Abstract:
A power converter has a first electrical circuit including a direct current (dc) voltage source, a first phase winding of an electrical machine, and a first switch operating in a conductive state. A second electrical circuit includes the first phase winding, a first unidirectional current device, and a capacitive storage element. A third electrical circuit includes the capacitive storage element, a second switch operating in a conductive state, and the first phase winding. A fourth electrical circuit includes the first phase winding, the dc voltage source, and a second unidirectional current device.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of priority provided by U.S. provisional application 61/705,566, which was filed on Sep. 25, 2012. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The invention relates to a power converter for an electrical machine and a method of operating the machine. 
       BACKGROUND OF THE RELATED ART 
       [0003]    Low-cost motor drives in vehicle applications, such as electric bikes (E-Bikes) operated with battery-stored energy, are sought because of their positive impact on the environment, the existing mass market of electric bikes, and the limited financial resources of the user community in China, India, and other developing nations. One of the significant cost elements of a motor drive is a power converter circuit, particularly its number of power devices, such as transistors and power diodes. Economy in the use of power devices translates into a reduced number of control circuit components, such as gate drives, logic power supplies, and device protection circuits; such economy also leads to reduced printed circuit board area, heat-sink volume, and weight. The use of fewer power devices also leads to lower cost of the power electronic system for the motor drive. 
         [0004]    The use of fewer power devices restricts the freedom of operation of individual machine phases. Further, the control of a power converter requires signals, such as current and voltage signals, for feedback control or for the motor drive system control. 
       SUMMARY OF THE INVENTION 
       [0005]    Inexpensive means of measuring and estimating currents and voltages in a converter circuit that is driving a switched reluctance or a permanent magnet brushless direct current (dc) motor and use of the measured current and voltage signals in the control of the motor drive system are aspects of this disclosure. The converter and machine described herein have two phases, and the converter is supplied energy from an electrical battery supply. An embodiment of the invention for a motor drive system with more than two phases is described and generalized for any number of phases. 
         [0006]    A control system, employing feedback current and voltage signals, is also disclosed for operating the converter circuit, such that energy in a storage capacitor of the converter circuit is kept within specified levels. The system is described in detail with application to a two-phase switched reluctance machine (SRM), which then is generalized for SRMs with more than two phases. 
         [0007]    Methods to estimate and predict phase-winding currents and voltages, voltages across a storage capacitor and battery pack, and currents in the storage capacitor and battery are also described. The measurements of the voltages and currents may be obtained continuously or discontinuously. 
         [0008]    One or more objects of the disclosed subject matter may be achieved by a power converter having: (1) a capacitive storage element; (2) first and second switches that each conducts current in a conductive state and does not conduct current in a non-conductive state; and (3) first and second unidirectional current devices that each conducts current unidirectionally. The capacitive storage element, first and second switches, and first and second unidirectional current elements are interconnected such that when interconnected with a dc voltage supply and a first phase winding of an electrical machine: (a) a first operational state exists in which energy is transferred from the dc voltage supply to the first phase winding when the first switch is in the conductive state, (b) a second operational state exists in which energy stored by the first phase winding during the first operational state is transferred to the capacitive storage element when the first switch is in the non-conductive state, (c) a third operational state exists in which energy stored by the capacitive storage element is transferred to the first phase winding when the second switch is in the conductive state, and (d) a fourth operational state exists in which energy stored by the first phase winding during the third operational state is transferred to dc voltage supply when the second switch is in the non-conductive state. 
         [0009]    One or more objects of the disclosed subject matter may also be achieved by a method of operating a power converter, the method including: (1) transferring energy from a dc voltage supply to a first phase winding of an electrical machine during a first operational state, (2) transferring energy stored by the first phase winding during the first operational state to a capacitive storage element during a second operational state, (3) transferring energy stored by the capacitive storage element to the first phase winding during a third operational state, and (4) transferring energy stored by the first phase winding during the third operational state to the dc voltage supply during a fourth operational state. 
         [0010]    One or more objects of the disclosed subject matter may also be achieved by a power converter including: (1) a first electrical circuit comprising a dc voltage source, a first phase winding of an electrical machine, and a first switch operating in a conductive state; (2) a second electrical circuit comprising the first phase winding, a first unidirectional current device, and a capacitive storage element; (3) a third electrical circuit comprising the capacitive storage element, a second switch operating in a conductive state, and the first phase winding; and (4) a fourth electrical circuit comprising the first phase winding, the dc voltage source, and a second unidirectional current device. 
         [0011]    One or more objects of the disclosed subject matter may also be achieved by a power converter including: (1) a dc voltage supply having a first terminal electrically connected directly to a first node and a second terminal electrically connected to a second node, either directly or through a first current sensor; and (2) a first phase module. The first phase module includes: (a) a first phase winding of an electrical machine having a first terminal electrically connected directly to the first node and a second terminal electrically connected directly to a third node, (b) a capacitive storage element having a first terminal electrically connected directly to the first node and a second terminal electrically connected directly to a fourth node, (c) a first switch having a first terminal electrically connected to the second node, either directly or through a second current sensor, and a second terminal electrically connected directly to the third node, (d) a first unidirectional current device having a first terminal electrically connected to the second node, either directly or through the second current sensor, (e) and a second terminal electrically connected directly to the third node, (f) a second switch having a first terminal electrically connected directly to the third node and a second terminal electrically connected directly to the fourth node, and (g) a second unidirectional current device having a first terminal electrically connected directly to the third node and a second terminal electrically connected directly to the fourth node. 
         [0012]    One or more objects of the disclosed subject matter may also be achieved by a method of controlling an electrical machine, the method including: (1) generating a first signal indicating whether a value representative of a voltage of a first voltage source is less than the difference between a value representative of a voltage of a second voltage source and a reference voltage value; (2) generating a second signal indicating whether the value representative of the voltage of the first voltage source equals or exceeds the sum of the value representative of the voltage of the second voltage source and the reference voltage value; (3) transferring energy from the second energy source to a phase winding of the electrical machine during a period that the first signal indicates an affirmative condition; and (4) transferring energy from the first energy source to the phase winding during a period that the second signal indicates an affirmative condition. 
         [0013]    One or more objects of the disclosed subject matter may also be achieved by a non-volatile storage medium storing instructions that, when executed by a processor, cause the processor to implement a method comprising: (1) transferring energy from a dc voltage supply to a first phase winding of an electrical machine during a first operational state, (2) transferring energy stored by the first phase winding during the first operational state to a capacitive storage element during a second operational state, (3) transferring energy stored by the capacitive storage element to the first phase winding during a third operational state, and (4) transferring energy stored by the first phase winding during the third operational state to the dc voltage supply during a fourth operational state. 
         [0014]    One or more objects of the disclosed subject matter may also be achieved by a non-volatile storage medium storing instructions that, when executed by a processor, cause the processor to implement a method comprising: (1) generating a first signal indicating whether a value representative of a voltage of a first voltage source is less than the difference between a value representative of a voltage of a second voltage source and a reference voltage value; (2) generating a second signal indicating whether the value representative of the voltage of the first voltage source equals or exceeds the sum of the value representative of the voltage of the second voltage source and the reference voltage value; (3) transferring energy from the second energy source to a phase winding of an electrical machine during a period that the first signal indicates an affirmative condition; and (4) transferring energy from the first energy source to the phase winding during a period that the second signal indicates an affirmative condition. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    Preferred embodiments of the invention are described in the following paragraphs of the specification and may be better understood when read in conjunction with the drawings, in which: 
           [0016]      FIG. 1  illustrates an embodiment of a power converter; 
           [0017]      FIG. 2  illustrates a modular unit M within the power converter of  FIG. 1 ; 
           [0018]      FIG. 3  illustrates a modular unit N within the power converter of  FIG. 1 ; 
           [0019]      FIG. 4  illustrates an embodiment of a power converter having any number of machine phases; 
           [0020]      FIG. 5  illustrates an embodiment of the power converter illustrated by  FIG. 1  having voltage and current sensors; 
           [0021]      FIG. 6  illustrates, for the power converter of  FIG. 5 , the relation of current i s  in phase winding A and a voltage V A  across phase winding A; 
           [0022]      FIG. 7  illustrates, for the power converter of  FIG. 5 , phase winding A current i a , voltage signal V ia1 , and a sampling of voltage signal V ia1 , identified by V ia1 (t s ), with respect to time for Mode 1 operation; 
           [0023]      FIG. 8  illustrates, for the power converter of  FIG. 5 , voltage signal V tc1  relative to voltage V A  across phase winding A and current i a  flowing through phase winding A for Mode 2 operation; 
           [0024]      FIG. 9  illustrates, for the power converter of  FIG. 5 , voltage signal V ia2  relative to voltage V A  across phase winding A and current i a  flowing through phase winding A for Mode 3 operation; 
           [0025]      FIG. 10  illustrates signal voltage V ia2  within  FIG. 9  in greater detail; 
           [0026]      FIG. 11  illustrates, for the power converter of  FIG. 5 , voltage V A  across phase winding A, phase winding A current i a , and voltage signal V tc1  with respect to time for Mode 3 operation; 
           [0027]      FIG. 12  illustrates the modularization of the phase A circuitry illustrated by  FIG. 5 ; 
           [0028]      FIG. 13  illustrates the modularization of the phase B circuitry illustrated by  FIG. 5 ; 
           [0029]      FIG. 14  illustrates an SRM having multiples ones of the phase units illustrated in  FIGS. 12 and 13 ; 
           [0030]      FIG. 15  illustrates a control system for controlling the power converter illustrated by  FIG. 14 ; and 
           [0031]      FIG. 16  illustrates the operation of the transistor selection block illustrated in  FIG. 15 . 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0032]      FIG. 1  illustrates an embodiment of a power converter. A power converter  1 , at its input terminals, has a battery pack  2  with voltage V b . A two-phase switched reluctance or a permanent magnet brushless direct current (dc) machine (PMBDCM) may be used in this embodiment. The description hereafter is only with reference to switched reluctance machine (SRM), but is equally applicable to the PMBDCM. 
         [0033]    Phase windings A and B are two, machine phase windings of an SRM. Battery  2  has a positive terminal connected to a first terminal of phase winding A, a first terminal of phase winding B, and a first terminal of a storage capacitor C. A negative terminal of battery  2  is connected to the anode of a diode D a1 , the emitter of a bipolar-junction transistor (BJT) T a1 , and the emitter of a BJT T b1 . A second terminal of phase winding A is connected to the cathode of diode D a1 , the collector of transistor T a1 , the anode of a diode D a2 , and the emitter of a BJT T a2 . A second terminal of phase winding B is connected to the collector of transistor T b1  and the anode of a diode D b2 . A second terminal of capacitor C is connected to the cathodes of diodes D a2  and D b2  and the collector of a BJT T a2 . 
         [0034]    Diode D a1  and transistor T a1  are available in one package, such as in a metal-oxide semiconductor field-effect transistor (MOSFET) device or an insulated-gate bipolar transistor (IGBT) device. Similarly, diode D a2  and transistor T a2  are also available in one package, such as in a MOSFET device or an IGBT device. Such packaging of the circuit elements leads to space savings in circuit realization and cost savings in manufacture. 
         [0035]    For simplicity of description, the devices described herein are assumed to be ideal. For example, the diodes, transistors, and interconnecting wires are considered to have a zero conduction voltage drop across them. In a practical embodiment, the conduction voltage drops may be considered. Neglecting these voltage drops and their associated losses does not change the essence of the description or the inferences drawn therefrom. 
         [0036]    Energization of phase winding A is achieved in two ways. One way is to energize phase winding A with battery  2 , and the other is to energize phase winding A with energy stored in capacitor C. Energization of phase winding A from battery  2  is designated Mode A 1 . Turning on transistor T a1  will apply battery voltage V b  across phase winding A, which will establish a current in phase winding A so as to generate a torque in the machine, say, in the clockwise (CW) direction and, hence, move a rotor of the machine in the CW direction. If phase winding A current exceeds a set limit, transistor T a1  may be turned off, which will cut off battery voltage V b  to phase winding A. As the current is nonzero at the turn-off time of transistor T a1 , there is energy storage in the inductance of phase winding A. The energy stored in the inductance of phase winding A must be transferred to a source or result in a high rise of voltage across transistor T a1 . The only way in which the energy in phase winding A can be transferred is through the flow of current through diode D a2  and capacitor C, resulting in an increase of voltage across capacitor C. The voltage of capacitor C is also applied across phase winding A and has a polarity that is conducive for current decay, not for build-up, as the current is charging capacitor C and flowing against a capacitor voltage V c . When the current falls below the set limit, so as to maintain current at a desired level, transistor T a1  is turned on again so that battery voltage V b  is applied across phase winding A, which is conducive for current build up. The net energy transferred to phase winding A is equal to the difference between the energy received from battery  2  and the energy delivered to capacitor C. For a machine to continue to generate torque in the CW direction, the energy transferred to the machine winding has to be positive. 
         [0037]    Energization of phase winding A from energy stored in capacitor C is designated Mode A 2 . Turing on transistor T a2  allows capacitor voltage V c  to be applied across phase winding A, resulting in a current through phase winding A. To control the current when it exceeds a set limit, transistor T a2  is turned off. The current in phase winding A is forced through a current path provided by battery  2  and diode D a1 . The voltage across phase winding A transitions from +V c  to −V b , thus forcing the current to decay in phase winding A. Phase winding A current charges battery  2 , such that the energy stored in the inductance of phase winding A is transferred to battery  2 . When the current in phase winding A falls below an established limit, transistor T a2  is turned on so as to reverse bias diode D a1  and transfer phase winding A current to capacitor C, rather than battery  2 . The voltage across phase winding A again is +V c , which increases the current in phase winding A. The net energy transferred to phase winding A is the difference between the energy transferred from capacitor C and the energy transferred to battery  2 . So long as this net energy is positive, the energy transfer to the machine is positive and some energy is transferred to battery  2  from the energy stored in capacitor C. 
         [0038]    Using Modes A 1  and A 2 , phase winding A can be energized in a controlled manner and receive energy from either battery  2  or capacitor C. When energy is transferred from battery  2  to the machine, a part of the energy is also transferred to capacitor C via phase winding A; and when the energy is transferred from capacitor C to phase winding A, a part of the energy stored by capacitor C is transferred to battery  2  via phase winding A. In a battery-operated motor drive for an electric-vehicle (EV) application, where the energy supply has to come from a battery pack, as it is the only source of energy, it is important to realize that Mode A 1  is the most dominant mode, but Mode A 2  is a secondary mode that serves to send energy recovered during Mode A 1  to a machine winding and the battery pack itself. 
         [0039]    Some distinct features of the above-described circuit controlling phase winding A are:
       (i) Currents of alternating polarity in phase winding A.   (ii) Energy transfer from battery  2  to phase winding A and then from phase winding A to storage capacitor C.   (iii) Energy transfer from storage capacitor C to phase winding A and then from phase winding A to battery  2 .   (iv) Only one transistor or a diode is conducting at any given time, in this part of the circuit, resulting in high-efficiency operation of the converter subsystem, which contributes to the high overall system efficiency of the motor drive system.   (v) Transistor T a1  and diode D a1  can be in one package and transistor T a2  and diode D a2  can be in one package, so as to achieve some compactness in the converter using packaging that is readily available commercially.   (vi) Transistor T a1 , diode D a1 , transistor T a2 , and diode D a2  can be realized in the form of a single phase leg of an inverter, within an integral package, for greater compactness.       
 
         [0046]    Energization of phase winding B by battery  2  is designated Mode B 1 . Turing on transistor T b1  will apply battery voltage V b  across phase winding B, which will establish a current in phase winding B that generates torque in the machine, say, in the CW direction and, hence, moves the rotor in the CW direction. If phase winding B current exceeds a set limit, transistor T b1  may be turned off, which will cut off battery voltage V b  to phase winding B. As the current is nonzero at the turn-off time of T b1 , there is energy storage in the inductance of phase winding B. The energy stored in the inductance of phase winding B must be transferred to a source or result in a high rise of voltage across transistor T b1 . The only manner in which the energy in phase winding B can be transferred is through the flow of current through diode D b2  and capacitor C, resulting in an increase of voltage across capacitor C. The voltage of capacitor C is also applied across phase winding B and has a polarity that is conducive for current decay, not for build-up, as the current is charging capacitor C and flowing against capacitor voltage V c . When the current falls below the set limit, so as to maintain current at a desired level, transistor T b1  is turned on again so that battery voltage V b  is applied across phase winding B, which is conducive for current build up. The net energy transferred to phase winding B is equal to the difference between the energy received from battery  2  and the energy delivered to capacitor C. For a machine to continue to generate torque in the CW direction, the energy transferred to the machine winding has to be positive. 
         [0047]    The energy stored in capacitor C cannot be used to energize phase winding B. In battery operated motor drives, most of the energy to power the motor drive has to come from the battery and the energy stored in the capacitor, due to commutation of the phase windings, may not be enough to feed two phases. Therefore, there may be no need to have the converter arrangement as employed with phase winding A. Transistor T b1  and diode D b2  may be sufficient to handle phase winding B, resulting in a saving of devices, control circuits, and associated logic power supply requirements. 
         [0048]    Distinct features of the phase winding B circuit are:
       (i) Phase winding B conducts only unidirectional current, not bidirectional current as in the case of phase winding A.   (ii) Phase winding B draws energy from battery  2 , and part of the energy stored in phase winding B is transferred to storage capacitor C.   (iii) Phase winding B cannot receive energy from storage capacitor C.   (iv) The circuit for phase winding B operation requires only one transistor and one diode.   (v) The transistor and diode can be packaged in one piece as a readily available chopper module. Such use of a chopper module leads to less assembly error in the electronics subsystem of the drive system, resulting in higher reliability of the electronics, compact packaging of the converter, and possible overall cost reduction in the electronics subsystem.       
 
         [0054]    The principles of the two-phase SRM can be applied to a multiphase SRM having greater than two phases. A generalized embodiment of a multiphase SRM is presented. 
         [0055]      FIG. 2  illustrates a modular unit M within the power converter of  FIG. 1 . Unit M comprises the above-described phase winding A and its related electronics of transistors T a1  and T a2  and diodes D a1  and D. Unit M is a three terminal device. A terminal  21  is connected to one end of phase winding A, a terminal  22  is connected to the emitter of transistor T a1  and anode of diode D a1 , and a terminal  23  is connected the collector of transistor T a2  and cathode of diode D a2 . The other end of phase winding A is connected to the collector of transistor T a1 , cathode of diode D a1 , emitter of transistor T a2 , and anode of diode D a2 . Thus, unit M has three external terminals  21 ,  22 , and  23 . To realize its operation, unit M&#39;s terminal  21  is connected to the positive terminal of battery  2  and capacitor C&#39;s terminal identified by symbol “−.” Terminal  22  is connected to the negative terminal of battery  2 , and terminal  23  is connected to the capacitor C&#39;s terminal identified by symbol “+.” 
         [0056]      FIG. 3  illustrates a modular unit N within the power converter of  FIG. 1 . Unit N comprises the above-described phase winding B and its related electronics of transistor T b1  and diode D b2 . Unit N is a three terminal device. A terminal  31  is connected to one end of phase winding B, a terminal  32  is connected to the emitter of T b1 , and a terminal  33  is connected to the cathode of diode D b2 . The other end of phase winding B is connected to the collector of transistor T b1  and anode of diode D b2 . Thus, unit N has three external terminals  31 ,  32 , and  33 . To realize its operation, unit N&#39;s terminal  31  is connected to the positive terminal of battery  2  and the terminal of capacitor C identified by symbol “−.” Terminal  32  is connected to the negative terminal of battery  2 , and terminal  33  is connected to the terminal of capacitor C identified by symbol “+.” 
         [0057]      FIG. 4  illustrates an embodiment of a power converter having any number of machine phases. Consider a machine having an integer number, h, of phases. Of these, j phases need to have energy supplied from battery  2  for some time and from a storage capacitor C for some time. Let j be less than h and k=h−j. In such a case, k phases have energy supplied only by battery  2 . Thus, j unit Ms and k unit Ns are integrated with battery  2  and storage capacitor C in a power converter  40 . The selection of integer values j and k is one of design based on application and cost requirements. 
         [0058]      FIG. 5  illustrates an embodiment of the power converter illustrated by  FIG. 1  having voltage and current sensors.  FIG. 5  differs from  FIG. 1  in the addition of such sensors. The addition of the sensors enables current and voltage measurements to be made for use in feedback control of a power converter  50  and, therefore, in the feedback control of the SRM. Battery pack  2  is connected to phase winding A through transistor T a1  and two current sensing resistors R a1  and R a2 . To sense the voltage of battery  2 , a potential divider comprising two resistors R b1  and R b2  is connected across battery  2 &#39;s positive terminal and terminal  22 . Likewise, to measure the potential between terminal  22  and a terminal  66 , a potential divider comprising resistors R c1  and R c2  is connected across terminals  66  and  22 . 
         [0059]    The current flowing through transistor T a1  or diode D a1  is measured by the voltage drop across resistor R a1  at the tap for a voltage signal V ia1 . This voltage, which is equal to the current flowing through resistor R a1  multiplied by the resistance of resistor R a1 , is with reference to terminal  22 . Similarly, the current flowing through battery  2 , which current is the same as that flowing through diode D a1  or transistor T a1 , is also measured by the voltage drop across resistor R a2  at the tap for a voltage signal V ia2 . The voltage of battery  2  is measured by tapping a voltage signal V bc , which is available at the junction of resistors R b1  and R b2 . The accuracy of the battery voltage measurement is not compromised by the voltage drop across current sensing resistor R a2 , because this voltage drop is negligible compared to the battery voltage. Similarly, the voltage across terminals  66  and  22  is given by tapping a voltage signal V tc1 . 
         [0060]    Similar insertion of a current resistor and resistors for voltage sensing is done for phase winding B. The current flowing through phase winding B and transistor T b1  is determined from the voltage drop across a resistor R b , which is inserted between the emitter of transistor T b1  and terminal  22 . A voltage signal V ib  indicates the current in transistor T b1 , according to the relation of voltage signal V 1b  equals the current flowing through phase winding B multiplied by the resistance of resistor R b . A voltage signal V tc2  across terminals  32  and  67  is measured using a potential divider comprising resistors R c1  and R c2 , and voltage signal V tc2  is with respect to terminal  22 . 
         [0061]    Three modes of operation for phase winding A are described. 
         [0062]    Mode 1: Phase winding A current flows from terminal  21  to terminal  66 , which is considered a positive current hereafter. The current in phase winding A, when transistor T a1  is turned on, is positive and represented by voltage signal V ia1 . Voltage signal V ia1  is positive for this condition with respect to terminal  22 . While transistor T a1  is on, voltage signal V tc1  indicates transistor T a1 &#39;s conduction voltage, which may not be of interest in a control system during this mode of operation. Phase winding A&#39;s current signal is derived as follows: 
         [0000]        V   ia1   −i   a   R   a1 ,  (1)
 
         [0000]    where i a  is the phase winding A current. From equation 1, the current in phase winding A is derived as: 
         [0000]    
       
         
           
             
               
                 
                   
                     i 
                     a 
                   
                   = 
                   
                     
                       
                         V 
                         
                           ia 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       
                         R 
                         
                           a 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0063]      FIG. 6  illustrates, for the power converter of  FIG. 5 , the relation of current i a  in phase winding A and a voltage V A  across phase winding A. When transistor T a1  is on, during a time period  71 , the voltage across phase winding A is V b . In period  71 , current i a  increases with time, because battery voltage V b  is continuously applied to phase winding A. During a period  72  that transistor T a1  is turned off at the end of period  71 , diode D a2  conveys current so as to discharge energy stored in phase winding A into capacitor C. During period  72 , current i a  decreases, as energy from phase winding A is supplying capacitor C and voltage V A  equals −V c , where V c  is positive with respect to terminal  21  of phase winding A. 
         [0064]      FIG. 7  illustrates, for the power converter of  FIG. 5 , phase winding A current i a , voltage signal V ia1 , and a sampling of voltage signal V ia1 , identified by V ia1 (t s ), with respect to time for Mode 1 operation. Phase winding A current i a  is shown for one phase conduction period, and the current follows a rectangular current reference, as is common in SRM drives. During a period  81 , transistor T a1  is turned on and current i a  and voltage signal V ia1  increase. During a period  82 , transistor T a1  is turned off and current i a  decreases and voltage signal V ia1  is zero. Current i a  and voltage signal V ia1  have similar waveforms during period  81 , though each is scaled by the resistance value of R a1  with respect to the other. Voltage signal V ia1  has a value of zero in period  82 , because no current flows through resistor R a1  during the non-conduction period of transistor T a1 . 
         [0065]    The waveform of current i a , illustrated in  FIG. 7 , occurs in one pulse width modulation (PWM) cycle. For feedback control purposes, an average value is desired for each PWM cycle. The average value can be obtained in many ways, such as by taking an average value of the beginning and the ending values of the conduction period only. Samples of voltage signal V ia1  may be taken at the turn-on and turn-off instances  85 ,  86  of transistor T a1  and averaged to provide a fairly accurate value of the average phase current for phase winding A. The algorithm can be more refined depending on the accuracy required for an application. 
         [0066]    Mode 2: When transistor T a1  is turned off, with current in phase winding A, the flow of current will transfer from transistor T a1  to diode D a2  and capacitor C, so as to charge capacitor C through a closed circuit with phase winding A. Ignoring the voltage drop across diode D a2 , the voltage across phase winding A is equal to the capacitor voltage V c , with its positive terminal being terminal  66  with respect to terminal  21 . Therefore, the voltage across terminals  22  and  66  is equal to the sum of battery voltage V b  and capacitor voltage V c  and is obtained by ignoring the resistance of resistor R a1  relative to the values of resistors R c1  and R c2 . Voltage signal V tc1  is determined from a current i sv1  that flows in resistors R c1  and R c2 . Current i sv1  is expressed by: 
         [0000]    
       
         
           
             
               
                 
                   
                     i 
                     
                       sv 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   = 
                   
                     
                       
                         
                           V 
                           b 
                         
                         + 
                         
                           V 
                           c 
                         
                       
                       
                         
                           R 
                           
                             c 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           R 
                           
                             c 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Therefore, voltage signal V tc1  is derived as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           V 
                           
                             tc 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         = 
                           
                          
                         
                           
                             i 
                             
                               sv 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                            
                           
                             R 
                             
                               c 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               R 
                               
                                 c 
                                  
                                 
                                     
                                 
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                                 1 
                               
                             
                             
                               
                                 R 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                               + 
                               
                                 R 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                             
                           
                            
                           
                             
                               ( 
                               
                                 
                                   V 
                                   b 
                                 
                                 + 
                                 
                                   V 
                                   c 
                                 
                               
                               ) 
                             
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0000]    A voltage signal V bc , which indicates the voltage of battery  2 , is determined by similar reasoning. A current i sv2  in resistors R b1  and R b2  is derived as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       i 
                       
                         sv 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     = 
                     
                       
                         V 
                         b 
                       
                       
                         
                           R 
                           
                             b 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           R 
                           
                             b 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    from which voltage signal V bc  is derived as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           V 
                           bc 
                         
                         = 
                           
                          
                         
                           
                             i 
                             
                               sv 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                            
                           
                             R 
                             
                               b 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               R 
                               
                                 b 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             
                               
                                 R 
                                 
                                   b 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                               + 
                               
                                 R 
                                 
                                   b 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                             
                           
                            
                           
                             
                               V 
                               b 
                             
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0000]    From equation 6, battery voltage V b  is derived in terms of voltage signal V bc  as: 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     b 
                   
                   = 
                   
                     
                       
                         
                           R 
                           
                             b 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           R 
                           
                             b 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       
                         R 
                         
                           b 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                      
                     
                       
                         V 
                         bc 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Similarly, from equation 2, the sum of the voltages of battery  2  and capacitor C is derived as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       V 
                       b 
                     
                     + 
                     
                       V 
                       c 
                     
                   
                   = 
                   
                     
                       
                         
                           R 
                           
                             c 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           R 
                           
                             c 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       
                         R 
                         
                           c 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                      
                     
                       
                         V 
                         
                           tc 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    From equations 7 and 8, capacitor voltage V c  is found as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           V 
                           c 
                         
                         = 
                           
                          
                         
                           
                             
                               
                                 
                                   R 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 + 
                                 
                                   R 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               
                                 R 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                              
                             
                               V 
                               
                                 tc 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                           - 
                           
                             V 
                             b 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 
                                   R 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 + 
                                 
                                   R 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               
                                 R 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                              
                             
                               V 
                               
                                 tc 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                           - 
                           
                             
                               
                                 
                                   R 
                                   
                                     b 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 + 
                                 
                                   R 
                                   
                                     b 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               
                                 R 
                                 
                                   b 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                              
                             
                               
                                 V 
                                 bc 
                               
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Equation 9 shows that capacitor voltage V c  is a function of voltage signal V bc  and voltage signal V tc1 . Capacitor voltage V c  is measured when phase winding A is charging capacitor C. Battery voltage signal V bc  is available all the time, whether phase winding A is being charged by battery  2  or capacitor C. 
         [0067]      FIG. 8  illustrates, for the power converter of  FIG. 5 , voltage signal V tc1  relative to voltage V A  across phase winding A and current i a  flowing through phase winding A for Mode 2 operation. A PWM cycle comprises periods  111  and  112 . During period  111 , transistor T a1  is turned on so that battery voltage V b  is applied across phase winding A and current i a  increases. During period  112 , transistor T a1  is turned off so that capacitor voltage V c  is applied across phase winding A and current i a  decreases. When transistor T a1  is turned on, the voltage across terminals  22  and  66  is almost equal to the conduction voltage drop of transistor T a1 , which conduction voltage drop is small compared to either battery voltage V b  or capacitor voltage V c  and, therefore, is treated as equal to zero in  FIG. 8 . When transistor T a1  is turned off, the voltage applied across phase A is equal to capacitor voltage V c . Therefore, the voltage across terminals  22  and  66  is approximately equal to the sum of battery voltage V b  and phase winding A voltage V A , which is equal to V c . Voltage signal V tc1  provides a scaled representation of the voltage across terminals  22  and  66 . 
         [0068]    Mode 3: The scenario of energy recovery from storage capacitor C, via the energization of phase winding A with transistor T a2 , is considered. When transistor T a2  is turned on, storage capacitor voltage V c  is applied to phase winding A, with terminal  66  being positive with respect to terminal  21 . Current i a  flows from terminal  66  to terminal  21  in phase winding A and through capacitor C and transistor T a2 . By this adopted convention, current i a  in phase winding A is negative. 
         [0069]    Current i a  is derived as follows. Phase winding A current i a  is measured for an instant, by turning off transistor T a2  for a short interval of time or during its turn-off time in a PWM switching cycle, during which time current i a  will transfer from transistor T a2  to diode D a1  via phase winding A, battery pack  2 , resistor R a2 , and resistor R a1 . 
         [0070]      FIG. 9  illustrates, for the power converter of  FIG. 5 , voltage signal V ia2  relative to voltage V A  across phase winding A and current i a  flowing through phase winding A for Mode 3 operation. A PWM cycle comprises periods  91  and  92 . During period  91 , transistor T a2  is turned on, the magnitude of voltage V A  across phase winding A is the same as capacitor voltage V c , phase winding A current i a  decreases, and voltage signal V ia1  is zero. Neither transistor T a1  nor diode D a1  conducts current during period  91 . 
         [0071]    During period  92 , transistor T a2  is turned off so that current i a  from phase winding A goes through battery  2 , resistors R a2  and R a1 , and diode D a1 . The voltage drop, represented by voltage signal V ia2 , across resistor R a2  with respect to terminal  22  is positive. Voltage V A  applied across phase winding A during period  92  is equal to battery voltage V b , ignoring the resistive voltage drop across resistors R a1  and R a2 , phase winding current i a  is increasing, and voltage signal V ia1  is positive with a decreasing value over time. Voltage signal V ia1  provides a scaled representation of battery voltage V b . 
         [0072]    Voltage signal V ia1  can be negative for Mode 3 operation, when transistor T a2  is turned off. It is preferable for sensor signals to provide positive values; therefore, voltage signal V ia2  is used during Mode 3. Voltage signal V ia2  is positive with respect to terminal  22  and is equal to phase winding A current i a  multiplied by the resistance of resistor R. Voltage signal V ia2  is given by: 
         [0000]        V   ia2   =i   a   R   a2 ,  (10)
 
         [0000]    where current i a  is the current flowing through phase winding A. Current i a  is derived from the measured voltage signal V ia1  as: 
         [0000]    
       
         
           
             
               
                 
                   
                     i 
                     a 
                   
                   = 
                   
                     
                       
                         V 
                         
                           ia 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       
                         R 
                         
                           a 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    After measuring voltage signal V ia2  for an instant, phase winding A can again be energized from storage capacitor C, by turning on transistor T a2 . 
         [0073]      FIG. 10  illustrates signal voltage V ia2  within  FIG. 9  in greater detail. The instantaneous value of current i a  in phase winding A at a moment t 1 , when transistor T a2  is turned off, is indicated by i 1 . Between moments t 1  and t 2 , voltage signal V ia1  has a decreasing value and the instantaneous value of current i a  at time t 2  is indicated by i 2 . At moment t 2 , transistor T a2  is turned on again and maintained in the on condition until moment t n , where the instantaneous value of current i a  is indicated by i 3  and transistor t a2  is turned off again. 
         [0074]    Between moments t 2  and t n , voltage signal V ia2  is zero and current i a  is not sensed. Instead, for Mode 3, current is sensed only when transistor T a2  is turned off and diode D a1  conducts current. This does not a create a problem in control, as most of the time an average signal is all that is required for feedback control. An average can be obtained for the period between moments t 1  and t 2  by taking an average of the currents i a  at those moments. Similarly, an average current between moments t n  and t n+1  can be obtained. If the current average is desired for the interval during transistor T a2 &#39;s conduction, such as between moments t 2  and t n , then it is obtained as the average of the currents i a  at the instances of t 2  and t n , which is the average of currents i 2  and i 3 . 
         [0075]      FIG. 11  illustrates, for the power converter of  FIG. 5 , voltage V A  across phase winding A, phase winding A current i a , and voltage signal V tc1  with respect to time for Mode 3 operation. A PWM cycle includes periods  121  and  122 . During transistor T a2 &#39;s period of non-conduction, voltage V A  applied across phase winding A, assuming there has been a current previously from capacitor C via transistor T a2  into phase winding A, amounts to battery voltage V b . Voltage V A  is considered positive, meaning terminal  21  is positive relative to terminal  66 . During time period  121 , the corresponding phase winding A current i a  increases and voltage signal V tc1  is zero. More specifically, the rate at which phase winding A current i a  increases declines as the energy stored in phase winding A charges battery  2 . Signal voltage V tc1  is zero because diode D a1  is conducting and its voltage drop is negligible. The voltage drop across diode D a1  is reflected across resistors R c1  and R c2 . 
         [0076]    When transistor T a2  is on, voltage V A  across phase winding A is −V c , that is from terminal  21  to terminal  66 . Ignoring resistor R a2 , the voltage across resistors R c1  and R c2  is equal to the sum of battery voltage V b  and capacitor voltage V c . Accordingly, voltage signal V tc1  is a scaled version of the sum of voltages V b  and V c , as expressed by Equation 4. 
         [0077]    Phase B operation of the SRM drive has only two modes, which are similar to Mode 1 and Mode 2 of phase winding A. 
         [0078]    Mode 1: A current i b  in phase winding B, when transistor T b1  is turned on, is obtained from voltage signal V ib . Voltage signal V ib  is positive for this condition, with respect to terminal  22 . Voltage signal V tc2  indicates transistor T b1 &#39;s conduction voltage. Phase winding B current signal i b  is derived as follows: 
         [0000]        V   ib1   =i   b   R   b .  (12)
 
         [0000]    From equation 12, current i b  in phase winding B is derived as: 
         [0000]    
       
         
           
             
               
                 
                   
                     i 
                     b 
                   
                   = 
                   
                     
                       
                         V 
                         ib 
                       
                       
                         R 
                         b 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0079]    Mode 2: When transistor T b1  is turned off with current in phase winding B, current i b  will transfer from transistor T b1  to diode D b2 , resulting in the charging of capacitor C and the closing of a circuit via phase winding B. Ignoring the voltage drop across diode D b2 , the voltage across phase winding B is equal to capacitor voltage V c , from the perspective of terminal  67  relative to a terminal  34 . Therefore, the voltage across terminals  32  and  67  is equal to the sum of battery voltage V b  and capacitor voltage V c  and is obtained by ignoring the resistance of resistor R a2 , relative to the values of resistors R c1  and R c2 . Voltage signal V tc2  is found from a current i sv2  that flows in resistors R c1  and R c2 , and current i sv2  is expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     i 
                     
                       sv 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   = 
                   
                     
                       
                         
                           V 
                           b 
                         
                         + 
                         
                           V 
                           c 
                         
                       
                       
                         
                           R 
                           
                             c 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           R 
                           
                             c 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Therefore, voltage signal V tc2  is derived as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           V 
                           
                             tc 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         = 
                           
                          
                         
                           
                             i 
                             
                               sv 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                            
                           
                             R 
                             
                               c 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               R 
                               
                                 c 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             
                               
                                 R 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                               + 
                               
                                 R 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                             
                           
                            
                           
                             
                               ( 
                               
                                 
                                   V 
                                   b 
                                 
                                 + 
                                 
                                   V 
                                   c 
                                 
                               
                               ) 
                             
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The state of battery voltage V b  is indicated by voltage signal V bc  and obtained by similar reasoning. A current i sv2  in resistors R b1  and R b2  is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       i 
                       
                         sv 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     = 
                     
                       
                         V 
                         b 
                       
                       
                         
                           R 
                           
                             b 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           R 
                           
                             b 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0000]    from which battery voltage signal V bc  is derived as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           V 
                           bc 
                         
                         = 
                           
                          
                         
                           
                             i 
                             
                               sv 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                            
                           
                             R 
                             
                               b 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               R 
                               
                                 b 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             
                               
                                 R 
                                 
                                   b 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                               + 
                               
                                 R 
                                 
                                   b 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                             
                           
                            
                           
                             
                               V 
                               b 
                             
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0000]    From equation 17, V b  is derived in terms of V bc  as 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     b 
                   
                   = 
                   
                     
                       
                         
                           R 
                           
                             b 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           R 
                           
                             b 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       
                         R 
                         
                           b 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                      
                     
                       
                         V 
                         bc 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Similarly, from equation 13, the sum of battery voltage V b  and capacitor voltage V c  is derived as 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       V 
                       b 
                     
                     + 
                     
                       V 
                       c 
                     
                   
                   = 
                   
                     
                       
                         
                           R 
                           
                             c 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           R 
                           
                             c 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       
                         R 
                         
                           c 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                      
                     
                       
                         V 
                         
                           tc 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
         [0000]    From equations 18 and 19, capacitor voltage V c  is found as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           V 
                           c 
                         
                         = 
                           
                          
                         
                           
                             
                               
                                 
                                   R 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 + 
                                 
                                   R 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               
                                 R 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                              
                             
                               V 
                               
                                 tc 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                           - 
                           
                             V 
                             b 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               
                                 
                                   R 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 + 
                                 
                                   R 
                                   
                                     c 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               
                                 R 
                                 
                                   c 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                              
                             
                               V 
                               
                                 tc 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                           - 
                           
                             
                               
                                 
                                   R 
                                   
                                     b 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 + 
                                 
                                   R 
                                   
                                     b 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                               
                               
                                 R 
                                 
                                   b 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                              
                             
                               
                                 V 
                                 bc 
                               
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
         [0080]    Equation 20 shows that capacitor voltage V c  is expressed as a function of voltage signal V bc  and voltage signal V tc2 . Capacitor voltage V c  is measured only when phase winding B is charging capacitor C. Having determined capacitor voltage V c  and battery voltage V b , voltage V A  applied across phase winding A, which is either battery voltage V b  or capacitor voltage V c , may be determined. 
         [0081]    The current in battery  2  is determined from measurements made using the current sensors, one of which gives the incoming and the other gives the outgoing current in battery  2 . Machine phase currents i a  and i b  and storage capacitor currents can be derived from current sensor measurements. Wherever measurements cannot be continuously made due to the nature of the circuit, the average currents in a PWM switching cycle may be determined. Such average values over a PWM switching cycle are sufficient for control purposes. 
         [0082]      FIG. 12  illustrates the modularization of the phase A circuitry illustrated by  FIG. 5 . Any number of phase modules MC may exist, with self-contained current sensing and voltage sensing circuits providing out-current signals, such as is provided by voltage signal V ia1 , and voltage signals, such as is provided by voltage signal V tc1 . 
         [0083]      FIG. 13  illustrates the modularization of the phase B circuitry illustrated by  FIG. 5 . Any number of phase modules NC may exist, with self-contained current sensing and voltage sensing circuits providing out-current signals, such as is provided by voltage signal V ib , and voltage signals, such as is provided by voltage signal V tc2 . 
         [0084]    Current sensing that occurs while storage capacitor C is charging a phase can be obtained from voltage signal V ia2  across resistor R a2 , and this could be common for the generalized circuit. Similarly, the generalized circuit may also have the potential divider, comprising resistors R b1  and R b2 , to measure battery voltage V b  via voltage signal V bc . 
         [0085]    Consider phase winding A, transistor T a1 , diode D a1 , resistors R a1 , R c1  and R c2 , transistor T a2 , and diode D a2  enclosed in dotted lines and identified as a unit MC. Unit MC has terminals,  21 ,  22 , and  23 . Similarly, a unit NC comprising transistor T b1 , current sensing resistor R b , voltage sensing resistors R c1  and R c2 , phase winding B, and diode Db 2  is a three terminal unit having terminals  32 ,  33 , and  34 . 
         [0086]      FIG. 14  illustrates an SRM having multiples ones of the phase units illustrated in  FIGS. 12 and 13 . A power converter  150  includes: (1) battery  2 , (2) capacitor C, (3) sensing resistor R a2 , to measure current when energy from capacitor C is transferred to phase winding A, (4) a common potential divider comprising resistors R b1  and R b2  to measure battery voltage V b  via voltage signal V bc , (5) j units MC connected between terminals  151 ,  152 , and  153 , where j is a desired number of phase windings A, and (6) k units NC connected between terminals  151 ,  152 , and  153 , where k is a desired number of phase windings B. Unit MC&#39;s terminals  151 ,  152 , and  153  correspond to, for example, terminals  22 ,  21 , and  23  in  FIG. 12 . Likewise, unit NC&#39;s terminals  151 ,  152 , and  153  correspond to terminals  32 ,  34 , and  33  in  FIG. 12 . Parameters j and k are any positive integer values. It is possible to have an equal number of units MC and units NC or zero units NC. 
         [0087]      FIG. 15  illustrates a control system for controlling the power converter illustrated by  FIG. 14 . Phase winding A draws energy from battery  2  or storage capacitor C. For one phase conduction period, only one of battery  2  and storage capacitor C provides energy to phase winding A. The selection of the source determines which of transistors T a1  and T a2  conducts. For Mode 1 of phase A operation, current i a  flowing through resistor R a1  produces voltage signal V ia1 . A current command i a *, corresponding to current i a , is translated to a voltage V ia ,* corresponding to V ia1 , by flowing through a resistor R a1  whose resistance is the same as that of resistor R a1 . Since feedback current i a  and reference current i a * are represented in the form of voltages, the difference between the reference and feedback current signals can be obtained by subtraction of their representative voltages using a summer  164 , whose output is fed to a current controller  165  of control system  160 . Current controller  165  may be a proportional-plus-integral controller or similar device. The output of current controller  165  provides a duty cycle signal d for transistor T a1  or T a2 . Duty cycle d is limited by current controller  165  to a maximum magnitude of one and a minimum magnitude of zero. 
         [0088]    A transistor selection block  167  selects which of transistors T a1  and T a2  to turn on, so as to determine which of energy sources, battery  2  and capacitor C, will energize phase winding A for a particular phase cycle. Transistor selection block  167  receives duty cycle signal d, voltage signals V tc1  and V bc , and a voltage signal ΔV indicating the allowable voltage change across storage capacitor C. The output of transistor selection block  167  provides control signals to the gates of bipolar junction transistors T a1  and T a2 . The selection of which transistor conducts during the phase cycle is based on whether voltage signal ΔV exceeds an allowable limit over battery voltage V b , which is represented by voltage signal V bc . Control system  160  may be implemented by a computer processor or programmable logic device. 
         [0089]      FIG. 16  illustrates the operation of the transistor selection block illustrated in  FIG. 15 . A summer  190  subtracts voltage signal V bc , representing battery voltage V b , from voltage signal V tc1 , which represents the sum of battery voltage V b  and capacitor voltage V c , to obtain a signal  183  representing capacitor voltage Y. Logic function blocks  191  and  192  receive signal  183  representing capacitor voltage V c , voltage signal ΔV, and a phase initiation signal  189 , which is derived from the starting edge of a phase dwell signal  187 . Phase dwell signal  187  is indicative of an angular duration of conduction for a phase winding, which is generated in a control system for a motor drive and determined by the rotational speed and absolute position of the rotor poles in an SRM. Phase dwell signal  187  may be a rectangular pulse that is processed through a sample and hold circuit  188 , so that only the leading edge of the pulse is output as phase initiation signal  189 . 
         [0090]    A logic function block  191  determines whether signal  183  representing capacitor voltage V c  is greater than or equal to the sum of battery voltage V b  and voltage signal ΔV. Logic function block  191  outputs a binary signal  185  indicating the determination. The value of signal  185  is held for one phase dwell period in accordance with phase initiation signal  189 . Similarly, logic function block  192  determines whether signal  183 , representing capacitor voltage V c , is less than the difference between battery voltage V b  and voltage ΔV. Logic function block  192  outputs a binary signal  186  indicating the determination. The value of signal  186  is held from the beginning to the end of the phase dwell duration in accordance with phase initiation signal  189 . Signal  185  is combined by an AND logic function block  193  with duty cycle signal d to generate a gate signal  170  for transistor T. 
         [0091]    When gate signal  170  is positive, capacitor C has enough energy to supply phase winding A. Therefore, when the phase dwell signal comes on, transistor T a2  is turned on to conduct current. Similarly, signal  186  is combined by an AND function block  194  with duty cycle signal d to generate a gate signal  169  for transistor T a2 . When gate signal  169  is positive, storage capacitor C will not be able to supply sufficient energy to phase winding A. Therefore, energy is supplied by battery  2 , by turning on transistor T a1 , via gate signal  169 , so as to conduct current. 
         [0092]    Control system  160  may similarly control phase B operation using current i b  indicated by voltage signal V ib  and control phase A and phase B operation using current i a  indicated by voltage sensor V ia2 . 
         [0093]    The machine phases discussed herein are those pertaining to switched reluctance machines, but are equally applicable to PMBDC machines. The voltage measurements and estimations described herein are also applicable for control purposes other than the ones described. Such an application is the use of machine-phase voltages and currents for estimating rotor position, via a computation of the phase-flux linkages and estimated phase currents. 
         [0094]    The disclosed method(s) may be implemented by instructions stored on a storage medium and executed by a computer processor or programmable logic device. 
         [0095]    The foregoing description illustrates and describes one or more preferred embodiments of the invention, but the invention may be used in various other combinations, modifications, and environments. The invention is capable of change or modification, within the scope of the inventive concept, as expressed herein, that is commensurate with the above teachings and the skill or knowledge of one skilled in the relevant art. Accordingly, the description is not intended to limit the invention to the embodiments disclosed herein.