In the hope of providing an explanation.
There are multiple types of cost relevant to this issue. First of, is the marginal cost. Basically, the marginal cost is the cost of electricity on the energy market, for which it is more economical for a power plant to shut down, than to operate. For non-subsidized renewable, the marginal cost is (just above) zero. For subsidized renewable, it is somewhere below zero, depending on the subsidy involved. For large nuclear and coal units, especially for models not build/prepared for load-following, the marginal cost can also be below zero, as cutting output then increasing it again would be more expensive.
Do note that an installation being able to provide energy at it's marginal cost doesn't mean that it's profitable. It just the point at which the finances look best and profits are maximized or losses are minimized. This is especially a problem for renewable power and nuclear, since (most of) their the investment is entirely up-front. If the electricity price isn't high enough during the lifetime of the plant, then the investement might never be recovered. Hence, feed-in subsidies.
The other relevant cost is lifecycle cost. This is a relatively simple system, where one looks at all the energy produced, looks at all the costs incurred, and thus calculates a cost per kwh. This is the average price the power plant needs to be profitable. Lifecycle costs vary heavily depending on design and location of a power plant, and some other factors. In practice, all power plant technologies (except solar PV) tend to be within the same range.
https://web.archive.org/web/20140419062707/http://report.mitigation2014.org/drafts/final-draft-postplenary/ipcc_wg3_ar5_final-draft_postplenary_annex-iii.pdfNow, there are 2 more important costs, relevant specifically to nuclear power and renewables.
First, is the Weighted Average Cost of Capital. Basically, how much interest and stuff you need to pay on your loans to be able to build something. For nuclear, this is the dominant aspect in price, accounting for about half of the lifecycle costs. Hence why a fast turn-over, as in China, results in low costs, and a prolonged construction (Finland) results in extremely high costs. This is also why most nuclear power plants have had governmental loan support.
For renewables, an important though oft ignored costs is the grid cost. This indirect cost, is the cost the useage of intermittent renewable energy inflicts on the grid. Most of the time, this isn't paid for by the renewable energy producers, but either by the grid operator (balancing payments) or by the owner of the non-profitable gas plants that provide energy when the wind is blowing. Note that nuclear and coal also have grid costs, these tend to be much smaller. Much discussion can be had about the size of these grid-level costs, or even their existence, but it remains a problem to be dealt with, and one not appropriately handled by the way the energy market works in many countries.
A quick cost analysis seems to suggest that too (but I may have failed it).
A cost analysis suggests what?
I think he means nuclear energy being cost efficient. It is - nuclear power plants are super expensive but for the fuel cost, they produce a lot of energy and since there is a lot of production in a single plant, less money goes into building the infra and energy network to the production itself. But one of the problems is that for that efficiency to work the power plants need to run basically at 100% power all the time, so everyone is still stuck with having to use gas/lng/oil/coal/water in significant amounts for all the adjustments and the times when that nuke plant is going through maintenance.
Well, not actually. A nuclear powerplant can be economically ran in a cost-following modus. In France, that is routinely done. Canada's Candu reactors even include a steam bypass system, in which the reactor is mostly decoupled from the generator, allowing them to vary power between 0.7-100% and technically making them the most versatile generation units on the entire generation grid.
For pratical purposes, that system isn't used that much though.