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Review on Maximum Power Point Tracking Control Strategy Algorithms for Offshore Floating Photovoltaic Systems

Lei Huang

^1,2,*

Baoyi Pan

^1,2,

Shaoyong Wang

³,

Yingrui Dong

³ and

Zihao Mou

^1,2

School of Electrical Engineering, Southeast University, Nanjing 210096, China

Marine Renewable Energy Engineering Center, Advanced Ocean Institute of Southeast University, Nantong 226010, China

China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd., Guangzhou 510663, China

Author to whom correspondence should be addressed.

J. Mar. Sci. Eng. 2024, 12(12), 2121; https://doi.org/10.3390/jmse12122121

Submission received: 29 September 2024 / Revised: 9 November 2024 / Accepted: 19 November 2024 / Published: 21 November 2024

(This article belongs to the Special Issue Offshore Renewable Energy, Second Edition)

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Browse Figures

Figure 1
Photovoltaic power generation development. "> Figure 2
Offshore floating photovoltaic systems. "> Figure 3
Basic structure of MPPT algorithm with boost converter. "> Figure 4
Single-diode equivalent circuit of PV cell. "> Figure 5
PV module characteristics under different irradiances and constant temperature (25 °C): (left) power–voltage curve and (right) current–voltage curve. "> Figure 6
PV module characteristics under partial shading conditions: (left) power–voltage curve and (right) current–voltage curve. "> Figure 7
Slope of wave surface under different wave models. (left) Airy wave and (right) Stokes wave. "> Figure 8
Irradiance under different wave models. (left) Airy wave and (right) Stokes wave. "> Figure 9
Output characteristics of photovoltaic model under influence of sea waves. (left) V-t curve, (middle) I-V-t diagram, and (right) P-V-t diagram. "> Figure 10
MPPT control structure: (left) direct control, (right) indirect control. "> Figure 11
Flowchart of P&O algorithm. "> Figure 12
The drift phenomena under continuously changing irradiance conditions. "> Figure 13
Flowchart of INC algorithm. "> Figure 14
Block diagram of FLC MPPT technique. "> Figure 15
Photovoltaic array structural diagram: (left) SP, (middle) BL, (right) TCT. "> Figure 16
Block diagram of ANN MPPT technique. "> Figure 17
Block diagram of PSO algorithms. ">

Versions Notes

Abstract

Floating photovoltaic systems are rapidly gaining popularity due to their advantages in conserving land resources and their high energy conversion efficiency, making them a promising option for photovoltaic power generation. However, these systems face challenges in offshore environments characterized by high salinity, humidity, and variable irradiation, which necessitate effective maximum power point tracking (MPPT) technologies to optimize performance. Currently, there is limited research in this area, and few reviews analyze it comprehensively. This paper provides a thorough review of MPPT techniques applicable to floating photovoltaic systems, evaluating the suitability of various methods under marine conditions. Traditional algorithms require modifications to address the drift phenomena under uniform irradiation, while different GMPPT techniques exhibit distinct strengths and limitations in partial shading conditions (PSCs). Hardware reconfiguration technologies are not suitable for offshore use, and while sampled data-based techniques are simple, they carry the risk of erroneous judgments. Intelligent technologies face implementation challenges. Hybrid algorithms, which can combine the advantages of multiple approaches, emerge as a more viable solution. This review aims to serve as a valuable reference for engineers researching MPPT technologies for floating photovoltaic systems.

Keywords:

floating photovoltaic (FPV) system; maximum power point tracking (MPPT); the drift phenomena; partial shading conditions (PSCs); intelligent algorithm

1. Introduction

Solar photovoltaic (PV) power generation offers several advantages, including abundant reserves, widespread distribution, and strong economic viability, making it one of the most prominent and promising renewable energy sources. The installed PV capacity is continually increasing, as shown in Figure 1, reaching approximately 1500 GW in 2022, with projections indicating that it could reach around 2500 GW by 2030 [1].

However, as the installed capacity of PV power generation continues to grow, the demand for land is also increasing, particularly in coastal areas where land resources are scarce, making it challenging to develop large-scale land-based PV projects [2]. Offshore PV presents a critical solution to this issue. Among these, floating photovoltaic (FPV) systems stand out for their ease of installation, low layout costs, convenient maintenance, and high power generation efficiency. The practical implementation of FPV systems is illustrated in Figure 2. Many countries are currently exploring large-scale applications of this technology [3,4].

To enhance the economic viability and stability of FPV systems, maximum power point tracking (MPPT) technology is crucial for the efficient operation of PV power generation systems. Figure 3 illustrates the basic structure of the MPPT algorithm application. It is also a key focus in the application of photovoltaic inverters, representing one of the main challenges in the field [5]. In FPV systems, the continuous oscillation of the solar panels causes the effective irradiance received by the panels to fluctuate, leading to constant changes in the power–voltage (P-V) curve of the PV array. The persistence and randomness of these environmental variations significantly increase the likelihood of the MPPT algorithm becoming trapped in local optima, thereby placing high demands on the algorithm’s adaptability and dynamic response.

Furthermore, offshore PV systems must account for the effects of partial shading conditions (PSCs) caused by complex environments. PSCs can lead to multiple peaks in the P-V curve of the PV array. Traditional MPPT control algorithms, such as Perturb and Observe (P&O) and Incremental Conductance (INC), are prone to getting stuck at local maximum power points (LMPPs), failing to perform global searches. This results in the PV array operating under suboptimal conditions, leading to significant power mismatch, energy loss, and potential damage to the PV modules. Such states need to be detected and, ideally, avoided.

While extensive research and engineering solutions have been developed for MPPT control algorithms in traditional land-based PV systems, their adaptability to offshore PV scenarios remains questionable. Current research on MPPT technology specific to offshore PV scenarios is limited. For instance, Reference [6] directly applied the P&O method, while Reference [7] combined a closed-loop and open-loop Fractional Short-Circuit Current (FSCC) method, where the closed-loop component essentially follows the P&O principle. However, neither approach overcomes the inherent drawbacks of the P&O method. Other studies have adapted swarm algorithms like the Bacterial Foraging Algorithm and Bat Algorithm for FPV systems [8], but these simulations lack real-time validation and practical relevance. A novel metaheuristic algorithm combining the Improved Grey Wolf Algorithm and Bat Algorithm was proposed in Reference [9], showing effectiveness in adapting to varying irradiance conditions, yet its evaluation methods are incomplete, and the computational complexity remains high.

In summary, the MPPT technology for FPV systems is still in its infancy, and no mature algorithms currently exist. Simple transplants of land-based MPPT technology to offshore scenarios face numerous challenges, and no reference has systematically compared MPPT techniques for land-based and offshore applications. Therefore, writing a review focused on MPPT technology suitable for FPV systems is highly necessary. This paper categorizes and summarizes the MPPT control algorithms proposed in recent years, discusses the challenges and solutions these algorithms face in FPV scenarios, and assesses their suitability for offshore applications.

This paper is organized as follows: Section 2 presents an analysis of the characteristics of photovoltaic arrays, with a focus on their behavior in offshore floating scenarios. Section 3 offers a comprehensive review of MPPT algorithms under uniform irradiance, with particular emphasis on the self-optimization control algorithm. Section 4 and Section 5 provide an in-depth analysis of global MPPT algorithms and hybrid algorithms in the context of partial shading conditions. Section 6 explores the current state of development and future prospects of MPPT control algorithms for floating photovoltaic systems. Finally, the conclusions are presented in Section 7.

2. Characteristics of Photovoltaic Arrays in Offshore Floating Scenarios

A PV array consists of multiple PV cells connected in series and parallel, where each PV cell serves as the smallest unit in the process of photoelectric conversion. Establishing a mathematical model for PV cells is fundamental to understanding the P-V characteristics of PV output and to implementing MPPT technology [10]. The single-diode equivalent circuit of a PV cell is illustrated in Figure 4.

Currently, PV cells are often modeled as an ideal current source in parallel with a diode, as illustrated in the figure. The internal losses of the PV cell are represented by a series resistor

R_{s}

and a parallel resistor

R_{s h}

. The output current

I_{p v}

can then be expressed as

I_{p v} = I_{p h} - I_{r} (e^{\frac{q (V_{p v} + I_{p v} R_{s})}{n * K^{*} T_{j}}} - 1) - \frac{V_{p v} + I_{p v} R_{s}}{R_{s h}}

(1)

where

I_{p v}

and

V_{p v}

are the output current (A) and voltage (V) of the PV cell, respectively;

I_{p h}

is the photocurrent (A) for the PV model;

I_{r}

is the diode reverse saturation current;

n

is the diode ideal factor;

q

is the charge (C) of the electron;

K

is the Boltzmann constant (J/K), with a value of

1.38 \times 10^{- 23}

; and

T_{j}

is the current temperature of the PV cell.

Under ideal conditions, if the internal losses of the PV cell are neglected and the photogenerated current

I_{p h}

is approximated as the short-circuit current

I_{s c}

, Equation (1) can be simplified to

I_{p ν} = I_{s c} (1 - C_{1} (e^{\frac{V_{p ν}}{C_{2} V_{o c}}} - 1))

(2)

where

V_{o c}

is the open-circuit voltage (V). At the maximum power point,

I_{p ν} = I_{m}, V_{p ν} = V_{m}

, while in the open state,

I_{p ν} = 0, V_{p ν} = V_{o c}

. The equation can be solved based on the above two working states, and the coefficients

C_{1}

and

C_{2}

can be obtained as

C_{1} = (1 - \frac{I_{m}}{I_{s c}}) \exp (- \frac{V_{m}}{C_{2} V_{o c}})

(3)

C_{2} = (\frac{V_{m}}{V_{o c}} - 1) {(\ln (- \frac{V_{m}}{C_{2} V_{o c}}))}^{- 1}

(4)

Under different irradiance and temperature conditions,

I_{s c}, I_{m}, V_{o c}, V_{m}

will vary within a certain range:

I_{s c} = I_{s c - r e f} \frac{s}{s_{r e f}} (1 + a Δ T)

(5)

I_{p ν} = I_{s c} (1 - C_{1} (e^{\frac{V_{p}}{C_{2} V_{o c}}} - 1))

(6)

I_{m} = I_{m - r e f} \frac{S}{S_{r e f}} (1 + a Δ T)

(7)

V_{o c} = V_{o c - r e f} (\ln (e + Δ S)) (1 - c Δ T)

(8)

V_{m} = V_{m - r e f} (\ln (e + b Δ S)) (1 - c Δ T)

(9)

where

S_{r e f}

and

T_{r e f}

are the standard irradiance and temperature, respectively;

Δ T = T - T_{r e f}

is the difference between current temperature and standard temperature;

Δ S = S - S_{r e f}

is the difference between current irradiance and standard irradiance;

I_{s c - r e f}, V_{o c - r e f}

are the short-circuit current (A) and open-circuit voltage (V) under a standard environment; and

a, b, c

are the constant parameters matched according to PV module data [11].

Under ideal conditions, where each PV cell in the array operates at the same irradiance and temperature, the output I-V (current–voltage) and P-V curves, as shown in Figure 5, exhibit a single power maximum point. In this scenario, traditional MPPT algorithms can successfully achieve maximum power capture.

When the array is under non-uniform irradiance conditions, known as partial shading conditions (PSCs), the activation of bypass diodes in the circuit causes current deviations, leading to a multi-peak phenomenon. A mathematical model for a PV array under three-segment shading can be established as follows:

I_{p ν} = \{\begin{array}{l} I_{s c 1} (1 - C_{1} (e^{\frac{V_{p ν}}{N_{s 1} C_{2} V_{o c 1}}} - 1)) \\ I_{s c 2} (1 - C_{1} (e^{\frac{V_{p ν}}{N_{s 2} C_{2} V_{o c 2}}} - 1)) \\ I_{s c 3} (1 - C_{1} (e^{\frac{V_{p ν}}{N_{s 3} C_{2} V_{o c 3}}} - l)) \end{array}

(10)

where

I_{s c 1}, I_{s c 2}, I_{s c 3}

are the short-circuit currents (A) under different irradiances, and

V_{o c 1}, V_{o c 2}, V_{o c 3}

are the open-circuit voltages (V) under different irradiances.

In this scenario, LMPPs will emerge, with the P-V curve displaying multiple peaks and the I-V curve appearing as a stepped curve. Additionally, when the irradiance continues to change, both the P-V and I-V curves will exhibit ongoing fluctuations, as illustrated in Figure 6.

In floating photovoltaic systems, wave motion continuously influences the angle of inclination of the photovoltaic panels, thereby affecting the irradiance they receive. Various floating platform designs have been proposed, but no mature solutions have been implemented for large-scale commercial deployment. Existing representative floating platform structures can be classified into two categories: the first category comprises structures that closely align with wave motion, such as submerged flexible membranes and flat floating platforms with flexible connections; the second category includes structures with inherent stability, where the amplitude of motion is less than that of the wave movement.

For the former type of floating structure design, it is composed of small-scale floating bodies connected flexibly, and its motion state is essentially consistent with that of the waves. The movement of the floating bodies can be regarded as the movement of water particles on the surface of the sea waves. Under parallel light conditions, the effect of translational motion on the irradiance received by the photovoltaic panels is minimal, and the focus is mainly on the impact of rotational motion.

In floating photovoltaic systems, the total solar irradiance that the photovoltaic surface receives can be categorized into direct irradiance

B_{β}

, diffuse irradiance

D_{β}

, and reflected irradiance

R_{β}

G_{β} = B_{β} + D_{β} + R_{β}

(11)

Since the irradiance on an inclined surface can be considered as a component of the irradiance on the water surface, it is necessary to first calculate the irradiance on the horizontal plane and the geometric relationship between the incident light and the inclined surface.

The geometric relationship is determined by the declination angle

δ

, latitude angle

φ

, hour angle

ω

, solar elevation angle

h

, solar azimuth angle

α

, and pitch angle

β

. The solar azimuth angle represents the angle between the projection of the photovoltaic surface’s normal vector on the horizontal plane and true south, while the pitch angle indicates the angle between the normal vector of the photovoltaic surface and the horizontal plane.

The declination angle

δ

can be calculated using the Cooper formula, while the latitude angle and hour angle can be directly determined based on the spatiotemporal position. The remaining two angles can be calculated as follows:

\sin h = \sin δ \sin φ + \cos δ \cos φ \cos ω

(12)

\sin α = \frac{- \cos δ \sin ω}{\cos h}

(13)

The angle

θ

between direct solar radiation and the normal vector of any inclined plane can be determined as follows:

\begin{matrix} \cos θ = & \cos β (\sin δ \sin φ + \cos δ \cos φ \cos ω) + \\ \sin β (\cos δ \sin α \sin ω + \cos δ \sin φ \cos α \cos ω - \sin δ \cos φ \cos α) \end{matrix}

(14)

The horizontal plane irradiance

G_{h}

is mainly divided into horizontal direct irradiance

B_{h}

and horizontal diffuse irradiance

D_{h}

, where the horizontal direct irradiance

B_{h}

is defined as

B_{h} = ξ_{0} S_{0} P^{m}

(15)

where

ξ_{0}

is the Earth’s orbital eccentricity correction factor, which can be calculated as

ξ_{0} = 1 + 0.033 \cos (\frac{2 π d_{n}}{365})

, and

d_{n}

is the day of the year, counted from 1 January.

S_{0}

is the solar constant, representing the amount of radiation received per unit area that is perpendicular to sunlight at the upper boundary of the atmosphere in a unit of time.

P

is the atmospheric transmittance coefficient.

m

is the atmospheric optical mass, which represents the ratio of the distance that sunlight travels through the atmosphere to reach sea level to the total thickness of the Earth’s atmosphere. In engineering calculations, it is typically computed as

m = \frac{1}{\sin h}

, and

h

is the solar elevation angle.

Theoretically, accurately calculating the solar diffuse irradiance on the Earth’s surface is quite difficult, so empirical formulas are generally used. The diffuse solar irradiance on the horizontal plane

D_{h}

is typically expressed as

D_{h} = 0.5 ξ_{0} S_{0} (\frac{1 - P^{m}}{1 - 1.4 \ln P}) \sin h

(16)

The intensity of the reflected radiation from solar radiation on the water surface, which is the sum of direct and diffuse radiation, is influenced by the reflection coefficient. Therefore, the formula for calculating the reflected irradiance is

R_{h} = ρ (B_{h} + D_{h})

(17)

In the formula,

ρ

represents the ocean reflectance, which is typically taken as 0.35.

By integrating the geometric relationships related to the horizontal plane irradiance and the inclined plane, the irradiance on the inclined surface can be calculated:

\begin{matrix} G_{β} & = B_{β} + D_{β} + R_{β} \\ = B_{h} \cos θ + D_{h} \frac{1 + \cos β}{2} + ρ (B_{h} + D_{h}) \frac{1 - \cos β}{2} \end{matrix}

(18)

In the formula,

B_{β}

denotes the direct irradiance on the inclined plane, and

D_{β}

represents the diffuse irradiance on the inclined plane, calculated under an isotropic model. In this model, diffuse radiation is assumed to result solely from dome scattering, uniformly distributed across the sky with equal intensity in all directions. Consequently, the diffuse irradiance is proportional to the dome area that faces the inclined plane.

R_{β}

signifies the reflected irradiance on the inclined plane.

For the consideration of an ideal scenario, the basic parameters selected for irradiance calculation in this paper are shown in Table 1.

Based on the analysis above and the data in Table 1, the irradiance calculation expression for the photovoltaic panel can be derived as follows:

\begin{matrix} G_{β} & = {768.426}^{*} \cos β + {639.334}^{*} \sin β + 242.6886 \\ = {768.426}^{*} \cos (τ + τ_{0}) + {639.334}^{*} \sin (τ + τ_{0}) + 242.6886 \end{matrix}

(19)

In this equation,

τ

represents the wave tilt angle, and

τ_{0}

is the tilt angle between the photovoltaic panel and the floating structure. Some studies have examined the impact of this tilt angle, showing that irradiance on the photovoltaic system is maximized at certain angles [12,13]. In this paper, we follow the setup of the aforementioned floating structure and set this tilt angle to 0.

To analyze the wave tilt angle variation in the floating body under ocean waves, this paper models the waves as Airy waves and second-order Stokes waves.

The surface wave expression for an Airy wave is as follows:

η (x, t) = \frac{H}{2} \cos (ω_{w} t - k_{w} x)

(20)

In this equation,

k_{w}

represents the wave number, with

k_{w} = 2 π / L

;

L

is the wavelength, and

H

is the wave amplitude;

ω_{w}

is the angular frequency of the wave. By taking the derivative of the Airy wave surface expression with respect to position and applying the arctangent function, the time-domain expression for the wave tilt angle of the Airy wave is obtained as follows:

τ (t) = \arctan [0.5 \cdot k_{w} H \sin (k_{w} x - ω_{w} t)]

(21)

The surface wave expression for the second-order Stokes wave is as follows:

\begin{matrix} η (x, t) = & \frac{π H}{8} (\frac{H}{L}) \frac{\cos h (k_{w} d_{w}) \cdot [\cos (2 k_{w} d_{w}) + 2]}{\sin h^{3} (k_{w} d_{w})} \cos 2 (k_{w} x - ω_{w} t) \\ + \frac{H}{2} \cos (k_{w} x - ω_{w} t) \end{matrix}

(22)

In this equation,

d_{w}

represents the water depth. Similarly, by taking the partial derivative of the second-order Stokes wave expression with respect to position and applying the arctangent function, the time-domain expression for the wave tilt angle of the second-order Stokes wave can be obtained:

τ (t) = \arctan [- \frac{π k_{w} H^{2}}{2 L} (- 1 + \frac{3}{2 \sin h^{2} k_{w} d_{w}}) \cot h k_{w} d_{w} \cdot \sin 2 (k_{w} x - ω_{w} t) - \frac{k_{w} H}{2} \sin (k_{w} x - ω_{w} t)]

(23)

The relationship between the wave angular frequency

ω_{w}

and wave number

k_{w}

can be determined by the dispersion relation

ω_{w}^{2} = g k_{w} \tan d_{w} (k_{w} d_{w})

, which simplifies under deep-water conditions to

ω_{w}^{2} = g k_{w}

, where

g

is the acceleration due to gravity.

Using China’s Yellow Sea as the reference region, with an average water depth of 44 m, latitude

φ = 36 °

, a monthly average wave period variation between 2 and 6 s, and an average significant wave height of 0.4–1.4 m, this study selects waves with a height of 1 m and periods of 3, 4, and 5 s for an analysis. The wave tilt angle images are shown in Figure 7.

From the above images, it can be seen that, compared to Airy waves, the second-order Stokes wave exhibits waveform distortion, while the amplitude and period remain similar to those of the Airy wave. Additionally, with the same wave height, the smaller the wave period, the greater the variation in the wave tilt angle.

The irradiance on the photovoltaic modules was calculated based on the wave tilt angle, and the results are shown in Figure 8. The figure shows that irradiance variation is consistent with wave tilt angle changes, and the smaller the wave period, the greater the amplitude of irradiance variation.

Based on the Airy wave model with a wave height of 1 m and a period of 3 s, this study analyzes the impact of irradiance on the photovoltaic system’s output characteristics. Figure 9 illustrates the time-varying output characteristics of the photovoltaic system under Airy wave conditions: the left panel shows the maximum power point voltage over time, the middle panel presents the I-V curve, and the right panel displays the P-V curve. As shown, over the 0–6 s period, the photovoltaic system’s I-V and P-V curves undergo two cycles of fluctuation, corresponding with the irradiance variation period. At 0.75 s, when irradiance reaches its peak, the system’s open-circuit voltage, short-circuit current, and maximum power also attain their maximum values. Furthermore, the left panel reveals that the photovoltaic system’s maximum power point voltage fluctuates over time.

3. MPPT Under Uniform Solar Irradiance

The current MPPT control structures, as shown in Figure 10, can be categorized into two types: Direct Duty Ratio-Based (DDR) and Voltage Reference-Based (VR). In the DDR type, the algorithm calculates the duty ratio, which then generates the switching signals to control the DC/DC circuit. In the VR type, the algorithm computes a voltage reference value, and a voltage controller adjusts the duty ratio accordingly. In almost all control strategies, these two control structures can be used interchangeably.

At present, Proportional–Integral (PI) regulators are commonly used for voltage control. However, Reference [14] proposes the use of a PR-P controller to replace the PI regulator. By leveraging the inheritance characteristics of signals generated by the controller’s resonant path, this approach integrates with the Model-Free Adaptive Control (MFAC) technique in the Extremum-Seeking Control (ESC) algorithm, resulting in reduced steady-state oscillations and faster response times.

When comparing these two structures, the DDR type does not require the design of additional parameters and adapts well to various environmental conditions. On the other hand, the VR type is less affected by load variations, offering stronger robustness and making it more suitable for industrial applications.

Reference [15] proposes a novel control structure that nests the MPPT algorithm module within a Proportional–Integral controller, allowing both to share the Analog-to-Digital Converter (ADC) sampling. This enables the MPPT algorithm module to benefit from a high sampling rate, significantly improving dynamic response performance while keeping costs low. This control structure is reliable, simple, and suitable for large-scale scenarios, making it directly applicable to existing photovoltaic systems.

Furthermore, the steady-state performance of photovoltaic MPPT algorithms can be evaluated under certain irradiance, temperature, and load conditions. However, assessing dynamic performance requires the consideration of more complex environmental conditions and experimental parameters. Currently, there are three main testing methods: the Step Operation Test, EN50530 Dynamic Test, and Daily Testing [16].

Among them, the Step Operation Test is simple but insufficient for a true evaluation of dynamic performance. The Daily Testing method simulates real operating conditions but comes with higher costs and experimental requirements. The EN50530 Dynamic Test involves changing the irradiance at a certain slope, closely resembling real operating conditions while keeping costs low, and thus has garnered significant attention. In particular, Reference [17] introduces a state-space simulation method to reduce the overall simulation time.

Before introducing specific methods, it is essential to outline the new demands that continuously fluctuating irradiance, induced by ocean waves, places on photovoltaic MPPT algorithms. For instance, with a wave height of 1 m and a period of 3 s, the irradiance exhibits a quasi-sinusoidal pattern with an approximate amplitude of 150 and a period of 3 s. Under such highly variable atmospheric conditions, the MPPT challenge effectively transforms into a time-constrained nonlinear optimization problem. Consequently, two critical performance metrics must be considered: the speed of tracking the maximum power point and the algorithm’s capability to escape from local optima.

3.1. MPPT Algorithms Based on Photovoltaic Cell Models

3.1.1. Constant Voltage (CV)

The Constant Voltage (CV) method is essentially an MPPT algorithm based on the photovoltaic cell model. As irradiance changes, the voltage at the maximum power point of a PV cell is approximately related to the open-circuit voltage by the following relationship:

U_{m p p} \approx 0.8 U_{o c}

(24)

Therefore, the Constant Voltage (CV) method simply maintains the output voltage at approximately 80% of the open-circuit voltage [18,19]. Clearly, this method has low control accuracy and is difficult to adjust for external environmental changes. Its accuracy further decreases when temperature fluctuations occur.

Currently, the CV method is often used to determine the initial value for other methods. For instance, in the P&O method, the initial reference voltage can be set as

U_{ref} = 0.78 U_{oc}

to speed up the tracking process [20]. However, some researchers argue that the initial reference voltage should slightly deviate from the voltage at the maximum power point, choosing

U_{ref} = 0.65 U_{α}

instead, which allows for recording different perturbation directions before converging to the MPP [21].

The I-V characteristics of a specific photovoltaic array are influenced by numerous parameters discussed in Section 1, all of which vary with temperature and irradiance. Consequently, variations in the I-V characteristic curve can be attributed to changes in the external parameters of the photovoltaic array. Reference [22] employs the measured voltage and current data in conjunction with the Newton–Raphson algorithm to estimate the values of irradiance and temperature, thereby calculating the voltage and current values corresponding to the maximum power point.

3.1.2. Sliding Mode Control (SMC)

Sliding Mode Control (SMC) is a variable structure control strategy that considers the system’s state changes, making it well suited for photovoltaic power generation systems with nonlinear characteristics. The sliding surface is defined as follows:

\frac{\partial P_{p ν}}{\partial I_{p ν}} = \frac{\partial I_{p ν}^{2} R_{p ν}}{\partial I_{p ν}} = I_{p ν} (2 R_{p ν} + I_{p ν} \frac{\partial R_{p ν}}{\partial I_{p ν}}) = 0

(25)

In the equation,

P_{p ν} = I_{p ν}^{2} R_{p ν}

represents the system’s output power, and

R_{p ν} = V_{p ν} / I_{p ν}

denotes the equivalent load directly connected to the solar cells.

As the photovoltaic system approaches the sliding surface, MPPT can be achieved. To confirm the existence of a sliding mode in this method and to ensure that it meets the reachability and stability requirements, it is necessary to select a Lyapunov function,

V = (1 / 2) S^{2}

. This function is used to demonstrate that the system satisfies the conditions for the existence of a generalized sliding mode,

\lim_{s \to 0} s \dot{s} \leq 0

[23].

SMC is designed based on the photovoltaic cell model, and compared to traditional MPPT algorithms, it is not limited by perturbation step size. This method offers significant advantages in terms of adaptability and disturbance rejection, leading to faster tracking speed and stronger dynamic response capabilities. However, due to the inherent discreteness of SMC, the system state switches at a very high frequency, causing a phenomenon known as chattering. This results in continuous oscillations in the steady-state output power of the PV system, leading to considerable energy loss.

SMC is heavily influenced by the choice of the sliding surface. In Reference [24], a Double Integral Sliding Mode Controller (DISMC) is utilized, with the sliding surface being continuously redefined to reduce chattering and improve the system’s dynamic response. Additionally, Reference [25] introduces a

θ

-modified Krill Herd method (

θ

-MDK) to optimize traditional SMC parameters, enhancing the algorithm’s performance.

The traditional constant rate of approach cannot simultaneously balance convergence speed and chattering. Although the exponential reaching law increases the approach speed, it fails to completely eliminate chattering. To address this, Reference [26] proposes a power reaching law with a saturation function, which combines the rapid convergence of the power term with the linear feedback within the boundary layer of the saturation function, achieving both rapid response and stability. Reference [27] further advances this by proposing a multi-power reaching law, integrating the speed of an exponential function with the smoothness of a power function, allowing the system to respond more quickly to disturbances.

3.1.3. Conclusions

Compared to traditional MPPT algorithms, MPPT algorithms based on the photovoltaic cell model do not require the consideration of perturbation step size, and they involve fewer parameters in the control system. This results in better tracking speed and steady-state accuracy. However, their principles are more complex, and they require a high level of precision in the photovoltaic cell model.

3.2. Traditional Self-Optimization MPPT Algorithm

Traditional extremum-seeking MPPT algorithms mainly refer to the Perturb and Observe (P&O) method and the Incremental Conductance (INC) method. These algorithms are based on the output characteristic curve of photovoltaic cells, optimizing according to the single-peak curve and the maximum power point (MPP) variation patterns. They offer relatively high accuracy and can achieve real-time control, meeting the needs of general applications. As a result, they are widely used in practical engineering scenarios.

3.2.1. Perturb and Observe (P&O)

The P&O method works by continuously applying perturbations to the duty ratio or voltage and comparing the change in output power before and after the perturbation. The direction of the next perturbation is determined based on whether the power increases or decreases, and this process continues until the change in output power becomes zero, indicating that the maximum power point (MPP) has been tracked. Its flowchart is shown in Figure 11. This algorithm is simple to implement and highly reliable, with good tracking efficiency under uniform irradiance conditions.

However, the traditional P&O method uses a fixed perturbation step size, which directly affects the tracking speed and steady-state accuracy of the algorithm, making it difficult to optimize both simultaneously. To overcome the limitations of the traditional fixed-step approach, many researchers have studied improved adaptive variable step-size P&O methods.

Depending on the MPPT control structure, the perturbation quantity can be chosen accordingly. The principle of variable step-size selection is as follows: a larger step size is chosen in the initial tracking stage, and the step size gradually decreases as the maximum power point is approached. It is worth noting that although different variable step-size choices may have different names or descriptions, they are fundamentally equivalent in principle [28].

Some researchers pre-divide the working region into zones based on the distance from the MPP. A larger step size is used when far from the MPP, and a variable step size is applied when closer to it, thereby increasing tracking speed while reducing computational complexity [29,30].

A significant challenge with variable step-size selection is the difficulty in determining the parameters, which are often set based on experience. For example, in Reference [31], the variable step size is simply set as

(I / V) Δ D

, which adheres to the aforementioned principles but lacks a sound mathematical basis. In Reference [29], the step size is chosen as

M (Δ P_{n} / Δ V_{n})

, which has been experimentally validated to perform well. However,

M

is a constant calculated during initialization, which may not fully account for continuous changes in irradiance. Reference [32] improves on this by correlating with current changes, indirectly linking it to irradiance changes and enhancing adaptive capability. Besides step-size selection based on formula calculations, some researchers choose step sizes based on geometric relationships. Reference [33] constructs a triangular relationship based on the photovoltaic output characteristic curve, where the step size is directly related to the working point position. Reference [34] constructs a centerline in the duty ratio change diagram, enabling the system to quickly operate near the MPP and then gradually smooth out oscillations through iterative step-size reduction.

When a single perturbation quantity is used, the operating point inevitably passes through regions far from the MPP, which slows down the tracking speed. Therefore, designing a reasonable initialization position or adopting a “jump” mechanism can be beneficial. Usually, the approximate initial position is obtained by an MPPT algorithm based on a photovoltaic cell model; the jump mechanism refers to skipping certain regions during the search process, including methods like a voltage window search (VWS) [35,36] and maximum power trapezium (MPT) [37]. Additionally, multi-perturbation is another feasible solution. Reference [38] accelerates tracking speed by simultaneously perturbing voltage and current based on the I-V curve, and its variable step-size selection is similar to that in Reference [34], where multiple iterations reduce steady-state oscillations.

To completely eliminate the impact of steady-state oscillations, a steady-state oscillation module is often added to the algorithm. This module detects when the system enters a steady-state oscillation condition using four sampling points and then designs a steady-state stop logic and restart mechanism [31,32,39].

In addition to the above improvements, researchers as early as 2004 proposed a method known as the beta method, which identifies an intermediate value between voltage and current and uses a variable coefficient

β

to achieve MPPT [40]. This approach can be combined with any standard MPPT method, adjusting the duty cycle by calculating the error between the maximum and minimum values of

β

. Reference [41] further refines the traditional beta method by introducing an adaptive scaling factor to enable variable step-size adjustment, which effectively enhances the system’s tracking speed.

The above improvements do not account for the drift phenomena that may occur with the P&O method under continuously changing irradiance conditions. As illustrated in Figure 12, at a certain moment, the photovoltaic cell operates on the left side of the maximum power point

U 1

with a power of

P 1

. If a negative perturbation is applied and the irradiance increases, the power after the perturbation changes from

P 2

P 3

. Since

P 3 > P 1

, the direction of the next perturbation changes from positive to negative, leading to a misjudgment and causing MPPT failure. The larger the step size, the higher the likelihood of misjudgment.

The key to solving the misjudgment problem lies in distinguishing whether the change in power is caused by the perturbation or by the change in irradiance.

The first method involves increasing the number of sampling points to make a determination. As early as 2008, Reference [42] proposed adding an additional power prediction value between two sampling points to compare power changes caused by different factors. References [43,44] further developed this into a multi-point power prediction method, although the underlying principle remains largely the same—irradiance changes during sampling are considered constant. Reference [45] introduced a method using multiple sampling, where multiple perturbations are applied continuously, and the sum of the perturbations is kept equivalent to a single perturbation. This helps distinguish between power changes caused by perturbations and those caused by irradiance changes. While this method is effective in making the distinction, it requires multiple iterations, resulting in a slower startup speed. The study in [46] employed a similar enhancement method and provided results on the tracking performance using the EN50530 testing protocol under fluctuating irradiance conditions. With a period of 15 s and power fluctuations exceeding 400 W, the results indicated commendable tracking performance, thereby validating the effectiveness of the proposed improvements.

The second method requires the simultaneous detection of both voltage and current. Reference [47] demonstrated that changes in operating conditions can be determined in real time based on the detected voltage and current variations. By adding an additional current change criterion to the traditional P&O method, misjudgments can be eliminated [32,39]. However, sudden load changes can also affect the accuracy of this judgment. To address this, Reference [38] further considers the impact of load changes and establishes a deviation avoidance loop, enabling accurate tracking without bias even when irradiance and load resistance change suddenly, either simultaneously or independently.

The third method sets a working region, and when the operating point crosses the boundary of this region, it indicates that irradiance has a significant impact on it. The perturbation step size is then adjusted accordingly. This method can be implemented by pre-setting voltage boundaries to divide the working region [30], or by designing a power boundary similar to an envelope curve alongside the P-V curve [34]. The limitation of this method is that when irradiance changes are minimal, misjudgments can occur within the working region.

The P&O method, due to its self-optimizing characteristics, is highly suitable for tracking the MPP in continuously fluctuating external environments. Reference [48] proposes a method that uses a Sliding Mode Controller (SMC) based on a particle swarm optimization (PSO) algorithm to adaptively adjust the step size of the P&O method. Simulation results demonstrate that this approach can effectively track the MPP even under conditions where irradiance and temperature undergo simultaneous abrupt changes every 0.1 s. These abrupt changes are significantly more frequent and intense than the typical variations in offshore environments, indicating that with certain improvements, the P&O method can indeed meet the requirements of floating photovoltaic systems.

These improvements can significantly enhance the tracking speed, steady-state accuracy, and dynamic performance of the traditional P&O method, but they are still limited to uniform irradiance conditions. Section 3.1 will further elaborate on global MPPT under PSCs.

3.2.2. Incremental Conductance (INC)

The principle of the Incremental Conductance (INC) method is based on the slope of the photovoltaic P-V curve, and its derivative is given by the following equation:

\frac{d P_{p ν}}{d V_{p ν}} = \frac{d (I_{p ν} V_{p ν})}{d V_{p ν}} = I_{p ν} + V_{p ν} \frac{d I_{p ν}}{d V_{p ν}} = I + V_{p ν} \frac{Δ I_{p ν}}{Δ V_{p ν}}

(26)

When the result of the above calculation is positive, it indicates that the selected point is on the left side of the MPP; if it is negative, the point is on the right side of the MPP. Therefore, the position of the MPP can be captured by comparing the instantaneous conductance with the Incremental Conductance.

The INC method is generally considered to have better dynamic and static performance compared to the P&O method, particularly in terms of smaller steady-state oscillations [49,50]. However, Reference [51] opposes this view and mathematically and experimentally verifies that these two methods are equivalent.

Both the INC and P&O methods are extremum-seeking MPPT techniques with similar principles. Their improvement methods are also very similar, and some can even be used interchangeably [32]. The flowchart of INC algorithm is shown in Figure 13.

In variable step-size algorithms based on the INC method, the step-size voltage formula often uses

d P / d U

or its variants [52]. However, this approach can result in slower tracking speeds on the left side of the maximum power point (MPP). Reference [53] fits a relationship curve between the step-size voltage and the output voltage based on photovoltaic cell parameters and designs a variable step size to improve tracking speed and computational efficiency. Reference [54] uses the ratio of the instantaneous conductance plus the difference between instantaneous current and voltage as a feedback criterion. In this method, the perturbation amount is not fixed but is an infinitely variable adaptive step size, making the calculation simple and more adaptable to complex environmental changes.

To address the misjudgment issue under changing environmental conditions, the INC method can also be improved by simultaneously measuring voltage and current [55]. Reference [56] proposes an intelligent detection of dynamic changes based on measurements from three consecutive operating points, forming an MPP operating region. This approach avoids misjudgment while significantly increasing tracking speed.

Additionally, in the algorithms mentioned above, the interval time between two perturbations is usually fixed and much longer than the system’s stabilization time. Under continuously changing environmental conditions, reducing this interval time can increase the system’s tracking speed [57].

3.3. Fuzzy Logic Control (FLC)

Photovoltaic power generation systems exhibit complex nonlinear output characteristics under the influence of environmental factors such as temperature and irradiance. Fuzzy Logic Control (FLC), which is based on experience and intuition rather than relying on an accurate mathematical model of the control object, is effective in managing time-varying, nonlinear complex systems. Its block diagram is shown in Figure 14.

FLC typically involves three steps: fuzzification, fuzzy rule processing, and defuzzification. In photovoltaic systems, a conventional fuzzy controller is usually implemented with traditional dual-input, single-output control. The inputs are the error signal

E (k)

and the difference in the error signal

C E (k)

, both of which are calculated from the output power and voltage measurements of the photovoltaic system:

E (k) = \frac{P_{p ν} (k) - P_{p ν} (k - 1)}{V_{p ν} (k) - V_{p ν} (k - 1)}

(27)

C E (k) = E (k) - E (k - 1)

(28)

After the input variables are fuzzified, the corresponding input fuzzy sets are obtained. These are then processed according to predefined fuzzy rules to generate an output fuzzy set, which is subsequently defuzzified to yield the output duty cycle.

The main issue with Fuzzy Logic Control is its heavy reliance on the designer’s experience, as the determination of initial parameters lacks a theoretical basis. The control effectiveness is significantly influenced by the controller’s parameters. Therefore, researchers have applied various techniques and methods to enhance the performance of fuzzy controllers, such as variable universe fuzzy control, asymmetric fuzzy control, and dual-mode fuzzy control.

For example, Reference [58] employs a variable universe adaptive fuzzy controller that automatically adjusts the universe of discourse based on changes in the photovoltaic output power deviation. Since the characteristics of the photovoltaic curve are inherently asymmetric on either side of the MPP, Reference [59] uses an asymmetric approach in designing the membership functions of the fuzzy controller to shorten search time. Reference [60] proposes a VWP interval fuzzy algorithm that establishes an optimization range to improve the algorithm’s steady-state performance and accuracy. Reference [61] categorizes the MPPT states of photovoltaic systems into four scenarios, designing specific fuzzy rules for each. Reference [62] fits maximum power point data under different environmental conditions, identifying the functional relationship between voltage, power, and temperature at the MPP, and designs a single-input single-output fuzzy controller with a fast tracking speed, though the accuracy and generality of the curve fitting pose issues.

In Reference [63], an intermediate variable is introduced, leading to a new three-input single-output fuzzy control algorithm that effectively addresses the challenges of rule quantity and applicability across various operating conditions, making it suitable for rapidly changing irradiance and low-irradiance environments.

Although these studies have made significant improvements in fuzzy control, many parameters are still adjusted based on the designer’s experience, making it difficult to coordinate multiple parameters and achieve optimal control. Furthermore, they cannot respond promptly to rapidly changing external environments.

Therefore, research on Fuzzy Logic Control is primarily focused on two directions: one is to optimize the parameters of other MPPT algorithms, and the other is to combine it with other intelligent algorithms to enhance control effectiveness. This will be further discussed in Section 5 of this paper.

4. MPPT Under Non-Uniform Solar Irradiance and Partial Shading Conditions

Land-based photovoltaic systems are affected by shading from clouds, trees, and pollutants, resulting in different irradiance levels received by various components of the photovoltaic array. In floating photovoltaic systems, the initial tilt angles of the photovoltaic modules vary due to their positions on the float and the impact of ocean waves, leading to differing and continuously changing irradiance levels across the modules.

Under non-uniform irradiance conditions, the P-V characteristic curve of the photovoltaic array becomes multi-peaked, making it difficult for the algorithms discussed in Section 2 to identify the global optimum, often causing them to fall into an LMPP. Therefore, global maximum power point tracking (GMPPT) under non-uniform irradiance is a critical area of MPPT algorithm research.

GMPPT can be implemented from both hardware and software perspectives. The software implementation can follow two approaches: one involves preprocessing sampled data to narrow the search range, followed by the application of MPPT algorithms designed for uniform irradiance; the other directly employs GMPPT algorithms with global search capabilities.

In 2014, Reference [64] provided a detailed discussion of algorithms in this area, though at the time, some algorithms were still underdeveloped, and no analysis of specific application environments was provided. Building on this, and considering the development of various algorithms in recent years, this paper offers a comprehensive evaluation and classification.

4.1. Hardware-Based GMPPT Control Method

Under PSCs, the structure of the photovoltaic array significantly impacts its output power. The basic series and parallel configurations have certain limitations [65,66]. Currently, as shown in Figure 15, common photovoltaic array structures include Series–Parallel (SP), Bridge-Link, Total-Cross-Tied (TCT), and Honey-Comb (HC) configurations.

References [67,68] studied the aforementioned structures and demonstrated that the TCT structure outperforms others in terms of average output power, loss, and stability under PSCs. Therefore, optimizing the TCT structure holds greater research value.

Reconfiguration methods can optimize photovoltaic array structures, enhancing the system’s immunity to PSCs and laying a foundation for improving photovoltaic system efficiency. Current photovoltaic array reconfiguration methods can be mainly divided into static reconfiguration, adaptive reconfiguration, and dynamic reconfiguration [69].

Static reconfiguration techniques involve changing the physical position of photovoltaic modules to effectively disperse local shading under typical local shading conditions. Several static reconfiguration techniques have been proposed, including the Sudoku method (SDK) [70,71], Optimal Sudoku method [72], Magic-Square method (MS) [73], Zig-Zag method [74], Square puzzle method [75], and Skyscraper method [76]. Additionally, Reference [77] proposed the Interleaving Row Cycle Static Reconfiguration technique, which reconstructs odd and even row arrays without changing the position of the modules in the column; Reference [78] proposed an Odd–Even Column (OEC) reconfiguration technique that improves average output power for asymmetric photovoltaic arrays.

These methods are not highly complex and perform well under typical local shading conditions. However, they face challenges such as complex wiring, making them difficult to apply to large-scale photovoltaic plants [79], and reduced effectiveness under dynamic shading conditions in actual systems.

Adaptive reconfiguration techniques use switch matrices to alter the electrical connections of adaptive parts of the photovoltaic array and connect them to a fixed part. Different software computing techniques [80,81] can be used to control the switch matrices for reconfiguration. Since only about 10% of the structure serves as the adaptive part, the requirements for sensors and control circuits are relatively low, but it is also challenging to achieve the optimal array configuration.

In dynamic reconfiguration techniques, each photovoltaic module is connected to a switch, and these switches are controlled by various algorithms, including heuristic algorithms [82], greedy algorithms [83], etc. Reference [84] proposed an SOPS-based reconfiguration algorithm for photovoltaic arrays in the TCT structure, which not only significantly improves the total output efficiency under PSCs but also keeps the global maximum power point near the open-circuit voltage, enabling traditional MPPT algorithms to complete the control. Dynamic reconfiguration methods effectively increase the array’s average output power and conversion efficiency but have high hardware requirements, are costly, and involve complex reconfiguration circuits.

In floating offshore systems, photovoltaic arrays rely on floating structures and face harsh external environments with high salinity and humidity, leading to higher hardware requirements. Therefore, selecting the most cost-effective hardware structure is crucial, making hardware reconfiguration techniques less suitable.

4.2. GMPPT Method Based on Sampled Data Preprocessing

The traditional MPPT control algorithms fail under PSCs as they get trapped in local extremum points. To overcome this limitation, the following three approaches are generally used to improve traditional algorithms: (1) a series of preprocessing methods based on scanning techniques; (2) system characteristic curve method; (3) segmental search method.

(1) The basic preprocessing technique is the I-V curve scanning method, which involves changing the reference voltage or duty cycle, measuring, and storing I-V data across the entire range to find the GMPP region. Although this method is straightforward in principle, it is too slow and unsuitable for rapidly changing external environments. Therefore, improvements to this technique are necessary to enhance search speed and efficiency. As early as 2008, a study [85] proposed moving the operating point with a suitable large interval on the P-V curve to locate the GMPP region. However, the choice of interval affects the probability of tracking GMPP and typically results in slower tracking speed. Another study [86] proved that the voltage difference between different peaks in a multi-peak curve is at least 0.8. To improve tracking speed, the window voltage search and maximum power trapezoidal method mentioned earlier can be used to skip some voltage ranges during the search [35,87]. Additionally, modifying the interval selection method has been explored; for example, Reference [88] used a ramp function to scan the photovoltaic array. Since the transient voltage of the array is negligible, this approach eliminates the need for sampling intervals and offers better tracking speed and dynamic performance. Reference [89] proposed an equal power curve scanning method, which avoids sampling and searching at non-MPP points, improving the algorithm’s tracking speed. However, its specific control performance can be influenced by the distribution of peak points, and the scanning method’s drawbacks are not entirely eliminated as continuous sampling and searching are still required. A fast Parabolic-Assumption algorithm is proposed in Reference [90], which utilizes a single current sensor and employs a fixed number of current scans equivalent to the number of series-connected PV modules. By leveraging a simplified parabolic equation, the algorithm enables the calculation of the GMPP with near-accuracy during PSCs.

It is worth noting that under fluctuating irradiance conditions, the scanning method may yield invalid sample data during the scanning process, leading to erroneous points or non-convergence. Furthermore, no research currently addresses this issue, making it unsuitable for application in floating photovoltaic systems.

(2) The system characteristic curve method locates the operating point near the GMPP using a predefined linear function related to various parameters of the photovoltaic array. Reference [91] used a virtual impedance characteristic disturbance (VICD) to initially locate the maximum power point, and a similar approach was taken in [92], which also proposed a calculation formula for cases of load variation. However, this method relies heavily on an accurate I-V curve of the photovoltaic array and may cause sudden changes in the reference voltage. Reference [93] introduced an improved global fractional characteristic curve technique, which accurately estimates the MPP voltage based on a precise diode model, but this method requires the inclusion of irradiance and temperature sensors. A common drawback of the system characteristic curve method is its heavy reliance on accurate photovoltaic cell parameters, making it prone to local optima due to high-model-accuracy requirements.

However, even with precise calculations, this method can only identify the globally optimal region at a specific instant. When environmental changes cause this optimal region to shift continuously, the algorithm must be repeatedly updated, resulting in power losses.

(3) The segmental search method includes techniques such as the dividing rectangle technique (DIRECT) [94], Fibonacci technique [95], and center point iteration technique. This method first determines the search range and then gradually narrows it down to finally pinpoint the exact location of the GMPP. However, this approach also carries the risk of selecting an incorrect range. References [96,97] proposed a new binary search method, which, by continuously bisecting the sampling points based on the current threshold range at each level of the I-V curve, effectively locates the GMPP region. This method can be extended to the preprocessing stage of any approach, with local optimization achieved using shrinkage and quantum-inspired algorithms.

4.3. Intelligent GMPPT Control Algorithm

4.3.1. Neural Network Algorithm

With the rise in artificial intelligence, some researchers have applied machine learning algorithms to the field of photovoltaic GMPPT. As early as 2008, there were studies that used neural network algorithm incorporating weather forecasting to predict the power generation of photovoltaic arrays [98]. A review in Reference [99] summarized various machine learning algorithms and conducted a comparative analysis of their control performance under different weather conditions.

With the continuous development of artificial neural networks (ANNs) and deep reinforcement learning (RL), traditional machine learning algorithms are gradually being replaced. These methods are data-driven and can achieve effective control when supported by sufficient data. Its block diagram is shown in Figure 16.

Reference [100] proposed a variable step-size MPPT technique based on ANN and compared its control effectiveness with ANN-based P&O and ANN-based INC algorithms. Reference [101] employed deep reinforcement learning (DRL), using a deep Q-network to handle discrete action spaces and the deep deterministic policy gradient algorithm to gather peak information, making it suitable for continuous state spaces. Reference [102] proposed an MPPT control algorithm based on an adaptive RBF neural network that can directly predict the maximum power point voltage based on external environmental changes; however, it requires the addition of irradiance and temperature sensors, which increases costs. Reference [103] introduced an adaptive neural network (DANC) MPPT algorithm, using the DANC online learning algorithm as the core of the PV system controller to achieve MPPT control in dynamic environments. Reference [104] further incorporated a feedback load voltage scanning method to handle partial shading conditions, but it could not avoid voltage and power fluctuations.

The challenge with neural network algorithms is that they require a large and reasonably accurate dataset as a training set, which is difficult to obtain in photovoltaic systems. Moreover, the training process lacks theoretical support, especially when adapting to external environmental changes, making the training process challenging and time-consuming.

Reference [105] proposed a Bayesian optimization (BO) convolutional neural network (CNN) algorithm that uses an image sensor instead of traditional voltage and current sensors to quickly predict the maximum power point voltage under rapidly changing random shading conditions. However, the prediction accuracy of this algorithm in practical applications still depends on the precision of the image sensor and the data conversion time.

Artificial intelligence algorithms undoubtedly represent one of the most promising future directions. However, for neural network algorithms specifically, there are notable challenges at this stage. When datasets are generated through simulations of PV arrays under varying environmental conditions, extensive information on both the array structure and PV module technology specifications is essential. Additionally, gathering actual PV curves for arrays under a wide range of real-world conditions can be highly time-consuming. If shading patterns cannot be comprehensively represented during training, there is no guarantee that the system will effectively respond to every possible shading scenario. The complexity of training and uncertainty in control performance currently limit the practical engineering applicability of these algorithms.

4.3.2. Swarm Intelligence Optimization Algorithms

Heuristic algorithms are inspired by bionics principles, abstracting natural phenomena and behaviors of animals into algorithms to solve corresponding problems. These mainly include swarm intelligence optimization algorithms (SIOAs) and evolutionary algorithms. Heuristic algorithms have excellent global search capabilities and can be widely applied to MPPT control under partial shading conditions.

Swarm intelligence optimization algorithms are a type of probabilistic search algorithm, including a particle swarm optimization (PSO) [106], cuckoo search (CS), ant colony optimization (ACO), butterfly optimization algorithm (BOA), snake optimizer algorithm [107], and Grey Wolf Optimization (GWO) [63], among others.

These swarm intelligence algorithms have significant similarities in structure and computation methods, with the primary differences lying in their update rules. Some algorithms update based on simulating the movement step length of social animals (such as PSO, GWO, etc.), while others set update rules based on certain algorithm mechanisms (such as ACO). Currently, there is no consensus on which algorithm is most suitable for photovoltaic MPPT control.

Various improvements have been made to different algorithms for the photovoltaic MPPT problem, and these algorithms can learn from each other. Taking the PSO algorithm as an example, the traditional PSO algorithm has a slow tracking speed and performs random searches during transients, leading to continuous fluctuations across the global range, resulting in significant power losses. Its block diagram is shown in Figure 17. To address this issue, PSO parameters can be adaptively adjusted to enhance its performance.

Reference [108] set two adaptive parameters to control particle velocity and search space, achieving tracking with minimal voltage and power fluctuations, making it suitable for large photovoltaic arrays. Reference [109] adaptively adjusted both the particle velocity and duty cycle step size while automatically sorting the particles, reducing the fluctuation of the duty cycle. Another major drawback of the PSO algorithm is that it is prone to getting stuck at a local maximum power point under continuously changing environmental conditions, so the initial position and movement range of particles need to be constrained. Various algorithms introduced in Section 3.2 of this paper can assist in determining the initial particle positions. Reference [110] designed two voltage boundaries that change with the external environment based on the estimation of the convex region on the P-V curve, enabling adaptation to changing external environments.

The main limitation of swarm intelligence optimization algorithms is not their tracking speed but rather their inherent requirement for stable environmental conditions to accurately track the global maximum power point (GMPP). None of the improvements mentioned above address this fundamental limitation. As a result, under fluctuating irradiance conditions, these algorithms require frequent restarts. The repeated restarts, along with the time-consuming search process following each restart, can result in energy loss and power surges, making them unsuitable for floating photovoltaic systems. However, when used in combination with other algorithms, either as an initial method for approximating the global maximum power region or as a parameter optimization tool, they can deliver effective results.

4.3.3. Evolutionary Algorithms

In the field of evolutionary algorithms, the most commonly used in MPPT are genetic algorithms (GAs) and differential evolution (DE).

The core of genetic algorithms lies in an iterative process. It begins with creating an initial population, followed by calculating the fitness of each individual. Next, selection, recombination, and mutation operators are applied to generate a new population. This process is repeated iteratively, with the fitness of each individual recalculated at each iteration. This process is repeated continuously to obtain the optimal fitness solution. Reference [111] developed an MPPT technique based on a real-time genetic algorithm, which performs well in tracking speed, steady-state accuracy, and convergence. However, it requires continuous measurement of open-circuit voltage and short-circuit current, as well as additional sensors and a pilot PV module, leading to higher hardware costs.

Compared to swarm intelligence algorithms, genetic algorithms have a discrete nature, with a minimum interval between feasible solutions. The size of this interval is determined by the range of optimization variables and the chromosome encoding length. Therefore, the chromosome encoding length must be carefully selected; otherwise, the algorithm may fail to track the global maximum power point (GMPP).

Differential evolution (DE) is a global optimization algorithm proposed in 1995, suitable for solving nonlinear problems with many local optima and randomness, making it applicable to MPPT problems. DE uses target vectors as the population, iterating through mutation, crossover, and selection steps, with each iteration’s solution corresponding to the photovoltaic output power.

Reference [112] improved the traditional DE based on the SEPIC converter by designing mutation rules for individuals in the population and adaptively calculating load changes, thereby improving the system’s tracking speed and load change adaptability. However, it is difficult to adapt to changes in irradiance. Reference [113] proposed the DE/rand-best/1 strategy during the iteration process, ensuring that the algorithm has strong global search capability in the early stages of evolution and avoids getting trapped in local optima in the later stages. They also introduced population individual sorting to reduce voltage fluctuations.

Reference [114] combines DE with the Jaya algorithm, where Jaya pushes all results away from the worst values, and DE pulls Jaya’s output toward the global optimum. Meanwhile, a mutation operator closely monitors this movement. This JayaDE algorithm creates a dual push-and-pull mechanism that accelerates convergence and enhances rapid decision making, enabling tracking under various environmental conditions. Although its simulation results show relative improvement, it remains far from sufficient.

Evolutionary algorithms often face challenges similar to those in swarm intelligence optimization algorithms, where they risk getting trapped in local optima. While many of the studies referenced claim improved dynamic performance, few provide simulation or experimental validation. In cases of sudden irradiance changes, certain algorithms require response times of over 0.5 s to locate a new maximum power point, which is a delay that is nearly impractical for floating photovoltaic systems.

5. Hybrid MPPT

The algorithms discussed above often exhibit suboptimal control performance in certain aspects. As a result, many studies have combined multiple algorithms to leverage their strengths and improve overall system control effectiveness.

Currently, two main approaches are used to integrate different algorithms:

Parameter-Improved Control Algorithms: Intelligent algorithms are employed to dynamically calculate and adjust the parameters of the original algorithms.

Multi-Mode Control Algorithms: A multilayer control model is established, with different layers dedicated to handling global search and local optimization.

5.1. Parameter-Improved Control Algorithms

Fuzzy Logic Control (FLC) does not necessitate an accurate mathematical model of the controlled system, making it particularly well suited for optimizing the parameters of various algorithms. In [115], FLC is employed for the adaptive step-size selection in the P&O method. Unlike traditional variable step-size techniques, FLC allows the step size to potentially reduce to zero, which can entirely eliminate oscillations near the maximum power point (MPP). Similarly, in [63], FLC is integrated with the Grey Wolf Optimization (GWO) algorithm, achieving a comparable effect in mitigating oscillations as observed in [115].

In [116], a genetic algorithm is utilized to optimize the number of neurons in a Multilayer Perceptron (MLP) neural network, which is subsequently applied to MPPT. However, this approach necessitates a substantial amount of training data. In the absence of adequate data, the model is prone to overfitting, wherein the neural network learns excessive details of the training samples but fails to generalize the underlying patterns, leading to information loss. Consequently, this limitation poses challenges for practical engineering applications.

5.2. Multi-Mode Control Algorithms

Swarm intelligence algorithms, known for their robust global search capabilities, are often integrated with traditional algorithms. In [117], particle swarm optimization (PSO) is combined with the P&O method. PSO is employed for global search, and once the duty cycle is confined within a narrower range, the P&O algorithm is utilized to find the optimal solution. However, this study does not address the dynamic performance of the method, and the inherent drawbacks of PSO appear to remain unmitigated during its operation. In [118], the Adaptive Cuckoo Search (ACS) algorithm is combined with P&O, where ACS handles global exploration and P&O is responsible for local optimization, demonstrating favorable performance under dynamic shading conditions.

In [119], the ant colony optimization (ACO) algorithm is integrated with FLC, employing an intelligent logic selection mechanism to adapt to varying external environments. ACO manages global search while FLC focuses on local optimization; however, the dynamic performance of this method has not been validated.

The study in [120] combines the Perturb and Observe method with PSO, but unlike other hybrid approaches, this method introduces a Search–Skip–Judge (SSJ) mechanism to ensure that regions are not redundantly searched, thereby enhancing the performance of the PSO algorithm. This approach shows strong tracking capabilities in complex partial shading conditions but is fundamentally incompatible with scenarios involving continuously varying irradiance, rendering it unsuitable for use in floating photovoltaic systems.

In [121], the Adaptive Bio-inspired Salp Swarm Algorithm (ASSA) is combined with P&O, where ASSA identifies the maximum power region, and variable step-size P&O is employed for tracking within this region. Upon irradiance changes, ASSA is re-applied for global search. However, to reduce power fluctuations during system operation, the historical results of previous global searches are retained, which constrains the updated global search space. This limitation adversely affects tracking performance under conditions of high-frequency and large-amplitude irradiance fluctuations.

6. Current Developments and Future Trends

This paper reviews the majority of existing terrestrial photovoltaic (PV) MPPT algorithms and summarizes the advancements in these algorithms for offshore environments. Current references lack specific MPPT control strategies tailored to floating PV systems; although some algorithms exhibit relative adaptability to such conditions, further simulation and experimental validation are required:

The P&O method, currently the most widely implemented in engineering applications, cannot be directly applied offshore. However, when combined with improvements targeting misjudgment issues and preprocessing techniques based on sampled data, this algorithm demonstrates high adaptability to floating PV systems and presents potential for further engineering development.
The harsh offshore environment, characterized by high salinity and humidity, significantly impacts PV system hardware. Present methods for PV array hardware reconfiguration are unsuitable for offshore scenarios. Moreover, prolonged exposure to such conditions may alter the intrinsic characteristics of PV cells, raising concerns about the feasibility and efficiency of algorithms based on PV cell models.
Intelligent algorithms hold considerable promise, with some existing approaches effectively achieving MPPT control in floating PV systems. However, neural network algorithms present significant training challenges, while heuristic algorithms involve complex computations. The question of which heuristic algorithm is optimal remains unresolved, necessitating further research and exploration.
Hybrid algorithms, which integrate the strengths of various approaches, can effectively enhance overall system control and represent the current mainstream and trend in MPPT algorithm research for floating PV systems.

Additionally, the evaluation methods for existing MPPT algorithms predominantly involve step response tests, EN50530 Dynamic Testing, and Daily Testing. However, in the context of floating PV systems, where irradiance fluctuates in high-frequency, near-sinusoidal patterns due to wave and wind influences, these conditions differ from current testing scenarios, indicating the need for further development and research.

7. Conclusions

Solar energy is among the most viable renewable energy sources, with its output power being contingent upon solar irradiation. Consequently, achieving maximum power extraction in floating photovoltaic systems presents the challenge of continuously varying irradiation. While numerous studies have proposed MPPT algorithms to enhance the efficiency of photovoltaic systems, few have addressed the impact of continuous changes in irradiation. This review examines the applicability of various MPPT algorithms in floating photovoltaic systems from two perspectives: uniform irradiation and partial shading conditions. Under uniform irradiance conditions, the self-optimizing algorithm stands out as the most widely used traditional MPPT technology, demonstrating unparalleled advantages. In response to drift phenomena induced by changes in irradiance, the three improvements summarized in this paper can significantly enhance tracking accuracy, making this algorithm the preferred choice for engineering applications. In non-uniform irradiance conditions, both the GMPPT technology based on sampling data and intelligent MPPT technology possess distinct strengths and weaknesses. These technologies can be integrated into a hybrid algorithm to capitalize on their advantages while mitigating their limitations, thereby improving overall algorithm performance. Several existing methods that demonstrate effective control in floating photovoltaic systems are highlighted in this review. Finally, this paper summarizes the research progress and outlines future development directions for MPPT technology in floating photovoltaic systems. The overarching aim of this research is to provide valuable insights for optimizing photovoltaic MPPT algorithms under offshore floating conditions.

Funding

This research was funded by the Key research and development project of Energy China, grant number CEEC2022-ZDYF-04.

Conflicts of Interest

Authors Shaoyong Wang and Yingrui Dong were employed by the company China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Photovoltaic power generation development.

Figure 2. Offshore floating photovoltaic systems.

Figure 3. Basic structure of MPPT algorithm with boost converter.

Figure 4. Single-diode equivalent circuit of PV cell.

Figure 5. PV module characteristics under different irradiances and constant temperature (25 °C): (left) power–voltage curve and (right) current–voltage curve.

Figure 6. PV module characteristics under partial shading conditions: (left) power–voltage curve and (right) current–voltage curve.

Figure 7. Slope of wave surface under different wave models. (left) Airy wave and (right) Stokes wave.

Figure 8. Irradiance under different wave models. (left) Airy wave and (right) Stokes wave.

Figure 9. Output characteristics of photovoltaic model under influence of sea waves. (left) V-t curve, (middle) I-V-t diagram, and (right) P-V-t diagram.

Figure 10. MPPT control structure: (left) direct control, (right) indirect control.

Figure 11. Flowchart of P&O algorithm.

Figure 12. The drift phenomena under continuously changing irradiance conditions.

Figure 13. Flowchart of INC algorithm.

Figure 14. Block diagram of FLC MPPT technique.

Figure 15. Photovoltaic array structural diagram: (left) SP, (middle) BL, (right) TCT.

Figure 16. Block diagram of ANN MPPT technique.

Figure 17. Block diagram of PSO algorithms.

Table 1. Irradiance calculation Parameters.

Name of Parameter	Quantitative Value	Name of Parameter	Quantitative Value
declination angle $δ$ (°)	0	the Earth’s orbital eccentricity correction factor $ξ_{0}$	1
latitude angle $φ$ (°)	0	the solar constant $S_{0}$ (W/m²)	1367
hour angle $ω$ (°)	36	the atmospheric transmittance coefficient $P$	0.7
solar azimuth angle $α$ (°)	0	the ocean reflectance $ρ$	0.35

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Huang, L.; Pan, B.; Wang, S.; Dong, Y.; Mou, Z. Review on Maximum Power Point Tracking Control Strategy Algorithms for Offshore Floating Photovoltaic Systems. J. Mar. Sci. Eng. 2024, 12, 2121. https://doi.org/10.3390/jmse12122121

AMA Style

Huang L, Pan B, Wang S, Dong Y, Mou Z. Review on Maximum Power Point Tracking Control Strategy Algorithms for Offshore Floating Photovoltaic Systems. Journal of Marine Science and Engineering. 2024; 12(12):2121. https://doi.org/10.3390/jmse12122121

Chicago/Turabian Style

Huang, Lei, Baoyi Pan, Shaoyong Wang, Yingrui Dong, and Zihao Mou. 2024. "Review on Maximum Power Point Tracking Control Strategy Algorithms for Offshore Floating Photovoltaic Systems" Journal of Marine Science and Engineering 12, no. 12: 2121. https://doi.org/10.3390/jmse12122121

APA Style

Huang, L., Pan, B., Wang, S., Dong, Y., & Mou, Z. (2024). Review on Maximum Power Point Tracking Control Strategy Algorithms for Offshore Floating Photovoltaic Systems. Journal of Marine Science and Engineering, 12(12), 2121. https://doi.org/10.3390/jmse12122121

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Review on Maximum Power Point Tracking Control Strategy Algorithms for Offshore Floating Photovoltaic Systems

Abstract

1. Introduction

2. Characteristics of Photovoltaic Arrays in Offshore Floating Scenarios

3. MPPT Under Uniform Solar Irradiance

3.1. MPPT Algorithms Based on Photovoltaic Cell Models

3.1.1. Constant Voltage (CV)

3.1.2. Sliding Mode Control (SMC)

3.1.3. Conclusions

3.2. Traditional Self-Optimization MPPT Algorithm

3.2.1. Perturb and Observe (P&O)

3.2.2. Incremental Conductance (INC)

3.3. Fuzzy Logic Control (FLC)

4. MPPT Under Non-Uniform Solar Irradiance and Partial Shading Conditions

4.1. Hardware-Based GMPPT Control Method

4.2. GMPPT Method Based on Sampled Data Preprocessing

4.3. Intelligent GMPPT Control Algorithm

4.3.1. Neural Network Algorithm

4.3.2. Swarm Intelligence Optimization Algorithms

4.3.3. Evolutionary Algorithms

5. Hybrid MPPT

5.1. Parameter-Improved Control Algorithms

5.2. Multi-Mode Control Algorithms

6. Current Developments and Future Trends

7. Conclusions

Funding

Conflicts of Interest

References

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