The Impact of Instrument Transformer Accuracy Class on the Accuracy of Hybrid State

Estimation

Elias Kyriakides and Markos AsprouKIOS Research and Innovation Center of Excellence

University of Cyprus

August 9, 20182018 PES General Meeting, Portland, Oregon

1

Panel Session: Addressing Uncertainty, Data Quality and Accuracy in State Estimation

Presentation Outline

• Hybrid state estimator overview

• Measurement uncertainties

• Impact of Instrument Transformer (IT)accuracy class on the hybrid state estimator

• Consideration of IT accuracy class inmeasurement weighting

2

Synchronized Measurement Technology• Present in the market since the early 1990s

• Synchronization of measurements

• The key element of SMT is the PhasorMeasurement Unit (PMU)

• GPS synchronized equipment

• Synchronized voltage and current phasors

• High reporting rate• 100 or 120 phasors per second depending on the system

operating frequency

• Conventional measurements are updated every 2-10seconds

• Angle measurements not possible with conventional measurement technology

Source: Arbiter

3

State Estimation in Power Systems

4

Measurements every 5-30 sNot synchronized

Active/reactive power flow measurement

Active/reactive injection measurement

Voltage magnitude measurement

State Estimation (SE) executed every 1-5 minusing asynchronous measurements

Goal of state estimation: Obtain an estimate ofthe “state” of the system (V and δ at every bus)

When the state is known, all MW and MVArflows can be calculated.

SE assumptions:• Balanced system• Line parameters perfectly known• No time-skew between measurements• Topology known

5

exhz += )(

e+

−=

+=

−−+−=

+−+=

=

1

)cossin(

)sincos(

),cossin()(

)sincos()(

2

2

i

i

j

ijijijijjii

j

ijijijijjii

ijijijijjiijsiiij

ijijijijjiijsiiij

inj

flow

flow

BGVVQ

BGVVP

bgVVbbVQ

bgVVggVP

V

Qinj

P

Q

P

⇓

Measurement errors are independent

following a normal distribution

The states of the system can be determined using a Weighted Least Squares (WLS) estimator

State Estimation in Power SystemsModel of the state estimator

=

PMU

VPMU

PMU

VPMU

inj

flow

inj

flow

hyb

I

θ

V

θ

Q

Q

P

P

z

Hybrid State Estimator

Conventional measurements

Idea: Take advantage of voltage and current phasor measurements from PMUsIncorporate these measurements into the existing state estimatorEmergence of a new state estimator: The Hybrid State Estimator

=

V

IIV

V

VVV

V

QQV

QQ

V

PPV

PP

xH

pmupmu

IpmuIpmu

pmupmu

VpmuVpmu

injinj

flowflow

injinj

flowflow

hyb

)(

PMU measurements

6

• The previous scheme may exhibit convergence problems during theiterative process

• The elements of the Jacobian matrix related to currents takerelatively large values for specific values of the voltage

Hybrid State Estimator

* S. Chakrabarti, E. Kyriakides, G. Ledwich, and A. Ghosh, “Inclusion of PMU current phasor measurements in a power system state estimator,”

IET Generation, Transmission, and Distribution, vol. 4, no. 10, pp. 1104-1115, Sep. 2010.

7

8

Use of Pseudo Flow MeasurementsAssuming that a PMU is connected to bus i, the voltage phasor at bus i, ഥ𝑉𝑖, as wellas the current phasor of the branch connecting bus i and bus j, 𝐼𝑖𝑗, are available.

To avoid the convergence problems, include indirectly the current phasormeasurements to the measurement vector.

* M. Asprou and E. Kyriakides, “Enhancement of hybrid state estimation using pseudo flow measurements,” IEEE Power and

Energy Society General Meeting, Detroit, MI, USA, paper no. 1022, pp. 1-7, July 2011.

WAN

PMUi j

GPS

gij+jbij

gsi+jbsi gsj+jbsj

ijij

ii

I

V

)sin(

)cos(

ijiijiij

ijiijiij

IVQ

IVP

pseudo

pseudo

−=

−=

9

Use of Pseudo Flow Measurements

=

pmu

Vpmu

inj

pse

flow

inj

pse

flow

V

θ

Q

Qflow

Q

P

Pflow

P

zhyb

Extremely accurate measurements

))cos()sin(()(

))sin()cos(()(

2

2

jiijjiijjiijsiiij

jiijjiijjiijsiiij

bgVVbbVQ

bgVVggVP

−−−−+−=

−+−−+=

Related to state variables similar to the conventional flow measurements

The use of pseudo flow measurements overcomes the convergence problem and improves the estimator accuracy

Measurement Chain Uncertainties

• The state estimator is based heavily on the measurements

• In practice, usually only the measurement device error is usedfor estimating the measurement uncertainty

• Important to look at the whole measurement chain (cables, ITs,measurement devices)

10

11

The Impact of Instrument TransformersInvestigate the effect of the accuracy class of the instrument transformers on

the accuracy of both the conventional and the hybrid state estimator

Case studies

• Measurement chain includes instrument transformers with good accuracy class (0.2S)

• Measurement chain includes instrument transformers with lower accuracy class (0.5)

Hybrid and conventional state estimators are executed every half hour for a wholeday for the IEEE 118 bus system, using a daily load profile

Metric of accuracy: Average sum of voltage magnitude and angle residuals

= =

−=

N

k

M

i

iiV kkMN

res

1 1

)(ˆ)(11

VV = =

−=

N

k

M

i

ii kkMN

res

1 1

)(ˆ)(11

θθ

N: Number of buses; M: Number of trials

Instrument Transformers Accuracy Class

0 4 8 12 16 20 24 28 32 36 40 44 480.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6x 10

-3

Voltage m

agnitude r

esid

uals

(p.u

)

Time instants

Conventional-IT accuracy 02

Conventional-IT accuracy 05

Hybrid-IT accuracy 02

Hybrid-IT accuracy 05

0 4 8 12 16 20 24 28 32 36 40 44 480.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

Voltage a

ngle

resid

uals

(degre

es)

Time instants

Conventional-IT accuracy 02

Conventional-IT accuracy 05

Hybrid-IT accuracy 02

Hybrid-IT accuracy 05

The instrument transformer accuracy class impacts only the hybrid state estimator accuracy

*M. Asprou, E. Kyriakides, and M. Albu, “The effect of instrument transformer accuracy class on the WLS state estimator accuracy,”

IEEE Power and Energy Society General Meeting, Vancouver, Canada, pp. 1-5, July 2013.

12

13

• In WLS state estimation, the measurements are weighted according tothe inverse of the square of their uncertainty. The instrumenttransformer uncertainty is ignored (as highlighted previously).

• In the case of current transformers, the measurement error depends onthe loading level – concept of variable weights

Current transformer maximum errors

Variable Weights in State Estimation

*M. Asprou, E. Kyriakides, and M. Albu, “The effect of variable weights in a WLS state estimator considering instrument transformer

uncertainties,” IEEE Transactions on Instrumentation and Measurement, vol. 63, no. 6, pp. 1484-1495, June 2014.

Weights for PMU Measurements

Uncertainty of PMU measurements22 )()( V

MUVVT

Vmeas uuu +=

22 )()( VVV

MUVTmeas uuu

+=

22 )()( IMU

IVT

Imeas uuu +=

22 )()( IIIMUVTmeas uuu

+=

The hybrid state estimator uses voltage phasor measurements andpseudo flow measurements

Derived from the sum of two Gaussian distributions

meas

VVTV

VT Ve

u96.1

=meas

ICTI

CT Ie

u96.1

=

meas

VMUV

MU Ve

u96.1

=meas

IMUI

MU Ie

u96.1

=

96.1

V

V VTVT

eu

=96.1

I

I CTCT

eu

=

96.1

V

V MUMU

eu

=96.1

I

I MUMU

eu

=

Angle uncertainty

Errors follow a normal distribution with

coverage factor 95%

Magnitude uncertainty

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Weights for PMU MeasurementsUncertainty of pseudo flow measurements

Use of uncertainty propagation theory

)cos( ijiijiij IVPpseudo

−=

)sin( ijiijiijIVQ

pseudo

−=

224

1))]((.[])(/[)( kukPPu

kijij pseudopseudo

pp ==

224

1))]((.[])(/[)( kukQQu

kijij pseudopseudo

pp ==

Diagonal elements of the weighting matrix

Pseudo flow measurements are correlated

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1))](([

)()(),( ku

k

Q

k

PQPu

k

ijij

ijijpseudopseudo

pseudopseudop

pp =

= Non-diagonal elements of the weighting

matrix

Imeas

Vmeasmeas meas

IVk =)(p IVmeas

Imeasmeas

Vmeas uuuuu

=)(p

15

Weights for Conventional Measurements

),0()cos( P

MU

I

transf

V

transftransftransfmeas uNIVP +−=

),0()sin( Q

MU

I

transf

V

transftransftransfmeas

uNIVQ +−=

( ) ( )2222

tantan

++

+

=

CTVT

ICT

VVT

meas

PIT uu

I

u

V

u

P

uV

meas

2222

tantan

+

+

+

=

CTVT

ICT

VVT

meas

QIT uu

I

u

V

u

Q

u Vmeas

meas

measP

Q=tan

2,2, )()( QP

MUIT

QP

meas uuu +=

24

1))](([

)()(),( ku

k

Q

k

PQPu trk

tr

meas

tr

measmeasmeas p

pp =

=

],,,[)( Itransf

Vtransftransftransftr IVk =p IV

CTVTICT

VVTtr uuuuu

=)(p

Diagonal elements

Non-diagonal elements

),(96.1

,,

measmeas

QPMUQP

MU QPe

u =

Inetwork

Vnetwork

Instrument

transformers

Power

meter

Itransf

Vtransf

16

Resulted Weighting MatrixThe measurement error covariance matrix R based on theinstrument transformer and measurement deviceuncertainties is formed as:

=

)(0000000

0)(000000

00)(00),(00

000)(00),(0

0000)(00),(

00),(00)(00

000),(00)(0

0000),(00)(

2

2

2

2

2

2

2

2

Vmeas

meas

injinjinj

pseflow

pseflow

pseflow

flowflowflow

injinjinj

pseflow

pseflow

pseflow

flowflowflow

V

QPQ

QPQ

QPQ

QPP

QPP

QPP

u

u

uu

uu

uu

uu

uu

uu

R

17

Case Study 1 – No Systematic Errors

= = =

−=

T

k

M

i

B

j

if

realf jj

PPMT

SPFM

1 1 1

ˆ11

• Weighting scheme 1 (current practice: only measurement device uncertainties,constant weights)

• Weighting scheme 2 (only measurement device uncertainties, variable weights)• Proposed weighting scheme (consider instrument transformers, variable weights)

Assume a daily load profile. Run hybrid state estimation every 30 minutesResults shown for 118 bus system

Metric of performance: Sum of Power FlowMismatches (SPFM)

18

19

SPFMS FOR HYBRID STATE ESTIMATOR

SPFM for optimal PMU locations

(MW)

SPFM for arbitrary PMU locations

(MW)

Weighting

scheme 1

Weighting

scheme 2

Proposed

weighting

scheme

Weighting

scheme 1

Weighting

scheme 2

Proposed

weighting

scheme

294.57 291.25 260.6 433.17 430.19 344.17

Case Study 1 – Results

Average of 86 MW better estimation for each time instant - 20% improvement

Average of 30.6 MW better estimation for each time instant - 10% improvement

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Case Study 2 – Erroneous PMU

Percentage error in power flows

Assume one PMU (out of the 20) provides measurements that are biased by a 10% systematic error from their actual values.

Average of 664.4 MW better estimation for each time instant-42% improvement

Type of weighting scheme SPFM (MW)Weighting scheme 1 1537.2Weighting scheme 2 1516.2

Proposed weighting scheme 851.8

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Conclusions – Lessons Learned• The accuracy of ITs did not play a major role in state estimation so far,

since we have been using the state estimation with conventionalmeasurements.

• The connection of an extremely accurate device (e.g., a PMU) to aninstrument transformer of low accuracy will deteriorate the accuracy ofthe measurements, overshadowing the true capabilities of the advancedmeasuring device.

• Weighting the measurements based on the combined uncertainty of theinstrument transformer and the measurement device improvesconsiderably the accuracy of the state estimator (even more important inthe case of erroneous measurements).

• With the addition of the more accurate PMU measurements we shoulduse ITs of higher accuracy class if we want to see improvement in ourstate estimator results.

Acknowledgements“This work has been supported by the European Union's Horizon 2020research and innovation programme under grant agreement No 739551(KIOS CoE) and from the Government of the Republic of Cyprus through theDirectorate General for European Programmes, Coordination andDevelopment.”

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