Patent Publication Number: US-10784041-B2

Title: Electromagnetic power converter

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 15/746,316 filed Jan. 19, 2018, which is a U.S. National Application of PCT/US2016/043150 filed Jul. 20, 2016, which claims priority to U.S. provisional patent application 62/195,093, filed on Jul. 21, 2015, which is incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This subject matter is generally related to electromagnetic power converters. 
     BACKGROUND 
     Power transformer is commonly used to convert the amplitude of the voltage of an alternating current (AC) source from one level to another. It plays an important role in electric power conversion, delivery, distribution, and utilization. In some implementations, the working principle of the power transformer is based on the magnetoelectric induction. When the primary windings of a power transformer are connected with an AC source, an AC voltage of the same frequency as that of the source voltage will be induced on the secondary windings. The voltage ratio of the power transformer, which is defined to be the ratio between the amplitudes of the input and output voltages, is determined by the turns ratio of the transformer. If the turns ratio of a power transformer is fixed, the voltage ratio will also be fixed. In some implementations, in order to change the voltage ratio of a power transformer, a tap-changing mechanism is used with the winding that allows a variable number of turns to be selected in discrete steps. The tap changer is a mechanical mechanism and can adjust the voltage ratio in discrete steps. 
     Power electronic converters can be used for variable-voltage and variable-frequency AC-AC power conversion. For example, power electronic converters can be made using power semiconductor devices, including insulated-gate bipolar transistors (IGBTs), metal-oxide-semiconductor field-effect transistors (MOSFETs), thyristors, and/or diodes, as well as passive components, such as inductors and capacitors. For example, AC-AC electric power conversion can be implemented using a variable frequency transformer (VFT). The VFT includes a rotary transformer (similar to an asynchronous generator) driven by an adjustable-speed DC motor drive. By adjusting the rotational speed of the VFT&#39;s rotor via the motor drive, two AC power systems with different frequencies or phases can be connected to the stator and rotor windings of the rotary transformer, respectively. The VFT can be used as a continuously variable phase-shifting transformer for power transfer between two asynchronous power networks with the same frequency. 
     SUMMARY 
     In general, in one aspect, a method for converting power is provided. The method includes providing an input signal to an electromagnetic (EM) power converter that comprises two or more core sections in which at least one core section comprises a magnetic flux valve having an adjustable reluctance, the EM power converter having one or more primary windings and one or more secondary windings wound around one or more core sections; providing one or more control signals to the one or more magnetic flux valves to control a reluctance or reluctances of the one or more magnetic flux valves, affecting magnetic coupling between the primary and secondary windings; and generating an output signal that is a function of the input signal and the one or more control signals. 
     Implementations of the method may include one or more of the following features. Each magnetic flux valve can include one or more layers of piezoelectric material, one or more layers of magnetostrictive material, and electrodes to receive one of the control signals. 
     The method can include using the control signal to provide electric charges to the one or more layers of piezoelectric material, and maintaining at least a portion of the electric charges at the one or more layers of piezoelectric material after removing the control signal. 
     The one or more layers of piezoelectric material can include a lead zirconate titanate (PZT) ceramic sheet, a PZT ceramic plate, PZT fibers, a polyvinylidene fluoride (PVDF) film, PMN-PT [Pb(Mg1/3Nb2/3)O3-PbTiO3] single crystals, or other materials that have the inverse piezoelectric effect. 
     The one or more layers of magnetostrictive material can include a Metglas® foil, a Terfenol-D (Tb0.30Dy0.70Fe1.92) foil, or other materials that have the converse magnetostrictive effect. 
     The two or more core sections can include a first core leg, a second core leg, and a third core leg, the second core leg can include a first magnetic flux valve, and the third core leg can include a second magnetic flux valve. 
     Providing one or more control signals can include providing a first control signal to the first magnetic flux valve and providing a second control signal to the second magnetic flux valve. 
     The method can include configuring the first and second control signals to provide a constant difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux valve. 
     The method can include configuring the first and second control signals to provide a time-varying difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux valve. 
     The difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux valve can have a sinusoidal waveform. 
     The input signal can have a sinusoidal waveform, square waveform, or triangular waveform, and the output signal can also have a corresponding sinusoidal, square, or triangular waveform. The input and output signals can also have other waveforms. 
     The method can include modifying the first and second control signals to modify an amplitude of the output signal. 
     The method can include modifying the first and second control signals to modify a frequency of the output signal. 
     The method can include modifying the first and second control signals to modify a waveform of the output signal. 
     The input signal can have a sinusoidal waveform, and the output signal can have a square waveform or a triangular waveform. 
     The two or more core sections can include a first core leg, a second core leg, a third core leg, and a fourth core leg, the second core leg can include a first magnetic flux valve, the third core leg can include a second magnetic flux valve, and the fourth core leg can include a third magnetic flux valve. 
     Providing one or more control signals can include providing a first control signal to the first magnetic flux valve, providing a second control signal to the second magnetic flux valve, and providing a third control signal to the third magnetic flux valve. 
     The EM power converter can include three power converter modules, providing the input signal to the EM power converter can include providing a three-phase input signal to the three power converter modules, and generating an output signal can include generating a single-phase output signal. 
     Each power converter module can include a first core leg, a second core leg, and a third core leg, the second core leg can include a first magnetic flux valve, and the third core leg can include a second magnetic flux valve. 
     For each power converter module, a primary winding can be wound around the first leg, a first secondary winding can be wound around the second core leg, and a second secondary winding can be wound around the third core leg. 
     The secondary windings can be electrically coupled in series, and the output signal can be generated across the secondary windings. 
     A negative terminal of the first secondary winding can be electrically coupled to a negative terminal of the second secondary winding. 
     The EM power converter can include nine power converter modules, providing the input signal to the EM power converter can include providing a three-phase input signal to the nine power converter modules, and generating an output signal can include generating a three-phase output signal. 
     Each power converter module can include a first core leg, a second core leg, and a third core leg, the second core leg includes a first magnetic flux valve, and the third core leg includes a second magnetic flux valve. 
     For each power converter module, a primary winding can be wound around the first core leg, a first secondary winding can be wound around the second core leg, and a second secondary winding can be wound around the third core leg. 
     The nine power converter modules can be grouped into three sets of power converter modules, each set of power converter modules can include three power converter modules, and the secondary windings of the three power converter modules in the set can be electrically coupled in series. 
     The method can include providing a three-phase input signal to each set of power converter modules. 
     The method can include controlling the control signals provided to the magnetic flux valves to provide a first phase output signal across the secondary windings of the first set of power converter modules, provide a second phase output signal across the secondary windings of the second set of power converter modules, and provide a third phase output signal across the secondary windings of the third set of power converter modules. 
     The EM power converter can include three power converter modules, providing the input signal to the EM power converter can include providing a three-phase input signal to the three power converter modules, and generating an output signal can include generating a three-phase output signal. 
     Each power converter module can include a first core leg, a second core leg, a third core leg, and a fourth core leg, the second core leg can include a first magnetic flux valve, the third core leg can include a second magnetic flux valve, and the fourth core leg can include a third magnetic flux valve. 
     For each power converter module, a primary winding can be wound around the first core leg, a first secondary winding can be wound around the second core leg, a second secondary winding can be wound around the third core leg, and a third secondary winding can be wound around the fourth core leg. 
     The method can include providing the three-phase input signal to the primary windings of the power converter modules. 
     The first secondary windings of the three power converter modules can be electrically coupled in series, the second secondary windings of the three power converter modules can be electrically coupled in series, and the third secondary windings of the three power converter modules can be electrically coupled in series. 
     A negative terminal of the first secondary winding of the first power converter module can be electrically coupled to a positive terminal of the second secondary winding of the second power converter module; a negative terminal of the second secondary winding of the second power converter module can be electrically coupled to the positive terminal of the third secondary winding of the third power converter module; and a positive terminal of the first secondary winding of the first power converter module and a negative terminal of the third secondary winding of the third power converter module can be two output terminals of one phase output of a three-phase EM power converter. 
     A negative terminal of the second secondary winding of the first power converter module can be electrically coupled to a positive terminal of the third secondary winding of the second power converter module; a negative terminal of the third secondary winding of the second power converter module can be electrically coupled to the positive terminal of the first secondary winding of the third power converter module; and a positive terminal of the second secondary winding of the first power converter module and a negative terminal of the first secondary winding of the third power converter module can be two output terminals of a second phase output of the three-phase EM power converter. 
     A negative terminal of the third secondary winding of the first power converter module can be electrically coupled to a positive terminal of the first secondary winding of the second power converter module; a negative terminal of the first secondary winding of the second power converter module can be electrically coupled to the positive terminal of the second secondary winding of the third power converter module; a positive terminal of the third secondary winding of the first power converter module and a negative terminal of the second secondary winding of the third power converter module can be two output terminals of a third phase output of the three-phase EM power converter. 
     A first phase of the three-phase output signal can be generated across the series-connected first secondary windings, a second phase of the three-phase output signal can be generated across the series-connected second secondary windings, and a third phase of the three-phase output signal can be generated across the series-connected third secondary windings. 
     The two or more core sections can include three or more core legs, each core leg can include a magnetic flux valve, and a primary winding and a secondary winding can be wound around each core leg. 
     The method can include providing a multi-phase input signal to the primary windings, and generating a multi-phase output signal at the secondary windings. 
     The method can include providing a three-phase input signal to the primary windings and generating a three-phase output signal at the secondary windings. 
     The two or more core sections can include nine core legs, each core leg can include a magnetic flux valve, the primary windings of the first, second, and third core legs can be connected in series, the primary windings of the fourth, fifth, and sixth core legs can be connected in series, and the primary windings of the seventh, eighth, and ninth core legs can be connected in series. 
     The secondary windings of the first, fourth, and seventh core legs can be connected in series, the secondary windings of the second, fifth, and eighth core legs can be connected in series, and the secondary windings of the third, sixth, and ninth core legs can be connected in series. 
     Providing the three-phase input signal can include providing a first phase input signal across the primary windings of the first, second, and third core legs, providing a second phase input signal across the primary windings of the fourth, fifth, and sixth core legs, and providing a third phase input signal across the primary windings of the seventh, eight, and ninth core legs. 
     Generating the three-phase output signal can include generating a first phase output signal across the secondary windings of the first, fourth, and seventh core legs, generating a second phase output signal across the secondary windings of the second, fifth, and eighth core legs, and generating a third phase output signal across the secondary windings of the third, sixth, and ninth core legs. 
     One of the core sections can include a magnetic flux valve and a magnetically permeable material, the magnetically permeable material can be coupled to the magnetic flux valve, the magnetic flux can travel in the magnetic flux valve and the magnetically permeable material in a same direction. 
     One of the core sections can include a magnetic flux valve and a magnetically permeable material, the magnetically permeable material can be spaced apart from the magnetic flux valve, the magnetic flux can travel in the magnetic flux valve along a first direction, and the magnetic flux can travel in the magnetically permeable material in a second direction opposite to the first direction. 
     The magnetically permeable material can include a ferrite ring core that surrounds the magnetic flux valve. 
     In general, in another aspect, an apparatus that includes a power converter having two or more core sections is provided. At least one core section includes a magnetic flux valve having an adjustable reluctance. The power converter has one or more primary windings and one or more secondary windings that are wound around one or more core sections. The core sections include magnetically permeable material, and the reluctance of the magnetic flux valve is a function of a control signal applied to the magnetic flux valve. 
     Implementations of the apparatus may include one or more of the following features. The magnetic flux valve can include one or more layers of piezoelectric material, one or more layers of magnetostrictive material, and electrodes to receive the control signal. 
     The one or more layers of piezoelectric material can hold electric charges provided by the control signal and maintain at least a portion of the electric charges after the control signal is removed. 
     The one or more layers of piezoelectric material can include a lead zirconate titanate (PZT) ceramic sheet, a PZT ceramic plate, PZT fibers, a polyvinylidene fluoride (PVDF) film, PMN-PT [Pb(Mg1/3Nb2/3)O3-PbTiO3] single crystals, or other materials that have the inverse piezoelectric effect. 
     The one or more layers of magnetostrictive material can include a Metglas® foil, a Terfenol-D (Tb 0.30 Dy 0.70 Fe 1.92 ) foil, or other materials that have the converse magnetostrictive effect. 
     The two or more core sections can include a first core leg, a second core leg, and a third core leg, the second core leg can include a first magnetic flux valve, and the third core leg can include a second magnetic flux valve. 
     The first magnetic flux valve can have a reluctance that is a function of a first control signal, and the second magnetic flux valve can have a reluctance that is a function of a second control signal. 
     The apparatus can include a driver circuit configured to generate the first and second control signals. 
     A primary winding can be wound around the first core leg, a first secondary winding can be wound around the second core leg, and a second secondary winding can be wound around the third core leg. 
     The first and second secondary windings can be connected in series, and the driver circuit can be configured to generate the first and second control signals having waveforms such that when the primary winding receives an input signal having a sinusoidal waveform, the first and second secondary windings generate an output signal having a sinusoidal waveform. 
     A negative terminal of the first secondary winding can be electrically coupled to a negative terminal of the second secondary winding. 
     The first and second secondary windings can be connected in series, and the driver circuit can be configured to generate the first and second control signals having waveforms such that when the primary winding receives an input signal having a sinusoidal waveform, the first and second secondary windings generate an output signal having at least one of a square or triangular waveform. 
     A negative terminal of the first secondary winding can be electrically coupled to a negative terminal of the second secondary winding. 
     The power converter can be configured such that a first portion of a magnetic flux generated by the primary winding passes the second core leg, a second portion of the magnetic flux generated by the primary winding passes the third core leg, and a ratio between the first and second portions is controlled by the first and second control signals. 
     The two or more core sections can include a first core leg, a second core leg, a third core leg, and a fourth core leg, the second core leg can include a first magnetic flux valve, the third core leg can include a second magnetic flux valve, and the fourth core leg can include a third magnetic flux valve. 
     The first magnetic flux valve can have a reluctance that is a function of a first control signal, the second magnetic flux valve can have a reluctance that is a function of a second control signal, and the third magnetic flux valve can have a reluctance that is a function of a third control signal. 
     The apparatus can include a driver circuit configured to generate the first, second, and third control signals. 
     The power converter can be configured such that a first portion of a magnetic flux generated by the primary winding passes the second core leg, a second portion of the magnetic flux generated by the primary winding passes the third core leg, a third portion of the magnetic flux generated by the primary winding passes the fourth core leg, and the relative amounts of the first, second, and third portions are controlled by the first, second, and third control signals. 
     The power converter can include three converter modules, each converter module can include a first core leg, a second core leg, and a third core leg, the second core leg can include a first magnetic flux valve, and the third core leg can include a second magnetic flux valve. 
     For each converter module, a primary winding can be wound around the first core leg, a first secondary winding can be wound around the second core leg, and a second secondary winding can be wound around the third core leg. 
     In each converter module, the secondary windings can be electrically coupled in series. 
     In each converter module, a negative terminal of the first secondary winding can be electrically coupled to a negative terminal of the second secondary winding. 
     The power converter can include nine converter modules, each converter module can include a first core leg, a second core leg, and a third core leg, the second core leg can include a first magnetic flux valve, and the third core leg can include a second magnetic flux valve. 
     For each converter module, a primary winding can be wound around the first core leg, a first secondary winding can be wound around the second core leg, and a second secondary winding can be wound around the third core leg. 
     The nine converter modules can be grouped into three sets of converter modules, each set of converter modules can include three converter modules, and the secondary windings of the three converter modules in each set can be electrically coupled in series. 
     A positive terminal of the second secondary winding of the first converter module can be electrically coupled to a positive terminal of the first secondary winding of the second converter module. 
     The power converter can include three converter modules, each converter module can include a first core leg, a second core leg, a third core leg, and a fourth core leg, the second core leg can include a first magnetic flux valve, the third core leg can include a second magnetic flux valve, and the fourth core leg can include a third magnetic flux valve. 
     For each converter module, a primary winding can be wound around the first core leg, a first secondary winding can be wound around the second core leg, a second secondary winding can be wound around the third core leg, and a third secondary winding can be wound around the fourth core leg. 
     The first secondary windings of the three converter modules can be electrically coupled in series, the second secondary windings of the three converter modules can be electrically coupled in series, and the third secondary windings of the three converter modules can be electrically coupled in series. 
     The two or more core sections can include three or more core legs, each core leg can include a magnetic flux valve, and a primary winding and a secondary winding can be wound around each core leg. 
     The two or more core sections can include nine core legs, each core leg can include a magnetic flux valve, the primary windings of the first, second, and third core legs can be connected in series, the primary windings of the fourth, fifth, and sixth core legs can be connected in series, and the primary windings of the seventh, eighth, and ninth core legs can be connected in series. 
     The secondary windings of the first, fourth, and seventh core legs can be connected in series, the secondary windings of the second, fifth, and eighth core legs can be connected in series, and the secondary windings of the third, sixth, and ninth core legs can be connected in series. 
     The apparatus can include a driver circuit configured to generate the control signal. 
     One of the core sections can include a magnetic flux valve and a magnetically permeable material, the magnetically permeable material can be coupled to the magnetic flux valve, the magnetic flux can travel in the magnetic flux valve and the magnetically permeable material in a same direction. 
     One of the core sections can include a magnetic flux valve and a magnetically permeable material, the magnetically permeable material can be spaced apart from the magnetic flux valve, the magnetic flux can travel in the magnetic flux valve along a first direction, and the magnetic flux can travel in the magnetically permeable material in a second direction opposite to the first direction. 
     The magnetically permeable material can include a ferrite ring core that surrounds the magnetic flux valve. 
     In general, in another aspect, a method for converting power is provided. The method includes applying a control signal to a magnetic flux valve that includes one or more layers of piezoelectric material and one or more layers of magnetostrictive material to provide one or more electric fields across the one or more layers of piezoelectric material to produce strain that is transferred to the one or more layers of magnetostrictive material, and modifying a permeability of the one or more layers of magnetostrictive material based on the strain; providing an input signal to a primary winding; controlling a magnetic coupling between the primary winding and a secondary winding based on the permeability of the one or more layers of magnetostrictive material; and controlling an output signal provided at least in part by the secondary winding based at least in part on the magnetic coupling between the primary and secondary windings. 
     Implementations of the method may include one or more of the following features. The method can include controlling an amplitude of the output signal based on the control signal. 
     The method can include controlling a frequency of the output signal based on the control signal. 
     The method can include controlling a waveform of the output signal based on the control signal. 
     In general, in another aspect, a method for converting power is provided. The method includes applying a control signal to a magnetic flux valve comprising one or more layers of piezoelectric material and one or more layers of magnetostrictive material to provide one or more electric fields across the one or more layers of piezoelectric material to produce strain that is transferred to the one or more layers of magnetostrictive material, and modifying a permeability of the one or more layers of magnetostrictive material based on the strain; controlling a distribution of magnetic flux among two or more core sections based at least in part on the permeability of the one or more layers of magnetostrictive material; and controlling an output signal based at least in part on the distribution of the magnetic flux among the two or more core sections. 
     Implementations of the method may include one or more of the following features. The method can include controlling an amplitude of the output signal based on the control signal. 
     The method can include controlling a frequency of the output signal based on the control signal. 
     The method can include controlling a waveform of the output signal based on the control signal. 
     A primary winding can be wound around a first core section, a first secondary winding can be wound around a second core section, a second secondary winding can be wound around a third core section, and the output signal can be provided by the first and second secondary windings. Controlling the distribution of magnetic flux can include controlling a distribution of magnetic flux between the second core section and the third core section, thereby controlling a first signal generated at the first secondary winding and a second signal generated at the second secondary winding, thereby controlling the output signal. 
     In general, in another aspect, an apparatus that includes a power converter is provided. The power converter includes a first converter module that includes a first core section; a primary winding wound around a portion of the first core section, the primary winding having a first terminal and a second terminal that are configured to receive a first input signal; a second core section comprising a first magnetic flux valve that has a reluctance that changes in response to a first control signal; and a first secondary winding wound around a portion of the second core section, the first secondary winding having a first terminal and a second terminal. 
     Implementations of the apparatus may include one or more of the following features. The apparatus can include a third core section; and a second secondary winding wound around a portion of the third core section, the second secondary winding having a first terminal and a second terminal. 
     The second terminal of the first secondary winding can be electrically coupled to the first terminal of the second secondary winding, and the first terminal of the first secondary winding and the second terminal of the second secondary winding can be configured to provide an output signal. 
     The third core section can include a second magnetic flux valve having a reluctance that changes in response to a second control signal. 
     The apparatus can include a driver circuit to generate the first and second control signals. 
     The first and second control signals can be configured to provide a constant difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux valve. 
     The first and second control signals can be configured to cause a difference between the first and second reluctances to vary over time. 
     The first and second control signals can be configured to cause the difference between the first and second reluctances to vary over time according to a sinusoidal waveform. 
     The apparatus can include a fourth core section that includes a third magnetic flux valve having a reluctance that changes in response to a third control signal; and a third secondary winding wound around a portion of the fourth core section, the third secondary winding having a first terminal and a second terminal. 
     The apparatus can include a driver circuit to generate the first, second, and third control signals. 
     The apparatus can include a driver circuit to generate the first control signal. 
     The first magnetic flux valve can include one or more layers of magnetostrictive material and one or more layers of piezoelectric material. 
     The one or more layers of piezoelectric material can hold electric charges provided by the control signal and maintain at least a portion of the electric charges after the control signal is removed. 
     In general, in another aspect, an apparatus that includes a power converter is provided. The power converter includes a plurality of converter modules, each converter module including a first core leg; a primary winding wound around a section of the first core leg, the primary winding having a first terminal and a second terminal that are configured to receive an input signal; a second core leg comprising a first magnetic flux valve having a reluctance that changes in response to a control signal; and a first secondary winding wound around a section of the second core leg, the secondary winding having a first terminal and a second terminal. 
     Implementations of the apparatus may include one or more of the following features. At least some of the secondary windings of the plurality of converter modules can be connected in series, and two terminals of the series-connected secondary windings can be configured to provide an output signal. 
     Each converter module can include a third core leg; and a second secondary winding wound around a section of the third core leg, the second secondary winding having a first terminal and a second terminal. The first secondary winding and the second secondary winding of at least some of the converter module can be connected in series. 
     The third core leg can include a second magnetic flux valve having a reluctance that changes in response to a second control signal. 
     Each converter module can include a fourth core leg and a third secondary winding wound around a section of the fourth core leg, the third secondary winding having a first terminal and a second terminal. 
     The fourth core leg can include a third magnetic flux valve having a reluctance that changes in response to a third control signal. 
     The apparatus can include a driver circuit to generate the first and second control signals. 
     The driver circuit can be configured to generate the first and second control signals to provide a constant difference between a first reluctance of the first magnetic flux valve and a second reluctance of the second magnetic flux valve. 
     The driver circuit can be configured to generate the first and second control signals to cause the first magnetic flux valve to have a first reluctance, the second magnetic flux valve to have a second reluctance, and a difference between the first and second reluctances to vary over time. 
     Within one converter module, a negative terminal of a first secondary winding can be electrically coupled to a negative terminal of a second secondary winding. 
     The first magnetic flux valve can include one or more layers of magnetostrictive material and one or more layers of piezoelectric material. 
     The one or more layers of piezoelectric material can hold electric charges provided by the control signal and maintain at least a portion of the electric charges after the control signal is removed. 
     In general, in another aspect, an apparatus that includes a power converter is provided. The power converter includes a plurality of converter modules, each converter module includes a first core leg; a primary winding wound around a section of the first core leg, the primary winding having a first terminal and a second terminal; a second core leg; a first secondary winding wound around a section of the second core leg, the secondary winding having a first terminal and a second terminal; a first magnetic flux valve having a reluctance that changes in response to a first control signal, in which the first core leg, the second core leg, and the first magnetic flux valve together provide a first magnetic flux path having an overall reluctance that changes in response to the first control signal; a third core leg; a second secondary winding wound around a section of the third core leg, the second secondary winding having a first terminal and a second terminal; and a second magnetic flux valve having a reluctance that changes in response to a second control signal, in which the first core leg, the third core leg, and the second magnetic flux valve together provide a second magnetic flux path having an overall reluctance that changes in response to the second control signal. 
     Implementations of the apparatus may include one or more of the following features. At least some of the secondary windings of the plurality of converter modules can be connected in series, and two terminals of the series-connected secondary windings can be configured to provide an output signal. 
     The plurality of converter modules can include three converter modules, the primary windings of the three converter modules can be configured to receive a three-phase input signal, and the series-connected secondary windings can be configured to provide a single phase output signal. 
     The plurality of converter modules can include three single-phase converter modules, each single-phase converter module can include three converter modules, and the three single-phase converter modules can be configured to provide a three-phase output signal. 
     The apparatus can include a driver circuit configured to generate the first and second control signals. 
     The driver circuit can be configured to generate the first and second control signals to provide a constant difference between a first reluctance of the first magnetic flux valve and a second reluctance of the second magnetic flux valve. 
     The driver circuit can be configured to generate the first and second control signals to cause the first magnetic flux valve to have a first reluctance, the second magnetic flux valve to have a second reluctance, and a difference between the first and second reluctances to vary over time. 
     Each of the magnetic flux valves can include one or more layers of magnetostrictive material and one or more layers of piezoelectric material. 
     The one or more layers of piezoelectric material can hold electric charges provided by the control signal and maintain at least a portion of the electric charges after the control signal is removed. 
     Each of the magnetic flux valves can include electrodes to receive one of the control signals and to provide an electric field across the one or more piezoelectric layers in response to the control signal. 
     Each converter module can includes a fourth core leg; a third secondary winding wound around a section of the fourth core leg, the third secondary winding having a first terminal and a second terminal; and a third magnetic flux valve having a reluctance that changes in response to a third control signal, in which the first core leg, the fourth core leg, and the third magnetic flux valve together provide a third magnetic flux path, and the third magnetic flux path has an overall reluctance that changes in response to the third control signal. 
     The plurality of converter modules can include three converter modules, the second terminal of the first secondary winding of the first converter module can be electrically coupled to the first terminal of the first secondary winding of the second converter module, the second terminal of the first secondary winding of the second converter module can be electrically coupled to the first terminal of the first secondary winding of the third converter module, and the first terminal of the first secondary winding of the first converter module and the second terminal of the first secondary winding of the third converter module can be configured to provide a first output signal. 
     The second terminal of the second secondary winding of the first converter module can be electrically coupled to the first terminal of the second secondary winding of the second converter module, the second terminal of the second secondary winding of the second converter module can be electrically coupled to the first terminal of the second secondary winding of the third converter module, and the first terminal of the second secondary winding of the first converter module and the second terminal of the second secondary winding of the third converter module can be configured to provide a second output signal. 
     The second terminal of the third secondary winding of the first converter module can be electrically coupled to the first terminal of the third secondary winding of the second converter module, the second terminal of the third secondary winding of the second converter module can be electrically coupled to the first terminal of the third secondary winding of the third converter module, and the first terminal of the third secondary winding of the first converter module and the second terminal of the third secondary winding of the third converter module can be configured to provide a third output signal. 
     The three primary windings can be configured to receive a three-phase input signal, and the first, second, and third output signals can be configured to be a three-phase output signal. 
     In general, in another aspect, a method for converting power is provided. The method includes providing an input signal to a primary winding that is wound around a section of a first core leg of a power converter; passing a first magnetic flux generated by the primary winding through a first magnetic flux path formed by the first core leg, a second core leg, and a first magnetic flux valve; generating a first signal across a first secondary winding that is wound around a section of the second core leg; and applying a first control signal to the first magnetic flux valve to control a reluctance of the first magnetic flux valve, in which the first signal is influenced by the reluctance of the first magnetic flux valve. 
     Implementations of the method may include one or more of the following features. The method can include passing a second magnetic flux generated by the primary winding through a second magnetic flux path formed by the first core leg and a third core leg; and generating a second signal across a second secondary winding that is wound around a section of the third core leg. 
     The first secondary winding and the second secondary winding can be connected in series, and the method can include providing an output signal at a first terminal of the first secondary winding and a second terminal of the second secondary winding. 
     The second magnetic flux path can be formed by the first core leg, the third core leg, and a second magnetic flux valve, and the method can include applying a second control signal to the second magnetic flux valve to control a reluctance of the second magnetic flux valve, in which the second signal is influenced by the reluctance of the second magnetic flux valve. 
     In general, in another aspect, a method for converting power is provided. The method includes providing a power converter that includes: a first core leg; a primary winding wound around a section of the first core leg, the primary winding having a first terminal and a second terminal; a second core leg; a first secondary winding wound around a section of the second core leg, the first secondary winding having a first terminal and a second terminal; a first magnetic flux valve, in which the first core leg, the second core leg, and the first magnetic flux valve form a first magnetic flux path; a third core leg; a second secondary winding wound around a section of the third core leg, the second secondary winding having a first terminal and a second terminal; and a second magnetic flux valve, in which the first core leg, the third core leg, and the second magnetic flux valve form a second magnetic flux path. The method includes providing an input signal to the primary winding; generating an output signal from terminals of the secondary windings; providing a first control signal to control a reluctance of the first magnetic flux valve; providing a second control signal to control a reluctance of the second magnetic flux valve; and controlling the output signal by controlling the reluctances of the first and second magnetic flux valves. 
     Implementations of the method may include one or more of the following features. The first magnetic flux valve can include one or more layers of piezoelectric material and one or more layers of magnetostrictive material, and providing the first control signal includes providing a first voltage signal to the one or more layers of piezoelectric material. 
     The method can include holding electric charges provided by the control signal at the one or more layers of piezoelectric material, and maintaining at least a portion of the electric charges at the one or more layers of piezoelectric material after the control signal is removed. 
     Providing the first and second control signals can include providing a first voltage signal to the first magnetic flux valve and a second voltage signal to the second magnetic flux valve. 
     A difference between the first and second voltage signals can be a constant. 
     A difference between the first and second voltage signals can vary over time. 
     Providing the input signal can include providing a sinusoidal input voltage signal. 
     Generating the output signal can include generating a sinusoidal output voltage signal. 
     The method can include controlling the first and second magnetic flux valves such that a difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux value is a constant, in which generating the output signal can include generating an output signal that has a frequency that is the same as the frequency of the input signal. 
     The method can include controlling the first and second magnetic flux valves such that a difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux value varies over time, in which generating the output signal can include generating an output signal having a modulated waveform that is a function of the input signal and the difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux valve. 
     In general, in another aspect, a method for converting power is provided. The method includes providing a power converter that includes: a first core leg and a primary winding wound around a section of the first core leg; a second core leg and a first secondary winding wound around a section of the second core leg; a third core leg and a second secondary winding wound around a section of the third core leg; and a first magnetic flux valve having a controllable reluctance. The method includes providing an input signal to the primary winding; providing a first control signal to the first magnetic flux valve to control the reluctance of the first magnetic flux valve, in which the magnetic fluxes passing the second and third core legs are influenced by the reluctance of the first magnetic flux valve; and generating an output signal at the secondary windings, in which the output signal is influenced by the magnetic fluxes passing the second and third core legs. 
     Implementations of the method may include one or more of the following features. The power converter can include a second magnetic flux valve, and the method can include providing a second control signal to the second magnetic flux valve to control the reluctance of the second magnetic flux valve, in which the magnetic fluxes passing the second and third core legs can be influenced by the reluctances of the first and second magnetic flux valves. 
     The first magnetic flux valve can include one or more layers of piezoelectric material, one or more layers of magnetostrictive material, and electrodes. Applying the first control signal can include applying a voltage signal across the electrodes to generate an electric field across the one or more layers of piezoelectric material. 
     The method can include holding electric charges provided by the control signal at the one or more layers of piezoelectric material, and maintaining at least a portion of the electric charges at the one or more layers of piezoelectric material after the control signal is removed. 
     In general, in another aspect, a method for converting power is provided. The method includes providing an input signal to a primary winding of a power converter that includes a first core leg and a second core leg, the second core leg comprising a first magnetic flux valve, the primary winding being wound around the first core leg; providing a first control signal to the first magnetic flux valve to control a reluctance of the first magnetic flux valve and affecting a reluctance of the second core leg; and inducing a first secondary signal across a first secondary winding that is wound around the second core leg, in which the first secondary signal is affected by the reluctance of the second core leg. 
     Implementations of the method may include one or more of the following features. The power converter can include a third core leg that includes a second magnetic flux value, and a second secondary winding wound around the third core leg. 
     The method can include providing a second control signal to the second magnetic flux valve to control a reluctance of the second magnetic flux valve and affecting a reluctance of the third core leg; and inducing a second secondary signal across the second secondary winding, in which the second secondary signal is affected by the reluctance of the third core leg. 
     The first and second secondary windings can be electrically coupled in series, and the method can include providing an output signal across the first and second secondary windings. 
     The method can include configuring the first and second control signals such that a difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux valve is a constant. 
     The input signal can have a sinusoidal waveform, and the output signal can also have a sinusoidal waveform. 
     The method can include configuring the first and second control signals such that a difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux valve varies over time. 
     The difference between the reluctance of the first magnetic flux valve and the reluctance of the second magnetic flux valve can have a sinusoidal waveform. 
     The method can include modifying the first and second control signals to modify an amplitude of the output signal. 
     The method can include modifying the first and second control signals to modify a frequency of the output signal. 
     The method can include modifying the first and second control signals to modify a waveform of the output signal. 
     The first voltage signal can have a sinusoidal waveform, and the method can include configuring the first and second control signals to cause the output voltage signal to have at least one of a square waveform or a triangular waveform. 
     The power converter can include a fourth core leg that includes a third magnetic flux valve, and a third secondary winding wound around the fourth core leg. 
     The method can include providing a third control signal to the third magnetic flux valve to control a reluctance of the third magnetic flux valve and affecting a reluctance of the fourth core leg, and inducing a third secondary signal across the third secondary winding, in which the third secondary signal can be affected by the reluctance of the fourth core leg. 
     In general, in another aspect, a method for converting power is provided. The method includes providing an input voltage signal to a primary winding of a power converter that includes a first core leg and a first magnetic flux valve, the primary winding being wound around the first core leg; providing a first control signal to the first magnetic flux valve to control a reluctance of the first magnetic flux valve and affecting magnetic flux that passes the first core leg; and inducing a second voltage signal across a first secondary winding that is wound around the first core leg, in which the second voltage signal is affected by the magnetic flux that passes the first core leg. 
     Implementations of the method may include one or more of the following features. The power converter can include additional core legs, each of the additional core legs can have a corresponding primary winding and a second secondary winding that are wound around the core leg, and each of the additional core legs can be coupled to a corresponding magnetic flux valve. 
     The method can include providing control signals to the magnetic flux valves coupled to the additional core legs to control reluctances of the magnetic flux valves and affecting magnetic fluxes that pass the additional core legs. 
     The method can include providing input voltage signals to the primary windings and generating output voltage signals at the secondary windings. 
     The input voltage signals can include a three-phase input voltage signal, and the output voltage signals can include a three-phase output voltage signal. 
     The power converter can include nine core legs, the primary windings of the first, second, and third core legs can be connected in series, the primary windings of the fourth, fifth, and sixth core legs can be connected in series, and the primary windings of the seventh, eighth, and ninth core legs can be connected in series. 
     The secondary windings of the first, fourth, and seventh core legs can be connected in series, the secondary windings of the second, fifth, and eighth core legs can be connected in series, and the secondary windings of the third, sixth, and ninth core legs can be connected in series. 
     The method can include providing a first phase input voltage signal across the primary windings of the first, second, and third core legs, providing a second phase input voltage signal across the primary windings of the fourth, fifth, and sixth core legs, and providing a third phase input voltage signal across the primary windings of the seventh, eight, and ninth core legs. 
     The method can include providing a first phase output voltage signal across the secondary windings of the first, fourth, and seventh core legs, providing a second phase output voltage signal across the secondary windings of the second, fifth, and eighth core legs, and providing a third phase output voltage signal across the secondary windings of the third, sixth, and ninth core legs. 
     In general, in another aspect, a method for converting power is provided. The method includes providing a multi-phase input voltage signal to primary windings of a plurality of power converter modules, each power converter module comprising a first magnetic flux valve; providing control signals to the magnetic flux valves to control reluctances of the magnetic flux valves; and inducing one or more voltage signals across secondary windings of the power converter modules, in which the voltage signals induced across the secondary windings are affected by the reluctances of the magnetic flux valves. 
     Implementations of the method may include one or more of the following features. The multi-phase input voltage signal can include a three-phase input voltage signal. 
     The secondary windings of three of the power converter modules can be connected in series, and the method can include providing a single-phase output voltage signal from the secondary windings of the three power converter modules. 
     The plurality of power converter modules can include nine power converter modules grouped into three single-phase power converter units, each single-phase power converter unit can include three power converter modules having secondary windings connected in series. The method can include providing a three-phase output voltage signal from the three single-phase power converter units. 
     Each converter module can include a first core leg and a second core leg, in which the first magnetic flux valve of the converter module can affect a magnetic flux that passes the first magnetic flux circuit. 
     Each converter module can include a third core leg, a secondary winding wound around the third core leg, and a second magnetic flux valve. 
     The method can include providing control signals to the second magnetic flux valves of each power converter module to control the reluctances of the second magnetic flux valves. 
     Each converter module can include a fourth core leg, a secondary winding wound around the fourth core leg, and a third magnetic flux valve. 
     The method can include providing control signals to the second and third magnetic flux valves of each power converter module to control the reluctances of the second and third magnetic flux valves. 
     The method can include providing a multi-phase output voltage signal from the secondary windings of the power converter modules. 
     The plurality of power converter modules can include three power converter modules, and the multi-phase output voltage signal includes a three-phase output voltage signal. 
     At least some of the secondary windings of the second core legs of the power converter modules can be connected in series, at least some of the secondary windings of the third core legs of the power converter modules can be connected in series, and at least some of the secondary windings of the fourth core legs of the power converter modules can be connected in series. 
     Each magnetic flux valve can include one or more layers of piezoelectric material, one or more layers of magnetostrictive material, and electrodes to receive one of the control signals and provide an electric field across the piezoelectric material. 
     The method can include holding electric charges provided by the control signal at the one or more layers of piezoelectric material, and maintaining at least a portion of the electric charges at the one or more layers of piezoelectric material after the control signal is removed. 
     The details of one or more of the above aspects and implementations are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages will become apparent from the description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic diagram of an electromagnetic (EM) power converter system. 
         FIG. 2A  is an exemplary configuration of an EM power converter module having three core legs. 
         FIG. 2B  is an exemplary configuration of an EM power converter module having four core legs. 
         FIG. 3A  is a diagram of the magnetic circuit of the three-leg EM power converter module of  FIG. 2A . 
         FIG. 3B  is a diagram of an equivalent circuit of the three-leg EM power converter module of  FIG. 2A . 
         FIGS. 4A to 4C  show magnetic flux variations in a three-leg EM power converter module. 
         FIGS. 5A and 5B  are graphs showing possible output voltages of a three-leg EM power converter module. 
         FIG. 6  is a graph showing the main flux in the central core leg and the fluxes in the two side core legs generated by modulation through a three-leg EM power converter module. 
         FIG. 7  is a diagram of a single-phase EM power converter that includes three three-leg modules. 
         FIGS. 8( a ) to 8( d )  are graphs of magnetic flux waveforms in the single-phase EM power converter formed by using three three-leg modules. 
         FIG. 9A  is a diagram showing a top view of the physical configuration of a four-leg EM power converter module. 
         FIG. 9B  is a diagram of the equivalent circuit of the power converter module of  FIG. 9A . 
         FIG. 10  is a diagram of a three-phase EM power converter that includes three four-leg modules. 
         FIGS. 11( a ) to 11( c )  are graphs showing waveforms of the magnetic fluxes in the four core legs of the three EM power converter modules. 
         FIG. 11( d )  is a graph showing the synthesized magnetic fluxes through the three secondary output windings of the three-phase EM power converter. 
         FIG. 12A  is a three-dimensional view an exemplary compact three-phase nine-leg EM power converter. 
         FIG. 12B  is a top view of the exemplary compact three-phase nine-leg EM power converter. 
         FIG. 12C  is a cross-sectional view of an exemplary core leg of the compact three-phase nine-leg EM power converter. 
         FIG. 12D  is a diagram of an equivalent circuit of the compact three-phase nine-leg EM power converter. 
         FIG. 13  is an exemplary winding connection diagram of the three-phase nine-leg EM power converter. 
         FIG. 14  is a diagram of an equivalent circuit of an n-leg EM power converter. 
         FIG. 15  is a diagram of an exemplary magnetic circuit containing a magnetic flux valve. 
         FIGS. 16A and 16B  are diagrams showing a side view and a three-dimensional view, respectively, of a first exemplary structure of a magnetic flux valve. 
         FIGS. 17A and 17B  are diagrams showing a side view and a three-dimensional view, respectively, of a second exemplary structure of a magnetic flux valve. 
         FIG. 18  is a diagram of a piezoelectric layer constructed by using piezoelectric fibers coupled to an interdigitated-pattern electrode. 
         FIG. 19  is a diagram showing exemplary directions of magnetic polarization and electric polarization in a magnetic flux valve with piezoelectric sheets. 
         FIG. 20  is a graph showing variations of the magnetization curves of a magnetic flux valve when different control voltages are applied to the magnetic flux valve. 
         FIG. 21  is a diagram of an exemplary power transformer. 
         FIG. 22  is a schematic diagram of the power transformer of  FIG. 21 . 
         FIG. 23  is a graph showing output waveforms of the power transformer of  FIG. 22 . 
         FIG. 24  is a graph showing a relationship between the voltage ratio of a transformer versus control voltage. 
         FIG. 25  is a diagram of an exemplary configuration for a controller. 
         FIG. 26  is a diagram of an exemplary configuration for a magnetic flux valve driver circuit. 
         FIG. 27  is a diagram showing an output triangular waveform of an EM power converter module being converted to a direct current waveform. 
         FIG. 28  is a photo of an exemplary magnetic flux valve. 
         FIG. 29  is a graph showing the relationship between the relative permeability of the magnetic flux valve versus the control voltage applied to the valve. 
         FIG. 30  is a diagram showing the magnetic flux line distribution in a magnetic flux valve and an adjacent magnetic core. 
         FIG. 31  is a diagram showing a compact configuration of an adjustable-voltage-ratio (AVR) transformer that has two magnetic flux valves. 
         FIG. 32  is a diagram showing the magnetic circuit of the AVR transformer in  FIG. 31 , and  FIG. 33  is a diagram showing the equivalent circuit of the AVR transformer. 
         FIG. 34  is a graph that shows the waveforms of v out  when different control voltages are applied. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     This disclosure provides a novel approach for an electromagnetic (EM) power converter for converting alternating current (AC) electric energy by actively controlling the magnetic flux in the device. The electromagnetic power converter can convert an AC input to an AC output with a different amplitude, frequency, and/or waveform, where the AC input and output can be single phase or have multiple phases. For example, from a sinusoidal input signal, the power converter can generate an output signal having an arbitrary waveform, e.g., sinusoid, square, or triangle waveform. The input signal waveform is not limited to sinusoidal and can also be an arbitrary waveform. In some implementations, the electromagnetic power converter includes one or more magnetic cores, coil windings wrapped on the magnetic cores, one or more controllable magnetic flux valves, and a driver circuit and a controller for the one or more magnetic flux valves. The power converter achieves conversion of amplitude, frequency, and/or waveform by electrically controlling magnetic fluxes without using mechanical moving parts. 
     In some implementations, the magnetic flux valve is a voltage-controlled static magnetic device made of magnetoelectric materials. The permeability of the magnetic flux valve is regulated by the control voltage applied to the valve, which is supplied by the driver circuit and controlled by the controller. The driver circuit can be implemented by using a power electronic converter or other devices that can output controllable voltages. A change of the permeability of the magnetic flux valve leads to changes of the reluctance of the magnetic flux valve and the reluctance of the magnetic core legs of the EM power converter containing the magnetic flux valve. The magnetic flux valve actively controls the magnetic flux distribution in the EM power converter. As the magnetic flux distribution changes, the flux linkage of each winding changes and thus the voltage induced across each winding can be controlled. The EM power converter can convert one or more AC inputs to one or more AC outputs with controllable amplitude, frequency, phase and waveform. 
     The power and energy needed to drive the magnetic flux valve are much lower than the power rating and energy flow, respectively, of the EM power converter. The output voltages of the magnetic flux valve driver circuit and the EM power converter are measured and used by a controller to control the driver circuit to supply desired voltages for the magnetic flux valves according to reference values provided to the controller. The reference values can be, e.g., the desired amplitude, frequency, etc., of the output voltages of the EM power converter. For example, the reference values can be provided by an operator, or by another system that sets the desired amplitude and frequency of the AC output voltage. 
     In some implementations, the EM power converter can have the following features. The voltage conversion ratio (i.e., ratio of output voltage to input voltage) of the EM power converter can be continuously adjustable. The EM power converter can perform frequency conversion. The EM power converter can have a power capacity ranging from low to high, a voltage rating ranging from low to high, and a current rating ranging from low to high. The EM power converter can have a static operation with no mechanical moving parts, have a low complexity of thermal management, and does not need a harmonic filter (which may be used in conventional power electronic converters to suppress harmonics). The EM power converter can have a fast dynamic response, low maintenance requirement, high reliability, and long life expectance, e.g., more than 25 years. 
     Referring to  FIG. 1 , in some implementations, an EM power converter system  100  includes an EM power converter  102 , a magnetic flux valve driver circuit  104 , and a controller  106 . The EM power converter  102  may include multiple modules, in which each module can include a magnetic core with multiple legs, one or more magnetic flux valves in some legs of the magnetic core, and coil windings wrapped on the core legs.  FIG. 1  shows an example in which the EM power converter  102  includes nine modules, but the EM power converter  102  can also include other numbers of modules. The numbers of core legs, magnetic flux valves, and coil windings in each module depend on the design. In this document, the term “core section” is used to refer to a section of the magnetic core, and can include a core leg and one or more magnetic flux valves. 
       FIGS. 2A and 2B  illustrate two exemplary configurations of an EM power converter module. Referring to  FIG. 2A , in some implementations, an EM power converter module  120  has three core legs—a center core leg  122 , a first side core leg  124 , and a second side core leg  126 . The first side core leg  124  has a first magnetic flux valve  128 , and the second side core leg  126  has a second magnetic flux valve  130 . A primary winding  132  is wound around the center core leg  122 , a first secondary winding  134  is wound around the first side core leg  124 , and a second secondary winding  136  is wound around the second side core leg  126 . 
     Referring to  FIG. 2B , in some implementations, an EM power converter module  140  has four core legs—a center core leg  142 , a first side core leg  144 , a second side core leg  146 , and a third side core leg  148 . Each of the side core legs has two magnetic flux valves. The first side core leg  144  has a first magnetic flux valve  150 A and a second magnetic flux valve  150 B. The second side core leg  146  has a first magnetic flux valve  152 A and a second magnetic flux valve  152 B. The third side core leg  148  has a first magnetic flux valve  154 A and a second magnetic flux valve  154 B. A primary winding  156  is wound around the center core leg  142 , a first secondary winding  158  is wound around the first side core leg  144 , a second secondary winding  160  is wound around the second side core leg  146 , and a third secondary winding  162  is wound around the third side core leg  148 . 
     The magnetic flux valve (e.g.,  128 ,  130 ,  150 A,  150 B,  152 A,  152 B,  154 A, and  154 B) is made of magnetoelectric materials, whose permeabilities can be regulated by controlling the external control voltage applied to the valve. The detailed structure and working principles of the three-leg EM power converter module  120  in  FIG. 2A  are illustrated in  FIGS. 3 to 7 . The detailed structure and working principles of the four-leg EM power converter module  140  in  FIG. 2B  are illustrated in  FIGS. 8 to 11 . 
     A Three-Leg EM Power Converter Module 
       FIG. 3A  shows the magnetic circuit of the three-leg EM power converter module  120  in  FIG. 2A . The primary winding  132  of the module is located on the central core leg  122  and connected to an AC voltage source v in    138  (v in =U in  sin ω 1 t) as the input. The turn number of the primary winding  132  is No. The two secondary windings  134 ,  136  of the module are located on the two side core legs  124 ,  126  and connected in series as the output. The turn numbers of the two secondary windings  134 ,  136  are N 1  and N 2 , respectively. In some examples, N 1 =N 2 . 
     As shown in  FIG. 3A , the power converter module  120  has two output terminals  170 ,  172  that are the two dotted terminals of the two secondary windings with the same polarity. Therefore, the output v out =v 1 −v 2 , where v 1  and v 2  are the voltages induced by the first secondary winding  134  and second secondary winding  136 , respectively. The two magnetic flux valves  128 ,  130  in the two side core legs  124 ,  126  are connected with the driver circuit  104 , which supplies controllable voltages to the magnetic flux valves  128 ,  130  to regulate their permeabilities. 
       FIG. 3B  shows an equivalent circuit  180  of the three-leg EM power converter module  120 . The two variable reluctances R x1    182  and R x2    184  represent the equivalent reluctances of the first and second magnetic flux valves  128 ,  130 . The equivalent offset reluctances of the two side core legs are R offset1    186  and R offset2    188 , which are mainly determined by the magnetic properties of the laminated magnetic core made by ferromagnetic or other magnetic materials. Therefore, the total reluctances R 1  of the left core leg and R 2  of the right core leg are
 
 R   1   =R   offset1   +R   x1   (Equ. 1)
 
 R   2   =R   offset2   +R   x2   (Equ. 2)
 
     In  FIG. 3B , R 0    190  is the equivalent reluctance of the central core leg  122  wrapped by the primary winding  132 , i n  is the current through the primary winding  132 , and ϕ 0  is the magnetic flux generated by the current i in  (called the main flux). The main flux ϕ 0  splits into two parts, which flow through the two side core legs  124  and  126 , respectively. The magnetic fluxes ϕ 1  and ϕ 2  (ϕ 1 +ϕ 2 =ϕ 0 ) through the two side core legs  124 ,  126  will change when the permeabilities of the two magnetic flux valves  128 ,  130  are changed. 
       FIGS. 4A to 4C  illustrate the flux variation process of the three-leg EM power converter module  120  in  FIG. 3A . Assume R offset1 =R offset2  and the two magnetic flux valves  128 ,  130  are the same. When the voltages applied to the two magnetic flux valves  128 ,  130  by the driver circuit  104  are equal, the reluctances of the two side core legs  124 ,  126  are the same (i.e., R 1 =R 2 ) and, therefore, the magnetic fluxes in the two side core legs  124 ,  126  are equal (i.e., ϕ 1 =ϕ 2 ), as illustrated in  FIG. 4A . 
     Referring to  FIG. 4B , when the voltage applied to the left magnetic flux valve  128  by the driver circuit  104  is higher than that applied to the right magnetic flux valve  130 , the left magnetic flux valve  128  has a lower permeability and, therefore, a larger reluctance (i.e., R 1 &gt;R 2 ). In this case, a larger portion of the magnetic flux generated by the current through the primary winding  132  will flow through the right core leg  126 . 
     Referring to  FIG. 4C , when the voltage applied to the left magnetic flux valve  128  by the driver circuit  104  is lower than that applied to the right magnetic flux valve  130 , the left magnetic flux valve  128  has a higher permeability and, therefore, a smaller reluctance (i.e., R 1 &lt;R 2 ). In this case, a larger portion of the magnetic flux generated by the current through the primary winding  132  will flow through the left core leg  124 . 
     If the dotted terminals with the same polarity of the two secondary windings  134 ,  136  are connected in series as shown in  FIG. 3A , the output voltage v out  of the EM power converter module  120  is the differential voltage induced by the two secondary windings  134 ,  136  and is determined by the difference of the magnetic fluxes in the two side core legs  124 ,  126  as well as the difference of the voltages applied to the two magnetic flux valves  128 ,  130 . 
     Suppose that the input voltage v in  applied to the primary winding  132  of the EM power converter module  120  in  FIG. 3A  is sinusoidal. If the difference of the voltages applied to the two magnetic flux valves  128 ,  130  is constant, the output voltage of the EM power converter module  120  will be a sinusoidal waveform, which has the same frequency as that of the input voltage applied on the primary winding  132 . The amplitude of the sinusoidal output voltage is affected by the difference of the voltages applied to the two magnetic flux valves  128 ,  130 , which is shown in  FIG. 5A . 
       FIGS. 5A and 5B  are graphs  200  and  210  that show possible output waveforms that can be provided by the power converter module  120 . In  FIG. 3A , when the magnetic flux valve  128  in the left core leg  124  is controlled such that the left core leg  124  constantly has the minimum reluctance while the magnetic flux valve  130  in the right core leg  126  is controlled such that the right core leg  126  constantly has the maximum reluctance, the minimum and maximum magnetic fluxes will flow through the left core leg and the right core leg, respectively. As a consequence, the voltage v 1  induced on the secondary winding of the left core leg will have the maximum amplitude U 1, max  while voltage v 2  induced on the secondary winding of the right core leg will have the minimum amplitude U 2, min . The output voltage v out , which is equal to v 1 −v 2  and labeled as Output  1  in  FIG. 5A , is a sinusoidal wave  202  and has the maximum amplitude (U 1, max −U 2, min ). On the contrary, when the magnetic flux valve  128  in the left core leg  124  is controlled such that the left core leg  124  constantly has the maximum reluctance while the magnetic flux valve  130  in the right core leg  126  is controlled such that the right core leg  126  constantly has the minimum reluctance, the output voltage v out , which is labeled as Output  3  in  FIG. 5A , is a sinusoidal wave  204  and also has the maximum amplitude (U 1, max −U 2, min ) but is out of phase with Output  1 . 
     The curves of Output  1  and Output  3  provide the two boundaries for the output voltage of the EM power converter module  120 . In other words, the actual output of the EM power converter module  120 , Output  2 , which has a waveform  206 , can be controlled between the two boundaries, as shown in  FIG. 5A . In this way, the EM power converter module  120  works like a controllable power transformer whose output voltage amplitude can be regulated continuously, i.e., a power transformer with continuous tap changing capability. If the differential voltage supplied by the driver circuit  104  of the two magnetic flux valves  128 ,  130  also varies, the output v out  will no longer be a pure sinusoidal waveform but a modulated waveform  212  of the input voltage and the differential voltage supplied by the driver circuit  104  of the two magnetic flux valves  128 ,  130 , as shown in  FIG. 5B . If the voltages applied to the magnetic flux valves  128 ,  130  are controlled dynamically, both the frequency and the amplitude of the output voltage can be regulated in real time via the modulation. However, the output v out  should still lie between Output  1  and Output  3 , as shown in  FIG. 5B . By synthesizing or superposing such modulated output waveforms from multiple EM power converter modules, the total output can be a pure sinusoidal waveform with controllable amplitude, frequency and phase. The operating principle of the EM power converter module  120  is based on magnetic flux and voltage modulation and synthesization, which is described below for sinusoidal input and output. 
     Consider the three-leg EM power converter module  120  in  FIG. 3A . Assume that the primary AC input is a sinusoidal voltage with the frequency ω 1  and the amplitude U in , the turn number of the primary winding  132  is N 0 , the turn numbers of the two secondary windings  134 ,  136  are N (i.e., N 1 =N 2 =N), and the main flux generated by the current through the primary winding  132  is ϕ 0 . Then the main flux can be expressed as 
                     ϕ   0     =       -       U   in         N   0     ⁢     ω   1           ⁢   sin   ⁢           ⁢     ω   1     ⁢   t             (     Equ   .           ⁢   3     )               
The main flux ϕ 0  splits into two parts, which flow through the two side core legs  124 ,  126 , respectively. The distribution of the magnetic flux in the left and right core legs  124 ,  126  is dependent on the reluctances R 1  and R 2  of the two core legs  124 ,  126 . Let R x1 =ΔR and R x2 =−ΔR. Then R 1  in Equation 1 and R 2  in Equation 5 can be expressed as follows.
 
 R   1   =R   offset1   +ΔR   (4)
 
 R   2   =R   offset2   −ΔR   (5)
 
     The reluctance R 1  (R 2 ) consists of two components: a fixed offset component R offset1  (R offset2 ) and a fluctuating component AR. The value of the offset component is mainly determined by the reluctance of the laminated magnetic core leg, while the value of ΔR depends on the permeability of the magnetic flux valve, which can be controlled by adjusting the voltage applied to the magnetic flux valve. In some examples, R offset1  and R offset2  have the same value and, therefore, are denoted as R offset  (i.e., R offset1 =R offset2 =R offset ) in the remaining text. 
     The flux ϕ 1  in the left core leg  124  and the flux ϕ 2  in right core leg  126  can be calculated as follows 
                     ϕ   1     =         ϕ   0     ⁢       R   2         R   1     +     R   2           =         ϕ   0     ⁢         R   offset     -     Δ   ⁢           ⁢   R           (       R   offset     +     Δ   ⁢           ⁢   R       )     +     (       R   offset     -     Δ   ⁢           ⁢   R       )           =       ϕ   0     ⁢         R   offset     -     Δ   ⁢           ⁢   R         2   ⁢     R   offset                       (   6   )                 ϕ   2     =         ϕ   0     ⁢       R   2         R   1     +     R   2           =         ϕ   0     ⁢         R   offset     +     Δ   ⁢           ⁢   R           (       R   offset     +     Δ   ⁢           ⁢   R       )     +     (       R   offset     -     Δ   ⁢           ⁢   R       )           =       ϕ   0     ⁢         R   offset     +     Δ   ⁢           ⁢   R         2   ⁢     R   offset                       (   7   )               
where ϕ 0 =ϕ 1 +ϕ 2 .
 
     By changing the fluctuating reluctance ΔR, ϕ 1  and ϕ 2  can be regulated. The voltages v 1  and v 2  induced on the two secondary windings  134 ,  136  are 
                     v   1     =         -   N     ⁢       d   ⁢           ⁢     ϕ   1       dt       =       -   N     ⁢     1     2   ⁢     R   offset         ⁢       d   ⁡     [       (       R   offset     -     Δ   ⁢           ⁢   R       )     ⁢     ϕ   0       ]       dt                 (   8   )                 v   2     =         -   N     ⁢       d   ⁢           ⁢     ϕ   2       dt       =       -   N     ⁢     1     2   ⁢     R   offset         ⁢       d   ⁡     [       (       R   offset     +     Δ   ⁢           ⁢   R       )     ⁢     ϕ   0       ]       dt                 (   9   )               
The output voltage v out  of this three-leg EM power converter module  120  is the difference of the voltages induced on the two secondary windings  134 ,  136  expressed as follows.
 
                     v   out     =         v   1     -     v   2       =         -   N     ⁢       d   ⁡     (       ϕ   1     -     ϕ   2       )       dt       =         -     N     2   ⁢     R   offset           ⁢     d   dt     ⁢     (       -   2     ⁢     ϕ   0     ⁢   Δ   ⁢           ⁢   R     )       =       N     R   offset       ⁢     d   dt     ⁢     (       ϕ   0     ⁢   Δ   ⁢           ⁢   R     )                     (   10   )               
where the flux term (ϕ 1 −ϕ 2 ) is called the synthesized flux through the two side (secondary) core legs  124 ,  126  of the three-leg EM power converter module  120 , which induces the output voltage of the three-leg EM power converter module  120 . Substituting the expression of ϕ 0  in Equation 3 into Equation 10, v out  can be expressed as follows
 
     
       
         
           
             
               
                 
                   
                     v 
                     out 
                   
                   = 
                   
                     
                       - 
                       
                         N 
                         
                           R 
                           offset 
                         
                       
                     
                     ⁢ 
                     
                       
                         U 
                         in 
                       
                       
                         
                           N 
                           0 
                         
                         ⁢ 
                         
                           ω 
                           1 
                         
                       
                     
                     ⁢ 
                     
                       
                         d 
                         dt 
                       
                       ⁡ 
                       
                         [ 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           R 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   ω 
                                   1 
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The value of ΔR can be controlled to be a time-varying function by the controller  106  of the magnetic flux valves. Assume that the value of ΔR is controlled to be the following sinusoidal function of time t with the frequency ω 2  and amplitude Ramp.
 
Δ R=R   amp  sin(ω 2   t )  (12)
 
Substituting Equation 12 into Equations 6 and 7, the flux ϕ 1  in the left core leg  124  and the flux ϕ 2  in right core leg  126  become
 
                     ϕ   1     =           ϕ   0     2     ⁢     (     1   -       Δ   ⁢           ⁢   R       R   offset         )       =           ϕ   0     2     ⁡     [     1   -         R   amp       R   offset       ⁢     sin   ⁡     (       ω   2     ⁢   t     )           ]       =       -       U   in       2   ⁢     N   0     ⁢     ω   1           ⁢       sin   ⁡     (       ω   1     ⁢   t     )       ⁡     [     1   -         R   amp       R   offset       ⁢     sin   ⁡     (       ω   2     ⁢   t     )           ]                     (   13   )                 ϕ   2     =           ϕ   0     2     ⁢     (     1   +       Δ   ⁢           ⁢   R       R   offset         )       =           ϕ   0     2     ⁡     [     1   +         R   amp       R   offset       ⁢     sin   ⁡     (       ω   2     ⁢   t     )           ]       =       -       U   in       2   ⁢     N   0     ⁢     ω   1           ⁢       sin   ⁡     (       ω   1     ⁢   t     )       ⁡     [     1   +         R   amp       R   offset       ⁢     sin   ⁡     (       ω   2     ⁢   t     )           ]                     (   14   )               
The magnetic flux ϕ 1  (ϕ 2 ) is a modulated waveform of the part of the main flux with the frequency ω 1  through the left (right) core leg and the fluctuating reluctance ΔR of the magnetic flux valve with the frequency ω 2  in the left (right) core leg generated by the time-varying voltage applied to the magnetic flux valve  120 .
 
       FIG. 6  is a graph  220  showing the waveforms of ϕ 0 , ϕ 1  and ϕ 2 . Substituting Equation 12 into Equation 11, then v out  can be written as 
                     v   out     =       -       NU   in         R   offset     ⁢     N   0     ⁢     ω   1           ⁢       d   dt     ⁡     [       R   amp     ⁢   sin   ⁢           ⁢     ω   1     ⁢   t   ⁢           ⁢   sin   ⁢           ⁢     ω   2     ⁢   t     ]                 (   15   )               
The output voltage of the three-leg EM power converter module  120  is a modulated waveform of a sinusoid with the frequency ω 1  (i.e., the frequency of the input voltage) and another sinusoid with the frequency ω 2  (i.e., the frequency of the variation of the fluctuating reluctance ΔR).
 
Single- or Three-Phase EM Power Converter Formed by Using Multiple Three-Leg Modules
 
     Referring to  FIG. 7 , a single-phase EM power converter  230  can be constructed using three identical three-leg EM power converter modules  232 ,  234 , and  236  (also referred to as module A, module B, and module C), in which their secondary (output) windings  238 ,  240 ,  242 ,  244 ,  246 ,  248  are connected sequentially and their primary (input) windings  250 ,  252 ,  254  are connected to balanced three-phase input voltage Sources v in1 , v in2 , and v in3   
                     v     in   ⁢           ⁢   1       =       U   in     ⁢   cos   ⁢           ⁢     ω   1     ⁢   t             (   16   )                 v     in   ⁢           ⁢   2       =       U   in     ⁢   cos   ⁢           ⁢     (         ω   1     ⁢   t     -       2   ⁢   π     3       )               (   17   )                 v     in   ⁢           ⁢   3       =       U   in     ⁢   cos   ⁢           ⁢     (         ω   1     ⁢   t     +       2   ⁢   π     3       )               (   18   )               
According to Equations 10, 11 and 15, the three-phase output voltages v out1 , v out2  and v out3  of the three EM power converter modules  232 ,  234 ,  236  are
 
                     v     out   ⁢           ⁢   1       =         -   N     ⁢           ⁢       d   ⁡     (       ϕ     A   ⁢           ⁢   1       +     ϕ     A   ⁢           ⁢   2         )       dt       =         -       NU   in         R   offset     ⁢           ⁢     N   0     ⁢     ω   1           ⁢       d   dt     ⁡     [     Δ   ⁢           ⁢     R   1     ⁢   sin   ⁢           ⁢     (       ω   1     ⁢   t     )       ]         =       -       NU   in         R   offset     ⁢           ⁢     N   0     ⁢     ω   1           ⁢       d   dt     ⁡     [       R   amp     ⁢           ⁢   sin   ⁢           ⁢     (       ω   1     ⁢   t     )     ⁢     sin   ⁡     (       ω   2     ⁢   t     )         ]                     (   19   )                 v     out   ⁢           ⁢   2       =         -   N     ⁢           ⁢       d   ⁡     (       ϕ     B   ⁢           ⁢   1       +     ϕ     B   ⁢           ⁢   2         )       dt       =         -       NU   in         R   offset     ⁢           ⁢     N   0     ⁢     ω   1           ⁢       d   dt     ⁡     [     Δ   ⁢           ⁢     R   2     ⁢   sin   ⁢           ⁢     (         ω   1     ⁢   t     -       2   ⁢           ⁢   π     3       )       ]         =       -       NU   in         R   offset     ⁢           ⁢     N   0     ⁢     ω   1           ⁢       d   dt     ⁡     [       R   amp     ⁢           ⁢   sin   ⁢           ⁢     (         ω   1     ⁢   t     -       2   ⁢           ⁢   π     3       )     ⁢   sin   ⁢           ⁢     (         ω   2     ⁢   t     -       2   ⁢           ⁢   π     3       )       ]                     (   20   )                 v     out   ⁢           ⁢   3       =         -   N     ⁢           ⁢       d   ⁡     (       ϕ     C   ⁢           ⁢   1       +     ϕ     C   ⁢           ⁢   2         )       dt       =         -       NU   in         R   offset     ⁢           ⁢     N   0     ⁢     ω   1           ⁢       d   dt     ⁡     [     Δ   ⁢           ⁢     R   3     ⁢   sin   ⁢           ⁢     (         ω   1     ⁢   t     +       2   ⁢           ⁢   π     3       )       ]         =       -       NU   in         R   offset     ⁢           ⁢     N   0     ⁢     ω   1           ⁢       d   dt     ⁡     [       R   amp     ⁢           ⁢   sin   ⁢           ⁢     (         ω   1     ⁢   t     +       2   ⁢           ⁢   π     3       )     ⁢   sin   ⁢           ⁢     (         ω   2     ⁢   t     +       2   ⁢           ⁢   π     3       )       ]                     (   21   )               
where ϕ A1 , ϕ B1 , and ϕ C1  are the magnetic fluxes through the left core legs of the three modules A, B, and C, respectively. The magnetic fluxes ϕ A1 , ϕ B1 , and ϕ C1  are generated by the modulation of the part of the main fluxes with the frequency ω 1  through the magnetic flux valves and the time-varying fluctuating reluctances of the magnetic flux valves with the frequency ω 2  in the left core legs of the three modules. The symbols ϕ A2 , ϕ B2 , and ϕ C2  represent the magnetic fluxes through the right core legs of the three modules A, B, and C, respectively. The magnetic fluxes ϕ A2 , ϕ B2 , and ϕ C2  are generated by the modulation of the part of the main fluxes with the frequency ω 1  through the magnetic flux valves and the time-varying fluctuating reluctances of the magnetic flux valves with the frequency ω 2  in the right core legs of the three modules A, B, and C.
 
     The fluctuating reluctances of the three EM power converter modules, ΔR 1 , ΔR 2 , and ΔR 3 , are controlled to be three balanced sinusoidal functions as follows 
                     Δ   ⁢           ⁢     R   1       =       R   amp     ⁢           ⁢   sin   ⁢           ⁢     (       ω   12     ⁢   t     )               (   22   )                 Δ   ⁢           ⁢     R   2       =       R   amp     ⁢           ⁢   sin   ⁢           ⁢     (         ω   2     ⁢   t     -       2   ⁢           ⁢   π     3       )               (   23   )                 Δ   ⁢           ⁢     R   3       =       R   amp     ⁢           ⁢   sin   ⁢           ⁢     (         ω   2     ⁢   t     +       2   ⁢           ⁢   π     3       )               (   24   )               
The total output voltage of the single-phase EM power converter  230 , v out_sum , is the summation of the outputs of the three modules A, B, C and is expressed as follows.
 
                     v     out   ⁢   _   ⁢   sum       =         v     out   ⁢           ⁢   1       +     v     out   ⁢           ⁢   2       +     v     out   ⁢           ⁢   3         =         -   N     ⁢           ⁢       d   ⁡     (       ϕ     A   ⁢           ⁢   1       +     ϕ     B   ⁢           ⁢   1       +     ϕ     C   ⁢           ⁢   1       -     ϕ     A   ⁢           ⁢   2       -     ϕ     B   ⁢           ⁢   2       -     ϕ     C   ⁢           ⁢   2         )       dt       =       3   2     ⁢     N     N   0       ⁢       R   amp       R   offset       ⁢         ω   2     -     ω   1         ω   1       ⁢     U     i   ⁢           ⁢   n       ⁢           ⁢     sin   ⁡     (       ω   2     -     ω   1       )       ⁢   t                 (   25   )               
where (ϕ A1 +ϕ B1 +ϕ C1 −ϕ A2 −ϕ B2 −ϕ C2 ) is called the synthesized magnetic flux through all secondary core legs of the EM power converter  230  shown in  FIG. 7 , which induces the output voltage of the EM power converter  230 . The synthesized magnetic flux has a sinusoidal waveform with the frequency of (ω 2 −ω 1 ). Thus, a sinusoidal voltage v out  sum with the frequency of (ω 2 −ω 1 ) is generated at the output of the EM power converter  230 , which is, therefore, called a single-phase EM power converter  230 .
 
     The amplitude of the output voltage v out_sum  is determined by the amplitude U in  of the voltages applied to the primary windings  250 ,  252 ,  254  of the modules A, B, C, the turn ratio N/No of each module, a frequency-related ratio (ω 2 −ω 1 )/ω 1 , and a reluctance ratio R amp /R offset . Both the frequency and amplitude of the output voltage v out  sum are controllable. Therefore, the EM power converter  230  in  FIG. 7  can perform single-phase variable-voltage and variable-frequency AC-AC electric power conversion. According to the relationship of voltage and magnetic flux (see Equations 8 and 9), as long as the synthesized flux (e.g., in Equation 10) is a sinusoidal function, the output voltage induced from the synthesized flux will be a sinusoidal function. Therefore, the general principle of the sinusoidal flux synthesization is to make the algebraic summation of the magnetic fluxes used to generate an output voltage of the EM power converter  230  be a sinusoidal function. However, the input and output of the EM power converter  230  are not limited to sinusoidal waveforms. Other AC waveforms, such as square wave, triangular wave, etc., can also be used and generated, as long as an appropriate magnetic flux modulation and synthesization method is used. 
       FIGS. 8( a ) to 8( c )  are graphs that show the waveforms of the magnetic fluxes inside the three modules A, B, and C of the EM power converter  230 , respectively, which include the main flux through the central core leg (e.g.,  268 ) and the fluxes through the two side (secondary) core legs (e.g.,  270 ,  272 ) generated by modulation of each power converter module. In each power converter module, the main flux generated by the current through the primary winding splits into two parts. By controlling the magnetic flux valves  256 ,  258 ,  260 ,  262 ,  264 ,  266 , the magnetic flux in each secondary core leg is generated by modulating the part of the main flux through the core leg with the fluctuating reluctance of the magnetic flux valve in the core leg, which is controlled by the time-varying voltage supplied by the driver circuit  104  of the magnetic flux valve. 
       FIG. 8( d )  is a graph that shows the waveforms of the main fluxes in the three modules A, B, C and the synthesized magnetic flux through all secondary windings (e.g.,  270 ,  272 ) of the EM power converter  230 . Both the main fluxes and the synthesized flux are pure sinusoidal waveforms. 
     A three-phase EM power converter can be constructed by using three single-phase EM power converters shown in  FIG. 7  for variable-voltage and variable-frequency three-phase AC-AC electric power conversion. If the inputs to the three single-phase EM power converters are a balanced three-phase AC voltage source, then the outputs of the three single-phase EM power converters, i.e., the output of the three-phase EM power converter, will be balanced three-phase AC voltages as well. 
     For example, suppose that the three modules in  FIG. 7  form the A phase of the three-phase EM power converter with the output voltage v outA  equal to v out_sum  in Equation (25), i.e., 
     
       
         
           
             
               v 
               
                 out 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 A 
               
             
             = 
             
               
                 3 
                 2 
               
               ⁢ 
               
                 N 
                 
                   N 
                   0 
                 
               
               ⁢ 
               
                 
                   R 
                   amp 
                 
                 
                   R 
                   offset 
                 
               
               ⁢ 
               
                 
                   
                     ω 
                     2 
                   
                   - 
                   
                     ω 
                     1 
                   
                 
                 
                   ω 
                   1 
                 
               
               ⁢ 
               
                 U 
                 
                   i 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   n 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 sin 
                 ⁡ 
                 
                   ( 
                   
                     
                       ω 
                       2 
                     
                     - 
                     
                       ω 
                       1 
                     
                   
                   ) 
                 
               
               ⁢ 
               t 
             
           
         
       
     
     The input terminals of the three modules in the B and C phases of the three-phase EM power converter are connected to the balanced three-phase voltage sources v in1 , v in2 , and v in3  in the same way as those in the A phase shown in  FIG. 7 . However, the fluctuating reluctances of the three modules A, B, and C in the B phase are controlled to be ΔR 2 , ΔR 3 , and ΔR 1 , respectively. Then, the output voltage v outB  of the B phase is: 
               v     out   ⁢           ⁢   B       =       3   2     ⁢     N     N   0       ⁢       R   amp       R   0       ⁢         ω   2     -     ω   1         ω   1       ⁢     U     i   ⁢           ⁢   n       ⁢           ⁢     sin   ⁡     [         (       ω   2     -     ω   1       )     ⁢   t     -       2   ⁢           ⁢   π     3       ]               
The fluctuating reluctances of the three modules A, B, and C in the C phase are controlled to be ΔR 3 , ΔR 1 , and ΔR 2 , respectively. Then, the output voltage v outC  of the C phase is:
 
               v     out   ⁢           ⁢   C       =       3   2     ⁢     N     N   0       ⁢       R   amp       R   0       ⁢         ω   2     -     ω   1         ω   1       ⁢     U     i   ⁢           ⁢   n       ⁢           ⁢     sin   ⁡     [         (       ω   2     -     ω   1       )     ⁢   t     +       2   ⁢           ⁢   π     3       ]               
Therefore, the three-phase EM power converter made of the nine identical modules shown in  FIGS. 2A and 3A  will output balanced three-phase sinusoidal voltages with controllable frequency and amplitude.
 
Four-Leg EM Power Converter Module
 
     The physical configuration, equivalent circuit, and operating principles of the four-leg EM power converter module  140  shown in  FIG. 2B  are described below. 
       FIG. 9A  is the top view of the physical configuration of the four-leg EM power converter module  140  shown in  FIG. 2B .  FIG. 9B  is the equivalent circuit of the module  140  shown in  FIG. 9A . As shown in  FIGS. 9A and 9B , the current iin through the primary winding  156  on the central core leg  142  generates the main magnetic flux, which then splits into three branches and flows through the three side (secondary) core legs  144 ,  146 ,  148 . The principle of regulating the reluctances of the magnetic flux valves for the magnetic flux redistribution and modulation is the same as that of the three-leg EM power converter module  120 . The magnetic flux will be redistributed if the reluctance(s) of any core leg(s) changes by controlling the magnetic flux valves. 
     Three-Phase EM Power Converter Formed by Using Multiple Four-Leg Modules 
     Referring to  FIG. 10 , an EM power converter  280  with a three-phase output can be implemented using three four-leg power converter modules  282 ,  284 ,  286  (which have the same configuration as power converter module  140  of  FIGS. 2B and 9 ). The notations of the fluxes and reluctances in each phase of the EM power converter are the same as those in  FIG. 9  by adding a phase index A, B or C in their subscripts, as in the following Equations 26 to 47. 
     Assume that the AC inputs on the primary windings (e.g.,  288 ) of the three modules  282 ,  284 ,  286  are balanced three-phase sinusoidal voltages with the frequency ω 1  and the amplitude U in , all of the primary windings have the same turn number N 0 , and all of the secondary windings (e.g.,  290 ) have the same turn number N 1 . If the main magnetic fluxes ϕ A0 , ϕ B0  and ϕ C0  of the three modules  282 ,  284 ,  286  generated by the currents through their primary windings are balanced three-phase sinusoidal functions as follows, 
                     ϕ     A   ⁢           ⁢   0       =         U   in         N   0     ⁢     ω   1         ⁢   sin   ⁢           ⁢     (       ω   1     ⁢   t     )               (   26   )                 ϕ     B   ⁢           ⁢   0       =       -       U   in         N   0     ⁢     ω   1           ⁢   sin   ⁢           ⁢     (         ω   1     ⁢   t     -       2   ⁢           ⁢   π     3       )               (   27   )                 ϕ     C   ⁢           ⁢   0       =       -       U   in         N   0     ⁢     ω   1           ⁢   sin   ⁢           ⁢     (         ω   1     ⁢   t     +       2   ⁢           ⁢   π     3       )               (   28   )               
then the distribution of the main flux in the three secondary (side) core legs of each module  282 ,  284 ,  286  is dependent on the reluctances of the three secondary core legs. Consider for example Module A  282 . Assume that the reluctances of the three secondary core legs are R A1 , R A2  and R A3  expressed as follows.
 
                     R     A   ⁢           ⁢   1       =       R   offset     +     Δ   ⁢           ⁢     R     A   ⁢           ⁢   1                   (   29   )                 R     A   ⁢           ⁢   2       =       R   offset     +     Δ   ⁢           ⁢     R     A   ⁢           ⁢   2                   (   30   )                 R     A   ⁢           ⁢   3       =       R   offset     +     Δ   ⁢           ⁢     R     A   ⁢           ⁢   3                   (   31   )               
Each of the reluctances R A1 , R A2  and R A3  consists of two components: a fixed offset component R offset  (i.e., assume R offset1 =R offset2 =R offset3 =R offset ) and a fluctuating component ΔR A1 , ΔR A2  and ΔR A3 , respectively. The value of R offset  is mainly determined by the reluctance of the laminated core leg, while the values of ΔR A1 , ΔR A2  and ΔR A3  are determined by the corresponding magnetic flux valve in the core leg.
 
     As described previously, the total reluctance of each secondary core leg of the power converter module can be controlled by changing the permeability (thus the fluctuating reluctance) of the magnetic flux valves in the core leg, which is achieved by the controlling the voltages applied to magnetic flux valves by the driver circuit (e.g.,  104 ). In this way, the magnetic fluxes ϕ A1 , ϕ A2 , and ϕ A3  in the three side core legs of Module A can be controlled via modulation: 
                     ϕ     A   ⁢           ⁢   1       =         ϕ     A   ⁢           ⁢   0       3     ⁡     [     1   +       K   ·   sin     ⁢           ⁢     (       ω   2     ⁢   t     )         ]               (   32   )                 ϕ     A   ⁢           ⁢   2       =         ϕ     A   ⁢           ⁢   0       3     ⁡     [     1   +       K   ·   sin     ⁢           ⁢     (         ω   2     ⁢   t     -       2   ⁢           ⁢   π     3       )         ]               (   33   )                 ϕ     A   ⁢           ⁢   3       =         ϕ     A   ⁢           ⁢   0       3     ⁡     [     1   +       K   ·   sin     ⁢           ⁢     (         ω   2     ⁢   t     +       2   ⁢           ⁢   π     3       )         ]               (   34   )               
where ϕ A0 =ϕ A1 +ϕ A2 +ϕ A3  and K is the split ratio of the modulated term of the main magnetic flux flowing through the three secondary core legs, and ω 2  is the frequency of the variations of the fluctuating reluctances of the magnetic flux valves. The magnetic fluxes ϕ A1 , ϕ A2 , and ϕ A3  are modulated waveforms of the main flux and the fluctuating reluctances. The value of K and the reluctances R A1 , R A2  and R A3  have the following relations:
 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           R 
                           
                             A 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       ⁢ 
                       
                         
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                         ⁡ 
                         
                           ( 
                           t 
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                             ( 
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                         ⁢ 
                         
                           
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                             ( 
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                   = 
                   
                     
                       1 
                       3 
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         + 
                         
                           K 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ω 
                             2 
                           
                           ⁢ 
                           t 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           R 
                           
                             A 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ⁡ 
                         
                           ( 
                           t 
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                           R 
                           
                             A 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                     
                       
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   = 
                   
                     
                       1 
                       3 
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           K 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   t 
                                 
                                 - 
                                 
                                   
                                     2 
                                     3 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           R 
                           
                             A 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           R 
                           
                             A 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                     
                       
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       + 
                       
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             R 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   = 
                   
                     
                       1 
                       3 
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           K 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     2 
                                     3 
                                   
                                   ⁢ 
                                   π 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
           
         
       
     
     When the value of K is given, the reluctances R A1 , R A2  and R A3  and therefore the fluctuating reluctances ΔR A1 , ΔR A2  and ΔR A3  can be calculated. The driver circuit of the magnetic flux valves can be controlled by the controller to supply proper voltages for the magnetic flux valves in the three secondary core legs to control their fluctuating reluctances at the desired values. 
     The magnetic fluxes ϕ B1 , ϕ B2  and ϕ B3  in the three secondary core legs of Module B  284  and the magnetic fluxes ϕ C1 , ϕ C2  and ϕ C3  in the three secondary core legs of Module C  286  can be controlled in the same way from the B and C phases of the balanced three-phase input source, respectively: 
     
       
         
           
             
               
                 
                   
                     ϕ 
                     
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       
                         ϕ 
                         
                           B 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       3 
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           K 
                           · 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   ω 
                                   2 
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       
                         ϕ 
                         
                           B 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       3 
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           K 
                           · 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   t 
                                 
                                 - 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     
                       B 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                   = 
                   
                     
                       
                         ϕ 
                         
                           B 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       3 
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           K 
                           · 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     
                       C 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       
                         ϕ 
                         
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       3 
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           K 
                           · 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   ω 
                                   2 
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   41 
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     
                       C 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       
                         ϕ 
                         
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       3 
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           K 
                           · 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   t 
                                 
                                 - 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     
                       C 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                   = 
                   
                     
                       
                         ϕ 
                         
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       3 
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           K 
                           · 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   43 
                   ) 
                 
               
             
           
         
       
     
       FIG. 10  also shows the flux lines of the three four-leg EM power converter modules  282 ,  284 ,  286 . The secondary windings of the three four-leg EM power converter modules  282 ,  284 ,  286  are connected in a specific sequence as illustrated in  FIG. 10  such that the synthesized magnetic fluxes ϕ out1 , ϕ out2  and ϕ out3  through the secondary windings of the EM power converter  280  are balanced three-phase sinusoidal functions expressed as follows. In some implementations, the secondary windings generating ϕ A1 , ϕ B2  and ϕ C3  are connected in series; the secondary windings generating ϕ A2 , ϕ B3  and ϕ C1  are connected in series; and the secondary windings generating ϕ A3 , ϕ B1  and ϕ C2  are connected in series. 
                     ϕ     out   ⁢           ⁢   1       =         ϕ     A   ⁢           ⁢   1       +     ϕ     B   ⁢           ⁢   2       +     ϕ     C   ⁢           ⁢   3         =         K   3     ⁡     [         ϕ     A   ⁢           ⁢   0       ⁢           ⁢     sin   ⁡     (       ω   2     ⁢   t     )         +       ϕ     B   ⁢           ⁢   0       ⁢           ⁢     sin   ⁡     (         ω   2     ⁢   t     -       2   ⁢   π     3       )         +       ϕ     C   ⁢           ⁢   0       ⁢           ⁢     sin   ⁡     (         ω   2     ⁢   t     +       2   ⁢   π     3       )           ]       =       -       K   ⁢           ⁢     ϕ   max       3       ⁢     3   2     ⁢     cos   ⁢           [       (       ω   2     -     ω   1       )     ⁢   t     ]                   (   44   )                 ϕ     out   ⁢           ⁢   2       =         ϕ     A   ⁢           ⁢   2       +     ϕ     B   ⁢           ⁢   3       +     ϕ     C   ⁢           ⁢   1         =         K   3     ⁡     [         ϕ     A   ⁢           ⁢   0       ⁢           ⁢     sin   ⁡     (         ω   2     ⁢   t     -       2   ⁢   π     3       )         +       ϕ     B   ⁢           ⁢   0       ⁢           ⁢     sin   ⁡     (         ω   2     ⁢   t     +       2   ⁢   π     3       )         +       ϕ     C   ⁢           ⁢   0       ⁢           ⁢     sin   ⁡     (       ω   2     ⁢   t     )           ]       =       -       K   ⁢           ⁢     ϕ   max       3       ⁢     3   2     ⁢     cos   ⁢           [         (       ω   2     -     ω   1       )     ⁢   t     -       2   ⁢   π     3       ]                   (   45   )                 ϕ     out   ⁢           ⁢   3       =         ϕ     A   ⁢           ⁢   3       +     ϕ     B   ⁢           ⁢   1       +     ϕ     C   ⁢           ⁢   2         =         K   3     ⁡     [         ϕ     A   ⁢           ⁢   0       ⁢           ⁢     sin   ⁡     (         ω   2     ⁢   t     +       2   ⁢   π     3       )         +       ϕ     B   ⁢           ⁢   0       ⁢           ⁢     sin   ⁡     (       ω   2     ⁢   t     )         +       ϕ     C   ⁢           ⁢   0       ⁢           ⁢     sin   ⁡     (         ω   2     ⁢   t     -       2   ⁢   π     3       )           ]       =       -       K   ⁢           ⁢     ϕ   max       3       ⁢     3   2     ⁢     cos   ⁢           [         (       ω   2     -     ω   1       )     ⁢   t     +       2   ⁢   π     3       ]                   (   46   )               
where ϕ max  is the amplitude of the main magnetic fluxes of the three four-leg EM power converter modules  282 ,  284 ,  286  defined as follows
 
     
       
         
           
             
               
                 
                   
                     ϕ 
                     max 
                   
                   = 
                   
                     
                        
                       
                         ϕ 
                         
                           A 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                        
                     
                     = 
                     
                       
                          
                         
                           ϕ 
                           
                             B 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                          
                       
                       = 
                       
                         
                            
                           
                             ϕ 
                             
                               C 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               0 
                             
                           
                            
                         
                         = 
                         
                           
                             U 
                             
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                             
                           
                           
                             
                               N 
                               0 
                             
                             ⁢ 
                             
                               ω 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   47 
                   ) 
                 
               
             
           
         
       
     
     The synthesized magnetic fluxes ϕ out1 , ϕ out2  and ϕ out3  will generate the following balanced three-phase sinusoidal voltages at the output of the three-phase EM power converter  280 . 
     
       
         
           
             
               
                 
                   
                     v 
                     
                       out 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   = 
                   
                     
                       K 
                       2 
                     
                     ⁢ 
                     
                       
                         N 
                         1 
                       
                       
                         N 
                         0 
                       
                     
                     ⁢ 
                     
                       
                         
                           ω 
                           2 
                         
                         - 
                         
                           ω 
                           1 
                         
                       
                       
                         ω 
                         1 
                       
                     
                     ⁢ 
                     
                       U 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         [ 
                         
                           
                             ( 
                             
                               
                                 ω 
                                 2 
                               
                               - 
                               
                                 ω 
                                 1 
                               
                             
                             ) 
                           
                           ⁢ 
                           t 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   48 
                   ) 
                 
               
             
             
               
                 
                   
                     v 
                     
                       out 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   = 
                   
                     
                       K 
                       2 
                     
                     ⁢ 
                     
                       
                         N 
                         1 
                       
                       
                         N 
                         0 
                       
                     
                     ⁢ 
                     
                       
                         
                           ω 
                           2 
                         
                         - 
                         
                           ω 
                           1 
                         
                       
                       
                         ω 
                         1 
                       
                     
                     ⁢ 
                     
                       U 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               ( 
                               
                                 
                                   ω 
                                   2 
                                 
                                 - 
                                 
                                   ω 
                                   1 
                                 
                               
                               ) 
                             
                             ⁢ 
                             t 
                           
                           - 
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             3 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   49 
                   ) 
                 
               
             
             
               
                 
                   
                     v 
                     
                       out 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                   = 
                   
                     
                       K 
                       2 
                     
                     ⁢ 
                     
                       
                         N 
                         1 
                       
                       
                         N 
                         0 
                       
                     
                     ⁢ 
                     
                       
                         
                           ω 
                           2 
                         
                         - 
                         
                           ω 
                           1 
                         
                       
                       
                         ω 
                         1 
                       
                     
                     ⁢ 
                     
                       U 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               ( 
                               
                                 
                                   ω 
                                   2 
                                 
                                 - 
                                 
                                   ω 
                                   1 
                                 
                               
                               ) 
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             3 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   50 
                   ) 
                 
               
             
           
         
       
     
     Compared to the single-phase EM power converter  230  formed by using three-leg modules in  FIG. 7 , the three-phase EM power converter  280  formed by using four-leg modules  282 ,  284 ,  286  has the advantages of being more compact, using less materials, and requiring only three modules to generate a three-phase AC output. 
       FIGS. 11( a ) to 11( d )  are graphs that show the magnetic flux waveforms in the four core legs of each power converter module A  282 , B  284 , C  286  and the synthesized flux waveforms through the secondary windings of the three phases of the EM power converter  280 . The main flux in each four-leg EM power converter module is a sinusoidal waveform. The fluxes through the three secondary core legs of each module are modulated sinusoidal waveforms, and the three synthesized fluxes through the secondary windings of the EM power converter  280  are balanced three-phase sinusoidal waveforms. 
     Other Structures of the EM Power Converter 
     The structure of the EM power converter module is not limited to the three-leg and four-leg structures shown in  FIGS. 2A and 2B . Other structures containing more legs can also be designed for the EM power converter module using the same magnetic flux and voltage modulation and synthesization principle. Structure design optimization can be performed to make the EM power converter more compact. 
       FIG. 12A  shows the configuration of a compact three-phase AC-AC EM power converter module  300 , which contains one EM power converter module (i.e., one magnetic core) having nine core legs (e.g.,  302 ). The nine core legs are labeled as A 1 , A 2 , A 3 , B 1 , B 2 , B 3 , C 1 , C 2 , and C 3 , as shown in  FIG. 12B . 
     The three-phase nine-leg EM power converter has a symmetric structure. The nine core legs have the same fixed offset reluctance R offset  as shown in  FIG. 12D . Each core leg has a primary winding  310  and a secondary winding  312  as shown in  FIG. 12C . The flux modulation and synthesization method of the three-phase EM power converter  300  in  FIG. 12A  is the same as that formed by using three three-leg modules in  FIG. 7  and that formed by using three four-leg modules in  FIG. 10 . The connection of the secondary windings on the nine core legs uses the same principle as that of the three-phase EM power converter  280  formed by using three four-leg modules in  FIG. 10 . The difference is that the three-phase nine-leg EM power converter  300  uses three distributed primary windings for each input phase instead of one concentrated primary winding in the EM power converter  140  shown in  FIG. 9A . Because the three-phase magnetic fluxes are symmetric, it is not necessary to wrap the primary windings on separate core legs. In other words, a primary winding and the corresponding secondary winding can be wrapped on the same core leg, as shown in  FIG. 13 . Thus, the core legs on the primary side of the EM power converter formed by using three-leg modules in  FIG. 7  or four-leg modules in  FIG. 10  can be saved, which is similar to a three-phase power transformer. 
       FIG. 13  shows the connection of the primary and secondary windings on the nine core legs of the EM power converter  300 . The connection of the secondary windings is the same as that of the EM power converter  280  in  FIG. 10 . The difference is that in  FIG. 13  the primary windings of each phase consist of three windings on three core legs connected in series. Although the structure of the EM power converter in  FIG. 13  is more compact than those in  FIGS. 7 and 10 , the principle of the flux redistribution, modulation, and synthesization remains the same as that of the EM power converters in  FIGS. 7 and 10 . 
     General Principle of the Magnetic Flux Modulation and Synthesization of a Generic n-Phase EM Power Converter (n=1, 2, 3, . . . ) 
     The working principle of the EM power converter is based on magnetic flux modulation and synthesization. The flux modulation and synthesization method is not limited to that described above and depends on the specific structures of the EM power converter. The flux modulation and synthesization methods share the same principle: the magnetic flux through each secondary core leg generated by the source current(s) through the primary winding(s) is modulated by the fluctuating reluctance(s) of magnetic flux valve(s) in the secondary core leg, which is controlled by the time-varying voltage(s) applied to the magnetic flux valve(s). The modulated magnetic fluxes in different secondary core legs are synthesized to form a desired waveform, such as a sinusoidal wave, a square wave, a triangular wave, or a pulse wave, depending on the input source and the voltages applied to the magnetic flux valves. 
     The magnetic flux modulation determines how the main flux splits into portions that are distributed in the secondary core legs. Consider a general n-leg EM power converter. Its equivalent circuit is shown in  FIG. 14 . If the main magnetic flux generated by the source current(s) i 0  through the primary winding(s) is ϕ 0 , the magnetic fluxes in the n secondary core legs of the n-leg EM power converter has the following relation: 
                       ϕ   1     ⁢     R   1       =         ϕ   2     ⁢     R   2       =     …   =         ϕ   i     ⁢     R   i       =     …   =       ϕ   n     ⁢     R   n                       (   51   )               
where i is the index of the secondary magnetic core leg, n is the total number of the secondary core legs, ϕ i  is the magnetic flux through the secondary core leg i, and R i  is the reluctance of the secondary core leg i. The summation of the magnetic fluxes through all secondary core legs is equal to ϕ 0 :
 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         0 
                       
                       n 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ϕ 
                       i 
                     
                   
                   = 
                   
                     ϕ 
                     0 
                   
                 
               
               
                 
                   ( 
                   52 
                   ) 
                 
               
             
           
         
       
     
     The synthesized magnetic fluxes determine the final output of the n-leg EM power converter because the output voltage(s) are the derivatives of the magnetic fluxes as follows. 
                     v   out     =         ∑     i   =   1     n     ⁢         N   i     ⁢   d   ⁢           ⁢     ϕ   i       dt       =         d   dt     ⁢       ∑     i   =   1     n     ⁢       N   i     ⁢     ϕ   i           ⁢     →         if   ⁢           ⁢     N   1       =     …   =       N   n     =   N         ⁢               ⁢     N   ⁢     d   dt     ⁢       ∑     i   =   1     n     ⁢     ϕ   i                     (   53   )               
where v out  is the final voltage output of some serially connected windings wrapped on the n secondary core legs, and N 1  is the turn number of the induced winding on the secondary core leg i. The synthesization (i.e., algebra summation) of the magnetic fluxes can be a sinusoidal wave, a triangular wave, a pulse wave, or any other waveform depending on the input source and the voltages applied to the magnetic flux valves. The output voltage can be sinusoidal when the synthesized magnetic flux is sinusoidal.
 
     The following describes the sinusoidal magnetic flux modulation and synthesization method. The magnetic flux ϕ i , the reluctance R i  and the split ratio K of the main magnetic flux flowing through the n secondary core legs have the following relation: 
                       ϕ   i       ϕ   0       =         1       R   i     ⁡     (   t   )                       ∑       i   =   1     n     ⁢     1       R   i     ⁡     (   t   )             =       1   n     ⁡     [     1   +     K   ⁢           ⁢     sin   ⁡     (         ω   out     ⁢   t     -           i   -   1     n     ·   2     ⁢           ⁢   π       )           ]                 (   54   )               
where ω ut  (e.g., (ω 2 −ω 1 ) in Equations 12, 25, 48 to 50, etc.) is the objective frequency of the output, which is determined by controlling the magnetic flux valve. When the main flux split ratio K is given, the reluctance R i (t) can be determined. The driver circuit of the magnetic flux valves can be controlled by the controller to supply a proper voltage for the magnetic flux valve in the core leg i to control the reluctance R i (t) at the desired value. By using an n-phase AC input, the EM power converter in  FIG. 14  can generate an n-phase AC output by applying the proper flux modulation and synthesization method.
 
     In some implementations, the EM power converter can also perform AC-DC power conversion. Consider Equation (10) for the single EM converter module in  FIG. 2A . Referring to  FIG. 27 , if ΔR is regulated such that the differential flux (ϕ 1 −ϕ 2 ) (=ϕ 0 ΔR/R offset ) is a triangular wave  460 , then the output voltage v out  is a rectangular wave  462 . By using a diode rectifier  464 , v out  can easily be rectified into a DC voltage v dc    466  without the need for a harmonic filter. A diode rectifier is low cost and reliable and can be built with a high power capacity using the emerging silicon carbide (SiC) diodes to achieve excellent performance. 
     For example, according to Equation (10), controlling (ϕ 1 −ϕ 2 ) to be a triangular wave is equivalent to controlling ϕ 0 ΔR to be a triangular wave, which can be expressed as a time-varying function ƒ, namely, ϕ 0 ΔR=ƒ or ΔR=ƒ/ϕ 0 . Suppose that the relationship between the control voltage v c  and ΔR is expressed mathematically to be v c =g(ΔR), where g is a function and its expression can be obtained from experiment. Therefore, v c =g(ƒ/ϕ 0 ). It indicates that v c  can be controlled according to g(ƒ/ϕ 0 ) such that ϕ 0 ΔR is a triangular wave ƒ and, thus, (ϕ 1 −ϕ 2 ) is a triangular wave. Alternatively, a feedback control system can be used to adjust the control voltage according to a measured feedback signal, such as the amplitude of the output signal, such that the output signal is a square waveform or a triangular waveform. 
     From the configuration prospective, the electromagnetic (EM) power converter is an electromagnetic device containing one or multiple modules for variable-frequency, variable-amplitude and/or variable-waveform AC-AC electric power conversion, in which each module is a magnetic circuit that includes magnetic cores, controllable magnetic flux valves, and coil windings wrapped on magnetic cores. The number of modules in an EM power converter can be one, two, three or more dependent on the specific design. The number of core legs in each EM power converter module can be one, two, three or more dependent on the specific design as well. In the above, three specific structures of the EM power converter module containing three legs, four legs, and nine legs are described. However, the EM power converter can also have other structures. 
     The working principle of the EM power converter is based on magnetic flux modulation and synthesization. The flux modulation and synthesization method is not limited to that described above and depends on the specific structures of the EM power converter. The flux modulation and synthesization methods share the same principle: the magnetic flux through each secondary core leg generated by the source current(s) through the primary winding(s) is modulated by the fluctuating reluctance(s) of magnetic flux valve(s) in the secondary core leg, which is controlled by the time-varying voltage(s) applied to the magnetic flux valve(s) by a driver circuit; the modulated magnetic fluxes in different secondary core legs are then synthesized to form a desired waveform, such as sinusoidal wave, square wave, triangular wave, pulse wave, etc., depending on the input source and the voltages applied to the magnetic flux valves. The magnetic flux modulation determines how the main flux splits and is distributed in the secondary core legs and the synthesized magnetic fluxes determine the final output of the EM power converter. 
     Structure of Magnetic Flux Valve 
     The following describes the structure of a magnetic flux valve (e.g.,  128  and  130  of  FIG. 2A ). A magnetic flux valve is a voltage-controlled static magnetoelectric device. As described above, the magnetic flux valve can be used in a magnetic circuit to actively control the magnetic flux through the magnetic circuit. In some implementations, a magnetic flux valve has a laminated structure that includes one or more magnetostrictive layers and one or more piezoelectric layers. Magnetostrictive materials are the materials whose shape or dimension will change when they are magnetized. The piezoelectric layers can be constructed using piezoelectric sheets or piezoelectric fibers. An external control voltage is applied to the piezoelectric layers. The permeability of the magnetostrictive layers will change when the external control voltage applied to the piezoelectric layers changes, which is referred to as the converse magnetoelectric effect. A permeability change of the magnetic flux valve will lead to a change of the reluctance of the magnetic flux valve and the reluctance of the magnetic circuit containing the magnetic flux valve and, therefore, will lead to a change of the magnetic flux or its distribution in the magnetic circuit. Based on this principle, a magnetic flux valve can be used to regulate the reluctance of a magnetic circuit and, therefore, control the magnetic flux in the magnetic circuit. This is achieved by regulating the external control voltage applied to the magnetic flux valve. This feature can be used for converting alternating current (AC) electric power from one frequency/amplitude/waveform to another frequency/amplitude/waveform. In the following, the concept of magnetic flux valve is first introduced, followed by a description of two feasible structures of the magnetic flux valve. The working principles of the magnetic flux valve are then discussed. 
     Magnetoelectric materials have electric (magnetic) polarization that can be changed by changing the external magnetic (electric) field applied to the materials. This is called the magnetoelectric (converse magnetoelectric) effect. In some implementations, compound multiphase magnetoelectric materials can gain a much stronger magnetoelectric effect than single-phase magnetoelectric materials. 
     Referring to  FIG. 15 , a magnetic circuit  320  includes a magnetic core  322 , a primary winding  324  and a secondary winding  326  wrapped around the magnetic core  322 , and a magnetic flux valve  328 . The magnetic flux valve  328  can be located anywhere in the magnetic loop, e.g., outside the windings, as shown in  FIG. 15 , or inside the windings. When the primary winding  324  is connected to an AC source  332  (i.e., the AC input), closed-loop magnetic flux will be produced and flow through the magnetic core  322  and the magnetic flux valve  328 . Similar to the case where a water valve controls the fluid flux through a pipe, the magnetic flux valve  328  is capable of continuously controlling the flow of the magnetic flux through the magnetic loop. This is achieved by controlling the voltage applied to the magnetic flux valve  328 , which is supplied by a driver circuit  330  connected with the magnetic flux valve  328 . The secondary winding  326  provides an AC output  334 . 
     Two feasible structures of the magnetic flux valve  328  are described below. One example is shown in  FIGS. 16A and 16B , a second example is shown in  FIGS. 17A and 17B . The two structures take advantage of the converse magnetoelectric effect. However, the structure of the magnetic flux valve is not limited to these two. The magnetic flux valve  328  can also have other structures with a controllable permeability. 
     Referring to  FIGS. 16A and 16B , in some implementations, a magnetic flux valve  340  has a laminated structure of two different types of layers made of magnetostrictive materials  342  and piezoelectric materials  344 , respectively. The piezoelectric layers  344  can be made by using thin piezoelectric (e.g., piezo ceramic) sheets or one-direction-aligned piezoelectric fibers. Materials that can be used as the piezoelectric layers include, e.g., lead zirconate titanate (PZT) ceramic sheets or plates, PZT fibers, polyvinylidene fluoride (PVDF) films, and PMN-PT [Pb(Mg 1/3 Nb 2/3 )O 3 —PbTiO 3 ] single crystals. 
     The magnetostrictive layers  342  can be made by using amorphous metal alloy ribbons or foils, such as Metglas iron-based alloy ribbons (or foils) or other materials (such as Terfenol-D (Tb 0.30 Dy 0.70 Fe 1.92 )) that have magnetostrictive effects. The piezoelectric layers  344  are plated with electrodes  346  on both sides. The electrodes  346  can be formed by using a solid pattern or an interdigitated (ID) pattern. 
     In the example of  FIGS. 16A, 16B , the piezoelectric layers  344  are made of thin piezoelectric sheets with solid-pattern electrodes  346  on both sides. The electrodes  346  are connected to two electrode collectors  348  on both sides of the layers using leads or conductive foils. Then, the piezoelectric layers  344  and the magnetostrictive layers  342  are placed alternatively. Depending on the specific design of the magnetic flux valve  340 , these layers can be bonded together with adhesives  350  or stacked in a confined space without bonding. In the former case, the adhesives  350  can be cyanoacrylate adhesives, epoxy resin, or any other type of materials which can perform such a bonding function. In the latter case, the layers can be stacked together tightly in a confined space with a fixed volume. The adjacent electrodes  346  have the same voltage polarity and are connected to the same electrode collector  348 . The two electrode collectors  348  are the positive and negative voltage terminals of the magnetic flux valve and will be connected to the driver circuit  330  ( FIG. 15 ). The polarities of the two electrode collectors  348  can be exchanged depending on the specific application. The circle with a dot in  FIG. 16A  indicates the direction of the magnetic field (flux line). The numbers of the piezoelectric layers and the magnetostrictive layers are dependent on the specific design of the magnetic flux valve. 
     Referring to  FIGS. 17A and 17B , in some implementations, a magnetic flux valve  360  includes piezoelectric layers  362  in which each side of a piezoelectric layer  362  is plated with an electrode  364  and then bonded with a magnetostrictive layer  366 . The three layers (two magnetostrictive layers  366  plus a piezoelectric layer  362 ) form a micro unit. Several micro units are stacked together without bonding. The adjacent electrodes  364  in any two adjacent micro units have the same voltage polarity and are connect to the same electrode collector  368 . The number of the micro units is determined by the specific design of a magnetic flux valve  360 . The two electrode collectors  368  are the positive and negative voltage terminals of the magnetic flux valve  360  and will be connected to the driver circuit  330  ( FIG. 15 ). The circle with a dot in  FIG. 17A  indicates the direction of the magnetic flux. 
     The piezoelectric layers  344 ,  362  in the structures shown in  FIGS. 16A and 17A  can be made by using thin piezoelectric sheets with solid-pattern electrodes. Referring to  FIG. 18 , the piezoelectric layers can also be made by using piezoelectric fibers with an interdigitated-pattern electrode  370 . The piezoelectric fibers are oriented along the longitudinal axis of the laminate. The interdigitated-pattern electrode  370  can be plated on either side or both sides of each piezoelectric fiber layer. When using piezoelectric fibers as the piezoelectric layers in the structures shown in  FIGS. 16A and 17A , respectively, a thin insulation layer  372  can be added between each piezoelectric fiber layer and the adjacent magnetostrictive layer  374  bonded with it, as shown in  FIG. 18 . 
     The following describes the working principles of the magnetic flux valve. The magnetic flux valve takes advantage of the converse magnetoelectric effect caused by the cross interaction between the piezoelectric phase and the magnetic phase in the magnetoelectric materials. The cross interaction is an elastic interaction that couples the electric polarization in the piezoelectric materials and the magnetic polarization in the magnetostrictive materials.  FIG. 19  shows the directions of the magnetic polarization (M) and electric polarization (P) inside the magnetic flux valve  340  shown in  FIG. 16A . When an electric field is applied to the piezoelectric materials  344 , electric polarization is generated in the piezoelectric materials  344  and cause the shape of the piezoelectric materials  344  to change. This is referred to as the inverse piezoelectric effect. In the magnetic flux valve  340 , the external control voltage applied to the piezoelectric layers  344  by the driver circuit  330  will generate an electric field across the piezoelectric layers  344 . The electric field will generate electric polarization in the piezoelectric layers  344 , which will change the shape of the piezoelectric layers  344  in the vertical direction. Since the piezoelectric layers  344  and the magnetostrictive layers  342  are bonded together using adhesives or stacked together tightly in a confined space with a fixed volume, the shape changes in the piezoelectric layers  344  will generate strain, which will be transferred to the magnetostrictive layers  342  immediately. Then, the magnetization of the magnetostrictive materials  342  in the horizontal direction will be altered by the strain. As a consequence, the permeability of the magnetostrictive layers  342  will be reduced. 
       FIG. 20  is a graph  380  showing the resulting magnetization curves of the magnetic flux valve  340  when an external control voltage at different levels of U 1 , U 2 , U 3 , . . . , and U n  is applied separately to the magnetic flux valve  340 , where 0&lt;U 1 &lt;U 2 &lt;U 3 &lt; . . . &lt;U n . The horizontal axis H denotes the magnetic field strength. The vertical axis B denotes the magnetic flux density. The slope of the B-H curve (i.e., magnetization curve) represents the permeability μ of the magnetic flux valve: 
     
       
         
           
             
               
                 
                   μ 
                   = 
                   
                     B 
                     H 
                   
                 
               
               
                 
                   ( 
                   55 
                   ) 
                 
               
             
           
         
       
     
     As shown in  FIG. 20 , on the B-H curves, the magnetic flux density B saturates when the magnetic field strength H increases over a certain value  382 . The magnetic flux valve mainly works in the unsaturated region  384  (i.e., linear region) of the B-H curves. When the voltage applied to the magnetic flux valve increases, the linear region  384  of the B-H curve becomes wider; while the slope of the curve in the linear region  384  becomes smaller, meaning a reduction in the permeability u. In the linear region  384 , the relation of the permeability u and the applied voltage U can be expresses as: 
                   μ   =       μ   0     -     f   ⁡     (   U   )                 (   56   )               
where μ 0  denotes the original permeability of the magnetic flux valve when there is no external control voltage applied, U is the external control voltage value, and ƒ(U) is the function of permeability variation with respect to the voltage U. The function ƒ(U) can be either linear or nonlinear, which depends on the structure of and the materials used in the magnetic flux valve.
 
     When the voltage U increases (decreases), the value of the function ƒ(U) increases (decreases) as well; while the permeability u decreases (increases). Thus, the permeability of the magnetic flux valve can be regulated continuously by changing the external control voltage. When the permeability of the magnetic flux valve changes, the reluctance of the magnetic flux valve and, therefore, the total reluctance of the magnetic circuit containing the magnetic flux valve, will change as well. The magnetic flux ϕ in a magnetic circuit is determined by the magnetomotive force F and the total magnetic reluctance R of the magnetic circuit as follows: 
                   ϕ   =     F   R             (   57   )               
where F is generally determined by the current through and the turn number of the windings of the magnetic circuit. Therefore, the magnetic flux in the magnetic circuit can be regulated by changing the total reluctance R of the magnetic circuit via controlling the permeability (therefore the reluctance) of the magnetic flux valve. This can be achieved by controlling the external control voltage applied to the magnetic flux valve by the driver circuit, as described by Equation 56.
 
       FIG. 28  is a photo of an exemplary magnetic flux valve  470  that includes electrode collectors  474 , magnetostrictive layers  476 , and piezoelectric layers  478 . Each magnetostrictive layer  476  includes a Metglas iron-based alloy ribbon, and each piezoelectric layer  478  includes a lead zirconate titanate (PZT) sheet. Twenty PZT sheets and forty Metglas ribbons are bonded together layer by layer using ethyl cyanoacrylate adhesives with the configuration in  FIGS. 16A and 16B . Each layer is 8 mm in width and 18 mm in length. Nickel foil electrodes attached on both sides of the PZT sheets are lead out and crimped by two screws and bolts to form the two electrode collectors  474 . An external control voltage is applied to the electrode collectors  474 . Windings  472  are wrapped on the magnetic flux valve  470  for measuring the permeability of the valve. 
       FIG. 29  is a graph  480  showing the relationship between the relative permeability of the magnetic flux valve  470  in  FIG. 28  versus the control voltage applied to the magnetic flux valve  470 . Experiments were conducted by applying a control voltage to the electrode collectors  474 , and measuring the relative permeability of the magnetic flux valve. The relative permeability of the magnetic flux valve (which is determined at least in part by the relative permeability of the amorphous alloy ribbons in the magnetic flux valve) decreased from 46300 to 11065 when the control voltage increased from 0 V to 400 V, showing a 76.1% variation range with respect to the maximum permeability at 0 V. On the other hand, when the control voltage decreased from 400 V to 0 V, the relative permeability increased from 11065 to 43910. Due to the piezoelectric hysteresis property of the PZT sheets, the permeability variation curves are slightly different when increasing and decreasing the control voltage. 
     Stacking Factor and Permeability Variation Range 
       FIG. 30  is a diagram showing the magnetic flux line  498  distribution in a magnetic flux valve  496  and an adjacent magnetic core  490 . The piezoelectric layers  492  of the magnetic flux valve  496  can be made of non-magnetic substances, so the magnetic flux flows mainly through the magnetostrictive layers  494  of the magnetic flux valve  496 . Therefore, the total cross-sectional area of the magnetostrictive layers  494  determines the equivalent cross-sectional area of the magnetic flux valve  496  for the magnetic flux to flow through. 
     In some implementations, each magnetostrictive layer in  FIGS. 16A, 16B, 17A, and 17B  can be formed by using multiple laminated amorphous (e.g., Metglas iron-based) alloy ribbons that are stacked together. Each piezoelectric layer can be formed using a PZT sheet. The thicknesses of one PZT sheet and one amorphous alloy ribbon are represented by the parameters dp and dm, respectively. The numbers of the PZT sheets and amorphous alloy ribbons used to form the magnetic flux valve are represented by parameters np and nm, respectively. Then, the total thicknesses of the PZT sheets (i.e., piezoelectric layers) and amorphous alloy ribbons (i.e., magnetostrictive layers) are dp×np and dm×nm, respectively. The stacking factor (also known as lamination factor) ks is defined as ks=dm×nm/(dm×nm+dp×np). The value of ks should be as high as possible to increase the effective cross-sectional area of the magnetic flux valve for the magnetic flux to flow through. In addition to the voltage, increasing the effective cross-sectional area of the magnetic flux valve such that more magnetic flux can flow through also increases the maximum current that can flow through the primary windings. Therefore, increasing the effective cross-sectional area of the magnetic flux valve such that more magnetic flux can flow through will increase the power capacity of the EM power converter. For example, the thickness of a single PZT sheet is usually from 100 μm to 300 μm and the thickness of one layer of amorphous alloy ribbon is usually 25 μm. If a magnetostrictive layer that includes multiple stacked amorphous alloy ribbons is bonded with one PZT sheet on each side, ks increases while the permeability variation range of the magnetic flux valve decreases because the deformation force produced by the PZT sheet is distributed into multiple amorphous alloy ribbons. 
     Table I shows the experimental results of the permeability variation ranges of a magnetic flux valve when the stacking factor is changed by stacking different numbers of amorphous alloy ribbons together to form the magnetostrictive layer. In this example, the thicknesses of one PZT sheet and one amorphous alloy ribbon are 190 μm and 25 μm, respectively. If one piece of amorphous alloy ribbon is bonded on each side of each PZT sheet, the stacking factor is (25+25)/(25+25+190)=0.208. The permeability decreases 76.1% as the control voltage increases from 0 V to 400 V. As shown in Table 1 below, the permeability variation range decreases quickly as the stacking factor increases. This is because the stress generated by each PZT sheet is transferred to multiple pieces of amorphous alloy ribbon. As a consequence, the permeability variation of each piece of amorphous alloy ribbon decreases. Therefore, the design of the magnetic flux valve should consider the trade-off between stacking factor and permeability variation range. 
                     TABLE 1                  PERMEABILITY VARIATION RANGES       AT DIFFERENT STACKING FACTORS                         Number of amorphous               ribbons on each side of one       Permeability variation       PZT sheet   Stacking factor k s     range*               1   0.208   76.1%       2   0.345   32.3%       3   0.441   18.0%               *Permeability variation range is the ratio of permeability variation (when the control voltage is increased from 0 V to 400 V) over the original permeability (when the control voltage is 0 V) of the magnetic flux valve (Δμ/μ).            
Application of the Magnetic Flux Valve: Adjustable-Voltage-Ratio (AVR) Transformer
 
       FIG. 31  is a diagram showing a novel compact configuration of an adjustable-voltage-ratio (AVR) transformer  500  that has two magnetic flux valves  502 , which is similar to a special case of the electromagnetic (EM) power converter. The AVR transformer  500  includes a magnetic E core  504  with three core legs  520 ,  522 , and  523 , a primary winding  508  on the central core leg, a secondary winding  510  or  511  on each of the side core legs, and a magnetic flux valve  502  or  503  between each of the two side (i.e., secondary) core legs and the central core leg. The permeability of each magnetic flux valve  502  or  503  can be altered by regulating the amplitude of the control voltage applied on the magnetic flux valve  502  or  503 . As a consequence, the reluctance of the magnetic flux valve  502  or  503  changes and, therefore, the magnetic fluxes through the legs of the magnetic core  504  can be regulated by the magnetic flux valves  502  and  503 . 
       FIG. 32  shows the magnetic circuit  524  of the AVR transformer  500  in  FIG. 31 . In this example, the primary winding  508  with No turns is located on the central core leg  520  and connected to an AC voltage source v in  as the input. The two secondary windings  510 ,  511  are located on the two side core legs  522 ,  523  and connected in series to output the voltage v out . The turn numbers of the two secondary windings  510 ,  511  are N 1  and N 2 , respectively. The two magnetic flux valves  502 ,  503  are connected with a driver circuit (not shown in the figure), which supplies control voltages v c , and v c2  to the magnetic flux valves  502  and  503  to regulate their permeability. As shown in  FIG. 32 , the two output terminals of the transformer  500  are the two dotted terminals of the two secondary windings  510 ,  511  with the same polarity. Therefore, the output v out =v 1 −v 2 , where v 1  and v 2  are the voltages induced by the secondary windings  510 ,  511  on the left and right core legs  522 ,  523 , respectively. The parameter i in  is the exciting current through the primary winding  520 , and ϕ 0  is the magnetic flux generated by the current i in  (called the main flux). The main flux ϕ 0  splits into two parts, which flow through the two side core legs  522 ,  523  respectively. The magnetic fluxes ϕ 1  and ϕ 2  (ϕ 1 +ϕ 2 =ϕ 0 ) through the two side core legs  522 ,  523  will change when the permeabilities of the two magnetic flux valves  502 ,  503  are changed. The distribution of the magnetic flux in the left and right core legs  522 ,  523  depends on the reluctances of the two side core legs  522 ,  523 . 
       FIG. 33  shows the equivalent circuit  530  of the AVR transformer  500 , where R 0  is the equivalent reluctance of the central core leg  520  wrapped by the primary winding  508 ; the two variable reluctances R x1  and R x2  represent the equivalent variable reluctances of the two magnetic flux valves  502 ,  503 ; the two fixed reluctances R offset1  and R offset2  represent the equivalent offset reluctances of the two side core legs  522 ,  523  and magnetic flux valves  502 ,  503 , which are mainly determined by the magnetic properties of the core legs  522 ,  523  and the magnetic flux valves  502 ,  503 . Therefore, the total reluctances R 1  of the left core leg  522  and R 2  of the right core leg  523  are 
                     R   1     =       R     offset   ⁢           ⁢   1       +     R     x   ⁢           ⁢   1                 (   58   )                 R   2     =       R     offset   ⁢           ⁢   2       +     R     x   ⁢           ⁢   2                 (   59   )               
Assume that the primary AC input is a time-varying sinusoidal voltage with the frequency ω and the amplitude U in , i.e., v in =U in  cos ωt. Then the main flux ϕ 0  is
 
                     ϕ   0     =       -       U     i   ⁢           ⁢   n           N   0     ⁢   ω         ⁢   sin   ⁢           ⁢   ω   ⁢           ⁢   t             (   60   )               
Therefore, the magnetic flux through the two secondary core legs  522 ,  523  can be expressed as:
 
     
       
         
           
             
               
                 
                   
                     ϕ 
                     1 
                   
                   = 
                   
                     
                       ϕ 
                       0 
                     
                     ⁢ 
                     
                       
                         R 
                         2 
                       
                       
                         
                           R 
                           1 
                         
                         + 
                         
                           R 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   61 
                   ) 
                 
               
             
             
               
                 
                   
                     ϕ 
                     2 
                   
                   = 
                   
                     
                       ϕ 
                       0 
                     
                     ⁢ 
                     
                       
                         R 
                         1 
                       
                       
                         
                           R 
                           1 
                         
                         + 
                         
                           R 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   62 
                   ) 
                 
               
             
           
         
       
     
     The voltages inducted by the two secondary windings  510 ,  511  are v 1 =−N 1 ·(dϕ 1 /dt) and v 2 =−N 2 ·(dϕ 2 /dt). Therefore, the output voltage v out  is 
                     v   out     =         v   1     -     v   2       =         -     d   dt       ⁢     (         N   1     ⁢           ⁢     ϕ   1       -       N   2     ⁢     ϕ   2         )       =       -     d   dt       ⁢     (             N   1     ⁢     R   2       -       N   2     ⁢     R   1             R   1     +     R   2         ⁢     ϕ   0       )                   (   63   )               
By replacing ϕ 0  with its expression in Equation (60), the output voltage v out  in Equation (63) is
 
     
       
         
           
             
               
                 
                   
                     v 
                     out 
                   
                   = 
                   
                     
                       
                         
                           
                             N 
                             1 
                           
                           ⁢ 
                           
                             R 
                             2 
                           
                         
                         - 
                         
                           
                             N 
                             2 
                           
                           ⁢ 
                           
                             R 
                             1 
                           
                         
                       
                       
                         
                           N 
                           0 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               R 
                               1 
                             
                             + 
                             
                               R 
                               2 
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       v 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   64 
                   ) 
                 
               
             
           
         
       
     
     Assume N 1 =N 2 =N and R offset1 =R offset2 =R offset . The voltage ratio v out /v in  of the transformer  500  is derived as 
     
       
         
           
             
               
                 
                   
                     
                       v 
                       out 
                     
                     
                       v 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                     
                   
                   = 
                   
                     
                       N 
                       
                         N 
                         0 
                       
                     
                     ⁢ 
                     
                       
                         
                           R 
                           
                             x 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         - 
                         
                           R 
                           
                             x 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             R 
                             offset 
                           
                         
                         + 
                         
                           R 
                           
                             x 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         + 
                         
                           R 
                           
                             x 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   65 
                   ) 
                 
               
             
           
         
       
     
     When the control voltages applied to the two magnetic flux valves  502 ,  503  are equal (v c1 =v c2 ), R x1 =R x2 , R 1 =R 2  and, therefore, ϕ 1 =ϕ 2  and v out =0. When the control voltage applied to the left magnetic flux valve  502  is higher than that applied to the right magnetic flux valve  503  (v c1 &gt;v c2 ), the left magnetic flux valve  502  has a lower permeability and, therefore, R 1 &gt;R 2 . In this case, a larger portion of the main flux generated by the current through the primary winding  508  will flow through the right core leg  523 . An opposite case (v c1 &lt;v c2 ) is that a larger portion of the magnetic flux flows through the left core leg  522  when R 1 &lt;R 2 . The output voltage v out  of the AVR transformer  500  is the differential voltage induced by the two secondary windings  510 ,  511  and is determined by the difference of the magnetic fluxes in the two side core legs  522 ,  523  due to the difference of the voltages applied to the two magnetic flux valves  502 ,  503 . 
     An AVR transformer  500  was developed and tested, in which the left magnetic flux valve  502  was connected with a controllable voltage source and the right magnetic flux valve  503  was not connected to any voltage source. When the control voltage was applied to the left magnetic flux valve  502 , the left magnetic flux valve  502  had a lower permeability and a larger portion of the main flux generated by the current through the primary winding  508  flowed through the right core leg  523 . By changing the control voltage applied on the left magnetic flux valve  502 , the output amplitude of the AVR transformer  500  can be regulated. 
       FIG. 34  is a graph  540  that shows the waveforms of v out  when different control voltages are applied. The amplitude of v out  varies from 0 V to 31.8 V continuously as the control voltage increases from 0 V to 300 V. The input voltage amplitude of this transformer is 15 V. Therefore, the voltage ratio v out /v in  of the AVR transformer varies from 0 to 2.12, indicating that it can be both a step-down transformer and a step-up transformer. The AVR transformer  500  has great potential for flexible voltage control in power electronics and electric power grid applications. 
     The following describes another example of a power transformer in which the windings are wound around the magnetic flux valves. Referring to  FIG. 21 , in some implementations, a power transformer  390  includes two modules, each module is a separate transformer with the primary windings  392  and secondary windings  394  wrapped on the same laminated PZT/Metglas composite core  396 , which is made of bonded PZT and Metglas layers. The Metglas layers can be, e.g., amorphous magnetic foils (Metglas 2605SA1). The PZT layers can be, e.g., thin piezoelectric sheets (Piezo Systems Inc. PSI-5E4H). 
     In this example, each PZT layer is 18.1 mm in length and 6.58 mm in width. The thicknesses of the Metglas foil and the PZT sheet are 25 μm and 0.191 mm, respectively. As shown in a diagram  402  (which shows an enlarged portion of the PZT/Metglas composite core  396 ), two layers of Metglas foils  404  are placed on each side of a PZT sheet layer  406  to form a micro sandwich-type unit  408 . The three layers are bonded together with Cyanoacrylate adhesives. Twenty two micro units are stacked together to form a laminated core. The electrodes on the PZT sheets of Module A are led out to form two terminals  398 , which are connected with a controllable voltage source. Kapton tapes are wrapped around each PZT/Metglas composite core  396  to provide insulation. A ferrite ring core  400  is placed outside each PZT/Metglas composite core  396  as a shell to provide a complete magnetic circuit for each module. 
       FIG. 22  shows a schematic diagram of the power transformer  390  in  FIG. 21 , in which N A1  and N B1  are the turns numbers of the primary windings  392  of Modules A and B, respectively; N A2  and N B2  are the turns numbers of the secondary windings  394  of Modules A and B, respectively; and Φ A  and Φ B  are the magnetic fluxes through the PZT/Metglas composite cores  396  of Modules A and B, respectively. 
     The primary windings  392  of the two modules are connected in series, e.g., the negative terminal of Module A&#39;s primary winding  392  is connected with the positive terminal of Module B&#39;s primary winding  392 . Therefore, the total input voltage v in  is the sum of the input voltages of the two modules, i.e., v in =v Ain +v Bin . The secondary windings  394  of the two modules are connected in an opposite way, e.g., the negative terminals of the secondary windings  394  of the two modules are connected together. Therefore, the final output voltage v out  is the subtraction of the output voltages of the two modules, i.e., v out =v Aout −v Bout . 
     Because the primary windings  392  of the two modules are connected in series, the exciting currents through them are equal and can be expressed as 
                       i     i   ⁢           ⁢   n       =       i   A     =       i   B     =           Φ   A     ⁢     R     m   ⁢           ⁢   A           N     A   ⁢           ⁢   1         =         Φ   B     ⁢     R     m   ⁢           ⁢   B           N     B   ⁢           ⁢   1                 ,           (   58   )               
where i A , i B , and i in  are the primary exciting currents (i.e., the current through the primary windings  392 ) of Module A, Module B, and the power transformer, respectively; and R mA  and R mB  are the magnetic reluctances of Modules A and B, respectively. The voltage v across a winding and the magnetic flux Φ through the core of a transformer have the relation v=N·dΦ/dt.
 
     By using the voltage-magnetic flux relation, the relations v in =v Ain +v Bin  and v out =v Aout −v Bout , and Equation 58, the voltage ratio v out /v in  can be derived as follows 
     
       
         
           
             
               
                 
                   
                     
                       
                         v 
                         out 
                       
                       
                         v 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           n 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             v 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               out 
                             
                           
                           - 
                           
                             v 
                             
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               out 
                             
                           
                         
                         
                           
                             v 
                             
                               A 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                             
                           
                           + 
                           
                             v 
                             
                               B 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               i 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                             
                           
                         
                       
                       = 
                       
                         
                           
                             
                               N 
                               
                                 A 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             ⁢ 
                             
                               N 
                               
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                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁢ 
                             
                               R 
                               
                                 m 
                                 ⁢ 
                                 
                                     
                                 
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                                 ⁢ 
                                 
                                     
                                 
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                                 1 
                               
                             
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                                 ⁢ 
                                 
                                     
                                 
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                               N 
                               
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                                 ⁢ 
                                 1 
                               
                             
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                                 1 
                               
                             
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                                 m 
                                 ⁢ 
                                 
                                     
                                 
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                           + 
                           
                             
                               N 
                               
                                 B 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁢ 
                             
                               N 
                               
                                 B 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
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                                 m 
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                                 A 
                               
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   59 
                   ) 
                 
               
             
           
         
       
     
     The magnetic reluctance R m  of a transformer can be replaced by the inductance L of the primary winding as R m =N 2 /L. Therefore, the voltage ratio can be rewritten as 
                         v   out       v     i   ⁢           ⁢   n         =           N     A   ⁢           ⁢   2       ⁢     N     A   ⁢           ⁢   1       ⁢     L   A       -       N     B   ⁢           ⁢   2       ⁢     N     B   ⁢           ⁢   1       ⁢     L   B               N     A   ⁢           ⁢   1       ⁢     N     A   ⁢           ⁢   1       ⁢     L   A       +       N     B   ⁢           ⁢   1       ⁢     N     B   ⁢           ⁢   1       ⁢     L   B             ,           (   60   )               
where L A  and L B  are the primary inductances of Modules A and B, respectively. According to Equation 60, the voltage ratio of the transformer can be regulated by changing the primary inductances of the two modules.
 
     In the exemplary power transformer  390  shown in  FIG. 21 , the PZT sheets  406  of the PZT/Metglas composite core  396  of Module A are connected with a controllable voltage source while the PZT/Metglas composite core  396  of Module B is not connected to any voltage source. With this design, the inductance L A  is adjustable by controlling the voltage applied on the PZT sheets  406  of the PZT/Metglas composite core  396  of Module A via the converse magnetoelectric effect, while the inductance L B  is a fixed value. Therefore, the voltage ratio can be regulated by the controlling the voltage applied on the PZT/Metglas composite core  396  of Module A. In this example, N A1 =N B1 =200, N A2 =150, and N B2 =207. 
     To test the power transformer  390 , its primary winding  392  is connected to a 10 kHz, 10 V sinusoidal voltage source and its secondary winding  394  is connected to a 1 kΩ resistive load. The output voltage induced in the secondary winding  394  is a 10 kHz sinusoidal wave whose amplitude varies according to the control voltage applied on the PZT sheets  406  of the PZT/Metglas composite core  396  of Module A. 
       FIG. 23  is a graph  410  showing output waveforms of the power transformer  390  when different control voltages are applied on the PZT sheets  406  of the PZT/Metglas composite core  396  in Module A. As the control voltage increases, the amplitude of the output voltage decreases from 0.33 V to 0 V first and then increases to the maximum value of 1.79 V continuously. According to Equation 60, this maximum value is determined by the variation range of the inductance L A  and the turns numbers of the two modules. 
     Table 2 below lists the measured inductance of Module A, measured and calculated amplitudes of v out , and the measured and calculated voltage ratios of the power transformer  390  when different control voltages are applied. The inductance L B  is a fixed value of 4.85 mH. The value of L A  decreases when the control voltage increases. The amplitudes of the output voltage calculated by Equation 60 match the measured values well. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Measured inductance of Module A, calculated and measured amplitudes of 
               
               
                 output voltage, and calculated and measured voltage ratios of the power transformer 
               
               
                 when different control voltages were applied. The inductance of Module B is fixed at 
               
               
                 4.85 mH. 
               
            
           
           
               
               
            
               
                   
                 Control voltage (V) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 0 
                 50 
                 100 
                 150 
                 200 
                 250 
                 300 
                 350 
                 400 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Inductance of Module A (mH) 
                 7.25 
                 6.99 
                 6.60 
                 6.04 
                 5.54 
                 5.10 
                 4.76 
                 4.50 
                 4.30 
               
               
                 Calculated amplitude of ν out   
                 0.35 
                 0.19 
                 0.06 
                 0.45 
                 0.83 
                 1.19 
                 1.50 
                 1.75 
                 1.95 
               
               
                 (V) 
               
               
                 Measured amplitude of ν out  (V) 
                 0.33 
                 0.24 
                 0.03 
                 0.47 
                 0.81 
                 1.13 
                 1.40 
                 1.61 
                 1.79 
               
               
                 Calculated voltage ratio 
                 3.5% 
                 1.9% 
                 0.6% 
                 4.5% 
                 8.3% 
                 11.9% 
                 15% 
                 18% 
                 20% 
               
               
                 (ν out /ν in ) 
               
               
                 Measured voltage ratio (ν out /ν in ) 
                 3.3% 
                 2.4% 
                 0.3% 
                 4.7% 
                 8.1% 
                 11.3% 
                 14% 
                 16% 
                 18% 
               
               
                   
               
            
           
         
       
     
       FIG. 24  is a graph showing the measured and calculated voltage ratios of the power transformer  390  versus the control voltage applied. The results show that the voltage ratio is continuously adjustable and the measured and calculated voltage ratios are close. The output voltage of the transformer  390  responds immediately when the control voltage is changed. Therefore, the voltage ratio of the transformer  390  can be adjusted rapidly without any delay (i.e., at a high frequency). In addition, once the PZT sheets are charged, the amplitude of the output voltage remains the same even if the control voltage source is removed. This means that the control process is an electrostatic process with a negligible power loss. 
     The magnetoelectric transformer  390  has a voltage ratio that can be adjusted from zero to the designed maximum value continuously and rapidly by changing the control voltage applied on the PZT sheets  406  of the PZT/Metglas composite core  396 . The control process is electrostatic and has negligible power consumption. The transformer  390  is useful in electric power control and conversion applications. 
       FIG. 25  is a diagram of an exemplary configuration for the controller  106  ( FIG. 1 ). The controller  106  includes an analog-to-digital (A/D) converter  430 , a central processing unit (CPU)  432  or a microcontroller unit (MCU), and a digital-to-analog (D/A) converter  434 . The A/D converter converts the analog signals  438  acquired from sensors, such as the AC output voltage(s) of the EM power converter  102  and the controllable voltages applied to the magnetic flux valves, into digital signals  440 . One or more reference inputs  436  provide reference values for the CPU/MUC  432 , in which the CPU/MCU  432  uses a control algorithm to process the digital sensor signals  440  to generate digital control signals  442  at the output. For example, the reference input can be the desired amplitude and frequency of the AC output voltage of the EM power converter  102 . For example, the reference input can be provided by an operator, or by another system that sets the desired amplitude and frequency of the AC output voltage. The control algorithm describes the relationship between the desired controllable voltages applied to the magnetic flux valves and the desired AC output voltage(s) of the EM power converter  102 . The digital control signals  442  are converted into analog control signals  444  by the D/A converter  434  for controlling the magnetic flux valve driver circuit  104 . 
     Referring to  FIG. 26 , in some implementations, a magnetic flux valve driver circuit  104  provides power amplification for the control signals. For example, the amplitudes of the analog control signals  444  may vary from 0 V to 1 V with only a 10 mA current, while the controllable voltages outputs of the driver circuit  104  may need to reach up to 400 V with a 1 A current according to the requirement of the magnetic flux valves (e.g.,  128 ,  130 ). Therefore, the driver circuit  104  includes a power amplifier  450  to amplify the analog control signals  444  into controllable voltages  452  for the magnet flux valves. The amplitude of the controllable voltages  452  is determined by the amplitude of the DC power supply  454  applied to the power amplifier  450 . The DC power supply  454  can be obtained from an AC power source  456  through a rectifier circuit  458 . The AC power source  456  can be the same as the AC input source of the EM power converter  102 . 
     The controller  106  may include additional components, such as a storage device to store program instructions for implementing the control algorithms. A user interface may be provided. For example, a touch screen and/or a keyboard and/or a pointer device (such as a computer mouse) may be provided to enable a user to specify an amplitude, frequency, and/or waveform of the output signal of the power converter  102 . 
     In some implementations, the controller  106  can include one or more processors and one or more computer-readable media (e.g., RAM, ROM, SDRAM, hard disk, optical disk, and flash memory). The one or more processors can perform various calculations described above. The calculations can also be implemented using application-specific integrated circuits (ASICs). The term “computer-readable medium” refers to a medium that participates in providing instructions to a processor for execution, including without limitation, non-volatile media (e.g., optical or magnetic disks), and volatile media (e.g., memory) and transmission media. Transmission media includes, without limitation, coaxial cables, copper wire, fiber optics and free space. 
     The features described above can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. A computer program is a set of instructions that can be used, directly or indirectly, in a computer to perform a certain activity or bring about a certain result. A computer program can be written in any form of programming language (e.g., C, Java), including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, a browser-based web application, or other unit suitable for use in a computing environment. 
     Suitable processors for the execution of a program of instructions include, e.g., general purpose microprocessors, special purpose microprocessors, digital signal processors, single-core or multi-core processors, of any kind of computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memories for storing instructions and data. Generally, a computer will also include, or be operatively coupled to communicate with, one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM, DVD-ROM, and Blu-ray BD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits). 
     Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous. 
     Although some examples have been discussed above, other implementations and applications are also within the scope of the following claims. For example, the power converter  140  in  FIG. 2B  has two magnetic flux valves (e.g.,  150 A,  150 B) on each leg of the magnetic core. It is possible to use a single magnetic flux valve on each core leg, or use three or more magnetic flux valves on each core leg. In the example of  FIG. 7 , three identical three-leg modules are used. It is possible to use three three-leg modules that have different characteristics, such as different core dimensions, primary windings with different numbers of turns, secondary windings with different numbers of turns, or magnetic flux valves with different functions ƒ(U) of permeability variation with respect to the applied voltage U. In the example of  FIG. 10 , three identical four-leg modules are used. It is also possible to use three four-leg modules that have different characteristics, such as different core dimensions, primary windings with different numbers of turns, secondary windings with different numbers of turns, or magnetic flux valves with different functions ƒ(U) of permeability variation with respect to the applied voltage U. In the example of  FIG. 12A , the different legs can have different characteristics, such as different core leg dimensions, primary windings with different numbers of turns, secondary windings with different numbers of turns, or magnetic flux valves with different functions ƒ(U) of permeability variation with respect to the applied voltage U. For power converters that have multiple core legs, different core legs can have different numbers of magnetic flux valves. For example, one of the core legs may have one magnetic flux valve, a second core leg may have two magnetic flux valves, and a third core leg may not have any magnetic flux valve. Different control signals applied to different magnetic flux valves of a power converter can have different amplitudes, frequencies, and/or waveforms. 
     While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what may be claimed, but rather as descriptions of features specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments.