METHOD AND APPARATUS FOR TRANSMISSION OF ELECTRICAL ENERGY

Abstract

The invention relates to electrical engineering, specifically to apparatuses and methods for transmission of electrical energy using resonant techniques between stationary objects, as well as between stationary power sources and movable devices that receive energy. The technical result is achieved by eliminating the occurrence, on the transmission line, of a potential antinode of a standing wave of potential, as well as by eliminating the occurrence, in the transmission line, of a current antinode of a standing wave of current, which fact simplifies operation and reduces the cost of the transmission system, improves environmental situation along the transmission line due to decreased intensity of electrical and magnetic fields, reduces the influence of the capacitance of the conductor of the transmission line on the resonant windings of Tesla transformers.

The use of the proposed invention results in increased efficiency of resonant transmission of electrical energy, and, primarily, over small and medium distances.

Claims

1. A method for transmission of electrical energy comprising: transmitting electrical energy from the source of electrical energy to the receiver of electrical energy using a frequency converter for converting electrical current from the source of electrical energy to elevated-frequency electrical current, transmitting and receiving resonant Tesla transformers, the low-potential terminals of the windings of said transformers being grounded, and an electrical energy transmission line, wherein the transmission line is included between the stationary or movable points of the resonant windings of the transmitting and receiving transformers, the output resistance in which corresponds to the input or output resistance of the transmission line, the frequency converter is connected to the transmitting transformer via an electrical capacitor using a coupling winding magnetically-inductively coupled to the winding of the transmitting transformer, the receiver of electrical energy is connected to the receiving transformer via an electrical capacitor using a coupling winding magnetically-inductively coupled to the winding of the receiving transformer, and said method further comprises: excitating, by means of electrical energy from the source of electrical energy, in the winding of the transmitting transformer, resonant oscillations with the provision of excitation of electrical current in the transmission line, transmitting the energy via the transmission line to the winding of the receiving transformer with excitation therein of resonant oscillations, which fact ensures transmission of energy from the receiving transformer to the receiver of electrical energy.

2. The method for transmission of electrical energy according to claim 1, wherein the energy is transmitted to the receiver of electrical energy further via a current inverter converting the energy of elevated-frequency current into the energy of electrical current suitable for supplying the load.

3. The method for transmission of electrical energy according to claim 1, wherein the high-potential terminals of the windings of the transmitting and receiving transformers are connected to solitary capacitors.

4. The method for transmission of electrical energy according to claim 3, wherein the solitary capacitors are made in the form of current-conducting spheres or toroids.

5. The method for transmission of electrical energy according to claim 1, wherein the transmission line is a single-wire transmission line.

6. A method for transmission of electrical energy comprising: transmitting electrical energy from the source of electrical energy to the receiver of electrical energy using a frequency converter for converting electrical current from the source of electrical energy to elevated-frequency electrical current, transmitting and receiving resonant Tesla transformers, and an electrical energy transmission line, wherein the transmission line is included between the stationary or movable points of the resonant windings of the transmitting and receiving transformers, the output resistance in which corresponds to the input or output resistance of the transmission line, the frequency converter is included between the low-potential terminal of the resonant winding of the transmitting transformer and the grounding connection, the receiver of electrical energy is included between the low-potential terminal of the resonant winding of the receiving transformer and the grounding connection, and said method further comprises: excitating, by means of electrical energy from the source of electrical energy, in the winding of the transmitting transformer, resonant oscillations with the provision of excitation of electrical current in the transmission line, and transmitting the energy via the transmission line to the winding of the receiving transformer with excitation therein of resonant oscillations, which fact ensures transmission of energy from the receiving transformer to the receiver of electrical energy.

7. The method for transmission of electrical energy according to claim 6, wherein the receiver of electrical energy is connected to the low-potential terminal of the resonant winding of the receiving transformer via a current inverter converting the energy of elevated-frequency current into the energy of electrical current suitable for supplying the load.

8. The method for transmission of electrical energy according to claim 6, wherein the high-potential terminals of the resonant windings of the transmitting and receiving transformers are connected to solitary capacitors.

9. The method for transmission of electrical energy according to claim 8, wherein the solitary capacitors are made in the form of current-conducting spheres or toroids.

10. The method for transmission of electrical energy according to claim 6, wherein the transmission line is a single-wire transmission line.

11. A method for transmission of electrical energy comprising: transmitting electrical energy from the source of electrical energy to the receiver of electrical energy using a frequency converter for converting electrical current from the source of electrical energy to elevated-frequency electrical current, transmitting and receiving resonant Tesla transformers, and two electrical energy transmission lines, wherein the both transmission lines are included between the stationary or movable points of the resonant windings of the transmitting and receiving transformers, the output resistance in which corresponds to the input or output resistance of the transmission line, the frequency converter is connected to the transmitting transformer via electrical capacitors using a coupling winding magnetically-inductively coupled to the winding of the transmitting transformer, the receiver of electrical energy is connected to the receiving transformer via electrical capacitors using a coupling winding magnetically-inductively coupled to the half-wave winding of the receiving transformer, and said method further comprises: excitating, by means of electrical energy from the source of electrical energy, in the winding of the transmitting transformer, resonant oscillations with the provision of excitation of electrical current in the transmission lines, transmitting the energy via the transmission lines to the winding of the receiving transformer with excitation therein of resonant oscillations, which fact ensures transmission of energy from the receiving transformer to the receiver of electrical energy.

12. The method for transmission of electrical energy according to claim 11, wherein the transmission lines are single-wire transmission lines.

13. The method for transmission of electrical energy according to claim 12, wherein the single-wire transmission lines are made separately from each other.

14. The method for transmission of electrical energy according to claim 12, wherein the single-wire transmission lines are made integral with each other in the form of isolated twisted pair with the required level of electric strength between the transmission lines and between the transmission lines and ground.

15. The method for transmission of electrical energy according to claim 11, wherein the middles of the windings of the transmitting and receiving Tesla transformers are grounded.

16. The method for transmission of electrical energy according to claim 11, wherein the energy is transmitted to the receiver of electrical energy further via a current inverter converting the energy of elevated-frequency current into the energy of electrical current suitable for supplying the load.

17. The method for transmission of electrical energy according to claim 11, wherein the high-potential terminals of the windings of the transmitting and receiving transformers are connected to solitary capacitors.

18. The method for transmission of electrical energy according to claim 17, wherein the solitary capacitors are made in the form of current-conducting spheres or toroids.

19. A method for transmission of electrical energy comprising: transmitting electrical energy from the source of electrical energy to the receiver of electrical energy using a frequency converter for converting electrical current from the source of electrical energy to elevated-frequency electrical current, transmitting and receiving resonant Tesla transformers, and two electrical energy transmission lines, wherein the both transmission lines are included between the stationary or movable points of the resonant windings of the transmitting and receiving transformers, the output resistance in which corresponds to the input or output resistance of the transmission line, the frequency converter is connected to the transmitting transformer by way of including the electrical output of the frequency converter in series with the conductor in the resonant winding of the transmitting transformer, the receiver of electrical energy is connected to the receiving transformer by way of including the electrical input of the receiver in series with the conductor in the resonant winding of the receiving transformer; and said method further comprises: excitating, by means of electrical energy from the source of electrical energy, in the winding of the transmitting transformer, resonant oscillations with the provision of excitation of electrical current in the transmission lines, transmitting the energy via the transmission lines to the winding of the receiving transformer with excitation therein of resonant oscillations, which fact ensures transmission of energy from the receiving transformer to the receiver of electrical energy.

20. The method for transmission of electrical energy according to claim 19, wherein the energy is transmitted to the receiver of electrical energy further via a current inverter converting the energy of elevated-frequency current into the energy of electrical current suitable for supplying the load.

21. The method for transmission of electrical energy according to claim 19, wherein the transmission lines are single-wire transmission lines.

22. The method for transmission of electrical energy according to claim 19, wherein the single-wire transmission lines are made separately from each other.

23. The method for transmission of electrical energy according to claim 19, wherein the single-wire transmission lines are made integral with each other in the form of isolated twisted pair with the required level of electric strength between the transmission lines and between the transmission lines and ground.

24. The method for transmission of electrical energy according to claim 19, wherein the high-potential terminals of the windings of the transmitting and receiving transformers are connected to solitary capacitors.

25. The method for transmission of electrical energy according to claim 24, wherein the solitary capacitors are made in the form of current-conducting spheres or toroids.

26. An apparatus for transmission of electrical energy comprising: a source and a receiver of electrical energy, a frequency converter for converting electrical current from the source of electrical energy to elevated-frequency electrical current, transmitting and receiving resonant Tesla transformers, the low-potential terminals of the windings of said transformers being grounded, and an electrical energy transmission line, wherein the transmission line is included between the stationary or movable points of the resonant windings of the transmitting and receiving transformers, the output resistance in which corresponds to the input or output resistance of the transmission line, the frequency converter is connected to the transmitting transformer via an electrical capacitor using a coupling winding magnetically-inductively coupled to the winding of the transmitting transformer, the receiver of electrical energy is connected to the receiving transformer via an electrical capacitor using a coupling winding magnetically-inductively coupled to the winding of the receiving transformer, the source of electrical energy provides the possibility of excitation, by means of electrical energy, in the winding of the transmitting transformer, of resonant oscillations with excitation of electrical current in the transmission line, and the transmission line provides the possibility of transmission of energy through same to the winding of the receiving transformer with excitation therein of resonant oscillations, which fact ensures transmission of energy from the receiving transformer to the receiver of electrical energy.

27. The apparatus for transmission of electrical energy according to claim 26, further comprising a current inverter through which energy is further transmitted to the receiver of electrical energy and which converts the energy of elevated-frequency current into the energy of electrical current suitable for supplying the load.

28. The apparatus for transmission of electrical energy according to claim 26, wherein the high-potential terminals of the windings of the transmitting and receiving transformers are connected to solitary capacitors.

29. The apparatus for transmission of electrical energy according to claim 28, wherein the solitary capacitors are made in the form of current-conducting spheres or toroids.

30. The apparatus for transmission of electrical energy according to claim 26, wherein the transmission line is a single-wire transmission line.

31. An apparatus for transmission of electrical energy comprising: a source and a receiver of electrical energy, a frequency converter for converting electrical current from the source of electrical energy to elevated-frequency electrical current, transmitting and receiving resonant Tesla transformers, and an electrical energy transmission line, wherein the transmission line is included between the stationary or movable points of the resonant windings of the transmitting and receiving transformers, the output resistance in which corresponds to the input or output resistance of the transmission line, the frequency converter is included between the low-potential terminal of the resonant winding of the transmitting transformer and the grounding connection, the receiver of electrical energy is included between the low-potential terminal of the resonant winding of the receiving transformer and the grounding connection, the source of electrical energy provides the possibility of excitation, by means of electrical energy, in the winding of the transmitting transformer, of resonant oscillations with excitation of electrical current in the transmission line, and the transmission line provides the possibility of transmission of energy through same to the winding of the receiving transformer with excitation therein of resonant oscillations, which fact ensures transmission of energy from the receiving transformer to the receiver of electrical energy.

32. The apparatus for transmission of electrical energy according to claim 31, wherein the receiver of electrical energy is connected to the low-potential terminal of the resonant winding of the receiving transformer via a current inverter converting the energy of elevated-frequency current into the energy of electrical current suitable for supplying the load.

33. The apparatus for transmission of electrical energy according to claim 31, wherein the high-potential terminals of the resonant windings of the transmitting and receiving transformers are connected to solitary capacitors.

34. The apparatus for transmission of electrical energy according to claim 33, wherein the solitary capacitors are made in the form of current-conducting spheres or toroids raised above the ground.

35. The apparatus for transmission of electrical energy according to claim 31, wherein the transmission line is a single-wire electrical energy transmission line.

36. An apparatus for transmission of electrical energy comprising: a source and a receiver of electrical energy, a frequency converter for converting electrical current from the source of electrical energy to elevated-frequency electrical current, transmitting and receiving resonant Tesla transformers, and two electrical energy transmission lines, wherein the both transmission lines are included between the stationary or movable points of the resonant windings of the transmitting and receiving transformers, the output resistance in which corresponds to the input or output resistance of the transmission line, the frequency converter is connected to the transmitting transformer via electrical capacitors using a winding magnetically-inductively coupled to the winding of the transmitting transformer, the receiver of electrical energy is connected to the receiving transformer via electrical capacitors using a coupling winding magnetically-inductively coupled to the half-wave winding of the receiving transformer, the source of electrical energy provides the possibility of excitation, by means of electrical energy, in the winding of the transmitting transformer, of resonant oscillations with excitation of electrical current in the transmission lines, and the transmission lines provides the possibility of transmission of energy through same to the winding of the receiving transformer with excitation therein of resonant oscillations, which fact ensures transmission of energy from the receiving transformer to the receiver of electrical energy.

37. The apparatus for transmission of electrical energy according to claim 36, wherein the transmission lines are single-wire transmission lines.

38. The apparatus for transmission of electrical energy according to claim 37, wherein the single-wire transmission lines are made separately from each other.

39. The apparatus for transmission of electrical energy according to claim 37, wherein the single-wire transmission lines are made integral with each other in the form of isolated twisted pair with the required level of electric strength between the transmission lines and between the transmission lines and ground.

40. The apparatus for transmission of electrical energy according to claim 36, wherein the middles of the windings of the transmitting and receiving Tesla transformers are grounded.

41. The apparatus for transmission of electrical energy according to claim 36, further comprising a current inverter through which energy is further transmitted to the receiver of electrical energy and which converts the energy of elevated-frequency current into the energy of electrical current suitable for supplying the load.

42. The apparatus for transmission of electrical energy according to claim 36, wherein the high-potential terminals of the windings of the transmitting and receiving transformers are connected to solitary capacitors.

43. The apparatus for transmission of electrical energy according to claim 42, wherein the solitary capacitors are made in the form of current-conducting spheres or toroids.

44. An apparatus for transmission of electrical energy comprising: a source and a receiver of electrical energy, a frequency converter for converting electrical current from the source of electrical energy to elevated-frequency electrical current, transmitting and receiving resonant Tesla transformers, and two electrical energy transmission lines, wherein the both transmission lines are included between the stationary or movable points of the resonant windings of the transmitting and receiving transformers, the output resistance in which corresponds to the input or output resistance of the transmission line, the frequency converter is connected to the transmitting transformer by way of including the electrical output of the frequency converter in series with the conductor in the resonant winding of the transmitting transformer, the receiver of electrical energy is connected to the receiving transformer by way of including the electrical input of the receiver in series with the conductor in the resonant winding of the receiving transformer, the source of electrical energy provides the possibility of excitation, by means of electrical energy, in the winding of the transmitting transformer, of resonant oscillations with excitation of electrical current in the transmission lines, and the transmission lines provides the possibility of transmission of energy through same to the winding of the receiving transformer with excitation therein of resonant oscillations, which fact ensures transmission of energy from the receiving transformer to the receiver of electrical energy.

45. The apparatus for transmission of electrical energy according to claim 44, further comprising a current inverter through which energy is further transmitted to the receiver of electrical energy and which converts the energy of elevated-frequency current into the energy of electrical current suitable for supplying the load.

46. The apparatus for transmission of electrical energy according to claim 44, wherein the transmission lines are single-wire transmission lines.

47. The apparatus for transmission of electrical energy according to claim 46, wherein the single-wire transmission lines are made separately from each other.

48. The apparatus for transmission of electrical energy according to claim 46, wherein the single-wire transmission lines are made integral with each other in the form of isolated twisted pair with the required level of electric strength between the transmission lines and between the transmission lines and ground.

49. The apparatus for transmission of electrical energy according to claim 44, wherein the high-potential terminals of the windings of the transmitting and receiving transformers are connected to solitary capacitors.

50. The apparatus for transmission of electrical energy according to claim 49, wherein the solitary capacitors are made in the form of current-conducting spheres or toroids.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0076] FIG. 1 is a schematic diagram of electrical connections for implementing the method and apparatus for transmission of electrical energy using two quarter-wave resonant Tesla transformers. The low-potential terminals of the resonant windings of the transmitting and receiving transformers are grounded, the high-potential terminals of the quarter-wave windings are remained unconnected. Electrical energy from the source of energy to the transmitting Tesla transformer is transmitted via a frequency converter, via an electrical capacitor and a low-voltage pumping winding, which provides magnetic-induction transmission of electrical energy to the region of current antinode of the quarter-wave resonant winding. Electrical energy from the transmitting transformer to the receiving transformer is transmitted using a single-wire transmission line between points A and B of the resonant windings of the transformers. The output resistance of the windings at points A and B is equal in absolute value to the wave resistance of the transmission line at the input and output of same. Electrical energy from the receiving transformer to the load is transmitted via an electrical capacitor using the magnetic-induction energy drain winding located in the region of current antinode of the resonant quarter-wave winding of the receiving Tesla transformer.

[0077] FIG. 2 is a schematic diagram of electrical connections for implementing the method and apparatus for transmission of electrical energy using two quarter-wave resonant Tesla transformers. The high-potential terminals of the resonant windings of the transmitting and receiving transformers are remained unconnected. The frequency converter with electrical output thereof is included immediately between the low-potential output and the grounding connection of the transmitting transformer. The load is included immediately between the low-potential terminal of the receiving transformer and the grounding connection. Electrical energy between the resonant quarter-wave Tesla transformers is transmitted using a single-wire transmission line between points A and B located on the quarter-wave windings at points where the output resistance of the windings is equal in absolute value to the resistance of the transmission line at the input of same.

[0078] FIG. 3 is a schematic diagram of electrical connections for implementing the method and apparatus for transmission of electrical energy from a transmitting quarter-wave Tesla transformer to a receiving quarter-wave Tesla transformer using a single-wire electrical energy transmission line, the length of the transmission line is one-half of the length of a standing wave excited on the line during the operation of the resonant quarter-wave windings in the resonance mode. Transmission of energy to the transmitting transformer, and of energy from the receiving transformer to the load is implemented via electrical capacitors using magnetic-induction coupling. The high-potential outputs of the resonant windings are connected using conductors to electrically conductive spheres.

[0079] FIG. 4 is a schematic diagram of electrical connections for implementing the method and apparatus for transmission of electrical energy from the source of electrical energy to the receiver of electrical energy using transmitting and receiving half-wave Tesla transformers and two single-wire transmission lines. The transmission of electrical energy from the frequency converter to the transmitting resonant transformer, as well as of energy from the receiving transformer to the load or to the inverter, is implemented via electrical capacitors using magnetic-induction windings. The high-potential terminals of half-wave resonant windings are remained unconnected. The beginning and ends of the two single-wire transmission lines are connected to points A, B, C, D on the half-wave windings of the resonant transformers, the output resistance in which is equal in absolute value to the wave resistances of the single-wire transmission lines at inputs and outputs of same.

[0080] FIG. 5 is a schematic diagram of electrical connections for implementing the method and apparatus for transmission of electrical energy from the source of electrical energy to the receiver using two half-wave Tesla transformers and two single-wire electrical energy transmission lines. The frequency converter and the load, or the inverter, are included immediately in series with the resonant half-wave windings. The single-wire transmission lines with beginnings and ends thereof are connected to the half-wave resonant windings of the Tesla transformers at points A, B, C, D, the output resistance in which is equal in absolute value to the wave resistances of the transmission line at inputs and outputs of same. One one-half of a standing wave of current rests on each one of the single-wire transmission lines, at the frequency of resonance of the half-wave windings.

[0081] FIG. 6 is a schematic diagram of electrical connections for implementing the method and apparatus for transmission of electrical energy using two single-wire lines made in the form of twisted pair and two resonant Tesla transformers, the middles of half-wave windings of which are grounded. The beginnings and ends of the single-wire transmission lines are connected to the half-wave windings of the Tesla transformers at points A, B, C, D, at which the output resistances of the windings are equal in absolute value to the wave resistances of the transmission lines at the inputs and outputs. The high-potential outputs of the half-wave resonant windings are connected using conductors to electrically conductive spheres.

EMBODIMENT OF INVENTION

[0082] FIG. 1 is an electrical diagram of the method and apparatus for transmission of electrical energy, where 1 is the source of electrical energy, 2 is the converter of electrical energy from the format of the source 1 to the format of alternating current of elevated and controlled frequency, the current frequency is set so that the following condition is fulfilled: f.sub.G=f.sub.01. Here, f.sub.G is the current frequency at the converter output, f.sub.01 is the resonance frequency of the quarter-wave winding 5 of the resonant transmitting Tesla transformer. 3 is an electrical capacitor that, together with a low-voltage winding 4, forms a resonant serial electrical power circuit of the transmitting Tesla transformer. The resonant frequency of the circuit is f.sub.P1=f.sub.01. The low-voltage winding 4 is disposed on top of the quarter-wave winding 5 at the low-potential terminal 6, in the region of current antinode. The high-potential terminal 7 of the winding 5 is electrically connected to the output high-potential terminal 9 of the quarter-wave resonant transmitting Tesla transformer, the terminal 9 is isolated and remained unconnected.

[0083] The low-potential terminal 6 of the winding 5 is connected to the grounding terminal 3 of the ground circuit on the transmitting side of the system and is connected to the grounding structure using a conductor 10. The terminal 8 of the winding 5 is arranged in that portion of the winding 5, where, during operation under load, the phases of current and potential are close to each other. The point 8 of the winding 5 is indicated by letter A. It is the beginning of a single wire transmission line 11. The end of the transmission line is point B. Point B is connected to a terminal 14 on the quarter-wave winding 15. In the region of the terminal 14, during operation under load, the phases of current and potential are opposed relative to each other. The low-potential terminal 12 of the quarter-wave winding 15 of the receiving Tesla transformer is connected to the grounding terminal 3 of the ground circuit on the receiving side using a conductor 17 that is electrically connected to the grounding structure. The high-potential terminal 13 of the winding 15 is electrically connected to the output high-potential terminal 16 of the quarter-wave resonant Tesla transformer, the terminal 16 is isolated and remained unconnected. The resonant frequency of the winding 15 is f.sub.02=f.sub.01. In the region of current antinode, a low-voltage winding 18 is disposed over the winding 15. The winding 18 via mutual inductance with the winding 15 removes electrical energy and passes same via an electric capacitor 19 to an inverter 20. The winding 18 together with the capacitor 19 forms a serial resonant circuit with its own resonant frequency f.sub.P2. Whereby, f.sub.P2=f.sub.02. The inverter 20 converts the energy of elevated-frequency electrical current into the energy of alternating current having the format that is required to supply the load 21. If the load 21 is indifferent to the format of the supply current, then the inverter 20 is no longer required. In this case, the winding 18 is designed and implemented so as to provide the load 21 with a voltage of the required magnitude. Provided that f.sub.G=f.sub.P1=f.sub.01=f.sub.02=f.sub.P2, the circuit of the low-voltage supply winding (3, 4), the quarter-wave winding 5 of the transmitting Tesla transformer, the quarter-wave winding 15 of the receiving Tesla transformer and the low-voltage energy-removing circuit (18, 19) operate in the resonant mode. Whereby, circuits (3, 4) and (18, 19) operate in the resonance mode on reactive elements with lumped parameters, and the quarter-wave windings 5 and 15 of the resonant Tesla transformers operate in the resonance mode on the segments of long lines with distributed reactive parameters. Accordingly, standing waves are formed on quarter-wave windings 5 and 15 in the form of quarter-wave implementations with potential antinodes at the terminals 7 and 13 (the terminals 9 and 16 of the Tesla transformers) and potential nodes at the terminals 6 and 12, as well as with current antinodes in the region of the grounding terminal 6 of the transmitting transformer 5 and the grounding terminal 12 of the receiving transformer 15, with current nodes at the terminals 7 of the transmitting transformer 5 and 13, of the receiving transformer 15. Thus, two independent wave objects are excited and coexist on the quarter-wave windings as follows: a quarter of a current wave and a quarter of a potential wave, which are two electrical characteristics of a single energy formation with an equal density per unit length of electromagnetic energy along the resonant winding. Thereby, the shift between the antinodes of current and potential along the windings is /4 of a standing wave of current or potential.

[0084] The theory and practice of the operation of quarter-wave transformers shows that the phases of current and potential in the nodes and antinodes are shifted, also in time, by T/4 (where T is the period of a current oscillation, T=1/f). Thereby, when moving along the winding, there is observed a rotation of the phases of current and potential in opposite directions such that at some points of the quarter-wave windings, at no load, the phases of current and potential, between the terminals (6, 7) and (12, 13), are the same (on the winding of the transmitting transformer, point 8) or are in antiphase (on the winding of the receiving transformer, point 14). If the line length is /2, the electrical energy transmission line 11 is included between points (8 and 14), wherein a most favorable, from the point of view of phase difference between current and voltage, electrical energy transmission mode is created on the transmission line 11.

[0085] When loading the load 21, the resonant frequency of the quarter-wave transformer 15 decreases, and the input resistance of the transmission line 11 at point A (line input) changes due to a change in the input resistance of the receiving quarter-wave transformer 15 at point B at the output of the line 11. Thus, there is occurred a mismatch of the output resistance at point 8 of the transmitting transformer 5 and the input resistance of the transmission line 11 at point A. To restore the matching mode, it is necessary to move the connection point 8 on the resonant winding 5. To this end, the tap at point 8 is not made as a single one, but is made as a series of taps along the entire length of the Tesla transformer. In the case of a constant load, the tap is made as a single connection point. In the case of a variable load, when tuning, a connection point that provides the optimal mode for the preferred load range is selected.

[0086] A similar situation takes place when changing the design parameters of the transmission line: lengthening or shortening the transmission distance, changing the diameter of a wire, changing the height of a suspension or changing the method, or the depth of embedding of the line into the ground. The input resistance at point A changes when connecting/disconnecting intermediate consumers to the transmission line. In the taps, the output resistance increases in absolute value when the connection point is moved from position 8 towards the high-voltage terminal of the resonant winding 5. Thereby, the resistance is of active-capacitive character. At the high-potential output (point 7), the output resistance reaches a value:

|Z.sub.OUT|=QZ.sub.W

[0087] Here: Z.sub.OUT is output resistance, absolute value;

[0088] Z.sub.W is wave resistance of the winding 5;

[0089] Q is quality factor of the winding 5;

[0090] The resistance at this point is of capacitive character.

[0091] When the connection point is moved from the position 8 towards the low potential terminal 6, the output resistance decreases in absolute value and the resistance character acquires the inductively-active type. The output resistance reaches a minimum value at the point 6:

[00002]$\left|Z_{O.Math.U.Math.T}\right|=\frac{Z_W}{Q}$

[0092] FIG. 2 is a schematic diagram of electrical connections of the method and apparatus for transmission of electrical energy, where 1 is the source of electrical energy, 2 is the frequency converter of the supply current to the current of elevated- and controlled-frequency for supplying a resonant transmission system comprising a transmitting resonant Tesla transformer 5, a receiving resonant Tesla transformer 15. Thereby, the frequency converter 2 is included immediately between the low-potential terminal 6 and the grounding conductor 10 on the transmitting side, the inverter 20 (or load 21) are included immediately between the low potential terminal 12 and the grounding conductor 17 on the receiving side. The electrical energy transmission line 11 is included between points 8 and 14 on the transmitting and receiving windings 5 and 15, i.e. between points A and B of the transmitting and receiving Tesla transformers. The principle of transmission of electrical energy between points A and B and tuning of the system is similar to that of FIG. 1.

[0093] FIG. 3 is a schematic diagram of electrical connections of the method and apparatus for transmission of electrical energy, where 1 is the source of electrical energy, 2 is the frequency converter of the supply current to the current of elevated- and controlled-frequency for supplying a resonant transmission system comprising a transmitting resonant Tesla transformer 5 and a receiving resonant Tesla transformer 15. Energy from the frequency converter 2 to the transmitting transformer 5 is transmitted via an electric capacitor 3 using magnetic-induction coupling of a low-voltage winding 4, which forms, together with the capacitor 3, a serial resonant circuit consisting of reactive elements with lumped parameters. Energy is transmitted to the load 21 or to the input of the inverter 20 from the receiving transformer 15 using magnetic-induction mutual coupling of the low-voltage winding 18, which forms, together with the capacitor 19, a serial resonant circuit formed from reactive elements with lumped parameters. The low-potential terminals 6, 12 of the quarter-wave windings 5 and 15 are grounded using conductors 10 and 17 immediately near the transformers. The high-potential terminals 7 and 13, via the high-voltage terminals 9 and 16 using the conductors 23 and 22 are connected to solitary capacitors in the form of spheres 25 and 24. Electrical energy from the transmitting transformer 5 to the receiving transformer 15 is transmitted using a single-wire line 11 connecting point A of transmission of energy and point B of reception of energy via terminals 8 on the transformer 5 and point 14 on the transformer 15.

[0094] FIG. 4 is a schematic diagram of the electrical connections of the method and apparatus for transmission of electrical energy from the source 1 of energy via a converter 2 using a half-wave transmitting Tesla transformer 5 and a receiving Tesla transformer 15 and two single-wire transmission lines 11 and 30. The energy from the converter 2 to a half-wave resonant winding 5 and from a half-wave resonant winding 15 to the inverter 20 (or to the load 21) is transmitted using magnetic-induction coupling of the low-voltage windings 4 and 18 via the electrical capacitors (3, 40) and (19, 35). The capacitors (3, 40) and (19, 35), together with the low-voltage windings 4 and 18, form serial resonant circuits. The high-potential terminals 7, 13, 27, 31 of the half-wave windings 5 and 15 are connected to the high-voltage terminals 9, 16, 29, 34, respectively, of the resonant half-wave transmitting Tesla transformer 5 and the resonant half-wave receiving Tesla transformer 15. The high-voltage terminals 9, 16, 29, 34 of the transformers 5 and 15 are remained unconnected. The beginnings and ends of the single-wire electric power transmission lines 11 and 30 are connected at points A, C and B, D to taps 8, 14, 28, 32 on the half-wave windings 5 and 15.

[0095] FIG. 5 is a schematic diagram of the electrical connections of the method and apparatus for transmission of electrical energy from the source 1 of electrical energy using two half-wave Tesla transformers 5 and 15 and two single-wire lines 11 and 30. The frequency converter 2 and the load 21, or inverter 20, are included immediately in interruptions 6 and 12 of the resonant half-wave windings 5 and 15. The transmission lines 11 and 30 are included between the terminals (8, 14) and (28, 32) of the windings 5 and 15. The terminals (8, 14) are connected to the terminal points (A, B), the terminals (28, 32) are connected to the points (C, D) between which the electrical energy is transmitted. One half-wave of a standing wave of current rests on each of the transmission lines (11, 30), at the frequency of resonance of the half-wave windings 5 and 15.

[0096] FIG. 6 is a schematic diagram of the electrical connections of the method and apparatus for transmission of electrical energy using two single-wire lines 11 and 30 made in the form of twisted pair and two resonant Tesla transformers 5 and 15, the middles of the half-wave windings at points 6 and 12 are grounded immediately near the transformers by conductors 10 and 17. The beginnings and ends of the transmission lines 11 and 30 are connected to points A, C, B, D of the half-wave Tesla transformers, in which the output resistances are equal in absolute value to the wave resistances of the windings 5, 15. The high-potential terminals 9, 29, 16, 34 of the resonant transformers 5, 15 are connected by conductors 23, 36, 22, 38 to electrically conductive spheres 25, 37, 24, 39. The lengths of the conductors 23, 36, 22, 38 are at least 5 times greater than the diameters of the spheres 25, 37, 24, 39.

[0097] The electromagnetic phenomena formed around the solenoidal windings of the quarter-wave Tesla transformers, when implementing the proposed methods and apparatuses for transmission of electrical energy, can be described using telegrapher's equations:

[00003]$\begin{array}{cc}\{\begin{array}{c}-\frac{u}{x}=r_0.Math.i+L_0.Math.\frac{i}{t},\\ -\frac{i}{x}=g_0.Math.u+C_0.Math.\frac{u}{t}..Math.\end{array}& \left(1\right)\end{array}$

[0098] Here: u is the potential with respect to ground in the coordinate x, at the moment of time t, [B];

[0099] i is the current in the conductor of the winding in the coordinate x, at the moment of time t, [A];

[0100] r.sub.0 is the resistance per unit length to the electrical current of the conductor of the winding, [Ohm/m];

[0101] g.sub.0 is the conductivity per unit length of the medium between the conductor of the winding and the ground, [S/m];

[0102] L.sub.0 is the inductance per unit length of the resonant winding, [H/m];

[0103] C.sub.0 is the ground capacitance per unit length of the resonant winding, [F/m].

[0104] Equations (1) are valid for any changes in current i and voltage U in time. Provided that the supply is performed by a sinusoidal voltage, in the steady state, using complex representations for currents and voltages, one obtains from (1):

[00004]$\begin{array}{cc}\{\begin{array}{c}-\frac{\stackrel{.}{U}}{x}=\left(r_0+j.Math..Math.L_0\right).Math.\stackrel{.}{I}=Z_0.Math.\stackrel{.}{I},\\ \\ -\frac{i}{x}=\left(g_0+j.Math..Math.C_0\right).Math.\stackrel{.}{U}=Y_0.Math.\stackrel{.}{U.}\end{array}& \left(2\right)\end{array}$

[0105] Here: Z.sub.0=(r.sub.0 jL.sub.0) is the complex resistance per unit length of the winding, [Ohm/m];

[0106] Y.sub.0=(g.sub.0+jC.sub.0) is the complex conductivity per unit length of the medium around the winding, [S/m].

[0107] In (2), the quantities {dot over (U)} and I are functions only of x.

[0108] After differentiation with respect to x, the system (2) becomes:

[00005]$\begin{array}{cc}\{\begin{array}{c}-\frac{d^2.Math.\stackrel{.}{U}}{d.Math.x^2}=Z_0.Math.\frac{d.Math.\stackrel{.}{I}}{\mathrm{dx}},\\ -\frac{d^2.Math.\stackrel{.}{I}}{d.Math.x^2}=Y_0.Math.\stackrel{.}{U}.Math.\mathrm{dx}.\end{array}& \left(3\right)\end{array}$

[0109] Using (1), the system (3) is transformed into a system of second-order differential equations with constant coefficients, the solution to which is as follows:

{dot over (U)}={dot over (A)}.sub.1e.sup.x{dot over (A)}.sub.2e.sup.x={dot over (A)}.sub.1e.sup.x.Math.e.sup.jx+{dot over (A)}.sub.2e.sup.x.Math.e.sup.jx(4)

[0110] Here, is the propagation constant, [m.sup.1];

=+j={square root over (Z.sub.0Y.sub.0)}={square root over ((r.sub.0+jL.sub.0)(g.sub.0+jC.sub.0))}(5)

[0111] is the attenuation coefficient, [dB/m];

[0112] is the phase coefficient, [rad/m];

[0113] {dot over (A)}.sub.1, {dot over (A)}.sub.2 are complex integration constants.

[00006]$\begin{array}{cc}\stackrel{.}{I}=-\frac{1}{Z_c}.Math.\frac{\stackrel{.}{U}}{x}=\frac{}{Z_c}.Math.\left({\stackrel{.}{A}}_1.Math.e^{-.Math.x}-{\stackrel{.}{A}}_2.Math.e^{.Math.x}\right)=\frac{{\stackrel{.}{A}}_1.Math.e^{-.Math.x}-{\stackrel{.}{A}}_2.Math.e^{.Math.x}}{\sqrt{\frac{Z_0}{y_0}}}& \left(6\right)\end{array}$

[0114] Here:

[00007]$\sqrt{\frac{Z_0}{Y_0}}=Z_c$

is the wave resistance of the winding, [Ohm];

[0115] After rearrangement and regrouping, (4) and (6) become:

[00008]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{U}={\stackrel{.}{U}}_1.Math.\mathrm{ch}.Math..Math.x-{\stackrel{.}{I}}_1.Math.Z_C.Math.\mathrm{sh}.Math..Math..Math..Math.x,\\ \stackrel{.}{I}=\frac{-{\stackrel{.}{U}}_1}{Z_C}.Math.\mathrm{sh}.Math..Math.x+{\stackrel{.}{I}}_1.Math..Math.c.Math.h.Math..Math..Math..Math.x..Math.\end{array}& \left(7\right)\end{array}$

[0116] Here: {dot over (U)}, are voltage and current complexes with current coordinates x along the winding;

[0117] {dot over (U)}.sub.1, .sub.1 are complexes of voltages and currents at the beginning of the winding (low-potential terminal);

[0118] ch, sh are hyperbolic functions of cosine and sine.

[0119] The expression (7) may be rearranged to become one using voltage and current at the end of the winding (high-potential terminal). Thereby, U.sub.2 and I.sub.2 of the end of the winding become independent. In this case, the coordinates are measured from the end of the winding:

[00009]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{U}={\stackrel{.}{U}}_2.Math..Math.c.Math.h.Math..Math.x+{\stackrel{.}{I}}_2.Math.Z_C.Math.\mathrm{sh}.Math..Math.x,\\ \stackrel{.}{I}=\frac{{\stackrel{.}{U}}_2}{Z_C}.Math.\mathrm{sh}.Math..Math.x+{\stackrel{.}{I}}_2.Math..Math.c.Math.h.Math..Math..Math..Math.x..Math.\end{array}& \left(8\right)\end{array}$

[0120] The input resistance of the winding in the coordinate x:

[00010]$Z_X=\frac{{\stackrel{.}{U}}_X}{{\stackrel{.}{I}}_X}.$

[0121] Thus, at the beginning of the winding:

[00011]$Z_{I.Math.N.Math.1}=\frac{{\stackrel{.}{U}}_1}{{\stackrel{.}{I}}_1};$

[0122] At the end of the winding:

[00012]$Z_{I.Math.N.Math.2}=\frac{{\stackrel{.}{U}}_2}{{\stackrel{.}{I}}_2};$

[0123] In case of small energy losses in the winding (r.sub.0=0, g.sub.0=0), the propagation constant and Z.sub.C will be equal to:

[00013]$=+j.Math.=\sqrt{\left(r_0+j.Math..Math.L_0\right).Math.\left(g_0+j.Math..Math.C_0\right)}=\sqrt{j.Math..Math.L_0.Math.j.Math.C_0}=j.Math..Math.\sqrt{L_0.Math.C_0}=j.Math.\frac{}{V_0}=j.Math..Math.;$

[0124] Here:

[00014]$V_0=\frac{1}{\sqrt{L_0.Math.C_0}}$

is the wave speed in the winding, [m/s];

[00015]$Z_C=\sqrt{\frac{Z_0}{Y_0}}=\frac{r_0+j.Math..Math.L_0}{g_0+j.Math..Math.C_0}=\sqrt{\frac{L_0}{C_0}}.$

[0125] Accordingly, (8), under assumption r.sub.0=0, g.sub.0=0, simplify to:

[00016]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{U}={\stackrel{.}{U}}_2.Math.\mathrm{chj}.Math..Math.\frac{}{V_0}.Math.x+{\stackrel{.}{I}}_2.Math.Z_C.Math.s.Math.h.Math.j.Math.\frac{}{V_0}.Math.x={\stackrel{.}{U}}_2.Math.c.Math.h.Math.\mathrm{jx}+{\stackrel{.}{I}}_2.Math.Z_C.Math.s.Math.h.Math.j.Math..Math.x,\\ \stackrel{.}{I}=\frac{{\stackrel{.}{U}}_2}{Z_C}.Math.s.Math.h.Math.j.Math.\frac{}{V_0}.Math.x+{\stackrel{.}{I}}_2.Math.\mathrm{ch}.Math..Math.j.Math.\frac{}{V_0}.Math.x=\frac{{\stackrel{.}{U}}_2}{Z_C}.Math.s.Math.\mathrm{hx}+{\stackrel{.}{I}}_2.Math.\mathrm{ch}.Math..Math..Math.x.\end{array}& \left(9\right)\end{array}$

[0126] The hyperbolic functions of imaginary argument are rearranged into circular ones:

[00017]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{U}={\stackrel{.}{U}}_2.Math..Math.\cos .Math.\left(\frac{}{V_0}.Math.x\right)+j.Math.{\stackrel{.}{I}}_2.Math.Z_C.Math.\sin \left(\frac{}{V_0}.Math.x\right)\\ \stackrel{.}{I}=j.Math.\frac{{\stackrel{.}{U}}_2}{Z_c}.Math.\sin \left(\frac{}{V_0}.Math.x\right)+{\stackrel{.}{I}}_2.Math..Math.\cos .Math.\left(\frac{}{V_0}.Math.x\right)\end{array}& \left(10\right)\end{array}$

[0127] For the case of no load, when .sub.2=0, Z.sub.2=, the relations (10) will become:

[00018]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{U}={\stackrel{.}{U}}_2.Math.\cos .Math.x\\ i=j.Math.\frac{{\stackrel{.}{U}}_2}{Z_C}.Math.\sin .Math.x\end{array}& \left(11\right)\end{array}$

[0128] By switching from complexes to instantaneous values u, i, one obtains:

[00019]$\begin{array}{cc}\{\begin{array}{c}u=U_{2.Math.\max }.Math.\cos .Math.x.Math.\sin .Math.t\\ i=\frac{U_{2.Math.\max }}{Z_c}.Math.\sin .Math.x.Math.\cos .Math.t\end{array}& \left(12\right)\end{array}$

[0129] The expression (12) is the equations of standing waves, the quantities of voltages and currents of which vary in time with angular frequency of alternating current and with a varying amplitude along the line under the law cos x and sin x.

[0130] In case of short circuit at the end of the line:

[00020]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{U}=j.Math.i_2.Math.Z_C.Math.\sin .Math.x\\ \stackrel{.}{I}={\stackrel{.}{I}}_2.Math.\cos .Math.x\end{array}& \left(13\right)\end{array}$

[0131] Or for instantaneous values:

[00021]$\begin{array}{cc}\{\begin{array}{c}u=I_{2.Math.\mathrm{ma}.Math.x}.Math.Z_C.Math.\sin .Math.x.Math.\cos .Math.t\\ i=I_{2.Math.\max }.Math.\cos .Math.x.Math.\sin .Math.t.Math.\end{array}& \left(14\right)\end{array}$

[0132] In accordance with (12) and (14), the input resistance of lossless lines, in the case of no load, is equal to:

[00022]$\begin{array}{cc}{Z}_{n.Math.l}=-j.Math.Z_{C.Math.}.Math.\mathrm{ctg}.Math..Math..Math.x=-j.Math.Z_C.Math..Math.\mathrm{ctg}.Math.\frac{2.Math.}{}.Math.x& \left(15\right)\end{array}$

[0133] The input resistance of a lossless line, in the case of a short circuit, at the end of the line will be:

[00023]$\begin{array}{cc}{Z}_{s.Math.c}=-j.Math.Z_{C.Math.}.Math.t.Math.g.Math..Math.x=-j.Math.Z_{c.Math.}.Math.t.Math.g.Math.\frac{2.Math.}{}.Math.x.Math..& \left(16\right)\end{array}$

[0134] The expression (12) can be presented as the sum and difference of two, opposed relative to each other, voltage and current waves:

[00024]$\begin{array}{cc}\{\begin{array}{c}u=\frac{U_{2.Math.\max }}{2}\left[\sin \left(t+.Math.x\right)+\sin \left(t-.Math.x\right)\right]\\ i=\frac{U_{2.Math.\max }}{2.Math.Z_C}\left[\sin \left(t+.Math.x\right)-\sin \left(t-.Math.x\right)\right]\end{array}& \left(17\right)\end{array}$

[0135] The expression (14), similarly, is the sum and difference of opposing waves:

[00025]$\begin{array}{cc}\{\begin{array}{c}u=\frac{I_{2.Math.\max }}{2}.Math.Z_C\left[\sin \left(t+.Math.x\right)+\sin \left(t-.Math.x\right)\right]\\ i=\frac{U_{2.Math.\max }}{2}\left[\sin \left(t+.Math.x\right)-\sin \left(t-.Math.x\right)\right]\end{array}& \left(18\right)\end{array}$

[0136] Since the phase constant of wave is equal to

[00026]$=\frac{}{V_0}=\frac{2.Math..Math.T}{T.Math.}=\frac{2.Math.}{},$

[0137] where is the length of wave in the winding, then the input resistance of the winding of X=/2 long and shorted at the end according to (16) will be:

[00027]$Z_{I.Math.N.Math.s.Math.c}=j.Math.Z_C.Math.t.Math.g.Math.\frac{2.Math.}{}.Math.\frac{}{2}=j.Math.Z_C.Math.t.Math.g.Math.=0.Math.\left[\mathrm{Ohm}\right]$

[0138] In case of no load, the input resistance of the half-wave segment of the winding according to (15) will be:

[00028]$\begin{array}{cc}{Z}_{I.Math.N.Math.n.Math.1}=-j.Math.Z_C.Math.c.Math.t.Math.g.Math.\frac{2.Math.}{}.Math.\frac{}{2}=-j.Math.Z_C.Math.c.Math.t.Math.g.Math.=.Math.\left[O.Math.\mathrm{hm}\right]& \end{array}$

[0139] Thus, the half-wave segment of the winding translates to the input the quantity of the output resistance.

[0140] For a winding having a length of a quarter of wavelength X=/4, the input resistance in case of interruption at the end (no load) according to (15):

[00029]$Z_{\mathrm{INn}.Math..Math.1}=-j.Math.Z_C.Math.c.Math.t.Math.g.Math.\frac{2.Math.}{}.Math.\frac{}{4}=-j.Math.Z_C.Math.c.Math.t.Math.g.Math.\frac{}{2}=0.Math.\left[O.Math.\mathrm{hm}\right]$

[0141] In the case of a short circuit, the quarter-wave winding, at the input, will have an input resistance according to (16):

[00030]$Z_{I.Math.N.Math.s.Math.c}=j.Math.Z_C.Math.t.Math.g.Math.\frac{2.Math.}{}.Math.\frac{}{4}=j.Math.Z_C.Math.\mathrm{tg}.Math.\frac{}{2}=.Math.\left[O.Math.\mathrm{hm}\right]$

[0142] Conclusion: the quarter-wave segment inverts, to the input, the resistance of output circuit. Since the resistance along the quarter-wave segment for the case of no load varies from infinity to zero, it is possible to determine in which coordinate X over the length of the winding the input resistance will be equal in absolute value to the wave one Z.sub.C. According to (15), one has:

[00031]$\left|Z_{I.Math.N.Math.n.Math.1}\right|=\left|-j.Math.Z_C.Math.c.Math.t.Math.g.Math.\frac{2.Math.}{}.Math.x\right|=\left|Z_C.Math.c.Math.t.Math.g.Math.\frac{2.Math.}{}.Math.x\right|=Z_C.Math.\left[O.Math..Math.\mathrm{hm}\right]$

[0143] From which:

[00032]$c.Math.t.Math.g.Math.\frac{2.Math.}{}.Math.x=1.$

Therefore,

[0144] [00033]$\frac{2.Math.}{}.Math.x=\frac{}{4},\mathrm{or}.Math..Math.x=\frac{}{8}.$

[0145] Thus, the point with the coordinate X from the unconnected high-potential end is located in the middle of the winding, since the entire length of the winding of the quarter-wave transformer is equal to

[00034]$\frac{}{4}.$

Voltage and current at the point

[00035]$x=\frac{}{8}$

can be determined by (12):

[00036]$\begin{array}{cc}\{\begin{array}{c}{u}_{/8}={\stackrel{.}{U}}_2.Math..Math.\cos .Math..Math.\frac{}{8}.Math.\sin .Math..Math..Math..Math.t=\frac{{\stackrel{.}{U}}_2}{\sqrt{2}}.Math.\sin .Math..Math..Math..Math.t\\ i_{/8}=\frac{{\stackrel{.}{U}}_2}{Z_C}.Math.\sin .Math..Math.\frac{}{8}.Math.\cos .Math..Math..Math..Math.t=j.Math.\frac{{\stackrel{.}{U}}_2}{\sqrt{2}}.Math.\frac{1}{Z_C}.Math.\sin .Math..Math..Math..Math.t\end{array}& \left(19\right)\end{array}$

[0146] The output resistance in absolute value at the point

[00037]$x=\frac{}{8}$

in accordance with (19) is indeed equal to Z.sub.C:

[00038]$\begin{array}{cc}\left|Z_{/8}\right|=\left|\frac{u}{i}\right|=\left|\frac{{\stackrel{.}{U}}_2.Math.\sqrt{2}.Math.Z_C.Math.\sin .Math..Math..Math..Math.t}{j.Math.\sqrt{2}.Math.{\stackrel{.}{U}}_2.Math.\sin .Math..Math..Math..Math.t}\right|=Z_C.& \left(20\right)\end{array}$

[0147] Points with the coordinates

[00039]$x=\frac{}{8}$

from the high-potential ends 7, 13, 27, 31 are indicated by numbers 8, 14, 28, 32. Since the points 8, 14, 28, 32 are the middles of the windings 5, 15, 26, 33, then the distance between the points 8, 14, 28, 32, low-potential terminals 6, 6, 12, 12, of windings 5, 15, 26, 33 is also equal to

[00040]$x=\frac{}{8}.$

The midpoints 8, 14, 28, 32 of the windings 5, 15, 26, 33 are output to the terminals A, B, C, D of the resonant transformers 5, 15, 26, 33 for connecting thereto the beginnings and ends of the transmission lines 11 and 30.

[0148] The expression (19) shows that in the midpoints 8, 14, 28, 32 of the windings 5, 15, 26, 33, the output resistances in absolute value are equal to Z.sub.C, the voltages are {square root over (2)} times lower than the potentials at the points 7, 13, 27, 31, i.e. at the high-potential terminals 9, 16, 29, 34, where potential antinodes are formed, and currents are {square root over (2)} less than those at the points 6, 6, 12, 12, where current nodes of the resonant quarter-wave Tesla transformers 5, 15, 26, 33 are formed. Thus, the voltage and current in the transmission line are reduced as compared to high-potential and low-potential transmission technologies, in which either a potential antinode, or a current antinode occur on the transmission line.

[0149] Examples of implementation of the method and apparatus for transmission of electrical energy.

Example 1

[0150] The transmitting 5 and receiving 15 Tesla transformers are made of copper single wire in insulation. The diameter of the wire over copper is d.sub.C=1.8 mm. The diameter of the wire in insulation is d.sub.I=2.27 mm. The winding density is n.sub.0=440 turns per meter. The diameter of the former is 300 mm. The tangent of the angle of approach of the winding is tg=2.41 10.sup.3. The winding length is 1.37 m. The inductance per unit length of the winding is L.sub.0=0.01724 (H/m). The design inductance of the resonant winding is 23.6 mH. The practical control of the inductance of the manufactured winding showed L=24.2 mH.

[0151] The design own ground capacitance of the winding was C=152 10.sup.12 F. The design wave resistance of the winding was:

[00041]$Z_C=\sqrt{\frac{L}{C}}=\sqrt{\frac{24.2.Math.{10}^{-3}}{152.Math.{10}^{-1.Math.2}}}=12.6.Math..Math.\mathrm{kOhm}.$

The design resonant frequency was

[00042]$f_{0.Math.d.Math.e.Math.s}=\frac{1}{2.Math..Math.\sqrt{L.Math.C}}=\frac{1}{2.Math..Math.\sqrt{24.2.Math.{10}^{-3}.Math.152.Math.{10}^{-1.Math.2}}}=83,025.Math..Math.\mathrm{kHz}.$

[0152] The real resonant frequency was f.sub.0=83.40 kHz. During transmission of energy, the voltage at the power terminal 8 of the resonant winding of the transmitting transformer 5 was 5 kV. The potential of the isolated high-voltage terminal 9 of the transmitting transformer 5 was 7.1 kV. The current in the transmission line 11 was 0.38 A. The power formed at the load was 1860 W. The power at the output of the generator 2 was 1980 W. The generator voltage was U.sub.G=380 volts, the generator current was I.sub.G=4.9 A. The transmission efficiency was 0.94.

Example 2

[0153] The transmitting 5 and receiving 15 Tesla transformers are made of copper single wire in insulation. The diameter of the wire over copper is d.sub.C=2.6 mm. The diameter of the wire in insulation is d.sub.I=10 mm. The winding density is n.sub.0=100 turns per meter. The total number of turns n is 300 turns. The winding length is 3.0 m. The length of the winding wire is 1130 m. The diameter of the former is 1.2 m. The former is made of impregnated vacuum-dried pine timber. The winding is formed in one layer, in turn to turn relation. The tangent of the angle of approach of the winding was tg=2,7 10.sup.3. The inductance per unit length of the winding was L.sub.0=0.0137 (H/m). The design inductance of the resonant winding was L=L.sub.0.Math.b=0.0137.Math.3.0=0.041 H. The design own capacitance of the winding to the ground was C=334 10.sup.12 F. The wave resistance of the winding was Z.sub.C=11.1 kOhm.

[0154] The design resonant frequency was f.sub.0=43.0 kHz.

[0155] During transmission of energy, the voltage at the power wire 8 of the resonant winding of the transmitting transformer 5 reached 25 kV. The potential of the isolated high-voltage terminal 9 of the transmitting transformer 5 was 35 kV. The current in the transmission line 11 was 10.5 A. The current in the grounding terminal was 15 A. The power in the load was 250 kW. The power at the generator output was 263 kW. The efficiency was =0.952.

[0156] Thus, the use of the proposed invention results in improved transmission efficiency. Due to the use of the full mechanism of transmission of electrical energy, there is arranged, in the transmission line between the terminals with natural parameters of the output resistances of the windings of the Tesla transformers, the transmission of energy with the voltage and current that are maximally similar in phase. Thereby, the voltage on the transmission line 11 is {square root over (2)} times lower than the potential at the high-voltage terminal 9, the current in the line 11 is {square root over (2)} times less than the current in the grounding terminal 6 of the resonant winding 5.

[0157] Absence of potential antinode and current antinode on the transmission line in the proposed methods and apparatuses for transmission of electrical energy results in reduced cost of the transmission system, reduced intensity of the electrical and magnetic fields under the transmission line, reduced cost of operation of the transmission lines. The fact that the voltage on the transmission line is reduced results in reduced requirements for the level of electrical strength of the fastening and supporting hardware, which fact ensures reduced capital costs during the construction of the transmission lines.