In recent years, as ecological issues have become increasingly significant, the excessive use of non-renewable energy has had a profound impact on the environment. For instance, severe smog in China has drawn attention to the necessity of clean and renewable energy sources. Among these, the photovoltaic (PV) industry has seen rapid development and widespread application in various aspects of daily life. The output characteristics of PV modules are influenced by factors such as light intensity and ambient temperature [1]. Typically, manufacturers provide only external output characteristics and electrical nameplate parameters under standard conditions. However, in practical applications, PV modules rarely operate under these ideal conditions. Therefore, it is crucial to obtain accurate external output characteristics and corresponding electrical parameters under different environmental conditions, which serves as a foundation for analyzing the performance of PV modules.
Due to the sensitivity of PV module output characteristics to environmental changes, selecting an appropriate model and accurately identifying its internal parameters remains a key challenge [2]. A commonly used single-diode model is known for its high accuracy in engineering applications [3]. Parameter identification methods can be broadly categorized into approximate mathematical analysis and optimization-based approaches. Some studies, such as [4-5], rely on mathematical approximation techniques. However, due to the presence of complex nonlinear functions and the direct approximation of certain parameters, the accuracy of calculated values tends to be limited. In contrast, [6] employs the CPSO algorithm, achieving good convergence but requiring a large number of iterations. Overall, intelligent optimization algorithms offer advantages in terms of accuracy and reliability, yet traditional algorithms often suffer from premature convergence or excessive computational time. To address this, an improved quantum particle swarm optimization (QPSO) algorithm is proposed for parameter identification of PV modules. This method not only avoids local optima but also reduces the number of iterations required during optimization. Moreover, the nonlinear relationship between PV module output characteristics and environmental factors makes accurate prediction of output curves and internal parameters under varying conditions highly significant.
The theoretical model of a photovoltaic cell is based on the single-diode model, as illustrated in Figure 1 [7]. The equivalent current and voltage expressions for the internal parameters are given as follows:
Where U represents the load voltage, I is the load current, Iph is the photo-generated current, Io is the diode reverse saturation current, A is the diode ideality factor, Rs is the series resistance, Rsh is the shunt resistance, T is the absolute temperature, K is Boltzmann's constant, and q is the elementary charge. The five unknown parameters—Iph, Io, A, Rs, and Rsh—need to be identified.
To improve the accuracy of parameter identification, an improved QPSO algorithm is introduced. Reference [8] uses the Lambert W function to simplify the expression for the photovoltaic current I:
Here, X = (Iph, Io, A, Rs, Rsh) represents the position vector of each particle, while Ical and Imea denote the calculated and measured currents, respectively. A smaller fitness value indicates more accurate parameter identification.
The Quantum Particle Swarm Optimization (QPSO) algorithm, proposed by Sun et al. in 2004, incorporates quantum mechanics principles to enhance particle movement. Unlike traditional PSO, QPSO describes particle behavior using quantum states, allowing particles to exist at any point with a probability density. However, the initial random distribution of particles in QPSO limits its exploration ability. To address this, chaos theory is integrated to improve the initialization process and prevent premature convergence. The Logistic chaotic equation is employed to generate sequences that enhance the ergodicity of the search space.
Experiments were conducted to validate the effectiveness of the improved algorithm. A simulation model of a PV module was created in MATLAB/Simulink, and parameter identification was performed using PSO, QPSO, CQPSO, and CPSO. The results showed that the CQPSO algorithm achieved a fitness value of 0.037014, significantly lower than that of PSO (0.5424), with only 18 iterations needed for convergence. This demonstrates the improved algorithm's superior performance in both speed and accuracy.
Further validation was carried out using real-world data under different temperature and irradiance conditions. The improved algorithm successfully identified the internal parameters and fitted the output characteristic curves. The predicted current error percentage was less than 0.5%, confirming the method’s reliability for PV module output prediction.
In conclusion, the improved quantum particle swarm optimization algorithm offers a robust solution for PV module parameter identification and output characteristic prediction. It effectively overcomes the limitations of traditional methods, providing high accuracy and efficiency. This approach has broad applications in areas such as maximum power point tracking and fault diagnosis, making it a valuable tool for future research and engineering projects in the solar energy sector.
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