  The non-linearity and non-convexity of power flow models and the phase
coupling challenge the analysis and optimization of unbalanced distribution
networks. To tackle the challenges, this paper proposes an online
feedback-based linearized power flow model for unbalanced distribution networks
with both wye-connected and delta-connected loads. The online feedback-based
linearized model is grounded on the first-order Taylor expansion of the branch
flow model, and updates the model parameters via online feedback by leveraging
the instantaneous measured voltages and load consumption at the previous time
step. Its closed-loop nature can asymptotically mitigate the model mismatch,
thus lending itself to a good performance. In addition, exploiting the
connection structure of unbalanced radial distribution networks, we provide a
unified matrix-vector compact form of the proposed linearized power flow model.
Finally, the numerical tests on the IEEE 123-bus test system validate the
effectiveness and superiority of the proposed model. A simple optimal power
flow case is also provided to illustrate the application of the online
feedback-based linearized model.
