Does this electricity charge a battery pack, which then is used to drive the electric motors which turn the screws? This would imply that the heat generation and turbine spin-up time merely need to respond before the batteries are discharged, potentially allowing response times of minutes or hours. It would give Tesla-like instant throttle response, where the operator would move the lever and the sub would jump forward.
Or does it directly power the engines? This would mean that your entire control loop would include the latency of the steam generation process. Move the lever, wait for the water to get hot, wait for the turbines to spin up, and then the screws would start to turn faster. Like the throttle response in an ancient diesel truck.
Given that the original diesel submarines used giant battery arrays to power the electric motors while the engines were off, and that the former gives much better control response, I'd assume that there are still large batteries in the loop. This paper [2] supports that assertion:
> The nominal cell voltage is 2.0 V. [1] The PDX-57 cell designed for Ohio-class submarines weights 2,100 pounds with a capacity of more than 10,000 Amp-hours and stored energy of 2.6 MWh. [1] The ASB-49 cell designed for the Los Angeles-class submarine weights 1,300 pounds with a capacity of 7,200 Amp-hours and stored energy of 1.8 MWh. [1] The LLL-69 type cell weights 1,500 pounds with a capacity of 8,100 Amp- hours and stored energy of 2.0 MHh. [1]
A couple megawatthours is plenty to run the screws while the steam loop and nuclear reactor respond.
Therefore, toomanybeersies comment:
> On a nuclear powered ship, yes, since you still essentially have a steam engine, the engine telegraph (throttle) isn't actually linked directly to the engine.
is technically correct but actually irrelevant. The nuclear reactor telegraph does control the steam turbine and eventually the battery charge, rather than the engine. But somewhere there's an electric motor controller which responds instantly.
[1] http://ieeexplore.ieee.org/document/1177196/?reload=true&tp=...
[2] http://large.stanford.edu/courses/2013/ph241/ditiangkin1/