Transmission Characteristics of Overhead MV/PLC Channels

Athanasios G. Lazaropoulos and Panayotis G. Cottis

Workshop on Applications for Powerline Communications, October 2008

Outline• Introduction and Review of to date Research Efforts

– Single Conductor over Lossy Earth– MTL Analysis

• Mathematical Analysis– Multiconductor Configuration– Modal Analysis– Derivation of the Propagation Matrix

• BPL Channel Model• Numerical Computation, Results and Discussion

Slide 2

Introduction• Typical Greek Overhead

MV configuration [1]• Basic Configurations

– Underground cables– Overhead lines

• Adverse properties of the overhead MV grid when viewed as a communications medium

Slide 3

Review of to date Research (1/2)• Single Conductor over Lossy Earth

– “A Thin Wire over Earth”– Quasi-transverse-electromagnetic (TEM) modes

• Transmission Characteristics– In 1926, the earliest solutions, Carson [2]

• Assumptions and Restrictions– In 1956, exact modal equations for very thin

overhead wires, Kikuchi [3-4]– In 1972, exact modal equation for thin wire above

earth, Wait [5-6]– In 1997, D’Amore’s solution [7]

Slide 4

Review of to date Research (2/2)

• MTL Analysis– Traveling Waves in MTL– Modes

• Common Mode (CM)• Differential Modes (DM)

– Line Coupling• Wire-to-Wire (W-T-W)• Wire-to-Ground (W-T-G)

Slide 5

(Fig.1)

(Fig.2)

Mathematical Analysis (1/4)• Multiconductor Configuration

i. V and I (matrices n×1)ii. P (matrix n×n)iii. Z and Y (matrices n×n)iv. Second-order differential equations governing

propagation via a conductor

v. P=ZY

Slide 6

( ) VPVYZV⋅=⋅′⋅′=2

2

dzd ( ) IPIZYI

⋅=⋅′⋅′= t

dzd

2

2

(1)

Slide 7

– γi, αi, βi and λi from P i=1,…,n( ) ( ) ( )fjff iii βαγ ⋅+=

Mathematical Analysis (2/4)• Modal Analysis

– Matrix Line Voltages V and Currents I (n×1)– Matrix Modal Voltages Vm and Currents Im (n×1)

(2)when Tv and TI matrices of similarity transformation [7-8]

mV VTV ⋅= m

I ITI ⋅=

(3)– Propagation constants

Slide 8

Mathematical Analysis (3/4)• Modal Analysis

– Equation for Modal Voltages

– General Equation for Modal Voltages

where

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−

−

+

+

−

−

mn

m

z

z

mn

m

z

z

mn

m

V

V

e

e

V

V

e

e

V

V

nn

M

L

MOM

L

M

L

MOM

L

M111

0

0

0

0 11

γ

γ

γ

γ

(4)

(5.1)( ) ( )0mmm z VFV ⋅=( ) ( )00 1 VTV ⋅= −

Vm (5.2)

Slide 9

Mathematical Analysis (4/4)• Propagation Matrix Derivation

– Propagation Matrix P [7], [9]• Internal, External, Ground Impedance• Admittance

( ) ( ) 111� −−− ′+′⋅′+′+′= gcgei YYZZZP

• Mode Characteristic Impedance and Admittance Matrices

[ ] { }[ ]eeInIeecmo diagZ

modmod

11modmod, ×

−× ⋅⋅⋅′== TTYZ λλ K

(6)

(7)

Slide 10

BPL Channel Model (1/5)• A priori and Deterministic (Modal)

Transfer Function [10-11]• Modal Frequency Response [12]• Reflection and Transmission Coefficients• Multipath Channel exhibiting Frequency

Selectivity– Multipath or Echo Model (LV [13-15] or modal

MV [16])

Slide 11

BPL Channel Model (2/5)(Fig.1)

(2)

( )( )3

31 tanh

tanhlZZlZZZZ

Lo

oLoin γ

γ++

=

( )( )2

22 tanh

tanhlZZlZZZZ

bo

oboin γ

γ++

=

( ) ( )( ) ( )121

121

tanh//tanh//

lZZZlZZZZZ

inino

oininoin γ

γ+

+=

oL

oL

ZZZZ

−−

=Γ1( )( ) oinin

oinin

ZZZZZZ

+−

=Γ21

212 //

//

• SM Method, Meng [17]

(Fig.2)

Slide 12

BPL Channel Model (3/5)• S-parameters [18]

oin

oin

ZZZZ

S+−

=11gg E

VVV

VV

EV

S 1

1

2

2

3321 22 ⋅⋅⋅=⋅=(8) (9)

• Shifting in the reference planes [19]

gin

in

g ZZZ

EV

+=1

( )3

3

1

1

2

3

11

l

l

ee

VV

⋅−

⋅−

⋅Γ+⋅Γ+

= γ

γ

( )1

1

2

2

1

2

11

l

l

ee

VV

⋅−

⋅−

⋅Γ+⋅Γ+

= γ

γ

(10)

(11)

Slide 13

BPL Channel Model (4/5)• Step 1: Evaluation of the

scattering matrices of the network modules Sk k=1,..,N

• Step 2: Evaluation of transmission matrices of the network modules Tk k=1,..,N

• Step 3: Evaluation of the end-to-end transmission matrix T

• Step 4: Evaluation of the end-to-end transfer function H(f)=S21(f)

Slide 14

BPL Channel Model (5/5)

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⋅−

−=

21

221112

21

11

21

22

21

1

SSSS

SS

SS

ST ∏=

=N

kkT

1

T

• T and S matrices for the whole network

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−=

11

12

11

11

122122

11

21

1TT

T

TTTT

TT

S(12) (13) (14)

Slide 15

Results and Discussion (1/5)• Three modes (CM and DMi ,i=1,2)• Separate Channels for each mode• Attenuation Constants and Phase Delays

0 20 35 40 60 80 1000

5

10

15

Frequency (MHz)

Atte

nuat

ion

cons

tant

α (d

B/k

m)

Common ModeDifferential Mode 1Differential Mode 2

(Fig.1) (Fig.2)

Slide 16

Results and Discussion (2/5)• MV/BPL Topologies

– Topology 1: L1=500m, L2=500m, Lb1=10m– Topology 2: L1=500m, L2=200m, L3=100m,

L4=200m, Lb1=6m, Lb2=1m, Lb3=6m (urban case)

– Topology 3: L1=500m, L2=200m, L3=100m, L4=200m, Lb1=300m, Lb2=150m, Lb3=200m (rural case)

– Topology 4, the same as Topology 3 but with no branches (“LOS” case)

0 10 20 30 40 50 60 70 80 90 100

0

20

40

60Cha

nnel atte

nuation (d

B)

Topology 1

0 10 20 30 40 50 60 70 80 90 100

0

20

40

60Cha

nnel atte

nuation (dB)

Topology 2

0 10 20 30 40 50 60 70 80 90 100

0

20

40

60Cha

nnel atte

nuation (d

B)

Topology 3

0 10 20 30 40 50 60 70 80 90 100

0

20

40

60Cha

nnel atte

nuation (d

B)

Frequency (MHz)

Topology 4

0 10 20 30 40 50 60 70 80 90 100

0

20

40

60Cha

nnel atte

nuation (d

B)

Topology 1

0 10 20 30 40 50 60 70 80 90 100

0

20

40

60Cha

nnel atte

nuation (d

B)

Topology 2

0 10 20 30 40 50 60 70 80 90 100

0

20

40

60Cha

nnel atte

nuation (d

B)

Topology 3

0 10 20 30 40 50 60 70 80 90 100

0

20

40

60Cha

nnel atte

nuation (d

B)

Frequency (MHz)

Topology 4

Slide 17

Results and Discussion (3/5)

• Topology 1, 2, 3 and 4

(Fig.3) (Fig.4)

Slide 18

Results and Discussion (4/5)

• Topology 3 and ‘LOS’ case• Multipath Propagation• Waste of Usable Bandwidth• Number and Behavior of Notches

(Fig.5)

(Fig.6)

Slide 19

Results and Discussion (5/5)

• Percentage Wasted Bandwidth

(Fig.7) (Fig.8)

References (1/3)1. T. A. Papadopoulos, Ch. G. Kaloudas and G. K. Papagiannis, “A Multipath

Channel Model for PLC Systems based on Nodal Method and Modal Analysis”, in Proc. 2007 IEEE International Conference on Power Line Communications and Its Applications, ISPLC’07, Pisa, Italy.

2. J. R. Carson, “Wave propagation in overhead wires with ground return,” Bell Syst. Tech. J., vol. 5, pp. 539–554, 1926.

3. H. Kikuchi, “Wave propagation along an infinite wire above ground at high frequencies,” Proc. Electrotech. J., vol. 2, pp. 73–78, Dec. 1956.

4. H. Kikuchi, “On the transition form a ground return circuit to a surface waveguide,” in Proc. Int. Congr. Ultrahigh Frequency Circuits Antennas, Paris, France, Oct. 1957, pp. 39–45.

5. J. R. Wait, “Theory of wave propagation along a thin wire parallel to an interface,” Radio Sci., vol. 7, pp. 675–679, Jun. 1972.

6. J. R. Wait and D. A. Hill, “Propagation along a braided coaxial cable in a circular tunnel,” IEEE Trans. Microw. Theory Tech., vol. 23, pp. 401–405, May 1975.

7. M. D’Amore and M. S. Sarto, “A new formulation of lossy ground return parameters for transient analysis of multi-conductor dissipative lines,” IEEE Trans. Power Del., vol. 12, no. 1, pp. 303–314, Jan. 1997.

Slide 20

References (2/3)8. R. P. Clayton, Analysis of Multi-Conductor Transmission Lines. New York:

Wiley, 1994.9. P. Amirshahi and M. Kavehrad, “High-Frequency Characteristics of Overhead

Multiconductor Power Lines for Broadband Communications,” IEEE Selected Areas in Communications, vol. 24, issue 7, pp. 1292–1303, Jul. 2006.

10. S. Galli, T. Banwell, "A Novel Approach to the Modeling of the Indoor Power Line Channel - Part II: Transfer Function and Its Properties," IEEE Transactions on Power Delivery, vol. 20, no. 3, July 2005.

11. T. Banwell, S. Galli, "A Novel Approach to the Modeling of the Indoor Power Line Channel - Part I: Circuit Analysis and Companion Model," IEEE Transactions on Power Delivery, vol. 20, no. 2, Apr. 2005.

12. D. K. Cheng, Fundamentals of Engineering Electromagnetic. New York: Addison-Wesley, 1992.

13. H. Philipps, “Modeling of powerline communication channels,” in Proc. Int. Symp. Power Line Commun. Appl., 2000, pp. 14–25.

14. H. Philipps, “Development of a statistical model for power-line communication channels,” in Proc. Int. Symp. Power Line Commun. Appl., 2000, pp. 153–160.

15. M. Zimmerman and K. Dostert, “A multipath model for the powerline channel,”IEEE Trans. Commun., vol. 50, no. 4, pp. 553–559, Apr. 2002.

Slide 21

References (3/3)16. P. Amirshahi and M. Kavehrad, “Transmission channel model and capacity of

overhead multi-conductor medium-voltage power-lines for broadband communications,” in Proc. CCNC, Las Vegas, NV, Jan. 2005, pp. 354–358.

17. Meng H., Chen S., Guan Y.L., Law C.L., So P.L., Gunawan E., Lie T.T, “Modeling of transfer Characteristics for the broadband power line communication channel,” Power Delivery, IEEE Transactions on Publication, July 2004, Volume 19, Issue 3, pages 1057- 1064.

18. G. Gonzalez, Microwave Transistor Amplifiers. Englewood Cliffs, NJ: Prentice-Hall, 1997.

19. D. M. Pozar, Microwave Engineering. New York: Wiley.

Slide 22

Workshop on Applications for Powerline Communications, October 2008

Slide 23

e-mail: thlazar@mail.ntua.gr

Transmission Characteristics of Overhead MV/PLC Channels

Athanasios G. Lazaropoulos and Panayotis G. Cottis