In existing estimation methods for utility harmonic impedance,it is commonly assumed that the harmonic impedance remains invariant,which often diverges from actual conditions. In practice,both the utility harmonic impedance and background harmonics typically time-varying with operating conditions. For the time interval between two sample points,large numerical value probably gives rise to more conspicuous difference between the impedance and the background harmonics at the corresponding time. Based upon the information of the sample points with a far gap,it is difficult to estimate the impedance value of the sample points of concern. As a consequence,a brand new time-varying utility harmonic impedance estimation method is put forward based on locally-geographically weighted regression. Firstly,a weight matrix is constructed based on time interval,assigning smaller weights to sample points with larger intervals from the points of interest. Locally weighted regression (LWR) is then applied to initially estimate the utility harmonic impedance and background harmonic reference values. Secondly,the impedance reference value is used to modify the regression equation to reduce the under determination of the original regression equation. To screen out the sample points that are similar to the background harmonics of the sample points of concern,the background harmonic reference value is simultaneously utilized as the prior information. On the basis of the screened samples,the background harmonic voltage and the utility harmonic impedance at each point are coped well with by geographically weighted regression (GWR). Under strong background harmonic fluctuations,the recommended method can not only identify abrupt changes in impedance,but also estimate the trend of utility harmonic impedance. Lastly,simulation and case studies demonstrate that the proposed method improves estimation accuracy by approximately 40% compared to traditional constant harmonic impedance estimation methods,and by around 30% compared to existing time-varying impedance estimation methods.