1. No category

University of Florida
March 19, 2105
Synchronized Phasor Measurement Data and
their Applications in Power Systems
Joe H. Chow
Professor, Electrical, Computer, and Systems Engineering
CURENT ERC Campus Director
Rensselaer Polytechnic Institute
chowj@rpi.edu
Topics
• NSF/DOE CURENT ERC
• Phasor measurement mechanism
• PMU data applications
• Phasor-only state estimation across power control regions
• Phasor data management using low rank matrices and
matrix completion algorithms
• Voltage stability analysis of wind farms using synchronized
phasor data
• Wide-area control with variable data latency
• Generator damping torque assessment from
measurements
University of Florida PMU Seminar
March 2015 JHC
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CURENT – NSF/DOE ERC
• Center for Ultra-Wide Area Resilient Electric Energy
Transmission Networks
• One of only two ERCs funded jointly by NSF and DOE.
• CURENT is the only ERC devoted to wide area controls and
one of only two in power systems.
• Partnership across four universities in the US and three
international partner schools. Many opportunities for
collaboration.
• Presently CURENT has over 20 industry members.
• Center began August 15, 2011
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CURENT Leadership
Council of Deans
Industry Advisory Board
Director
K. Tomsovic, UTK
Scientific Advisory Board
Administrative Director
Deputy Director
Y. Liu, UTK
Internal Academic Board
Technical Director
F. Wang, UTK
ERC Research Thrusts
Education & Diversity Program
Monitoring
F. Li, UTK
Y. Liu, UTK
Pre-College & Assessment
Program C. Chen, UTK
Modeling
A. Abur, NEU
Control
Innovation & Industrial
Collaboration Program
J. Chow, RPI
B. Trento, UTK
T. King, UTK
Actuation
F. Wang, UTK
Engineered Systems
L. Tolbert, UTK
UTK Campus
Director
RPI Campus
Director
NEU Campus
Director
TU Campus
Director
THU Campus
Director
UWA Campus
Director
NTUA Campus
Director
L. Tolbert
J. Chow
A. Abur
G. Murphy
Y. Min
C. Canizares
N. Hatziargyriou
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CURENT Engineering Research Center
• Program elements include:
• Outreach (K-12 education) – summer camps
• Research experience for undergraduates
• Entrepreneurship training
• Industry program
• Systems engineering approach
• International collaboration
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US Wind and Solar Resources
Wind
Population
Best wind and solar sources are
far from load centers.
Transmission networks
must play a central role in
integration.
Solar
http://www.eia.doe.gov/cneaf/solar.renewables/ilands/fig12.html
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CURENT Vision
• A nation-wide transmission grid that is fully monitored and dynamically controlled for
high efficiency, high reliability, low cost, better accommodation of renewable sources,
full utilization of storage, and responsive load.
• A new generation of electric power and energy systems engineering leaders with a
global perspective coming from diverse backgrounds.
Monitoring and
sensing
Communication
Control and
Actuation
Computation
Multi-terminal HVDC
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PMU Locations in North America
Installations:
•
1100+ PMUs
•
150+ data
concentrators
(PDCs)
New challenges:
•
Data quality
•
Networking
•
Control room
integration
•
Wide-area
monitoring &
control
Source: NASPI,
October 2013
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What is CURENT?
Wide Area Control of
PowerGrid
Grid
Power
HVDC
WAMS
PMU
Measurement
&Monitoring
FDR
Storage
Communication
Communication
Solar Farm
PSS
Responsive Load
Actuation
FACTS
Wind Farm
Generator
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Major Control Research Questions
•


•


•


•
Control objectives
Near 100% renewable penetration
Primary frequency control: frequency regulation using
renewable resources
Information flow and system monitoring
PMU data, smart meter data, …: Big data?
How do we make get the most information out of the data?
Control architecture
Ultra-wide-area control with communication systems
Integration of renewable resources
Control equipment economics and optimization
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Phasor Measurement: Introduction
• All power systems operate with 3-phase sinusoidal AC voltages
and currents at a frequency of 50 or 60 Hz
• Phase a quantities (voltages and currents) lead phase b
quantities by 120 degrees, which leads phase c by 120 degrees
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Voltage and Current Measurements
• What operators see on traditional EMS screens
• V and P,Q are sampled every 5 sec (or less frequently). An RTU will
transmit the data via modems, microwave, or internet (ICCP) directly
to control rooms or NERC Net.
• The data from different locations are not captured at precisely the
same time. However, V, P, and Q normally do not change abruptly,
unless there is a large disturbance nearby. These data can be used in
the State Estimator to validate the measured data and calculate the
non-metered voltages and line power flows.
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What is a Phasor?
• A sinusoidal signal can be represented by a cosine function
with a magnitude A, frequency ω, and phase φ.
• A is the rms value of the voltage/current signal
• A phasor (or the positive sequence value) cannot be computed
instantaneously from single data points
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Phasor Representations
• Two phasor representations

Polar coordinates:

Rectangular coordinates:
A  A j  ( A,  )
A  Are  jAim  ( Are , Aim )
• Both formats acceptable for phasor data streaming
• The frequency of the phasor is not communicated, but
normally the bus frequency is computed and sent out as a
separate data channel
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Virginia Tech PMUs
From Arun Phadke
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Measured 3-Phase Signals
Load rejection test
during generator
testing with breaker
not opening properly –
sampling at 2.88 kHz
(48 points per cycle)
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Phasor Calculation
• Sample the continuous voltage or
current signal. The figure shows 12
points per cycle (the sampling rate
is 12x60 = 720 Hz).
• Use Discrete Fourier Series
(DFS/DFT) method to compute the
magnitude and phase  of the
signal (i.e., applying DFS formula).
• Calculate magnitude and phase for
each phase of the 3-phase quantity
• Using one period of data reduces
the effect of measurement noise
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Anatomy of a PMU
f
Adapted from Ken Martin and Arun Phadke
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Using Phasors – Example 1: Flow Calculation
• From the synchronized measurement of the adjacent bus
voltage phasors at the same time instants, the P,Q flow can be
computed (linear state estimator)
V1  V2
VV
*
1 2 sin(1  2 )
I12 
, S12  V1  I12  P12  jQ12 , P12 
jX L
XL
• Note: The two voltage phasors have to be measured at exactly
the same time
• Looking at angle separation between generator and load buses
can provide a way to assess system stress
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Using Phasors – Example 2: Increase Visibility
• Suppose the voltage V2 on Bus 2 is not measured, but there is
a PMU on Bus 1 to measure V1 , I12 . Then V2 can be calculated
from
V2  V1  jX L I12
• Note: This is a direct calculation, not requiring a state
estimator solution. Thus by measuring the phasor data on a
bus, one can calculate the voltages of the neighboring buses
using the line parameters from the loadflow data .
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Using Phasors – Example 3: Interarea Oscillations
• Suppose Buses 1 and 2 are a thousand miles apart in different
control regions. A big disturbance occurs on the power system.
• By measuring the bus frequencies f1 and f 2 (separately but
synchronized), we can calculate the frequency difference
f  f1  f 2
• Any interarea oscillations of generators near Bus 1 against
generators near Bus 2 will show up in f
• This interarea mode oscillation monitoring is possible because
of the high sampling rate of the PMU (30 samples/sec).
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Using Phasors – Example 3: EI Interarea Oscillations
• The Florida event on Feb 26, 2008
• Note: the time progression of the frequency disturbance
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FNET Visualization
FDR recordings in Eastern Interconnection – Feb 2, 2008: plot of
frequencies at various locations
Prof. Yilu Liu, University of Tennessee, Knoxville
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Using Phasors – Example 3: WECC Interarea
Oscillations (much less damped 0.578 Hz mode)
2.5
-3
2
Machine Speed Difference (pu)
Angular Difference  (deg)
74
x 10
70
66
62
1.5
1
0.5
0
-0.5
-1
-1.5
58
0
50
100
150
Time (sec)
200
250
-2
300
0
50
Swing Component of Angular Difference (deg)
Quasi-Steady State of Angular Difference (deg)
70
65
60
55
50
100
150
200
Time (sec)
250
300
Quasi-steady state of angle difference
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Time (sec)
200
250
300
Machine speed difference
Angle difference between machine internal nodes
75
100
10
5
0
-5
-10
50
100
150
200
Time (sec)
250
300
Swing component of angle difference
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State Estimation and EMS Systems
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State Estimation with Synchrophasor Data
• Two possibilities
 Phasor assisted/augmented state estimation
 Phasor data only state estimation
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PMUs Enable Dynamic Visibility
Comparison of SCADA vs. PMU data for a
loss-of-generation event
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Phasor Data Only State Estimation (PSE)
• State estimation using synchrophasor data only
 How many PMUs are needed to achieve observability?
 How many PMUs are needed to achieve redundancy so
PMU data error (such as due to loss of GPS clock signal)
can be corrected, so that the PSE can be robust
 Impact of loss of PMU data on PSE
• Benefit of PSE – If a bus voltage phasor or a line current
phasor is not measured, it can be calculated from other
phasor measurements – virtual PMU data
• Dynamic state estimation – calculate the internal states of
synchronous machines
• Generator model validation and identification
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Extending Visibility
PMU
• If the PMU on Bus 1 measure the voltage phasor V1 and the
current phasor I12 , then the voltage phasor on Bus 2 can be
directly calculated as
V2  V1  jX L I12
• That is, a PMU “sees” the voltage phasor of neighboring buses
• Basis for a non-iterative linear state estimator (Phadke, Thorp,
Karimi, 1986)
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Number of PMUs for PSE Observability
• Bus voltage phasor measurements are important, but current
phasor measurements are just as important.
• In fact, to achieve PSE observability, the minimum number of
line current phasor measurements needed is half of the number
of buses, and is independent of the number of lines in the
system; in essence, half of the bus voltage phasors are
measured and the other half can be calculated from the
current phasor measurements
• For a system with 1000 buses (69, 115, 230, 345 kV), one needs
500 current phasor measurements. However, if only the 100 or
so 345 kV buses need to be monitored, then about 50 current
phasors are needed.
• In general, a PMU measures several line current phasors. Thus
a rule of thumb is to have PMUs on 1/3 of the buses (A. Abur).
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March 2015 JHC
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Phase Angle Errors in PMU Data
• RPI has worked with phasor data from over 30 (older) PMUs and have the
following observations:
 Voltage and current magnitude data are quite accurate (~1% error).
 Voltage and current phase angle errors occur in some PMUs
 “Random” jumps of 7.5 degrees or integer multiples of it, followed
by resets at a later time
 Slew/ramp with periodic resets (not the ±180 deg wrap-around
situation)
• The errors are attributed to
 Wrong phase connection to a PMU: a constant bias, trivial to correct
 Signal processing algorithms used in the PMU: off-nominal frequency
values and phase-lock loop implementation
 Error with time synchronization: GPS clock signal overload or temporary
loss of GPS signal
 Delays due to instrumentation cables and filter time constants
 Without such errors, the linear state estimator would be the ideal tool
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Phase Errors Observed in PMU Data
Persistent, random, and drift errors in PMU phase data
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Phase Angle Bias – Equations
PMU A
PMU B
PMU A at Bus 1
Voltage
Angle
PMU B at Bus 2
1  1meas   A  e
1
13  13meas   A  e
Current
Angles
 2   2meas  B  e
13
Same angle bias
variable  Afor all
PMU channels
1n  1meas
  A  e
n
1n
University of Florida PMU Seminar
2
 23   2meas
 B  e
3
23
 2 k   2mek as  B  e
2k
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Current Scaling Factors
• Line current flows have a wide range of values
 No simple “sanity check” as a voltage measurement (e.g.,
0.95-1.05 p.u.)
• Current transformers (CTs) are in general quite nonlinear
 Readings not trustworthy at low current values
• In case there are redundant measurements such as current
measurements on both ends of the line or to the same bus, it
is possible to use a scaling factor to improve the accuracy of
the line current measurements
University of Florida PMU Seminar
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Current Scaling Factors – Equations
PMU A
PMU B
PMU A at Bus 1
PMU B at Bus 2
 eI
1  c13  I13  I1meas
3
meas
I 23  I 23
 eI 23
13
Independent scaling
for each current
channel
s
 eI
1  c1n  I1n  I1mea
n
1n
Current
Magnitudes
 eI
1  c2k  I 2k  I 2meas
k
2k
Independent estimates of V3 should agree.
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RT-PSE
• NSF project to implement this phasor-only state estimator with
Grid Protection Alliance (GPA)
• New York (excluding NYC and LI) and New England
765/345/230 kV system: from Buffalo to Maine
• Connect NY and NE as a single SE – possible as NY and NE
have PMUs “looking at” buses in the other system
• The angle bias correction feature is critical – there are a few
close-by buses with angle differences of the order of 0.08
degree.
• Based on PMU data provided by NYISO and ISO-NE, the total
vector error (TVE) between the corrected voltage data and the
PSE voltage solution is normally less than 1%
• It will be implemented as an action adaptor on the GPA’s
OpenPDC for real-time operation.
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Big Data Analysis in Power Systems
• Phasor Measurement Data is considered to be a source of Big
Data in power systems
• 30/50/60 points per second, 24/7/365: GB/TB per day
• Control regions such as New York and New England, will have
about 40 PMUs each, with 6-12 data channels per PMU
• PMU data is envisioned to provide the following capabilities:
• Disturbance triggering
• Disturbance location and recognition (what kind of
disturbance, e.g., loss of generation, loss of line)
• Assessing the severity of the disturbance and its impact on
the power system
• Avoiding cascading failure in interconnected power systems
• What kind of Big Data tools can be used? Is there a Big Data
Toolbox somewhere?
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Space-Time View of PMU Data
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PMU Data Quality Improvement
• Fill in missing data
• Correct bad data
• Detect cyber attacks – beyond the routine black-hole and
gray-hole types of attacks
• Check on system oscillations
• Alarm on disturbances
• Identify what kind of disturbances using disturbance
characterization
• Figure out if there are any correlations between the
disturbances and the possibility of cascading blackouts
• Can all these tasks be done on a single platform? Singlechannel processing will be hopeless.
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PMU Data Single-Channel Analysis
• From a 2003 article with Alex Bykhovsky (ISO-NE) using PMU data from
Northfield Mountain
• Frequency at
Northfield for
loss of NE HVDC
1 pole
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PMU Block Data Analysis
• Power system is an interconnected network – data measured at
various buses will be driven by some underlying system
condition
• The system condition may change, but some consistent relationship
between the PMU data from different nearby buses will always be there
• If one gets some PMU data values at time t at a particular bus, it is
possible to estimate roughly what the PMU values at the nearby buses are.
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Low-Rank Power System Data Matrix
•
•
•
Joint work with Prof. Meng Wang at RPI
Previous work by Dahal, King, and Madani 2012; Chen, Xie,
and Kumar 2013
Example: well-known Netflix Prize problem
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Low-Rank Matrix Analysis for
Block PMU Data
• Analyze PMU data of multiple time instants collectively from
PMUs in electrically close regions and distinct control regions.
• Process spatial-temporal blocks of PMU data for




PMU data compression – singular value decomposition: keep
only significant singular values and vectors
Missing PMU data recovery – matrix completion using convex
programming
Detection of PMU data substitution – sum of a low-rank matrix
and a sparse matrix, using convex programming decomposition
algorithm
Disturbance and bad data detection – when second and third
singular values become large
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Data Compression
• A matrix 𝐿 of multiple channel PMU data for a certain time
period
• SVD:
𝐿 = 𝑈Σ𝑉 𝑇
• If 𝐿 is low rank, it can be approximated by retaining only the
largest singular values in Σ
𝐿 = 𝑈 Σ 𝑉𝑇
• Reduced storage using smaller number of singular vectors
• Reconstruct the data for each channel using the SVD formula
• Lossy compression
• Illustration: 6 frequency channels for 20 seconds (𝐿 is 6x600)
during a disturbance
• SVD of 𝐿
𝐿 = [3597.1, 0.086, 0.022, 0.010, 0.0084, 0.0078]
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Data Compression Example
original
Two SVs
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One SV
RMS error
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Missing Data Recovery Formulation
• Problem formulation: given part of the entries of a matrix,
need to identify the remaining entries
• Assumption: the rank of the matrix is much less than its
dimension
• Intuitive approach: among all the matrices that comply with
the observations, search for the matrix with lowest rank
• Technical approach: reconstruct the missing values by solving
an optimization problem: nuclear norm minimization (Fazel
2002, Candes and Recht 2009)
• Many good reconstruction algorithms are available using
convex programming, e.g., Singular Value Thresholding (SVT)
(Cai et al. 2010), Information Cascading Matrix Completion
(ICMC) (Meka et al. 2009)
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Missing Data Example
• 6 PMUs, 37 channels,
30 sps, 20 sec data
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Results: Temporal Correlated Erasures
• If a channel in a particular
PMU is lost at a particular
time, there is a probability
that 𝜏 trailing data points will
also be lost.
SVT
ICMC
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Data Substitution Attacks
• Measurements: the phasors 𝑉1 ,
𝑉2 , 𝐼12 , 𝐼23 . Estimate the phasor
𝑉3 .
• Redundancy in measurements can
be used to detect bad data.
• Cyber data attack: manipulate the
phasors 𝐼12 and 𝐼23
simultaneously.
• Can result in significant error in
the phasor 𝑉3 , yet cannot be
detected by state estimation
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Cyber Data Attacks
• Worst-case interacting bad data (Liu, Ning, & Reiter 2011)
• An intruder with the system topology information (not
necessarily, Kim, Tong, & Thomas 2013) simultaneously
manipulate multiple measurements so that these attacks
cannot be detected by any bad data detector.
• Cyber data attacks can potentially lead to significant errors to
the outcome of state estimation.
• Existing approaches


Usually protect key PMUs to avoid these attacks (Kosut, Jia,
Thomas, & Tong 2010, Kim & Poor 2011, Bobba et al. 2010, Dán
& Sandberg 2010)
Sedghi & Jonckheere 2013: Detection of cyber data attacks in
SCADA system. Assume the measurements at different time
instants are i.i.d. distributed.
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Attack model
• At each instant, the intruder injects errors to the estimation of
system states by manipulating multiple measurements.
• Voltage and current phasor measurements can be represented by
linear functions of state variables.
• The additive errors to phasor measurements are consistent with
each other and cannot be detected by bad data detectors.
• The intruder can only attack a small number of PMUs continuously.
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Attack model
• At each instant, the intruder injects errors to the estimation of
system states by manipulating multiple measurements.
• Voltage and current phasor measurements can be represented by
linear functions of state variables.
• The additive errors to phasor measurements are consistent with
each other and cannot be detected by bad data detectors.
• The intruder can only attack a small number of PMUs continuously.
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Attack model
• At each instant, the intruder injects errors to the estimation of
system states by manipulating multiple measurements.
• Voltage and current phasor measurements can be represented by
linear functions of state variables.
• The additive errors to phasor measurements are consistent with
each other and cannot be detected by bad data detectors.
• The intruder can only attack a small number of PMUs continuously.
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Assumptions
𝑀 = 𝐿 + 𝐶𝑊 𝑇 + 𝑁
Measurement under attack
• 𝐿: low-rank. From correlations in measurements.
• 𝐶: column sparse. The intruder has limited access to the system
• 𝑁: 𝑁 𝐹 ≤ 𝜀
Given 𝑀 and 𝑊, how could we identify 𝐿 and 𝐶?
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Connection to Related Work
• Xu, Caramanis, & Sanghavi 2012: Decomposition of a low-rank
matrix and a column-sparse matrix.
• Our methods and proofs are built upon those in Xu,
Caramanis, & Sanghavi 2012, with extension to general cases
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Connection to Related Work
• Mardani, Mateos & Giannakis 13: Decomposition of a lowrank matrix plus a compressed sparse matrix. Internet traffic
anomaly detection.
• Our focus: column-sparse matrices, W is arbitrary.
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Our Approach
• Find (𝐿∗ , 𝐶 ∗ ), the optimum solution to the following
optimization problem
𝐿∈ℂ
•
•
•
•
•
•
min𝑡×𝑛 𝐿
𝑡×𝑝
,𝐶∈ℂ
∗
+𝜆 𝐶
1,2
s.t. 𝐿 + 𝐶𝑊 𝑇 − 𝑀
𝐹
≤ 𝜀 (1)
𝐿 ∗ : sum of singular values of 𝐿
𝐶 1,2 : sum of column norms of 𝐶
Compute the SVD of 𝐿∗ = 𝑈 ∗ Σ ∗ 𝑉 ∗ †
Find column support of 𝐷∗ = 𝐶 ∗ 𝑊 𝑇 , denoted by ℐ∗
Return 𝐿∗ , 𝑈 ∗ , and ℐ∗
(1) is convex and can be solved efficiently.
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Theoretical Guarantee
Theorem (Noiseless measurements, 𝑛 = 0)
With a properly chosen 𝜆, the solution returned by our method
1. identifies the PMU channels under attack.
2. identifies the measurements that are not attacked.
3. recovers the correct subspace spanned by actual phasors.
Theorem (Noisy measurements, 𝑛 ≠ 0)
With a properly chosen 𝜆, the solution returned by our method
is sufficiently close (with distance depending on the noise level)
to a solution that meets 1-3.
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Numerical Results
• Simulate the case that the
intruder alters the PMU
channels that measure the
phasors 𝐼12 , 𝐼52 , 𝐼13 , and 𝐼43 .
• The voltage phasor estimates of
Buses 2 and 3 are corrupted
Actual values and corrupted values
University of Florida PMU Seminar
Column norms of the recovered error matrix
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Disturbance Detection using PMU Data and
Singular Value Analysis
• Organize PMU date into different regions, like Central New York,
West NY, North NY, etc.
• Analyze voltage magnitude or frequency channels from PMUs
in a region with Singular Value Decomposition (SVD)
• Steady state: relationships between measurements at different
PMUs remain the same → one large singular value, and the
rest are very small singular values
• During a disturbance, the relationships between different
PMUs will start to differ → 2nd and 3rd largest singular values
will increase
• Disturbance location: region with the largest 2nd largest
singular value
• Analysis and plots by Josh Klimaszewski and Tony Jiang
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Disturbance 2 (Voltage Magnitudes)
2nd largest SV
Window Size (3.33 seconds/100 samples)
Step Size (1.66 seconds/50 samples)
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March 2015 JHC
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Disturbance 2 (Voltage Magnitudes)
2nd largest SV
Window Size (3.33 seconds/100 samples)
Step Size (1.66 seconds/50 samples)
2nd largest SV
Window Size (.67 seconds/20 samples)
Step Size (.67 seconds/20 samples)
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March 2015 JHC
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Voltage Stability Analysis of A Wind Hub
• Voltage stability analysis of a wind hub in the BPA
service area



Wind farms tend to be integrated to sub-transmission
(115/230 kV) networks
Some of these renewable integration seem to be lacking
reactive power support, i.e., power transfer is voltage
stability limited
PMU/SCADA data is used to develop Thevenin equivalents
• AQ-bus voltage stability analysis method


For quasi-steady state voltage stability analysis
An alternative to the Continuation Power Flow Method
University of Florida PMU Seminar
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BPA Wind Hub Diagram
G
Thévenin equiv.
(swing bus)
G
Thévenin equiv.
Measurements
Edge of the
observable
network
AQ bus (negative load)
PQ
PQ
PV
PQ
PQ
PV
Unobservable
Credit: E. Heredia, D. Kosterev, M. Donnelly, “Wind Hub Reactive
Resource Coordination and Voltage Control Study by Sequence Power
Flow,” 2013 IEEE PES General Meeting, July 2013.
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Voltage Variations with Outage of Strong Link
• SCADA data showing
voltage response on
Buses 21, 22, and 25,
with Line 22-25 out of
service. The voltage
jumps are WTG trips.
• The project is to
determine wind turbine
reactive power control
models and voltage
stability limit.
• The wind farms cannot
produce full output in
this scenario.
Capacitor
switchings
~ 3 hours
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Estimating Wind Plant Models and Shunts
•
•
•
•
Compute ΔQ and ΔP from measurements
Using ΔP, calculate maximum possible ΔQ from WT (threshold value)
If ΔQ is larger than the WT threshold, shunt switching is detected
Compute the total ΔQ due to shunt switching, quantize according to shunts
0.05
-0.05
WT Reactive Power (p.u.)
WT Reactive Power (p.u.)
0
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
Measurements
Measurements w/ est. shunt Q removed
PQ model
-0.4
-0.45
0
0.2
0.4
0.6
0
-0.05
Shunt action
-0.1
-0.15
-0.2
Measurements
Measurements w/ est. shunt Q removed
PQ model
-0.25
0.8
WT Active Power (p.u.)
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0
0.2
0.4
0.6
0.8
1
WT Active Power (p.u.)
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BPA JC VS Analysis
• 24-hour data at 2-second intervals
 SCADA data at JC: V,P,Q, and also V at East and West Buses
• No shunt capacitor information at the wind farms
• Intent is to perform offline computation on a daily basis to
verify the reliability and usefulness of the computation
algorithm before considering the tool for real-time
information support
• Performs a new VS margin calculation every 5 minutes




Complex code to figure out the shunt compensation in the wind
farms
The AQ-technique works well, readily going beyond the voltage
collapse point
Thevenin equivalent estimation (ETH and XTH) is difficult during
periods when the voltages and flows are stationary or vary
widely.
24-hour data requires about 15 minutes to compute
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BPA JC 24-hr VS Analysis
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Wide-area Monitoring and Control
Slide 1 - Vision
Monitoring and Sensing
Communication
Control and Actuation
Computation
RTO
Regional Transmission Organization
credit: NPR & UTK
Proposal 1041877
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Wide-area Networked Control with PMUs
• Closed-loop control using remote phasor measurements
 Measurement filter delays
 Communication issues: packet loss, network congestion
100-200 ms total delay
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Estimate of Data Latency
From Dr. Innocent Kamwa, IREQ
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Adaptive Wide-area Controller
• Adaptive controller to account for time-varying data latency [1]:
• Multiple phase-lead compensators:



Each compensator tuned for a specific level of latency
Measure incoming data latency using GPS time stamps
Switch between compensators according to measured data latency
[1] J. H. Chow and S. G. Ghiocel, “An Adaptive Wide-Area Power System Damping
Controller using Synchrophasor Data,” in Control and Optimization Methods for
Electric Smart Grids, pp. 327-342. Editors: A. Chakrabortty and M. Ilic. New York,
NY: Springer Science+Business Media, 2012.
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Compensator Design
• Each compensator is designed for a fixed delay (Td ):
• Compensators are selected based on the incoming data
latency, such that:
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Adaptive Algorithm
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Delay-Based Compensator Switching
Question: how
long should the
adaptive
control wait to
switch to a
lower latency
controller?
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Proof of Stability
• Proof of stability using the concept of average dwell time
( d):
• Considering switched-delay systems of the form:
where  (t ) is the switching signal.
• Find a minimum  d that guarantees stability of the system
• Proof provided by Dr. Farshad Pour Safaei and Prof. Joao
Hespanha of UCSB
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Linear Matrix Inequalities
• Consider a set of linear matrix inequalities (LMIs) for
all controllers:
• Solve an LMI feasibility
problem for a fixed
value of
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Average Dwell Time
• The feasibility of the LMIs guarantees stability for a minimum
average dwell time
where:
• Proof: Choose Lyapunov function such that
• Lyapunov function decreases at switching instants:
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Example Two-Area System
• Dampen inter-area oscillations between Areas 1 and 2
• Control action is applied to a TCSC on an intertie between the
areas
• Use remote signals with latency, measured near the
generators (average angle in each area)
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Computation of Average Dwell Time
• The average dwell time can be computed for an
arbitrary number of controllers.
• For the controllers in the two-area example, the
average dwell time is computed by solving the LMI
feasibility problem and minimizing using a line
search.
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Simulation
• The two-area system was simulated using a random
latency applied to the remote signals:
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Comparison to Previous Work
• B. Demirel, C. Briat, and M. Johansson, “Deterministic and
stochastic approaches to supervisory control design for
networked systems with time-varying communication delays,”
Nonlinear Analysis: Hybrid Systems, 10 (2013) 94–110:
proposes a similar result
 Demirel’s ADT is less conservative than ours.
 The formulation here is simpler.
University of Florida PMU Seminar
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Damping assessment using relative phase
information from PMU data
• Power systems with long transmission lines for power
transfer tend to have lightly damping interarea modes, e.g.,
Western US power system (WECC), Nordel power grid
• The interarea mode damping is achieved by application of
power system stabilizers (PSSs) on multiple generators.
• Unfortunately, some of these PSSs may be poorly tuned
because the interarea mode shapes have changed.
• As a result, WECC wants to develop model identification
techniques for generators, excitation systems, and PSSs, so
that the damping contribution to the interarea modes can
be properly assessed.
• However, generator testing requires taking it off-line, which
can be costly.
University of Florida PMU Seminar
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Damping assessment using relative phase
information from PMU data
• Is it possible to assess the damping contribution of a
particular generator (with its PSS) by measuring disturbance
or ambient response?
• We have recently developed a technique using linearized
power system models to assess such damping contributions
• The method looks at the phase differences between the
generator rotor angle (or speed) and its terminal bus angle
(or frequency)
• The method can be applied to disturbance simulation or
PMU data (requiring methods such as Prony, Eigensystem
Realization Algorithm, or N4SID to extract the modal
components)
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Linearized Model Block Diagram of a SingleMachine infinite-Bus System


Heffron and Phillips
de Mello and Concordia
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Synchronizing and Damping Torque
Decomposition - SMIB
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Interarea Mode Damping Result
• For each generator, find the phase difference between the
interarea mode content of the terminal bus voltage angle and the
generator angle, for example, for generator 1:
 m1   m1
• If this difference is
• Positive and large, then PSS contributes good damping
• Negative, then this machine is contributing negative damping torque
• Positive but small – need to look at the setting of the PSS
• The damping for each generator is assessed using its own
measurements
• To apply the method in real time – after any disturbance resulting
in sustained interarea mode oscillation, use the PMU data to check
this phase difference for all critical generators. Note that the rotor
angle can be measured with a regular digital recording device.
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WECC Simulation
• A BPA engineer provided a disturbance scenario with
significant oscillations
• 2 cases for the scenario:
• No PSS’s
• A few PSS’s turned on
• RPI was provided with the time response of a selected set of
generators (rotor angle, rotor speed, generator terminal bus
angle, generator terminal bus frequency).
• RPI was not told which generators had the PSS turned on.
The intent is to use the modal angle difference to find those
generators with their PSS’s turned on.
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Case 1: All PSS’s off
Case 1 OFF
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
0.3
0.2
0.1
10
Rot or angle (rad)
0.4
15
20
25
30
60.1
35
5
10
15
20
25
T ime (sec)
Time (sec)
Case 1 OFF
Case 1 OFF
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
0.3
0.2
0.1
0
-0.1
30
1.008
35
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
1.006
1.004
1.002
1
0.998
-0.2
0
60.2
59.9
0
Rot or Speed (pu)
5
60.3
60
0
0
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
60.4
Bus Freq (Hz)
Bus angle (rad)
Case 1 OFF
5
10
15
20
25
30
35
0
10
30
T ime (sec)
T ime (sec)
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Case 1: A Few PSS’s On
Case 1 ON
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
0.3
0.2
0.1
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
60.4
Bus Freq (Hz)
Bus angle (rad)
Case 1 ON
60.3
60.2
60.1
60
0
0
5
10
15
20
25
30
35
0
5
10
T ime (sec)
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
0.3
0.2
0.1
0
-0.1
-0.2
10
15
20
25
25
30
30
35
1.008
Rot or Speed (pu)
Rot or angle (rad)
0.4
5
20
35
Time (sec)
Case 1 ON
Case 1 ON
0
15
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
1.006
1.004
1.002
1
0.998
0
10
30
T ime (sec)
T ime (sec)
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Case 1: All PSS’s Off – Gen 1
blue: term. bus angle, green: rotor angle
blue: term. bus frequency, green: rotor speed
1.01
0.45
0.4
0.35
1.005
0.3
0.25
1
0.2
0.15
0.1
-5
0
5
10
15
20
25
30
35
40
University of Florida PMU Seminar
0.995
-5
0
5
10
March 2015 JHC
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20
25
30
35
40
90
Test Case Results
• For each generator, compute the relative phase change
between no PSS on to some PSS’s on.
• Machines with large phase increases have effective PSS’s
Generator
Angle diff change (deg)
PSS
1
3.03
N
2
12.09
Y
3
11.21
Y
4
1.79
N
5
1.11
N
6
5.00
7
5.24
8
-0.03
N
9
12.29
Y
10
-6.80
N
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References
•
•
•
•
•
•
L. Vanfretti, J. H. Chow, S. Sarawgi, and B. Fardanesh, “A Phasor-Data Based
Estimator Incorporating Phase Bias Correction,” IEEE Transactions on Power
Systems, vol. 26, no. 1, pp. 111-119, Feb. 2011.
S. G. Ghiocel, J. H. Chow, G. Stefopoulos, B. Fardanesh, D. Maragal, M. Razanousky,
and D. B. Bertagnolli, “Phasor State Estimation for Synchrophasor Data Quality
Improvement and Power Transfer Interface Monitoring,” IEEE Transactions on Power
Systems, vol. 29, no. 2, pp. 881-888, 2014.
M. Wang, P. Gao, S. Ghiocel, and J. Chow, “Modeless Reconstruction of Missing
Synchrophasor Measurements,” accepted for publication in IEEE Transactions on
Smart Grid.
M. Wang, el al., “Identification of “Unobservable” Cyber Data Attacks on Power
Grids,” presented at the IEEE SmartGridComm, Venice, November 2014.
M. Wang, el al., “A Low-Rank Matrix Approach for the Analysis of Large Amounts of
Power System Synchrophasor Data,” presented at HICSS, Lihue, January 2015.
S. G. Ghiocel and J. H. Chow, “A Power Flow Method using a New Bus Type for
Computing Steady-State Voltage Stability Margins,” IEEE Transactions on Power
Systems, vol. 29, no. 2, pp. 958-965, 2014.
University of Florida PMU Seminar
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References
•
•
•
•
•
•
S. G. Ghiocel, J. H. Chow, R. Quint, D. Kosterev, and D. J. Sobajic, “Computing
Measurement-Based Voltage Stability Margins for a Wind Power Hub using the AQBus Method,” Proc. of Power and Energy Conference at Illinois (PECI), 2014.
S. G. Ghiocel, J. H. Chow, G. Stefopoulos, B. Fardanesh, D. Maragal, D. B. Bertagnolli,
M. Swider, M. Razanousky, D. J. Sobajic, and J. H. Eto, “Phasor-Measurement-Based
Voltage Stability Margin Calculation for a Power Transfer Interface with Multiple
Injections and Transfer Paths,” Proc. of Power System Computation Conference,
Wroclaw, Poland, 2014.
NASPI Voltage Stability Workshop Oct. 22, 2014:
https://www.youtube.com/watch?v=LBXvjv0XnuA&feature=youtu.be
J. H. Chow and S. G. Ghiocel, “An Adaptive Wide-Area Power System Damping
Controller using Synchrophasor Data,” in Control and Optimization Methods for
Electric Smart Grids, pp. 327-342. Editors: A. Chakrabortty and M. Ilic. New York, NY:
Springer Science+Business Media, 2012.
F. R. Pour Safaei, S. G. Ghiocel, J. P. Hespanha, and J. H. Chow, “Stability of an
adaptive switched controller for power system oscillation damping using remote
synchrophasor signals,” Proceedings of the 2014 IEEE Conference on Decision and
Control, Los Angeles, Dec. 2014.
X. T. Jiang, J. H. Chow, F. Wilches-Bernal, “A Synchrophasor Measurement Based
Method for Assessing Damping Torque Contributions from Power System
Stabilizers,” submitted to 2015 Power Tech Conference, Eindhoven.
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Acknowledgements
This work was supported primarily by the ERC Program of the
National Science Foundation and DOE under NSF Award Number
EEC-1041877. Other US government and industrial sponsors of
CURENT research are also gratefully acknowledged.
Other industry/agency collaborators: NYPA, NYSERDA, Hitachi,
Grid Protection Alliance, BPA, SCE, GCEP, ORNL
Phasor Measurement Process
60 Hz
Component
Timing
GPS
DFT
Frequency & Rate-ofChange Frequency
Algorithm
SYMMETRICAL
DFT
COMPONENT
Frequency
dfreq/dt
TRANSFORMATION
Phasors
DFT
Time synchronized sampling
of three phase waveform.
REAL TIME
DATA OUTPUT
12 samples/cycle (720/sec)
Discrete Fourier Transform
uses 12 samples for each
phasor conversion.
Disturbance and
transient detectors,
data table storage
Trigger
flags
Ken Martin
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