WO2001011751A1 - Impedance-compensated power transmission circuit - Google Patents

Impedance-compensated power transmission circuit Download PDF

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Publication number
WO2001011751A1
WO2001011751A1 PCT/KR2000/000843 KR0000843W WO0111751A1 WO 2001011751 A1 WO2001011751 A1 WO 2001011751A1 KR 0000843 W KR0000843 W KR 0000843W WO 0111751 A1 WO0111751 A1 WO 0111751A1
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Prior art keywords
transmission line
present
impedance
series
equation
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PCT/KR2000/000843
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French (fr)
Korean (ko)
Inventor
In-Gyu Park
Original Assignee
Park In Gyu
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Priority to AU61876/00A priority Critical patent/AU6187600A/en
Publication of WO2001011751A1 publication Critical patent/WO2001011751A1/en

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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1807—Arrangements for adjusting, eliminating or compensating reactive power in networks using series compensators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30—Reactive power compensation

Definitions

  • the present invention relates to 3-phase ac power systems, and more particularly to impedance compensation techniques of transmission circuits for solving power flow control problems of transmission circuits.
  • Electric power is transmitted from generation centers to loads through transmission circuits comprising transmission lines, and in most cases, generation centers and loads are geographically widely spread. Accordingly, most transmission circuits become complex, and the control of power flow becomes difficult as well.
  • the power flow through a transmission line is determined by the magnitudes and the phase angles of the voltages of both the ends of the transmission line, and the impedance of the transmission line.
  • the power flow through a transmission circuit is determined by the magnitudes and the phase angles of the bus voltages of the transmission circuit, and the bus admittance matrix YBUS which can be called the impedance of the transmission circuit.
  • the impedance of a transmission line cannot be designed at will, but is determined one-sidedly by the length of the transmission line, and the control of the magnitudes and the phase angle difference of the voltages is possible only in some limited range, so that there occur the cases in which the power flow of the transmission circuit cannot be controlled as needed, [references 1, 4, 8, 14].
  • FIG. 1 is a transmission circuit in which both the ends of the first transmission line (11) and both the ends of the second transmission line (12 ) are respectively connected to the first bus (13) and the second bus (14).
  • FIG. 1 shows only one phase of the 3-phase transmission circuit, as is all the same in the following figures.
  • all of the voltage and the current symbols in capitals are phasors.
  • Vs and 7s are phasors.
  • FIG. 1 is an example, and in such cases where the currents of transmission lines cannot be controlled individually, there occurs the problems especially as follows. Firstly, if the current inclines to one transmission line so that this transmission line is overloaded, the other transmission lines cannot be sufficiently used though they have extra capacities. Secondly, if the current inclines to a transmission line having a relatively large resistance, the total of the power losses in the transmission lines is larger and the operating cost increases in comparison with the cases where it does not. [references 1, 4, 8, 14].
  • the impedance compensation technique of the transmission circuit is to solve the power flow control problems above, and is basically the one in which a series compensator is connected with the transmission line.
  • the series inductor is shown in FIG. 2.
  • the series inductor (21) compensates the impedance of the first transmission line with a positive reactance and increases the total impedance of the first transmission line, so that it causes the effect of reducing the current 7 ⁇ of the first transmission line.
  • the series inductor has the disadvantages that it increases the reactive power of the transmission line, and especially it lowers the maximum transmissible power and the stability limit, [references 1-3].
  • the series capacitor is shown in FIG. 3.
  • the series capacitor (31) compensates the impedance of the second transmission line (12) with a negative reactance and decreases the total impedance of the second transmission line (12), so that it causes the effect of reducing relatively the current of the first transmission line.
  • the series capacitor has the effect of reducing the reactive power of the transmission line, differing from the series inductor.
  • the series capacitor has the disadvantage that it causes the subsynchronous resonance phenomena of other components of the power system, especially generators, [references 1-7].
  • phase shifting transformer As still another conventional technique, there is the technique that connects the phase shifting transformer to the transmission line. This technique has the effect of changing the current of the transmission line by compensating the phase angle difference between the voltages of both the ends of the transmission line.
  • the phase shifting transformer has the disadvantage that it should change the phase angle by changing the tap according to the change of the load in order to cause the effect of the impedance compensation, [references 1, 3, 4, 8-11].
  • the techniques have been proposed, which connect a static power converter comprising high power GTO's to the transmission line through a series transformer.
  • the series static compensators have the advantage that they not only compensate the steady-state impedance of the transmission line, but also control the transient.
  • the series static compensators have the disadvantages that the high power technology of the static power converters is difficult and their costs are very high, [references 1, 12-21].
  • the present invention is to overcome the disadvantages of said conventional techniques, and it is a new impedance compensation technique which does not use said conventional series inductor, said series capacitor, said phase shifting transformer, or said series static compensator, but uses only a series transformer (or a autotransformer).
  • the present invention has the aspects that the two windings of the series transformer are respectively connected in series with the two transmission lines which need the impedance compensation, and the turns ratio of the two windings is set to compensate the impedances of the transmission lines.
  • FIG. 1 is an example of power transmission circuits.
  • FIG. 2 is a power transmission circuit of which the impedance is compensated by the conventional series inductor.
  • FIG. 3 is a power transmission circuit of which the impedance is compensated by the conventional series capacitor.
  • FIG. 4 is a first embodiment of the present invention.
  • FIG. 5A is the structure of the series transformer of FIG. 4.
  • FIG. 5B is the circuit symbol of FIG. 5A.
  • FIG. 6 is the equivalent circuit of FIG. 4.
  • FIG. 9 is an example where R + jX, and a - 2 in FIG. 6.
  • FIG. 10 is a second embodiment of the present invention.
  • FIG. 11 is the equivalent circuit of FIG. 10.
  • FIG. 12 is a circuit where the shunt impedances of the transmission lines are added to the transmission circuit of FIG. 10.
  • FIG. 13 is the series transformer to which a mechanical tap changer is added.
  • FIG. 14 is the series transformer to which a static tap changer is added.
  • FIG. 15 is a third embodiment of the present invention.
  • FIG. 16A is the structure of the autotransformer of FIG. 15.
  • FIG. 16B is the circuit symbol of FIG. 16A.
  • FIG. 17 is the autotransformer to which a mechanical tap changer is added.
  • FIG. 18 is the autotransformer to which a static tap changer is added.
  • FIG. 19 is a fourth embodiment of the present invention.
  • FIG. 20 is a fifth embodiment of the present invention.
  • 101 third bus. 102 fourth bus.
  • 171 mechanical tap changer of autotransformer.
  • 181 static tap changer of autotransformer.
  • 201 fifth bus.
  • 202 sixth bus.
  • FIG. 4 A first embodiment of the present invention is shown in FIG. 4.
  • the structure and the circuit symbol of the series transformer (41) of FIG. 4 are shown in FIG. 5A and FIG. 5B, respectively.
  • the first embodiment of the present invention is the one in a power transmission circuit of an ac power system, comprising: a first transmission line (11); a second transmission line (12); a series transformer (41) comprising a core (51), a first winding (52) wound on said core, a second winding (53) wound on said core, and the turns ratio a of said first winding and said second winding being set to compensate the impedances Z ⁇ and 2 of said first transmission line and said second transmission line; and said first winding (52) being connected in series with said first transmission line (11), and said second winding (53) being connected in series with said second transmission line (12).
  • the series transformer (41) can be located not only at both the ends of the transmission line, but also anywhere between them, as in the case of the conventional series inductor, the series capacitor, and so on. But, when it is located in the middle of the transmission line, if the first transmission line (11) and the second transmission line (12) are far away, this is not good because the transmission lines (11) and (12), and the series transformer (41) should be connected through long lines. And, although some transmission lines or transmission circuits can be additionally connected between the bus (13) and the bus (14), they are not the essential elements of the present invention.
  • the present invention provides the first transmission line (11) with a compensation voltage V ⁇ and provides the second transmission line (12) with a compensation voltage V 2 .
  • the series transformer (41) can be modeled as an ideal one, that is, the case where the magnetizing inductance is so large, and the copper loss and the core loss are so small, and the leakage flux is also so small that they can be ignored. Then, the voltage -current relation of the series transformer (41) can be written as follows.
  • V 2 - a V ⁇
  • a is the turns ratio of the series transformer (41).
  • the number of the winding of the first winding (52) be m
  • the number of the winding of the second winding (53) be m
  • a As shown in the equation (1), the present invention controls the ratio of the current 7 ⁇ of the first transmission line and the current I 2 of the second transmission line according to the turns ratio a of the series transformer.
  • V s - V R V 2 + Z 2 I 2 .
  • the compensation voltage V ⁇ is proportional to the current 7 ⁇ of the first transmission line
  • the compensation voltage V is proportional to the current I 2 of the second transmission line.
  • the compensation voltages V ⁇ and V can be modeled as the compensation impedances respectively.
  • FIG. 6 The equivalent circuit of FIG. 4 where the compensation voltages and V 2 are modeled as the compensation impedances respectively is shown in FIG. 6.
  • the present invention provides the first transmission line (11) and the second transmission line (12) with the compensation impedances.
  • the values of the compensation impedances are determined by the impedances Z ⁇ and Z 2 of the transmission lines, and the turns ratio a of the series transformer.
  • the present invention can compensate the impedances of the transmission lines by setting the turns ratio a of the series transformer appropriately to compensate the impedances of the transmission lines.
  • the present invention compensates the impedance with a positive reactance J1/2X in the first transmission line (11), and compensates the impedance with a negative reactance -J1/2X in the second transmission line (12).
  • FIG. 8 where the turns ratio a of the series transformer is set to 1 in order to compensate the impedances Z ⁇ - R + jX and Z 2 - 2R + j2X of the transmission lines and make the impedances equal.
  • the present invention compensates the impedance with a positive resistance 1/27? and a positive reactance J1/2X in the first transmission line (11), and compensates the impedance with a negative resistance -1/27?
  • the present invention compensates the impedance with a negative resistance -1/67?
  • the conventional series inductor has the disadvantage that it increases the reactive power of the transmission line because it compensates the transmission line with a positive reactance.
  • the present invention does not increase the total reactive power of the transmission lines because it compensates the impedance with a positive reactance in the one transmission line, whereas it compensates the impedance with a negative reactance of the same amount of the power in the other transmission line.
  • the conventional phase shifting transformer has the disadvantage that it should change the phase angle by changing the tap according to the change of the load in order to cause the effect of the impedance compensation.
  • the present invention does not need to change the tap according to the change the load because, if the turns ratio a of the series transformer is fixed, the values of the compensation impedances are fixed.
  • the present invention compensates not only the reactance component of the impedance of the transmission line, but also the resistance component. This characteristic is useful especially in compensating the impedance of the transmission line having a large resistance component.
  • the positive resistance is the circuit element which consumes energy in the form of heat or the like
  • the negative resistance is the circuit element which, on the contrary, generates energy.
  • neither the positive resistance nor the negative resistance in the present invention actually consumes or generates energy.
  • neither the positive reactance nor the negative reactance in the present invention actually stores energy.
  • the energy in the present invention is transferred from the one winding of the series transformer (41) to the other winding by the magnetic coupling.
  • the energy which is emitted from the one winding in the form of a positive resistance is absorbed by the other winding in the form of a negative resistance, and the energy which is emitted from the one winding in the form of a positive reactance is absorbed by the other winding in the form of a negative reactance.
  • the negative reactance of the present invention is different from that of the conventional series capacitor. While the conventional series capacitor compensates the impedance of the transmission line by a capacitance, the present invention compensates the impedance of the transmission line by a negative inductance.
  • the capacitance and the negative inductance operates identically at the source frequency. However, the capacitance causes the resonant phenomena in the frequency range except the source frequency, especially in the low frequency range, whereas the negative inductance does not.
  • the description for the negative inductance of the present invention is as follows.
  • the present invention compensates the transmission line with a positive resistance and a negative resistance, and a positive inductance and a negative inductance.
  • V ⁇ j ⁇ L m I ⁇ — j ⁇ aL m I 2 (8)
  • the equation (9) corresponds the equation (1) in which the magnetizing inductance L m is ignored. Substituting L m - °° into the equation (9), the equation (9) becomes equal with the equation (1).
  • the compensation voltage V ⁇ of the first transmission line and the compensation voltage V of the second transmission line are obtained as follows.
  • the equation (10) corresponds the equation (3) in which the magnetizing inductance L m is ignored. Substituting L m - ⁇ into the equation (10), the equation (10) becomes equal with the equation (3). As shown in the equation (9) and the equation (10), the present invention can obtain the similar compensation effect to the equation (1) and the equation (3), even in the case where the magnetizing inductance L m of the series transformer (41) cannot be ignore.
  • the core of ac inductors has an air gap. This is to reduce the nonlinearity due to the core, that is the magnetic saturation and the hysteresis phenomena.
  • the core of ordinary transformers usually does not have an air gap. This is because the magnetizing inductance becomes smaller and the exciting current becomes larger if it has an air gap.
  • the series transformer (41) of the present invention differing from ordinary transformers, can have an air gap in the core (51) to reduce the magnetic saturation and the hysteresis phenomena.
  • the consideration of the copper loss, the core loss, and the leakage flux in the series transformer (41) can be done in the same way as ordinary transformers.
  • the copper loss, the core loss, and the leakage flux though the less the better, do not have large influence on the operation of the present invention.
  • FIG. 10 A second embodiment of the present invention is shown in FIG. 10.
  • the second embodiment of the present invention differing from the first embodiment, is the transmission circuit in which only the one end of the first transmission line (11) and the one end of the second transmission line (12) are connected to the first bus (13).
  • some transmission lines or transmission circuits can be additionally connected between the bus (13), the bus (101), and the bus (102), they are not the essential elements of the present invention.
  • Vs - V ⁇ V l + Z l
  • FIG. 11 is identical with FIG. 6 except that there is a compensation impedance between the bus (101) and the bus (102). If the bus (101) and the bus (102) are united, FIG. 11 is identical with FIG. 6.
  • the present invention compensates the impedances of the first transmission line (11) and the second transmission line (12), and compensates the bus admittance matrix YBUS-
  • the values of the compensation impedances are determined by the impedances and Z 2 of the transmission lines, and the turns ratio a of the series transformer. Accordingly, the present invention can compensate the bus admittance matrix YBUS by setting the turns ratio a of the series transformer appropriately to compensate the impedances of the transmission lines.
  • FIG. 12 is a circuit where the shunt impedances of the transmission line, that is Zio's and 2o's, are added to the transmission circuit of FIG. 10. Applying the Kirchhoff's voltage law to the circuit of FIG. 12, the following equation is obtained.
  • the equation (16) can be arranged as follows.
  • Iu V ⁇ - Zr 2 ( Vs + aV 1 - V v ) .
  • the bus admittance matrix YBUS of the equation (20) is similar to the bus admittance matrix YBUS of the equation (15). If the shunt impedances Zio and Z20 of the transmission lines are larger than the impedances Zi and Z2 of the transmission lines respectively so that Zi ' and Z 2 of the equation (17) is approximated to Zi and Z2 respectively, the equation (20) becomes identical with the equation (15). As shown in the equation (20), the present invention compensates the impedances of the first transmission line (11) and the second transmission line (12), and compensates the bus admittance matrix YBUS even in the case where the shunt impedances of the transmission lines cannot be ignored.
  • the values of the compensation impedances are fixed. It is useful in many cases that the values of the compensation impedances are fixed. However, there also are the cases where it is required to change the values of the compensation impedances, that is the turns ratio a, according to the operating condition.
  • To change the turns ratio a according to the operating condition can be done by a mechanical tap changer or a static tap changer, as in the case of voltage regulating transformers or phase shifting transformers.
  • FIG. 13 is shown briefly the series transformer to which a mechanical tap changer (131) is added
  • FIG. 14 is shown briefly the series transformer to which a static tap changer (141) is added.
  • the turns ratio a of the series transformer defined in the equation (1) is always a positive value in the case where the first winding (52) and the second winding (53) are wound as FIG. 5A and FIG. 5B. However, in the case where one of the windings of the series transformer is wound in the opposite direction, differing from FIG. 5A and FIG. 5B, the turns ratio a becomes a negative value. If the turns ratio a becomes a negative value, the direction of the current 7i of the first transmission line and the direction of the current 72 of the second transmission line become opposite, as shown in the equation (1). That the direction of 7 ⁇ and the direction of 72 become opposite has usefulness especially in the case where the power is transmitted from the bus (101) to the bus (102) via the bus (13) in such a circuit as FIG. 10.
  • FIG. 15 A third embodiment of the present invention is shown in FIG. 15.
  • the third embodiment of the present invention is the transmission circuit using an autotransformer instead of a series transformer of the first embodiment of FIG. 4.
  • the structure and the circuit symbol of the autotransformer (151) of FIG. 15 are shown in FIG. 16A and FIG. 16B, respectively.
  • FIG. 15A, and FIG. 16A, and FIG. 16A are shown in FIG. 15A, and FIG.
  • the third embodiment of the present invention is the one in a power transmission circuit of an ac power system, comprising: a first bus (13); a first transmission line (11); a second transmission line (12); an autotransformer (151) comprising a core (161), a winding (162) wound on said core, a tap (163) connected to said winding, and the turns ratio a of said winding being set to compensate the impedances Z ⁇ and Z 2 of said first transmission line and said second transmission line; and the first terminal (164) of said winding (162) being connected to the one end of said first transmission line (11), the second terminal (165) of said winding (162) being connected to the one end of said second transmission line (12), and said tap (163) being connected to said first bus (13).
  • the autotransformer (151) because of its structure, can be located only at both the ends of the transmission lines, which are the bus (13) or the bus (14), differing from the series transformer of the first embodiment of FIG. 4.
  • the description for the operation of the third embodiment of the present invention is identical with that of the first embodiment of FIG. 4. But, let the number of the winding between the tap (163) and the first terminal (164) be m and the number of the winding between the tap (163) and the second terminal (165) be n 2 , then the turns ratio a of the autotransformer is given as a - n 2 Jn ⁇ .
  • FIG. 17 is shown briefly the autotransformer to which a mechanical tap changer (171) is added
  • FIG. 18 is shown briefly the autotransformer to which a static tap changer (181) is added.
  • mechanical tap changer (171) or the static tap changer (181) of the autotransformer are already widely used in voltage regulating transformers or phase shifting transformers, so that they will become apparent to those skilled in the art without describing their composition and operation in detail in this description.
  • FIG. 19 A fourth embodiment of the present invention is shown in FIG. 19. As shown in FIG. 19, the fourth embodiment of the present invention is the transmission circuit using an autotransformer instead of a series transformer of the second embodiment of FIG. 10. The description for the operation of the fourth embodiment of the present invention is identical with that of the second embodiment of FIG. 10.
  • FIG. 20 A fifth embodiment of the present invention is shown in FIG. 20.
  • the fifth embodiment of the present invention is the transmission circuit in which neither both the ends of the first transmission line nor both the ends of the second transmission line is connected to the same buses. This is the most general embodiment among those of the present invention. Although some transmission lines or transmission circuits can be additionally connected between the bus (101), the bus (102), the bus (201), and the bus (202), they are not the essential elements of the present invention.
  • V y - V ⁇ V x Y Z ⁇ I x
  • V w - Vu V 2 + Z 2 7 2 .
  • V ⁇ [ Z 2 V V — Z x a V w — Z 2 V ⁇ + Z a V ⁇ ]
  • the equation (25) is identical with the equation (15).
  • the present invention compensates the impedances of the first transmission line (11) and the second transmission line (12), and compensates the bus admittance matrix YBUS-
  • the values of the compensation impedances are determined by the impedances i and Z 2 of the transmission lines, and the turns ratio a of the series transformer. Accordingly, the present invention can compensate the bus admittance matrix YBUS by setting the turns ratio of the series transformer appropriately to compensate the impedances of the transmission lines.
  • the transmission circuits of the other two phases are identical with the transmission circuit of this one phase. But, a little more explanation for the 3-phase transformer is necessary.
  • the 3-phase transformer is the one having three core legs, and is generally smaller, lighter, and cheaper than the bank of three single-phase transformers.
  • the bank of three single-phase transformers is advantageous instead.
  • the 3-phase series transformer(or the 3-phase autotransformer) of the present invention there is one more point to be considered in the 3-phase series transformer (or the 3-phase autotransformer) of the present invention.
  • the voltage between the first winding and the second winding of each single-phase transformer becomes the difference between the compensation voltage V ⁇ of the first transmission line and the compensation voltage V 2 of the second transmission line.
  • the voltage between the windings becomes the line-to-line voltage of the transmission lines.
  • the line-to ⁇ line voltage of the transmission lines generally is much higher than the compensation voltages of the transmission lines. Accordingly, the case of three phase transformer requires much higher voltage of the insulation between the windings than the case of the bank of three single-phase transformers, and is disadvantageous as much.
  • the present invention has the advantages that, according to the turns ratio, it, on the one hand, provides the two transmission lines with compensation voltages, on the other hand, controls the ratio of the currents of the two transmission lines, and consequently, provides the two transmission lines with compensation impedances.
  • the conventional series inductor has the disadvantage that it increases the reactive power of the transmission line because it compensates the impedance of the transmission line with a positive reactance.
  • the present invention has the advantage that it does not increase the total reactive power of the transmission lines because it compensates the impedance with a positive reactance in the one transmission line whereas it compensates the impedance with a negative reactance of the same amount of the power in the other transmission line.
  • the conventional series capacitor has the disadvantage that it causes the subsynchronous resonance phenomena because it compensates the impedance of the transmission line by a capacitance.
  • the present invention has the advantage that it does not cause the subsynchronous resonance phenomena because it compensates the impedance of the transmission line by not a capacitance but a negative inductance.
  • the conventional phase shifting transformer has the disadvantage that it should change the phase angle by changing the tap according to the change of the load in order to cause the effect of the impedance compensation.
  • the present invention has the advantage that it does not need to change the tap according to the change the load because, if the turns ratio of the series transformer (or the autotransformer) is fixed, the values of the compensation impedances are fixed.
  • the conventional phase shifting transformer has the disadvantages that the connection of its windings is complex, it is composed of two apparatus of an exciting transformer and a series transformer, and high voltage insulation is required between the first winding and the second winding of the exiting transformer.
  • the series transformer (or the autotransformer) of the present invention has the advantages that the connection of its windings is simple, it is composed of one apparatus, and high voltage insulation is not required between the first winding and the second winding.
  • the recent series static compensators are composed of a static power converter and a series transformer, and they have the disadvantages that the high power technology of the static power converters is difficult and their costs are very high.
  • the present invention has the advantage that the high power technology is not difficult and its cost is not high because only a series transformer(or an autotransformer) is used.
  • the present invention has the advantage that it compensates not only the reactance component of the impedance, but also the resistance component of the transmission line. This characteristic is useful especially in compensation the impedance of the transmission line having a large resistance component.
  • the present invention has the advantage that it can control the compensating impedances by changing the turns ratio of the series transformed or the autotransformer) through a mechanical or a static tap changer, which is similar to the conventional series inductor or the phase shifting transformer.
  • the present invention is a new impedance compensation technique which does not use the conventional series inductor, the series capacitor, the phase shifting transformer, or the series static compensator, but uses only a series transformer (or autotransformer), and provides various superior advantages to the conventional techniques. Therefore, the present invention is expected to be able to substitute the conventional techniques well in many applications where these advantages are desirable.
  • the voltage level of the first transmission line and the voltage level of the second transmission line in the present invention may differ from each other.
  • the present invention can be applied to single-phase or generalized poly-phase ac power systems besides 3-phase ones.
  • the turn ration a of the series transformer(or the autotransformer) of the present invention can be set to control the ratio of the currents of the two transmission lines, this becomes equal with compensating the impedances of the two transmission lines in the result.
  • the present invention can also be applied to the cases where the third transmission line and more transmission lines are added to the first transmission line and the second transmission line, by adding series transformers (or autotransformers).
  • series transformers or autotransformers
  • all the impedances of the first transmission line, the second transmission line, and the third transmission line can be compensated by adding a series transformer(or an autotransformer) between the first transmission line and the third transmission line, or by adding a series transformer (or an autotransformer) between the second transmission line and the third transmission line, and the present invention can be applied to the cases where more transmission lines are added, by the similar way.

Abstract

The present invention is to compensate the impedances of power transmission lines and control the power flow of the transmission circuit. The present invention comprises a series transformer connected between two transmission lines, of which the two windings are connected in series with the two transmission lines respectively, and of which the turns ratio is set to compensate the impedances of the two transmission lines. According to the turns ratio, the present invention, on the one hand, provides the two transmission lines with compensation voltages, on the other hand, controls the ratio of the currents of the two transmission lines, and consequently, provides the two transmission lines with compensation impedances. The present invention, especially, compensates the impedances of the transmission lines with a positive inductance and a negative inductance, so that it does not cause the subsynchronous resonance phenomena, differing from the conventional series capacitor. Considering the high power technology of transformers is established and their costs are relatively low, the present invention is expected to be easily put to practical use.

Description

D E S C R I P T I O N
IMPEDANCE-COMPENSATED POWER TRANSMISSION CIRCUIT TECHNICAL FIELD The present invention relates to 3-phase ac power systems, and more particularly to impedance compensation techniques of transmission circuits for solving power flow control problems of transmission circuits. BACKGROUND ART
Electric power is transmitted from generation centers to loads through transmission circuits comprising transmission lines, and in most cases, generation centers and loads are geographically widely spread. Accordingly, most transmission circuits become complex, and the control of power flow becomes difficult as well. The power flow through a transmission line is determined by the magnitudes and the phase angles of the voltages of both the ends of the transmission line, and the impedance of the transmission line. Likewise, the power flow through a transmission circuit is determined by the magnitudes and the phase angles of the bus voltages of the transmission circuit, and the bus admittance matrix YBUS which can be called the impedance of the transmission circuit. The impedance of a transmission line cannot be designed at will, but is determined one-sidedly by the length of the transmission line, and the control of the magnitudes and the phase angle difference of the voltages is possible only in some limited range, so that there occur the cases in which the power flow of the transmission circuit cannot be controlled as needed, [references 1, 4, 8, 14].
As an example, suppose that there is a part like FIG. 1 in a power system. FIG. 1 is a transmission circuit in which both the ends of the first transmission line (11) and both the ends of the second transmission line (12) are respectively connected to the first bus (13) and the second bus (14). FIG. 1 shows only one phase of the 3-phase transmission circuit, as is all the same in the following figures. In addition, in FIG. 1 and the following figures and the equations, all of the voltage and the current symbols in capitals (for example, Vs and 7s) are phasors. In the transmission circuit of FIG. 1, even though we control both the voltage Vs of the bus (13) and the voltage VR of the bus (14) which are the voltages of both the ends of the transmission line, the current 7ι of the first transmission line and the current of the second transmission line cannot be controlled individually. FIG. 1 is an example, and in such cases where the currents of transmission lines cannot be controlled individually, there occurs the problems especially as follows. Firstly, if the current inclines to one transmission line so that this transmission line is overloaded, the other transmission lines cannot be sufficiently used though they have extra capacities. Secondly, if the current inclines to a transmission line having a relatively large resistance, the total of the power losses in the transmission lines is larger and the operating cost increases in comparison with the cases where it does not. [references 1, 4, 8, 14]. The impedance compensation technique of the transmission circuit is to solve the power flow control problems above, and is basically the one in which a series compensator is connected with the transmission line. As a conventional technique, the series inductor is shown in FIG. 2. In FIG. 2, the series inductor (21) compensates the impedance of the first transmission line with a positive reactance and increases the total impedance of the first transmission line, so that it causes the effect of reducing the current 7ι of the first transmission line. However, the series inductor has the disadvantages that it increases the reactive power of the transmission line, and especially it lowers the maximum transmissible power and the stability limit, [references 1-3].
As another conventional technique, the series capacitor is shown in FIG. 3. In FIG. 3, the series capacitor (31) compensates the impedance of the second transmission line (12) with a negative reactance and decreases the total impedance of the second transmission line (12), so that it causes the effect of reducing relatively the current of the first transmission line. The series capacitor has the effect of reducing the reactive power of the transmission line, differing from the series inductor. However, the series capacitor has the disadvantage that it causes the subsynchronous resonance phenomena of other components of the power system, especially generators, [references 1-7].
As still another conventional technique, there is the technique that connects the phase shifting transformer to the transmission line. This technique has the effect of changing the current of the transmission line by compensating the phase angle difference between the voltages of both the ends of the transmission line. However, the phase shifting transformer has the disadvantage that it should change the phase angle by changing the tap according to the change of the load in order to cause the effect of the impedance compensation, [references 1, 3, 4, 8-11].
On the other hand, recently, the techniques have been proposed, which connect a static power converter comprising high power GTO's to the transmission line through a series transformer. The series static compensators have the advantage that they not only compensate the steady-state impedance of the transmission line, but also control the transient. However, the series static compensators have the disadvantages that the high power technology of the static power converters is difficult and their costs are very high, [references 1, 12-21].
[reference 1] N. G. Hingorani, "Flexible ac transmission," IEEE Spect. vol. 30, no. 4, pp. 40-45, 1993
[reference 2] T. J. E Miller, Reactive power control in electric systems, John Wiley & Sons, Inc., 1982.
[reference 3] P. Kundur, Power system stability and control, McGraw-Hill, Inc., 1994. [reference 4] M. Noroozian and G. Andersson, "Power flow control by use of controllable series components," IEEE Trans. Power Delivery, vol. 8, no. 3, pp. 1420-1429, 1993.
[reference 5] H. A. Othman and L. Angquist, "Analytical modeling of thyristor- controlled series capacitors for SSR studies," IEEE Trans. Power Systems, vol. 11, no. 1, pp. 119-125, 1996.
[reference 6] R. J. Piwko, C. A. Wegner, S. J. Kinney, and J. D. Eden, "Subsynchronous resonance performance tests of the Slatt thyristor-controlled series capacitor," IEEE Trans. Power Delivery, vol. 11, no. 2, pp. 1112-1119, 1996.
[reference 7] D. N. Kosterev, W. A. Mittelstadt, R. R. Mohler and W. J. Kolodziej, "An application study for sizing and rating controlled and conventional series compensation," LEEE Trans. Power Delivery, vol. 11, 5 no. 2, pp. 1105-1111, 1996.
[reference 8] J. Bladow and A. Montoya, "Experiences with parallel EHV phase shifting transformers," IEEE Trans. Power Delivery, vol. 6, no. 3, pp. 1096-1100, 1991.
[reference 9] M. R. Iravani and D. Maratukulam, "Applications of 10 static phase shifters in power systems," IEEE Trans. Power Delivery, vol. 9, no. 3, pp. 1600-1608, 1994.
[reference 10] M. R. Iravani and D. Maratukulam, "Review of semiconductor-controlled (static) phase shifters for power system applications," IEEE Trans. Power Systems, vol. 9, no. 4, pp. 1833-1839, 15 1994.
[reference 11] E. V. Larsen, "Power flow control with rotary transformers," U.S. Patent No. 5,841,267, 1998.
[reference 12] L. Gyugyi, "Unified power control concept for flexible AC transmission systems," LEE proc. Generation, Transmission 20 and Distribution, vol. 139, no. 4, pp. 323-331, 1992.
[reference 13] B. T. Ooi, S. Z. Dai, and X. Wang, "Solid-state series capacitive reactance compensators," IEEE Trans. Power Delivery, vol. 7, no. 2, pp. 914-919, 1992.
[reference 14] L. Gyugyi, "Dynamic compensation of ac 25 transmission lines by solid-state synchronous voltage sources," LEEE Trans. Power Delivery, vol. 9, no. 2, pp. 904-911, 1994.
[reference 15] L. Gyugyi, C. D. Schauder, S. L. Williams, T. R. Rietman, D. R. Torgerson, and A. Edris, "The unified power flow controller: A new approach to power transmission control," IEEE Trans. 30 Power Delivery, vol. 10, no. 2, pp. 1085-1097, 1995.
[reference 16] L. Gyugyi, C. D. Schauder, and K. K. Sen, "Static synchronous series compensator: a solid-state approach to the series compensation of transmission lines," IEEE Trans. Power Delivery, vol. 12, no. 1, pp. 406-417, 1997.
[reference 17] K. K. Sen, "SSSC-Static Synchronous Series Compensator: theory, modeling, and applications," IEEE Trans. Power Delivery, vol. 13, no. 1, pp. 241-246, 1998. [reference 18] C. D. Schauder, L. Gyugyi, M. R. Lund, D. M.
Hamai, T. R. Rietman, D. R. Torgerson, and A. Edris, "Operation of the unified power controller (UPFC) under practical constraints," LEEE Trans. Power Delivery, vol. 13, no. 2, pp. 630-639, 1998.
[reference 19] L. Gyugyi, "Transmission line dynamic impedance compensation system," U.S. Patent No. 5,198,746, 1993.
[reference 20] L. Gyugyi, "Generalized fast, power flow controller," U.S. Patent No. 5,343,139, 1994.
[reference 21] C. D. Schauder, S. L. Williams, and L. Gyugyi, "Transmission line power controller with a continuously controllable voltage source responsive to a real power demand and a reactive power demand," U.S. Patent No. 5,734,257, 1998.
SUMMARY. OBJECTS. AND ADVANTAGES OF THE PRESENT INVENTION
The present invention is to overcome the disadvantages of said conventional techniques, and it is a new impedance compensation technique which does not use said conventional series inductor, said series capacitor, said phase shifting transformer, or said series static compensator, but uses only a series transformer (or a autotransformer).
The present invention has the aspects that the two windings of the series transformer are respectively connected in series with the two transmission lines which need the impedance compensation, and the turns ratio of the two windings is set to compensate the impedances of the transmission lines.
It is a basic object and advantage of the present invention that, according to the turns ratio, it, on the one hand, provides the two transmission lines with compensation voltages, on the other hand, controls the ratio of the currents of the two transmission lines, and consequently, provides the two transmission lines with compensation impedances. Objects and advantages of the present invention are listed below, one by one in comparison with the conventional techniques.
It is an object and advantage of the present invention to provide the impedance compensation technique which does not increase the total reactive power of the transmission lines, compared to the conventional series inductor.
It is another object and advantage of the present invention to provide the impedance compensation technique which does not cause the subsynchronous resonance phenomena by compensating the impedance of the transmission line with not a capacitance but a negative inductance, compared to the conventional series capacitor.
It is still another object and advantage of the present invention to provide the impedance compensation technique which does not need to change the tap according to the change of the load, compared to the conventional phase shifting transformer
It is still another object and advantage of the present invention to provide the impedance compensation technique of which the high power technology is not difficult and its cost is not high, compared to the recent series static compensators. It is still another object and advantage of the present invention to provide the impedance compensation technique which compensates not only the reactance component, but also the resistance component of the impedance of the transmission line, compared to the conventional techniques. It is an additional object and advantage of the present invention to provide the impedance compensation technique which can control the compensation impedances by changing the turns ratio of the series transformer through a mechanical or a static tap changer, which is similar to the conventional series inductor or the phase shifting transformer.
The present invention relates to the above objects and advantages individually as well as collectively. These and other objects and advantages of the present invention will become apparent to those skilled in the art from the accompanying drawings and the following detailed description.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 is an example of power transmission circuits. FIG. 2 is a power transmission circuit of which the impedance is compensated by the conventional series inductor.
FIG. 3 is a power transmission circuit of which the impedance is compensated by the conventional series capacitor.
FIG. 4 is a first embodiment of the present invention. FIG. 5A is the structure of the series transformer of FIG. 4.
FIG. 5B is the circuit symbol of FIG. 5A.
FIG. 6 is the equivalent circuit of FIG. 4.
FIG. 7 is an example where
Figure imgf000008_0001
= jX, Zt - j2X, and a = 1 in FIG. 6.
FIG. 8 is an example where R + j2X, and a = 1 in FIG. 6.
FIG. 9 is an example where
Figure imgf000008_0002
R + jX, and a - 2 in FIG. 6.
FIG. 10 is a second embodiment of the present invention.
FIG. 11 is the equivalent circuit of FIG. 10. FIG. 12 is a circuit where the shunt impedances of the transmission lines are added to the transmission circuit of FIG. 10.
FIG. 13 is the series transformer to which a mechanical tap changer is added.
FIG. 14 is the series transformer to which a static tap changer is added.
FIG. 15 is a third embodiment of the present invention.
FIG. 16A is the structure of the autotransformer of FIG. 15.
FIG. 16B is the circuit symbol of FIG. 16A.
FIG. 17 is the autotransformer to which a mechanical tap changer is added.
FIG. 18 is the autotransformer to which a static tap changer is added.
FIG. 19 is a fourth embodiment of the present invention. FIG. 20 is a fifth embodiment of the present invention. BRIEF DESCRIPTION OF REFERENCE NUMERALS
11 first transmission line. 12 : second transmission line, 13 first bus. 14 : second bus. 21 series inductor. 31 : series capacitor, 41 series transformer, 51 core of series transformer, 52 first winding of series transformer. 53 : second winding of series transformer.
101 third bus. 102 : fourth bus. 131 mechanical tap changer of series transformer, 141 static tap changer of series transformer, 151 autotransformer. 161 core of autotransformer. 162 winding of autotransformer. 163 : tap of autotransformer. 164 first terminal of autotransformer. 165 : second terminal of autotransformer.
171 : mechanical tap changer of autotransformer. 181 : static tap changer of autotransformer. 201 : fifth bus. 202 : sixth bus.
BRIEF DESCRIPTION OF SYMBOLS
Vs '■ voltage of bus (13). 7s : voltage of bus (13) VR '■ voltage of bus (14).
7ι : current of first transmission line. current of second transmission line.
Zx impedance of first transmission line, z2 impedance of second transmission line,
Vi compensate voltage of first transmission line, v2 compensate voltage of second transmission line, a '■ turns ratio of series transformer(or autotransformer).
VT '■ voltage of bus (101). IT '■ current of bus (101). Vu '■ voltage of bus (102). Iu '■ current of bus (102). YBUS '■ bus admittance matrix. '■ shunt impedance of first transmission line.
Z20 '■ shunt impedance of second transmission line.
Vv ■ voltage of bus (201). Iγ '■ current of bus (201).
Vw '■ voltage of bus (202). Iw '■ current of bus (202). DETAILED DESCRIPTION OF THE PRESENT INVENTION
A first embodiment of the present invention is shown in FIG. 4. The structure and the circuit symbol of the series transformer (41) of FIG. 4 are shown in FIG. 5A and FIG. 5B, respectively. As shown in FIG. 4, FIG. 5A, and FIG. 5B, the first embodiment of the present invention is the one in a power transmission circuit of an ac power system, comprising: a first transmission line (11); a second transmission line (12); a series transformer (41) comprising a core (51), a first winding (52) wound on said core, a second winding (53) wound on said core, and the turns ratio a of said first winding and said second winding being set to compensate the impedances Z\ and 2 of said first transmission line and said second transmission line; and said first winding (52) being connected in series with said first transmission line (11), and said second winding (53) being connected in series with said second transmission line (12).
And, it is the one, wherein the one end of said first transmission line and the one end of said second transmission line are connected to a first bus (13), and the other end of said first transmission line and the other end of said second transmission line are connected to a second bus
(14).
The series transformer (41) can be located not only at both the ends of the transmission line, but also anywhere between them, as in the case of the conventional series inductor, the series capacitor, and so on. But, when it is located in the middle of the transmission line, if the first transmission line (11) and the second transmission line (12) are far away, this is not good because the transmission lines (11) and (12), and the series transformer (41) should be connected through long lines. And, although some transmission lines or transmission circuits can be additionally connected between the bus (13) and the bus (14), they are not the essential elements of the present invention.
The description for the operation of the first embodiment of the present invention is as follows.
First, as shown in FIG. 4, the present invention provides the first transmission line (11) with a compensation voltage V\ and provides the second transmission line (12) with a compensation voltage V2.
Now, consider the case where the series transformer (41) can be modeled as an ideal one, that is, the case where the magnetizing inductance is so large, and the copper loss and the core loss are so small, and the leakage flux is also so small that they can be ignored. Then, the voltage -current relation of the series transformer (41) can be written as follows.
V2 = - a Vλ
(1)
Iχ ah
In the equation (1), FIG. 4, FIG. 5A, and FIG. 5B, a is the turns ratio of the series transformer (41). Let the number of the winding of the first winding (52) be m and the number of the winding of the second winding (53) be m, then it is given that a =
Figure imgf000011_0001
As shown in the equation (1), the present invention controls the ratio of the current 7ι of the first transmission line and the current I2 of the second transmission line according to the turns ratio a of the series transformer.
Applying the Kirchhoff's voltage law to the circuit of FIG. 4, the following equation is obtained.
vs - VR = V Y Zλ Iλ
(2) Vs - VR = V2 + Z2I2 . From the equation (1) and the equation (2), the compensation voltage V\ of the first transmission line and the compensation voltage V of the second transmission line are obtained as follows.
Figure imgf000012_0001
What can be known from the equation (3) is that the compensation voltage V\ is proportional to the current 7ι of the first transmission line, and the compensation voltage V is proportional to the current I2 of the second transmission line. This means that the compensation voltages V\ and V can be modeled as the compensation impedances respectively. The equivalent circuit of FIG. 4 where the compensation voltages
Figure imgf000012_0002
and V2 are modeled as the compensation impedances respectively is shown in FIG. 6. As shown in the equation (3) and FIG. 6, the present invention provides the first transmission line (11) and the second transmission line (12) with the compensation impedances. And the values of the compensation impedances are determined by the impedances Z\ and Z2 of the transmission lines, and the turns ratio a of the series transformer. Accordingly, the present invention can compensate the impedances of the transmission lines by setting the turns ratio a of the series transformer appropriately to compensate the impedances of the transmission lines. As an example of FIG. 6, FIG. 7 is shown, where the turns ratio a of the series transformer is set to 1 in order to compensate the impedances Z\ - j'X and Z2 = j2X of the transmission lines and make the impedances equal. In FIG. 7, the present invention compensates the impedance with a positive reactance J1/2X in the first transmission line (11), and compensates the impedance with a negative reactance -J1/2X in the second transmission line (12). Then, the total impedance of the first transmission line (11) becomes J3/2X, and the total impedance of the second transmission line (12) becomes J3/2X, so that the impedances become the same. As another example of FIG. 6, FIG. 8 is shown, where the turns ratio a of the series transformer is set to 1 in order to compensate the impedances Z\ - R + jX and Z2 - 2R + j2X of the transmission lines and make the impedances equal. In FIG. 8, the present invention compensates the impedance with a positive resistance 1/27? and a positive reactance J1/2X in the first transmission line (11), and compensates the impedance with a negative resistance -1/27? and a negative reactance -jl/2X in the second transmission line (12). Then, the total impedance of the first transmission line (11) becomes 3/27? +J3/2X, and the total impedance of the second transmission line (12) becomes 3/27? + J3/2X, so that the impedances become the same. As still another example of FIG. 6, FIG. 9 is shown, where the turns ratio a of the series transformer is set to 2 in order to compensate the impedances Z\ = 7? + jX and Z - R + j'X of the transmission lines and make the total impedance of the first transmission line (11) 1/2 the total impedance of the second transmission line (12). In FIG. 9, the present invention compensates the impedance with a negative resistance -1/67? and a negative reactance -jl/6X in the first transmission line (11), and compensates the impedance with a positive resistance 2/37? and a positive reactance J2/3X in the second transmission line (12). Then, the total impedance of the first transmission line (11) becomes 5/6R + J5/6X, and the total impedance of the second transmission line (12) becomes 5/3R +J5/3X, so that the total impedance of the first transmission line (11) becomes 1/2 the total impedance of the second transmission line (12). The conventional series inductor has the disadvantage that it increases the reactive power of the transmission line because it compensates the transmission line with a positive reactance. Compared to this, the present invention does not increase the total reactive power of the transmission lines because it compensates the impedance with a positive reactance in the one transmission line, whereas it compensates the impedance with a negative reactance of the same amount of the power in the other transmission line.
The conventional phase shifting transformer has the disadvantage that it should change the phase angle by changing the tap according to the change of the load in order to cause the effect of the impedance compensation. Compared to this, the present invention does not need to change the tap according to the change the load because, if the turns ratio a of the series transformer is fixed, the values of the compensation impedances are fixed.
Differing from the conventional techniques, the present invention compensates not only the reactance component of the impedance of the transmission line, but also the resistance component. This characteristic is useful especially in compensating the impedance of the transmission line having a large resistance component.
Generally, the positive resistance is the circuit element which consumes energy in the form of heat or the like, and the negative resistance is the circuit element which, on the contrary, generates energy. However, neither the positive resistance nor the negative resistance in the present invention actually consumes or generates energy. Also, neither the positive reactance nor the negative reactance in the present invention actually stores energy. By multiplying two equations of the equation (3) by 7ι and I2, and substituting the second equation 7ι = al of the equation (2) into them, it can be seen that the signs of the powers of the two compensation impedances are opposite to each other and the magnitudes are the same. As shown in the equation (1), this coincides with the facts that the sum of the power of the first winding of the ideal series transformer and the power of the second winding is always 0. That is, the energy in the present invention is transferred from the one winding of the series transformer (41) to the other winding by the magnetic coupling. The energy which is emitted from the one winding in the form of a positive resistance is absorbed by the other winding in the form of a negative resistance, and the energy which is emitted from the one winding in the form of a positive reactance is absorbed by the other winding in the form of a negative reactance.
The negative reactance of the present invention is different from that of the conventional series capacitor. While the conventional series capacitor compensates the impedance of the transmission line by a capacitance, the present invention compensates the impedance of the transmission line by a negative inductance. The capacitance and the negative inductance operates identically at the source frequency. However, the capacitance causes the resonant phenomena in the frequency range except the source frequency, especially in the low frequency range, whereas the negative inductance does not. The description for the negative inductance of the present invention is as follows.
Consider the case where the first transmission line (11) and the second transmission line (12) are modeled as the 7?ι -
Figure imgf000015_0001
series circuit and the 7?2 - L2 series circuit, respectively. Then, the equation (1), the equation (2), and the equation (3) are respectively written in the time domain as follows.
Figure imgf000015_0002
(4) aι2 .
Figure imgf000015_0003
Figure imgf000015_0004
As shown in the equation (6), the present invention compensates the transmission line with a positive resistance and a negative resistance, and a positive inductance and a negative inductance. An example where 7?ι = 7?, = L, 7?2 = 27?, L2 - 2L, and a = 1 is shown in the following equation.
Figure imgf000016_0001
Now, consider the case where the magnetizing inductance Lm of the series transformer (41) is considered. In this case, the voltage-current relation of the series transformer (41) is written as follows.
Vλ = jωLmIλ — jωaLmI2 (8)
V2 — — jωaLmI + jωa LmI2 .
From the equation (8) and the equation (2), the following equation is obtained.
V2 aV
( a + l)a + Z2l(jωLmm) (9)
' I w- ' - α , +4- 11 + 4- Z 7. /{(j,Vω,Lm) h
The equation (9) corresponds the equation (1) in which the magnetizing inductance Lm is ignored. Substituting Lm - °° into the equation (9), the equation (9) becomes equal with the equation (1).
From the equation (9) and the equation (2), the compensation voltage V\ of the first transmission line and the compensation voltage V of the second transmission line are obtained as follows.
Figure imgf000016_0002
(10) v - ( 2 - Zxd)a
The equation (10) corresponds the equation (3) in which the magnetizing inductance Lm is ignored. Substituting Lm - ∞ into the equation (10), the equation (10) becomes equal with the equation (3). As shown in the equation (9) and the equation (10), the present invention can obtain the similar compensation effect to the equation (1) and the equation (3), even in the case where the magnetizing inductance Lm of the series transformer (41) cannot be ignore.
Generally, the core of ac inductors has an air gap. This is to reduce the nonlinearity due to the core, that is the magnetic saturation and the hysteresis phenomena. On the contrary, the core of ordinary transformers usually does not have an air gap. This is because the magnetizing inductance becomes smaller and the exciting current becomes larger if it has an air gap. In the present invention, when the core (51) has an air gap and the magnetizing inductance becomes small, there occurs no problem except that the values of the compensation impedances are more or less changed, as shown in the equation (10). Accordingly, the series transformer (41) of the present invention, differing from ordinary transformers, can have an air gap in the core (51) to reduce the magnetic saturation and the hysteresis phenomena.
The consideration of the copper loss, the core loss, and the leakage flux in the series transformer (41) can be done in the same way as ordinary transformers. As in the case of ordinary transformers, the copper loss, the core loss, and the leakage flux, though the less the better, do not have large influence on the operation of the present invention.
A second embodiment of the present invention is shown in FIG. 10. As shown in FIG. 10, the second embodiment of the present invention, differing from the first embodiment, is the transmission circuit in which only the one end of the first transmission line (11) and the one end of the second transmission line (12) are connected to the first bus (13). Although some transmission lines or transmission circuits can be additionally connected between the bus (13), the bus (101), and the bus (102), they are not the essential elements of the present invention.
The description for the operation of the second embodiment of the present invention is as follows. First, applying the Kirchhoff's current law to FIG. 10, the following equation is obtained.
Is = Iχ + h
Figure imgf000018_0001
Iu = - h .
And, the voltage -current relation of the series transformer (41) is identical with the equation (1). Substituting the equation (1) into the equation (11), the following is obtained.
Figure imgf000018_0002
Iτ = - al2 (12)
Iu = ~ •
Applying the Kirchhoff's voltage law to the circuit of FIG. 10, the following equation is obtained.
Vs - Vτ = Vl + Z l
(13) Vs - Vu = 2 + Z272 .
Substituting the equation (1) into the equation (13), and obtaining V\ and 72, the following is obtained.
V,
h
Figure imgf000018_0003
Substituting the equation (14) into the equation (12), the following bus equation is obtained.
Figure imgf000019_0001
where, 1)
Figure imgf000019_0002
From the equation (15), the equivalent circuit of FIG. 10 can be obtained as FIG. 11. FIG. 11 is identical with FIG. 6 except that there is a compensation impedance between the bus (101) and the bus (102). If the bus (101) and the bus (102) are united, FIG. 11 is identical with FIG. 6. As shown in FIG. 11 and the equation (15), the present invention compensates the impedances of the first transmission line (11) and the second transmission line (12), and compensates the bus admittance matrix YBUS- The values of the compensation impedances are determined by the impedances
Figure imgf000019_0003
and Z2 of the transmission lines, and the turns ratio a of the series transformer. Accordingly, the present invention can compensate the bus admittance matrix YBUS by setting the turns ratio a of the series transformer appropriately to compensate the impedances of the transmission lines.
Now, suppose the case where the shunt impedances of the transmission line are considered.
FIG. 12 is a circuit where the shunt impedances of the transmission line, that is Zio's and 2o's, are added to the transmission circuit of FIG. 10. Applying the Kirchhoff's voltage law to the circuit of FIG. 12, the following equation is obtained.
Figure imgf000020_0001
The equation (16) can be arranged as follows.
Figure imgf000020_0002
where,
Z\ Z10 + Z\
z2 z20 z2
Substituting the equation (1) into the equation (17), and obtaining
Figure imgf000020_0003
and 72, the following is obtained.
Figure imgf000020_0004
Applying the Kirchhoff's current law to FIG.12, the following equation is obtained.
s = +1)72
IT = ~2T vτ~ ~7~ Vs ~ Vι~ Vτ) QQ)
Iu = Vυ-
Figure imgf000020_0005
Zr2( Vs + aV1 - Vv) .
Substituting the equation (18) into the equation (19), the following bus equation is obtained.
Figure imgf000021_0003
Figure imgf000021_0001
where,
Y BUS
Z2 ' Z{al
Figure imgf000021_0002
The bus admittance matrix YBUS of the equation (20) is similar to the bus admittance matrix YBUS of the equation (15). If the shunt impedances Zio and Z20 of the transmission lines are larger than the impedances Zi and Z2 of the transmission lines respectively so that Zi ' and Z2 of the equation (17) is approximated to Zi and Z2 respectively, the equation (20) becomes identical with the equation (15). As shown in the equation (20), the present invention compensates the impedances of the first transmission line (11) and the second transmission line (12), and compensates the bus admittance matrix YBUS even in the case where the shunt impedances of the transmission lines cannot be ignored.
In the present invention, if the turns ratio a of the series transformer is fixed, the values of the compensation impedances are fixed. It is useful in many cases that the values of the compensation impedances are fixed. However, there also are the cases where it is required to change the values of the compensation impedances, that is the turns ratio a, according to the operating condition. To change the turns ratio a according to the operating condition can be done by a mechanical tap changer or a static tap changer, as in the case of voltage regulating transformers or phase shifting transformers. In FIG. 13 is shown briefly the series transformer to which a mechanical tap changer (131) is added, and in FIG. 14 is shown briefly the series transformer to which a static tap changer (141) is added. There are various kinds in the mechanical tap changer (131) or the static tap changer (141). However, these are already widely used in voltage regulating transformers or phase shifting transformers, so that they will become apparent to those skilled in the art without describing their composition and operation in detail in this description.
The turns ratio a of the series transformer defined in the equation (1) is always a positive value in the case where the first winding (52) and the second winding (53) are wound as FIG. 5A and FIG. 5B. However, in the case where one of the windings of the series transformer is wound in the opposite direction, differing from FIG. 5A and FIG. 5B, the turns ratio a becomes a negative value. If the turns ratio a becomes a negative value, the direction of the current 7i of the first transmission line and the direction of the current 72 of the second transmission line become opposite, as shown in the equation (1). That the direction of 7ι and the direction of 72 become opposite has usefulness especially in the case where the power is transmitted from the bus (101) to the bus (102) via the bus (13) in such a circuit as FIG. 10.
Among the case where the turns ratio a has a negative value, a somewhat interesting phenomenon occurs when a - -1. In such a transmission circuit as FIG. 4, as shown in FIG. 6, a phenomenon that both the compensation impedances become infinity and the transmission lines (11) and (12) are broken occurs. And, in such a transmission circuit as FIG. 10, as shown in FIG. 11, a phenomenon that both the compensation impedances become infinity and the transmission lines (11) and (12) are separated from the bus (13) occurs.
A third embodiment of the present invention is shown in FIG. 15. As shown in FIG. 15, the third embodiment of the present invention is the transmission circuit using an autotransformer instead of a series transformer of the first embodiment of FIG. 4. The structure and the circuit symbol of the autotransformer (151) of FIG. 15 are shown in FIG. 16A and FIG. 16B, respectively. As shown in FIG. 15, FIG. 16A, and FIG. 16B, the third embodiment of the present invention is the one in a power transmission circuit of an ac power system, comprising: a first bus (13); a first transmission line (11); a second transmission line (12); an autotransformer (151) comprising a core (161), a winding (162) wound on said core, a tap (163) connected to said winding, and the turns ratio a of said winding being set to compensate the impedances Z\ and Z2 of said first transmission line and said second transmission line; and the first terminal (164) of said winding (162) being connected to the one end of said first transmission line (11), the second terminal (165) of said winding (162) being connected to the one end of said second transmission line (12), and said tap (163) being connected to said first bus (13).
And, it is the one, wherein the other end of said first transmission line and the other end of said second transmission line are connected to a second bus (14).
The autotransformer (151), because of its structure, can be located only at both the ends of the transmission lines, which are the bus (13) or the bus (14), differing from the series transformer of the first embodiment of FIG. 4. The description for the operation of the third embodiment of the present invention is identical with that of the first embodiment of FIG. 4. But, let the number of the winding between the tap (163) and the first terminal (164) be m and the number of the winding between the tap (163) and the second terminal (165) be n2, then the turns ratio a of the autotransformer is given as a - n2Jn\.
In FIG. 17 is shown briefly the autotransformer to which a mechanical tap changer (171) is added, and in FIG. 18 is shown briefly the autotransformer to which a static tap changer (181) is added. There are various kinds in the mechanical tap changer (171) or the static tap changer (181) of the autotransformer. However, these also are already widely used in voltage regulating transformers or phase shifting transformers, so that they will become apparent to those skilled in the art without describing their composition and operation in detail in this description.
A fourth embodiment of the present invention is shown in FIG. 19. As shown in FIG. 19, the fourth embodiment of the present invention is the transmission circuit using an autotransformer instead of a series transformer of the second embodiment of FIG. 10. The description for the operation of the fourth embodiment of the present invention is identical with that of the second embodiment of FIG. 10.
A fifth embodiment of the present invention is shown in FIG. 20. As shown in FIG. 20, the fifth embodiment of the present invention is the transmission circuit in which neither both the ends of the first transmission line nor both the ends of the second transmission line is connected to the same buses. This is the most general embodiment among those of the present invention. Although some transmission lines or transmission circuits can be additionally connected between the bus (101), the bus (102), the bus (201), and the bus (202), they are not the essential elements of the present invention.
The description for the operation of the fifth embodiment of the present invention is as follows.
First, applying the Kirchhoff's current law to FIG. 20, the following equation is obtained.
Iv =
Iw = h
(21)
Figure imgf000024_0001
Iu = - h And, the voltage-current relation of the series transformer (41) is identical with the equation (1). Substituting the equation (1) into the equation (21), the following is obtained.
Iv = al2
Figure imgf000025_0001
(22) Iτ = — ali
I ■ un = ~
Applying the Kirchhoff's voltage law to the circuit of FIG. 20, the following equation is obtained.
Vy - Vτ = Vx Y Zλ Ix
(23) Vw- Vu = V2 + Z272 .
Substituting the equation (1) into the equation (23), and obtaining
Figure imgf000025_0002
and , the following is obtained.
1
Vι = [ Z2 VV — Zx a Vw— Z2 Vτ + Z a Vυ ]
Z2 + Zx a
(24)
Figure imgf000025_0003
Substituting the equation (24) into the equation (22), the following bus equation is obtained.
Figure imgf000026_0001
where,
Figure imgf000026_0002
If the bus (201) and the bus (202) are united, the equation (25) is identical with the equation (15). As shown in the equation (25), the present invention compensates the impedances of the first transmission line (11) and the second transmission line (12), and compensates the bus admittance matrix YBUS- The values of the compensation impedances are determined by the impedances i and Z2 of the transmission lines, and the turns ratio a of the series transformer. Accordingly, the present invention can compensate the bus admittance matrix YBUS by setting the turns ratio of the series transformer appropriately to compensate the impedances of the transmission lines.
All the figures so far are those which show only one phase of the 3-phase transmission circuits. The transmission circuits of the other two phases are identical with the transmission circuit of this one phase. But, a little more explanation for the 3-phase transformer is necessary. As is well-known, there are mainly two types in the 3-phase transformer. The first type is a bank of three single-phase transformers, and the second type is one 3-phase transformer. The 3-phase transformer is the one having three core legs, and is generally smaller, lighter, and cheaper than the bank of three single-phase transformers. However, in the case where an extra transformer against the fault is added, the bank of three single-phase transformers is advantageous instead. These points are true in the 3-phase series transformer(or the 3-phase autotransformer) of the present invention, but there is one more point to be considered in the 3-phase series transformer (or the 3-phase autotransformer) of the present invention. In the case of the bank of three single-phase transformers, the voltage between the first winding and the second winding of each single-phase transformer becomes the difference between the compensation voltage V\ of the first transmission line and the compensation voltage V2 of the second transmission line. However, in the case of the 3-phase transformer, the voltage between the windings becomes the line-to-line voltage of the transmission lines. And, the line-to^line voltage of the transmission lines generally is much higher than the compensation voltages of the transmission lines. Accordingly, the case of three phase transformer requires much higher voltage of the insulation between the windings than the case of the bank of three single-phase transformers, and is disadvantageous as much.
As described above, the present invention has the advantages that, according to the turns ratio, it, on the one hand, provides the two transmission lines with compensation voltages, on the other hand, controls the ratio of the currents of the two transmission lines, and consequently, provides the two transmission lines with compensation impedances.
The advantages of the present invention are listed below, one by one in comparison with the conventional techniques
The conventional series inductor has the disadvantage that it increases the reactive power of the transmission line because it compensates the impedance of the transmission line with a positive reactance. Compared to this, the present invention has the advantage that it does not increase the total reactive power of the transmission lines because it compensates the impedance with a positive reactance in the one transmission line whereas it compensates the impedance with a negative reactance of the same amount of the power in the other transmission line.
The conventional series capacitor has the disadvantage that it causes the subsynchronous resonance phenomena because it compensates the impedance of the transmission line by a capacitance. Compared to this, the present invention has the advantage that it does not cause the subsynchronous resonance phenomena because it compensates the impedance of the transmission line by not a capacitance but a negative inductance.
The conventional phase shifting transformer has the disadvantage that it should change the phase angle by changing the tap according to the change of the load in order to cause the effect of the impedance compensation. Compared to this, the present invention has the advantage that it does not need to change the tap according to the change the load because, if the turns ratio of the series transformer (or the autotransformer) is fixed, the values of the compensation impedances are fixed. In addition, the conventional phase shifting transformer has the disadvantages that the connection of its windings is complex, it is composed of two apparatus of an exciting transformer and a series transformer, and high voltage insulation is required between the first winding and the second winding of the exiting transformer. Compared to this, the series transformer (or the autotransformer) of the present invention has the advantages that the connection of its windings is simple, it is composed of one apparatus, and high voltage insulation is not required between the first winding and the second winding.
The recent series static compensators are composed of a static power converter and a series transformer, and they have the disadvantages that the high power technology of the static power converters is difficult and their costs are very high. Compared to this, the present invention has the advantage that the high power technology is not difficult and its cost is not high because only a series transformer(or an autotransformer) is used. Differing from the conventional techniques, the present invention has the advantage that it compensates not only the reactance component of the impedance, but also the resistance component of the transmission line. This characteristic is useful especially in compensation the impedance of the transmission line having a large resistance component.
In addition, the present invention has the advantage that it can control the compensating impedances by changing the turns ratio of the series transformed or the autotransformer) through a mechanical or a static tap changer, which is similar to the conventional series inductor or the phase shifting transformer.
The present invention relates to the above advantages individually as well as collectively. These and other advantages of the present invention will become apparent to those skilled in the art from the accompanying drawings and the above detailed description.
In conclusion, the present invention is a new impedance compensation technique which does not use the conventional series inductor, the series capacitor, the phase shifting transformer, or the series static compensator, but uses only a series transformer (or autotransformer), and provides various superior advantages to the conventional techniques. Therefore, the present invention is expected to be able to substitute the conventional techniques well in many applications where these advantages are desirable.
While my above description contains many specificities, these should not be construed as limitations on the scope of the present invention, but rather as an exemplification of preferred embodiment thereof. For example, the voltage level of the first transmission line and the voltage level of the second transmission line in the present invention may differ from each other. And, the present invention can be applied to single-phase or generalized poly-phase ac power systems besides 3-phase ones. And, as can be seen in the equation (1), although the turn ration a of the series transformer(or the autotransformer) of the present invention can be set to control the ratio of the currents of the two transmission lines, this becomes equal with compensating the impedances of the two transmission lines in the result. And, the present invention can also be applied to the cases where the third transmission line and more transmission lines are added to the first transmission line and the second transmission line, by adding series transformers (or autotransformers). For instance, in the case where the third transmission line is added, all the impedances of the first transmission line, the second transmission line, and the third transmission line can be compensated by adding a series transformer(or an autotransformer) between the first transmission line and the third transmission line, or by adding a series transformer (or an autotransformer) between the second transmission line and the third transmission line, and the present invention can be applied to the cases where more transmission lines are added, by the similar way. And, various protective equipments which are used in the conventional series inductor, the series capacitor, the phase shifting transformer, or the series static compensators can be added to the series transformer(or the autotransformer) of the present invention. Therefore, it is to be understood that the present invention is not limited to the disclosed embodiments, but it is intended to cover various simple modifications, extensions, additions, and equivalents, as far as they are within the spirit of the present invention.

Claims

C L A I M S
1. An impedance-compensated power transmission circuit in a power transmission circuit of an ac power system, comprising: a first transmission line; a second transmission line; a series transformer comprising a core, a first winding wound on said core, a second winding wound on said core, and the turns ratio of said first winding and said second winding being set to compensate the impedances of said first transmission line and said second transmission line! and said first winding being connected in series with said first transmission line, and said second winding being connected in series with said second transmission line.
2. An impedance-compensated power transmission circuit of claim
1, wherein the one end of said first transmission line and the one end of said second transmission line are connected to a first bus.
3. An impedance-compensated power transmission circuit of claim
2, wherein the other end of said first transmission line and the other end of said second transmission line are connected to a second bus.
4. An impedance-compensated power transmission circuit of claim 1, claim 2, or claim 3, further comprising means for changing said turns ratio.
5. An impedance-compensated power transmission circuit of claim 4, wherein said means for changing said turns ratio is a mechanical tap changer.
6. An impedance-compensated power transmission circuit of claim 4, wherein said means for changing said turns ratio is a static tap changer.
7. An impedance-compensated power transmission circuit in a power transmission circuit of an ac power system, comprising: a first bus! a first transmission line; a second transmission line; an autotransformer comprising a core, a winding wound on said core, a tap connected to said winding, and the turns ratio of said winding being set to compensate the impedances of said first transmission line and said second transmission line; and the first terminal of said winding being connected to the one end of said first transmission line, the second terminal of said winding being connected to the one end of said second transmission line, and said tap being connected to said first bus.
8. An impedance-compensated power transmission circuit of claim
7, wherein the other end of said first transmission line and the other end of said second transmission line are connected to a second bus.
9. An impedance-compensated power transmission circuit of claim 7 or claim 8, further comprising means for changing said turns ratio.
10. An impedance-compensated power transmission circuit of claim
9, wherein said means for changing said turns ratio is a mechanical tap changer.
11. An impedance-compensated power transmission circuit of claim 9, wherein said means for changing said turns ratio is a static tap changer.
PCT/KR2000/000843 1999-08-05 2000-08-02 Impedance-compensated power transmission circuit WO2001011751A1 (en)

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