DE1613753C - Circuit arrangement for Spei solution of a symmetrical multi-phase utility circuit from an emphasis alternating voltage - Google Patents

Description

30th

The invention relates to a circuit arrangement for feeding a symmetrical multi-phase utility circuit from a single-phase alternating voltage, with at least one phase of the useful electric circuit a reactance in series to determine the respective phase shift angle is connected upstream between the phase current and the single-phase AC voltage and wherein the single-phase alternating voltage via a single-phase transformer with secondary-side taps is fed to individual phases of the utility circuit.

One application for such circuit arrangements is, for example, the supply of special Multi-phase inductors for induction heating with medium frequency of workpieces which are one of the Phase number have appropriate symmetry. The generators used for these applications are well known for reasons of the simple design and the cost price almost exclusively single-phase. This Circuit arrangements are also applicable when it comes to the frequency of one To increase the voltage supplied to the alternator by means of a static frequency multiplier, which, for example, due to three-phase currents, a single-phase current of three times the frequency can generate, this multiplication can take place in several stages, so that one finally receives a relatively high frequency.

A circuit arrangement of the type specified at the beginning is from German Patent 107 844 known. The taps are taken from the taps and the phases of the utility circuit conducted phase currents via a common line containing a reactance to another secondary-side terminal of the single-phase transformer fed back. The phase shift angles are essentially determined by the position of the taps. With such a circuit arrangement a symmetrical multiphase system with more than three phases is obviously not possible.

On the other hand, circuit arrangements of a similar type are known in which each phase has its own Reactance is assigned to determine the phase shift angle, one of these reactances possibly zero or is replaced by an effective resistor. That's how it is in German Patent specification 682 531 an arrangement for feeding a three-phase rectifier arrangement from a Single-phase alternating current network described in which a three-phase transformer is used in a special design which is designed so that the sum of the three secondary stress components at all Loads of the rectifier is zero, two primary-side phases each with a reactance Phase shift is connected upstream. The special solution, however, is not one for the general case Multi-phase utility circuit can be used with any number of phases.

With one from the French patent specification. 964 962 known circuit arrangement is for each Phase a separate single-phase transformer is provided, the primary winding of which is a reactance is upstream. The effort is due to the number of single-phase transformers required the greater the number of phases, the greater.

Finally, from US Pat. No. 3,258,673, a circuit arrangement is known in which the RC phase shifters are used. This solution is only suitable for small services.

The object of the invention is to provide an arrangement that is simple and economical the completely symmetrical supply of a multi-phase utility circuit with any number of phases from a single-phase AC voltage source.

According to the invention, this is achieved in a circuit arrangement of the type specified at the outset achieves that the single-phase alternating voltage at the taps per phase, based on a zero point of the useful circuit, is dimensioned so that it corresponds to the cosine of the respective phase shift angle is inversely proportional.

In the circuit arrangement according to the invention, only a single single-phase transformer is used for the Generation of any number of phase voltages required. They determine the phases of the useful circuit upstream reactive resistances the phase shift angle, while the special dimensioning of the single-phase alternating voltages tapped at the taps the effect shows that the performance of all phases is the same.

A particularly simple structure with a small number of taps in relation to the number of phases of the single-phase transformer can be achieved according to an advantageous development of the subject matter of the invention that the individual Phases are shifted symmetrically to the vectorial position of the single-phase alternating voltage and the Phases shifted by negative and positive phase shift angles of the same amount on the same Tap lie.

Embodiments of the invention are shown in the drawing. In it shows

F i g. 1 the vector diagram of a five-phase utility circuit,

F i g. 2 shows a five-phase circuit arrangement according to the invention, the phase currents of which correspond to the vector diagram from F i g. 1 correspond to

F i g. 3 the vector diagram of a three-phase utility circuit,

F i g. 4 shows a three-phase circuit arrangement according to the invention, the phase currents of which correspond to the vector diagram from F i g. 3 correspond,

F i g. 5 the vector diagram of a two-phase utility circuit,

F i g. 6 shows a two-phase circuit arrangement according to the invention, the phase currents of which correspond to the vector diagram from F i g. 5 correspond,

F i g. 7 the vector diagram of a four-phase utility circuit and

F i g. 8 shows a four-phase circuit arrangement according to the invention, the phase currents of which correspond to the vector diagram from F i g. 7 correspond.

F i g. 1 shows five vectors J ₁ to J ₆ , which represent the currents which are to flow in the phases of a five-phase utility circuit. These vectors have the same size and are shifted by 72 ° in relation to each other. F i g. 2 schematically shows this useful circuit with five star-connected phases 1 to 5, each of which contains a resistor R connected in series with an inductance L, as well as a zero point N. This circuit is to be fed from a single-phase alternating voltage U via a single-phase transformer T. The vector system of FIG. 1 has an axis of symmetry which coincides with the vector J ₁ , the direction of which is intended to represent the phase of the voltage V ₁ taken from the secondary winding of the single-phase transformer T. The current J ₁ must therefore be in phase with the voltage V ₁ , for which a capacitor C _{1 is connected} between the terminal 1 and the tap of the transformer T which supplies the voltage V ₁ and has the following value:
1 _ ■

CuC ₁

The currents J ₂ and J ₅ of phases 2 and 5 must be phase shifted by 72 ° forwards and backwards with respect _{to J 1.} To achieve these phase shifts when phases 2 and 5 are fed from a voltage in-phase with V _1, pure reactances must be added to the impedance of the phases, as shown in FIG. 2 are represented by the inductance L ₅ and the capacitor C ₅ , which corresponds to the case that the inductance L is not too large compared to the resistance R. The values of these elements can easily be calculated from the formulas below:

¹ = R ■ tg72 ° + L = 3.0777 R + mL

ω C =

ω L + ojl ₂ = R · ° tg72
ω L ₂ = 3.0777 R - u, L.

If the above value of > L _{2 is} negative, the inductance L ₂ must of course be replaced by a capacitor with an impedance equal to the absolute value.

Furthermore, the performance of phases 2 and 5 must be the same as the performance of phase 1. If V is the voltage applied to any impedance Z, I is the current flowing through that impedance, and η is the phase shift angle of that current with respect to the voltage, then is the power developed

W + VI cos φ

The following applies:

V _ V cos φ ~~ Z ~ R '

where R is the effective resistance of the impedance, one obtains

so:

W =

V ² COS ² φ

COS <f

Applying this relationship to phase 1 one obtains

V ₁ = WR,

where W is phase 1 power, while capacitor C _{1 is} not consuming any power.

For phases 2 and 5, the power factor seen from the transformer T is : cos 72 ° = 0.309, so that the following voltage must be applied to these phases in order to obtain the same power W:

WR 1

= 3.24 YWr.

V ₂₅ =

0.309

This means that K ₂₅ = 3.24 V ₁ . This voltage can be taken from a suitable tap on the secondary winding of the transformer T.

For phases 3 and 4, currents I ₃ and I ₄ . be phase-shifted by 144 ° backwards or forwards with respect to V _1. The argument of any complex impedance can only be between a shift of 90 ° backwards and 90 ° forwards, these limits being excluded if, as is the case, the impedance has a real component. However, this angle of 144 ° can be produced by connecting phases 3 and 4 of transformer T to a voltage V _{24 in} phase opposition to V ₁ . are fed so that these phases _{absorb currents -J 3} and -Z ₄ , which are shifted forward or backward by 36 ° with respect to V _1. If again it is assumed that c> L is not so large compared to R , a capacitor C ₃ must be connected in series with phase 3 and an inductance L ₄ with phase 4, which satisfy the following formulas:

and

ω Ci

so:

= mL + R ■ tg 36 ° = 0.727 R + mL

> L + CoL ₄ . = R- tg 36 ° = 0.727 R ,
o> L ₄ = 0.727 R - mL.

As already stated, if this value O) L _{4 is} negative, ie if OL is too large compared to R , the inductance L _{4 must be} replaced by a capacitor with an impedance equal to the absolute value.

The magnitude of the voltage F _{34 in phase opposition to the voltage K 1} , which must be applied to the line in phases 3 and 4. Obtaining W results in

cos 36 °

= 1,236

= 1.236 V ₁ .

In this way it is possible to obtain balanced currents in the five phases, so that in this case the connection between the zero point N and the point O of the secondary winding of the single-phase transformer T can obviously be omitted. Since the currents are balanced, so are the voltages at terminals 1 to 5 of the five phases, as the impedances are identical.

3 and 4 relate to a star-connected three-phase utility circuit with the three phases 1 to 3 and a zero point N. The system of the three vectors J ₁ , I ₂ , 13 representing the currents of the three phases again has an axis of symmetry coinciding with the vector J ₁ . Analogously to the previous example, a capacitor C _{1 is connected} in series with phase 1 in order to bring the power factor seen by the single-phase transformer T down to 1, it being furthermore arranged so that the currents -I ₂ and - / ₃ µm 60 ° forwards or backwards with respect to Z _{1 are} phase-shifted, which takes place in that a capacitor C ₂ and an inductance L _{3 are connected} in series with the corresponding phases, the inductance can be replaced by a capacitor when mL to is large compared to R. For the reasons explained above, phases 2 and 3 must be _{fed via these parts with a voltage F 23} , which is in phase opposition to F ₁ and has the following value:

_v _ V WR
²³ ~ cos 60 °

■ y

The case of the FIG. 7 and 8 illustrated four-phase circuit can be easily understood. Phases 3 and 4 are in series with pure reactive resistances, which are identical to those connected in series with phases 1 and 2, and are fed with voltage F ₃₄ , which is the same as the voltage F _{12 feeding the other two phases} has, but is in opposite phase to this, the size of each S T his pannungen, is as in the previous case, FTWR. If the four currents are well balanced, the connections of the neutral point and possibly the transformer can be omitted.

Other circuits with any number of phases are conceivable. In all cases the axis of symmetry must of the vector system representing the currents are chosen so that the phase shift angle should be avoided in the vicinity of 90 °, as this would lead to unrealizable supply voltages comes because, as can be seen from the above, these voltages each correspond to the cosine these angles are inversely proportional.

The above examples concerned multiphase connections in star connection; However, the circuit arrangement described can also be used for polygonal circuits, since a polygon can always be replaced by an equivalent star. In the general case of a circuit with m phases with impedances Z in polygonal connection, which is fed with a phase voltage E and takes up a line current J, a star connection with impedances Z ', which is fed with the same phase voltage E , is equivalent to the first if it absorbs the same line currents. If i is the current in an impedance Z of the polygon circuit, one obtains

j _. . π ~ E. π
I = 2i sin - = 2 - sin -.

When the currents are well balanced, as in the previous example, the connection between the neutral point and the single-phase transformer are omitted, so that even the transformer itself can be omitted if the primary voltage has a suitable value.

FIGS. 5 and 6 show a two-phase utility circuit. The system of the two currents in the two phases 1 and 2 representing the vectors I ₁ and I ₂ has a symmetry axis which is the bisector of the angle formed by them, so that I ₁ and I ₂ in relation to the supply voltage by 45 ° to the are forward or backward out of phase. In series with phase 1 there must be a capacitor C ₁ with the value

Furthermore, if e denotes the voltage at the terminals of an impedance Z 'in the star connection, it can be written:

E = 2 e sin - = 2 Z ' I sin
m

ω C ₁

= mL + R ■ tg 45 ° = mL + R

One inferred from these relationships

4 sur -
m

In a three-phase circuit z. B. becomes this relationship

Z "

and in phase 2 an inductance L ₂ with the value

o> L ₂ = R ■ tg 45 ° - mL = R - mL

switched when this value is positive, and a capacitor when this is not the case.

The common voltage applied to these two phases has the value

Assuming that the impedances of the circuit of FIG. 4 are connected in delta, the equivalent resistance in the star

circuit -γ-, and the voltages to be applied have the values

fWR

ν V ^WR

^Kl2 ~ cos 45 °

= π-

V ₂₃ =

The reactances connected in series with the various phases of the power circuits described were either inductors or con-

capacitors, but of course they can also be created by combining these elements in series or parallel connection. In particular, for the purpose of regulation can be changeable Inductors are used, which z. B. saturable and with fixed inductors or capacitors are connected in series or in parallel to produce adjustable inductive reactances.

1 sheet of drawings

209 529/149

Claims (2)

Patent claims: 1. Circuit arrangement for feeding a symmetrical multi-phase utility circuit from a single-phase alternating voltage, with at least one phase of the utility circuit being preceded by a series reactance to determine the respective phase shift angle between the phase current and the single-phase alternating voltage, and the single-phase alternating voltage via a single-phase transformer with secondary-side taps Phases of the useful circuit is supplied, characterized in that the single-phase alternating voltage (U) at the taps per phase, based on a zero point (N) of the useful circuit, is dimensioned so that it is inversely proportional to the cosine of the respective phase shift angle. 2. Circuit arrangement according to claim 1, characterized in that the individual phases are shifted symmetrically to the vectorial position of the single-phase alternating voltage (U) and the phases shifted by negative and positive phase shift angles of the same amount are at the same tap.