the impact of instrument transformer accuracy class on the...
TRANSCRIPT
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
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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
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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
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.
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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
−=
−=
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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)
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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.
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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
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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
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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)
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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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