Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 111 (2017) 954 – 963
8th International Conference on Sustainability in Energy and Buildings, SEB-16, 11-13 September 2016, Turin, ITALY
Optimization of Scaling Factors of Fuzzy–MPPT Controller for Stand-alone Photovoltaic System by Particle Swarm Optimization Arfaoui Joudaa*,Feki Elyesb,Abdelhamid Rabhic,Mami Abdelkaderb a
National School of Engineering of Tunis, BP 37,1002 Tunis, University of Tunis ELMANAR,Tunisia b Department of Physics, Faculty of Sciences, University Tunis El Manar, Tunisia c University of Picardie Jules Verne (UPJV), 33 rue Saint Leu, 80039 Amiens Cedex 1, France
Abstract In this paper, we present a novel fuzzy logic controller, for tracking the maximum power point of boost-based PV system. The fuzzy logic controller is used to improve its dynamic response with sudden irradiations and temperature conditions. This paper deals with the optimal adjustment of scaling factors for fuzzy controllers, these parameters affects the controller performance in term of speed, accuracy and stability .Hence, scaling factors are optimized by using Particle Swarm Optimization algorithm. Numerical simulations are carried out to highlight the tracking control performance of the fuzzy-MPPT using PSO algorithm for tuning the scaling factors. Then the optimized FLC is applied to DC-DC Boost converter. This paper provides reliable information on the performance of the optimized fuzzy-MPPT strategy which can be used by system designers to improve the overall efficiency and reduce the cost of PV system application. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of KES International. Keywords:Photovoltaic (PV); Fuzzy logic control (FLC); Maximum power point tracking(MPPT); DC-DC Boost converter; Particle Swarm Optimization (PSO); MATLAB/Simulink ; Scaling Factors;
1. Introduction The shortage of energy resources and environmental issues associated with it such as global warming and increasing air pollution has attracted much attention in renewable energy. Photovoltaic solar energy is one form of renewable energy which can help overcome these problems. A great attention has been drawn towards solar photovoltaic systems in research. Currently, to increase the output efficiency of a photovoltaic energy source, a maximum power point tracker (MPP) is often used to maximize the delivered power from the PV generator, which
* Corresponding author. Tel.: +21621003783. E-mail address:
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1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of KES International. doi:10.1016/j.egypro.2017.03.258
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depends on solar irradiance, cell temperature and load conditions. The maximum power point tracking is the most important aspect of control and design especially for PV production. The MPPT is substantially a nonlinear control problem. This is due to the nonlinearity nature of the I-V characteristic of the solar cell with the unpredictable variations of the environmental conditions. Therefore, DC-DC converters are considered the means by which in many applications the maximum power point tracker maintains the PV module operates at it is maximum power point voltage, (Vmpp), to extract the maximum power. Recently, a great number of MPPT techniques have been proposed in the literature such as the Perturb and Observe method and the incremental conductance methods which are widely used [1]. In order to overcome the aforementioned limitations regarding the fuzzy-MPPT, artificial intelligence based methods using (fuzzy logic, neural network) [2],[3],[4], sliding mode [5], genetic algorithms [6],[7] and particle swarm optimizer [8],[9] have been introduced, in order to improve the overall efficiency of tracking. MPPT fuzzy logic controllers (FLC) are relatively simple for design because they do not necessitate the knowledge of the exact model. They have also the advantage of being a robust and fast controller which is implemented in order to obtain the peak power point and having quite good performance (time response, stability, speed tracking and small oscillations) under changing atmospheric conditions, The most commonly used input variables for the MPPT algorithms would be the slope of the power-versus-voltage (P-V) curve of the PV cell characteristics curves and change of this slope, the output is a duty cycle or its variation [10],[11],[12]. In a previous study [13], P-V slope and variation of power ∆(Ppv) were selected as the input variables, while another study [14], [15] selected variations of power and voltage (∆(Ppv) and ∆(Vpv)) as the input variables instead. Other studies also used variations of power and current (∆(Ppv) and ∆(Ipv)) [16]. Previous investigations adopting the incremental conductance method used conductance and increment of conductance as the fuzzy input variables for MPP evaluation [17]. Another reported fuzzy MPPT algorithm used the sum of the arctangent of the conductance and arctangent of the conductance increment as the input variable [18]. In this paper, the design scheme for the fuzzy-MPPT logic controller through the scaling factors adaptation is proposed. Hence, optimizing the input scaling factors of the proposed fuzzy logic controller by using particle swarm optimization is developed in order to analyze the effects of these parameters on the controller's performance. In fact, the input scaling factors in a fuzzy control system are commonly used to conduct proper transformations between the real input data and the pre-specified universe of discourses of the fuzzy input variables in the system [19]. The optimized FLC is applied to a DC-DC Boost converter and the performance of the proposed method is evaluated under varying climatic conditions such as solar irradiance and temperature using Matlab/Simulink. The paper is organized as follows. In Section 2, we present the stand-alone photovoltaic system which consists of a photovoltaic panel connected to a boost converter for providing solar energy to a resistive load. In order to track the MPP of the PV system, an optimized MPPT method based on a fuzzy controller, using PSO is developed in section 3 while in section 4, we present the obtained simulation results using the Matlab/Simulink which are given to compare the performance of the optimized fuzzy controller in terms of speed and accuracy. The final section concludes the work. 2. Photovoltaic system It is necessary to describe the different components of PV system, before proceeding to develop our control. Modeling of PV model: A PV model is composed of solar cells connected in series or parallel which are arranged to form a module.The efficiency of PV modules depends on PV module temperature and load conditions. In fact, to simplify the analysis, a resistive load was considered in this study. In general, when a PV module is directly connected to a load, the operating point is seldom the MPP. Power converters were needed to adjust the energy flow from the PV array to the charge. The evolution of the generated power curves as a function of voltage are shown in Figures 1 and 2 , respectively, for a given constant irradiation and different values of temperature and then for a given constant temperature and different values of irradiation. It might be seen that the operating point can be adjusted by changing the values of the load resistance.
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Fig.1. P_V power curves with different T (G=100w/m²). Fig.2. P_V power curves with different G (T=27°C).
In order to model the photovoltaic module, a photovoltaic cell must be initially established, as depicted in Figure 3.
Fig.3. Equivalent circuit for PV cell
The electrical equivalent circuit of the PV cell consists of a current generator, in parallel with a diode and connected to a serial resistance, namely Rs and a shunt resistance, namely Rsh. The PV cell model is described by the following equations [20], [21]: ª º § V pv Rs I pv · § V pv Rs I pv · I ph I 0 «exp ¨ ¸ 1» ¨ ¸ V Rsh K (1) t © ¹ ¹ ¬ ¼ © m.K .T Vt (2) q m is the number of cells that are electrically connected in series so as to provide the desired power and voltage, K is the Boltzmann's constant, T the absolute temperature and q the electronic charge.The expression of the generated current which depends on solar radiation (G) and temperature (T), is given by the following equation [22], [21]; I pv
I ph
G ª¬ I sc K t T Tr º¼ G
r
I0
(3)
I ph § qVoc · exp ¨ ¸ 1 © KT ¹
(4)
Gr , Tr are respectively the reference solar radiation and temperature of the cell. Vt , K t are respectively the thermal voltage and the coefficient temperature of the short circuit current. Voc is the open circuit voltage, I sc is the short circuit current. I ph represents the light current (A), represents the ideality factor.
I 0 that represents the diode reverse saturation current and K that
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3. Maximum power point tracker MPPT is a switch mode power converter used as interface between the PV generator and the load. In fact, MPPT designers contain two parts: hardware (DC-DC converter) and software (MPPT algorithm). A typical scheme of MPPT system is depicted in Figure 4, where the photovoltaic voltage and current are serve as inputs to the MPPT block.
Fig.4. Structure of MPPT Algorithm.
3.1. DC-DC Boost Converter: DC-DC converter is used in PV systems to regulate the PV voltage by varying the duty cycle by means of MPPT technique in order to maintain the operating point of the PV panel at the MPP. The great importance that the dc converters have gained in many applications, it started from low to high-powers applications. In this paper, a boost converter is chosen to perform two major tasks; it regulates the fluctuating input voltage coming from the PV panel and assumes the tracking of the maximum power point by the adjusting of the duty cycle. The solar power generation system under study consists of a photovoltaic panel feeding into a resistive load through a boost converter. The system's average model is given in (5).
R Rm I L VD VB u Rb V 1 I L V pv D b L L L L I 1 I L pv C1 C1 I 1 1 IL VB L u C2 RLC 2 C2
dI L ° ° dt ° dV pv ® ° dt ° dVB ° dt ¯
Where V pv and I pv are the PV panel voltage and current. L , current. Rm is a resistance characterizing IGBT loses C1 ,
(5)
Rb and I L are the self inductance, resistance and
C 2 , VD and VB are respectively the input capacitance,
the output capacitance , the diode forward voltage and the load voltage, u is the control input. Considering the PV current as an exogenous input, we get the following state representation (6).
§ dI L ¨ dt ¨ ¨ dV pv ¨ dt ¨ ¨ dVB ¨ dt ©
· ¸ ¸ ¸ ¸ ¸ ¸ ¸ ¹
§ Rb 1 1 · § Rb Rm I L VD VB ¨ ¸ ¨ L L L ¸ § IL · ¨ L ¨ 1 ¸¨ ¸ ¨ 00 0 V ¨ ¨ C1 ¸ ¨ pv ¸ ¨ ¸ ©¨ VB ¹¸ ¨ I L ¨¨ 1 ¸ ¨ 1 ¨ C2 0 R C2 ¸ © C2 L © ¹
§ VD · ¨ L ¸ ¨ ¸ ¨ I pv ¸u ¨ C1 ¸ ¨ ¸¸ 0 ¨ ¨ ¹ ©
· ¸ ¸ ¸ ¸ ¸ ¸ ¸ ¹
(6)
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Control of the boost converter switch is achieved by an MPPT controller that will assure the variation of the duty cycle of the converter in order to extract the maximum possible power from the PV array. The output voltage of the boost which is also the voltage across the load, obtained by the MPPT algorithm is described by (7).
Vout
1 Vin 1 D
(7)
Where D is the duty cycle of the converter. 3.2. MPPT control strategy In order to operate a solar array within its MPP, an MPPT method is needed to find and maintain the peak power. These methods find the voltage or current on which the solar array provides the maximum output power [8]. In this section, a PSO-based MPPT is presented. Numerical simulations are carried out to highlight the tracking control performance and the advantages of the optimized fuzzy-MPPT compared to a P&O as one of the most widely conventional methods. These algorithms are described in the following sections. 3.2.1. Perturb and Observe algorithm:
Fig.5. Flowchart of P&O algorithm
In order to assess the performance of the proposed fuzzy-MPPT controller in comparison with a classic method of maximum power point tracking, the Perturb and Observe is presented, is popular because of its ease of implementation. The principle of this controller is to track the maximum power point (MPP) by repeatedly increasing or decreasing the module voltage and observing its effects on the output PV power that is compared with that at the previous perturbing cycle. The flowchart of the P&O algorithm is shown in Figure 5. A comparison between the power values of the present and the previous states occurs. If the differential is positive the duty cycle is changing in order to maintain the same direction of perturbation. If the power's difference is negative, the duty cycle is changing in order to reverse the direction of perturbation [23]. 3.2.2. Fuzzy-MPPT controller optimization using PSO Particle swarm optimization technique: Particle swarm optimization is a stochastic search method developed by
[24]. This recent metaheurstic technique was inspired by the social behavior of birds flocking and fish schooling
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[25], [26]. In fact, PSO is considered one of the strong optimization techniques based on evolutionary computation; it allows solving various complex optimization problems. The PSO method maintains a swarm of individuals; where a number of particles are used that constitute a group and move in search space to find the best solution. Each particle in PSO flies through the search space to find the best solution. Each particle in PSO flies through the search space with an adoptable velocity that is dynamically modified according to its own flying experience and also to the flying experience of the other particles. Inputs of fuzzy controller: Fuzzy logic models are appropriates for nonlinear control especially the TS fuzzy models (Takagi-Sugeno), due to their capability to approximate any nonlinear behavior and it does not use complex mathematical equations. The performances of a TS fuzzy model depend on its complexity (Number of fuzzy rules), on the type of membership functions and also on the antecedent variables and the consequent regressors. The structure of the fuzzy-MPPT logic controller is presented in Figure 6.
Fig.6. Structure of fuzzy logic controller Table.1. Rule base used in the fuzzy logic controller
Input 1
Input 2
Input 3
Input 4
Output
N
N
Z
N
mf4
N
N
G
N
mf1
N
Z
Z
Z
mf3
N
Z
G
Z
mf1
N
P
Z
P
mf5
N
P
G
P
mf4
Z
N
Z
N
mf4
Z
N
G
N
mf2
Z
Z
Z
Z
mf5
Z
P
L
P
mf8
Z
P
Z
P
mf6
Z
P
G
P
mf4
P
N
L
N
mf7
P
N
Z
N
mf5
P
Z
L
Z
mf7
P
Z
Z
Z
mf6
P
P
L
P
mf9
P
P
Z
P
mf7
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This algorithm of MPPT uses two input variables; the slope S (k) of the power (P-V curve) and variation of slope S (k) and the duty cycle as the output which controls the boost converter. These variables were defined using the following equations:
Ppv (k ) Ppv (k 1)
(8)
'Vpv Vpv (k ) Vpv (k 1) 'S (k ) S (k ) S (k 1)
(9)
S (k )
'Ppv
Where Ppv and V pv are respectively the photovoltaic power and voltage of the panel. The input membership functions (MFs) for S (k) and ∆S (k) are defined using trapezoidal MFs. In fact, we define three fuzzy sets: Positive (P), zero (Z) and negative (N) to describe each linguistic variable. In this paper, an optimized fuzzy-MPPT logic method for photovoltaic systems is proposed, to track the maximum power of the PV module under rapidly changing weather conditions. The database for fuzzy rules designed according to the fuzzy input variables, are shown in Table 1. According to fuzzy logic, the selection of the universe of discourse of the inputs and outputs will also directly affect the results. 3.2.3. Optimization of FLC using S-function based PSO algorithm:
The diagram of the proposed algorithm is shown in Figure 7.
Fig.8. Flowchart of PSO algorithm.
Fig.7. Block diagram of the proposed algorithm.
In our case, PSO approach is used instead of traditional methodology trial and error to find the optimal adjustment of scaling factors for fuzzy-MPPT controllers, based on closed loop system performance specifications. In the proposed strategy, PSO is used to perform satisfactory in steady state and improve transient performance whenever the system exhibits an oscillatory or overshoot behavior. Obviously, we show that the adjustment of the input scaling factors can be interpreted as the change of the universe of discourse for input variables. In fact, the bandwidth of the overall performance of the controller are greatly affected by the choice of the scaling factors KS(k) and K∆S(k).The factor KS(k) determines the sensitivity of the controller to changes in power while K∆S(k) determines the sensitivity to change in duty cycle. Suitable values of KS(k) and were chosen based on simulation results using PSO algorithm. In fact, fuzzy logic toolbox is used to formulate the fuzzy logic algorithm and the rules were fine tuned by simulations. This involved the choice of the number of rules, setting memberships function boundaries and determining suitable values for the scale factors KS(k) and K∆S(k). The optimization algorithm using PSO approach is explained as follow: the tracking process is started with an initial
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duty cycle. The boost converter input current Ipv and voltage Vpv are measured and used to compute the module power Ppv(k) . Then, the duty cycle is increased by the controller based on the initial changes in power and duty cycle. At stage two, Ipv and Vpv are measured and used to compute Ppv(k+1). After gathering the past and the present information of the module power, the controller makes a decision on whether to increase or decrease the duty cycle. This tracking process repeats itself continuously until the peak power point is reached [27].Figure 8 shows the flowchart of PSO. The objective of optimization the scaling factors (KS(k) and K∆S(k)) is to acquire fast dynamic response and smaller steady state error. The integral absolute error (IAE) as expressed in (10) is used as the cost function. Where e (t) indicates the output power error (e (t) =Pmax-Ppv). A low value of the performance index corresponds to a small settling time, a small steady error and small overshoot.
IAE
³
f
0
(10)
e(t )dt
Where Ppv is the power obtained from PV array, Pmax is the maximum power. 4. Simulation results The proposed system is composed of photovoltaic panel of 62W, a DC/DC boost converter and resistive load.
Fig.9. PV panel platform. Table.2. Boost converter parameters.
Table.3.PV module parameters.
Self inductance
L
4470 μH
Leakage resistance
Rb
0.54 :
Resistance characterizing IGBT loses
Rm
22 m:
current at Pmax (Vmp)
4.1 A 21 V 5.1 A
Maximum power (Pmax) voltage at Pmax (Vmp)
Input capacitance
C1
1 mF
Open-circuit voltage (Voc)
output capacitance
C2
47 μF
Short-circuit current (Isc)
diode forward voltage
VD
1.9 V
resistive load
RL
20 :
62 W 15V
Performances of MPP tracker under real conditions: In this scenario, we compare by simulations, the convergence of the output power of the PV system under test, to the MPPT using P&O and proposed fuzzy logic algorithms. In fact, both control algorithms P&O and optimized fuzzy-MPPT controllers are simulated and tested on the Matlab/Simulink environment, under illumination and temperature, modulated according to one day. On Figures 10 and 11, we present the evolution of measured weathers conditions.
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Fig.10. Temperature for a day.
Fig.11. The solar radiation for a day.
Fig.12. Maximum power point obtained by P&O and optimized fuzzy method
Tuning of input scaling factors using PSO: As discussed in the prior section, scaling factors can be optimized by using
PSO algorithm. Similar to other heuristic optimization algorithms, PSO estimates the optimal variable through iterations by minimizing of a cost function. In fact, PSO accepts error as a continuous value and calculates scaling factors iteratively during operation. Reaching optimal solution can be determined by utilizing an error based performance index as indicated in the previous paragraph. After using PSO for optimization scaling factors of the FLC controller, we can notice that the convergence time or response time of the proposed controller is faster than the classical one. Therefore, Fuzzy-MPPT method tracked the MPP of the PV module successfully as shown in Figure 12. x Response Time: In fact, the proposed algorithm shows a significant improvement in the time interval when we have a sudden changing atmospheric conditions. In addition, the proposed algorithm shows a better transient response. Figure 12 demonstrates the high efficiency, on terms of stability and response time, of the proposed controller compared to the P&O algorithm. In fact, the photovoltaic power obtained by the proposed method is around 55 W for the maximum level of solar radiation, mentioned in Figure 12, meaning an increase of up 6 W compared to the previous power generated by the P&O method.Obviously, we can say that our control law gets there pretty well, which explains the 13% gain of power. 5. Conclusion This paper presents a photovoltaic model using Matlab/Simulink and illustrates the design of the appropriate boost converter with a maximum power tracker. The optimized fuzzy-MPPT method has been implemented under disturbance in the photovoltaic irradiation levels after using PSO for optimization scaling factors of this FLC. In fact, we adopt PSO method in this paper because it is an efficient global optimizer for continuous variable problems and it is easily implemented with very little parameters to fine-tune. Simulations results showed that for the same weather conditions, the produced PV power by the P&O-MPPT algorithm is less than the power produced when the fuzzy algorithm is used. These results proved that the proposed controller tracks successfully and accurately the maximum power under real atmospheric conditions.
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