Power Systems Model Developments for Power Quality ...about.cleaned-usth.com/files/Anh_Tuan_Phan_power_systems_model... · Power Systems Model Developments for Power ... A.T. Phan

In front of the jury: M. Moamar Sayed-Mouchaweh

M. Laurent Rambault

M. Malek Ghanes

M. Edouard Laroche

M. Gilles Hermann

M. Patrice Wira

by Anh Tuan Phan

Laboratoire MIPS, Université de Haute Alsace

1

PhD Defense 16 September 2016

Power Systems Model Developments for Power

Quality Monitoring: Application to Fundamental

Frequency and Unbalance Estimation

Power quality problems:-fundamental frequency deviation-unbalance

-harmonics-voltage swell/sag

photovoltaicpanel

windgenerator

eletrical

car

home

generation

... ...

power plant

engine

other loadsother

generator

consumptiontransmission and distribution

2

A.T. Phan PhD defense

Power quality is a central issue for the whole

grid’s reliability

3

The research of the thesis aims to improve the power quality of power systems


1. Power quality disturbances and monitoring of power quality

2. Well-known methods for power quality improvement

3. New state-space representations for frequency estimation

4. New state-space representations for symmetrical

components identification

5. Conclusions and perspectives

Content

4



I. Power quality problems

II. Power quality control

III. Problematic






Content

5


Ideal three phase signals of a three phase

power system

6

Principle of an ideal three phase generator:

Current waveforms: ( ) sin( )

( ) sin( 2 / 3)

( ) sin( 2 / 3)

a

b

c

i t I t

i t I t

i t I t

1. Power quality disturbances and

monitoring of power quality


Power quality problems:

Unbalance of three phase systems

7

Bala

nce

Unbala

nce

( ) sin( )

( ) sin( 2 / 3)

( ) sin( 2 / 3)

a

b

c

i t I t

i t I t

i t I t

( ) sin( )

( ) sin( )

( ) sin( )

a

b

c

a

b

a

b

c c

i t t

i t t

i It t

I

I

Consequences:

1. power losses, heating, reduced productivity and vibration to asynchronous

motors and synchronous generators.

2. limited line transmission capacity because of additional heating.





Frequency deviation

8

The value of the fundamental frequency depends on the equilibrium of the

power generation and the power demand.

Power generation Power demand

Ideally:

generated power = consumed power

The frequency rises if the power

generation is higher than the power

demand.

The frequency falls otherwise.

50Hzof

Sou

rce

: ww

w.v

ente

ea.f

r 50.87Hzof

49.19Hzof




The effects of frequency deviation

• Large errors occur in protective relays due to the frequency variation

• The magnetic characteristic of transformers can get into non-linear zones

when the fundamental frequency varies in time.

9

• The operation of rotating machinery, or processes using their timing from the

power frequency will be affected when the frequency changes



Frequency variation has great impact to normal operation of electrical devices,

among them:


0 100 200 300-8

-6

-4

-2

0

2

4

6

8Distorted current waveform

0 100 200 300-8

-6

-4

-2

0

2

4

6

8Equivalent harmonic components

fundamental

7th harmonic

11th harmonic


Harmonics

10




The effects of harmonics

• Heating in electrical machines

• Insulation failure in power cables

• Decrease in response speed and mis-operation of relays

• Mis-operation and/or malfunction in electronic equipment

11

The propagation of harmonics in power systems leads to many negative

effects such as:




Power quality control:

Active power filter

12

automatic and control power

electronics signal

processing

POWER LINE

SHUNT ACTIVE FIL TER

NONLINEAR

LOAD

CONTROL LAW

PARAMETER

ESTIMATION

POWER SOURCE

INVERTER

measured line current

compensating current

harmonic

components

reference

signal




Objective of the thesis

13

automatic and control power

electronics signal

processing

POWER LINE

SHUNT ACTIVE FIL TER

NONLINEAR

LOAD

CONTROL LAW

PARAMETER

ESTIMATION

POWER SOURCE

INVERTER

measured line current

compensating current

harmonic

components

reference

signal • Frequency estimation

• Symmetrical components

estimation

• Harmonic current estimation

• Reactive power estimation

signal processing

PARAMETER

ESTIMATION






I. Extended Kalman Filter for balanced three phase power

signals (3P EKF)

II. Extended Kalman Filter for one phase power signal (1P EKF)





Content

14


Extended Kalman Filter for balanced three

phase power signals (3P EKF)

( ) sin( )

( ) sin( 2 / 3)

( ) sin( 2 / 3)

a s

b s

c s

i k I kT

i k I kT

i k I kT

1( ) sj kTy k A e

Clark’s transform

15

2. Well-known methods for power

quality improvement

• Clark’s transform: 2 1 1

3 2 2

1( )

2

( ) ( ) ( ) ( )a b c

b c

i i i i

i i i

k k k k

( ) ( ) ( )y k i jik k

• Complex representation:

power

system


Extended Kalman Filter for balanced three

phase power signals (3P EKF)

( ) sin( )

( ) sin( 2 / 3)

( ) sin( 2 / 3)

a s

b s

c s

i k I kT

i k I kT

i k I kT

1( ) sj kTy k A e

Clark’s transform

1. Selection of the state variables

1

2 ( ) : sj kTq k Ae

1( ) : sj Tq k e

2. Definition of the state-space representation

1 1

2 1 2

( 1) 1 0 ( )

( 1) 0 ( ) ( )

q k q k

q k q k q k

2( ) ( )y k q k

16


quality improvement


Extended Kalman Filter for one phase power

signal (1P EKF)

( ) sin( ) 0.5 0.5 s sj kT j kTsi k I kT j Ie j Ie

17


quality improvement


Extended Kalman Filter for one phase power

signal (1P EKF)

( ) sin( ) 0.5 0.5 s sj kT j kTsi k I kT j Ie j Ie

18


1( ) : sj Tq k e

2( ): sj kT jq k Ie

1 1

2 21

1

13 3

( 1) ( )1 0 0

( 1) ( )0 ( ) 0

0 0 ( )( 1) ( )

q k q k

q k q kq k

q kq k q k

2 3( ) ( ) 0.5 ( ) 0.5 ( )y k i k j q k j q k

3:( ) sj kT j

q Iek


quality improvement

2. Definition of the state-space representation


Characteristics of the well-known methods

Methods Characteristics

Underlying model Advantages Disadvantages Applications

3P EKF Nonlinear state-

space model

Sample based,

robust to noise

- Difficult to choose

initial values of

the state

variables.

- Balanced three

phase signals

1P EKF Nonlinear state-

space model

Sample based,

robust to noise

- Difficult to choose

initial values of

the state

variables.

- Single phase

signals

19


quality improvement

Comments:

• The models of these two methods are not suitable to unbalanced systems

• We have compared them with Adaptive Prony’s method and Adaptive

Notch Filter in [1]

A.T. Phan PhD defense 2. Well-known methods for power

quality improvement

Discussion

20

Balanced

three

phase

systems

One phase

signals

Unbalanced three

phase systems

Main problems:

• Frequency fluctuation

• Harmonics

• Unbalance

• Reactive power

Tools and solutions:

• Symmetrical

Components

• Our proposed

state-space models

Main problems:


• Harmonics

• Reactive power


• 3P EKF

Main problems:


• Harmonics

• Reactive power


• 1P EKF

• Adaptive Notch Filter

• Adaptive Prony’s

method

One

phase

systems





I. Theory of symmetrical components

II. New state-space representations and algorithms

III. Initialization scheme for the state variables

IV. Simulation tests and results




Content

21


Analysis tools for unbalanced three phase

signals: symmetrical components

aI

bI

cI

120o

120o120o

aI

cI

bI

120o

120o120oo

bIo

aI

ocI

22 3. New state-space representations

for frequency estimation

positive components

(balanced three

phase system)

negative components

(balanced three

phase system)

zero components

(symmetrical)

aI

bI

cI

An unbalanced three

phase system

Any unbalanced three phase systems can be represented as a unique sum of

three symmetrical components:


New state-space models modeling unbalanced

three phase systems

( )

( )

( )

( ) sin

( ) sin

( ) sin

a s

b s

c s

b

a

c

a

c

b

I

I

kT

kT

kTI

i k

i k

i k

( ) 0s sj kT j j kT jy k A e A e

23

Clark’s transform

power system

3. New state-space representations




three phase systems


24

Clark’s transform ( )

( )

( )

( ) sin

( ) sin

( ) sin

a s

b s

c s

b

a

c

a

c

b

I

I

kT

kT

kTI

i k

i k

i k





three phase systems [4]


25


1( ) : sj Tq k e

2. Definition of a state-space representation

1 1

2 21

1

13 3

( 1) ( )1 0 0

( 1) ( )0 ( ) 0

0 0 ( )( 1) ( )

q k q k

q k q kq k

q kq k q k

2 3( ) ( ) ( )y k q k q k

Clark’s transform

2( ) sj kT j

q A ek

3( ) sj kT j

q A ek

( )

( )

( )

( ) sin

( ) sin

( ) sin

a s

b s

c s

b

a

c

a

c

b

I

I

kT

kT

kTI

i k

i k

i k




Properties of the new state-space model

Meaning of the

state variables

Model of 3P

EKF

Model of 1P

EKF

Proposed

model

Represents the

fundamental

frequency

Represents the

fundamental

frequency

Represents the

fundamental

frequency

Represents the

positive

components

No physical

meaning

Represents the

positive

components

Does not exist No physical

meaning

Represents the

negative

components

1( )q k

2( )q k

3( )q k

26



The proposed model and its properties have been presented in [3].


Method to estimate the fundamental frequency

using the proposed model: Extended Kalman Filter

11

1ˆ ( ) sin img( ( ))2

o

s

f k q kT

27

Iterative

estimator



This approach has been published in a conference [4]


How to initialize the state variables in EKF?

28

Assign ( )

a value near

the nominal value

Estimate states ,

in several iterations

by Kalman Filter (KF)

Use the estimated

state variables

for tracking stage

3q

of

2q

1

2

3

1q

2 2

3 3

0( 1) ( )

1( 1) ( )0

aq k q k

q k q ka

2 3( ) ( ) ( )y k q k q k

1( ) sj Ta kq e

State-space model when is

assigned a fixed value: of




Algorithm diagram of the new proposed

method to estimate the fundamental frequency

12

0

1ˆ( ) [ ( ) ( )]

L

i

k y k i y k iL

1 1

2 21

3 3

1

( 1) ( )1 0 0

( 1) ( )0 ( ) 0

1( 1) ( )0 0

( )

q k q k

q k q kq k

q k q k

q k

2 3( ) ( ) ( )y k q k q k

Initialization stage

Tracking stage

( )k threshold

?

Y

N

State-space representation of unbalanced

three phase systems:

Definition of : ( )k

29 3. New state-space representations



Simulation tests and results

a) Unbalanced three phase sinusoidal signals

b) Unbalanced three phase sinusoidal signals disturbed by 30 dB noise

c) Unbalanced three phase sinusoidal signals disturbed by harmonics

a) b) c)

30

I. Performance of the proposed method compared to 1P EKF and 3P EKF

(without employing the proposed initialization scheme) in estimating

the fundamental frequency of:




Results of estimating fundamental

frequency of an unbalanced system a)



31


Results of estimating fundamental

frequency of an unbalanced system

Methods time to reach the

reference

frequency with

+/- 0.1 Hz (ms)

MSE at steady-

state

3P EKF 100 10−4

1P EKF 57 10−6

Proposed method 49 10−7

a)



32

* The time of one period of the signal is 20 (ms)


Results of estimating fundamental frequency

of an unbalanced system with an additional

30 dB noise

33

b)





of an unbalanced system with an additional

30 dB noise

34

b)




reference

frequency with

+/- 0.1 Hz (ms)

MSE at steady-

state

3P EKF 115 10−4

1P EKF 47 10−6





of an unbalanced system disturbed by

harmonics

35

c)



Phase A Phase B Phase C Phase

sequence

0° 120° 240° A-B-C

3x0° (0°)

3x120° (360°=0°)

3x240° (720°=0°)

In phase

5x0° (0°)

5x120° (-120°)

5x240° (-240°)

C-B-A

7x0°

(0°) 7x120° (120°)

7x240°

(240°)

A-B-C

Fundamental

3rd harmonic

5th harmonic

7th harmonic

sou

rce:

ww

w.a

llab

ou

tcir

cuit

s.co

m

This table shows the harmonic phase sequences of some harmonics




harmonics

36

c)






harmonics

37

c)




reference

frequency with

+/- 0.1 Hz (ms)

MSE at steady-

state

3P EKF 135 10−4

1P EKF 150 10−4





II. The performance of the proposed method combined with the initialization

scheme is evaluated in estimating the fundamental frequency for:

38

a) Unbalanced three phase sinusoidal signals with the frequency and

amplitudes experiencing step changes.

b) Unbalanced three phase sinusoidal signals with the frequency varying

as a sinusoidal wave.




Case a) Signals for test

50o

f 50.5o

f

1A 0.8A

0.2A 0.3A

Before load change After load change

time (s)

39




Results of estimating the fundamental

frequency

49.5(Hz)

45(Hz)

40

Initial value of the

fundamental frequency:

Initial value of the

fundamental frequency:




Results of estimating the fundamental

frequency

Initialization time to reach the

reference

frequency with

+/- 0.1 Hz (ms)

MSE at steady-

state

49.5 Hz 3 10−10

45 Hz 5.8 10−7

41





Case b) Frequency tracking

The estimated frequency

and the real one

(the frequency is

initialized at 49.5 Hz)

The estimation error

42




Discussion

• The proposed method is an accurate frequency estimator even in time-

varying environments and unbalanced conditions.

• The initialization scheme helps to solve the problems of choosing initial

values for the state variables.

43

• The performance of 3P EKF is degraded when the system is unbalanced.



• Unlike the other two methods, 1P EKF is unable to eliminate the impact of

the harmonics whose three phase signals are in phase with each others.

• The proposed nonlinear model has been published in [2].







I. New state-space representations and algorithms

II. Initialization scheme for the state variables

III. Simulation tests and results


Content

44


Clark’s transform of unbalanced three phase

signals

45


Clark’s transform

4. New state-space representations for

symmetrical components identification

( )

( )

( )

( ) sin

( ) sin

( ) sin

a s

b s

c s

b

a

c

a

c

b

I

I

kT

kT

kTI

i k

i k

i k

Power system



three phase systems

Fundamental frequency

is unknown Fundamental frequency

is known

46

1 1

2 21

3 3

1

( 1) ( )1 0 0

( 1) ( )0 ( ) 0

1( 1) ( )0 0

( )

q k q k

q k q kq k

q k q k

q k

2 3( ) ( ) ( )y k q k q k

1( ) : sj Tkq e

Nonlinear model

1 2

Linear model

2 2

3 3

0( 1) ( )

1( 1) ( )0

aq k q k

q k q ka

2 3( ) ( ) ( )y k q k q k

1( ): sj Ta kq e



The nonlinear model is published in [2]


Methods to estimate the symmetrical components

using the proposed models: EKF and KF

2. The proposed linear state space model is combined with KF

abc 3 q

2 q

1 q abc

i

i Clark’s

transformation

inverse Clark’s transformation

symmetrical components

average

proposed nonlinear state space representation

EKF

, , a b c i i i

, , a b c i i i

, , a b c i i i

o o o

+ + +

- - -

state variables

measured line currents

, , a b c i i i

+

47

1. The proposed nonlinear state space model is combined with EKF

1

2

abc 3 q

2 q abc

i

i Clark’s

transformation



average

proposed linear state space

representation KF

, , a b c i i i

, , a b c i i i

, , a b c i i i

o o o

+ + +

- - -

state variables


, , a b c i i i

+

of



computing of


Algorithm diagram of the new proposed method to

estimate the symmetrical components

Initialization stage

Tracking stage

( )k threshold

?

Y

N

48





I. The fundamental frequency is known, the proposed method for this

case is used to estimate the symmetrical components of unbalanced three

phase sinusoidal signals. The results are compared with that of method

MO-Adaline.

49

2 2

3 3

0( 1) ( )

1( 1) ( )0

aq k q k

q k q ka

2 3( ) ( ) ( )y k q k q k

This is a linear model 1




Results of estimating the symmetrical components

of unbalanced three phase sinusoidal signals

The unbalanced three-

phase signals

Estimated amplitudes

of positive and

negative components

Estimated phase

angles of positive and

negative components

50






51

Amplitudes MSE at steady-

state

MO-Adaline 10−7

Proposed method 10−14

Amplitudes MSE at steady-

state

MO-Adaline 10−8

Proposed method 10−15

Positive

components:

Negative

components:





a) Unbalanced sinusoidal three phase signals with the frequency and the

amplitudes experiencing step changes.

b) Unbalanced sinusoidal three phase signals during frequency variation.

52

II. The fundamental frequency is unknown, the proposed method for this case is used to estimate the symmetrical components of:

is a nonlinear model

1 1

2 21

3 3

1

( 1) ( )1 0 0

( 1) ( )0 ( ) 0

1( 1) ( )0 0

( )

q k q k

q k q kq k

q k q k

q k

2 3( ) ( ) ( )y k q k q k

2 4. New state-space representations for



Case a) Signals for test

50o

f 50.5o

f

1A 0.8A

0.2A 0.3A


time (s)

53




Estimation of the symmetrical components of

unbalanced three phase sinusoidal signals

experiencing step changes

Estimation error

of the positive

components

Estimation error

of the negative

components

54






Case b) Estimation of the symmetrical components

of unbalanced three phase sinusoidal signals with

the frequency varying

55

Estimation error of

the positive

components

Estimation error of

the negative

components


Discussion

• With the fundamental frequency supposed to be available, the linear

method is able to estimate effectively the three symmetrical

components.

• The nonlinear method , when combined with the proposed initialization scheme, is efficient in estimating the symmetrical components of time-varying unbalanced power systems.

56

1

2



• The method and its applications in frequency and unbalance estimation

have been presented in a journal article to appear [5].








Content

57


Conclusions

• Power quality is a central issue for the whole grid’s reliability.

• Signal processing methods are useful to monitor and control of power

quality effectively, however, most of them concern one phase signals

and/or balanced three phase signals.

58 5. Conclusions and perspectives


Conclusions

• The thesis proposes new methods to estimate the parameters of unbalanced

three phase power systems. The methods are based on new state-space

modeling of the unbalanced systems and applied to:

– Estimate the fundamental frequency of the power systems

– Estimate the symmetrical components of the power systems

59

• Simulation results have proven that the new methods are efficient and robust in estimating the fundamental frequency and the symmetrical components of a time-varying power system under various severe unbalanced conditions.

• The work developed during this thesis has been published in 4 international conferences and 1 international journal.



Perspectives

• Expand the proposed state-space models in order to take into account the

harmonic components, as each component of three phases could be

considered as a positive or negative sequence.

60 5. Conclusions and perspectives

• Look to associate to the proposed state space model another identification

algorithm, e.g., Artificial Neural Networks, to improve the performance of

the method in disturbed and time-varying environment of power systems.

• Enhance the proposed state-space models for higher order unbalanced

harmonics, the purpose is to come up to a general and uniform state-space

model able to include in one concept or model the unbalanced fundamental

component, the unbalanced harmonics, and the harmonic sequences.


Publications and Authors’ contributions

61

Conference papers published in international conferences with review and proceedings:

[1]. Anh Tuan Phan, Gilles Hermann, and Patrice Wira. “Online Frequency Estimation in

Power Systems: A Comparative Study of Adaptive Methods”. In: 40th Annual Conference of the IEEE

Industrial Electronics Society (IECON 2014), Dallas, TX - USA, pages 4352–4357, 2014

[ 2]. Anh Tuan Phan, Gilles Hermann, and Patrice Wira. Kalman filtering with a new state-space model for

three-phase systems: Application to the identification of symmetrical components. In IEEE Conference on

Evolving and Adaptive Intelligent Systems (EAIS 2015), Douai-France, pages 216–221, 2015

[ 3]. Anh Tuan Phan, Duc Du Ho, Gilles Hermann, and Patrice Wira. A new state-space model for three-

phase systems for kalman filtering with application to power quality estimation. In 11th International

Conference of Computational Methods in Sciences and Engineering (ICCMSE 2015), Athens-Greece, 2015

[ 4]. Anh Tuan Phan, Gilles Hermann, and Patrice Wira. A new state-space for unbalanced

three-phase systems: Application to fundamental frequency tracking with kalman filtering. In 18th IEEE

Mediterranean Electrotechnical Conference (MELECON 2016), Limassol Cyprus, 2016

Article published in international journals:

[ 5]. Anh Tuan Phan, Patrice Wira, and Gilles Hermann. A Dedicated State Space for Power

System Modeling and Frequency and Unbalance Estimation, Evolving Systems, to appear in 2016

THANK YOU contact: [email protected]

62


Results of estimating the positive components

of an unbalanced system: load change

50o

f 50o

f

1.2A 1A

0A 0.2A


time (s)

63


Results of estimating the positive components


Phase A

Phase B

Phase C

64


Results of estimating the negative components


Phase A

Phase B

Phase C

65


Adaptive Prony’s method

( )u k k

ˆ( )i k1

0 1

1

1

...( )

1 ...

m

m

n

n

b b z b zH z

a z a z

( )i k

( )e k

( )u k

update iaib

( )i k measured line current :

Input: Reference signal:

by Least Square Method

66


Adaptive Notch Filter

1 2

1 2 2

1 2cos( )( , )

1 2cos( )

z zH z

z z

(1 )

Frequency response of

( )jH e

( , )H z

( )i k ( , )e k ( , )H z

measured line

current update

by Least Mean Square Method 67


68


Algorithm

abc 3 q

2 q

1 q abc

i

i Clark’s

transformation



average

proposed state space

representation KF

, , a b c i i i

, , a b c i i i

, , a b c i i i

o o o

+ + +

- - -

state variables


, , a b c i i i

+

69


Tracking of a fundamental frequency varying

constantly in time

Real and estimated

frequency (Hz)

Frequency estimation

error (Hz)

70



Frequency deviation

Fundamental frequency varies in time

71



Harmonics

72



Frequency deviation

Sweden

Singapore

73 https://en.wikipedia.org

Central Europe

China

Great Britain



Unbalance of three phase systems

74

Balance Unbalance

( ) sin( )

( ) sin( 2 / 3)

( ) sin( 2 / 3)

a

b

c

i t I t

i t I t

i t I t

( ) sin( )

( ) sin( )

( ) sin( )

a

b

c

a

b

a

b

c c

i t t

i t t

i It t

I

I

• power losses, heating, reduced productivity and vibration to

asynchronous motors and synchronous generators. • limited line transmission capacity because of additional heating.

Unbalance leads to:


Power quality control:

Passive power filter

75

PASSIVE FILTER


Algorithm to estimate state variables of the

proposed model: Extended Kalman Filter

11

1ˆ ( ) sin img( ( ))2

o

s

f k q kT

+

76

Iterative

estimator




77

Amplitudes Mean at steady-

state

MSE at steady-

state

Error max.

at steady-

state

MO-Adaline 1.0000 10−7 10−5

Proposed method 0.9999 10−14 10−7

Amplitudes Mean at steady-

state

MSE at steady-

state

Error max.

at steady-

state

MO-Adaline 0.2000 10−8 0.0013

Proposed method 0.2000 10−15 10−7

Positive components:

Negative components:



three phase systems

Measured

line currents

a b ci i i

Symmetrical component decomposition

State-space modeling



Model synthesis

a b ci i i a b ci i i

o o o

a b ci i i

78

zzzz 1 1

2 1 2

( 1) 1 0 ( )

( 1) 0 ( ) ( )

q k q k

q k q k q k

2( ) ( )y k q k

State space model of balanced

three phase signals:




Properties of the new state-space model

Characteristics Model of 3P EKF Model of 1P

EKF

Proposed

model

Linearity Nonlinear Nonlinear Nonlinear

Number of states 2 3 3

Output

Clark’s transform of

balanced three

phase signals

One phase

signal

Clark’s

transform of

unbalanced

three phase

signals

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Power Systems Model Developments for Power Quality ...about.cleaned-usth.com/files/Anh_Tuan_Phan_power_systems_model... · Power Systems Model Developments for Power ... A.T. Phan