# Harmony Search-Assisted Perturb-and-Observe MPPT Algorithm for PV Systems

Geon Hee Lee, Seungho Choi, Zong Woo Geem, Jehyuk Won

► To cite this version:

Geon Hee Lee, Seungho Choi, Zong Woo Geem, Jehyuk Won. Harmony Search-Assisted Perturb-and-Observe MPPT Algorithm for PV Systems. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/3y2nb658. hal-05089019

HAL Id: hal-05089019

https://utc.hal.science/hal-05089019v1

Submitted on 28 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
## Main Title:

# Harmony Search-Assisted Perturb-and-Observe MPPT Algorithm for PV Systems

Geon hee lee

Gachon

University

Seongnam-si,

South Korea

ghlee490@gmail.

com

Seungho Choi

Gachon

University

Seongnam-si,

South Korea

chltmdgh89@gac

hon.ac.kr

Zong Woo Geem

Gachon

University

Seongnam-si,

South Korea

geem@gachon.ac

.kr

Jehyuk Won

Kangwon

National

University

Chuncheon-si

South Korea

jhwon@kangwon

.ac.kr

## Acknowledgements

This work was supported in part by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea RS-2024-00441420 and in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education RS-2023-00237518.

## Keywords

«Photovoltaic (PV) system», «maximum power point tracking (MPPT)», «harmony search (HS), perturb-and-observe (P&O)», «partial shading condition (PSC)»

## Abstract

Nonuniform irradiation in photovoltaic (PV) systems can cause multiple power peaks, where traditional maximum power point tracking (MPPT) methods like perturb-and-observe (P&O) are only effective under uniform conditions. Accurate global MPPT is crucial under partial shading conditions (PSCs). This paper proposes a hybrid MPPT algorithm integrating harmony search (HS) with P&O. This approach reduces power loss during searches and avoids getting stuck at local maxima under PSCs, a common issue with standard P&O methods. A parameter-setting-free HS (PSF-HS) is introduced to enhance search efficiency, followed by variable-step-size P&O to fine-tune the GMPP location. Experiments on a 250 W PV system under various PSCs using a PV emulator demonstrate the algorithm's effectiveness.

## I. Introduction

<figure><img src="image_2.png" /><figcaption>Fig. 1: Structure of typical PV system with MPPT algorithm.</figcaption></figure>

Global warnings, the depletion of coal, and rising fossil fuel prices have increased attention to renewable energy. Solar energy, in particular, is favored for its abundance, renewability, and non-polluting nature. These benefits have spurred the rapid global adoption of photovoltaic (PV) systems, which are popular for their environmental cleanliness, low maintenance, and falling costs. Moreover, their integration into power grids reduces reliance on fossil fuels [1]. The typical structure PV system with maximum power point tracking (MPPT) algorithm is shown in Fig. 1. Generally, a PV system comprises a PV array, a DC-DC converter to regulate the DC-link voltage, a DC-AC inverter to interface with the AC grid, and a controller, which includes voltage and current information for the MPPT algorithm block to generate the maximum power point (MPP) of duty cycle.

Conventional MPPT techniques optimize PV system output by methods such as perturbation and observation (P&O), incremental conductance
(IC), constant voltage (CV), and advanced approaches like fuzzy logic and neural networks, each balancing complexity, efficiency, and adaptability to varying conditions [2]. In general, the P&O method is effective and preferred because of its simplicity and high tracking speed. However, P&O performs poorly in tracking global MPPs (GMPPs) under partial shading conditions (PSC) involving multiple local MPPs (LMPPs).

To overcome the limitations of traditional MPPT algorithms [3], metaheuristic algorithms have been developed to effectively tackle multivariable nonlinear problems. Metaheuristic algorithms are widely utilized in power systems to solve various optimization problems, including optimal power flow, economic and emission dispatches, reactive power dispatches, and distribution network optimization. They can effectively address complex constraints and multipurpose optimization problems. In recent years, various methods have been introduced, such as the grey wolf algorithm [4], Harris hawks optimization [5], the crow search algorithm [6], the bat algorithm [7], particle swarm optimization (PSO) [8], and normal harmony search (NHS) [9].

Among these nature-inspired algorithms, the harmony search (HS) method stands out for its simplicity and minimal parameter requirements. Despite this, it has not been extensively investigated in the context of MPPT algorithms.

In recent, hybrid MPPT was proposed to improve the problems of conventional MPPT. A literature review on hybrid MPPT algorithms shows that conventional methods, such as P&O (often adopted because of its ease of implementation), are assisted by various metaheuristic algorithms, such as PSO [10], adaptive butterfly PSO [11], enhanced leader PSO [12], the artificial bee colony [13], gray wolf optimization [14], and the flower pollination algorithm [15], [16]. Hybrid algorithms mainly aim to improve tracking accuracy and convergence time for GMPPs. In [10] and [11], the P&O method was initially used to find the nearest LMPP. Then, starting from the LMPP, the PSO method is adopted to identify the GMPP. However, this approach cannot effectively reduce the overall convergence time in cases with multiple LMPPs. In some past articles [12]-[16], two-stage approaches were developed by integrating metaheuristic algorithms in the first stage and then P&O in the second stage.

A review of the literature on PV applications revealed only one article discussing the use of the NHS method [9]. Initially, the NHS method

benefits from an expanded bandwidth, allowing for faster tracking of a closer GMPP. However, in the final stage, reducing the bandwidth may lengthen the time required to accurately identify the exact GMPP. Therefore, simply adjusting the bandwidth does not ensure improved tracking performance.

In this study, a hybrid algorithm (HS-assisted P&O) is created to address the shortcomings of the NHS method and compensate for the partial shading problem in the P&O method. Based on a metaheuristic algorithm, an affordable range of GMPPs can be narrowed down via the parameter-setting-free (PSF) HS method. Then, the GMPP can be identified accurately through fast-tracking using variable-step-size P&O.

## II. Harmony search (HS) method

<figure><img src="image_3.png" /><figcaption>Fig. 2: Principle of HS method in MPPT control.</figcaption></figure>

The HS method simulates creating new harmonies akin to jazz improvisation, with solution vectors termed as harmonies and their storage space as harmony memory (HM). An essential operator involves HM consideration, where a random HM value influences the creation of a new harmony. Decision variables, compared to pitches, are adjusted subtly through a "pitch adjustment" operator to introduce minor variations. Fig. 2 shows the principle of using the HS method for MPPT control.

<table><caption>**Table I: Definition of hyperparameter in HS method**</caption><thead><tr><td>Hyperparameter</td><td>Definition</td></tr></thead><tbody><tr><td>HM size (HMS)</td><td>Number of harmonies stored.</td></tr><tr><td>HM consideration rate (HMCR)</td><td>Possibility of executing HM consideration.</td></tr><tr><td>Pitch adjustment rate (PAR)</td><td>Possibility of executing HM consideration with pitch adjustment.</td></tr><tr><td>Number of segmentations (N<sub>seg</sub>)</td><td>Determines the bandwidth (bw) during pitch adjustment.</td></tr></tbody></table>
An HM is represented as follows.

$$ 
\begin{array}{l}
x_1^1 \quad x_2^1 \quad \dots \quad x_n^1 \\
x_1^2 \quad x_2^2 \quad \dots \quad x_n^2 \\
\vdots \quad \vdots \quad \ddots \quad \vdots \\
x_1^{HMS} \quad x_2^{HMS} \quad \dots \quad x_n^{HMS}
\end{array}
\quad
\begin{array}{l}
f(x^1) \\
f(x^2) \\
\vdots \\
f(x^{HMS})
\end{array}
\qquad (1) $$

This means a number n of decision variables x up to the HMS are included in HM. $f(x)$ is the objective function for this study. The three major operators are listed in Table II.

<table><caption>**Table II: Three major operators in HS method**</caption><thead><tr><th>Operator</th><th>Description and equation</th></tr></thead><tbody><tr><td>Random generation</td><td>Generate a portion of the new harmony randomly within the range of the decision variables<br>$x'_n = LB_n + r \times (UB_n - LB_n)$</td></tr><tr><td>HM consideration</td><td>A portion of the new harmony is copied randomly from the stored HM values<br>$x'_n = x'_n \in \{x_n^1, x_n^2, \dots, x_n^{HMS}\}$</td></tr><tr><td>Pitch adjustment</td><td>Apply fine-tuning to the copied values using the HM consideration operator.<br>$x'_n = x'_n \pm r \cdot bw_n$</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Fig. 3: Process of HS method.</figcaption></figure>

### III. Proposed hybrid MPPT algorithm

The method suggested in this paper has two stages. In the first step, PSF-HS is implemented to find the nearest GMPP, followed by the second stage to retrieve the exact GMPP using P&O with variable step size.

#### A. Applied variable-step-size P&O method

Fixed-step-size P&O is used in most studies on P&O-based hybrid MPPT algorithms combined with metaheuristic approaches [10], [12]-[16]. Variable-step-size versions have been proposed in a few studies. In [11], the step size was changed according to the power-voltage (P-V) relationship, such as $\Delta P/\Delta V$. An adaptive-step-size version was proposed in [8] based on the $\Delta P/P_{k-1}$ relationship. These methods can improve

the performance of conventional fixed-step-size P&O, which may deteriorate the average MPPT efficiency with oscillation after the MPP is reached. The main reason for adopting a variable step size is the mitigation of the oscillation problem as the MPP is approached. However, oscillation may be worsened by a rather enlarged step size due to the sensing noise when the step size is too small. Predefined values were set for the minimum and maximum step sizes in [8] and the voltage and current threshold values in [11], but this approach can reduce the reliability of the system and increase the dependence of performance on the predefined values.

A variable-step-size SS is used in this study ($SS_k=0.9 \times SS_{k-1}$) to avoid the noise problem and simplify the methods in [8] and [11]. As the applied P&O method is only used in the second stage to finalize the GMPP, the value of 90% is reasonable for tracking speed and accuracy based on experimental validation in Section IV.

#### B. Applied PSF-HS method

PV systems typically consist of various types of panels and generate power at different scales. Additionally, the challenge of MPPT is compounded by the fact that the shape of the P-V curve—the objective function—continuously shifts due to changing weather conditions during operation. As a result, the PSF-HS method [17] proves more effective in solving MPPT issues than other harmony search approaches. In the PSF-HS method, the parameters HMCR and PAR are automatically determined by the method itself, rather than being user-defined. Initially, the PSF-HS method follows the same procedure as the traditional HS method until the harmony memory (HM) is established. Afterward, a “rehearsal” phase occurs, during which HMCR and PAR are set to 0.5, and the harmony is regenerated to match the size of the HM.

<table><caption>**Table III: Comparison of parameters among HS methods**</caption><thead><tr><th>Parameter</th><th>HS</th><th>NHS</th><th>PSF-HS</th></tr></thead><tbody><tr><td>HMS</td><td>D/U</td><td>D/U</td><td>D/U</td></tr><tr><td>Max iteration</td><td>D/U</td><td>D/U</td><td>D/U</td></tr><tr><td>bw</td><td>D/U</td><td>Automatic</td><td>D/U</td></tr><tr><td>bw<sub>min</sub> bw<sub>max</sub></td><td>N/U</td><td>D/U</td><td>N/U</td></tr><tr><td>HMCR</td><td>D/U</td><td>D/U</td><td>Automatic</td></tr><tr><td>PAR</td><td>D/U</td><td>Automatic</td><td>Automatic</td></tr><tr><td>PAR<sub>min</sub> PAR<sub>max</sub></td><td>N/U</td><td>D/U</td><td>N/U</td></tr></tbody></table>
In Table III, ‘D/U’ means a parameter value defined by the user. The relatively higher number of D/U means high complexity. ‘Automatic’ means that the value is automatically determined by a specific equation used in the algorithm. 'N/U' means that the parameter is not used in the algorithm.

## C. Implementation of proposed algorithm

<figure><img src="image_5.png" /><figcaption>Fig. 4: Block diagram of proposed hybrid MPPT algorithm.</figcaption></figure>

The pseudocode of the proposed hybrid MPPT algorithm is as follows.

```
Proposed MPPT Algorithm

begin HS_stage
    for each index in Harmony Memory (HM)
        Generate duty cycle ($d_{index}$) and calculate power for
        initializing the HM
    end for
    for each iteration until the early stop condition is satisfied or
        reached the limit
            if the HMC operator is not performed by probability HMCR
                then
                    Generate a new duty cycle ($d_{new}$) with a random value
                else
                    Generate new $d_{new}$ with a value stored in the HM
                    $d_{new} \leftarrow d_{new} \pm r \times bw$ (r is a random real number
                    between 0 and 1)
                end if
                if new harmony's power is higher than worst harmony's
                    power then
                        Replace the worst harmony in HM with a new harmony
                        end if
                        if rehearsal phase is over then
                            Count the number of harmonies that created by the
                            HMC&PA operator in HM($N_{HMC&PA}$)
                            HMCR $\leftarrow N_{HMC&PA}/HMS$
                        end if
                    end for
                    end HS_stage
                begin P&O_stage
                    Start P&O from the best harmony($d_{best}$) found in the HS stage
                    Calculate power($P_{old}$) with sensed voltage($V_{old}$) and current value
                    $d \leftarrow d_{best} + initial\_step\_size$
                    Check the voltage($V_{new}$) and power($P_{new}$) again after moving.
                    for each iteration until the step size becomes smaller than the limit
                        if the power has increased compared to before moving then
                            if the voltage has increased compared to before moving then
                                $d \leftarrow d_{best} - initial\_step\_size \times 0.8^{iteration}$
                            else
                                $d \leftarrow d_{best} + initial\_step\_size \times 0.8^{iteration}$
                        end if
                    else
```

```
    if the voltage has increased compared to before moving then
        $d \leftarrow d_{best} + initial\_step\_size \times 0.8^{iteration}$
    else
        $d \leftarrow d_{best} - initial\_step\_size \times 0.8^{iteration}$
    end if
    end if
    $P_{old} \leftarrow P_{new}$, $V_{old} \leftarrow V_{new}$
    Calculate power($P_{new}$) with sensed voltage($V_{new}$) and current value
    value
    end for
    end P&O_stage
```

As shown in Fig. 4, the two-stage approach involves implementing PSF-HS in the first stage to find the nearest GMPP and variable-step-size P&O in the second stage to reach the exact GMPP rapidly. This proposed block diagram replaces the conventional PV system controller in Fig. 1.

A flowchart of the proposed hybrid MPPT algorithm is presented in Fig. 5, which is based on Fig. 3 and the pseudocode.

In the HS algorithm for optimizing solar panel output, the objective function represents the solar panel's output, while the decision variable is the duty cycle. In other words, the optimization algorithm in the MPPT problem aims to identify the duty cycle that allows the PV system to generate maximum power. In the first stage, the initial duty cycles ($d_{H1}$-$d_{H5}$) are applied to the boost converter through the PWM block. The corresponding current and voltage outcomes in the PV system are collected through the ADC block and stored in HM. The results are calculated with their respective powers and are stored or replaced by comparing them with the power of new harmony. The process of creating a new harmony and updating HM is repeated, approaching the GMPP. In the second stage, HS-assisted P&O works with a smaller range to explore than if P&O were used alone, so a small initial step size of 0.02 is feasible. As this is a variable-step-size scheme, the step size is reduced by 20% per duty cycle update, and the algorithm is set to terminate when the step size becomes smaller than the minimum value of 0.0002.

## IV. Experimental results

A 250 W experimental setup was built and tested to evaluate the performance of the proposed hybrid MPPT algorithm in tracking the global maximum power point (GMPP). The setup, as illustrated in Fig. 6, includes a GaN-based DC-DC boost converter operating at a switching frequency of 100 kHz. The hybrid MPPT algorithm is implemented using a TMS320F280049 microcontroller from Texas Instruments. Rather than using a physical photovoltaic (PV) array, a PV array simulator
<figure><img src="image_6.png" /><figcaption>Fig. 5: Flowchart for proposed hybrid MPPT algorithm.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6: Experimental setup of PV system.</figcaption></figure>

(IT6012C-500-80 from iTEC) was used. Additionally, the SAS1000 solar array simulation software was utilized to simulate different PSCs. The experiment tested the algorithm's performance under three conditions: a scenario without partial shading (non-PSC) and two scenarios with partial shading (PSC-1 and PSC-2). In the non-PSC scenario, only one MPP was present. PSC-1 had one LMPP and one GMPP, while PSC-2 had four LMPPs and one GMPP. The performance of various algorithms, including P&O, HS, NHS, PSF-HS, PSO, and the proposed hybrid algorithm (PSF-HS+P&O), was compared in terms of time and accuracy over ten consecutive tests.

The average values of time and accuracy are tabulated in Table IV under three different PSCs. A basic form of P&O was used and it can be noted that it is only applicable for non-PSC since it failed to find MPP under PSC-1 and PSC-2. Two kinds of hyperparameter sets (HMCR, PAR) are used, namely, (0.95, 0.7) and (0.8, 0.5), respectively, to show parameter sensitivity for HS.

<table><caption>Table IV: Average values of time & accuracy under non-PSC, PSC-1, -2</caption><thead><tr><th>Non-PSC/PSC-1/PSC-2<br>191.61/127.73/84.89 [W]</th><th colspan="3">Time [s]</th><th colspan="3">Accuracy [%]</th></tr></thead><tbody><tr><td>P&O</td><td>3.25</td><td>N/A</td><td>N/A</td><td>99.9</td><td>N/A</td><td>N/A</td></tr><tr><td>HS (0.95/0.7)</td><td>6.21</td><td>6.74</td><td>7.37</td><td>99.8</td><td>99.8</td><td>99.9</td></tr><tr><td>HS (0.8/0.5)</td><td>7.38</td><td>6.97</td><td>7.91</td><td>99.8</td><td>99.8</td><td>99.8</td></tr><tr><td>NHS (0.8/-)</td><td>10.92</td><td>9.28</td><td>10.35</td><td>99.5</td><td>99.8</td><td>99.8</td></tr><tr><td>PSF-HS (-/-)</td><td>6.25</td><td>6.10</td><td>6.84</td><td>99.8</td><td>99.8</td><td>99.8</td></tr><tr><td>PSO (0.4.1.2.1.6)</td><td>6.71</td><td>6.76</td><td>6.92</td><td>99.8</td><td>99.9</td><td>99.8</td></tr><tr><td>Proposed algorithm</td><td>3.58</td><td>3.25</td><td>3.78</td><td>99.9</td><td>99.9</td><td>99.9</td></tr></tbody></table>

According to the NHS parameter setting [9], the HMCR is set to 0.8 in this test. The PSO parameters are set $w=0.4$, $c_1=1.2$, $c_2=1.6$ with reference to [18].

<figure><img src="image_8.png" /><figcaption>Fig. 7: Boxplots of HS, NHS, PSF-HS, PSO, and proposed hybrid algorithm under PSC-2: (a) time, (b) accuracy.</figcaption></figure>
The parameters during the comparative experiment are defined in Table III. The proposed hybrid algorithm is much more beneficial in terms of the number of hyperparameters than conventional HS and NHS methods. In this paper, the results of PSC-2 will be highlighted using boxplots as summarized in Fig. 7.

It can be noted that the parameter setting for conventional HS, HS (0.8, 0.5) performs better in the median time than HS (0.95, 0.7). Also, the box of HS (0.95, 0.7) is wider than HS (0.8, 0.5), indicating that there is more variability in the time it takes to reach the GMPP. The wider box that the performance is less consistent. However, HS (0.95, 0.7) shows better accuracy than HS (0.8, 0.5), which means its results are more closely clustered around 100%. This result is caused by the difference in HMCR. A lower HMCR increases the probability of using random generation, thus shortening the tracking time needed to reach the nearest GMPP. A higher HMCR enhances the accuracy of tracking the exact GMPP because HM consideration is executed instead of random generation.

NHS has the highest median time and widest box among the compared methods under PSC-2. As for accuracy, NHS was slightly better with a narrower box than HS (0.8, 0.5). However, the long whiskers indicate that NHS can occasionally result in much lower accuracy, leading to inconsistent performance. The NHS method, with its slower processing times and higher variability in accuracy, is less efficient and less reliable compared to the other methods examined.

PSF-HS has a lower median time than NHS and HS methods. The box is smaller than the NHS and HS methods, indicating less variability and consistent performance. However, there is one outlier, the method's accuracy can drop significantly, although this occurs infrequently. The median accuracy for PSF-HS is the lowest of the other methods and the box is wider than NHS. The whiskers of the box plot for PSF extend to a lower accuracy value, which indicates that the method can sometimes perform slightly below its median accuracy. PSF-HS performs with moderate consistency and occasional minor drops in accuracy.

PSO is similar to PSF-HS in terms of median time, and it is better than NHS and the HS methods. The box of PSO is comparable to that of PSF-HS, showing moderate variability, which is less than NHS and the HS methods. PSO achieves a high median accuracy, it has a relatively small box area. PSO has an outlier, where accuracy

drops to around 99.60%. This suggests that in some rare cases, the method's performance can significantly decline, making it less reliable in maintaining consistently high accuracy. PSO offers a balance between speed and accuracy, with moderately fast processing times and generally high accuracy. However, it has greater variability in accuracy, as evidenced by the presence of an outlier. The proposed method has the lowest median time, making it the fastest on average compared to all other methods.

<figure><img src="image_9.png" /><figcaption>Fig. 8: Experimental results of PSF-HS under PSC-2: (a) I–V and P–V curves in SAS1000, (b) measured waveforms.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 9: Experimental results of the proposed hybrid algorithm under PSC-2: (a) I–V and P–V curves in SAS1000, (b) measured waveforms.</figcaption></figure>
The box of the proposed method is the smallest, indicating the least variability.

This means it is not only faster but also more consistent in its performance. Also, the proposed method achieves an exceptionally high median accuracy, close to 99.9%. This demonstrates that it consistently delivers precise results across various trials.

The box of the proposed method is nonexistent, indicating that the accuracy is extremely consistent.

The results are tightly clustered around the median, showing minimal variability in performance. The proposed method excels in both speed and accuracy, offering the fastest processing times and the most consistent accuracy among the methods evaluated. It has the most accurate performance in finding the GMPP among the HS methods only except for similar accuracy with HS (0.95, 0.7) under PSC-2, as seen in Table IV.

Among the comparative experimental results, the outcomes of HS (0.95, 0.7) are selected since it could be regarded as optimized tracking performance using the conventional HS method compared to the case of HS (0.8, 0.5).

The I–V and P–V curves (captured by SAS1000) and measured experimental waveforms (voltage, current, and power of the PV system with duty cycles) are presented in Figs. 8–9. Further, the PSC-2 is only included in this Section to highlight the most severe case study of partial shading.

The shading pattern, PV array parameters, generated power, and tracking accuracy (efficiency) are confirmed in Figs. 8(a)–9(a). The GMPP is successfully located regardless of the applied method.

As indicated in Fig. 8(b), at the duty cycle, once the initial harmony is generated, the consecutive iterations follow. In Fig. 9(b), *max iter* = 13 is identified in the first stage and P&O is implemented in the second stage. Under PSC-2, the accuracies of 99.77% (HS (0.95, 0.7)) is improved to 99.93% (proposed algorithm) and the tracking times are significantly reduced from 7.8 s (HS (0.95, 0.7)) to 3.2 s (proposed algorithm).

## V. Conclusion

This paper introduces a hybrid MPPT algorithm that integrates harmony search (HS) with the P&O algorithm to address partial shading in photovoltaic (PV) systems. The key contributions of the research are as follows: (a) Given the limited application of HS in PV systems,

conceptual illustrations are provided to explain its working principles; (b) This study is the first to propose a hybrid MPPT algorithm that combines HS with P&O; (c) The algorithm incorporates the PSF scheme, reducing the parameter-setting complexity compared to conventional HS and NHS methods; (d) A robust, variable-step-size P&O algorithm is integrated into the hybrid model to enhance tracking efficiency; and (e) A detailed flowchart and pseudocode are included for practical implementation. Extensive experimental testing demonstrates that the proposed hybrid MPPT algorithm achieves the fastest convergence time compared to P&O, HS, NHS, PSF-HS, and PSO. Specifically, the proposed algorithm improves tracking accuracy to an average of 99.89% under non-PSC condition, 99.88% under PSC-1, and 99.89% under PSC-2. Additionally, the proposed algorithm reduces average tracking time by 2.63s, 3.49s, and 3.59s compared to the conventional HS method under non-PSC, PSC-1, and PSC-2 respectively.

## References

[1] L. Liu, D. Zhou, J. Zou and W. Wang, "Zero-Vector-Regulation-Based Closed-Loop Power Distribution Strategy for Dual-DC-Port DC-AC Converter-Connected PV-Battery Hybrid Systems," in IEEE Transactions on Power Electronics, vol. 38, no. 6, pp. 6956-6968, June 2023.

[2] S. E. Babaa, M. Armstrong, and V. Pickert, "Overview of maximum power point tracking control methods for PV Systems," Journal of Power and Energy Engineering, vol. 02, no. 08, pp. 59-72, 2014.

[3] I. Pervez, I. Shams, S. Mekhilef, A. Sarwar, M. Tariq and B. Alamri, "Most Valuable Player Algorithm based Maximum Power Point Tracking for a Partially Shaded PV Generation System," in IEEE Transactions on Sustainable Energy, vol. 12, no. 4, pp. 1876-1890, Oct. 2021.

[4] H. Gundogdu, A. Demirci, S. M. Tercan and U. Cali, "A Novel Improved Grey Wolf Algorithm Based Global Maximum Power Point Tracker Method Considering Partial Shading," in IEEE Access, vol. 12, pp. 6148-6159, 2024.

[5] N. A. N. Aldin, W. S. E. Abdellatif, Z. M. S. Elbarbary, A. I. Omar and M. M. Mahmoud, "Robust Speed Controller for PMSG Wind System Based on Harris Hawks Optimization
via Wind Speed Estimation: A Real Case Study," in IEEE Access, vol. 11, pp. 5929-5943, 2023.

[6]. M. A. Zeddini, S. Krim, M. Mansouri, M. F. Mimouni and A. Sakly, "Fuzzy Logic Adaptive Crow Search Algorithm for MPPT of a Partially Shaded Photovoltaic System," in IEEE Access.

[7]. I. Pervez, C. Antoniadis, H. Ghazzai and Y. Massoud, "A Modified Bat Algorithm with Reduced Search Space Exploration for MPPT under Dynamic Partial Shading Conditions," 2023 IEEE International Symposium on Circuits and Systems (ISCAS), Monterey, CA, USA, 2023, pp. 1-5.

[8]. J. S. Koh, R. H. G. Tan, W. H. Lim and N. M. L. Tan, "A Modified Particle Swarm Optimization for Efficient Maximum Power Point Tracking Under Partial Shading Condition," in IEEE Transactions on Sustainable Energy, vol. 14, no. 3, pp. 1822-1834, July 2023.

[9]. N. Kumar, I. Hussain, B. Singh and B. K. Panigrahi, "Normal Harmonic Search Algorithm-Based MPPT for Solar PV System and Integrated With Grid Using Reduced Sensor Approach and PNKLMS Algorithm," in IEEE Transactions on Industry Applications, vol. 54, no. 6, pp. 6343-6352, Nov.-Dec. 2018.

[10]. K. L. Lian, J. H. Jhang and I. S. Tian, "A Maximum Power Point Tracking Method Based on Perturb-and-Observe Combined With Particle Swarm Optimization," in IEEE Journal of Photovoltaics, vol. 4, no. 2, pp. 626-633, March 2014.

[11]. Mathi DK, Chinthamalla R., "A hybrid global maximum power point tracking method based on butterfly particle swarm optimization and perturb and observe algorithms for a photovoltaic system under partially shaded conditions." Int Trans Electr Energ Syst. 2020.

[12]. J. P. Ram, D. S. Pillai, N. Rajasekar and S. M. Strachan, "Detection and Identification of Global Maximum Power Point Operation in Solar PV Applications Using a Hybrid ELPSO-P&O Tracking Technique," in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 8, no. 2, pp. 1361-1374, June 2020.

[13]. D. Pilakkat and S. Kanthalakshmi, "An improved P&O algorithm integrated with artificial bee colony for photovoltaic systems

under partial shading conditions," Sol. Energy, vol. 178, pp. 37-47, 2019.

[14]. S. Mohanty, B. Subudhi and P. K. Ray, "A Grey Wolf-Assisted Perturb & Observe MPPT Algorithm for a PV System," in IEEE Transactions on Energy Conversion, vol. 32, no. 1, pp. 340-347, March 2017.

[15]. J. P. Ram, D. S. Pillai, A. M. Ghias, and N. Rajasekar, "Performance enhancement of solar PV systems applying P&O assisted flower pollination algorithm (FPA)," Sol. Energy, vol. 199, pp. 214-229, 2020.

[16]. D. S. Pillai, J. P. Ram, A. M. Y. M. Ghias, M. A. Mahmud and N. Rajasekar, "An Accurate, Shade Detection-Based Hybrid Maximum Power Point Tracking Approach for PV Systems," in IEEE Transactions on Power Electronics, vol. 35, no. 6, pp. 6594-6608, June 2020.

[17]. Z.W. Geem and K.B. Sim, "Parameter setting free harmony search algorithm," Applied Mathematics and Computation, vol. 217, pp. 3881-3889, 2010.

[18]. M. Seyedmahmoudian, T. K. Soon, B. Horan, A. Ghandhari, S. Mekhilef and A. Stojcevski, "New ARMO-based MPPT Technique to Minimize Tracking Time and Fluctuation at Output of PV Systems under Rapidly Changing Shading Conditions," early access in IEEE Transactions on Industrial Informatics.