Ultra-high-voltage（UHV） long distance transmission lines have unique characteristics on distributed parameters. While considering lines with lumped parameter models， the conventional distance protection may mal-operate on the long distance transmission lines. The paper proposes a novel principle of distance protection for long distance transmission lines based on Bergeron model. The proposed principle can reflect fault distance truly under the internal or external faults. Furthermore， it will not be influenced by load current， power swing， etc. Compared with conventional distance protection methods， the proposed principle does not mal-operate in the cases when external fault with transition resistance occurs. Finally， the interpolation algorithm of Bergeron equation， and the shunt reactors current calculation in time domain are given as well.