A new quadratic form based frequency measurement algorithm

A new algorithm to measure both off-nominal and small frequency deviations is presented. The technique uses quadratic forms of sampled signals. It does not require a fixed sampling frequency. This property is very important since it leads to a simple algorithm to measure both off-nominal and small frequency deviations very accurately without requiring a look-up table. Also, because of this adaptive sampling property, the accuracy of the algorithm is immune to harmonic distortion which may be present in the signal. The algorithm is easy to implement and requires only seven multiplications per frequency estimate. The number of samples required per estimate is four. Unlike some algorithms using the same technique, the proposed algorithm is relatively insensitive to DC offsets and random noise, since it uses a data window length of a complete cycle. The method is fast since fewer estimates are needed to produce a stable result. This will accelerate the time for a tripping decision in a frequency protective relay. Some test results are presented. These results demonstrate that when random noise is present in the signal, the proposed algorithm has superior performance when compared with other algorithms using the same quadratic form based approach. Test results also show that using an adaptive sampling frequency improves the insensitivity to harmonic distortion