The number of measurements is often smaller than that of states in harmonic state estimation (HSE). This is a difficulty in HSE

which makes the measurement-state equation underdetermined

and the system incompletely observable. In light of the problem

three aspects are studied. Firstly

the equation is turned from underdetermined to determined or even overdetermined by combining mathematical analysis and power system analysis

and proceeding from reducing the quantity of states. On the premise that system complete observability

is ensured

the number of measurement will be greatly reduced. Secondly

singular value decomposition (SVD) is applied to finding the observable islands and their calculation. Thirdly

by referring to the matrix condition number

a practical linearly independent ranking method is proposed. The method is applied to guiding the adjustment and increase of equipment to realize fine observability. Finally

the Heze-Fangshan 220 kV-110 kV-35 kV distribution system is presented to illustrate the application of SVD and the proposed method. This work is supported by National Natural Science Foundation of China (No. 11201179).