  Transmission lines are vital components in power systems. Tripping of
transmission lines caused by over-temperature is a major threat to the security
of system operations, so it is necessary to efficiently simulate line
temperature under both normal operation conditions and foreseen fault
conditions. Existing methods based on thermal-steady-state analyses cannot
reflect transient temperature evolution, and thus cannot provide timing
information needed for taking remedial actions. Moreover, conventional
numerical method requires huge computational efforts and barricades system-wide
analysis. In this regard, this paper derives an approximate analytical solution
of transmission-line temperature evolution enabling efficient analysis on
multiple operation states. Considering the uncertainties in environmental
parameters, the region of over-temperature is constructed in the environmental
parameter space to realize the over-temperature risk assessment in both the
planning stage and real-time operations. A test on a typical conductor model
verifies the accuracy of the approximate analytical solution. Based on the
analytical solution and numerical weather prediction (NWP) data, an efficient
simulation method for temperature evolution of transmission systems under
multiple operation states is proposed. As demonstrated on an NPCC 140-bus
system, it achieves over 1000 times of efficiency enhancement, verifying its
potentials in online risk assessment and decision support.
