Power System Frequency Measurement And Its Application In Authentication Of Digital Audio Recordings

Frequency is one of the fundamental parameters of power system since it canfaithfully reflect the dynamic behavior of system generation and load. Fast and accuratefrequency estimation plays a critical role in system operation, monitoring and control.Frequency variation not only embodies system’s dynamic behaviors but contains plentyof time information. From different time scales, the variation is uniform and unique.The electric network frequency criterion (ENF) makes good use of this feature byincorporating power system frequency with forensic digital audio authentication (DAA).This paper analyzes power system frequency measurement methods and then applies thefrequency measurements in DAA on the basis of the North American power systemfrequency monitoring system FNET.Based on brief introduction of the FNET system, recursive discrete Fouriertransform (DFT) used in the second generation of frequency disturbance recorder (FDR)is deduced followed by a re-sampling strategy. The re-sampling strategy adjusts eachdata sample in one data window according to the coarse estimation given by therecursive DFT. It guarantees that the number of sample points within one cycle remainsconstant regardless of frequency change of a real voltage signal; hence, the sampling isnearly a synchronized sampling and as a consequence the frequency and voltage phasorcan be estimated accurately. Simulation results indicate that the FDR algorithm is robustto white noise and harmonics, and that the frequency tracking ability in static anddynamic condition is excellent. Further improvement of the accuracy of the FDRalgorithm lies in reduction of sinusoidal term in the phase angle estimation error,whereas the increase of sampling frequency, polynomial fitting order of phase anglesand word length of the A/D converter do not necessarily refine the accuracy.An improved frequency estimation algorithm is proposed using least squaremethod. A sampling interval parameter k is introduced, and four neighboring sampleswith interval k are adopted to establish the mathematic relationship between voltagesamples and system frequency. Noise and harmonics are considered separately whichhelps to deduce the final explicit formula for frequency estimation. The samplinginterval is the key parameter of this algorithm, and its optimal value is obtained if theproduction of signal radian frequency and sapling interval equals to π3. If thiscondition is met during estimation, the algorithm will then possess the best performance of noise and3rd-harmonics suppression. Simulation results validate this theoretical value;the performance of this proposed method is close to that of the FDR algorithm in staticscenarios, but has better frequency tracking ability. It can estimate frequency withoutiteration, and needs a few sampling points; hence, the frequency is measured in a fastermanner with a shorter time delay, which implies that the proposed method is suitable forfast frequency estimation of a short data window.An entire procedure of DAA is proposed. Robust statistical method is introduced toidentify the spikes contained in FDR raw data, and a series of B-spline basis functionsare used to replace the missing segments; an ad hoc standard power system frequencydatabase for DAA is then established when outliers are removed. An iterative oscillatorerror correction algorithm is proposed by introducing value offset and time intervaloffset, and this method overcomes mismatch problem of the extracted ENF sequenceagainst the FDR data. A two-step method for ENF estimation is used by adjusting thecurrent short-time Fourier transform. To learn the accuracy and precision of any ENFestimator, a procedure considering windowing function, zero-padding factor, noisyinfluence and frequency bin offset is proposed. Testing results indicate that the ENFestimator in this paper needs neither windowing function nor zero-padding factor, and isnearly an unbiased estimator, which avoids the intensive computation withoutcompromising the accuracy. Determination of production time of an audio recording istested by frequency database matching and the entire authentication procedure isvalidated by case studies.Phase estimation is introduced as an alternative method for DAA. Considering thenegative frequency component of the DFT output, a phase angle estimation method withhigh precision is deduced. Based on the signal derivative method for frequencyestimation, another phase estimation method using phase angle of derivative signal isproposed. Massive testing indicates that the phase information is an effective feature forthe DAA, and that the two methods can detect change near the tampering points. Bychecking the rate of change of phase sequence the tampering points can be located then.