1. Introduction
The integration of renewable energy sources into power systems has become critical for achieving global decarbonization goals. Among these, solar photovoltaic (PV) systems, particularly solar grid-tied inverters, play a pivotal role due to their scalability and cost-effectiveness. Accurate identification of control parameters in these inverters is essential for optimizing their transient response and ensuring grid stability. Traditional parameter identification methods, such as Least Squares (LS), Maximum Likelihood (ML), Differential Evolution (DE), and Simplex Method (SM), face challenges in balancing accuracy and convergence efficiency. This study proposes a hybrid Simplex-Tabu Search (STS) algorithm to address these limitations, offering superior convergence rates while maintaining high precision for solar grid-tied inverter control parameter identification.
2. Structure and Control Strategy of Solar Grid-Tied Inverters
A typical solar grid-tied inverter system comprises three components: a PV array, a DC-AC inverter, and a control system. The inverter employs a dual-loop control strategy (inner current loop and outer voltage loop) to regulate active power (PP) and reactive power (QQ). The inner loop dynamics are governed by:Vdq(s)=(kP+kIs)[Idqref−Idq(s)]−ωLIdq(s)+Vdq(s)Vdq(s)=(kP+skI)[Idqref−Idq(s)]−ωLIdq(s)+Vdq(s)
where kPkP and kIkI are the proportional and integral coefficients, IdqrefIdqref is the reference current, and ωLωL represents the cross-coupling term. The outer loop adjusts the DC-link voltage (UdcUdc) and reactive power:Idqref(s)=(kPouter+kIouters)[Udcref−Udc(s)]Idqref(s)=(kPouter+skIouter)[Udcref−Udc(s)]
Accurate identification of kPkP and kIkI parameters is critical for ensuring stable operation of solar grid-tied inverters.
3. Traditional Parameter Identification Methods
3.1 Least Squares (LS)
The LS method minimizes the sum of squared errors between measured and simulated outputs:xi=xi−1+Ai(yi−θiTxi−1)xi=xi−1+Ai(yi−θiTxi−1)
Limitations: Poor performance in nonlinear systems and sensitivity to input signal noise.
3.2 Maximum Likelihood (ML)
ML maximizes the likelihood function:L(θ)=∏j=1lf(yj∣θ)L(θ)=j=1∏lf(yj∣θ)
Limitations: Computationally intensive for high-dimensional systems.
3.3 Differential Evolution (DE)
DE involves mutation, crossover, and selection steps:Mutation: v=x1+F⋅(x2−x3)Mutation: v=x1+F⋅(x2−x3)
Limitations: Premature convergence to local minima due to reduced population diversity.
3.4 Simplex Method (SM)
SM iteratively refines a simplex in NN-dimensional space. For a 2D case:Reflection: xr=xc+α(xc−xh)Reflection: xr=xc+α(xc−xh)
Limitations: Slow convergence near optima due to local cycling.
4. Hybrid Simplex-Tabu Search (STS) Algorithm
4.1 Algorithm Workflow
- Initialization: Use SM to rapidly approach the convergence region.
- Transition: Switch to Tabu Search (TS) when SM stagnates.
- Tabu Search: Explore non-tabu neighbors to escape local minima.
The termination criterion is defined as:ε=∣kj−kj−1∣kj−1×100%<5%ε=kj−1∣kj−kj−1∣×100%<5%
4.2 Mathematical Formulation
- Objective Function: Minimize the error between simulated and reference trajectories:
F=∑i=1N(Mi−Si)2F=i=1∑N(Mi−Si)2
- Tabu List: Stores recently visited solutions to avoid revisiting.
5. Case Studies: Inner and Outer Loop Parameter Identification
5.1 Inner Loop Results
The STS algorithm reduced iterations from 46 (SM) to 21, achieving a relative error below 1% (Table 1).
Table 1: Inner Loop Parameter Identification Performance
| Method | Iterations | kPkP Error (%) | kIkI Error (%) |
|---|---|---|---|
| SM | 46 | 0.64 | 0.04 |
| STS | 21 | 0.23 | 0.70 |
5.2 Outer Loop Results
STS achieved a 47% reduction in iterations (36 to 19) with errors under 1% (Table 2).
Table 2: Outer Loop Parameter Identification Performance
| Method | Iterations | kPkP Error (%) | kIkI Error (%) |
|---|---|---|---|
| SM | 36 | 2.45 | 1.05 |
| STS | 19 | 0.59 | 0.43 |
5.3 Comparative Analysis
STS outperformed existing methods in both accuracy and efficiency (Table 3).
Table 3: Benchmarking Against Existing Methods
| Method | Avg. Error (%) | Avg. Iterations |
|---|---|---|
| Frequency-Domain ML [8] | 1.21 | 42 |
| Genetic-PSO [11] | 2.93 | 45 |
| BPNN-PID [12] | 2.98 | 30 |
| STS (Proposed) | 0.43 | 19 |
6. Conclusion
This study introduces a hybrid Simplex-Tabu Search (STS) algorithm for identifying control parameters in solar grid-tied inverters. By synergizing the rapid initial convergence of SM with the local optima evasion capability of TS, STS achieves:
- Relative errors below 1% for both inner and outer loop parameters.
- 60–119% improvement in convergence efficiency compared to traditional methods.
- Robust performance across diverse initial conditions.
The STS algorithm is a promising tool for enhancing the operational stability and efficiency of solar grid-tied inverters, particularly in large-scale renewable energy systems. Future work will explore its application to multi-inverter networks and real-time parameter adaptation.