# Influence of the electric reactor magnetic field on the electromagnetic relays/Elektrinio reaktoriaus magnetinio lauko itaka elektromagnetinems relems.

Introduction

One of the mean criterions of power system reliability is capability of system to keep the satisfactory level of voltage in the time of the short circuit. Ad hoc the special inductive elements without ferromagnetic core--electric reactors--are used. Simultaneously they limit the short circuit current.

Electric reactor is the source of the strong magnetic field. The magnetic field of the reactor arises especially in the time of short circuit action. When the rated current of electric reactor is equal to 1,6 kA, in the moment of the short circuit it can reach 50 kA. The modeling results of the magnetic field, which creates electric reactor, are presented in [1, 2]. We can see that in the places where the cases with protection relays are mounted the magnetic field grows to the value 70 kA/m.

The short circuit is emergency action dangerous for all power system and it must be quickly localized. The relay protection system is used for this. All equipment is arranged compactly in the power plants. The some part of the relays of the protection system is situated in the close vicinity of the electric reactor. The magnetic field is used for the electromagnetic relay control. Therefore the strong outer magnetic field can disturb the action of the electromagnetic relays.

The electric reactor is the three-phase device. The rotating magnetic field with variable direction of field arises near the reactor, usually. But the magnetic field can be directed along the concrete direction in the short circuit action especially when the short circuit is in one phase. This direction is not known in advance. The relays can be acted by the magnetic field of other power equipment, too. Therefore when the relays are mounted the every its position can be dangerous in the short circuit case.

To warrant the reliability of relay protection system we must to explain what influence can do the outer magnetic field for the electromagnetic relays of different sorts which are used in the relay protection system [3, 4].

The action of outer magnetic field to the relay of the direct current

The typical design of the electromagnetic relay of the direct or alternating current is showed in the Fig 1. The main parts of relay are: magnetic circuit M, the moving part of magnetic circuit--armature A and the excitation coil of the magnetic field EC. Because the current is not passing in the excitation coil EC between the magnetic circuit M and armature A is air gap AG. When the current [i.sub.0] is passing in the EC the armature A is attracting to magnetic circuit M the contacts related with A are connected or disconnected and the required electric circuit is connecting.

[FIGURE 1 OMITTED]

The current [i.sub.0]=[I.sub.0]=const is invariable in the electromagnetic direct-current relay. This current creates the magnetic flux [[PSI].sub.0]=const, which attracts the armature A.

We suppose that in the air gap AG and excitation coil the outer alternating magnetic flux [[PSI].sub.ex] acts and it is parallel to the flux [[PSI].sub.0]. Therefore, in the half period of flux [[PSI].sub.ex] alternation the directions of the fluxes [[PSI].sub.ex] and [[PSI].sub.0] are the same and in the other half period these fluxes are directed on the contrary. We choose the initial phase of the flux [[PSI].sub.ex] equal to [pi]

[[PSI].sub.ex] = [[PSI].sub.m] sin([omega]t + [pi]). (1)

Some part of the outer flux acts in the air gap AG but it is not passed inside the excitation coil EC. We name this flux as leakage flux and note as [[PSI].sub.d]

[[PSI].sub.d] = [[PSI].sub.dm] sin([omega]t + [pi]). (2)

Magnetic flux [[PSI].sub.ex] creates the internal voltage [u.sub.0] in the excitation coil EC

[u.sub.0] = d[PSI]/dt = [omega] [[PSI].sub.exm] sin([omega]t + [pi]/2). (3)

The internal voltage [u.sub.0] creates the current [i.sub.2] in the excitation coil

[i.sub.2] = [omega][[PSI].sub.exm]/[square root of [([omega]L).sup.2] + [R.sup.2]] sin([omega]t + [phi]), (4)

where the R and L are the resistance and the inductance of the excitation current, accordingly

[phi] = arctan R/[omega]L. (5)

The current [i.sub.2] creates the magnetic flux [[PSI].sub.2], which can be expressed as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

Evaluating that:

sin [phi] = sin(arctan R/[omega]L) = R/[omega]L/[square root of 1 + [(R/[omega]L).sup.2]], (7)

cos [phi] = cos(arctan R/[omega]L) = 1/[square root of 1 + [(R/[omega]L).sup.2]], (8)

we obtain

[[PSI].sub.2] = [[PSI].sub.exm]/1 + [(R/[omega]L).sup.2] sin [omega]t + [[psi].sub.exm](R/[omega]L)/1 + [(R/[omega]L).sup.2] cos [omega]t. (9)

In the ideal case when R/[omega]L [right arrow] 0 and [[PSI].sub.d] [right arrow] 0 the flux [[PSI].sub.2] will be equal to flux [[PSI].sub.ex] and will be directed contrary. Therefore it could be compensate the flux [[PSI].sub.ex].

In the real relay we must evaluate the R and [[PSI].sub.d]. Flux [[PSI].sub.ex] expressed by (1) we can present by two components

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (10)

Evaluating, that [[PSI].sub.d] = [[PSI].sub.dm] sin [omega]t, total magnetic flux of air gap [[PSI].sub.[SIGMA]] can be expressed of (9) and (10)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (11)

This magnetic flux is pulsated. When the amplitude of [[PSI].sub.ex] is big, the action of relay can be delayed to 10 ms. The contacts of relay can be periodically connected and disconnected independently on the relay control current [I.sub.0].

The disruptive alternating magnetic flux can evoke other negative effect. The excitation coil EC will be heating by the current [i.sub.2] complementary to the heating by control current [I.sub.0]. The complementary heat power P can be calculated as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (12)

When the outer magnetic flux is large the relay can quickly overheat.

The action of outer magnetic field to the relay of the alternating current

The design of the alternating-current relay is the same as the direct-current relay (see Fig. 1). The control current in the alternating-current relay is sinusoidal

[i.sub.0] = [I.sub.m0] sin [omega]t. (13)

This current creates the sinusoidal magnetic field in the air gap AG. The flux [[PSI].sub.0] of this field is sufficient for the armature attraction

[[PSI].sub.0] = [[PSI].sub.0m] sin [omega]t. (14)

Suppose that in the air gap AG and excitation coil EC of this relay acts the outer magnetic flux [[PSI].sub.ex], analogically with direct-current relay. The flux [[PSI].sub.ex] is expressed by (1). It is directed contrary to magnetic flux [[PSI].sub.0]. In the air gap AG acts the leakage flux [[PSI].sub.d], too. It is expressed by (2). The flux [[PSI].sub.ex] evokes the current [i.sub.2] and magnetic flux [[PSI].sub.2], expressed by (9). We obtain the total magnetic flux [[PSI].sub.[SIGMA]] of the air gap AG summing [[PSI].sub.0], [[PSI].sub.ex], [[PSI].sub.d] and [[PSI].sub.2]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (15)

It consists of sinusoidal [[PSI].sub.I] and cosinusoidal [[PSI].sub.II] components. These components create the electromagnetic forces [F.sub.I] and [F.sub.II], accordingly

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (16)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (17)

We can express the sum Fn of unvarying components of the forces [F.sub.In] and [F.sub.IIn] as follow

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (18)

The force [F.sub.0] acts in the alternating-current relay when the outer magnetic flux is absent ([F.sub.0] = [F.sub.n], when [[PSI].sub.exm] [right arrow] 0 and [[PSI].sub.dm] [right arrow] 0). The coefficient [K.sub.n] shows the relative variation of force [F.sub.n] because the outer magnetic fluxes [[PSI].sub.ex] and [[PSI].sub.d]. The dependence of [K.sub.n] on the ratios [[PSI].sub.exm]/ [[PSI].sub.0m], [[PSI].sub.dm/[[PSI].sub.exm] and R/[omega]L is complicated. The dependences of [K.sub.n] on the ratio [[PSI].sub.m]/[[PSI].sub.exm] are presented in Fig. 2 for ratio R/[omega]L=0,1 and in Fig.3 for ratio R/[omega]L=0,05.

[FIGURE 2 OMITTED]

We can see of Fig. 2 and 3 that the coefficient [K.sub.n] considerably decreases, when amplitude of the outer magnetic flux [[PSI].sub.exm] is some times more than amplitude [[PSI].sub.0m] of flux created by excitation coil. The increase of leakage flux [[PSI].sub.d] decreases [K.sub.p] especially when [[PSI].sub.exm]/[[PSI].sub.0m]>5.

[FIGURE 3 OMITTED]

The action of the outer magnetic field to the induction relay

In the induction relay the influence of the outer magnetic field is important when the excitation coil is arranged in the branch of the magnetic circuit which the induction disc is not intersect. In the Fig. 2 it is showed the induction relay with two poles: screened P1 and non-screened P2. The induction disc ID is under these poles. When the sinusoidal excitation coil [i.sub.0] is passed to the excitation coil EC, the magnetic fluxes [[PSI].sub.01] and [[PSI].sub.02] are created in the magnetic circuit branches with P1 and P2, correspondingly. They intersect the induction disc.

We suppose that the outer alternating magnetic flux [[PSI].sub.ex] acts perpendicular to the induction disc ID and parallel to the excitation coil EC axis. We divide this flux into three parallel fluxes: [[PSI].sub.ex0] in the branch with coil EC, [[PSI].sub.ex1] in the branch with pole P1 and [[PSI].sub.ex2] in the branch with pole P2. Let the initial phases of fluxes [[PSI].sub.ex0], [[PSI].sub.01] and [[PSI].sub.02] coincide in the magnetic circuit branch with excitation coil EC. In the branches with poles P1 and P2 the flux [[PSI].sub.ex1]([[PSI].sub.ex2]) will be directed contrary than flux [[PSI].sub.01]([[PSI].sub.02]) (see Fig. 4).

[FIGURE 4 OMITTED]

The flux [[PSI].sub.ex0] inducts the electromotive force [e.sub.2] and current [i.sub.2] in EC. The current [i.sub.2] creates the flux [[PSI].sub.21] in the branch with pole P1 and [[PSI].sub.22] in the branch with pole P2. Analogically as in the direct-current relay we find that difference between the initial phases of fluxes [[PSI].sub.21]( [[PSI].sub.22]) and [[PSI].sub.01]([[PSI].sub.02]) is equal to [phi]-[pi]. The angle [phi] is expressed by (5), where R and L are the resistance and inductance of EC.

The fluxes [[PSI].sub.21] and [[PSI].sub.22] are parts of flux [[PSI].sub.2]

[[PSI].sub.2] = [[PSI].sub.21] + [[PSI].sub.22], [[PSI].sub.21] = [k.sub.1] [[PSI].sub.2], [[PSI].sub.21] = [k.sub.2] [[PSI].sub.2]. (19)

There [k.sub.1]=const., [k.sub.2]=const., [k.sub.1] + [k.sub.2] = 1.

The total fluxes [[PSI].sub.[SIGMA]1] and [[PSI].sub.[SIGMA]2] in the branches with poles P1 and P2 can be expressed as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (20)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (21)

We can write by (9):

[[PSI].sub.21m] cos [phi] = [k.sub.1] [[PSI].sub.ex0m]/1 + [(R/[omega]L).sup.2], (22)

[[PSI].sub.22m] cos [phi] = [k.sub.2] [[PSI].sub.ex0m]/1 + [(R/[omega]L).sup.2]. (23)

When the magnitude of outer magnetic flux [[PSI].sub.exm] is equal to (20-30) % of magnetic flux created by excitation coil EC, the total magnetic flux can be too small for induction relay action. Therefore, the induction relays are more sensitive to outer magnetic field than direct- or alternating-current relays.

Conclusions

1. The strongest magnetic fields are near electric reactors in electric plants. These fields can disturb the electromagnetic relays action.

2. In the direct-current relay the outer magnetic field can delay the action and evoke the contacts disconnection.

3. The alternating-current relay can not act when the outer magnetic flux is some times more than the inner magnetic flux. The especially dangerous is leakage magnetic flux which is not intersected the excitation coil.

4. Induction relay can not act, when outer magnetic flux reach some tens percentages of the magnetic flux created by relay excitation coil.

Received 2010 03 25

References

[1.] Morozionkov J., Virbalis J. A. Investigation of electric reactor magnetic field using Finite Element Method // Electronics and Electrical Engineering.--Kaunas: Technologija, 2008.--No. 5(85).--P. 9-12.

[2.] Morozionkov J., Virbalis J. A. Shielding of electric reactor magnetic field // Electronics and Electrical Engineering.--Kaunas: Technologija, 2009.--No. 8(96).--P. 15-18.

[3.] Gecys S., Smolskas P. Design Aspects of Electric motors for Borehole Investigating Mechatronic System // Electronics and Electrical Engineering.--Kaunas: Technologija, 2007. No. 2(74).--P. 75-78.

[4.] BukSnaitis J. Methods for determination of Windings Factors of Alternating-Current Electric Machines // Electronics and Electrical Engineering.--Kaunas: Technologija, 2009.--No. 1(89).--P. 83-86.

J. Morozionkov, J. A. Virbalis

Departement of Electrical Engineering, Kaunas University of Technology, Studentu str. 48, LT-51367 Kaunas, Lithuania, phone: +370 3 7 300267, e-mail: arvydas.virbalis@ktu.lt

One of the mean criterions of power system reliability is capability of system to keep the satisfactory level of voltage in the time of the short circuit. Ad hoc the special inductive elements without ferromagnetic core--electric reactors--are used. Simultaneously they limit the short circuit current.

Electric reactor is the source of the strong magnetic field. The magnetic field of the reactor arises especially in the time of short circuit action. When the rated current of electric reactor is equal to 1,6 kA, in the moment of the short circuit it can reach 50 kA. The modeling results of the magnetic field, which creates electric reactor, are presented in [1, 2]. We can see that in the places where the cases with protection relays are mounted the magnetic field grows to the value 70 kA/m.

The short circuit is emergency action dangerous for all power system and it must be quickly localized. The relay protection system is used for this. All equipment is arranged compactly in the power plants. The some part of the relays of the protection system is situated in the close vicinity of the electric reactor. The magnetic field is used for the electromagnetic relay control. Therefore the strong outer magnetic field can disturb the action of the electromagnetic relays.

The electric reactor is the three-phase device. The rotating magnetic field with variable direction of field arises near the reactor, usually. But the magnetic field can be directed along the concrete direction in the short circuit action especially when the short circuit is in one phase. This direction is not known in advance. The relays can be acted by the magnetic field of other power equipment, too. Therefore when the relays are mounted the every its position can be dangerous in the short circuit case.

To warrant the reliability of relay protection system we must to explain what influence can do the outer magnetic field for the electromagnetic relays of different sorts which are used in the relay protection system [3, 4].

The action of outer magnetic field to the relay of the direct current

The typical design of the electromagnetic relay of the direct or alternating current is showed in the Fig 1. The main parts of relay are: magnetic circuit M, the moving part of magnetic circuit--armature A and the excitation coil of the magnetic field EC. Because the current is not passing in the excitation coil EC between the magnetic circuit M and armature A is air gap AG. When the current [i.sub.0] is passing in the EC the armature A is attracting to magnetic circuit M the contacts related with A are connected or disconnected and the required electric circuit is connecting.

[FIGURE 1 OMITTED]

The current [i.sub.0]=[I.sub.0]=const is invariable in the electromagnetic direct-current relay. This current creates the magnetic flux [[PSI].sub.0]=const, which attracts the armature A.

We suppose that in the air gap AG and excitation coil the outer alternating magnetic flux [[PSI].sub.ex] acts and it is parallel to the flux [[PSI].sub.0]. Therefore, in the half period of flux [[PSI].sub.ex] alternation the directions of the fluxes [[PSI].sub.ex] and [[PSI].sub.0] are the same and in the other half period these fluxes are directed on the contrary. We choose the initial phase of the flux [[PSI].sub.ex] equal to [pi]

[[PSI].sub.ex] = [[PSI].sub.m] sin([omega]t + [pi]). (1)

Some part of the outer flux acts in the air gap AG but it is not passed inside the excitation coil EC. We name this flux as leakage flux and note as [[PSI].sub.d]

[[PSI].sub.d] = [[PSI].sub.dm] sin([omega]t + [pi]). (2)

Magnetic flux [[PSI].sub.ex] creates the internal voltage [u.sub.0] in the excitation coil EC

[u.sub.0] = d[PSI]/dt = [omega] [[PSI].sub.exm] sin([omega]t + [pi]/2). (3)

The internal voltage [u.sub.0] creates the current [i.sub.2] in the excitation coil

[i.sub.2] = [omega][[PSI].sub.exm]/[square root of [([omega]L).sup.2] + [R.sup.2]] sin([omega]t + [phi]), (4)

where the R and L are the resistance and the inductance of the excitation current, accordingly

[phi] = arctan R/[omega]L. (5)

The current [i.sub.2] creates the magnetic flux [[PSI].sub.2], which can be expressed as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

Evaluating that:

sin [phi] = sin(arctan R/[omega]L) = R/[omega]L/[square root of 1 + [(R/[omega]L).sup.2]], (7)

cos [phi] = cos(arctan R/[omega]L) = 1/[square root of 1 + [(R/[omega]L).sup.2]], (8)

we obtain

[[PSI].sub.2] = [[PSI].sub.exm]/1 + [(R/[omega]L).sup.2] sin [omega]t + [[psi].sub.exm](R/[omega]L)/1 + [(R/[omega]L).sup.2] cos [omega]t. (9)

In the ideal case when R/[omega]L [right arrow] 0 and [[PSI].sub.d] [right arrow] 0 the flux [[PSI].sub.2] will be equal to flux [[PSI].sub.ex] and will be directed contrary. Therefore it could be compensate the flux [[PSI].sub.ex].

In the real relay we must evaluate the R and [[PSI].sub.d]. Flux [[PSI].sub.ex] expressed by (1) we can present by two components

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (10)

Evaluating, that [[PSI].sub.d] = [[PSI].sub.dm] sin [omega]t, total magnetic flux of air gap [[PSI].sub.[SIGMA]] can be expressed of (9) and (10)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (11)

This magnetic flux is pulsated. When the amplitude of [[PSI].sub.ex] is big, the action of relay can be delayed to 10 ms. The contacts of relay can be periodically connected and disconnected independently on the relay control current [I.sub.0].

The disruptive alternating magnetic flux can evoke other negative effect. The excitation coil EC will be heating by the current [i.sub.2] complementary to the heating by control current [I.sub.0]. The complementary heat power P can be calculated as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (12)

When the outer magnetic flux is large the relay can quickly overheat.

The action of outer magnetic field to the relay of the alternating current

The design of the alternating-current relay is the same as the direct-current relay (see Fig. 1). The control current in the alternating-current relay is sinusoidal

[i.sub.0] = [I.sub.m0] sin [omega]t. (13)

This current creates the sinusoidal magnetic field in the air gap AG. The flux [[PSI].sub.0] of this field is sufficient for the armature attraction

[[PSI].sub.0] = [[PSI].sub.0m] sin [omega]t. (14)

Suppose that in the air gap AG and excitation coil EC of this relay acts the outer magnetic flux [[PSI].sub.ex], analogically with direct-current relay. The flux [[PSI].sub.ex] is expressed by (1). It is directed contrary to magnetic flux [[PSI].sub.0]. In the air gap AG acts the leakage flux [[PSI].sub.d], too. It is expressed by (2). The flux [[PSI].sub.ex] evokes the current [i.sub.2] and magnetic flux [[PSI].sub.2], expressed by (9). We obtain the total magnetic flux [[PSI].sub.[SIGMA]] of the air gap AG summing [[PSI].sub.0], [[PSI].sub.ex], [[PSI].sub.d] and [[PSI].sub.2]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (15)

It consists of sinusoidal [[PSI].sub.I] and cosinusoidal [[PSI].sub.II] components. These components create the electromagnetic forces [F.sub.I] and [F.sub.II], accordingly

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (16)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (17)

We can express the sum Fn of unvarying components of the forces [F.sub.In] and [F.sub.IIn] as follow

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (18)

The force [F.sub.0] acts in the alternating-current relay when the outer magnetic flux is absent ([F.sub.0] = [F.sub.n], when [[PSI].sub.exm] [right arrow] 0 and [[PSI].sub.dm] [right arrow] 0). The coefficient [K.sub.n] shows the relative variation of force [F.sub.n] because the outer magnetic fluxes [[PSI].sub.ex] and [[PSI].sub.d]. The dependence of [K.sub.n] on the ratios [[PSI].sub.exm]/ [[PSI].sub.0m], [[PSI].sub.dm/[[PSI].sub.exm] and R/[omega]L is complicated. The dependences of [K.sub.n] on the ratio [[PSI].sub.m]/[[PSI].sub.exm] are presented in Fig. 2 for ratio R/[omega]L=0,1 and in Fig.3 for ratio R/[omega]L=0,05.

[FIGURE 2 OMITTED]

We can see of Fig. 2 and 3 that the coefficient [K.sub.n] considerably decreases, when amplitude of the outer magnetic flux [[PSI].sub.exm] is some times more than amplitude [[PSI].sub.0m] of flux created by excitation coil. The increase of leakage flux [[PSI].sub.d] decreases [K.sub.p] especially when [[PSI].sub.exm]/[[PSI].sub.0m]>5.

[FIGURE 3 OMITTED]

The action of the outer magnetic field to the induction relay

In the induction relay the influence of the outer magnetic field is important when the excitation coil is arranged in the branch of the magnetic circuit which the induction disc is not intersect. In the Fig. 2 it is showed the induction relay with two poles: screened P1 and non-screened P2. The induction disc ID is under these poles. When the sinusoidal excitation coil [i.sub.0] is passed to the excitation coil EC, the magnetic fluxes [[PSI].sub.01] and [[PSI].sub.02] are created in the magnetic circuit branches with P1 and P2, correspondingly. They intersect the induction disc.

We suppose that the outer alternating magnetic flux [[PSI].sub.ex] acts perpendicular to the induction disc ID and parallel to the excitation coil EC axis. We divide this flux into three parallel fluxes: [[PSI].sub.ex0] in the branch with coil EC, [[PSI].sub.ex1] in the branch with pole P1 and [[PSI].sub.ex2] in the branch with pole P2. Let the initial phases of fluxes [[PSI].sub.ex0], [[PSI].sub.01] and [[PSI].sub.02] coincide in the magnetic circuit branch with excitation coil EC. In the branches with poles P1 and P2 the flux [[PSI].sub.ex1]([[PSI].sub.ex2]) will be directed contrary than flux [[PSI].sub.01]([[PSI].sub.02]) (see Fig. 4).

[FIGURE 4 OMITTED]

The flux [[PSI].sub.ex0] inducts the electromotive force [e.sub.2] and current [i.sub.2] in EC. The current [i.sub.2] creates the flux [[PSI].sub.21] in the branch with pole P1 and [[PSI].sub.22] in the branch with pole P2. Analogically as in the direct-current relay we find that difference between the initial phases of fluxes [[PSI].sub.21]( [[PSI].sub.22]) and [[PSI].sub.01]([[PSI].sub.02]) is equal to [phi]-[pi]. The angle [phi] is expressed by (5), where R and L are the resistance and inductance of EC.

The fluxes [[PSI].sub.21] and [[PSI].sub.22] are parts of flux [[PSI].sub.2]

[[PSI].sub.2] = [[PSI].sub.21] + [[PSI].sub.22], [[PSI].sub.21] = [k.sub.1] [[PSI].sub.2], [[PSI].sub.21] = [k.sub.2] [[PSI].sub.2]. (19)

There [k.sub.1]=const., [k.sub.2]=const., [k.sub.1] + [k.sub.2] = 1.

The total fluxes [[PSI].sub.[SIGMA]1] and [[PSI].sub.[SIGMA]2] in the branches with poles P1 and P2 can be expressed as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (20)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (21)

We can write by (9):

[[PSI].sub.21m] cos [phi] = [k.sub.1] [[PSI].sub.ex0m]/1 + [(R/[omega]L).sup.2], (22)

[[PSI].sub.22m] cos [phi] = [k.sub.2] [[PSI].sub.ex0m]/1 + [(R/[omega]L).sup.2]. (23)

When the magnitude of outer magnetic flux [[PSI].sub.exm] is equal to (20-30) % of magnetic flux created by excitation coil EC, the total magnetic flux can be too small for induction relay action. Therefore, the induction relays are more sensitive to outer magnetic field than direct- or alternating-current relays.

Conclusions

1. The strongest magnetic fields are near electric reactors in electric plants. These fields can disturb the electromagnetic relays action.

2. In the direct-current relay the outer magnetic field can delay the action and evoke the contacts disconnection.

3. The alternating-current relay can not act when the outer magnetic flux is some times more than the inner magnetic flux. The especially dangerous is leakage magnetic flux which is not intersected the excitation coil.

4. Induction relay can not act, when outer magnetic flux reach some tens percentages of the magnetic flux created by relay excitation coil.

Received 2010 03 25

References

[1.] Morozionkov J., Virbalis J. A. Investigation of electric reactor magnetic field using Finite Element Method // Electronics and Electrical Engineering.--Kaunas: Technologija, 2008.--No. 5(85).--P. 9-12.

[2.] Morozionkov J., Virbalis J. A. Shielding of electric reactor magnetic field // Electronics and Electrical Engineering.--Kaunas: Technologija, 2009.--No. 8(96).--P. 15-18.

[3.] Gecys S., Smolskas P. Design Aspects of Electric motors for Borehole Investigating Mechatronic System // Electronics and Electrical Engineering.--Kaunas: Technologija, 2007. No. 2(74).--P. 75-78.

[4.] BukSnaitis J. Methods for determination of Windings Factors of Alternating-Current Electric Machines // Electronics and Electrical Engineering.--Kaunas: Technologija, 2009.--No. 1(89).--P. 83-86.

J. Morozionkov, J. A. Virbalis

Departement of Electrical Engineering, Kaunas University of Technology, Studentu str. 48, LT-51367 Kaunas, Lithuania, phone: +370 3 7 300267, e-mail: arvydas.virbalis@ktu.lt

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Title Annotation: | ELECTRICAL ENGINEERING/ELEKTROS INZINERIJA |
---|---|

Author: | Morozionkov, J.; Virbalis, J.A. |

Publication: | Elektronika ir Elektrotechnika |

Article Type: | Report |

Geographic Code: | 4EXLT |

Date: | Oct 1, 2010 |

Words: | 2260 |

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