When the high voltage short-circuit tests for circuit-breakers and other switchgears is performed

enve-lopes of transient recovery voltage（TRV）need to be computed rapidly and accurately

so as to obtain the parameterssuch as U

c

t

2

and t

d

. The key and difficulty point of the four parameter TRV waveform envelope calculation is to ob-tain the straight line L

2

with two tangents to the TRV waveform. There are some deficiencies of current algorithms incalculating the L

2

such as needing curve fitting and poor convergence. In this paper

a novel algorithm of calculatingthe intersection of two straight lines

and then using successive approximation to compute the L

2

is discussed

and asimplified algorithm of delay line is presented. Theoretical analysis and comparison with the existing algorithms showthat the new algorithms have good convergence and applicability.