training on power frequency electric and magnetic field ......power lines are both electric and...

Training on power frequency electric and

magnetic field strength prediction model

Enrica Caputo – Arpa Piemonte, Radiation Department

• Macro geographical analysis

• Exposition evaluation without measurements

• Exposition evaluation on new sources

• Past exposition evaluation

• Minimun distance from sources calculation

Electric and Magnetic field strength

prediction model

Why?

Energy Infrastructure

FOCUS: Overhead transmission power lines

Primary exposition source

Italy:70000 km HV (120-132-150 kV) and VHV (220-380 kV) transmission lines

GLOSSARY

1. Insulator.

2. Bundle of two conductors (some lines have 4).

3. Spacer to hold the two conductors apart.

4. Earth wire at top of tower or pylon.

5. The three bundles on one side of the tower make

up one electrical circuit. Most lines have two

circuits, one each side.

6. Identity plate saying which line it is and who owns

it. Also usually has a safety warning notice about

the dangers of electrocution.

7. Anti-climbing device - barbed wire to stop

unauthorised climbing

GLOSSARY

Ammarro

singoloSospensione

singola

Sospensione a V

singola

Ammarro

doppioSospensione

doppiaSospensione a V

doppia

In technical documentation :

SS; ┴ Single vertical insulator

DS; ╨ Double vertical insulator

SA; /\ Single horizontal insulator

DA; //\\ Double horizontal insulator

V \\// V-shape insulator (for 380 kV)

Conductors height

GLOSSARY

h1: conductor height on start pylon

h2: conductor height on end pylon

L: Span length

SAG: difference in level between the points of support and the lowest point on the

conductor

GC: minimum ground clearance (minimum height)

GC

h h

GLOSSARY

Conductors width is fixed by geometrichal pylons shape

Conductors height (cfr Sag and minimum Ground clearance) depends

on cables weight and length and environmental boundary conditions

GC

h h

CATENARY

T=Cable Tension (N)

H*= Horizontal Tension (N)

W= Cable Weight (N/m)

𝑧 (𝜉) =𝑘cosh (𝜉/𝑘+𝐶1) +𝐶2

k=Catenary Constant (m)

k= H/W (m)

C1, C2 calculated by h1,h2

h1 h2

z

𝜉

*the horizontal tension is assumed to be constant throughout the conductor at a given temperature

B-E CALCULATION

Power lines are both ELECTRIC and MAGNETIC FIELD sources

ELECTRIC FIELD

• VOLTAGE

• Conductors TYPE and SIZE

• Pylons geometrical SHAPE

• phase DISPOSITION

• DISTANCE by conductors

No time variations

Screened by most building

materials and by trees, hedges

etc

MAGNETIC FIELD

• CURRENT

• Pylons geometrical SHAPE

• phase DISPOSITION

• DISTANCE by conductors

Time variations (Current variation

by energy needs)

Not screened

3D MAGNETIC FIELD CALCULATION

Ampère-Laplace law

m0 air magnetic permeability constant (4p 10-7 H/m)

I current

dl element of length along the path taken by the current

r position vector of the point at which B is being determined

Γ Conductors curve shape (catenary)

3D MAGNETIC FIELD CALCULATION - Γ

Yv= minimum height in xy plane

X axis origin in x catenary minimum

V

V

Y

x

Y

x

V

Y

xcoshY)ee(

2

Y)x(Y VV


Simplified 2D models based on the Biot-Savart law.

If power line conductors satisfy a thin-wire approximation are treated as infinite

line sources positioned at a constant distance from the earth’s surface.

Thin-wire approximation: straight horizontal parallel wires with span length

>>distance between conductors

r

IB

pm

40 Biot-Savart law*

*for a simple conductor


Power lines: single or double three-phase balanced system (phase shift 120°)

-1.5

-1

-0.5

0

0.5

1

1.5

0 100 200 300 400 500 600

50 HzRS

T


Superposition principle:

Biot-Savart law to each phase + Sum as fasors (complex vectors)

0

)()(2

)()(2

22

0

22

0

zB

yyxx

xxIB

yyxx

yyIB

i ii

iiy

i ii

iix

p

m

p

m


• Rxi=

• Ryi=

• di=

• radi= k=

• Re(Bx)= (Rx1 cos rad1 + Rx2 cos rad2 + Rx3 cos rad3 )

• Im(Bx)= (Rx1 sin rad1 + Rx2 sin rad2 + Rx3 sin rad3 )

I*2

0

p

m

22 )()( ii

i

yyxx

xx

22 )()( hyxx i

ikd

p2

I*2

0

p

m

22 )()( ii

i

yyxx

yy

• Bx=

• By=

• Bz=0

• B=22 ByBx

22 )Im()Re( BxBx

22 )Im()Re( ByBy

Two three-phase balanced system :

Re(Bxi), Im(Bxi), Re(Byi), Im(Byi)

Re(Bx)=Re(Bx1)+Re(Bx2)

Im(Bx)=Im(Bx1)+Im(Bx2)

Re(By)=Re(By1)+Re(By2)

Im(By)=Im(By1)+Im(By2)

Bx=

By=

B=

22 )Im()Re( BxBx

22 )Im()Re( ByBy

22 ByBx


PROS

• Simple computation (self made)

• Few input

• Perfect for underground cables

CONS

• Overestimation near conductors

• Just for parallel wires

• Just transverse plane


https://arpapiemontenir.shinyapps.io/Single-circuit-B-calculation/


WEP APPLICATION developed by ARPA Piemonte

Developed in R CRAN environment (free and open source),

published in ARPA debian server (Linux) or in public hosting server

Based on R script (it is possible to run R scripts on local machine)

Simple two-dimensional model with one or two three-phase circuit

Calculation on section plane or at one heigt in a transverse axys

PROS

•Simple computation (self made) excel spreadsheet or other tools



Extract of R script


SEGMENTATION OF THE OVERHEAD POWER LINE CONDUCTORS

Ampère-Laplace law

Superposition principle

Each segment

+

Each phase

The magnetic induction at any point in space

can be numerically computed using a discrete

approximation of eq. having discretised each

conductor into elementary straight

segments,

PROS

• Calculation in complex configuration (multiple lines, power lines

intersection, …)

• Multiple output (horizontal plane, transverse plane, …)

CONS

• A lot of input

• Complex computation (commercial tools)

• Calculation time is proportional to catenary segmentation



MAGIC

394100 394150

394200 394250

394300 394350

394400 394450

394500 394550

394600 4.98198e+006 4.982e+006 4.98202e+006 4.98204e+006 4.98206e+006 4.98208e+006 4.9821e+006 4.98212e+006 4.98214e+006

230

235 240

245

250 255

260

265 270

275

asse Z (m)

asse X (m) asse Y (m)

asse Z (m)


MAGIC


MAGIC


MAGIC

Output + Geographical Information System= Simple exposition evaluation

2D-3D Model Comparison

Twin three-phase circuit 132 kV, span 242m, elevation gap 8m, catenary

constant 1079m

Percentual deviation

-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 10 20 30 40 50 60

distanza da asse linea (m)

sca

rto

%

sostegno

metà campata

Pylon

Midspan

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60


sca

rto

%

sostegno

metà campata

height = 4.5m

from the ground

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0 10 20 30 40 50 60


sca

rto

%

sostegno

metà campataheight = 1.5m

from the ground

Single three-phase circuit 132 kV,

triangle shape, span 210m, no

elevation gap, catenary constant

1050m

Percentual deviation

2D-3D Model Comparison

Pylon

Midspan

Pylon

Midspan


2D MODEL = TWO SYSTEMS OF PARALLEL CONDUCTORS

3D MODEL= COMPLEX WIRES CONFIGURATION

Two or more three-phase balanced system

Is calculation correct?

V1

I1

150 Hz

V1=V2=V3

Balanced line: I1=I2=I3, 1= 2= 3

Phase Voltage

Current

load angle

Three phase AC power lines: phase shifts

Phase shift between Current and Voltage is given to the load nature

Inductive load current LAGS Voltage: <0

Capacitive load current LEADING Voltage: >0

Real load?...



Phase shift in 220 kV power line (Torino city)

For single circuit lines, the choice of the reference current

phasor is arbitrary (e.g. phase a) and, under the hypothesis of

balanced conditions, the phase angle displacement of the other

two currents is simply 2/3π.



Differently, when two or more circuits are present, it is necessary to refer each current

phasor to a unique reference phasor (or to determine the relative phase angle between

the reference phasors of each circuit). It is useful to express the generic current phasor

as:

Twin three-phase AC power lines: phase shift


21221

12

2

12

(* Maurizio Albano, Roberto Benato, Roberto Turri, “DETERMINATION OF LINE CURRENT PHASE ANGLE

DISPLACEMENT FROM MAGNETIC FIELD MEASUREMENTS IN MULTIPLE-CORRIDOR POWER LINES” )

Application

Single three-phase circuit 220 kV (line 2) + Twin three-phase circuit 132 kV (line 1)

Method application trouble:

• Exact catenary status knowledge during measurement perform for

both lines (in order to separately calculate X-axis magnetic induction

contributions of each power line)

• Precision in determining measurement point in span reference system

0

0.2

0.4

0.6

0.8

1

1.2

1.4

00:00 02:24 04:48 07:12 09:36 12:00 14:24 16:48 19:12 21:36 00:00

ora

B (

µT

)

B1

B2

Bsfas

Binfase

Some results

0

5

10

15

20

25

-5.86 3.72 13.29 22.87 32.44 42.02 51.59 61.17 70.74

scarto % tra Bsfas e Binfase

Fre

qu

en

za

Mean: 37.5%

Median: 41.4%

Standard deviation:

22.1

Results

Percentual deviation between calculated B (phase shifts) and

calculated B (no phase shifts)

Conductors height in a point is given by catenary constant (weight and horizontal tension ratio) and span length.

Conductors elongation depends on material elastic properties and temperature (environmental + Joule effect current flow dissipation)

Thermal elongation:

at = thermal expansion coefficient

EDS = everyday stress (t=15°C and I=0)

Elastic elongation :

ec = elastic modulus

Sc = conductor section

Pc = conductor weight per unit length

k = catenary constant

)( EDScEDSttermico ttLL a

)(1

edscc

EDS

celastico kkP

S

LL

e

Model influence parameters

0

1

2

3

4

5

6

7

8

9

10

11

12

-100 -80 -60 -40 -20 0 20 40 60 80 100

distanza dall'asse della linea (m)

ind

uz

ion

e m

ag

ne

tic

a (

µT

)

EDS Temp

Catenary curve variation

Double three-phase circuit 220 kV side by side phase.

Aluminium-Steel conductors Span =300 m – 1 m Sag increase

Section B calculation in everyday stress condition (EDS) and real condition ( I=1000 A , Tenv 50°C) for

ground clearence level

2D ELECTRIC FIELD CALCULATIONCampo elettrico

Coulomb law

2

0rπε2

QE

Q conductor electric charge

r distance conductor- point

ε0 vacuum dielectric constant

Earth effect= Each of the overhead conductors

can be considered as a line charge near a

plane conductor.

Image technique: each conductor has specular

conductor with opposite charge (same distance from plane).

This situation is equivalent to the original setup, and so the force on the

real charge can now be calculated with Coulomb's law between two point

charges

Superposition principle

How can we calculate conductors charge Q? Or, better, linear charge density *?

VPπε2Q1

0

[P] Maxwell capacitance matrix

[V] Voltage fasors matrix

*charge in conductors core , const, for distance >>conductors radius

2D ELECTRIC FIELD CALCULATION

Thin-wire approximation: straight horizontal parallel wires with span

length >>distance between conductors

λ as fasor, λ image conductors= λ conductors (realistic hypothesis for

most of soil typology, but we can consider different conditions)

Gauss law



2D ELECTRIC FIELD CALCULATION STEP BY STEP

1. [P] Maxwell capacitance matrix

2. [P]-1 matrix inverse

3. i i’ ‘ as fasors

4.Combining i i’ for x and y

5.Ex,Ey

6.E

• E calculation is more complex than B calculation : additional step is

calculation knowing Voltage fasors (hardest part);

• Each conductor, even not in voltage, modify electric field (Earth wires );

• Conductors radius and spacing is needed (Bundle of n conductors :

equivalent radius)


Critical issues

• RMS Voltage from ground

• Equivalent radius

• Geometric data input (same as B calculation)

2D ELECTRIC FIELD CALCULATION: INPUT DATA

For each conductor (even Earth wires)

campo elettrico

0

1000

2000

3000

4000

5000

6000

-50 -40 -30 -20 -10 0 10 20 30 40 50


E (

V/m

)Example: Electric field value under different power lines typologies

tensione

220 kV

380 kV

380 kV

campo elettrico doppia terna

0

1000

2000

3000

4000

5000

6000

7000

-50 -40 -30 -20 -10 0 10 20 30 40 50


E (

V/m

)Double three-phase circuit : phase layout

240

120

0

240

120

0

240

120

0

0

120

240

NON-OPTIMIZED PHASES

OPTIMIZED PHASES

Electric field value depends on geometric conductors disposition, but also on

environmental conditions.

Investigation on:

• Temperature

• Soil electrical conductivity

• relative humidity.

ELECTRIC FIELD CALCULATION:Environmental Conditions

ELECTRIC FIELD CALCULATION:Temperature

)( EDScEDSttermico ttLL aThermal elongation:

at = thermal expansion coefficient

EDS = everyday stress (t=15°C and I=0)

TS= thermal stress (90°C :–t=50°C and I=1000)

ΔL= 70 cm

ΔE= 750 V/m

ELECTRIC FIELD CALCULATION: Soil conductivity

Image technique : soil is considered infinit plane perfectly conductive

Soil electric properties depends on water percentage in the form of

electrolytic solution, and since it depends on the soil type and on its

capacity to retain it, different type of soil has different conductivity .

Soil = complex dielectric medium

With some passages it’s possible to prove than electric field in air is given by

superposition of real conductors with charge density λ and Imagine conductors

with charge density λ’, assuming air permittivity as 1


Soil electrical conductivity: Soil type

In standard environmental conditions soil conductivity has small effect

campo elettrico E

0

1000

2000

3000

4000

5000

6000

7000

8000

0 5 10 15 20 25 30 35 40 45

distanza asse linea (m)

E (

V/m

)

RH 90% In blue: measured E

In pink: calculated E

E measure >E calculation ???

Hypotesis: Wider cable charge distribution

ELECTRIC FIELD CALCULATION: relative humidity

ELECTRIC FIELD CALCULATION: relative humidity

Hypotesis: Wider cable charge distribution

Possible solution: increase equivalent radius

ELECTRIC FIELD CALCULATION: Soil conductivity+RH

(a) Paved road (b) Low grass (c) Ground

Electric field variations

Red= HR 100% (fog), blue=HR 90%, green=HR<50%

With high RH, difference between measurements increase for conductive soils

https://arpapiemontenir.shinyapps.io/single-circuit-E-calculation/


https://arpapiemontenir.shinyapps.io/single-circuit-E-calculation/

training on power frequency electric and magnetic field ......power lines are both electric and...

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