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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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Figure: Two area, four generator, 10 bus system.

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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 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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