DE260521C - - Google Patents

Description

IMPERIAL

PATENT OFFICE.

PATENT LETTERING

- M 260521 CLASS 21 c. GROUP

switched on inductance sources.

Patented in the German Empire on June 19, 1912.

In the process of reducing energy loss in lines for variable electrical currents with between the outgoing and return lines at preferably equal intervals Switched on, acting as inductance sources compensators must, as the inventor has shown that the expansion joints are arranged in such a number and so distributed be that on the wavelength which at

ίο the vibration to be transmitted before Switching on the shunts (compensators) would be present on the line, several expansion joints are omitted, for practical purposes at least eight. as well As with the distance, incorrect information about the dimensioning is given in the literature made of the resistance of the expansion joints. Thompson demands a greater resistance for the shunts than he owns the whole line, and Roeber gives its rules regardless of the actual task of the shunts. Due to the practical conditions, however, the theoretically desired smallest possible smallness the effective resistance compared to the inductive resistance drawn a limit, and the question arises when is the effective (effective ohmic) resistance an inductance source according to the Thompson method as cheap and sufficient can be considered small. In doing so, consideration must also be given to economic efficiency, d. H. to discuss the question of whether the expense of a far-off compensation to the savings in energy and the other investment costs in the right relationship place.

On the basis of the known definition of the equivalent uniform conductor given by the inventor and its method of calculation, together with permissible approximations taking into account the special conditions, the present invention determines that the effective ohmic resistance of the compensators is less than 0.415 times the capacitance resistance of the section of the conductor element must be, if at all the losses resulting from the wattless currents in the line are to be reduced by switching on the compensators. How much smaller the effective ohmic resistance has to be depends on the particular purposes of use and the requirement to what extent the attenuation of the line is reduced, ie to what extent it should be reduced. It is found that the total ohmic resistance of the compensator acting as an inductance ^{source may be at most equal to j / y 4} + 1 - y ² times the impedance of the capacitance of the associated conductor element for the number of periods to be transmitted, where y represents the denominator of the fraction to which the attenuation by the compensators should be reduced.

In the long-distance transmission of time-varying electrical currents of low strength

55

60

(Low current) is the electrical efficiency of the line because of the low cost for the generation of the required electrical energy on the profitability of the Plant usually without any significant influence, such as B. with remote switching, telegraphy etc. In many cases all that matters is to transfer a certain amount of energy to the desired distance,

ίο such as when telephoning. the Line is then to be calculated regardless of the degree of efficiency from the point of view that it is as cheap as possible. at Low-voltage systems is now generally through the Thompson system only a significant economic advantage compared to the reduction in attenuation by Gain reinforcement of the conductor when it is about a third and. more decreased shall be. According to the invention, it is necessary in these systems, the entire The effective ohmic resistance of the shunt is not more than 0.2 times the value the impedance of the capacitance of the associated conductor element in the case of the to be forwarded To make period number.

In the case of power transmissions (heavy current) over longer distances, however, the line must be measured from the point of view that the cost of depreciation and Interest on the line system and the costs of expanding the generating system a minimum value to cover the loss in the line and its additional operating costs own. Since both the system costs and the efficiency of the Thompsonian conductor depend on the energy loss in the expansion joints, the reduction must be here the attenuation of the line by the compensators is much greater and the effective ohmic resistance of the compensators can be significantly smaller than for low-voltage transmissions, provided that the compensators are not preferred for Serve to reduce overvoltages. For practical implementations of power transmissions the attenuation of the line must be reduced to at least the third part by switching on the compensators, if the transmission is to be significantly improved. According to the invention, the effective one must therefore be used in these systems The ohmic resistance of the compensators is not more than 0.05 times the value of the impedance the line capacitance of the associated conductor element in the case of the Be period number. From practical experiments it has now been found that the production of Compensators are possible in which the value of the total ohmic effective resistance is up to about 0.0015 times Value of the impedance of the capacitance of the associated conductor element for the relevant number of periods to be forwarded goes down.

The new dimensioning is based on the following mathematical and physical consideration justified.

Below the so-called "critical" ohmic resistance of the expansion joints is the one Understand the value below which the total effective ohmic resistance of each compensator must be, if with a certain compensation of the wattless currents originating from the line at the same time a reduction in the losses in the line is to be achieved. The "critical" Resistance results from the condition that the attenuation constant of the conductor element of the Thompson conductor is equal to that must be the same route of the relevant line without compensators. the Equation 1 for this is:

² ) - \ - a'-w '- sk)

ι.

ir {V (a ^a + P * -C »)> (w * + j> *. L ') + • p * .L.C}

The left side of the equation is the attenuation constant for that of the Thompson ladder equivalent uniform line, the right side the attenuation constant for the same Line without compensators. With the Thompson leader it denotes:

w 'is the effective ohmic resistance in the main circuit (i.e. conductor),

s = pL ' the effective inductive resistance in the main circuit,

= p-C = p- [C-

² - the effective conductive resistance between the forward and return lines (shunt),

L _{0 is} the effective inductance between the outgoing and return lines,

a ' the effective discharge between the outgoing and return lines. For the same line without compensators:

w is the effective ohmic resistance of the conductor,

p L is the effective inductive resistance of the conductor,

pC is the conductive resistance between the forward and return lines,

a is the effective derivative between the outward and return lines and in both terms of the equation

p = 2 π η is the angular frequency.

All sizes in both links are related to the length of the ladder element.

The "critical resistance" has a maximum value in the resonance case, which should always be aimed for and is therefore of particular importance. For this purpose, the variable k is zero. Cable lines are also assumed, as these are mainly used for the Thompson system. With these lines, s can be neglected against w ' and p · L against w. Furthermore, the calculation should be carried out on an artificial line which does not have a discharge, since it is simpler and sufficiently accurate for the present purpose given the practically possible distances between the compensators. The derivation of the line can also be neglected, since only the losses resulting from the charging currents are reduced by the compensators and therefore only their contribution to the attenuation is taken into account here. Under these conditions, equation 1 reads:

2.

: I / -WpC.

The attenuation constant of the conductor element of the Thompson conductor results from idling 80 20 and short circuit sufficiently accurate to:

3 ·

ßl = l / «":

Ρ ² ^ (2 rf + (2p

.T ^ ² I ^:

where means:

r is the effective ohmic resistance of the compensator, L _{n is} the effective inductance of the compensator, or it becomes:

In most practical cases, - ^ - against

be so that
4-

p ² -C ²

^ r- neglected

= ι / w ■

wp ' ¹ · C ² + P ² ■ V _n

can be set. With this value equation 2 gives:

v _m τ ^ "wp ² -C ²

From the resonance condition

6th

becomes when —5— small against

Φ-L _n

p.c

(w

(4) ² ' P ² ' C ²

~ T is: PL _n

r ² + p * -V _n * ^r ~ ' or expanded according to pL _n to the fourth power of r :

! 07-2 ^I -

p ² · C ² - r ⁴ .

The last link can be neglected compared to the other two, so that

7- P * -Ln-Ji ₇ C ₂ --2-r *

will. Substituting this value into equation 5 gives:

-C *

or

■ In + - O.

-C- w -p ² -C ² p ² -C ² Thus, the "critical value" for the resistance of the compensators: ι ι

(4 - wpC) pC or sufficiently approximated: {/ 32 - 8w · p - C + w ² - p ² ■ C ² -4},

Vm =

(4-wpC) pC - · - ^ - { 1.66-0.707-wp -C).

In most applications of the Thompson ladder system , wpC against the unit can be neglected. Then the "critical resistance" is:

10.

r _m = 0.415 PC

The value of the effective ohmic resistance that the compensators must have if the attenuation of the line is to be ^{reduced to the yth} part is obtained with the help of equation 5 from the relationship:

ι pC w -p ² -C ²

11.

p ² -c ²

or if this equation is solved for r _x in the earlier way, to:

12th

r _x =

(4th

C) t y · w - p · C

or with sufficient accuracy for most practical designs:

It is then possible to dimension the electrical parameters of the expansion joints so that that in all practical cases they give a good result for Thompson's method. The dissipation losses resulting from the expansion joints, based on the unit of length of the line, however, are not entirely independent of the number of expansion joints, i.e. with any number not constant, but take more or more with the subdivision less because the cost of the expansion joints, if they can be implemented at all, in the case of a very strong subdivision grow so disproportionately that this is why this 110 condition cannot be realized with practical explanations of the Thompson leader. Therefore it is not possible to arbitrarily increase the effect of the expansion joints by increasing them to increase, but the same is for a certain line, number of periods and type of compensator with a certain number, based on the length unit of the line, the biggest. When dimensioning the expansion joints, this aspect must be taken into account 120 carried. The best distance between the expansion joints is also obtained from the

above calculation, especially if in equation 4 the dependency of the derivative resulting from the compensators per unit length of the line on the number of compensators is used. Assuming that ζ. B. the derivation of the compensators on the unit length of the line is inversely proportional to the length of the conductor element or the distance I between the compensators, the most favorable value of I is approximately

i, 59

•1/

where r represents the effective ohmic or loss resistance of the compensators and w the effective ohmic resistance of the line, here both based on its unit length. For economic reasons, the distance between the compensators is often not measured according to the minimum of the attenuation of the line, but in such a way that the ratio of the attenuation reduction through

the compensators at their cost for the line in question as inexpensive as possible, or in the case of power transmissions, that the operating profit is a percentage of the investment capital is as large as possible. These values are also dependent on the costs of the expansion joints, etc. 30 result with the help of the specified mathematical relationship in a corresponding extension.

Claims (1)

Patent claim: Method for reducing the energy loss in lines for variable electrical currents with inductance sources connected between the forward and return lines, characterized in that the total effective ohmic resistance of each compensator is at most equal to j / y ⁴ -f ι-y ² times the apparent resistance of the capacitance of the associated conductor element is at the number of periods to be forwarded, where y represents the denominator of the fraction to which the attenuation by the compensators is to be reduced.