  Enhancing the spatio-temporal observability of residential loads is crucial
for achieving secure and efficient operations in distribution systems with
increasing penetration of distributed energy resources (DERs). This paper
presents a joint inference framework for residential loads by leveraging the
real-time measurements from distribution-level sensors. Specifically, smart
meter data is available for almost every load with unfortunately low temporal
resolution, while distribution synchrophasor data is at very fast rates yet
available at limited locations. By combining these two types of data with
respective strengths, the problem is cast as a matrix recovery one with much
less number of observations than unknowns. To improve the recovery performance,
we introduce two regularization terms to promote a low rank plus sparse
structure of the load matrix via a difference transformation. Accordingly, the
recovery problem can be formulated as a convex optimization one which is
efficiently solvable. Numerical tests using real residential load data
demonstrate the effectiveness of our proposed approaches in identifying
appliance activities and recovering the PV output profiles.
