Transformers for controlling independent active and reactive power flows in transmission lines

Abstract

An exemplary transformer includes an exciter unit (EU) and a compensating voltage unit (CVU). The EU includes a three-phase transformer with a shunt-Y connected primary winding. The CVU includes multiple series-connected secondary windings, each having one secondary winding from each phase of the EU, and multiple load tap changers. Each load tap changer is associated with a group of secondary windings, each containing one secondary winding from each phase of the EU. Each secondary winding in the group is located at the same distance from the associated primary winding of the EU. All secondary windings, sub-windings between two consecutive taps, and primary windings have similar heights. The sub-windings may or may not be interleaved. Each load tap changer can vary the effective number of turns in the associated group of secondary windings by connecting to one of multiple taps associated with each secondary winding, according to a selected operating point.

Description

[Technical Field]

[0001] This disclosure relates to transformers, and more particularly to transformers that generate a compensating voltage. [Background technology]

[0002] In the past, electrical engineering techniques implemented power flow control methods using inductors, capacitors, transformers, and load tap changers. In recent years, power electronics-based solutions have become the preferred means of addressing power flow control schemes. Power flow control solutions can vary widely in cost and complexity, ranging from constructing new transmission lines to more efficiently utilizing existing ones. A key consideration for any solution is identifying underutilized transmission lines and leveraging their unused capacity to increase power flow to the thermal limits of the line using the most cost-effective and long-proven solution.

[0003] Power flow control in a line is performed either by adjusting the effective line reactance with respect to a series-connected capacitor or reactor in that line, and / or by adjusting the effective phase angle between the voltage at the transmitting end and the voltage at the receiving end of that line. In either case, the active and reactive power flows in that line change simultaneously, meaning that the active and reactive power flows cannot be controlled independently.

[0004] Independent control of active and reactive power flows in a line, as needed, can only be achieved by using an impedance regulator (IR) to emulate independently tuned resistance and reactance.

[0005] A feasible power flow controller uses a compensation voltage at an arbitrary phase angle to the line current flowing through it, and controls the four-quadrant impedance (-R, +R, X C and X L ) emulates the current. The ratio of the compensation voltage to the current line current is the emulated impedance. This compensation voltage exchanges active and reactive power with the line. For the exchanged power to flow freely, the compensation voltage is either linked to a shunt connection voltage to the same line, as in the case of power electronics-based integrated power flow controllers, electromechanical-based rotary transformers, and transformer / LTC-based Sen transformers, or to a series connection voltage, as in the case of power electronics-based interline power flow controllers or transformer / LTC-based multiline Sen transformers. In special cases, when the compensation voltage and the line current flowing through it are orthogonal, the compensation voltage made on a power electronics-based or electromechanical-based system does not need to be linked to another voltage source. These special cases are equivalent to using a capacitor or reactor for compensation.

[0006] Patent Document 1 proposes a Distributed Series Reactor (DSR) that inserts the magnetization inductance of a transformer into a conductor when the conductor current reaches a predetermined value, and removes the magnetization inductance when the conductor current returns below the predetermined value. The disclosed method merely inserts a reactor in series with the line to reduce the power flow in the line. Since a capacitor cannot be inserted in series with the line using this method, the system cannot increase the power flow in the line. Furthermore, this system does not implement -R or +R, and therefore it is not an impedance adjuster and cannot independently control the active and reactive power flows in the line.

[0007] Patent Document 2 discloses a technique for emulating a series capacitor or reactor by connecting a compensation voltage in series with a line and maintaining its phase angle lagging or leading the current line current by 90°. Through control actions, the magnitude of the series compensation voltage is varied to vary the emulated capacitor or reactor. It has been proposed that a series compensation voltage of variable magnitude be implemented by the use of a power electronics inverter. Impedance compensation is achieved on the basis of using energy storage across the inverter's DC capacitor so that additional active power can be transiently exchanged with the line. Impedance compensation depends on the rating of the storage device and therefore its operating duration is limited. Continuous impedance compensation is required for power flow controllers that can implement four-quadrant impedance and control active and reactive power independently. The disclosed technique also uses a reactance control method used to operate a reactance regulator (RR), and therefore the series compensation voltage (V s’s ) is proportional to the current line current (I), and the emulated reactance (X se) becomes a constant of proportionality. For this control algorithm to function correctly, a line current must exist. Also, in reactance control methods, the polarity of the reactance is defined before the desired control action is to be performed. If it is defined as inductive, the best that can be achieved is to reduce the line current to slightly below the corresponding uncompensated value. Since the normal operation of the control algorithm depends on the presence of a line current, the line current can never be reduced to nearly zero by the controller. If the emulated reactance is to be defined as capacitive, the line current will initially increase. If the required emulated capacitive reactance is higher than the inductive reactance of the line, the effective line reactance becomes capacitive, and the power flow in the line reverses. However, reversing the power flow while the line current is high causes several problems. During the transition, when the power flow is reversed, the line may operate beyond its maximum thermal capacity. Furthermore, during the emulation of higher capacitive reactance, there is a point where the inductive reactance of the line equals the capacitive reactance emulated by the reactance regulator, which can cause instability in the power flow of the line. The reactance control method provides the basic characteristics of RR in terms of reducing or increasing the power flow in the line. However, an undesirable characteristic of this control method appears during the reversal of the power flow in the line when the line current is too high, causing even greater transients. In practical implementations, if the current through the RR exceeds its rating, the inverter base RR will be bypassed.

[0008] Patent Document 3 discloses a voltage control method that provides all the desirable features offered by reactance control methods with respect to controlling power flow in a line. Furthermore, the voltage control method provides absolute stability in the power flow, causing the power to pass near zero while changing its direction of flow.

[0009] Patent Document 4 discloses a Phase Angle Regulator (PAR) that provides a series compensation voltage at a relative phase angle of ±90° with respect to the line voltage. The purpose of the PAR is to adjust the phase shift angle of the line voltage to control the power flow in the line, but the phase angle adjustment cannot independently control the active and reactive power flows in the line. The inability of the PAR to use relative phase angles other than ±90°, within the range of 0° to 360°, prevents it from independently promoting the active and reactive power flows. Power electronics-based PARs can provide millisecond-level dynamic compensation, such as the power electronics-based impedance regulator (integrated power flow controller) demonstrated at American Electric Power's Inez substation in 1998. In contrast, the dynamic performance of a PAR is limited by the operating speed of the mechanical LTC, which responds in seconds, although this level of response time has been acceptable in most utility model applications for several decades.

[0010] A PAR (Performance Amplifier) ​​injects a compensation voltage in series with the line, thereby emulating a compensation impedance, which is the ratio of the compensation voltage to the current line current. However, this emulated impedance is not an independently adjustable resistance and reactance, and therefore, a PAR cannot independently control the active and reactive power flows in the line. An impedance regulator (IR), on the other hand, provides independent control of the active and reactive power flows in the line as needed.

[0011] Patent Document 5 discloses independent control of active and reactive power flows, such that the compensation voltage is generated using electromechanical means.

[0012] Patent Document 6 discloses an electromechanical-based independent active and reactive power flow controller. The machine uses a shunt-shunt configuration, which results in a much higher power rating and cost than an equivalent shunt-series power flow controller.

[0013] Figure 1 shows a Sen transformer in a known implementation. Patent documents 7-10 disclose Sen transformers in a shunt-series configuration used as general-purpose power flow transformers for compensating power flow in transmission lines. Sen transformers provide independent control of active and reactive power flow using IR in a low-cost manner by employing redesigned transformer / LTC technology. This is because transformer / LTC technology has been proven to be efficient, simple, and reliable in utility model applications for decades. Sen transformers use three primary windings and nine secondary windings to create a compensation voltage that modifies the line voltage to a specific magnitude and phase angle, whereas conventional transformers only modify the magnitude of the line voltage, and PARs only modify the phase angle of the line voltage. As a result, by using a Sen transformer, the active and reactive power flows in the line can be independently adjusted to maximize the revenue-generating active power flow and minimize the reactive power flow while maintaining line voltage stability.

[0014] Transformers used in power system applications generally include two types: voltage-regulating transformers (VRTs) and phase angle adjusters (PARs). VRTs primarily adjust the magnitude of line voltage (i.e., increase or decrease in line voltage) without significantly altering its original phase angle. In symmetrical configurations, PARs (sym) primarily adjust the phase angle of line voltage with little to no change to its original voltage magnitude. In asymmetrical configurations, PARs primarily adjust the phase angle of line voltage with some increase in line voltage magnitude.

[0015] Figures 2A and 2B show voltage regulating transformers in known configurations. A VRT can be of two types: (a) an autotransformer 202 as shown in Figure 2A, and (b) a twin-turn transformer 204 as shown in Figure 2B. Since a transformer is configured to convert electrical energy from one voltage and current level at its input to another voltage and current level at its output, the primary voltage (vp ) is applied across the primary winding having n p turns, and the secondary voltage (v s ) is induced across the secondary winding having n s turns, an ideal transformer operates on the following principle.

Number

[0016] Depending on the transformer configuration, the output voltage (v out ) is related to the input voltage (v in ) as follows.

Number

[0017] In the above equation, the primary voltage (v p ) is applied across the primary winding having n p turns, and the secondary voltage (v s ) is induced across the secondary winding having n s turns. The input current (i in ) is related to the output current (i out ) as follows.

Number

[0018] Use the fact that the magnetomotive force is balanced in the primary and secondary windings as follows. n p × i p = n s × i s (6)

[0019] In both the configurations of FIGS. 2A and 2B, it can be verified from Eqs. (2), (3), (4), and (5) that the input power is the same as the output power. In other words, v in × iin =v out ×i out (7)

[0020] In a two-winding transformer, the primary and secondary voltages are electrically isolated. The induced voltage in the secondary winding is connected by a wire and a shunt. In a voltage boosting transformer, n s >n p This is useful for increasing the voltage from the generator's output before transmitting electrical energy through a high-voltage AC transmission line. In a voltage step-down transformer, n s <n p This is useful for reducing the voltage of the transmission line before using it at various lower voltages required by the load. p =n s When this is the case, the primary voltage and secondary voltage and the primary current and secondary current are the same, and the transformer is used as an isolated transformer because the primary voltage and secondary voltage are electrically isolated from each other. In both autotransformers and two-turn transformers, the effective number of turns in the secondary winding is varied using LTC.

[0021] From equations (1) and (6), it can be written as follows: v p ×i p =v s ×i s (8)

[0022] This ensures power balance in both the primary and secondary windings, since an ideal transformer neither generates nor absorbs power.

[0023] The autotransformer in Figure 2A has an excitation (i.e., primary) winding 206 p The shunt connects to the wire, and the compensating (i.e., secondary) winding 206 s Since they are connected in series, it is called having a shunt-series configuration. The two-turn transformer in Figure 2B has an excitation (i.e., primary) winding 208 p and compensation (i.e., secondary) winding 208 sSince both windings are connected to the wire via a shunt, it is called a shunt-shunt configuration. In a shunt-series configuration, the primary and secondary windings are electrically connected, whereas in a shunt-shunt configuration, the primary and secondary windings are electrically isolated from each other.

[0024] Figure 3 shows a transformer circuit in a known implementation. As shown in Figure 3, the transformer circuit 300 may include both a voltage regulator 302 and a phase angle regulator 304. The voltage regulator (VR) or autotransformer 302 adjusts the line voltage by connecting a variable magnitude compensation voltage in series with the line at 0° or 180° relative to the line voltage. The phase angle regulator (PAR) 304 adjusts the phase angle of the line voltage by connecting a variable magnitude compensation voltage in series with the line at 90° or -90° relative to the line voltage. Compensation voltage (V) in autotransformer 302 1s The compensation voltage (V) in PAR304 is varied by LTC306 in phase (0°) or out of phase (180°) with respect to the line voltage, and thus adjusts the magnitude of the transmission line voltage. s’1 ) is varied by LTC308 perpendicular to the line voltage (90° or -90°), and thus adjusts the phase angle of the transmission line voltage. Figure 3 shows these two perpendicular compensation voltages, i.e., V from autotransformer 302. 1s and V from PAR304 s’1 However, a new compensation voltage (V) is variable in both magnitude and phase angle. s’s This shows how they can be combined to generate a new compensation voltage (V s’s The voltage (V) is not limited to a specific phase angle such as 0°, 180°, or ±90°. Due to its variable magnitude and variable phase angle compensation voltage, the line voltage can be modified to be in a variable magnitude and phase angle. Creating two orthogonal voltages using an autotransformer and a PAR is possible with a single unit of the Sen transformer having the same compensation voltage (V). s’s It requires more hardware than what would be needed to create it.

[0025] Figures 4A and 4B show the single-line diagram and associated phasor diagram of the Sen transformer, respectively, in known implementation configurations. The Sen transformer 400 combines the functions of an autotransformer and a PAR into a smaller physical package, resulting in a reduced amount of hardware compared to what would be required separately for an autotransformer and a PAR. As shown in Figure 4A, the Sen transformer 400 uses a shunt unit (exciter unit) 402 and a series unit (compensating voltage unit) 404, and is sized (V s’s ) and the series compensation voltage (V) which is variable in relative phase angle (β) s’s Create a line voltage (V) s ) from (V s’ ) was modified to achieve independent control of active and reactive power flows in the line, and the magnitude (V s’ It controls both the magnitude (V) and the phase shift angle (ψ) simultaneously. As shown in Figures 4A and 4B, the Sen transformer 400 has a variable magnitude (V) s’s By connecting a compensation voltage of ) in series with the line at any relative phase angle of 0°≦β≦360°, the magnitude of the line voltage (V s’ ) and the phase shift angle (ψ) are adjusted simultaneously.

[0026] Returning to Figure 1A, the Sen transformer includes an exciter unit 102 and a three-phase transformer with Y-connected primary windings (108A, 108B, and 108C). The compensating voltage unit 104 has nine secondary windings (three windings in each phase, i.e., 106 on the core of phase A). a1 , 106 a2 , and 106 a3 , 106 on the core of phase B b1 , 106 b2 , and 106 b3 , and 106 on the core of the C phase c1 , 106 c2 , and 106 c3 ) includes. Compensation secondary winding 106 a1 , 106 a2 , 106 a3 , 106 b1 , 106 b2 , 106 b3 , 106 c1, and 106 c2 , and 106 c3 is assigned in a group arranged for taps at a specified interval. By selecting the number of turns of the group of secondary windings using the LTC110 associated with that group, the magnitude of the compensation voltage (V s’s ) is varied within a specified range, and the relative phase angle (β) is varied between 0° and 360°. The three-phase transmission-end voltages (V sA , V sB , and V sC ) are applied to the exciter unit 102. The LTC changes their positions stepwise, and the compensation points are discrete within an acceptable control range of the relative phase angle of 0° ≤ β ≤ 360°.

[0027] The LTC can be grouped as follows. · 106 for the first three-phase LTC1 a1 , 106 b2 and 106 c3 · 106 for the second three-phase LTC2 b1 , 106 c2 and 106 a3 · 106 for the third three-phase LTC3 c1 , 106 a2 and 106 b3

[0028] It means that each of the windings (106 a1 , 106 b2 and 106 c3 ) is tapped at the same number of turns through LTC1, each of the windings (106 b1 , 106 c2 and 106 a3 ) is tapped at the same number of turns through LTC2, and each of the windings (106 c1 , 106 a2 and 106 b3 ) is tapped at the same number of turns through LTC3. However, 106 a1 - 106 b2 - 106 c3 set, 106[[ID=6�]] b1 - 106c2 -106 a3 set, and 106 c1 -106 a2 -106 b3 The number of turns in the set can be different from each other.

[0029] By selecting the number of turns from each of the three windings through three LTCs (LTC1, LTC2, and LTC3), and thus by selecting the magnitudes of the components of the three 120° phase-shifted induced voltages, the compensation voltage (V s’s ) in any phase is derived from the phasor sum of the voltages induced in a three-phase secondary winding set (106 for compensation in phase A a1 , 106 b1 , and 106 c1 , 106 for compensation in phase B a2 , 106 b2 , and 106 c2 , and 106 for compensation in phase C a3 , 106 b3 , and 106 c3 ). The magnitude of the induced voltage (V) in the secondary winding, the voltage (x) across each tap of the LTC, and the number of taps (N) in the LTC are related by the following equation.

Equation

[0030] The magnitude (V s’s ) and relative phase angle (β) of the compensation voltage (V s’s ) can be calculated for the tap associated with a particular phase. The corrected sending-end voltage (V s’ ) is generated by connecting the compensation voltage (V s’s ) having the magnitude (V s’s ) and relative phase angle (β) in series with the sending-end voltage (V s ). This can be written for phase A as follows. V s’A =V sA +V s’sA (10) Or V s’A∠ψ A =V sA ∠0°+V s’sA ∠β A (11) Here, V s’sA ∠β A =V s’sA =V a1 +V b1 +V c1 (12) or V s’sA ∠β A =k a1 V sA +k b1 V sB +k c1 V sC =k a1 V sA +k b1 e -j2π / 3 V sA +k c1 e j2π / 3 V sA (13) In the above equation,

[0031] V a1 , V b1 , and V c1 This is the effective voltage in the series compensation windings (a1, b1, and c1) of phase A,

[0032] k a1 =0.05, k b1 =0, and k c1 =0.20 is an arbitrarily selected effective turns ratio between the secondary series compensation winding and the corresponding primary winding in phase A.

[0033] V s’sA This is the magnitude of the series compensation voltage in phase A,

[0034] β A This is the relative phase angle of the series compensation voltage in phase A.

[0035] Figures 5A to 5F show several single-phase transformers in known implementation configurations. Each single-phase transformer in Figures 5A to 5B is an ideal transformer in which an alternating current (AC) source voltage is applied to the input or primary winding, resulting in an AC current flowing through the primary winding. Primary current (i p ) is the AC primary magnetic flux (φ p Creates the primary voltage (v). p ) and primary magnetic flux (φ p ) and the number of turns in the primary winding (n p ) can be related to the following, according to Faraday's law of induction:

number

[0036] In reality, leakage primary magnetic flux (φ lp The primary magnetic flux (φ) is called p Since some of the φ does not flow through the magnetic core, an ideal transformer does not exist. The remaining portion is the mutual magnetic flux (φ) as shown in Figure 5C. m ) is called.

[0037] Two voltages, namely the primary voltage (v p ) and the corrected primary voltage (v' p The difference between ) is the leakage primary reactance (X) as shown in Figure 5D. lp Voltage (v) across ) lp It is expressed as ). Leakage primary magnetic flux (φ lp To take this into account, a portion of the excitation primary voltage is used to account for the equivalent leakage primary reactance (X) within the transformer before the ideal transformer action occurs. lp ) will be considered over time.

[0038] The primary winding acts as a load relative to the source. The secondary winding acts as a source relative to the load. When the secondary winding supplies current to the load, the polarity of the current in the secondary winding is the secondary current (i s The magnetic flux created by ) is the mutual magnetic flux (φ m This would be contrary to the principle of mutual magnetic flux. In order to maintain the same mutual magnetic flux, the primary current (ip ) is the secondary current (i s When ) increases, it increases. A portion of the secondary magnetic flux (φs) that does not flow through the magnetic core increases, as shown in Figure 5E, the mutual magnetic flux (φ m ) opposing secondary leakage flux (φ ls ) is called.

[0039] Two voltages, namely the modified secondary voltage (v' s ) and secondary voltage (v s The difference between this and the leakage secondary reactance (X ls Voltage (v) across ) ls It is expressed as (φ). Leakage secondary flux (φ ls To take this into account, a portion of the induced secondary voltage is absorbed before the remaining voltage becomes available at the output terminal, as shown in Figure 5F, by the equivalent leakage secondary reactance (X) within the transformer. ls ) will be considered over time.

[0040] Figures 6A to 6C show three single-phase transformers in known configurations. As shown in Figure 6A, the three single-phase transformers 602A, 602B, and 602C have a three-phase primary voltage (v pA , v pB , and v pC The system is excited by ), where the phase voltages are shifted by a phase angle of 120°, and the induced three-phase secondary voltage (v sA , v sB , and v sC In this configuration, the phase voltages are also shifted by a phase angle of 120°. The number of windings in the primary and secondary windings for each phase is n pA and n sA , n pB and n sB , and n pC and n sC Figures 6B and 6C show the single-phase transformer of Figure 6A configured as a three-phase transformer 604, with only one primary winding and one secondary winding on each leg of the core 606, the same leakage impedance in each phase, and the same voltage across the leakage impedance in each phase.

[0041] Figures 7A and 7B show a three-phase transformer in another known configuration. As shown in Figures 7A and 7B, each leg of the core has a single primary and secondary winding in a nested configuration, where the primary and secondary windings are concentric around each core leg. Even in nested and concentric configurations, the leakage impedance in each phase is the same whether the primary winding is an inner winding located next to the core and the secondary winding is an outer winding, as shown in Figure 7A, or vice versa, as shown in Figure 7B. Generally, lower voltage windings may be located next to the core, and higher voltage windings may be located further away from the core. However, if the windings consist of taps, it may be a better design to place the windings on the outside, regardless of their voltage, for other benefits, such as easier access to the taps. As shown in Figures 7A and 7B, all primary windings in the transformer have the same internal diameter (ID) and outer diameter (OD). Furthermore, all secondary windings in the transformer have the same ID and OD.

[0042] A Sen transformer may have a configuration in which at least several secondary windings are arranged on each leg of the core. In this configuration, special care must be taken to ensure that the leakage impedance in each phase is the same so that the voltage across the leakage impedance is balanced in each phase; otherwise, the voltages in the three phases at the output will be unbalanced, which is undesirable. Also, the compensation voltages in each of the three phases are equal in magnitude and shifted by a phase angle of 120°. [Prior art documents] [Patent Documents]

[0043] [Patent Document 1] U.S. Patent No. 7,835,128 [Patent Document 2] U.S. Patent No. 5,198,746 [Patent Document 3] U.S. Patent No. 5,754,035 [Patent Document 4] U.S. Patent No. 9,197,065 [Patent Document 5] U.S. Patent No. 5,841,267 [Patent Document 6] U.S. Patent No. 8,054,011 [Patent Document 7] Strength Patent No. 6,335,613 [Patent Document 8] U.S. Patent No. 6,384,581 [Patent Document 9] U.S. Patent No. 6,396,248 [Patent Document 10] U.S. Patent No. 6,420,856 [Overview of the Initiative]

[0044] An exemplary transformer for generating a compensating voltage is disclosed, comprising an exciter unit and a compensating voltage unit, wherein the exciter unit comprises three single-phase transformers or a three-phase transformer having a shunt Y-connected primary winding, and the compensating voltage unit comprises a plurality of series-connected secondary windings, each comprising one secondary winding from each phase of the exciter unit, and a plurality of load tap changers, each load tap changer associated with a group of secondary windings, each of which comprises one secondary winding from each phase of the exciter unit, and each secondary winding in the group of secondary windings is connected to the exciter unit. The load tap changer includes a plurality of load tap changers, each configured to vary the effective number of turns of an associated group of secondary windings by connecting to one of a plurality of taps associated with each secondary winding, according to a selected operating point, all secondary and sub-windings between two consecutive taps, and the primary windings having similar heights, with the sub-windings being interleaved or not.

[0045] An exemplary method for generating a compensating voltage through a transformer is disclosed, the transformer comprising an exciter unit and a compensating voltage unit, the exciter unit comprising a plurality of series-connected secondary windings, each comprising one secondary winding from each phase of the exciter unit, and a plurality of load tap changers, each load tap changer associated with a group of secondary windings, each secondary winding in the group of secondary windings being associated with the primary winding of the exciter unit The method includes selecting the operating point of the transformer, selecting the load tap position for each secondary winding in the group of secondary windings associated with each load tap changer based on the operating point, and generating a compensation voltage by calculating the sum of the effective voltages induced in the group of secondary windings for each load tap changer.

[0046] A patent or application file must include at least one color drawing. A copy of the published patent or patent application containing one or more color drawings will be provided by the Patent Office upon request and payment of the required fees.

[0047] The exemplary embodiments are best understood from the following detailed description when read in conjunction with the accompanying drawings. These drawings include the following figures: [Brief explanation of the drawing]

[0048] [Figure 1A] This figure shows a Sen transformer in a shunt-series configuration, according to known implementations. [Figure 1B] These are the relevant phasor diagrams based on known implementations. [Figure 2A] This diagram shows a voltage regulator transformer, i.e., an autotransformer, in a known implementation configuration. [Figure 2B]This figure shows a two-turn transformer in a known configuration. [Figure 3] This diagram shows a transformer circuit incorporating an autotransformer and a phase angle adjuster (asymmetrical) in a known implementation configuration. [Figure 4A] This is a single-line diagram of a Sen transformer in a shunt-series configuration, based on known implementations. [Figure 4B] These are related phasor diagrams based on known implementations. [Figure 5A] This figure shows a single-phase transformer in a known implementation configuration. [Figure 5B] This is an equivalent circuit diagram of a single-phase transformer in a known implementation. [Figure 5C] This figure shows a single-phase transformer in a known implementation configuration. [Figure 5D] This is an equivalent circuit diagram of a single-phase transformer in a known implementation. [Figure 5E] This figure shows a single-phase transformer in a known implementation configuration. [Figure 5F] This is an equivalent circuit diagram of a single-phase transformer in a known implementation. [Figure 6A] This figure shows three single-phase transformers in known implementation configurations. [Figure 6B] This is a diagram showing a single three-phase transformer in a known implementation configuration. [Figure 6C] This is a diagram showing a single three-phase transformer in a known implementation configuration. [Figure 7A] This diagram shows the arrangement of the primary and secondary windings (closest to the core) in known implementation configurations. [Figure 7B] This diagram shows the arrangement of the primary winding and the secondary winding (closest to the core) in known implementation configurations. [Figure 8A] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8B] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8C] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8D] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8E] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8F] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8G] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8H] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8I] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8J] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8K] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8L] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8M] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8N] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8O] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 8P] This figure shows an exemplary winding arrangement for a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9A] This figure shows modified transmit-end voltage operating points numbered 0 to 60 according to exemplary embodiments of the present disclosure. [Figure 9B] This figure shows the respective active and reactive power flow (Pr and Qr) operating points, numbered 0 to 60, according to exemplary embodiments of the present disclosure. [Figure 9C] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9D] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9E] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9F] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9G] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9H] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9I] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9J] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9K] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9L] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9M] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9N] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9O] This figure shows the maximum active power flow amplification and doubling capability of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9P] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9Q] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9R] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9S] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9T] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9U] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9V] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9W] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9X] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9Y] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9Z] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9AA] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9AB] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 9AC] A diagram showing the maximum effective power flow enhancement multiple capacity of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 10A] This is a table showing the operating points of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 10B] This is a table showing the operating points of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 10C] This is a table showing the operating points of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 10D] This is a table showing the operating points of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 10E] This is a table showing the operating points of a Sen transformer according to an exemplary embodiment of the present disclosure. [Figure 11] This figure shows an exemplary winding layout and the distribution of amperages at β=0° according to an exemplary embodiment of the present disclosure. [Figure 12] This figure shows an exemplary winding layout and the distribution of amperages at β=60° according to an exemplary embodiment of the present disclosure. [Figure 13] This figure shows an exemplary winding layout and the distribution of amperages at β=120° according to an exemplary embodiment of the present disclosure. [Figure 14] This figure shows an exemplary winding layout and the distribution of amperages at β=180° according to an exemplary embodiment of the present disclosure. [Figure 15] This figure shows an exemplary winding layout and the distribution of amperages at β=240° according to an exemplary embodiment of the present disclosure. [Figure 16] This figure shows an exemplary winding layout and the distribution of amperages at β=300° according to an exemplary embodiment of the present disclosure. [Figure 17A] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17B] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17C]A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17D] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17E] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17F] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17G] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17H] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17I] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17J] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17K] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17L] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17M] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17N] A diagram showing a Sen transformer arranged in a shunt-shunt configuration and having a winding arrangement according to an exemplary embodiment of the present disclosure. [Figure 17O]This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17P] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17Q] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17R] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17S] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17T] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17U] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17V] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17W] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17X] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17Y] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17Z] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AA]This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AB] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AC] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AD] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AE] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AF] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AG] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AH] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AI] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AJ] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AK] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AL] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AM]This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 17AN] This figure shows a Sen transformer having a winding configuration, arranged in a shunt-shunt configuration, according to an exemplary embodiment of the present disclosure. [Figure 18A] This figure shows a series-to-series transformer configuration according to an exemplary embodiment of the present disclosure. [Figure 18B] This figure shows a series-to-series transformer configuration according to an exemplary embodiment of the present disclosure. [Figure 19] This figure shows a generalized Sen transformer (GST) configured to generate both a shunt-compensated voltage and a series-compensated voltage in a single unit, according to an exemplary embodiment of the present disclosure. [Figure 20] This figure shows a method for generating a compensation voltage according to an exemplary embodiment of the present disclosure. [Modes for carrying out the invention]

[0049] Further areas of applicability of this disclosure will become apparent from the detailed description provided below. It should be understood that the detailed description of exemplary embodiments is for illustrative purposes only and therefore does not necessarily limit the scope of this disclosure.

[0050] An exemplary embodiment of this disclosure relates to a Sen transformer in which the compensating voltage is the phasor sum of three voltages induced in the secondary windings, each from a different phase, A, B, or C. The windings are strategically arranged around the legs of the transformer so that balanced leakage impedances in each phase are achieved. According to the exemplary embodiment described in further detail, all primary windings have the same inner diameter (ID1) and outer diameter (OD1), as well as substantially similar heights, and all secondary and sub-windings between two consecutive taps associated with a group according to a designated load tap changer have the same inner diameter and outer diameter and substantially similar heights (i.e., lengths). The sub-windings may or may not be interleaved.

[0051] An exemplary embodiment of the present disclosure is based on the Sen transformer 800 of Figure 8A, which can be configured to control independent active and reactive power flows in a transmission line as described herein. The transformer 800 includes an exciter unit 802 and a compensating voltage unit 804. According to the exemplary embodiment, the exciter unit 802 includes a three-phase transformer having shunt Y-connected primary windings 808A, 808B, and 808C. The compensating voltage unit 804 includes a plurality of series-connected secondary windings 806 in each phase of the exciter unit 802. The compensating voltage unit 804 also includes a plurality of load tap changers 810, each load tap changer 810 having a plurality of secondary windings 806 a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 It is associated with one of the following. The secondary windings may be assigned to three groups of LTC control, each group having one secondary winding from each phase (A, B, and C) of the exciter unit 802, and each secondary winding in the group is set to the same load setting. Each secondary winding 806 in the group of secondary windings associated with LTC1, LTC2, and LTC3 a1 ,806 a2 ,806 a3,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 The respective primary windings 808A, 808B, and 808C of the excitation unit 802 are located at the same distance from each secondary winding 806, and each load tap changer operates according to the selected operating point. a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 It is configured to vary the effective number of turns of the associated secondary winding groups LTC1, LTC2, and LTC3 by connecting to one of the multiple taps 810 associated with it.

[0052] Figures 8A to 8P show exemplary winding arrangements for a Sen transformer according to exemplary embodiments of the present disclosure.

[0053] As shown in Figure 8C, the three excitation windings 808A, 808B, and 808C may be the innermost windings. The winding arrangement (placement) in Figure 8C may be configured such that all primary windings have the same inner diameter (ID) and outer diameter (OD), and all secondary windings have the same inner diameter ID and outer diameter OD. Furthermore, all windings (i.e., primary and secondary windings) may have substantially the same height or length. In addition, the secondary windings may be positioned above the primary windings in a sequence according to LTC grouping. According to an exemplary embodiment, nine compensatory windings 806 a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 The secondary winding can be arranged as follows: As shown in Figures 8C, 8D, and 8E, secondary winding 806 connected to LTC1 a1 ,806 b2 , and 806 c3 These have the same inner diameter (ID2) and outer diameter (OD2) and can be arranged on the excitation windings 808A, 808B, and 808C, respectively. As shown in Figures 8C, 8D, and 8G, secondary winding 806 connected to LTC3 a2 ,806 b3 , and 806 c1 These have the same inner diameter (ID3) and outer diameter (OD3), and each is a secondary winding 806 a1 ,806 b2 , and 806 c3 It can be placed above. As shown in Figures 8C, 8D, and 8F, secondary winding 806 connected to LTC2 a3 ,806 b1 , and 806 c2 These have the same inner diameter (ID4) and outer diameter (OD4), and each is a secondary winding 806 a2 ,806 b3 , and 806 c1 It can be placed above.

[0054] According to an exemplary embodiment, the LTC windings may be concentric with one another, and the exciter windings 808A, 808B, and 808C are fully rated. The three sets of compensating windings (806a1, 806b2, and 806c3), (806b1, 806c2, and 806a3), and (806c1, 806a2, and 806b3) are each fully rated.

[0055] Figures 8A and 8B show the series compensation voltage generated by a Sen transformer 800 having the winding arrangement of Figure 8A, according to an exemplary embodiment of the present disclosure. Based on the winding arrangement of Figure 8A, the series compensation voltage (V s’sA ) is the three available induced voltages V from the excitation phases separated by 120°. a1 , V b1 , and V c1 It is constructed by taking and summing them. Similarly, the series compensation voltage (V s’sB) is the three available induced voltages V from the excitation phases separated by 120°. a2 , V b2 , and V c2 It is constructed by taking and calculating the sum of these values, and the series compensation voltage (V s’sC ) is the three available induced voltages V from the excitation phases separated by 120°. a3 , V b3 , and V c3 It is constructed by finding the sum of the following. Using LTC (LTC1, LTC2, and LTC3), three sets of secondary (i.e., compensating) windings (806) in each phase. a1 ,806 b2 , and 806 c3 ), (806 b1 ,806 c2 , and 806 a3 ), and (806 c1 ,806 a2 , and 806 b3 The effective number of turns in each secondary (i.e., compensating) winding in the ) is varied, and the combined voltage is variable in magnitude and phase angle.

[0056] The magnitude (V) of the induced voltage in one or more of the active secondary windings 806a1, 806a2, 806a3, 806b1, 806b2, 806b3, 806c1, 806c2, and 806c3, the voltage (x) across each tap of LTC1, LTC2, and LTC3, and the number of taps in the LTC (N) are related by the following equation:

number

[0057] According to the exemplary embodiments of this disclosure, the transmitting end voltage V s = 1, the allowable magnitude (V) of the induced voltage (V) can be set to 0.2, and the voltage (x) across each tap of the LTC can be 0.05. Therefore, the Sen transformer 800 has each secondary winding 806 a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2,806 b3 ,806 c1 ,806 c2 , and 806 c3 In this configuration, there are N=0.2 / 0.05 or N=4 taps. Therefore, according to the exemplary configuration of the Sen transformer 800, the secondary winding 806 a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 Each of these can be tapped at one of tap positions 0, 1, 2, 3, or 4. The selected tap position determines the primary, i.e., the percentage of the exciting voltage, for example, 0%, 5%, 10%, 15%, and 20%, respectively, and the secondary winding 806 a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 Each of them is effective in that proportion. The selected tap position is associated with the secondary winding 806 a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 However, this also determines how much it contributes to forming the compensation voltage. For example, for tap positions 0, 1, 2, 3, or 4, the contribution of the secondary winding to the compensation voltage could be 0.0 (0%), 0.05 (5%), 0.10 (10%), 0.15 (15%), or 0.20 (20%), respectively.

[0058] The tap positions for load tap changers LTC1, LTC2, and LTC3 for any operating point of the Sen transformer 800 are shown in Figures 8E to 8G. For example, the secondary windings associated with the first phase of the exciter unit 802, the compensating winding 806a1 is tapped for a voltage of 0.05 pu, the compensating winding 806b1 is tapped for a voltage of 0.0 pu, and the compensating winding 806c1 is tapped for a voltage of 0.20 pu.

[0059] According to exemplary embodiments of this disclosure, moving the contacts of the LTC to higher tap positions (i.e., towards the dots) (e.g., 0→1, 1→2, 2→3, 3→4, etc.) results in a series compensation voltage V s’s Increase the primary windings 808A, 808B, and 808C, and the secondary winding 806 a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 These are considered to have voltage ratings of 1 pu and 0.20 pu, respectively. According to the exemplary embodiments described herein, secondary winding 806 a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 Each of these may have LTC contacts located at tap positions at 5% intervals, and includes five taps marked 0 to 4. At tap position 0, each secondary winding is bypassed.

[0060] Figure 8H shows an exemplary winding arrangement in which multiple secondary windings for each primary winding are arranged having the same inner diameter (ID2) and outer diameter (OD2). For example, in phase A of the Sen transformer 800, the primary winding 808A is arranged as an inner winding on the core leg, and the secondary winding 806 a1 ,806 a2 , and 806a3 The primary winding 808A forms multiple rings. Each of the secondary windings has the same inner diameter (ID2) and outer diameter (OD2). Similarly, in phase B, the primary winding 808B is the inner winding on the corresponding core leg, and the secondary winding 806 b1 ,806 b2 , and 806 b3 In phase C, the primary winding 808C is an outer winding that forms multiple rings around the primary winding 808B, and the secondary winding 806 is an inner winding on the corresponding core leg. c1 ,806 c2 , and 806 c3 This is the outer winding that forms multiple rings around the primary winding 808C. Just as in the case of phase A, the secondary windings for phases B and C of the Sen transformer 800 have the same ID and OD.

[0061] Figures 8I and 8J show a winding arrangement for the Sen transformer of Figure 8A, including a tertiary winding, according to an exemplary embodiment of the present disclosure. As shown in Figure 8I, the winding arrangement in phase A is such that the tertiary winding 812 is the innermost winding and is located closest to the core legs, with three secondary windings 806 a1 ,806 a2 , and 806 a3 This is the outer winding, and the secondary winding 806 a3 It may include multiple nests and concentric windings such that the outermost winding is 806. a1 It is positioned as an intermediate winding between the two. The winding arrangement in Figure 8J is similar to the arrangement shown in Figure 8H, with the addition of a tertiary winding 812. As shown in Figure 8J, the tertiary winding 812 is the innermost winding, and the secondary winding 806 a1 ,806 a2 , and 806 a3 This set is the outermost winding. Primary winding 808A is connected to tertiary winding 812 and secondary winding 806. a1 ,806 a2 , and 806 a3 It is positioned as an intermediate winding between the sets. Secondary winding 806 a1 ,806 a2 , and 806a3 The set forms multiple rings around the primary winding 808A. Although the tertiary winding 812 is shown only with respect to phase A, it should be understood that the arrangements shown in Figures 8I and 8J are equally applicable and available for phases B and C of the Sen transformer 800. According to the exemplary embodiment in Figures 8I and 8J, the tertiary winding 812 is delta-connected, meaning that the tertiary winding 812 is a delta winding, with only one of its terminals exiting the transformer for grounding purposes. Furthermore, the tertiary winding 812 does not supply power to the load and is always closed. The tertiary winding remains closed, while the secondary winding 806 can be open during the LTC switching transition from one tap position to the next. a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 It acts as a safety measure under the condition of switching the upper tap. This condition creates an unbalanced current flow through the secondary winding, which is undesirable. The tertiary winding 812 has a zero-sequence impedance that creates a zero-sequence voltage drop when zero-sequence current flows through the tertiary winding. The tertiary winding 812 is a stabilizing winding that acts as a "bridge" when a switching transition occurs from one tap position to the next.

[0062] Figure 8K shows nine secondary windings (806) in a Sen transformer according to an exemplary embodiment of the present disclosure. a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3This indicates one of the following non-interleaved arrangements. Subwindings between any two tap positions of each secondary winding may be arranged in a non-interleaved arrangement. For example, the taps of each winding are associated with a sequential arrangement of tap sequences (i.e., 0-3 and 4-1).

[0063] Figure 8L shows nine secondary windings (806) in a Sen transformer according to an exemplary embodiment of the present disclosure. a1 ,806 a2 ,806 a3 ,806 b1 ,806 b2 ,806 b3 ,806 c1 ,806 c2 , and 806 c3 This indicates one of the interleaved arrangements. Subwindings between any two tap positions of each secondary winding may be arranged in an interleaved arrangement. For example, the taps of each winding are associated with a non-sequential arrangement of tap sequences (i.e., 0, 2, 3, 1 and 2, 4, 3, 1).

[0064] Figure 8M shows a winding arrangement for a set of three single-phase Sen transformers with tertiary windings according to an exemplary embodiment of the present disclosure. As shown in Figure 8M, the windings may be arranged such that for each single-phase transformer, the primary winding 808A, 808B, or 808C is the innermost winding (closest to the core) on one rim, with ID1 and OD1, and the tertiary winding 812, with ID5 and OD5, is also located closest to the core on another rim. For a single-phase transformer with an A-phase excitation voltage, the secondary winding 806 a1 These windings can be arranged concentrically on one of the excitation windings 808A (closest to the core) on a single rim. Furthermore, the secondary winding 806 a2 and 806 a3 It may be located on a tertiary winding 812 on another rim, and on a secondary winding 806 a3 This is the outermost winding, and the three windings 812, 806 a2 , and 806 a3 They are concentric on the same rim. In a single-phase transformer with a B-phase excitation voltage, the secondary winding 806 b2These windings can be arranged concentrically on one of the excitation windings 808B (closest to the core) on a rim. Furthermore, the secondary winding 806 b3 and 806 b1 It may be located on a tertiary winding 812 on another rim, and on a secondary winding 806 b1 This is the outermost winding, and the three windings 812, 806 b3 , and 806 b1 They are concentric on the same rim. Similarly, in a single-phase transformer with a C-phase excitation voltage, the secondary winding 806 c3 These windings can be arranged concentrically on one of the excitation windings 808C (closest to the core) on a rim. Furthermore, the secondary winding 806 c1 and 806 c2 It may be located on a tertiary winding 812 on another rim, and on a secondary winding 806 c2 This is the outermost winding, and the three windings 812, 806 c1 , and 806 c2 The windings are concentric on the same rim. Secondary windings connected to the same LTC have the same inner diameter (ID) and outer diameter (OD). For example, based on the winding arrangement shown in Figure 8M, secondary winding 806 has ID2 and OD2. a1 ,806 b2 , and 806 c3 However, secondary winding 806, which may be connected to LTC1 and has ID3 and OD3 a2 ,806 b3 , and 806 c1 However, secondary winding 806, which may be connected to LTC3 and has ID4 and OD4 a3 ,806 b1 , and 806 c2 However, it can be connected to LTC2.

[0065] Figure 8N shows a winding arrangement for a set of three single-phase Sen transformers with tertiary windings according to an exemplary embodiment of the present disclosure. As shown in Figure 8N, the windings may be arranged such that for each single-phase transformer, the primary winding 808A, 808B, or 808C is the innermost winding (closest to the core) on one rim, with ID1 and OD1, and the tertiary winding 812, with ID5 and OD5, is also located closest to the core on another rim. For a single-phase transformer with an A-phase excitation voltage, the secondary winding 806 a1 ,806 a2 , and 806 a3 The secondary winding forms multiple rings around the primary winding 808A. Each of the secondary windings has the same inner diameter (ID2) and outer diameter (OD2). In a single-phase transformer with a B-phase excitation voltage, the secondary winding 806 b2 ,806 b3 , and 806 b1 This forms multiple rings around the primary winding 808B. Each of the secondary windings has the same inner diameter (ID2) and outer diameter (OD2). Similarly, in a single-phase transformer with a C-phase excitation voltage, the secondary winding 806 c3 ,806 c1 , and 806 c2 This forms multiple rings around the primary winding 808C. Each of the secondary windings has the same inner diameter (ID2) and outer diameter (OD2).

[0066] The exemplary embodiments shown in Figures 8A to 8N disclose a core-type transformer structure in which the transformer windings are wound around a core. It should be understood that the exemplary embodiments of this disclosure are applicable to and can be implemented in a shell-type transformer structure in which the core encloses the transformer windings. Figures 8O and 8P show the winding arrangement of a core-type transformer compared to a shell-type transformer according to the exemplary embodiments of this disclosure. As shown in Figures 8O and 8P, the primary windings 808A, 808B, and 808C, and the secondary windings 806a, 806b, and 806c of the shell-type transformer are enclosed within the transformer core by an outer rim.

[0067] Figure 9A shows the theoretically possible compensation points for the modified transmit-end voltage using the Sen transformer 800. Figure 9B shows the corresponding active and reactive power flows at the receive end within the entire relative phase angle range of 0° ≤ β ≤ 360°. Figure 9B also shows that the maximum active power flow enhancement at the receive end is 0.40 pu (from 1 pu to 1.4 pu) in this particular example. Figure 9A shows that when the Sen transformer is used, the theoretically circular control area with a fixed compensation voltage of 0.20 pu is hexagonal. The more taps in the LTC, the closer the compensation points are to each other, and vice versa.

[0068] Figure 9A shows the modified transmit-end voltage phasor V s’ , also showing the location of the tip. Figure 9B shows the active and reactive power flows (P) according to an exemplary embodiment of the present disclosure. r and Q r The operating points are shown. Each modified transmit-end voltage operating point shown in Figure 9A corresponds to the power flow operating point in the PQ plane shown in Figure 9B. A subset of the operating points (1, 7, 19, 37, 4, 13, 28, and 49) represents the operating points of the voltage regulator (VR). The VR operating points lie on a straight line relating to relative phase angles β=0° and β=180°, while the Sen Transformer 800 operating point is in a two-dimensional operating plane. In practical applications, the desired active and reactive power flows (PQ) from 61 possible operating points are used. r and Q r ) For the requirements, the corresponding modified transmit terminal voltage (V s’ The phasor tip may be mapped in Figure 9A, and an appropriate tap position for the LTC may be selected from the table shown in Figures 10A to 10E.

[0069] Figures 9C and 9D show the modified transmit-end voltage operating point for limited relative phase angle operation within the range of β=0° to β=120°, as well as the respective active and reactive power flows (P r and Q r The operating point is indicated. The relative phase angle operation at β=60° provides the maximum active power flow operating point.

[0070] Figures 9E and 9G show the Sen transformer of Figure 8A configured for limited relative phase angle operation in the range β=0° to β=120° according to an exemplary embodiment of the present disclosure for a voltage operating point as shown in Figure 9F. As shown in Figure 9E, since the Sen transformer 800 is configured to operate within the limited relative phase angle range β=0° to β=120°, the compensating voltage unit 804 may be modified by removing secondary windings associated with phases outside the relative phase angle range of interest. For example, in the compensating voltage unit 804 of Figure 9E, secondary windings 806b1, 806c2, and 806a3 may be deactivated during operation or omitted or removed from the transformer configuration. Omitting or removing secondary windings from the transformer, or deactivating them during operation, can result in more thermally efficient operation of the Sen transformer 800. Furthermore, omission and / or removal may lead to a reduction in the size and cost of the transformer. The tap positions for load tap changers LTC1 and LTC3 for the maximum active power flow operating point of the Sen transformer 800 (1.4 pu in this particular example) are shown in Figures 9H and 9I. Since one secondary winding corresponding to a phase outside a limited range of phase angles is deactivated during operation or omitted or removed from the transformer configuration as already described, only two tap changers are required for operation.

[0071] Figures 9J and 9K show the modified transmit-end voltage operating point for limited relative phase angle operation at β=240°, which provides the minimum active power flow operating point, as well as the respective active and reactive power flows (P r and Q r ) Indicates the operating point.

[0072] Figures 9L and 9N show the Sen transformer of Figure 8A for limited relative phase angle operation at β=240° according to an exemplary embodiment of the present disclosure for a voltage operating point as shown in Figure 9M. As shown in Figure 9L, since the Sen transformer 800 is configured to operate in limited relative phase angle operation at β=240°, the compensating voltage unit 804 may be modified by removing secondary windings associated with phases outside the relative phase angle of interest. For example, in the compensating voltage unit 804 of Figure 9L, secondary windings 806a1, 806c1, 806a2, 806b2, and 806b3, 806c3 may be deactivated during operation or omitted or removed from the transformer configuration. Omitting or removing secondary windings from the transformer, or deactivating them during operation, can result in more thermally efficient operation of the Sen transformer 800. Furthermore, omission and / or removal may lead to a reduction in the size and cost of the transformer. The tap position for the load tap changer LTC2 for the minimum active power flow operating point of the Sen transformer 800 (0.6 pu in this particular example) is shown in Figure 9O. Since the two secondary windings corresponding to phases outside the limited phase angle are deactivated during operation or removed or omitted from the transformer configuration as already described, only one tap changer is required for operation.

[0073] Figures 9P and 9Q show the modified transmit-end voltage operating point for limited relative phase angle operation at β=60°, which provides the maximum active power flow operating point, as well as the respective active and reactive power flows (P r and Q r ) Indicates the operating point.

[0074] Figures 9R and 9T show the secondary winding 806 b1 ,806 c2 , and 806 a3Figure 8A shows a Sen transformer for limited relative phase angle operation at β=60° according to an exemplary embodiment of the present disclosure, for a voltage operating point as shown in Figure 9S, when the voltage applied to is reversed using switch 901. As shown in Figure 9R, since the Sen transformer 800 is configured to operate in limited relative phase angle operation at β=60°, the compensating voltage unit 804 may be modified by removing secondary windings associated with phases outside the phase angle of interest. For example, in the compensating voltage unit 804 of Figure 9R, secondary windings 806a1, 806c1, 806a2, 806b2, and 806b3, 806c3 may be disabled during operation or omitted or removed from the transformer configuration. The tap positions for the load tap changer LTC2 for the maximum active power flow operating point of the Sen transformer 800 (1.4 pu in this particular example) are shown in Figure 9U. Since the two secondary windings corresponding to phases outside the limited phase angle are either deactivated during operation or omitted or removed from the transformer configuration as already described, only one tap changer is required for operation.

[0075] Figures 9V and 9W show the modified transmit-end voltage operating point for limited relative phase angle operation within the range of β=0° to β=120°, with a feature enabled to double the maximum active power flow enhancement, as well as the respective active and reactive power flows (P r and Q r The operating point is shown. Figure 9W also shows that the maximum active power flow enhancement at the receiving end is 0.80 pu (from 1 pu to 1.8 pu) in this particular example.

[0076] Figures 9X and 9Z show the Sen transformer of Figure 8A configured for limited relative phase angle operation in the range of β=0° to β=120°, with the feature of doubling the maximum active power flow enabled, according to an exemplary embodiment of the present disclosure for a voltage operating point as shown in Figure 9Y. The tap positions for load tap changers LTC1, LTC2, and LTC3 for the doubling maximum active power flow enhancement operating point of the Sen transformer 800 (1.8 pu in this particular example) are shown in Figures 9AA to 9AC.

[0077] Figure 11 shows an exemplary winding layout and the distribution of ampere turns at β=0° according to an exemplary embodiment of the present disclosure. As shown in Figures 8D and 11, primary windings A, B, and C, and secondary winding 806 associated with LTC1. a1 ,806 b2 , and 806 c3 This is enabled, and LTC2 and LTC3 are set at their minimum tap positions. A magnetomotive force (mmf) is generated in the primary winding and applied across the secondary winding associated with LTC1.

[0078] Figure 12 shows an exemplary winding layout and the distribution of ampere turns at β=60° according to an exemplary embodiment of the present disclosure. As shown in Figures 8D and 12, primary windings A, B, and C, and secondary winding 806 associated with LTC1. a1 ,806 b2 , and 806 c3 , as well as secondary winding 806 associated with LTC3 c1 ,806 a2 , and 806 b3 It is enabled, and LTC2 is set at its minimum tap position. mmf is generated in the primary winding and applied across the secondary windings associated with LTC1 and LTC3.

[0079] Figure 13 shows an exemplary winding layout and the distribution of ampere turns at β=120° according to an exemplary embodiment of the present disclosure. As shown in Figures 8D and 13, primary windings A, B, and C, and secondary winding 806 associated with LTC3. c1 ,806 a2 , and 806 b3 This is enabled, and LTC1 and LTC2 are set at their minimum tap positions. mmf is generated in the primary winding and applied across the secondary winding associated with LTC3.

[0080] Figure 14 shows an exemplary winding layout and the distribution of ampere turns at β=180° according to an exemplary embodiment of the present disclosure. As shown in Figures 8D and 14, primary windings A, B, and C, and secondary winding 806 associated with LTC3. c1 ,806 a2 , and 806 b3 The secondary windings 806b1, 806c2, and 806a3 associated with LTC2 are enabled, and LTC1 is set at its minimum tap position. mmf is generated in the primary winding and applied across the secondary windings associated with LTC3 and LTC2.

[0081] Figure 15 shows an exemplary winding layout and the distribution of ampere turns at β=240° according to an exemplary embodiment of the present disclosure. As shown in Figures 8D and 15, primary windings A, B, and C, and secondary winding 806 associated with LTC2. b1 ,806 c2 , and 806 a3 This is enabled, and LTC1 and LTC3 are set at their minimum tap positions. mmf is generated in the primary winding and applied across the secondary winding associated with LTC2.

[0082] Figure 16 shows an exemplary winding layout and the distribution of ampere turns at β=300° according to an exemplary embodiment of the present disclosure. As shown in Figures 8D and 16, primary windings A, B, and C, and secondary winding 806 associated with LTC2. b1 ,806 c2 , and 806 a3 , as well as secondary winding 806 associated with LTC1 a1 ,806 b2 , and 806 c3 It is enabled, and LTC3 is set at its minimum tap position. mmf is generated in the primary winding and applied across the secondary windings associated with LTC2 and LTC1.

[0083] Figures 17A to 17AN show a Sen transformer having a winding arrangement in a shunt-shunt configuration according to an exemplary embodiment of the present disclosure. As shown in Figures 17A and 17B, the Sen transformer 1700 includes an exciter unit 1702 and a compensating voltage unit 1704 arranged in a shunt-shunt configuration. Figure 17A shows the Sen transformer 1700, the single-phase exciter unit 1702, and three compensating windings 1706 in a single-phase configuration. a , 1706 b , 1706 c Figures 17C and 17E show the Sen transformer of Figure 17A in a three-phase configuration. The exciter unit 1702 in Figures 17C and 17E consists of three shunt Y-connected primary windings 1708A, 1708B, and 1708C, and the exciter unit 1704 consists of nine secondary windings (three windings in each phase, i.e., 1706 on the core of phase A). a1 , 1706 a2 , and 1706 a3 , 1706 on the core of phase B b1 , 1706 b2 , and 1706 b3 , and 1706 on the core of the C phase c1 , 1706 c2 , and 1706 c3 ) consists of 3-phase transmitting terminal voltage (V sA , V sB , and V sC A voltage is applied to the exciter unit 1702. The Sen transformer 1700 can achieve the power flow operating point shown in Figures 10A to 10E by calculating the sum of the three available induced voltages from phases A, B, and C of the primary windings (one or more) of the exciter unit 1702, which are 120° apart. The Sen transformers in Figures 17A, 17C, and 17E also include LTC1710 (LTC1, LTC2, and LTC3). When using LTCs, the effective number of turns in each compensating winding in each phase is varied, and the combined voltage is variable in magnitude and phase angle.

[0084] According to an exemplary embodiment, the transmitting terminal voltage for the Sen transformer 1700 is V sThe allowable magnitude (V) of the induced voltage (V) can be 1 pu and should be 0.2 pu, and the voltage (x) across each tap of LTC1710 is 0.05 pu, with N=4 taps associated with each secondary winding 1706a1, 1706a2, 1706a3, 1706b1, 1706b2, 1706b3, 1706c1, 1706c2, and 1706c3. Thus, each of the taps in LTC2 and LTC3 is set at 0, 1, 2, 3, or 4, and the corresponding secondary winding is effective by only 0, 5, 10, 15, or 20%, respectively, contributing 0.0, 0.05, 0.10, 0.15, or 0.20 pu to form the compensation voltage. However, each of the taps in LTC1 is set to 0, 1, 2, 3, or 4, and the corresponding secondary winding is effective only at 100, 105, 110, 115, or 120%, respectively, with a compensation voltage V s’A , V s’B , and V s’C It contributes 1.00, 1.05, 1.10, 1.15, or 1.20 pu to forming [the specified value].

[0085] Combined voltage (V s’ ) can be at any phase angle with respect to the current line current (I). Therefore, the active and reactive powers (P) exchanged between the line and shunt are 2sh and Q 2sh A compensating voltage (V) at an arbitrary phase angle with respect to the current line current flows bidirectionally through the magnetic core. s’ The ) acts as an impedance regulator (IR). The exciter controls the line and active and reactive power (P 1sh and Q 1sh Note that the ) is replaced and flows bidirectionally through the magnetic core.

[0086] As shown in Figures 17E to 17H, the secondary winding (1706 a1 , 1706 b2 , and 1706 c3 Each of the ) is tapped through LTC1 at the same number of turns, winding (1706 b1 , 1706 c2 , and 1706 a3Each of the ) is tapped through LTC2 at the same number of turns, winding (1706 c1 , 1706 a2 , and 1706 b3 Each of these is tapped through LTC3 with the same number of turns. However, the number of turns in each set of secondary windings for LTC1, LTC2, and LTC3 may differ from one another.

[0087] As shown in Figures 17B and 17D, the number of turns from each of the three windings is selected through the three LTCs (LTC1, LTC2, and LTC3), and therefore the magnitude of the three 120° phase-shifted induced voltage components is selected, thereby obtaining the compensation voltage (V) in any phase. s’ ) is a 3-phase secondary winding set (1706 for compensation in phase A) a1 , 1706 b1 , and 1706 c1 , 1706 for compensation in Phase B a2 , 1706 b2 , and 1706 c2 , and 1706 for compensation in Phase C a3 , 1706 b3 , and 1706 c3 It is derived from the phasor sum of the voltages induced in ).

[0088] According to an exemplary embodiment, each of the taps in LTC1, LTC2, and LTC3 may be set to 0, 1, 2, 3, or 4. Each of the secondary windings associated with LTC2 and LTC3 may be effective only 0, 5, 10, 15, or 20%, respectively, and may contribute 0.0, 0.05, 0.10, 0.15, or 0.20 pu to forming the compensation voltage. At the same time, each of the secondary windings associated with LTC1 may be effective only 100, 105, 110, 115, or 120%, respectively, and the compensation voltage V s’A , V s’B , and V s’C It contributes 1.00, 1.05, 1.10, 1.15, or 1.20 pu to forming [the specified value].

[0089] Based on the exemplary winding configuration in Figure 8A, the Sen transformer 1700 operates as follows: • ψ=0° and V s’ >V s In that case, only LTC1 is required to operate. • ψ=0° and V s’ <V s In that case, only LTC2 and LTC3 are required to be operational. ψ A ψ B , and ψ C This is the corrected phase shift angle of the transmit end voltage with respect to the transmit end voltage in phases A, B, and C.

[0090] As shown in Figures 17E and 11, the phase shift angle and V are 0°. s’ >V s When selecting an operating point having primary windings A, B, and C, and secondary winding 1706 associated with LTC1 of Sen transformer 1700, a1 , 1706 b2 , and 1706 c3 The taps are active (i.e., tap positions 1, 2, 3, or 4), and LTC2 and LTC3 are set at their minimum tap position (i.e., tap position 0). A magnetomotive force (mmf) is generated in the primary winding and applied across the secondary winding associated with LTC1.

[0091] As shown in Figures 17E and 12, when selecting an operating point with a phase shift angle of 2.42°, 4.72°, 6.89°, or 8.95°, primary windings A, B, and C, and secondary winding 1706 associated with LTC1 are used. a1 , 1706 b2 , and 1706 c3 , as well as secondary winding 1706 associated with LTC3 c1 , 1706 a2 , and 1706 b3 It is enabled, and LTC2 is set at its minimum tap position. mmf is generated in the primary winding and applied across the secondary windings associated with LTC1 and LTC3.

[0092] As shown in Figures 17E and 13, when selecting an operating point with a phase shift angle of 2.54°, 5.21°, 7.99°, or 10.89°, primary windings A, B, and C, and secondary winding 1706 associated with LTC3 are used. c1 , 1706 a2 , and 1706 b3 This is enabled, and LTC1 and LTC2 are set at their minimum tap positions. mmf is generated in the primary winding and applied across the secondary winding associated with LTC3.

[0093] As shown in Figures 17E and 14, the phase shift angle and V are 0°. s’ <V s When selecting an operating point having primary windings A, B, and C, and secondary winding 1706 associated with LTC3, c1 , 1706 a2 , and 1706 b3 The secondary windings 1706b1, 1706c2, and 1706a3 associated with LTC2 are enabled, and LTC1 is set at its minimum tap position. mmf is generated in the primary winding and applied across the secondary windings associated with LTC3 and LTC2.

[0094] As shown in Figures 17E and 15, when selecting an operating point with a phase shift angle of -2.54°, -5.21°, -7.99°, or -10.89°, primary windings A, B, and C, and secondary winding 1706 associated with LTC2 are used. b1 , 1706 c2 , and 1706 a3 This is enabled, and LTC1 and LTC3 are set at their minimum tap positions. mmf is generated in the primary winding and applied across the secondary winding associated with LTC2.

[0095] As shown in Figures 17E and 16, when selecting an operating point with a phase shift angle of -2.42°, -4.72°, -6.89°, or -8.95°, primary windings A, B, and C, and secondary winding 1706 associated with LTC2 are used. b1 , 1706 c2 , and 1706 a3 , as well as secondary winding 1706 associated with LTC1 a1 , 1706 b2 , and 1706 c3 This is enabled, and LCT3 is set at its minimum tap position. mmf is generated in the primary winding and applied across the secondary windings associated with LTC2 and LTC1.

[0096] Figure 17I shows Sen transformer 1700 configured for a modified transmit-end voltage with the same operating point as shown in Figure 17A. As shown in Figure 17I, all taps on the compensating voltage windings 1706a, 1706b, and 1706c of the compensating voltage unit 1704 are configured to operate closer to ground potential. This configuration can be compared to the transformer configuration shown in Figure 17A, where the taps on the compensating voltage windings 1706b and 1706c are configured to operate closer to ground potential as shown in Figure 17A, but the tap on the compensating voltage winding 1706a of the compensating voltage unit 1704 is configured to operate closer to ground potential, not closer to line potential as shown in Figure 17A. Both Figures 17A and 17I are set up for operation at the same operating point as shown in the corresponding phasor diagrams in Figures 17B and 17J. As explained with respect to the transformer in Figure 17A, moving the contacts (LTC1) of the compensating voltage winding 1706a to higher tap positions in the direction toward the dot (e.g., 0→1, 1→2, 2→3, 3→4, etc.) increases the compensating voltage in winding 1706a of the compensating voltage unit 1704. However, the transformer in Figure 17I operates differently in that moving the contacts (LTC1) of the compensating voltage winding 1706a to higher tap positions in the direction toward the dot (e.g., 0→1, 1→2, 2→3, 3→4, etc.) increases the compensating voltage in winding 1706a of the compensating voltage unit 1704. However, both Figures 17A and 17I show that moving the contacts (LTC2 and LTC3) of the compensating voltage windings 1706b and 1706c to higher tap positions in the direction toward the dot (e.g., 0→1, 1→2, 2→3, 3→4, etc.) increases the compensating voltage in windings b and c of the compensating voltage unit 1704. That is, in Figure 17A, the compensating voltage is increased in each of the secondary windings by moving the contacts of the LTC1, LTC2, and LTC3 tap positions in the same direction toward the dot.For the same operating point using the transformer in Figure 17I, the compensating voltage is increased by changing the direction of the tap movement for LTC1 to a higher tap position away from the dot, unlike the corresponding directional movement for LTC2 and LTC3 toward the dot to a higher tap position.

[0097] Figures 17K and 17M show the Sen transformer of Figure 17I in a three-phase configuration for any voltage operating point as shown in Figure 17L. The tap positions for load tap changers LTC1, LTC2, and LTC3 for any operating point of the Sen transformer 1700 are shown in Figures 17N to 17P. In the compensating voltage unit 1704, the compensating voltages of the secondary windings 1706a1, 1712b2, and 1714c3 can be increased by moving the contacts of LTC1 to higher tap positions in the direction away from the dot (e.g., 0→1, 1→2, 2→3, 3→4, etc.). In the secondary windings 1706b1, 1706c1, 1706a2, 1706c2, 1706a3, and 1706b3, the compensation voltage can be increased by moving the contacts of LTC2 and LTC3 to higher tap positions in the direction toward the dot (e.g., 0→1, 1→2, 2→3, 3→4, etc.).

[0098] Figures 17Q and 17R show modified transmit-end voltage operating points numbered 0 to 60, and their respective active and reactive power flows (P), according to exemplary embodiments of the present disclosure, with 10% allowable upper and lower voltage limits. r and Q r ) Indicates the operating point.

[0099] Figure 17S shows each of the LTC1 taps for the transformer configuration in Figure 17I, set at -1, 0, 1, 2, or 3, with the corresponding secondary windings being effective at 95, 100, 105, 110, or 115%, respectively, and the compensation voltage V s’A , V s’B , and V s’CIt contributes 0.95, 1.00, 1.05, 1.10, or 1.15 pu to forming. The operating point shown in Figure 17T is the same as that in Figure 17B or Figure 17J.

[0100] Figures 17U and 17W show the winding configuration of the Sen transformer in Figure 17S in a three-phase arrangement for the voltage operating point shown in Figure 17V. The tap positions for the load tap changers LTC1, LTC2, and LTC3 for any operating point of the Sen transformer 1700 are shown in Figures 17X to 17Z. The secondary windings in each phase are configured to produce the modified transmit-end voltage, as already described in Figure 17I.

[0101] Figures 17AA and 17AB show a modified set of transmit-end voltage operating points in the power flow increase region according to an exemplary embodiment of the present disclosure, as well as the respective active and reactive power flows (P r and Q r The operating point is shown. As shown in Figures 17AA and 17AB, the power flow increase region is operable in a relative phase angle range of approximately β=0° to β=120°.

[0102] Figures 17AC and 17AE show a Sen transformer in a three-phase configuration for a voltage operating point as shown in Figure 17AD, requiring only six compensating secondary windings. Based on the winding configuration of the compensating voltage unit 1704, the phase angle range also corresponds to the power flow increase region. Since the Sen transformer 1700 is configured to operate within a limited phase angle range as shown in Figures 17AA and 17AB, the compensating voltage unit 1704 can be modified by removing or deactivating secondary windings associated with phases outside the phase angle range of interest. For example, in the compensating voltage unit 1704 of Figure 17AC, secondary windings 1706b1, 1706c2, and 1706a3 can be deactivated or omitted / removed from the transformer configuration. The deactivated secondary windings are grouped with LTC2. The tap positions for load tap changers LTC1 and LTC3 for any operating point of the Sen transformer 1700 are shown in Figures 17AF to 17AG. Since one secondary winding corresponding to a phase outside the limited range of phase angles of interest is disabled during operation or omitted or removed from the transformer configuration as already described, only two tap changers are required for operation.

[0103] Figures 17AH and 17AI show a modified set of transmit-end voltage operating points in the power flow reduction region according to an exemplary embodiment of the present disclosure, as well as the respective active and reactive power flows (P r and Q r The operating point is shown. As shown in Figures 17AH and 17AI, the power flow reduction region is operable in a relative phase angle range of approximately β=240° to β=360°.

[0104] Figures 17AJ and 17AL show a Sen transformer in a three-phase configuration for a voltage operating point as shown in Figure 17AK, requiring only six compensating secondary windings. Based on the winding configuration of the compensating voltage unit 1704, the phase angle range also corresponds to the power flow reduction region. Since the Sen transformer 1700 is configured to operate within a limited phase angle range as shown in Figures 17AH and 17AI, the compensating voltage unit 1704 can be modified by removing or deactivating secondary windings associated with phases outside the phase angle range of interest. For example, in the compensating voltage unit 1704 of Figure 17AJ, secondary windings 1706c1, 1706a2, and 1706b3 can be deactivated or omitted / removed from the transformer configuration. The deactivated secondary windings are grouped with LTC3. The tap positions for load tap changers LTC1 and LTC2 for any operating point of the Sen transformer 1700 are shown in Figures 17AM to 17AN. Since one secondary winding corresponding to a phase outside the limited range of phase angles of interest is disabled during operation or omitted or removed from the transformer configuration as previously described, only two tap changers are required for operation.

[0105] Controlling power flow in a single line using a power flow controller with a shunt-series or shunt-shunt configuration has a side effect: neighboring lines must adjust their power flows to maintain an unchanging overall power flow from source to load. However, power from one line can be precisely transmitted to another line through a series-series configuration without altering the power flow in any other line.

[0106] Figure 18A shows a single-line diagram of a Sen transformer in a series-series configuration according to an exemplary embodiment of the present disclosure. As shown in Figure 18A, the Sen transformer 1800 includes an exciter unit 1802 and two compensating voltage units 1804A and 1804B connected in series with the exciter unit 1802. Each compensating voltage in the “leader” line is of any magnitude within its permissible limits and at any phase angle with respect to the line voltage and current line current, so that the active and reactive power flows in that line can be controlled independently as needed. Furthermore, each series compensating voltage in the “follower” line is of a specific magnitude and phase angle with respect to the current line current, so that the active and reactive power from the “leader” line are transmitted bidirectionally to the “follower” line. This technique provides desirable power flow management for multi-line transmission systems by reducing power flow in overloaded lines and increasing power flow in underloaded lines, with minimal impact on other uncompensated lines.

[0107] Figure 18B shows a Sen transformer 1800 having a series-series connection between the exciter unit 1802 and the compensating voltage units 1804A and 1804B. As shown in Figure 18B, the line voltage (V s ) is applied to the Y-connected primary windings 1808A, 1808B, and 1808C of the shunt-connected three-phase transformer in the exciter unit 1802. A total of nine secondary windings (1806 on the A-phase core) a11 , 1806 a12 , and 1806 a13 , 1806 on the core of phase B b11 , 1806 b12 , and 1806 b13 , and 1806 on the core of the C phase c11 , 1806 c12 , and 1806 c13 In the compensation voltage unit 1804A, which has a 3-phase compensation voltage, each phase is deriveted from a 3-winding set (1806 for the compensation voltage in phase A). a11 , 1806 b11 , and 1806 c11 , 1806 for compensation voltage in phase B a12 , 1806b12 , and 1806 c12 , and 1806 for compensation voltage in phase C a13 , 1806 b13 , and 1806 c13 This is the phasor sum of the voltages induced in ). The combined compensation voltage magnitude and relative phase angle with respect to the line voltage can be selected by selecting the number of turns from each of the three windings via the respective LTC control for each group (LTC1, LTC2, and LTC3), and therefore the magnitude of the three 120° phase-shifted induced voltage components. A total of nine secondary windings (1806 on the core of phase A). a21 , 1806 a22 , and 1806 a23 , 1806 on the core of phase B b21 , 1806 b22 , and 1806 b23 , and 1806 on the core of the C phase c21 , 1806 c22 , and 1806 c23 In the compensation voltage unit 1804B, which has a 3-phase compensation voltage, each phase is a 3-winding set (1806 for the compensation voltage in phase A). a21 , 1806 b21 , and 1806 c21 , 1806 for compensation voltage in phase B a22 , 1806 b22 , and 1806 c22 , and 1806 for compensation voltage in phase C a23 , 1806 b23 , and 1806 c23 This is the phasor sum of the voltages induced in ). The combined compensation voltage magnitude and relative phase angle with respect to the line voltage can be selected by selecting the number of turns from each of the three windings via the respective LTC control for each group (LTC1, LTC2, and LTC3), and therefore the magnitudes of the three 120° phase-shifted induced voltage components.

[0108] Figure 19 shows a generalized Sen transformer (GST) configured to generate both shunt-compensated voltage and series-compensated voltage in a single unit, according to an exemplary embodiment of the present disclosure. As shown in Figure 19, the GST 1900 includes an exciter unit 1902 and a compensating voltage unit 1904. The compensating voltage unit 1904 is connected to a plurality of shunt compensator units 1906 m and multiple series compensator units 1908 n This includes each shunt compensator unit 1906. m and series compensator unit 1908 n Each is connected to its respective power line. Series Compensator Unit 1908 n It is configured to independently control the active and reactive power flows in each line and to transmit active and reactive power from one or more "leader" lines to one or more "follower" lines. Shunt Compensator Unit 1906 m It is configured to independently control the active and reactive power flows in each line and to connect isolated networks with different voltages and phase angles to transmit active and reactive power from one or more "leader" lines to one or more "follower" lines. Series Compensator Unit 1908 n and shunt compensator unit 1906 m Each of these is induced from the excitation voltage through the transformer action. Therefore, the mismatch between active and reactive power between the various compensation voltages flows into the lines supplying the excitation unit 1902 of the GST1900.

[0109] Control 1910 and / or control operations for switching the LTC based on a desired operating point may be performed by a computing device. According to exemplary embodiments, the computing device may include one or more processing devices, as necessary, such as a microprocessor, a central processing unit, a microcomputer, a programmable logic unit, or any other suitable hardware processing device. The computing device may consist of computer program code for performing the specific functions described herein. The program code may be stored in a computer-usable medium, which may refer to memory, such as a memory device for the computing device, which may be a memory semiconductor (e.g., DRAM). These computer program products may be tangible, non-transient means for providing software to various hardware components of each device as necessary to perform the tasks associated with the exemplary embodiments described herein. The computer program (e.g., computer control logic) or software may be stored in a memory device. According to exemplary embodiments, the computer program may also be received and / or accessed remotely via other components of the computing device, such as a receiver or receiving device. Such a computer program, when executed, can enable a processor to implement the Method and the exemplary embodiments described herein, and may represent a controller of the processor. If the Disclosure is implemented using software, the software may be stored on a non-temporary computer-readable medium and, where applicable, may be loaded onto a computing device using a removable storage drive, interface, hard disk drive, or communication interface, etc.

[0110] One or more processors in a computing device may include one or more modules or engines configured to perform the functions of the exemplary embodiments described herein. Each of these modules or engines may be implemented using hardware, and in some cases, software may also be available, such as program code and / or programs stored in memory. In such cases, the program code may be compiled by each processor (e.g., by a compilation module or engine) before execution. For example, the program code may be source code written in a programming language that is translated into a lower-level language, such as assembly language or machine code, for execution by one or more processors and / or any additional hardware components. The compilation process may include the use of any other techniques that may be suitable for lexical analysis, preprocessing, parsing, semantic analysis, syntactic-oriented translation, code generation, code optimization, and translation of the program code into a lower-level language suitable for controlling the computing device to perform the functions disclosed herein. It will be apparent to those skilled in the art that such a process results in a computing device which is a specially configured computing device independently programmed to perform the functions described above.

[0111] Figure 20 shows a method for generating a compensating voltage according to an exemplary embodiment of the present disclosure. The method may be implemented through a transformer configured as shown in Figures 8A, 17C, 17K, 17U, 17AC, 17AJ, 18B, or 19. As shown in the above figures, the transformer has an exciter unit and a compensating voltage unit. The exciter unit includes a three-phase transformer with a shunt Y-connected primary winding. The compensating voltage unit includes a plurality of series-connected secondary windings, each containing one secondary winding from each phase of the exciter unit. The compensating voltage unit also includes a plurality of load tap changers. Each load tap changer is associated with a group of secondary windings, each containing one secondary winding from each phase of the exciter unit. According to the exemplary embodiment, each secondary winding is assigned to a group of secondary windings, and each secondary winding is located at the same distance (i.e., positioned) from the associated primary winding of the exciter unit. In another exemplary embodiment, all secondary and sub-windings between two consecutive taps in the compensating voltage unit and the primary winding in the exciter unit have substantially similar heights. The sub-windings may or may not be interleaved. When performing this method, the controller is configured to select the operating point of the transformer (step 2000). The operating point may be selected based on inputs received by the controller (e.g., 1910) from an operator or user. Figures 10A to 10E show various operating points for generating a compensating voltage according to one or more parameters of the transformer. In another exemplary embodiment, the inputs may be automatically generated by an external computing system configured to monitor the operation of the power system and automatically select the operating point based on the desired power flow control. Based on the selected operating point, the controller (e.g., 1910) selects, based on the operating point, a load tap position for each secondary winding in the group of secondary windings associated with each load tap changer (step 2010). The transformer's compensation voltage unit generates the compensation voltage by calculating the sum of the effective voltages induced in the secondary winding group for each load tap changer (step 2020).Figures 11 to 16 show the resulting compensation voltages generated by the secondary winding of the compensation voltage unit for each operating point. This operation can be repeated when the conditions in (one or more) power lines, grids, and / or the desired compensation voltage change.

[0112] Those skilled in the art will understand that the present invention can be embodied in other specific forms without departing from its spirit or essential characteristics. Accordingly, the embodiments of this disclosure are considered illustrative and not restrictive in all respects. The scope of the present invention is indicated not by the above description but by the appended claims, encompassing all modifications that fall within their meaning, scope, and equivalence.

Claims

1. A transformer that generates a compensation voltage, wherein the transformer is Excitator unit and Compensation voltage unit and Equipped with, The excitation unit includes three single-phase transformers, or a three-phase transformer having a shunt Y-connected primary winding. The aforementioned compensation voltage unit is Multiple secondary windings connected in series, including one secondary winding from each phase of the excitation unit, Multiple load tap changers, each load tap changer associated with a group of secondary windings including one secondary winding from each phase of the excitation unit, each secondary winding in the group of secondary windings being at the same distance from the associated primary winding of the excitation unit, all windings being of similar height, and each load tap changer configured to vary the effective number of turns of the associated group of secondary windings by connecting to one of a plurality of taps associated with each secondary winding according to a selected operating point. A transformer, including one.

2. The excitation unit and the compensation voltage unit are electrically connected in a shunt-series configuration. The transformer according to claim 1, comprising:

3. The excitation unit and the compensation voltage unit are electrically isolated in a shunt-shunt configuration. The transformer according to claim 1, comprising:

4. The excitation unit is connected to a transmission line and a plurality of compensation voltage units, and each compensation voltage unit is electrically connected to one of the plurality of transmission lines, in a series-to-series configuration. The transformer according to claim 1, comprising:

5. The transformer according to claim 1, wherein the compensation voltage is the sum of the effective voltages induced by the plurality of secondary windings for each phase in the compensation voltage unit.

6. The transformer according to claim 1, wherein the plurality of taps associated with each secondary winding are separated at x% intervals.

7. The transformer according to claim 6, wherein x is an integer value such that x > 0.

8. The transformer according to claim 5, based on the spacing arrangement of five taps numbered 0, 1, 2, 3, and 4, and each tap being isolated by 5%, wherein the effective voltage in each secondary winding varies as follows: the series compensation voltage varies in magnitude from 0 to 20% of the primary voltage and in relative phase angle from 0° to 360°, and the shunt compensation voltage varies in magnitude from 80 to 120% of the primary voltage and in phase shift angle from -ψ to +ψ.

9. The transformer according to claim 1, wherein the load tap changer is configured as a single-phase load tap changer, and the three single-phase load tap changers are connected to the same number of turns in the group of the secondary winding.

10. The transformer according to claim 1, wherein the load tap changer is configured as a plurality of three-phase load tap changers, and each load tap changer is connected to the same number of turns in the group of secondary windings.

11. The aforementioned compensation unit is A tertiary winding for each phase, wherein the tertiary windings for the three phases are delta-connected, and only one terminal exits the transformer for grounding purposes. The transformer according to claim 1, further comprising:

12. The transformer according to claim 11, wherein each tertiary winding is the innermost winding adjacent to the core of the transformer.

13. The transformer according to claim 11, wherein the tertiary winding is configured to enable the circulation of zero-sequence current.

14. A method for generating a compensating voltage through a transformer having an exciter unit and a compensating voltage unit, the exciter unit comprising: a plurality of series-connected secondary windings, each comprising one secondary winding from each phase of the exciter unit; and a plurality of load tap changers, each load tap changer associated with a group of secondary windings, each comprising one secondary winding from each phase of the exciter unit, each secondary winding in the group of secondary windings being at the same distance from the associated primary winding of the exciter unit, and all windings being at similar heights; the method is, Selecting the operating point of the transformer, Based on the aforementioned operating point, the load tap position is selected for each secondary winding in the group of secondary windings associated with each load tap changer, A compensation voltage is generated by calculating the sum of the effective voltages induced in the aforementioned group of secondary windings for each load tap changer. Methods that include...

15. The method according to claim 14, wherein each three-phase load tap changer varies the magnitude of the series compensation voltage and the relative phase angle of the series compensation voltage based on the selected load tap position.

16. Each secondary winding has a total of five taps separated at 5% intervals, and the method is The magnitude of the series compensation voltage is varied from 0% to 20% of the primary voltage. The method according to claim 15, further comprising:

17. The relative phase angle of the series compensation voltage is varied between 0° and 360°. The method according to claim 15, further comprising:

18. The relative phase angle of the series compensation voltage is varied between 0° and 120°, Using an additional switch on the transformer, the voltage applied to the secondary winding is reversed in order to double the maximum active power flow enhancement at a relative phase angle of 60°. The method according to claim 15, further comprising:

19. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a relative phase angle of 0°, The first load tap changer is set to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The second load tap changer is set to connect load tap position 0 on each secondary winding, The third load tap changer is set to connect load tap position 0 on each secondary winding. The method according to claim 17, including the method described in claim 17.

20. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a relative phase angle of 60°, The first load tap changer is set to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The second load tap changer is set to connect load tap position 0 on each secondary winding, The third load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding. The method according to claim 17, including the method described in claim 17.

21. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a relative phase angle of 120°, The first load tap changer is set to connect load tap position 0 on each secondary winding, The second load tap changer is set to connect load tap position 0 on each secondary winding, The third load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding. The method according to claim 17, including the method described in claim 17.

22. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a relative phase angle of 180°, The first load tap changer is set to connect load tap position 0 on each secondary winding, The second load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The third load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding. The method according to claim 17, including the method described in claim 17.

23. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a relative phase angle of 240°, The first load tap changer is set to connect load tap position 0 on each secondary winding, The second load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The third load tap changer is set to connect load tap position 0 on each secondary winding. The method according to claim 17, including the method described in claim 17.

24. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a relative phase angle of 300°, The first load tap changer is set to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The second load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The third load tap changer is set to connect load tap position 0 on each secondary winding. The method according to claim 17, including the method described in claim 17.

25. The method according to claim 14, wherein each three-phase load tap changer varies the magnitude of the shunt compensation voltage and the phase shift angle of the shunt compensation voltage based on the selected load tap position.

26. Each secondary winding has a total of five taps separated at 5% intervals, and the method is The magnitude of the shunt compensation voltage is varied from 80% to 120% of the primary voltage. The method according to claim 24, further comprising:

27. The phase shift angle of the shunt compensation voltage is varied between -ψ and +ψ. The method according to claim 24, further comprising:

28. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a phase shift angle of 0°, The first load tap changer is set to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The second load tap changer is set to connect load tap position 0 on each secondary winding, The third load tap changer is set to connect load tap position 0 on each secondary winding. The method according to claim 26, including the method described in claim 26.

29. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is 2. Selecting the operating point having a phase shift angle of 2.42°, 4.72°, 6.89°, or 8.95°, The first load tap changer is set to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The second load tap changer is set to connect load tap position 0 on each secondary winding, The third load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding. The method according to claim 26, including the method described in claim 26.

30. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a phase shift angle of 2.54°, 5.21°, 7.99°, or 10.89°, The first load tap changer is set to connect load tap position 0 on each secondary winding, The second load tap changer is set to connect load tap position 0 on each secondary winding, The third load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding. The method according to claim 26, including the method described in claim 26.

31. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a phase shift angle of 0°, The first load tap changer is set to connect load tap position 0 on each secondary winding, The second load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The third load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding. The method according to claim 26, including the method described in claim 26.

32. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a phase shift angle of -2.54°, -5.21°, -7.99°, or -10.89°, The first load tap changer is set to connect load tap position 0 on each secondary winding, The second load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The third load tap changer is set to connect load tap position 0 on each secondary winding. The method according to claim 26, including the method described in claim 26.

33. Each load tap changer includes load tap positions 0, 1, 2, 3, and 4, and the method is Selecting the operating point having a phase shift angle of -2.42°, -4.72°, -6.89°, or -8.95°, The first load tap changer is set to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The second load tap changer is configured to connect load tap positions 1, 2, 3, or 4 on each secondary winding, The third load tap changer is set to connect load tap position 0 on each secondary winding. The method according to claim 26, including the method described in claim 26.

34. All taps of the compensation voltage unit are configured to vary the phase shift angle of the shunt compensation voltage between -ψ and +ψ when they are closer to ground potential, in the most cost-effective configuration of the transformer. The method according to claim 24, further comprising:

35. Vary the phase shift angle of the shunt compensation voltage between -ψ and 0. The method according to claim 24, further comprising:

36. Vary the phase shift angle of the shunt compensation voltage between 0 and +ψ. The method according to claim 24, further comprising:

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