As renewable energy integration accelerates, solar inverter play a pivotal role in converting DC power from photovoltaic panels to grid-compatible AC power. However, weak grid conditions—characterized by low short-circuit ratios and high impedance—often lead to harmonic distortions, resonance phenomena, and instability. Traditional linear control methods, such as proportional-integral-derivative (PID) controllers, struggle to address these nonlinear challenges. This paper proposes a novel harmonic compensation framework for solar inverter by integrating particle swarm optimization (PSO)-enhanced backpropagation (BP) neural networks with adaptive PID control. The method aims to suppress harmonics, improve dynamic response, and ensure stability under abrupt load or voltage variations.
1. Methodology
1.1 Enhanced BP Neural Network Architecture
The BP neural network, a multi-layer feedforward structure, is optimized to handle nonlinear dynamics in solar inverter. Its three-layer architecture (input, hidden, output) employs weighted connections and activation functions to map input-output relationships. The output of neurons in the hidden and output layers is defined as:yj=f(∑i=0nwijxi),zj=g(∑i=0hwijyi)(1)yj=f(i=0∑nwijxi),zj=g(i=0∑hwijyi)(1)
where yjyj and zjzj are outputs of the hidden and output layers, ff and gg are activation functions, and wijwij denotes weights. To mitigate oscillations during training, a momentum term is introduced:Δw(n)=−η∂ϵ(n)∂w(n)+αΔw(n−1)(2)Δw(n)=−η∂w(n)∂ϵ(n)+αΔw(n−1)(2)
Here, ηη is the learning rate, ϵ(n)ϵ(n) is the loss function, and αα is the momentum factor.
1.2 Hybrid PSO-GA Optimization
Standard BP networks suffer from sensitivity to initial weights and fixed hyperparameters. To overcome this, a hybrid PSO-genetic algorithm (GA) optimizes the network’s weights and learning parameters. The PSO algorithm updates particle velocities and positions as:vij(t+1)=wvij(t)+c1r1(pbest,ij−xij(t))+c2r2(gbest,ij−xij(t))(3)vij(t+1)=wvij(t)+c1r1(pbest,ij−xij(t))+c2r2(gbest,ij−xij(t))(3)xij(t+1)=xij(t)+vij(t+1)(4)xij(t+1)=xij(t)+vij(t+1)(4)
where ww is an adaptive inertia weight, c1c1 and c2c2 are learning factors, and r1,r2∈[0,1]r1,r2∈[0,1]. To enhance population diversity, GA-style mutation is applied with a 20% probability, perturbing particle positions to escape local optima.
1.3 Adaptive PID Control Integration
The optimized BP network dynamically adjusts PID parameters (Kp,Ki,KdKp,Ki,Kd) to minimize tracking errors. The PID control law is:u(t)=Kpe(t)+Ki∑j=0ke(j)Δt+Kde(t)−e(t−1)Δt(5)u(t)=Kpe(t)+Kij=0∑ke(j)Δt+KdΔte(t)−e(t−1)(5)
where e(t)e(t) is the error signal. The neural network continuously refines Kp,Ki,KdKp,Ki,Kd based on real-time grid conditions.
2. Experimental Validation
2.1 Test Setup
A quasi-Z-source solar inverter prototype was tested under weak grid conditions. Key parameters include:
- Grid impedance: 30 Ω (simulating weak grid)
- DC input voltage: 25–30 V
- Load variation: 20 Ω ↔ 30 Ω
2.2 Performance Metrics
The proposed method was compared against traditional BP, GA-BP, PSO-PID, and SOA-PID models. Key metrics include tracking error, phase synchronization time, and settling time.
| Model | Tracking Error | Phase Sync Time (s) | Settling Time (s) |
|---|---|---|---|
| Traditional BP | 2.2 | 0.11 | 0.37 |
| GA-BP | 1.5 | 0.06 | 0.22 |
| Proposed PSO-BP | 1.2 | 0.04 | 0.19 |
2.3 Dynamic Response Analysis
- Voltage surge (25 V → 30 V): Capacitor voltage deviation was limited to 9.8 V, stabilizing within 4.37 ms (Figure 4a).
- Load step (20 Ω → 30 Ω): Output remained stable without oscillations or sawtooth waveforms (Figure 4b).
The fitness value and objective function of the proposed method outperformed alternatives:FitnessProposed=13.2(vs. 10.3 for SOA-PID, 9.9 for PSO-PID)FitnessProposed=13.2(vs. 10.3 for SOA-PID, 9.9 for PSO-PID)Objective FunctionProposed=5×10−6(vs. 10−4 for others)Objective FunctionProposed=5×10−6(vs. 10−4 for others)
3. Discussion
The integration of PSO-GA with BP neural networks addresses critical limitations in solar inverter control:
- Nonlinear Adaptation: Enhanced BP networks model inverter dynamics more accurately (R2=0.98508R2=0.98508) than traditional BP (R2=0.95442R2=0.95442).
- Robustness: The hybrid optimizer ensures global convergence while maintaining population diversity.
- Real-Time Performance: Adaptive PID tuning reduces settling time by 48.6% compared to GA-BP.
This method is particularly suited for solar inverter in weak grids, where harmonic suppression and rapid stabilization are critical.
4. Conclusion
This study demonstrates a neural network-based harmonic compensation strategy that significantly enhances the stability and power quality of solar inverter in weak grids. By synergizing PSO-GA optimization with BP networks, the framework achieves:
- Lower harmonic distortion under voltage/load transients.
- Faster dynamic response (4.37 ms recovery time).
- Superior convergence in parameter optimization.
Future work will explore hardware-in-loop validation and scalability for large-scale solar farms.