Figure 1.
Illustration of a photovoltaic system.
Citation: Ajitanshu Vedrtnam, Kishor Kalauni, Sunil Dubey, Aman Kumar. A comprehensive study on structure, properties, synthesis and characterization of ferrites[J]. AIMS Materials Science, 2020, 7(6): 800-835. doi: 10.3934/matersci.2020.6.800
| [1] | Nalin Fonseka, Jerome Goddard Ⅱ, Alketa Henderson, Dustin Nichols, Ratnasingham Shivaji . Modeling effects of matrix heterogeneity on population persistence at the patch-level. Mathematical Biosciences and Engineering, 2022, 19(12): 13675-13709. doi: 10.3934/mbe.2022638 |
| [2] | Nazanin Zaker, Christina A. Cobbold, Frithjof Lutscher . The effect of landscape fragmentation on Turing-pattern formation. Mathematical Biosciences and Engineering, 2022, 19(3): 2506-2537. doi: 10.3934/mbe.2022116 |
| [3] | Nancy Azer, P. van den Driessche . Competition and Dispersal Delays in Patchy Environments. Mathematical Biosciences and Engineering, 2006, 3(2): 283-296. doi: 10.3934/mbe.2006.3.283 |
| [4] | James T. Cronin, Jerome Goddard II, Amila Muthunayake, Ratnasingham Shivaji . Modeling the effects of trait-mediated dispersal on coexistence of mutualists. Mathematical Biosciences and Engineering, 2020, 17(6): 7838-7861. doi: 10.3934/mbe.2020399 |
| [5] | Eric Ruggieri, Sebastian J. Schreiber . The Dynamics of the Schoener-Polis-Holt model of Intra-Guild Predation. Mathematical Biosciences and Engineering, 2005, 2(2): 279-288. doi: 10.3934/mbe.2005.2.279 |
| [6] | Robert Stephen Cantrell, Chris Cosner, William F. Fagan . The implications of model formulation when transitioning from spatial to landscape ecology. Mathematical Biosciences and Engineering, 2012, 9(1): 27-60. doi: 10.3934/mbe.2012.9.27 |
| [7] | Chang-Yuan Cheng, Kuang-Hui Lin, Chih-Wen Shih . Coexistence and extinction for two competing species in patchy environments. Mathematical Biosciences and Engineering, 2019, 16(2): 909-946. doi: 10.3934/mbe.2019043 |
| [8] | Kuang-Hui Lin, Yuan Lou, Chih-Wen Shih, Tze-Hung Tsai . Global dynamics for two-species competition in patchy environment. Mathematical Biosciences and Engineering, 2014, 11(4): 947-970. doi: 10.3934/mbe.2014.11.947 |
| [9] | Jesus R. Artalejo, A. Economou, M.J. Lopez-Herrero . Evaluating growth measures in an immigration process subject to binomial and geometric catastrophes. Mathematical Biosciences and Engineering, 2007, 4(4): 573-594. doi: 10.3934/mbe.2007.4.573 |
| [10] | Jacques A. L. Silva, Flávia T. Giordani . Density-dependent dispersal in multiple species metapopulations. Mathematical Biosciences and Engineering, 2008, 5(4): 843-857. doi: 10.3934/mbe.2008.5.843 |
There has been significant progress in conducting research in the photovoltaic (PV) field over the last decade [1,2,3,4]. PV energy is generated by the conversion of sunlight and temperature. The particular interest in PV energy has driven researchers to enhance and optimize the efficiency of energy conversion within PV systems [5,6,7,8]. The autonomous functioning of a PV system in optimal conditions requires the optimization of several physical parameters related to the PV generator used [9,10,11]. Therefore, introducing an electronic converter between the PV generator and the load is essential. A step-up converter is suitable to achieve the goal of the studied work [12,13,14]. Indeed, as defined by the duty cycle, the factor characterizing the step-up device should be controlled by a specific technique of the PV power maximization [15,16].
In the literature, the numerous documented power maximization techniques are classified into three categories namely: Classical iterative methods, revolutionary methods based on artificial intelligence and hybrid methods [17,18,19,20]. The first class is mainly based on processing instantaneous values of power, currents and voltages, such as Perturb & Observe (P & O) and Incremental Conductance (INC). The second class includes techniques based on artificial intelligence, such as Artificial Neural Networks (ANN) and Fuzzy Logic (FL). On the other hand, the third class includes the techniques defined by the combination of two or more maximum power point tracker (MPPT) methods, namely the following: The hybrid two-stage adaptive method, the novel Lyapunov-based rapid and ripple-free method, and the adjustable variable step based MRAC method. In [21], the P & O method was observed with an oscillatory convergence around the maximum power point (MPP), thus causing instability and a margin of error in the found power value. These oscillations are explained by the difference between two instantaneous power values. Loukriz et al. [22] presented the INC method, known by its damped oscillation due to the small convergence step generated by the ratio of the instantaneous variation of current to the instantaneous variation of voltage. On the other hand, Goel et al. [23] displayed the ability of the ANN tool to rapidly and intelligently predict the value of the duty cycle to control the used converter. Moreover, [24] describes the converter control strategy as a set of linguistic rules that allow the value to reach the desired MPP quickly with a better performance. The hybrid, two-stage, adaptive MPPT method proposed by [25] is formed by two stages: The first stage presents a control block to find the reference voltage for each MPP; and the second stage is an adaptive model reference controller block that determines concise values of the duty cycle to hold on stable the found MPP. This strategy shows high performances under varying irradiances and temperatures. Manna et al. [26] suggested a Lyapunov-based robust model reference adaptive controller to quickly find the MPP for rapid variations in irradiance, temperature and output load. Singh et al. [27] experimented with an efficient technique for different weather scenarios defined by an adjustable P & O variable step.
In a detailed study, we separately applied P & O and ANN as an MPPT method to control a boost converter and closely observed their efficiencies and performances. We found that P & O is accurate, unstable, and sensitive to initial values while ANN is less accurate, stable, and did not require initial values. We combined these two techniques with the aim to start the convergence by ANN trained by the Levenberg-Marquardt (LM) method to approach the optimum of the duty cycle and then hand it over to P & O to continue the convergence. Therefore, the obtained method is sensitive to the irradiance changes considerably affecting the precision. These results can be explained by the high sensitivity of P & O toward the changing climatic conditions [28].
While trying to take advantage of the intelligent prediction quality of ANN and its low sensitivity towards initial values, we thought of improving its training process to enhance its low precision. In principle, the LM is the most used method to ensure the learning of ANNs. In the literature, the convergence of gradient descent methods, such as LM and Gauss-Newton (GN) tends towards a local minimum knowing that the shape of the error function to be optimized can have either a single global minimum or several local minimums [29]. This can explain the low precision observed when searching for MPP by an ANN trained by LM. On the other hand, in [30], we proposed an LM combined with simulated annealing (SA) for the parameter identification of the single diode model of the solar cell and we obtained the most accurate results compared to those reported in the literature. The interest behind the use of SA is interpreted by the existence of several local minima in the shape of the error function according to the damping factor, thus characterizing the equation of the LM method. In the present paper, for the first time, we proposed to combine the conventional GN method with the heuristic technique SA (GNSA) to guarantee global convergence during the optimization process treated in the training of ANN. Indeed, GNSA is proposed to ensure the training of the ANN network by adjusting the characteristic weights and bias wij, wjm, bij and bjm to predict the correct value of the duty cycle corresponding to a defined value of temperature and irradiance.
The three techniques (i.e., P & O, ANN and ANN-P & O) were studied to establish a comparative study and highlight the effectiveness of the proposed ANN trained by the GNSA (ANN-GNSA) approach. After an in-depth study under variable irradiance and temperature, it is observed that the proposed ANN-GNSA method demonstrates a significant efficiency, a good accuracy during the search for the MPP and a high robustness towards the meteorological condition's variation.
The main contributions of this work are presented as follows:
√ For the first time, this paper proposed the novel ANN-GNSA approach to precisely track the right MPP into a PV system based on a step-up converter with a high speed of convergence under variable irradiance and temperature values.
√ The idea behind the proposition of the improved GNSA to train the ANN network is explained by its descent directions quality guided by the globally convergent SA method to adjust correctly the weights and the bias of the hidden and the output layer of ANN tool at each iteration.
√ A fair comparison is carried out between the outcomes of the proposed method and those obtained by the P & O, ANN and ANN-P & O approaches to demonstrate the high performances of ANN-GNSA in terms of its outstanding accuracy and the speed of convergence toward the desired MPP.
• First, the ANN-GNSA is studied at fixed meteorological conditions (G = 1000 W/m2 and T = 25℃), where it reaches the right MPP = 18.59 W during a convergence time of 0.04832 s.
• The proposed method controls the step-up converter under variable irradiances G = [200 W/m2, 300 W/m2, 700 W/m2, 1000 W/m2, 800 W/m2, 400 W/m2], with an efficiency of 99.54% and under variable temperatures T = [15℃, 35℃, 45℃, 5℃] with an efficiency of 99.98%. The tracking of MPP in the both cases is ensured with a high speed compared to P & O, ANN and ANN-P & O.
The functioning within a direct connection between a PV generator (GPV) and a load is carried out according to a non-optimal power. Certainly, the power transmitted by a GPV to the output might not align with the maximum power [31].
For this purpose, it is essential to utilize an impedance adaptation stage in direct-direct mode (DC-DC) in order to optimize the power at the output of the GPV. In this context, a step-up (Boost) chopper-type static electronic converter presents the most appropriate device for this work. A suitable MPPT settling the duty cycle of the boost device to its optimal values presents the appropriate solution to maximize the power and enable the optimal operation of the PV system.
A PV module is a collection of solar cells generating continuous electrical energy. The mode of connection of the cells, either in series or in parallel, is carried out according to the energy requirement of the PV voltage or the PV current [32].
The equivalent circuit of a PV module based on a single diode is simply the same circuit of the PV cell but scaled by Ns. The latter presents the count of solar cells linked in series. The multiplication by Ns is applied for series resistance (Rs), parallel resistance (Rsh) and the diode's ideality factor (n) [33].
Iph is the photocurrent, Is denotes the diode's saturation current, IPV indicates the PV current and VPV presents the PV voltage.
The mathematical equation deduced from the electrical characterization of the PV module, formulating Rs, Rsh, Iph, Is and n parameters as a function of IPV and VPV is presented by Eq 1 [34].
| IPV=Iph−Is[exp(VPVNs+RsIPVnVth)−1]−VPVNs+RsIPVRsh | (1) |
where Vth is the thermal voltage calculated using (A. T)/q, A presents the Boltzmann constant equal to 1.3806503 × 10-23 J/°K, q denotes the charge of the electron equal to 1.60217646 × 10-19 C and T is the temperature of the cell measured in Kelvin.
The expression of the five intrinsic parameters of the PV module in terms of climatic factors is crucial to establish a faithful representative model. Eqs (2) and (3) allow the modelling of a GPV, and show the relation with the irradiance (G) and the temperature (T) [35,36]:
| IPV=(IPV,n+KiΔT)GGn | (2) |
| Is=Isc,n+KiΔTexp(q(Voc,n+KiΔT)nVth)−1 | (3) |
where ΔT denotes the variation between the given T and Tn which is the nominal value of T, Voc, n is the nominal value of the open circuit voltage, Gn presents the nominal value of the irradiation, IPV, n indicates the nominal value of the photovoltaic current, Ki is the coefficient of the current and Isc, n presents the short circuit current of the solar cell.
In this study, a boost type static electronic converter was used to increase the energy coming from the module intended to supply the output load. Figure 3 illustrates an electrical circuit of the boost converter based on an inductance L, an input capacitance Cint, an output capacitance Cout, a diode D, and a Mosfet K controlled by the duty cycle at its trigger [37].
VPV is the generated voltage by the PV module, Vs is the voltage at the output load and ipv is the input current.
The duty cycle D is calculated as follows:
| D=VD−VPV+VsVD+Vs−Vsw | (4) |
where VD is the diode voltage, Vs is the output voltage at the load, Vsw is the Mosfet voltage and VPV is the voltage at the output of the PV module.
The inductance L is found by Eq 5 using ripple current inductors ΔiL [38]:
| L=VPV(Vs−VPV)ΔiL×fs×Vs | (5) |
where fs is the switching frequency of the step-up device.
The value of the input capacitance can be found by the following equation [38]:
| C=Is(max)×Dfs×ΔVs | (6) |
To guide the module towards its operating MPP, the power optimization process requires a specific mechanism called the "maximum power point tracker" (MPPT) settling an adaptation stage [39,40,41].
To achieve this, the implementation of a specific MPPT method is crucial. The most prevalent power maximization methods reported in the literature include the following:
• The conventional perturbation & observation (P & O) method,
• The classical artificial neural network (ANN) method,
• The ANN in conjunction with the P & O method.
These methods have been studied to underscore the performance of the novel ANN-GNSA methods.
As its name indicates, the P & O method applies perturbations at the VPV voltage and observes the sign of the instantaneous power variation in order to decide the convergence direction [21].
The perturbation is ensured by applying either positive or negative adjustments, depending on the convergence orientation towards the MPP point. This process first begins by incrementing the voltage by adding a positive step. This increment addition operation is adopted if the adjusted value of the generated power is always positive. Once this variation turns negative, the voltage is either decreased or increased by either a negative step or by a positive step, respectively, depending on the position of the functioning point, placed either on the left or on the right of the MPP, respectively.
Due to its black box characteristic, this tool allows us to model problems without any prior knowledge of the physical or theoretical functioning of a system. The ANN helps to establish a significant liaison between its inputs and outputs. This connection is ensured by updating the characteristic parameters, named "weights" (wij and wjm) and "bias" (bij, bjm), thus marking its internal structure formed by layers of neurons [23].
The neural network operates as a MPPT command to automatically generate the exact duty cycle according to the temperature (T) and the irradiance (G) values given at the input. The effectiveness of an ANN highly depends on the success of the learning process as well as on the optimal number of hidden neurons, which was fixed at six neurons in this study. The learning process is generally ensured by the LM method whose training principle is based on the backpropagation technique. Typically, the inputs of the ANN network are T and G, and the output is simply represented by the duty cycle D, which is intended to control the activation of the chopper Mosfet. The proposed ANN network aimed to find the PPM point, which is illustrated as follows:
where i refers to the index of the output layer, j pertains to the index of the hidden layer, m denotes the index of the input layer, wij signifies the weight linking the hidden neurons to the output, wjm represents the weight linking the input neurons to the hidden ones, bij indicates the bias of the output neurons and bjm denotes the bias of the hidden neurons.
The generation of the exact value of the duty cycle strongly depends on the learning accuracy of the network and the optimal number of the hidden neurons. The training process mainly requires an experimental database presenting the examples (T, G), as well as the corresponding values of the duty cycle D. The database D = f (G, T) used in this paper includes 600 examples sweeping a large margin of T and G, thus allowing the network to be able to predict the exact value of D regardless of the value of T and G.
The training process is divided into two stages: the learning stage and the testing stage. During the learning stage, almost 500 examples are provided to the network during the convergence of the classical LM algorithm. During this phase, the network intelligently learns how to predict the value of the D factor according to T and G, which are given as inputs. The prediction capacity and efficiency of the network are demonstrated during the test phase using 100 examples of data D = f (G, T), which are completely different from the examples already processed during the learning stage.
The studied objective function "mean of sum squared errors (MSSE)" is defined as follows [42]:
| MSSE=1N∑Nr=1[∑Nsi=1[(Dpredicted(i,r)−Dtarget(i,r))2]] | (7) |
where N is the number of examples, Ns is the number of output neurons, r denotes the index of the used target data, I indicates the index of the used output, Dpredicted presents the output value computed by the network and Dtarget is the target value of the output.
The principle of this approach consists of starting the execution of the algorithm with the ANN model. The predicted value of D, which is close to the optimal one, is taken by the P & O method as an initial value to continue its convergence and judiciously seek the exact value of D corresponding to the MPP [43].
After correctly training the ANN network with approximately 600 examples of D = f (T, G) during the two phases (i.e., learning and testing in the optimization process and identification of the correct values of the weights and the bias), the ANN tool provides the well-determined wij, wjm, bij and bjm, which are able to predict the correct value of the duty D for any value of T and G.
The ANN executed first in the ANN-P & O algorithm is merely presented as a feedforward equation Eq 8 based on the well-identified wij, wjm, bij and bjm, thus resulting from the training process [44].
| D=Fs[∑Nsi=1[wijFc(∑Ncj=1(wjmxm+bjm))+bij]] | (8) |
I denotes the index of the output neurons, j presents the index of the hidden neurons, m is the index of the input neurons, yi indicates the output of the network, xm is the inputs of the network [T, G], Fs is the activation function of the output neurons, Fc is the activation function of the hidden neurons and Nc is the number of hidden neurons.
The GN method is a conventional iterative technique aimed to ensure a parameter identification using descent directions dn. In this paper, GN is used to train the ANN network through the adjustment of the weights and the biases wij, wjm, bij and bjm at each iteration n during the optimization process of the MSSE error function, according to the following expressions cited in [45]:
| θn+1=θn+αdn | (9) |
| dn=−J'ϵJ'J | (10) |
where dn is the descent direction at an iteration n, J is a matrix formed by four Jacobeans or the first four derivatives functions of Eq 8, J' presents the transpose of the Jacobean, α indicates either the step size factor or the length of descent direction, ϵ denotes the generated error between the computed Eq 8 and the experimental Dtarget, θ is the vector of the fours weights and biases to be adjusted [wij, wjm, bij, bjm] and n is the number of iterations.
The convergence of the GNSA algorithm requires declares the initial value of θ and the expression of either the four first derivatives or the Jacobeans "J" of Eq 8 at the start of its code. The latter presents D(θ). Each Jacobean among the four ones is obtained by deriving D(θ) according to a parameter from the four (wij, wjm, bij, bjm) parameters, such as: J = [δD/δwijδD/δwjmδD/δbijδD/δbjm]. During its execution, at an iteration n, GNSA determines the optimal value of αn by the SA technique and multiplies this value to the calculated value of the descent direction dn (Eq 10). The resulting value is added to the previously found value of θn to generate the adjusted value θn+1 to be processed during the next iteration. Just after, the iteration of n increments and this principle of GNSA functioning loops until finding the good value of θ, corresponding to the minimum error of MSSE.
The SA approach was chosen after a further study of the behavior of MSSE according to large marge of α values at each iteration n of GNSA convergence during the training of the ANN. From this, the MSSE is observed with many local minima. To reach the global minimum, the SA is executed at each run of GN to find the most precise α value that leads to a good identification of the weights and the biases wij, wjm, bij and bjm. This combination between the GN and SA techniques defined by GNSA is used in this research as a new neural network training approach presented by the enhanced ANN-GNSA method.
The training process of the ANN by the novel optimization GNSA technique is illustrated in the following flowchart and then explained in detail step by step.
Step 1: - Give the experimental samples of the inputs (T, G) and the output D,
- iteration n = 1,
- Simultaneously start the two stages of learning and the test,
Step 2: - Learn the ANN model by the improved GNSA method using the characteristic equations Eq. 9 and Eq. 10 to adjust the four parameters θ = [wij, wjm, bij, bjm],
-The learning phase is carried out using its own experimental data of D and (T, G), fixed at 500 examples,
Step 3: - Compute the MSSElearning criterion at an iteration n based on 100 examples of test.
Step 4: - Give the adjusted weights θn at an iteration n,
Step 5: - Compute the feedforward equation Eq 8 based on the learning examples and by using the adjusted weights θn at a fixed iteration n,
- Compute the feedforward equation Eq 8 based on the 100 examples of the test data and by using the adjusted weights θn obtained at the same iteration n,
Step 6: - Compute the H(n) = MSSEtest criterion,
Step 7: - If H(n) < H(n - 1)
• Reset a counter variable "c = 0",
• Increment the iteration n = n + 1,
• Loop to step 2.
- Otherwise, increment the counter variable c = c + 1
Step 8: - If c different to 6
• Loop to step 2,
- Otherwise, if c equal to 6
• Stop the training process,
Step 9: Give the optimal and the well-adjusted value of the θ parameter.
To emphasize the efficiency of the new method, three techniques (P & O, ANN and ANN-P & O) have been examined in a detailed study to compare their results with those obtained by the new ANN-GNSA method.
The used PV module is Solarex MSX-20L. It is comprised of 36 cells attached in series and characterized by the parameter's values shown in Table 1. On the other hand, the overall parameters values characterizing the structure of the step-up converter is shown in Table 2.
| Parameters | Values |
| Maximum power Pmax | 20 W |
| Current at maximum power IMPP | 1.17 A |
| Voltage at maximum power VMPP | 17.1 V |
| Short-circuit current Icc | 1.27 A |
| Open-circuit voltage Vcc | 20.8 V |
DownLoad:
CSV
| Parameters | Values |
| Input capacitor Cin | 771.6 µF |
| Inductance L | 189.8 µH |
| Switching frequency f | 30 kHz |
| Output capacitor Cout | 57.16 µF |
DownLoad:
CSV
The control of a PV system is given by the "MPPT" subsystem which contains the code of the algorithm being processed (P & O, ANN, ANN-P & O or ANN-GNSA). The load connected to the output is a 30 Ω resistor.
Equations (1), (2) and (3) have been implemented as blocks in the "Solarex module" subsystem to emulate the PV module, as shown in Figure 11.
The graphical presentation of the boost converter is shown in the model illustrated in Figure 4. The corresponding model is presented by the hereby illustration.
A fixed value of the pair (G, T) corresponds to a given value of the response IPV(VPV). In this study, several responses measured experimentally for 600 different values of the pair (G, T) of the Solarex module were taken into consideration. Figures 13 and 14 show some experimental curves of IPV(VPV) for the variables G and T.
In order to extract all 600 values of D to be called out during the training of ANN at its output, we proposed to execute a P & O algorithm to generate the corresponding value of D for a precise curve of PPV (VPV). PPV is obtained by multiplying the VPV and the IPV. The P & O algorithm used is performed 600 times for 600 different PPV (VPV) curves obtained for 600 different values of T and G. The examples considered during the training process are formed by (G, T) and D.
Five hundred examples of D = f (G, T) are used during the learning of ANN-GNSA and 100 examples D = f (G, T) are employed during the test of its effectiveness.
The number of hidden neurons have been judiciously studied by observing MSSEtest for different number of hidden neurons, where 15 is the optimal number at which the obtained MSSEtest is the lowest one, as shown in Figure 15.
The learning process of ANN-GNSA is based on the minimization of the objective function MSSElearning. Figure 16 shows a decreasing curve until the iteration 270. The learning stop is decided at iteration 223 instead of 270 to avoid over-learning caused by the memorization of the network of the set of examples D = f (G, T), which leads to an erroneous prediction of the values of D at the output.
A good decision of the learning stop is made based on the convergence of ANN-GNSA during the test phase. Indeed, when the MSSEtest curve successively increases six times during a decrease of MSSElearning, the learning of the ANN should stop (Figure 17).
The values of D found by ANN-GNSA are shown in Figure 18. An illustration of the target values and the predicted values of D in the same figure shows the compatibility amongst the two, which proves the effectiveness of ANN-GNSA.
To shed light on the exact maximum power value reached by each MPPT method (P & O, ANN, ANN-P & O or ANN-GNSA), the PPV have been presented according to time in Figure 19. The real target maximum power PPV corresponding to G = 1000 W/m2 and T = 25℃ is set at 18.59 W. As it is clearly seen, the ANN-GNSA method runs into an MPP equal to 18.59 W during 0.04382 s as compared to 18.55 W at 0.06667 s for the ANN-P & O, 18.28 W at 0.08008 s for the ANN and a range of power [18.31 W – 18.57 W] during [0.05808 s – 0.09156 s] for the P & O. Therefore, the proposed MPPT technique is the fastest and the most precise to track the right MPP value.
The generated value of the control factor D of the step-up converter varies depending on the used MPPT method. Indeed, Figure 20 shows that the values of D given by the P & O are changeable, thus leading to oscillations at the PPV curve (Figure 19). D is fixed at 0.3103 for the ANN and at 0.28 for the ANN-GNSA, where the second one is best explained by the achieved power PPV = 18.59 W, which is considered the desired value. On the other hand, the ANN-P & O starts from the value of D = 0.3103 generated by the ANN and converges to a value of D = 0.2863 close to that provided by the ANN-GNSA. From these observations, we deduce that the value of D = 0.28 is the most optimal value for G = 1000 W/m2 and T = 25℃.
In Figure 21, the evolutions of PPV(VPV) obtained by the four studied MPPT methods were also taken into consideration. In the latter a vertical offset of 0.5 W is established between the four curves to shed light on the tracking accuracy provided by the improved ANN-GNSA method.
The P & O, ANN and ANN-P & O methods can't correctly achieve the right MPPs, as is the case of G = 300 W/m2 and G = 400 W/m2. On other hand, the ANN method is less efficient at tracking the desired MPPs; it remains stuck in its neighborhood, especially in the case of G = 200 W/m2, G = 300 W/m2, G = 1000 W/m2 and G = 400 W/m2. However, the ANN-P & O and the proposed ANN-GNSA are more efficient in reaching the correct MPP values.
To evaluate the performance of the P & O, ANN, ANN-P & O and ANN-GNSA techniques to reach to optimal value of MPP, we are based on the convergence time to be concluded from Figure 22 and on the tracking efficiency η to be calculated from the obtained maximum PPV (MPP) of each MPPT method through the following expression [46]:
| η=PPVmeanPPVmax | (11) |
where PPVmean is the mean PV power delivered by the photovoltaic module, and PPVmax is either the maximum PV power or the MPP.
Table 3 shows the optimal power MPP to achieve at each irradiance, as well as the maximum power generated by each method among the four methods. The quality of the tracking of MPP by each technique is illustrated by the calculated efficiency values and by the reached convergence time (tc).
| G(W/m2) |
Target MPP (W) |
P & O | ANN | ANN-P & O | ANN-GNSA | ||||
| Obtained MPP (W) |
tc(s) | ObtainedMPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | ||
| 200 | 1.858 | 1.586 | 0.1095 - 0.1152 | 0.4517 | 0.0239 | 1.553 | 0.1766 | 1.613 | 0.1 |
| 300 | 4.026 | 3.437 | 0.5772 - 0.5831 | 2.243 | 0.5659 | 3.371 | 0.6028 | 4.026 | 0.5887 |
| 700 | 12.72 | 12.68 | 1.045 - 1.047 | 12.7 | 1.038 | 12.72 | 1.105 | 12.72 | 1.04 |
| 1000 | 18.59 | 18.55 | 1.541 - 1.549 | 18.28 | 1.547 | 18.55 | 1.66 | 18.59 | 1.517 |
| 800 | 14.69 | 14.61 | 2.025 - 2.039 | 14.63 | 2.032 | 14.67 | 2.082 | 14.67 | 2.005 |
| 400 | 6.676 | 5.9 | 2.598 - 2.604 | 5.766 | 2.606 | 6.076 | 2.624 | 6.676 | 2.594 |
| η (%) | 96.93 | 92.34 | 97.28 | 99.54 | |||||
DownLoad:
CSV
The P & O, ANN and ANN-P & O approaches take the longest time to reach the MPPs with a significant gap compared to their target values. The proposed ANN-GNSA is faster and tracks the MPP with high efficiency. The convergence time margins for the P & O are [0.1095 s-0.1152 s], [0.5772 s-0.5831 s], [1.045 s-1.047 s], [1.541 s-1.549 s], [2.025 s-2.039 s] and [2.598 s-2.604 s]. For the ANN method, the convergence times are 0.0239 s, 0.5659 s, 1.038 s, 1.547 s, 2.032 s and 2.606 s and for the ANN-P & O method, the convergence times are 0.1766 s, 0.6028 s, 1.105 s, 1.66 s, 2.082 s and 2.624 s. The speed of tracking the MPP by the proposed ANN-GNSA method is considered faster than the other three techniques for G set at (1000 W/m2, 800 W/m2 and 400 W/m2), as it is shown by the convergence times: 1.517 s, 2.005 s, 2.594 s. For a G defined at (200 W/m2, 300 W/m2 and 700 W/m2), the ANN is observed faster than the ANN-GNSA, though less precise in the reached MPP values. The MPP search efficiencies are as follows: 96.93% for the P & O, 92.34% for the ANN, 97.28% for the ANN-P & O and 99.54% for the proposed approach. From these all outcomes, the ANN-GNSA demonstrates its outstanding and its superiority to track the optimal MPP with a high efficiency during less convergence time.
From Figure 24 and Table 4, the ANN-GNSA outperforms the other comparative methods in terms of the convergence times and the efficiency. Indeed, the proposed method has an efficiency of 99.98% as compared to 99.87% for the P & O, 95.98% for the ANN and 99.16% for the ANN-P & O. Moreover, the ANN-GNSA demonstrates its high speed in tracking the MPP for different temperature values: For T = 15℃ the tc = 0.2096 s, for T = 35℃ the tc = 0.8198 s, for T = 45℃ the tc 1.549 s and for T = 5℃ the tc = 2.301 s.
| T(℃) |
Target MPP (W) |
P & O | ANN | ANN-P & O | ANN-GNSA | ||||
| Obtained MPP (W) |
tc(s) | ObtainedMPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | ||
| 15 | 19.39 | 19.32 | 0.2589 | 17.890 | 0.2657 | 19.16 | 0.2266 | 19.37 | 0.2096 |
| 35 | 17.77 | 17.77 | 0.8724 | 17.61 | 0.8741 | 17.61 | 0.8849 | 17.77 | 0.8198 |
| 45 | 17.35 | 17.32 | 1.559 | 16.84 | 1.608 | 17.31 | 1.558 | 17.35 | 1.549 |
| 5 | 20.19 | 20.2 | 2.329 | 19.36 | 2.404 | 20.02 | 2.418 | 20.2 | 2.301 |
| η (%) | 99.87 | 95.98 | 99.19 | 99.98 | |||||
DownLoad:
CSV
A novel and enhanced method, named the ANN trained by GNSA, is proposed in this paper to control a step-up converter within a PV system under varying irradiances and temperatures. The ANN-GNSA is evolved to ensure the fast and accurate tracking of the MPP, under variable irradiance and temperature values, without oscillations. Some MPPT methods such as the P & O, ANN and ANN-P & O are used to shed light on the performances of the proposed controller. For a fixed G = 1000 W/m2 and T = 25℃, the ANN-GNSA has the smallest tracking time (0.04382 s) compared to other MPPT methods [0.05808 s – 0.09156 s] for the P & O, 0.08008 s for the ANN and 0.06667 s for the ANN-P & O. Under a variable irradiance, the obtained efficiency is 99.54% compared to 96.93% for the P & O, 92.34% for the ANN and 97.28% for the ANN-P & O; on other side, the variable temperature is equal to 99.98% as compared to 99.87% for the P & O, 95.98% for the ANN and 99.19% for the ANN-P & O. By varying the irradiance in the margin [200 W/m2, 300 W/m2, 700 W/m2, 1000 W/m2, 800 W/m2, 400 W/m2], the proposed MPPT controller converges faster toward the MPP with convergence times of 0.1 s, 0.5887 s, 1.04 s, 1.517 s, 2.005 s and 2.594 s, respectively. A similar behavior is observed by varying the temperature in the margin [15℃, 35℃, 45℃, 5℃]; the convergence times are 0.2096 s, 0.8198 s, 1.549 s and 2.301 s, respectively. From these outcomes, the enhanced ANN-GNSA is considered a promising MPPT technique due to its outstanding performance under variable irradiances and temperatures.
In a future study, we will lead a comparative study of the behavior and the tracking time of the ANN-GNSA implemented on FPGA, Arduino and on a microcontroller.
The author declares that Artificial Intelligence (AI) tools are not used in the creation of this article.
The author declares that there is no conflict of interest in this paper.
| [1] | Adam JD, Davis LE, Dionne GF, et al. (2002) Ferrite devices and materials. IEEE T Microw Theory 50: 721-737. |
| [2] | Pullar RC (2012) Hexagonal ferrites: A review of the synthesis, properties and applications of hexaferrite ceramics. Prog Mater Sci 57: 1191-1334. |
| [3] | Dairy ARA, Al-Hmoud LA, Khatatbeh HA (2019) Magnetic and structural properties of barium hexaferrite nanoparticles doped with titanium. Symmetry 11: 732. |
| [4] | Snelling EC (1988) Soft Ferrites, Properties and Applications, Butterworth-Heinemann Ltd. |
| [5] | Smit J, Wijn HPJ (1959) Ferrites, Eindhoven: Philips Technical Library, 150. |
| [6] | Issa B, Obaidat I, Albiss B, et al. (2013) Magnetic nanoparticles: Surface effects and properties related to biomedicine applications. Int J Mol Sci 14: 21266-21305. |
| [7] | Ammar S, Helfen A, Jouini N, et al. (2001) Magnetic properties of ultrafine cobalt ferrite particles synthesized by hydrolysis in a polyol medium. J Mater Chem 11: 186-192. |
| [8] | Šutka A, Gross KA (2016) Spinel ferrite oxide semiconductor gas sensors. Sensor Actuat B-Chem 222: 95-105. |
| [9] | Veena M, Somashekarappa A, Shankaramurthy GJ, et al. (2016) Effect of 60Co gamma irradiation on dielectric and complex impedance properties of Dy3+ substituted Ni-Zn nanoferrites. J Magn Magn Mater 419: 375-385. |
| [10] | Krishnan V, Selvan RK, Augustin CO, et al. (2007) EXAFS and XANES investigations of CuFe2O4 Nanoparticles and CuFe2O4-MO2 (M = Sn, Ce) Nanocomposites. J Phys Chem C 111: 16724-16733. |
| [11] | Vaidyanathan G, Sendhilnathan S (2008) Characterization of Co1-xZnxFe2O4 nanoparticles synthesized by co-precipitation method. Physica B 403: 2157-2167. |
| [12] | Valenzuela R (2012) Novel applications of ferrites. Phys Res Int 2012: 591839. |
| [13] | Kaur M, Kaur N, Verma V (2016) Ferrites: synthesis and applications for environmental remediation, Ferrites and Ferrates: Chemistry and Applications in Sustainable Energy and Environmental Remediation, American Chemical Society, 1238: 113-136. |
| [14] | Haspers JM (1962) Ferrites: Their properties and applications, In: Hausner HH, Modern Materials, Elsevier, 3: 259-341. |
| [15] | Shaikh PA, Kambale RC, Rao AV, et al. (2010) Structural, magnetic and electrical properties of Co-Ni-Mn ferrites synthesized by co-precipitation method. J Alloy Compd 492: 590-596. |
| [16] | Jaswal L, Singh B (2014) Ferrite materials: A chronological review. J Int Sci Technol 2: 69-71. |
| [17] | Saville P (2005) Review of radar absorbing materials. Defence Research and Development Atlantic Dartmouth (Canada). Available from: https://www.researchgate.net/publication/235178242_Review_of_Radar_Absorbing_Materials. |
| [18] | Meng F, Wang H, Huang F, et al. (2018) Graphene-based microwave absorbing composites: A review and prospective. Compos Part B-Eng 137: 260-277. |
| [19] | Abu-Dief AM, Abdel-Fatah SM (2018) Development and functionalization of magnetic nanoparticles as powerful and green catalysts for organic synthesis. BJBAS 7: 55-67. |
| [20] | Kharisov BI, Dias HR, Kharissova OV (2019) Mini-review: Ferrite nanoparticles in the catalysis. Arab J Chem 12: 1234-1246. |
| [21] | Kefeni KK, Mamba BB, Msagati TAM (2017) Application of spinel ferrite nanoparticles in water and wastewater treatment: A review. Sep Purif Technol 188: 399-422. |
| [22] | Kumar M, Dosanjh HS, Singh J, et al. (2020) Review on magnetic nanoferrites and their composites as alternatives in waste water treatment: synthesis, modifications and applications. Environ Sci-Water Res 6: 491-514. |
| [23] | Reddy DHK, Yun YS (2016) Spinel ferrite magnetic adsorbents: Alternative future materials for water purification. Coordin Chem Rev 315: 90-111. |
| [24] | Stephen ZR, Kievit FM, Zhang M (2011) Magnetite nanoparticles for medical MR imaging. Mater Today 14: 330-338. |
| [25] | Shokrollahi H, Khorramdin A, Isapour G (2014) Magnetic resonance imaging by using nano-magnetic particles. J Magn Magn Mater 369: 176-183. |
| [26] | Pegoretti VCB, Couceiro PRC, Gonçalves CM, et al. (2010) Preparation and characterization of tin-doped spinel ferrite. J Alloy Compd 505: 125-129. |
| [27] | Shokrollahi H, Avazpour L (2016) Influence of intrinsic parameters on the particle size of magnetic spinel nanoparticles synthesized by wet chemical methods. Particuology 26: 32-39. |
| [28] | Ramimoghadam D, Bagheri S, Hamid SBA (2014) Progress in electrochemical synthesis of magnetic iron oxide nanoparticles. J Magn Magn Mate 368: 207-229. |
| [29] | Sechovsky V (2001) Magnetism in solids: General introduction, In: Jürgen Buschow KH, Cahn RW, Flemings MC, et al., Encyclopedia of Materials: Science and Technology, Elsevier, 5018-5032. |
| [30] | Gregersen E (2011) The Britannica Guide to Electricity and Magnetism, New York: Britannica Educational Publishing and Rosen Educational Services. |
| [31] | Ferrimagnetism, Engineering LibreTexts (2020) Avaliable from: https://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Science)/Magnetic_Properties/Ferrimagnetism. |
| [32] | Cullity BD, Graham CD (2008) Introduction to Magnetic Materials, 2 Eds., Wiley-IEEE Press. |
| [33] | Hench LL, West JK (1990) Principles of Electronic Ceramics, Wiley. |
| [34] | Biagioni C, Pasero M (2014) The systematics of the spinel-type minerals: An overview. Am Mineral 99: 1254-1264. |
| [35] | Spinel: mineral, Encyclopedia Britannica (2020) Available from: https://www.britannica.com/science/spinel. |
| [36] | Mineral gallery—The spinel group. Avaliable from: http://www.galleries.com/spinel_group. |
| [37] | Biagioni C, Pasero M (2014) The systematics of the spinel-type mineralas: An overview. Am Mineral 99: 1254-1264. |
| [38] | About: cuprospinel. Avaliable from: http://dbpedia.org/page/Cuprospinel. |
| [39] | Nickel EH (1973) The new mineral cuprospinel (CuFe2O4) and other spinels from an oxidized ore dump at Baie Verte, Newfoundland. Can Mineral 11: 1003-1007. |
| [40] | Pekov IV, Sandalov FD, Koshlyakova NN, et al. (2018) Copper in natural oxide spinels: The new mineral thermaerogenite CuAl2O4, cuprospinel and Cu-enriched varieties of other spinel-group members from fumaroles of the Tolbachik Volcano, Kamchatka, Russia. Minerals 8: 498. |
| [41] | Fleischer M, Mandarino JA (1974) New mineral names. Am Mineral 59: 381-384. |
| [42] | Manju BG, Raji P (2018) Synthesis and magnetic properties of nano-sized Cu0.5Ni0.5Fe2O4 via citrate and aloe vera: A comparative study. Ceram Int 44: 7329-7333. |
| [43] | Liu Y, Wu Y, Zhang W, et al. (2017) Natural CuFe2O4 mineral for solid oxide fuel cells. Int J Hydrogen Energ 42: 17514-17521. |
| [44] | Estrella M, Barrio L, Zhou G, et al. (2009) In situ characterization of CuFe2O4 and Cu/Fe3O4 water-gas shift catalysts. J Phys Chem C 113: 14411-14417. |
| [45] | The mineral Franklinite. Avaliable from: http://www.galleries.com/Franklinite. |
| [46] | Abdulaziz A, Wael HA, Kirk S, et al. (2020) Novel franklinite-like synthetic zinc-ferrite redox nanomaterial: synthesis, and evaluation for degradation of diclofenac in water. Appl Catal B-Environ 275: 119098. |
| [47] | Lucchesi S, Russo U, Giusta AD (1999) Cation distribution in natural Zn-spinels: franklinite. Eur J Mineral 11: 501-512. |
| [48] | Palache C (1935) The Minerals of Franklin and Sterling Hill, Sussex County, New Jersey, US Government Printing Office. |
| [49] | Jacobsite. Avaliable from: https://www.mindat.org/min-2061.html. |
| [50] | Deraz NM, Alarifi A (2012) Novel preparation and properties of magnesioferrite nanoparticles. J Anal Appl Pyrol 97: 55-61. |
| [51] | Magnesioferrite. Avaliable from: https://www.mindat.org/min-2501.html. |
| [52] | Banerjee SK, Moskowitz BM (1985) Ferrimagnetic properties of magnetite, In: Kirschvink JL, Jones DS, MacFadden BJ, Magnetite Biomineralization and Magnetoreception in Organisms: A New Biomagnetism, Boston: Springer, 17-41. |
| [53] | Wasilewski P, Kletetschka G (1999) Lodestone: Natures only permanent magnet-What it is and how it gets charged. Geophys Res Lett 26: 2275-2278. |
| [54] | Blaney L (2007) Magnetite (Fe3O4): Properties, synthesis, and applications. Lehigh Rev 15: 33-81. |
| [55] | O'Driscoll B, Clay P, Cawthorn R, et al. (2014) Trevorite: Ni-rich spinel formed by metasomatism and desulfurization processes at Bon Accord, South Africa? Mineral Mag 78: 145-163. |
| [56] | About: Trevorite. Avaliable from: http://dbpedia.org/page/Trevorite. |
| [57] | de Paiva JAC, Graça MPF, Monteiro J, et al. (2009) Spectroscopy studies of NiFe2O4 nanosized powders obtained using coconut water. J Alloy Compd 485: 637-641. |
| [58] | Mogensen F (1946) A ferro-ortho-titanate ore from Södra Ulvön. Geol Fören Stockh Förh 68: 578-587. |
| [59] | Ulvöspinel. Avaliable from: https://www.mindat.org/min-4089.html. |
| [60] | Rossiter MJ, Clarke PT (1965) Cation distribution in Ulvöspinel Fe2TiO4. Nature 207: 402-402. |
| [61] | Mineralienatlas —Fossilienatlas. Avaliable from: https://www.mineralienatlas.de/lexikon/index.php/MineralData?lang = de & mineral = Cuprospinel. |
| [62] | Magnetite. Avaliable from: https://www.mindat.org/min-2538.html. |
| [63] | Trevorite. Avaliable from: https://www.mindat.org/min-4012.html. |
| [64] | Bromho TK, Ibrahim K, Kabir H, et al. (2018) Understanding the impacts of Al+3-substitutions on the enhancement of magnetic, dielectric and electrical behaviors of ceramic processed nickel-zinc mixed ferrites: FTIR assisted studies. Mater Res Bull 97: 444-451. |
| [65] | Burdett JK, Price GD, Price SL (1982) Role of the crystal-field theory in determining the structures of spinels. J Am Chem Soc 104: 92-95. |
| [66] | Verwey EJW, Heilmann EL (1947) Physical properties and cation arrangement of oxides with spinel structures I. cation arrangement in spinels. J Chem Phys 15: 174-180. |
| [67] | Greenberg E, Rozenberg GK, Xu W, et al. (2009) On the compressibility of ferrite spinels: a high-pressure X-ray diffraction study of MFe2O4 (M = Mg, Co, Zn). High Pressure Res 29: 764-779. |
| [68] | Yadav RS, Havlica J, Hnatko M, et al. (2015) Magnetic properties of Co1-xZnxFe2O4 spinel ferrite nanoparticles synthesized by starch-assisted sol-gel autocombustion method and its ball milling. J Magn Magn Mater 378: 190-199. |
| [69] | Paramesh D, Kumar KV, Reddy PV (2016) Influence of nickel addition on structural and magnetic properties of aluminium substituted Ni-Zn ferrite nanoparticles. Process Appl Ceram 10: 161-167. |
| [70] | Antao SM, Hassan I, Parise JB (2005) Cation ordering in magnesioferrite, MgFe2O4, to 982 ℃ using in situ synchrotron X-ray powder diffraction. Am Mineral 90: 219-228. |
| [71] | O'neill H, St C (1992) Temperature dependence of the cation distribution in zinc ferrite (ZnFe2O4) from powder XRD structural refinements. Eur J Mineral 571-580. |
| [72] | Singh S, Ralhan NK, Kotnala RK, et al. (2012) Nanosize dependent electrical and magnetic properties of NiFe2O4 ferrite. IJPAP 50: 739-743. |
| [73] | Nejati K, Zabihi R (2012) Preparation and magnetic properties of nano size nickel ferrite particles using hydrothermal method. Chem Cent J 6: 23. |
| [74] | Melagiriyappa E, Jayanna HS (2009) Structural and magnetic susceptibility studies of samarium substituted magnesium-zinc ferrites. J Alloy Compd 482: 147-150. |
| [75] | Morán E, Blesa MC, Medina ME, et al. (2002) Nonstoichiometric spinel ferrites obtained from α-NaFeO2 via molten media reactions. Inorg Chem 41: 5961-5967. |
| [76] | Lazarević ZŽ, Jovalekić Č, Sekulić D, et al. (2012) Characterization of nanostructured spinel NiFe2O4 obtained by soft mechanochemical synthesis. Sci Sinter 44: 331-339. |
| [77] | Sáez-Puche R, Fernández MJ, Blanco-gutiérrez V, et al. (2008) Ferrites nanoparticles MFe2O4 (M = Ni and Zn): Hydrothermal synthesis and magnetic properties. Bol Soc Esp Cerámica Vidr 47: 133-137. |
| [78] | Gözüak F, Köseoğlu Y, Baykal A, et al. (2009) Synthesis and characterization of CoxZn1−xFe2O4 magnetic nanoparticles via a PEG-assisted route. J Magn Magn Mater 321: 2170-2177. |
| [79] | Souriou D, Mattei JL, Chevalier A, et al. (2010) Influential parameters on electromagnetic properties of nickel-zinc ferrites for antenna miniaturization. J Appl Phys 107: 09A518. |
| [80] | Went JJ, Rathenau GW, Gorter EW, et al. (1952) Hexagonal iron-oxide compounds as permanent-magnet materials. Phys Rev 86: 424-425. |
| [81] | Belrhazi H, Hafidi MYE, Hafidi ME (2019) Permanent magnets elaboration from BaFe12O19 hexaferrite material: Simulation and prototype. Res Dev Mater Sci 11: 1-5. |
| [82] | Stergiou CA, Litsardakis G (2016) Y-type hexagonal ferrites for microwave absorber and antenna applications. J Magn Magn Mater 405: 54-61. |
| [83] | Jotania R (2014) Crystal structure, magnetic properties and advances in hexaferrites: A brief review. AIP Conf Proc 1621: 596-599. |
| [84] | Mahmood SH, Al-Shiab Q, Bsoul I, et al. (2018) Structural and magnetic properties of (Mg, Co)2W hexaferrites. Curr Appl Phys 18: 590-598. |
| [85] | Izadkhah H, Zare S, Somu S, et al. (2017) Utilizing alternate target deposition to increase the magnetoelectric effect at room temperature in a single phase M-type hexaferrite. MRS Commun 7: 97-101. |
| [86] | Kitagawa Y, Hiraoka Y, Honda T, et al. (2010) Low-field magnetoelectric effect at room temperature. Nat Mater 9: 797-802. |
| [87] | Muleta G (2018) The study of optical, electrical and dielectric properties of cadmium and zinc substituted copper ferrite nanoparticles. Ethiopia: Arba Minch University. |
| [88] | Albanese G (1977) Recent advances in hexagonal ferrites by the use of nuclear spectroscopic methods. J Phys Colloq 38: C1-85. |
| [89] | Maswadeh Y, Mahmood S, Awadallah A, et al. (2015) Synthesis and structural characterization of non-stoichiometric barium hexaferrite materials with Fe:Ba ratio of 11.5-16.16. IOP Conf Ser Mater Sci Eng 92: 23. |
| [90] | Kruželák J, Hudec I, Dosoudil R, et al. (2015) Investigation of strontium ferrite activity in different rubber matrices. J Elastom Plast 47: 277-290. |
| [91] | Wartewig P, Krause MK, Esquinazi P, et al. (1999) Magnetic properties of Zn- and Ti-substituted barium hexaferrite. J Magn Magn Mater 192: 83-99. |
| [92] | Kanagesan S, Jesurani S, Velmurugan R, et al. (2012) Structural and magnetic properties of conventional and microwave treated Ni-Zr doped barium strontium hexaferrite. Mater Res Bull 47: 188-192. |
| [93] | Xia A, Zuo C, Chen L, et al. (2013) Hexagonal SrFe12O19 ferrites: Hydrothermal synthesis and their sintering properties. J Magn Magn Mater 332: 186-191. |
| [94] | Ghahfarokhi SM, Ranjbar F, Shoushtari MZ (2014) A study of the properties of SrFe12-xCoxO19 nanoparticles. J Magn Magn Mater 349: 80-87. |
| [95] | Nga TTV, Duong NP, Hien TD (2009) Synthesis of ultrafine SrLaxFe12-xO19 particles with high coercivity and magnetization by sol-gel method. J Alloy Compd 475: 55-59. |
| [96] | Zhang Z, Liu X, Wang X, et al. (2012) Electromagnetic and microwave absorption properties of Fe-Sr0.8La0.2Fe11.8Co0.2O19 shell-core composites. J Magn Magn Mater 324: 2177-2182. |
| [97] | Zhang Z, Liu X, Wang X, et al. (2012) Effect of Nd-Co substitution on magnetic and microwave absorption properties of SrFe12O19 hexaferrites. J Alloy Compd 525: 114-119. |
| [98] | Chen N, Yang K, Gu M (2010) Microwave absorption properties of La-substituted M-type strontium ferrites. J Alloy Compd 490: 609-612. |
| [99] | Šepelák V, Myndyk M, Witte R, et al. (2014) The mechanically induced structural disorder in barium hexaferrite, BaFe12O19, and its impact on magnetism. Faraday Discuss 170: 121-135. |
| [100] | Yuan CL, Tuo YS (2013) Microwave adsorption of Sr(MnTi)xFe12-2xO19 particles. J Magn Magn Mater 342: 47-53. |
| [101] | Handoko E, Iwan S, Budi S, et al. (2018) Magnetic and microwave absorbing properties of BaFe12-2xCoxZnxO19 (x = 0.0; 0.2; 0.4; 0.6) nanocrystalline. Mater Res Express 5: 064003. |
| [102] | Mallick KK, Shepherd P, Green RJ (2007) Magnetic properties of cobalt substituted M-type barium hexaferrite prepared by co-precipitation. J Magn Magn Mater 312: 418-429. |
| [103] | Liu Q, Liu Y, Wu C (2017) Investigation on Zn-Sn co-substituted M-type hexaferrite for microwave applications. J Magn Magn Mater 444: 421-425. |
| [104] | Tyagi S, Baskey HB, Agarwala RC, et al. (2011) Synthesis and characterization of microwave absorbing SrFe12O19/ZnFe2O4 nanocomposite. Trans Indian Inst Met 64: 607-614. |
| [105] | Tyagi S, Verma P, Baskey HB, et al. (2012) Microwave absorption study of carbon nano tubes dispersed hard/soft ferrite nanocomposite. Ceram Int 38: 4561-4571. |
| [106] | Sharbati A, Khani JMV, Amiri GR (2012) Microwave absorption studies of nanocrystalline SrMnx/2(TiSn)x/4Fe12-xO19 prepared by the citrate sol-gel method. Solid State Commun 152: 199-203. |
| [107] | Reddy NK, Mulay VN (2002) Magnetic properties of W-type ferrites. Mater Chem Phys 76: 75-77. |
| [108] | Ahmed MA, Okasha N, Kershi RM (2010) Dramatic effect of rare earth ion on the electrical and magnetic properties of W-type barium hexaferrites. Phys B Condens Matter 405: 3223-3233. |
| [109] | Ul-ain B, Zafar A, Ahmed S (2015) To explore a new class of material (X-type hexaferrites) for N2O decomposition. Catal Sci Technol 5: 1076-1083. |
| [110] | Ueda H, Shakudo H, Santo H, et al. (2018) Magnetocrystalline anisotropy of single crystals of M-, X-, and W-type strontium hexaferrites. J Phys Soc Jpn 87: 104706. |
| [111] | Mohebbi M, Vittoria C (2013) Growth of Y-type hexaferrite thin films by alternating target laser ablation deposition. J Magn Mag. Mater 344: 158-161. |
| [112] | Rama KK, Vijaya KK, Dachepalli R (2012) Structural and electrical conductivity studies in nickel-zinc ferrite. Adv Mater Phys Chem 2012: 23241. |
| [113] | M. Ben Ali et al. Effect of zinc concentration on the structural and magnetic properties of mixed Co-Zn ferrites nanoparticles synthesized by sol/gel method. J Magn Magn Mater 398: 20-25. |
| [114] | Raut AV, Barkule RS, Shengule DR, et al. (2014) Synthesis, structural investigation and magnetic properties of Zn2+ substituted cobalt ferrite nanoparticles prepared by the sol-gel auto-combustion technique. J Magn Magn Mater 358-359: 87-92. |
| [115] | Mu G, Chen N, Pan X, et al. (2008) Preparation and microwave absorption properties of barium ferrite nanorods. Mater Lett 62: 840-842. |
| [116] | Li Y, Huang Y, Qi S, et al. (2012) Preparation, magnetic and electromagnetic properties of polyaniline/strontium ferrite/multiwalled carbon nanotubes composite. Appl Surf Sci 258: 3659-3666. |
| [117] | Chen N, Mu G, Pan X, et al. (2007) Microwave absorption properties of SrFe12O19/ZnFe2O4 composite powders. Mater Sci Eng B 139: 256-260. |
| [118] | Chang S, Kangning S, Pengfei C (2012) Microwave absorption properties of Ce-substituted M-type barium ferrite. J Magn Magn Mater 324: 802-805. |
| [119] | Rane AV, Kanny K, Abitha VK, et al. (2018) Methods for synthesis of nanoparticles and sabrication of nanocomposites, In: Bhagyaraj MS, Oluwafemi OS, Kalarikkal N, et al., Synthesis of Inorganic Nanomaterials, Woodhead Publishing, 121-139. |
| [120] | Gu Y, Sang S, Huang K, et al. (2000) Synthesis of MnZn ferrite nanoscale particles by hydrothermal method. J Cent South Univ Technol 7: 37-39. |
| [121] | Xia A, Liu S, Jin C, et al. (2013) Hydrothermal Mg1-xZnxFe2O4 spinel ferrites: Phase formation and mechanism of saturation magnetization. Mater Lett 105: 199-201. |
| [122] | He HY (2011) Magnetic properties of Co0.5Zn0.5Fe2O4 nanoparticles synthesized by a template-assisted hydrothermal method. J Nanotechnol 2011: 182543. |
| [123] | Mostafa NY, Zaki ZI, Heiba ZK (2013) Structural and magnetic properties of cadmium substituted manganese ferrites prepared by hydrothermal route. J Magn Magn Mater 329: 71-76. |
| [124] | Köseoğlu Y, Alan F, Tan M, et al. (2012) Low temperature hydrothermal synthesis and characterization of Mn doped cobalt ferrite nanoparticles. Ceram Int 38: 3625-3634. |
| [125] | Mostafa NY, Hessien MM, Shaltout AA (2012) Hydrothermal synthesis and characterizations of Ti substituted Mn-ferrites. J Alloy Compd 529: 29-33. |
| [126] | Rashad MM, Mohamed RM, Ibrahim MA, et al. (2012) Magnetic and catalytic properties of cubic copper ferrite nanopowders synthesized from secondary resources. Adv Powder Technol 23: 315-323. |
| [127] | Tyagi S, Agarwala RC, Agarwala V (2011) Reaction kinetic, magnetic and microwave absorption studies of SrFe11.2N0.8O19 hexaferrite nanoparticle. J Mater Sci-Mater El 22: 1085-1094. |
| [128] | Mattei JL, Huitema L, Queffelec P, et al. (2011) Suitability of Ni-Zn ferrites ceramics with controlled porosity as granular substrates for mobile handset miniaturized antennas. IEEE T Magn 47: 3720-3723. |
| [129] | Moscoso-Londoñ o O, Tancredi PABLO, Muraca D, et al. (2017) Different approaches to analyze the dipolar interaction effects on diluted and concentrated granular superparamagnetic systems. J Magn Magn Mater 428: 105-118. |
| [130] | Harzali H, et al. (2016) Structural and magnetic properties of nano-sized NiCuZn ferrites synthesized by co-precipitation method with ultrasound irradiation. J Magn Magn Mater 419: 50-56. |
| [131] | Iqbal MJ, Ashiq MN, Hernandez-Gomez P, et al. (2007) Magnetic, physical and electrical properties of Zr-Ni-substituted co-precipitated strontium hexaferrite nanoparticles. Scr Mater 57: 1093-1096. |
| [132] | Thanh NK, Loan TT, Anh LN, et al. (2016) Cation distribution in CuFe2O4 nanoparticles: Effects of Ni doping on magnetic properties. J Appl Phys 120: 142115. |
| [133] | Gomes JA, Sousa MH, Da Silva GJ, et al. (2006) Cation distribution in copper ferrite nanoparticles of ferrofluids: A synchrotron XRD and EXAFS investigation. J Magn Magn Mater 300: e213-e216. |
| [134] | Arulmurugan R, Vaidyanathan G, Sendhilnathan S, et al. (2006) Thermomagnetic properties of Co1-xZnxFe2O4 (x = 0.1-0.5) nanoparticles. J Magn Magn Mater 303: 131-137. |
| [135] | Arulmurugan R, Jeyadevan B, Vaidyanathan G, et al. (2005) Effect of zinc substitution on Co-Zn and Mn-Zn ferrite nanoparticles prepared by co-precipitation. J Magn Magn Mater 288: 470-477. |
| [136] | Gordani GR, Ghasemi A, Saidi A (2014) Enhanced magnetic properties of substituted Sr-hexaferrite nanoparticles synthesized by co-precipitation method. Ceram Int 40: 4945-4952. |
| [137] | Baniasadi A, Ghasemi A, Nemati A, et al. (2014) Effect of Ti-Zn substitution on structural, magnetic and microwave absorption characteristics of strontium hexaferrite. J Alloy Compd 583: 325-328. |
| [138] | Modi KB, Shah SJ, Pujara NB, et al. (2013) Infrared spectral evolution, elastic, optical and thermodynamic properties study on mechanically milled Ni0.5Zn0.5Fe2O4 spinel ferrite. J Mol Struct 1049: 250-262. |
| [139] | Tehrani MK, Ghasemi A, Moradi M, et al. (2011) Wideband electromagnetic wave absorber using doped barium hexaferrite in Ku-band. J Alloy Compd 509: 8398-8400. |
| [140] | Ohnishi H, Teranishi T (1961) Crystal distortion in copper ferrite-chromite series. J Phys Soc Jpn 16: 35-43. |
| [141] | Tachibana T, Nakagawa T, Takada Y, et al. (2003) X-ray and neutron diffraction studies on iron-substituted Z-type hexagonal barium ferrite: Ba3Co2-xFe24+xO41 (x = 0-0.6). J Magn Magn Mater 262: 248-257. |
| [142] | Sözeri H, Deligöz H, Kavas H, et al. (2014) Magnetic, dielectric and microwave properties of M-Ti substituted barium hexaferrites (M = Mn2+, Co2+, Cu2+, Ni2+, Zn2+). Ceram Int 40: 8645-8657. |
| [143] | González-Angeles A, Mendoza-Suarez G, Grusková A, et al. (2005) Magnetic studies of Zn-Ti-substituted barium hexaferrites prepared by mechanical milling. Mater Lett 59: 26-31. |
| [144] | Zou H, Li S, Zhang L, et al. (2011) Determining factors for high performance silicone rubber microwave absorbing materials. J Magn Magn Mater 323: 1643-1651. |
| [145] | Lixi W, Qiang W, Lei M, et al. (2007) Influence of Sm3+ substitution on microwave magnetic performance of barium hexaferrites. J Rare Earth 25: 216-219. |
| [146] | Ghasemi A, Hossienpour A, Morisako A, et al. (2008) Investigation of the microwave absorptive behavior of doped barium ferrites. Mater Design 29: 112-117. |
| [147] | Choopani S, Keyhan N, Ghasemi A, et al. (2009) Static and dynamic magnetic characteristics of BaCo0.5Mn0.5Ti1.0Fe10O19. J Magn Magn Mater 321: 1996-2000. |
| [148] | Pradhan AK, Saha S, Nath TK (2017) AC and DC electrical conductivity, dielectric and magnetic properties of Co0.65Zn0.35Fe2-xMoxO4 (x = 0.0, 0.1 and 0.2) ferrites. Appl Phys A-Mater 123: 715. |
| [149] | Silva LG, Solis-Pomar F, Gutiérrez-Lazos CD, et al. (2014) Synthesis of Fe nanoparticles functionalized with oleic acid synthesized by inert gas condensation. J Nanomater 2014: 643967. |
| [150] | Zheng X, Yu SH, Sun R, et al. (2012) Microstructure and properties of ferrite/organic nanocomposite prepared with microemulsion method. Maters Sci Forum 722: 31-38. |
| [151] | Košak A, Makovec D, Žnidaršič A, et al. (2004) Preparation of MnZn-ferrite with microemulsion technique. J Eur Ceram Soc 24: 959-962. |
| [152] | Malik MA, Wani MY, Hashim MA (2012) Microemulsion method: A novel route to synthesize organic and inorganic nanomaterials: 1st Nano Update. Arab J Chem 5: 397-417. |
| [153] | Mazario E, Herrasti P, Morales MP, et al. (2012) Synthesis and characterization of CoFe2O4 ferrite nanoparticles obtained by an electrochemical method. Nanotechnology 23: 355708. |
| [154] | Rivero M, del Campo A, Mayoral A, et al. (2016) Synthesis and structural characterization of ZnxFe3-xO4 ferrite nanoparticles obtained by an electrochemical method. RSC Adv 6: 40067-40076. |
| [155] | Saba A, Elsayed E, Moharam M, et al. (2012) Electrochemical synthesis of nanocrystalline Ni0.5Zn0.5Fe2O4 thin film from aqueous sulfate bath. ISRN 2012: 532168. |
| [156] | Bremer M, Fischer ST, Langbein H, et al. (1992) Investigation on the formation of manganese-zinc ferrites by thermal decomposition of solid solution oxalates. Thermochim Acta 209: 323-330. |
| [157] | Angermann A, Töpfer J, Silva K, et al. (2010) Nanocrystalline Mn-Zn ferrites from mixed oxalates: Synthesis, stability and magnetic properties. J Alloy Compd 508: 433-439. |
| [158] | Li D, Herricks T, Xia Y (2003) Magnetic nanofibers of nickel ferrite prepared by electrospinning. Appl Phys Lett 83: 4586-4588. |
| [159] | Na KH, Kim WT, Park DC, et al. (2018) Fabrication and characterization of the magnetic ferrite nanofibers by electrospinning process. Thin Solid Films 660: 358-364. |
| [160] | Nam JH, Joo YH, Lee JH, et al. (2009) Preparation of NiZn-ferrite nanofibers by electrospinning for DNA separation. J Magn Magn Mater 321: 1389-1392. |
| [161] | Phulé PP, Wood TE (2001) Ceramics and glasses, sol-gel synthesis of, In: Buschow KHJ, Cahn RW, Flemings MC, et al., 2 Eds., Encyclopedia of Materials: Science and Technology, Oxford: Elsevier, 1090-1095. |
| [162] | Peterson DS (2013) Sol-gel technique, In: Li D, Encyclopedia of Microfluidics and Nanofluidics, New York: Springer Science + Business Media, 1-7. |
| [163] | Muresan LM (2015) Corrosion protective coatings for Ti and Ti alloys used for biomedical implants, In: Tiwari A, Rawlins J, Hihara LH, Intelligent Coatings for Corrosion Control, Boston: Butterworth-Heinemann, 585-602. |
| [164] | Xu P (2001) Polymer-ceramic nanocomposites: ceramic phases, In: Buschow KHJ, Cahn RW, Flemings MC, et al., Encyclopedia of Materials: Science and Technology, Oxford: Elsevier, 7565-7570. |
| [165] | Allaedini G, Tasirin SM, Aminayi P (2015) Magnetic properties of cobalt ferrite synthesized by hydrothermal method. Int Nano Lett 5: 183-186. |
| [166] | Gan YX, Jayatissa AH, Yu Z, et al. (2020) Hydrothermal synthesis of nanomaterials. J Nanomater 2020: 8917013. |
| [167] | O'Hare D (2001) Hydrothermal synthesis, In: Buschow KHJ, Cahn RW, Flemings MC, et al., Encyclopedia of Materials: Science and Technology, Oxford: Elsevier, 3989-3992. |
| [168] | Kumar A, Nanda D (2019) Methods and fabrication techniques of superhydrophobic surfaces, In: Samal SK, Mohanty S, Nayak SK, Superhydrophobic Polymer Coatings, Elsevier, 43-75. |
| [169] | Liu S, Ma C, Ma MG, et al. (2019) Magnetic nanocomposite adsorbents, In: Kyzas GZ, Mitropoulos AC, Composite Nanoadsorbents, Elsevier, 295-316. |
| [170] | Šepelák V, Bergmann I, Feldhoff A, et al. (2007) Nanocrystalline nickel ferrite, NiFe2O4: Mechanosynthesis, nonequilibrium cation distribution, canted spin arrangement, and magnetic behaviour. J Phys Chem C 111: 5026-5033. |
| [171] | Rao CNR, Biswas K (2015) Ceramic methods, Essentials of Inorganic Materials Synthesis, John Wiley & Sons, 17-21. |
| [172] | Chatterjee AK (2001) X-ray diffraction, In: Ramachandran VS, Beaudoin JJ, Handbook of Analytical Techniques in Concrete Science and Technology: Principles, Techniques and Applications, Norwich, New York: William Andrew Publishing, 275-332. |
| [173] | Sudha D, Dhanapandian S, Manoharan C, et al. (2016) Structural, morphological and electrical properties of pulsed electrodeposited CdIn2Se4 thin films. Results Phys 6: 599-605. |
| [174] | Kumar A, Agarwala V, Singh D (2013) Effect of particle size of BaFe12O19 on the microwave absorption characteristics in X-band. Prog Electromagn Res 29: 223-236. |
| [175] | Kambale RC, Adhate NR, Chougule BK, et al. (2010) Magnetic and dielectric properties of mixed spinel Ni-Zn ferrites synthesized by citrate-nitrate combustion method. J Alloy Compd 491: 372-377. |
| [176] | Singhal S, Singh J, Barthwal SK, et al. (2005) Preparation and characterization of nanosize nickel-substituted cobalt ferrites (Co1-xNixFe2O4). J Solid State Chem 178: 3183-3189. |
| [177] | Tyagi S, Baskey HB, Agarwala RC, et al. (2011) Reaction kinetic, magnetic and microwave absorption studies of SrFe12O19/CoFe2O4 ferrite nanocrystals. Trans Indian Inst Met 64: 271-277. |
| [178] | Swamy PP, Basavaraja S, Lagashetty A, et al. (2011) Synthesis and characterization of zinc ferrite nanoparticles obtained by self-propagating low-temperature combustion method. Bull Mater Sci 34: 1325-1330. |
| [179] | Sharma R, Agarwala RC, Agarwala V (2008) Development of radar absorbing nano crystals by microwave irradiation. Mater Lett 62: 2233-2236. |
| [180] | Thakur A, Singh RR, Barman PB (2013) Structural and magnetic properties of La3+ substituted strontium hexaferrite nanoparticles prepared by citrate precursor method. J Magn Magn Mater 326: 35-40. |
| [181] | Tang X, Yang Y, Hu K (2009) Structure and electromagnetic behavior of BaFe12-2x(Ni0.8Ti0.7)xO19-0.8x in the 2-12 GHz frequency range. J Alloy Compd 477: 488-492. |
| [182] | Sigh P, Andola HC, Rawat MSM, et al. (2011) Fourier transform infrared (FT-IR) spectroscopy in an-overview. Res J Med Plants 5: 127-135. |
| 1. | Daniel Coombs, Michael A. Gilchrist, Colleen L. Ball, Evaluating the importance of within- and between-host selection pressures on the evolution of chronic pathogens, 2007, 72, 00405809, 576, 10.1016/j.tpb.2007.08.005 | |
| 2. | Kazuhiko Nara, Five questions about Streptococcus mutans: Theoretical study of its transmission and colonisation, 2012, 57, 00039969, 1498, 10.1016/j.archoralbio.2012.03.008 |
Figures(16) / Tables(12)
Ajitanshu Vedrtnam, Kishor Kalauni, Sunil Dubey, Aman Kumar. A comprehensive study on structure, properties, synthesis and characterization of ferrites[J]. AIMS Materials Science, 2020, 7(6): 800-835. doi: 10.3934/matersci.2020.6.800
| Parameters | Values |
| Maximum power Pmax | 20 W |
| Current at maximum power IMPP | 1.17 A |
| Voltage at maximum power VMPP | 17.1 V |
| Short-circuit current Icc | 1.27 A |
| Open-circuit voltage Vcc | 20.8 V |
DownLoad:
CSV
| Parameters | Values |
| Input capacitor Cin | 771.6 µF |
| Inductance L | 189.8 µH |
| Switching frequency f | 30 kHz |
| Output capacitor Cout | 57.16 µF |
DownLoad:
CSV
| G(W/m2) |
Target MPP (W) |
P & O | ANN | ANN-P & O | ANN-GNSA | ||||
| Obtained MPP (W) |
tc(s) | ObtainedMPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | ||
| 200 | 1.858 | 1.586 | 0.1095 - 0.1152 | 0.4517 | 0.0239 | 1.553 | 0.1766 | 1.613 | 0.1 |
| 300 | 4.026 | 3.437 | 0.5772 - 0.5831 | 2.243 | 0.5659 | 3.371 | 0.6028 | 4.026 | 0.5887 |
| 700 | 12.72 | 12.68 | 1.045 - 1.047 | 12.7 | 1.038 | 12.72 | 1.105 | 12.72 | 1.04 |
| 1000 | 18.59 | 18.55 | 1.541 - 1.549 | 18.28 | 1.547 | 18.55 | 1.66 | 18.59 | 1.517 |
| 800 | 14.69 | 14.61 | 2.025 - 2.039 | 14.63 | 2.032 | 14.67 | 2.082 | 14.67 | 2.005 |
| 400 | 6.676 | 5.9 | 2.598 - 2.604 | 5.766 | 2.606 | 6.076 | 2.624 | 6.676 | 2.594 |
| η (%) | 96.93 | 92.34 | 97.28 | 99.54 | |||||
DownLoad:
CSV
| T(℃) |
Target MPP (W) |
P & O | ANN | ANN-P & O | ANN-GNSA | ||||
| Obtained MPP (W) |
tc(s) | ObtainedMPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | ||
| 15 | 19.39 | 19.32 | 0.2589 | 17.890 | 0.2657 | 19.16 | 0.2266 | 19.37 | 0.2096 |
| 35 | 17.77 | 17.77 | 0.8724 | 17.61 | 0.8741 | 17.61 | 0.8849 | 17.77 | 0.8198 |
| 45 | 17.35 | 17.32 | 1.559 | 16.84 | 1.608 | 17.31 | 1.558 | 17.35 | 1.549 |
| 5 | 20.19 | 20.2 | 2.329 | 19.36 | 2.404 | 20.02 | 2.418 | 20.2 | 2.301 |
| η (%) | 99.87 | 95.98 | 99.19 | 99.98 | |||||
DownLoad:
CSV
| Parameters | Values |
| Maximum power Pmax | 20 W |
| Current at maximum power IMPP | 1.17 A |
| Voltage at maximum power VMPP | 17.1 V |
| Short-circuit current Icc | 1.27 A |
| Open-circuit voltage Vcc | 20.8 V |
| Parameters | Values |
| Input capacitor Cin | 771.6 µF |
| Inductance L | 189.8 µH |
| Switching frequency f | 30 kHz |
| Output capacitor Cout | 57.16 µF |
| G(W/m2) |
Target MPP (W) |
P & O | ANN | ANN-P & O | ANN-GNSA | ||||
| Obtained MPP (W) |
tc(s) | ObtainedMPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | ||
| 200 | 1.858 | 1.586 | 0.1095 - 0.1152 | 0.4517 | 0.0239 | 1.553 | 0.1766 | 1.613 | 0.1 |
| 300 | 4.026 | 3.437 | 0.5772 - 0.5831 | 2.243 | 0.5659 | 3.371 | 0.6028 | 4.026 | 0.5887 |
| 700 | 12.72 | 12.68 | 1.045 - 1.047 | 12.7 | 1.038 | 12.72 | 1.105 | 12.72 | 1.04 |
| 1000 | 18.59 | 18.55 | 1.541 - 1.549 | 18.28 | 1.547 | 18.55 | 1.66 | 18.59 | 1.517 |
| 800 | 14.69 | 14.61 | 2.025 - 2.039 | 14.63 | 2.032 | 14.67 | 2.082 | 14.67 | 2.005 |
| 400 | 6.676 | 5.9 | 2.598 - 2.604 | 5.766 | 2.606 | 6.076 | 2.624 | 6.676 | 2.594 |
| η (%) | 96.93 | 92.34 | 97.28 | 99.54 | |||||
| T(℃) |
Target MPP (W) |
P & O | ANN | ANN-P & O | ANN-GNSA | ||||
| Obtained MPP (W) |
tc(s) | ObtainedMPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | Obtained MPP (W) |
tc(s) | ||
| 15 | 19.39 | 19.32 | 0.2589 | 17.890 | 0.2657 | 19.16 | 0.2266 | 19.37 | 0.2096 |
| 35 | 17.77 | 17.77 | 0.8724 | 17.61 | 0.8741 | 17.61 | 0.8849 | 17.77 | 0.8198 |
| 45 | 17.35 | 17.32 | 1.559 | 16.84 | 1.608 | 17.31 | 1.558 | 17.35 | 1.549 |
| 5 | 20.19 | 20.2 | 2.329 | 19.36 | 2.404 | 20.02 | 2.418 | 20.2 | 2.301 |
| η (%) | 99.87 | 95.98 | 99.19 | 99.98 | |||||
