Analysis,design and implementation of analog circuitry-based maximum power point tracking for photovoltaic boost DC/DC converter

Abstract

Currently, research is being devoted towards the development of fast and precise maximum power point tracking (MPPT) methods for various photovoltaic (PV) applications. Due to rapidly varying solar irradiation and cell temperature, traditional MPPT algorithms are unable to track the optimum power from PV modules. In this paper, an analog circuitry-based fast and robust MPPT method utilizing a boost DC/DC converter is presented to improve the tracking capability. The mathematical model of a PV module and design expressions for converter elements are presented. To trace the desired maximum power point (MPP), a control law is derived by synthesizing the PV characteristic curves. The steady-state and transient responses of the PV-integrated boost converter are demonstrated under various conditions of source and load using the MATLAB/Simulink platform. Furthermore, a laboratory prototype is developed to validate the proposed control strategy in the real-time application. A satisfactory agreement has been exhibited among simulation and experimental results. The superiority of the proposed MPP tracker over different existing methods is investigated. Additionally, the proposed controller distributes the energy spectrum over a wider range of frequencies and simultaneously reduces the energy concentration at the clock frequency and its multiples, so that the effect of electromagnetic interference (EMI) is reduced for certain range of loads.

Keywords

Boost DC/DC converter maximum power point tracking (MPPT)photovoltaic (PV) system

Introduction

Recently, solar energy as a non-conventional resource of energy is more significant for reducing the dependency on conventional sources. Photovoltaic (PV) systems are used to convert inexhaustible solar energy into electricity. The electric power generation from the PV module is expected to become essential for mitigating global warming and greenhouse gases (Miyatake et al., 2011). The practical applications of PVs are grid-connected power generation, electric vehicles, spacecraft, remote sensing, charging the battery, and so on (Shaw et al., 2016). However, the cost, conversion efficiency, load impedance, environment conditions (i.e. irradiance level and cell temperature) and non-linear voltage-power (V–P) characteristics are the main constraints in the utilization of PV modules (Badoud et al., 2007; Raj and Jeyakumar; 2014; Solarex, 1997; Villalva et al.; 2009; Wang et al., 2016).

Over the past few decades, research has been devoted towards the design of fast and accurate maximum power point (MPP) trackers for various PV applications. Tracking the global peak of a PV module in any conditions is necessary to guarantee the maximum obtainable power. The MPP tracking (MPPT) is a non-linear control algorithm to tune the interfacing converter’s duty ratio continuously, so that it can draw maximum power from the solar arrays irrespective of load or weather conditions (Garraoui et al., 2017; Jiang et al., 2013; Lim and Hamil, 2000; Maity and Sahu, 2016). Over the last two decades, research on several MPPT methods using DC/DC converters has been reported in the literature (Enany et al., 2016; Esram and Chapman, 2007; Subudhi and Pradhan, 2013; Xiao et al., 2007). The reviews were mostly directed towards perturb and observe (P&O) (Abdelsalam et al., 2011; Brito et al., 2013; Femia et al., 2005; Tajuddin et al., 2015) and incremental conductance (INC) (Fesharaki et al., 2017; Safari and Mekhilef, 2011; Zakzouk et al., 2016); these are implemented using a microcontroller, field programmable gate array (FPGA) or digital signal processor (DSP). The P&O-based MPPT method has an inherent limitation is that with gradual changes in input parameters, the operating point oscillates around the MPP giving rise to a waste of some amount of the available energy. Some well-documented MPPT approaches using modified P&O algorithms have been suggested to scale down the number of oscillations. Conversely, they reduce the speed of convergence and system efficiency during environment change. However, the system employing the INC algorithm has good accuracy and efficiency. It can track the MPP by comparing the INC with its instantaneous value. The computational complexity of the INC algorithm is higher than that of P&O; thus the required response time for finding the MPP is considerably increased and its hardware realization is too expensive. Ripple correlation control (RCC) yields a fast and parameter-insensitive MPPT method, which has low implementation cost for PV applications (Esram et al., 2006). Under the rapid change in weather conditions, all above-mentioned methods become confused. During this time interval, the operating point can move away from the MPP instead of keeping close to it. Duan et al. (2015), Ishaque et al. (2012) and Miyatake et al. (2011) suggested an efficient MPPT method based on the particle swarm optimization (PSO) approach. This method is complicated and some parameters must be set by the user. Veerachary et al. (2003) and Zhang and Bai (2008) proposed an artificial neural network (ANN) for an MPP tracker. The main disadvantage of ANN-based methods is that the accuracy is highly dependent on the amount of available training data and they need to be retrained when the parameters are varied.

To minimize the cost and circuit complexity, and at the same time accelerate the speed of convergence, a novel MPPT method utilizing a boost DC/DC converter is proposed. This recommended architecture is implemented with an analog circuit that provides a fast and efficient MPP tracker under rapidly changing environmental conditions. The mathematical model is presented to understand the V–I and V–P characteristics of a typical 60-W PV module by varying solar irradiance and cell temperature. The boost DC/DC converter is used to track the MPP of the PV module and deliver a higher voltage to the load/DC bus. The components and semiconductors of the boost power stage are selected based on their design expressions (Gules et al., 2008; Hauke, 2014; Pires et al., 2017). A control law is established from the V–P curve to generate the appropriate duty ratio of the converter. This MPPT control law is realized using sensing circuits, an analog multiplier, differentiator circuits, comparator circuits, an exclusive-OR (XOR) gate and a D-type flip-flop. The choice of this analog solution is interesting due to its low cost and easy to implement with DC/DC converter for low power PV applications. The switching dynamics of a positive edge-triggered D-type flip-flop is presented to explain the ON/OFF state of a metal-oxide-semiconductor field-effect transistor (MOSFET) based on the control logic generated by the XOR gate. Extensive simulations and experiments are carried out to show the tracking performance of the PV-integrated boost converter under various demanding situations. The simulation results obtained by employing the proposed algorithm are compared with the results based on P&O and INC algorithms to demonstrate better tracking capability. Finally, we briefly discuss the aperiodic mode of operation for spreading the spectra of the PV voltage to reduce the electromagnetic interference (EMI) problem (Li et al., 2007; Qin et al., 2015; Stankovic et al., 1995).

The remaining of this paper is organized in the following way. The following section expresses the mathematical modelling of PV cell and design aspects of boost DC/DC converter. Then the theoretical analysis and steps for hardware implementation of the proposed analog circuitry-based MPPT controller are discussed. The peak power tracking performance is demonstrated through numerical simulations and a laboratory prototype, and finally the conclusions are presented.

PV-integrated boost DC/DC converter

A block diagram of the stand-alone PV system for DC load applications is presented in Figure 1. It comprises a PV module, a boost DC/DC converter with an MPPT control circuit and a load. The sensed PV current and voltage are fed to the controller and the generated gating pulse is employed to drive the boost converter for MPPT operation. In this system, load dissipates the PV power at a higher voltage level than the source.

Figure 1.

Block diagram of a stand-alone photovoltaic (PV) system with maximum power point tracking (MPPT) controller.

Mathematical modelling of PV Cell

The equivalent circuit of a single diode-based practical PV cell is illustrated in Figure 2. It consists of a light generated current source $(I_{ph})$ in parallel with a diode $(D_{1})$ , a shunt resistance $(R_{sh})$ and a resistance $(R_{s})$ in series (Badoud et al., 2007; Raj and Jeyakumar; 2014; Villalva et al.; 2009; Wang et al., 2016). By applying Kirchhoff's voltage law (KVL) at node ‘ $a$ ’, the current generated by the PV cell $(i_{PV})$ is obtained as

i_{PV} = I_{ph} - i_{D 1} - i_{sh}

(1)

where $i_{D 1}$ and $i_{sh}$ are the average current through the diode $D_{1}$ and leakage current in the shunt resistor, respectively. $I_{ph}$ , which is directly proportional to the solar irradiation $(G)$ and temperature $(T)$ , can be expressed as

I_{ph} = [I_{ph, n} + K_{i} (T - T_{n})] \frac{G}{G_{n}}

(2)

where $I_{ph, n}$ , $T_{n}$ , $G_{n}$ and $K_{i}$ are the photon current, operating temperature, irradiance and short-circuit current coefficient at the standard test condition (STC), 300 K and 1000 W/m². Referring to the theory of semiconductors, $i_{D 1}$ can be expressed as

i_{D 1} = I_{r} [\exp (\frac{v_{D 1}}{η \cdot N_{s} \cdot V_{T}}) - 1]

(3)

where

I_{r} = \frac{I_{sc, n} + K_{i} (T - T_{n})}{\exp (\frac{V_{oc, n} + K_{v} (T - T_{n})}{η \cdot N_{s} \cdot V_{T}}) - 1}

is the reverse saturation current of the diode, $v_{D 1}$ is the voltage imposed on the diode equal to $v_{PV} + R_{s} \cdot i_{PV}$ , $η$ is the diode ideality factor, $N_{s}$ is the number of cells connected in series, $V_{T} = k \cdot T / q$ is the thermal voltage imposed on the diode, $k$ is the Boltzmann’s constant (1.381×10⁻²³ J/K), $T$ is the operating temperature in Kelvin, $q$ is the electron charge (1.602×10⁻¹⁹ C), $I_{sc, n}$ is the short-circuit current at STC, $V_{oc, n}$ is the open-circuit voltage at STC, $K_{v}$ is the open-circuit voltage coefficient. Substituting (2) and (3) into (1), the I–V characteristic equation of a PV cell is written as

i_{PV} = I_{ph} - I_{r} [\exp (\frac{v_{PV} + R_{s} \cdot i_{PV}}{η \cdot N_{s} \cdot V_{T}}) - 1] - \frac{v_{PV} + R_{s} \cdot i_{PV}}{R_{sh}}

(4)

Figure 2.

Equivalent circuit of a photovoltaic (PV) cell.

The range of the operating voltage and current of the cell can be determined from the open-circuit and short-circuit conditions, respectively. From the preceding equation, the open-circuit voltage $(V_{oc})$ and short-circuit current $(I_{sc})$ can be computed as

\begin{matrix} V_{oc} |_{i_{PV} = 0} = η \cdot N_{s} \cdot V_{T} \cdot \ln (\frac{I_{ph}}{I_{r}} + 1) \\ I_{sc} |_{v_{PV} = 0} = I_{ph} / (1 + \frac{R_{s}}{R_{sh}}) \end{matrix}

(5)

As the ratio between $V_{oc}$ and $R_{sh}$ is negligible, $V_{oc}$ can be derived from $i_{D 1}$ . Also, by considering $i_{D 1} \approx 0$ under short-circuit conditions, $I_{sc}$ can be determined. Finally, the output power of the PV module $(p_{PV})$ is expressed as $p_{PV} = v_{PV} \cdot i_{PV}$ .

The Solarex MSX60 PV module is considered the reference module for simulation (Solarex, 1997) and the detailed parameters are summarized in Table 1. The electrical characteristics of the V–I and V–P curves of the PV module for different irradiances are shown in Figures 3(a) and (b), respectively. It is noted that with the increase of irradiation level from 250 to 1000 W/m², the magnitude of short-circuit current $I_{sc}$ is effectively increased from 0.9 to 3.8 A by using (2) and (4), whereas the open-circuit voltage $V_{oc}$ is slightly varied from 19.57 to 21.1 V. Therefore, the maximum power $P_{\max}$ is raised from 13.28 to 59.73 W, shown in Figure 3(b). Similarly, the V–I and V–P characteristics of the PV module by varying temperature levels at STC irradiance are demonstrated in Figures 3(c) and (d), respectively. Figure 3(d) implies the rise of $P_{\max}$ from 53.18 to 59.73 W with subsequent variations of $T$ from 25° to 55°C.

Table 1.

Electrical parameters of the Solarex MSX60 photovoltaic (PV) module.

Parameters	Symbol	values
Maximum power	$P_{\max}$	$60$ W
Voltage at MPP	$V_{MPP}$	$17.1$ V
Current at MPP	$I_{MPP}$	$3.5$ A
Guaranteed minimum $P_{\max}$	–	$58$ W
Open circuit voltage	$V_{oc}$	$21.1$ V
Short circuit current	$I_{sc}$	$3.8$ A
Open circuit voltage coefficient	$K_{v}$	$- (80 \pm 10)$ mV/°C
Short circuit current coefficient	$K_{i}$	$(0.065 \pm 0.015)$ %/°C
Number of cells connected in series	$N_{s}$	36

MPP, maximum power point.

Figure 3.

V–I and V–P characteristics of Solarex MSX60 photovoltaic (PV) module: (a) and (b) for different irradiation levels at temperature of 25°C; (c) and (d) for different temperature levels at irradiance of 1000 W/m².

Selection and design of boost converter

Figure 4(a) exhibits the schematic diagram of a boost DC/DC converter, consisting of a MOSFET $(SW)$ , a power diode $(D_{2})$ , two capacitors $(C_{1}, C_{2})$ and an inductor $(L)$ . $L$ and $C_{2}$ are used to reduce the ripples contained in the input current and output voltage waveforms, respectively. The converter is operated in continuous conduction mode with two different modes based on the status of the MOSFET. In the first mode of operation, $SW$ is turned ON, $D_{2}$ is reversed biased and the load is disconnected from the source, as demonstrated in Figure 4(b). During this period, as the PV voltage $(v_{PV})$ appears across the inductor, the current flowing through the inductor $(i_{L})$ linearly increases by storing magnetic energy. When the MOSFET is OFF, $D_{2}$ is forward biased and the voltage across $L$ $(v_{L})$ is added to the PV voltage $(v_{PV})$ to generate high output voltage $(v_{o})$ , shown in Figure 4(c). The reasons for the selection of the boost converter in renewable power generation have following advantages over the buck converter:

The boost converter is used to step-up the voltage level of PV module by maintaining the same input power as per the load requirement.

It requires a smaller and more economical input capacitor $(C_{1})$ than the buck converter to smooth the continuous input current from the PV array (Xiao et al., 2007).

Driving a boost converter is easier than the buck converter, as the power switch has a ground terminal.

In the boost topology, the diode $(D_{2})$ can act as a blocking diode to avoid reverse current flows, which causes leakage loss or huge damage in case of the battery load.

Figure 4.

Equivalent circuits of a boost DC/DC converter: (a) boost converter circuit configuration; (b) mode I: SW–ON; (c) mode II: SW–OFF.

The power stage design of the boost converter is particularly based on the average voltage and current values of the converter (Gules et al., 2008; Hauke, 2014; Pires et al., 2017). The parameters associated with the design of the PV-integrated step-up converter are average input voltage $(V_{PV})$ , input current $(I_{PV})$ , output voltage $(V_{o})$ , load resistance $(R_{o})$ and switching frequency $(f_{s})$ , and their corresponding values are 17.56 V, 3.3 A, 33.4 V, 20 Ω and 50 kHz. The design equations are stated below.

Duty ratio

The steady-state duty ratio $(D)$ is the faction of switching period $(T_{s})$ during which SW is in the ON state. For the boost converter, $D$ can be calculated in terms of input and output voltages as follows

D = \frac{V_{o} - V_{PV}}{V_{o}} = \frac{33.4 - 17.56}{33.4} = 0.474

(6)

Inductor

Referring to Figure 4(b), during $(0 \leq t \leq D T_{s})$ , the voltage across the inductor $(v_{L} = L \cdot Δ i_{L} / D T_{s})$ is equal to $V_{PV}$ . The value of the estimated inductor ripple current $(Δ i_{L})$ is assumed to be ≤20% of $I_{PV}$ , i.e. $Δ i_{L} = 0.66$ A. Thus, the inductance is calculated by

L \geq \frac{V_{PV} \cdot D}{Δ i_{L} \cdot f_{s}} = \frac{17.56 \cdot 0.474}{0.66 \cdot 50 \cdot 10^{3}} = 0.252 mH

(7)

An inductance of 0.3 mH is utilized in the prototype.

Input capacitor

The input capacitor, $C_{1}$ is mainly designed to filter out the current ripples produced by the inductor, resulting a smooth input current $(i_{PV})$ from the PV module. In a switching period $T_{s}$ , the charge $(Δ Q_{1} = C_{1} \cdot Δ v_{c 1})$ stored in $C_{1}$ is $Δ i_{L} \cdot T_{s} / 8$ . The input voltage ripple is denoted $Δ v_{c 1}$ , which is considered $\leq 10$ % of the $V_{PV}$ . The value of $C_{1}$ is realized using the following expression

C_{1} \geq \frac{Δ i_{L}}{8 \cdot Δ v_{c 1} \cdot f_{s}} = \frac{0.66}{8 \cdot 1.75 \cdot 50 \cdot 10^{3}} = 0.942 μ F

(8)

The selected value of $C_{1}$ is 1 µF.

Output capacitor

The output capacitor $(C_{2})$ is designed such that the ripple contained in $v_{o}$ is negligible. The output voltage ripple $(Δ v_{c 2})$ is restricted by $\leq 1$ % of $V_{o}$ , assuming $Δ v_{c 2} = 0.334$ V. The expression for $Δ v_{c 2}$ is $D \cdot I_{o, \max} / (C_{2} \cdot f_{s})$ , where $I_{o, \max} = (V_{o} / R_{o, \min}) = 1.67$ A. Thus, the capacitance is calculated by

C_{2} \geq \frac{D \cdot I_{o, m a x}}{Δ v_{c 2} \cdot f_{s}} = \frac{0.474 \cdot 1.67}{0.334 \cdot 50 \cdot 10^{3}} = 47.4 μ F

(9)

A value of 100 µF is chosen in this paper. This value may increase if the load demands a ripple free output voltage.

Power switch

In Figure 4(b), the switch $(SW)$ carries a peak current of $i_{SW, peak}$ called the maximum current flowing through the MOSFET. It is defined as

i_{SW, peak} = I_{PV} + \frac{Δ i_{L}}{2} = 3.3 + \frac{0.66}{2} = 3.63 A

(10)

In general, the current rating of MOSFET should be greater than $i_{SW, peak}$ . Similarly, in mode II of the operation, the voltage across the power switch is equal to $V_{o}$ , as shown in Figure 4(c). Therefore, the $SW$ voltage rating should be much greater than 33.4 V. The power switch adopted in the experimental analysis is an N-channel MOSFET IRF540 whose current and voltage ratings are 21 A and 500 V, respectively.

Diode

The desired current rating of the diode $(D_{2})$ is equal to peak output current $(i_{0, peak})$ . Generally, a Schottky diode is used to reduce losses and its peak current rating is higher than the average rating. The power dissipation of $D_{2}$ is $i_{D 2} \cdot v_{D 2}$ .

Efficiency

The efficiency of the system is defined by (11), considering the PV module as the power input and output is the load.

η (%) = (\frac{p_{o}}{p_{PV}}) \times 100

(11)

Proposed MPPT controller

MPPT control is essential for estimating the maximum power available from a PV module and for finding a satisfactory result when the parameters drift (particularly temperature and irradiance) or STC values vary (Lim and Hamil, 2000). By employing this controller, an appropriate duty cycle is developed, which is utilized to drive the boost converter. To obtain MPP, a robust analog technique has been recommended in this research, and its synthesis and implementation are outlined below.

Synthesis of MPPT controller

Figure 5(a) represents the V–P characteristics of PV module. This curve attains a maximum power $(P_{\max})$ at MPP whose coordinates are given by $(V_{MPP}, P_{\max})$ . The derivative of the V–P curve is shown in Figure 5(b). It is observed that the MPP is located where the power slope of the PV is null. Mathematically, this characteristic can be represented as

\frac{\partial p_{PV}}{\partial v_{PV}} = {\begin{matrix} + ve & if (V_{MPP} - v_{PV}) > 0 \\ - ve & if (V_{MPP} - v_{PV}) < 0 \\ 0 & otherwise \end{matrix}

(12)

Figure 5.

Maximum power point tracking (MPPT) curves: (a) V–P characteristic; (b) V– $\partial P$ / $\partial V$ characteristic.

From the preceding equation, it is ensured that the voltage across the input capacitor $v_{PV}$ starts to increase (decrease) towards $V_{MPP}$ for a positive (negative) value of power gradient $\partial p_{PV} / \partial v_{PV}$ . The voltage derivative with respect to $t$ can be written as

\frac{d v_{PV}}{dt} = {\begin{matrix} + ve & if (V_{MPP} - v_{PV}) > 0 \\ - ve & if (V_{MPP} - v_{PV}) < 0 \\ 0 & otherwise \end{matrix}

(13)

Equation (13) can be defined in an alternative way as $w_{vt} = (V_{MPP} - v_{PV}) / k_{1}$ , where $k_{1}$ is a positive constant that controls the convergence rate; the smaller the value of $k_{1}$ , the faster the speed of convergence. It is noted that the right-hand sides of (12) and (13) have similar structures. Thus, we can establish a simple relation between left-hand sides.

w_{vt} \propto \frac{\partial p_{PV}}{\partial v_{PV}} = k_{2} \cdot \frac{\partial p_{PV}}{\partial v_{PV}}

(14)

where $k_{2} > 0$ is a constant value. $p_{PV}$ depends on the intermediate variable $v_{PV}$ and $v_{PV}$ depends on $t$ ; therefore $p_{PV}$ and $v_{PV}$ are considered dependent variables. Applying the chain rule

\frac{d p_{PV}}{dt} = \frac{\partial p_{PV}}{\partial v_{PV}} \cdot \frac{d v_{PV}}{dt} \Rightarrow \frac{\partial p_{PV}}{\partial v_{PV}} = \frac{w_{pt}}{w_{vt}}

(15)

On simplification of (15) using (14), we have

w_{vt} = k_{2} \cdot \frac{w_{pt}}{w_{vt}}

(16)

In practice, the hardware implementation of the above-mentioned equation is slightly problematic due to the existence of an algebraic loop and appearance of $w_{vt}$ on both the sides of (16), which creates a high-frequency oscillation. In addition to, the analog divider circuit causes imperfect operations and a singularity problem when $w_{vt}$ becomes null (i.e. $v_{PV} = V_{MPP}$ ). To overcome these drawbacks, the preceding equation can be rearranged into the form ${w_{vt}}^{2} = k_{2} \cdot w_{pt}$ . However, squaring of $w_{vt}$ ignores the necessary sign information.

To escape from the singularity problem and at the same time enhance the speed of convergence, the authors recommended a function $f (\cdot)$ to realize (16) in a unique manner. It can be defined as

f (m) = {\begin{matrix} + 1 & if m > 0 \\ - 1 & if m \leq 0 \end{matrix}

(17)

Equation (16) can be rewritten as

f (w_{vt}) \leftarrow f (\frac{w_{pt}}{w_{vt}}) \equiv \frac{f (w_{pt})}{f (w_{vt})} \equiv f (w_{pt}) \cdot f (w_{vt})

(18)

In the above equation, the right-hand side information is assigned to the left-hand side. The result determines whether $v_{PV}$ should be increased or decreased such that $\partial p_{PV} / \partial v_{PV} = 0$ . Additionally, the use of $f (\cdot)$ can avoid the necessity of an analog divider circuit. The truth table of the control law is summarized in Table 2. In the table, when $f (w_{pt}) \cdot f (w_{vt}) = + 1$ , $v_{PV}$ should be increased; otherwise $v_{PV}$ should be decreased.

Table 2.

Truth table of the control law.

Test cases	Right-hand side of (18)					Left-hand side of (18)	State of $v_{PV}$
Test cases	$w_{vt}$	$w_{pt}$	$f (w_{vt})$	$f (w_{pt})$	$f (w_{pt}) \cdot f (w_{vt})$	$f (w_{vt})$	State of $v_{PV}$
1	$> 0$	$> 0$	$+ 1$	$+ 1$	$+ 1$	$+ 1$	Increase
2	$\leq 0$	$> 0$	$- 1$	$+ 1$	$- 1$	$- 1$	Decrease
3	$\leq 0$	$\leq 0$	$- 1$	$- 1$	$+ 1$	$+ 1$	Increase
4	$> 0$	$\leq 0$	$+ 1$	$- 1$	$- 1$	$- 1$	Decrease

Implementation of analog MPPT controller

The hardware implementation of proposed controller is illustrated in Figure 6. The necessary voltage and current waveforms of the PV module are measured through analog sensors constructed with op-amps, which are further considered test signals for the MPPT controller. A low-cost analog multiplier AD633 is utilized to evaluate the output power $(p_{PV})$ from these signals. The calculated $p_{PV}$ and measured $v_{PV}$ are fed to the inverting differentiator circuit to obtain the first derivatives $- w_{pt}$ and $- w_{vt}$ , correspondingly. This circuit is designed by a first-order high-pass filter using Op-amp TL084 IC, which has a pass band gain of $- R_{f} / R_{1}$ and a cut-off frequency of $1 / (2 π \cdot R_{1} \cdot C_{1})$ . Instead of adopting −1/ $+ 1$ to express the sign of a value, it is more convenient to use a logic signal with two distinguishable levels (i.e. 0/1). Therefore, two comparators are assigned to determine their individual sign, by producing Boolean logic $w_{p}$ and $w_{v}$ . In practice, the references $- w_{pt}$ and $- w_{vt}$ are applied to the inverting input of the LM311 comparator ICs and their non-inverting input is grounded. When $w_{pt} > 0$ , the output of comparator $(w_{P})$ . is drawn a logic $1$ (HIGH), else $0$ (LOW). Similarly, the second comparator output $w_{vt}$ has produced two logic states. The sign multiplication of $w_{pt}$ and $w_{vt}$ is represented by a Boolean function, which is executed using an XOR gate. The logic output of the XOR gate $(Z)$ indicates whether the PV voltage $(v_{PV})$ should increase or decrease to achieve MPP. If $Z = 0$ (SW is open) then $v_{PV}$ will increase and vice-versa.

Figure 6.

Implementation of proposed architecture for maximum power point (MPP) tracker.

On the other hand, $v_{PV}$ can be varied by controlling the power switch $SW$ automatically. When $SW$ is opened, $C_{1}$ starts charging so that $v_{PV}$ increases, as shown in Figure 4(c). To decrease $v_{PV}$ , $C_{1}$ is made to discharge by closing the MOSFET, as depicted in Figure 4(b). The ON and OFF position of MOSFET can be made to correlate perfectly with the logic value of $Z$ to vary the input capacitor voltage, i.e. $v_{PV}$ . This output is sampled by a positive edge-triggered D-type flip-flop at a clock frequency of $f_{s}$ and produces a Boolean output $(Q)$ to drive the power MOSFET IRF540. Simultaneously, it also reduces the effect of certain interference generated by the converter’s switching action. In this D-type flip-flop, the data input $(D)$ is connected to $+ V_{cc}$ (logic HIGH) and logic $Z$ is treated as the control input $(\bar{CLR})$ . The switching regulator SG3524 is incorporated to generate the clock pulse. The switching dynamics of analog MPPT technique using D-type flip-flop are shown in Figure 7.

Figure 7.

Switching dynamics of proposed maximum power point tracking (MPPT) controller using positive edge-triggered D-type flip-flop.

Two comparators have four permissible test cases, discussed in Table 3. Analysing test cases 1 and 2, the locations of the operating point are moving towards the MPP. This can be accomplished by corresponding charging and discharging of $C_{1}$ . Considering test case 3, both $v_{PV}$ and $p_{PV}$ are decreasing and the operating point is departing from the MPP. To achieve this, the controller should open the switch automatically to charge $C_{1}$ . Furthermore, with an increase in $v_{PV}$ (i.e. $w_{vt} > 0$ ) and a decrease in $p_{PV}$ (i.e. $w_{pt} \leq 0$ ) corresponding to case 4, the controller closes the switch so that $C_{1}$ can discharge and $v_{PV}$ will decrease. It is concluded that at any point of starting location on the V–P curve, $v_{PV}$ converges upon $V_{MPP}$ .

Table 3.

Investigation of four permissible test cases.

Test cases	$w_{vt}$	$w_{pt}$	$w_{v}$	$w_{p}$	$Z$	Status of $SW$	Condition of $C_{1}$	State of $v_{PV}$
1	$> 0$	$> 0$	$1$	$1$	$0$	Open	Charging	Increase
2	$\leq 0$	$> 0$	$0$	$1$	$1$	Close	Discharging	Decrease
3	$\leq 0$	$\leq 0$	$0$	$0$	$0$	Open	Charging	Increase
4	$> 0$	$\leq 0$	$1$	$0$	$1$	Close	Discharging	Decrease

SW, switch.

Results and discussion

Simulation results

To evaluate the efficacy of the PV-integrated boost converter, the system is modelled and analysed in the time-domain-based MATLAB/Simulink environment. The parameters of the boost converter were as designed previously. In this study, the tracking performance of the MPPT controller is verified under various operating conditions.

The steady-state periodic waveforms of the MPPT system under nominal load conditions (i.e. 20 Ω) are demonstrated in Figures 8(a)–(f). In this case, the value of solar irradiation and cell temperature are taken as 1000 W/m² and 25°C, respectively. The figures from top to bottom represent PV current $(i_{PV})$ , PV voltage $(v_{PV})$ , input power $(p_{PV})$ , output current $(i_{o})$ , output voltage $(v_{o})$ and output power $(p_{o})$ , and their corresponding mean values are 3.49 A, 17.12 V, 59.74 W, 1.66 A, 33.43 V and 55.49 W. It confirms that the proposed MPPT controller efficiently tracks the PV voltage and current at the true MPP.

Figure 8.

Steady-state response of photovoltaic (PV) integrated boost converter at $R_{o} = 20$ Ω: (a) PV current $(i_{PV})$ ; (b) PV voltage $(v_{PV})$ ; (c) input power $(p_{PV})$ ; (d) output current $(i_{o})$ ; (e) output voltage $(v_{o})$ ; (f) output power $(p_{o})$ .

The switching dynamics of the recommended architecture using a positive edge-triggered D-type flip-flop are displayed in Figure 9. Here a 50 kHz signal with 1.2 μs pulse width, logic 1 (HIGH) and XOR output $Z$ are considered $CLK$ , data and $\bar{CLR}$ inputs of the D-type flip-flop, respectively, and their corresponding waveforms are shown in Figures 9(a)–(c). By analysing the logic state of flip-flop output $Q$ , the proposed MPPT decides the nature of inductor current $(i_{L})$ and input capacitor voltage $(v_{c 1})$ accordingly.

Figure 9.

Switching dynamics of proposed maximum power point tracking (MPPT) under nominal load condition, i.e. periodic mode: (a) clock pulse $(CLK)$ ; (b) control input $(\bar{CLR})$ ; (c) flip-flop output $(Q)$ ; (d) inductor current $(i_{L})$ ; (e) input capacitor voltage $(v_{c 1})$ .

Figures 10(a)–(f) demonstrate the current, voltage and power waveforms of the MPPT system at $R_{o} = 40$ Ω. It is observed that for a higher value of load resistance, the system goes to aperiodic mode due to the fast-scale instability of MPPT system (Maity and Sahu, 2016). Thus, non-uniform ripples appeared in the PV waveforms. The average values of $i_{PV}$ , $v_{PV}$ and $p_{PV}$ are measured as 2.95 A, 18.32 V and 54.04 W, respectively. Furthermore, the system efficiency is reduced than the periodic mode that results in a decrease in load power $(p_{o})$ . In this mode, the digital signals $\bar{CLR}$ and $Z$ are aperiodic in nature, so an abnormal ripple is observed in the $i_{L}$ and $v_{c 1}$ waveforms. The switching patterns under aperiodic mode are illustrated in Figures 11(a)–(e).

Figure 10.

Steady-state performance, when $R_{o}$ is sufficiently large, i.e. for 40 Ω: (a) photovoltaic (PV) current $(i_{PV})$ ; (b) PV voltage $(v_{PV})$ ; (c) input power $(p_{PV})$ ; (d) output current $(i_{o})$ ; (e) output voltage $(v_{o})$ ; (f) output power $(p_{o})$ .

Figure 11.

Switching patterns of the proposed maximum power point tracking (MPPT) controller under light load condition, i.e. aperiodic mode: (a) clock pulse $(CLK)$ ; (b) control input $(\bar{CLR})$ ; (c) flip-flop output $(Q)$ ; (d) inductor current $(i_{L})$ ; (e) input capacitor voltage $(v_{c 1})$ .

Figures 12(a)–(f) depict the dynamic performance of the proposed MPPT system under an irradiance level variation. In this study, the irradiance level is subjected to a decrease of 25% (i.e. from 1000 to 750 W/m²) at $t = 0.23$ s, and maintained constant during $t = 0.23$ – $0.27$ s; then it comes back to the initial level. It is observed that both $i_{PV}$ and $v_{PV}$ exhibit fast transient response and stable operation. With the decrease in $G$ , the magnitude of $I_{MPP}$ effectively decreases compared with $V_{MPP}$ ; hence $P_{\max}$ is decreased (referred to Figures 3a and b). It is observed from the figures that the settling time for $i_{PV}$ and $v_{PV}$ under this test case is instantaneous.

Figure 12.

Dynamic response of proposed maximum power point tracking (MPPT) with an irradiation level variation during $0.23 s \leq t \leq 0.27 s$ : (a) photovoltaic (PV) current $(i_{PV})$ ; (b) PV voltage $(v_{PV})$ ; (c) input power $(p_{PV})$ ; (d) output current $(i_{o})$ ; (e) output voltage $(v_{o})$ ; (f) output power $(p_{o})$ .

The tracking performances of INC, P&O and the proposed MPPT methods under varying irradiance, cell temperature and load impedance are shown in Figures 13 –15. The step size ( $Δ D$ ) adopted in INC and P&O is 1%. In general, as the switching converter intrinsically contains a switching ripple on the PV voltage, an optimum value of ( $Δ D$ ) should be chosen, such that the voltage variation due to perturbation of D ( $Δ D$ ) should be greater than the amplitude of the switching ripple of the PV voltage (Femia et al., 2005). In Figure 13, the tests comprise four step changes of irradiance level: STC, 500 W/m² during 0.035 s≤t<0.09 s, 350 W/m² during 0.09 s≤t<0.13 s and 750 W/m²t≥0.13 s. Similarly, Figures 14 and 15 show the performance comparison under the variation in cell temperature and load impedance. From the figures, it can be visualized that the proposed drift-free analog MPPT controller is able to extract the global peaks of the PV variables ( $i_{PV}$ , $v_{PV}$ and $p_{PV}$ ) with a shorter time in all four scenarios, whereas tracking based on the conventional INC suffers from wide oscillation and its average values are less than the MPP. However, the conventional P&O exhibits successful tracking performance, but it needs more time to track MPP during the step changes. In terms of both steady-state and transient responses, the proposed MPPT technique shows excellent behaviour in comparison with the traditional methods under variation in source and load parameters. The proposed MPPT controller provides a relatively larger bandwidth than P&O and INC to eliminate the low-frequency limit cycle oscillation, and reduces the cross-coupling effects. Hence, this method does not show any low frequency oscillations when there is a change in parameters.

Figure 13.

Tracking performances of incremental conductance (INC), perturb and observe (P&O) and proposed maximum power point tracking (MPPT) controller under step changes in solar irradiance at T=25°C and $R = 20$ Ω: (a) photovoltaic (PV) current $(i_{PV})$ behaviour; (b) PV voltage $(v_{PV})$ behaviour; (c) input power $(p_{PV})$ behaviour.

Figure 14.

Tracking performances of incremental conductance (INC), perturb and observe (P&O) and proposed maximum power point tracking (MPPT) controller under step changes in cell temperature at $G = 1000$ W/m² and $R = 20$ Ω: (a) photovoltaic (PV) current $(i_{PV})$ behaviour; (b) PV voltage $(v_{PV})$ behaviour; (c) input power $(p_{PV})$ behaviour.

Figure 15.

Tracking performances of incremental conductance (INC), perturb and observe (P&O) and proposed maximum power point tracking (MPPT) controller under step changes in load impedance at STC: (a) photovoltaic (PV) current $(i_{PV})$ behaviour; (b) PV voltage $(v_{PV})$ behaviour; (c) input power $(p_{PV})$ behaviour.

Experimental implementation and results

To evaluate the performance of the proposed MPPT system equipped with the PV module, a prototype is developed and tested in the laboratory under various operating conditions, such as steady-state and transients. A photograph of the test set-up developed for experimental study is shown in Figure 16. The boost converter parameters used for real-time analysis were described previously. A clock frequency of 50 kHz has been selected for the D-type flip-flop operation. This frequency is used to sample the XOR gate output so that the output of the flip-flop produces a digital data that decides to switch ON or OFF the power switch only at regular intervals in time. As a result, the power MOSFET IRF540 is switched at a 50 kHz gating signal through the driver circuit. The input and output waveforms are captured and stored by a 100-MHz, four-channel DSOX3014A digital storage oscilloscope (DSO). Detail realization of the circuitry have been discussed previously.

Figure 16.

Photograph of hardware set-up for implementing the proposed maximum power point tracking (MPPT) controller.

The steady-state performances of the MPPT system at the following operating conditions of the PV source and load: $G = 350$ W/m², T=35°C and $R_{o} = 75$ Ω, are depicted in Figures 17(a)–(c). Under these operating conditions, the average voltage and current provided by the PV module, $v_{PV}$ and $i_{PV}$ are maintained around 15.7 V and 0.8 A, respectively, as shown in Figure 17(a). These steady-state values are close to their analytical values and indicate the coordinates of MPP. The maximum power $(P_{\max})$ extracted from the PV module is approximately 12.56 W. It can be observed that by the action of proposed analog MPPT technique, the boost converter input voltage $(v_{PV})$ and input current $(i_{PV})$ are varied to track the MPP of the PV source. The waveforms of expected output voltage $(v_{o})$ and output current $(i_{o})$ of the MPPT system are illustrated in upper and lower traces of Figure 17(b), respectively, and their corresponding values are found to be 28 V and 0.37 A. It can be noted that the analytical and measured values of output parameters were in good agreement. The efficiency of the boost DC/DC converter prototype is around 83% at nominal load. Figures 17(c) and (d) show the experimental switching dynamics of the D-type flip-flop under periodic mode (here $R_{o}$ is chosen as 75 Ω) and aperiodic mode (where $R_{o} = 105$ Ω) of operation, respectively. In each figure, from top to bottom traces identify $v_{PV}$ , $i_{PV}$ and $CLK$ (the clock signal whose frequency is 50 kHz). From the figures, it can be demonstrated that at two different values of $R_{o}$ , $v_{PV}$ and $i_{PV}$ accurately track their corresponding MPP values. Under aperiodic mode, the average values of $v_{PV}$ and $i_{PV}$ are approximated as 14.3 V and 0.75 A, respectively, as displayed in Figure 17(d). The extracted PV power is around 10.7 W, which is slightly less than the power obtained in periodic mode. This power loss happens due to the abnormal ripples appearing in the current and voltage waveforms. Hence, the proposed MPPT system prefers to operate in the periodic mode to achieve better efficiency and lower smooth ripple.

Figure 17.

Experimental waveforms under steady weather conditions at G=350 W/m² and T=35°C: (a) periodic mode of operation, upper trace: photovoltaic (PV) voltage $(v_{PV})$ and lower trace: PV current $(i_{PV})$ ; (b) periodic mode of operation, upper trace: output voltage $(v_{o})$ and lower trace: output current $(i_{o})$ ; (c) periodic mode of operation, upper trace: PV voltage $(v_{PV})$ , middle trace: PV current $(i_{PV})$ and lower trace: clock pulse $(CLK)$ ; (d) aperiodic mode of operation, upper trace: PV voltage $(v_{PV})$ , middle trace: PV current $(i_{PV})$ and lower trace: clock pulse $(CLK)$ .

Figure 18 demonstrates the dynamic tracking performance of the proposed analog MPPT under a realistic example of variation in irradiance $G$ . In this study, the PV panel is illuminated artificially by three levels of irradiance such as 350 W/m² during $t_{1} \leq t < t_{2}$ , 80 W/m² during $t_{2} \leq t < t_{3}$ and again 350 W/m² during $t_{3} \leq t < t_{4}$ . It can be observed that the PV-integrated boost converter regulates the input capacitor voltage $v_{c 1}$ towards its new set points (i.e. 15.7 V for $t < t_{2}$ , 9.2 V for $t_{2} \leq t < t_{3}$ and 15.7 V for $t \geq t_{3}$ ) within $390$ and $190$ ms, following a step decrease and increase of irradiance level. When irradiance is decreased, the input capacitor $C_{1}$ discharges to compensate for the power supplied by the PV source. In this transition, the trajectory of $v_{c 1}$ is converged exponentially. For a increase in irradiance, the generated PV power is more than the demand load power, so that one may expect a lower oscillatory dynamic response during the reaching phase. The trajectory evolution from one level to another is governed by a simple first-order linear differential equation. The irradiance level change does not produce any undesirable response (i.e. unstable behaviour or spikes); thus the proposed MPPT system associated with the PV source manages this transient situation smoothly.

Figure 18.

Experimental waveform of photovoltaic (PV) voltage $(v_{PV})$ under dynamic weather conditions at T=35°C.

EMI reduction: a further study of MPPT system

The semiconductor device of the MPP tracker is mainly driven by a high-frequency switching signal that results in various unwanted harmonics at multiples of the converter switching frequency $(f_{s})$ . These undesirable harmonics are often associated with EMI, which may degrade the performance of the MPPT system (Stankovic et al., 1995). Conceptually, this EMI is mainly due to the energy typically concentrated at the clock and its multiple frequencies. Some application, where many functional blocks having mixed-signal power management circuits, are integrated on the same substrate or nearby (Qin et al., 2015), and these switching harmonics may disturb the sensitive blocks through EMIs. Therefore, the solar MPP tracker should also provide EMI regulation along with fast and accurate tracking under rapidly changing solar irradiation and cell temperature. The most efficient approach for suppressing the spectral peaks is spread-spectrum clock generation (Li et al., 2007), where instead of maintaining a constant frequency, this method modulates the system clock across a much smaller frequency that creates a frequency spectrum with side band harmonics.

The energy spectrums of the PV voltage $(v_{PV})$ , under both periodic and aperiodic modes of operations, are shown in Figures 19(a) and (b), respectively. Figure 19(a) implies that the energy is mainly concentrated at the switching frequency $f_{s}$ and its multiples, which shows the EMI problem. When the system operates in the aperiodic mode, the proposed MPPT can spread the energy spectrum of switching signal over a wider range of frequencies and the energy concentration at the clock frequency and its harmonics is also reduced simultaneously, as shown in Figure 19(b). Experimental validation of this concept using the proposed MPPT is illustrated in Figure 20. From the figures, it is observed that at the periodic mode of operation, spectral peaks occur at switching frequency $f_{s}$ and integral multiples of $f_{s}$ , as shown in Figure 20(a). However, in Figure 20(b), these spectral peaks are considerably reduced under the aperiodic mode of operation. Such a reduction of peaks represents an additional benefit of lower EMI, which is achieved without any extra hardware circuitry adding to the proposed MPPT controller.

Figure 19.

The magnitude spectrum of simulated photovoltaic (PV) voltage waveform $(v_{PV})$ at STC: (a) periodic mode of operation when $R_{o} = 20$ Ω; (b) aperiodic mode of operation when $R_{o} = 40$ Ω.

Figure 20.

The magnitude spectrum of experimental photovoltaic (PV) voltage waveform $(v_{PV})$ at G=350 W/m² and T=35°C: (a) periodic mode of operation when $R_{o} = 75$ Ω; (b) aperiodic mode of operation when $R_{o} = 105$ Ω.

Performance assessment

The comparative performances of various existing MPPT techniques with the recommended method are summarized in Table 4. It is observed that the PI-based controllers and adaptive P&O methods are most suitable for extracting maximum power with a high tracking performance, fast convergence and low ripple voltage in steady state. From an experimental point of view, PI-based P&O has a medium level of complexity, whereas adaptive P&O has the highest level of complexity. However, as these techniques are implemented in the digital domain by using either the microcontroller or FPGA platform, they require more computation time and as a result the closed-loop PV system exhibits quantization-induced limit cycle oscillations (Venturini et al., 2008). Moreover, analog RCC (Esram et al., 2006) techniques used to deliver peak available power in the steady state is not suitable, as the MPP of PV module will vary as the solar insolation varies. Therefore, RCC also fails to track the maximum power accurately under rapidly changing environmental conditions, whereas the proposed analog circuitry-based MPPT technique is easy to implement by using low-cost analog ICs, and free from delay and quantization effects. Furthermore, it can quickly and accurately converge to the desired peak under varying environmental conditions.

Table 4.

Comparative performances of proposed maximum power point tracking (MPPT) with existing techniques.

MPPT methods	Tracking performance	Steady state oscillation	Convergence time	Accurate	Implementation	Computation time
P&O (Femia et al., 2005; Tajuddin et al., 2015)	Good	Varies	Varies	Yes	Simple	Less
INC (Fesharaki et al., 2017; Safari and Mekhilef, 2011; Zakzouk et al., 2016)	Good	Less	Medium	Yes	Medium	More
RCC (Esram et al., 2006)	Good	Less	Varies	Yes	Simple	Nil
Load $i_{0} / v_{0}$ maximization (Jiang et al., 2013)	Good	Varies	Fast	No	Medium	More
Adaptive P&O (Abdelsalam et al., 2011)	Very good	Less	Fast	Yes	Complex	More
PI-based P&O (Brito et al., 2013)	Excellent	Varies	Varies	Yes	Medium	More
Proposed	Excellent	Less	Very Fast	Yes	Simple	Nil

P&O, perturb and observe; INC, incremental conductance; RCC, ripple correlation control; PI, proportional–integral.

Conclusions

This research suggested a low-cost analog circuitry-based MPPT technique for fast and accurate tracking of PV power using a boost DC/DC converter. The MPPT control law is derived from the non-linear V–P characteristics and implemented by using $\bar{CLR}$ pin of a D-type flip-flop for pulse width modulation. Moreover, modelling of the PV module and operational principles of proposed method have been discussed in detail. Extensive simulation studies have been performed using a MATLAB/Simulink tool to appraise the speed of convergence and tracking capability of the MPPT algorithm. The findings affirm that the recommended MPPT controller is fast and robust under variations of irradiance level, cell temperature and load impedance, compared with various existing methods. To validate the efficacy of the MPPT controller, an experimental prototype has been developed and tested under both steady-state and dynamic conditions. Experimental results show that the proposed MPPT system provides high tracking performances under rapidly changing environmental conditions. The EMI problem has also been studied under different load conditions, both in simulation and in experiment platforms. As a conclusion, this proposed MPPT contributes toward improved tracking and power harvesting from the PV module.

Footnotes

Declaration of conflicting interest

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Priyabrat Garanayak

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