research article electromagnetic interference between cranes and … · 2019. 7. 31. · wire x y z...

Research ArticleElectromagnetic Interference between Cranes andBroadcasting Antennas

V. Javor

Faculty of Electronic Engineering, University of Nis, A. Medvedeva 14, 18000 Nis, Serbia

Correspondence should be addressed to V. Javor; [email protected]

Received 22 July 2015; Accepted 18 October 2015

Academic Editor: Felipe Cátedra

Copyright © 2015 V. Javor. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

An interesting phenomenon was noticed in some cases by workers operating with cranes in electromagnetic field of broadcastingantennas. They experienced electrical shock or burning pain at distances of kilometers away from powerful transmitters becausecranes act as unintentional receiving antennas. The solution to this problem depends on dimensions and positioning of thecrane structure, electromagnetic field strength at the site, frequency, and directional characteristic of the transmitting antenna.Electromagnetic interference between such structures is analyzed in this paper. Computational results for the induced currentsand voltages in crane, treated as wire antenna problem, are determined using integrodifferential equations for the current alongconductive structure, satisfying boundary condition for the electric field. Pointmatchingmethod as theMethod ofMoments (MoM)is applied for solving these equations and polynomial approximation of the current is used. Results are presented for different cranestructures and possible solutions to this problem are given.

1. Introduction

When considering interference between natural electro-magnetic sources of disturbances (terrestrial, as lightningdischarges, or extraterrestrial, as cosmic radiation and solarwind) and various man-made objects (such as equipment,electronic devices, electric systems, power lines, commu-nication and automation systems, and installations), thekey issues are electromagnetic field strength, amplitudes ofvoltages and currents, electrical properties of the medium,dimensions and positioning of the structure, distances, andfrequency. An adequate modeling would take into accounta wide variety of configurations of the observed systems.In the last few decades rapid advance has been achieveddue to development of numerical programs and moderncomputers possibilities. The analysis in this paper is basedon the wire antenna approach and the ground is treated asperfectly conducting. Finite ground conductivity has someinfluence on induced voltages and currents, so it could beconsidered using the same procedure as in this paper, butthe solution to this problem is what matters. However, theseelectromagnetic interference (EMI) problems were rarelynoticed and described just in a few papers [1–7]. Large

conductive structures permanently or temporarily positionedin electromagnetic field of powerful medium wave (MW)transmitters, if their dimensions are of the order of wave-length, might be dangerous for humans and equipment. AMtransmission is nowadays mostly used for sports, news, andtalk radio, whereas FM is better for sound. Digital audiobroadcasting is advancing in many countries all over theworld. Although there is a shift to higher frequencies for allsystems, MW transmitters are still in operation throughoutthe world. AM carrier frequencies are assigned to stationsin the frequency range from 531 to 1611 kHz, and, just inEurope, there are still more than a hundred of them withpower ranging from 1 kW to 1MW [8], depending on thetargeted area (local, regional, or international).

2. Some EMI Problems

The lifting crane of height 60m and jib of length about25m was operating in Progar (Serbia), 8 km away from thetransmitter, when the problem was noticed by crane workers.Themeasured open-circuit voltagewas 450V. Radio Belgradewas operating at the frequency𝑓=684 kHzup to 1999, havingpowerful 2 MW transmitter and main antenna of height ℎ =

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2015, Article ID 452962, 10 pageshttp://dx.doi.org/10.1155/2015/452962

2 International Journal of Antennas and Propagation

Z

C

(a)

(b)

(c)

Figure 1: Possible places (a), (b), and (c) for inserting impedanceinto the crane contour.

Figure 2: Rail-mounted 65 t crane in Tenerife (Spain).

230m (half-wave monopole). The electric field strength was𝐸0= 2.1V/m at the crane’s site. The solution to that problem

was an egg-insulator inserted above the hook (Figure 1),thus disturbing the resonance of the formed contour. Thelimitation of this solution is its mechanical strength.

Values of the induced voltages were measured in somesimilar situations throughout the world. There are rail-mounted container cranes in the harbor of Tenerife, Spain,having 30.5m span and capacity of 65 t. At one of them, theindustrial bus was faulty each timewhen it was in the positionto take the load from ship, or if its spreader descended nearcontainers. Sensors and actuators were grounded to the cranestructure, but the problem in control system persisted. In2013, the induced current of 500mA was measured, as wellas 50V voltage at the frequency 𝑓 = 621 kHz due to AMantenna broadcasting at this frequency (Spanish nationalradio broadcast) from the nearby mountain [6]. When theylubricated the wires of steel cables supporting the spreaderand thus isolated the spreader from crane structure byinserting some impedance, the problem was temporarilysolved. The crane structure is presented in Figure 2, and theinstrument measuring the induced voltage is presented inFigures 3 and 4.The further work presented in this paper wasinitiated by coworking on this problem.

At the island Oahu (Hawaii), the crane operator experi-enced electrical shock while using it to lower steel peelingsinto the canal [2]. The crane had the boom of 33.5m length

Figure 3: Measurement site.

Figure 4: Instrument measuring induced voltage of about 50V atabout 621 kHz.

and was near transmitter broadcasting five AM and one FMchannel at the frequencies from 30 to 100MHz with the totalpower 117 kW and antenna of height ℎ = 122m.

In 50 t rough-terrain crane in Japan [3] induced voltagesin the hook up to 1.2 kV and several amperes measured in theboom of this crane were noticed. It was positioned in the farfield of the transmitter operating at frequency 𝑓 = 624 kHz,at the distance where the measured electric field was 𝐸

0=

0.79V/m. The case is examined further in this paper. In [3]the solution to put acrylic plate under outrigger floats is given,and also another solution to add a plain knit grounding wirein the hook was suggested.

On the building site in Rio de Janeiro (Brazil) wheretwo cranes were used, workers reported electrical shock andskin burns when they touched the boom of the large crawlercrane, and electronic systems of the smaller truck-basedcrane became inoperative [7]. The grounding of the vehicledid not solve the problem. It was due to AM transmittersoperating with the power of 100 kW at 𝑓

1= 1280 kHz (station

1) and at 𝑓2= 900 kHz (station 2), approximately 230 meters

from the building site. Practical solution to the problem wasa coil wounded around the hydraulic jack of the crane, withone end connected to the hook and the other grounded to anearby point.

EMI problem was noticed also by workers using a largecrane during the assembly phase of the turbine component,while building wind power plant in Turkey [5], nearby AMtransmitter operating at 𝑓 = 702 kHz with the power of550 kW. Steel tower of the turbine had 80 meters of height,and the rotor with three blades 44 meters long. The mainboom of the crane was 110m long and there was also a shorterauxiliary boom. Crane site was 8 km from the transmitter.Additional grounding was used to mitigate the inducedeffects.

International Journal of Antennas and Propagation 3

Z

Boom

Wire

x y

z

𝜑

𝜃

�̂�

�̂�r̂

h1

h2

Jib

h3

2a1

2a2

2a3

Figure 5: Simple wire antenna model of the crane in externalelectromagnetic field.

All the mentioned problems may be treated as receivingwire antenna in external electromagnetic field, so that someof the codes may be used as NEC [9], AWAS [10], andso forth. Programs AWAS and SPAN [11] are used in thispaper to calculate induced currents and voltages for the givenexamples.

3. Crane Acting as Receiving Antenna inExternal Electromagnetic Field

To model the crane structure as wire antenna in externalelectromagnetic field, it is necessary to determine if the fieldis near or far. For all the mentioned cases, the constructionwork is done in the far field of transmitting antenna, at afew hundreds of meters or even kilometers away [12, 13].Near field is in fact prohibited area with electric field valuesmuch over the occupational/controlled limits according toregulations. It should be noticed that mentioned problemsoccur in the area with electric field values below the publiclimits for these frequencies [14]. Let us assume that receivingantenna is in a plane wave electromagnetic field, so thatelectric field is

𝐸𝑠= 𝐸0

⋅ exp [−𝑗𝑘 (𝑥 sin 𝜃 cos𝜑 + 𝑦 sin 𝜃 sin𝜑 + 𝑧 cos 𝜃)] ,(1)

where 𝜃 and 𝜑 are spherical coordinates, 𝑥, 𝑦, and 𝑧 areDescartes coordinates given in Figure 5, 𝐸

0is the maximum

electric field strength, 𝑘 = 2𝜋/𝜆 is the phase constant,𝜆 = 𝑐/𝑓is the wavelength, and 𝑐 is the speed of light.

The crane is treated as wire antenna structure at perfectlyconducting ground. To model a 50 t rough-terrain crane [3]with cylindrical segments, the boom segment is taken ofheight ℎ

1= 50.5m and radius 𝑎

1= 37.5 cm, the jib of length

ℎ2= 26m and radius 𝑎

2= 20 cm, and the wire of length ℎ

3

Table 1: Induced voltages in case A.

Voltage (V)𝑓 (kHz) 𝜃 = 0, 𝜑 = 0 𝜃 = 𝜋/2, 𝜑 = 0 𝜃 = 𝜋/2, 𝜑 = 𝜋/2500 25.74 48.61 41.20550 33.85 70.55 61.65600 47.77 110.66 99.10650 78.30 203.10 185.60700 196.40 574.84 533.95720 346.53 1067.93 997.05726 370.75 1159.83 1085.61727 370.34 1161.98 1087.43728 368.51 1159.19 1085.32735 325.62 1043.23 1069.28750 207.44 691.59 978.15800 76.63 294.23 650.84850 44.39 198.67 512.33900 29.95 158.59 421.281000 16.15 125.72 279.76

= 48m and radius 𝑎3= 1.5 cm. This is the first examined

crane, denoted by case A. For the second examined crane,denoted by case B, lengths are the same for all segments,but radii are 𝑎

1= 15 cm, 𝑎

2= 10 cm, and 𝑎

3= 2.5 cm. The

hook is at height 2.5m above the ground, in both cases. Ifusing FDTD method as in [3], calculated induced voltagesare about 600V, whereas measured results from [3] are upto 1.2 kV, and induced currents are of several amperes, if themaximum electric field is 𝐸

0= 0.79V/m and 𝑓 = 624 kHz.

Results for this crane are calculated in this paper using AWAS[10], based on Pocklington’s equation [15] and polynomialapproximation of the currents [16]. The induced voltages aregiven in Table 1 for case A and in Table 2 for case B, for therange of frequencies of interest and the three propagationdirections.These show that frequencies producing the largestvoltages differ in the two cases, so as themaximumof inducedvoltages. At𝑓 = 727 kHzmaximumvoltage𝑈maxA = 1161.98Vis calculated in case A, whereas at 𝑓 = 676 kHz voltage𝑈maxB= 1433.24V in case B, both for the propagation directions𝜃 = 𝜋/2, 𝜑 = 0.

The induced currents along the structure are given inFigures 6–11, starting from the base of the boom, along the jib,and down the wire to the hook at the end. These results aregiven in Figure 6 for the electric field 𝐸

𝜃= 0.79V/m, 𝐸

𝜑= 0,

for the propagation directions 𝜃 = 0, 𝜑 = 0, in Figure 7 for𝜃 = 𝜋/2, 𝜑 = 0, and in Figure 8 for 𝜃 = 𝜋/2, 𝜑 = 𝜋/2, forcase A (total length along the crane in that case is 124.5m).For 𝐸

𝜃̸= 0, 𝐸𝜑= 0, 𝜃 = 0, 𝜑 = 𝜋/2, there are no voltages or

currents induced, but this is not the case in real situation. Infact 𝜃 is near 𝜋/2 and any 𝜑may exist during crane operation,as both antenna structures are vertically positioned at theground.

It is shown that at some frequencies the phenomenon willnot be noticed at all. The maximum of induced current at thebase of the boom is about 5 amperes, and it occurs for thefrequency 𝑓 = 727 kHz and the propagation directions 𝜃 =


Table 2: Induced voltages in case B.

Voltage (V)𝑓 (kHz) 𝜃 = 0, 𝜑 = 0 𝜃 = 𝜋/2, 𝜑 = 0 𝜃 = 𝜋/2, 𝜑 = 𝜋/2500 28.59 58.06 50.83550 40.80 91.95 82.68600 68.07 171.31 157.33640 139.45 385.12 358.90670 420.36 1248.21 1174.41675 474.24 1426.01 1343.43676 475.32 1433.24 1350.07677 472.50 1427.73 1345.88680 443.51 1350.95 1274.10700 194.54 623.25 590.86750 67.36 246.68 236.49800 39.12 165.53 160.24850 26.58 131.73 128.43900 19.34 114.05 111.791000 11.03 97.61 96.55

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Curr

ent (

A)

JibBoomDistance along the structure (m)

20 40 60 80 100 120 1400Wire

700kHz650kHz600kHz550kHz500kHz

1000 kHz900kHz800 kHz750kHz727kHz

𝜃 = 0, 𝜑 = 0

Figure 6: Induced currents versus length from the boom base, caseA, directions 𝜃 = 0, 𝜑 = 0.

𝜋/2, 𝜑 = 0, in case A. This current is about 5.7 amperes for𝑓 = 676 kHz in case B. It should be noticed that for ±30 kHzcurrents along the structure are about one-half of the value at𝑓 = 727 kHz, as shown in Figure 7.

There is a difference in current results at segmentsbeginnings/ends, if compared to FDTD results [3]. Thereare no discontinuities in currents results due to Kirchhoff ’slaw for currents at nodes which is satisfied in the appliedprocedure. The chosen polynomial degree is 𝑛 = 3. In case B,for ±30 kHz, currents along the structure are about one-thirdof the value at 𝑓 = 676 kHz, as shown in Figure 10. Resonant


20 40 60 80 100 120 1400Wire

𝜃 = 𝜋/2, 𝜑 = 0



0

1

2

3

4

5

Curr

ent (

A)

Figure 7: Induced currents versus length from the boom base, caseA, directions 𝜃 = 𝜋/2, 𝜑 = 0.


20 40 60 80 100 120 1400Wire



0

1

2

3

4

5

Curr

ent (

A)

𝜃 = 𝜋/2, 𝜑 = 𝜋/2

Figure 8: Induced currents versus length from the boom base, caseA, directions 𝜃 = 𝜋/2, 𝜑 = 𝜋/2.

characteristics of this structure may be noticed also in resultsfor the induced voltages versus frequency in Figures 12 and13, for the two cases A and B.

From the calculation of induced currents and voltages forthese two cases it may be noticed that the change in segmentscross section dimensions has great influence. Change ofwire diameter, determined also with mechanical constraints,changes resonant frequency and in this way the problem



20 40 60 80 100 120 1400Wire


1000 kHz900 kHz800kHz700kHz

𝜃 = 0, 𝜑 = 0

0.0

0.5

1.0

1.5

2.0

2.5

Curr

ent (

A)

Figure 9: Induced currents versus length from the boom base, caseB, directions 𝜃 = 0, 𝜑 = 0.


20 40 60 80 100 120 1400Wire



0

1

2

3

4

5

6

Curr

ent (

A)

𝜃 = 𝜋/2, 𝜑 = 0

Figure 10: Induced currents versus length from the boom base, caseB, directions 𝜃 = 𝜋/2, 𝜑 = 0.

might be mitigated. Another approach may be an adequatechoice of crane configuration after the structure is analyzedand induced voltages and currents are computed.

4. Computation Procedure Based onHallen’s Equation

Magnetic vector-potential of a wire antenna structure with𝑛 linear cylindrical segments, having current distribution


20 40 60 80 100 120 1400Wire



0

1

2

3

4

5

6

Curr

ent (

A)

𝜃 = 𝜋/2, 𝜑 = 𝜋/2

Figure 11: Induced currents versus length from the boom base, caseB, directions 𝜃 = 𝜋/2, 𝜑 = 𝜋/2.

𝜃 = 𝜋/2, 𝜑 = 𝜋/2

𝜃 = 0, 𝜑 = 0

𝜃 = 𝜋/2, 𝜑 = 0

600 700 800 900 1000500Frequency (kHz)

0

200

400

600

800

1000

1200

1400

Volta

ge (V

)

Figure 12: Open-circuit voltage in case A for 𝐸𝜃= 0.79V/m, 𝐸

𝜑= 0

and propagation directions: 𝜃 = 0 and 𝜑 = 0; 𝜃 = 𝜋/2 and 𝜑 = 0;𝜃 = 𝜋/2 and 𝜑 = 𝜋/2.

𝐼𝑧𝑚

(𝑧𝑚) along 𝑚th segment, is obtained as the sum of 𝑛

components. Each component 𝐴(𝑧𝑚) is in the direction of

𝑚th segment, having length ℎ𝑚and radius 𝑎

𝑚, so that

𝐴 (𝑧𝑚) =𝜇

4𝜋∫ℎ𝑚

0

𝐼𝑧𝑚

(𝑧𝑚)exp (−𝑗𝑘𝑟

𝑚,𝑚)

𝑟𝑚,𝑚

d𝑧𝑚, (2)


𝜃 = 𝜋/2, 𝜑 = 𝜋/2

𝜃 = 0, 𝜑 = 0

𝜃 = 𝜋/2, 𝜑 = 0

600 700 800 900 1000500Frequency (kHz)

0

200

400

600

800

1000

1200

1400

1600

Volta

ge (V

)

Figure 13: Open-circuit voltage in case B for 𝐸𝜃= 0.79V/m, 𝐸

𝜑= 0

and propagation directions: 𝜃 = 0 and 𝜑 = 0; 𝜃 = 𝜋/2 and 𝜑 = 0;𝜃 = 𝜋/2 and 𝜑 = 𝜋/2.

where 𝑟𝑚,𝑚= [𝑥𝑚

2 + 𝑦𝑚

2 + (𝑧𝑚− 𝑧𝑚)2]1/2 is the distance

between the point 𝑀(𝑥𝑚, 𝑦𝑚, 𝑧𝑚) and the point 𝑃(0, 0, 𝑧

𝑚)

along the axis of the𝑚th segment, for𝑚 = 1, . . . , 𝑛.The total magnetic vector-potential is

𝐴 =𝑛

∑𝑚=1

𝐴 (𝑧𝑚) . (3)

Descartes components of magnetic vector-potential originat-ing from the 𝑙th segment current are recalculated into the𝑚thsegment Descartes coordinate system as

𝐴𝑥𝑚

= ∑𝑙,𝑙 ̸=𝑚

sin𝜓𝑙,𝑚

sin 𝜃𝑙,𝑚𝐴 (𝑧𝑙) ,

𝐴𝑦𝑚

= − ∑𝑙,𝑙 ̸=𝑚

cos𝜓𝑙,𝑚

sin 𝜃𝑙,𝑚𝐴 (𝑧𝑙) ,

𝐴𝑧𝑚

= 𝐴 (𝑧𝑚) + ∑𝑙,𝑙 ̸=𝑚

cos 𝜃𝑙,𝑚𝐴 (𝑧𝑙) ,

(4)

where 𝜃𝑙,𝑚, 𝜓𝑙,𝑚, and 𝜑

𝑙,𝑚are Euler’s angles between the

𝑙th and 𝑚th segments of Descartes coordinate systems.Boundary condition for the tangential component of electricfield at the conductive surface and Lorenz gauge condition areused, so that

𝐴𝑧𝑚

= 𝐶1𝑚

cos (𝑘𝑧𝑚) + 𝐶2𝑚

sin (𝑘𝑧𝑚) − 𝐹 (𝑧

𝑚) , (5)

𝐹 (𝑧𝑚)

= ∫𝑧𝑚

0

(𝜕𝐴𝑥𝑚

𝜕𝑥𝑚

+𝜕𝐴𝑦𝑚

𝜕𝑦𝑚

)𝑥𝑚=𝑎𝑚

𝑦𝑚=0

𝑧𝑚=𝑠

cos [𝑘 (𝑧𝑚− 𝑠)] d𝑠

−1

𝑗𝑐∫𝑧𝑚

0

𝐸𝑧𝑚𝑠

𝑥𝑚=𝑎𝑚𝑦𝑚=0

𝑧𝑚=𝑠

sin [𝑘 (𝑧𝑚− 𝑠)] d𝑠,

(6)

where 𝐶1𝑚

and 𝐶2𝑚

are complex constants and 𝐸𝑧𝑚𝑠is the

external electric field component at the surface of the 𝑚thsegment. Function (6) is written as

𝐹 (𝑧𝑚) = −

1

𝑗𝑐∫𝑧𝑚

0

𝐸𝑧𝑚𝑠


𝑧𝑚=𝑠

sin [𝑘 (𝑧𝑚− 𝑠)] d𝑠 +

𝜇

4𝜋

⋅ ∫ℎ𝑙

0

𝐼𝑧𝑙

(𝑧𝑙) ∫𝑧𝑚

0

cos [𝑘 (𝑧𝑚− 𝑠)]

⋅ (𝜕

𝜕𝑧𝑙

+ cos 𝜃𝑙,𝑚

𝜕

𝜕𝑧𝑚

)

⋅exp (−𝑗𝑘𝑟

𝑙,𝑚)

𝑟𝑙,𝑚

𝑥𝑚=𝑎𝑚

𝑦𝑚=0

𝑧𝑚=𝑠

d𝑠 d𝑧𝑙,

(7)

which results in the system of integrodifferential equations ofHallen’s type [17] for the currents along this structure:

𝑛

∑𝑙=1

∫ℎ𝑙

0

𝐼𝑧𝑙

(𝑧𝑙)𝐾𝑚,𝑙(𝑧𝑚, 𝑧𝑙) d𝑧𝑙−4𝜋𝐶1𝑚

𝜇cos (𝑘𝑧

𝑚)

−4𝜋𝐶2𝑚

𝜇sin (𝑘𝑧

𝑚)

=4𝜋

𝑗𝑐𝜇∫𝑧𝑚

0

𝐸𝑧𝑚𝑠


𝑧𝑚=𝑠

sin [𝑘 (𝑧𝑚− 𝑠)] d𝑠

−4𝜋

𝑗𝑐𝜇

𝑛𝑍

∑𝑖=1

𝑍(𝑖)𝐼 (𝑧𝑚

(𝑖)) sin [𝑘 (𝑧𝑚− 𝑧𝑚

(𝑖))] ,

(8)

for𝑚 = 1, . . . , 𝑛, whereas integral kernels are for 𝑙 ̸= 𝑚

𝐾𝑚,𝑙(𝑧𝑚, 𝑧𝑙) = cos 𝜃

𝑙,𝑚

exp (−𝑗𝑘𝑟𝑙,𝑚)

𝑟𝑙,𝑚


− ∫𝑧𝑚

0

cos [𝑘 (𝑧𝑚− 𝑠)] [

𝜕

𝜕𝑧𝑙

+ cos 𝜃𝑙,𝑚

𝜕

𝜕𝑧𝑚

]

⋅exp (−𝑗𝑘𝑟

𝑙,𝑚)

𝑟𝑙,𝑚

𝑥𝑚=𝑎𝑚

𝑦𝑚=0

𝑧𝑚=𝑠

d𝑠,

(9)

and for 𝑙 = 𝑚

𝐾𝑙,𝑙(𝑧𝑙, 𝑧𝑙) =

exp (−𝑗𝑘𝑟𝑙,𝑙)

𝑟𝑙,𝑙

𝑥𝑙=𝑎𝑙𝑦𝑙=0

. (10)

In (8),𝑍(𝑖) is the concentrated impedance at point 𝑧𝑚

(𝑖) alongthe 𝑖th segment, for 𝑖 = 1, . . . , 𝑛

𝑧, where 𝑛

𝑧is the total

number of concentrated impedances for that segment. Thissystem of equations is solved by Point matching method asthe Method of Moments (MoM) [18] and matching pointsare equidistantly positioned at the surface of each segment,including the beginnings and ends of segments. Currentsare assumed to be distributed along the axes of segments,although they are flowing along the conductive surface of


the structure, in order to avoid singularities in integrals.Distributions of the currents are unknowns and they areapproximated by polynomials [16].

The distance between the matching point𝑀(𝑥𝑚, 𝑦𝑚, 𝑧𝑚)

at 𝑚th segment surface and the point 𝑃𝑙(0, 0, 𝑧

𝑙) along the

axis of 𝑙th segment, where the elementary current source ispositioned, for 𝑙 ̸= 𝑚 is

𝑟𝑙,𝑚= [(𝑥

𝑚− 𝑥𝑏𝑙,𝑚− 𝑧𝑙sin𝜓𝑙,𝑚

sin 𝜃𝑙,𝑚)2

+ (𝑦𝑚− 𝑦𝑏𝑙,𝑚− 𝑧𝑙cos𝜓𝑙,𝑚

sin 𝜃𝑙,𝑚)2

+ (𝑧𝑚− 𝑧𝑏𝑙,𝑚− 𝑧𝑙cos 𝜃𝑙,𝑚)2

]1/2

,

(11)

and for 𝑙 = 𝑚

𝑟𝑙,𝑙= [𝑥𝑙

2 + 𝑦𝑙

2 + (𝑧𝑙− 𝑧𝑙)2

]1/2

. (12)

𝑃𝑏(𝑥𝑏𝑙,𝑚, 𝑦𝑏𝑙,𝑚, 𝑧𝑏𝑙,𝑚) is the beginning of the 𝑙th segment,

that is, its coordinate system origin, recalculated into the𝑚th segment coordinate system. Kirchhoff ’s current law issatisfied for all the nodes. For 𝑛

𝐷antenna segments incident

to node𝐷, Kirchhoff ’s law is𝑛𝐷

∑𝑟=1

𝑛𝑟

∑𝑠=1

𝐵𝑟𝑠(𝑧𝑟

ℎ𝑟

)𝑠

= 0, (13)

for unknown complex coefficients𝐵𝑟𝑠and chosen polynomial

degree 𝑛𝑟in the approximation of current along the 𝑟th

segment. Coordinate of the beginning/end of 𝑟th segment is𝑧𝑟and ℎ𝑟is the segment length. Electric potential is calculated

from the following expression:

𝑉𝑧𝑚

= −𝑗𝑐 [𝐶1𝑚

sin (𝑘𝑧𝑚) − 𝐶2𝑚

cos (𝑘𝑧𝑚)]

+ ∫𝑧𝑚

0

𝐸𝑧𝑚𝑠


𝑧𝑚=𝑠

cos [𝑘 (𝑧𝑚− 𝑠)] d𝑠

+ 𝑗𝑐 ∫𝑧𝑚

0

(𝜕𝐴𝑥𝑚

𝜕𝑥𝑚

+𝜕𝐴𝑦𝑚

𝜕𝑦𝑚

)𝑥𝑚=𝑎𝑚

𝑦𝑚=0

𝑧𝑚=𝑠

⋅ sin [𝑘 (𝑧𝑚− 𝑠)] d𝑠 −

𝑛𝑍

∑𝑖=1

𝑍(𝑖)𝐼 (𝑧𝑚

(𝑖))

⋅ cos [𝑘 (𝑧𝑚− 𝑠)] .

(14)

5. Tower Crane and Turn-OverCrane Examples

More complex crane structures are modelled and system of(8) is solved for each example using the presented procedure.Some interesting results for tower crane and turn-over crane[1] are obtained. For the crane in Figure 14 in far electromag-netic field, 𝐸

𝜃= 1V/m, 𝐸

𝜑= 0, for 𝑓 = 1MHz and different

propagation directions, effective current along main towersegment of the height 𝑙 = 34m is presented in Figure 15, for

1m

46m

23m

22m6m

34m

1.5m

0.1m0.1m

Z

0.1m

Figure 14: Tower crane model.

𝜃 = 𝜋/2

𝜃 = 𝜋/4

𝜃 = 0

𝜑 = 0

𝜑 = 𝜋/4

𝜑 = 𝜋/2

10 20 300Distance along the tower segment l (m)

0

50

100

150

200

250

300

Indu

ced

curr

entI

ef(m

A)

Figure 15: Induced current along the main tower segment of thetower crane.

the polynomial degree 𝑛 = 5 and impedance 𝑍 = 100Ω. Ifthe turn-over crane given in Figure 16 is in the same field, theeffective current along boom segment of the height 𝑙 = 32mis presented in Figure 17.

For 𝑓 = 1MHz the wavelength is 𝜆 = 300m. Theresults for different frequencies are analyzed and it is obtainedthat for the tower crane example the maximum currentsalong the structure and maximum touch voltages at the hookare at 𝑓 = 725.8 kHz and for the turn-over crane are at𝑓 = 1.49MHz. Eight segments and seven nodes were chosento model the tower crane at perfectly conducting ground,whereas six segments and six nodes were chosen for the turn-over crane.

6. Reloading Bridge and Portal-HarborCrane Examples

It is important to consider reloading bridges, portal-harborcranes, and container cranes, as they may be permanently inthe field of MW transmitter a few kilometers from the crane’s


32m

0.1m0.5m

9.1m

0.1m

5m

1m

12m

16m

0.3m

Z

Figure 16: Turn-over crane model.

𝜃 = 𝜋/2

𝜃 = 𝜋/4

𝜃 = 0

𝜑 = 0

𝜑 = 𝜋/4

𝜑 = 𝜋/2

0

5

10

15

20

25

30

35

Indu

ced

curr

entI

ef(m

A)

5 10 15 20 25 300Distance along the boom segment l (m)

Figure 17: Induced current along the boom segment of the turn-over crane.

site. Electric fields in such cases are often of the order of V/m,depending on the transmitter power and vicinity. Positions ofsuch cranes should be carefully selected based on modelingof the specific problem. Induced effects may pose great riskin some cases [19, 20].

An example of the reloading bridge with its dimensionsis given in Figure 18. Portal-harbor crane of dimensions verysimilar to the described rail-mounted container crane ispresented in Figure 19. For these cranes positioned in thefar field, for 𝐸

𝜃= 1V/m, 𝐸

𝜑= 0, 𝜃 = 𝜋/2, and 𝜑 =

𝜋/2, touch voltages and induced currents are calculated forthe polynomial degree 𝑛 = 5 and impedance 𝑍 = 1000Ω.Results are presented in Figures 20 and 21. Induced voltagefor the portal-harbor crane is about 50V for frequency 𝑓 =621 kHz, as measured in Tenerife (Spain), although this is justa simplified model.

The impedancewhichmodels a human touching the hookmay be chosen according to the frequency of interest andusing results from [21–25].

It may be concluded that the reloading bridge is moresuitable, as it has less resonant frequencies, smaller values of

32m5m 5m

7m5m

35m38m38m30m

5m5m0.1m

Z

Figure 18: Reloading bridge model.

1.5m0.05m

10m

2m

2m

1m1m

2m18m

7m

3m16m

5m

1m

Z

Figure 19: Portal-harbor crane model.

induced currents, and smaller values of touch voltages exceptin the narrow bandwidth around resonant frequency.

7. Conclusion

Currents up to several amperes and touch voltages up to about1 kVmay be induced in large cranes nearbyMW transmitters.At such frequencies these values may result in electricalshock, painful burns, and dangerous involuntary movementsof workers, but also in faults in the automation and controlsystems of cranes. Analysis of such problems is presented inthis paper as well as results for induced current and voltagesfor different configurations of crane structures.

Current distribution along the crane structure is deter-mined using wire antenna model of the crane and elec-tromagnetic theory approach. Currents along segments areapproximated by polynomials. System of integral equationsfor the currents is solved using Point matching method.Results are in agreement with measured currents and volt-ages.

This approach may be used to analyze specific prob-lems, especially before positioning of reloading bridges andcontainer cranes nearby MW transmitters. Some practicalsolutions to this problem are also given in the paper.

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper.

Acknowledgment

This paper is in the frame of research within ProjectsHUMANISM III 44004 and TR33008 (2011–2015) financed


Reloading bridgePortal-harbor crane

𝜃 = 𝜋/2, 𝜑 = 𝜋/2

0

50

100

150

200

250

300

350

U (V

)

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.5f (MHz)

Figure 20: Induced voltage for reloading bridge and portal-harborcrane versus 𝑓.

Reloading bridgePortal-harbor crane

𝜃 = 𝜋/2, 𝜑 = 𝜋/2

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.5f (MHz)

0

50

100

150

I (m

A)

Figure 21: Induced current for reloading bridge and portal-harborcrane versus 𝑓.

by Ministry of Education, Science and Technological Devel-opment of the Republic of Serbia.

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