Time-Domain Harmonic State Estimation Using Filtered

Measurements based on Fourier Transform for Unbalanced Power

System Conditions Ismael Molina-MorenoAurelio Medina-Ríos

Rafael Cisneros-Magaña

AgendaO IntroductionO ProposalsO ResultsO Conclusions

IntroductionO Harmonic state estimation (HSE) has

conventionally been formulated in the frequency-domain, i.e. using power quality meters. However, it is possible doing similar analysis in the time-domain, i.e. using voltage and current waveform meters.

O Power quality meter has two main parts: data acquisition systems (DAQ) and a processing units to determine the harmonics components. So, if only the DAQ is used then the meters become more economical.

IntroductionO The estimation implies a limited

number of monitoring devices, so the placement of them is another challenge task. Prior works have not considered this limitation.

O The initial state is also required by prior methodologies due to formulation is based on numerical integration methods.

IntroductionO A particular prior technique in the

time-domain for HSE has been based on Kalman Filter.

O This methodology requires the harmonic sources, the error matrices associated with the measuring process and the plant model.

O The optimal meter placement and the initial state are also required.

Proposed methodologyO The proposed methodology to estimate

the harmonic state is shown in Fig. 1.

O Time-domain harmonic state estimation (TDHSE) is in the discrete time and is based on filtered measurements.

Proposed methodologyO The proposed methodology to estimate

the harmonic state is shown in Fig. 1.

O Time-domain harmonic state estimation (TDHSE) is in the discrete time and is based on filtered measurements.

Proposed methodologyO The mathematical formulation for

the proposed methodology is given in (1) and (2)

O k is de kth sample. N samples are taken to complete a cycle.

O The first step is to filter z to mitigate the error e.

Proposed methodologyO The filter is based on Fourier transform:O Function represented by Fourier coefficients

O In the discrete time-domain

O The key consist in consider only the harmonic coefficients of interest when the measurement be rebuilt

Proposed methodologyO The second step is develop a mathematical formulation

to relate the measurements with state variable in the discrete-time.

O To discretize the continuous time differential equations, the central method is used

O Preliminary results have been reported in the North American Power Symposium 2015.

O The proposed method has been extended to unbalanced case where it is necessary model the network by a three-phase circuit.

ResultsO 12 measurements

instead of 27 to obtain similar results.

O Unbalanced condition.

ConclusionsO A methodology for time domain harmonic state estimation for

unbalanced case assessment in power networks using filtered measurements based on Fourier transform has been proposed.

O The performance of the proposed methodology has been validated through direct comparison of the estimated state variables against the actual variables response. In all the analyzed cases a close agreement between the estimated and the actual response has been achieved.

O The proposed methodology does not require an accurate previous knowledge of the harmonic sources nor initial conditions. It only needs of a snapshot of voltage and current during at time interval of interest to estimate the harmonic state.

O Although the accuracy of estimation depends on device placement, the error due to location has been relatively small, i.e. for the analyzed cases it has been kept below 0.23%.