To enhance the speed and accuracy of maximum power point tracking (MPPT) while reducing power loss and harmonic distortion in partially shaded photovoltaic (PV) systems, this study proposes a hybrid control method integrating the Cuckoo Search Algorithm (CSA) and Incremental Conductance (INC) method. The CSA performs global exploration to avoid local optima, while the INC method refines the search near potential maxima. This approach is further validated through grid-connected control simulations to ensure compliance with harmonic standards.
1. Output Characteristics of PV Modules Under Partial Shading
The PV array model consists of 3×1 cells under non-uniform irradiance (1,000 W/m², 400 W/m², and 800 W/m²). The P-V curve exhibits three peaks, with only one global maximum power point (GMPP). Key parameters are listed below:
| Parameter | Value |
|---|---|
| Temperature | 25°C |
| Cell Configuration | 4×2 series-parallel |
| Peak Power per Cell | 238.7 W |
The nonlinear P-V relationship under shading creates multiple local maxima (5,761 W, 238 W, 24.14 W), necessitating robust MPPT strategies.
2. CSA-INC Hybrid Algorithm for MPPT
The CSA-INC algorithm combines global and local search capabilities:
2.1 Cuckoo Search Algorithm (CSA)
CSA models parasitic breeding behavior with Lévy flights for global optimization:
$$x_i^{t+1} = x_i^t + \alpha \oplus L(\beta),$$
where \(L(\beta)\) represents Lévy-distributed step sizes:
$$L(\beta) = \frac{u\sigma}{|v|^{1/\beta}}(x_i^t – x_{best}^t),$$
with \(\sigma\) derived from Gamma functions. Host nests are updated probabilistically with abandonment rate \(P_a\).
2.2 Incremental Conductance (INC) Method
Upon approaching GMPP, INC executes precise local search using:
$$\frac{dP}{dV} = 0 \Rightarrow \frac{I}{V} + \frac{dI}{dV} = 0.$$
The duty cycle \(D\) of the DC-DC converter is adjusted as:
$$D_{k+1} = D_k \pm \Delta D \cdot \text{sign}\left(\frac{\Delta P}{\Delta V}\right).$$
2.3 Hybridization Strategy
The transition from CSA to INC occurs when:
$$\max(|x_{best} – x_i|) < \epsilon,$$
where \(\epsilon\) is a threshold (e.g., 2% voltage deviation).
3. Simulation Results and Analysis
A 16 kW grid-connected PV system was modeled in MATLAB/Simulink with LCL filters. Key outcomes include:
3.1 MPPT Performance Comparison
| Algorithm | Settling Time (s) | Power Error (%) | THD (%) |
|---|---|---|---|
| CSA-INC | 0.21 | 0.02 | 2.3 |
| Standard CSA | 0.25 | 0.15 | 3.8 |
The hybrid method achieves 99.98% tracking accuracy at 5,762 W output, outperforming standalone CSA in convergence speed (16% faster) and stability.
3.2 Grid Integration Performance
Harmonic analysis of grid current shows:
$$THD = \sqrt{\sum_{h=2}^{50} \left(\frac{I_h}{I_1}\right)^2} = 2.3\%,$$
which complies with IEEE 1547 standards (<5%). DC-link voltage stabilizes at 211 V (theoretical: 207 V), demonstrating effective MPPT-inverter coordination.
4. Conclusion
The CSA-INC hybrid algorithm effectively addresses partial shading challenges in PV systems by synergizing global exploration and localized refinement. Simulations confirm its superiority in tracking speed (0.21 s settling), accuracy (0.02% error), and grid compatibility (2.3% THD). This methodology provides a viable solution for optimizing renewable energy integration in smart grids.