A charge protection circuit with a timing function is disclosed. The systems and methods relate to selecting a centroid document from a group of structured documents, selecting a subset of the group of structured documents in order to form a cluster of the subset of documents about the centroid document. The primary angle preferably satisfies the condition arcsin, where d is a width of the waveguide and is a wavelength of the primary beam. The invention also discloses methods for black start of the dchp during a mains power loss, and also modification of the operating voltage on start up of electrical equipment during a power loss, to prevent the Stirling engine stalling.