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In high-voltage dc power systems of advanced aircraft, most of the electrical motor drives and power electronic converters behave as constant power loads (CPLs) when tightly regulated and usually cause negative impedance instability problems. This paper presents stability criteria for an electrical system constituted of a dc power supply, multistage LC filters, and an ideal CPL. The derived criteria are based on the Brayton-Moser mixed potential theory and can be extended to actual CPLs. The dynamic negative incremental impedance of the CPL is used to place design constraints on the filter parameters to prevent instabilities. Simulation and experimental results confirm that the proposed criteria would guarantee system stability under different voltage disturbances.