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Real-time study of a photovoltaic system with boost converter using the PSO-RBF neural network algorithms in a MyRio controller
Solar Energy 183 (2019) 1–16
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Real-time study of a photovoltaic system with boost converter using the PSO-RBF neural network algorithms in a MyRio controller
T
Hichem Hamdi , Chiheb Ben Regaya, Abderrahmen Zaafouri ⁎
University of Tunis, Higher National Engineering School of Tunis (ENSIT), Engineering Laboratory of Industrial Systems and Renewable Energies (LISIER), 5 Avenue Taha Hussein, PO Box 56, 1008 Tunis, Tunisia
ARTICLE INFO
ABSTRACT
Keywords: MPPT MyRio RBF neural network PSO
Given the nonlinear feature of a photovoltaic generator, a maximum power point tracking algorithm (MPPT) is required in a photovoltaic system leading to maximum power point (MPP) operation and maximizing the power generated. The tracking MPP techniques are based on an actual or estimated research mechanism using experimental data. Conventional MPPT techniques like perturbe and observe (P&O), incremental conductance, etc., are good enough to track the maximum power for the PV systems, but they are less stable, more oscillating around the MPP. Generally, techniques based on the estimated research mechanisms, such as the Artificial Neural Network (ANN), the Adaptive Neuro-Fuzzy Inference System (ANFIS), and the Radial Basis Function Neural Network (RBFNN), etc., are supervised automatic learning techniques, which aims to create a model for an unknown function in order to find a relationship between input data and output data. In the case of RBF Neural Network, the center of the radial base function, the variance of the radial function base and the weight must be chosen. If these variables are not chosen appropriately, the RBF neural network can degrade the validity and accuracy of the modeling. On the other hand the RBF network suffers from a growth in the size of the hidden layer comparable to that of a set of learning data which also implies more computational time. The solution of these two problems is the motivation of this research. The PSO algorithm is used to optimize the parameters of the RBFNN by introducing a new adaptive strategy of particle swarm optimizer to dynamically adjust the inertia weight factor ω and the new velocity vid (t + 1) with a new µ coefficient. The obtained results based on RBFNN hybrid approach with PSO (PSO-RBFNN approach) were compared with the results obtained with the adaptive Neuro-Fuzzy Inference System (ANFIS). The experimental test bench of the PSO-RBFNN approach has been implemented using a MyRio card, which prove the good performances of the new proposed technique in terms of the average relative errors of the learning, test and control data, for the model PSO-RBFNN which converge approximately to 0.26%, 0.294% and 0.8% respectively, and energy efficiency MPPT in the case of atmospheric parameters varying over time can reach 99.04%.
1. Introduction A photovoltaic generator can work in a wide range of output current and voltage but the photovoltaic panel can provide maximum power only for a particular voltage and current. Indeed, the output power of photovoltaic (PV) array depends on solar irradiation levels and ambient temperature. These climatic variations cause a fluctuation in the power output and the maximum power point, which makes it necessity to insert a controlled static converter for the pursuit of the maximum power point. These commands are known under the name of MPPT (Maximum Power Point Tracking). An MPPT, or maximum power point tracker is an electronic DC-DC converter that optimizes the effectiveness between the solar array (PV panels), and the receiver (Babu et al., ⁎
2015; Rezk and Eltamaly, 2015). In the literature, several MPPT techniques are used in photovoltaic systems to improve efficiency, so that the maximum power can be delivered to the load. To solve this problem, many researchers have proposed different techniques of search for optimum power points, we can mention the widely used Perturb and Observe algorithm (P&O), which is a conventional algorithm that follows the MPP with a constant step of service cycle. The time response to reach the MPP depends on the value of the duty cycle. If the cycle is too small, the time response will be large and vice versa. For this method, MPP operation is less efficient than other systems (Rezk and Eltamaly, 2015; Ezinwanne et al., 2017; Sera et al., 2013). Recently, the number of fuzzy logic applications have increased significantly especially for uncertain
Corresponding author. E-mail address: [email protected] (H. Hamdi).
https://doi.org/10.1016/j.solener.2019.02.064 Received 14 August 2018; Received in revised form 16 February 2019; Accepted 25 February 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.
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Nomenclature
r1 and r2 random numbers MPPT maximum power point tracker RBFNN Radial Basis Function Neural Networks ANFIS Adaptive neuro fuzzy inference system ANN artificial neural network UDP User Datagram Protocol TCP/IP Transmission Control Protocol/Internet Protocol ISE Integral Square Error MSE mean squared error PV Photovoltaic DSP Digital Signal Processor MPP Maximum power point LABVIEW Laboratory Virtual Instrument Engineering Workbench
PSC partial shading condition GMPP global maximum power point LMPP local maximum power point PSO particle swarm optimization fuzzy logic controller FLC pbest , i particle’s personal best solution gbest global best of Pbest , i x id (t ) position vector of PSO vid (t ) velocity vector of PSO ω inertia weight c1 and c2 the learning factors nonlinear systems (Chakchouk et al., 2017; Ben Regaya et al., 2012). With control systems such as Fuzzy Logic Control (FLC ) proposed by Othman et al. (2012) and Liu et al. (2014), the performance of the system can be better than the conventional algorithm because the time response for MPP tracking is faster than the P&O MPPT method and also more efficient for MPP tracking. Both methods used the I PV and V PV control sensors as inputs for system optimization. In Duman and Yorukeren (2018), Varnham et al. (2007) and Bouraiou et al. (2015), the solar irradiance and the temperature of the cell are transmitted to ANFIS and the output differs from the reference to another. Some authors use Vmax as the output of ANFIS and others use Pmax . The advantage of this method is the fast and accurate tracking of the MPP without interrupting PV power, using trial and error search, or approximating the MPP (Gaboriault and Notman, 2004; Chaouachi et al., 2010). The ANFIS technique (Esen et al., 2008a,b) and a novel maximum power point tracking combining both the Radial Basis Function Neural Network with the Particle Swarm Optimization (PSO RBFNN ) and fuzzy logic are used in this study for controlling duty cycle of the electronic switch of DC DC boost converter. The PV system has been used under varying temperature and insolation conditions, to provide maximum power to the resistive load. The different steps of the controller design are presented together with simulation and their experimental results are presented to demonstrate the main characteristics of
the proposed MPPT, and it’s compared with the Conventionnel P&O, ANFIS, FL control and P&O Algorithm. The main contributions of the proposed control scheme can be summarized as follows: 1. The proposition of a new MPPT technique based radial basis function (RBF) neural network model optimized using particle swarm optimization (PSO), by introducing a new adaptive strategy of particle swarm optimizer to dynamically adjust the inertia weight factor ω and the new velocity vid (t + 1) with a new µ coefficient. A modified PSO algorithm is used to determine the centers, widths, and connection weights of RBF neural network to ensure a good follow-up of the MPPT; 2. Guarantee the effectiveness of maximum power point tracking (MPPT) and amelioration of MPPT efficiency; 3. A simulation benchmarking study was carried on; 4. A real time experimental comparative study using My RIO 1900 board of the proposed method of MPPT is performed. 2. Structure of PV system with MPPT As the PV conversion chain illustrates in Fig. 1, MPP is reached through controlling the DC-DC converter with a system using a MPPT controller. The strategy of the MPPT controller allows to optimize the transfer of power from the PV panel to the load. FLC
LABVIEW LABVIE UDP Receive
UDP Send
MATLA MATLAB PSO-RBFNN
MPPT
Voltage divider
USB connection US
Whether Link Davis Vantage Fig. 1. Elementary chain of photovoltaic conversion. 2
Load
WIFI Communication
DC-DC Boost converter
Current sensor ACS712
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2.1. Photovoltaic model In order to model the PV panel, we start with a simple model which represents a PV elementary cell. The configuration that Fig. 2 presents is the most common equivalent schema of a solar cell. It is composed of a variable source current Iph , connected in parallel with a diode D , characterizing the junction of semi-conductors which make the solar cell, and a parallel resistance Rp . To this assembly, another resistance Rs is added in series. From Fig. 2, the generated current (IPV ) by the PV cell is given by: Fig. 2. Solar cell circuit diagram.
IPV = Iph
(1)
IRp
The value of Iph is heavily dependent on the irradiance (G ) and solar cell temperature (Tc ). The Iph equation can be expressed by the following equation (El Hammoumi and Motahhir, 2018; Ginart et al., 2013):
Table 1 The main parameters of PLM-300M-72 PV module. The voltage at MPP (VMPP ) The current at MPP (IMPP ) Open-circuit voltage (Voc ) Short-circuit current (Isc ) Maximum power generated from the module Peak Efficiency Temp. Coefficient of Isc : µsc Temp. Coefficient of VOc Temp. Coefficient of Pmax Number of Cells
Id
36.59 V 08.20 A 45.60 V 08.78 A 300 W 15.37% 0.06%/°C −0.34%/°C −0.45%/°C 72
Iph =
G (Isc, ref + µsc · T ) Gref
(2)
The current flowing through the diode Id , is given by Eq. (3):
VPV + IPV · Rs A· VT
Id = I0 exp
1
(3)
where
Hardware part of the system consists of National Instruments (NI) myRIO module and Whether Link Davis Vantage. Application circuits for the current and voltage sensor is shown on Fig. 1. Power supply, data exchange and output logic levels measurement are implemented on the base of NI myRIO input/output lines. Whether Link Davis Vantage is used for temperature and solar irradiation measurement of the PV panel and is controlled via USB interface from myRIO card. Custom software was developed in LabVIEW development system. The MPPT is divided into two steps, first will lift the response of the MPPT to deliver the voltage and the maximum current corresponds to the MPP by using the proposed method PSO-RBFNN in matlab/ Simulink, and the second will lift to reduce the strong oscillations around the steady state by using the fuzzy logic controller (FLC) in LABVIEW part. The communication of both parties is done by the UDP protocol.
VT =
kB T q
(4)
Saturation current (I0 ) of solar cells can be expressed in a mathematical equation that has a relationship with the temperature of the solar cell as follows (Esen et al., 2016):
I0 =
Isc, ref
exp
( ) Voc, ref a
Tc 3 ) exp T c 1 , ref (
q· Eg
(
1 Tc, ref
1 Tc
)
A· kB
(5)
The thermal voltage a is presented by the following equation:
a=
Ns ·A· kB· Tc q
(6)
The current IRp in a closed loop can be determined by using Kirchhoff's voltage law analysis, which is expressed in Eq. (7):
Fig. 3. Changing of MPP with: (a) solar irradiation and (b) temperature. 3
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Fig. 4. Boost converter. PV Arrays
PV Current Sense
Boost Converter
=
LOAD
=
PV Voltage Sense Solar Irradiation diation Sense Temperature Sense
DC Load
+ -
RBFNN
+ PSO
Fig. 5. PV system with hybrid PSO-RBFNN based MPPT.
Photovoltaic panel +
RBFNN
-
Σ
Training algorithm Fig. 7. Block diagram of a RBF network.
The equivalent circuit of a PV array is expressed as follows: Fig. 6. Architecture of used RBF neural network.
IRp
V + IPV · Rs = PV Rp
IPV = Np I ph
I0 exp
VPV + IPV · Rs A· VT
1
VPV + IPV · Rs Rp
VPV /Ns + IPV · Rs / Np A·VT
1
VPV Np/ Ns + IPV · Rs
(7)
Rp
Therefore, the output current (IPV ) were previously expressed by Eq. (1), can be restated by Eq. (8):
IPV = Iph
Np I0 exp
(9)
where IPV is the output current of solar cells (Ampere), Iph is photocurrent (Ampere), I0 is saturation current of solar cells (Ampere), VPV is output voltage of solar cells (Volt), µsc is the temperature coefficient of the short circuit current ( A/ K ), provided by the manufacturer, Eg is the Silicon bandgap energy (Eg = 1.12 eV), Tc is the temperature of the solar cell (Kelvin), Tc, ref is the reference temperature of Solar Cells
(8)
A PV array is a group of several PV modules which are electrically connected in series (Ns ) and parallel (Np ) for generating more power. 4
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Step 1: Initialization Initialize each particle of the swarm, with random values for position ( ) and velocity ( ) in the search space according to the dimensionality of problem. Step 2: Evaluation Evaluate fitness value of particle by using fitness function. Step 3: Comparison Compare the value obtained from the fitness function from particle with the value of If the value of the fitness function is better than the value, then update the particle position to takes . the place of form any particle is better than , then update = . If the value of Step 4: Compute inertia weight using Eq. (18) and using Eq. (21). Step 5: Adaptation Modify the position and velocity of the particles using Eq. (16) and Eq. (17), respectively. Step 6: Stop test If the maximum number of iterations or the ending criteria is not achieved so far, then return to step 2. Fig. 8. The pseudocode of the proposed PSO clustering for RBF unit center.
Step 1. Start with one RBF. Initialize RBF parameters. Start optimizing centers of RBFs using PSO (Algorithme1) Initialize particles position and velocity randomly Step 2. Compute mean of squared distances between the center of cluster and -nearest neighbors using Eq. (22) Step 3. Compute coefficient factor:
, where
is the number of hidden units and
is the
maximum distance between those centers. Step 4. Find the maximum distance from each center and normalize the distance vector Step 5. Multiply the distance vector obtained from step 4 by the coefficient factor Step 6. Compute the average of reference dense distances of all the center nodes using (Eq. (23)) as the widths of the improved PSO-RBFNN are given by (Eq. (24)). Fig. 9. The Algorithm of the proposed width adjustment.
Temperature Zone
Irradiance Zone
Fig. 10. PSO
RBF as compared to the actual trajectory and RBF trajectory.
(Kelvin), G and Gref are the irradiance and the irradiance reference (kW/m2) , kB is Boltzmann’s constant (1.381 × 10 23 J/K) , q is electron charge (1.60222 × 10 19 C) , A is ideality factor of PV technology (1 A < 2) , Isc , V0c , Vmpp and Impp represent the short circuit current, the open circuit voltage, the maximum power point current and voltage which are shown in Table 1. The typical current-voltage (I-V) curve
characteristics under 10, 25, 40, 55 and 70 °C, and for 200, 400, 600, 800 and 1000 W/m2 changes for no-load condition of PV panel is examined in Fig. 3.
5
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Fig. 11. Voltage error with PSO
RBFNN compared with RBF .
10
PSO-RBF Fitness value
1
RBF
0.1
0.01
0.001
0
50
100
150
200
Iteration Fig. 12. Comparison of convergence profiles for PSO
RBF and traditional RBF.
Table 2 Summary table of simulation models.
knowledge base
Model
Training time/ s
Number of iterations
Test time/ s
Precision
MSE
RBF PSO-RBF
0.958 0.746
180 130
0.318 0.239
0.001 0.001
0.0053 0.0026
Input
fuzzification
inference
defuzzification
Output
Fig. 14. Fuzzy Inference System.
Filters made of capacitors are normally added to the output of the converter to reduce output voltage ripple. The boost converter is used to regulate a chosen level of the solar photovoltaic module output voltage and to keep the system at the maximum possible power from solar panels at all times. The SIMULINK model of the boost converter used in the simulation is shown in Fig. 4.
2.2. DC-DC boost converter A boost converter (step-up converter) is a DC to DC power converter with an output voltage is greater than its input voltage. It is a class of switched-mode power supply (SMPS) containing at least two semiconductor switches (a diode and a transistor) and at least one energy storage element, a capacitor, inductor, or the two in combination.
Fig. 13. Architecture of RBFNN . 6
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Fig. 15. Membership functions of (a) error E , (b) Change of error CE and (c) duty cycle D .
where D is the duty cycle of converter. For the switching frequency f , the ripple of the output voltage can be obtained as:
Table 3 Fuzzy rules base. E/CE
NL
NM
NS
ZE
PS
PM
PL
NL NM NS ZE PS PM PL
ZE ZE NS NM PS PM PL
ZE ZE ZE NS PM PM PL
ZE ZE ZE ZE PM PM PL
NL NS ZE ZE PS ZE ZE
NL NM NS ZE ZE ZE ZE
NL NM NS PS ZE ZE ZE
NM NM NS PM ZE ZE ZE
V0 D = V0 RfC To ensure a continuous conduction, the minimum inductance
L>
2.2.1. Design calculation The Boost converter parameter values are calculated by the following formulae (Wu et al., 2015; Zainuri et al., 2012):
V0 =
1 1
D
Vin
(11)
(1
D) 2Rload 2f
(12)
3. MPPT controller The proposed PSO RBFNN based MPPT block diagram is shown in Fig. 5. The objective of the controller is to determine the converter duty cycle D , by which the converter delivers the maximum attainable power to the load at any given temperature and irradiance (Li, 2015;
(10) 7
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number of hidden units; i (x ) is the radial basis function. There are different types of radial basis function, and the normalized Gaussian function is usually used as the radial basis function, which is defined as follows (Esen et al., 2008): i (x )
= exp [ ||xi
ci ||2 /(2 i2]
(14)
where x i = [x1, x2, , xN ]T is the input vector of the neural network; ci is the center of the ith basis function in the hidden layer; i is the width of the ith node. In RBFNN to reach the best accuracy results, a measured fitness function is used which takes the error between the output (target) of the RBF and the real output. There are many fitness functions which can be used to calculate the error, such as, Mean Square Error (MSE), Root Mean Square Error (RMSE), Sum Square Error (SSE), and Normalized/ Root Mean Squared Error (N/RMSE). In this paper, the MSE fitness function is used which is given by the following equation: Fig. 16. The fuzzy rule surfaces.
MSE =
1 n
n i=1
(Yi
Ti ) 2
(15)
where n is the number of input data, T is the target output and Y is the real output. A general block diagram of an RBF network is illustrated in Fig. 7. 3.1.2. Particle Swarm Optimization (PSO) Particle swarm optimization (PSO), introduced by Collotta and Pau (2017) mimics the behavior of a swarm of insects or a school of fish. If one of the particles discovers a good path to food, the rest of the swarm will be able to follow instantly even if they are far away in the swarm. Swarm behavior is modeled by particles in multidimensional space that have two characteristics: a position and a velocity. These particles wander around the hyperspace and remember the best position that they have discovered. They communicate good positions to each other and adjust their own position and velocity based on these good positions. If we would like to describe the process used in this algorithm more technically, we would follow these steps (Algorithm1) (Collotta and Pau, 2017; Mohandes, 2012; Montazer and Giveki, 2015; Park and Kim, 2016): The position x id and velocity vid of the particles are given resectevily by:
Fig. 17. Diagram showing the sensors interface from the MyRio card.
Zhao et al., 2015). The first part of the controller, Radial Basis Function Neural Network with the particle swarm optimization (PSO RBFNN ), works as a reference model of the PV array and finds the suitable maximum voltage under a given temperature and irradiance. While the FLC fit into a regulation loop, by comparing the maximum voltage and current of reference model and those of the output of the PV array. Subsequently, control loop errors are used to produce the change of D , which is the objective of the third block controller.
vid (t + 1) = wi (t ) vid (t ) + c1 r1 (pbestid (t ) + c2 r2 (gbestd (t )
x id (t )) (16)
x id (t ))
3.1. Particle swarm optimization and radial basis function neural network
x id (t + 1) = xid (t ) + µi (t )·vid (t + 1)
3.1.1. Radial Basis Function Neural Network (RBFNN) Feed-forward layered neural networks have increasingly been used in many areas, such as, modeling and control of nonlinear systems. One example of a feed forward neural network is the Radial Basis Function (RBF ) network. The typical structure of an RBF neural network is shown in Fig. 6. Input units distribute the values to the hidden layer units uniformly, without multiplying them with weights. Hidden units are known as RBF units because their transfer function is a monotonous radial basis function in which the number of hidden units is determined by the described problems. Hidden layer outputs are led to the output units and summed with appropriate weight, to yield a vector y = [y1 , y2 , , ym ]T for m outputs by linear combination of the outputs of hidden nodes to produce the final output (Wilamowski, 2009; Liu, 2013; Montazer and Giveki, 2015; Esen et al., 2008c). RBF neural networks can be expressed by Eq. (13):
where i = 1, 2, …, M ; d = 1, 2, …, n , t + 1 is the current iteration number, t is the previous iteration number, c1 and c2 are the learning factors which are usually between [0, 2], r1 and r2 are two independent random numbers uniformly distributed in the range of [0, 1], pbestid (t ) is the best previous position along the d th dimension of the particle i in the iteration t (memorized by every particle), gbestd (t ) is the best previous position among all the particles along the d th dimension in the iteration t (memorized in a common repository), wi (t ) is the inertia weight factor and µi (t ) is a coefficient (see Fig. 8). In order to get better search performance, the dynamic adjustment strategy for ω and µ is proposed as follows (Montazer and Giveki, 2015):
wi i (x ) i=1
(18)
wi (t ) = k1 hi (t ) + k2 bi (t ) + w0 hi (t ) = |(max {Fid (t ), Fid (t
k
y=
(17)
(13)
bi (t ) =
where, wi is the weight of the connection for each hidden unit; k is the 8
1 n
1)}
min {Fid (t ), Fid (t
1)})/ f1 |
(19)
n
(Fi (t ) i=1
Favg )/ f2
(20)
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Fig. 18. Virtual instrument developed to obtain the monitored data.
Fi (t ) is the current fitness of the i th particle, Favg is the mean fitness of all particles in the swarm at the k th iteration, k1 and k2 coefficients given in Eq. (18) are typically selected experimentally within the range of [0, 1], The µ parameter used in Eq. (17) adaptively adjust the value of vid (t + 1) by considering the value of vid (t ) . (see Fig. 9).
2
if vi (t ) > vmax (vmax / vi (t )) e (t / tmax ) µi (t ) = 1 if vmin < vi (t ) < vmax
(vmin/vi (t )) e
(t / tmax )2
if
vi (t ) < vmin
(21)
where w0 [0, 1] is the inertia factor which manipulates the impact of the previous velocity history on the current velocity (in most cases is set to 1), tmax is the maximum number of iterations, hi (t ) is the speed of evolution, bi (t ) is the average fitness variance of the particle swarms, Fid (t ) is the fitness value of pbestid (t ) namely F (pbestid (t )) , Fid (t 1) is the fitness value of pbestid (t 1) namely F (pbestid (t 1)) , f1 = f1 is the normalization function, max { F1, F1, , Fn}, Fn = |Fid (t ) Fid (t 1)|, f2 f2 is the normalization function, max {|F1 (t ) Favg|, |F2 (t ) Favg |, , |Fn (t ) Favg |} . n is the size of the particle swarms,
3.1.3. Hybrid RBFNN with PSO (PSO RBFNN ) PSO has been used to improve RBF Network in several sides like network architecture, learning algorithm, and network connections. Every single solution of PSO called a particle. Using fitness function (MSE) to evaluate the particles for optimal solution. In this paper, we present an approach to evolve the optimization accuracy. This approach is a combined RBF with PSO to reduce the number of neurons and error value between target and real output in Radial Base Function Neural Network, as well as select the best values of RBF centers by using PSO. This approach is described by the following steps (Algorithm2) (Xie et al., 2012; Xuan et al., 2011): 9
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2
3
1 2 3 4
1
6
5
5 6
4 Fig. 19. Front panel of the PV interface under the LabVIEW environment.
Fig. 20. UDP: the Simulink model.
The mean of squared distances between the center of cluster j and pnearest neighbors is given by (Esen et al., 2017):
1 ri = p
trajectory and RBF trajectory is shown in Fig. 10, which indicate a good pursuit of the real voltage output. From Fig. 11, we can note that the PSO RBF neural network error percentage changes uniformly at a rate between 0.2% and 0.5%. Consequently, the prediction precision using the model psoriatic RBF model is better than the traditional RBF model. The fitness function value changes in Fig. 12 and it shows that PSO RBF neural network is more precise. It shows as well that relative time of application PSO RBF is shorter than RBF with a high accuracy under the same samples set. The PSO RBF algorithm can optimize quickly and can be used for short-term forecasting. The quantitative performances comparison of the simulation results produced by the RBF and PSO-RBF models is given in Table 2. In this work, the best performance is achieved by using one- layer neural network with 2 inputs and 2 outputs, and the optimal number of neurons in hidden layer is qual to 200 neurons as shown in Fig. 13.
1 2
p
||cj
ci
||2
(22)
j =1
where cj are the p -nearest neighboring nodes of ci . The average of reference dense distances of all the center nodes and the widths of the improved PSO-RBFNN are given, respectively, by the following equations:
r¯ =
i
=
1 N
N
ri
(23)
i=1
dmax ri 1 · N r¯ 1 + f '' (ci )
1/4
(24)
3.2. Fuzzy logic controller
3.1.4. Validation results The strategy of the PSO RBFNN method is the optimization of RBF parameters via the PSO optimization process. To determine the optimal location of the vector particles and the leading particle decoding individual series, the best particles receive the corresponding parameters of the RBF network in every iteration. To prove the performance determining results of the PSO RBF network, a simulation tests were carried out under the same condition of RBF and PSO RBF network hybrid algorithm in order to make comparison between them. Simulation results of the PSO-RBFNN compared to the real
To precisely adjust the power and output voltage of the photovoltaic system, and to reduce the strong oscillations around the steady state, a fuzzy logic controller (FLC) can be used. The process of FLC can be classified into three stages, fuzzification, rule evaluation and defuzzification. These components and the general architecture of a FLC are shown in Fig. 14. The proposed inputs of the FLC are defined as in Eqs. (25) and (26). The proposed output from FLC is (D ) which corresponds to the modulation signal which is applied to the PWM modulator in order to 10
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Fig. 21. Block diagram of the acquisition system.
produce the switching pulses. During fuzzification, the numerical input variables which are converted into linguistic variables are based on the membership functions. Fig. 15(a), (b) and (c) show the membership functions of error E , change of error CE , and D , respectively. The error E and the change of error CE are defined by the following equations:
E (k ) =
Ppv (k )
Ppv (k
1)
Ipv (k )
Ipv (k
1)
CE (k ) = E (k )
E (k
1)
The control surface of the output variable D is shown in Fig. 16. 3.3. Code generation in LabVIEW/MATLAB programming The data acquisition system that collects the meteorological and electrical parameters of the photovoltaic system through a development system designed around the MyRio card is given in Fig. 17. The communication module including the stack of TCP protocols/IP allows MyRio to transfer data to the Ethernet network. The MyRio card will have to update the data available on a LabVIEW GUI every minute (Srinivas et al., 2016). The MyRio card sends information received from the different sensors via Wi-Fi network. The PC powered by LabVIEW must process these strings (Gade and Angal, 2018). From the interface developed by LabVIEW, we visualize the data of the digital and analog inputs, and the recording of all the data in Excel files using the computer memory as shown in Fig. 18. In this study, PV system supervision is designed and co-simulations are performed using LabVIEW and MATLAB/Simulink. Solar irradiation and operating temperature are transferred from LabVIEW to MATLAB/ Simulink, so that the reference voltage output from the PSO-RBFNN controller is then transferred from Simulink to LabVIEW. The communication between these two programs is provided by the UDP block that runs in MATLAB and LabVIEW. The front panel of the PV interface is shown in Fig. 19.
(25) (26)
where Ppv (k ) and Ipv (k ) are the instant power and current of the photovoltaic module respectively. Seven fuzzy levels are used for all the input and output variables: NL (Negative Large), NM (Negative Medium), NS (Negative Small), ZE (Zero), PS (Positive Small), PM (Positive Medium) and PL (Positive Large). The theoretical rules design is based on the fact that if the change in the current causes the power to increase, the moving of the next change is kept in the same direction, otherwise the next change is reversed. After the theoretical design, all the MFs and the rules were adjusted by the trialand error to obtain the desired performance. The proposed rules are shown in Table 3. The fuzzy rules are designed to track the maximum power point of the photovoltaic system under changing weather conditions. Rapidly changing solar radiation is taken into account while designing these rules.
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photovoltaic generator
Current sensor ACS712 + voltage divider
Whether Link Davis Vantage
Load
PC WITH UDP LABVIEW MATLAB DC-DC Boost Converter
MyRio Card
Fig. 22. Experimental setup of the virtual instrumentation system.
To evaluate the performance of the proposed MPPT system, by an experimental study, it is necessary to give the LabVIEW model carried out which is indicated in Fig. 21.
Table 4 Parameters of the boost converter. Input Voltage
Vin = 20 70 V
Designed Parameter
Rated Output Voltage Rated Output Current Rated Output Power Switching Frequency
V0 = 100 V I0 = 6 A P0 = 600 W fs = 50 KHz
C1 Q1 L1 D1
4. Experimental results and discussion
66 μf IRFP460 2 mH STPS20150CT
In order to validate the LABVIEW model, the PV test system of Fig. 22 is installed. It consists of a DC-DC converter witch is connected with a solar system of two HYM 250 W panels mounted in series, a resistive load of 20 Ω and a control myRio board on which the control algorithms are implemented. The open circuit voltage (Voc ) and the short-circuit current (Isc ) of the PV panel are respectively 45.6 V and 8.78 A. The parameters of the PV panel are listed in Table 1, and the specifications of the power converter are listed in Table 4. To check the designed system, an experiment was performed. The experiment consists in checking the response time and the operational efficiency of the MPP search when the load is subjected to different test conditions. Fig. 23 shows solar irradiation and ambient temperature versus time for typical sunny day delivered by pro-Weather Link Advantage.
There are many parameters, information and data shown on the LabVIEW front panel interfaces. They are illustrated as follows: Area 1: Parameter input areas of irradiance, temperature. Area 2: Display electrical data at panel output (output voltage, current) and waveforms. Area 3: View electricity data at the output of the DC DC converter and waveforms. Area 4: Display the reference voltage that corresponds to the maximum power. Area 5: Display area of duty cycle at the input of the DC DC converter. Area 6: The efficiency of tracking of MPPT. The Simulink blocks of UDP send and UDP receive from the DSP System Toolbox is shown in Fig. 20. MATLAB data are received in a subsystem and the vector is decomposed in the control variables (temperature, irradiation) used in the controller block. The block output, manipulated variables (voltage and current reference) are merged into a vector and sended to LabVIEW.
4.1. Behavior of the system In this section, we compare through the application experience, the convergence towards the MPP concerning the output power of the studied PV system by using one of the four controllers Conventionnel P &O, ANFIS (Esen et al., 2008d), FL control and P&O Algorithm (AlMajidi et al., 2018) and the proposed method PSO-RBFNN.
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Irradiation (w/m²)
800 600 400 200
8:00 8:21 8:42 9:03 9:24 9:45 10:06 10:27 10:48 11:09 11:30 11:51 12:12 12:33 12:54 13:15 13:36 13:57 14:18 14:39 15:00 15:21 15:42 16:03 16:24 16:45 17:06 17:27 17:48
0
Time (HH:mm)
(a)
Temperature (°C)
30
20
10
8:00 8:21 8:42 9:03 9:24 9:45 10:06 10:27 10:48 11:09 11:30 11:51 12:12 12:33 12:54 13:15 13:36 13:57 14:18 14:39 15:00 15:21 15:42 16:03 16:24 16:45 17:06 17:27 17:48
0
Time (HH:mm)
(b) Fig. 23. Pro-Weather Link Advantage data collection: (a) Temperature of PV and (b) Solar irradiance.
As shown in Figs. 24a and 25a, the power tracking of the proposed method turned out to be fast and accurate in finding the right direction, whilst that of the conventional P&O algorithm, ANFIS and FL control and P&O algorithm was lost when there is a rapid change in irradiance and temperature. As a result, the latter methods takes a longer time than the proposed method PSO-RBFNN one to address the phenomenon of research MPP, as shown in Fig. 25a. In addition, the proposed method is more accurate in finding the new MPP after the changes in weather conditions, and it has a smooth oscillation around this value for steady-state conditions compared to others methods, as shown in the zoom of Fig. 25a. The average difference between maximum power and tracking power is less than 5 W with the PSO-RBFNN, but it can reach 10 W with the FLC and P&O algorithm and 15 W with ANFIS controller. Table 5 summarizes the experimental results about tracked power with the studied MPPT controllers for different Irradiations and temperature. It is clear that the power generated when using the PSORBFNN technique was greater than 99% under all test conditions.
where P (t ) is the generated power at certain time, and Pmax (t ) is the theoretical maximum generated power at the same time. The actual power is calculated using the PV array current and voltage sensors. The theoretical maximum power calculated using Eqs. (1), (2), (5) and (8). The tracking time (t) is calculated according to the ability of the power tracking to reach the MPP under varying weather conditions. Whilst the MPPT efficiency of the proposed method appears to be lower, it achieves an average tracking efficiency of 99.04% under all the varying weather condition, whereas those for FL control and P& O algorithm and P&O-MPPT methods are 98.7%, and 97.1%, respectively. ii. The Integral of the Squared Error (ISE): It is an analytical manipulation method using linear quadratic weights to minimize the difference between the system output and a value of a desired order. This difference may be due to either a change of order or perturbations in the system. It is calculated using Parseval’s theorem that states the integral or sum of the squares of the function equals to the square of its transform. The Integral of the Squared Error (ISE) is given by:
4.2. Performance criteria of MPPT controllers In order to evaluate the performances of differents types of the studied controllers, a comparison of the efficiency criterion was made.
ISE =
i. The efficiency criterion η of a MPPT controller defined by:
=
P (t ) Pmax (t )
100
t 0
[e (t )]2 dt
(28)
where
e (t ) =
(27)
13
Ppv Vpv
(29)
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(a)
Rapid change in values of meteorological
(b) Fig. 24. PV module system for the proposed method versus conventional P&O under rapidly changing weather conditions: (a) power and (b) voltage.
In our research, for the different studied MPPT controllers, Table 6 sums up the calculation results of the performance and the ISE criterion. According to the definitions above of η and ISE criteria, we note that for obtain the more efficient and faster MPPT, we must have a higher η and lower ISE. The obtained results show that the use of proposed MPPT controller improves considerably and efficiently the performance of the PV plants. The comparison made between these four types of controllers confirm that the use of PSO-RBFNN controller enables not only the minimization of ISE criteria, which reduces the response time of the controller, but also improve the MPPT controller performance η, which aims at diminishing fluctuations in transients operation mode. This increases the efficiency of the MPPT controller type PSORBFNN and definitely ensures the improvement of stability around the MPP.
power points. among maximum power point tracking methods for photovoltaic systems include those based on an estimated search mechanism such as the adaptive neural network with a fuzzy system inference system (ANFIS) and the radial base function neural Network (RBFNN) which can easily reach PPGM as soon as the search algorithm is launched. These last techniques suffer from two problems; the first problem is the robustness and the stability (strong oscillations around the GMPP) of the controller according to the climatic changes. The second problem is that the PSO can be trapped in a local optimum which slows down the convergence speed. In addition, the use of the nearest p-neighbor algorithm to calculate RBF unit widths results in loss of information about the spatial distribution of the training data set. To overcome these drawbacks, a new adaptive version of particle swarm optimizer in high-dimensional data has been applied. This combination method based on the RBF neural network, and PSO showed a better MPPT energy efficiency compared to the proposed approaches. The MPPT energy efficiencies for RBFNN-FLC, FLC and P& O algorithm, and ANFIS based on weather variations are 99.04%, 98.7% and 97.1%, respectively. The Experimental results obtained from PV system show a fast convergence speed and a considerable reduction of the oscillations of the output power.
5. Conclusions The weather, complicit with its many weather variations such as temperature and solar irradiation, generates many peaks in the P-V curve, one maximum global power point and several local maximum
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(a)
Rapid change in values of meteorological
(b) Fig. 25. PV module system for the proposed method versus ANFIS and (FL control and P&O Algorithm) under rapidly changing weather conditions: (a) power and (b) voltage. Table 5 Tracked power under various values of irridation G and temperature T. Time HH:mm
11:30 14:40 14:03 12:45 11:15
Irradiance level (w/m2)
350 450 580 600 680
Temperature (°C)
16 18.4 17.8 17.7 16
Max Tracked PV power (W)
130 310 405 380 250
Parameters
PSORBFNN
ANFIS
FLC and P&O algorithm
Conventionnel P&O
η (%)
99.04 0.185
97.1 0.94
98.7 0.202
96.3 5.324
6
Tracking efficiency (%)
PSO-RBFNN
FLC and P&O
ANFIS
PSO-RBFNN
FLC and P&O
ANFIS
126.5 305.5 401.2 377 247.7
125.2 302.2 398 374 245
122.8 297 391.7 370 243
97.30 98.54 99.06 99.21 99.08
96.3 97.48 98.27 98.42 98.00
94.46 95.80 96.71 97.36 97.20
References
Table 6 Performance criteria of MPPT controller.
ISE·10
Tracked PV power (W)
Al-Majidi, S.D., Abbod, M.F., Al-Raweshidy, H.S., 2018. A novel maximum power point tracking technique based on fuzzy logic for photovoltaic systems. Int. J. Hydrogen Energy 43 (31), 14158–14171. Babu, T.S., Rajasekar, N., Sangeetha, K., 2015. Modified particle swarm optimization technique based maximum power point tracking for uniform and under partial shading condition. Appl. Soft Comput. 34, 613–624. Ben Regaya, C., Farhani, F., Zaafouri, A., Chaari, A., 2012. Comparison between two methods for adjusting the rotor resistance. Int. Rev. Model. Simul. 5 (2), 938–944.
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H. Hamdi, et al. Bouraiou, A., Hamouda, M., Chaker, A., Sadok, M., Mostefaoui, M., Lachtar, S., 2015. Modeling and simulation of photovoltaic module and array based on one and two diode model using Matlab/Simulink. Energy Procedia 74, 864–877. Chakchouk, W., Ben Regaya, C., Zaafouri, A., Sellami, A., 2017. Fuzzy supervisor approach design based-switching controller for pumping station: experimental validation. Math. Probl. Eng. 1–12. Chaouachi, A., Kamel, R.K., Nagasaka, K., 2010. A novel multi-model neuro-fuzzy-based MPPT for three-phase grid-connected photovoltaic system. Sol. Energy 84, 2219–2229. Collotta, M., Pau, G., 2017. A fuzzy logic approach by using particle swarm optimization for effective energy management in IWSNs. IEEE Trans. Ind. Electron. 9496–9506. Duman, S., Yorukeren, N., 2018. A novel MPPT algorithm based on optimized artificial neural network by using FPSOGSA for standalone photovoltaic energy systems. Neural Comput. Appl. 29 (1), 257–278. El Hammoumi, A., Motahhir, S., 2018. Low-cost Virtual Instrumentation of PV Panel Characteristics using Excel and Arduino in Comparison with Traditional Instrumentation. Renewables: Wind, Water, and Solar. Springer, pp. 1–16. Esen, H., Inalli, M., Sengur, A., Esen, M., 2008b. Performance prediction of a groundcoupled heat pump system using artificial neural networks. Expert Syst. Appl. 35, 1940–1948. Esen, H., Inalli, M., Sengur, A., Esen, M., 2008a. Modelling a ground-coupled heat pump system using adaptive neuro-fuzzy inference systems. Int. J. Refrig. 31, 65–74. Esen, H., Inalli, M., Sengur, A., Esen, M., 2008c. Predicting performance of a groundsource heat pump system using fuzzy weighted pre-processing-based ANFIS. Build. Environ. 43, 2178–2187. Esen, H., Inalli, M., Sengur, A., Esen, M., 2008d. Artificial neural networks and adaptive neuro-fuzzy assessments for ground-coupled heat pump system. Energy Build. 40, 1074–1083. Esen, H., Kapicioglu, A., Ozsolak, O., 2016. Design and implementation of automatic wheat mower based on smart sensor fed by a photovoltaic. Int. J. Photoenergy 10 Article ID 5410759. Esen, H., Esen, M., Ozsolak, O., 2017. Modelling and experimental performance analysis of solar- assisted ground source heat pump system. J. Exp. Theor. Artif. Intell. 29, 1–17. Ezinwanne, O., Zhongwen, F., Zhijun, L., 2017. Energy performance and cost comparison of MPPT techniques for photovoltaics and other applications. Energy Procedia 107, 297–303. Gaboriault, M., Notman, A., 2004. A high efficiency, noninverting, buck boost DC-DC converter. In: Nineteenth Annual IEEE Applied Power Electronics Conference and Exposition, pp. 1411–1415. Gade, A., Angal, Y., 2018. Real-Time Intelligent NI MyRio-Based Library Management Robotic System Using LabVIEW. Springer, pp. 387–399. Ginart, A., Riley, R.W., Hardman, B., Ernst, M., 2013. Closed forms solution for simplified PV modeling and voltage evaluation including irradiation and temperature
dependence. In: IEEE Green Technologies Conference, pp. 105–112. Li, S., 2015. A variable-weather-parameter optimization strategy to optimize the maximum power point tracking speed of photovoltaic system. Sol. Energy 113, 1–13. Liu, J., 2013. Radial Basis Function (RBF) Neural Network Control for Mechanical Systems. Springer, pp. 71–112. Liu, Y., Li, M., Ji, X., Luo, X., Wang, M., Zhang, Y., 2014. A comparative study of the maximum power point tracking methods for PV systems. Energy Convers. Manage. 85, 809–816. Mohandes, M.A., 2012. Modeling global solar radiation using Particle Swarm Optimization (PSO). Sol. Energy 86 (11), 3137–3145. Montazer, G.A., Giveki, D., 2015. An improved radial basis function neural network for object image retrieval. Neurocomputing 168, 221–233. Othman, A., Fathy, A., Ghitas, A., 2012. Realworld maximum power point tracking simulation of PV system based on Fuzzy Logic control. NRIAG J. Astron. Geophys. 186–194. Park, J., Kim, K.Y., 2016. Instance variant nearest neighbor using particle swarm optimization for function approximation. Appl. Soft Comput. 40, 331–341. Rezk, H., Eltamaly, A.M., 2015. A comprehensive comparison of different MPPT techniques for photovoltaic systems. Sol. Energy 112, 1–11. Sera, D., Mathe, L., Kerekes, T., Teodorescu, R., 2013. The perturb-and-observe and incremental conductance MPPT methods for PV systems. IEEE J. Photovolt. 3, 1070–1078. Srinivas, P., Kodali, L.V., Ramesh, C., 2016. Simulation of incremental conductance MPPT algorithm for PV systems using LabVIEW. Int. J. Innov. Res. Electr. Electron. Instrument. Control Eng. 4 (1), 34–38. Varnham, A., Al-Ibrahim, A.M., Azzi, D., 2007. Soft-computing model-based controllers for increased photovoltaic plant efficiencies. IEEE Trans. Energy Convers. 22, 873–880. Wilamowski, B.M., 2009. Neural network architectures and learning algorithms: how not to be frustrated with neural networks. IEEE Ind. Electron. Mag. 56–63. Wu, Z.Q., Jia, W.J., Zhao, L.R., Wu, C.H., 2015. Maximum wind power tracking based on cloud RBF neural network. Renew. Energy 86, 466–472. Xie, T., Yu, H., Hewlett, J., Rozycki, P., Wilamowski, B., 2012. Fast and efficient secondorder method for training radial basis function networks. IEEE Trans. Neural Netw. Learn. Syst. 23 (4), 609–619. Xuan, H.H., Hien, D.T.T., Huynh, T., 2011. Efficient algorithm for training interpolation RBF networks with equally spaced nodes. IEEE Trans. Neural Netw. 22 (6), 982–988. Zainuri, M.M., Radzi, M.M., Soh, A.C., Rahim, N.A., 2012. Adaptive P&O-fuzzy control MPPT for PV boost Dc-Dc converter. In: IEEE International Conference on Power and Energy, pp. 524–529. Zhao, J., Zhou, X., Ma, Y., Liu, W., 2015. A novel maximum power point tracking strategy based on optimal voltage control for photovoltaic systems under variable environmental conditions. Sol. Energy 640–649.
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Contents lists available at ScienceDirect
Solar Energy journal homepage: www.elsevier.com/locate/solener
Real-time study of a photovoltaic system with boost converter using the PSO-RBF neural network algorithms in a MyRio controller
T
Hichem Hamdi , Chiheb Ben Regaya, Abderrahmen Zaafouri ⁎
University of Tunis, Higher National Engineering School of Tunis (ENSIT), Engineering Laboratory of Industrial Systems and Renewable Energies (LISIER), 5 Avenue Taha Hussein, PO Box 56, 1008 Tunis, Tunisia
ARTICLE INFO
ABSTRACT
Keywords: MPPT MyRio RBF neural network PSO
Given the nonlinear feature of a photovoltaic generator, a maximum power point tracking algorithm (MPPT) is required in a photovoltaic system leading to maximum power point (MPP) operation and maximizing the power generated. The tracking MPP techniques are based on an actual or estimated research mechanism using experimental data. Conventional MPPT techniques like perturbe and observe (P&O), incremental conductance, etc., are good enough to track the maximum power for the PV systems, but they are less stable, more oscillating around the MPP. Generally, techniques based on the estimated research mechanisms, such as the Artificial Neural Network (ANN), the Adaptive Neuro-Fuzzy Inference System (ANFIS), and the Radial Basis Function Neural Network (RBFNN), etc., are supervised automatic learning techniques, which aims to create a model for an unknown function in order to find a relationship between input data and output data. In the case of RBF Neural Network, the center of the radial base function, the variance of the radial function base and the weight must be chosen. If these variables are not chosen appropriately, the RBF neural network can degrade the validity and accuracy of the modeling. On the other hand the RBF network suffers from a growth in the size of the hidden layer comparable to that of a set of learning data which also implies more computational time. The solution of these two problems is the motivation of this research. The PSO algorithm is used to optimize the parameters of the RBFNN by introducing a new adaptive strategy of particle swarm optimizer to dynamically adjust the inertia weight factor ω and the new velocity vid (t + 1) with a new µ coefficient. The obtained results based on RBFNN hybrid approach with PSO (PSO-RBFNN approach) were compared with the results obtained with the adaptive Neuro-Fuzzy Inference System (ANFIS). The experimental test bench of the PSO-RBFNN approach has been implemented using a MyRio card, which prove the good performances of the new proposed technique in terms of the average relative errors of the learning, test and control data, for the model PSO-RBFNN which converge approximately to 0.26%, 0.294% and 0.8% respectively, and energy efficiency MPPT in the case of atmospheric parameters varying over time can reach 99.04%.
1. Introduction A photovoltaic generator can work in a wide range of output current and voltage but the photovoltaic panel can provide maximum power only for a particular voltage and current. Indeed, the output power of photovoltaic (PV) array depends on solar irradiation levels and ambient temperature. These climatic variations cause a fluctuation in the power output and the maximum power point, which makes it necessity to insert a controlled static converter for the pursuit of the maximum power point. These commands are known under the name of MPPT (Maximum Power Point Tracking). An MPPT, or maximum power point tracker is an electronic DC-DC converter that optimizes the effectiveness between the solar array (PV panels), and the receiver (Babu et al., ⁎
2015; Rezk and Eltamaly, 2015). In the literature, several MPPT techniques are used in photovoltaic systems to improve efficiency, so that the maximum power can be delivered to the load. To solve this problem, many researchers have proposed different techniques of search for optimum power points, we can mention the widely used Perturb and Observe algorithm (P&O), which is a conventional algorithm that follows the MPP with a constant step of service cycle. The time response to reach the MPP depends on the value of the duty cycle. If the cycle is too small, the time response will be large and vice versa. For this method, MPP operation is less efficient than other systems (Rezk and Eltamaly, 2015; Ezinwanne et al., 2017; Sera et al., 2013). Recently, the number of fuzzy logic applications have increased significantly especially for uncertain
Corresponding author. E-mail address: [email protected] (H. Hamdi).
https://doi.org/10.1016/j.solener.2019.02.064 Received 14 August 2018; Received in revised form 16 February 2019; Accepted 25 February 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.
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Nomenclature
r1 and r2 random numbers MPPT maximum power point tracker RBFNN Radial Basis Function Neural Networks ANFIS Adaptive neuro fuzzy inference system ANN artificial neural network UDP User Datagram Protocol TCP/IP Transmission Control Protocol/Internet Protocol ISE Integral Square Error MSE mean squared error PV Photovoltaic DSP Digital Signal Processor MPP Maximum power point LABVIEW Laboratory Virtual Instrument Engineering Workbench
PSC partial shading condition GMPP global maximum power point LMPP local maximum power point PSO particle swarm optimization fuzzy logic controller FLC pbest , i particle’s personal best solution gbest global best of Pbest , i x id (t ) position vector of PSO vid (t ) velocity vector of PSO ω inertia weight c1 and c2 the learning factors nonlinear systems (Chakchouk et al., 2017; Ben Regaya et al., 2012). With control systems such as Fuzzy Logic Control (FLC ) proposed by Othman et al. (2012) and Liu et al. (2014), the performance of the system can be better than the conventional algorithm because the time response for MPP tracking is faster than the P&O MPPT method and also more efficient for MPP tracking. Both methods used the I PV and V PV control sensors as inputs for system optimization. In Duman and Yorukeren (2018), Varnham et al. (2007) and Bouraiou et al. (2015), the solar irradiance and the temperature of the cell are transmitted to ANFIS and the output differs from the reference to another. Some authors use Vmax as the output of ANFIS and others use Pmax . The advantage of this method is the fast and accurate tracking of the MPP without interrupting PV power, using trial and error search, or approximating the MPP (Gaboriault and Notman, 2004; Chaouachi et al., 2010). The ANFIS technique (Esen et al., 2008a,b) and a novel maximum power point tracking combining both the Radial Basis Function Neural Network with the Particle Swarm Optimization (PSO RBFNN ) and fuzzy logic are used in this study for controlling duty cycle of the electronic switch of DC DC boost converter. The PV system has been used under varying temperature and insolation conditions, to provide maximum power to the resistive load. The different steps of the controller design are presented together with simulation and their experimental results are presented to demonstrate the main characteristics of
the proposed MPPT, and it’s compared with the Conventionnel P&O, ANFIS, FL control and P&O Algorithm. The main contributions of the proposed control scheme can be summarized as follows: 1. The proposition of a new MPPT technique based radial basis function (RBF) neural network model optimized using particle swarm optimization (PSO), by introducing a new adaptive strategy of particle swarm optimizer to dynamically adjust the inertia weight factor ω and the new velocity vid (t + 1) with a new µ coefficient. A modified PSO algorithm is used to determine the centers, widths, and connection weights of RBF neural network to ensure a good follow-up of the MPPT; 2. Guarantee the effectiveness of maximum power point tracking (MPPT) and amelioration of MPPT efficiency; 3. A simulation benchmarking study was carried on; 4. A real time experimental comparative study using My RIO 1900 board of the proposed method of MPPT is performed. 2. Structure of PV system with MPPT As the PV conversion chain illustrates in Fig. 1, MPP is reached through controlling the DC-DC converter with a system using a MPPT controller. The strategy of the MPPT controller allows to optimize the transfer of power from the PV panel to the load. FLC
LABVIEW LABVIE UDP Receive
UDP Send
MATLA MATLAB PSO-RBFNN
MPPT
Voltage divider
USB connection US
Whether Link Davis Vantage Fig. 1. Elementary chain of photovoltaic conversion. 2
Load
WIFI Communication
DC-DC Boost converter
Current sensor ACS712
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2.1. Photovoltaic model In order to model the PV panel, we start with a simple model which represents a PV elementary cell. The configuration that Fig. 2 presents is the most common equivalent schema of a solar cell. It is composed of a variable source current Iph , connected in parallel with a diode D , characterizing the junction of semi-conductors which make the solar cell, and a parallel resistance Rp . To this assembly, another resistance Rs is added in series. From Fig. 2, the generated current (IPV ) by the PV cell is given by: Fig. 2. Solar cell circuit diagram.
IPV = Iph
(1)
IRp
The value of Iph is heavily dependent on the irradiance (G ) and solar cell temperature (Tc ). The Iph equation can be expressed by the following equation (El Hammoumi and Motahhir, 2018; Ginart et al., 2013):
Table 1 The main parameters of PLM-300M-72 PV module. The voltage at MPP (VMPP ) The current at MPP (IMPP ) Open-circuit voltage (Voc ) Short-circuit current (Isc ) Maximum power generated from the module Peak Efficiency Temp. Coefficient of Isc : µsc Temp. Coefficient of VOc Temp. Coefficient of Pmax Number of Cells
Id
36.59 V 08.20 A 45.60 V 08.78 A 300 W 15.37% 0.06%/°C −0.34%/°C −0.45%/°C 72
Iph =
G (Isc, ref + µsc · T ) Gref
(2)
The current flowing through the diode Id , is given by Eq. (3):
VPV + IPV · Rs A· VT
Id = I0 exp
1
(3)
where
Hardware part of the system consists of National Instruments (NI) myRIO module and Whether Link Davis Vantage. Application circuits for the current and voltage sensor is shown on Fig. 1. Power supply, data exchange and output logic levels measurement are implemented on the base of NI myRIO input/output lines. Whether Link Davis Vantage is used for temperature and solar irradiation measurement of the PV panel and is controlled via USB interface from myRIO card. Custom software was developed in LabVIEW development system. The MPPT is divided into two steps, first will lift the response of the MPPT to deliver the voltage and the maximum current corresponds to the MPP by using the proposed method PSO-RBFNN in matlab/ Simulink, and the second will lift to reduce the strong oscillations around the steady state by using the fuzzy logic controller (FLC) in LABVIEW part. The communication of both parties is done by the UDP protocol.
VT =
kB T q
(4)
Saturation current (I0 ) of solar cells can be expressed in a mathematical equation that has a relationship with the temperature of the solar cell as follows (Esen et al., 2016):
I0 =
Isc, ref
exp
( ) Voc, ref a
Tc 3 ) exp T c 1 , ref (
q· Eg
(
1 Tc, ref
1 Tc
)
A· kB
(5)
The thermal voltage a is presented by the following equation:
a=
Ns ·A· kB· Tc q
(6)
The current IRp in a closed loop can be determined by using Kirchhoff's voltage law analysis, which is expressed in Eq. (7):
Fig. 3. Changing of MPP with: (a) solar irradiation and (b) temperature. 3
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Fig. 4. Boost converter. PV Arrays
PV Current Sense
Boost Converter
=
LOAD
=
PV Voltage Sense Solar Irradiation diation Sense Temperature Sense
DC Load
+ -
RBFNN
+ PSO
Fig. 5. PV system with hybrid PSO-RBFNN based MPPT.
Photovoltaic panel +
RBFNN
-
Σ
Training algorithm Fig. 7. Block diagram of a RBF network.
The equivalent circuit of a PV array is expressed as follows: Fig. 6. Architecture of used RBF neural network.
IRp
V + IPV · Rs = PV Rp
IPV = Np I ph
I0 exp
VPV + IPV · Rs A· VT
1
VPV + IPV · Rs Rp
VPV /Ns + IPV · Rs / Np A·VT
1
VPV Np/ Ns + IPV · Rs
(7)
Rp
Therefore, the output current (IPV ) were previously expressed by Eq. (1), can be restated by Eq. (8):
IPV = Iph
Np I0 exp
(9)
where IPV is the output current of solar cells (Ampere), Iph is photocurrent (Ampere), I0 is saturation current of solar cells (Ampere), VPV is output voltage of solar cells (Volt), µsc is the temperature coefficient of the short circuit current ( A/ K ), provided by the manufacturer, Eg is the Silicon bandgap energy (Eg = 1.12 eV), Tc is the temperature of the solar cell (Kelvin), Tc, ref is the reference temperature of Solar Cells
(8)
A PV array is a group of several PV modules which are electrically connected in series (Ns ) and parallel (Np ) for generating more power. 4
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Step 1: Initialization Initialize each particle of the swarm, with random values for position ( ) and velocity ( ) in the search space according to the dimensionality of problem. Step 2: Evaluation Evaluate fitness value of particle by using fitness function. Step 3: Comparison Compare the value obtained from the fitness function from particle with the value of If the value of the fitness function is better than the value, then update the particle position to takes . the place of form any particle is better than , then update = . If the value of Step 4: Compute inertia weight using Eq. (18) and using Eq. (21). Step 5: Adaptation Modify the position and velocity of the particles using Eq. (16) and Eq. (17), respectively. Step 6: Stop test If the maximum number of iterations or the ending criteria is not achieved so far, then return to step 2. Fig. 8. The pseudocode of the proposed PSO clustering for RBF unit center.
Step 1. Start with one RBF. Initialize RBF parameters. Start optimizing centers of RBFs using PSO (Algorithme1) Initialize particles position and velocity randomly Step 2. Compute mean of squared distances between the center of cluster and -nearest neighbors using Eq. (22) Step 3. Compute coefficient factor:
, where
is the number of hidden units and
is the
maximum distance between those centers. Step 4. Find the maximum distance from each center and normalize the distance vector Step 5. Multiply the distance vector obtained from step 4 by the coefficient factor Step 6. Compute the average of reference dense distances of all the center nodes using (Eq. (23)) as the widths of the improved PSO-RBFNN are given by (Eq. (24)). Fig. 9. The Algorithm of the proposed width adjustment.
Temperature Zone
Irradiance Zone
Fig. 10. PSO
RBF as compared to the actual trajectory and RBF trajectory.
(Kelvin), G and Gref are the irradiance and the irradiance reference (kW/m2) , kB is Boltzmann’s constant (1.381 × 10 23 J/K) , q is electron charge (1.60222 × 10 19 C) , A is ideality factor of PV technology (1 A < 2) , Isc , V0c , Vmpp and Impp represent the short circuit current, the open circuit voltage, the maximum power point current and voltage which are shown in Table 1. The typical current-voltage (I-V) curve
characteristics under 10, 25, 40, 55 and 70 °C, and for 200, 400, 600, 800 and 1000 W/m2 changes for no-load condition of PV panel is examined in Fig. 3.
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Fig. 11. Voltage error with PSO
RBFNN compared with RBF .
10
PSO-RBF Fitness value
1
RBF
0.1
0.01
0.001
0
50
100
150
200
Iteration Fig. 12. Comparison of convergence profiles for PSO
RBF and traditional RBF.
Table 2 Summary table of simulation models.
knowledge base
Model
Training time/ s
Number of iterations
Test time/ s
Precision
MSE
RBF PSO-RBF
0.958 0.746
180 130
0.318 0.239
0.001 0.001
0.0053 0.0026
Input
fuzzification
inference
defuzzification
Output
Fig. 14. Fuzzy Inference System.
Filters made of capacitors are normally added to the output of the converter to reduce output voltage ripple. The boost converter is used to regulate a chosen level of the solar photovoltaic module output voltage and to keep the system at the maximum possible power from solar panels at all times. The SIMULINK model of the boost converter used in the simulation is shown in Fig. 4.
2.2. DC-DC boost converter A boost converter (step-up converter) is a DC to DC power converter with an output voltage is greater than its input voltage. It is a class of switched-mode power supply (SMPS) containing at least two semiconductor switches (a diode and a transistor) and at least one energy storage element, a capacitor, inductor, or the two in combination.
Fig. 13. Architecture of RBFNN . 6
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Fig. 15. Membership functions of (a) error E , (b) Change of error CE and (c) duty cycle D .
where D is the duty cycle of converter. For the switching frequency f , the ripple of the output voltage can be obtained as:
Table 3 Fuzzy rules base. E/CE
NL
NM
NS
ZE
PS
PM
PL
NL NM NS ZE PS PM PL
ZE ZE NS NM PS PM PL
ZE ZE ZE NS PM PM PL
ZE ZE ZE ZE PM PM PL
NL NS ZE ZE PS ZE ZE
NL NM NS ZE ZE ZE ZE
NL NM NS PS ZE ZE ZE
NM NM NS PM ZE ZE ZE
V0 D = V0 RfC To ensure a continuous conduction, the minimum inductance
L>
2.2.1. Design calculation The Boost converter parameter values are calculated by the following formulae (Wu et al., 2015; Zainuri et al., 2012):
V0 =
1 1
D
Vin
(11)
(1
D) 2Rload 2f
(12)
3. MPPT controller The proposed PSO RBFNN based MPPT block diagram is shown in Fig. 5. The objective of the controller is to determine the converter duty cycle D , by which the converter delivers the maximum attainable power to the load at any given temperature and irradiance (Li, 2015;
(10) 7
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number of hidden units; i (x ) is the radial basis function. There are different types of radial basis function, and the normalized Gaussian function is usually used as the radial basis function, which is defined as follows (Esen et al., 2008): i (x )
= exp [ ||xi
ci ||2 /(2 i2]
(14)
where x i = [x1, x2, , xN ]T is the input vector of the neural network; ci is the center of the ith basis function in the hidden layer; i is the width of the ith node. In RBFNN to reach the best accuracy results, a measured fitness function is used which takes the error between the output (target) of the RBF and the real output. There are many fitness functions which can be used to calculate the error, such as, Mean Square Error (MSE), Root Mean Square Error (RMSE), Sum Square Error (SSE), and Normalized/ Root Mean Squared Error (N/RMSE). In this paper, the MSE fitness function is used which is given by the following equation: Fig. 16. The fuzzy rule surfaces.
MSE =
1 n
n i=1
(Yi
Ti ) 2
(15)
where n is the number of input data, T is the target output and Y is the real output. A general block diagram of an RBF network is illustrated in Fig. 7. 3.1.2. Particle Swarm Optimization (PSO) Particle swarm optimization (PSO), introduced by Collotta and Pau (2017) mimics the behavior of a swarm of insects or a school of fish. If one of the particles discovers a good path to food, the rest of the swarm will be able to follow instantly even if they are far away in the swarm. Swarm behavior is modeled by particles in multidimensional space that have two characteristics: a position and a velocity. These particles wander around the hyperspace and remember the best position that they have discovered. They communicate good positions to each other and adjust their own position and velocity based on these good positions. If we would like to describe the process used in this algorithm more technically, we would follow these steps (Algorithm1) (Collotta and Pau, 2017; Mohandes, 2012; Montazer and Giveki, 2015; Park and Kim, 2016): The position x id and velocity vid of the particles are given resectevily by:
Fig. 17. Diagram showing the sensors interface from the MyRio card.
Zhao et al., 2015). The first part of the controller, Radial Basis Function Neural Network with the particle swarm optimization (PSO RBFNN ), works as a reference model of the PV array and finds the suitable maximum voltage under a given temperature and irradiance. While the FLC fit into a regulation loop, by comparing the maximum voltage and current of reference model and those of the output of the PV array. Subsequently, control loop errors are used to produce the change of D , which is the objective of the third block controller.
vid (t + 1) = wi (t ) vid (t ) + c1 r1 (pbestid (t ) + c2 r2 (gbestd (t )
x id (t )) (16)
x id (t ))
3.1. Particle swarm optimization and radial basis function neural network
x id (t + 1) = xid (t ) + µi (t )·vid (t + 1)
3.1.1. Radial Basis Function Neural Network (RBFNN) Feed-forward layered neural networks have increasingly been used in many areas, such as, modeling and control of nonlinear systems. One example of a feed forward neural network is the Radial Basis Function (RBF ) network. The typical structure of an RBF neural network is shown in Fig. 6. Input units distribute the values to the hidden layer units uniformly, without multiplying them with weights. Hidden units are known as RBF units because their transfer function is a monotonous radial basis function in which the number of hidden units is determined by the described problems. Hidden layer outputs are led to the output units and summed with appropriate weight, to yield a vector y = [y1 , y2 , , ym ]T for m outputs by linear combination of the outputs of hidden nodes to produce the final output (Wilamowski, 2009; Liu, 2013; Montazer and Giveki, 2015; Esen et al., 2008c). RBF neural networks can be expressed by Eq. (13):
where i = 1, 2, …, M ; d = 1, 2, …, n , t + 1 is the current iteration number, t is the previous iteration number, c1 and c2 are the learning factors which are usually between [0, 2], r1 and r2 are two independent random numbers uniformly distributed in the range of [0, 1], pbestid (t ) is the best previous position along the d th dimension of the particle i in the iteration t (memorized by every particle), gbestd (t ) is the best previous position among all the particles along the d th dimension in the iteration t (memorized in a common repository), wi (t ) is the inertia weight factor and µi (t ) is a coefficient (see Fig. 8). In order to get better search performance, the dynamic adjustment strategy for ω and µ is proposed as follows (Montazer and Giveki, 2015):
wi i (x ) i=1
(18)
wi (t ) = k1 hi (t ) + k2 bi (t ) + w0 hi (t ) = |(max {Fid (t ), Fid (t
k
y=
(17)
(13)
bi (t ) =
where, wi is the weight of the connection for each hidden unit; k is the 8
1 n
1)}
min {Fid (t ), Fid (t
1)})/ f1 |
(19)
n
(Fi (t ) i=1
Favg )/ f2
(20)
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Fig. 18. Virtual instrument developed to obtain the monitored data.
Fi (t ) is the current fitness of the i th particle, Favg is the mean fitness of all particles in the swarm at the k th iteration, k1 and k2 coefficients given in Eq. (18) are typically selected experimentally within the range of [0, 1], The µ parameter used in Eq. (17) adaptively adjust the value of vid (t + 1) by considering the value of vid (t ) . (see Fig. 9).
2
if vi (t ) > vmax (vmax / vi (t )) e (t / tmax ) µi (t ) = 1 if vmin < vi (t ) < vmax
(vmin/vi (t )) e
(t / tmax )2
if
vi (t ) < vmin
(21)
where w0 [0, 1] is the inertia factor which manipulates the impact of the previous velocity history on the current velocity (in most cases is set to 1), tmax is the maximum number of iterations, hi (t ) is the speed of evolution, bi (t ) is the average fitness variance of the particle swarms, Fid (t ) is the fitness value of pbestid (t ) namely F (pbestid (t )) , Fid (t 1) is the fitness value of pbestid (t 1) namely F (pbestid (t 1)) , f1 = f1 is the normalization function, max { F1, F1, , Fn}, Fn = |Fid (t ) Fid (t 1)|, f2 f2 is the normalization function, max {|F1 (t ) Favg|, |F2 (t ) Favg |, , |Fn (t ) Favg |} . n is the size of the particle swarms,
3.1.3. Hybrid RBFNN with PSO (PSO RBFNN ) PSO has been used to improve RBF Network in several sides like network architecture, learning algorithm, and network connections. Every single solution of PSO called a particle. Using fitness function (MSE) to evaluate the particles for optimal solution. In this paper, we present an approach to evolve the optimization accuracy. This approach is a combined RBF with PSO to reduce the number of neurons and error value between target and real output in Radial Base Function Neural Network, as well as select the best values of RBF centers by using PSO. This approach is described by the following steps (Algorithm2) (Xie et al., 2012; Xuan et al., 2011): 9
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2
3
1 2 3 4
1
6
5
5 6
4 Fig. 19. Front panel of the PV interface under the LabVIEW environment.
Fig. 20. UDP: the Simulink model.
The mean of squared distances between the center of cluster j and pnearest neighbors is given by (Esen et al., 2017):
1 ri = p
trajectory and RBF trajectory is shown in Fig. 10, which indicate a good pursuit of the real voltage output. From Fig. 11, we can note that the PSO RBF neural network error percentage changes uniformly at a rate between 0.2% and 0.5%. Consequently, the prediction precision using the model psoriatic RBF model is better than the traditional RBF model. The fitness function value changes in Fig. 12 and it shows that PSO RBF neural network is more precise. It shows as well that relative time of application PSO RBF is shorter than RBF with a high accuracy under the same samples set. The PSO RBF algorithm can optimize quickly and can be used for short-term forecasting. The quantitative performances comparison of the simulation results produced by the RBF and PSO-RBF models is given in Table 2. In this work, the best performance is achieved by using one- layer neural network with 2 inputs and 2 outputs, and the optimal number of neurons in hidden layer is qual to 200 neurons as shown in Fig. 13.
1 2
p
||cj
ci
||2
(22)
j =1
where cj are the p -nearest neighboring nodes of ci . The average of reference dense distances of all the center nodes and the widths of the improved PSO-RBFNN are given, respectively, by the following equations:
r¯ =
i
=
1 N
N
ri
(23)
i=1
dmax ri 1 · N r¯ 1 + f '' (ci )
1/4
(24)
3.2. Fuzzy logic controller
3.1.4. Validation results The strategy of the PSO RBFNN method is the optimization of RBF parameters via the PSO optimization process. To determine the optimal location of the vector particles and the leading particle decoding individual series, the best particles receive the corresponding parameters of the RBF network in every iteration. To prove the performance determining results of the PSO RBF network, a simulation tests were carried out under the same condition of RBF and PSO RBF network hybrid algorithm in order to make comparison between them. Simulation results of the PSO-RBFNN compared to the real
To precisely adjust the power and output voltage of the photovoltaic system, and to reduce the strong oscillations around the steady state, a fuzzy logic controller (FLC) can be used. The process of FLC can be classified into three stages, fuzzification, rule evaluation and defuzzification. These components and the general architecture of a FLC are shown in Fig. 14. The proposed inputs of the FLC are defined as in Eqs. (25) and (26). The proposed output from FLC is (D ) which corresponds to the modulation signal which is applied to the PWM modulator in order to 10
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Fig. 21. Block diagram of the acquisition system.
produce the switching pulses. During fuzzification, the numerical input variables which are converted into linguistic variables are based on the membership functions. Fig. 15(a), (b) and (c) show the membership functions of error E , change of error CE , and D , respectively. The error E and the change of error CE are defined by the following equations:
E (k ) =
Ppv (k )
Ppv (k
1)
Ipv (k )
Ipv (k
1)
CE (k ) = E (k )
E (k
1)
The control surface of the output variable D is shown in Fig. 16. 3.3. Code generation in LabVIEW/MATLAB programming The data acquisition system that collects the meteorological and electrical parameters of the photovoltaic system through a development system designed around the MyRio card is given in Fig. 17. The communication module including the stack of TCP protocols/IP allows MyRio to transfer data to the Ethernet network. The MyRio card will have to update the data available on a LabVIEW GUI every minute (Srinivas et al., 2016). The MyRio card sends information received from the different sensors via Wi-Fi network. The PC powered by LabVIEW must process these strings (Gade and Angal, 2018). From the interface developed by LabVIEW, we visualize the data of the digital and analog inputs, and the recording of all the data in Excel files using the computer memory as shown in Fig. 18. In this study, PV system supervision is designed and co-simulations are performed using LabVIEW and MATLAB/Simulink. Solar irradiation and operating temperature are transferred from LabVIEW to MATLAB/ Simulink, so that the reference voltage output from the PSO-RBFNN controller is then transferred from Simulink to LabVIEW. The communication between these two programs is provided by the UDP block that runs in MATLAB and LabVIEW. The front panel of the PV interface is shown in Fig. 19.
(25) (26)
where Ppv (k ) and Ipv (k ) are the instant power and current of the photovoltaic module respectively. Seven fuzzy levels are used for all the input and output variables: NL (Negative Large), NM (Negative Medium), NS (Negative Small), ZE (Zero), PS (Positive Small), PM (Positive Medium) and PL (Positive Large). The theoretical rules design is based on the fact that if the change in the current causes the power to increase, the moving of the next change is kept in the same direction, otherwise the next change is reversed. After the theoretical design, all the MFs and the rules were adjusted by the trialand error to obtain the desired performance. The proposed rules are shown in Table 3. The fuzzy rules are designed to track the maximum power point of the photovoltaic system under changing weather conditions. Rapidly changing solar radiation is taken into account while designing these rules.
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photovoltaic generator
Current sensor ACS712 + voltage divider
Whether Link Davis Vantage
Load
PC WITH UDP LABVIEW MATLAB DC-DC Boost Converter
MyRio Card
Fig. 22. Experimental setup of the virtual instrumentation system.
To evaluate the performance of the proposed MPPT system, by an experimental study, it is necessary to give the LabVIEW model carried out which is indicated in Fig. 21.
Table 4 Parameters of the boost converter. Input Voltage
Vin = 20 70 V
Designed Parameter
Rated Output Voltage Rated Output Current Rated Output Power Switching Frequency
V0 = 100 V I0 = 6 A P0 = 600 W fs = 50 KHz
C1 Q1 L1 D1
4. Experimental results and discussion
66 μf IRFP460 2 mH STPS20150CT
In order to validate the LABVIEW model, the PV test system of Fig. 22 is installed. It consists of a DC-DC converter witch is connected with a solar system of two HYM 250 W panels mounted in series, a resistive load of 20 Ω and a control myRio board on which the control algorithms are implemented. The open circuit voltage (Voc ) and the short-circuit current (Isc ) of the PV panel are respectively 45.6 V and 8.78 A. The parameters of the PV panel are listed in Table 1, and the specifications of the power converter are listed in Table 4. To check the designed system, an experiment was performed. The experiment consists in checking the response time and the operational efficiency of the MPP search when the load is subjected to different test conditions. Fig. 23 shows solar irradiation and ambient temperature versus time for typical sunny day delivered by pro-Weather Link Advantage.
There are many parameters, information and data shown on the LabVIEW front panel interfaces. They are illustrated as follows: Area 1: Parameter input areas of irradiance, temperature. Area 2: Display electrical data at panel output (output voltage, current) and waveforms. Area 3: View electricity data at the output of the DC DC converter and waveforms. Area 4: Display the reference voltage that corresponds to the maximum power. Area 5: Display area of duty cycle at the input of the DC DC converter. Area 6: The efficiency of tracking of MPPT. The Simulink blocks of UDP send and UDP receive from the DSP System Toolbox is shown in Fig. 20. MATLAB data are received in a subsystem and the vector is decomposed in the control variables (temperature, irradiation) used in the controller block. The block output, manipulated variables (voltage and current reference) are merged into a vector and sended to LabVIEW.
4.1. Behavior of the system In this section, we compare through the application experience, the convergence towards the MPP concerning the output power of the studied PV system by using one of the four controllers Conventionnel P &O, ANFIS (Esen et al., 2008d), FL control and P&O Algorithm (AlMajidi et al., 2018) and the proposed method PSO-RBFNN.
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Irradiation (w/m²)
800 600 400 200
8:00 8:21 8:42 9:03 9:24 9:45 10:06 10:27 10:48 11:09 11:30 11:51 12:12 12:33 12:54 13:15 13:36 13:57 14:18 14:39 15:00 15:21 15:42 16:03 16:24 16:45 17:06 17:27 17:48
0
Time (HH:mm)
(a)
Temperature (°C)
30
20
10
8:00 8:21 8:42 9:03 9:24 9:45 10:06 10:27 10:48 11:09 11:30 11:51 12:12 12:33 12:54 13:15 13:36 13:57 14:18 14:39 15:00 15:21 15:42 16:03 16:24 16:45 17:06 17:27 17:48
0
Time (HH:mm)
(b) Fig. 23. Pro-Weather Link Advantage data collection: (a) Temperature of PV and (b) Solar irradiance.
As shown in Figs. 24a and 25a, the power tracking of the proposed method turned out to be fast and accurate in finding the right direction, whilst that of the conventional P&O algorithm, ANFIS and FL control and P&O algorithm was lost when there is a rapid change in irradiance and temperature. As a result, the latter methods takes a longer time than the proposed method PSO-RBFNN one to address the phenomenon of research MPP, as shown in Fig. 25a. In addition, the proposed method is more accurate in finding the new MPP after the changes in weather conditions, and it has a smooth oscillation around this value for steady-state conditions compared to others methods, as shown in the zoom of Fig. 25a. The average difference between maximum power and tracking power is less than 5 W with the PSO-RBFNN, but it can reach 10 W with the FLC and P&O algorithm and 15 W with ANFIS controller. Table 5 summarizes the experimental results about tracked power with the studied MPPT controllers for different Irradiations and temperature. It is clear that the power generated when using the PSORBFNN technique was greater than 99% under all test conditions.
where P (t ) is the generated power at certain time, and Pmax (t ) is the theoretical maximum generated power at the same time. The actual power is calculated using the PV array current and voltage sensors. The theoretical maximum power calculated using Eqs. (1), (2), (5) and (8). The tracking time (t) is calculated according to the ability of the power tracking to reach the MPP under varying weather conditions. Whilst the MPPT efficiency of the proposed method appears to be lower, it achieves an average tracking efficiency of 99.04% under all the varying weather condition, whereas those for FL control and P& O algorithm and P&O-MPPT methods are 98.7%, and 97.1%, respectively. ii. The Integral of the Squared Error (ISE): It is an analytical manipulation method using linear quadratic weights to minimize the difference between the system output and a value of a desired order. This difference may be due to either a change of order or perturbations in the system. It is calculated using Parseval’s theorem that states the integral or sum of the squares of the function equals to the square of its transform. The Integral of the Squared Error (ISE) is given by:
4.2. Performance criteria of MPPT controllers In order to evaluate the performances of differents types of the studied controllers, a comparison of the efficiency criterion was made.
ISE =
i. The efficiency criterion η of a MPPT controller defined by:
=
P (t ) Pmax (t )
100
t 0
[e (t )]2 dt
(28)
where
e (t ) =
(27)
13
Ppv Vpv
(29)
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(a)
Rapid change in values of meteorological
(b) Fig. 24. PV module system for the proposed method versus conventional P&O under rapidly changing weather conditions: (a) power and (b) voltage.
In our research, for the different studied MPPT controllers, Table 6 sums up the calculation results of the performance and the ISE criterion. According to the definitions above of η and ISE criteria, we note that for obtain the more efficient and faster MPPT, we must have a higher η and lower ISE. The obtained results show that the use of proposed MPPT controller improves considerably and efficiently the performance of the PV plants. The comparison made between these four types of controllers confirm that the use of PSO-RBFNN controller enables not only the minimization of ISE criteria, which reduces the response time of the controller, but also improve the MPPT controller performance η, which aims at diminishing fluctuations in transients operation mode. This increases the efficiency of the MPPT controller type PSORBFNN and definitely ensures the improvement of stability around the MPP.
power points. among maximum power point tracking methods for photovoltaic systems include those based on an estimated search mechanism such as the adaptive neural network with a fuzzy system inference system (ANFIS) and the radial base function neural Network (RBFNN) which can easily reach PPGM as soon as the search algorithm is launched. These last techniques suffer from two problems; the first problem is the robustness and the stability (strong oscillations around the GMPP) of the controller according to the climatic changes. The second problem is that the PSO can be trapped in a local optimum which slows down the convergence speed. In addition, the use of the nearest p-neighbor algorithm to calculate RBF unit widths results in loss of information about the spatial distribution of the training data set. To overcome these drawbacks, a new adaptive version of particle swarm optimizer in high-dimensional data has been applied. This combination method based on the RBF neural network, and PSO showed a better MPPT energy efficiency compared to the proposed approaches. The MPPT energy efficiencies for RBFNN-FLC, FLC and P& O algorithm, and ANFIS based on weather variations are 99.04%, 98.7% and 97.1%, respectively. The Experimental results obtained from PV system show a fast convergence speed and a considerable reduction of the oscillations of the output power.
5. Conclusions The weather, complicit with its many weather variations such as temperature and solar irradiation, generates many peaks in the P-V curve, one maximum global power point and several local maximum
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(a)
Rapid change in values of meteorological
(b) Fig. 25. PV module system for the proposed method versus ANFIS and (FL control and P&O Algorithm) under rapidly changing weather conditions: (a) power and (b) voltage. Table 5 Tracked power under various values of irridation G and temperature T. Time HH:mm
11:30 14:40 14:03 12:45 11:15
Irradiance level (w/m2)
350 450 580 600 680
Temperature (°C)
16 18.4 17.8 17.7 16
Max Tracked PV power (W)
130 310 405 380 250
Parameters
PSORBFNN
ANFIS
FLC and P&O algorithm
Conventionnel P&O
η (%)
99.04 0.185
97.1 0.94
98.7 0.202
96.3 5.324
6
Tracking efficiency (%)
PSO-RBFNN
FLC and P&O
ANFIS
PSO-RBFNN
FLC and P&O
ANFIS
126.5 305.5 401.2 377 247.7
125.2 302.2 398 374 245
122.8 297 391.7 370 243
97.30 98.54 99.06 99.21 99.08
96.3 97.48 98.27 98.42 98.00
94.46 95.80 96.71 97.36 97.20
References
Table 6 Performance criteria of MPPT controller.
ISE·10
Tracked PV power (W)
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