The special Hankel matrix is structured from interharmonic sampling, which is described by state space model. A method of parameters estimation based on state space model is proposed, which can achieve interharmonics frequency, amplitude and, phase of the joint estimation. The simulation results show that the method can effectively restrain white Gaussian noise, with superior performance.
Traditional power system harmonic analysis method based on Fourier transform (FFT) has the frequency spectrum revelation and the stockade effect, so there are limitations in the detection of harmonic [
The parameter estimation method based on state space model (SSM) can inhibit the channel between any zero-mean noise, and it also improves the resolution of parameter estimation [
The interharmonics are defined as follows in IEC-61000-2-2: there is not an integer multiple signal between the frequency and the fundamental frequency in the voltage and current signal harmonic. Power system harmonics and inter-harmonic detection signal can be expressed as [
Consider the following:
Equation (
Equation (
The
The
Consider the following:
The ‘‘
Define a new matrix
Then
Consider the following:
The substitution into (
Make the following:
The algorithm steps of estimate model pole based on SSM method will be described as follows: constructing data matrix singular value decomposition with data matrix calculating the model order estimation of calculating approximation of calculating the eigenvalues of the matrix calculating inter-harmonic component of amplitude according to (
The experiment sampling signal that is inter-harmonic is described in (
Interharmonic parameters.
|
1 | 2 | 3 |
---|---|---|---|
|
0.1 | 0.2 | 0.3 |
|
0.2 | 0.4 | 0.8 |
|
|
|
|
The results of this experiment are shown in Table
White Gaussian noise, 200 simulations, and interharmonics parameter estimation bias.
SNR/dB |
|
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|---|---|
8 |
|
|
|
|
|
|
|
|
|
10 |
|
|
|
|
|
|
|
|
|
15 |
|
|
|
|
|
|
|
|
|
20 |
|
|
|
|
|
|
|
|
|
|
— | — | — |
|
|
|
|
|
|
The comparison of logarithm mean square error (MSE) of estimation frequency at different SNR between these methods with the traditional SSM algorithm is shown in Figure
Logarithm mean square error at different method and SNR.
Figure
MSE of estimation frequency at different method and SNR.
Traditional inter-harmonic detection method needs to search for peaks in the frequency domain that did not realize the frequency, amplitude, and other parameters of the joint estimation. Parameter estimation method based on SSM achieves damped frequency, damped factor of the joint estimation, which avoids the search in the frequency domain spectra with superior performance.
The authors declare that there is no conflict of interests regarding the publication of this paper.