Download Non-Intrusive Parameter Estimation for Single-Phase Induction Motors Using Transient Data

2015 POWER AFFILIATES
Non-Intrusive Parameter Estimation for Single-Phase
Induction Motors Using Transient Data
P. Huynh1, H. Zhu1, and D. Aliprantis2
Dept. of ECE, Univ. of Illinois, Urbana, IL, USA
2 School of ECE, Purdue Univ., West Lafayette, IN, USA
1
February 20th, 2015
[email protected]
Acknowledgement: Texas Instruments (TI) ESP group
Single-Phase Induction Motors
(SPIMs)
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Research Motivation

Accurate SPIM dynamic
modeling is crucial for studying
and mitigating Fault-Induced
Delayed Voltage Recovery
(FIDVR) events in distribution
systems [Liu et al’14]

Recent developments of smart
meter infrastructure allows
transient measurements.

Existing non-intrusive methods
developed for three-phase
motors, but not yet for SPIMs!

FIDVR illustration [NERC’2009].
Parameter identification can
help motor prognostics and
diagnostics [Ghial et al’14]
Goal: A non-intrusive framework for estimating SPIM parameters using transient data
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SPIM Winding Configuration
a-axis
ar-axis
br-axis




Identical rotor
windings
Asymmetric stator
windings
(main/auxiliary)
Several possible
topologies
Equivalent circuit
obtained from
stationary dq
reference frame
transformation
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m’
𝜃𝑟
br’
ar’
a’
ROTOR
Rotation
ar
a
m-axis
br
STATOR
m
SPIM capacitor-start
– capacitor-run winding configuration.
4
Dynamic Modeling of CSCR SPIMs

State vector

System dynamics

Output model

Matrices B and C are constant, M and A depend on parameters

Construction of the first equation
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SPIM Start-Up Transients
 4-pole, 1 4-HP SPIM
 Free acceleration
 120V/60Hz
20
z [A]
10
0
-10
-20
0
0.2
0.4
Switching
time
0.6
0.8
Time [sec]
1
1.2
wm [rpm]
1500
1000
Start
phase
Run
phase
500
0
0
0.2
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0.4
0.6
0.8
Time [sec]
1
6
1.2
Start-up transient current z and
mechanical rotational speed 𝜔𝑚
SPIM Parameter Estimation

Goal: Estimate the parameterized model (M and A) to fit the input
voltage u and output current z

Key steps
‒ Discretization using first-order approximation
‒ State augmentation by the parameters of interest
‒ Estimating the augmented state vector to obtain the parameters

Challenges
‒ Non-linear system  Extended Kalman Filtering
‒ Parameters identifiability  Test with the most critical parameters
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Extended Kalman Filtering Algorithm (EKF)
 EKF extends the
clairvoyant Kalman
Filtering to adaptively
estimate the states of
non-linear systems
 Implementing EKF
requires minimal
storage and
computing resources
 Each iteration has
‒ Prediction step to form
the best estimate given
all prior information
‒ Correction step to
incorporate the latest
measurement
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EKF detailed steps
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30
 Various initial
guesses
 Fast convergence
with high accuracy –
1.5% error
 Compared to initial
guesses, estimated 𝑟𝑠
value significantly
improves the SPIM
transient response
Percentage Error
 Main winding
resistance 𝑟𝑠
10
0
-10
-20
-30
0
200
400
600
Iteration index
-30 percent
-20 percent
-10 percent
10 percent
20 percent
30 percent
800
1000
Estimated parameter
Initial parameter
2
Output error [A]
Single Parameter
Estimation
20
1
0
-1
-2
0
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0.5
9
1
Time [sec]
1.5
2
• Add main winding
leakage reluctance
[𝑟𝑠 , 𝐿𝑙𝑠 ]
• Initial guess: +30%
error for 𝑟𝑠 and -30%
error for 𝐿𝑙𝑠
20
Percentage Error
Dual Parameters
Estimation
10
0
-10
-20
-30
0
• Similar results to the
single-parameter
testing (3% error)
200
400
600
Iteration index
800
1000
Estimated parameters
Initial parameters
2
Output error [A]
• Estimated
parameters greatly
improve the SPIM
transient response as
well
rs
Lls
1
0
-1
-2
0
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0.5
10
1
Time [sec]
1.5
2
40
 Initial guess with ± 30%
error
 Estimates for 𝐿𝑙𝑆 , and
𝐶1 fail to achieve the
actual values
 However, the transient
response still accurately
produced using the
estimates
Percentage Error
 Account for auxiliary
winding [𝑟𝑠 , 𝑟𝑆 , 𝐿𝑙𝑠 , 𝐿𝑙𝑆 ,
𝐶1 ]
30
20
10
0
-10
-20
-30
0
2
8
10
4
x 10
Estimated parameters
Initial parameters
4
2
0
-2
-4
-6
0
0.5
 Parameter identifiability
issue!!
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6
Iteration index
6
Output error [A]
Multiple Parameters
Estimation
rs
rS
Lls
LlS
C1
11
1
Time [sec]
1.5
2
Conclusions


Improving SPIM dynamic modeling important for
distribution systems FIDVR studies
Non-intrusive framework for SPIM parameter
estimation
‒ Dynamic SPIM modeling allows to estimate parameters using
EKF
‒ More critical parameters lead to better estimation accuracy
‒ Some parameters cannot be identified simultaneously

On-going work
‒ Verify the effectiveness of the algorithm in a laboratory setting
‒ Study the parameter identifiability issue
‒ Investigate reduced-complexity algorithm by using the dynamic
model at single frequency (i.e., dynamic phasor model)
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References
[1] North American Electric Reliability Corporation (NERC), “A Technical
Reference Paper Fault-Induced Delayed Voltage Recovery,” NERC,
Tech. Rep., June 2009.
[2] Y. Liu, V. Vittal, J. Undrill, and J.H. Eto, “Transient Model of AirConditioner Compressor Single Phase Induction Motor,” IEEE Trans.
Power Syst. , vol.28, no.4, pp.4528-4536, Nov. 2013.
[3] P. C. Krause, “Simulation of unsymmetrical 2-phase induction
machines,” IEEE Trans. Power App. Syst. (until 1985), vol. 84, no. 11,
pp. 1025-1037, 1965.
[4] V. K. Ghial, L. M. Saini, and J. S. Saini, “Parameter estimation
of permanent-split capacitor-run single-phase induction motor using
computed complex voltage ratio,”IEEE Trans. Ind. Electron., vol. 61,
no. 2, pp. 682–692, 2014.
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Single Phase Induction Motor Model [Krause’1965]
 Start phase
 Run phase
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Tranformation to dq reference frame [Krause’1965]
 For the stator
 For the rotor
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Voltage and Flux Linkage Equations in dq reference
frame [Krause’1965]
 Voltages
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 Currents
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Voltage and Flux Linkage Equations in original
reference frame [Krause’1965]
 Voltages
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 Flux
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Motor’s Parameters
1
4
Table 1: -HP SPIM Parameters
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