Fault Location on HVDC Transmission Lines Using Dynamic

Fault Location on HVDC Transmission Lines Using

Dynamic State Estimation (DSE)

上海科技大学ShanghaiTech University

Panel Session: State Estimation for Power Electronics-Dominated

Systems: Challenges and Solutions

Presenter: Yu Liu

Power System Protection and Automation Laboratory (PSPAL)

School of Information Science and Technology

ShanghaiTech UniversityEmail: [email protected]; [email protected]

1

Power System Protection and

Automation LaboratoryP PAL电力系统保护与自动化实验室

P PAL

mailto:[email protected]


Personal Info

2

Education

2017 Ph.D. Electrical Engineering Georgia Institute of Technology

2013 M.S. Electrical Engineering Shanghai Jiao Tong University

2011 B.S. Electrical Engineering Shanghai Jiao Tong University

Working experiences

2017 Assistant Professor ShanghaiTech University

2012 Visiting Scholar Georgia Institute of Technology

Research Interests

• Power System Protection, Fault Location

• State and Parameter Estimation of Power Systems

• Condition Monitoring of Power Electronic Systems

P PAL

01 Introduction

02 Review of Existing DSE Based Fault Location Method

03 Proposed New DSE Based Fault Location Method

04 Numerical Experiments

05 Conclusion

Outline

3

01 Introduction




05 Conclusion

Outline

4

Advantages of HVDC over HVAC

• No reactive power loss

• No stability problem

• Long distance, large capacity transmission

• Flexible power control

5

IntroductionWhy HVDC transmission? Development of HVDC transmission

Point-to-Point

• LCC-HVDC transmission

• VSC-HVDC transmission

-- Two-level VSC-HVDC

-- Three-level VSC-HVDC

-- MMC-HVDC

Advantages of MMC-HVDC transmission

• Compatible with weak AC systems

• Independent control of active/reactive power

• Lower switching frequency

• Lower harmonics

compared to LCC-HVDC

compared to other VSC-

HVDC topologies

MMC 1

MMC 2

MMC 3

MMC 4

DC link 12 DC link 34

DC link 24

Line of interest

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

6

Introduction

Point-to-point MMC-HVDC

After occurrence of line faults in MMC-HVDC grids:

• Operation of DC circuit breakers, to isolate the line with fault

• Accurate fault location within the isolated line (using line terminal measurements

during faults) (focus of this presentation)

Development of HVDC transmission MMC-HVDC grids

MMC 1 MMC 2

Line of interest

us(t)is(t)

ur(t)ir(t)S R

Improve power supply

reliability of the system

lf

7

Introduction

MMC-HVDC grids

MMC 1

MMC 2

MMC 3

MMC 4


DC link 24

Line of interest

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

Accurate fault location within the isolated line

Challenges (Compared to HVAC fault location)

Power Electronics Dominated System

• Low Inertia:

-- Severe transients during faults

• Vulnerable Power Electronic Devices:

-- Short data window (several milliseconds, to prevent MMC shutdown)

• DC system:

-- Absence of fundamental frequency (50 or 60 Hz) components

lf

Fundamental frequency phasor based methods

-- Steady state assumptions at system fundamental frequency (50 or 60 Hz);

-- Not Applicable for HVDC lines

Travelling wave based methods

-- Limited wavefront detection reliability (especially high impedance faults)

-- Require very high sampling rate (100khz -> systematic error ≈ 1.5 km)

Natural frequency based methods

-- Mode mixing phenomenon (especially during single pole to ground faults)

-- Frequency extraction errors

Time domain model based methods

-- Traditional methods: utilize models with lumped parameters

-- Dynamic state estimation (DSE) based fault location method

Existing transmission line fault location methods

8

Introduction

01 Introduction




05 Conclusion

Outline

9

Review of Existing DSE Based Fault Location Method

Section

1

( )1

1 ( )ai t

( )1

1 ( )v t

( )1

1 ( )bi t

( )1

2 ( )v t

Section

m

( )1( )ami t

( )1( )mv t

( )1( )bmi t

Section

1

( )2

1 ( )ai t( )2

1 ( )bi t

( )2

2 ( )v t

Section

n

( )2( )ani t

( )2( )nv t

( )2( )bni t

( )2

1 ( )nv t+

( )1

1 ( )mv t+

Rf

( )2

1 ( )v tor

( )fl t ( )fl l t−

Location

of the faultSide 1 Side 2

Parameter to be

determined

Model of section k

Left part

Model of section k

Right part

10

• Works well in HVAC systems

• Introduce the fault location as

a parameter (extended state) of

the dynamic model

• Use DSE to solve the states of

the dynamic model, including

fault location

Details of transmission line modeling :

• Multi-section π model

• Very accurate approximation of fully distributed parameter line model, with large m and n

Yu Liu*, Sakis Meliopoulos, Zhenyu Tan, Liangyi Sun and Rui Fan, “Dynamic State Estimation-Based Fault Locating on Transmission

Lines”, IET Generation, Transmission & Distribution, vol. 11, no. 17, pp. 4184-4192, Nov. 2017. (*: corresponding author)

Model of section k, left part

Section

k

( )1( )aki t

( )1( )kv t

( )1( )bki t

( )1

1 ( )kv t+

( )1( )aki t

( )1( )kv t

1 ( ) /fl t m R 1 ( ) /fl t mL

( )1( )Lki t

1 ( ) /fl t mG 1 ( ) /fl t mC 1 ( ) /fl t mG 1 ( ) /fl t mC

( )1( )bki t

( )1

1 ( )kv t+

Model of section k,

left side part

( )( )

( ) ( )1

1 1 11 1( )( ) ( ) ( )vk

ak vk Lk

d tt t t

m dt m= + +

yC Gi y i

( ) ( )( )

( )( ) ( )

1

11 1 11 11

( )( ) ( ) ( )

v k

bk Lkv k

d tt t t

m dt m

+

+= + −

yC Gi y i

( ) ( ) ( )( )1

1 1 11 11

( )( ) ( ) ( ) Lk

k k Lk

d tt t t

m m dt+= − + + +

yR L0 v v y

( ) ( )1 1( ) ( ) ( )vk f kt l t t= − 0 y v

( )( ) ( )1 1

11( ) ( ) ( )f kv kt l t t++

= − 0 y v

( ) ( )1 1( ) ( ) ( )Lk f Lkt l t t= − 0 y i


Fault location lf(t) is

strongly coupled

with the states of the

dynamic model

High nonlinearity of

the dynamic model



Section

k

( )2( )aki t

( )2( )kv t

( )2( )bki t

( )2

1 ( )kv t+

Model of section k, right part


Fault location lf(t) is

strongly coupled

with the states of the

dynamic model

High nonlinearity of

the dynamic model

( )2( )aki t

( )2( )kv t

( )1 ( ) /fl l t n −R ( )1 ( ) /fl l t n −L

( )2( )Lki t

( )1 ( ) /fl l t n −G ( )1 ( ) /fl l t n −C ( )1 ( ) /fl l t n −G ( )1 ( ) /fl l t n −C

( )2( )bki t

( )2

1 ( )kv t+

Model of section k,

right side part

( )( ) ( )

( ) ( ) ( )2 2

2 2 2 21 1 1 1( ) ( )( ) ( ) ( ) ( )k vk

ak k vk Lk

d t d tl lt t t t

n dt n dt n n

= − + − +

v yC C G Gi v y i

( )( )

( )( )

( )( )

( ) ( )

2212 2 2 211 1 1 1

1 1

( )( )( ) ( ) ( ) ( )

v kkbk k Lkv k

d td tl lt t t t

n dt n dt n n

+++ +

= − + − −

yvC C G Gi v y i

( ) ( ) ( ) ( )( ) ( )2 2

2 2 2 21 1 1 11

( ) ( )( ) ( ) ( ) ( ) Lk Lk

k k Lk Lk

d t d tl lt t t t

n n n dt n dt+

= − + + − + −

i yR R L L0 v v i y

( ) ( )2 2( ) ( ) ( )vk f kt l t t= − 0 y v

( )( ) ( )2 2

11( ) ( ) ( )f kv kt l t t++

= − 0 y v

( ) ( )2 2( ) ( ) ( )Lk f Lkt l t t= − 0 y i




13

1 1 1 1

2 2 2 2

3 3

( )( ) ( ) ( )

( )( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( )

eqx eqp eqx eqc

eqx eqp eqx eqc

T i T ieqx eqp eqxx eqpp

T ieqpx

d tt t t

dt

d tt t

dt

t t t t t t

t t

= + + +

= + + +

= + + +

+

xz Y x Y p D C

x0 Y x Y p D C

0 Y x Y p x F x p F p

p F x

State vector:

Standard syntax of the dynamic model (Differential and Algebraic Equations):

Parameter vector

( )tx

( )tp

( )tz Measurement vector

Nonlinear model

(Instantaneous voltages at each node;

Instantaneous currents through each branch)

(Fault location, fault resistances)

(Instantaneous voltages and currents at

terminals of the transmission line)



( , ) ( ( , ))m mt t t t=z h xp

After discretization of the dynamic model (Algebraic Equation):

Dynamic state estimation (DSE) procedure (batch mode regression formulation):

1 1( , ) ( , ) ( ) ( ( ( , ) ) ( , ))T T

m m m mt t t t h t t t t + −= − −xp xp H WH H W xp z

( , ) [ ( , ), ( , )]T

m m mt t t t t t=xp x p

Solution is given with following Newton’s iterative algorithm until convergence,

where H is the Jacobian matrix ( )( ) ( ) ( ) ( ), ., ,m m

m m t t t th t t t t == xp xpH xp xp

14


where the extended state vector is

( )

,min ( ) ( , ) ( ( , )) ( , ) ( ( , ))

m

T

m m m mt t

J t t t t t t t t t= − −xp

z h xp W z h xp



The existing method does not work in HVDC lines, due to

• Large condition number of the inverse matrix and large numerical error

• High computational burden

15




Limitations when applying this method in HVDC lines:

Specific Characteristics of (1) DSE Problem and (2) HVDC system

(1) DSE Problem:

• Highly nonlinear DSE problem

• High-dimensional matrix inverse in every Newton’s iteration and

DSE time step; Matrix dimension: (16m+16n+24)×(16m+16n+24)

(2) HVDC system:

• Requires small DSE time step, to accurately track severe transients during faults

• Large section number m and n to ensure model accuracy

1

1

( , ) ( , )

( )

( ( ( , ) ) ( , ))

m m

T T

m m

t t t t

h t t t t

+

−

=

−

−

xp xp

H WH H W

xp z

01 Introduction




05 Conclusion

Outline

16

17

Proposed New DSE Based Fault Location Method

The DSE formulation of the existing method:

• Highly nonlinear DSE problem

• High-dimensional matrix inverse in every Newton’s iteration and DSE time step

The DSE formulation of the proposed method:

• Linear DSE problem;

• No Newton’s iterations;

• Avoid re-calculation of matrix inverse: constant matrix in all DSE time steps

Key Idea: Reformulate the DSE problem for fault location

With given fault location lf and resistance Rf :

linear dynamic model of the line

( ) ( )( )

( )( )

1 1

2 2

eqx eqx

eqx eqx

d tt t

dt

d tt

dt

= +

= +

xz Y x D

x0 Y x D

18


2 2 (2 2 ) 2 (2 ) 2 (2 )

2 (2 2 ) 2 2 (2 ) 2 (2 )

1

2 (2 2 ) 2 2 (2 2 2)

2 (2 2 ) 2 (2 2 2) 2

, , ,

, , ,

/2, , ,

, /2, ,

m n m n

m n m n

eqx

l m n m n

m n r m n

+

+

+ + −

+ + −

=

−

I 0 0 0

0 I 0 0Y

G 0 I 0

0 G 0 I

2 (2 2) 2 (2 ) 2 (2 ) 2 (2 )

2 (2 2) 2 (2 ) 2 (2 ) 2 (2 )

1

2 (2 2 ) 2 (2 ) 2 (2 )

2 (2 2 ) 2 (2 ) 2 (2 )

, , ,

, , ,

/2, , ,

, /2, ,

m n m n

m n m n

eqx

l m n m n

m n r m n

+

+

+

+

=

0 0 0 0

0 0 0 0D

C 0 0 0

0 C 0 0

11 (2 2) (2 +2) 2 2 (2 2) (2 )

(2 2) (2 2) 22 (2 2) (2 2) 2 2

2 2 (2 ) (2 ) 33 (2 ) (2 )

(2 ) (2 ) 2 (2 ) (2 ) 44

51 2 (2 2 2) 53 2 (2 2)

m n m m n

n m n m n

eqx m m n m n

n m n n m

m n n

− − −

− + − + −

+ − −

=

Y 0 E 00 Y 0 E

Y E 0 Y 00 E 0 Y

Y 0 Y 0

11 (2 2) (2 2) (2 2) (2 ) (2 2) (2 )

(2 2) (2 2) 22 (2 2) (2 2) (2 2) (2 )

2 (2 ) (2 2) (2 ) (2 ) 33 (2 ) (2 )

(2 ) (2 ) (2 ) (2 2) (2 ) (2 ) 44

51 2 (2 2 -2) 2 4 2 (2 2)

m n m m m n

n m n m n n

eqx m m m n m n

n m n n n m

m n n

− + − −

− + − + −

+

+

+ −

=

D 0 0 00 D 0 0

D 0 0 D 00 0 0 D

D 0 0 0

Binglin Wang, Yu Liu*, Dayou Lu, Kang Yue and Rui Fan, “Transmission Line Fault Location in MMC-HVDC Grids Based on

Dynamic State Estimation and Gradient Descent”, IEEE Trans. Power Del., 2020, early access. (*: corresponding author)

the coefficient matrices are functions

of lf , Rf , and other constant parameter

matrices of the transmission line.

where

Section

1

Section

1

Section

m

Section

n

Multi section model, left part

(m sections)

Multi section model, right part

(n sections)

...

...

...

...

Fault

Fault

model

lf l-lf

( ) ( )1

lti

( ) ( )2

rti

( ) ( )1

l

L ti( ) ( )l

Lm ti( ) ( )1

r

L ti( ) ( )r

Ln ti

( ) ( )1

ltv

( ) ( )2

ltv

( ) ( )l

m tv( ) ( )1

l

m t+v( ) ( )1

rtv

( ) ( )2

rtv

( ) ( )r

n tv( ) ( )1

r

n t+v

19




( ) ( ), ,z Y x Bm eqx m eqt t t t= −

Discretization of the dynamic model,

Dynamic state estimation (DSE) procedure (batch mode regression formulation):

1ˆ ( , ) ( ) ( ( , ) )T Tm eqx eqx eqx m eqt t t t−= +x Y WY Y W z B



( ) ( )( )

( )( )

1 1

2 2

eqx eqx

eqx eqx

d tt t

dt

d tt

dt

= +

= +

xz Y x D

x0 Y x D

( )( ) ( )

,min ( ) ( , ) , ( , ) ,

m

T

m eqx m eq m eqx m eqt t

J t t t t t t t t t= − + − + xz Y x B W z Y x B

Solution can be directly obtained without iterations,Constant matrix in all

DSE time steps;

No Newton’s iterations

evaluates the consistency between the measurement and the dynamic model( ) ( )ˆ, ,

ˆ ( ) ( )m mt t t t

J t J t=

=x x

20




How to determine the fault location?The best consistency corresponds to correct fault location lf and fault resistance Rf .

,min ( , )

f ff f

l Ry l R=

where function expresses the average chi-square value y as functions of lf and Rf .( )



evaluates the consistency between the measurement and the dynamic model( ) ( )ˆ, ,

ˆ ( ) ( )m mt t t t

J t J t=

=x x

Solution can be obtained through Gradient Descent algorithm,

( 1) ( 1) ( ) ( ) ( ) ( ) ( )[ , ] [ , ] ( , )f f f f f fl R l R l R + + = −

Existing method

Reach last measurement?

No

No

Yes

Yes

Proposed method

Output fault location result

Newton

interation

DSE Procedure

(Highly Nonlinear)

No

No

Yes

Yes

Gradient

Decent

Initial with 1 =

Output fault location result

DSE Procedure

(Linear)

( ) ( ), ,z Y x Bm eqx m eqt t t t= −

( )Store the average chi-square value: ,f fy l R=

0Initialize with t t=0 0Initialize with ,f f f fl l R R= =

0Initialize with t t=

( ) ( ) ( )( )1

ˆ , = ,x Y WY Y W z BT T

m eqx eqx eqx m eqt t t t−

+

( ) ( ) ( )ˆ , , ,=r Y x B zm eqx m eq mt t t t t t− −

( ) ( ) ( )ˆ ˆ ˆ= , ,r WrT

m mJ t t t t t

Reach last measurement?

Generate the nonlinear line model:

( ) ( )( ), ,z h xm mt t t t=

Generate the linear dynamic model:

1 1( , ) ( , ) ( )

( ( ( , ) ) ( , ))

xp xp H WH

H W xp z

T

m m

T

m m

t t t t

h t t t t

+ −= −

−

Constant matrixduing DSE

Newton's Iteration Converges?

Updated in each iteration and each

DSE time step

Reach minimum ?y

Update

, f fl Rt t t= +

1 = +

t t t= +

Flow chart

comparison

between the

existing method

and the proposed

method

21



01 Introduction




05 Conclusion

Outline

22

MMC 1

MMC 2

MMC 3

MMC 4


DC link 24

Line of interest

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

• 320 KV MMC-HVDC grid

• Line of interest: Line S-R, 200 km

• Two-pole instantaneous (sampled value) voltage and current measurements at both

terminals of the line,

• Sampling rate: 20 kilo-samples/sec

• Available time window:

5 ms after the occurrence of the fault

Existing DSE based method v.s.

proposed DSE based method

23

Numerical Experiments

• Section number: selected as m = n = 200 for

both the existing and the proposed method



MMC 1 MMC 3

Line of interests

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

1. 0.01 Ω P-G fault, 50km from side S

Large

condition

number

Unreliable

fault location

results

Existing method Proposed method

24

Positive pole to ground faults (P-G)

Best

Consistency:

(lf , Rf ) =

(49.42 km,

0.0023 Ω)

Fault Location

Error = 0.29 %



MMC 1 MMC 3

Line of interests

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

1. 0.01 Ω P-G fault, 50km from side S

25

Positive pole to ground faults (P-G)

2. P-G faults, through the line

Proposed method

Fault

resistance (Ω)

Average absolute

error (%)

Max absolute

error (%)

0.01 0.1827 0.3738

1 0.1877 0.3636

5 0.1747 0.3628

10 0.1595 0.4554

Accurate Fault Location Results



MMC 1 MMC 3

Line of interests

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

1. 0.01 Ω P-P fault, 50km from side S

Large

condition

number

Unreliable

fault location

results


26

Pole to Pole faults (P-P)

Best

Consistency:

(lf , Rf ) =

(50.48 km,

0.8803 Ω)

Fault Location

Error = 0.24 %



MMC 1 MMC 3

Line of interests

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

1. 0.01 Ω P-P fault, 50km from side S

27

Pole to Pole faults (P-P)

2. P-P faults, through the line

Proposed method

Fault

resistance (Ω)

Average absolute

error (%)

Max absolute

error (%)

0.01 0.1420 0.5507

1 0.1991 0.5446

5 0.1889 0.5728

10 0.1985 0.5345




MMC 1 MMC 3

Line of interests

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

1. 200 Ω P-G fault, 50km from side S

Large

condition

number

Unreliable

fault location

results


28

High Resistance Faults

Best

Consistency:

(lf , Rf ) =

(49.36 km,

199.6725 Ω)

Fault Location

Error = 0.32 %



MMC 1 MMC 3

Line of interests

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

1. 200 Ω P-G fault, 50km from side S

29

High Resistance Faults

2. High resistance P-G faults, through the line

Proposed method

Fault

resistance (Ω)

Average absolute

error (%)

Max absolute

error (%)

200 0.2469 0.6966

300 0.2782 0.8249

400 0.3084 1.0679

500 0.4211 1.2898




Measurement

errorsParameter

errors

30

Discussions

MMC 1 MMC 3

Line of interests

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

• 0.01 Ω P-G faults, through the line

• Different measurement errors

• Different parameter errors



Proposed method

Different

section

numbers

Different

time

window

lengths

31

Discussions

MMC 1 MMC 3

Line of interests

us(t)is(t)

ur(t)ir(t)S R

B1 B2

B3 B4

• 0.01 Ω P-G faults, through the line

• Different section numbers m and n

• Different available time window length



Proposed method

01 Introduction




05 Conclusion

Outline

32

• A new dynamic state estimation based fault location method is proposed for

transmission lines in MMC-HVDC grids.

• The method solves the limitations of the existing DSE based fault location

methods, including large numerical errors and high computational burden,

especially when applied to transmission lines in MMC-HVDC grids.

• The methods present accurate fault location results, independent of fault

types, fault locations and fault resistances, and only requires a short data

window of several milliseconds.

33

Conclusions

• Power electronic dominated systems (for example HVDC

systems) bring additional challenges due to special

characteristics of electromagnetic transients in those systems.

• We need to re-examine the effectiveness of the existing

approaches when applied to power electronic dominated systems.

34

Some Observations

Thank You!

35

P PAL

Should you have any questions, please feel free to contact:

Yu Liu

Power System Protection and Automation Laboratory (PSPAL)

School of Information Science and Technology

ShanghaiTech University

Email: [email protected]; [email protected]



Documents

Fault Location on HVDC Transmission Lines Using Dynamic