research highlights
A Low-Rank Matrix Approach for the Analysis of Large Amounts of
Power System Synchrophasor Data
by Dr. Joe Chow ([email protected]) and Dr. Meng Wang ([email protected])
With the installation of many new multi-channel phasor measurement units (PMUs), utilities and power
grid operators are collecting an unprecedented amount of high-sampling-rate measurements of bus
frequency, bus voltage phasor, and line current phasor with accurate time stamps. The data owners are
interested in efficient algorithms to process and extract as much information as possible from such data
for real-time and off-line analysis. Traditional data analysis methods typically analyze one channel of PMU
data at a time and then combine the results from the individual analysis to arrive at some conclusions. We
proposed a spatial-temporal framework for efficient processing of blocks of PMU data. A key property of
these PMU data matrices is that they are low rank. Using this low-rank property, various data management
issues such as data compression, missing data recovery, data substitution detection, and disturbance
triggering and location can be processed using singular-value based algorithms and convex programming.
Fig. 1 illustrates data management through processing spatial-temporal blocks of PMU data. Figs. 2-4
illustrate the low-rank property of PMU data blocks from PMU data obtained from six multi-channel
PMUs deployed in the Central New York (NY) Power System (Fig. 2). Six PMUs measure thirty-seven bus
voltage and line current phasors in total. Fig. 3 shows the current magnitudes of PMU measurements
in twenty seconds at a rate of thirty samples per second. Fig. 4 shows the singular values of the data
matrix. Despite its high dimensionality (37 by 600), the number of significant singular values is very small.
Therefore, the data matrix can be approximated by a low-rank matrix.
0-5ÅDATAÅPOINTS
3PACE
0-5ÅCHANNELS
(ISTORICALÅBLOCK
.9Å0-5SÅ
q
.%Å0-5SÅ
q
q
q
12
8
1
2
3
E
A
Stability
interfaces
C
7
2EALÅTIME
$ISTURBANCEÅ
4
RELATEDÅTOÅ$ISTURBANCEÅ
Fig. 1 - Spatial-temporal PMU data blocks
for multiple tasks
Interface
to external
system
10
B
5
D
9
0
5
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time(s)
To load center
Fig. 2 - Locations of Six PMU ́