Time domain harmonic state estimation using filtered measurements based on fourier transform for unbalanced power system conditions

1. Time-Domain Harmonic State Estimation
Using Filtered Measurements based on
Fourier Transform for Unbalanced Power
System Conditions
Ismael Molina-Moreno
Aurelio Medina-Ríos
Rafael Cisneros-Magaña

2. Agenda
O Introduction
O Proposals
O Results
O Conclusions

3. Introduction
O 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.

4. Introduction
O 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.

5. Introduction
O 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.

6. Proposed methodology
O 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.

7. Proposed methodology
O 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.

8. Proposed methodology
O 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.

9. Proposed methodology
O 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

10. Proposed methodology
O 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.

11. Results
O 12 measurements
instead of 27 to obtain
similar results.
O Unbalanced condition.

12. Conclusions
O 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%.