The smart grid isn't a single thing, or even a bound-able set of technologies. To give a non-physics example, you can watch a Google Tech Talk from someone who's largely focused on the communications, as in TCP/IP sort of stuff, as it applies to the smart grid.
Physical underpinnings are important, but I would say that what you want is more a "generalist engineer" background built around smart grid applications. Then a focus that will develop with whatever direction you take or mathematical optimization subset you're interested in.
The part of Electrical Engineering you're interested in is power systems. The bread and butter of this is electrical network analysis, but there are other physical principles behind it which come from manifestations of Maxwell's Laws. For generators, a broad sense of inductance is necessary, even with reference frame transformations applied to them. You should know about mutual inductance, leakage inductance, and general matrix formulation. You should also be privy to the basics of 3-phase power and how it ties in with electrical network analysis.
Particularly for the smart grid, the field is expanding, and you should expect a short half-life for a degree in the "new" stuff. In studying the basics of power systems, you should have a good deal of comfort with inductance and the mechanism of operation for conventional transformers, but there's ongoing interest in solid state transformers. But this isn't all. Not only are solid state transformers exciting because the technology is getting better - but they can do different tasks, tasks that will be relevant to a more heterogeneous smart grid. Specifically, I would suggest getting a strong background in IGBTs. A part of the thinking is that this kind of new technology will prove a general purpose power converter box, which can do DC-DC, AC-DC, and lots of switching.
The physical basis of that is all semiconductor technology. If you're interested in smart grid, you should be braced for hearing a lot of this, even if it's not your own focus. From your mathematical background and interest in mathematical optimization, I would predict you're more interested in dispatch algorithms and multilayer control systems. But this doesn't really point to any particular physics mastery that's needed.
In all cases, grid management is tied in with the physics of the components tied into it. For instance, grid-connected batteries have their own physics. These physics are simplified and lumped into a mathematical model which can be plugged right into the system-level simulation. At its core, however, it relies on ion transport. In other cases, we still have conventional power plants. Beyond the heat production you should be very interested in the fuel source or combustion physics unless it's direct use like a combustion turbine. Thermal cycles are more directly relevant, and how that energy gets communicated to the generator through expansion and torque. In a more fine-detail, you should be interested in the dynamical aspect of rotor (prime mover) inertia and the oscillations that those are subject to when plugged into the rest of the system. There are even more levels of oscillation you should be worried about, as the next generation electrical conversion systems, HVDC equipment, and things like that often employ high-frequency switching which contributes oscillations that are problems for other components. Of course, you'll also probably be interested in photovoltaic, taking you back to semiconductor physics.
This is so much that it might be better to ask yourself what your priorities are. I would go through something like this:
- Maxwell's equations and the principle behind inductors/generators
- A broad foundation in semiconductor physics
- EM wave propagation, and the physical limits of AC network matrix representations