Centralized node controllers in accordance with embodiments of the invention enable linear approximation of optimal power flow. One embodiment includes a centralized node controller including: a network interface, a processor, and a memory containing: a centralized power control application a network topology, where the network is multiphase unbalanced and comprises a plurality of connected nodes; wherein the processor is configured by the centralized controller application to: request node operating parameters from the plurality of connected nodes; calculate network operating parameters using a linear approximation of optimal power flow and the node operating parameters from the plurality of connected nodes; send network operating parameters to the plurality of connected nodes.
STATEMENT OF FEDERALLY SPONSORED RESEARCH
 This invention was made with government support under DE-AR0000226/T-106986 & DE-AR0000226/T-107186 awarded by the Department of Energy. The government has certain rights in the invention.