Patent Publication Number: US-2023147142-A1

Title: Power Conversion System

Description:
TECHNICAL FIELD 
     The present disclosure relates to a power conversion system. 
     BACKGROUND ART 
     A modular multilevel converter (hereinafter, also referred to as “MMC converter”) in which a plurality of unit converters are cascaded can easily deal with a higher voltage by increasing the number of unit converters. “Unit converter” is also referred to as “submodule” or “converter cell”. The MMC converter is widely applied to a power transmission and distribution system as a large-capacity static VAR compensator or a power conversion device for high-voltage DC power transmission. 
     In Japanese Patent Laying-Open No. 2012-228025 (PTL 1), suppressing fluctuations in DC capacitor voltage caused by a cycle of a fundamental frequency of a power-supply-side or load-side voltage is under study. 
     CITATION LIST 
     Patent Literature 
     PTL 1: Japanese Patent Laying-Open No. 2012-228025 
     SUMMARY OF INVENTION 
     Technical Problem 
     A power conversion system including MMC-type power converters is used, for example, as a system for controlling electric power of a DC power transmission system. Typically, electric power is exchanged between two AC systems through a DC circuit, and these AC systems may be different in system conditions (e.g., a fundamental frequency and a power request). In this case, a power converter connected to one AC system and a power converter connected to the other AC system are different in required specifications. However, from the perspective of maintainability, it is preferable to use a submodule composed of the same components (e.g., a DC capacitor) in each power converter. 
     For example, when these AC systems have different fundamental frequencies, voltage fluctuations of a first DC capacitor on the AC system side having a lower fundamental frequency are greater than voltage fluctuations of a second DC capacitor on the AC system side having a higher fundamental frequency. Therefore, a capacitance required to suppress the voltage fluctuations of the second DC capacitor is smaller than a capacitance required to suppress the voltage fluctuations of the first DC capacitor. Thus, when the same DC capacitor is used, it is necessary to adopt the capacitance required to suppress the voltage fluctuations of the first DC capacitor. In this case, the voltage fluctuations of the second DC capacitor are suppressed more greatly than the required specifications, and thus, a difference (i.e., margin) between a maximum voltage and a withstand voltage becomes large, which causes waste. PTL 1 neither teaches nor suggests a solution to such a problem. 
     An object in an aspect of the present disclosure is to provide a power conversion system capable of reducing a size of the entire system while ensuring maintainability of a plurality of power converters connected to a plurality of AC systems having different system conditions, respectively. 
     Solution To Problem 
     A power conversion system according to an embodiment includes: a first power converter to perform power conversion between a first AC system and a DC circuit; and a second power converter to perform power conversion between a second AC system and the DC circuit. Each of the first power converter and the second power converter includes a plurality of submodules connected in series. Each of the plurality of submodules includes a plurality of switching elements and a capacitor. A first fundamental frequency of the first AC system is greater than a second fundamental frequency of the second AC system. A first average voltage value of a capacitor in a first submodule included in the first power converter is larger than a second average voltage value of a capacitor in a second submodule included in the second power converter. 
     A power conversion system according to another embodiment includes: a first power converter to perform power conversion between a first AC system and a DC circuit; and a second power converter to perform power conversion between a second AC system and the DC circuit. Each of the first power converter and the second power converter includes a plurality of submodules connected in series. Each of the plurality of submodules includes a plurality of switching elements and a capacitor. A current effective value of a capacitor in a first submodule included in the first power converter based on a power factor and an apparent power requested from the first AC system is smaller than a current effective value of a capacitor in a second submodule included in the second power converter based on a power factor and an apparent power requested from the second AC system. A first average voltage value of the capacitor in the first submodule is larger than a second average voltage value of the capacitor in the second submodule. 
     ADVANTAGEOUS EFFECTS OF INVENTION 
     According to the present disclosure, the power conversion system is capable of reducing a size of the entire system while ensuring maintainability of a plurality of power converters connected to a plurality of AC systems having different system conditions, respectively. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a schematic configuration diagram of a power conversion system according to the present embodiment. 
         FIG.  2    is a schematic configuration diagram of a power converter. 
         FIG.  3    is a circuit diagram showing an example of a submodule. 
         FIG.  4    is a diagram for illustrating voltage fluctuations of capacitors. 
         FIG.  5    shows changes in capacitor voltages according to the present embodiment. 
         FIG.  6    shows a change in capacitor voltage before and after a fault occurs in an AC system. 
         FIG.  7    is a diagram for illustrating a relationship between a current flowing to the positive electrode side and a current flowing to the negative electrode side in the submodule. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiments will be described hereinafter with reference to the drawings. In the following description, the same components are denoted by the same reference characters. Their names and functions are also the same. Therefore, detailed description about them will not be repeated. 
     First Embodiment 
     &lt;Overall Configuration of System&gt; 
       FIG.  1    is a schematic configuration diagram of a power conversion system  100  according to a first embodiment. Referring to  FIG.  1   , power conversion system  100  includes power conversion devices  10 _ 1  and  10 _ 2  (hereinafter, also collectively referred to as “power conversion device  10 ”), AC systems  12 _ 1  and  12 _ 2  (hereinafter, also collectively referred to as “AC system  12 ”), transformers  13 _ 1  and  13 _ 2  (hereinafter, also collectively referred to as “transformer  13 ”), and a DC circuit  14 . A configuration in which two systems each including AC system  12 , transformer  13  and power conversion device  10  are connected to common DC circuit  14  will be described below. However, three or more systems may be connected to DC circuit  14 . 
     In power conversion system  100 , electric power is received and transmitted between AC system  12 _ 1  and AC system  12 _ 2  through DC circuit  14 . AC system  12 _ 1  and AC system  12 _ 2  are three-phase AC systems having different system conditions. Specifically, a fundamental frequency F1 of AC system  12 _ 1  is higher than a fundamental frequency F2 of AC system  12 _ 2 , and fundamental frequencies F1 and F2 are, for example, 60 Hz and 50 Hz, respectively. DC circuit  14  is a DC line or a DC bus. 
     Power conversion device  10 _ 1  includes a power converter  2 _ 1  to perform power conversion between AC system  12 _ 1  and DC circuit  14 , and a controller  3 _ 1 . Power conversion device  10 _ 2  includes a power converter  2 _ 2  to perform power conversion between AC system  12 _ 2  and DC circuit  14 , and a controller  3 _ 2 . Each of power converters  2 _ 1  and  2 _ 2  is implemented by a power converter of MMC conversion type. Controller  3 _ 1  controls the operation of power converter  2 _ 1 . Controller  3 _ 2  controls the operation of power converter  2 _ 2 . In the following description, power converters  2 _ 1  and  2 _ 2  will be also collectively referred to as “power converter  2 ” and controllers  3 _ 1  and  3 _ 2  will be also collectively referred to as “controller  3 ”. 
     Transformer  13 _ 1  is connected between AC system  12 _ 1  and power converter  2 _ 1 . Transformer  13 _ 2  is connected between AC system  12 _ 2  and power converter  2 _ 2 . 
     When electric power is transmitted from AC system  12 _ 1  to AC system  12 _ 2 , power converter  2 _ 1  operates as a rectifier (REC) and power converter  2 _ 2  operates as an inverter (INV). Specifically, AC power is converted into DC power by power converter  2 _ 1 , and the converted DC power is DC-transmitted through DC circuit  14 . The DC power is converted into AC power by power converter  2 _ 2  at a power reception end, and the converted AC power is supplied to AC system  12 _ 2  through transformer  13 _ 2 . When power converter  2 _ 1  operates as an inverter and power converter  2 _ 2  operates as a rectifier, the conversion operation opposite to the above-described conversion operation is performed. 
     &lt;Configuration of Power Conversion Device&gt; 
       FIG.  2    is a schematic configuration diagram of power converter  2 . Referring to  FIG.  2   , power converter  2  is implemented by an MMC converter including a plurality of submodules (corresponding to “SM” in  FIG.  2   )  7  connected in series to each other. 
     Power converter  2  includes a plurality of leg circuits  4   u,    4   v  and  4   w  (hereinafter, denoted as “leg circuit  4 ” when leg circuits  4   u,    4   v  and  4   w  are collectively mentioned or when any one of leg circuits  4   u,    4   v  and  4   w  is mentioned) connected in parallel with each other between a positive electrode DC terminal (i.e., higher-potential-side DC terminal) Np and a negative electrode DC terminal (i.e., lower-potential-side DC terminal) Nn. 
     Leg circuit  4  is provided for each of a plurality of phases that form an alternating current. Leg circuit  4  is connected between AC system  12  and DC circuit  14 , to perform power conversion therebetween. In power converter  2 , three leg circuits  4   u,    4   v  and  4   w  are provided to correspond to a U phase, a V phase and a W phase, respectively. 
     AC input terminals Nu, Nv and Nw provided in leg circuits  4   u,    4   v  and  4   w , respectively, are connected to AC system  12  through transformer  13 . For ease of illustration,  FIG.  2    does not show the connection between AC input terminals Nv and Nw and transformer  13 . Positive electrode DC terminal Np and negative electrode DC terminal Nn commonly connected to each leg circuit  4  are connected to DC circuit  14 . 
     Leg circuit  4   u  includes an upper arm  5  from positive electrode DC terminal Np to AC input terminal Nu, and a lower arm  6  from negative electrode DC terminal Nn to AC input terminal Nu. AC input terminal Nu, which is a connection point of upper arm  5  and lower arm  6 , is connected to transformer  13 . Since leg circuits  4   v  and  4   w  are configured similarly, leg circuit  4   u  will be representatively described below. 
     Upper arm  5  includes a plurality of submodules  7  that are cascaded, and a reactor  8 A. The plurality of submodules  7  and reactor  8 A are connected in series to each other. Lower arm  6  includes a plurality of submodules  7  that are cascaded, and a reactor  8 B. The plurality of submodules  7  and reactor  8 B are connected in series to each other. Instead of the reactor, each of upper arm  5  and lower arm  6  may be connected to AC system  12  through a three-winding transformer having an impedance equivalent to that of the reactor. 
     Power conversion system  100  is provided with detectors that measure an amount of electricity (e.g., a current, a voltage and the like) used for control. Examples of the detectors include an AC voltage detector  18 , an AC current detector  16 , DC voltage detectors  11 A and  11 B, arm current detectors  9 A and  9 B provided in each leg circuit  4 , and the like. Signals detected by these detectors are input to controller  3 . 
     Based on these detected signals, controller  3  outputs operation commands for controlling operation states of submodules  7  in power converter  2 . The operation commands are generated to correspond to the arms (e.g., the U-phase upper arm, the U-phase lower arm, the V-phase upper arm, the V-phase lower arm, the W-phase upper arm, and the W-phase lower arm). In addition, controller  3  receives various types of information from each submodule  7 . The various types of information are internal information of submodule  7 , and include a voltage value of a capacitor in submodule  7 , state information indicating a state of submodule  7 , and the like. The state information includes information indicating whether submodule  7  is in a normal operation state in which submodule  7  is operating normally, or in a stop state, information indicating the presence or absence of a failure of submodule  7 , and the like. 
     Controller  3  typically includes, as hardware configurations, an auxiliary transformer, an Analog to Digital (AD) conversion unit, a processor and the like. The processor includes a central processing unit (CPU), a random access memory (RAM) and a read only memory (ROM). The AD conversion unit includes an analog filter, a sample hold circuit, a multiplexer and the like. Controller  3  may be implemented by, for example, a digitally-protected controller. 
     For ease of illustration,  FIG.  2    collectively shows a part of the signal lines for the signals input from the detectors to controller  3  and the signal lines for the signals input and output between controller  3  and submodules  7 . Actually, however, the signal lines are provided for each detector and for each submodule  7 . The signal lines for transmission and the signal lines for reception may be separately provided between submodules  7  and controller  3 . Each signal line is implemented by, for example, an optical fiber. 
     AC voltage detector  18  detects a U-phase AC voltage Vacu, a V-phase AC voltage Vacv, and a W-phase AC voltage Vacw of AC system  12 . AC current detector  16  detects a U-phase AC current lacu, a V-phase AC current lacy, and a W-phase AC current Iacw of AC system  12 . DC voltage detector  11 A detects a DC voltage Vdcp of positive electrode DC terminal Np connected to DC circuit  14 . DC voltage detector  11 B detects a DC voltage Vdcn of negative electrode DC terminal Nn connected to DC circuit  14 . A difference between DC voltage Vdcp and DC voltage Vdcn is referred to as “DC voltage Vdc”. 
     Arm current detectors  9 A and  9 B provided in leg circuit  4   u  for the U phase detect an arm current Ipu flowing through upper arm  5  and an arm current Inu flowing through lower arm  6 , respectively. Similarly, arm current detectors  9 A and  9 B provided in leg circuit  4   v  for the V phase detect an arm current Ipv and an arm current Inv, respectively. Arm current detectors  9 A and  9 B provided in leg circuit  4   w  for the W phase detect an arm current Ipw and an arm current Inw, respectively. In the following description, arm currents Ipu, Inu, Ipv, Inv, Ipw, and Inw are collectively referred to as “arm current Iarm”. 
     &lt;Configuration of Submodule&gt; 
       FIG.  3    is a circuit diagram showing an example of the submodule. Submodule  7  shown in  FIG.  3 ( a )  has a circuit configuration called “half bridge configuration”. This submodule  7  includes a series body formed by connecting two switching elements  31   p  and  31   n  in series, a capacitor  32  serving as an energy accumulator, a voltage detector  33 , and a bypass switch  34 . The series body and capacitor  32  are connected in parallel. Voltage detector  33  detects a capacitor voltage Vc, which is a voltage across capacitor  32 . 
     Submodule  7  shown in  FIG.  3 ( b )  has a circuit configuration called “full bridge configuration”. This submodule  7  includes a first series body formed by connecting two switching elements  31   p   1  and  31   n   1  in series, a second series body formed by connecting two switching elements  31   p   2  and  31   n   2  in series, and capacitor  32 , and voltage detector  33 . The first series body, the second series body and capacitor  32  are connected in parallel. Voltage detector  33  detects capacitor voltage Vc. 
     Each of two switching elements  31   p  and  31   n  in  FIG.  3 ( a )  and four switching elements  31   p   1 ,  31   n   1 ,  31   p   2 , and  31   n   2  in  FIG.  3 ( b )  is, for example, formed by connecting a freewheeling diode (FWD) in antiparallel with a semiconductor switching element of self arc-extinguishing type, such as an insulated gate bipolar transistor (IGBT), a gate commutated turn-off (GCT) thyristor and a metal oxide semiconductor field-effect transistor (MOSFET). In addition, in  FIGS.  3 ( a ) and  3 ( b ) , a capacitor such as a film capacitor is mainly used as capacitor  32 . 
     In the following description, switching elements  31   p,    31   n,    31   p   1 ,  31   n   1 ,  31   p   2 , and  31   n   2  will be also collectively referred to as “switching element  31 ”. In addition, on and off of the semiconductor switching element in switching element  31  will be simply denoted as “on and off of switching element  31 ”. 
     Referring to  FIG.  3 ( a ) , opposing terminals of switching element  31   n  are referred to as “input/output terminals P 1  and P 2 ”. By the switching operation of switching elements  31   p  and  31   n,  the voltage across capacitor  32  and a zero voltage are output. 
     For example, when switching element  31   p  is turned on and switching element  31   n  is turned off, the voltage across capacitor  32  is output. When switching element  31   p  is turned off and switching element  31   n  is turned on, the zero voltage is output. Although the opposing terminals of switching element  31   n  are referred to as “input/output terminals P 1  and P 2 ” in  FIG.  3 ( a ) , opposing terminals of switching element  31   p  may be referred to as “input/output terminals P 1  and P 2 ”, and in this case, the operation is reversed. 
     Bypass switch  34  is connected between input/output terminals P 1  and P 2 . In  FIG.  3 ( a ) , bypass switch  34  is connected in parallel with switching element  31   n . However, when the opposing terminals of switching element  31   p  are referred to as “input/output terminals P 1  and P 2 ”, bypass switch  34  is connected in parallel with switching element  31   p.  By turning on bypass switch  34 , submodule  7  is short-circuited. Bypass switch  34  is also used to short-circuit submodule  7  when each element in this submodule  7  fails. Thus, even when any one of the plurality of submodules  7  fails, power converter  2  can continue to operate by using another submodule  7 . 
     Next, referring to  FIG.  3 ( b ) , a midpoint between switching element  31   p   1  and switching element  31   n   1  and a midpoint between switching element  31   p   2  and switching element  31   n   2  are referred to as “input/output terminals P 1  and P 2 ” of submodule  7 . 
     By keeping switching element  31   n   2  in a constantly on state, keeping switching element  31   p   2  in a constantly off state, and alternately turning on switching elements  31   p   1  and  31   n   1 , submodule  7  shown in  FIG.  3 ( b )  outputs a positive voltage or a zero voltage. In addition, by keeping switching element  31   n   2  in a constantly off state, keeping switching element  31   p   2  in a constantly on state, and alternately turning on switching elements  31   p   1  and  31   n   1 , submodule  7  shown in  FIG.  3 ( b )  can also output a zero voltage or a negative voltage. 
     Bypass switch  34  is connected between input/output terminals P 1  and P 2 . Bypass switch  34  is connected in parallel with the series bodies of switching elements  31   n   1  and  31   n   2 . By turning on bypass switch  34 , submodule  7  is short-circuited. 
     The case in which submodule  7  has a half bridge cell configuration shown in  FIG.  3 ( a )  and the semiconductor switching elements and the capacitor serving as an energy accumulation element are used will be described below as an example. However, submodule  7  may have a full bridge configuration shown in  FIG.  3 ( b ) . Alternatively, a submodule other than the submodules having the above-described configurations, e.g., a submodule having a circuit configuration also called “1.5 half bridge configuration” in which one of switching elements  31  in  FIG.  3 ( b )  is replaced only by a diode may be used. 
     &lt;Capacitor Voltage of Submodule&gt; 
     An output DC voltage of power converter  2  implemented by an MMC converter is DC voltage Vdc between positive electrode DC terminal Np and negative electrode DC terminal Nn. DC voltage Vdc is determined by a product sum of an instantaneous capacitor voltage Vcj of j-th submodule  7   j  that forms each leg circuit  4  and a switching state Si. A switching state Sj is “1” when switching element  31   p  is on, and “0” when switching element  31   p  is off. 
     For ease of explanation, variations in capacitor voltages Vc of submodules  7  between the arms and in the arm are ignored. Here, Vav represents a time average voltage value of capacitor voltage Vc, Mdc represents a DC modulation rate, and n represents the number of submodules per arm (i.e., included in each arm). Then, the following equation (1) holds. In this case, the number of submodules included in each leg circuit  4  is 2n. 
       Vdc=Σ(Vcj×Sj)=Vav×2n×Mdc . . .   (1)
 
     According to the equation (1) above, when DC modulation rate Mdc is constant (typically, 0.5), the number n of submodules is proportional to Vdc/Vav, and thus, the number n of submodules can be reduced by increasing average voltage value Vav. 
     Time average voltage value Vav (hereinafter, also simply referred to as “average voltage value Vav”) is obtained by dividing a total sum of instantaneous capacitor voltages Vcj of submodules  7   j  in the arm by the number n of submodules, and is expressed by the following equation (2). The symbol “&lt; &gt;” in the equation (2) represents a time average. 
       Vav=&lt;(ΣVcj)/n&gt;. . .   (2)
 
     During the normal power conversion operation (i.e., normal operation), controller  3  controls each submodule  7  in the arm such that the time average voltage value of capacitor voltage Vc of each submodule  7  in the arm is set to value Vav expressed by the equation (2). 
     However, in power converter  2 , a current having an AC component mainly composed of a fundamental frequency component flows into capacitor  32  mounted on each submodule  7 . Therefore, a ripple voltage actually occurs in capacitor  32  and capacitor voltage Vc fluctuates around average voltage value Vav. 
       FIG.  4    is a diagram for illustrating voltage fluctuations of the capacitors. Referring to  FIG.  4   , a waveform  210  represents a temporal change in a capacitor voltage Vc1 of capacitor  32  (hereinafter, also referred to as “capacitor  32 _ 1 ”) mounted on submodule  7  in power converter  2 _ 1 . A waveform  220  represents a temporal change in a capacitor voltage Vc2 of capacitor  32  (hereinafter, also referred to as “capacitor  32 _ 2 ”) mounted on submodule  7  in power converter  2 _ 2 . Capacitors  32 _ 1  and  32 _ 2  are implemented by capacitors having an equal rating (e.g., having an equal capacitance, an equal withstand voltage and the like). 
     In the example in  FIG.  4   , the number n1 of submodules included in each arm of power converter  2 _ 1  is equal to the number n2 of submodules included in each arm of power converter  2 _ 2 . In addition, power converter  2 _ 1  and power converter  2 _ 2  are connected to common DC circuit  14 . Therefore, based on the equation (1), an average voltage value Vav1 of capacitor voltage Vc1 is equal to an average voltage value Vav 2  of capacitor voltage Vc2. 
     Here, C represents a capacitance of the capacitor, F represents a fundamental frequency, and Icap represents a current flowing through the capacitor. Then, a ripple voltage Vrp that occurs in the capacitor has a relationship as expressed by the following equation (3): 
       Vrp∝(1/C)×(1/F)×Icap . . .   (3).
 
     In the first embodiment, fundamental frequency F1 of AC system  12 _ 1  is 60 Hz and fundamental frequency F 2  of AC system  12 _ 2  is 50 Hz. Therefore, a ripple voltage Vrp 1  of capacitor  32 _ 1  in power converter  2 _ 1  connected to AC system  12 _ 1  is smaller than a ripple voltage Vrp 2  of capacitor  32 _ 2  in power converter  2 _ 2  connected to AC system  12 _ 2 . Ripple voltage Vrp 1  refers to a difference between a maximum voltage value Vmax1 of capacitor voltage Vc1 and average voltage value Vav1. Ripple voltage Vrp 2  refers to a difference between a maximum voltage value Vmax2 of capacitor voltage Vc2 and average voltage value Vav2. Capacitors  32 _ 1  and  32 _ 2  composed of the same component have an equal capacitance. Assuming that current Icap is the same, ripple voltage Vrp 1  is 5/6 times as great as ripple voltage Vrp 2 . 
     In addition, since capacitors  32 _ 1  and  32 _ 2  are composed of the same component, capacitors  32 _ 1  and  32 _ 2  have an equal withstand voltage Vov. Therefore, a voltage margin Vg 1  (=Vov−Vmax 1 ) in capacitor  32 _ 1  is greater than a voltage margin Vg 2  (=Vov−Vmax 2 ) in capacitor  32 _ 2 . 
     When the same capacitor is applied as capacitors  32 _ 1  and  32 _ 2 , capacitance C is determined to satisfy the specifications based on greater ripple voltage Vrp 2  (i.e., such that voltage margin Vg 2  becomes equal to or greater than a reference margin). In this case, it is understood that voltage margin Vg 1  of capacitor  32 _ 1  is excessive, although voltage margin Vg 1  of capacitor  32 _ 1  satisfies the specifications. Specifically, capacitor  32 _ 1  includes an extra voltage margin corresponding to a difference value Vdi (=Vrp 2 −Vrp 1 ) between ripple voltage Vrp 2  and ripple voltage Vrp 1 . 
     In the first embodiment, difference value Vdi is used to adjust the average voltage value of capacitor  32 _ 1  and reduce the number of submodules included in power converter  2 _ 1  connected to the AC system  12 _ 1  side on the high frequency side. As a result, the size of the entire power conversion system is reduced. 
       FIG.  5    shows changes in capacitor voltages according to the first embodiment. Referring to  FIG.  5   , a waveform  210 A represents a temporal change in capacitor voltage Vc1 of capacitor  32 _ 1 . Waveform  210 A is formed by adding difference value Vdi to waveform  210  in  FIG.  4   , and thus, an average voltage value Vav1* of capacitor voltage Vc1 shown in  FIG.  5    is larger by difference value Vdi than average voltage value Vav1 shown in  FIG.  4   . In contrast, average voltage value Vav2 of capacitor voltage Vc2 of capacitor  32 _ 2  is equal to average voltage value Vav2 (=Vav1) in  FIG.  4   . Therefore, it is understood that average voltage value Vav1* is larger by difference value Vdi than average voltage value Vav2. In other words, average voltage value Vav1* is a value obtained by adding difference value Vdi to average voltage value Vav2. 
     As expressed by the equation (1) above, average voltage value Vav of the capacitor changes depending on the number n of submodules per arm. Here, X % represents a rate of change in average voltage value Vav1* with respect to average voltage value Vav1 of capacitor  32 _ 1 . Then, the following equation (4) holds: 
         X =((Vav1*−Vav1)/Vav1)×100 . . .   (4).
 
     Since DC voltage Vdc in the equation (1) does not change, it is understood that the number n of submodules is reduced by X % when average voltage value Vav increases by X %. Therefore, in the example in  FIG.  5   , the number n1* of submodules included in each arm of power converter  2 _ 1  is smaller by Y (=n1×X/100) than the number n1 of submodules in the example in  FIG.  4   . 
     In the present embodiment, the number of submodules per phase of power converter  2 _ 1  included in power conversion device  10 _ 1  is set at n1*. During the normal operation, controller  3 _ 1  controls each submodule  7  in the arm such that the time average voltage value of capacitor voltage Vc of each submodule  7  included in the arm of power converter  2 _ 1  is set to average voltage value Vav1*. On the other hand, the number of submodules per phase of power converter  2 _ 2  included in power conversion device  10 _ 2  is set at n2. During the normal operation, controller  3 _ 2  controls each submodule  7  in the arm such that the time average voltage value of capacitor voltage Vc of each submodule  7  included in the arm of power converter  2 _ 2  is set to average voltage value Vav2. As a result, capacitor voltages Vc1 and Vc2 of capacitors  32 _ 1  and  32 _ 2  change as shown in  FIG.  5   . 
     In the example in  FIG.  5   , a maximum voltage value Vmax1* of capacitor voltage Vc1 is equal to maximum voltage value Vmax2 of capacitor voltage Vc2, and thus, a voltage margin Vg 1 * of capacitor  32 _ 1  is equal to voltage margin Vg 2  of capacitor  32 _ 2 . Therefore, it is understood that voltage margin Vg 1 * of capacitor  32 _ 1  does not include an extra voltage margin, although capacitor  32 _ 1  ensures a voltage margin that satisfies the specifications. 
     As described above, in the first embodiment, submodules  7  in power converters  2 _ 1  and  2 _ 2  connected to AC systems  12 _ 1  and  12 _ 2  having different fundamental frequencies, respectively, are the same, and difference value Vdi between the ripple voltage of capacitor  32 _ 1  and the ripple voltage of capacitor  32 _ 2  caused thereby can be used to reduce the number of submodules in power converter  2 _ 1 . Therefore, it is possible to reduce the size of power converter  2 _ 1  while ensuring maintainability of power converters  2 _ 1  and  2 _ 2 , and as a result, the size of the entire power conversion system can be reduced. 
     &lt;When Submodule Fails&gt; 
     A method for adjusting average voltage value Vav when submodule  7  fails will be described. 
     Controller  3  receives, as state information of each submodule  7 , a healthy state determination signal indicating a healthy state of submodule  7 . When submodule  7  is in a healthy state, the healthy state determination signal is “1”. When submodule  7  is in a failure state, the healthy state determination signal is “0”. A failure of submodule  7  is not limited to an element failure, and means that submodule  7  no longer operates in accordance with a command from controller  3 . Examples of the failure of submodule  7  include a failure of a switching element, a failure of a gate driver, a breakage of a capacitor, a breakage of a bus bar, a communication error and the like. 
     Controller  3  outputs a corresponding operation command to each arm (e.g., the U-phase upper arm, the U-phase lower arm, the V-phase upper arm, the V-phase lower arm, the W-phase upper arm, and the W-phase lower arm), thereby controlling each arm. Therefore, on the arm including submodule  7  that has failed, controller  3  performs various types of control for dealing with the failure. 
     Let us assume that the number of submodules in leg circuit  4   u  corresponding to the U phase is  2   m  (m is an integer equal to or greater than 2), the number of submodules in the U-phase upper arm is m, and the number of submodules in the U-phase lower arm is m. For example, when the healthy state determination signals received from k (k is an integer equal to or greater than 1 and k&lt;m) submodules  7 _i, of m submodules  7  in the U-phase upper arm, are “0”, controller  3  detects a failure of each submodule  7 _i. By turning on bypass switch  34  of each submodule  7 _i, controller  3  bypasses each submodule  7 _i that has failed. 
     Next, based on the number (i.e., k) of submodules  7 _i that have failed, controller  3  increases average voltage value Vav in each submodule  7  included in the U-phase upper arm. Specifically, controller  3  increases average voltage value Vav by a factor of m/(m−k). That is, (average voltage value Vav after failure)/(average voltage value Vav before failure)=m/(m−k). In this case, controller  3  controls (m−k) submodules  7  such that the time average voltage value of capacitor voltage Vc of each of (m−k) healthy submodules  7  in the U-phase upper arm is set to increased average voltage value Vav. As a result, a voltage output by k submodules  7  can be compensated for by remaining (m−k) healthy submodules  7  before failure. 
     &lt;When Fault Occurs in AC System&gt; 
     A method for adjusting average voltage value Vav when a fault occurs in AC system  12  will be described. Let us assume that a fault occurs in AC system  12 _ 1 . However, this fault is a temporary fault that will be removed after a certain period of time from the occurrence of the fault. 
       FIG.  6    shows a change in capacitor voltage before and after a fault occurs in the AC system. Referring to  FIG.  6   , a waveform  250  represents average voltage value Vav1* of capacitor  32 _ 1 . For the sake of convenience, average voltage value Vav1* before a fault occurs is denoted as “V0”. Average voltage value V0 is equal to average voltage value Vav1* in  FIG.  5   . A waveform  260  represents capacitor voltage Vc1 including voltage fluctuations (i.e., ripple voltage Vrp 1 ) of capacitor  32 _ 1 . 
     At time t1, a fault occurs in AC system  12 _ 1  and controller  3 _ 1  detects the fault. For example, controller  3 _ 1  determines that the fault has occurred in AC system  12 _ 1 , when at least one of absolute values of arm currents Ipu, Ipv, Ipw, Inu, Inv, and Inw detected by arm current detectors  9 A and  9 B exceeds a threshold value Th1, or when a total value of the arm currents flowing through the respective phases exceeds a threshold value Th2. Alternatively, controller  3 _ 1  may determine that the fault has occurred, when any one of the AC voltages detected by AC voltage detector  18  exceeds (or falls below) a threshold value Th3. 
     From time t0 to time t1, controller  3 _ 1  controls each submodule  7  such that the time average voltage value of capacitor voltage Vc of each submodule  7  in the arm is set to average voltage value V0. However, when controller  3 _ 1  detects the fault at time t1, controller  3 _ 1  controls each submodule  7  such that the time average voltage value of capacitor voltage Vc of each submodule  7  in the arm is set to a value obtained by subtracting a reference value D1 from average voltage value V0 (i.e., V0−D1). Thus, controller  3 _ 1  decreases average voltage value Vav1*. 
     When the fault is removed at time t2, a current flows from AC system  12 _ 1  to power converter  2 _ 1 , and thus, capacitor voltage Vc1 increases abruptly. In the present embodiment, controller  3 _ 1  intentionally decreases capacitor voltage Vc1 at the occurrence of the fault, which can prevent capacitor voltage Vc1 from exceeding withstand voltage Vov after the fault is removed. 
     When a fault occurs in AC system  12 _ 2 , controller  3 _ 2  performs the operation similar to the above-described operation of controller  3 _ 1 . Specifically, when controller  3 _ 2  detects the fault in AC system  12 _ 2 , controller  3 _ 2  controls each submodule  7  such that the time average voltage value of capacitor voltage Vc of each submodule  7  in the arm is set to a value obtained by subtracting a reference value D2 from the average voltage value before the fault occurs. Reference value D2 may be equal to reference value D1. Thus, controller  3 _ 2  decreases average voltage value Vav2. 
     Controller  3 _ 2  may also decrease average voltage value Vav2 when a fault has occurred in AC system  12 _ 1 . In this case, controller  3 _ 2  receives, from controller  3 _ 1  (or another higher-level device), information indicating that the fault has occurred in AC system  12 _ 1 . After controller  3 _ 2  receives the information, controller  3 _ 2  decreases average voltage value Vav2. Thus, even when the fault in AC system  12 _ 1  may affect capacitor voltage Vc2 of each submodule  7  in power converter  2 _ 2 , it is possible to prevent capacitor voltage Vc2 from exceeding withstand voltage Vov. 
     &lt;When Dielectric Strength of DC Circuit Decreases&gt; 
     A method for adjusting average voltage value Vav when a dielectric strength of DC circuit  14  decreases will be described. Let us assume that DC circuit  14  is a DC power transmission line, and the dielectric strength of DC circuit  14  decreases due to salt-containing snow and the like that adhere to the DC power transmission line. 
     Each of transformers  13 _ 1  and  13 _ 2  is implemented by a transformer having a variable transformation ratio. The transformer having a variable transformation ratio is implemented by, for example, a transformer having a tap switching function, and the like. In addition, controller  3  is configured to be capable of communicating with transformer  13 , and transmits, to transformer  13 , various commands such as a command to change the transformation ratio. 
     When a system operator determines that the dielectric strength of DC circuit  14  has decreased, the system operator inputs, to controllers  3 _ 1  and  3 _ 2 , information indicating that the dielectric strength of DC circuit  14  has decreased. Then, DC voltage Vdc of DC circuit  14  is decreased by ΔVdc. 
     In this case, controller  3 _ 1  decreases, by ΔVav1*, average voltage value Vav1* of capacitor  32 _ 1  in each submodule  7  included in power converter  2 _ 1 . Similarly, controller  3 _ 2  decreases, by ΔVav2, average voltage value Vav2 of capacitor  32 _ 2  in each submodule  7  included in power converter  2 _ 2 . Since the number of submodules included in each arm of power converter  2 _ 1  is n1*, ΔVav1*=ΔVdc/(Mdc×2n1*) based on the relationship expressed by the equation (1). Since the number of submodules included in leg circuit  4  of power converter  2 _ 2  is n2, ΔVav2=ΔVdc/(Mdc×2n2) based on the relationship expressed by the equation (1). 
     It is necessary to maintain the voltages of AC systems  12 _ 1  and  12 _ 2 , while decreasing DC voltage Vdc by ΔVdc. Here, V 1 _ 1  represents an AC voltage on the primary side (i.e., AC system  12 _ 1  side) of transformer  13 _ 1 . In addition, V 2 _ 1  represents an AC voltage on the secondary side (i.e., power converter  2 _ 1  side) of transformer  13 _ 1  before DC voltage Vdc decreases, and V 2 _ 1 * represents an AC voltage on the secondary side of transformer  13 _ 1  after DC voltage Vdc decreases. 
     In this case, controller  3 _ 1  adjusts a transformation ratio al of transformer  13 _ 1  such that AC voltage V 1 _ 1  on the primary side of transformer  13 _ 1  is maintained. Specifically, controller  3 _ 1  instructs transformer  13 _ 1  to change transformation ratio α1 from (V 2 _ 1 )/(V 1 _ 1 ) to (V 2 _ 1 *)/(V 1 _ 1 ). 
     Similarly, V 1 _ 2  represents an AC voltage on the primary side (i.e., AC system  12 _ 2  side) of transformer  13 _ 2 , V 2 _ 2  represents an AC voltage on the secondary side (i.e., power converter  2 _ 2  side) of transformer  13 _ 2  before DC voltage Vdc decreases, and V 2 _ 2 * represents an AC voltage on the secondary side of transformer  13 _ 2  after DC voltage Vdc decreases. In this case, controller  3 _ 2  adjusts a transformation ratio α2 of transformer  13 _ 2  such that AC voltage V 1 _ 2  on the primary side of transformer  13 _ 2  is maintained. Specifically, controller  3 _ 2  instructs transformer  13 _ 2  to change transformation ratio α2 from (V 2 _ 2 )/(V 1 _ 2 ) to (V 2 _ 2 *)/(V 1 _ 2 ). 
     As a result, when the dielectric strength of DC circuit  14  decreases, it is possible to prevent damage to DC circuit  14  by decreasing DC voltage Vdc, and to maintain the voltage on the AC system  12  side. 
     Second Embodiment 
     In the first embodiment, description has been given of the case in which the plurality of AC systems  12 _ 1  and  12 _ 2  have different fundamental frequencies. In a second embodiment, description will be given of the case in which power requests from the plurality of AC systems  12 _ 1  and  12 _ 2  are different from each other. 
     According to the above-described equation (3), the ripple voltage increases in proportion to current Icap flowing through the capacitor. Capacitors  32 _ 1  and  32 _ 2  composed of the same component have an equal capacitance. Therefore, when fundamental frequency F1 of AC system  12 _ 1  is equal to fundamental frequency F2 of AC system  12 _ 2 , ripple voltage Vrp becomes greater as current Icap becomes greater. In the second embodiment, attention is focused on a difference in currents Icap flowing through the capacitors in power converters  2 _ 1  and  2 _ 2 , which is caused by a difference in power requests from AC systems  12 _ 1  and  12 _ 1 . Here, power converters  2 _ 1  and  2 _ 2  operate to meet the power requests from AC systems  12 _ 1  and  12 _ 2 , respectively. 
     Arm current Iarm flowing in power converter  2  flows through each of the positive electrode side (i.e., the switching element  31   p  side) and the negative electrode side (i.e., the switching element  31   n  side) of submodule  7 . In the following description, the semiconductor switching element of each of switching elements  31   p  and  31   n  is implemented by an IGBT. 
     A current Isp flowing through the positive electrode side is a summed current of a current flowing through the IGBT of switching element  31   p  and a current flowing through the FWD of switching element  31   p.  This summed current corresponds to current Icap flowing through capacitor  32 . On the other hand, a current Isn flowing through the negative electrode side is a summed current of a current flowing through the IGBT of switching element  31   n  and a current flowing through the FWD of switching element  31   n.  In switching elements  31   p  and  31   n,  the current flowing through the FWD is opposite in direction to the current flowing through the IGBT. 
     A current sharing ratio between current Isp (i.e., current Icap) and current Isn changes depending on a power factor (PF) of AC system  12 . Arm current Iarm is a sum of current Isp and current Isn, and an effective value expression thereof is Iarm=(Isp 2 +Isn 2 ) 1/2 . In  FIG.  3   , a positive direction of current Isp corresponds to a direction from input/output terminal P 1  to switching element  31   p   1 , and a positive direction of current Isn corresponds to a direction from input/output terminal P 1  to switching element  31   n   1 . 
       FIG.  7    is a diagram for illustrating a relationship between current Isp flowing through the positive electrode side and current Isn flowing through the negative electrode side in the submodule. In  FIG.  7   , the vertical axis represents an effective value of current Isp (=Icap), and the horizontal axis represents an effective value of current Isn. A straight line  302  is a straight line that satisfies current Isp=current Isn. 
     Straight lines  304 ,  306  and  308  are straight lines indicating the relationship between current Isp and current Isn when the power factor of AC system  12  is 0, 0.95 and 1.00, respectively. Current effective values {=(Isp 2 +Isn 2 ) 1/2 } of arm current Iarm at points  354 ,  356  and  358  on straight lines  304 ,  306  and  308 , respectively, are the same. A curved line  362  represents points at which the current effective values of arm current Iarm are the same. 
     According to straight lines  304  to  308 , as the power factor at the AC output of power converter  2  becomes greater, the current disproportionately flows through the negative electrode side, which makes current Isn greater and current Isp smaller. In contrast, as the power factor becomes smaller, current Isp (i.e., current Icap) becomes greater. When the power factor is constant, current Icap becomes greater as arm current Iarm becomes greater. The magnitude of arm current Iarm is proportional to the magnitude of an apparent power input and output between power converter  2  and AC system  12 . Therefore, it is also said that when the power factor is constant, current Icap becomes greater as the input and output apparent power becomes greater. When the input apparent power input to power converter  2  is different from the output apparent power output from power converter  2 , the magnitude of current Icap depends on the greater one of the input apparent power and the output apparent power. 
     Therefore, when the power requests (e.g., an input/output request of the apparent power and a requested power factor) from AC systems  12 _ 1  and  12 _ 2  are different, currents Icap flowing through capacitors  32  in power converters  2 _ 1  and  2 _ 2  are different in magnitude, and as a result, the ripple voltages of capacitors  32  are different in magnitude. By referring to  FIG.  7   , current Icap based on the power factor and the apparent power requested from AC system  12  can be obtained. 
     Let us assume that a power factor requested from AC system  12 _ 1  is equal to a power factor requested from AC system  12 _ 2 . In this case, when input and output of an apparent power requested from AC system  12 _ 1  is smaller than input and output of an apparent power requested from AC system  12 _ 2 , a current Icap 1  flowing through capacitor  32 _ 1  in power converter  2 _ 1  is smaller than a current Icap 2  flowing through capacitor  32 _ 2  in power converter  2 _ 2 . 
     Therefore, ripple voltage Vrp 1  of capacitor  32 _ 1  is smaller than ripple voltage Vrp 2  of capacitor  32 _ 2 . Therefore, as described in the first embodiment with reference to  FIG.  5   , the number of submodules in power converter  2 _ 1  can be reduced by making the average voltage value of capacitor voltage Vc1 of capacitor  32 _ 1  greater by difference value Vdi (=Vrp 2 —Vrp 1 ) than the average voltage value of capacitor voltage Vc2 of capacitor  32 _ 2 . 
     Next, let us assume that the input and output of the apparent power requested from AC system  12 _ 1  is equal to the input and output of the apparent power requested from AC system  12 _ 2 . In this case, when the power factor requested from AC system  12 _ 1  is greater than the power factor requested from AC system  12 _ 2 , current Icap 1  flowing through capacitor  32 _ 1  in power converter  2 _ 1  is smaller than current Icap 2  flowing through capacitor  32 _ 2  in power converter  2 _ 2 . Therefore, ripple voltage Vrp 1  of capacitor  32 _ 1  is smaller than ripple voltage Vrp 2  of capacitor  32 _ 2 . 
     Therefore, the number of submodules in power converter  2 _ 1  can be reduced by making the average voltage value of capacitor voltage Vc1 of capacitor  32 _ 1  greater by difference value Vdi than the average voltage value of capacitor voltage Vc2 of capacitor  32 _ 2 . 
     In the above-described example, description has been given of the case in which the power factor requested from AC system  12 _ 1  is equal to the power factor requested from AC system  12 _ 2  and the case in which the input and output of the apparent power requested from AC system  12 _ 1  is equal to the input and output of the apparent power requested from AC system  12 _ 2 . However, the power factor and the input and output of the apparent power requested from AC system  12 _ 1  may be different from the power factor and the input and output of the apparent power requested from AC system  12 _ 2 . For example, in  FIG.  7   , a point  371  corresponds to the current values (Isn 1  and Icap 1 ) based on the power factor and the input and output of the apparent power requested from AC system  12 _ 1 , and a point  372  corresponds to the current values (Isn 2  and Icap 2 ) based on the power factor and the apparent power requested from AC system  12 _ 2 . Based on the positional relationship between point  371  and point  372 , the power factor requested from AC system  12 _ 1  is smaller than the power factor requested from AC system  12 _ 2 , and the input and output of the apparent power requested from AC system  12 _ 1  is smaller than the input and output of the apparent power requested from AC system  12 _ 2 . 
     Referring to  FIG.  7   , current Icap 1  at point  371  is smaller than current Icap 2  at point  372 . Therefore, ripple voltage Vrp 1  of capacitor  32 _ 1  is smaller than ripple voltage Vrp 2  of capacitor  32 _ 2 . Therefore, the number of submodules in power converter  2 _ 1  can be reduced by making the average voltage value of capacitor voltage Vc1 of capacitor  32 _ 1  greater by difference value Vdi than the average voltage value of capacitor voltage Vc2 of capacitor  32 _ 2 . 
     As described above, the effective value of the current (i.e., current Icap 1 ) of capacitor  32 _ 1  in power converter  2 _ 1  based on the power factor and the apparent power requested from AC system  12 _ 1  is compared with the effective value of the current (i.e., current Icap 2 ) of capacitor  32 _ 2  in power converter  2 _ 2  based on the power factor and the apparent power requested from AC system  12 _ 2 . When current Icap 1  is smaller than current Icap 2 , for example, ripple voltage Vrp 1  is smaller than ripple voltage Vrp 2 , and thus, the number of submodules in power converter  2 _ 1  can be reduced. 
     In the above-described example, submodules  7  in power converters  2 _ 1  and  2 _ 2  connected to AC systems  12 _ 1  and  12 _ 2  that are different in power requests, respectively, are the same, and difference value Vdi between the ripple voltage of capacitor  32 _ 1  and the ripple voltage of capacitor  32 _ 2  caused thereby can be used to reduce the number of submodules in power converter  2 _ 1 . Therefore, in the second embodiment as well, it is possible to reduce the size of one power converter while ensuring maintainability of power converters  2 _ 1  and  2 _ 2 , and as a result, the size of the entire power conversion system can be reduced. 
     Other Embodiments 
     In the first embodiment, the method for adjusting average voltage value Vav in each of &lt;When Submodule Fails&gt;, &lt;When Fault Occurs in AC System&gt;and &lt;When Dielectric Strength of DC Circuit Decreases&gt;has been described. However, in the second embodiment as well, the method for adjusting average voltage value Vav in each case can be used. 
     The configurations illustrated as the embodiments above are merely examples of the configuration of the present disclosure, and can be combined with another known technique or can be modified by being omitted partially, for example, without going beyond the scope of the present disclosure. Moreover, the embodiments described above may be implemented, employing the processes and configurations described in other embodiments as appropriate. 
     It should be understood that the embodiments disclosed herein are illustrative and non-restrictive in every respect. The scope of the present disclosure is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims. 
     REFERENCE SIGNS LIST 
       2  power converter;  3  controller;  4   u,    4   v,    4   w  leg circuit;  5  upper arm;  6  lower arm;  7  submodule;  8 A,  8 B reactor;  9 A,  9 B detector;  10  power conversion device;  11 A,  11 B DC voltage detector;  12  AC system;  13  transformer;  14  DC circuit;  16  AC current detector;  18  AC voltage detector;  31   n,    31   n   1 ,  31   n   2 ,  31   p,    31   p   1 ,  31   p   2  switching element;  32  capacitor;  33  voltage detector;  34  bypass switch;  100  power conversion system.