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I am trying to close a gap in my answer to this question: Are there general accuracy requirements for aircraft power supplies?

There is MIL-STD-704(F) Aircraft Electrical Power Characteristics for military aircraft.

Which standard is applicable to the electrical power system for civilian aircraft under the authority of the FAA?

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The answer is not straightforward. Power supplies used in commercial aircraft LRUs are required to meet RTCA DO-160G, sections: 16 Power Input, 17 Voltage Spike, and 18 Audio Frequency Conducted Susceptibility - Power Inputs.

The issue is this is what the consumers of aircraft power have to deal with. It doesn't actually specify what the aircraft power distribution system has to provide. Though by inference, the power generation system must deliver power within the bounds of what the consumers can accept.

In my experience, aircraft OEMs design their power distribution system and then levy specific requirements on the power supply design of all consumers on the aircraft. While DO-160 covers the majority of the need, the OEM requirements will include additional requirements deemed necessary by their design and analysis. As a Boeing engineer explained to me, "The requirements are not to protect your power supply. They're there to protect my power bus."

The reality is aircraft power is a small dynamic system and it is impacted by everything on the bus. It has to be designed as a system unique to each aircraft. Since it's part of the aircraft, the aircraft rules come into play. For air transport aircraft, that means 14 CFR Part 25. The applicable portions include 14 CFR 25.1310 and the Electrical Systems and Equipment subject section.

Additional guidance is available in Advisory Circular AC 25.1353-1a ELECTRICAL EQUIPMENT AND INSTALLATIONS.

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You are probably looking for RTCA DO-160G.

Note that there is no legal obligation to apply such engineering standards under the authority of the FAA. It is the choice of the manufacturer and the customer which standards shall apply.

Of course there are many reasons to apply well established standards, including but not limited to cost-savings during development, testing, and certification.

The FAA strongly encourages the use of RTCA/DO-160G through Advisory Circular no. 21-16G:

[...]

a. This advisory circular (AC) identifies RTCA Document No. (RTCA/DO)-160 versions D, E, F, and G, Environmental Conditions and Test Procedures for Airborne Equipment, dated July 27, 1997, December 20, 2005, December 6, 2007, and December 8, 2010, respectively, as containing acceptable environmental qualifications to show compliance with certain airworthiness requirements. The FAA strongly encourages the use of RTCA/DO-160G for new articles.

[...]

 c. This AC is not mandatory and does not constitute a regulation. This AC describes a means, but not the only means, to comply with airworthiness requirements.

[...]

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