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On Solar Photovoltaic Parameter Estimation: Global Optimality Analysis and a Simple Efficient Differential Evolution Method

Shuhua Gao, Yunyi Zhao, Cheng Xiang, Yu Ming, Tan Kuan Tak, Tong Heng Lee

TL;DR

The paper investigates two key questions in PV parameter estimation: whether current results are globally optimal and whether a simple optimization method suffices. It combines a deterministic interval branch-and-bound (B&B) approach with an intentionally simple differential evolution (DE) to evaluate SDM and DDM parameter fitting on two standard I-V datasets. The main findings are that the interval B&B method certifies the global minimum RMSE for the SDM and yields a tight upper bound for the DDM, while the simple DE can attain the global minimum or the best-known results with far less computational effort, often under 1 second. Practically, this work suggests that overly sophisticated metaheuristics may be unnecessary for PV parameter estimation and positions simple DE as a robust, fast default for industrial deployment, with the interval bounds serving as valuable evaluation references for future methods.

Abstract

A large variety of sophisticated metaheuristic methods have been proposed for photovoltaic parameter extraction. Our aim is not to develop another metaheuristic method but to investigate two practically important yet rarely studied issues: (i) whether existing results are already globally optimal; (ii) whether a significantly simpler metaheuristic can achieve equally good performance. We take the two widely used I-V curve datasets for case studies. The first issue is addressed using a branch and bound algorithm, which certifies the global minimum rigorously or locates a fairly tight upper bound, despite its intolerable slowness. These values are useful references for fair evaluation and further development of metaheuristics. Next, extensive examination and comparison reveal that, perhaps surprisingly, an elementary differential evolution (DE) algorithm can either attain the global minimum certified above or obtain the best-known result. More attractively, the simple DE algorithm takes only a fraction of the runtime of state-of-the-art metaheuristic methods and is particularly preferable in time-sensitive applications. This novel, unusual, and notable finding also indicates that the employment of increasingly complicated metaheuristics might be somewhat overkilling for regular PV parameter estimation. Finally, we discuss the implications of these results for future research and suggest the simple DE method as the first choice for industrial applications.

On Solar Photovoltaic Parameter Estimation: Global Optimality Analysis and a Simple Efficient Differential Evolution Method

TL;DR

The paper investigates two key questions in PV parameter estimation: whether current results are globally optimal and whether a simple optimization method suffices. It combines a deterministic interval branch-and-bound (B&B) approach with an intentionally simple differential evolution (DE) to evaluate SDM and DDM parameter fitting on two standard I-V datasets. The main findings are that the interval B&B method certifies the global minimum RMSE for the SDM and yields a tight upper bound for the DDM, while the simple DE can attain the global minimum or the best-known results with far less computational effort, often under 1 second. Practically, this work suggests that overly sophisticated metaheuristics may be unnecessary for PV parameter estimation and positions simple DE as a robust, fast default for industrial deployment, with the interval bounds serving as valuable evaluation references for future methods.

Abstract

A large variety of sophisticated metaheuristic methods have been proposed for photovoltaic parameter extraction. Our aim is not to develop another metaheuristic method but to investigate two practically important yet rarely studied issues: (i) whether existing results are already globally optimal; (ii) whether a significantly simpler metaheuristic can achieve equally good performance. We take the two widely used I-V curve datasets for case studies. The first issue is addressed using a branch and bound algorithm, which certifies the global minimum rigorously or locates a fairly tight upper bound, despite its intolerable slowness. These values are useful references for fair evaluation and further development of metaheuristics. Next, extensive examination and comparison reveal that, perhaps surprisingly, an elementary differential evolution (DE) algorithm can either attain the global minimum certified above or obtain the best-known result. More attractively, the simple DE algorithm takes only a fraction of the runtime of state-of-the-art metaheuristic methods and is particularly preferable in time-sensitive applications. This novel, unusual, and notable finding also indicates that the employment of increasingly complicated metaheuristics might be somewhat overkilling for regular PV parameter estimation. Finally, we discuss the implications of these results for future research and suggest the simple DE method as the first choice for industrial applications.

Paper Structure

This paper contains 15 sections, 11 equations, 4 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System modeling and problem formulation
  3. Modeling of PV systems
  4. Optimization problem formulation
  5. Optimization methods
  6. Deterministic global optimization with an interval arithmetic based branch and bound algorithm
  7. Stochastic global optimization with a simple DE
  8. Experimental results and discussions
  9. Datasets and experimental settings
  10. Global optimality analysis via interval B&B
  11. SDM results
  12. DDM results
  13. Optimization via simple differential evolution (DE)
  14. Comparison with existing algorithms
  15. Conclusion

Figures (4)

  • Figure 1: Equivalent circuit of a PV cell. (a) SDM; (b) DDM.
  • Figure 2: Measured and estimated I-V curves using parameter values optimized by interval B&B. (a) RT; (b) PW.
  • Figure 3: Convergence curves of DE with RT: (a) SDM (b) DDM.
  • Figure 4: Runtime comparison of different algorithms.