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• Proposing comprehensive equivalent electric circuit of polluted insulator. • Considering dynamic behavior for arc parameters instead of static one. • Evaluating proposed mathematical model with experimental results for real insulators. • Comparing the proposed mathematical model with static models for the same frame of real insulators. • Analyzing leakage current behavior under various pollution and humidity. This paper presents an improved dynamic mathematical model of critical parameters for ceramic insulators based on an extended equivalent electric circuit model of a polluted insulator. The extended equivalent electric circuit model introduces a capacitance in dry band. The model proposes that the electric arc constants (n, N) of critical parameters (voltage and current) in the mathematical model are not static. These factors depend on insulator's profile, pollution intensity and thermal characteristic of insulator discharge. The dynamic values of electric arc parameters are suggested based on the analysis of the experimental data and mathematical calculation of critical voltage of the polluted insulators. The calculated critical voltage of the proposed mathematical model is compared against the experimentally measured values of the critical voltage under different operating conditions. The experimental test results validate the competency of the proposed dynamic model in an accurate performance prediction of the polluted insulators. [ABSTRACT FROM AUTHOR]