A Comparative Study Of Maximum.pdf

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A comparative study of maximum power point tracking methods for a photovoltaic-based water pumping system a

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Bhavnesh Kumar , Yogesh K. Chauhan & Vivek Shrivastava

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School of Engineering, Gautam Buddha University, Greater Noida, India Published online: 28 Feb 2013.

To cite this article: Bhavnesh Kumar, Yogesh K. Chauhan & Vivek Shrivastava (2014) A comparative study of maximum power point tracking methods for a photovoltaic-based water pumping system, International Journal of Sustainable Energy, 33:4, 797-810, DOI: 10.1080/14786451.2013.769990 To link to this article: http://dx.doi.org/10.1080/14786451.2013.769990

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International Journal of Sustainable Energy, 2014 Vol. 33, No. 4, 797–810, http://dx.doi.org/10.1080/14786451.2013.769990

A comparative study of maximum power point tracking methods for a photovoltaic-based water pumping system Bhavnesh Kumar*, Yogesh K. Chauhan and Vivek Shrivastava

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School of Engineering, Gautam Buddha University, Greater Noida, India (Received 30 July 2012; final version received 18 January 2013) In this paper the performance of the proposed fuzzy-based maximum power point tracking (MPPT) is investigated and compared with incremental conductance and constant voltage controller for a photovoltaic (PV) pumping system. A fuzzy logic controller with a mamdani inference engine using only nine rules is designed to track the optimum power point. An induction motor has been used to drive the centrifugal pump. The system performance is analysed for different weather conditions. A detailed comparative study presenting the merits and demerits of each technique is also presented in order to develop a relative relationship. Simulation results obtained indicate better performance of the fuzzy-based MPPT algorithm for the PV pumping system. Keywords: centrifugal pump; constant voltage controller; fuzzy logic controller; induction motor; MPPT; PV array.

Introduction In this era, due to the growing energy concerns search for new and promising sources of energy has been ignited. Photovoltaic (PV) energy generation has remarkably attracted the researchers as it has advantages of abundant, free and easily available fuel. Furthermore, the major drawback of high cost is also reduced with the maturity of technology in the field of power electronics (Benlarbi, Mokrani, and Nait-Said 2004; Ghoneim 2006; Kuo and Liang 2001; Omar and Makhlomo 2003). The PV array can be used either in a standalone or grid-connected mode. Grid-connected PV systems are commonly used in the distributed generation system to inject power into the grid (El-Shafy and Nafeh 2010; Chouder et al. 2012; Silva, Motta, and Tofoli 2011). The standalone PV systems are more suitable in remote areas for water pumping. Several studies have also been carried out on the choice of electric motors and pumps in order to optimise the water pumping system (Choi and Lee 2012; Kini, Bansal, and Aithal 2008; Leyva et al. 2011). Earlier, DC motors were mainly employed to drive the PV-based water pumps. The permanent magnet and separately excited DC motors were found more suitable for the PV array-based water pumping systems (Akbaba, Qamber, and Kamal 1988; Mummadi 2000; Singer and Appelbaum 1993). However, DC motors suffer from the common disadvantage of frequent maintenance, which results in increased running cost and decreased reliability. In comparison with the DC motors, the induction motors are preferred as it offers higher ruggedness, lower maintenance, higher reliability, wider range and lower cost. Although, additional stage of DC–AC conversion is *Corresponding author. Email: [email protected] © 2013 Taylor & Francis

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involved with induction motor-based PV pumping systems (Akbaba 2007; Betka and Moussi 2004; Bhat, Pittet, and Sonde 1987; Daud and Mahmoud 2005; Eskander and Zaki 1997; Olorunfemi 1991). The output from a PV array is nonlinearly varying and dependent on the intensity of sunlight, temperature and cell area. Therefore, for the the full exploitation of the PV array its maximum power has to be tracked with the help of a controller under different operating conditions (Koutroulis, Kalaitzakis, and Voulgaris 2001). Various conventional maximum power point tracking (MPPT) techniques are available in the literature, among which much focus has been on perturb and observe (PO) methods and incremental conductance (IC) methods (Chiang, Chang, and Yen 1998; Huaa and Lin 2004; Tafticht, Agbossou, and Doumbia 2007). PO involves a perturbation in the operating voltage of the PV array by perturbing the duty ratio of the power converter. The implementation of PO is much simpler, but fails during the rapidly changing conditions particularly due to sunlight intensity. The IC method is based on the fact that the slope of the PV array power curve is zero at MPP, positive on the left and negative on the right of MPP. This technique is more commonly used; however its operating point oscillates around the MPP. Elgendy, Zahawi, and Atkinson (2010) used constant voltage controller (CVC) for tracking of the maximum power from the PV array for a directly connected DC motor pump system. The method utilises the fact that the maximum power line is almost linear in a narrow band of a particular voltage. However, the complex circuit was required for the significant improvements. Artificial intelligent techniques have also been used for the optimisation of the PV water pumping systems. Bahgat et al. (2005), Hiyama and Kitabayashi (1997), Lin, Hong, and Chen (2011), and Veerachary and Yadaiah (2000)) used neural network to track the maximum power and to identify the PV array optimal point. However, more data requirement restricts the optimal operation under practical conditions. Fuzzy logic controller (FLC) is found more suitable for the development of classical MPPT methods. Ansari, Chatterji, and Iqbal (2010) have proposed an FLC-based MPPT for a PV array system, but marked the superior performance with DC load only. Other than the input/output selection, one factor which generally influences the performance of the fuzzy controller is the size of the rule base. In general, there is direct relation between the size of the rule base and the performance of the FLC-based system. Commonly, the rule base of 25 rules is used for the fuzzy-based MPPT. A rule base of minimum 15 rules is reported in the literature; however, its tracking performance was not found satisfactory (Alajmi et al. 2011). In view of the literature gap, the aim of this paper is to present an FLC with the reduced rule base and superior performance for a PV supplied induction motor-driven water pumping system. In addition, the performance of the proposed FLC in the system under investigation is compared with IC and CVC techniques and a comparative study is presented.

System description and modelling The system under investigation consists of a PV array, DC–DC converter, pulse width modulated (PWM) inverter, induction motor and centrifugal pump as load. A simple model of PV array and centrifugal pump is derived in order to simulate the system. All components are modelled separately and then joined together. The schematic diagram of the system under investigation is shown in Figure 1. PV array model PV array is a group of interconnected PV modules which are formed by interconnecting the solar cell in series/parallel combinations.

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VL PV Array

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Figure 1.

Schematic diagram of PV water pumping system with MPPT.

I pv

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Ir

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Figure 2.

Equivalent circuit of solar cell.

For describing the electrical behaviour of the solar cell different mathematical models had been introduced. Perhaps, the most commonly used equivalent model is the one diode equivalent model shown in Figure 2. The output voltage from one diode model of solar cell is given by   Isc + Ir − Ipv nkTC VPV = − Ipv Rs , (1) ln q Ir where VPV and Ipv are output voltage and current of the cell, respectively, Rs is the cell resistance, Isc is the photocurrent or short circuit current, Ir is the reverse saturation current of the diode, q is the electron charge, k is the Boltzmann constant, Tr is the reference operating temperature of the cell and n is the ideality factor. The solar cell operating temperature varies as a function of solar insolation level and ambient temperature. The effects of change in temperature and insolation level on PV array voltage are incorporated with the help of the following equations (Altas and Sharaf 2008): TV = 1 + β(Tc − Ta ), γ TI = (Ta − TC ), Gc

(2)

CV = 1 + βα(GX − GC ),

(4)

1 (GX − GC ), GC

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CI = 1 +

TC = α(GX − GC ),

(3)

(6)

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where TV and TI are the temperature coefficients of solar cell output voltage and current, respectively, Ta and Tc are the ambient and operating temperatures, respectively, and β and γ are the constants, CV and CI are the correction factors for output voltage and current of solar cell, respectively, GX and GC are the standard and operating insolation levels, respectively, α is a constant and Tc is change in the operating temperature.

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Power conditioning model In this work, a DC–DC boost converter along with a PWM inverter is connected in between the PV array and induction motor for power conditioning and is shown in Figure 1. The boost converter used is designed to operate in a continuous conduction mode which means that the inductor current will always be more than zero. When switch (S) is on (VL = Vin ), due to the positive inductor voltage (VL ) the current builds up in the inductor L. When S is off (VL = Vin − V0 ), the voltage across the inductor reverses and adds to the input voltage, thus makes the output (DC-link) voltage greater than the input (PV array) voltage. For steady-state operations, the input–output voltage relation is given in terms of on/off duty ratio (D) of the switching period as 1 V0 = . Vin 1−D

(7)

A three-phase inverter is used for converting the DC output of the boost converter into a threephase AC supply to feed the induction motor. The output is controlled by a pulse width modulation control circuit with a fixed modulation index. Induction motor model The dynamic equivalent circuit of a three-phase induction motor expressed in a d-q synchronously rotating reference frame is shown in Figure 3 (Daud and Mahmoud 2005). In Figure 3, Rs and Rr are the stator and rotor resistances, respectively, Lls and Llr are the stator and rotor leakage inductances, respectively, Lm is the mutual inductance, Vds and Vdr are the d-axis stator and rotor voltages, respectively, Vqs and Vqr are the q-axis stator and rotor voltages, respectively, ψqs and ψqr are the q-axis stator and rotor flux linkages, respectively, ψds and ψdr are the d-axis stator and rotor flux linkages, respectively. The electromagnetic torque developed by an induction motor is given by Te =

3P Lm (Iqs Idr − Ids Iqr ). 22

(8)

The mechanical part modelling of an electric motor is given by Te = Jpωm + Bωm + TL .

(9)

where J is the total inertia of the motor shaft, B is the friction coefficient and TL is the load torque. Centrifugal pump model Generally, centrifugal pumps are preferred over volumetric pumps for pumping applications because of three important advantages: (i) high PV energy utilisation, (ii) ability to operate for longer periods and (iii) proximity of load line to the MPP line. A centrifugal pump is characterised by its head-flow rate (H-Q) performance curve at the nominal speed. Affinity laws describe that the flow rate (Q) is directly proportional to the speed, the head (H) is proportional to the square

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of speed and the power is directly proportional to the cube of the speed (Kini, Bansal, and Aithal 2008). The selection of the pump size is crucial as it represents the mechanical load of the induction motor and it identifies the ratings of the other system components. A dynamic centrifugal pump load torque (TP ) is generally modelled in the form of a load torque requirement on a motor shaft. This load torque (TL ) depends on the square of the operating speed (ωr ) and is given by TP = TL = Kωr2 .

(10)

Here, K is defined in terms of nominal pump power Pn and speed ωn as K=

Pn ωn3

Fuzzy-based MPPT technique FLC has the advantages of working with imprecise inputs, not needing an accurate mathematical model and capability to handle nonlinearity as mentioned by Iskender (2005). In this work, the FLC-based algorithm is used for the modification of the conventional PO technique. The motive behind the designing of the proposed controller is to eliminate the above-mentioned drawback while keeping the advantageous features. Fuzzy logic control generally consists of three stages: fuzzification, rule base inference and defuzzification. The two input control variables selected for the FLC are the error E(k), and change in error E(k) at the kth sampling period. Both inputs are normalised by the scaling factors Ge , Gce and

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Fuzzy inference rule matrix. E(k)

E(k)

NE

ZE

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NE ZE PE

ZE NE PE

NE ZE PE

NE PE ZE

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VPV (k ), I PV (k )

PPV (k )

E(k ), E(k )

Normalisation

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Defuzzification D

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ZE

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Membership function for inputs NE

1

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(a) Flow chart of the fuzzy-based algorithm. (b) Inputs and output membership function.

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updated using the following equations:  E(k) = Ge

 PPV (k) − PPV (k − 1) , VPV (k) − VPV (k − 1)

(11)

E = Gce (E(k) − E(k − 1)).

(12)

The output control signal, change in duty cycle D generated by the controller regulates the duty cycle of the boost converter and is given by (13)

where Go is the output scaling factor. The inputs and output scaling factors are very crucial parameters and can be optimised by the trial-and-error method. For deciding the value of the output control signal, the fuzzy controller uses the rules provided in the fuzzy inference rule matrix shown in Table 1. The universe of discourse for the inputs and output is divided into three fuzzy subset functions: NE (negative), ZE (zero) and PE (positive). Therefore, it requires only nine rules in the inference matrix for regulating the duty ratio of the boost converter. The flowchart of the fuzzy-based algorithm is shown in Figure 4(a). In this paper, triangular and trapezoidal membership functions for the inputs and output variables are used and shown in Figure 4(b). To convert the fuzzy output value into a numeric value required by the boost converter, defuzzification is performed using the centre for the area algorithm.

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D = Go (D(k) − D(k − 1)),

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Figure 5.

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(a) P–V (b) I–V characteristics for different insolation levels.

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Results and discussion To study the steady state and transient state performance of the system under investigation, the different components of the system such as PV array, DC–DC boost converter, induction motor, centrifugal pump and different MPPT techniques are designed using Equations (1)–(13) in the Simulink/MATLAB software environment. The parameter of induction motor and the boost converter are given in the appendix. The results are obtained after simulating the system in the discrete mode with a sampling frequency of 20 kHz under various operating conditions. The results and their discussion are as follows:

The P–V and I–V characteristics of PV array are shown in Figure 5 for different insolation levels of 1000, 800, 600, 400 W/m2 at a constant temperature of 20◦ C. The decrease in the insolation level from its reference value of 1000 W/m2 is evident from the figure, the short circuit current sharply decreases, whereas the open circuit voltage slowly decreases. Therefore, the maximum power depends mainly upon the short circuit current and moderately on the voltage during the insolation level variations. Figure 6 shows the P–V and I–V characteristics of the PV array for different operating temperatures of 0, 10, 20, 30, 40◦ C with a constant insolation level of 1000 W/m2 . It is evident from

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Characteristics of PV array at different operating conditions

30 20 10 0

Figure 6.

(a) P–V (b) I–V characteristics for different temperature levels.

250

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the figure that the open circuit voltage decreases with the increase in the operating temperature above the reference value of 20◦ C, whereas it increases with the decrease in the temperature from the reference value. However, the short circuit current is very less affected by the temperature variations. As far as maximum power from the PV array is concerned, it primarily depends upon the array voltage during the temperature variations.

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Figure 7.

System performance using IC (a) for slow change in insolation (b) for fast change in insolation.

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(a) Sins (W/m 2)

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Figure 8.

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System performance using CVC (a) for slow change in insolation (b) for fast change in insolation.

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Figure 9.

System performance using FLC (a) for slow change in insolation (b) for fast change in insolation.

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The performance of the IC technique under varying insolation levels for the PV pumping system is investigated for slow (shiny day) and fast (cloudy day) changing insolation levels as shown in Figure 7. For both cases, the insolation level changes in the range of 1000–550 W/m2 . In order to examine the change in system dynamics under varying operating conditions, the key parameters such as Vpv , Ipv , ωrm are obtained. The system is started under loaded condition, with a threephase induction motor driving a pump load. The PV array side parameters Vpv and Ipv vary in the range of 7.8 V and 14.6 A, respectively, for the slow changing insolation level as shown in Figure 7(a). The change in the insolation level changes the system dynamics which results in a motor speed variation of 2 rad/s. For fast step changing insolation as shown in Figure 7(b), the variations of 11.4 V and 19.1 A are measured in Vpv and Ipv , respectively. In order to examine the robustness of the IC technique, the system is investigated under the fast changing insolation level. Correspondingly, the performance of the system is illustrated in Figure 7(b). System performance using CVC The transient and steady-state characteristics of the PV pumping system under investigation employing CVC are measured. The time response of the quantities under observation on the above stated operating conditions is shown in Figure 8. The converter duty ratio is adjusted using a proportional-integral controller to keep the PV array voltage constant at a reference value of 180 V. As the region of the optimal voltage for MPPT is around 180 V, the same is chosen as the reference value. Figure 8 shows that when the system is started, the operating voltage point moves towards the reference value of 180 V from the open circuit voltage and remains constant for different operating conditions. It is also evident from the figure that the rotor of induction motor slowly settles on the speed of around 105 rad/s with a variation of 1.4 rad/s. System performance with FLC The responses of the PV pumping system employing an FLC for MPPT for slow and fast changes in insolation levels are shown in Figure 9. The measured values of the parameters are given in Table 1. The insolation level varies in the range of 1000–480 W/m2 . As shown in Figure 9, when 0.2 0 –0.2 Error

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System performance using the IC technique

–0.4 –0.6 CVC FLC IC

–0.8 –1

0

0.2

0.4

0.6 Time(s)

Figure 10.

Response of normalised error of different controllers.

0.8

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the system is started, the operating voltage moves away from the open circuit voltage to the optimal voltage and correspondingly the array current is settled. The array current is directly influenced by the insolation level variation. However, the array voltage is maintained on the optimal point by varying the duty ratio of the boost converter. After a brief starting transient period, the ωrm gradually increases to a steady-state value of 132.5 and less affected by the insolation variation. A comparison of error settling response for all three MPPT techniques under investigation, carried out at a constant insolation level of 1000 W/m2 , is shown in Figure 10. The calculated error for each controller is normalised corresponding to their respective MPP values. It is evident from Figure 10 that the proposed FLC has better transient and steady-state response in comparison with other two techniques.

Conclusion The analysis on a three-phase induction motor-driven water pumping system supplied by a PV array for maximum energy transfer is carried out through a developed mathematical model. A minimal rule base FLC for maximum power tracking is proposed. The performance of the proposed controller for the system under consideration is compared with IC and CVC. In order to analyse the steady-state performance, the whole system is modelled in time domain. The performance of the proposed controller is found satisfactory. Following are the salient points of this study: • The simulation model of the PV array has been designed and the effect of insolation level and operating temperature has been studied. • Three MPPT techniques, namely IC, CVC and FLC have been developed and simulated for different operating conditions. • The simulation results prove that the performance of the proposed FLC with minimal rule base is found superior in comparison with other developed techniques. References Akbaba, M. 2007. “Matching Induction Motors to PVG for Maximum Power Transfer.” Desalination 209 (1–3): 31–38. Akbaba, M., I. Qamber, and A. Kamal. 1988. “Matching of Separately Excited DC Motor to Photovoltaic Generators for Maximum Power Output.” Solar Energy 63 (6): 375–385. Alajmi, B. N., K. H. Ahmed, S. J. Finney, and B. W. Williams. 2011. “Fuzzy Logic Control Approach of a Modified HillClimbing Method for Maximum Power Point in Microgrid Standalone Photovoltaic System.” IEEE Transactions on Power Electronics 26 (4): 1022–1030. Altas, I. H., and A. M. Sharaf. 2008. “A Novel Maximum Power Fuzzy Logic Controller for Photovoltaic Solar Energy Systems.” Renewable Energy 33 (3): 388–399. Ansari, F., S. Chatterji, and A. Iqbal. 2010. “A Fuzzy Logic Control Scheme for a Solar Photovoltaic System for a Maximum Power Point Tracker.” International Journal of Suistainable Energy 29 (4): 245–255. Bahgat, A. B. G., N. H. Helwa, G. E. Ahmad, and E. T. El-Shenawy. 2005. “Maximum Power Point Tracking Controller for PV Systems Using Neural Networks.” Renewable Energy 30 (8): 1257–1268. Benlarbi, K., L. Mokrani, and M. Nait-Said. 2004. “A Fuzzy Global Efficiency Optimization of a Photovoltaic Water Pumping System.” Solar Energy 77 (2): 203–216. Betka, A., and A. Moussi. 2004. “Performance Optimization of a Photovoltaic Induction Motor Pumping System.” Renewable Energy 29 (14): 2167–2181. Bhat, S. R., A. Pittet, and B. S. Sonde. 1987. “Performance Optimization of Induction Motor-Pump System Using Photovoltaic Energy Source.” IEEE Transactions on Industrial Applications 23 (6): 995–1000. Chiang, S. J., K. T. Chang, and C. Y. Yen. 1998. “Residential Photovoltaic Energy Storage System.” IEEE Transactions on Industrial Electronics 45 (3): 385–394. Choi, W., and C. Lee. 2012. “Photovoltaic Panel Integrated Power Conditioning System Using a High Efficiency Step-up DC–DC Converter.” Renewable Energy 41 (1): 227–234. Chouder, A., S. Silvestre, N. Sadaoui, and L. Rahmani. 2012. “Modeling and Simulation of a Grid Connected PV System Based on the Evaluation of Main PV Module Parameters.” Simulation Modelling Practice and Theory 20 (1): 46–58. Daud, A., and M. M. Mahmoud. 2005. “Solar Powered Induction Motor-Driven Water Pump Operating on a Desert Well, Simulation and Field Tests.” Renewable Energy 30 (5): 701–714.

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Appendix Parameters of induction motor: 3 HP, 3-phase, 4 pole, 220 V, 50 Hz, stator resistance (Rs) = 0.435 , rotor resistance (Rr ) = 0.816 , stator inductance (Lls ) = 2.0 mH, rotor inductance (Llr ) = 2.0 mH, mutual inductance (Lm ) = 69.3 mH, inertia constant (J) = 0.02 kg m2 , friction factor (F) = 0.002 N-m-s Parameters of centrifugal pump: Nominal power (Pn ) = 1.5 kW, nominal speed (ωn ) = 145.5 rad/s Parameters of PV array: Open circuit voltage (Voc ) = 230 V, short circuit current (Isc ) = 40 A, cell resistance (RS ) = 0.001  Parameters of boost converter: Inductor (L) = 790 mH, capacitor (C) = 2.7 mF, switching frequency = 5 kHz