This document summarizes research on applying compressive sampling (CS) techniques to synchrophasor data communication. CS can reduce bandwidth requirements by reconstructing synchrophasors at a higher rate from a sub-Nyquist reporting rate. Simulation results show CS enables reconstruction of phasor dynamics from sub-Nyquist data with errors below IEEE standards, allowing system monitoring with lower bandwidth. The research aims to improve wide area monitoring systems by applying CS to transmit synchrophasor data over long distances using less network bandwidth.

1. Sarasij Das
The University of Western Ontario, Canada
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2. 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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3.  Synchrophasor communication
 Aim
 Basic Theory
 Results
 Conclusion
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4.  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

5.  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

6.  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


7.  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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8. Use of Compressive Sampling for synchrophasor
communication
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9.  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 N
y f  


1 1N N N N
f x  
 
y x A x  

10.  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 N
y x A x      
 
1m
y 
1
0
0
0
0
0
0
N
N Z e r o
x
N Z e r o

 
 
 
 
 
 
 
 
 
 
 
  
Example

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PMU PMU PMU PMU
Substation PDC Substation PDC
Super-PDC (Control Center PDC)
Substation-PDC
Substation-PDC

12.  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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13.  Practical Synchrophasors = Near-Sparse
 CS should be designed considering sparsity
of synchrophasors
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14.  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

15.  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

16. • 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)

17. 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 * co s( )] co s( )]m x a
X X k t k t     

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Maximum TVE = 0.32%

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22.  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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23. Thank You
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