Simulations of the Performance of Maximum Power Point Tracking Algorithms Based on Experimental Data According to the Topologies of DC-DC Converters

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1. Introduction

Energy extracted from a solar panel depends on weather conditions which bring it to be an intermittent energy source [1] [2] [3]. However, the direct connection of a solar panel to a direct current (DC) load or to an alternating current (AC) load via an inverter becomes weak because the transfer of the maximum power will be difficult when the irradiance changes. The direct connected photovoltaic system is the cheapest and the worldwide one. The operating point of the solar panel depends on the impedance of the load. It is the intersection between the I-V (or P-V) characteristic of the solar panel and that of the load. In order to prevent the reverse flow of the current, a diode is connected between the solar panel and the load. This system does not offer any possibility to limit or to set the voltage at the terminals of the load. Meanwhile, it is not evident to transfer the maximum power to the load [4] - [9]. That is why it is necessary to insert an impedance match block between the load and the photovoltaic (PV) panel. This block can be a DC-DC converter which is controlled by an electronic system in order to follow the maximum power point of the solar panel. The maximum power point tracking (MPPT) command system which can be analogue or digital, changes the duty ratio of the command pulses of the DC-DC converter in order to bring the operating point to the maximum power point when the irradiance is changing. There are various topologies of DC-DC converters:

• A buck converter with the DC output voltage lower than or equal to the DC input voltage.

• A boost converter with the DC output voltage greater than or equal to the DC input voltage.

• A buck-boost converter with the DC output voltage greater than or lower than or equal to the DC input voltage.

Since 1968 with the first MPPT algorithm, many other types of MPPT algorithms have been developed: Perturb and Observe (P & O), Incremental Conductance (INC), Hill Climbing (HC), Voltage or Current fraction, Fussy logic, Neural network, Ripple correlation control (RCC), etc. [10] - [15]. All these MPPT algorithms are implemented to control a boost converter in a PV system. Preliminary studies are necessary for the choice of a topology of DC-DC converters. Most recent works are only based on a boost converter [16] [17] [18] [19] [20]. This means that the performance of MPPT algorithms is evaluated particularly on this topology mostly used in a PV system. However, it will be necessary to evaluate the performance of MPPT algorithms when another topology of DC-DC converter is used.

This paper evaluates four of the various MPPT algorithms according to the buck and the boost converter, under normal weather conditions. The four MPPT algorithms are: P & O, HC and INC (fixed step, INCF and variable step, INCV). The main objective is to determine which MPPT algorithm and which DC-DC converter topology are suitable for sub-Saharan (tropical) weather conditions. In the second section, methods used for this work are presented. Then the results are presented and discussed.

2. Methods

2.1. Experimental System and Material

In order to collect data for this research work, the system represented in Figure 1(a) was used, with the image shown in Figure 1(b). This system is a direct-connected stand-alone PV system. The various components are:

• A pyranometer for the measurement of the global irradiance (in W/m^{2}). Its specifications are given in Table 1.

• Voltage and current sensors (ALMEMO^{®}) for the measurement of voltage and current respectively.

• A temperature sensor (ALMEMO^{®}) for the measurement of the temperature at the surface of the solar panel. Its specifications are given in Table 2.

(a) (b)

Figure 1. (a) Block diagram of the experimental system; (b) Image of the outdoor system.

Table 1. Specifications of the pyranometer.

Table 2. Specifications of the temperature sensor.

• An ALMEMO^{®} data acquisition unit having five inputs, two outputs, an EEPROM of 1 MB (200,000 measures).

2.2. Methods

1) DC-DC converters

Two topologies of DC-DC converters are used in this work: the buck and the boost converters.

• The buck converter is represented in Figure 2. Its operating principle is based on the two conduction modes: continuous conduction mode (CCM) and discontinuous conduction mode (DCM). The output voltage and current of the buck converter are given in Equations (1) and (2) respectively.

${V}_{S}=\alpha {V}_{pv}$ (1)

${I}_{S}=\frac{{I}_{pv}}{\alpha}$ (2)

With *α* the duty ratio (
$0<\alpha \le 1$ ).

• The boost converter is represented in Figure 3. Its operating principle is also based on the two conduction modes. And its output voltage and current can be obtained as shown in Equations (3) and (4) respectively.

${V}_{S}=\frac{{V}_{pv}}{1-\alpha}$ (3)

${I}_{S}=\left(1-\alpha \right){I}_{pv}$ (4)

With *α* the duty ratio (
$0<\alpha \le 1$ ).

2) MPPT algorithms

Many MPPT algorithms have been developed. In this paper, the focus was only on the most popular and the worldwide algorithms: P & O, HC and INC (fixed and variable steps).

Figure 2. Circuit of a buck converter [21] [22].

Figure 3. Circuit of a boost converter [21] [22].

• The Hill Climbing algorithm is based on the perturbation of the duty ratio. Its flow chart is represented in Figure 4. The main advantage of this method is that it is easy to implement. However, when the weathers conditions are changing rapidly, this algorithm is no more accurate because of oscillations around the maximum power point [23] [24] [25].

• The Perturb and Observe (P & O) algorithm with its flowchart represented in Figure 5 is based on the perturbation of the output voltage of the PV source. This MPPT algorithm is easy to implement and is also the most used nowadays. However, due to the rapidly change of the weather conditions, it becomes inaccurate with an oscillation occurred around the maximum power point [23] [24] [25].

• The Incremental Conductance (INC) algorithm which is divided into two types: the fixed step one and the variable step one. The fixed step incremental conductance (INCF) algorithm operates like the P & O algorithm with the same performance. Its flowchart is shown in Figure 6. The variable step incremental conductance (INCV), represented in Figure 7, has been developed in order to solve the problem occurred during the operation of the INCF algorithm. In fact, the INCF algorithm becomes inaccurate when the weather conditions change rapidly, leading energy lost. With a variable step (INCV), there is no more energy lost and the maximum power point is tracked accurately. However, the INCV is difficult to implement. Liu *et al.* in 2008 developed the first INCF with the variation step (*D*_{step}) given in Equation (5). Coefficient *N* is determined according the condition given in Equation (6) [23] - [28].

Figure 4. Flowchart of the HC algorithm.

Figure 5. Flowchart of the P & O algorithm.

Figure 6. Flowchart of the INCF algorithm.

Figure 7. Flowchart of the INCV algorithm.

${D}_{\text{step}}=N\left|\frac{{P}_{pv}\left(k\right)-{P}_{pv}\left(k-1\right)}{{V}_{pv}\left(k\right)-{V}_{pv}\left(k-1\right)}\right|$ (5)

$N<\frac{{D}_{\text{stepmax}}}{{\left|\frac{\text{d}{P}_{pv}}{\text{d}{V}_{pv}}\right|}_{\text{fixedstep}={D}_{\text{stepmax}}}}$ (6)

Jae-Hoon and Won-Pyo developed in 2013 [10] another expression of the step given in Equation (7). *N _{p}*,

${D}_{\text{step}}={N}_{p}\left|1-\frac{1}{1+\mathrm{exp}\left[-a\left(\Delta {P}_{pv}-c\right)\right]}\right|$ (7)

3) Modelling of the PV system

The electrical model of a PV panel is widely known. In this research paper, the single-diode model is used because the experimental data were recorded on a monocrystalline silicon PV panel. The equivalent circuit of this panel is given by Dandoussou *et al.*, 2015 [4]. The whole model of the PV system is given in Figure 8 below. There are four different blocks (or subsystems):

Figure 8. Simulink^{®} model of the PV system.

• The first block is the PV panel having nine input variables. The surface temperature was recorded during one day as shown in Figure 9(a). The irradiance is also represented in Figure 9(a). These weather conditions were recorded on the 23rd of January 2013 in Ngaoundere, Cameroon (Latitude 7.3˚N and Longitude 13.3˚E). The ideality factor, the series resistance and the reverse saturation current (see Figures 9(b)-(d) respectively) were extracted by Dandoussou *et al.*, 2015 [4].

• The second block is the DC-DC converter. Each of the two topologies (boost and buck converters) has been implemented.

• The third block is the MPPT block. Using Stateflow under Simulink®, the four MPPT algorithms (HC, P & O, INCF and INCV) have been implemented.

• The fourth block is the load block which is a rheostat of 7.5 Ω.

3. Results

3.1. Hill Climbing (HC) Algorithm

Figure 10 shows the output powers produced by the PV system according to the design parameters of the buck converter, using HC algorithm. The waveform in red (PoutHVBuck1) is obtained when L = 935 µH and C = 2.67 µF, and the blue waveform (PoutHVBuck2) is obtained when L = 935 µH and C = 26.7 µH. This means that during the design process of the buck converter with HC algorithm control method, it is important to focus on the values of the components so that it will avoid unstable output power.

Figure 11 shows the waveforms of the output powers of the PV system, using HC algorithm, according to the design parameters of the boost converter. The

Figure 9. Input parameters of the PV system [4].

Figure 10. Output powers for HC algorithm according to the design of the buck converter.

Figure 11. Output powers for HC algorithm according to the design of the boost converter.

red waveform (PoutHVBoost2) is for L = 9350 µH and C = 2.67 µF and the blue waveform is for L = 935 µH and C = 2.67 µH. It’s clear that when increasing the value of the inductance (L), even though the output power becomes more stable, the response time of the algorithm becomes too high. For a very small value of the inductance (L), the output power becomes very unstable.

3.2. Perturb and Observe (P & O) and Fixed Step Increment of Conductance (INCF) Algorithms

Figure 12 shows the waveforms of the output powers produced by the PV system using P & O or INCF algorithm, according to the design parameters of the buck converter. The red waveform (PoutINCFBuck1) is for L = 935 µH and C = 2.67 µF and the blue waveform (PoutINCFBuck2) is for L = 935 µH and C = 267 µF. It’s clear that the value of the capacitor (C) affects the performance of the algorithm. When C is small, the output power is oscillating, with a small response time of the algorithm. When C is increasing, the output power becomes slightly stable, but the response time of the algorithm is high.

Figure 13 shows the output powers produced by the PV system using P & O or INCF algorithm, according to the design parameters of the boost converter. The red waveform (PoutINCFBoost2) is for L = 935 µH and C = 2.67 µF and the blue waveform (PoutINCFBoost1) is for L = 9350 µH and C = 2.67 µF. For the boost converter, it is the value of the inductance (L) that affects the performance of the P & O or INCF algorithm. When L is small, the output power is stable, following normally the fluctuation of the weather conditions (G and T). When L is increasing, the output power is more stable, but the response time of the algorithm is high. This leads to power losses.

Figure 12. Output powers for INCF algorithm according to the design of the buck converter.

Figure 13. Output powers for INCF algorithm according to the design of the boost converter.

3.3. Variable Step Increment of Conductance Algorithm (INCV)

Figure 14 shows the waveforms of the output powers of the PV system using INCV algorithm, according to the design parameters of the buck converter. The red waveform (PoutINCVBuck1) is for L = 935 µH and C = 2.67 µF, and the blue

Figure 14. Output powers for INCV algorithm according to the design of the buck converter.

waveform (PoutINCVBuck2) is for L = 935 µH and C = 26.7 µF. This means that the value of the capacitor (C) affects the performance of the INCV algorithm, controlling a buck converter. When C is small, the output power is unstable. When C is increasing, the output power is still oscillating, with power losses decreasing. The response time is not affected.

Figure 15 shows the output powers of the PV system using INCV algorithm, according to the design parameters of the boost converter. The red waveform (PoutINCVBoost2) is for L = 935 µH and C = 2.67 µF, and the blue waveform (PoutINCVBoost1) is for L = 9350 µH and C = 2.67 µF. Therefore, the value of the inductance (L) affects the stability of the algorithm only when the system has been put on. This means that there are power losses only at the beginning when the value of L is decreasing.

4. Discussion

Figure 16 shows the output powers obtained from the simulations, compared to the measured power on the direct-connected PV system (without MPPT block). As shown, it is clear that the HC algorithm has slightly increased the output power. However, the boost DC-DC converter is more efficient than the buck DC-DC converter. In fact, the buck converter loses energy at some moments of the day even if there is no fluctuation of the weather conditions (irradiance and temperature).

The simulated results for these two algorithms are shown in Figure 17. It should be recalled that these two algorithms have the same performance as

Figure 15. Output powers for INCV algorithm according to the design of the boost converter.

Figure 16. Comparison between the two converters with HC algorithm.

proved by Dandoussou *et al.*, 2017 [5]. With these two algorithms, the buck converter produces power that is fluctuating during the whole day. This means that power losses are high compare to the boost converter.

The output powers are shown in Figure 18. Known as the best, compare to the first three algorithms (HC, P & O and INCF), the INCV algorithm is no

Figure 17. Comparison between the two converters with INCF algorithm.

Figure 18. Comparison between the two converters with INCV algorithm.

more suitable for the buck converter. There are power losses during the whole day.

Table 3 shows the calculated energy produced by each MPPT algorithm with respect to the DC-DC converter topology. This energy was calculated from Equation (8) using Matlab^{®} command: *E* = trapz(*t*, *P*), with *t* the time (from 10:00 to 15:30) and *P* the produced power (in W). The measured energy is given by Emes =

Table 3. The daily energy produced each MPPT algorithm.

160.93 Wh. With the buck converter controlled by P & O or INCF algorithm, the output energy is low compare to the measured energy on the system without MPPT. Once more the INCV algorithm has the best performance whatever which converter is used.

$\text{d}E=P\text{d}t\Rightarrow E={\displaystyle {\int}_{{t}_{0}}^{{t}_{1}}P\text{d}t}$ (8)

5. Conclusion

This paper focused on the simulations of MPPT algorithms according to two topologies of DC-DC converters. Recorded temperature and irradiance and extracted PV parameters (ideality factor, series resistance and reverse saturation current) were used to simulate the PV systems using Matlab^{®}/Simulink^{®}. From the obtained results, it is clear that there are some power losses during the whole day, independent from the weather conditions, when the buck converter is used. The output powers fluctuate during the whole day. The boost converter is suitable for all the MPPT algorithms, with the INCV algorithms having the best performance. However, in further works, it would be better to take into consideration others factors like the PV technologies, the other DC-DC converter topologies, additional electronics circuits (a stabiliser for example).

Acknowledgements

Authors thank the Director of HTTTC Kumba for providing some key equipment for this research work to be realized smoothly.

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