Patent Publication Number: US-9425679-B2

Title: Inverter apparatus and solar power generation system

Description:
The contents of the following Japanese patent application are incorporated herein by reference: NO. 2012-111802 filed on May 15, 2012. 
     BACKGROUND 
     1. Technical Field 
     The present invention relates to an inverter apparatus and a solar power generation system. 
     2. Related Art 
     A power conditioner converts DC power from solar cells into AC power, by turning ON and OFF a plurality of switches forming an inverter circuit. Patent Documents 1 and 2 each disclose a power conditioner that improves the efficiency of the conversion from DC power to AC power by decreasing switching loss caused by the switches in the inverter circuit.
     Patent Document 1: Japanese Patent Application Publication No. 2010-220320   Patent Document 2: Japanese Patent Application Publication No. 2010-220321   

     In these power conditioners, more efficient conversion of the DC power from the solar cells into AC power is desired. 
     SUMMARY 
     According to a first aspect of the present invention, provided is an inverter apparatus comprising a first switch group that is connected to a DC power source and includes a first switch and a second switch connected in series; a capacitor that has one end thereof connected to a first connection point between the first switch and the second switch; a second switch group that is connected in parallel with the capacitor and includes a third switch and a fourth switch that are connected in series; a switch control section that controls an ON/OFF state of the first switch, the second switch, the third switch, and the fourth switch to convert DC voltage from the DC power source into AC voltage and output the AC voltage from a second connection point between the third switch and the fourth switch; and a smoothing circuit that is connected to the second connection point and normalizes a pulse waveform of the AC voltage. 
     In the inverter apparatus, the switch control section may turn the first switch and the second switch ON and OFF in an alternating manner, and may turn the third switch and the fourth switch ON and OFF in an alternating manner. After turning the first switch and the second switch ON and OFF in an alternating manner and turning the third switch and the fourth switch ON and OFF in an alternating manner, the switch control section may turn the third switch and the fourth switch ON and OFF in an alternating manner while the first switch is OFF and the second switch is ON. 
     In the inverter apparatus, the switch control section may turn the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF, and may turn the third switch and the fourth switch ON and OFF in an alternating manner while the first switch is ON and the second switch is OFF. After turning the third switch and the fourth switch ON and OFF in an alternating manner while the first switch is ON and the second switch is OFF, the switch control section may turn the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF. After turning the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF, the switch control section may turn the third switch and the fourth switch ON and OFF in an alternating manner while the first switch is OFF and the second switch is ON. 
     The inverter apparatus may further comprise a voltage measuring section that measures voltage of a system power source connected on the output side of the smoothing circuit. The switch control section may determine a timing for switching from an operation of turning the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF to an operation of turning the third switch and the fourth switch ON and OFF in an alternating manner while the first switch is ON and the second switch is OFF, based on the voltage of the system power source. 
     The inverter apparatus may be connected to a three-phase AC power source. The switch control section may control the ON/OFF state of the first switch, the second switch, the third switch, and the fourth switch to output from the smoothing circuit shifted AC voltage obtained by shifting a reference AC voltage, with which the AC voltage is to be phase-synchronized, in a positive direction by a predetermined potential, from a reference potential of the reference AC voltage. 
     In the inverter apparatus, after turning the third switch and the fourth switch ON and OFF in an alternating manner while the first switch is OFF and the second switch is ON, the switch control section may turn the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF. 
     In the inverter apparatus, after turning the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF, the switch control section may turn ON the first switch, turn OFF the second switch, turn OFF the third switch, turn ON the fourth switch, and maintain the switches in this state. 
     In the inverter apparatus, if the state in which the first switch is ON, the second switch is OFF, the third switch is OFF, and the fourth switch is ON is maintained for an interval greater than 2π/3, the switch control section may turn the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF and then, after turning the first switch and the second switch ON and OFF in an alternating manner while the third switch is OFF and the fourth switch is ON, turn ON the first switch, turn OFF the second switch, turn OFF the third switch, turn ON the fourth switch, and maintain the switches in this state. 
     In the inverter apparatus, after maintaining the state in which the first switch is ON, the second switch is OFF, the third switch is OFF, and the fourth switch is ON, the switch control section may turn the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF. 
     In the inverter apparatus, if the state in which the first switch is ON, the second switch is OFF, the third switch is OFF, and the fourth switch is ON is maintained for an interval greater than 2π/3, the switch control section may turn ON the first switch, turn OFF the second switch, turn OFF the third switch, turn ON the fourth switch, maintain the switches in this state and then, after turning the first switch and the second switch ON and OFF in an alternating manner while the third switch is OFF and the fourth switch is ON, turn the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF. 
     In the inverter apparatus, after turning the first switch and the second switch ON and OFF in an alternating manner while the third switch is ON and the fourth switch is OFF, the switch control section may turn the third switch and the fourth switch ON and OFF in an alternating manner while the first switch is OFF and the second switch is ON. 
     According to a first aspect of the present invention, provided is a solar power generation system comprising a solar cell; and the inverter apparatus of the first aspect that converts DC voltage from the solar cell into AC voltage. 
     The summary clause does not necessarily describe all necessary features of the embodiments of the present invention. The present invention may also be a sub-combination of the features described above. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a circuit configuration of a power conditioner according to an embodiment of the present invention. 
         FIG. 2A  shows an exemplary first voltage command value used in Control Technique 1. 
         FIG. 2B  shows an exemplary second voltage command value used in Control Technique 1. 
         FIG. 2C  shows an exemplary reference AC voltage to be output from the power conditioner. 
         FIG. 3A  shows an exemplary first voltage command value used in Control Technique 2. 
         FIG. 3B  shows an exemplary second voltage command value used in Control Technique 2. 
         FIG. 4  shows exemplary switching conditions for each of the switches in Control Technique 2. 
         FIG. 5  shows a circuit configuration when the power conditioner is applied to a three-phase four-wire power source. 
         FIG. 6  shows exemplary voltage waveforms output from a power conditioner for each phase when applied in a three-phase four-wire power source. 
         FIG. 7A  shows an exemplary first voltage command value used in Control Technique 3. 
         FIG. 7B  shows an exemplary second voltage command value used in Control Technique 3. 
         FIG. 8  shows exemplary switching conditions for each of the switches in Control Technique 3. 
         FIG. 9A  shows an exemplary first voltage command value used in Control Technique 3. 
         FIG. 9B  shows an exemplary second voltage command value used in Control Technique 3. 
         FIG. 10  shows exemplary switching conditions for each of the switches in Control Technique 3. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Hereinafter, some embodiments of the present invention will be described. The embodiments do not limit the invention according to the claims, and all the combinations of the features described in the embodiments are not necessarily essential to means provided by aspects of the invention. 
       FIG. 1  shows a circuit configuration of a power conditioner  100  according to an embodiment of the present invention. The power conditioner  100  is used in a solar power generation system, for example. The power conditioner  100  is one example of an inverter apparatus. The power conditioner  100  is connected to a DC power source  70  and a system power source  80 . The DC power source  70  may be a solar cell, for example. The power conditioner  100  converts the DC voltage from the DC power source  70  into AC voltage, and operates together with the system power source  80 . 
     The power conditioner  100  includes a first capacitor  30 , a first switch group  10 , a second capacitor  32 , a second switch group  20 , a smoothing circuit  40 , a switch control section  50 , a first voltage sensor  34 , a second voltage sensor  35 , and a third voltage sensor  36 . The first capacitor  30  is connected in parallel with the DC power source  70 , via an input terminal  61  at one end and an input terminal  62  at the other end, and normalizes the DC voltage output from the DC power source  70 . The input terminal  62  is connected to a ground, which is a reference potential. 
     The first switch group  10  is connected in parallel with the DC power source  70  and the first capacitor  30 . The first switch group  10  includes a first switch  12  and a second switch  14 , which are connected in series. The first switch  12  and the second switch  14  may include switching elements such as a MOS field effect transistor or an insulated gate bipolar transistor (IGBT), for example. As another example, the first switch  12  and the second switch  14  may include diodes, and the diodes may be connected inversely in parallel to the switching elements. One end of the first switch  12  is connected to the input terminal  61 , and the other end of the first switch  12  is connected to one end of the second switch  14 . The other end of the second switch  14  is connected to the input terminal  62 . In other words, the other end of the second switch  14  is connected to the ground. 
     One end of the second capacitor  32  is connected to a first connection point  16  between the first switch  12  and the second switch  14 . The second switch group  20  is connected in parallel with the second capacitor  32 . The second switch group  20  includes a third switch  22  and a fourth switch  24  that are connected in series. The third switch  22  and the fourth switch  24  may include switching elements such as a MOS field effect transistor or an insulated gate bipolar transistor (IGBT), for example. As another example, the third switch  22  and the fourth switch  24  may include diodes, and the diodes may be connected inversely in parallel to the switching elements. One end of the third switch  22  is connected to one end of the second capacitor  32 . The other end of the third switch  22  is connected to one end of the fourth switch  24 . The other end of the fourth switch  24  is connected to the other end of the second capacitor  32 . 
     The switch control section  50  converts the DC voltage from the DC power source  70  into AC voltage by turning ON and OFF the first switch  12 , the second switch  14 , the third switch  22 , and the fourth switch  24 , and causes the AC voltage to be output from a second connection point  26  between the third switch  22  and the fourth switch  24 . The smoothing circuit  40  is connected to the second connection point  26  and normalizes the pulse wave of the AC voltage. The smoothing circuit  40  includes a coil  42  and a third capacitor  44 . One end of the coil  42  is connected to the second connection point  26 , and the other end of the coil  42  is connected to one end of the third capacitor  44 . The one end of the third capacitor  44  is also connected to an output terminal  63 . The other end of the third capacitor  44  is connected to an output terminal  64 . The other end of the third capacitor  44  is also connected to the ground. 
     The first voltage sensor  34  measures the voltage E 1  of the DC power source  70  input to the power conditioner  100 . The second voltage sensor  35  measures the voltage E 2  of the second capacitor  32 . The third voltage sensor  36  measures the AC voltage output from the power conditioner  100 , which is the voltage of the system power source  80 , i.e. the system voltage. The switch control section  50  performs PWM control of the first switch  12 , the second switch  14 , the third switch  22 , and the fourth switch  24  based on voltage information acquired from the first voltage sensor  34 , the second voltage sensor  35 , and the third voltage sensor  36 , thereby converting the DC voltage from the DC power source  70  into AC voltage having a phase in synchronization with the phase of reference AC voltage output by the system power source  80 . 
     The following describes three Control Techniques by which the switch control section  50  performs ON/OFF control of the first switch  12 , the second switch  14 , the third switch  22 , and the fourth switch  24 . 
     &lt;Control Technique 1&gt; 
     During interval I, which is the half-period during which the reference AC voltage is positive, the switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner, and also turns the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner. After turning the first switch  12  and the second switch  14  ON and OFF in an alternating manner and turning the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner during the half-period in which the reference AC voltage is positive, the switch control section  50  turns the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner while keeping the first switch  12  OFF and the second switch  14  ON during interval II, which is the half-period during which the reference AC voltage is negative. 
     The switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner based on a first voltage command value  200 , such as shown in  FIG. 2A , that indicates the positive half waveform having a phase synchronized with the phase of the reference AC voltage. When the first switch  12  is ON and the second switch  14  is OFF, the potential of the first connection point  16  is the potential of the input terminal  61 , i.e. the voltage E 1  of the DC power source  70 . On the other hand, when the first switch  12  is OFF and the second switch  14  is ON, the potential of the first connection point  16  is the potential of the input terminal  62 , i.e. the ground potential. 
     The switch control section  50  turns the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner based on a second voltage command value  202 , such as shown in  FIG. 2B , that indicates the negative half waveform having a phase synchronized with the phase of the reference AC voltage. When the third switch  22  is ON and the fourth switch  24  is OFF, the potential of the second connection point  26  is the potential at one end of the second capacitor  32 , i.e. the potential of the first connection point  16 . On the other hand, when the third switch  22  is OFF and the fourth switch  24  is ON, the potential of the second connection point  26  is a potential obtained by subtracting the potential difference between the ends of the second capacitor  32  (the voltage E 2  of the second capacitor  32 ) from the potential of the first connection point  16 . 
     Here, the maximum value of the voltage indicated by the first voltage command value  200  is double the maximum value of the reference AC voltage. On the other hand, the minimum voltage indicated by the second voltage command value  202  is the same as the minimum value of the reference AC voltage. Accordingly, the PWM control of the first switch  12  and the second switch  14  is based on the first voltage command value  200  and the PWM control of the third switch  22  and the fourth switch  24  is based on the second voltage command value  202 , and therefore the power conditioner  100  can output AC voltage that is synchronized with the reference AC voltage, such as shown by reference numeral  210  in  FIG. 2C . 
     Here, the first voltage command value  200  used in Technique 1 can be expressed as shown below. 
     
       
         
           
             
               
                 
                   
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     Furthermore, the second voltage command value  202  used in Technique 1 can be expressed as shown below. 
     
       
         
           
             
               
                 
                   
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     Here, v 1ref  represents the first voltage command value, v 2ref  represents the second voltage command value, and V s  represents the reference AC voltage. 
     The switch control section  50  determines a timing for switching between a state in which the first switch  12  and the second switch  14  are turned ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF to a state in which the third switch  22  and the fourth switch  24  are turned ON and OFF in an alternating manner while the first switch  12  is ON and the second switch  14  is OFF, based on the voltage of the system power source measured by the third voltage sensor  36 . More specifically, by detecting the zero-cross point of the voltage measured by the third voltage sensor  36 , the switch control section  50  controls the timing for switching between interval I, during which the first switch  12  and the second switch  14  are turned ON and OFF in an alternating manner, and interval II, during which the first switch  12  is kept OFF and the second switch  14  is kept ON. Furthermore, the switch control section  50  controls the pulse width when performing PWM control by turning the first switch  12  and the second switch  14  ON and OFF in an alternating manner or turning the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner such that the magnitude of the peak voltage of the voltage E 2  of the second capacitor  32  measured by the second voltage sensor  35  is at least √2 times the magnitude of the reference AC voltage V s . 
     With Control Technique 1, the power conditioner  100  can be used for a single-phase two-wire, single-phase three-wire, three-phase three-wire, or three-phase four-wire power source. Furthermore, with Control Technique 1, there is no need to perform ON/OFF control of the first switch  12  and the second switch  14  during the half-period where the reference AC voltage is negative. Accordingly, the switching loss that occurs due to the first switch  12  and second switch  14  being turned ON and OFF during the half-period where the reference AC voltage is negative can be eliminated. 
     &lt;Control Technique 2&gt; 
     The switch control section  50  turns the first switch  12 , the second switch  14 , the third switch  22 , and the fourth switch  24  ON and OFF according to ON/OFF conditions, such as shown in  FIG. 4 , during each of the intervals I, II, III, and IV, based on the first voltage command value  200  shown in  FIG. 3A  and the second voltage command value  202  shown in  FIG. 3B . In this way, the switch control section  50  converts the DC voltage from the DC power source  70  into a reference AC voltage to be output by the power conditioner  100 , i.e. an AC voltage that is synchronized with the AC voltage output by the system power source  80 . 
     The first voltage command value  200  used in Control Technique 2 can be expressed as shown below. The switch control section  50  performs PWM control of the first switch  12  and the second switch  14  during intervals I and III based on the first voltage command value  200 . 
     
       
         
           
             
               
                 
                   
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     Furthermore, the second voltage command value  202  used in Control Technique 2 can be expressed as shown below. The switch control section  50  performs PWM control of the third switch  22  and the fourth switch  24  during intervals II and IV based on the second voltage command value  202 . 
     
       
         
           
             
               
                 
                   
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                   I 
                 
               
             
           
         
       
     
     Here, v 1ref  represents the first voltage command value, v 2ref  represents the second voltage command value, V s  represents the reference AC voltage, V in  represents the voltage E 1  of the DC power source  70  input to the power conditioner  100 , and δ 1  represents an interval with a width that is half the width of interval II. 
     During interval I, the switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF. When the third switch  22  is ON, the fourth switch  24  is OFF, the first switch  12  is ON, and the second switch  14  is OFF, the potential of the second connection point  26  is the voltage E 1  of the DC power source  70 , which is the potential of the input terminal  61 . Furthermore, when the third switch  22  is ON, the fourth switch  24  is OFF, the first switch  12  is OFF, and the second switch  14  is ON, the potential of the second connection point  26  is the ground potential GND. Accordingly, during interval I, a voltage having a repeating pulse waveform that alternates between the voltage E 1  of the DC power source  70  and the ground potential GND is output from the second connection point  26 . 
     During interval II, which follows interval I, the switch control section  50  turns the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner while the first switch  12  is ON and the second switch  14  is OFF. When the first switch  12  is ON, the second switch  14  is OFF, the third switch  22  is ON, and the fourth switch  24  is OFF, the potential of the second connection point  26  is the voltage E 1  of the DC power source  70 . When the first switch  12  is ON, the second switch  14  is OFF, the third switch  22  is OFF, and the fourth switch  24  is ON, the potential of the second connection point  26  is the difference E 1 −E 2  between the voltage E 1  of the DC power source  70  and the voltage E 2  of the second capacitor  32 . Accordingly, during interval II, a voltage having a repeating pulse waveform that alternates between the voltage E 1  of the DC power source  70  and the voltage difference E 1 −E 2  is output from the second connection point  26 . 
     After the third switch  22  and the fourth switch  24  are turned ON and OFF in an alternating manner while the first switch  12  is ON and the second switch  14  is OFF during interval II, during the following interval III, the switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF, under the same conditions as used for interval I. As a result, during interval III, a voltage having a repeating pulse waveform that alternates between the voltage E 1  of the DC power source  70  and the ground voltage GND is output from the second connection point  26 . 
     After the first switch  12  and the second switch  14  are turned ON and OFF while the third switch  22  is ON and the fourth switch  24  is OFF during interval III, during the following interval IV, the switch control section  50  turns the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner while the first switch  12  is OFF and the second switch  14  is ON. When the first switch  12  is OFF, the second switch  14  is ON, the third switch  22  is ON, and the fourth switch  24  is OFF, the potential of the second connection point  26  is the ground potential GND. When the first switch  12  is OFF, the second switch  14  is ON, the third switch  22  is OFF, and the fourth switch  24  is ON, the potential of the second connection point  26  is the potential −E 2  at the other end of the second capacitor  32 . Accordingly, during interval IV, a voltage having a repeating pulse waveform that alternates between the ground potential GND and the voltage potential −E 2  is output from the second connection point  26 . 
     In this way, the switch control section  50  performs PWM control by controlling the intervals during which each switch is ON and OFF, based on the respective switching conditions of the intervals, and converts the DC voltage from the DC power source  70  into AC voltage having a phase that is synchronized with the phase of the reference AC voltage. 
     The switch control section  50  determines the timing for switching between a state in which the first switch  12  and the second switch  14  are turned ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF to a state in which the third switch  22  and the fourth switch  24  are turned ON and OFF in an alternating manner while the first switch  12  is ON and the second switch  14  is OFF, based on the voltage E 1  of the DC power source  70  and the voltage E 2  of the second capacitor  32 . In other words, the switch control section  50  determines the timing for switching from interval I to interval II based on the voltage E 1  of the DC power source  70  and the voltage E 2  of the second capacitor  32 . 
     More specifically, the switch control section  50  determines interval I to be the period from the zero-cross timing at which the reference AC voltage switches from negative to positive to the timing at which the reference AC voltage is E 1 −E 2 . In the same manner, the switch control section  50  determines the timing for switching from interval II to interval III based on the voltage E 1  of the DC power source  70  and the voltage E 2  of the second capacitor  32 . More specifically, after switching to interval II, the switch control section  50  determines interval II to be a period lasting until the reference AC voltage again becomes E 1 −E 2 . The switch control section  50  then determines interval III to be a period from the timing at which the reference AC voltage again becomes E 1 −E 2  to the zero-cross timing at which the reference AC voltage switches from positive to negative. Furthermore, the switch control section  50  determines interval IV to be a period from the zero-cross timing at which the reference AC voltage switches from positive to negative to the zero-cross timing at which the reference AC voltage switches from negative to positive. 
     Here, if the DC power source  70  is a solar cell, the power conditioner  100  alters the input voltage from the DC power source  70  in order to output the maximum power from the solar cell. Accordingly, the voltage E 1  of the DC power source  70  fluctuates. Therefore, the switch control section  50  may acquire voltage information indicating the voltage E 1  of the DC power source  70  from the first voltage sensor  34 , for example. Furthermore, the switch control section  50  may acquire the voltage E 2  of the second capacitor  32  stored in advance in a memory or the like provided to the power conditioner  100 . The switch control section  50  calculates the difference E 1 −E 2  between the voltage E 1  and the voltage E 2 . The switch control section  50  references the predetermined voltage command value indicating the waveform of the reference AC voltage, calculates the time from the zero-cross timing at which the reference AC voltage switches from negative to positive to the timing at which the reference AC voltage becomes E 1 −E 2 , and sets this time as interval I. The switch control section  50  calculates the time from when the reference AC voltage becomes E 1 −E 2  to the timing at which the reference AC voltage again becomes E 1 −E 2 , and sets this time as interval II. 
     If the voltage of the second capacitor  32  is a fixed value, each interval indicating the timing at which switching conditions are changed is determined using the voltage E 1  of the DC power source  70  as a parameter. Accordingly, each interval may be calculated in advance for each magnitude of the voltage E 1  and stored in a memory. In this case, the switch control section  50  references the memory and determines the time associated with the magnitude of the voltage E 1  of the DC power source  70  measured by the first voltage sensor  34  to be the interval indicating the timing at which the switching conditions are to be changed. 
     On the other hand, if the input voltage from the DC power source  70  fluctuates, the voltage of the second capacitor  32  also fluctuates. Due to the voltage fluctuation of the second capacitor  32 , there is a possibility that the output from the power conditioner  100  will become unstable. Therefore, in order to stabilize the output from the power conditioner  100 , the voltage of the second capacitor  32  is preferably made constant. In order to achieve a constant voltage for the second capacitor  32 , the average value P 2  of the power output from the second connection point  26  may be controlled to be zero, for example. Here, the effective value V 2f  of the fundamental frequency component of the output voltage from the second connection point  26  can be expressed as shown below. 
     
       
         
           
             
               
                 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           V 
                           
                             2 
                             ⁢ 
                             f 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             1 
                             
                               2 
                             
                           
                           ⁢ 
                           
                             1 
                             π 
                           
                           ⁢ 
                           
                             
                               ∫ 
                               0 
                               
                                 2 
                                 ⁢ 
                                 π 
                               
                             
                             ⁢ 
                             
                               
                                 v 
                                 
                                   2 
                                   ⁢ 
                                   ref 
                                 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                               ⁢ 
                               
                                 ⅆ 
                                 θ 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               2 
                             
                             π 
                           
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   - 
                                   
                                     V 
                                     in 
                                   
                                 
                                 ⁢ 
                                 sin 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   δ 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   2 
                                 
                                 ⁢ 
                                 
                                   
                                     V 
                                     S 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           sin 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           2 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             δ 
                                             1 
                                           
                                         
                                         4 
                                       
                                       + 
                                       
                                         
                                           δ 
                                           1 
                                         
                                         2 
                                       
                                       + 
                                       
                                         π 
                                         4 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     By calculating a value for δ 1  that results in the average value P 2 =V 2f I=0, the average value P 2  of the power output from the second connection point  26  can be controlled to be zero, thereby stabilizing the output from the power conditioner  100 . Here, the δ 1  that results in the average value P 2 =V 2f I=0 may be calculated using a third-order approximation, for example, and does not need to be calculated directly from the above Expression. 
     With Control Technique 2, the power conditioner  100  can be used for a single-phase two-wire, single-phase three-wire, three-phase three-wire, or three-phase four-wire power source. Furthermore, with Control Technique 2, when the third switch  22  and the fourth switch  24  are being turned ON and OFF in an alternating manner during interval II, the output voltage has a pulse waveform that alternates between the voltage E 1  of the DC power source  70  and the voltage difference E 1 −E 2 . Accordingly, the switching loss in the third switch  22  and fourth switch  24  can be decreased by a greater amount than in a case where the output voltage has a pulse waveform that alternates between the voltage E 1  of the DC power source  70  and the ground voltage GND. Furthermore, ripple current is input to the second capacitor  32  only during intervals II and IV. Accordingly, the generation of heat by the second capacitor  32  due to the input of ripple current can be restricted, and therefore deterioration of the second capacitor  32  can be restricted. 
     &lt;Control Technique 3&gt; 
     With Control Technique 3, the power conditioner  100  can be used for a three-phase AC power source having a three-phase three-wire or three-phase four-wire configuration.  FIG. 5  shows a circuit configuration of the system when applied to a three-phase four-wire power source. The system includes power conditioners  100   u ,  100   v , and  100   w . The power conditioners  100   u ,  100   v , and  100   w  are connected to a DC power source  70  and three-phase AC power sources  80   u ,  80   v , and  80   w . The power conditioner  100  shown in  FIG. 1  can be used as each of the power conditioners  100   u ,  100   v , and  100   w.    
     If a three-phase three-wire or three-phase four-wire power source is used, the voltage usage efficiency of the DC power source  70  can be improved by using a third-order harmonic. Therefore, in Control Technique 3, the switch control section  50  turns the first switch  12 , the second switch  14 , the third switch  22 , and the fourth switch  24  ON and OFF such that the phase output voltages vxu, vxv, and vxw output respectively from the power conditioners  100   u ,  100   v , and  100   w  have voltage waveforms such as shown in  FIG. 6 . Each voltage waveform shown in  FIG. 6  represents a voltage waveform obtained by adding an offset voltage v f  to a voltage waveform obtained by subtracting the maximum phase voltage from the three-phase power source voltage in a three-phase four-wire configuration. 
     The switch control section  50  converts the DC voltage from the DC power source  70  into AC voltage by turning the first switch  12 , the second switch  14 , the third switch  22 , and the fourth switch  24  ON and OFF according to ON/OFF conditions, such as shown in  FIG. 8 , during each of the intervals I, II, III, IV, V, VI, and VII, based on the first voltage command value  200  shown in  FIG. 7A  and the second voltage command value  202  shown in  FIG. 7B . As another example, the switch control section  50  converts the DC voltage from the DC power source  70  into AC voltage by turning the first switch  12 , the second switch  14 , the third switch  22 , and the fourth switch  24  ON and OFF according to ON/OFF conditions, such as shown in  FIG. 10 , during each of the intervals I, II, III, IV, V, VI, and VII, based on the first voltage command value  200  shown in  FIG. 9A  and the second voltage command value  202  shown in  FIG. 9B .  FIGS. 7A and 7B  show the voltage command value when δ 1  is less than or equal to π/3 (when interval IV is no greater than 2π/3), and  FIGS. 9A and 9B  show the voltage command value when δ 1  is greater than π/3 (when interval IV is less than 2π/3). 
     With Control Technique 3, the first voltage command value  200  when δ 1  is less than or equal to π/3 (when interval IV is no greater than 2π/3) can be expressed in each of the intervals I to VII as shown below. The switch control section  50  performs PWM control of the first switch  12  and the second switch  14  in intervals II, III, V, and VI based on the first voltage command value  200 . 
     
       
         
           
             
               
                 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     u_v 
                     
                       1 
                       ⁢ 
                       ref 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 π 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 φ 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     + 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 φ 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 
                                   π 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             v 
                             f 
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 
                                   π 
                                   3 
                                 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             V 
                             in 
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 δ 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             v 
                             f 
                           
                         
                         
                           
                             ( 
                             
                               
                                 δ 
                                 1 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 π 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     - 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 π 
                                 3 
                               
                               &lt; 
                               θ 
                               &lt; 
                               φ 
                             
                             ) 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               φ 
                               &lt; 
                               θ 
                               &lt; 
                               π 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Furthermore, with Control Technique 3, the second voltage command value  202  when δ 1  is less than or equal to π/3 (when interval IV is no greater than 2π/3) can be expressed in each of the intervals I to VII as shown below. The switch control section  50  performs PWM control of the third switch  22  and the fourth switch  24  in intervals I and VII based on the second voltage command value  202 . 
     
       
         
           
             
               
                 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     u_v 
                     
                       2 
                       ⁢ 
                       ref 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     + 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 π 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 φ 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 φ 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 
                                   π 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 
                                   π 
                                   3 
                                 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               - 
                               
                                 V 
                                 in 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 δ 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 δ 
                                 1 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 π 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 π 
                                 3 
                               
                               &lt; 
                               θ 
                               &lt; 
                               φ 
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     - 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               φ 
                               &lt; 
                               θ 
                               &lt; 
                               π 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Here, v 1ref  represents the first voltage command value, v 2ref  represents the second voltage command value, V s  represents the reference AC voltage, V in  represents the voltage E 1  of the DC power source  70  input to the power conditioner  100 , and δ 1  represents an interval with a width that is half the width of interval II. Furthermore, v f  represents the offset voltage, φ represents the θ that results in the u-phase output vxu equaling 0, and φ can be calculated using the following Expression. 
     
       
         
           
             
               
                 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   φ 
                   = 
                   
                     
                       
                         sin 
                         
                           - 
                           1 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             v 
                             f 
                           
                           
                             
                               6 
                             
                             ⁢ 
                             
                               V 
                               S 
                             
                           
                         
                         ) 
                       
                     
                     + 
                     
                       π 
                       3 
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     When δ 1  is less than or equal to π/3, during interval I, the switch control section  50  turns the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner while the first switch  12  is OFF and the second switch  14  is ON. After the third switch  22  and the fourth switch  24  are turned ON and OFF in an alternating manner while the first switch  12  is OFF and the second switch  14  is ON during Interval I, during the following intervals II and III, the switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF. 
     After the first switch  12  and the second switch  14  are turned ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF, during interval IV that follows interval III, the switch control section  50  turns ON the first switch  12 , turns OFF the second switch  14 , turns OFF the third switch  22 , and turns ON the fourth switch  24 , and keeps the switches in this state. After the first switch  12  is turned ON, the second switch  14  is turned OFF, the third switch  22  is turned OFF, and the fourth switch  24  is turned ON, during intervals V and VI that follow interval IV, the switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF. 
     After the first switch  12  and the second switch  14  are turned ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF, during interval VII that follows interval VI, the switch control section  50  turns the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner while the first switch  12  is OFF and the second switch  14  is ON. 
     With Control Technique 3, the first voltage command value  200  when δ 1  is greater than π/3 (when interval IV is greater than 2π/3) can be expressed as shown below for each of the intervals I to VII. The switch control section  50  performs PWM control of the first switch  12  and the second switch  14  during intervals II, III, V, and VI based on the first voltage command value  200 . 
     
       
         
           
             
               
                 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     u_v 
                     
                       1 
                       ⁢ 
                       ref 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 π 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 φ 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     + 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 φ 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     + 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               V 
                               in 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 
                                   π 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             V 
                             in 
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 
                                   π 
                                   3 
                                 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 π 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     - 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               V 
                               in 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 π 
                                 3 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 δ 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     - 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 δ 
                                 1 
                               
                               &lt; 
                               θ 
                               &lt; 
                               φ 
                             
                             ) 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               φ 
                               &lt; 
                               θ 
                               &lt; 
                               π 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     Furthermore, with Control Technique 3, the second voltage command value  202  when δ 1  is greater than π/3 (when interval IV is greater than 2π/3) can be expressed as shown below for each of the intervals I to VII. The switch control section  50  performs PWM control of the third switch  22  and the fourth switch  24  during intervals I and VII based on the second voltage command value  202 . 
     
       
         
           
             
               
                 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     u_v 
                     
                       2 
                       ⁢ 
                       ref 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     + 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 π 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 φ 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 φ 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               - 
                               
                                 V 
                                 in 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 - 
                                 
                                   π 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               - 
                               
                                 V 
                                 in 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 - 
                                 
                                   π 
                                   3 
                                 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 π 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               - 
                               
                                 V 
                                 in 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               
                                 π 
                                 3 
                               
                               &lt; 
                               θ 
                               &lt; 
                               
                                 δ 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             ( 
                             
                               
                                 δ 
                                 1 
                               
                               &lt; 
                               θ 
                               &lt; 
                               φ 
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               
                                 V 
                                 S 
                               
                               ⁢ 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     θ 
                                     - 
                                     
                                       
                                         2 
                                         3 
                                       
                                       ⁢ 
                                       π 
                                     
                                   
                                   ) 
                                 
                               
                             
                             + 
                             
                               v 
                               f 
                             
                           
                         
                         
                           
                             ( 
                             
                               φ 
                               &lt; 
                               θ 
                               &lt; 
                               π 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     When δ 1  is greater than π/3, during interval I, the switch control section  50  turns the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner while the first switch  12  is OFF and the second switch  14  is ON. After the third switch  22  and the fourth switch  24  are turned ON and OFF in an alternating manner while the first switch  12  is OFF and the second switch  14  is ON during Interval I, during the following interval II, the switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF. 
     After the first switch  12  and the second switch  14  are turned ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF, during interval III that follows interval II, the switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner, while the third switch  22  is OFF and the fourth switch  24  is ON. After the first switch  12  and the second switch  14  are turned ON and OFF in an alternating manner while the third switch  22  is OFF and the fourth switch  24  is ON, during interval IV that follows interval III, the switch control section  50  turns ON the first switch  12 , turns OFF the second switch  14 , turns OFF the third switch  22 , and turns ON the fourth switch  24 , and keeps the switches in this state. 
     After the first switch  12  is turned ON, the second switch  14  is turned OFF, the third switch  22  is turned OFF, and the fourth switch  24  is turned ON, during interval V that follows interval IV, the switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner while the third switch  22  is OFF and the fourth switch  24  is ON. After the first switch  12  and the second switch  14  are turned ON and OFF in an alternating manner while the third switch  22  is OFF and the fourth switch  24  is ON, during interval VI that follows interval V, the switch control section  50  turns the first switch  12  and the second switch  14  ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF. 
     After the first switch  12  and the second switch  14  are turned ON and OFF in an alternating manner while the third switch  22  is ON and the fourth switch  24  is OFF, during interval VII that follows interval VI, the switch control section  50  turns the third switch  22  and the fourth switch  24  ON and OFF in an alternating manner while the first switch  12  is OFF and the second switch  14  is ON. 
     Control Technique 3 differs from Control Technique 2 in that the AC voltage output from the smoothing circuit  40  is obtained by shifting the reference AC voltage in a positive direction by a predetermined potential (offset voltage v f ) from the reference potential of the reference AC voltage with which the AC voltage is to be phase-synchronized. With Control Technique 3, the sum of the voltage E 1  and the voltage E 2  need only be greater than or equal to the reference AC voltage Vp-p, which is the AC voltage of the system power source  80 . Accordingly, compared to Control Technique 2, the voltage E 1  and the voltage E 2  can be lower. Therefore, the switching loss can be further decreased. 
     In the same manner as Control Technique 2, in order to stabilize the output from the power conditioners  100   u ,  100   v , and  100   w , the voltage of each second capacitor  32  is preferably made constant. In order to achieve a constant voltage for a second capacitor  32 , the average value P 2  of the power output from the second connection point  26  may be controlled to be zero, for example. In Control Technique 3, the effective value V 2f  of the fundamental frequency component of the output voltage from each second connection point  26  can be expressed as shown below. 
     
       
         
           
             
               
                 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           V 
                           
                             2 
                             ⁢ 
                             f 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             1 
                             
                               2 
                             
                           
                           ⁢ 
                           
                             1 
                             π 
                           
                           ⁢ 
                           
                             
                               ∫ 
                               0 
                               
                                 2 
                                 ⁢ 
                                 π 
                               
                             
                             ⁢ 
                             
                               
                                 v 
                                 
                                   2 
                                   ⁢ 
                                   ref 
                                 
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                               ⁢ 
                               
                                 ⅆ 
                                 θ 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               2 
                             
                             π 
                           
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             - 
                                             
                                               V 
                                               in 
                                             
                                           
                                           + 
                                           
                                             v 
                                             f 
                                           
                                         
                                         ) 
                                       
                                       ⁢ 
                                       sin 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         δ 
                                         1 
                                       
                                     
                                     + 
                                     
                                       
                                         
                                           3 
                                           ⁢ 
                                           
                                             2 
                                           
                                           ⁢ 
                                           
                                             v 
                                             S 
                                           
                                         
                                         4 
                                       
                                       ⁢ 
                                       π 
                                     
                                     + 
                                     
                                       
                                         
                                           6 
                                         
                                         ⁢ 
                                         
                                           V 
                                           S 
                                         
                                       
                                       8 
                                     
                                     - 
                                     
                                       
                                         
                                           
                                             2 
                                           
                                           ⁢ 
                                           
                                             V 
                                             S 
                                           
                                         
                                         4 
                                       
                                       ⁢ 
                                       sin 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                       ⁢ 
                                       φ 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             3 
                                             ⁢ 
                                             
                                               2 
                                             
                                             ⁢ 
                                             
                                               V 
                                               S 
                                             
                                           
                                           4 
                                         
                                         ⁢ 
                                         φ 
                                       
                                       + 
                                       
                                         
                                           
                                             
                                               2 
                                             
                                             ⁢ 
                                             
                                               V 
                                               S 
                                             
                                           
                                           4 
                                         
                                         ⁢ 
                                         
                                           sin 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 2 
                                                 ⁢ 
                                                 φ 
                                               
                                               - 
                                               
                                                 
                                                   2 
                                                   3 
                                                 
                                                 ⁢ 
                                                 π 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       + 
                                       
                                         
                                           v 
                                           f 
                                         
                                         ⁢ 
                                         sin 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         φ 
                                       
                                     
                                     ⁢ 
                                     
                                         
                                     
                                   
                                 
                               
                             
                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     By calculating a value for δ 1  that results in the average value P 2 =V 2f I=0, the average value P 2  of the power output from the second connection point  26  can be controlled to be zero, thereby stabilizing the output from the power conditioner  100 . By expanding δ 1  in the above Expression, the following Expression can be formed. 
     
       
         
           
             
               
                 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ⁢ 
                   
                       
                   
                 
               
             
             
               
                 
                   
                     δ 
                     1 
                   
                   = 
                   
                     
                       sin 
                       
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     3 
                                     ⁢ 
                                     
                                       2 
                                     
                                     ⁢ 
                                     
                                       V 
                                       S 
                                     
                                   
                                   4 
                                 
                                 ⁢ 
                                 π 
                               
                               + 
                               
                                 
                                   
                                     6 
                                   
                                   ⁢ 
                                   
                                     V 
                                     S 
                                   
                                 
                                 8 
                               
                               - 
                               
                                 
                                   
                                     
                                       2 
                                     
                                     ⁢ 
                                     
                                       V 
                                       S 
                                     
                                   
                                   4 
                                 
                                 ⁢ 
                                 sin 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                                 ⁢ 
                                 φ 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     3 
                                     ⁢ 
                                     
                                       2 
                                     
                                     ⁢ 
                                     
                                       V 
                                       S 
                                     
                                   
                                   4 
                                 
                                 ⁢ 
                                 φ 
                               
                               + 
                               
                                 
                                   
                                     
                                       2 
                                     
                                     ⁢ 
                                     
                                       V 
                                       S 
                                     
                                   
                                   4 
                                 
                                 ⁢ 
                                 
                                   sin 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         φ 
                                       
                                       - 
                                       
                                         
                                           2 
                                           3 
                                         
                                         ⁢ 
                                         π 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   v 
                                   f 
                                 
                                 ⁢ 
                                 sin 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 φ 
                               
                             
                           
                         
                       
                       
                         
                           V 
                           in 
                         
                         - 
                         
                           v 
                           f 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     While the embodiments of the present invention have been described, the technical scope of the invention is not limited to the above described embodiments. It is apparent to persons skilled in the art that various alterations and improvements can be added to the above-described embodiments. It is also apparent from the scope of the claims that the embodiments added with such alterations or improvements can be included in the technical scope of the invention. 
     The operations, procedures, steps, and stages of each process performed by an apparatus, system, program, and method shown in the claims, embodiments, or diagrams can be performed in any order as long as the order is not indicated by “prior to,” “before,” or the like and as long as the output from a previous process is not used in a later process. Even if the process flow is described using phrases such as “first” or “next” in the claims, embodiments, or diagrams, it does not necessarily mean that the process must be performed in this order.