WO2012163841A1

WO2012163841A1 - A voltage source converter for a hvdc transmission system

Info

Publication number: WO2012163841A1
Application number: PCT/EP2012/059863
Authority: WO
Inventors: Praveen Kumar Barupati; Sasitharan Subramanian; Subhasish Mukherjee; Tomas Jonsson
Original assignee: Abb Technology Ltd
Priority date: 2011-05-30
Filing date: 2012-05-25
Publication date: 2012-12-06

Abstract

The invention concerns a voltage source converter comprising a plurality of switching elements to effectively convert between AC and DC for a high voltage direct current (HVDC) system. The voltage source converter has a bridge (42) having one or more phase legs comprising switching elements (44) connected between a first DC terminal (52) and a second DC terminal (54), each phase leg of said one or more phase legs comprises an AC terminal provided at a midpoint (A, B, C) of each phase leg to connect to AC equipment (50). The voltage source converter also has at least one converter leg (48) comprising switching elements connected between the first and second DC terminals, the at least one converter leg having a midpoint, and has at least one switching element (46) provided between the midpoint of the at least one converter leg and the midpoint of each phase leg. A method for operating the voltage source converter is also provided.

Description

A VOLTAGE SOURCE CONVERTER FOR A HVDC TRANSMISSION SYSTEM FIELD OF INVENTION

The present invention relates generally to a converter for high voltage direct current (HVDC) transmission, and more specifically to a voltage source converter for a HVDC system. The present invention also relates to a method for operating a voltage source converter.

BACKGROUND

A high-voltage direct current (HVDC) power transmission system uses direct current for the bulk transmission of electrical power, in contrast with the more common alternating current systems. The advantage of HVDC systems is that the high voltage used for electric power transmission reduces the energy lost in the transmission considerably.

The input power supply for HVDC system is usually AC, and therefore AC needs to be converted to high voltage DC for the transmission. Power transfer and conversion between a three phase AC power line and a DC power line for the HVDC system are well known in the art. Similarly, at the other end of the transmission, the HVDC needs to be converted to high voltage AC for distribution. Power transfer and conversion of DC power to a three phase AC power are also well known in the art.

In such systems, for converting AC power to DC power and vice- versa, converters are used. One form of converter used in HVDC systems is a voltage source converter (VSC) and may be implemented in the HVDC system in a converter station, also referred to as a terminal. Converter stations may use high power electronic semiconductor devices such as thyristors, insulated-gate bipolar transistors (IGBTs) and gate turn-off thyristors (GTOs), and in earlier generation systems, also mercury arc valves. These electronic devices are also generally referred to as valves or switches.

For high voltage transmission, a large number of valves (e.g. IGBTs) are connected in series, and this is challenging for switching with reduced loss, specifically, when two level or three level converters are used.

Another limitation has been current capability of the switch devices. Typical rating of the available IGBT is about 4000A maximum turn-off current, effectively giving 1800A DC transmission. Multilevel VSC technology without IGBT series connection has been introduced on the market, but extra equipment is required in order to safely handle different fault scenarios.

Recent developments in the field have presented the use of multi-level converters based on cascaded two level (CTL) cells, available as modules. The CTL cells include at least two semiconductor director valves ( IGBTs ) and diodes along with a storage element (capacitor). The use of CTL cells, apart from being modular, reduces significantly loss in the system and also reduces the amount of filtering equipment needed for conversion with less ripple/harmonics.

Figures 1 A-B illustrate prior- art converters using CTL cells. In Figure 1 A. the configuration 12 is a three phase bridge, having three phase legs 14. 16. 1 8 having cascaded converter cells for each of the three phases 20, 22, 24. Each phase leg of the converter is divided in two arms, an upper arm and a lower arm. which respectively connect the positive and negative DC poles. 26 and 28. This converter, though based on the three phase bridge with CTL cells for reduced losses, has the limitation that each CTL is in main power (current ) path and requires devices with higher current rating.

Another prior art configuration is shown in Figure 1 B. This configuration has three phase legs 14. 16. 1 8 having three-level full-bridge or chain -link cells in series with IGBT switches 36. While the IGBT switches of a phase leg is ON, the associated series multilevel converter adds or subtracts finite voltage steps to or from the voltage at the DC network to construct a half sinusoidal voltage which is directed to the AC network and forms the main power path. The converter may be operated such that each series strings are switched at near zero voltage, thereby reducing losses and other undesirable effects caused by di/dt or dv/dt events. DC capacitors 32 are also illustrated in this configuration.

However, the prior art voltage source converter configurations still suffer from considerable losses, including switching losses and conduction losses. There exists a continued need to further simplify these converter topologies and to reduce said losses and the number of circuit components of the voltage source converter.

SUMMARY OF THE INVENTION

One object of the present invention is to minimize losses in a converter that operates to convert between high voltage AC and DC in a high voltage direct current (HVDC) system. The present invention provides a new arrangement for the converter that minimizes use of cascaded cells (for example, converter two level (CTL) cells ) in the converter arrangement to make the converter arrangement cost and weight effective.

The above-mentioned object of the present invention is attained by providing a voltage source converter comprising a plural ity of switching elements, the voltage source converter having a first direct current. DC. terminal and a second direct current. DC. terminal for connection to a high voltage direct current. HVDC. system, where the first and second DC terminals have between them

a bridge having one or more phase legs comprising switching elements, each phase leg of said one or more phase legs comprises an AC terminal provided at a midpoint of each phase leg for connection to AC equipment, wherein the voltage source converter comprises at least one converter leg comprising switching elements, the at least one converter leg having a midpoint, and

at least one switching element provided between the midpoint of the at least one converter leg and the midpoint of each phase leg.

The above-mentioned object of the present invention is also attained by providing a method for operating a voltage source converter comprising a plurality of switching elements, the voltage source converter comprising a first direct current. DC. terminal and a second direct current. DC. terminal for connection to a high voltage direct current. HVDC. system, where the first and second DC terminals have between them

- a bridge having one or more phase legs, each phase leg comprising switching elements and an AC terminal provided at a midpoint of each phase leg for connection to AC equipment, and

- at least one converter leg comprising switching elements, a midpoint and at least one switching element provided between the midpoint of the at least one converter leg and the midpoint of each phase leg. the method comprising

a) operating switching elements of each phase leg of the bridge to connect the midpoint of each phase leg to the first DC terminal or the second DC terminal for a predetermined duration; and

b) operating the switching element of the at least one converter leg. the method being characterized in that the midpoint of each phase leg is connected to the midpoint of the at least one converter leg for the predetermined duration in an AC cycle by operating the at least one switching element provided between the midpoint of the at least one converter leg and the midpoint of each phase leg.

As an aspect of the invention, a voltage source converter comprising a plural ity of switching elements arranged in the manner described in the invention is disclosed. The voltage source converter may have a bridge having one or more phase legs including switching elements (director valves in the phase legs ), in which each phase leg from said one or more phase legs comprises an AC terminal provided at midpoint of each phase leg to connect with an AC equipment. The voltage source converter may also have at least one converter leg including switching elements (cascaded cells in the converter leg), in which the at least one converter leg has a midpoint; and may have at least one switching element of the plurality of the switching elements, provided between the midpoint of said at least one converter leg and the mid points of each of the phase legs. The bridge and the at least one converter leg may be placed between the high voltage DC terminals.

According to an advantageous embodiment of the voltage source converter according to the present invention, the at least one switching element provided between the midpoint of the at least one converter leg and the midpoint of each phase leg comprises at least one bidirectional switch

In one embodiment, the switching elements of said one or more phase legs comprise at least one Insulated-gate bipolar transistor (IGBT).

In another embodiment, the switching elements of the at least one converter leg comprise an energy storage device, such as capacitor, battery or any other device that in a suitable arrangement produces an effect of cascaded cells.

In yet another embodiment, the switching elements of the at least one converter leg comprise at least one cascaded cell, or a plurality of cascaded cells. The at least one cascaded cell can be at least one full bridge cell or at least one half bridge cell.

In another embodiment, the at least one switching element of the plurality of switching elements provided between the midpoint of the at least one converter leg and the midpoints of the each of the phase legs of the voltage source converter comprises at least one bidirectional switch.

According to an advantageous embodiment of the voltage source converter according to the present invention, the AC equipment is a transformer.

Thus. AC equipment that connects with the each phase leg of the voltage source converter may be a transformer.

According to an advantageous embodiment of the voltage source converter according to the present invention, the voltage source converter comprises a DC filter between the bridge and the at least one converter leg.

In yet another embodiment of the voltage source converter, the voltage source converter further comprises a DC filter between the bridge and the at least one converter leg at the first and second DC terminals or/and after the at least one converter leg on the first and second DC terminals.

According to an advantageous embodiment of the voltage source converter according to the present invention, the voltage source converter comprises at least one capacitor connected between the first and second DC terminals. The at least one capacitor may be connected across the first and second DC terminals.

According to a further advantageous embodiment of the voltage source converter according to the present invention, the at least one switching element provided between the midpoint of the at least one converter leg and the midpoints of each phase leg comprises a DC filter.

In yet another embodiment, the voltage source converter comprises an AC filter between the AC terminals and the AC equipment.

In another aspect, a method for operating a voltage source converter for an HVDC system is provided. In one embodiment, the voltage source converter comprises a bridge connected between a first DC terminal and a second DC terminal along with a converter leg. The three- phase bridge may comprise three-phase legs, having corresponding AC terminals at midpoints of the phase legs connecting to a three-phase AC equipment, in which each phase leg may comprise two arms, and each arm of the three phase bridge may have IGBTs.

According to an advantageous embodiment of the method according to the present invention, the at least one converter leg comprises cascaded cells providing multi-level configuration, wherein the at least one switching element provided between the midpoint of the at least one converter leg and the midpoint of each phase leg comprises at least one bi-directional switch, wherein the method comprises the step of operating the cascaded cells, and wherein operating the at least one switching element comprises operating the at least one bidirectional switch.

The converter leg may comprise cascaded CTL modules (or cascaded cells), and may have a mid-point terminal of the converter leg connected to midpoints of each of the three phase legs through a bi-directional switch.

According to an advantageous embodiment of the method according to the present invention, the switching elements of said one or more phase legs are operated at around the voltage phase cross over.

According to a further advantageous embodiment of the method according to the present invention, the method further comprises decoupling between AC voltage peak and DC voltage by accounting for triplet! harmonics in the operation of the voltage source converter.

According to another advantageous embodiment of the method according to the present invention, the predetermined time period is the duration of approximately 120 degree of the applied voltage.

According to yet another advantageous embodiment of the method according to the present invention, the voltage source converter is operated such that at any instance switching elements of one phase leg of the bridge are operated to connect the midpoint of said one phase leg to the first DC terminal or the second DC terminal, and said one phase leg is swapped with another phase leg of the bridge at the instant when the phase voltage at the midpoint of said one phase leg is approximately the same as that at the midpoint of the another phase leg. The method for operating the voltage source converter according to one embodiment comprises switching the IGBTs of each arm of the three phase legs, bi-directional switch and the cascaded CTL modules of the converter leg for the converter operation to convert between AC and DC with proper wave shaping. The method may comprise having the AC terminals of each of the phase legs connect to the midpoint terminal of the at least one converter leg and the first or second DC terminals for a predetermined duration in an AC cycle ( appro for duration corresponding to 120 degree of the AC cycle ) by operating the IGBTs and the bi-directional switch provided between each of the phase legs and the converter leg. The cascaded cells of the converter leg may be operated as per a sine wave to control wave shaping.

The method may further involve operating the IGBTs of the phase legs at around zero crossing of the AC cycle and also decouples AC voltage peak and DC voltage by accounting for triplet! harmonics in the operation of the voltage source converter. Also, the voltage source converter is operated such that for any two phases, the connection between the midpoint terminal of the converter leg with the first or second DC terminal is swapped at around same potential to minimize dv/dt effects.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings, in which like characters represent like parts throughout the drawings, wherein:

Figure l A is a schematic representation of an exemplary prior art configuration of a multilevel voltage source converter;

Figure I B is a schematic representation of another exemplary prior art configuration of a multi-level voltage source converter;

Figure 2 is a schematic representation of an exemplary embodiment of the present invention;

Figure 3 is an exemplary waveform representation to explain the working of the present invention; Figure 4 is an exemplary waveform representation of an output voltage waveform relating to the embodiment of the present invention;

Figure 5 is a schematic representation of another exemplary embodiment of the voltage source converter showing additional filters and converter leg; and

Figure 6 a schematic representation of yet another exemplary embodiment of the voltage source converter.

DETAILED DESCRIPTION

As used herein and in the claims, the singular forms "a," "an." and "the" may include the plural reference unless the context clearly indicates otherwise.

An exemplary embodiment of the voltage source converter 40 is shown in Figure 2 and may include a three phase bridge 42 comprising switching elements, for example. IGBTs 44 connected in series for each arm of the three phase legs. Each phase leg has a midpoint A. B and C. AC terminals are provided corresponding to the midpoints A. B and C. DC terminals, namely a first DC terminal 52 and a second DC terminal 54, are shown as X and Z terminals in FIG. 2. The bridge may further be provided with an additional leg 48 (also referred as converter leg. or CTL leg ) having cascaded cells, herein cascaded two level (CTL) modules.

It may be noted here that only a single leg of CTL modules is advantageously provided, which reduces cell capacitance, and this may further reduce costs.

In another embodiment, the converter leg 48 may comprise an energy storage device, for example a capacitor, used suitably, as an example with diode clamps, or any other circuit arrangement, which is able to produce multilevel voltage. Anther example of an energy storage device is be a battery, which when connect in a suitable circuit arrangement, produces an equivalent effect of a cascaded cell.

Further, in another embodiment, more than one converter leg may be provided and operated suitably. Similarly, the bridge of another embodiment may be a single or multi-phase bridge.

The midpoint terminal Y of the converter leg 48 is connected to each phase A ,B, C through switching elements 46. In one embodiment shown in Figure 2. the switching elements 46 are capable to operate bi-directionally and are referred herein as bi-directional switches. The midpoint terminal Y of the converter leg and the midpoints A, B, C of the phase legs denote electrically symmetry around the midpoints for the respective converter leg 48 and the phase leg. i.e. irrespective of the number of switches connected in each arm of the converter leg or the phase leg. the arms are electrically equivalent in each of the legs (phase or converter legs).

In another embodiment of the present invention, the AC terminals are connected to three- phase AC equipment 50 The three-phase AC equipment 50 may be a transformer.

As would be appreciated by those skilled in the art. the three-phase bridge 42 can be operated in rectifier or inverter mode. The switching elements of the upper and lower arms of the phase legs may be alternately operated to connect DC terminals X. Y to AC terminals A. B. C. The bi-directional switches may be used to connect one of the AC terminals A. B or C to the midpoint Y of the converter leg. Each phase A. B. C may be connected at X. Y and Z for a duration of 120" as depicted in Figure 3, illustrating phase A 62 connection to X. Y and Z depending on the AC voltage. The highest voltage terminal may be connected to point X and the lowest voltage terminal may be connected to point Z. The other AC terminal may be connected to point Y.

The upper and lower arms of the converter leg may be operated to produce a multilevel voltage as per the desired AC sine wave.

The bi-directional switches may be operated during 1 50 degree to 2 10 degree and 330 degree to 30 degree of the corresponding phase voltage. If the current is in-phase with the AC voltage (for active power transfer), the current in the converter leg is expected to be small. Furthermore, the bi-directional switch may be operated near to zero voltage across it which reduces the switching loss.

In the configuration of Figure 2, the switching elements of the three-phase bridge 42 switch from one phase to the other at phase crossover of voltage (instant at which one phase voltage crosses other phase voltage ). As the phase legs are switched at the same potential, there is no rate of change of voltage (dv/dt ). The bidirectional switches may be operated at zero voltage across them and hence they will have very low dv/dt. Also, as during phase transition of midpoint Y the incoming bidirectional switch can be turned on before turning off the outgoing bidirectional switch (due to switching at same potential ), and no di/dt problem will appear in the bidirectional switches. Therefore, with this configuration, further advantages of reduced EMI (Electro-Magnetic Interference ), reduced losses due to switching, and negligible di/dt and dv/dt (requiring comple management schemes across devices otherwise ) are realized.

Figure 3 shows an exemplary voltage waveform for the voltage source converter in operation. The phase A waveform 62 is obtained with phase A at X between 30° to 150° as indicated by reference numeral 64, phase A at Y between 1 50 to 2 10 as indicated by reference numeral 66 and phase A at Z between 2 10 to 330 as indicated by reference numeral 68, and phase A at Y for 330 to 30 in one cycle, as indicated by reference numeral 70. The waveform 72 for phase B follows the similar pattern with the given phase shift (e.g., 120 for balanced three phase system ).

It would be appreciated by those skilled in the art that the decoupling between AC voltage peak and DC voltage can be achieved by adding triplet! harmonic in the reference voltage, which is used for controll ing the voltage source converter.

The multi-level nature in the line- line AC voltage may be obtained for 240 of the AC waveform. The output voltage waveform 82 is. as shown in Figure 4. having multi-level nature 84 in the line-line AC voltage. As shown in Figure 4. the output voltage waveform is a flat-top wave for remaining 120 ( in positive cycle at 60 to 120 and in negative cycle at 240 to 300). Further, in an exemplary non limiting implementation, the flat top nature of the AC output voltage can be avoided by adding a DC side filter on the DC link.

It would be further appreciated by those skilled in the art. that a DC filter may be added between the converter leg and DC terminals, between the converter leg and three phase bridge, in series with the bidirectional switches or in any combination of these places to smoothen out the AC voltage. The DC filter may be passive or active. Figure 5 is an exemplary non-limiting schematic representation of the present invention, with the addition of AC filter 91 and DC filters 92. 94. 96 and 98. It may be noted that the converter leg is depicted having full bridge cell instead of the half bridge cells as depicted in Figure 2.

Figure 6 is another exemplary schematic representation of the embodiment of Figure 2 with the AC filter 102 on the AC side and the DC filters 104 provided between the converter leg 48 and the DC terminals, along with capacitors 108 that is provided across the DC bus and is grounded at mid-point.

Instead of bi-directional switches, controlled switches 106 may be provided. The controlled switches can be a DC filter, which will function as bidirectional switch also. In this configuration, the triplet! harmonic current circulates between star point of the transformer to mid-point of the capacitor and gives the required PQ capabilities. However, if the transformer is delta connected, then the triplet! harmonic current circulates within the phases.

The advantages of the exemplary voltage source converter, as described in Figures 2 to 6. include reduced losses due to very small switching losses and lesser conduction losses compared to prior art configurations.

The conduction losses in the converter leg are small as only the difference between the DC and AC current flows through it. By means of the present invention, there is a fewer number of switching per level change in the AC voltage compared to prior art. and thereby, the present invention provides reduced switching losses.

In the exemplary embodiment of Figure 2, the cell capacitance is reduced to almost one third in comparison with prior art configurations and this further reduces the cost and weight. Further, the voltage source converter does not require any significant components to handle issues related with rate of change of current and voltage (di/dt and dv/dt ).

As explained above, since the three phase bridge switches are operated at phase crossover of the AC voltage there is no or negligible dv/dt. Since the switching happens at zero voltage across the switches, the switching losses are considerably reduced.

In contrast to other voltage source converters relying on high frequency switching in the three phase bridge, in accordance with the present invention the switches in the three phase bridge, as shown in Figures 2, 5, and 6. may switch once in a fundamental frequency cycle (this is referred to as fundamental frequency switching) and at zero voltage across them. This reduces switching losses and simplifies dynamic voltage sharing along the series string of switches. Further, in the converter leg, only a small amount of current (the difference between ac and dc current ) flows, and therefore the current rating of switching elements in the converter leg is reduced.

Based on the arrangement of the voltage source converter and the method for operating the voltage source converter, a High Voltage Direct Current (HVDC) system may be operated advantageously with low loss.

While only certain features and embodiments of the present invention have been illustrated and described herein, the invention shall not be considered limited to the embodiments illustrated, but can be modified and altered in many ways by one skilled in the art. without departing from the scope of the appended claims. It is. therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.

Claims

1. A voltage source converter comprising a plurality of switching elements, the voltage source converter having a first direct current. DC. terminal (52) and a second direct current. DC. terminal (54) for connection to a high voltage direct current. HVDC. system, where the first and second DC terminals have between them a bridge (42) having one or more phase legs comprising switching elements (44), each phase leg of said one or more phase legs comprises an AC terminal provided at a midpoint (A, B. C) of each phase leg for connection to AC equipment (50), characterized in that the voltage source converter comprises

at least one converter leg (48) comprising switching elements, the at least one converter leg having a midpoint (Y), and

at least one switching element (46) provided between the midpoint (Y) of the at least one converter leg and the midpoint (A, B. C ) of each phase leg.

2. The voltage source converter according to claim 1 . wherein the at least one switching element (46) provided between the midpoint (Y) of the at least one converter leg (48) and the midpoint (A, B, C) of each phase leg comprises at least one bidirectional switch.

3. The voltage source converter according to claim 1 or 2, wherein the switching elements of said one or more phase legs comprise at least one Insulated-gate bipolar transistor. IGBT.

4. The voltage source converter according to any of the claims 1 to 3, wherein the switching elements of the at least one converter leg (48) comprise an energy storage device.

5. The voltage source converter according to any of the claims 1 to 4. wherein the switching elements of the at least one converter leg (48) comprise at least one full bridge cell.

6. The voltage source converter according to any of the claims 1 to 4, wherein the switching elements of the at least one converter leg (48) comprise at least one half bridge cell.

7. The voltage source converter according to any of the claims 1 to 6. wherein the voltage source converter comprises a DC filter between the bridge and the at least one converter leg (48).

8. The voltage source converter according to any of the claims 1 to 7. wherein the voltage source converter comprises a DC filter at the first and second DC terminals (52, 54).

9. The voltage source converter according to any of the claims 1 to 8. wherein the voltage source converter comprises at least one capacitor connected between the first and second DC terminals (52, 54).

10. The voltage source converter according to any of the claims 1 to 9. wherein the at least one switching element (46) provided between the midpoint (Y) of the at least one converter leg (48) and the midpoints (A, B, C) of each phase leg comprises a DC filter.

1 1 . The voltage source converter according to any of the claims 1 to 10, wherein the voltage source converter comprises an AC filter between the AC terminals and the AC equipment.

12. A method for operating a voltage source converter comprising a plurality of switching elements, the voltage source converter comprising a first direct current. DC. terminal (52) and a second direct current. DC. terminal (54) for connection to a high voltage direct current. HVDC. system, where the first and second DC terminals have between them

- a bridge (42) having one or more phase legs, each phase leg comprising switching elements (44) and an AC terminal provided at a midpoint (A, B. C ) of each phase leg for connection to AC equipment (50), and

- at least one converter leg (48) comprising switching elements, a midpoint (Y) and at least one switching element (46) provided between the midpoint (Y) of the at least one converter leg and the midpoint (A, B, C) of each phase leg. the method comprising

a) operating switching elements of each phase leg of the bridge (42) to connect the midpoint (A, B.C ) of each phase leg to the first DC terminal (52) or the second DC terminal (54) for a predetermined duration; and b) operating the switching element of the at least one converter leg (48),

the method being characterized in that the midpoint (A, B, C) of each phase leg is connected to the midpoint (Y) of the at least one converter leg for the predetermined duration in an AC cycle by operating the at least one switching element (46) provided between the midpoint of the at least one converter leg and the midpoint of each phase leg.

13. The method according to claim 12, wherein the at least one converter leg (48) comprises cascaded cells providing multi-level configuration, wherein the at least one switching element (46) provided between the midpoint (Y) of the at least one converter leg (48) and the midpoint (A, B, C) of each phase leg comprises at least one bi-directional switch, wherein the method comprises the step of operating the cascaded cells, and wherein operating the at least one switching element (46) comprises operating the at least one bidirectional switch.

14. The method according to claim 13, wherein the method comprises operating the cascaded cells of the converter leg as per a sine wave to control wave shaping.

15. The method according to any of the claims 12 to 14. wherein the switching elements of said one or more phase legs are operated at around the voltage phase cross over.

16. The method according to any of the claims 12 to 15. wherein the method further comprises decoupling between AC voltage peak and DC voltage by accounting for triplet! harmonics in the operation of the voltage source converter.

17. The method according to any of the claims 12 to 16. wherein the predetermined time period is the duration of approximately 1 20 degree of the applied voltage.

1 8. The method according to any of the claims 12 to 17. wherein the voltage source converter is operated such that at any instance switching elements of one phase leg of the bridge (42) are operated to connect the midpoint (A, B, C) of said one phase leg to the first DC terminal (52) or the second DC terminal (54). and said one phase leg is swapped with another phase leg of the bridge at the instant when the phase voltage at the midpoint of said one phase leg is approximately the same as that at the midpoint of the another phase leg.