# Construction and Application of a Five-Level Inverter for Maximum Power Point Tracking (MPPT) of the Photovoltaic Systems (PV)

Alireza Siadatan, Hamed Karimi, Maryam Sepehrinour

► To cite this version:

Alireza Siadatan, Hamed Karimi, Maryam Sepehrinour. Construction and Application of a Five-Level Inverter for Maximum Power Point Tracking (MPPT) of the Photovoltaic Systems (PV). The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0214. hal-05095945

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# Construction and Application of a Five-Level Inverter for Maximum Power Point Tracking (MPPT) of the Photovoltaic Systems (PV)

Alireza Siadatan, SMIEEE

Department of Electrical and
Computer Science,
York University,
Toronto, Canada.

siadatan@yorku.ca

Hamed Karimi, MIEEE

Department of Electrical Engineering,
Khatam University,
Tehran, Iran.

h.karimi@khatam.ac.ir

Maryam Sepehrinour

Department of Computer Science
and Technology,

Algoma University, Brampton
Campus, Ontario, Canada.

maryam.sepehrinour@algomau.ca

## Keywords

DC-DC Converter, Multi-level Inverter, Maximum Power Point Tracking (MPPT), Photovoltaic, Switching, Incremental Conductance (INC).

## Abstract

Considering the high initial cost of a solar system, achieving maximum power output is crucial. In this paper, the Nemo conduction method is utilized to reach the maximum power point of an 80W solar module. This method is also used to supply power to an Ohmic inductor load from a five-level inverter with an active diode barrier at the output of a boost converter. With this setup, a two-level five-level inverter has been developed, and a predictive control method is employed to regulate the inverter, resulting in a five-level waveform at the output. The predictive control simulation successfully generates a five-level three-phase voltage while ensuring that the output current closely tracks the reference current and the voltage of the floating capacitors is controlled. The construction and simulation results demonstrate the accuracy and speed of locating the optimal point to maximize energy production.

## Introduction

Considering the increasing need for electric energy and the exhaustion of non-renewable energies, the importance of new energies is increasing. Among new energies, solar energy is very important due to its abundance and availability. In order to make maximum use of this energy and increase the efficiency of the whole system, it is necessary to receive maximum power from solar modules. Due to the non-linear feature and the dependence of solar cells on the temperature and radiation conditions of the environment, the maximum power that can be received from a solar cell will change and a specific working point will be obtained in each situation.

Various fans have been presented to Maximum Power Point Tracking (MPPT). To reach the maximum power point, an interface converter must be used. This converter can supply DC or AC output according to the user's needs. In this method, the control is indirect (Open Loop) and it is very difficult to predict all working conditions [1-2]. Also, in some studies, intelligent methods such as fuzzy logic, neural networks and particle optimization method have been used. These methods are based on sampling and have a very fast response without overshoot and also have the least fluctuation in the steady state when the environmental conditions change. But on the other hand, they are associated with complex calculations and require a more expensive microprocessor. The particle optimization method, which is suitable for solving multivariable equations, is very suitable for the shadow condition that occurs in the P-V curve with several peaks [3-4]. Deviation-based methods such as Perturbation and Observation (P&O) and Hill-Climbing (HC) are also common methods. In these methods, first the voltage and current are measured and the corresponding power ($P1$) is calculated. Then a small voltage deviation ($\Delta V$) in the P&O method or duty cycle deviation ($\Delta d$) in the HC method is created in the DC-DC converter in one direction and $P2$ is calculated. Then $P1$ and $P2$ are compared and the direction of deviation is determined to calculate the value of MPPT [5].

One of the biggest problems of these methods is the momentary deviation due to changing weather conditions in finding the maximum power, and also the amount of deviation cannot be controlled [6]. To determine the size of the deviation, the deviation estimation method, which is an extended mode of the P&O method, is used [7]. The purpose of this research is to provide a proposed structure to achieve maximum power from PV. Also, many methods have been presented for this purpose. Considering the advantages and disadvantages of the mentioned methods, the aim of this research is to use a method that has a suitable reaction to sudden changes in
weather conditions and also uses the direct control method and performs power control operations with moment-to-moment sampling; Therefore, in this research, the growth guidance method, which includes the mentioned features, has been used to extract the maximum power. One of the prominent features of the mentioned method is to consider two parameters of voltage and current simultaneously, which can be used in many analyzes and analyzes used for the ideal and optimal design of the solar cell.

## Incremental guidance method

Incremental Conductance method (InC), the main advantage of this method is its simplicity, and it works based on the slope of the P-V curve in Fig. 3. In addition, when the solar radiation does not change very quickly, it will show good performance.

$$ \left\{ \begin{array}{l} \frac{dP}{dv} = 0 = at \text{ MPP} \\ \frac{dP}{dv} \rangle 0 = \text{MPP} = \text{In the left} \\ \frac{dp}{dv} \langle 0 = \text{MPP} = \text{In the right} \end{array} \right. \qquad (1) $$

For a solar system, the $dP/dV$ ratio is obtained as follows:

$$ \frac{dp}{dv} = \frac{d(IV)}{dv} = I + V \frac{di}{dv} \approx I + V \frac{\Delta I}{\Delta V} \qquad (2) $$

However, if we consider Equation (2) equal to zero and positive on the left side and negative on the right side, we will have MPP in this case.

$$ \left\{ \begin{array}{l} \frac{\Delta I}{\Delta V} = \frac{-I}{V} \rightarrow \text{in MPP} \\ \frac{\Delta I}{\Delta V} \rangle \frac{-I}{V} \rightarrow \text{MPP} \rightarrow \text{In the left} \\ \frac{\Delta I}{\Delta V} \langle \frac{-I}{V} \rightarrow \text{MPP} \rightarrow \text{In the right} \end{array} \right. \qquad (3) $$

This method is suitable in case of sudden changes in weather conditions [8-9]. In this method, like the P&O method, there is a problem of deviation size, and a solution that was presented for this problem is the use of variable step size, which, of course, requires complex and expensive control circuits [12-13].

<figure><img src="image_2.png" /><figcaption>Fig. 1. Flowchart InC algorithm.</figcaption></figure>

## Suggested method

In this paper, in order to use the incremental conduction method, first, the resistance values of Rs and Rp, which are actually the resistances of the solar cell model, should be calculated with the approach of extracting the maximum power from the solar cell. For this purpose, the proposed method of this research is presented in two parts [18]. In the first part, the PV cell modeling and the expression of the mathematical model for it, as well as the calculations related to the internal resistances of the solar cell model Rs and Rp are presented. In the second part, using the boost converter and the InC control method, the maximum power is extracted from the solar cell.

## Calculation amount of Rs and Rp in PV

In most papers, the same model is considered for the solar cell, which is given in Fig. 2, and its mathematical model is also expressed according to Equation (4) [14].

<figure><img src="image_3.png" /><figcaption>Fig. 2. Block diagram MPPT of a solar cell.</figcaption></figure>
$$I = I_{pv} - I_{o} \left[ \exp\left(\frac{V + R_{s} \cdot I}{V_{t} \cdot a}\right) - 1 \right] - \frac{V + R_{s} \cdot I}{R_{p}} \quad (4)$$

In Equation (4), $I_{pv}$ is the production current through the sun and $I_o$ is the saturation current of the diode in the solar array and $V_t=N_s kT/q$ is the thermal voltage of the array with $N_s$ cells that are connected in series with each other, $q$ is the charge electron (1.6×10⁻¹⁹C), $k$ is Boltzmann's constant (1.38×10⁻²³J/K)², $T$ is the temperature of the p-n junction based on Kelvin units, and $a$ is the ideal diode constant. Considering the Equation $P_{max,m}=V_{mp} \cdot I_{mp}=P_{max,e}$ computational power is equal to experimental power we can write [10-18].

$$P_{max,m} = V_{mp} \left\{ I_{pv} - I_{o} \left[ \exp\left(\frac{q}{k \cdot T} \frac{V_{mp} + R_{s} I_{mp}}{a \cdot N_{s}}\right) - 1 \right] - \frac{V_{mp} + R_{s} I_{mp}}{R_{p}} \right\} = P_{max,e} \quad (5)$$

$$R_p = \frac{V_{mp}(V_{mp} + R_s I_{mp})}{V_{mp} I_{pv} - V_{mp} I_o \exp\left(\frac{q}{k \cdot T} \frac{V_{mp} + R_s I_{mp}}{a \cdot N_s}\right) + V_{mp} I_o - P_{max,e}}$$

As is evident from Equation (5), a value of $R_p$ is determined for each value of $R_s$, allowing the I-V curve to be plotted using Equation (4). By employing an iterative method to calculate $R_s$ and $R_p$, we can achieve $P_{max,m} = P_{max,e}$. To do so, we gradually increase the value of $R_s$ from zero in each step, paying close attention. Additionally, Equation (5) provides the value of $R_p$ at each step, along with the corresponding $P_{max}$ value [16-17].

<figure><img src="image_4.png" /><figcaption>Fig. 3. Standard current and power.</figcaption></figure>

The curve in which the value of $P_{max}$ and $V_{mp}$ for the specified $R_s$ and $R_p$ is equal to the tested value expresses the exact value of the series and parallel

resistances. Now using the Equation (4) we can draw the I-V curve. The block diagram in Fig. 4, shows how to calculate $R_s$ and $R_p$ in general.

<figure><img src="image_5.png" /><figcaption>Fig. 4. Block diagram for calculation of $R_s$ and $R_p$.</figcaption></figure>

## Boost converter control method to achieve MPPT

In this converter, the INC algorithm is used to reach the MPP point. In similar algorithms, the power difference and the voltage difference between the two measured values in the sampling period are received, and according to the ratio of these two differences, according to the Equation (1), it can be determined that the working point of the module at this moment is on the left side [21-22]. The MPP point is located or to the right of the MPP point; Therefore, if we are on the right side of the MPP point, we decrease the reference voltage, and if we are on the left side of the MPP point, we increase the reference voltage. In the INC method, in addition to the voltage, the current is also sampled and the position relative to the MPP point is measured using Equation (3), and the shift in the P-V curve in this method is also done by changing the voltage and using a boost converter. Fig. 5, shows the control method used to reach the MPP point. After reaching the reference voltage, the error voltage, which is calculated from the difference between the reference voltage and the module voltage, is passed through the PI controller to increase the resulting error, and by comparing the output wave of the PI controller with the triangular wave, the PWM wave required for Keying produced the boost converter [19].

In Fig. 5, the MPPT block with the INC control method is responsible for determining the reference voltage using the information received from the PV module. According to Fig. 1, the sampling of the voltage and current of the solar cell is done at a certain
moment, and at the next moment, the values are measured and recorded again, and then the values are subtracted, and each time they are inserted and checked in Equation (3), and the controller by inserting Measured values in Equation and determining the position in the diagram, you decide in which direction to shift in the P-V curve, actually increase or decrease the reference voltage. According to Equation (3), in fact, MPP can be followed by comparing the instantaneous velocity (I/V) with the incremental conduction (ΔI/ΔV), which is called the incremental conductance method or the INC method. This method is very suitable in case of sudden changes in weather conditions [11-13]. In fact, the boost converter, in addition to increasing the voltage level of the solar cell at its output, also adjusts the voltage of the solar module at the input in order to reach maximum power.

<figure><img src="image_6.png" /><figcaption>Fig. 5. Block diagram of boost converter control.</figcaption></figure>

In this converter, switches S1 and S3, as well as switches S2 and S4, operate simultaneously. Additionally, switches S1 and S2, S5 and S6, and S7 and S8 complement each other [15-20]. As a result, three independent pulses are required in each phase, leading to a total of 2³ = 8 switching modes.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Single-phase five-level active converter.</figcaption></figure>

As shown in table (1), in these 8 modes, they produce five different voltage levels that are normalized to Vdc and are equal to (1, 0, 1, -2, -2). Also, Equation (6) of the output voltage shows relative to the neutral point.

$$ 
\begin{aligned}
V_{xn} &= (S_{x1} \times S_{x5}) \times V_{cu} + ((S_{x1} - 1) \times (S_{x5} - 1)) \\
\Rightarrow V_{dc} &= (S_{x5} - S_{x7}) \times V_{cfx}
\end{aligned} 
\quad (6) $$

<table><caption>TABLE I. The state of the switches and their effect on the output voltage.</caption><thead><tr><th>Switches</th><th>Effect on the capacitor</th><th>Normalized phase</th><th colspan="3">State of the switches</th></tr></thead><tbody><tr><td>Vx</td><td>I<sub>x</sub> &lt; 0</td><td>V<sub>xN</sub></td><td>S<sub>x1</sub></td><td>S<sub>x5</sub></td><td>S<sub>x6</sub></td></tr><tr><td>0</td><td>---</td><td>-2</td><td>-2</td><td>0</td><td>0</td></tr><tr><td>1</td><td>Charge</td><td>-1</td><td>-1</td><td>0</td><td>1</td></tr><tr><td>2</td><td>Dis</td><td>-1</td><td>-1</td><td>0</td><td>1</td></tr><tr><td>3</td><td>---</td><td>0</td><td>0</td><td>0</td><td>1</td></tr><tr><td>4</td><td>---</td><td>0</td><td>0</td><td>1</td><td>0</td></tr><tr><td>5</td><td>Charge</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>6</td><td>Dis</td><td>1</td><td>1</td><td>1</td><td>0</td></tr><tr><td>7</td><td>---</td><td>2</td><td>2</td><td>1</td><td>1</td></tr></tbody></table>

Fig. 7, shows the input and output voltages of the boost converter for a 54 Ω load. As it can be seen, the generated input voltage is equal to the PV output voltage, also the value of the input voltage range of the desired converter at the MPP of the module is adjusted according to the controller used.

<figure><img src="image_8.png" /><figcaption>Fig. 7. Input and output voltage waveforms of the boost converter.</figcaption></figure>

Fig. 8, shows the input and output power of the boost converter [23]. Considering that the elements used in the simulation are not ideal, the output power is slightly lower than the input power due to losses. Considering the input and output power of the system, the efficiency of the converter is 94%, considering the conduction losses of the key and the inductor. graph, you decide which direction to shift in the P-V curve, actually increasing or decreasing the reference voltage. According to Equation (3), in fact, MPP can be followed by comparing the instantaneous velocity (I/V) with the incremental conductance (ΔI/ΔV), which is called the incremental conductance method or the INC method. This method is very suitable in case of sudden changes in weather conditions [12-14].
In fact, the boost converter, in addition to increasing the voltage level of the solar cell at its output, also adjusts the voltage of the solar module at the input in order to reach maximum power.

<figure><img src="image_9.png" /><figcaption>Fig. 8. Input and output power waveforms of the boost converter.</figcaption></figure>

## Simulation

In this part of the research, the results of the implementation of the proposed method are presented. In the performed simulation, the desired module is the KC85T model, the specifications of which are listed in the manual of this module in Table 2. As can be seen the maximum power of the cell tested in the laboratory is 87.34 V, and the current and voltage of the MPP are 5.02 A and 17.4 V, respectively. The environmental conditions that are the inputs of the solar cell are temperature and radiation. The temperature is in Kelvin and is equivalent to 25 degrees Celsius or 298 degrees Kelvin, and the radiation is between 0 and 1000 W/m², which is considered 1000 W/m² in the simulation. Radiation has a direct effect on the output current of the cell, and in the best case, $I_{MPP}$ = 5.02 A is received from the cell. The temperature has a direct effect on the output voltage, and in the assumed temperature conditions, the voltage received from the cell is $V_{MPP}$ = 17.4 V which using nemo conduction control method INC to reach the maximum power of the solar module, as seen in Fig. 12, in the simulation, it is 87.34, which is the maximum power predicted for the KC85T module is, we have reached and the MPP of the solar module has been followed with proper accuracy.

<figure><img src="image_10.png" /><figcaption>Fig. 9. Experimental setup to obtain the maximum power.</figcaption></figure>

<table><caption>TABLE II. Solar module parameters.</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>(I<sub>SC,n</sub>)</td><td>5.35 A</td></tr><tr><td>(V<sub>OC,n</sub>)</td><td>21.8 V</td></tr><tr><td>(I<sub>mp</sub>)</td><td>5.05 A</td></tr><tr><td>(V<sub>mp</sub>)</td><td>17.6 V</td></tr><tr><td>(P<sub>max,e</sub>)</td><td>87.35 W</td></tr></tbody></table>

Fig. 10 and 11, show the current and voltage of solar module at the maximum power point, respectively. also be can see that the voltage and current frequency oscillate around the MPP.

<figure><img src="image_11.png" /><figcaption>Fig. 10. Solar cell output current.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 11. Solar cell voltage.</figcaption></figure>

Fig. 12, shows the power received from the solar module in the steady state of the circuit. As you can see in the figure, the power of the solar module in this condition is the same as the power that was stated in the manual of the solar module, which indicates the correct operation of the MPP tracking method. Fig. 13, shows the output voltage of the boost converter. As you can see, with a proper timing, the voltage waveform reaches a stable point.

<figure><img src="image_13.png" /><figcaption>Fig. 12. Power received from the solar cell in steady state.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. 13. Boost converter output voltage.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 14. Phase A output voltage relative to the middle point of the DC link.</figcaption></figure>

Fig. 15, shows the line voltage between A and B. As we expect, AB line voltage consists of 9 levels. Other line voltages also have 9 levels like this figure, but they have 120 degrees' difference from each other.

<figure><img src="image_16.png" /><figcaption>Fig. 15. AB line voltage.</figcaption></figure>

Fig. 16, also shows the voltage of these two capacitors in the steady state of the circuit more precisely. As you can see in this figure, the voltage of these two capacitors are almost equal to each other.

<figure><img src="image_17.png" /><figcaption>Fig. 16. Voltage of DC link capacitors in steady state.</figcaption></figure>

Fig. 17, also shows the voltage of these three floating capacitors in the steady state of the circuit more precisely. In this figure, the voltage balance of three capacitors can be seen.

<figure><img src="image_18.png" /><figcaption>Fig. 17. Voltage of floating capacitors in steady state.</figcaption></figure>

## Conclusion

Among the renewable sources, solar energy is one of the largest sources. Therefore, considering the high cost of building a PV system, obtaining the maximum power from this energy is crucial. Many control methods have been proposed to achieve the maximum power from the solar cell, some of the most significant of which were reviewed in this paper. The implementation of most of these methods is associated with high complexity and cost. Additionally, previous methods of tracking the MPPT during sudden changes in weather conditions resulted in measurement deviations and unfavorable outcomes. In this research, the nemo guidance method was utilized to reach the MPP of the KC 85 T solar module. With this control method, the circuit receives 87% of the output power from the solar cell in the steady state, as indicated by the results. The simulation demonstrates that the MPPT was achieved with a high degree of accuracy, confirming the effectiveness of the proposed MPPT method. Furthermore, the output voltage of the boost converter maintains a constant voltage at its output. This constant voltage can be utilized to power the DC link of multi-level inverters. By using the inverter, the generated power can be efficiently delivered to the AC consumer, resulting in a high-efficiency and cost-effective solar system. In the first stage, the maximum power is extracted from the solar cell, and this power is then used by the boost converter as a battery or constant voltage source for the DC link in the second stage, which involves a multi-level inverter.
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