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Synchrophasor Analytics for Electrical TransmissionSystems
Prof S A Soman
Indian Institute of Technology Bombay
04/04/2013
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Agenda
SCADA based State Estimation
Synchrophasor Analytics
Transmission Line Parameter Estimation
Linear State EstimationSupervised Zone-3 Distance Protection
CT/CVT Calibration
Control Schemes to improve System Security
Online Vulnerability Analysis of Distance Relays
Summary
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Traditional State Estimation Implemented using SCADA technology Measurements comprise bus voltage magnitude at substations
and complex flow or injection measurements If zi is a voltage magnitude measurement at bus k, then
zi = fi(V) = eTk V
If zi is a MW bus injection measurement at bus k, then
zi = fi(V) =n
j=1
VkVj|Ykj| cos (k j kj)
The measurement vector can be written as,
Z = f(V) +
Least Squares (LS) estimate of V is given by
min1
2||Z f(V)||
2
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SCADA based SE- Disadvantages
Scan time of RTU measurements is high (1-5 seconds) and
time skew errors are significant
During power swings (electromechanical oscillations in the
0.5-2 Hz range) limited situational awareness, no controlactions can be taken
Lack of a common reference phasor is a primary reason for
non-linear state estimator
Non-linearity slows down overall computation and can lead toconvergence difficulty
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Transmission Line Parameter Estimation (1)
Accurate line parameter information of transmission lines isessential for the following reasons Distance relays use impedance information of the lines for proper
zone settings SE softwares use line parameters for estimating system states Location of faults in a transmission line. Fault locating algorithms
use the parameter models for locating faults Tools like online LFA, etc. would have inaccuracies if the
parameters are not precise
Application of TLS method to estimate line parameters has
been proposed in literature, using a moving window techniqueto use voltage, current, active and reactive power
measurements from PMUs and other measuring devices
The method has been further developed for estimation of +ve
sequence parameters, using only phasor measurements5 of 29
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Transmission Line Parameter Estimation (2) Offline process, voltage and current phasors obtained from
PMUs over a span of time are processed to estimate lineparameters
Formulation: we take the condition where PMUs monitor line
current and bus voltages at both ends of the line
B2
sh B2
sh
PMU PMUr + jx
I12
I21
V1
V2
Bus 1 Bus 2
Figure: Two bus system with PMUs at both end of the line.
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Transmission Line Parameter Estimation (3) Measurements available to us are the positive sequence
phasors V1, V2, I12 and I21 Our objective is to estimate the line parameters r, x and Bsh2 In rectangular form, equation that connects the phasors is given
by
Ir12 +jIi12 =
(Vr1 Vr2) +j(Vi1 Vi2)
(g+jb) + j Bsh2
.(Vr1 +jVi1).
We get two sets of equations for voltage and current
measurements. Together, they constitute a block for a given
time instant
(Vr1 Vr2) (V
i1 V
i2) V
i1
(Vi1 Vi2) (V
r1 V
r2) V
r1
(Vr2 Vr1) (V
i2 V
i1) V
i2
(Vi2 Vi1) (V
r2 V
r1) V
r2
. gb
Bsh2
=
Ir12Ii12Ir21Ii21
.
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Transmission Line Parameter Estimation (4)
Figure: Two area, four generator, 10 bus system.
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Transmission Line Parameter Estimation (5)
Table: Average Estimation results with normal CVTs
R = 0.0529/km, L = 1.6835 mH/km, C = 0.0090258 F/km
g = 0.4119 pu, b = 4.1692 pu, Bsh2 = 0.1519 pu.
Parameters g b Bsh
2LS 0.4034 4.1588 0.1514Weighted TLS 0.4137 4.1673 0.1505TLS (No weights) 0.4153 4.1689 0.1535
RMS LS Error % 4.0513 0.5120 2.9200
RMS TLS Error % 2.0179 0.1267 2.7625RMS TLS Error (No weights) % 4.2406 0.2798 3.0929
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Stages in Synchrophasor based State Estimation
PDC NTP
Observability
Analyzer
State
Estimator
Bad Data
Detector
PMUs
Figure: Various stages in state estimation computation.
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Synchrophasor based Linear State Estimator With PMUs measurement vector includes voltage phasors Vpmu
and current phasors IpmuVpmuIpmu
=
I
Ybranch
[V] +
vi
The matrix Ybranch is given by
Ybranch = yA + ys
Consider the following example
I23I13
I21
I12
3
21
Vpmu1
Vpmu2
Ipmu12
Ipmu13
Ipmu23
=
11
y12 y12y13 y13
y23
y23
V1V2V3
+
1234
5
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Synchrophasor State Estimator
The SynSE model can be compactly written as,
Z = MV +
If the system is observable, the least square estimate viz.,
solution of the problem min 12 Z MV 22 is given by,
V = M+Z = (MHM)1MHZ
The measurement estimate and residual vector are given by
Z = M(MHM)1MHZ = PZ
r = Z Z = (I P)Z
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Computational aspects of linear SE (1)
LS squares solution of SE problem can be found by LUfactorization
Preferable to use a numerically stable factorization approach
e.g., QR decomposition
Givens rotation is preferred over Householder reflection Column ordering of matrix M can done by Minimum Degree
Algorithm (MDA)
Dynamic row ordering technique like VPAIR can be used to
minimize intermediate fills M has complex elements, it is not possible to perform standard
Givens rotation. However with proper choice of alignment
matrices, Complex Given Rotations can be performed
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Computational aspects of linear SE (2)
For a case study on NEW Indian grid with PMUs at all buses,
the following timings were obtained
The time taken for the QR factorization on a Pentium i3 dual
core personal computer with 3 gigabytes of RAM, is
approximately 300 msec Forward/backward substitution takes approximately 2 msec
Factorization is only required when the topology changes and
the M matrix is updated
The actual state estimation problem can thus be solved in 2-3msec
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Supervised Zone-3 Distance protection - Issues
with Zone 3 A distance relay, zone-3 element, can maloperate on power
swings. Power swings are electromechanical oscillations with
0.5- 2.0 Hz frequency It can maloperate under low voltage and high line loading
conditions:
Zapp =|Vi|
2
P2ij + Q2ij
Pij +jQij
10 % voltage drop implies a 19 % reduction in Zapp
10 % increase in load implies 10 % reduction in Zapp Simultaneous application of above leads to 24 % reduction in Zapp
Specially an issue when a short line terminates into a long line
and with lines having significant infeed
Can SynSE be used to improve securityof distance relays?15 of 29
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Overview of Proposed Synchrophasor
Supervisory System Yes because
1. PMU reporting rate - 20ms -0.1 sec or 10-50 Hz; Nyquist criteriasatisfied
2. communication latency is of the order of 100 ms;3. zone-3 operating time 90 cycles
SynSE is a faster than the slower backup protection
PMU
Synchrophasor -State Estimator
Fault
detectionlogic
AND
PMU
PMU BackupRelay
Trip/ No
Trip
Trip/ NoTrip
Trip/ No
Trip
AND logic is used to improve security Dependability depends upon accuracy of fault detection logic16 of 29
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PMU placement vis-a-vis Transmission Line
For an observable system, PMU placement vis-a-vis atransmission line can happen in three configurations
21PMU
I12 I43
43 PMU
F
Configuration - 1
21 PMU
I43
43 PMU
F
Configuration - 2
I21
21 PMU 43PMU
F
Configuration - 3
I34I21
Depending upon CB status, this leads to five modes of
operation in SynSE based backup protection system
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Case Studies: Results
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500
2000
2500
time(s)
||r
||
Modes1 and 4
Mode1 failure
Mode4 failure
20
fault duration 0.5 s
Power Swing
LLL fault atmidpoint of line L
3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500
2000
2500
time(s)
||r||
Modes2 and 5
20
fault duration 0.5s
Remote (non PMU)end trip in 0.1s
Mode2 failure
Mode5 failure LLL fault atmidpoint of L
3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
200
400
600
800
1000
1200
1400
1600
1800
2000
time(s)
||r||
Mode3
PMU end breakertrip (0.1 s)
Residual withbus side VT
Residual withbus side VT
Residual withbus side VT
Residual withline side VT
LLL fault atmidpoint of line L
3
0 20 40 60 80 100 120 140 160 180 200 220
50
100
150
200
250
Line Length(km)
||r||
Fault Obseravbility Modes for LG fault
20
RF= 600 ohms
Mode4
Mode1Mode3
Modes 2,5
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CT/CVT Calibration (1)
The SE equation is Z = MV +
Consider a complex calibration factor for each measurement
and its vector
Let ZD represent a diagonal matrix with entries from Z SE equation can be modified to account for calibration factors
ZD= MV +
Or equivalently
[M ZD]
V
=
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CT/CVT Calibration (2)
As a result, we can formulate following constrained least square
problem
min H
s.t. 0.5 real() 1.5
0.5 imag() 1.5
The limits on calibration is to safeguard against some
impractical calibration values.
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Control Schemes to improve System Security
PDCState
Estimator
Detector
Predictor
Voltage Instability
Control Actions
Predefined Islanding,
Balancing
Network ControlActions (FACTS,
HVDCs)Islanding in
Extreme Cases
Generator Control
Actions
Load Control
Actions
Adaptive or
Generator, LoadDirectly to Islanding
Control Action
AGC
Simulator
DSA
Module
Historian
Online Power
System Oscillation
Mode Identifier
FrequencyInstabilityDetector
Detector
RelayVulnerability
Analyser
Predictor
PMUs
Trigger
,
*
OOS
Event Based
or Periodic
DSA Trigger
Manual Preventive
Action
AutomaticPreventive Action
*
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Control Schemes to improve System Security (1)
Power systems can suffer from voltage, angle and frequency
instabilities. There could be both small and large disturbance
aspects to these stability problems
Inadvertent relay operations and hidden failures can also
trigger or create cascade outages leading to above instabilities
In a preventive control mode, DSA is a tool which is used todetermine the stress level in the system and likelihood of an
instability in near future
DSA may be run every few minutes. However, it could be
triggered from PMU data DSA module could also be triggered by vulnerability analysis of
distance relay module
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Control Schemes to improve System Security (2) Different stability margin indices can be obtained from DSA
module In case of an alert system state, control actions to remedy and
return to normal operating state have to be designed
In addition, based on PMU data, one could envisage thefollowing.
1. Out-of-step detection and prediction analytic2. Voltage instability and prediction analytic3. Frequency instability analytic
An oscillation monitoring tool can detect poorly damped
oscillations which could be consequence of small signal
oscillations
Various control actions which can be envisaged are as follows
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Control Schemes to improve System Security (3)
1. Controlled system separation
2. Use of wide-area signals for damping oscillations with HVDC,FACTS controllers or PSS
3. Adaptation of relays and control systems using wide areainformation
4. To determine set-point (operating point) changes for alleviatingpoor damping of swings detected during actual operation
5. Detection of islanding and using centre-of-inertia frequency (orweighted averaged frequency) for df/dt relaying
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Online Vulnerability Analysis - Distance Relays (1)
When a transmission line fault occurs, there are several relaysin the vicinity of the relay that get started
If the fault gets cleared by primary protection (zone-1) then
other timers stop
Several other relays come close to starting. These are termedas vulnerable relays
It is possible that in subsequent faults in same line or during
some other network operating conditions they start and operate
Relay characteristics will be obtained from the actual relays andmodelled in simulated computer environment
Synchrophasor measurements will be obtained for situation
when fault event occurred
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Online Vulnerability Analysis - Distance Relays (2)
Events will be replayed to simulated relays and risk of starting
will be checked
Vulnerability index will be then computed where the relays are
ranked based on their risk
Vulnerability of relays during stressed conditions can be
continuously checked
Hidden failures can be exposed
Suitable changes can be made in settings of vulnerable relays
to make them more secure
If a power swing characteristic is found to come close to the
relay, it can be used to trigger DSA to evaluate system
weakness
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Overall PMU Analytics inter linkage
Various Control Signalsto Stabilize System
Block/UnblockSignal to Relays
Result
B
roadcast
Receive
Result
Estimator
Trigger Signal toDSA Module
PDC
Historian
Services
ClientInteraction
Zone 3Back Up
Control Schemesfor Improving
System Security
LogsRelay SettingsNetwork Database
Linear State
EstimatorLine Parameter
Calibrator
CT/CVT
Detector
Vulnerability
Relay
TriggerDSA
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Summary
Analytic modules, envisaged under the synchrophasor
analytics project are described
An architecture of control schemes for improving system
security has been presented Simulation results on following modules are presented,
displaying their utility Line parameter estimation Linear state estimation Supervised zone-3 relay element operation
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Thank You
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