Sarasij Das The University of Western Ontario, Canada

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This presentation is based on the following papers

Sarasij Das and Tarlochan Sidhu. ‘Application of Compressive Sampling in

Synchrophasor Data Communication in WAMS’, IEEE Transactions on Industrial

Informatics, http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6553079

Sarasij Das and Tarlochan Sidhu. 'Reconstruction of Phasor Dynamics at

Higher Sampling Rates using Synchrophasors Reported at Sub-Nyquist Rate.'

Innovative Smart Grid Technologies (ISGT), 2013 IEEE PES, 24-27 Feb 2013,

Washington, D.C

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Synchrophasor communication

Aim

Basic Theory

Results

Conclusion

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Dedicated networks preferred due to security

Utility substations located geographically far away

Wide area monitoring is time critical application, communication delay matters

Fibre optic preferred for low latency

Fibre optic + long distance + dedicated = High cost

At present, 40-300 PMUs installed in a grid

Number of installed PMUs increasing at higher rates (1000-10000 in future)

Higher reporting rate (>60 frames/s) limited by available bandwidth

Higher reporting rate and larger no. of PMUs will lead to huge bandwidth requirement

Fibre optic networks are costly

Better network utilization delays requirement of network upgradation

Nyquist sampling theorem :

To avoid aliasing :

Synchrophasor reporting rate twice the maximum frequency in synchrophasor domain

System dynamics monitoring not possible with synchrophasors of Sub-Nyquist reporting rate

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2s

f f

To reduce the bandwidth requirement for synchrophasor communication

To reconstruct synchrophasors at a higher rate from a sub-Nyquist reporting rate

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Use of Compressive Sampling for synchrophasor communication

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Suppose, signal f is sampled at higher than Nyquist rate

,(y is vector of ‘N’ samples)

Sensing Matrix

f can be expressed using basis matrix

,(x is coefficient of basis )

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1 1N N N Ny f

1 1N N N Nf x

y x A x

Suppose, ‘m’ samples (corresponding to sub-Nyquist rate) are randomly selected from ‘N’ samples.

So,

If ‘x’ is sparse/near-sparse, ‘x’ can be recovered from using Compressive Sampling

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1 1 1m m N N N N m N Ny x A x

1my

1

0

0

0

0

0

0

N

N Z e ro

x

N Z e ro

Example

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PMU PMU PMU PMU

Substation PDC Substation PDC

Super-PDC (Control Center PDC)

Substation-PDC

Substation-PDC

PMUs use low pass filters to remove high frequencies from estimated synchrophasors

Std C37.118.1-2011 considers synchrophasor domain oscillations up to 5 Hz

1-3 oscillation modes (dominant) usually appear simultaneously in synchrophasor domain

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Practical Synchrophasors = Near-Sparse

CS should be designed considering sparsity of synchrophasors

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Block coding : Compresses block of data and transmits

Issues with block coding are

- 1 packet loss means loss of multiple phasors

- Additional communication delays

- Need additional processing capability at PMU

Adaptive coding : Compresses and transmits data as soon as generated

Issues are

- Compression ratio low (usually 1.5-2)

- Overall bandwidth savings low due to

communication payloads

- Need additional processing capability at PMU

• Interpolation assumes a signal structure

• Interpolation affected by noise

• Missing data aggravates interpolation

• Consider:

- Bandwidth saving 4

- Phasor reporting rate of PMU 5 frames/s

- Phasor receiving rate@ PDC 20 frames/s

- Interpolation not possible (violation of

Nyquist theorem)

Modulation

frequency

(Hz)

Maximum TVE (%)

Spline Cubic Fourier

Interpolation

CS

5 24 12 7 1

• Synchrophasor reporting rate 10 frames/s

• Synchrophasors reconstructed at PDC 30 frames/s

* IEEE C37.118.1-2011 : specifies maximum 5 Hz

modulation frequency

[1 * c o s ( )] c o s ( )]m x a

X X k t k t

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Maximum TVE = 0.32%

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CS performs satisfactorily during oscillations, large step changes, exponentially decay and steady state

System dynamics monitoring also be possible with sub-Nyquist rate

CS reduces bandwidth requirements

Please consult the papers for more results

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Thank You

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