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After I've finished my Master's degree in mathematics, I too want to use my powers for good.

One endeavour I consider good is the pursuit of the design and implementation of a Smart Grid which will, supposedly, allow us to use our electricity more efficiently and connect decentralized energy sources (such a solar panels and wind-mills) to the grid.

I am wondering, though, to what extent studying mathematics is useful for this. The wikpedia article on Smart Grids includes a section on "Smart Grid Modelling". It mentions that, amongst other things, Percolation Theory, Kuramoto Oscillators, Maximum Entropy Methods and Markov Procecesses are studied within the context of designing a Smart Grid. However, most other subjects are more computer science-y.

So I could study these subjects so I can contribute to Smart Grid research when I'm a bit older. My question is, though, are there more subjects I should study to be able to contribute to Smart Grid research? What about (delay) (partial) differential equations, difference equations, optimization theory and operations research? Are these subjects useful as well? Should I study some topics in physics as well? (Such as electromagnetism?) Are there any Master's Programmes in Applied Mathematics that incorporate courses that specifically deal with Smart Grids?

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    $\begingroup$ Most of us here don't know the answer. (So don't be disappointed if there are no replies.) But we can hope that someone working on Smart Grids will see it and give you some pointers. Which is probably a good use of this site! $\endgroup$ – GEdgar Jul 12 '13 at 15:40
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I'm a graduate student in power systems, so while I'm not in industry, I figure I could give you my perspective on Smart Grid research as a student who's asking similar "applications" questions to those in my field.

I would first say that, from my perspective, mathematics is quite useful for the S.G.; for such a large-scale system modernization/transformation, interdisciplinary research is essential. The most common mathematical subjects I see brought up in presentations, sessions, conferences, and courses include:

  • Numerical Analysis and Integration
  • Random Processes (e.g.: Markov)
  • Linear and Nonlinear Optimization
  • Neural Networks

The most common power course I see being taken by students from other fields is (1) Introductory Power Systems Analysis (less so electromagnetics, although it does help you understand the physics behind the system). You can maybe take (2) Large-Scale Systems Analysis, although that somewhat depends on what aspect of the grid you would like to work on.

Courses outside of Power Systems that I (and my peers) have taken or plan on taking include:

  • Control Systems Theory and Design
  • Numerical Analysis
  • Optimization Theory
  • Random Processes
  • Graph/Network Theory
  • Real and Complex Analysis
  • Robust Control Theory
  • Nonlinear Control Systems

I say "intro-level" because you can certainly take another course or two in the area and still apply what you learn to the S.G.

Examples of applied mathematics in S.G. research include Cornell's Applied Mathematics Colloquia and University Research Programs Funded by the DoE. It may say "computational", but at the core of it all is analysis improved/sped-up using applied mathematics techniques. Hope this gives you some ideas!

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There are perhaps many ways to approach these "smart grid" problems, and one way is to approach it from a "networking theory" point of view.

But, and this is a big but, hot topics like these smart grids, well, they come and go. The way they are advertised is cool, "it is going to solve all of our problems, yay," but it does not work this way. So, unless you are doing research in the area "today," I would keep my options open, and try to read about different problems at your stage. Why is smart grid research so active today? Is it because it is so "promising?". Well, maybe, but you should also keep in mind that there exists a class of network theorists $\mathcal{N}$, such that they first pick their favorite network theory problem, and then change regular network flows to power flows, resource allocation to power allocation, replace vertices with high degrees with power stations or refrigerators, and there they go, they now have more papers (i.e. pressure to publish). Of course, this does not mean that smart grid presents no new interesting research challenges and there is no original work to be done.

Going back to your original question, it comes to me as a surprise that you have never mentioned graph theory in the topics you listed. Pick your favorite graph; the power demands of each node is a stochastic process (peaking for example in the daylight hours where people use more electricity). There also power providers in this network and the power they can provide is also random (these power providers may include individual users). You first have to define a communication protocol among these nodes on how and when they provide power to each other. Indeed, the "smartness" of the grid comes from the hope that these nodes can communicate with each other and decide on the most efficient way to distribute power. The way to define efficiency maybe to minimize the maximum load of the power grid (i.e. the flows), minimize the power transmission losses (which is actually very important as most of the power you produce in the stations gets lost in today's "stupid" grids) or to maximize the total profits of the big power companies, whichever you prefer.

To summarize, I think "communication" is the key in smart grid research (big respect though for the electromagnetics, and power electronics side of things that I know nothing about). If you would like to do research in this side of the story, I would go with learning some (network) information theory, networking (protocols, TCP, etc), stochastic optimization, etc.

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