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Background:  Smart grid systems require high-quality phasor measurement unit (PMU) data for proper operation, control, and decision-making. Missing PMU data may lead to improper actions or even blackouts. While the conventional cubic interpolation methods based on the solution of a set of linear equations to solve for the cubic spline coefficients have been applied by many researchers for interpolation of missing data, the computational complexity increases non-linearly with increasing data size.    Methods:  In this work, a modified recurrent equation-based cubic spline interpolation procedure for recovering missing PMU data is proposed. The recurrent equation-based method  makes the computations of spline constants simpler. Using PMU data from the State Load Despatch Center (SLDC) in Madhya Pradesh, India, a comparison of the root mean square error (RMSE) values and time of calculation (ToC) is calculated for both methods.    Results:  The modified recurrent relation method could retrieve missing values 10 times faster when compared to the conventional cubic interpolation method based on the solution of a set of linear equations.  The RMSE values have shown the proposed method is effective even for special cases of missing values (edges, continuous missing values).    Conclusions:  The proposed method can retrieve any number of missing values at any location using observed data with a minimal number of calculations.

Modified recurrent equation-based cubic spline interpolation for missing data recovery in phasor measurement unit (PMU)