  We present a method for joint phase identification and topology recovery in
unbalanced three phase radial networks using only voltage measurements. By
recovering phases and topology jointly, we utilize all three phase voltage
measurements and can handle networks where some buses have a subset of three
phases. Our method is theoretically justified by a novel linearized formulation
of unbalanced three phase power flow and makes precisely defined and reasonable
assumptions on line impedances and load statistics. We validate our method on
three IEEE test networks simulated under realistic conditions in OpenDSS,
comparing our performance to the state of the art. In addition to providing a
new method for phase and topology recovery, our intuitively structured
linearized model will provide a foundation for future work in this and other
applications.
