I just linked a new paper in our reports section entitled Hamiltonian control design for DC microgrids with stochastic sources and loads with applications. This paper resulted from a collaboration between Sandia, Michigan Tech, and myself at OptimoJoe.
The paper itself is the combination of a few different pieces of work. First, we describe a very cool hardware setup that Sandia constructed in order to test ideas regarding microgrids. Second, we discuss how to model these microgrids using Kirchhov circuit laws. Now, part of the reason why these models are nice is that it enables us to formulate an optimal control problem, so that we can improve and optimize the performance of the microgrid. For example, we may want to minimize the dependency of the microgrid on our storage devices, which are essential, but costly in terms of losses. Alternatively, we may want to minimize the parasitic losses. In addition, we describe a modular setup on how to divide the microgrid into discrete components that we can quickly combine into new configurations. This vastly simplifies the formulation of the optimal control formulations. Basically, given a microgrid configuration, we can automatically generate a new optimal control problem.
On the optimization side, we solved each of the optimal control problems using Optizelle. Since these were fully constrained optimization problems, which contain both equality and inequality constraints, we used the composite-step trust-region SQP algorithm combined with a primal-dual interior point method. In short, things worked well and we were able to generate solutions quickly and accurately. I will mention that microgrid optimization is a nice application area for optimization. Basically, these are ODE constrained optimization problems, which are slightly easier to solve structurally than PDE constrained optimization problems, since they lack a spatial domain, but still contain some interesting nuances that make them fun to work with.
In any case, both the Sandia and MTU groups were easy to work with and very knowledgeable. If anyone is looking to do some exploratory research in microgrids, they’re a great crowd to know. And, of course, if any other groups are looking to solve some optimal control or design problems related to microgrids, I consult as well.