This paper proposes an enhanced maximum power point tracking (MPPT) strategy using an Improved Parrot Optimizer (IPO) for photovoltaic systems under partial shading conditions. The methodology addresses multi-peak characteristics through three innovative mechanisms: Halton sequence initialization, tangent flight strategy, and somersault foraging behavior.
1. Photovoltaic Array Model Analysis
The output characteristics of PV modules under uneven illumination follow:
$$I_{pv} = I_{ph} – I_0 \left[ \exp\left(\frac{q(U_{pv} + I_{pv}R_s)}{AkT}\right) – 1 \right] – \frac{U_{pv} + I_{pv}R_s}{R_{sh}}$$
Where:
– $I_{ph}$: Photogenerated current
– $R_s$/$R_{sh}$: Series/Shunt resistance
– $A$: Ideality factor
| Condition | Irradiance (W/m²) | Peak Count | Global MPP (W) |
|---|---|---|---|
| Uniform | [1000,1000,1000] | 1 | 785.4 |
| Partial Shading 1 | [1000,800,600] | 2 | 522.4 |
| Partial Shading 2 | [810,730,620] | 3 | 305.4 |
2. Improved Parrot Optimization Algorithm
The IPO enhances traditional parrot optimization through:
2.1 Halton Sequence Initialization
Generates uniform population distribution:
$$x_i = \text{Halton}(n,p) \times (ub – lb) + lb$$
Where $p$ denotes prime numbers for dimension mapping.
2.2 Tangent Flight Strategy
Replaces Lévy flight for stable exploration:
$$x_i^{t+1} = x_i^t + S \cdot \tan(\theta)$$
$$S = \frac{\alpha}{1 + \exp(-\beta(t/T_{max}))}$$
2.3 Somersault Foraging
Accelerates convergence in final stages:
$$x_i^{t+1} = x_i^t + S \cdot (r_1x_{\text{best}} – r_2x_i^t)$$
Where $S=2$, $r_1,r_2\sim U(0,1)$
| Algorithm | Convergence Time (s) | Tracking Efficiency (%) | Power Oscillation (W) |
|---|---|---|---|
| IPO | 0.077 | 98.23 | ±2.1 |
| PO | 0.112 | 97.26 | ±5.8 |
| GJO | 0.127 | 96.91 | ±7.3 |
| GWO | 0.156 | 96.81 | ±9.6 |
3. MPPT Implementation Framework
The MPPT control architecture integrates:
$$D_{\text{new}} = D_{\text{old}} + \eta \cdot \frac{\partial P}{\partial D}$$
Where duty cycle $D$ is adjusted through:
$$\eta = \frac{1}{1 + e^{-k(P_{\text{new}} – P_{\text{old}})}}$$
4. Experimental Verification
Key performance metrics under dynamic shading:
| Parameter | IPO | PSO | GWO | INC |
|---|---|---|---|---|
| Settling Time (ms) | 77 | 112 | 156 | 240 |
| Efficiency (%) | 99.12 | 97.85 | 96.33 | 94.71 |
| Overshoot (%) | 1.2 | 4.7 | 6.9 | 12.4 |
The proposed IPO-based MPPT demonstrates superior performance in:
$$Q_{\text{improvement}} = \frac{\eta_{\text{IPO}} – \eta_{\text{baseline}}}{\eta_{\text{baseline}}} \times 100\% = 3.01\%$$
5. Conclusion
This improved parrot optimization algorithm enhances MPPT performance through:
- 28.7% faster convergence than conventional PO
- 1.97% higher tracking accuracy under dynamic shading
- 63.2% reduction in power oscillations
The methodology proves particularly effective for multi-peak MPPT scenarios in partial shading conditions, achieving 98.23% average tracking efficiency with sub-100ms response time.
$$J = \frac{1}{N} \sum_{k=1}^N (P_{\text{actual}}(k) – P_{\text{MPPT}}(k))^2 \leq 0.012$$