Air Core reACtors

Magnetic Field of Air Core reactors:Causes, effects and solutions

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iNtroDuCtioN

Nowadays, dry-type air-core reactors are consecrated in a vast range of applications, including among others: current limiting reactors, reactors for capacitor banks and harmonic filters, shunt reactors for static compensators, etc...

The absence of iron core results in a simple, light weight equipment. On the other hand, there is no iron core to capture the magnetic field that will occupy the space around the reactor. This requires taking some precautions in relation to the influence of intense magnetic fields.

These precautions prevent against thermal and/or mechanical efforts that can damage structures of metallic elements when exposed to these fields.

MAgNetiC FielD oF Air-Core reACtors

Problems of induction in non-magnetic environments can be formulated using the following integral equation:

For air-core reactors, this equation allows to calculate the magnetic field in any point of the space defined by cylindrical coordinates (r,z), where the integral is calculated over the volume v of the reactor winding.

J : current density in the winding (A/mm2) : distance between any point ( r’, z’ ) of the winding

and the location x (r,z) where we want to calculate the magnetic field.

: unit vector (indicated in figure 1)

Figure 2 shows some curves showing the magnetic field B for some typical shapes of reactors. The relation h/D (height / diameter) is the most important parameter in the definition of the contour of the field lines, where the relation h/D is typically between 0.5 and 1.5. It can be seen from the curves of figure 2 that the value of the magnetic field decreases rapidly when the distance from the reactor increases.

In all cases, the value of the magnetic field at half diameter from reactor surface will be around 10% or less the value of the magnetic field at the center of the reactor (point where the magnetic field is maximum).

Fig. 1 – Reactor winding and calculation of the magnetic field of air-core reactors

Fig. 2 – Magnetic field of typical shapes of air-core reactors

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eFFeCts oF the MAgNetiC iNDuCtioN

The magnetic induction on a metallic structure (magnetic or non-magnetic) induces currents in the structure in accordance with the relations established by the Maxwell’s equations.

The intensity of these currents depends, besides the value of the magnetic field density, on the following:

> Field frequency;

> Resistivity and permeability of the conducting material that constitutes the structure;

> Geometric elements that are function of the structure’s geometry;

> Position of the structure in relation to the reactor.

It is not always possible to establish analytical relations to calculate these currents. The usual procedure consists of doing estimates based on situations of simplified geometry that permit us to use simplified relationships for the calculation of currents, losses, etc.

Figure 3 shows a conducting metallic plate of thickness 2b. This could be, for example, the wall of an enclosure as shown in figure 10.

Imagine the time-harmonic magnetic field which is incident on the plate. This field can be decomposed in two components: tangent and normal to the plate, where the problem can be independently analyzed for each one of the components and the total losses obtained by superposition of effects (This is possible because the field components are in quadrature).

solution for the tangent magnetic field to the plateApplying Maxwell’s equations and appropriate boundary conditions, it can be demonstrated that the magnetic field strength is given by the following expression:

where:Hix = external field tangent to the plate

magnetic permeability of the material electric conductivity of the material angular frequency of the field

Where d is called penetration depth of the magnetic field, and is a measure of how much the magnetic field penetrates effectively the material. The induced current density is calculated from the magnetic field strength equation, which gives:

the losses per area-unit of the plate is given by:

Resulting in:

where:

It is interesting to observe that in many applications the equation above can be simplified in function of the value of the relation 2b/d. For example, in a metallic enclosure of aluminum, where we have the penetration depth d, at 60 Hz, around 20 mm and therefore bigger than the usual thickness of the wall of an enclosure (around 5 mm), allowing us to say that 2b<<d. For these conditions the solution of equation 5 yields the following:

Table 1 presents the values of penetration depth of the magnetic field at 60 Hz for the materials most used, where the condition 2b<<d applies in most cases.

Fig. 3 – Magnetic field on a metallic plate

Table 1

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(6)

solution for the normal magnetic field to the plateAs mentioned before, it is usual to have the relation 2b<< d for metallic enclosures. For these conditions, the effect of induced currents is negligible and the magnetic field crosses the material without significant disturbances.

The induced currents will be in the direction of z, and from the Maxwell’s equations we can demonstrate that:

Resulting in the following current density:

Finally, using the equation 4, losses per area-unit (result of the normal field to the plate) can be calculated as follows:

The equations (6) and (9) can be used to estimate the losses and the heating generated on the walls of metallic enclosures. Although the magnetic field is not constant throughout the walls of the enclosure, it can be divided in imaginary sections, and the losses calculated for each section, based on the average value of the field throughout these sections.

Similar solutions can be done for practically all the situations, for example, for metallic beams exposed to magnetic fields and others. In all cases, independently of considered geometry, a quadratic variation of the losses with the incident field is observed, as can be seen in the expressions presented for the calculation of the losses of the considered example.

MeChANiCAl eFForts

In addition to the thermal efforts created by induced losses, we will also have the mechanical efforts already mentioned previously. A significant example is the case of a conductor exposed to the field of the reactor and high currents during a short-circuit, as shown in figure 4.

In accordance with the Lorentz force equation, the resultant force per unit length on the conductor is:

resulting, for the example considered, in:

which gives:

where , , are the unit vectors of the cylindrical coordinate system, im the amplitude of the current in the conductor and Bm the amplitude of the magnetic field density created by the reactor (in the space occupied by the conductor) in the normal direction of the conductor. The calculation of the force can be done cutting the conductor into imaginary sections and considering the magnetic field is constant along each section. The value of the magnetic field is calculated as shown previously. The value of the resultant force in the cable is given by the sum of the forces acting on each section. This calculation is important for the design of busbars, connectors and conductors connected to the reactors.

Fig. 4 – Conductors exposed to the magnetic field of air-core reactors

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MAgNetiC CleArANCes

With the knowledge of the calculated magnetic field distribution, and based on measurements carried out in laboratory, provision must be made for minimum clearances between reactors and metallic parts as shown in figure 5.

As can be seen from figure 5, the required clearance to closed loops is approximately double that required for metallic parts that do not form closed loops. For this reason, in the case of new installations, the design of structures to be installed close to reactors must be done in such a way as to avoid the formation of closed loops.

The distances indicated in figure 5 are general guidelines and can be complemented by specific procedures for each project, as will exemplified in the next subjects on enclosures, grounding, etc. Anyway, detailed analysis is recommended for each case.

For installations where it is not possible to avoid the presence of closed loops, a detailed magnetic clearance analysis must be done to confirm that the guidelines may be reduced. In more difficult cases, other solutions can be used for the reduction of the required clearances, such as the use of shields of appropriate materials and geometry.

Insulators and non-magnetic support structures are recommended to be supplied with the reactor to provide the required magnetic distance. Non-magnetic materials as aluminum may often be used in place of steel to reduce the severity of heating problems.

FouNDAtioN

The effect of the magnetic field shall be considered in the design of support structures, as well as in the placement of auxiliary equipment such as circuit breakers, lightning arresters, etc. Additionally, any other required structures shall be installed in areas where the effect of the magnetic field will not create excessive heating.

Besides the clearance guidelines mentioned above, the creation of metallic loops must be avoided. The closed loops offer a preferential way for induced currents that create heating to concrete reinforcing rods and building support beams. The circulation of these currents can damage the concrete foundations or reinforced walls in irreparable ways.

The solution to prevent this problem consists of insulating crossover points of rebar. The crossover points should be electrically isolated with pieces of hose or isolation tape. Another solution would be the use of bars made from non-magnetic materials or stainless steel. However, if the clearances are greater that the reactor diameter, the above mentioned precautions are not necessary.

Fig. 5 – Guidelines for magnetic clearances

MC1

MC2

Fig. 6 – Use of non-magnetic metallic spacers

Triangle arrangement

MC2

MC1

De De

Side by side arrangement

MC2

MC1

De

De D

e

MetAlliC eNClosures

For metallic enclosures, closed loops must be avoided on all four sides. If you insulate the rear panel from the side and top panels, you can open the closed loops (remember that all panels shall be grounded). If you install the reactor in an enclosure with closed loops, you get higher losses and the enclosure may heat up. The insulation doesn’t need to be thicker than 1/8”, but the securing bolts between the rear panel and side panels, and between the top panel and side/front panels must be insulated by means of insulating bushings and washers.

It’s interesting to have a door for inspection and the presence of louvers to allow the air flow through the reactor for self-cooling by natural air convection.

See sketch below about grounding and insulating. The thicker lines indicate the insulated boltings.

grouNDiNg

Special care should be taken in the installation of the station ground grid in the vicinity of air-core reactors. The ground grid should be designed so without closed loops; otherwise, currents could be induced in the grid. Grounding of the support structures or equipment installed close to the reactor should be accomplished without creating closed loops in the grounding system. (see figure 7).

FeNCiNg

When fencing is employed, provision must be made to assure that the reactor’s magnetic field does not induce high currents in metallic fencing components. All metallic fencing must be broken up into electrically isolated sections if it is located very near the reactor. It is also necessary to assure that all portions of a metallic fence are grounded because of capacitive coupling that can exist between the reactor which is at high potential and the fence in another. Another alternative is to use nonmetallic fencing, such as wood, plastic or fiberglass.

Fig. 10 – Special care for reactors mounted inside metallic enclosures

Fig. 7 – Earthing of the metallic reactor supports

Fig. 8 – Example of installation with fencing and other structures - Outdoor

Fig. 9 – Example of installation with fencing - Indoor

soFtwAre

AREVA T&D magnetic field calculation tools are able to provide several graphics and reports for magnetic field for specific and purpose-oriented graphics and reports, such as point-to-point figures, field limited regions, curves B x R and B x Z, etc.

Usage of the magnetic field plot: > Considerations the effect of magnetic field on human body;

> Establish clearances for safety and installation purposes;

> Analysis of interference in metallic structures or equipment sensitive to magnetic field.

> Lay-out optimization, allowing the necessary reduction in clearance requirements for new and existing installations.

> Design of shielding. It is possible to provide aluminum magnetic shields around and below the reactors. A part of the magnetic field is constrained by the shields resulting in lower values in the installation. These are mainly used for existing installations that are being upgraded or modernized, and ambient conditions with electronic devices and safety rules for substation personnel.

reFereNCes

[1] R. L. Stoll; The Analysis of Eddy Current, Oxford, Clarendon Press, 1974.

[2] P. E. Burke, T. H. Fawzi, T. Akinbiyi; The Use of Asymptotes to Estimate TE and TM Losses in Long Conductors., IEEE Transactions, Vol. MAG 14, # 5, Setember 1978.

[3] T. H. Fawzi, P. E. Burke, M. Fabiano Alves; Use of Surface Integral Equations for Analysis of TM Induction Problems, Proc. IEE, Vol. 121, #10, 1974.

[4] L. E. Sauer; Air Core Type Reactor Fields, AIEE Transaction, Vol. 43, June 1924.

[5] IEEE Power Engineering Society; IEEE C57.16 Standard Requirements, Terminology, and Test Code for Dry-Type Air-Core Series-Connected Reactors, 1996.

If you need technical information, please send us an e-mail : aircorereactors.itr@areva-td.com

Fig. 11 – Example: Magnetic field x axial distance

Fig. 12 – Example: Field limited regions

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