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If your inverter requires a 60 OCPD, then that is the minimum rating for all OCPD devices between the inverter and the utility.
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Where did you pull this requirement from? I agree this is a good design guideline, but I do not see it required by the NEC.
If your main panel is rated 150A and has a 150 OCPD, then the maximum inverter OCPD is 30A.
Looks like you need to upgrade the main panel to 200A...
If the inverter is backfeeding a subpanel, the main panel rating has no correlation (unless there are some really bad design issues). I'll explain later...
...the minimum rating for the subpanel is 100A (assuming 2008 or 2011 NEC applies).
The minimum rating of a subpanel, when backfed by a 60A inverter, is 100A only because that is the next standard size above 60A. It could be 72.5A if they made one. The math:
(60A + 15A) ? 120% = 72.5A
...using 15A for the utility supply only because it is the smallest standard rating for a fuse or fixed-trip breaker [240.6(A)].
Actually we could use a 60A-rated panel and fuse the utility feed at 10A [1, 3, 6, and 10 are standard fuse sizes per 240.6(A)]... and the math: (60A + 10A) ? 120% = 58.3A. But for obvious reasons, this, the preceding, and other similar would be a very poor design for typical loading.
Getting back to the requirement extending to the main panel, I believe you've been misguided in 705.12(D)(2)'s interpretation. For reference, it states:
(2) Bus or Conductor Rating. The sum of the ampere
ratings of overcurrent devices in circuits supplying power
to a busbar or conductor shall not exceed 120 percent of the
rating of the busbar or conductor.
There are two typical scenarios to discuss regarding subpanels: 1) mcb, and 2) mlo. In each scenario, consider which are the "...overcurrent devices supplying power to a busbar or conductor..." regarding the utility-connected feeder.
In the case of the mcb subpanel, when the inverter is backfeeding power to the grid, the utility is not supplying power through the feeder conductor. Current can only travel in one direction at any one instance on a wire conductor. As such, the only overcurrent device supplying power to the utility feeder at that instance is the subpanel's mcb. So as long as the mcb is not more than 120% of the ampacity of the feeder conductor, it is good to go regardless of the inverter output and ocpd rating.
In the case of the mlo panel, there is no mcb, so the feeder must be of an ampacity not less than the utility end ocpd plus the inverter output ocpd divided by 120%. This is true of the panel busbar rating in either scenario.