The short-term AC breakdown strength of laminated polypropylene insulating Paper (PPLP) has been studied for cold dielectric of high temperature superconductivity power cables. The design and operating conditions of the electrode system for studying of short-term breakdown strength of one-layer and multi-layer PPLP samples are discussed in liquid nitrogen(LN2) state. The influence of various operating factors (geometry and dimension of electrodes, speed of tested voltage, thickness of test sample) on the value of short-term AC breakdown strength at cryogenic temperature has been established.