  Ad hoc electrical networks are formed by connecting power sources and loads
without planning the interconnection structure (topology) in advance. They are
designed to be installed and operated by individual communities---without
central oversight---and as a result are well-suited to addressing the lack of
electricity access in rural and developing areas. However, ad hoc networks are
not widely used, and a major technical challenge impeding their development
(and deployment) is the difficulty of certifying network stability without a
priori knowledge of the topology. We develop conditions on individual power
sources and loads such that a microgrid comprised of many units will be stable.
We use Brayton-Moser potential theory to develop design constraints on
individual microgrid components that certify transient stability---guaranteeing
that the system will return to a suitable equilibrium after load switching
events. Our central result is that stability can be ensured by installing a
parallel capacitor at each constant power load, and we derive an expression for
the required capacitance.
