MPPT Design of Photovoltaic Power Generation System Based on Improved Fibonacci Linear Search Algorithm

Abstract

At present, photovoltaic power generation is becoming increasingly popular, and one of its major drawbacks is the low photoelectric conversion efficiency of photovoltaic cells. In order to improve power generation efficiency, an equivalent circuit model of photovoltaic cells and a simulation structure of photovoltaic power generation systems have been established. The working principle and MPPT (Maximum Power Point Tracking) control process of the improved Fibonacci linear search algorithm have been analyzed to achieve the goal of improving power generation efficiency. The improved Fibonacci linear search algorithm is applied in the MPPT technology of photovoltaic power generation system, and simulation experiments are conducted. Through analysis and simulation, MPPT can quickly track the maximum power point when the external lighting conditions change and has good tracking effect.

1. Introduction

One of the main disadvantages of PV (photovoltaic) power generation systems is the low photoelectric conversion efficiency of PV cells. Typically, the conversion efficiency of polycrystalline silicon cells ranges from 12% to 14%, while that of monocrystalline silicon cells ranges from 14% to 18%. Considering inverter efficiency, the overall efficiency of PV systems is only slightly above 10% [1]. To improve solar energy utilization, methods include enhancing the conversion efficiency of PV arrays or modifying the structure and control strategies of inverters to ensure the PV array operates near the maximum power point, known as Maximum Power Point Tracking (MPPT).

PV arrays are power-unstable devices with complex nonlinear output characteristics, influenced by external environmental conditions such as solar irradiance, temperature, and load. Therefore, ensuring the PV array operates at the maximum power point is crucial for improving photoelectric conversion efficiency [2]. This paper provides a detailed introduction to the basic principles and main algorithms of MPPT in PV power generation systems.

The traditional MPPT methods for photovoltaic power generation systems mainly include the constant voltage tracking method, conductance increment method, and interference observation method (also known as the hill climbing method). These methods have certain effects under different lighting intensities and temperature conditions, but there are also some limitations [3].

For example, the limitations of the constant voltage tracking method are prominent. In total, 76% of the open circuit voltage is selected as the fixed voltage, and the photovoltaic panel is operated at this voltage to approximate the maximum power tracking. When the temperature is the same under different light intensities, the maximum power point of the solar panel almost falls on both sides of the same vertical line, which may make it difficult to accurately track the maximum power line at specific temperature moments.

The advantage of the incremental conductance method is that the direction of the reference voltage change at the next moment depends entirely on the instantaneous impedance and the magnitude of the impedance change at that moment and is independent of the operating point voltage and power at the previous moment, so there will be no misjudgment in the disturbance observation method. Therefore, it can adapt to rapid changes in light intensity, with small voltage fluctuations and high control accuracy. The disadvantage is that it is susceptible to interference from clutter signals and can cause significant misoperation [4]. In practical operation, usually very small values of dI and dU are taken, which requires high precision in the collection of parameters such as the output voltage and output current of photovoltaic devices. The accuracy of sensors is also required to be high, and the calculation process is relatively complex. It must be adjusted gradually to approach the maximum power point and cannot be quickly adjusted to the maximum power point.

Although the perturbation observation method has the advantages of simple logic and easy implementation, it may make errors in the case of changes in light intensity. When the illumination rapidly decreases, the output power of the photovoltaic module will also change due to the characteristics presented by the P-V curve of the photovoltaic module, which may affect the judgment of the disturbance direction [5].The comparison of the performance of various MPPT algorithms is shown in

Table 1. Performance comparison of MPPT algorithm for photovoltaic power generation system.

Algorithm Type	Tracking Accuracy	Response Speed	Complexity	Hardware Cost	Anti- Interference	Applicable Scenarios
Improved Fibonacci	±0.8%	110 ms	middle	middle	excellent	Local shadow/rapid change irradiation
Disturbance observation method (P&O)	±2.5%	200 ms	low	low	middle	Stable lighting conditions
Incremental conductance method (INC)	±1.2%	150 ms	high	middle	good	Uniform irradiation environment
Neural network control	±0.5%	80 ms	extremely high	high	excellent	Complex and ever-changing environment
Fuzzy logic control	±1.5%	180 ms	rising– falling	rising– falling	good	Nonlinear system
Particle swarm optimization (PSO)	±0.7%	300 ms	high	high	middle	Multi peak curve scene

.

Overall, various MPPT methods have their advantages and disadvantages, and the choice of method depends on specific application scenarios and environmental conditions. This article introduces an improved Fibonacci search algorithm that can accurately and quickly track the maximum power of photovoltaic arrays under different tracking strategies for uniform lighting and shadow conditions and is applicable to photovoltaic arrays of any topology.

2. Principle of Maximum Power Point Tracking Control Technology for Photovoltaic Power Generation System

In photovoltaic power generation systems, the voltage values at both ends of photovoltaic cells are not fixed when outputting maximum power under different light intensities. Moreover, when the operating temperature changes, the voltage values will also change for the same maximum power under the same light intensity. The output of a photovoltaic cell is closely related to the intensity of light and the temperature of the environment. In order to ensure that the photovoltaic cell can have maximum power output at any light intensity and temperature, that is, the photovoltaic cell always operates at the maximum power point, the first step is to determine the position of the maximum power point on the photovoltaic cell’s volt ampere characteristic curve [6].

Figure 1 shows the current (power)–voltage relationship curve of a photovoltaic cell, which represents the relationship between the output current I (power P) and voltage U of the cell under specific light intensity and temperature. From the previous analysis of the output characteristics of photovoltaic cells, it can be seen that both curve 1 and curve 2 indicate the characteristics of the cells and have obvious nonlinear features. Curve 2 is similar to a parabola; that is, when the photovoltaic cell outputs the maximum power Pm (I_mU_m), the maximum power point voltage (maximum operating voltage) Um is less than the open circuit voltage U_OC, and the current (maximum operating current) I_m at the maximum power point is less than the short-circuit current I_SC. When the battery voltage varies between 0 and U_m, the power curve is an increasing function, and when the battery voltage is between U_m and U_OC, the power curve is a decreasing function. The output power of photovoltaic cells mainly depends on the intensity of light and their operating temperature. According to the I-U and P-U characteristic curves of photovoltaic cells at different temperatures, as the operating temperature increases, the short-circuit current I_SC slightly increases, the open circuit voltage U_OC and the maximum power point voltage U_m decrease, and the maximum output power Pm of the photovoltaic cell decreases. According to the I-U and P-U characteristic curves under different light intensities, it can be concluded that the I_SC value of the same battery is directly proportional to the light intensity; the maximum output power P_m also increases with the increase in light intensity [7].

In order to achieve the maximum energy output of photovoltaic arrays under current illumination under any external conditions, the maximum power point tracking problem of photovoltaic arrays is proposed [8]. With the increasing popularity of photovoltaic power generation systems, the high cost and low conversion efficiency of photovoltaic power generation systems make the research on maximum power point tracking technology increasingly important. The maximum power point tracking (MPPT) control strategy is to detect the output power of the photovoltaic array in real time, use a certain control algorithm to predict the possible maximum power output of the photovoltaic array under the current working conditions, and meet the requirements of maximum power output by changing the current impedance situation. In this way, even if the junction temperature of the photovoltaic cell increases and the output power of the array decreases, the system can still operate at its optimal state under the current operating conditions [9]. Due to the nonlinear output characteristics of photovoltaic cells, mathematical analysis is not easy. Simple linear circuits can be used to study the basic principles of maximum power point tracking.

According to the impedance matching principle in circuit theory, in a linear circuit, when the equivalent resistance of the external load is equal to the internal resistance of the power supply, the external load can obtain the maximum output power. That is to say, when the load resistance is equal to the internal resistance of the power supply, the power supply has the maximum power output. Although photovoltaic cells and power electronic converters are both nonlinear, they can be considered linear circuits in the short term [10]. The photovoltaic cell is modeled as a DC power source and the power electronic converter as an external resistive load, the equivalent resistance of the power electronic converter is adjusted to always follow the internal resistance changes in the photovoltaic cell in different external environments, and the two loads are dynamically matched to obtain the maximum output power on the output side of the power electronic converter, achieving MPPT of the photovoltaic cell [11].

3. Modeling of Photovoltaic Power Generation System

3.1. Equivalent Circuit Model of PV Cells

The PV cell can be described using the equivalent circuit model shown in Figure 2. When connected to a load R, the generated photocurrent I_L flows through the load, producing terminal voltage U [12].

From the equivalent circuit model in Figure 1, the output characteristic equation is as follows:

$${\mathrm{I}=\mathrm{I}}_{\mathrm{L}}-{\mathrm{I}}_0\left\{\exp \left[{\displaystyle \frac{\mathrm{q}\left(\mathrm{U}+{\mathrm{r}}_{\mathrm{S}}\mathrm{I}\right)}{\mathrm{n}\mathrm{k}\mathrm{T}}}\right]-1\right\}-{\displaystyle \frac{\mathrm{U}+{\mathrm{r}}_{\mathrm{S}}\mathrm{I}}{{\mathrm{r}}_{\mathrm{s}\mathrm{h}}}}$$

(1)

where i is the output current of the PV cell; r_s is the internal equivalent series resistance; I_L is the photocurrent source current; n is the diode ideality factor; I_o is the reverse saturation current of the diode; k is the Boltzmann constant; q is the electron charge; T is the operating temperature of the PV cell; U is the output voltage of the PV cell; and r_gh is the internal equivalent parallel impedance.

3.2. Simulation Structure of PV Power Generation System

The MPPT structure of the PV power generation system consists of PV cells, a boost converter, an MPPT controller, and a PWM (Pulse Width Modulation) drive circuit, as shown in Figure 3. The MPPT controller adjusts the switching state of the IGBT (insulated gate bipolar transistor) in the Boost circuit by receiving the output current I and voltage U of the PV cell to generate PWM drive pulses [13].

4. Improved Fibonacci Linear Search Algorithm

4.1. Basic Principles of the Fibonacci Search Method

An integer sequence {F_k}(k = 0, 1, …) satisfying the following conditions is called a Fibonacci sequence:

$$\left\{\begin{array}{l}{\mathrm{F}}_{\mathrm{K}+2}={\mathrm{F}}_{\mathrm{K}}+{\mathrm{F}}_{\mathrm{K}+1},\mathrm{K}\ge 0\\ {\mathrm{F}}_0={\mathrm{F}}_1=1\end{array}\right.$$

(2)

Assume f(x) has only one minimum point in the closed interval [a₀, b₀]. The Fibonacci search method for finding the optimal value of a single-variable unimodal function involves the following steps: first, select two test points x₁ and x₂ and within the initial interval [a₀,b₀], calculate f(x₁) and f(x₂), compare their values, narrow the search range, and repeat the process iteratively until the search interval is smaller than a predefined threshold [14].

During the first iteration, the test points $x_1^1$ and $x_2^1$ are selected within the interval [a₀, b₀] as follows:

$$x_1^1=a_0+{\displaystyle \frac{F_{n-2}}{F_n}}\left(b_0-a_0\right)=b_0+{\displaystyle \frac{F_{n-1}}{F_n}}\left(a_0-b_0\right)$$

(3)

$${\mathrm{x}}_2^1={\mathrm{a}}_0+{\displaystyle \frac{{\mathrm{F}}_{\mathrm{n}-1}}{{\mathrm{F}}_{\mathrm{n}}}}\left({\mathrm{b}}_0-{\mathrm{a}}_0\right)={\mathrm{b}}_0+{\displaystyle \frac{{\mathrm{F}}_{\mathrm{n}-2}}{{\mathrm{F}}_{\mathrm{n}}}}\left({\mathrm{a}}_0-{\mathrm{b}}_0\right)$$

(4)

where the definition of parameter n is the number of iterations, the length of the interval $\lfloor {\mathrm{x}}_1^1,{\mathrm{b}}_0\rfloor$ equals that of $\lfloor {\mathrm{a}}_0,{\mathrm{x}}_1^1\rfloor$, and ${\mathrm{x}}_1^1+{\mathrm{x}}_2^1=\mathrm{a}+\mathrm{b}$. By comparing f(x₁) and f(x₂), the search interval is reduced iteratively until the relative precision is met [15].

If $\mathrm{f}\left({\mathrm{x}}_1^1\right)\le \mathrm{f}\left({\mathrm{x}}_2^1\right)$, then eliminate the interval $\lfloor {\mathrm{x}}_2^1,{\mathrm{b}}_0\rfloor$ and select the second trial points ${\mathrm{x}}_1^2$ and ${\mathrm{x}}_2^2$ within the remaining interval $\lfloor {\mathrm{a}}_0,{\mathrm{x}}_2^1\rfloor$, as shown in Figure 4. At this point ${\mathrm{a}}_1={\mathrm{a}}_0$, ${\mathrm{b}}_1={\mathrm{x}}_2^1$, and ${\mathrm{x}}_2^2={\mathrm{x}}_1^1$, and the formula for selecting the second trial point is

$${\mathrm{x}}_1^2={\mathrm{b}}_1+{\displaystyle \frac{{\mathrm{F}}_{\mathrm{n}-2}}{{\mathrm{F}}_{\mathrm{n}-1}}}\left({\mathrm{a}}_1-{\mathrm{b}}_1\right)$$

(5)

$${\mathrm{x}}_2^2={\mathrm{a}}_1+{\displaystyle \frac{{\mathrm{F}}_{\mathrm{n}-2}}{{\mathrm{F}}_{\mathrm{n}-1}}}\left({\mathrm{b}}_1-{\mathrm{a}}_1\right)$$

(6)

From the equation above ${\mathrm{x}}_1^2={\mathrm{a}}_1+{\mathrm{b}}_1-{\mathrm{x}}_2^2$, and if $\mathrm{f}\left({\mathrm{x}}_1^1\right)>\mathrm{f}\left({\mathrm{x}}_2^1\right)$, the interval $\lfloor {\mathrm{a}}_0,{\mathrm{x}}_1^1\rfloor$ is eliminated. The remaining interval $\lfloor {\mathrm{x}}_1^1,{\mathrm{b}}_0\rfloor$ is then searched by selecting new trial points ${\mathrm{x}}_1^2$ and ${\mathrm{x}}_2^2$ (see Figure 4b), where ${\mathrm{a}}_1={\mathrm{x}}_1^1$, ${\mathrm{b}}_1={\mathrm{b}}_0$, and ${\mathrm{x}}_1^2={\mathrm{x}}_2^1$ (or an equivalent update rule) [16]. The same principle applies in further steps, ${\mathrm{x}}_2^2={\mathrm{a}}_1+{\mathrm{b}}_1-{\mathrm{x}}_1^2$.

After multiple iterations following the aforementioned rules, the search range gradually converges toward the optimal value of the function. At this point, the optimal value needs to be determined based on the relative precision δ of the interval reduction [17]. A relative precision threshold δ is defined, and its selection principle is as follows: Assuming the final search interval is [a_n−1, b_n−1], the condition (b_n−1 − a_n−1) ≤ δ(b₀ − a₀) must be satisfied. Once the required relative precision δ is achieved, the search can terminate. A smaller δ improves the accuracy of the optimal value but slows down convergence. By iteratively computing function values, the search interval can be narrowed down to meet the desired relative precision. When the number of function evaluations reaches F_n ≥ 1/δ, the optimal value of the function f(x) is obtained [18].

When the Fibonacci search algorithm is applied for maximum power point tracking (MPPT) in photovoltaic (PV) arrays, the output voltage of the PV array can be represented as the independent variable x, while the output power is expressed as f(x). By leveraging the P-U characteristic curve of the PV array, the maximum output power can be tracked and achieved in real time by adjusting the output voltage. In the traditional Fibonacci search method, the relative precision δ determines the optimal value by constraining the range of the independent variable. However, from the perspective of the optimal value itself, it is not precisely quantified [19]. The ultimate goal of MPPT is to locate the maximum output power of the PV array. If the traditional Fibonacci search method is used for PV array MPPT, a significant issue arises near the maximum power point: the output voltage exhibits a high sensitivity to power variations. As a result, the tracked maximum power may deviate from the true value, leading to inaccuracies.

To address the aforementioned issues, the concept of absolute precision ε can be introduced, and the iteration termination condition can be modified as follows: Iteration stops when both conditions (b_n−1 − a_n−1) ≤ δ(b₀ − a₀) and $\mathrm{f}\left({\mathrm{x}}_2^{\mathrm{n}-1}\right)-\mathrm{f}\left({\mathrm{x}}_1^{\mathrm{n}-1}\right)\le \mathrm{\epsilon }$ are satisfied, thereby obtaining the maximum power point (MPP) voltage and the maximum output power of the array. By adding the supplementary condition $\mathrm{f}\left({\mathrm{x}}_2^{\mathrm{n}-1}\right)-\mathrm{f}\left({\mathrm{x}}_1^{\mathrm{n}-1}\right)\le \mathrm{\epsilon }$, the function f(x) is constrained in its value range. This enhancement not only increases the output power of the PV array but also makes the improved search method more precise than traditional approaches, effectively reducing errors [20].

Meanwhile, the use of high-precision measurement systems further ensures the accuracy of the results. The accuracy and sampling rate of different sensors are shown in

Table 2. Key sensors.

Sensor Type	Accuracy	Sampling Rate
Voltage measurement	±0.1% FS(full span)	100 kHz
Current measurement	±0.2% FS	100 kHz
Temperature sensor	±0.5 °C	10 kHz

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When using the traditional Fibonacci search algorithm for MPPT in photovoltaic power generation systems, there is a problem of computational complexity. The quantitative analysis of the computational complexity comparison of the improved Fibonacci search algorithm in photovoltaic MPPT is as follows:

(1) The complexity of the traditional Fibonacci algorithm.

① Time complexity: $\mathrm{O}\left({\displaystyle \frac{1}{\mathsf{\delta }}}\right)$, where δ is the relative accuracy.

② Under typical parameters, the following applies:

Each iteration requires two power calculations (f(x₁), f(x₂));

The number of iterations required for convergence is ${\mathrm{N}}_{\mathrm{tradition}}\approx 1.44\ln \left({\displaystyle \frac{{\mathrm{b}}_0-{\mathrm{a}}_0}{\mathsf{\delta }}}\right)$.

For example, when the initial interval is [0, 50 V] and δ = 0.01 V, approximately 24 iterations are required.

(2) Improved algorithm optimization.

① Dynamic accuracy adjustment: δ k = max (0.02, 0.1e − αt).

② The complexity is reduced to $\mathrm{O}\left({\displaystyle \frac{1}{{\mathsf{\delta }}_{\mathrm{eff}}}}\right)\left({\mathsf{\delta }}_{\mathrm{eff}}=0.05\right)$.

③ The number of iterations decreased by 38% (measured from 24 to 15 times).

The performance quantification comparison of different indicators is shown in

Table 3. Performance quantitative comparison.

Index	Traditional Algorithm	Improvement Algorithm	Increase Amplitude
Average number of iterations	24	15	37.5%
Function evaluation times	48	22	54.2%
Convergence time	8.6 ms	3.2 ms	62.8%

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4.2. MPPT Control Flow

It is assumed that the structure of the PV Array is m × n, there are m groups of series-connected PV arrays with n PV arrays in each group, and the open circuit voltage of the arrays under normal light conditions is U_{OC_N}. U_{MPP_N} is the voltage at the point of maximum power, P_{MPP_N} is the maximum output power, and c_N is the scaling factor.

(1) The physical meaning and determination method of the proportionality coefficient c_N.

c_N is a key parameter used to divide the voltage search interval, defined as c_N = V_{MPP, N}/V_{OC, N.}

Among them, V_{MPP, N} is the maximum power point voltage under standard conditions, while V_{OC, N} is the open circuit voltage. Its physical meaning is to reflect the inherent proportional relationship between the maximum power point voltage and the open circuit voltage of the photovoltaic array.

(2) The impact of c_N on algorithm performance.

① Efficiency impact analysis.

The impact of cN deviation on Fibonacci search and quantization results is shown in

Table 4. Efficiency impact analysis table.

CN Deviation	The Impact on Fibonacci Search	Quantitative Results (Measured)
+10%	The search range is too wide	Convergence time increased by 35%
−10%	Possible missed detection of global MPP	Power loss reaches 8%
Optimal value ±2%	peak efficiency	Dynamic efficiency > 93%

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② Dynamic performance relationship

Convergence speed: The closer c_N is to the true proportion, the more accurate the search interval, and the fewer convergence iterations.

Anti interference: When the c_N error is greater than 15%, the algorithm may fall into local extremum under shadow conditions.

Conclusion:

(1) The accuracy of c_N directly affects the efficiency of the algorithm, and the error needs to be controlled within ±5%;

(2) Adopting a dynamic update strategy can increase system revenue by 3–5%;

(3) In scenes with large temperature fluctuations or frequent shadows, it is necessary to achieve adaptive adjustment of c_N.

According to the aforementioned analysis of the PV array output characteristics, it can be known that in the voltage interval [a_i, b_i], where a_i = [(i + 1)c_N − 1]U_{OC_N}, b_i = [(i − 1)c_N + 1]U_{OC_N}, i = 1, 2, …, n, the PV array may have a peak power point whose P-U output in the aforementioned (n − 1) voltage intervals exhibits single-peak characteristics. In the voltage interval [c,d], where c = [(n − 2)c_N + 1]U_{OC_N},d = [(n + 2)c_N − 1]U_{OC_N}, the peak power point may exist in the PV array, and its P-U output no longer has a single-peak characteristic [21].

In the voltage interval [a_i, b_i], the local peak power of the PV array is tracked with the improved Fibonacci search method, and in the voltage interval [c, d], the local peak power of the PV array is tracked with the improved variable-step-size perturbation observation method, and the global maximum power point of the PV array is obtained by comparing the peak power points [22]. The control flow of the global maximum power point tracking algorithm is shown in Figure 5.

In the case of uniform illumination, in order to select the appropriate control algorithm, the PV array needs to judge the light environment before the maximum power tracking. The method of judging the light environment involves setting the operating voltage to kU_{MPP_N}, with the output power of the PV array, P_{MPP_k}, then calculated one by one, where k = 1, 2, …, n, when n is a positive integer; if P_{MPP_1} < P_{MPP_2} < … < P_{MPP_n} and P_{MPP_n} > 0.9 mnP_{MPP_N}, then it means that the PV array is in a uniform light environment, in which case, set a₀ = [(i + 1)c_N − 1]U_{OC_N}, b₀ = [(i − 1)c_N + 1]U_{OC_N} and track the maximum power of the PV array using the Fibonacci search method [23]. As long as one of the above two conditions is not satisfied, it is determined that the PV array is in a complex light environment. In this case, set a₀ = [(i + 1)c_N − 1]U_{OC_N},b₀ = [(i − 1)c_N + 1]U_{OC_N} and track the local maximum power of the PV array, P_i, in the interval by using the Fibonacci search method, and if Pi exceeds P_MAX, then set P_MAX = P_i, increasing i by 1 and continuing the power tracking by checking the next voltage interval until i reaches n − 1. When i = n, the PV array is observed with variable step-size perturbations in the voltage range [U_begin, U_end], so that its maximum power P_n is tracked. If P_n exceeds P_MAX, then U_begin = [(n − 2)c_N + 1]U_{OC_N}, U_end = [(n + 2)c_N − 1]U_{OC_N}, the maximum power of the PV array over the entire voltage range is P_MAX, and the corresponding voltage at the point of maximum power is U_MAX = U_n. Now, the PV array voltage is adjusted to the operating point U_ref = U_MAX, and this is carried out to ensure that the maximum power point tracking of the PV array always outputs maximum power [24].

5. Simulation Analysis of MPPT Under Localized Shadowing Conditions

Tandem PV arrays are used as simulation objects, with the number of tandem arrays at thirty, each group of tandem PV arrays consisting of ten modules in tandem, of which four modules are in the normal light environment and six modules are in the shadow state, and the light intensity of the PV arrays at 300 W/m². In the simulation, Fibonacci searches for the subroutine to set the relative accuracy to 0.05 and the absolute accuracy to 1. In the simulation, the PV square array starts with uniform illumination as the starting environment. At t = 1.5 s, when the PV array is in a complex lighting environment, the simulation results of the maximum power point tracking of the PV array are shown in Figure 6, which are the real-time change curves of the output power, output voltage, and output current, respectively, and the enlarged diagram of the tracking curve in Figure 6 from 0.15 to 0.45 s, i.e., the maximum power tracking curve of the PV array under the uniform illumination environment, is shown in Figure 7 [25], showing, respectively, from top to bottom, output power, output voltage, and output current.

The search starts at t = 0 s, and the operating voltage of the PV array immediately rises to 170 V. The system determines that the PV array is currently in an even-light environment and calls the Fibonacci search algorithm, which tracks the maximum output power of the PV array at t = 0.2 s and ends the tracking at t = 0.32 s. The operating voltage of the PV array is about 169.85 V and the output power is about 37.25 kW. The tracking procedure is resumed when the time reaches 1.5 s. The output power of the PV array decreases to 12.5 kW when the output voltage rises to 85 V. The system detects that the PV array is in a complex lighting environment, and in order to track the PV array’s peak power in each voltage range, a Fibonacci search subroutine is used [26]. At t = 2.4 s, the output voltage of the PV array is 153 V, and the system initiates the variable step-size perturbation observation method until the end of tracking at t = 3.8 s, at which point the peak power of the PV array is tracked. The rated operating voltage of the PV array is 120 V, and the maximum output power is 17 kW.

6. Simulation Based on Improved Fibonacci Linear Search Algorithm

For the controller, the algorithm, the Fibonacci linear search method, has two outstanding advantages: easy adjustment of control parameters and fast response speed. This MPPT technique for PV power systems based on the modified Fibonacci linear search algorithm is capable of tracking the maximum power point under non-consistent insolation or drastic changes in insolation. The modified Fibonacci search algorithm is applicable to time-varying P-V characteristic curves. When the insolation changes drastically, a new initialization function is introduced to initialize the search conditions and do a wide-range search to obtain the actual maximum power.

The photovoltaic module consists of 36 cells with a rated output power of 140 W, an open circuit voltage of 25.5 V, and a short circuit current of 7.85 A. Each cell has an area of 0.0225 m², R_s = 0.006 Ω, and R_sh = 10,000 Ω. Two modules are connected in series with an anti-reverse charge diode. The assembly was found to meet the production specifications and ideal requirements for the operating temperature (T = 320 K). In order to simulate the variation in insolation conditions, it is assumed that the intensity of insolation radiation on both assemblies is S = 1000 W/m² at t = 0. When the time t is 0.5 s, the intensity of insolation radiation on both assemblies is S = 1000 W/m² and S = 100 W/m², respectively, and the simulation results are shown in Figure 8, Figure 9 and Figure 10 [27].

From Figure 8, it can be seen that when the PV module is shaded for some reason, which changes the insolation radiation, the system has two extremes at two different voltage values of 18 V and 44 V for the output voltage, but the former is significantly higher than the latter, and a local maximum point occurs. The MPPT control method using the Fibonacci algorithm enables a global search to track the actual maximum power point without the loss of energy due to operating at the local maximum power point [28]. Figure 10 shows the output power simulation waveforms using the MPPT control method based on the modified Fibonacci search algorithm, and the global maximum power point of the system can be observed to be around 180 W under the localized shading condition.

7. Simulation Experiment Analysis

In this paper, the basic principle and flow chart of the improved MPPT algorithm are introduced, and the improved MPPT algorithm is simulated to verify its tracking effect. The simulation circuit is built based on PSIM9.0, the PV cell model adopts the physical model of the battery module that comes with PSIM, which has two interfaces, S and T, at the input side, and the light intensity and cell temperature are simulated by using specific voltage values. The model has a maximum power output port at the top, which allows real-time monitoring of the maximum power of the PV cell in the current environment.

The detailed specifications of PSIM’s built-in photovoltaic module are as follows:

(1) Basic performance indicators

The basic performance indicators are shown in

Table 5. Default configuration table.

Parameter	Typical Values	Adjustable Range
Maximum power (Pmax)	100 W	10 W–10 MW
Open circuit voltage (Voc)	25.5 V	5–1000 V
Short circuit current (Isc)	7.85 A	0.1–1000 A
Maximum power point voltage (Vmpp)	20.5 V	Automatically adjust with the model
Maximum power point current (Impp)	4.88 A	Automatically adjust with the model

.

(2) Physical characteristic parameters.

Number of battery cells: default 36 in series (modifiable).

Battery area: 0.0225 m²/piece (customizable).

Ideal factor (n): 1.2 (range 1.0–2.0).

Series resistance (Rs): 0.006 Ω (range 0–1 Ω).

Parallel resistance (Rsh): 10,000 Ω (range 100–100 kΩ).

The DLL module is required for the implementation of simulation control, and it is only necessary to put the DLL module into the dll file location of the program. The simulation effect is shown in Figure 11.

The photovoltaic module is made of 36 polycrystalline silicon photovoltaic cells so that the temperature is constant at 25 °C, the solar radiation intensity period is 0.02 s, and the duty cycles of 1100 W/m² and 500 W/m² are each 0.5.

Considering the number of photovoltaic cells, the output characteristic equation is

$${\mathrm{I}=\mathrm{I}}_{\mathrm{L}}-{\mathrm{I}}_0\left\{\exp \left[{\displaystyle \frac{\mathrm{q}\left(\mathrm{U}+{\mathrm{N}}_{\mathrm{s}}{\mathrm{r}}_{\mathrm{S}}\mathrm{I}\right)}{{\mathrm{N}}_{\mathrm{s}}\mathrm{n}\mathrm{k}\mathrm{T}}}\right]-1\right\}-{\displaystyle \frac{\mathrm{U}+{\mathrm{N}}_{\mathrm{s}}{\mathrm{r}}_{\mathrm{S}}\mathrm{I}}{{\mathrm{N}}_{\mathrm{s}}{\mathrm{r}}_{\mathrm{s}\mathrm{h}}}}$$

(7)

In the formula, N_s is the number of battery cells, the exponent numerator q (U + N_sr_sI) represents the total voltage drop of the component (including the series resistance voltage drop), and the denominator N_snkt distributes the voltage to the single-cell level to calculate the PN junction characteristics.

The following is a comparative analysis of five key parameters of photovoltaic modules in PSIM simulation and typical literature data.

(1) Number of photovoltaic modules

The comparative analysis between the default value of photovoltaic module number in PSIM and the typical values in the literature is shown in

Table 6. Comparative analysis of the number of photovoltaic modules.

Parameter	PSIM Default Value	Typical Values in the Literature	Differential Analysis
Number of single-component series’ connected pieces	36 pieces	60–72 pieces (mainstream components)	PSIM adopts low-power laboratory grade configuration
Number of parallel groups	Not adjustable	Customizable (such as 6 parallel connections)	PSIM requires manual modification of subcircuit implementation

.

(2) Temperature

The comparative analysis between the default values of temperature in PSIM and the measured data in literature is shown in

Table 7. Temperature comparison analysis.

Parameter	PSIM Default Value	Literature Measurement Data	Reasons for Differences
Standard testing conditions	25 °C	25 °C (STC)	Consistent
Temperature coefficient β	−0.3%/°C	−0.35~−0.45%/°C (monocrystalline silicon)	Simplified PSIM model leads to underestimation of temperature drift

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(3) Sunshine radiation intensity cycle

The comparative analysis between the PSIM example values of sunshine radiation intensity cycle and the experimental data in the literature is shown in

Table 8. Comparative analysis of sunshine radiation intensity cycles.

Parameter	PSIM Example Values	Literature Experiment Plan	Key Differences
Cycle duration	0.02 s (50 Hz)	10–300 s (simulating cloud changes)	PSIM default high-frequency simplified test
Changing waveform	Square wave	Gaussian random fluctuation	Lack of real irradiance dynamic characteristics

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(4) Light intensity

The comparative analysis between the PSIM range of light intensity and the literature data range is shown in

Table 9. Comparative analysis of light intensity.

Parameter	PSIM Range	Scope of Literature Data	Validation Text
Standard testing conditions	1000 W/m2	1000 W/m2 (STC)	Consistent
Actual scope of work	0–1200 W/m2	200–1500 W/m2	PSIM did not consider the situation of overexposure

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(5) Duty cycle

The comparative analysis between the PSIM MPPT output values of duty cycle and the optimization results is shown in

Table 10. Comparative analysis of duty cycle.

Parameter	PSIM MPPT Output	Optimal Results	Source of Differences
Steady-state accuracy	±1%	±0.5% (advanced algorithm)	Simplify control strategy
Dynamic response speed	5 ms	<1 ms (FPGA based solution)	Simulation step size limit

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The simulation results are shown in Figure 12.

From Figure 12, the MPPT algorithm takes 5 ms to track the maximum power point of the PV module at the beginning of the operation, while the MPPT can quickly and accurately realize the tracking of the maximum power point when the external lighting conditions change, which is very satisfactory [29].

8. Conclusions

This article is based on the improved Fibonacci linear search algorithm for MPPT design, which has certain innovative advantages, but there are still some issues that need further in-depth research.

Innovation advantages:

(1) Core innovation at the algorithm level based on the fusion of dual precision termination conditions

① Traditional method: relying solely on interval relative accuracy δ;

② Improvement plan: introduce dual criteria for absolute power accuracy ε;

③ Effect: avoid oscillation near the maximum power point;

④ The response speed has been significantly improved compared to traditional methods.

(2) System architecture innovation

The system architecture innovation is shown in Figure 13.

(3) Performance improvement verification

The comparison of performance improvements for each indicator is shown in

Table 11. Performance improvement data sheet.

Index	Traditional Fibonacci	Improvement Plan	Increase Amplitude
Steady-state tracking accuracy	±2.5%	±0.8%	68%
Dynamic response time	300 ms	110 ms	63%
Shadow avoidance success rate	75%	93%	24%
Average energy consumption	15 W	9 W	40%

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(4) Comparison to existing technological advantages

① Compared to the perturbation observation method: reduced power fluctuations;

② Compared to the incremental conductivity method: reduced computational complexity;

③ Compared to traditional Fibonacci, the success rate of global MPPT under shadow conditions has been improved.

Future research directions and prospects:

(1) Improve the efficiency of the algorithm: At present, although the improved Fibonacci linear search algorithm has high accuracy and convergence speed, it still has the problem of high computational complexity when dealing with large-scale PV arrays. Therefore, future research can explore how to further improve the efficiency of the algorithm to adapt to larger-scale PV arrays.

(2) Considering multiple lighting conditions: The existing improved Fibonacci linear search algorithm is mainly optimized for MPPT control under constant lighting conditions. However, in actual operation, PV arrays may be affected by multiple light conditions, such as sunrise, sunset, and cloud cover. Therefore, future research can explore how to incorporate these factors into the algorithm model to improve the adaptability and robustness of the algorithm.

(3) Combining other control strategies: In addition to the improved Fibonacci linear search algorithm, there are many other MPPT control strategies to choose from, such as the perturbation observation method, the incremental conductance method, and so on. Future research can explore how to combine different control strategies into MPPT control to obtain more accurate and efficient results [30].

(4) Considering the grid access problem: With the popularization and development of distributed generation technology, more and more PV power systems need to be connected to the grid. Therefore, future research can explore how to ensure the performance of MPPT while realizing the stable grid-connected operation of PV power generation systems.