energies Article

Fuzzy Logic Based MPPT Controller for a PV System Carlos Robles Algarín *

ID

, John Taborda Giraldo and Omar Rodríguez Álvarez

Facultad de Ingeniería, Universidad del Magdalena, Carrera 32 No. 22-08, 470004 Santa Marta, Colombia; [email protected] (J.T.G.); [email protected] (O.R.Á.) * Correspondence: [email protected]; Tel.: +57-5-421-7940 Received: 19 October 2017; Accepted: 22 November 2017; Published: 2 December 2017

Abstract: The output power of a photovoltaic (PV) module depends on the solar irradiance and the operating temperature; therefore, it is necessary to implement maximum power point tracking controllers (MPPT) to obtain the maximum power of a PV system regardless of variations in climatic conditions. The traditional solution for MPPT controllers is the perturbation and observation (P&O) algorithm, which presents oscillation problems around the operating point; the reason why improving the results obtained with this algorithm has become an important goal to reach for researchers. This paper presents the design and modeling of a fuzzy controller for tracking the maximum power point of a PV System. Matlab/Simulink (MathWorks, Natick, MA, USA) was used for the modeling of the components of a 65 W PV system: PV module, buck converter and fuzzy controller; highlighting as main novelty the use of a mathematical model for the PV module, which, unlike diode based models, only needs to calculate the curve fitting parameter. A P&O controller to compare the results obtained with the fuzzy control was designed. The simulation results demonstrated the superiority of the fuzzy controller in terms of settling time, power loss and oscillations at the operating point. Keywords: fuzzy logic controller; maximum power point tracking (MPPT); dc-dc converter; photovoltaic system

1. Introduction In recent years, the use of photovoltaic (PV) energy has experienced significant progress as an alternative to solve energy problems in places with high solar density, which is due to pollution caused by fossil fuels and the constant decrease of prices of the PV modules. Unfortunately, the energy conversion efficiency of the PV modules is low, which reduces the cost-benefit ratio of PV systems. The maximum power that a PV module can supply is determined by the product of the current and the voltage at the maximum power point, which depends on the operating temperature and the solar irradiance. The short-circuit current of a PV module is directly proportional to the solar irradiance, decreasing considerably as the irradiation decreases, while the open circuit voltage varies moderately due to changes in irradiation. In contrast, the voltage decreases considerably when the temperature increases, while the short circuit current increases moderately. In summary, increases in solar irradiation produce increases in the short-circuit current, while increases in temperature decrease the open circuit voltage, which affects the output power of the PV module. This variability of the output power means that in the absence of a coupling device between the PV module and the load, the system does not operate at the maximum power point (MPP). According to the previous context, the use of maximum power point (MPPT) controllers is currently increasing [1]. These devices are responsible for regulating the charge of the batteries, controlling the point at which the PV modules produces the greatest amount of energy possible, regardless of variations in climatic conditions. The use of MPPT controllers in PV systems has the following advantages: 1. They yield more power, depending on weather and temperature; 2. They allow the connection of PV modules in series to increase the voltage of the system, which reduces the Energies 2017, 10, 2036; doi:10.3390/en10122036

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wiring gauge and adds flexibility; 3. They offer a cost savings in the transmission wire needed for the installation of the PV system. In contrast to MPPT controllers, traditional controllers make a direct connection of the PV modules to the batteries, which requires that the modules operate in a voltage range that is below to the voltage in maximum power point. For example, in the case of a 12 V system, the battery voltage can vary between 11 V and 15 V, but the voltage at the maximum power point is a typical value between 16 V and 17 V. Due to this situation, with the traditional controllers the energy that the PV modules can deliver is not maximized. Taking into account the above, different researches have been carried out using traditional algorithms for the modeling and implementation of MPPT controllers [2], of which the following are highlighted: perturb and observe (P&O) [3,4], modified P&O [5,6], fractional short circuit current [7], fractional open circuit voltage [8], sliding mode control [9,10] and incremental conductance [11]. The P&O algorithm has been used traditionally, but it has been shown that this method has problems for tracking the MPP when there are sudden changes in solar irradiance [12]. Also, algorithms based on artificial intelligence techniques such as fuzzy logic [13–19] and neural networks [20–22] have been used, as well as the implementation of optimization algorithms such as glowworm swarm [23], ant colony [24,25] and bee colony [26–28]. These algorithms are part of soft computing techniques and have the advantage of being easily implemented using embedded systems. Additionally, MPPT controllers are widely used in hybrid power systems, in which different control techniques based on neural networks, fuzzy logic and particle swarm optimization have been evaluated. In [29–31], the effectiveness of these control techniques was demonstrated in order to achieve a fast and stable response for real power control and power system applications. The implementation of new control and optimization techniques that are detailed in [32–35] for electrical power and energy systems can be studied in the modeling and implementation of MPPT controllers. This paper presents the design and modeling of a fuzzy controller to track the maximum power point of a PV module, using the characteristics of fuzzy logic to represent a problem through linguistic expressions [36]. This paper presents as a novelty the use of the mathematical model proposed in [37,38] for modeling the PV module, which, unlike diode based models, only needs to calculate the curve fitting parameter. The results were compared with the P&O controller, which demonstrated that the proposed approach presents less energy losses and ensures MPP in all cases evaluated in simulation. It is worth mentioning that this work is part of a set of intelligent control techniques being evaluated in the research group Magma Ingeniería of the Universidad del Magdalena in order to implement a MPPT controller of low cost and high efficiency. The main objective of this work is the design, modeling and simulation of a fuzzy logic controller and a dc-dc converter for an off-grid PV system. In a second stage, the fuzzy logic controller will be implemented using the low-cost Arduino platform [38], taking as a reference the input variables, output, fuzzification, inference system and defuzzification evaluated during the modeling stage. The dc-dc converter will also be implemented according to the design conditions evaluated in the simulations. This work is structured as follows: Section 2 presents the design and modeling of PV system. Section 3 shows the simulation results for different operating conditions established in Matlab-Simulink. Finally, Section 4 summarizes the main conclusions. 2. Design and Modeling of PV System Figure 1 shows the general diagram of the PV system, which is composed of the 65 W PV module, the buck converter, the battery and the MPPT algorithm (fuzzy or P&O).

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PV Module (65W)

Io

I V

+ Vo -

DC-DC Converter (Buck)

Battery

D MPPT Algorithm

Figure 1. Block diagram of the photovoltaic (PV) system.

Figure 1. Block diagram of the photovoltaic (PV) system. 2.1. Modeling of the PV Module

2.1. Modeling the PV (1) Module In of Equation the mathematical model of the PV module is shown [37,38]. With this model, it only necessary to calculate the curve fitting parameter that can be obtained directly from the In is Equation (1) the mathematical model of the PV module is shown [37,38]. With this model, Equation (1). The other parameters are obtained from the electrical data of the PV module. it is only necessary to calculate the curve fitting parameter that can be obtained directly from the V 1 Ix − ) bVx b ] Equation (1). The other parameters are I(V) obtained from the (electrical data of the PV module. (1) = −1 [1 − e 1 − e( bh )

(

V

−1)

i

Ix b where Vx and Ix are the open circuit short with dynamic values for solar I(Vvoltage 1 −circuit e bVx current ) = and ( −1 ) b 1 − e irradiance and temperature, which are defined by Equations (2) and (3); b is the characteristic constant, it does not have units and is the unique parameter that has to be calculated.

(1)

where Vx and Ix are the open circuit voltage and short circuit current with dynamic values for solar E Vmax −Voc ( i(3); ln( b Ei irradiance and temperature, which are defined by Equations (2) and is the))characteristic(2)constant, Vx = s TCv (T − TN ) + sVmax − s(Vmax − Vmin )e EiN Vmax−Vmin E it does not have units and is the iN unique parameter that has to be calculated. I =p

Ei

[I + TC (T − T )]

sc i N Vx = s EEiNi TCv (T − TN ) x+ sVEmax iN − s(Vmax − Vmin )e

Ei iN

(E

max −Voc )) ln ( VVmax −V min

(3)

(2)

where; s: number of PV modules connected in series; p: number of PV modules connected in parallel; i Ix = p EEiN (3) + TCi (T − TN )] of 1000 W/m2; T: temperature of Ei: effective irradiation of the PV module; EiN[I: scirradiation constant the PV module; TN: temperature constant of 25 °C; Tcv: temperature coefficient of voltage; Tci: where; s: number of PV modules connected in series; p: number of PV modules connected in parallel; temperature coefficient of current; Voc: open circuit voltage; Isc: short-circuit current; Vmax: voltage for 2 Ei : effective irradiation the of 1000 W/m temperature of the iN : irradiation irradiations underof 200 WPV andmodule; operatingEtemperature of 25constant °C (this value is 103% of V;ocT: ); V min: voltage ◦ PV module; TN : temperature of 25 C; Tcv : temperature coefficient voltage; for irradiations over 1200constant W and operating temperature of 25 °C (this value is of 85% of Voc). Tci : temperature electrical parameters of thevoltage; 65 W PVImodule (Yingli Solar, Baoding, China) are illustrated coefficient ofThe current; Voc : open circuit current; Vmax : voltage for irradiations sc : short-circuit ◦ in Table 1. To find b, Equation (1) and the parameters of Table 1 were used. Knowing the: value under 200 W and operating temperature of 25 C (this value is 103% of Voc );that Vmin voltage for of b is in the range of 0.01 to 0.18 [39], the approximation of ◦Equation (4) can be done.

irradiations over 1200 W and operating temperature of 25 C (this value is 85% of Voc ). −1 (4) The electrical parameters of the 65 W PV module (Yingli Solar, Baoding, China) are illustrated in 1 − e( b ) ≈ 1 Table 1. To find b, Equation (1) and the parameters of Table 1 were used. Knowing that the value of b Therefore, for Vx = 21.7 V; Ix = 4 A; I = 3.71 A and V = 17.5 V; the value of b is 0.07375. is in the range of 0.01 to 0.18 [39], the approximation of Equation (4) can be done. Table 1. Electrical parameters of the PV module type YL65P-17b.

Therefore, for

−1 Parameter Value 1 − e( b ) ≈ 1 Short-circuit current (Isc) 4A Open circuit voltage (Voc) 21.7 V Vx = 21.7 V; Ix =Voltage 4 A; I at=P3.71 A and V = 17.5 V; the value max (Vmpp) 17.5 V of b Current at Pmax (Impp) 3.71 A Table 1.Temperature Electrical parameters the PV type−0.0802 YL65P-17b. coefficient of of voltage (Tcvmodule ) V/°C Temperature coefficient of current (Tci) 0.0024 A/°C Maximum voltage (Vmax) 22.35 V Parameter Value Minimum voltage (Vmin) 18.44 V

Short-circuit current (Isc ) Open circuit voltage (Voc ) Voltage at Pmax (Vmpp ) Current at Pmax (Impp ) Temperature coefficient of voltage (Tcv ) Temperature coefficient of current (Tci ) Maximum voltage (Vmax ) Minimum voltage (Vmin )

4A 21.7 V 17.5 V 3.71 A −0.0802 V/◦ C 0.0024 A/◦ C 22.35 V 18.44 V

(4) is 0.07375.

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Figure Figure 2a 2a shows shows the the modeling modeling of the PV module with the Simulink function blocks (MathWorks, Natick, MA, USA). Figure 2b 2b presents the PV in a subsystem, which was evaluated for different Natick, MA, USA). Figure presents themodule PV module in a subsystem, which was evaluated for values of solar and temperature. different valuesirradiance of solar irradiance and temperature. (s*(u(1)/1000)*(TCv)*(u(2)-25))+(s*Vmax)-((s*(VmaxVmin))*(exp((u(1)/1000)*(log((Vmax-Voc)/(Vmax-Vmin))))))

1

[Vx]

Vx

Fcn Vx

Ei 2

p*(u(1)/1000)*(Isc+(TCi*(u(2) -25)))

T

[Ix]

Ix

Fcn Ix [Vx]

From2 ((u(2)/(1-(exp(-1/b))))*(1(exp((u(3)/b*u(1)))-(1/b)))))

[Ix]

From3 3

1

I

Fcn I

V

(a) [Ip] Imodule

Ei

1

1

V+

Ei (W/m2)

Isource2 2

2

T

V-

2

I

Imodule1

T °C

3

Pmodule Pmodule1

V Memory

3

Ref_V

PV Module

1

Vmodule1

(b)

Figure Figure 2. 2. PV module in Matlab. (a) Model implemented with Simulink Simulink function function blocks; blocks; (b) (b) Subsystem Subsystem implemented implemented for for the the simulation. simulation.

Table22shows shows values obtained the mathematical of the PV module, using Table thethe values obtained withwith the mathematical modelmodel of the PV module, using variable ◦ variable solar irradiance and operating temperature of 25 °C. Itbecan be that seen the thatvalues the values obtained solar irradiance and operating temperature of 25 C. It can seen obtained for 2, T = 25 °C) 2 ◦ for standard test conditions (E i = 1000 W/m correspond to the electrical parameters of standard test conditions (Ei = 1000 W/m , T = 25 C) correspond to the electrical parameters the of PV PV module presented in in Table 1. 1. Additionally, it itisisworth the solar solar the module presented Table Additionally, worthnoting notingthat thatthe the decreases decreases in in the irradiance considerably considerably affect affect the the short-circuit short-circuit current, current, while while the the open open circuit circuit voltage voltage is is affected affected in in irradiance smaller proportion. smaller proportion. Table 2. Parameters of the PV module for variable solar irradiance. Table 2. Parameters of the PV module for variable solar irradiance.

Parameter 1000 W/m2 800 W/m2 600 W/m2 400 W/m2 200 W/m2 2 2 2 2 Parameter 400 W/m1.6 200 W/m Short-circuit current Isc (A) 1000 W/m4.0 800 W/m23.2 600 W/m2.4 0.8 Open circuit current voltageIscVoc (V) Short-circuit (A) 4.0 21.70 3.2 21.42 2.4 21.02 1.6 20.44 0.819.62 Open circuit Voc(V) (V) 21.7017.66 21.42 17.55 21.0217.37 20.4416.78 19.62 Voltage at voltage Pmax Vmpp 16.08 Voltage at P V (V) 17.66 17.55 17.37 16.78 16.08 max mpp Current at Pmax Impp (A) 3.679 2.924 2.171 1.459 0.730 Current at Pmax Impp (A) 3.679 2.924 2.171 1.459 0.730 Maximum Power Point (W) 64.98 51.31 37.72 24.48 11.75 Maximum Power Point (W) 64.98 51.31 37.72 24.48 11.75 Table 3 shows the data obtained with the mathematical modeling of the PV module for solar Table 3ofshows the data obtained the mathematical modeling PV module for solar 2 and irradiance 1000 W/m variablewith temperature. In this case, it canofbethe noted that increases in 2 and variable temperature. In this case, it can be noted that increases in irradiance of 1000 W/m temperature considerably affect the open circuit voltage, while the short-circuit current is affected in a smaller proportion. Tables 2 and 3 will be used as references in the results and discussion section,

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temperature Energies 2017, 10,considerably 2036

affect the open circuit voltage, while the short-circuit current is affected 5 of in 18 a smaller proportion. Tables 2 and 3 will be used as references in the results and discussion section, in in which which aa comparison comparison with with the the fuzzy fuzzy and and P&O P&O controllers controllers will will be be made; made; with with variations variations of of the the solar solar irradiance temperature of of the the PV PV module. module. irradiance and and the the operating operating temperature Table 3. Parameters of the PV module for variable temperature. Table 3. Parameters of the PV module for variable temperature.

Parameter Parameter Short-circuit current Isc (A) Open circuitcurrent voltage oc (V) Short-circuit Isc V (A) Open circuit voltage V (V) oc (V) Voltage at Pmax Vmpp Voltage at Pat Vmpp max Current Pmax Impp(V) (A) Current at Pmax Impp (A) Maximum Power Point Maximum Power Point (W)(W)

0 °C 0 3.94 3.9423.71 23.7119.39 19.393.606 3.606 69.9269.92 ◦C

25 °C 25 4.00 4.0021.7 21.7 17.66 17.66 3.679 3.679 64.98 64.98 ◦C

50 °C 50 ◦4.06 C 19.69 4.06 19.69 16.47 16.47 3.617 3.617 59.59 59.59

75 °C ◦C 754.12 17.69 4.12 17.69 14.47 14.47 3.771 3.771 54.55 54.55

2.2. DC-DC Converter Model 2.2. DC-DC Converter Model A buck converter as control device was used. Figure 3 shows the circuit that was designed to A buck converter as control device was used. Figure 3 shows the circuit that was designed to ensure that the converter operates in the continuous conduction mode (CCM); in order to avoid that, ensure that the converter operates in the continuous conduction mode (CCM); in order to avoid that, the current in the inductor reaches zero during a time interval. the current in the inductor reaches zero during a time interval. Vo

Figure 3. Buck converter circuit. Figure 3. Buck converter circuit.

In the CCM, thethe diode is in circuit (Ton(T ).onUsing Equation (5), CCM,when whenthe thetransistor transistorisisconducting, conducting, diode is open in open circuit ). Using Equation the ripple of the is obtained as shown in Equation (6). (6). (5), the ripple of inductor the inductor is obtained as shown in Equation LΔIL L∆I L L = VLV= ∆t∆t −ILILRRLL))− −V Voo s− DS− (V(V VV s− DS Ton ∆IL∆I == T L (+) (+) on LL The inductor current decreases during the off off state state as as shown shown in in Equation Equation (7). (7).

(5) (5) (6) (6)

V + (V + I R ) Vo o+ (Vdd+ ILLRLL) Toff (7) ∆IL (−) = ∆IL (−) = Toff (7) L L Assuming that Vd, RL y VDS are very small values, Equations (8) and (9) are obtained. Assuming that Vd , RL y VDS are very small values, Equations (8) and (9) are obtained. (Vs − Vo ) (8) ∆IL (+) = T (Vs −LVo ) on ∆IL (+) = Ton (8) L Vo (9) ∆IL (−) =V Toff o ∆IL (−) = LToff (9) L Equating Equations (8) and (9); using Ts = Toff + Ton, Equation (10) for the duty cycle D is obtained. Equating Equations (8) and (9); using Ts = Toff + Ton , Equation (10) for the duty cycle D is obtained. Ton Vo D= = (10) TonTs VVos D= = (10) Ts Vs 2.2.1. Inductor Design The inductor was designed to maintain the balance volts per second of the converter and to reduce ripple in the output current. Using an improper inductor produces an alternating current ripple in the direct current output, causing a change between continuous and discontinuous

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2.2.1. Inductor Design The inductor was designed to maintain the balance volts per second of the converter and to reduce 6 of 18 ripple in the output current. Using an improper inductor produces an alternating current ripple in the direct current output, causing a change between continuous and discontinuous conduction modes. conduction modes. To operate in the continuous conduction mode, the critical output current must To operate in the continuous conduction mode, the critical output current must be greater than or be greater than or equal to half the inductor current ripple. See Equation (11) and Figure 4. equal to half the inductor current ripple. See Equation (11) and Figure 4. ∆IL (11) io (crit) ≥ ∆I io (crit) ≥ 2 L (11) 2 Energies 2017, 10, 2036

I L Solid io Dashed= io(crit) ΔI L

Ton

Toff Ts

Figure Critical output current. Figure 4. 4. Critical output current.

Replacing Equation (8)(8) inin (12), using Ton = DT s, the Equation (12) forfor thethe design of of thethe inductor Replacing Equation (12), using Ton = DT Equation (12) design inductor s , the is is obtained. obtained. o Vo ( 1 − V V )Ts Lmin ≥ Vo (1 − Vos)Ts (12) Vs ) 2i0 (crit (12) Lmin ≥ 2i0 (crit) To calculate L, the maximum power and voltage according to the MPP of the PV module were used: Vs = 17.71 W, ioand = 5.41 A, fsaccording = 20 KHz. Using a ripple value of 10% for a To calculate L, V, thePmaximum power voltage to the MPP of the PV module were max = 64.984 maximum output current, Equation (13) A, is obtained. used: Vs = 17.71 V, Pmax = 64.984 W, io = 5.41 fs = 20 KHz. Using a ripple value of 10% for a maximum output current, Equation (13) is obtained. ∆IL = 0.1 × io (max) = 0.541 A (13) (13) ∆IL = 0.1 × io (max) = 0.541 A

Using Equations (12) and (13), minimum value of the inductor as shown in Equation (14) Using Equations (12) and (13), thethe minimum value of the inductor as shown in Equation (14) is is obtained. obtained. 12 ) × 50 µS 12 × (1 − 17.71 L≥ ≥ 357.57 µH (14) 12 2 × 0.2705 12 × (1 − ) × 50 μS 17.71 (14) L≥ ≥ 357.57 μH 2 × 0.2705 2.2.2. Capacitor Design The current in the capacitor is defined as the variation of the charge with respect to time. 2.2.2. Capacitor Design See Equation (15). ∆Q variation ∆Vc of the charge with respect to time. See The current in the capacitor is defined as the i= =C (15) ∆t ∆t Equation (15). Using Figure 5 and Equation (15), the expression the variation of the load ∆Q is obtained. ∆Q ∆Vfor c (15) i= =C See Equation (16). ∆t ∆t ∆IL Ts ∆Q = for (16) Using Figure 5 and Equation (15), the expression 8 the variation of the load ΔQ is obtained. See Equation (16). ∆Q =

∆IL Ts 8

(16)

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I LI L

L/2 ΔIΔIL/2

Figure 5. Timevariation variation ofthe the currentininthe the inductor. Figure Figure5.5.Time Time variationof of thecurrent current in theinductor. inductor.

Therefore,Equation Equation(17) (17)for forthe thedesign designofofthe thecapacitor capacitorisisobtained. obtained. Therefore, Therefore, Equation (17) for the design of the capacitor is obtained. ∆I∆IL T LT ss CC≥≥ ∆I8∆V Tsc c 8∆V L C≥ 8∆Vc Usingaaripple ripplevalue valueofof0.1%, 0.1%,Equation Equation(18) (18)isisobtained. obtained. Using

(17) (17) (17)

Using a ripple value of 0.1%, Equation (18) is obtained. (0.001)(V ∆V==(0.001)(V 0.012VV ∆V o )==0.012 o)

(18) (18)

FromEquations Equations(13), (13),(17) (17)and and(18), (18), the(minimum minimum value the capacitorisisobtained. obtained.See SeeEquation Equation From ofofthe ∆Vthe = 0.001 = 0.012 V capacitor (18) )(Vo )value (19). (19). From Equations (13), (17) and (18), the minimum value of the capacitor is obtained. See Equation (19). ∆I∆IL T LT ss 279.63μF μF (19) CC≥≥ ≥≥279.63 (19) 8∆V ∆I8∆V L Tsc c C≥ ≥ 279.63 µF (19) 8∆Vc 2.2.3.Modelling ModellingofofBuck BuckConverter Converter 2.2.3. 2.2.3. Modelling of Buck Converter Figure66shows showsthe thebuck buckconverter converterthat thatwas wasmodeled modeledusing usingthe thefundamental fundamentalblocks blocksofofSimulink. Simulink. Figure Figure 6 shows the buck converter that was modeled using the fundamental blocks of Simulink.

Dutty Dutty

V+V+

PWMGenerator Generator PWM (DC-DC)20KHz (DC-DC)20KHz

LL

Switch Switch

Ammeter2 Ammeter2

Scope1 Scope1

Diode Diode SeriesRLC RLCBranch Branch Series

Battery Battery

P_Out P_Batt P_Out P_Batt

V_out V_out

V-V-

Figure6.6.6.Buck Buckconverter convertermodeled modeledin inSimulink. Simulink. Figure Figure Buck converter modeled in Simulink.

Figure77shows showsthe thecurrent currentininthe thebattery batterywith withthe thebuck buckconverter converterininopen openloop, loop,with withsolar solar Figure Figure 7 shows the current in the battery with the buck converter in open loop, with solar 2 and temperature of 25 °C; in which it is observed that the converter works in 2 irradiance of 200 W/m irradiance of 200 W/m 2and temperature of 25 °C; in which it is observed that the converter works in irradiance of 200 W/m and temperature of 25 ◦ C; in which it is observed that the converter works in theCCM CCMaccording accordingtotothat thatestablished establishedininthe thedesign designconditions. conditions. the the CCM according to that established in the design conditions.

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22 1.04 1.04

1.5 1.5

1.02 1.02

Battery Current (A) Battery Current (A)

Battery Current (A) Battery Current (A)

11

0.5 0.5 00

-0.5 -0.5 -1-1 -1.5 -1.5 00

11 0.98 0.98 0.96 0.96 0.94 0.94 0.92 0.92

0.90.9 0.88 0.88

0.05 0.05

0.1 0.1

0.15 0.2 0.15 0.2 Time(seconds) (seconds) Time

0.25 0.25

0.3 0.3

0.35 0.35

0.2214 0.2214 0.2215 0.2215 0.2215 0.2214 0.2214 0.2215 0.2215 0.2213 0.2213 0.2213 0.2213 0.2213 0.2214 0.2214 0.2214 0.2214 0.2215 0.2214 0.2214 0.2213

Time(seconds) (seconds) Time (b) (b)

(a)(a)

Figure7.7. 7.(a) (a)Battery Batterycurrent currentfor foropen openloop; loop;(b) (b)Extended Extendedsection sectionfor forrange range(0.2213–0.2215 (0.2213–0.2215s). s). Figure Figure current for open loop; (b) Extended section for range (0.2213–0.2215 s).

2.3.Fuzzy FuzzyController ControllerDesign Design 2.3. 2.3. Fuzzy Controller Design Fuzzycontrol controlis isaaamethod methodthat thatallows allowsthe theconstruction constructionof ofnonlinear nonlinearcontrollers controllersfrom fromheuristic heuristic Fuzzy Fuzzy control is method that allows the construction of nonlinear controllers from heuristic informationthat that comes from the knowledge ofan anexpert. expert. Figure shows theblock block diagram ofaafuzzy fuzzy information the knowledge of Figure 88shows the diagram of information thatcomes comesfrom from the knowledge of an expert. Figure 8 shows the block diagram of a controller. The fuzzification block is responsible for processing the input signals and assign them controller. The fuzzification block is responsible for processing the input signals and assign them aa fuzzy controller. The fuzzification block is responsible for processing the input signals and assign fuzzyavalue. value. The setof ofrules rules allows alinguistic linguistic description ofthe thevariables variables tobe becontrolled controlled andisis fuzzy set allows description of to and them fuzzyThe value. The set of rulesaallows a linguistic description of the variables to be controlled based on the knowledge of the process. The inference mechanism is responsible for making an based on the knowledge of the process. The inference mechanism is responsible for making an and is based on the knowledge of the process. The inference mechanism is responsible for making interpretation of the data taking into account the rules and their membership functions. With the interpretation of the data taking into account the rules and their membership functions. With the an interpretation of the data taking into account the rules and their membership functions. With the defuzzificationblock, block,the thefuzzy fuzzyinformation informationcoming comingfrom fromthe theinference inferencemechanism mechanismisis isconverted convertedinto into defuzzification defuzzification block, the fuzzy information coming from the inference mechanism converted into non-fuzzy information that is useful for the process to be controlled. non-fuzzy information that is useful for the process to be controlled. non-fuzzy information that is useful for the process to be controlled.

Inference Inference

Defuzzification Defuzzification

Input Input

Fuzzification Fuzzification

FuzzyControler Controler Fuzzy

Process Process

Output Output

Rules Rules

Figure8.8.Block Blockdiagram diagramfor foraafuzzy fuzzycontroller. controller. Figure Figure 8. Block diagram for a fuzzy controller.

Takinginto intoaccount accountthe theabove, above,the thedesign designof offuzzy fuzzycontroller controllerfor forthis thiswork workisispresented. presented.AAfuzzy fuzzy Taking Taking intotwo account the above, the design fuzzy controller for this variables work is presented. fuzzy controller with two inputs and oneoutput output wasofdesigned. designed. Thetwo two input variables areError ErrorA (E) and controller with inputs and one was The input are (E) and controller with two inputs and one output was designed. The two input variables are Error (E) and Change of Error (CE), which are shown in Equations (20) and (21) for sample times k. Change of Error (CE), which are shown in Equations (20) and (21) for sample times k. Change of Error (CE), which are shown in Equations (20) and (21) for sample times k. P(k)−−P(k P(k−−1) 1) ∆P ∆P P(k) (20) E(k)== (20) E(k) == V(k) − V(k − 1) ∆V P(V(k) k) −−P(V(k k −−1)1) ∆P ∆V E(k) = = (20) V(k) − V(k − 1) ∆V (21) CE(k)==E(k) E(k)−−E(k E(k−−1) 1)==∆E ∆E (21) CE(k) CE(k) = E(k) − E(k − 1) = ∆E (21) Theinput inputE(k) E(k)isisthe theslope slopeof ofthe theP-V P-Vcurve curveand anddefines definesthe thelocation locationof ofthe theMPP MPPin inthe thePV PVmodule. module. The TheCE(k) CE(k) input defines whether themovement movement ofthe the operating pointisisof inthe theMPP MPPin direction ornot. not. The input E(k) is thewhether slope ofthe P-V curve and defines the location the PV module. The input defines of operating point in the MPP direction or The CE(k) defines whether the movement of (ΔD), the operating point is positive in the MPP direction or not. Theoutput outputinput variable the increment induty dutycycle cycle (ΔD), whichcan can take positive ornegative negativevalues values The variable isisthe increment in which take or depending on thelocation location ofthe theoperating operating point. This output sent tothe the dc-dcor converter tovalues drive The outputon variable is the of increment in duty cycleThis (∆D), which take positive negative depending the point. output isiscan sent to dc-dc converter to drive theload. load.Using Using thelocation valueof of ΔD delivered by thecontroller, controller, anis accumulator wasmade made toobtain obtain the depending on the ofΔD thedelivered operatingby point. This output sent to the dc-dc converter to drive the the value the an accumulator was to the valueof ofthe theduty dutycycle. cycle.See SeeEquation Equation(22). (22). value D(k)==D(k D(k−−1) 1)++∆D(k) ∆D(k) D(k)

(22) (22)

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the load. Using the value of ∆D delivered by the controller, an accumulator was made to obtain the value of the duty cycle. See Equation (22). D(k) = D(k − 1) + ∆D(k)

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2.3.1. 2.3.1. Membership Membership Functions Functions Triangular Triangular membership membership functions functions for for the the fuzzification fuzzification process process were were used. used. For For the the inputs inputs E, E, CE CE and and for for the the output output ∆D, ΔD, 55 membership membership functions functions were were defined defined in in terms terms of of the the following following linguistic linguistic variables: (B), Neutral (N), High (A)(A) andand VeryVery HighHigh (MA). The range for the error variables:Very VeryLow Low(MB), (MB),Low Low (B), Neutral (N), High (MA). The range for the is ( − 60 to 100), for the change of error is ( − 10 to 10) and for the increment in duty cycle is ( − 0.01 to error is (−60 to 100), for the change of error is (−10 to 10) and for the increment in duty cycle is (−0.01 0.01). Figure 9 shows thethe membership functions for for thethe inputs andand outputs of the controller. to 0.01). Figure 9 shows membership functions inputs outputs of the controller. VH

H

L

0.5

VL

1

N

Degree of Membership

Degree of Membership

1 VL

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VL

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H

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-0.01

-0.008 -0.006

0 0.002 -0.004 -0.002 Output Variable: ΔD

0.004

0.006

0.008

0.01

(c)

Figure 9. 9. Membership Membership functions. functions. (a) Error; Error; (b) (b) Change Change of of error; error; (c) (c) Increment Increment of of duty duty cycle. cycle. Figure

2.3.2. Fuzzy Fuzzy Rules Rules 2.3.2. Table 44shows shows the the 25 25 fuzzy fuzzy rules rules applied applied in in the the controller. controller. The The rows rows and and columns columns represent represent the the Table two inputs inputs EE and and ∆E. ΔE. The The output output ∆D ΔD is is aa variable variable located located at at the the intersection intersectionof ofaarow rowwith withaacolumn. column. two Table 4. Fuzzy associative matrix. Table 4. Fuzzy associative matrix.

E/ΔE Very Low E/∆E Very Low Very Low VH Low Very Low H VH NeutralLow H H HighNeutral H H High H Very High H Very High

H

Low Low VH H VH HH HH H H H

Neutral Neutral H HH HN NL L L L

High

Very High

High VL Very High VL VL VL L L L

VL L L L

VL L L VL VL

L L VL VL

2.3.3. Fuzzy Controller Modelling 2.3.3. Fuzzy Controller Modelling The controller was modeled with the Matlab Fuzzy Logic Toolbox (MathWorks, Natick, MA, The controller was modeled with the Matlab Fuzzy Logic Toolbox (MathWorks, Natick, MA, USA). A Mamdani controller with the centroid defuzzification method was used. This procedure was USA). A Mamdani controller with the centroid defuzzification method was used. This procedure carried out using the fuzzy inference system editor (FIS editor) (MathWorks, Natick, MA, USA). was carried out using the fuzzy inference system editor (FIS editor) (MathWorks, Natick, MA, USA). Figure 10 shows the controller modeled in Simulink, for which a subsystem was performed to Figure 10 shows the controller modeled in Simulink, for which a subsystem was performed to calculate calculate ΔV and ΔP in order to obtain the inputs E and ΔE. ∆V and ∆P in order to obtain the inputs E and ∆E.

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T T

12:34 12:34

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V V 2 2

I I

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I I

ΔP ΔP

Dutty Dutty Cycle Cycle

Change of Change Error of Error

Error Error Subtract3 Subtract3

Zero-Order Zero-Order Hold2 Hold2

ΔV and ΔP ΔV and ΔP

Subtract1 Subtract1 Memory2 Memory2

Change of Error Memory1 Change of Error Memory1

Figure Fuzzy logic logic controller. controller. Figure 10. 10. Fuzzy Figure 10. Fuzzy logic controller.

2.4. 2.4.P&O P&OController ControllerDesign Design 2.4. P&O Controller Design The the operating operating point point of of the the PV PV module moduleby byincreasing increasing TheP&O P&Oalgorithm algorithm consists consists of modifying modifying the The P&O algorithm consists of modifying the operating point of the PV module by increasing or order to to measure measure the the output outputpower powerbefore before and ordecreasing decreasingthe the duty duty cycle cycle of of aa dc-dc dc-dc converter converter in order and or decreasing the duty cycle of a dc-dc converter in order to measure the output power before and after the algorithm algorithmperturbs perturbsthe thesystem systemininthe thesame samedirection; direction; afterthe theperturbance. perturbance. If If the the power increases, the after the perturbance. If the power increases, the algorithm perturbs the system in the same direction; otherwise Figure 11 11 shows showsthe the44possible possibleoptions options otherwisethe thesystem system is is perturbed perturbed in the the opposite direction. direction. Figure otherwise the system is perturbed in the opposite direction.1 Figure 11 shows the 4 possible options that thatare arepresented presentedduring duringthe thetracking trackingof ofthe theMPP, MPP,with withpoint point 1being beingthe theprevious previousposition positionand andpoint point2 that are presented during theof tracking of(A, the MPP, with point 1 being the previous position and point being thethe current position of each case (A, B,B, C and D). 2 being current position each case C and D). 2 being the current position of each case (A, B, C and D). CaseA: A:∆P ΔP < 0 y ∆V ΔV 0 y ∆V >> 0. Case C: ΔP > 0 y ΔV 0. Case D: ΔP > 0 y ΔV < 0. • Case CaseD: D:∆P ΔP>>00yy∆V ΔV0 V(x)-V(x-1)>0

No No

Duty Duty++ ++

Duty Duty++ ++

Ye Yess

ΔP>0 ΔP>0 Ye Yess

No No

V(x)-V(x-1)>0 V(x)-V(x-1)>0

Duty Duty----

Duty Duty----

Duty Duty++ ++

V(x-1)=V(x) V(x-1)=V(x) P(x-1)=P(x) P(x-1)=P(x)

Figure 12. Flowchartofof ofthe theperturbation perturbation and observation (P&O) controller. Figure Figure12. 12.Flowchart Flowchart the perturbationand andobservation observation(P&O) (P&O)controller. controller.

2.5. PV SystemModelling Modelling 2.5. 2.5.PV PVSystem System Modelling Figure 13 showsthe thePV PVsystem systemimplemented implemented Matlab/Simulink, which is composed of PV the Figure in Matlab/Simulink, which isiscomposed of Figure13 13shows shows the PV system implemented inin Matlab/Simulink, which composed ofthe the PV PV module, buck converter and the fuzzy/P&O controller. The signal builderblock blockwas wasused usedto to module, the buck converter and the fuzzy/P&O controller. The signal builder module, thethe buck converter and the fuzzy/P&O controller. The signal builder block was used to generate the temperature and irradiance signals in order to evaluate the controller performance. generate the temperature and irradiance signals in order to evaluate the controller performance. generate the temperature and irradiance signals in order to evaluate the controller performance. Additionally, this system was used to evaluate the standard standard P&O controller and and perform perform the the Additionally, Additionally, this this system system was was used used to to evaluate evaluate the standard P&O P&O controller comparison with the fuzzy controller. comparison comparisonwith withthe thefuzzy fuzzycontroller. controller. 1000 1000

Irradiance Irradiance

powergui powergui

VV

VV

II

II

EiEi(W/m2) (W/m2)

DD

EiEi(W/m2) (W/m2)

TT °C°C

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PP

T T(°C) (°C)

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Dutty_Cycle Dutty_Cycle P_Out P_Out

Power Power

Switch1 Switch1 V+ V+

V+ V+

V-V-

V-V-

Reference_Volt Reference_Volt

PV PVModule Module

V_Out V_Out

DC-DC DC-DCConverter Converter

Figure 13. PV system modelling. Figure Figure13. 13.PV PVsystem systemmodelling. modelling.

2.6. Limitations 2.6. 2.6.Limitations The dc-dc designed based onon the electrical parameters of the PV The fuzzy control were designed based the electrical parameters of Thedc-dc dc-dcconverter converterand andfuzzy fuzzycontrol controlwere were designed based on the electrical parameters ofthe the module under study; for this reason, the calculations made apply to PV modules with powers up to PV module under study; for this reason, the calculations made apply to PV modules with powers up PV module under study; for this reason, the calculations made apply to PV modules with powers up 65 W. of theof inputs of the fuzzy controller is the change of error, which requires a differentiation to W. the of fuzzy isis the change of requires to 65 65 One W. One One of the inputs inputs of the the fuzzy controller controller the change of error, error, which which requires aa operation that operation increases complexity in calculations and can generateand errors measuring differentiation that increases complexity in can generate errors differentiation operationthe that increasesthe thethe complexity inthe thecalculations calculations and canwhen generate errors small powers thatsmall are sensitive to noise. when powers are whenmeasuring measuring small powersthat that aresensitive sensitiveto tonoise. noise.

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3. 3. Results Results and and Discussion Discussion

3. Results and Discussion To the performance To test test the performance of of the the PV PV system, system, different different scenarios scenarios were were simulated simulated in in which which the the traditional P&O control is evaluated in comparison with the fuzzy controller. Four scenarios that traditional P&O control is evaluated in comparison with the fuzzy controller. Four scenarios that To test the performance of the PV system, different scenarios were simulated in which the simulate changes in solar irradiance and operating temperature of the PV are presented. simulatesudden sudden changes in solar irradiance and operating temperature ofmodule the module are traditional P&O control is evaluated in comparison with the fuzzy controller. FourPV scenarios that In all cases, the following elements were used: 65 W PV module, 12 V battery, inductor of 416 µH and presented.sudden In all cases, the following elements were 65 W temperature PV module, 12 battery, inductor of simulate changes in solar irradiance and used: operating of Vthe PV module are capacitor of 500 µF; with a sampling frequency of frequency 20 KHz forofthe dc-dc converter. 416 μH and capacitor of 500 μF; with a sampling 20 KHz for the dc-dc converter. presented. In all cases, the following elements were used: 65 W PV module, 12 V battery, inductor of 416 μH and capacitor of 500 μF; with a sampling frequency of 20 KHz for the dc-dc converter. 1:1:standard conditions Case Case standardtest test conditions 2 and temperature Case 1:case, standard test conditions In thethe two controllers were evaluated for solarfor irradiance of 1000 W/m In this this case, two controllers were evaluated solar irradiance of 1000 W/m2 and ◦ C. Figure 14a shows the results obtained for the power delivered to the battery with a simulation of 25 2 and temperature of 25 °C. 14a shows were the results obtained theirradiance power delivered to W/m the battery In this case, the Figure two controllers evaluated for for solar of 1000 time of 0.03 s. It can be seen that the two controllers extract the maximum power of 65 W with a good with a simulation of 0.0314a s. Itshows can bethe seen that the two controllers extract the maximum power temperature of 25 time °C. Figure results obtained for the power delivered to the battery stabilization time of 0.005 s, which is consistent with the results obtained in [15,16]. In Figure 14b, it in is of 65aW with a good timebeofseen 0.005 s, the which consistent extract with the obtained with simulation timestabilization of 0.03 s. It can that twoiscontrollers theresults maximum power observed that the14b, dutyitcycle of the P&O control small oscillations between 0.6926 and 0.7, [15,16]. Figure is observed that the duty presents cycle of the P&O control presents small oscillations of 65 WIn with a good stabilization time of 0.005 s, which is consistent with the results obtained in in contrast to the fuzzy control that is stabilized at a value of D = 0.694. betweenIn0.6926 inobserved contrast to thethe fuzzy stabilized a value of D = oscillations 0.694. [15,16]. Figureand 14b,0.7, it is that dutycontrol cycle ofthat theisP&O controlatpresents small between 0.6926 and 0.7, in contrast to the fuzzy control that is stabilized at a value of D = 0.694. 0.702

60 50

0.702 0.7

40 50

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Power Power (W) (W)

Duty Cycle Duty Cycle

60

40 30

0.698 0.696

30 20

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P&O 0.035 Fuzzy

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(b)

(a)

2 and 2T Figure 14. 14. PV W/m = 25T°C. (a)◦Output power of the PV Duty Figure PVsystem systemwith withEiE=i 1000 = 1000 W/m and = 25 C. (a) Output power ofmodule; the PV (b) module; 2 cycle. Figure 14.cycle. PV system with Ei = 1000 W/m and T = 25 °C. (a) Output power of the PV module; (b) Duty (b) Duty cycle.

Case 2: changes in solar irradiance, temperature of 25 °C Case 2:2:changes in solar temperature ofof2525◦ C Case changes solarirradiance, irradiance, °C In this case, the in performance of the temperature controllers was evaluated with an operating temperature of this case, the performance of the controllers was evaluated with an was operating temperature of 25 °CIn and sudden changes in solar irradiance. Initially, an irradiance signal used with increments In this case, the performance of the controllers was evaluated with an operating temperature of ◦ C and sudden 2 2 2 25 changes in solar irradiance. Initially, an irradiance signal was used with increments of °C 200and W/m , starting at 200 and endingInitially, at 1000 W/m . Changes in irradiance every 25 sudden changes inW/m solar irradiance. an irradiance signal was usedwere with made increments 2 , starting at 200 W/m2 and ending at 1000 W/m2 . Changes in irradiance were made every of W/m 2. Changes in 0.2200 s with simulation time2of 1 sending (see Figure 15a). Subsequently, a irradiance test signal were with decreases in of 200 W/ma2total , starting at 200 W/m and at 1000 W/m made every 21and 215a). 0.2 s with a total simulation time of s (see Figure Subsequently, a test signal with decreases in solar irradiance between 1000 W/m 200 W/m was used (see Figure 15b). 0.2 s with a total simulation time of 1 s (see Figure 15a). Subsequently, a test signal with decreases in 2 and 200 W/m2 was used (see Figure 15b). solar solar irradiance irradiance between between 1000 1000 W/m W/m2 and 200 W/m2 was used (see Figure 15b).

200 0

0

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0.1 0.1

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1000 800 1000 600 800 400 200 600 4000 0 200 0 0

Irradiance Irradiance (W/m2) (W/m2)

Irradiance Irradiance (W/m2) (W/m2)

1000 800 600 1000 400 800 200 600 4000

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Figure 15. (a) Increases in solar irradiance; (b) Decreases in solar irradiance. Figure 15. (a) Increases in solar irradiance; (b) Decreases in solar irradiance.

Figure 16a shows the output power for increments in the irradiance signal. In general terms it can be noted that the two controllers present a good performance in the signal. different instants of time. Figure 16a shows the output output power for increments increments in the the irradiance irradiance Figure 16a shows the power for in signal. In In general general terms terms it it The power obtained is between 11.7 W and 64.9 W, which corresponds to the values presented in can be noted that the two controllers present a good performance in the different instants of time. can be noted that the two controllers present a good performance in the different instants of time. Table 2. However, it should be noted that the P&OW, controller presented small oscillations for E i = 200 The power obtained between 11.7 W and which corresponds the values presented The power obtained isisbetween 11.7 W and 64.964.9 W, which corresponds to the to values presented in Tablein 2. W/m2,2.which is evidenced dutythat cycle Figure 16b, in times between 0 oscillations and 0.2 s. for E i = 200 Table However, it shouldinbethe noted theofP&O controller presented small However, it should be noted that the P&O controller presented small oscillations for Ei = 200 W/m2 , W/m2, which is evidenced in the duty cycle of Figure 16b, in times between 0 and 0.2 s. which is evidenced in the duty cycle of Figure 16b, in times between 0 and 0.2 s.

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0.78 0.74 0.76 0.72 0.74 0.72 0.7 0.7 0.68 0.78 0.68 0.66 0.76 0.66 0.74 0.05 0.1 0 0.72 0.05 0.1 0.15 0 0.7

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(a) power of the PV module for increases in solar irradiance; (b) (b) Duty cycle. Figure 16.Output (a) Output Figure 16. (a) power of the PV module for increases in solar irradiance; (b) Duty cycle.

Figure 16. (a) Output power of the PV module for increases in solar irradiance; (b) Duty cycle.

In Figure 17a, the output power for decreases in the irradiance signal is shown. As with the In Figure 17a, the output power for decreases in the irradiance signal is shown. As with the In Figure 17a, the thetwo output power for decreases in the irradiance shown. increase signal, controllers exhibit good performance with outputsignal power is between 64.9As Wwith and the In Figure output power forgood decreases in the irradiance signalpower is shown. As with increase signal, the17a, twothe controllers exhibit performance with output between 64.9the W and increase the17b two controllers good performance with power between 64.9 W 11.7 signal, W. Figure shows the dutyexhibit cycle, in which it is noted that theoutput P&O controller presents the increase signal, the two controllers exhibit good performance with output power between 64.9 W and 11.7 W. Figure 17b shows the duty cycle, in which it is noted that the P&O controller presents the oscillations that 17b characterize this duty method, but in that do notitsignificantly affect performance of the and 11.7 Figure showsthethe cycle, which is noted that thethe P&O controller 11.7 W. W.that Figure 17b shows duty cycle, in which it is noted that the P&O controller presentspresents theof the oscillations characterize this method, but that do not significantly affect the performance system. the oscillations characterizethis this method, dosignificantly not significantly affect the performance oscillations that that characterize method, butbut thatthat do not affect the performance of the of system. the system. system. 70 0.76

64.9W

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Figure 17. (a) Output power of the PV module for decreases in solar (a)

(b)

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0.9 Fuzzy P&O

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cycle.

Figure 17. Output (a) Output power of thePV PVmodule module for for decreases in solar irradiance; (b) Duty cycle. Figure 17. (a) power ofcase the decreases solar irradiance; Duty cycle. With 17. the(a) tests carried out inof it module is evident the twoin controllers exhibit a(b) similar Figure Output power the 2, PV forthat decreases in solar irradiance; (b) Duty behavior cycle. for sudden changes in solar irradiance. In addition, it was found that the P&O control has small With the tests carried out in case 2, it is evident that the two controllers exhibit a similar behavior oscillations thatcarried do not significantly affect the power delivered to controllers the battery. With the tests case 2, two With it isInevident that the two controllers exhibit a similar behavior for sudden changes in out solarinirradiance. addition, it was found that the P&O control has small 2 for sudden changes innot solar irradiance. Inthe addition, it1000 wasW/m found oscillations do affect power delivered to the battery. Case 3:that changes in significantly temperature, solar irradiance ofit In addition, was found that the P&O control has small

oscillations that do not significantly affect the power delivered to battery. affect power delivered to the battery. 2 the Case 3: point, changes temperature, irradiance 1000 W/m At this theinperformance ofsolar thethe system wasof evaluated for sudden changes in temperature 2. Initially, the signal shown 2 with3:a3:constant solar irradiance of 1000 W/m in Figure 18a was used, with Case ininthe temperature, irradiance ofof 1000 Case changes temperature, solar irradiance 1000W/m W/m Atchanges this point, performancesolar of the system was evaluated for2sudden changes in temperature

temperature increases every 0.2 s between 02 °C and 100 °C, for a test time of 1 s. Subsequently, the

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0.1

0.2

0.3

0.8

0.4 Figure (a) 0.5 18. 0.6 Time (s)

0.7

0.9

1

100°C

75°C 0.6

50°C Time (s) (a) (a) Figure 18.

0°C 0

0.7

0.8

0.9

1

Temperature TemperatureTemperature (°C) (°C) (°C)

Temperature Temperature (°C) (°C)

with a constant solar irradiance of 1000 W/m . Initially, the signal shown in Figure 18a was used, with At thisshown point,inthe performance of the system wasinevaluated forbetween sudden100 changes temperature signal Figure 18b was used, with decreases temperature °C and in 0 °C. temperature increases every 0.2 s between 0 °C and 100 °C, for a test time of 1 s. Subsequently, the 2 2 with a constant constantsolar solarirradiance irradianceofof1000 1000 W/m . Initially, the signal shown in Figurewas 18a was used, . Initially, signal shown in Figure signal shown in Figure 18b was used, W/m with decreases inthe temperature between 100 °C 18a and 0 °C.used, with 100 ◦ C 100 ◦ C, for 100°C with temperature increases s between and 100for test time 1 s. Subsequently, 75°C 80 80 temperature increases everyevery 0.2 s 0.2 between 0100°C °C 0and 100 °C, a 75°C testa time of 1 of s. Subsequently, the 60 60 50°C ◦ C and 0 ◦ C. 100 100 40 40 50°C the signal shown in Figure 18b was used, with decreases in temperature between 100 signal shown in Figure in temperature between 100 °C and 0 °C. 25°C 18b was used, 100°C 100°C 75°Cwith decreases 80 80 20 60 0 400 20 100 0 80 0

60

25°C

75°C

0.1

0.2

0.3

0.4

100°C 0.1

0.5 50°C Time (s)

0.6

0.3 75°C0.4

0.5 Time (s)

0°C

0.8

25°C

(b) 0.2

0.7

0.6

0.7

(b) 50°C Increases in temperature;40 (b) Decreases in temperature. 20

0.8

0.9

25°C

0

0.1 0.4 0.5 0.2 in 0.3 0 Decreases Increases (b) temperature. 0.9 0.7 0.8 in temperature; 1

0.9

0.6

1

0°C

0.7

1

0°C

0.8

0.9

1

In Figure 19a, the power delivered to the battery is shown, where it is evident the oscillations (a) (b) and power losses that are obtained with the P&O control. Sudden changes in temperature In Figure 19a, the power delivered to the battery is shown, where it is evident the oscillations significantly affect the P&O whichtemperature; is confirmed(b) by Decreases the duty cycle signal shown in Figure 19b. Figure 18.are (a)control, Increases temperature. in temperature. and power losses that obtained inwith the P&O control. Sudden changes in temperature In contrast, the fuzzy control delivers stable power with duty cycle values that adapt to changes in significantly affect the P&O control, which is confirmed by the duty cycle signal shown in Figure 19b. theFigure operating temperature ofdelivered the PV module. With the P&O control, there it areisaverage power losses In 19a, the power to thepower battery is duty shown, where evident the oscillations In Figure contrast,19a, thethe fuzzy control deliversto stable cycle values adapt changes in and In power delivered the batterywith is shown, where it is that evident thetooscillations and power losses that are obtained with the P&O control. Sudden changes in temperature the operating temperature of the PV module. With the P&O control, there are average power losses power losses that are obtained with the P&O control. Sudden changes in temperature significantly Time (s)

significantly affect the P&O control, which is confirmed by the duty cycle signal shown in Figure 19b. affect the P&O control, which is confirmed by the duty cycle signal shown in Figure 19b. In contrast, In contrast, the fuzzy control delivers stable power with duty cycle values that adapt to changes in the fuzzy control delivers stable power with duty cycle values that adapt to changes in the operating the operating temperature of the PV module. With the P&O control, there are average power losses

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Energiesof 2017, 2036module. With the P&O control, there are average power losses of 3.15 14 ofW, 18 2.13 W, temperature the10,PV 2.84 W, 4.122017, W and 6.38 W for each of the simulation intervals. The losses were calculated taking Energies 2036 Energies 10, 2036 of14 18of 18 as of 3.15 2017, W,10,2.13 W, 2.84 W, 4.12 W and 6.38 W for each of the simulation intervals. The losses14were reference the power obtained withthe the fuzzy controller five operating temperatures between calculated taking as reference power obtained withfor the the fuzzy controller for the five operating ◦W, of 3.15 2.13 W,2.84 2.84W, W,4.12 4.12 W W and W for each of the simulation intervals. The losses were of temperatures 3.15 W, W, and 6.38 W for each of the simulation intervals. The losses were 0 ◦ C and 100 C,2.13 which correspond to the values presented in Table 3. between 0 °C and 100 °C, which correspond to the values presented in Table 3.

calculatedtaking takingasasreference reference the the power power obtained forfor thethe five operating calculated obtained with withthe thefuzzy fuzzycontroller controller five operating 1 temperatures between 0 °C and 100 °C, which correspond to the values presented in Table 3. temperatures between 0 °C and 100 °C, which correspond to the values presented in Table 3. 69.9W 70 59.5W

60

69.9W 64.9W

59.5W

54.5W

40 50

54.5W

48.6W

48.6W

40

40 20 30

30 10 20 20 0 0 10

0.2

0.1

0.4

0.3

0.5 Time (s)

0.7

0.7

Fuzzy P&O Fuzzy 0.8P&O 0.9

(a)

10 0

0

0.6

Fuzzy P&O 0.8 0.9

0

0

0.1

0.1

0.2

0.4

0.3

0.5 Time (s)

0.6

0.83 0.64

0.8 0.6

0.8

0.75

0.69

0.7 0.64

0.6 0.4

0.64

0.6

0.5 0.3

0.5

0.4 0.2

0.4

0.3 0.1

Fuzzy P&O

0.3

0 0.2 0 0.2 0.1

1

0.94

0.83

0.75

0.69

0.7 0.5

Duty Cycle

50 30 Power (W)

0.9

59.5W

0.94

0.69

0.9 0.7

48.6W

64.9W

0.75

1

54.5W

69.9W

50 60

0.83

0.8 1

Duty Cycle Duty Cycle

Power (W)Power (W)

70

0.94

0.9

64.9W

60 70

0.1

0.6 0.5 Time (s)

0.4

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0.9 Fuzzy P&O

0.7

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(b)

00.1 0

1

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0

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0.6 0.5 Time (s)

0.4

0.8 0 0.7 0.1 0.6 0.3 0.4 0.2 temperature; 0.8 module 0.9 1 0.5(a)power 0.6 0.2 0.3 (a) 0.4 Figure 19. Output of0.7the PV para increases in (b) Duty cycle. (b)0.5 Time (s)

1

Fuzzy 1 P&O 0.9

Time (s) Figure 19. (a) Output power of the PV module para increases in temperature; (b) Duty cycle.

1

(b)

(a)

Figure 19. (a) Output power of the PVfor module para increases in temperature; (b) Duty Figure 20 shows the power obtained decreases in operating temperature. As incycle. the scenario

19. the (a) Output power of the PV module para increases in temperature; (b) DutyAs cycle. Figure 20Figure shows power obtained decreases in operating temperature. in the proposed in Figure 19, the P&O controlfor presents oscillations. The worst scenario occurs when thescenario Figure 20 shows the power obtained for decreases in operating temperature. As in the scenario temperature fromP&O 100 °Ccontrol to 75 °C,presents where theoscillations. system does not reach stabilization and there are proposed in Figuredrops 19, the The worst scenario occurs when the Figure 20 shows 19, thethe power for decreases in operating temperature. As in when the scenario proposed in Figure P&Oobtained control presents oscillations. The worst scenario occurs the ◦C ◦ C,With oscillations between 20 W and 52 W. the P&O control, does there are average power losses ofand 46.18 temperature drops from 100 to 75 where the system not reach stabilization there temperatureFigure drops 19, from 100P&O °C tocontrol 75 °C, where the oscillations. system does not stabilization and there are proposed the presents Thereach worst scenario occurs when the are W, 17.32in W, 0 W, 1.11 W and 1.2 W. oscillations between 20 from W20 and 52 the P&O there arereach average power losses of 46.18 oscillations between W and 52 W.°C, With the P&O control,does therenot are average power losses 46.18 temperature drops 100 °CW. to With 75 where thecontrol, system stabilization andofthere are W, 1 W, 17.32 W, 0 W, 1.11 W and 17.32 W, 0 W, 1.11 W and 1.2 oscillations between 20 WW. and1.2 52W. W. With the P&O control, there are average power losses of 46.18 69.9W 70

0.9

64.9W

60

Power (W)

50

40 30

0.7 0.9

64.9W 59.5W

69.9W

54.5W

64.9W 59.5W

54.5W

0.4

0.3

0.5 Time (s)

0.6

0.7

0.8

0

10

0

1

0.9

Fuzzy P&O

20

0.83

0.75

0.83

0.75

0.94

1

0.6 0.8

0.9 0.5 0.7

0.69 0.64

0.94 0.83

0.8 0.4 0.6

0.69

0.75

0.64

0.7 0.3 0.5

0.69 0.64

0.6 0.2 0.4 0.5 0.1 0.3

Fuzzy P&O 0.2

0.94

0.8 1

69.9W Duty Cycle Duty Cycle

70

70 48.6W 50 60 40 48.6W 50 30 40 48.6W 20 30 10 20 0 0.1 0 10

54.5W

Duty Cycle

Power (W)Power (W)

W, 17.32 W, 0 W, 1.11 W and 59.5W1.2 W. 60

00.4 0.2 0 0.1 0.3

0.1

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0.1

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0.7

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Fuzzy P&O 0.9

0.8

Fuzzy P&O 0.9

0.8 1 0.9 0.6 0.4 0.2 0.5 Figure 20.0.3(a) Output power of0.7the PV module for decreases in temperature;Time (b)(s)Duty cycle. Time (s) 0.1

0.1

Fuzzy P&O

0

0

0

0.1

0.3

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1

1

Fuzzy P&O 0.9

0.2 0.5 power of the PV module for decreases in temperature; (b) Duty cycle. 0.1 Figure 0.3 (a)0.4 Output Time (s) 0 Figure Case 4: variations inTime solar irradiance temperature (s) 20. (a)20. Output power of the PVand module for decreases in temperature; (b) Duty cycle.

0.7

0.6

0.8

1

0.9

0.2

1

Finally, the of the was evaluated for sudden changes (b) in temperature Case 4: variations in solar irradiance and temperature Figure 20. performance (a) Output power of system the PV module for decreases in temperature; Duty cycle. and solar irradiance in different time values between 0 and 1 s, as seen in Figure 21. Case 4: variations solar irradiance and temperature Finally, the in performance of the system was evaluated for sudden changes in temperature and Case 4: variations in solar irradiance and temperature solar irradiance in 1000 different time values between 0 and 1 s, as seen in Figure 21.

Irradiance (W/m2) Te mpe rature (°C)

rature (°C) Irradiance Te mpe Irradiance Te mpe rature (°C) (W/m2) (W/m2)

Finally, the performance of of thethe system was evaluated for sudden changes in temperature and 800 Finally, the performance system was evaluated for sudden changes in temperature and 600 1000 solar irradiance in different time values between as seen seenininFigure Figure21.21. solar irradiance in different time values between00and and 11 s, s, as 400 800 200 600

1000 0 400

(a)

800 200 80

600 0

75°C

75°C

60

(a)

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400

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80

20040

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60

20 0

40

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80

0.1 0°C

0 0

25°C

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0.3 75°C 0.4

0.2

50°C 0.2

(a)

0.4

25°C

0.5 0.6 Time (s)0°C 0.5

25°C Time (s)

50°C 25°C 50°C

0°C

(b)

0.3

75°C

25°C

50°C

0°C

40 0

60

25°C

50°C

020

0.6

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25°C0°C 0.8 75°C 0.9

50°C 0.7

0.8

25°C

50°C 0.9

1 0°C

25°C

1

20 Figure 21. Irradiance and temperature signals to(b)evaluate the performance of fuzzy and P&O 0°C controllers. (a) 0Increases in solar irradiance; (b) Variable0°C temperature. 0°C Figure 21. Irradiance and temperature signals to 0.5evaluate the 0.7 performance of fuzzy1 and P&O 0 0.1 0.2 0.3 0.4 0.6 0.8 0.9 Time (s) controllers. (a) Increases in solar irradiance; (b) Variable temperature. (b)

21. Irradiance and temperature signals to evaluate the performance of and fuzzy andcontrollers. P&O FigureFigure 21. Irradiance and temperature signals to evaluate the performance of fuzzy P&O controllers. (a) Increases in solar irradiance; (b) Variable temperature. (a) Increases in solar irradiance; (b) Variable temperature.

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For Forthe thedescribed describedtest testconditions, conditions,the thepower powerobtained obtainedfrom fromthe thePV PVmodule moduleusing usingfuzzy fuzzyand andP&O P&O controllers is shown in Figure 22. The results prove that the fuzzy controller tracks the MPP without controllers is shown in Figure 22. The results prove that the fuzzy controller tracks the MPP without oscillations losses. InIn contrast, thethe P&O controller exhibits power losses and and oscillations for oscillationsand andpower power losses. contrast, P&O controller exhibits power losses oscillations changes in solar and temperature. The worst scenario, for the P&O control, betweenis for changes in irradiance solar irradiance and temperature. Thecase worst case scenario, for the P&Oiscontrol, 2, 0.3 and 0.40.3 s when the temperature changes from 50 tofrom 75 ◦50 C with solar of 1000 W/m between and 0.4 s when the temperature changes to 75a°C withirradiance a solar irradiance of 1000 2, inthe inW/m which power oscillates between 11.5 and 37.5 The average power losseslosses with with the which the power oscillates between 11.5 andW. 37.5 W.highest The highest average power P&O control occurred between the times 0.2 s to 0.3 s and 0.3 s to 0.4 s with values of 8.52 W and the P&O control occurred between the times 0.2 s to 0.3 s and 0.3 s to 0.4 s with values of 8.52 W and 30.48 30.48W, W,respectively. respectively. 70

64.9W

P&O Fuzzy

69.9W 59.5W

60

54.5W

Power (W)

50 40

39.3W

37.7W 38.1W

30 20 11.7W

10 0

0

11.6W 11.9W 11.7W

11.3W

0.1

0.2

0.3

0.4

0.5 Time (s)

0.6

0.7

0.8

0.9

1

Figure Figure22. 22.Output Outputpower powerofofthe thePV PVmodule modulewith withthe thefuzzy fuzzyand andP&O P&Ocontrollers. controllers.

Conclusions 4.4.Conclusions this paper, a fuzzy controller to the track the maximum power of a PV module was InInthis paper, a fuzzy controller to track maximum power point of apoint PV module was presented, presented, for performance which their performance waswith compared a P&OAll controller. All components of the for which their was compared a P&O with controller. components of the PV system PV system modeled in Matlab/Simulink (PVconverter, module,fuzzy buckand converter, fuzzy andIn P&O were modeledwere in Matlab/Simulink (PV module, buck P&O controllers). this controllers). way, different test scenarios with signals of irradiance temperature and solar irradiance way, different In testthis scenarios with signals of temperature and solar variables were used in variables were used order to evaluate of demonstrated the PV system.that It was that order to evaluate the in performance of the the PV performance system. It was thedemonstrated fuzzy controller thean fuzzy controller has an excellent performance there changes in the of operating has excellent performance when there are suddenwhen changes in are the sudden operating temperature the PV temperature of the PV module, in contrast P&O controlaffected, that is considerably affected, presenting module, in contrast with P&O control thatwith is considerably presenting power losses up to power losses up to 46.18 W. On the other hand, it was also evidenced that in the presence of variations 46.18 W. On the other hand, it was also evidenced that in the presence of variations in solar irradiance in two solarcontrollers irradiancepresented the two controllers presented aand good performance and extracted maximum the a good performance extracted the maximum powerthe according to power according to the electrical of the module; P&O control the electrical characteristics of the PVcharacteristics module; although thePV P&O control although presented the the well-known presented the well-known oscillations, mainly in the sudden changes of irradiance. In this way, the oscillations, mainly in the sudden changes of irradiance. In this way, the main contribution of this main contribution of this manuscript is the supplying theto maximum power manuscript is the guarantee of supplying theguarantee maximumof possible power a battery possible in an off-grid PVto a battery in an off-grid PV system, using a fuzzy controller. As future work, in the second stage system, using a fuzzy controller. As future work, in the second stage of the project, the fuzzy controllerof the be project, the fuzzyin controller will be implemented in the low-cost Arduino platform; emphasizing will implemented the low-cost Arduino platform; emphasizing that fuzzy control offers the that fuzzyof control advantagein ofmicrocontrollers. being easily programmed in microcontrollers. advantage being offers easily the programmed Acknowledgments: supported by by the theVicerrectorí Vicerrectoría Investigaciónof of Universidad Acknowledgments: This This work was supported a dedeInvestigación thethe Universidad del del Magdalena. Magdalena. Author Contributions: Carlos Robles Algarín conceived and modeled the PV module and the fuzzy controller. Author Contributions: Carlos Robles Algarín conceived and modeled the PV module and the fuzzy controller. John Taborda Giraldo designed the P&O controller and dc-dc converter. Omar Rodríguez Álvarez contributed in John Taborda Giraldo designed the P&O controller and dc-dc converter. Omar Rodríguez Á lvarez contributed the design of the dc-dc converter and data analysis. All authors contributed in writing the manuscript. in the design of the dc-dc converter and data analysis. All authors contributed in writing the manuscript. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations Vx

Open circuit voltage for variable values of solar irradiance and operating temperature.

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Abbreviations Vx Ix MPP Pmax Vmpp Impp s p Ei EiN T TN Tcv Tci Voc Isc Vmax Vmin VL RL Rc Ton Toff Ts D Vs Vdc Vd Vo ∆IL ∆IL (+) ∆IL (−) Io ∆Q ∆V

Open circuit voltage for variable values of solar irradiance and operating temperature. Short-circuit current for variable values of solar irradiance and operating temperature. Maximum power point of the PV module. Maximum power of the PV module. Voltage at Pmax . Current at Pmax . Number of PV modules connected in series. Number of PV modules connected in parallel. Effective irradiation of the PV module. Irradiation constant of 1000 W/m2 . Temperature of the PV module. Temperature constant of 25 ◦ C. Temperature coefficient of voltage. Temperature coefficient of current. Open circuit voltage. Short-circuit current. Voltage for irradiations under 200 W and operating temperature of 25 ◦ C. Voltage for irradiations over 1200 W and operating temperature of 25 ◦ C. Voltage in the inductor. Internal resistance of the inductor. Internal resistance of the capacitor. The on time in the dc-dc converter. The off time in the dc-dc converter. Sampling time. Duty cycle. Input voltage in dc-dc converter. Transistor voltage in the on mode. Diode forward voltage. Output voltage of the dc-dc converter. Ripple current in the inductor. Ripple current in Ton . Ripple current in Toff . Critical output current. Charge variation in the capacitor. Voltage variation in the capacitor.

References 1. 2. 3.

4.

5. 6.

Karami, N.; Moubayed, N.; Outbib, R. General review and classification of different MPPT Techniques. Renew. Sustain. Energy Rev. 2017, 68, 1–18. [CrossRef] Mohapatra, A.; Nayak, B.; Das, P.; Mohanty, K.B. A review on MPPT techniques of PV system under partial shading condition. Renew. Sustain. Energy Rev. 2017, 80, 854–867. [CrossRef] Bianconi, E.; Calvente, J.; Giral, R.; Mamarelis, E.; Petrone, G.; Ramos, C.A.; Spagnuolo, G.; Vitelli, M. Perturb and Observe MPPT algorithm with a current controller based on the sliding mode. Int. J. Electr. Power 2013, 44, 346–356. [CrossRef] Chen, M.; Ma, S.; Wu, J.; Huang, L. Analysis of MPPT Failure and Development of an Augmented Nonlinear Controller for MPPT of Photovoltaic Systems under Partial Shading Conditions. Appl. Sci. 2017, 7, 95. [CrossRef] Kwan, T.H.; Wu, X. High performance P&O based lock-on mechanism MPPT algorithm with smooth tracking. Sol. Energy 2017, 155, 816–828. [CrossRef] Alik, R.; Jusoh, A. Modified Perturb and Observe (P&O) with checking algorithm under various solar irradiation. Sol. Energy 2017, 148, 128–139. [CrossRef]

Energies 2017, 10, 2036

7. 8.

9. 10.

11.

12. 13.

14. 15. 16. 17.

18. 19. 20. 21. 22. 23.

24.

25. 26.

27. 28.

17 of 18

Bounechba, H.; Bouzid, A.; Snani, A.; Lashab, A. Real time simulation of MPPT algorithms for PV energy system. Int. J. Electr. Power 2016, 83, 67–78. [CrossRef] Huang, Y.P.; Hsu, S.Y. A performance evaluation model of a high concentration photovoltaic module with a fractional open circuit voltage-based maximum power point tracking algorithm. Comput. Electr. Eng. 2016, 51, 331–342. [CrossRef] Cortajarena, J.A.; Barambones, O.; Alkorta, P.; De Marcos, J. Sliding mode control of grid-tied single-phase inverter in a photovoltaic MPPT application. Sol. Energy 2017, 155, 793–804. [CrossRef] Tobón, A.; Peláez-Restrepo, J.; Villegas-Ceballos, J.P.; Serna-Garcés, S.I.; Herrera, J.; Ibeas, A. Maximum Power Point Tracking of Photovoltaic Panels by Using Improved Pattern Search Methods. Energies 2017, 10, 1316. [CrossRef] Loukriz, A.; Haddadi, M.; Messalti, S. Simulation and experimental design of a new advanced variable step size Incremental Conductance MPPT algorithm for PV systems. ISA Trans. 2016, 62, 30–38. [CrossRef] [PubMed] Mellit, A.; Rezzouk, H.; Messai, A.; Medjahed, B. FPGA-based real time implementation of MPPT-controller for photovoltaic systems. Renew. Energy 2011, 36, 1652–1661. [CrossRef] Ramalu, T.; Mohd Radzi, M.A.; Mohd Zainuri, M.A.A.; Abdul Wahab, N.I.; Abdul Rahman, R.Z. A Photovoltaic-Based SEPIC Converter with Dual-Fuzzy Maximum Power Point Tracking for Optimal Buck and Boost Operations. Energies 2016, 9, 604. [CrossRef] Hassan, S.Z.; Li, H.; Kamal, T.; Arifoglu, ˘ U.; Mumtaz, S.; Khan, L. Neuro-Fuzzy Wavelet Based Adaptive MPPT Algorithm for Photovoltaic Systems. Energies 2017, 10, 394. [CrossRef] Nabipour, M.; Razaz, M.; Seifossadat, S.; Mortazavi, S. A new MPPT scheme based on a novel fuzzy approach. Renew. Sustain. Energy Rev. 2017, 74, 1147–1169. [CrossRef] Bendib, B.; Krim, F.; Belmili, H.; Almi, M.F.; Boulouma, S. Advanced Fuzzy MPPT Controller for a Stand-alone PV System. Energy Procedia 2014, 50, 383–392. [CrossRef] Belaidi, R.; Haddouche, A.; Fathi, M.; Larafi, M.M.; Kaci, G.M. Performance of grid-connected PV system based on SAPF for power quality improvement. In Proceedings of the International Renewable and Sustainable Energy Conference (IRSEC), Marrakech, Morocco, 14–17 November 2016; pp. 1–4. Chekired, F.; Larbes, C.; Rekioua, D.; Haddad, F. Implementation of a MPPT fuzzy controller for photovoltaic systems on FPGA circuit. Energy Procedia 2011, 6, 541–549. [CrossRef] Na, W.; Chen, P.; Kim, J. An Improvement of a Fuzzy Logic-Controlled Maximum Power Point Tracking Algorithm for Photovoltic Applications. Appl. Sci. 2017, 7, 326. [CrossRef] Messaltia, S.; Harrag, A.; Loukriz, A. A new variable step size neural networks MPPT controller: Review, simulation and hardware implementation. Renew. Sustain. Energy Rev. 2017, 68, 221–233. [CrossRef] Dounis, A.I.; Kofinas, P.; Papadakis, G.; Alafodimos, C. A direct adaptive neural control for maximum power point tracking of photovoltaic system. Sol. Energy 2015, 115, 145–165. [CrossRef] Muthuramalingam, M.; Manoharan, P.S. Comparative analysis of distributed MPPT controllers for partially shaded stand alone photovoltaic systems. Energy Convers. Manag. 2014, 86, 286–299. [CrossRef] Jin, Y.; Hou, W.; Li, G.; Chen, X. A Glowworm Swarm Optimization-Based Maximum Power Point Tracking for Photovoltaic/Thermal Systems under Non-Uniform Solar Irradiation and Temperature Distribution. Energies 2017, 10, 541. [CrossRef] Titri, S.; Larbes, C.; Toumi, K.Y.; Benatchba, K. A new MPPT controller based on the Ant colony optimization algorithm for Photovoltaic systems under partial shading conditions. Appl. Soft Comput. 2017, 58, 465–479. [CrossRef] Jiang, L.L.; Maskell, D.L.; Patra, J.C. A novel ant colony optimization-based maximum power point tracking for photovoltaic systems under partially shaded conditions. Energy Build. 2013, 58, 227–236. [CrossRef] Benyoucef, A.S.; Chouder, A.; Kara, K.; Silvestre, S.; Sahed, O.A. Artificial bee colony based algorithm for maximum power point tracking (MPPT) for PV systems operating under partial shaded conditions. Appl. Soft Comput. 2015, 32, 38–48. [CrossRef] Fathy, A. Reliable and efficient approach for mitigating the shading effect on photovoltaic module based on Modified Artificial Bee Colony algorithm. Renew. Energy 2015, 81, 78–88. [CrossRef] Atawi, I.E.; Kassem, A.M. Optimal Control Based on Maximum Power Point Tracking (MPPT) of an Autonomous Hybrid Photovoltaic/Storage System in Micro Grid Applications. Energies 2017, 10, 643. [CrossRef]

Energies 2017, 10, 2036

29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.

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Ou, T.-C.; Hong, C.-M. Dynamic operation and control of microgrid hybrid power systems. Energy 2014, 66, 314–323. [CrossRef] Hong, C.-M.; Ou, T.-C.; Lu, K.-H. Development of intelligent MPPT (maximum power point tracking) control for a grid-connected hybrid power generation system. Energy 2013, 50, 270–279. [CrossRef] Shiau, J.-K.; Wei, Y.-C.; Lee, M.-Y. Fuzzy Controller for a Voltage-Regulated Solar-Powered MPPT System for Hybrid Power System Applications. Energies 2015, 8, 3292–3312. [CrossRef] Ou, T.-C.; Su, W.-F.; Liu, X.-Z.; Huang, S.-J.; Tai, T.-Y. A Modified Bird-Mating Optimization with Hill Climbing for Connection Decisions of Transformers. Energies 2016, 9, 671. [CrossRef] Ou, T.-C. A novel unsymmetrical faults analysis for microgrid distribution systems. Electr. Power Energy Syst. 2012, 43, 1017–1024. [CrossRef] Ou, T.-C. Ground fault current analysis with a direct building algorithm for microgrid distribution. Electr. Power Energy Syst. 2013, 53, 867–875. [CrossRef] Ou, T.-C.; Lu, K.-H.; Huang, C.-J. Improvement of Transient Stability in a Hybrid Power Multi-System Using a Designed NIDC (Novel Intelligent Damping Controller). Energies 2017, 10, 488. [CrossRef] Robles Algarín, C.; Callejas Cabarcas, J.; Polo Llanos, A. Low-Cost Fuzzy Logic Control for Greenhouse Environments with Web Monitoring. Electronics 2017, 6, 71. [CrossRef] Ortiz, E. Modeling and Analysis of Solar Distributed Generation. Ph.D. Thesis, Michigan State University, Michigan, MI, USA, 2006. Gil, O. Modelado Y Simulación de Dispositivos Fotovoltaicos. Master’s Thesis, Universidad de Puerto Rico, San Juan, Puerto Rico, 2008. Robles, C.; Ospino, A.; Casas, J. Dual-Axis Solar Tracker for Using in Photovoltaic Systems. Int. J. Renew. Energy Res. IJRER 2017, 10, 137–145. © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Fuzzy Logic Based MPPT Controller for a PV System Carlos Robles Algarín *

ID

, John Taborda Giraldo and Omar Rodríguez Álvarez

Facultad de Ingeniería, Universidad del Magdalena, Carrera 32 No. 22-08, 470004 Santa Marta, Colombia; [email protected] (J.T.G.); [email protected] (O.R.Á.) * Correspondence: [email protected]; Tel.: +57-5-421-7940 Received: 19 October 2017; Accepted: 22 November 2017; Published: 2 December 2017

Abstract: The output power of a photovoltaic (PV) module depends on the solar irradiance and the operating temperature; therefore, it is necessary to implement maximum power point tracking controllers (MPPT) to obtain the maximum power of a PV system regardless of variations in climatic conditions. The traditional solution for MPPT controllers is the perturbation and observation (P&O) algorithm, which presents oscillation problems around the operating point; the reason why improving the results obtained with this algorithm has become an important goal to reach for researchers. This paper presents the design and modeling of a fuzzy controller for tracking the maximum power point of a PV System. Matlab/Simulink (MathWorks, Natick, MA, USA) was used for the modeling of the components of a 65 W PV system: PV module, buck converter and fuzzy controller; highlighting as main novelty the use of a mathematical model for the PV module, which, unlike diode based models, only needs to calculate the curve fitting parameter. A P&O controller to compare the results obtained with the fuzzy control was designed. The simulation results demonstrated the superiority of the fuzzy controller in terms of settling time, power loss and oscillations at the operating point. Keywords: fuzzy logic controller; maximum power point tracking (MPPT); dc-dc converter; photovoltaic system

1. Introduction In recent years, the use of photovoltaic (PV) energy has experienced significant progress as an alternative to solve energy problems in places with high solar density, which is due to pollution caused by fossil fuels and the constant decrease of prices of the PV modules. Unfortunately, the energy conversion efficiency of the PV modules is low, which reduces the cost-benefit ratio of PV systems. The maximum power that a PV module can supply is determined by the product of the current and the voltage at the maximum power point, which depends on the operating temperature and the solar irradiance. The short-circuit current of a PV module is directly proportional to the solar irradiance, decreasing considerably as the irradiation decreases, while the open circuit voltage varies moderately due to changes in irradiation. In contrast, the voltage decreases considerably when the temperature increases, while the short circuit current increases moderately. In summary, increases in solar irradiation produce increases in the short-circuit current, while increases in temperature decrease the open circuit voltage, which affects the output power of the PV module. This variability of the output power means that in the absence of a coupling device between the PV module and the load, the system does not operate at the maximum power point (MPP). According to the previous context, the use of maximum power point (MPPT) controllers is currently increasing [1]. These devices are responsible for regulating the charge of the batteries, controlling the point at which the PV modules produces the greatest amount of energy possible, regardless of variations in climatic conditions. The use of MPPT controllers in PV systems has the following advantages: 1. They yield more power, depending on weather and temperature; 2. They allow the connection of PV modules in series to increase the voltage of the system, which reduces the Energies 2017, 10, 2036; doi:10.3390/en10122036

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wiring gauge and adds flexibility; 3. They offer a cost savings in the transmission wire needed for the installation of the PV system. In contrast to MPPT controllers, traditional controllers make a direct connection of the PV modules to the batteries, which requires that the modules operate in a voltage range that is below to the voltage in maximum power point. For example, in the case of a 12 V system, the battery voltage can vary between 11 V and 15 V, but the voltage at the maximum power point is a typical value between 16 V and 17 V. Due to this situation, with the traditional controllers the energy that the PV modules can deliver is not maximized. Taking into account the above, different researches have been carried out using traditional algorithms for the modeling and implementation of MPPT controllers [2], of which the following are highlighted: perturb and observe (P&O) [3,4], modified P&O [5,6], fractional short circuit current [7], fractional open circuit voltage [8], sliding mode control [9,10] and incremental conductance [11]. The P&O algorithm has been used traditionally, but it has been shown that this method has problems for tracking the MPP when there are sudden changes in solar irradiance [12]. Also, algorithms based on artificial intelligence techniques such as fuzzy logic [13–19] and neural networks [20–22] have been used, as well as the implementation of optimization algorithms such as glowworm swarm [23], ant colony [24,25] and bee colony [26–28]. These algorithms are part of soft computing techniques and have the advantage of being easily implemented using embedded systems. Additionally, MPPT controllers are widely used in hybrid power systems, in which different control techniques based on neural networks, fuzzy logic and particle swarm optimization have been evaluated. In [29–31], the effectiveness of these control techniques was demonstrated in order to achieve a fast and stable response for real power control and power system applications. The implementation of new control and optimization techniques that are detailed in [32–35] for electrical power and energy systems can be studied in the modeling and implementation of MPPT controllers. This paper presents the design and modeling of a fuzzy controller to track the maximum power point of a PV module, using the characteristics of fuzzy logic to represent a problem through linguistic expressions [36]. This paper presents as a novelty the use of the mathematical model proposed in [37,38] for modeling the PV module, which, unlike diode based models, only needs to calculate the curve fitting parameter. The results were compared with the P&O controller, which demonstrated that the proposed approach presents less energy losses and ensures MPP in all cases evaluated in simulation. It is worth mentioning that this work is part of a set of intelligent control techniques being evaluated in the research group Magma Ingeniería of the Universidad del Magdalena in order to implement a MPPT controller of low cost and high efficiency. The main objective of this work is the design, modeling and simulation of a fuzzy logic controller and a dc-dc converter for an off-grid PV system. In a second stage, the fuzzy logic controller will be implemented using the low-cost Arduino platform [38], taking as a reference the input variables, output, fuzzification, inference system and defuzzification evaluated during the modeling stage. The dc-dc converter will also be implemented according to the design conditions evaluated in the simulations. This work is structured as follows: Section 2 presents the design and modeling of PV system. Section 3 shows the simulation results for different operating conditions established in Matlab-Simulink. Finally, Section 4 summarizes the main conclusions. 2. Design and Modeling of PV System Figure 1 shows the general diagram of the PV system, which is composed of the 65 W PV module, the buck converter, the battery and the MPPT algorithm (fuzzy or P&O).

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PV Module (65W)

Io

I V

+ Vo -

DC-DC Converter (Buck)

Battery

D MPPT Algorithm

Figure 1. Block diagram of the photovoltaic (PV) system.

Figure 1. Block diagram of the photovoltaic (PV) system. 2.1. Modeling of the PV Module

2.1. Modeling the PV (1) Module In of Equation the mathematical model of the PV module is shown [37,38]. With this model, it only necessary to calculate the curve fitting parameter that can be obtained directly from the In is Equation (1) the mathematical model of the PV module is shown [37,38]. With this model, Equation (1). The other parameters are obtained from the electrical data of the PV module. it is only necessary to calculate the curve fitting parameter that can be obtained directly from the V 1 Ix − ) bVx b ] Equation (1). The other parameters are I(V) obtained from the (electrical data of the PV module. (1) = −1 [1 − e 1 − e( bh )

(

V

−1)

i

Ix b where Vx and Ix are the open circuit short with dynamic values for solar I(Vvoltage 1 −circuit e bVx current ) = and ( −1 ) b 1 − e irradiance and temperature, which are defined by Equations (2) and (3); b is the characteristic constant, it does not have units and is the unique parameter that has to be calculated.

(1)

where Vx and Ix are the open circuit voltage and short circuit current with dynamic values for solar E Vmax −Voc ( i(3); ln( b Ei irradiance and temperature, which are defined by Equations (2) and is the))characteristic(2)constant, Vx = s TCv (T − TN ) + sVmax − s(Vmax − Vmin )e EiN Vmax−Vmin E it does not have units and is the iN unique parameter that has to be calculated. I =p

Ei

[I + TC (T − T )]

sc i N Vx = s EEiNi TCv (T − TN ) x+ sVEmax iN − s(Vmax − Vmin )e

Ei iN

(E

max −Voc )) ln ( VVmax −V min

(3)

(2)

where; s: number of PV modules connected in series; p: number of PV modules connected in parallel; i Ix = p EEiN (3) + TCi (T − TN )] of 1000 W/m2; T: temperature of Ei: effective irradiation of the PV module; EiN[I: scirradiation constant the PV module; TN: temperature constant of 25 °C; Tcv: temperature coefficient of voltage; Tci: where; s: number of PV modules connected in series; p: number of PV modules connected in parallel; temperature coefficient of current; Voc: open circuit voltage; Isc: short-circuit current; Vmax: voltage for 2 Ei : effective irradiation the of 1000 W/m temperature of the iN : irradiation irradiations underof 200 WPV andmodule; operatingEtemperature of 25constant °C (this value is 103% of V;ocT: ); V min: voltage ◦ PV module; TN : temperature of 25 C; Tcv : temperature coefficient voltage; for irradiations over 1200constant W and operating temperature of 25 °C (this value is of 85% of Voc). Tci : temperature electrical parameters of thevoltage; 65 W PVImodule (Yingli Solar, Baoding, China) are illustrated coefficient ofThe current; Voc : open circuit current; Vmax : voltage for irradiations sc : short-circuit ◦ in Table 1. To find b, Equation (1) and the parameters of Table 1 were used. Knowing the: value under 200 W and operating temperature of 25 C (this value is 103% of Voc );that Vmin voltage for of b is in the range of 0.01 to 0.18 [39], the approximation of ◦Equation (4) can be done.

irradiations over 1200 W and operating temperature of 25 C (this value is 85% of Voc ). −1 (4) The electrical parameters of the 65 W PV module (Yingli Solar, Baoding, China) are illustrated in 1 − e( b ) ≈ 1 Table 1. To find b, Equation (1) and the parameters of Table 1 were used. Knowing that the value of b Therefore, for Vx = 21.7 V; Ix = 4 A; I = 3.71 A and V = 17.5 V; the value of b is 0.07375. is in the range of 0.01 to 0.18 [39], the approximation of Equation (4) can be done. Table 1. Electrical parameters of the PV module type YL65P-17b.

Therefore, for

−1 Parameter Value 1 − e( b ) ≈ 1 Short-circuit current (Isc) 4A Open circuit voltage (Voc) 21.7 V Vx = 21.7 V; Ix =Voltage 4 A; I at=P3.71 A and V = 17.5 V; the value max (Vmpp) 17.5 V of b Current at Pmax (Impp) 3.71 A Table 1.Temperature Electrical parameters the PV type−0.0802 YL65P-17b. coefficient of of voltage (Tcvmodule ) V/°C Temperature coefficient of current (Tci) 0.0024 A/°C Maximum voltage (Vmax) 22.35 V Parameter Value Minimum voltage (Vmin) 18.44 V

Short-circuit current (Isc ) Open circuit voltage (Voc ) Voltage at Pmax (Vmpp ) Current at Pmax (Impp ) Temperature coefficient of voltage (Tcv ) Temperature coefficient of current (Tci ) Maximum voltage (Vmax ) Minimum voltage (Vmin )

4A 21.7 V 17.5 V 3.71 A −0.0802 V/◦ C 0.0024 A/◦ C 22.35 V 18.44 V

(4) is 0.07375.

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Figure Figure 2a 2a shows shows the the modeling modeling of the PV module with the Simulink function blocks (MathWorks, Natick, MA, USA). Figure 2b 2b presents the PV in a subsystem, which was evaluated for different Natick, MA, USA). Figure presents themodule PV module in a subsystem, which was evaluated for values of solar and temperature. different valuesirradiance of solar irradiance and temperature. (s*(u(1)/1000)*(TCv)*(u(2)-25))+(s*Vmax)-((s*(VmaxVmin))*(exp((u(1)/1000)*(log((Vmax-Voc)/(Vmax-Vmin))))))

1

[Vx]

Vx

Fcn Vx

Ei 2

p*(u(1)/1000)*(Isc+(TCi*(u(2) -25)))

T

[Ix]

Ix

Fcn Ix [Vx]

From2 ((u(2)/(1-(exp(-1/b))))*(1(exp((u(3)/b*u(1)))-(1/b)))))

[Ix]

From3 3

1

I

Fcn I

V

(a) [Ip] Imodule

Ei

1

1

V+

Ei (W/m2)

Isource2 2

2

T

V-

2

I

Imodule1

T °C

3

Pmodule Pmodule1

V Memory

3

Ref_V

PV Module

1

Vmodule1

(b)

Figure Figure 2. 2. PV module in Matlab. (a) Model implemented with Simulink Simulink function function blocks; blocks; (b) (b) Subsystem Subsystem implemented implemented for for the the simulation. simulation.

Table22shows shows values obtained the mathematical of the PV module, using Table thethe values obtained withwith the mathematical modelmodel of the PV module, using variable ◦ variable solar irradiance and operating temperature of 25 °C. Itbecan be that seen the thatvalues the values obtained solar irradiance and operating temperature of 25 C. It can seen obtained for 2, T = 25 °C) 2 ◦ for standard test conditions (E i = 1000 W/m correspond to the electrical parameters of standard test conditions (Ei = 1000 W/m , T = 25 C) correspond to the electrical parameters the of PV PV module presented in in Table 1. 1. Additionally, it itisisworth the solar solar the module presented Table Additionally, worthnoting notingthat thatthe the decreases decreases in in the irradiance considerably considerably affect affect the the short-circuit short-circuit current, current, while while the the open open circuit circuit voltage voltage is is affected affected in in irradiance smaller proportion. smaller proportion. Table 2. Parameters of the PV module for variable solar irradiance. Table 2. Parameters of the PV module for variable solar irradiance.

Parameter 1000 W/m2 800 W/m2 600 W/m2 400 W/m2 200 W/m2 2 2 2 2 Parameter 400 W/m1.6 200 W/m Short-circuit current Isc (A) 1000 W/m4.0 800 W/m23.2 600 W/m2.4 0.8 Open circuit current voltageIscVoc (V) Short-circuit (A) 4.0 21.70 3.2 21.42 2.4 21.02 1.6 20.44 0.819.62 Open circuit Voc(V) (V) 21.7017.66 21.42 17.55 21.0217.37 20.4416.78 19.62 Voltage at voltage Pmax Vmpp 16.08 Voltage at P V (V) 17.66 17.55 17.37 16.78 16.08 max mpp Current at Pmax Impp (A) 3.679 2.924 2.171 1.459 0.730 Current at Pmax Impp (A) 3.679 2.924 2.171 1.459 0.730 Maximum Power Point (W) 64.98 51.31 37.72 24.48 11.75 Maximum Power Point (W) 64.98 51.31 37.72 24.48 11.75 Table 3 shows the data obtained with the mathematical modeling of the PV module for solar Table 3ofshows the data obtained the mathematical modeling PV module for solar 2 and irradiance 1000 W/m variablewith temperature. In this case, it canofbethe noted that increases in 2 and variable temperature. In this case, it can be noted that increases in irradiance of 1000 W/m temperature considerably affect the open circuit voltage, while the short-circuit current is affected in a smaller proportion. Tables 2 and 3 will be used as references in the results and discussion section,

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temperature Energies 2017, 10,considerably 2036

affect the open circuit voltage, while the short-circuit current is affected 5 of in 18 a smaller proportion. Tables 2 and 3 will be used as references in the results and discussion section, in in which which aa comparison comparison with with the the fuzzy fuzzy and and P&O P&O controllers controllers will will be be made; made; with with variations variations of of the the solar solar irradiance temperature of of the the PV PV module. module. irradiance and and the the operating operating temperature Table 3. Parameters of the PV module for variable temperature. Table 3. Parameters of the PV module for variable temperature.

Parameter Parameter Short-circuit current Isc (A) Open circuitcurrent voltage oc (V) Short-circuit Isc V (A) Open circuit voltage V (V) oc (V) Voltage at Pmax Vmpp Voltage at Pat Vmpp max Current Pmax Impp(V) (A) Current at Pmax Impp (A) Maximum Power Point Maximum Power Point (W)(W)

0 °C 0 3.94 3.9423.71 23.7119.39 19.393.606 3.606 69.9269.92 ◦C

25 °C 25 4.00 4.0021.7 21.7 17.66 17.66 3.679 3.679 64.98 64.98 ◦C

50 °C 50 ◦4.06 C 19.69 4.06 19.69 16.47 16.47 3.617 3.617 59.59 59.59

75 °C ◦C 754.12 17.69 4.12 17.69 14.47 14.47 3.771 3.771 54.55 54.55

2.2. DC-DC Converter Model 2.2. DC-DC Converter Model A buck converter as control device was used. Figure 3 shows the circuit that was designed to A buck converter as control device was used. Figure 3 shows the circuit that was designed to ensure that the converter operates in the continuous conduction mode (CCM); in order to avoid that, ensure that the converter operates in the continuous conduction mode (CCM); in order to avoid that, the current in the inductor reaches zero during a time interval. the current in the inductor reaches zero during a time interval. Vo

Figure 3. Buck converter circuit. Figure 3. Buck converter circuit.

In the CCM, thethe diode is in circuit (Ton(T ).onUsing Equation (5), CCM,when whenthe thetransistor transistorisisconducting, conducting, diode is open in open circuit ). Using Equation the ripple of the is obtained as shown in Equation (6). (6). (5), the ripple of inductor the inductor is obtained as shown in Equation LΔIL L∆I L L = VLV= ∆t∆t −ILILRRLL))− −V Voo s− DS− (V(V VV s− DS Ton ∆IL∆I == T L (+) (+) on LL The inductor current decreases during the off off state state as as shown shown in in Equation Equation (7). (7).

(5) (5) (6) (6)

V + (V + I R ) Vo o+ (Vdd+ ILLRLL) Toff (7) ∆IL (−) = ∆IL (−) = Toff (7) L L Assuming that Vd, RL y VDS are very small values, Equations (8) and (9) are obtained. Assuming that Vd , RL y VDS are very small values, Equations (8) and (9) are obtained. (Vs − Vo ) (8) ∆IL (+) = T (Vs −LVo ) on ∆IL (+) = Ton (8) L Vo (9) ∆IL (−) =V Toff o ∆IL (−) = LToff (9) L Equating Equations (8) and (9); using Ts = Toff + Ton, Equation (10) for the duty cycle D is obtained. Equating Equations (8) and (9); using Ts = Toff + Ton , Equation (10) for the duty cycle D is obtained. Ton Vo D= = (10) TonTs VVos D= = (10) Ts Vs 2.2.1. Inductor Design The inductor was designed to maintain the balance volts per second of the converter and to reduce ripple in the output current. Using an improper inductor produces an alternating current ripple in the direct current output, causing a change between continuous and discontinuous

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2.2.1. Inductor Design The inductor was designed to maintain the balance volts per second of the converter and to reduce 6 of 18 ripple in the output current. Using an improper inductor produces an alternating current ripple in the direct current output, causing a change between continuous and discontinuous conduction modes. conduction modes. To operate in the continuous conduction mode, the critical output current must To operate in the continuous conduction mode, the critical output current must be greater than or be greater than or equal to half the inductor current ripple. See Equation (11) and Figure 4. equal to half the inductor current ripple. See Equation (11) and Figure 4. ∆IL (11) io (crit) ≥ ∆I io (crit) ≥ 2 L (11) 2 Energies 2017, 10, 2036

I L Solid io Dashed= io(crit) ΔI L

Ton

Toff Ts

Figure Critical output current. Figure 4. 4. Critical output current.

Replacing Equation (8)(8) inin (12), using Ton = DT s, the Equation (12) forfor thethe design of of thethe inductor Replacing Equation (12), using Ton = DT Equation (12) design inductor s , the is is obtained. obtained. o Vo ( 1 − V V )Ts Lmin ≥ Vo (1 − Vos)Ts (12) Vs ) 2i0 (crit (12) Lmin ≥ 2i0 (crit) To calculate L, the maximum power and voltage according to the MPP of the PV module were used: Vs = 17.71 W, ioand = 5.41 A, fsaccording = 20 KHz. Using a ripple value of 10% for a To calculate L, V, thePmaximum power voltage to the MPP of the PV module were max = 64.984 maximum output current, Equation (13) A, is obtained. used: Vs = 17.71 V, Pmax = 64.984 W, io = 5.41 fs = 20 KHz. Using a ripple value of 10% for a maximum output current, Equation (13) is obtained. ∆IL = 0.1 × io (max) = 0.541 A (13) (13) ∆IL = 0.1 × io (max) = 0.541 A

Using Equations (12) and (13), minimum value of the inductor as shown in Equation (14) Using Equations (12) and (13), thethe minimum value of the inductor as shown in Equation (14) is is obtained. obtained. 12 ) × 50 µS 12 × (1 − 17.71 L≥ ≥ 357.57 µH (14) 12 2 × 0.2705 12 × (1 − ) × 50 μS 17.71 (14) L≥ ≥ 357.57 μH 2 × 0.2705 2.2.2. Capacitor Design The current in the capacitor is defined as the variation of the charge with respect to time. 2.2.2. Capacitor Design See Equation (15). ∆Q variation ∆Vc of the charge with respect to time. See The current in the capacitor is defined as the i= =C (15) ∆t ∆t Equation (15). Using Figure 5 and Equation (15), the expression the variation of the load ∆Q is obtained. ∆Q ∆Vfor c (15) i= =C See Equation (16). ∆t ∆t ∆IL Ts ∆Q = for (16) Using Figure 5 and Equation (15), the expression 8 the variation of the load ΔQ is obtained. See Equation (16). ∆Q =

∆IL Ts 8

(16)

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I LI L

L/2 ΔIΔIL/2

Figure 5. Timevariation variation ofthe the currentininthe the inductor. Figure Figure5.5.Time Time variationof of thecurrent current in theinductor. inductor.

Therefore,Equation Equation(17) (17)for forthe thedesign designofofthe thecapacitor capacitorisisobtained. obtained. Therefore, Therefore, Equation (17) for the design of the capacitor is obtained. ∆I∆IL T LT ss CC≥≥ ∆I8∆V Tsc c 8∆V L C≥ 8∆Vc Usingaaripple ripplevalue valueofof0.1%, 0.1%,Equation Equation(18) (18)isisobtained. obtained. Using

(17) (17) (17)

Using a ripple value of 0.1%, Equation (18) is obtained. (0.001)(V ∆V==(0.001)(V 0.012VV ∆V o )==0.012 o)

(18) (18)

FromEquations Equations(13), (13),(17) (17)and and(18), (18), the(minimum minimum value the capacitorisisobtained. obtained.See SeeEquation Equation From ofofthe ∆Vthe = 0.001 = 0.012 V capacitor (18) )(Vo )value (19). (19). From Equations (13), (17) and (18), the minimum value of the capacitor is obtained. See Equation (19). ∆I∆IL T LT ss 279.63μF μF (19) CC≥≥ ≥≥279.63 (19) 8∆V ∆I8∆V L Tsc c C≥ ≥ 279.63 µF (19) 8∆Vc 2.2.3.Modelling ModellingofofBuck BuckConverter Converter 2.2.3. 2.2.3. Modelling of Buck Converter Figure66shows showsthe thebuck buckconverter converterthat thatwas wasmodeled modeledusing usingthe thefundamental fundamentalblocks blocksofofSimulink. Simulink. Figure Figure 6 shows the buck converter that was modeled using the fundamental blocks of Simulink.

Dutty Dutty

V+V+

PWMGenerator Generator PWM (DC-DC)20KHz (DC-DC)20KHz

LL

Switch Switch

Ammeter2 Ammeter2

Scope1 Scope1

Diode Diode SeriesRLC RLCBranch Branch Series

Battery Battery

P_Out P_Batt P_Out P_Batt

V_out V_out

V-V-

Figure6.6.6.Buck Buckconverter convertermodeled modeledin inSimulink. Simulink. Figure Figure Buck converter modeled in Simulink.

Figure77shows showsthe thecurrent currentininthe thebattery batterywith withthe thebuck buckconverter converterininopen openloop, loop,with withsolar solar Figure Figure 7 shows the current in the battery with the buck converter in open loop, with solar 2 and temperature of 25 °C; in which it is observed that the converter works in 2 irradiance of 200 W/m irradiance of 200 W/m 2and temperature of 25 °C; in which it is observed that the converter works in irradiance of 200 W/m and temperature of 25 ◦ C; in which it is observed that the converter works in theCCM CCMaccording accordingtotothat thatestablished establishedininthe thedesign designconditions. conditions. the the CCM according to that established in the design conditions.

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22 1.04 1.04

1.5 1.5

1.02 1.02

Battery Current (A) Battery Current (A)

Battery Current (A) Battery Current (A)

11

0.5 0.5 00

-0.5 -0.5 -1-1 -1.5 -1.5 00

11 0.98 0.98 0.96 0.96 0.94 0.94 0.92 0.92

0.90.9 0.88 0.88

0.05 0.05

0.1 0.1

0.15 0.2 0.15 0.2 Time(seconds) (seconds) Time

0.25 0.25

0.3 0.3

0.35 0.35

0.2214 0.2214 0.2215 0.2215 0.2215 0.2214 0.2214 0.2215 0.2215 0.2213 0.2213 0.2213 0.2213 0.2213 0.2214 0.2214 0.2214 0.2214 0.2215 0.2214 0.2214 0.2213

Time(seconds) (seconds) Time (b) (b)

(a)(a)

Figure7.7. 7.(a) (a)Battery Batterycurrent currentfor foropen openloop; loop;(b) (b)Extended Extendedsection sectionfor forrange range(0.2213–0.2215 (0.2213–0.2215s). s). Figure Figure current for open loop; (b) Extended section for range (0.2213–0.2215 s).

2.3.Fuzzy FuzzyController ControllerDesign Design 2.3. 2.3. Fuzzy Controller Design Fuzzycontrol controlis isaaamethod methodthat thatallows allowsthe theconstruction constructionof ofnonlinear nonlinearcontrollers controllersfrom fromheuristic heuristic Fuzzy Fuzzy control is method that allows the construction of nonlinear controllers from heuristic informationthat that comes from the knowledge ofan anexpert. expert. Figure shows theblock block diagram ofaafuzzy fuzzy information the knowledge of Figure 88shows the diagram of information thatcomes comesfrom from the knowledge of an expert. Figure 8 shows the block diagram of a controller. The fuzzification block is responsible for processing the input signals and assign them controller. The fuzzification block is responsible for processing the input signals and assign them aa fuzzy controller. The fuzzification block is responsible for processing the input signals and assign fuzzyavalue. value. The setof ofrules rules allows alinguistic linguistic description ofthe thevariables variables tobe becontrolled controlled andisis fuzzy set allows description of to and them fuzzyThe value. The set of rulesaallows a linguistic description of the variables to be controlled based on the knowledge of the process. The inference mechanism is responsible for making an based on the knowledge of the process. The inference mechanism is responsible for making an and is based on the knowledge of the process. The inference mechanism is responsible for making interpretation of the data taking into account the rules and their membership functions. With the interpretation of the data taking into account the rules and their membership functions. With the an interpretation of the data taking into account the rules and their membership functions. With the defuzzificationblock, block,the thefuzzy fuzzyinformation informationcoming comingfrom fromthe theinference inferencemechanism mechanismisis isconverted convertedinto into defuzzification defuzzification block, the fuzzy information coming from the inference mechanism converted into non-fuzzy information that is useful for the process to be controlled. non-fuzzy information that is useful for the process to be controlled. non-fuzzy information that is useful for the process to be controlled.

Inference Inference

Defuzzification Defuzzification

Input Input

Fuzzification Fuzzification

FuzzyControler Controler Fuzzy

Process Process

Output Output

Rules Rules

Figure8.8.Block Blockdiagram diagramfor foraafuzzy fuzzycontroller. controller. Figure Figure 8. Block diagram for a fuzzy controller.

Takinginto intoaccount accountthe theabove, above,the thedesign designof offuzzy fuzzycontroller controllerfor forthis thiswork workisispresented. presented.AAfuzzy fuzzy Taking Taking intotwo account the above, the design fuzzy controller for this variables work is presented. fuzzy controller with two inputs and oneoutput output wasofdesigned. designed. Thetwo two input variables areError ErrorA (E) and controller with inputs and one was The input are (E) and controller with two inputs and one output was designed. The two input variables are Error (E) and Change of Error (CE), which are shown in Equations (20) and (21) for sample times k. Change of Error (CE), which are shown in Equations (20) and (21) for sample times k. Change of Error (CE), which are shown in Equations (20) and (21) for sample times k. P(k)−−P(k P(k−−1) 1) ∆P ∆P P(k) (20) E(k)== (20) E(k) == V(k) − V(k − 1) ∆V P(V(k) k) −−P(V(k k −−1)1) ∆P ∆V E(k) = = (20) V(k) − V(k − 1) ∆V (21) CE(k)==E(k) E(k)−−E(k E(k−−1) 1)==∆E ∆E (21) CE(k) CE(k) = E(k) − E(k − 1) = ∆E (21) Theinput inputE(k) E(k)isisthe theslope slopeof ofthe theP-V P-Vcurve curveand anddefines definesthe thelocation locationof ofthe theMPP MPPin inthe thePV PVmodule. module. The TheCE(k) CE(k) input defines whether themovement movement ofthe the operating pointisisof inthe theMPP MPPin direction ornot. not. The input E(k) is thewhether slope ofthe P-V curve and defines the location the PV module. The input defines of operating point in the MPP direction or The CE(k) defines whether the movement of (ΔD), the operating point is positive in the MPP direction or not. Theoutput outputinput variable the increment induty dutycycle cycle (ΔD), whichcan can take positive ornegative negativevalues values The variable isisthe increment in which take or depending on thelocation location ofthe theoperating operating point. This output sent tothe the dc-dcor converter tovalues drive The outputon variable is the of increment in duty cycleThis (∆D), which take positive negative depending the point. output isiscan sent to dc-dc converter to drive theload. load.Using Using thelocation valueof of ΔD delivered by thecontroller, controller, anis accumulator wasmade made toobtain obtain the depending on the ofΔD thedelivered operatingby point. This output sent to the dc-dc converter to drive the the value the an accumulator was to the valueof ofthe theduty dutycycle. cycle.See SeeEquation Equation(22). (22). value D(k)==D(k D(k−−1) 1)++∆D(k) ∆D(k) D(k)

(22) (22)

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the load. Using the value of ∆D delivered by the controller, an accumulator was made to obtain the value of the duty cycle. See Equation (22). D(k) = D(k − 1) + ∆D(k)

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2.3.1. 2.3.1. Membership Membership Functions Functions Triangular Triangular membership membership functions functions for for the the fuzzification fuzzification process process were were used. used. For For the the inputs inputs E, E, CE CE and and for for the the output output ∆D, ΔD, 55 membership membership functions functions were were defined defined in in terms terms of of the the following following linguistic linguistic variables: (B), Neutral (N), High (A)(A) andand VeryVery HighHigh (MA). The range for the error variables:Very VeryLow Low(MB), (MB),Low Low (B), Neutral (N), High (MA). The range for the is ( − 60 to 100), for the change of error is ( − 10 to 10) and for the increment in duty cycle is ( − 0.01 to error is (−60 to 100), for the change of error is (−10 to 10) and for the increment in duty cycle is (−0.01 0.01). Figure 9 shows thethe membership functions for for thethe inputs andand outputs of the controller. to 0.01). Figure 9 shows membership functions inputs outputs of the controller. VH

H

L

0.5

VL

1

N

Degree of Membership

Degree of Membership

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-0.01

-0.008 -0.006

0 0.002 -0.004 -0.002 Output Variable: ΔD

0.004

0.006

0.008

0.01

(c)

Figure 9. 9. Membership Membership functions. functions. (a) Error; Error; (b) (b) Change Change of of error; error; (c) (c) Increment Increment of of duty duty cycle. cycle. Figure

2.3.2. Fuzzy Fuzzy Rules Rules 2.3.2. Table 44shows shows the the 25 25 fuzzy fuzzy rules rules applied applied in in the the controller. controller. The The rows rows and and columns columns represent represent the the Table two inputs inputs EE and and ∆E. ΔE. The The output output ∆D ΔD is is aa variable variable located located at at the the intersection intersectionof ofaarow rowwith withaacolumn. column. two Table 4. Fuzzy associative matrix. Table 4. Fuzzy associative matrix.

E/ΔE Very Low E/∆E Very Low Very Low VH Low Very Low H VH NeutralLow H H HighNeutral H H High H Very High H Very High

H

Low Low VH H VH HH HH H H H

Neutral Neutral H HH HN NL L L L

High

Very High

High VL Very High VL VL VL L L L

VL L L L

VL L L VL VL

L L VL VL

2.3.3. Fuzzy Controller Modelling 2.3.3. Fuzzy Controller Modelling The controller was modeled with the Matlab Fuzzy Logic Toolbox (MathWorks, Natick, MA, The controller was modeled with the Matlab Fuzzy Logic Toolbox (MathWorks, Natick, MA, USA). A Mamdani controller with the centroid defuzzification method was used. This procedure was USA). A Mamdani controller with the centroid defuzzification method was used. This procedure carried out using the fuzzy inference system editor (FIS editor) (MathWorks, Natick, MA, USA). was carried out using the fuzzy inference system editor (FIS editor) (MathWorks, Natick, MA, USA). Figure 10 shows the controller modeled in Simulink, for which a subsystem was performed to Figure 10 shows the controller modeled in Simulink, for which a subsystem was performed to calculate calculate ΔV and ΔP in order to obtain the inputs E and ΔE. ∆V and ∆P in order to obtain the inputs E and ∆E.

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T T

12:34 12:34

Digital Clock1 Clock1 Digital 1 1

V V 2 2

I I

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V V Divide Divide

I I

ΔP ΔP

Dutty Dutty Cycle Cycle

Change of Change Error of Error

Error Error Subtract3 Subtract3

Zero-Order Zero-Order Hold2 Hold2

ΔV and ΔP ΔV and ΔP

Subtract1 Subtract1 Memory2 Memory2

Change of Error Memory1 Change of Error Memory1

Figure Fuzzy logic logic controller. controller. Figure 10. 10. Fuzzy Figure 10. Fuzzy logic controller.

2.4. 2.4.P&O P&OController ControllerDesign Design 2.4. P&O Controller Design The the operating operating point point of of the the PV PV module moduleby byincreasing increasing TheP&O P&Oalgorithm algorithm consists consists of modifying modifying the The P&O algorithm consists of modifying the operating point of the PV module by increasing or order to to measure measure the the output outputpower powerbefore before and ordecreasing decreasingthe the duty duty cycle cycle of of aa dc-dc dc-dc converter converter in order and or decreasing the duty cycle of a dc-dc converter in order to measure the output power before and after the algorithm algorithmperturbs perturbsthe thesystem systemininthe thesame samedirection; direction; afterthe theperturbance. perturbance. If If the the power increases, the after the perturbance. If the power increases, the algorithm perturbs the system in the same direction; otherwise Figure 11 11 shows showsthe the44possible possibleoptions options otherwisethe thesystem system is is perturbed perturbed in the the opposite direction. direction. Figure otherwise the system is perturbed in the opposite direction.1 Figure 11 shows the 4 possible options that thatare arepresented presentedduring duringthe thetracking trackingof ofthe theMPP, MPP,with withpoint point 1being beingthe theprevious previousposition positionand andpoint point2 that are presented during theof tracking of(A, the MPP, with point 1 being the previous position and point being thethe current position of each case (A, B,B, C and D). 2 being current position each case C and D). 2 being the current position of each case (A, B, C and D). CaseA: A:∆P ΔP < 0 y ∆V ΔV 0 y ∆V >> 0. Case C: ΔP > 0 y ΔV 0. Case D: ΔP > 0 y ΔV < 0. • Case CaseD: D:∆P ΔP>>00yy∆V ΔV0 V(x)-V(x-1)>0

No No

Duty Duty++ ++

Duty Duty++ ++

Ye Yess

ΔP>0 ΔP>0 Ye Yess

No No

V(x)-V(x-1)>0 V(x)-V(x-1)>0

Duty Duty----

Duty Duty----

Duty Duty++ ++

V(x-1)=V(x) V(x-1)=V(x) P(x-1)=P(x) P(x-1)=P(x)

Figure 12. Flowchartofof ofthe theperturbation perturbation and observation (P&O) controller. Figure Figure12. 12.Flowchart Flowchart the perturbationand andobservation observation(P&O) (P&O)controller. controller.

2.5. PV SystemModelling Modelling 2.5. 2.5.PV PVSystem System Modelling Figure 13 showsthe thePV PVsystem systemimplemented implemented Matlab/Simulink, which is composed of PV the Figure in Matlab/Simulink, which isiscomposed of Figure13 13shows shows the PV system implemented inin Matlab/Simulink, which composed ofthe the PV PV module, buck converter and the fuzzy/P&O controller. The signal builderblock blockwas wasused usedto to module, the buck converter and the fuzzy/P&O controller. The signal builder module, thethe buck converter and the fuzzy/P&O controller. The signal builder block was used to generate the temperature and irradiance signals in order to evaluate the controller performance. generate the temperature and irradiance signals in order to evaluate the controller performance. generate the temperature and irradiance signals in order to evaluate the controller performance. Additionally, this system was used to evaluate the standard standard P&O controller and and perform perform the the Additionally, Additionally, this this system system was was used used to to evaluate evaluate the standard P&O P&O controller comparison with the fuzzy controller. comparison comparisonwith withthe thefuzzy fuzzycontroller. controller. 1000 1000

Irradiance Irradiance

powergui powergui

VV

VV

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II

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PP

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Power Power

Switch1 Switch1 V+ V+

V+ V+

V-V-

V-V-

Reference_Volt Reference_Volt

PV PVModule Module

V_Out V_Out

DC-DC DC-DCConverter Converter

Figure 13. PV system modelling. Figure Figure13. 13.PV PVsystem systemmodelling. modelling.

2.6. Limitations 2.6. 2.6.Limitations The dc-dc designed based onon the electrical parameters of the PV The fuzzy control were designed based the electrical parameters of Thedc-dc dc-dcconverter converterand andfuzzy fuzzycontrol controlwere were designed based on the electrical parameters ofthe the module under study; for this reason, the calculations made apply to PV modules with powers up to PV module under study; for this reason, the calculations made apply to PV modules with powers up PV module under study; for this reason, the calculations made apply to PV modules with powers up 65 W. of theof inputs of the fuzzy controller is the change of error, which requires a differentiation to W. the of fuzzy isis the change of requires to 65 65 One W. One One of the inputs inputs of the the fuzzy controller controller the change of error, error, which which requires aa operation that operation increases complexity in calculations and can generateand errors measuring differentiation that increases complexity in can generate errors differentiation operationthe that increasesthe thethe complexity inthe thecalculations calculations and canwhen generate errors small powers thatsmall are sensitive to noise. when powers are whenmeasuring measuring small powersthat that aresensitive sensitiveto tonoise. noise.

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3. 3. Results Results and and Discussion Discussion

3. Results and Discussion To the performance To test test the performance of of the the PV PV system, system, different different scenarios scenarios were were simulated simulated in in which which the the traditional P&O control is evaluated in comparison with the fuzzy controller. Four scenarios that traditional P&O control is evaluated in comparison with the fuzzy controller. Four scenarios that To test the performance of the PV system, different scenarios were simulated in which the simulate changes in solar irradiance and operating temperature of the PV are presented. simulatesudden sudden changes in solar irradiance and operating temperature ofmodule the module are traditional P&O control is evaluated in comparison with the fuzzy controller. FourPV scenarios that In all cases, the following elements were used: 65 W PV module, 12 V battery, inductor of 416 µH and presented.sudden In all cases, the following elements were 65 W temperature PV module, 12 battery, inductor of simulate changes in solar irradiance and used: operating of Vthe PV module are capacitor of 500 µF; with a sampling frequency of frequency 20 KHz forofthe dc-dc converter. 416 μH and capacitor of 500 μF; with a sampling 20 KHz for the dc-dc converter. presented. In all cases, the following elements were used: 65 W PV module, 12 V battery, inductor of 416 μH and capacitor of 500 μF; with a sampling frequency of 20 KHz for the dc-dc converter. 1:1:standard conditions Case Case standardtest test conditions 2 and temperature Case 1:case, standard test conditions In thethe two controllers were evaluated for solarfor irradiance of 1000 W/m In this this case, two controllers were evaluated solar irradiance of 1000 W/m2 and ◦ C. Figure 14a shows the results obtained for the power delivered to the battery with a simulation of 25 2 and temperature of 25 °C. 14a shows were the results obtained theirradiance power delivered to W/m the battery In this case, the Figure two controllers evaluated for for solar of 1000 time of 0.03 s. It can be seen that the two controllers extract the maximum power of 65 W with a good with a simulation of 0.0314a s. Itshows can bethe seen that the two controllers extract the maximum power temperature of 25 time °C. Figure results obtained for the power delivered to the battery stabilization time of 0.005 s, which is consistent with the results obtained in [15,16]. In Figure 14b, it in is of 65aW with a good timebeofseen 0.005 s, the which consistent extract with the obtained with simulation timestabilization of 0.03 s. It can that twoiscontrollers theresults maximum power observed that the14b, dutyitcycle of the P&O control small oscillations between 0.6926 and 0.7, [15,16]. Figure is observed that the duty presents cycle of the P&O control presents small oscillations of 65 WIn with a good stabilization time of 0.005 s, which is consistent with the results obtained in in contrast to the fuzzy control that is stabilized at a value of D = 0.694. betweenIn0.6926 inobserved contrast to thethe fuzzy stabilized a value of D = oscillations 0.694. [15,16]. Figureand 14b,0.7, it is that dutycontrol cycle ofthat theisP&O controlatpresents small between 0.6926 and 0.7, in contrast to the fuzzy control that is stabilized at a value of D = 0.694. 0.702

60 50

0.702 0.7

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Power Power (W) (W)

Duty Cycle Duty Cycle

60

40 30

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2 and 2T Figure 14. 14. PV W/m = 25T°C. (a)◦Output power of the PV Duty Figure PVsystem systemwith withEiE=i 1000 = 1000 W/m and = 25 C. (a) Output power ofmodule; the PV (b) module; 2 cycle. Figure 14.cycle. PV system with Ei = 1000 W/m and T = 25 °C. (a) Output power of the PV module; (b) Duty (b) Duty cycle.

Case 2: changes in solar irradiance, temperature of 25 °C Case 2:2:changes in solar temperature ofof2525◦ C Case changes solarirradiance, irradiance, °C In this case, the in performance of the temperature controllers was evaluated with an operating temperature of this case, the performance of the controllers was evaluated with an was operating temperature of 25 °CIn and sudden changes in solar irradiance. Initially, an irradiance signal used with increments In this case, the performance of the controllers was evaluated with an operating temperature of ◦ C and sudden 2 2 2 25 changes in solar irradiance. Initially, an irradiance signal was used with increments of °C 200and W/m , starting at 200 and endingInitially, at 1000 W/m . Changes in irradiance every 25 sudden changes inW/m solar irradiance. an irradiance signal was usedwere with made increments 2 , starting at 200 W/m2 and ending at 1000 W/m2 . Changes in irradiance were made every of W/m 2. Changes in 0.2200 s with simulation time2of 1 sending (see Figure 15a). Subsequently, a irradiance test signal were with decreases in of 200 W/ma2total , starting at 200 W/m and at 1000 W/m made every 21and 215a). 0.2 s with a total simulation time of s (see Figure Subsequently, a test signal with decreases in solar irradiance between 1000 W/m 200 W/m was used (see Figure 15b). 0.2 s with a total simulation time of 1 s (see Figure 15a). Subsequently, a test signal with decreases in 2 and 200 W/m2 was used (see Figure 15b). solar solar irradiance irradiance between between 1000 1000 W/m W/m2 and 200 W/m2 was used (see Figure 15b).

200 0

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Irradiance Irradiance (W/m2) (W/m2)

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Figure 15. (a) Increases in solar irradiance; (b) Decreases in solar irradiance. Figure 15. (a) Increases in solar irradiance; (b) Decreases in solar irradiance.

Figure 16a shows the output power for increments in the irradiance signal. In general terms it can be noted that the two controllers present a good performance in the signal. different instants of time. Figure 16a shows the output output power for increments increments in the the irradiance irradiance Figure 16a shows the power for in signal. In In general general terms terms it it The power obtained is between 11.7 W and 64.9 W, which corresponds to the values presented in can be noted that the two controllers present a good performance in the different instants of time. can be noted that the two controllers present a good performance in the different instants of time. Table 2. However, it should be noted that the P&OW, controller presented small oscillations for E i = 200 The power obtained between 11.7 W and which corresponds the values presented The power obtained isisbetween 11.7 W and 64.964.9 W, which corresponds to the to values presented in Tablein 2. W/m2,2.which is evidenced dutythat cycle Figure 16b, in times between 0 oscillations and 0.2 s. for E i = 200 Table However, it shouldinbethe noted theofP&O controller presented small However, it should be noted that the P&O controller presented small oscillations for Ei = 200 W/m2 , W/m2, which is evidenced in the duty cycle of Figure 16b, in times between 0 and 0.2 s. which is evidenced in the duty cycle of Figure 16b, in times between 0 and 0.2 s.

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(a) power of the PV module for increases in solar irradiance; (b) (b) Duty cycle. Figure 16.Output (a) Output Figure 16. (a) power of the PV module for increases in solar irradiance; (b) Duty cycle.

Figure 16. (a) Output power of the PV module for increases in solar irradiance; (b) Duty cycle.

In Figure 17a, the output power for decreases in the irradiance signal is shown. As with the In Figure 17a, the output power for decreases in the irradiance signal is shown. As with the In Figure 17a, the thetwo output power for decreases in the irradiance shown. increase signal, controllers exhibit good performance with outputsignal power is between 64.9As Wwith and the In Figure output power forgood decreases in the irradiance signalpower is shown. As with increase signal, the17a, twothe controllers exhibit performance with output between 64.9the W and increase the17b two controllers good performance with power between 64.9 W 11.7 signal, W. Figure shows the dutyexhibit cycle, in which it is noted that theoutput P&O controller presents the increase signal, the two controllers exhibit good performance with output power between 64.9 W and 11.7 W. Figure 17b shows the duty cycle, in which it is noted that the P&O controller presents the oscillations that 17b characterize this duty method, but in that do notitsignificantly affect performance of the and 11.7 Figure showsthethe cycle, which is noted that thethe P&O controller 11.7 W. W.that Figure 17b shows duty cycle, in which it is noted that the P&O controller presentspresents theof the oscillations characterize this method, but that do not significantly affect the performance system. the oscillations characterizethis this method, dosignificantly not significantly affect the performance oscillations that that characterize method, butbut thatthat do not affect the performance of the of system. the system. system. 70 0.76

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Figure 17. (a) Output power of the PV module for decreases in solar (a)

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0.8

0.8

0.7

0.9 Fuzzy P&O

1

0.9

Fuzzy P&O 1

0.8

0.9

1

cycle.

Figure 17. Output (a) Output power of thePV PVmodule module for for decreases in solar irradiance; (b) Duty cycle. Figure 17. (a) power ofcase the decreases solar irradiance; Duty cycle. With 17. the(a) tests carried out inof it module is evident the twoin controllers exhibit a(b) similar Figure Output power the 2, PV forthat decreases in solar irradiance; (b) Duty behavior cycle. for sudden changes in solar irradiance. In addition, it was found that the P&O control has small With the tests carried out in case 2, it is evident that the two controllers exhibit a similar behavior oscillations thatcarried do not significantly affect the power delivered to controllers the battery. With the tests case 2, two With it isInevident that the two controllers exhibit a similar behavior for sudden changes in out solarinirradiance. addition, it was found that the P&O control has small 2 for sudden changes innot solar irradiance. Inthe addition, it1000 wasW/m found oscillations do affect power delivered to the battery. Case 3:that changes in significantly temperature, solar irradiance ofit In addition, was found that the P&O control has small

oscillations that do not significantly affect the power delivered to battery. affect power delivered to the battery. 2 the Case 3: point, changes temperature, irradiance 1000 W/m At this theinperformance ofsolar thethe system wasof evaluated for sudden changes in temperature 2. Initially, the signal shown 2 with3:a3:constant solar irradiance of 1000 W/m in Figure 18a was used, with Case ininthe temperature, irradiance ofof 1000 Case changes temperature, solar irradiance 1000W/m W/m Atchanges this point, performancesolar of the system was evaluated for2sudden changes in temperature

temperature increases every 0.2 s between 02 °C and 100 °C, for a test time of 1 s. Subsequently, the

20 60 0 40 0 20

Temperature (°C)

100 80 60 40 20 0

0

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75°C 0.6

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0°C 0

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1

Temperature TemperatureTemperature (°C) (°C) (°C)

Temperature Temperature (°C) (°C)

with a constant solar irradiance of 1000 W/m . Initially, the signal shown in Figure 18a was used, with At thisshown point,inthe performance of the system wasinevaluated forbetween sudden100 changes temperature signal Figure 18b was used, with decreases temperature °C and in 0 °C. temperature increases every 0.2 s between 0 °C and 100 °C, for a test time of 1 s. Subsequently, the 2 2 with a constant constantsolar solarirradiance irradianceofof1000 1000 W/m . Initially, the signal shown in Figurewas 18a was used, . Initially, signal shown in Figure signal shown in Figure 18b was used, W/m with decreases inthe temperature between 100 °C 18a and 0 °C.used, with 100 ◦ C 100 ◦ C, for 100°C with temperature increases s between and 100for test time 1 s. Subsequently, 75°C 80 80 temperature increases everyevery 0.2 s 0.2 between 0100°C °C 0and 100 °C, a 75°C testa time of 1 of s. Subsequently, the 60 60 50°C ◦ C and 0 ◦ C. 100 100 40 40 50°C the signal shown in Figure 18b was used, with decreases in temperature between 100 signal shown in Figure in temperature between 100 °C and 0 °C. 25°C 18b was used, 100°C 100°C 75°Cwith decreases 80 80 20 60 0 400 20 100 0 80 0

60

25°C

75°C

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0.1 0.4 0.5 0.2 in 0.3 0 Decreases Increases (b) temperature. 0.9 0.7 0.8 in temperature; 1

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In Figure 19a, the power delivered to the battery is shown, where it is evident the oscillations (a) (b) and power losses that are obtained with the P&O control. Sudden changes in temperature In Figure 19a, the power delivered to the battery is shown, where it is evident the oscillations significantly affect the P&O whichtemperature; is confirmed(b) by Decreases the duty cycle signal shown in Figure 19b. Figure 18.are (a)control, Increases temperature. in temperature. and power losses that obtained inwith the P&O control. Sudden changes in temperature In contrast, the fuzzy control delivers stable power with duty cycle values that adapt to changes in significantly affect the P&O control, which is confirmed by the duty cycle signal shown in Figure 19b. theFigure operating temperature ofdelivered the PV module. With the P&O control, there it areisaverage power losses In 19a, the power to thepower battery is duty shown, where evident the oscillations In Figure contrast,19a, thethe fuzzy control deliversto stable cycle values adapt changes in and In power delivered the batterywith is shown, where it is that evident thetooscillations and power losses that are obtained with the P&O control. Sudden changes in temperature the operating temperature of the PV module. With the P&O control, there are average power losses power losses that are obtained with the P&O control. Sudden changes in temperature significantly Time (s)

significantly affect the P&O control, which is confirmed by the duty cycle signal shown in Figure 19b. affect the P&O control, which is confirmed by the duty cycle signal shown in Figure 19b. In contrast, In contrast, the fuzzy control delivers stable power with duty cycle values that adapt to changes in the fuzzy control delivers stable power with duty cycle values that adapt to changes in the operating the operating temperature of the PV module. With the P&O control, there are average power losses

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Energiesof 2017, 2036module. With the P&O control, there are average power losses of 3.15 14 ofW, 18 2.13 W, temperature the10,PV 2.84 W, 4.122017, W and 6.38 W for each of the simulation intervals. The losses were calculated taking Energies 2036 Energies 10, 2036 of14 18of 18 as of 3.15 2017, W,10,2.13 W, 2.84 W, 4.12 W and 6.38 W for each of the simulation intervals. The losses14were reference the power obtained withthe the fuzzy controller five operating temperatures between calculated taking as reference power obtained withfor the the fuzzy controller for the five operating ◦W, of 3.15 2.13 W,2.84 2.84W, W,4.12 4.12 W W and W for each of the simulation intervals. The losses were of temperatures 3.15 W, W, and 6.38 W for each of the simulation intervals. The losses were 0 ◦ C and 100 C,2.13 which correspond to the values presented in Table 3. between 0 °C and 100 °C, which correspond to the values presented in Table 3.

calculatedtaking takingasasreference reference the the power power obtained forfor thethe five operating calculated obtained with withthe thefuzzy fuzzycontroller controller five operating 1 temperatures between 0 °C and 100 °C, which correspond to the values presented in Table 3. temperatures between 0 °C and 100 °C, which correspond to the values presented in Table 3. 69.9W 70 59.5W

60

69.9W 64.9W

59.5W

54.5W

40 50

54.5W

48.6W

48.6W

40

40 20 30

30 10 20 20 0 0 10

0.2

0.1

0.4

0.3

0.5 Time (s)

0.7

0.7

Fuzzy P&O Fuzzy 0.8P&O 0.9

(a)

10 0

0

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Fuzzy P&O 0.8 0.9

0

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0.83 0.64

0.8 0.6

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0.69

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50 30 Power (W)

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59.5W

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64.9W

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1

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Duty Cycle Duty Cycle

Power (W)Power (W)

70

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0.8 0 0.7 0.1 0.6 0.3 0.4 0.2 temperature; 0.8 module 0.9 1 0.5(a)power 0.6 0.2 0.3 (a) 0.4 Figure 19. Output of0.7the PV para increases in (b) Duty cycle. (b)0.5 Time (s)

1

Fuzzy 1 P&O 0.9

Time (s) Figure 19. (a) Output power of the PV module para increases in temperature; (b) Duty cycle.

1

(b)

(a)

Figure 19. (a) Output power of the PVfor module para increases in temperature; (b) Duty Figure 20 shows the power obtained decreases in operating temperature. As incycle. the scenario

19. the (a) Output power of the PV module para increases in temperature; (b) DutyAs cycle. Figure 20Figure shows power obtained decreases in operating temperature. in the proposed in Figure 19, the P&O controlfor presents oscillations. The worst scenario occurs when thescenario Figure 20 shows the power obtained for decreases in operating temperature. As in the scenario temperature fromP&O 100 °Ccontrol to 75 °C,presents where theoscillations. system does not reach stabilization and there are proposed in Figuredrops 19, the The worst scenario occurs when the Figure 20 shows 19, thethe power for decreases in operating temperature. As in when the scenario proposed in Figure P&Oobtained control presents oscillations. The worst scenario occurs the ◦C ◦ C,With oscillations between 20 W and 52 W. the P&O control, does there are average power losses ofand 46.18 temperature drops from 100 to 75 where the system not reach stabilization there temperatureFigure drops 19, from 100P&O °C tocontrol 75 °C, where the oscillations. system does not stabilization and there are proposed the presents Thereach worst scenario occurs when the are W, 17.32in W, 0 W, 1.11 W and 1.2 W. oscillations between 20 from W20 and 52 the P&O there arereach average power losses of 46.18 oscillations between W and 52 W.°C, With the P&O control,does therenot are average power losses 46.18 temperature drops 100 °CW. to With 75 where thecontrol, system stabilization andofthere are W, 1 W, 17.32 W, 0 W, 1.11 W and 17.32 W, 0 W, 1.11 W and 1.2 oscillations between 20 WW. and1.2 52W. W. With the P&O control, there are average power losses of 46.18 69.9W 70

0.9

64.9W

60

Power (W)

50

40 30

0.7 0.9

64.9W 59.5W

69.9W

54.5W

64.9W 59.5W

54.5W

0.4

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20

0.83

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1

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0.69 0.64

0.94 0.83

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0.69

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0.69 0.64

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Fuzzy P&O 0.2

0.94

0.8 1

69.9W Duty Cycle Duty Cycle

70

70 48.6W 50 60 40 48.6W 50 30 40 48.6W 20 30 10 20 0 0.1 0 10

54.5W

Duty Cycle

Power (W)Power (W)

W, 17.32 W, 0 W, 1.11 W and 59.5W1.2 W. 60

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Fuzzy P&O 0.9

0.8 1 0.9 0.6 0.4 0.2 0.5 Figure 20.0.3(a) Output power of0.7the PV module for decreases in temperature;Time (b)(s)Duty cycle. Time (s) 0.1

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Fuzzy P&O

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0.2 0.5 power of the PV module for decreases in temperature; (b) Duty cycle. 0.1 Figure 0.3 (a)0.4 Output Time (s) 0 Figure Case 4: variations inTime solar irradiance temperature (s) 20. (a)20. Output power of the PVand module for decreases in temperature; (b) Duty cycle.

0.7

0.6

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1

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0.2

1

Finally, the of the was evaluated for sudden changes (b) in temperature Case 4: variations in solar irradiance and temperature Figure 20. performance (a) Output power of system the PV module for decreases in temperature; Duty cycle. and solar irradiance in different time values between 0 and 1 s, as seen in Figure 21. Case 4: variations solar irradiance and temperature Finally, the in performance of the system was evaluated for sudden changes in temperature and Case 4: variations in solar irradiance and temperature solar irradiance in 1000 different time values between 0 and 1 s, as seen in Figure 21.

Irradiance (W/m2) Te mpe rature (°C)

rature (°C) Irradiance Te mpe Irradiance Te mpe rature (°C) (W/m2) (W/m2)

Finally, the performance of of thethe system was evaluated for sudden changes in temperature and 800 Finally, the performance system was evaluated for sudden changes in temperature and 600 1000 solar irradiance in different time values between as seen seenininFigure Figure21.21. solar irradiance in different time values between00and and 11 s, s, as 400 800 200 600

1000 0 400

(a)

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1

20 Figure 21. Irradiance and temperature signals to(b)evaluate the performance of fuzzy and P&O 0°C controllers. (a) 0Increases in solar irradiance; (b) Variable0°C temperature. 0°C Figure 21. Irradiance and temperature signals to 0.5evaluate the 0.7 performance of fuzzy1 and P&O 0 0.1 0.2 0.3 0.4 0.6 0.8 0.9 Time (s) controllers. (a) Increases in solar irradiance; (b) Variable temperature. (b)

21. Irradiance and temperature signals to evaluate the performance of and fuzzy andcontrollers. P&O FigureFigure 21. Irradiance and temperature signals to evaluate the performance of fuzzy P&O controllers. (a) Increases in solar irradiance; (b) Variable temperature. (a) Increases in solar irradiance; (b) Variable temperature.

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For Forthe thedescribed describedtest testconditions, conditions,the thepower powerobtained obtainedfrom fromthe thePV PVmodule moduleusing usingfuzzy fuzzyand andP&O P&O controllers is shown in Figure 22. The results prove that the fuzzy controller tracks the MPP without controllers is shown in Figure 22. The results prove that the fuzzy controller tracks the MPP without oscillations losses. InIn contrast, thethe P&O controller exhibits power losses and and oscillations for oscillationsand andpower power losses. contrast, P&O controller exhibits power losses oscillations changes in solar and temperature. The worst scenario, for the P&O control, betweenis for changes in irradiance solar irradiance and temperature. Thecase worst case scenario, for the P&Oiscontrol, 2, 0.3 and 0.40.3 s when the temperature changes from 50 tofrom 75 ◦50 C with solar of 1000 W/m between and 0.4 s when the temperature changes to 75a°C withirradiance a solar irradiance of 1000 2, inthe inW/m which power oscillates between 11.5 and 37.5 The average power losseslosses with with the which the power oscillates between 11.5 andW. 37.5 W.highest The highest average power P&O control occurred between the times 0.2 s to 0.3 s and 0.3 s to 0.4 s with values of 8.52 W and the P&O control occurred between the times 0.2 s to 0.3 s and 0.3 s to 0.4 s with values of 8.52 W and 30.48 30.48W, W,respectively. respectively. 70

64.9W

P&O Fuzzy

69.9W 59.5W

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54.5W

Power (W)

50 40

39.3W

37.7W 38.1W

30 20 11.7W

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1

Figure Figure22. 22.Output Outputpower powerofofthe thePV PVmodule modulewith withthe thefuzzy fuzzyand andP&O P&Ocontrollers. controllers.

Conclusions 4.4.Conclusions this paper, a fuzzy controller to the track the maximum power of a PV module was InInthis paper, a fuzzy controller to track maximum power point of apoint PV module was presented, presented, for performance which their performance waswith compared a P&OAll controller. All components of the for which their was compared a P&O with controller. components of the PV system PV system modeled in Matlab/Simulink (PVconverter, module,fuzzy buckand converter, fuzzy andIn P&O were modeledwere in Matlab/Simulink (PV module, buck P&O controllers). this controllers). way, different test scenarios with signals of irradiance temperature and solar irradiance way, different In testthis scenarios with signals of temperature and solar variables were used in variables were used order to evaluate of demonstrated the PV system.that It was that order to evaluate the in performance of the the PV performance system. It was thedemonstrated fuzzy controller thean fuzzy controller has an excellent performance there changes in the of operating has excellent performance when there are suddenwhen changes in are the sudden operating temperature the PV temperature of the PV module, in contrast P&O controlaffected, that is considerably affected, presenting module, in contrast with P&O control thatwith is considerably presenting power losses up to power losses up to 46.18 W. On the other hand, it was also evidenced that in the presence of variations 46.18 W. On the other hand, it was also evidenced that in the presence of variations in solar irradiance in two solarcontrollers irradiancepresented the two controllers presented aand good performance and extracted maximum the a good performance extracted the maximum powerthe according to power according to the electrical of the module; P&O control the electrical characteristics of the PVcharacteristics module; although thePV P&O control although presented the the well-known presented the well-known oscillations, mainly in the sudden changes of irradiance. In this way, the oscillations, mainly in the sudden changes of irradiance. In this way, the main contribution of this main contribution of this manuscript is the supplying theto maximum power manuscript is the guarantee of supplying theguarantee maximumof possible power a battery possible in an off-grid PVto a battery in an off-grid PV system, using a fuzzy controller. As future work, in the second stage system, using a fuzzy controller. As future work, in the second stage of the project, the fuzzy controllerof the be project, the fuzzyin controller will be implemented in the low-cost Arduino platform; emphasizing will implemented the low-cost Arduino platform; emphasizing that fuzzy control offers the that fuzzyof control advantagein ofmicrocontrollers. being easily programmed in microcontrollers. advantage being offers easily the programmed Acknowledgments: supported by by the theVicerrectorí Vicerrectoría Investigaciónof of Universidad Acknowledgments: This This work was supported a dedeInvestigación thethe Universidad del del Magdalena. Magdalena. Author Contributions: Carlos Robles Algarín conceived and modeled the PV module and the fuzzy controller. Author Contributions: Carlos Robles Algarín conceived and modeled the PV module and the fuzzy controller. John Taborda Giraldo designed the P&O controller and dc-dc converter. Omar Rodríguez Álvarez contributed in John Taborda Giraldo designed the P&O controller and dc-dc converter. Omar Rodríguez Á lvarez contributed the design of the dc-dc converter and data analysis. All authors contributed in writing the manuscript. in the design of the dc-dc converter and data analysis. All authors contributed in writing the manuscript. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations Vx

Open circuit voltage for variable values of solar irradiance and operating temperature.

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Abbreviations Vx Ix MPP Pmax Vmpp Impp s p Ei EiN T TN Tcv Tci Voc Isc Vmax Vmin VL RL Rc Ton Toff Ts D Vs Vdc Vd Vo ∆IL ∆IL (+) ∆IL (−) Io ∆Q ∆V

Open circuit voltage for variable values of solar irradiance and operating temperature. Short-circuit current for variable values of solar irradiance and operating temperature. Maximum power point of the PV module. Maximum power of the PV module. Voltage at Pmax . Current at Pmax . Number of PV modules connected in series. Number of PV modules connected in parallel. Effective irradiation of the PV module. Irradiation constant of 1000 W/m2 . Temperature of the PV module. Temperature constant of 25 ◦ C. Temperature coefficient of voltage. Temperature coefficient of current. Open circuit voltage. Short-circuit current. Voltage for irradiations under 200 W and operating temperature of 25 ◦ C. Voltage for irradiations over 1200 W and operating temperature of 25 ◦ C. Voltage in the inductor. Internal resistance of the inductor. Internal resistance of the capacitor. The on time in the dc-dc converter. The off time in the dc-dc converter. Sampling time. Duty cycle. Input voltage in dc-dc converter. Transistor voltage in the on mode. Diode forward voltage. Output voltage of the dc-dc converter. Ripple current in the inductor. Ripple current in Ton . Ripple current in Toff . Critical output current. Charge variation in the capacitor. Voltage variation in the capacitor.

References 1. 2. 3.

4.

5. 6.

Karami, N.; Moubayed, N.; Outbib, R. General review and classification of different MPPT Techniques. Renew. Sustain. Energy Rev. 2017, 68, 1–18. [CrossRef] Mohapatra, A.; Nayak, B.; Das, P.; Mohanty, K.B. A review on MPPT techniques of PV system under partial shading condition. Renew. Sustain. Energy Rev. 2017, 80, 854–867. [CrossRef] Bianconi, E.; Calvente, J.; Giral, R.; Mamarelis, E.; Petrone, G.; Ramos, C.A.; Spagnuolo, G.; Vitelli, M. Perturb and Observe MPPT algorithm with a current controller based on the sliding mode. Int. J. Electr. Power 2013, 44, 346–356. [CrossRef] Chen, M.; Ma, S.; Wu, J.; Huang, L. Analysis of MPPT Failure and Development of an Augmented Nonlinear Controller for MPPT of Photovoltaic Systems under Partial Shading Conditions. Appl. Sci. 2017, 7, 95. [CrossRef] Kwan, T.H.; Wu, X. High performance P&O based lock-on mechanism MPPT algorithm with smooth tracking. Sol. Energy 2017, 155, 816–828. [CrossRef] Alik, R.; Jusoh, A. Modified Perturb and Observe (P&O) with checking algorithm under various solar irradiation. Sol. Energy 2017, 148, 128–139. [CrossRef]

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27. 28.

17 of 18

Bounechba, H.; Bouzid, A.; Snani, A.; Lashab, A. Real time simulation of MPPT algorithms for PV energy system. Int. J. Electr. Power 2016, 83, 67–78. [CrossRef] Huang, Y.P.; Hsu, S.Y. A performance evaluation model of a high concentration photovoltaic module with a fractional open circuit voltage-based maximum power point tracking algorithm. Comput. Electr. Eng. 2016, 51, 331–342. [CrossRef] Cortajarena, J.A.; Barambones, O.; Alkorta, P.; De Marcos, J. Sliding mode control of grid-tied single-phase inverter in a photovoltaic MPPT application. Sol. Energy 2017, 155, 793–804. [CrossRef] Tobón, A.; Peláez-Restrepo, J.; Villegas-Ceballos, J.P.; Serna-Garcés, S.I.; Herrera, J.; Ibeas, A. Maximum Power Point Tracking of Photovoltaic Panels by Using Improved Pattern Search Methods. Energies 2017, 10, 1316. [CrossRef] Loukriz, A.; Haddadi, M.; Messalti, S. Simulation and experimental design of a new advanced variable step size Incremental Conductance MPPT algorithm for PV systems. ISA Trans. 2016, 62, 30–38. [CrossRef] [PubMed] Mellit, A.; Rezzouk, H.; Messai, A.; Medjahed, B. FPGA-based real time implementation of MPPT-controller for photovoltaic systems. Renew. Energy 2011, 36, 1652–1661. [CrossRef] Ramalu, T.; Mohd Radzi, M.A.; Mohd Zainuri, M.A.A.; Abdul Wahab, N.I.; Abdul Rahman, R.Z. A Photovoltaic-Based SEPIC Converter with Dual-Fuzzy Maximum Power Point Tracking for Optimal Buck and Boost Operations. Energies 2016, 9, 604. [CrossRef] Hassan, S.Z.; Li, H.; Kamal, T.; Arifoglu, ˘ U.; Mumtaz, S.; Khan, L. Neuro-Fuzzy Wavelet Based Adaptive MPPT Algorithm for Photovoltaic Systems. Energies 2017, 10, 394. [CrossRef] Nabipour, M.; Razaz, M.; Seifossadat, S.; Mortazavi, S. A new MPPT scheme based on a novel fuzzy approach. Renew. Sustain. Energy Rev. 2017, 74, 1147–1169. [CrossRef] Bendib, B.; Krim, F.; Belmili, H.; Almi, M.F.; Boulouma, S. Advanced Fuzzy MPPT Controller for a Stand-alone PV System. Energy Procedia 2014, 50, 383–392. [CrossRef] Belaidi, R.; Haddouche, A.; Fathi, M.; Larafi, M.M.; Kaci, G.M. Performance of grid-connected PV system based on SAPF for power quality improvement. In Proceedings of the International Renewable and Sustainable Energy Conference (IRSEC), Marrakech, Morocco, 14–17 November 2016; pp. 1–4. Chekired, F.; Larbes, C.; Rekioua, D.; Haddad, F. Implementation of a MPPT fuzzy controller for photovoltaic systems on FPGA circuit. Energy Procedia 2011, 6, 541–549. [CrossRef] Na, W.; Chen, P.; Kim, J. An Improvement of a Fuzzy Logic-Controlled Maximum Power Point Tracking Algorithm for Photovoltic Applications. Appl. Sci. 2017, 7, 326. [CrossRef] Messaltia, S.; Harrag, A.; Loukriz, A. A new variable step size neural networks MPPT controller: Review, simulation and hardware implementation. Renew. Sustain. Energy Rev. 2017, 68, 221–233. [CrossRef] Dounis, A.I.; Kofinas, P.; Papadakis, G.; Alafodimos, C. A direct adaptive neural control for maximum power point tracking of photovoltaic system. Sol. Energy 2015, 115, 145–165. [CrossRef] Muthuramalingam, M.; Manoharan, P.S. Comparative analysis of distributed MPPT controllers for partially shaded stand alone photovoltaic systems. Energy Convers. Manag. 2014, 86, 286–299. [CrossRef] Jin, Y.; Hou, W.; Li, G.; Chen, X. A Glowworm Swarm Optimization-Based Maximum Power Point Tracking for Photovoltaic/Thermal Systems under Non-Uniform Solar Irradiation and Temperature Distribution. Energies 2017, 10, 541. [CrossRef] Titri, S.; Larbes, C.; Toumi, K.Y.; Benatchba, K. A new MPPT controller based on the Ant colony optimization algorithm for Photovoltaic systems under partial shading conditions. Appl. Soft Comput. 2017, 58, 465–479. [CrossRef] Jiang, L.L.; Maskell, D.L.; Patra, J.C. A novel ant colony optimization-based maximum power point tracking for photovoltaic systems under partially shaded conditions. Energy Build. 2013, 58, 227–236. [CrossRef] Benyoucef, A.S.; Chouder, A.; Kara, K.; Silvestre, S.; Sahed, O.A. Artificial bee colony based algorithm for maximum power point tracking (MPPT) for PV systems operating under partial shaded conditions. Appl. Soft Comput. 2015, 32, 38–48. [CrossRef] Fathy, A. Reliable and efficient approach for mitigating the shading effect on photovoltaic module based on Modified Artificial Bee Colony algorithm. Renew. Energy 2015, 81, 78–88. [CrossRef] Atawi, I.E.; Kassem, A.M. Optimal Control Based on Maximum Power Point Tracking (MPPT) of an Autonomous Hybrid Photovoltaic/Storage System in Micro Grid Applications. Energies 2017, 10, 643. [CrossRef]

Energies 2017, 10, 2036

29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.

18 of 18

Ou, T.-C.; Hong, C.-M. Dynamic operation and control of microgrid hybrid power systems. Energy 2014, 66, 314–323. [CrossRef] Hong, C.-M.; Ou, T.-C.; Lu, K.-H. Development of intelligent MPPT (maximum power point tracking) control for a grid-connected hybrid power generation system. Energy 2013, 50, 270–279. [CrossRef] Shiau, J.-K.; Wei, Y.-C.; Lee, M.-Y. Fuzzy Controller for a Voltage-Regulated Solar-Powered MPPT System for Hybrid Power System Applications. Energies 2015, 8, 3292–3312. [CrossRef] Ou, T.-C.; Su, W.-F.; Liu, X.-Z.; Huang, S.-J.; Tai, T.-Y. A Modified Bird-Mating Optimization with Hill Climbing for Connection Decisions of Transformers. Energies 2016, 9, 671. [CrossRef] Ou, T.-C. A novel unsymmetrical faults analysis for microgrid distribution systems. Electr. Power Energy Syst. 2012, 43, 1017–1024. [CrossRef] Ou, T.-C. Ground fault current analysis with a direct building algorithm for microgrid distribution. Electr. Power Energy Syst. 2013, 53, 867–875. [CrossRef] Ou, T.-C.; Lu, K.-H.; Huang, C.-J. Improvement of Transient Stability in a Hybrid Power Multi-System Using a Designed NIDC (Novel Intelligent Damping Controller). Energies 2017, 10, 488. [CrossRef] Robles Algarín, C.; Callejas Cabarcas, J.; Polo Llanos, A. Low-Cost Fuzzy Logic Control for Greenhouse Environments with Web Monitoring. Electronics 2017, 6, 71. [CrossRef] Ortiz, E. Modeling and Analysis of Solar Distributed Generation. Ph.D. Thesis, Michigan State University, Michigan, MI, USA, 2006. Gil, O. Modelado Y Simulación de Dispositivos Fotovoltaicos. Master’s Thesis, Universidad de Puerto Rico, San Juan, Puerto Rico, 2008. Robles, C.; Ospino, A.; Casas, J. Dual-Axis Solar Tracker for Using in Photovoltaic Systems. Int. J. Renew. Energy Res. IJRER 2017, 10, 137–145. © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).