centrifugal pump opposes to the motor a resistant torque Cr that is given by the following equation [13]:
Cm - Cr= Kr Q2, (7)
where K r - the proportionality coefficient.
The mechanical equation of the system is given by:
Cm - Cr = jdQ , (8)
dt
where J - the group inertia.
Fuzzy logic controller structure and design
The fuzzy logic permits to define control laws of any process starting from a linguistic description of the control strategy to be adopted. Fuzzy logic uses instead of numerical variables linguistic a variables whose
values (fuzzy subsets) are labels or sentences in a natural or artificial language.
Fuzzy logic controller structure
In a typical basic configuration of a fuzzy logic controller (FLC) one can find:
- Fuzzification or linguistic coding of input variables, which transforms a given set of numerical inputs (measured or calculated) into a fuzzy linguistic variables set composed of fuzzy subset called also membership functions.
- Inference fuzzy rules which contains a set of fuzzy rules in linguistic form as well as the database which is a collection of expert control objectives. This control rules base can be set up using IF-THEN rules, based on expert experience and/or engineering knowledge, and learning rule-based system which has learning capabilities.
- Defuzzification of the inference engine, which evaluates the rules based on a set of control actions for a given fuzzy inputs set. This operation converts the inferred fuzzy control action into a numerical value at the output by forming the "union" of the outputs resulting from each rule. The deffuzification produces a non-fuzzy output control action that best represents the recommended control actions of the different rules.
Fuzzy logic control design
The typical power-voltage characteristic of photovoltaic generator is shown in Fig. 3 and Fig. 4. The MPP is reached when the PVG output voltage Vg for given conditions equals its optimal value Vop. One has also Pu = KrQ3 the centrifugal pump power that must be maximum. Then at the MPP the rotation speed is maximum. The boost converter with an adjusted duty cycle permits the maximization of the rotation speed by an online adaptation of the PVG output voltage to steer in finite time at its optimal value. The duty cycle a of the converter, which is chosen as controller law is adjusted by using fuzzy logic controller (FLC), is proposed to keep the rotation speed at its maximum according to the solar irradiation (k) and the temperature (T) variations. Fig. 6 shows the block diagram of this fuzzy controller.
a
The two input control variables of this fuzzy controller are the rotation speed variation dQ and the PVG output voltage variation dVg; dQ and dVg are normalized using the two input scaling factors gQ and gv. The output of the controller is the duty cycle variation da that is normalized by scaling factor ga.
In the fuzzification process the numerical variable is converted into a linguistic variable or subset. The following five fuzzy levels are chosen for the controlling inputs and output of the fuzzy controller (dQ, dVg and da ) in fuzzification {NB (Negative Big), NS (Negative Small), ZE (Zero), PS (Positive Small) and PB (Positive Big)}. Membership functions for both controller inputs and output variables are defined on the common normalized range of [-1, 1]. In this paper, asymmetric triangular membership functions are considered and their representation is shown in Fig. 7.
NS
|(da)
|(dQ) ZE PS
PB
-1 -0.5 0 0.5 1 dVg
Fig. 7. Membership functions of dVg, dQ. and da
► da
corresponding output membership function weighted by the rule strength. The gravity center deffuzification method is used to convert the fuzzy output of the fuzzy controller into a numerical value. In this case, the change of the controller output is computed by the following equation:
da =
] i,y,s,
with (1< i < 25),
where p,- - represents the ith rule degree of the fulfillment at the kth sampling period, yi - the gravity center abscissa of the output fuzzy membership function corresponding to the ith rule and Si - its surface. The final control signal sent to the system is: a(K) = = a(K-1)+ ga da (K-1).
Table 1
Rule base of fuzzy logic controller
Change of PVG output voltage (dVg) Change of the rotation speed (dß)
NB NS EZ PS PB
NB NB NB EZ PB PB
NS NB NS EZ PS PS
EZ PS PS EZ PS PS
PS PB PS EZ NS NB
PB PB PB EZ NB NB
The generated rules should be done properly and arranged in a fuzzy matrix table. Twenty five rules have been deduced from a qualitative analysis of the influence of the rotation speed variation dQ and the PVG output voltage variation dVg which are given in Table 1. This rule table can reflect experiences of the human experts basis of Fig. 8. The fuzzy rules are designed to incorporate the following considerations keeping in view overall tracking performance.
1 - If a negative variation of the rotation speed is accompanied with a negative variation of PVG output voltage and vice versa, then we would decrease the duty cycle.
2 - If the variation of the rotation speed is sufficiently close to zero which means that its maximum is reached, then we would not make any variation in the duty cycle.
3 - If a positive variation of the rotation speed is going with a negative variation of PVG output voltage and vice versa, then we would increase the duty cycle.
During the inference process, the product-sum inference mechanism is used to calculate the fuzzy output of the controller. This is achieved by forming the union of the fuzzy output resulting from each rule, which is the
Fig. 8. Fuzzy rules deduction from versus Vg function
Simulation results
For the simulation we consider the parameters of the system:
- The photovoltaic panel SM55:
Rs = 0.1124 Q, Rsh = 6500 Q, y = 1.7404, ISCR = 3.45 A, I0r = 4.842 pA, K = 4-10-4 A/K, N = 36, Ns = 20, Np = 5 and Tr = 298.15 K.
- DC motor: ABB DMI 180B: Vmn = 400 V, Imn = 12.2 A, Qn = 104.7 rad/s, R = 9.84 W, L = 0.12 H, J = 0.06 Kg m2.
- Chopper parameters: L0 = 3.5 mH, C0 = 4.7 mF, r0 = 60 mQ, Rds = 85 mQ .
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- Centrifugal pump parameter: Kr = 28-10-4 W (s/rad)3, On = 104.7 rad/s.
- Fuzzy logic controller parameters: gO = 10-4, gv = 7-10-4, ga = 1.2.
Fig. 9, 10, Fig. 11, 12 and Fig. 13, 14 show respectively the good concordance between the rotation speed Q, the PVG power Pg and the duty cycle control a with the
theoretical results when the irradiation and the temperature increase (decrease) (Table 2). It is noted that when the irradiation and temperature vary, the duty cycle control is judiciously adjusted to its optimal value. Consequently the rotation speed converge to their optimal values which is corresponding to maximum power.
110
105
•100
T1
e e 95
u
e 90
o
85
m 80
75
70
800 W/m2
900 W/m2
298.15 K
298.15 K
900 W/m2
338.15 K
Theoretical Simulated I
0 1 2 3 4 5 6
Time (s)
Fig. 9. Rotation speed with increasing irradiation and temperature
1000 W
298.15 K
900 W
298.15 K
900 W 278.15 K
Theoretical Simulated
4 5 6
Time (s)
Fig. 10. Rotation speed with decreasing irradiation and temperature
Ph
O
5000 900 W/m2
4500 800 W/m2 298.15 K
4000 f 298.15 K 900 W/mt .
3500 ^ 338.15 K
3000 2 Theoretical Simulated 1
2500
1
4 5 . 6
Tim e (s)
Fig. 11. PVG power with increasing irradiation and temperature
Ph
O
>
Ph
5500 5000 4500 4000
3500 3000
900 W -
f 1000 W
900 W 278.15 K
298.15 K
Theoretical Simulated
1 2 3 4 5 6
Time (s)
Fig. 12. PVG power with decreasing irradiation and temperature
0.2
0.18
0.16
<D 0.14
O 0 12
ït
5 0.1
U
0.08
0.06
0.04
0.02
900 W/m2
900 W/m2 f 338.15 K .
800 W/m2
C 298.15 K
/ 298.15 K Theoretical
! Simulated
0 1 2 3 4 5 6
Time (s)
Fig. 13. Duty cycle with increasing irradiation and temperature
02
0.18
0.16
rj 0.14
c 0.12
3 0 1
U
0.08
0.06
0.04
0.02
0
1000 W
- f298.15 K; ^ 900 W
\ 298.15 K 900W
j 278.15 K :
Theoretical
— Siimulatedd
1 2 3 4 5 6
Time (s)
Fig. 14. Duty cycle with decreasing irradiation and temperature
Table 2
Theoretical results for given irradiation and temperature
Irradiation X and temperature T PVG Power Pg (W) Rotation speed Q (rad/s) Duty cycle a
X = 800 W/m2 T = 298.15 K 4313 101.1 0.1039
X = 900 W/m2 T = 278.15 K 5409 108.3 0.0964
X = 900 W/m2 T = 298.15 K 4897 105.1 0.1405
X = 900 W/m2 T = 338.15 K 3384 97.94 0.1830
X = 1000 W/m2 T = 298.15 K 5484 108.8 0.1720
Conclusion
In this paper, a fuzzy logic controller is derived and applied to a photovoltaic pumping system in order to track the optimal operating point. The system is consisting of a photovoltaic generator with a power electronic converter that assure maximum power point tracking (MPPT). The converter feed a DC motor coupling with a centrifugal pump. The PV generator is forced to operate at its maximum power point by using fuzzy logic controller that adjusts the duty cycle of the converter to control the motor rotation speed to reach its maximum value. The drive system performance has been simulated at different solar irradiations and temperatures. The simulation shows that the use of the proposed controller gives good results for the maximum power tracking.
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