Patent Publication Number: US-7898829-B2

Title: Rectifier circuit and three-phase rectifier device

Description:
TECHNICAL FIELD 
     The present invention relates to rectification techniques, and particularly to a field called multiple rectification. 
     BACKGROUND ART 
     With the widespread use of inverter equipment, increasing amounts of harmonics are generated due to the loads of rectifiers. This increases the possibility of overheating or breakage of phase advance capacitors and transformers of power systems due to the harmonic current. Therefore, there is a demand to suppress harmonics of the rectified current obtained on the basis of a three-phase power supply (for example, JIS standard JISC61000-3-2). 
     In a common three-phase rectifier circuit, six steps appear in one period of the current waveform. In general, with an n-step current waveform, the lowest-order harmonic is of the (n−1)th. Then, the harmonic content with respect to the fundamental wave is 1/n, and so the fifth and seventh harmonics significantly appear. 
     Accordingly, techniques for suppressing harmonics are proposed, for example by Non-Patent Documents 1 and 2 and Patent Document 1. These schemes adopt a technique called multiple rectification, and Non-Patent Documents 1 and 2 disclose techniques in which each of polyphase currents generates 12 pulses in one period, and two rectifier circuits are connected in parallel to the load (this technique is hereinafter referred to as “12-pulse rectification”). Also, Patent Document 1 discloses a technique in which each of polyphase currents generates 18 pulses in one period, and three rectifier circuits are connected in parallel to the load (this technique is hereinafter referred to as “18-pulse rectification”). Adopting these techniques eliminates the fifth, seventh, or eleventh, thirteenth harmonic components. 
     Non-Patent Document 2 provides an additional coil to an interphase reactor connecting the outputs of two rectifier circuits together, in order to improve the current waveform in 12-pulse rectification. Alternating current is applied to the coil, so as to inject a current into the interphase reactor. This improves the current waveform inputted to the transformer for obtaining the 12 pulses of current. 
     However, injecting a current into an interphase reactor with an additional coil, as described in Non-Patent Document 2, requires applying a complicated waveform to the coil. Non-Patent Document 2 avoids such a complicated waveform, and applies a triangular wave to the coil, but then distortion remains in the input current as a natural result. Also, the device for injecting current into the interphase reactor is configured complicatedly, or a separate voltage source is required. 
     Choppers described later in the preferred embodiments are introduced in Non-Patent Document 3. 
     Patent Document 1: Japanese Patent Laid Open No. 59-15475 (1984) 
     Non-Patent Document 1: Hisao Matsumoto, “Twelve-pulse Converter with Autotransformer Connection”, The Institute of Electrical Engineers of Japan, Transactions B, vol. 96, no. 8, pp. 406-412 
     Non-Patent Document 2: Sewan Choi, P. N. Enjeti, H. Lee and I. L. Pitel: “A new active interphase reactor for 12-pulse rectifiers provides clean power utility interface”, IEEE Trans. Ind. Applicat., vol. 32, no. 6, pp. 1304-1311 (1996) 
     Non-Patent Document 3: Takao Hirasa, “Power Electronics”, Kyoritsu Shuppan Co., Ltd, pp. 77-90, 1992 
     DISCLOSURE OF THE INVENTION 
     The present invention has been made by considering the problems above, and an object of the present invention is to provide a technique by which currents flowing in a transformer for outputting plural sets of three-phase currents given to a multiple rectifier circuit are easily made close to sinusoidal waves. 
     According to a first aspect of the rectifier circuit of the present invention, a rectifier circuit comprises: a first three-phase diode bridge ( 31 ) having three input ends ( 31 U,  31 V,  31 W) and a pair of output ends ( 31 P,  31 N), said first three-phase diode bridge applying full-wave rectification to currents (i u1 , i v1 , i w1 ) inputted to said input ends to obtain a first rectified current (i d1 ), and outputting said first rectified current from one ( 31 P) of said output ends; a first chopper ( 41 ;  43 ) having a pair of output ends ( 41 P,  41 N;  43 P,  43 N), said first chopper performing a first chopper operation to receive a current having a fundamental frequency of a first value as said first rectified current; a second three-phase diode bridge ( 32 ) having three input ends ( 32 U,  32 V,  32 W) and a pair of output ends ( 32 P,  32 N), said second three-phase diode bridge applying full-wave rectification to currents (i u2 , i v2 , i w2 ) inputted to said input ends to obtain a second rectified current (i d2 ), and outputting said second rectified current from one ( 32 P) of said output ends; and a second chopper ( 42 ;  44 ) having a pair of output ends ( 42 P,  42 N;  44 P,  44 N), said second chopper performing a second chopper operation to receive a current having a fundamental frequency of said first value as said second rectified current. Said pair of output ends of said first chopper and said pair of output ends of said second chopper are connected in parallel. 
     According to a second aspect of the rectifier circuit of the present invention, the rectifier circuit of the first aspect further comprises an interphase reactor ( 71 ) which is connected to said input ends of said first three-phase diode bridge ( 31 ) and in which the currents (i u1 , i v1 , i w1 ) inputted to said input ends flow. 
     According to a third aspect of the rectifier circuit of the present invention, the rectifier circuit of the first aspect or the second aspect further comprises an interphase reactor ( 72 ) which is connected between said first three-phase diode bridge and said first chopper and in which said first rectified current (i d1 ) flows. 
     According to a fourth aspect of the rectifier circuit of the present invention, in the rectifier circuit of the first aspect, said first chopper ( 43 ) comprises: a first inductor ( 411 ) in which said first rectified current (i d1 ) flows; a first diode ( 413 ) having an anode connected to said one ( 31 P) of said output ends of said first three-phase diode bridge ( 31 ) through said first inductor, and a cathode connected to one ( 43 P) of said output ends of said first chopper; a second inductor ( 431 ) connected to the other ( 31 N) of said output ends of said first three-phase diode bridge; a second diode ( 434 ) having a cathode connected to said other ( 31 N) of said output ends of said first three-phase diode bridge through said second inductor, and an anode connected to the other ( 43 N) of said output ends of said first chopper; and a switching element ( 412 ) having a first end connected to the anode of said first diode and a second end connected to the cathode of said second diode, said switching element opening/closing between said first end and said second end. Said second chopper ( 44 ) comprises: a third inductor ( 421 ) in which said second rectified current (i d2 ) flows; a third diode ( 423 ) having an anode connected to said one ( 32 P) of said output ends of said second three-phase diode bridge ( 32 ) through said third inductor, and a cathode connected to one ( 44 P) of said output ends of said second chopper; a fourth inductor ( 441 ) connected to the other ( 32 N) of said output ends of said second three-phase diode bridge; a fourth diode ( 444 ) having a cathode connected to said other ( 32 N) of said output ends of said second three-phase diode bridge through said fourth inductor, and an anode connected to the other ( 44 N) of said output ends of said second chopper; and a switching element ( 422 ) having a first end connected to the anode of said third diode and a second end connected to the cathode of said fourth diode, said switching element opening/closing between its said first end and said second end. 
     According to a fifth aspect of the rectifier circuit of the present invention, in the rectifier circuit of any of the first to fourth aspects, said first chopper and said second chopper are both step-up choppers. 
     According to a sixth aspect of the rectifier circuit of the present invention, in the rectifier circuit of any of the first to fourth aspects, said first chopper operation is controlled by pulse width modulation on the basis of a first modulation wave having a carrier frequency, and said second chopper operation is controlled by pulse width modulation on the basis of a second modulation wave having said carrier frequency and being in opposite phase to said first modulation wave. 
     According to a seventh aspect of the rectifier circuit of the present invention, the rectifier circuit of any of the first to sixth aspects further comprises a smoothing capacitor ( 5 ) connected in parallel to said output ends of said first chopper and said output ends of said second chopper. 
     According to an eighth aspect of the rectifier circuit of the present invention, in the rectifier circuit of any of the first to seventh aspects, first three-phase alternating currents (i u1 , i v1 , i w1 ) are inputted to said input ends ( 31 U,  31 V,  31 W) of said first three-phase diode bridge ( 31 ), a fundamental frequency of said first three-phase alternating currents is a second value that is ⅙ of said first value and said first three-phase alternating currents having mutual phase differences of 120 degrees at the fundamental frequency, and second three-phase alternating currents (i u2 , i v2 , i w2 ) are inputted to said input ends ( 32 U,  32 V,  32 W) of said second three-phase diode bridge ( 32 ), a fundamental frequency of said second three-phase alternating currents is said second value and having mutual phase differences of 120 degrees at the fundamental frequency, and wherein there is a phase difference of 30 degrees at the fundamental frequency between said first three-phase alternating currents and said second three-phase alternating currents, and wherein said first three-phase alternating currents and said second three-phase alternating currents each have a waveform which: (i) exhibits a crest in each of first and second sections both of which continue in correspondence with a phase length of 60 degrees at the fundamental frequency; (ii) exhibits a trough in each of continuous two 60-degree sections, in each of third and fourth sections both of which continue in correspondence with a phase length of 60 degrees at the fundamental frequency; and (iii) exhibits a flatter form as compared with said crests and troughs, in each of fifth and sixth sections which correspond to a phase length of 60 degrees at the fundamental frequency and which are separated by said first and second sections or by said third and fourth sections. 
     According to a ninth aspect of the rectifier circuit of the present invention, in the rectifier circuit of the eighth aspect, the waveform of each of said first three-phase alternating currents and said second three-phase alternating currents exhibits a triangular wave in said first to fourth sections. 
     According to a tenth aspect of the rectifier circuit of the present invention, in the rectifier circuit of the eighth aspect, in said first to fourth sections, the waveform of each of said first three-phase alternating currents and said second three-phase alternating currents exhibits a waveform formed by combining a curve that is similar to a waveform that a sinusoidal wave exhibits from 0 degree to 30 degrees and a waveform that is left-right symmetrical to the curve. 
     According to a first aspect of the three-phase rectifier device of the present invention, a three-phase rectifier device comprises: the rectifier circuit according to any of the first to tenth aspects of the present invention; and a three-phase transformer ( 2 ) that receives three-phase currents (i u , i v , i w ), a fundamental frequency of said three-phase currents is a second value that is ⅙ of said first value and said three-phase currents having mutual phase differences of 120 degrees at the fundamental frequency, and that outputs first three-phase alternating currents (i u1 , i v1 , i w1 ) having phase differences of 15 degrees at the fundamental frequency respectively from said three-phase currents, and that also outputs second three-phase alternating currents (i u2 , i v2 , i w2 ) having phase differences of 30 degrees at the fundamental frequency from said first three-phase alternating currents. 
     According to a second aspect of the three-phase rectifier device of the present invention, in the three-phase rectifier device of the first aspect, said three-phase transformer ( 2 ) comprises three autotransformers ( 21 ,  22 ,  23 ) each having a primary winding ( 211 ,  221 ,  232 ) and a secondary winding ( 212 ,  222 ,  232 ) coupled with said primary winding and having a center tap, said primary windings of said three autotransformers are delta-connected, and said center tap of each said autotransformer is connected to a connection point (U, V, W) that connects a pair of said primary windings other than said primary winding coupled with said secondary winding to which said center tap belongs. 
     According to a third aspect of the three-phase rectifier device of the present invention, in the three-phase rectifier device of the first aspect, said three-phase transformer ( 2 ) comprises: three primary windings ( 211 ,  221 ,  231 ) corresponding to respective phases; and three secondary windings ( 212 ,  222 ,  232 ) coupled with all of said primary windings and each having a center tap, and wherein said primary windings are delta-connected, and said three center taps are individually connected to three connection points (U, V, W) at which a pair of said primary windings are connected together. 
     According to the first aspect, particularly the eighth to tenth aspects, of the rectifier circuit of the present invention, when a smoothing capacitor is connected in parallel to the pair of output ends of the first chopper and the pair of output ends of the second chopper, and first three-phase alternating currents having a fundamental frequency of a second value that is ⅙ of the first value are provided to the first three-phase diode bridge, and second three-phase alternating currents having phase differences of 30 degrees from the first three-phase alternating currents are provided to the second three-phase diode bridge, then the currents flowing in the transformer for outputting the first and second three-phase alternating currents is made close to sinusoidal waves. Also, the dc component of voltage can be controlled easily because the control is performed by using choppers. 
     According to the second aspect and the third aspect of the rectifier circuit of the present invention, even when a neutral point corresponding to the first three-phase alternating currents and a neutral point corresponding to the second three-phase alternating currents are not insulated and zero-phase voltage having a fundamental frequency of a third value that is ½ of the first value is generated, it is possible to suppress current flowing on the basis of the zero-phase voltage. 
     According to the fourth aspect of the rectifier circuit of the present invention, no interphase reactor is required. 
     According to the fifth aspect of the rectifier circuit of the present invention, the dc component of voltage is controlled, and dc voltage higher than the peak value of the power-supply voltage is obtained. 
     According to the sixth aspect of the rectifier circuit of the present invention, ripple having the carrier frequency is reduced. 
     According to the seventh aspect of the rectifier circuit of the present invention, the output voltage is smoothed. 
     According to the first aspect to the third aspect of the three-phase rectifier device of the present invention, it is possible to provide appropriate inputs respectively to the first three-phase diode bridge and the second three-phase diode bridge. 
     These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a circuit diagram used to describe a first preferred embodiment of the present invention. 
         FIG. 2  is a circuit diagram illustrating the configuration of a first three-phase diode bridge. 
         FIG. 3  is a circuit diagram illustrating the configuration of a second three-phase diode bridge. 
         FIG. 4  is a circuit diagram illustrating the details of a three-phase transformer. 
         FIG. 5  is a phasor diagram illustrating voltages in individual parts of the three-phase transformer. 
         FIG. 6  is a graph illustrating desired waveforms of currents. 
         FIG. 7  is a graph illustrating the waveforms of currents. 
         FIG. 8  is a graph illustrating the waveforms of first and second rectified currents. 
         FIG. 9  is a graph illustrating the waveform of current. 
         FIG. 10  is a graph illustrating the waveforms of currents. 
         FIG. 11  is a circuit diagram illustrating parts of the configuration shown in  FIG. 1 . 
         FIG. 12  is a circuit diagram illustrating a configuration for generating signals on the basis of data pieces. 
         FIG. 13  is a circuit diagram used to describe a second preferred embodiment of the present invention. 
         FIG. 14  is a circuit diagram illustrating a modification of the second preferred embodiment of the present invention. 
         FIG. 15  is a circuit diagram used to describe a third preferred embodiment of the present invention. 
         FIG. 16  is a circuit diagram illustrating a configuration for generating signals on the basis of data pieces in a fourth preferred embodiment of the present invention. 
         FIG. 17  is a circuit diagram illustrating the acquisition of data conducted when a circuit described in the third preferred embodiment of the invention is used. 
         FIG. 18  is a graph illustrating current values exhibited when the configuration shown in  FIG. 12  and the configuration of  FIG. 17  are used. 
         FIG. 19  is a graph illustrating current values exhibited when the configuration shown in  FIG. 16  and the configuration of  FIG. 17  are used. 
         FIG. 20  is a circuit diagram illustrating a modification of the fourth preferred embodiment of the present invention. 
     
    
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     First Preferred Embodiment 
       FIG. 1  is a circuit diagram used to describe a first preferred embodiment of the present invention. A first three-phase diode bridge  31 , a second three-phase diode bridge  32 , a first chopper  41 , and a second chopper  42  constitute a rectifier circuit. The rectifier circuit may be grasped as including a smoothing capacitor  5 . A three-phase transformer  2  constitutes a three-phase rectifier device together with the rectifier circuit. 
     The three-phase transformer  2  receives three-phase currents i u , i v , i w  from a three-phase power supply  1 , and outputs first three-phase alternating currents i u1 , i v1 , i w1  and second three-phase alternating currents i u2 , i v2 , i w2 . 
     The three-phase power supply  1  includes a U-phase power supply  101 , a V-phase power supply  102 , and a W-phase power supply  103 , respectively generating three-phase voltages e u , e v , e w . The U-phase power supply  101 , the V-phase power supply  102 , and the W-phase power supply  103  respectively supply the three-phase currents i u , i v , i w . 
     The first three-phase diode bridge  31  receives the three-phase currents i u1 , i v1 , i w1 , and outputs a first rectified current i d1 . The second three-phase diode bridge  32  receives the three-phase currents i u2 , i v2 , i w2 , and outputs a second rectified current i d2 . 
       FIG. 2  is a circuit diagram illustrating the configuration of the first three-phase diode bridge  31 . The first three-phase diode bridge  31  has input ends  31 U,  31 V,  31 W and output ends  31 P and  31 N. It applies full-wave rectification to the currents inputted to the input ends  31 U,  31 V,  31 W, and outputs the first rectified current i d1  from the output end  31 P. In this preferred embodiment, the three-phase currents i u1 , i v1 , i w1  are inputted to the input ends  31 U,  31 V,  31 W. 
       FIG. 3  is a circuit diagram illustrating the configuration of the second three-phase diode bridge  32 . The second three-phase diode bridge  32  has input ends  32 U,  32 V,  32 W and output ends  32 P and  32 N. It applies full-wave rectification to the currents inputted to the input ends  32 U,  32 V,  32 W, and outputs the second rectified current i d2  from the output end  32 P. In this preferred embodiment, the three-phase currents i u2 , i v2 , i w2  are inputted to the input ends  32 U,  32 V,  32 W. 
     The first chopper  41  performs a first chopper operation to receive the first rectified current i d1  as a current whose fundamental frequency has a first value. Then it outputs part of the first rectified current id, as a first chopper current i c1 . The second chopper  42  performs a second chopper operation to receive the second rectified current i d2  as a current whose fundamental frequency has the first value. Then it outputs part of the second rectified current i d2  as a second chopper current i c2 . 
     In this preferred embodiment, the first chopper  41  and the second chopper  42  are step-up choppers. Specifically, the first chopper  41  has output ends  41 P and  41 N, and outputs the first chopper current i c1  from the output end  41 P. The first chopper  41  has an inductor  411  that is connected to the output end  31 P of the first three-phase diode bridge  31  and receives the first rectified current i d1 . The collector of an insulated gate bipolar transistor (IGBT)  412  and the anode of a diode  413  are connected in common, and connected to the output end  31 P through the inductor  411 . The cathode of the diode  413  is connected to the output end  41 P. The output ends  31 N and  41 N are connected in common to the emitter of the IGBT  412 . The IGBT  412  functions as a switching element that opens/closes between its collector and emitter. 
     In correspondence with the output ends  41 P and  41 N, inductor  411 , IGBT  412 , and diode  413 , the second chopper  42  includes output ends  42 P and  42 N, an inductor  421 , an IGBT  422 , and a diode  423 , and the second chopper  42  outputs the second chopper current i c2  from the output end  42 P. 
     The output ends  41 P and  41 N are connected in parallel to the output ends  42 P and  42 N, and also in parallel to the smoothing capacitor  5 . A load  6  is connected in parallel to the smoothing capacitor  5 , and supplied with the both-end voltage v dc  of the smoothing capacitor  5 . 
     As described above, the first chopper  41  and the second chopper  42  have their output ends connected in parallel with the smoothing capacitor  5 , and so the current of the first chopper current i c1  and the second chopper current i c2  are continuous to function as a current source. Also, by adopting step-up type as the first chopper  41  and the second chopper  42 , it is possible to obtain dc voltage that is higher than the peak values of the three-phase voltages e u , e v , e w . Also, by providing the smoothing capacitor  5 , it is possible to smooth the output voltage. 
       FIG. 4  is a circuit diagram illustrating the details of the three-phase transformer  2 , which is illustrated in Non-Patent Document 1, for example. The three-phase transformer  2  includes three autotransformers  21 ,  22 ,  23 . The autotransformer  21  has a primary winding  211  connected between a U-phase input end U and a W-phase input end W, and a secondary winding  212  coupled with it and having a center tap. The secondary winding  212  is divided into secondary windings  2121  and  2122  by the center tap. The center tap is connected to a V-phase input end V. While the number of turns of the primary winding  211  is n 1 , the number of turns of both of the secondary windings  2121  and  2122  is n 2 , and the value shown by Expression (1) is adopted as the ratio. 
     [Expression 1] 
     
       
         
           
             
               
                 
                   
                     
                       n 
                       2 
                     
                     
                       n 
                       1 
                     
                   
                   = 
                   
                     a 
                     = 
                     
                       
                         tan 
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                           ( 
                           
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                             12 
                           
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                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
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     In the same way, the autotransformer  22  has a primary winding  221  connected between the U-phase input end U and the V-phase input end V, and a secondary winding  222  coupled with it and having a center tap. The secondary winding  222  is divided into secondary windings  2221  and  2222  by the center tap. The center tap is connected to the W-phase input end W. While the number of turns of the primary winding  221  is n 1 , the number of turns of both of the secondary windings  2221  and  2222  is n 2 . 
     The autotransformer  23  has a primary winding  231  connected between the W-phase input end W and the V-phase input end V, and a secondary winding  232  coupled with it and having a center tap. The secondary winding  232  is divided into secondary windings  2321  and  2322  by the center tap. The center tap is connected to the U-phase input end U. While the number of turns of the primary winding  231  is n 1 , the number of turns of both of the secondary windings  2321  and  2322  is n 2 . 
     The primary windings  211 ,  221  and  231  are delta-connected. The three-phase currents i u , i v , i w  from the three-phase power supply  1  flow respectively into the U-phase input end U, the V-phase input end V, and the W-phase input end W. On the other hand, a current i uw  flows in the primary winding  211  from the W-phase input end W to the U-phase input end U, a current i vu  flows in the primary winding  221  from the U-phase input end U to the V-phase input end V, and a current i wv  flows in the primary winding  231  from the V-phase input end V to the W-phase input end W. Expression (2) holds about the currents i wv , i uw , i vu , flowing in the primary windings  231 ,  211   221 . 
     [Expression 2] 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             i 
                             wv 
                           
                           = 
                           
                             a 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   i 
                                   
                                     u 
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                                     v 
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     The currents i v1  and i v2  are outputted from the center tap of the secondary winding  212  respectively through the secondary windings  2121  and  2122 , the currents i w1  and i w2  are outputted from the center tap of the secondary winding  222  respectively through the secondary windings  2221  and  2222 , and the currents i u1  and i u2  are outputted from the center tap of the secondary winding  232  respectively through the secondary windings  2321  and  2322 . Accordingly, Expression (3) holds. 
     [Expression 3] 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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                   } 
                 
               
               
                 
                   ( 
                   3 
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       FIG. 5  is a phasor diagram illustrating the voltages in individual parts of the three-phase transformer  2 , which is illustrated in Non-Patent Document 1. The three-phase voltages e u , e v , e w  have phase differences of 120 degrees relative to each other, and the phase lags in this order. The voltage e u1  on the side opposite to the center tap of the secondary winding  2321  leads in phase by 15 degrees with respect to the voltage e u , the voltage e v1  on the side opposite to the center tap of the secondary winding  2121  leads in phase by 15 degrees with respect to the voltage e v , and the voltage e w1  on the side opposite to the center tap of the secondary winding  2221  leads in phase by 15 degrees with respect to the voltage e w . Also, the voltage ea on the side opposite to the center tap of the secondary winding  2322  lags in phase by 15 degrees with respect to the voltage e u , the voltage e v2  on the side opposite to the center tap of the secondary winding  2122  lags in phase by 15 degrees with respect to the voltage e v , and the voltage e w2  on the side opposite to the center tap of the secondary winding  2222  lags in phase by 15 degrees with respect to the voltage e w . 
     With the autotransformer  23 , the absolute value E 1  of the voltage applied to the primary winding  231  is the absolute value of the difference between the voltage e v  and the voltage e w , and a voltage having an absolute value a·E 1  is excited in the secondary winding  2322 . Accordingly, because its center tap is connected to the U-phase input end U and the voltage e u  is applied, the absolute value E t  of the difference between the voltage e u2  and the voltage e u  is equal to the absolute value a·E 1 . The same is true for the other phases. 
     Such voltage relations are determined by the relative coupling and connection of the autotransformers  21 ,  22  and  23 . Accordingly, as long as the three-phase voltages e u , e v , e w  are stable, the voltage relations are maintained regardless of the waveforms of the currents i u1 , i v1 , i w1 , i u2 , i v2 , i w2 . In other words, by controlling the current waveforms, there is room to improve the waveforms of the three-phase currents i u , i v , i w  inputted to the three-phase transformer  2  from the three-phase power supply  1 . The currents i u1 , i v1 , i w1 , i u2 , i v2 , i w2  can be controlled on the basis of how they are inputted with the operations of the first chopper  41  and the second chopper  42 . 
     Now, a desired waveform of the currents i u1 , i v1 , i w1 , i u2 , i v2 , i w2  will be illustrated first, and a description will be made to illustrate that such currents can be inputted on the basis of the operations of the first chopper  41  and the second chopper  42 . 
       FIG. 6  is a graph illustrating a desired waveform i(θ) of the currents i u1 , i v1 , i w1 , i u2 , i v2 , i w2 . Where, the phase of the angle θ differs depending on the six currents. Specifically, the waveform i(θ) is represented by Expression (4). 
     [Expression 4] 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             0 
                             ≤ 
                             θ 
                             ≤ 
                             
                               π 
                               6 
                             
                           
                           , 
                           
                             
                               
                                 π 
                                 ≤ 
                                 θ 
                                 ≤ 
                                 
                                   
                                     7 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   6 
                                 
                               
                               : 
                               
                                 i 
                                 ⁡ 
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                             
                             = 
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 I 
                                 d 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               π 
                               6 
                             
                             ≤ 
                             θ 
                             ≤ 
                             
                               π 
                               3 
                             
                           
                           , 
                           
                             
                               
                                 
                                   
                                     7 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   6 
                                 
                                 ≤ 
                                 θ 
                                 ≤ 
                                 
                                   
                                     4 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                               
                               : 
                               
                                 i 
                                 ⁡ 
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                             
                             = 
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 I 
                                 d 
                               
                               ⁢ 
                               
                                 sin 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     + 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               π 
                               3 
                             
                             ≤ 
                             θ 
                             ≤ 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                               3 
                             
                           
                           , 
                           
                             
                               
                                 
                                   
                                     4 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                                 ≤ 
                                 θ 
                                 ≤ 
                                 
                                   
                                     5 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                               
                               : 
                               
                                 i 
                                 ⁡ 
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                             
                             = 
                             0 
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                               3 
                             
                             ≤ 
                             θ 
                             ≤ 
                             
                               
                                 5 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                               6 
                             
                           
                           , 
                           
                             
                               
                                 
                                   
                                     5 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   3 
                                 
                                 ≤ 
                                 θ 
                                 ≤ 
                                 
                                   
                                     11 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   6 
                                 
                               
                               : 
                               
                                 i 
                                 ⁡ 
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                             
                             = 
                             
                               
                                 - 
                                 2 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 I 
                                 d 
                               
                               ⁢ 
                               
                                 sin 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     - 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 5 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                               6 
                             
                             ≤ 
                             θ 
                             ≤ 
                             π 
                           
                           , 
                           
                             
                               
                                 
                                   11 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   π 
                                 
                                 6 
                               
                               ≤ 
                               θ 
                               ≤ 
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   π 
                                   : 
                                   
                                     i 
                                     ⁡ 
                                     
                                       ( 
                                       θ 
                                       ) 
                                     
                                   
                                 
                               
                             
                             = 
                             
                               
                                 - 
                                 2 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 I 
                                 d 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     The waveform i(θ) can be roughly explained as shown below: 
     (i) It exhibits a crest in each of the first and second sections (the section from 5π/3 to 2π and the section from 0 to π/3) both of which continue in correspondence with a phase length of 60 degrees at the fundamental frequency; 
     (ii) It exhibits a trough in each of continuous two 60-degree sections, in each of the third and fourth sections (the section from 2π/3 to π and the section from π to 4π/3) both of which continue in correspondence with a phase length of 60 degrees at the fundamental frequency; and 
     (iii) It exhibits a flatter form as compared with the crests and troughs, in each of the fifth and sixth sections (the section from π/3 to 2π/3 and the section from 4π/3 to 5π/3) which correspond to a phase length of 60 degrees at the fundamental frequency and which are separated by the first and second sections or by the third and fourth sections. 
     Expression (5) is obtained by applying Fourier expansion to Expression (4). 
     [Expression 5] 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             i 
                             ⁡ 
                             
                               ( 
                               θ 
                               ) 
                             
                           
                           = 
                           
                             
                               
                                 
                                   I 
                                   d 
                                 
                                 
                                   3 
                                 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             + 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   2 
                                 
                                 ∞ 
                               
                               ⁢ 
                               
                                 
                                   I 
                                   mn 
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 n 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             I 
                             mn 
                           
                           = 
                           
                             
                               32 
                               
                                 
                                   ( 
                                   
                                     
                                       n 
                                       2 
                                     
                                     - 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 π 
                               
                             
                             ⁢ 
                             
                               I 
                               d 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                               
                                 n 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                               2 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                               
                                 n 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 π 
                               
                               3 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                               
                                 
                                   ( 
                                   
                                     n 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 π 
                               
                               12 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                               
                                 
                                   ( 
                                   
                                     n 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 π 
                               
                               12 
                             
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     As can be seen from Expression (5), the waveform i(θ) has a fundamental component of cos θ, and the components of even order, (3 n)th, (12 n+1)th, and (12 n−1)th are zero. Accordingly, it is seen that the main harmonic components are (6 m+1)th and (6 m−1)th, with an odd number m. 
     Considering the phase differences about the angle θ of Expression (5), the currents i u1 , i v1 , i w1 , i u2 , i v2 , i w2  are shown by Expression (6). Where the angular frequency of the three-phase voltages e u , e v , e w  is taken as c, and the voltage e u  is assumed to be proportional to the sinusoidal function sin(ωt) of time t. 
     [Expression 6] 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             i 
                             
                               u 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           = 
                           
                             
                               
                                 I 
                                 m 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       t 
                                     
                                     + 
                                     
                                       π 
                                       12 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   2 
                                 
                                 ∞ 
                               
                               ⁢ 
                               
                                 
                                   I 
                                   mn 
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   n 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         t 
                                       
                                       + 
                                       
                                         π 
                                         12 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             i 
                             
                               u 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           = 
                           
                             
                               
                                 I 
                                 m 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       t 
                                     
                                     - 
                                     
                                       π 
                                       12 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   2 
                                 
                                 ∞ 
                               
                               ⁢ 
                               
                                 
                                   I 
                                   mn 
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   n 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         t 
                                       
                                       - 
                                       
                                         π 
                                         12 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             i 
                             
                               v 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           = 
                           
                             
                               
                                 I 
                                 m 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       t 
                                     
                                     + 
                                     
                                       π 
                                       12 
                                     
                                     - 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   2 
                                 
                                 ∞ 
                               
                               ⁢ 
                               
                                 
                                   I 
                                   mn 
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   n 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         t 
                                       
                                       + 
                                       
                                         π 
                                         12 
                                       
                                       - 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           π 
                                         
                                         3 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             i 
                             
                               v 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           = 
                           
                             
                               
                                 I 
                                 m 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       t 
                                     
                                     - 
                                     
                                       π 
                                       12 
                                     
                                     - 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   2 
                                 
                                 ∞ 
                               
                               ⁢ 
                               
                                 
                                   I 
                                   mn 
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   n 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         t 
                                       
                                       - 
                                       
                                         π 
                                         12 
                                       
                                       - 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           π 
                                         
                                         3 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             i 
                             
                               w 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           = 
                           
                             
                               
                                 I 
                                 m 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       t 
                                     
                                     + 
                                     
                                       π 
                                       12 
                                     
                                     + 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   2 
                                 
                                 ∞ 
                               
                               ⁢ 
                               
                                 
                                   I 
                                   mn 
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   n 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         t 
                                       
                                       + 
                                       
                                         π 
                                         12 
                                       
                                       + 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           π 
                                         
                                         3 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             i 
                             
                               w 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           = 
                           
                             
                               
                                 I 
                                 m 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       t 
                                     
                                     - 
                                     
                                       π 
                                       12 
                                     
                                     + 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         π 
                                       
                                       3 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   2 
                                 
                                 ∞ 
                               
                               ⁢ 
                               
                                 
                                   I 
                                   mn 
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   n 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         t 
                                       
                                       - 
                                       
                                         π 
                                         12 
                                       
                                       + 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           π 
                                         
                                         3 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
       FIG. 7  is a graph illustrating the currents i u1  and i u2 . The graph is based on the phase of the voltage e u . The minimum value of each is −I d  and the maximum value is I d . Due to the phase relation of voltages shown in the phasor diagram of  FIG. 5 , the currents i u1  and i u2  respectively lead in phase by 15 degrees and lag in phase by 15 degrees. Though not shown graphically, due to the phase relation of voltages shown in the phasor diagram of  FIG. 5 , the currents i u1 , i v11 , i w1  have phase differences of 120 degrees with each other, and the currents i u2 , i v2 , i w2  have phase differences of 120 degrees with each other. 
       FIG. 8  is a graph illustrating the waveforms of the first rectified current i d1  and the second rectified current i d2  together with the voltage e u . The first rectified current i d1  is obtained by applying full-wave rectification to the currents i u1 , i v1 , i w1 , and so it exhibits an approximately triangular wave that repeats in periods of 60 degrees in terms of the fundamental frequency of the voltage e u . In other words, the fundamental frequency of the three-phase alternating currents i u1 , i v1 , i w1  inputted to the input ends  31 U,  31 V,  31 W of the first three-phase diode bridge  31  is ⅙ of the fundamental frequency of the first rectified current i d1 . 
     More accurately, the currents i u1 , i v1 , i w1  have the waveforms shown by Expression (6), and so the waveform of the first rectified current i d1  in a rising region exhibits a sine θ waveform in the section of 0≦θ≦π/6, and the waveform in a falling region exhibits a sine θ waveform in the section of 5π/6≦θ≦π. That is, it exhibits a waveform formed by combining a curve that is similar to the waveform that a sinusoidal wave exhibits from 0 degree to 30 degrees and a waveform that is left-right symmetrical to the curve. The same is true for the second rectified current i d2 . A near triangular waveform configured on the basis of a waveform commonly called “middle-phase”, not a maximum phase nor a minimum phase of a sinusoidal wave, is herein referred to as a three-phase ac middle-phase waveform. 
     From Expressions (2), (3) and (6), the current i u  is represented by Expression (7). This shows that the current i u  contains the fundamental frequency component only. The same is true for the currents i v  and i w . 
     [Expression 7] 
     
       
         
           
             
               
                 
                   
                     
                       i 
                       u 
                     
                     = 
                     
                       
                         
                           
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               I 
                               m 
                             
                           
                           
                             cos 
                             ⁢ 
                             
                               π 
                               12 
                             
                           
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         t 
                       
                       = 
                       
                         
                           2 
                         
                         ⁢ 
                         
                           I 
                           rms 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         t 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   Where 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         I 
                         m 
                       
                       = 
                       
                         
                           1 
                           d 
                         
                         
                           3 
                         
                       
                     
                     , 
                     
                       
                         I 
                         rms 
                       
                       = 
                       
                         
                           
                             
                               2 
                             
                             ⁢ 
                             
                               I 
                               m 
                             
                           
                           
                             cos 
                             ⁢ 
                             
                               π 
                               12 
                             
                           
                         
                         = 
                         
                           0.845 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             d 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
       FIG. 9  is a graph illustrating the waveform obtained by obtaining the current i wv  from Expressions (2) and (6).  FIG. 10  is a graph illustrating the waveforms of currents (i u1 +i u2 ), (−i uw +i vu ), i u  obtained from Expressions (2), (3), (6) and (7). 
     Now, as described above, the rectified currents i d1  and i d2  are close to a triangular wave, and so it is possible to receive these currents respectively from the three-phase diode bridges  31  and  32 , with the chopper operations of the choppers  41  and  42 . It is thus possible to input the currents i u1 , i v1 , i w1 , i u2 , i v2 , i w2  from the three-phase transformer  2  to the three-phase diode bridges  31  and  32 , and it is possible for the three-phase transformer  2  to remove harmonic components of the currents i u , i v , i w . 
     Then, next, an example configuration for the chopper operations of the choppers  41  and  42  for receiving of the rectified currents i d1  and i 2d  will be described. An example that obtains desired waveforms by pulse width modulation will be described. 
       FIG. 11  is a circuit diagram illustrating parts of the configuration shown in  FIG. 1 , showing parts for obtaining parameters on which the control of the chopper operations is based. Specifically, the values of the rectified currents i d1  and i d2  flowing respectively through the inductors  411  and  421  are detected respectively as data I d1  and data I d2 , and the value of the both-end voltage v dc  of the smoothing capacitor  5  is detected as data V dc . Signals T 1  and T 2  for controlling the turning on/off of the IGBTs  412  and  422  are given to the gates of the IGBTs  412  and  422  through the buffers shown with triangular signs in the diagram. 
       FIG. 12  is a circuit diagram illustrating a configuration for generating the signals T 1  and T 2  on the basis of the data I d1 , I d2 , and V dc . This configuration can be roughly divided into a voltage control block  81 , a current command generating block  82 , a current control block  83 , and a PWM modulation block  84 . 
     A voltage command generator  801  obtains a voltage command value V dc * corresponding to a desired both-end voltage V dc , which is inputted to the voltage control block  81  together with the data V dc . In the voltage control block  81 , an operator  802  obtains a difference between the voltage command value V dc * and the data V dc , which is outputted to the current command generating block  82  through the processings in a PI controller  803  and a limiter  804 . 
     The current command generating block  82  includes waveform generators  805  and  806  for generating three-phase ac middle-phase waveforms, both of which generate a three-phase ac middle-phase waveform. However, the waveforms generated by the waveform generators  805  and  806  are in opposite phase to each other.  FIG. 12  shows this opposite phase relation with the circles located in different positions near the waveform generators  805  and  806  (this sign does not indicate the inversion of polarity). The three-phase ac middle-phase waveforms generated by the waveform generators  805  and  806  have a frequency that is six times the fundamental frequency of the three-phase voltages e u , e v , e w  (accordingly, of the currents i u1 , i v1 , i w1 , i u2 , i v2 , i w2 ), and so they can be grasped as having a mutual phase difference of 30 degrees, with reference to the fundamental frequency. 
     In the current command generating block  82 , the output of the voltage command generator  801  is inputted to a multiplier  807  and multiplied with the output of the waveform generator  805 . Similarly, the output of the voltage command generator  801  is inputted to a multiplier  808  and multiplied with the output of the waveform generator  806 . The results of multiplication are outputted to the current control block  83  respectively as current command values I d1 * and I d2 * about the rectified currents i d1  and i d2 . 
     In the current control block  83 , an operator  809  obtains a difference between the current command value I d1 * and the data I d1 , which is outputted to the PWM modulation block  84  through the processing in a PI controller  810 . Similarly, an operator  811  obtains a difference between the current command value I d2 * and the data I d2 , which is outputted to the PWM modulation block  84  through the processing in a PI controller  812 . 
     The PWM modulation block  84  includes a carrier generator  813  for generating a modulation carrier C and differential amplifiers  815  and  816 . The differential amplifier  815  is provided with the modulation carrier C and the output of the PI controller  810 , and generates the signal T 1 . The differential amplifier  816  is provided with the modulation carrier C and the output of the PI controller  812 , and generates the signal T 2 . The signals T 1  and T 2  control on/off of the IGBTs  412  and  422  such that rectified currents i d1  and i d2  corresponding to the current command values I d1 * and I d2 * flow and a both-end voltage V dc  corresponding to the voltage command value V dc * is generated in the smoothing capacitor  5 , whereby the operations of the choppers  41  and  42  are controlled. 
     Second Preferred Embodiment 
       FIG. 13  is a circuit diagram used to describe a second preferred embodiment of the present invention. The configuration illustrated here differs from the configuration of the first preferred embodiment in that an interphase reactor  71  is additionally interposed between the three-phase transformer  2  and the first three-phase diode bridge  31 . 
     When explained by referring to  FIGS. 2 and 4 , the input ends  31 U,  31 V,  31 W of the first three-phase diode bridge  31  are connected respectively to the secondary windings  2321 ,  2121 ,  2221 , each through one interphase reactor. That is, the three-phase currents i u1 , i v1 , i w1  flow in the interphase reactor  71 . 
     Though not described in the first preferred embodiment, zero-phase voltage is generally generated between a neutral point on the input side of a three-phase diode bridge and an intermediate potential on the output side. This voltage is a triple component of the fundamental frequency of the three-phase voltage on the input side. When explained by referring to  FIGS. 2 and 5 , in the first three-phase diode bridge  31 , zero-phase voltage is generated at a frequency of ½ of the fundamental frequency of the first rectified current i d1 , between the neutral point potential of the three-phase voltages e u1 , e v1 , e w1  given respectively to the input ends  31 U,  31 V,  31 W and the intermediate potential of the voltage applied between the output ends  31 P and  31 N. Zero-phase voltage is similarly generated in the second three-phase diode bridge  32 . 
     When parallel-connected multiple rectifier circuitry is adopted as in the present invention, and when the two neutral points are not insulated on the side supplying the two sets of three-phase currents inputted to the rectifier circuits, then current due to the zero-phase voltage is generated (hereinafter referred to as “zero-phase current”). This is because the three-phase currents become unbalanced with the generation of zero-phase voltage. 
     In this preferred embodiment, as can be seen from  FIG. 4 , the three-phase transformer  2  adopts the autotransformers  21 ,  22  and  23 , and so the neutral points of the three-phase voltages e u1 , e v1 , e w1  and the three-phase voltages e u2 , e v2 , e w2  (see  FIG. 5 ) respectively corresponding to the three-phase currents i u1 , i v1 , i w1  and the three-phase currents i u2 , i v2 , i w2  are common. 
     Accordingly, it is desirable to cut the zero-phase current by adopting the interphase reactor  71  to provide large impedance for the imbalance of the three-phase currents. 
       FIG. 14  is a circuit diagram illustrating a modification of this preferred embodiment, where an interphase reactor  72  is provided between the first three-phase diode bridge  31  and the first chopper  41 . Thus, the first rectified current i d1  flows through the interphase reactor  72 . More specifically, the first rectified current i d1  flows in a reactor interposed between the output end  31 P of the first three-phase diode bridge  31  and the inductor  411  of the first chopper  41 . A reactor is provided also between the output end  31 N of the first three-phase diode bridge  31  and the emitter of the IGBT  412 . 
     It is desirable to provide the interphase reactor  72  located in this position because it cuts the zero-phase current in the same way as the interphase reactor  71 . 
     The interphase reactors  71  and  72  described above are both provided for the first three-phase diode bridge  31 , but they may be provided for the second three-phase diode bridge  32  on its input side or output side. 
     Third Preferred Embodiment 
       FIG. 15  is a circuit diagram used to describe a third preferred embodiment of the present invention. The configuration shown here differs from the configuration of the first preferred embodiment in that the first chopper  41  and the second chopper  42  are replaced respectively by a first chopper  43  and a second chopper  44 . 
     As compared with the first chopper  41 , the first chopper  43  additionally includes an inductor  431  and a diode  434 . More specifically, the inductor  431  is interposed between the output end  31 N of the first three-phase diode bridge  31  and the emitter of the IGBT  412 . Also, the diode  434  has its anode connected to the output end  43 N, and its cathode connected to the emitter of the IGBT  412 . The second chopper  44 , too, includes an inductor  441  and a diode  444  that are connected in the same way as the inductor  431  and the diode  434 . 
     With this configuration, in the first chopper  43  and the second chopper  44 , it is also possible to control the currents flowing to the negative side of the first three-phase diode bridge  31  and to the negative side of the second three-phase diode bridge  32 , and no zero-phase current flows. This eliminates the need for an interphase reactor. 
     Fourth Preferred Embodiment 
     When pulse width modulation is adopted in order to obtain desired waveforms of the rectified currents i d1  and i d2  as described in the first preferred embodiment, ripple due to the modulation carrier C is superimposed on the rectified currents i d1  and i d2 . This causes ripple in the currents i u1 , i v1 , i w1 , i u2 , i v2 , i w2 , and further in the three-phase currents i u , i v , i w . Accordingly, this preferred embodiment describes a scheme for reducing the ripple due to the carrier C. 
       FIG. 16  is a circuit diagram illustrating a configuration adopted in this preferred embodiment and for generating the signals T 1  and T 2  on the basis of the data I d1 , I d2  and V dc . Unlike the PWM modulation block  84  of the first preferred embodiment described with  FIG. 12 , the differential amplifier  816  of this preferred embodiment is provided not with the carrier C but with a carrier D that is in opposite phase relative to the carrier C. The carrier D is generated by a carrier generator  814 . 
     That is, in this preferred embodiment, the operation of the first chopper  41  is controlled by pulse width modulation on the basis of the carrier C, and the operation of the second chopper  42  is controlled by pulse width modulation on the basis of the carrier D having the same carrier frequency as, and in opposite phase to, the carrier C. This cancels the ripple having the carrier frequency in the rectified currents i d1  and i d2 . 
       FIG. 17  is a circuit diagram illustrating the acquisition of the data I d1 , I d2  and V dc  when the circuit described in the third preferred embodiment is adopted, which corresponds to  FIG. 11 . 
       FIG. 18  is a graph illustrating the values of the currents i u1 , i u2  and i u  exhibited when the configuration exhibited in  FIG. 12  and the configuration exhibited in  FIG. 17  are used.  FIG. 19  is a graph illustrating the values of the currents i u1 , i u2  and i u  exhibited when the configuration exhibited in  FIG. 16  and the configuration exhibited in  FIG. 17  are used. The graph of  FIG. 19  shows that the ripple is reduced as compared with the graph of  FIG. 18 . 
       FIG. 20  is a circuit diagram illustrating a modification of this preferred embodiment, which is a circuit diagram illustrating a configuration for generating the signals T 1  and T 2  on the basis of the data I d1 , I d2  and V dc . Unlike the configuration described with  FIG. 16 , the waveform generator  806  and the multiplier  808  are omitted in the current command generating block  82 , and a phase shifter  817  is additionally provided. The phase shifter  817  shifts by 15 degrees the phase of the current command value I d1 * outputted by the multiplier  807 . Then, the phase shifter  817  outputs a current command value I d2 * that is in opposite phase to the current command value I d1 *. 
     With this configuration, the signals T 1  and T 2  are generated in the same way as in the configuration of  FIG. 12  when the carrier generator  814  generates the same carrier C as the carrier generator  813  and PWM modulation is performed. In this case, the carrier generator  814  can be merged with the carrier generator  813  as in  FIG. 12 . 
     When the carrier generator  814  generates the carrier D in opposite phase to the carrier generator  813  and PWM modulation is performed, the signals T 1  and T 2  are generated in the same way as in the configuration of  FIG. 16 , and the ripple having the carrier frequency is canceled in the rectified currents i d1  and i d2 . 
     Modifications 
     The description above has shown examples in which the three-phase currents i u1 , i v1 , i w1  lead in phase by 30 degrees with respect to the three-phase currents i u2 , i v2 , i w2 , but the present invention can be constituted in the same way also when they lag in phase. 
     Also, three-phase ac middle-phase waveforms have been suggested as the first rectified current i d1 , and the second rectified current i d2 , but ordinary triangular waves may be used instead. In this case, the choppers  41  to  44  can be controlled easily. 
     Also, configurations adopting three autotransformers  21 ,  22  and  23  as the three-phase transformer  2  have been described, but the applications of the present invention are not limited thereto. A three-phase transformer may be adopted in which primary windings  211 ,  221 ,  231  and secondary windings  212 ,  222 ,  232  are coupled with each other. For example, it is possible to adopt a three-phase transformer having three primary windings  211 ,  221  and  231  and three secondary windings  212 ,  222 ,  232  coupled with them. The secondary windings  212 ,  222 ,  232  are all provided with center taps. The primary windings  211 ,  221 ,  231  are delta-connected, and the three center taps are individually connected to a connection point at which the primary windings  211  and  221  are connected together, a connection point at which the primary windings  221  and  231  are connected together, and a connection point at which the primary windings  231  and  232  are connected together. Such a three-phase transformer is illustrated in FIG. 7 of Non-Patent Document 2, for example. 
     While the invention has been described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is understood that numerous other modifications and variations can be devised without departing from the scope of the invention.