Abstract:
Current of a three-phase multilevel modular converter (MMC) is controlled. The control is a division-summation (D-Σ) method yet uses integration to replace the two steps of division and summation. Common D-Σ characteristic equations are used for all areas. Inductance changes are considered in the characteristic equations. Current source is used to control converter. Therefore, the current of the converter can be traced to sinusoidal reference current even when the inductance changes become big. The modulation method and the capacitor-voltage balancing method are submodule unified pulse width modulation (SUPWM) and sorted voltage-balancing method, respectively. The current control directly obtains a law of the current change on each conducting module of an arm. It does not need complex sector judgments and table look-ups. Thus, the amount of computation and memory for a processor can be relatively reduced.

Description:
TECHNICAL FIELD OF THE INVENTION 
     The present invention relates to current control of MMC; more particularly, relates to a division-summation (D-Σ) method for controlling a three-phase modular multilevel converter (MMC) with inductance changes allowed. 
     DESCRIPTION OF THE RELATED ARTS 
     As an up-and-coming high-pressure multilevel converter, MMC shares DC side voltage and has modular design with low switching frequency and stress and low harmony distortion. Furthermore, its applications in high-voltage DC power supply, virtual power compensation, motor drives and low voltage ride through (LVRT) are studied. Among them, the current control of MMC is a more popular research topic. 
     Traditional MMC current control method is transplanted from the DC control method of two multilevel converters, where mathematical models of abc-to-dq vector conversions for the abc three phases are calculated to obtain corresponding control methods for d-axis and q-axis. (Zhao Yan; Hu Xue-hao; Tang Guang-fu; He Zhi-yuan, “A study on MMC model and its current control strategies,” Power Electronics for Distributed Generation Systems (PEDG), 2010 2nd IEEE International Symposium on, vol., no., pp. 259,264, 16-18 Jun. 2010.). In a practical engineering application, when current flowing through each arm of the MMC is changed, inductance of the inductor will be significantly changed as following the current change. Such a situation of inductance change is not considered in the abc-dq conversion, so that error on current control will happen by using the DC control method of the d-q axis conversion. 
     In order to solve the problem for accurate current control under big inductance changes, three documents (Wu T F, Chang C H, Lin L C, et al. A D-Σ Digital Control for Three-Phase Inverter to Achieve Active and Reactive Power Injection[J]. Power Electronics, IEEE Transactions on, 2014, 31(8): 3879-3890; Wu T F, Chang C H, Lin L C, et al. Two-Phase Modulated Digital Control for Three-Phase Bidirectional Inverter With Wide Inductance Variation[J]. Power Electronics, IEEE Transactions on, 2013, 28(4): 1598-1607; Wu T F, Sun K H, Kuo C L, et al. Predictive current controlled 5-kW single-phase bidirectional inverter with wide inductance variation for dc-microgrid applications[J]. Power Electronics, IEEE Transactions on, 2010, 25(12): 3076-3084) provide D-Σ control methods for single-phase and three-phase converters (two-level converters). The methods consider the inductance changes under the current changes to build mathematical models of two-level converters and obtain corresponding duty ratios of all switches of each submodule in the present control cycle for controlling the three-phase MMC. But, as compared to the two-level converter, MMC is more complex, whose mathematical models have many differences. If a D-Σ control method of two-level converter is directly applied to the MMC, complex multilevel space phasor-order modulation is required with memory and calculation greatly increased in the processor. 
     For an existing multilevel converter, when the inductance significantly changes as the current flows through the inductor, the traditional d-q axis conversion does not consider inductance change and, therefore, error compensation would happen. As a result, mains current is easily affected by big inductance change to generate oscillation and further lead to serious distortion. 
     Hence, the prior arts do not fulfill all users&#39; requests on actual use. 
     SUMMARY OF THE INVENTION 
     The main purpose of the present invention is to provide a D-Σ method for controlling a three-phase MMC with inductance changes allowed. 
     Another purpose of the present invention is to calculate voltages corresponding to the current changes by obtaining inductance values following the current changes and building a table in a single chip, where, with consideration of inductance changes during calculation, circuit gains are quickly adjusted to resolve mains current distortion owing to big inductance changes; the present invention does not need coordinate conversions, sector judgments and directly calculates a number of conducted submodules of each arm according to a characteristic equation; and the present invention has a simple process, a small amount of calculation and an easy digital control. 
     To achieve the above purposes, the present invention is a method of current control of a three-phase MMC with inductance changes allowed, where the method is execution in a device of the three-phase MMC to control the three-phase MMC and the three-phase MMC has a plurality of inductance values of upper and lower arms at different phases; and the method comprises the following steps: (a) three-phase reference currents of three-phase mains side are sine functions of a fundamental frequency; after feedback voltages and feedback currents of the three-phase mains side are separately obtained through a voltage feedback circuit and a current feedback circuit, the reference currents in a next control cycle of the three-phase mains side are separately subtracted by corresponding ones of the feedback currents in a present control cycle to obtain current changes of corresponding inductors in the present control cycle; through storing changes of inductance values of the upper and lower arms into a single chip as following the current changes, equivalent inductance values of the mains side are calculated with the corresponding inductance values of three phases of the MMC; (b) an average number of submodules conducted by each one of the upper and lower arms in the present control cycle is calculated by using a digital division-summation (D-Σ) control method; (c) a law of number change of submodules of each one of the upper and lower arms in the present control cycle is figured out by using a method of submodule unified pulse width modulation (SUPWM); and (d) corresponding duty ratios of all switches of each one of the submodules in the present control cycle are calculated by using a voltage-balancing method based on sorted submodule capacitances and the method is looped to execute step (a). Accordingly, a novel method of current control of a three-phase MMC with inductance changes allowed is obtained. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
       The present invention will be better understood from the following detailed description of the preferred embodiment according to the present invention, taken in conjunction with the accompanying drawings, in which 
         FIG. 1  is the view showing the equivalent circuit and the control blocks of the preferred embodiment according to the present invention; 
         FIG. 2  is the view showing the submodule of the three-phase modular multilevel converter (MMC); 
         FIG. 3  is the flow view showing the control of the three-phase MMC based on division-summation (D-Σ); 
         FIG. 4  is the view showing the control blocks in the S field for controlling the three-phase MMC; 
         FIG. 5  is the view showing the law of number change of the submodules of the arm in the control cycle; and 
         FIG. 6A  and  FIG. 6B  are the views showing the simulated waveforms of the mains currents and those of the A-phase mains voltage under the parallel connection with mains. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The following description of the preferred embodiment is provided to understand the features and the structures of the present invention. 
     Please refer to  FIG. 1 - FIG. 5 , which are a view showing an equivalent circuit and control blocks of a preferred embodiment according to the present invention; a view showing a submodule of a three-phase MMC; a flow view showing control of the three-phase MMC based on D-Σ; a view showing control blocks in an S field for controlling the three-phase MMC; and a view showing a law of number change of submodules of an arm in a control cycle. As shown in the figures, the present invention is a method of current control of a three-phase MMC with inductance changes allowed, where the method is execution in a device of three-phase MMC to control the three-phase MMC. The device controlling the three-phase MMC comprises the three-phase MMC  11 , a city grid circuit  12 , a single chip  13 , a current feedback circuit  14 , a voltage feedback circuit  15  and a drive circuit  16 . 
     The three-phase MMC  11  has a plurality of inductance values of upper and lower arms of different phases. 
     The city grid circuit  12  is electrically connected with the three-phase MMC  11  to receive currents converted by and outputted from the three-phase MMC  11 . 
     The single-chip  13  is electrically connected with the drive circuit  16 , the current feedback circuit  14 , and the voltage feedback circuit  15 . 
     The current feedback circuit  14  is electrically connected with the city grid circuit  12  and the single-chip  13  for receiving the currents outputted from the city grid circuit  12  and generating feedback currents accordingly. 
     The voltage feedback circuit  15  is electrically connected with the three-phase MMC  11 , the city grid circuit  12  and the single-chip  13  to receive voltages outputted from the city grid circuit  12  and generating a feedback voltage accordingly while receiving voltages of DC side for the three-phase MMC  11 . 
     The drive circuit  16  is electrically connected with the three-phase MMC  11  and the single chip  13  for driving the three-phase MMC  11 . 
     On using, the present invention comprises the following steps: 
     (a) Step S 10 : According to Eq. 1, three-phase currents (i a , i b , i c ) of three-phase mains side for the three-phase MMC  11  are calculated to obtain reference currents (i aref , i bref , i cref ), which are sine functions of a fundamental frequency. After feedback voltages (u ab , u bc , u ca ) and feedback currents (i a , i b , i c ) of the mains side are separately obtained through the voltage feedback circuit  15  and the current feedback circuit  14 , the reference currents in a next control cycle of the three-phase mains side for the three-phase MMC  11  are separately subtracted by corresponding ones of the feedback currents in a present control cycle (T) to obtain current changes (Δi a , Δi b , Δi c ) of corresponding inductors in the present control cycle according to Eq. 2. Therein, since inductance values have big changes as the currents flow through the corresponding inductors, changes of inductance value are taken into consideration for achieving a precise control of the currents. Through storing changes of the inductance values (L ap , L bp , L cp , L an , L bn , L cn ) of the upper and lower arms into the single chip  13  with off-line measurements as following changes of the currents, equivalent inductance values (L a , L b , L c ) of the mains side are calculated according to Eq. 3 with the corresponding inductance values of three phases. 
                   {             i   aref     =       I   M     ⁢     sin   ⁡     (     ω   ⁢           ⁢   t     )                       i   bref     =       I   M     ⁢     sin   ⁡     (       ω   ⁢           ⁢   t     -     120   ⁢   °       )                       i   cref     =       I   M     ⁢     sin   ⁡     (       ω   ⁢           ⁢   t     +     120   ⁢   °       )                         Eq   .           ⁢   1               
Therein, i a (k), i b (k) and i c (k) are sampled values of reference currents of phase a, b and c of connected grid in the present control cycle, whose amplitude is I M .
 
                   {             Δ   ⁢           ⁢     i   a       =         i   aref     ⁡     (     k   +   1     )       -       i   a     ⁡     (   k   )                       Δ   ⁢           ⁢     i   b       =         i   bref     ⁡     (     k   +   1     )       -       i   b     ⁡     (   k   )                       Δ   ⁢           ⁢     i   c       =         i   cref     ⁡     (     k   +   1     )       -       i   c     ⁡     (   k   )                         Eq   .           ⁢   2               
Therein, i aref (k+1), i bref (k+1) and i cref (k+1) are sampled values of the reference currents of the phase a, b and c of the connected grid in the next control cycle; i a , i b , i c  are feedback values of the reference currents of the phase a, b and c of the connected grid in the present control cycle; and, Δi a , Δi b  and Δi c  are to-be-traced deviation values of currents of the phase a, b and c.
 
                   {             L   a     =         L   ap     ⁢     L   an           L   ap     +     L   an                       L   b     =         L   bp     ⁢     L   bn           L   bp     +     L   bn                       L   c     =         L   cp     ⁢     L   cn           L   cp     +     L   cn                         Eq   .           ⁢   3               
Therein, L a , L b , L c  are equivalent inductances of the phase a, b and c; L ap , L bp , L cp  are the inductances of the upper arms of the phase a, b and c; and, L an , L bn , L cn  are the inductance of the upper arms of the phase a, b and c.
 
     (b) Step S 11 : According to Eq. 4(a) and Eq. 4(a), by using a D-Σ digital control, an average number of conducted submodules of each upper or lower arm in the present current cycle is figured out. 
     For the upper arms of three phases: 
     
       
         
           
             
               
                 
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     Therein, N ap , N bp , N cp  are the conducted submodules of the upper arms of the phase a, b and c; N an , N bn , N cn  are the conducted submodules of the lower arms of the phase a, b and c; N is the total number of submodules; u ab  and u bc  are voltages of mains lines between phases a,b and b,c; u ab =u ao −u bo  and u bc =u bo −u co  while u ao , u bo  and u co  are feedback values of voltages of the phase a, b and c in the present current cycle; U c  is the rated voltage of capacitor of submodule; and, T is the time length of control cycle. 
     (c) Step S 12 : According to Eq. 5(a)˜Eq. 5(f), by using a method of submodule unified pulse width modulation (SUPWM), a law of number change of submodules of each arm in the present control cycle is figured out as shown in  FIG. 5 . 
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                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ⁢ 
                   
                     ( 
                     b 
                     ) 
                   
                 
               
             
           
         
       
     
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             t 
                             
                               a 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   
                                     N 
                                     _ 
                                   
                                   
                                     a 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     p 
                                   
                                 
                                 - 
                                 
                                   N 
                                   
                                     a 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     p 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             t 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   
                                     N 
                                     _ 
                                   
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     p 
                                   
                                 
                                 - 
                                 
                                   N 
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     p 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             t 
                             
                               c 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   
                                     N 
                                     _ 
                                   
                                   
                                     c 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     p 
                                   
                                 
                                 - 
                                 
                                   N 
                                   
                                     c 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     p 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ⁢ 
                   
                     ( 
                     c 
                     ) 
                   
                 
               
             
           
         
       
     
     For the lower arms of three phases: 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             N 
                             
                               a 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               0 
                             
                           
                           = 
                           
                             floor 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   N 
                                   _ 
                                 
                                 an 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             N 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               0 
                             
                           
                           = 
                           
                             floor 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   N 
                                   _ 
                                 
                                 bn 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             N 
                             
                               c 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               0 
                             
                           
                           = 
                           
                             floor 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   N 
                                   _ 
                                 
                                 cn 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ⁢ 
                   
                     ( 
                     d 
                     ) 
                   
                 
               
             
           
         
       
     
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             t 
                             
                               a 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   
                                     N 
                                     _ 
                                   
                                   
                                     a 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                   
                                 
                                 + 
                                 
                                   N 
                                   
                                     a 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             t 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   
                                     N 
                                     _ 
                                   
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                   
                                 
                                 + 
                                 
                                   N 
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             t 
                             
                               c 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   
                                     N 
                                     _ 
                                   
                                   
                                     c 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                   
                                 
                                 + 
                                 
                                   N 
                                   
                                     c 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ⁢ 
                   
                     ( 
                     e 
                     ) 
                   
                 
               
             
           
         
       
     
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             t 
                             
                               a 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   
                                     N 
                                     _ 
                                   
                                   
                                     a 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                   
                                 
                                 - 
                                 
                                   N 
                                   
                                     a 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             t 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   
                                     N 
                                     _ 
                                   
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                   
                                 
                                 - 
                                 
                                   N 
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             t 
                             
                               c 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   
                                     N 
                                     _ 
                                   
                                   
                                     c 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                   
                                 
                                 - 
                                 
                                   N 
                                   
                                     c 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     n 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     0 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               / 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ⁢ 
                   
                     ( 
                     f 
                     ) 
                   
                 
               
             
           
         
       
     
     Therein, function floor(x) is rounded down to take a maximum integer not greater than parameter x. 
     (d) Step S 13 : At last, by using a voltage-balancing method based on sorted submodule capacitances, corresponding duty ratios of all switches of each submodule in the present control cycle are calculated for controlling the three-phase MMC. Therein, the three-phase MMC converts electricity between the DC side and the mains side according to the duty ratios of all switches of each submodule. 
     Thus, a novel method of current control of a three-phase MMC with inductance changes allowed is obtained. 
     In  FIG. 4 , the traditional method controls current according to the dq-axis conversion; yet, the present invention directly controls current under the abc coordinates after obtaining feedback values of voltages and currents through feedback circuits. 
     In  FIG. 5 , in the present control cycle, a low of change of submodule number (N xk ) of an arm (x phase k arm, x=a,b,c) is shown. The number of submodules for the arm is changed twice in the present control cycle, where N xk0  is changed into N xk0 +1 at time t xk1  and N xk0 +1 is changed into N xk0  at time t xk2 . 
     Please refer to  FIG. 6A  and  FIG. 6B , which are views showing simulated waveforms of mains currents and those of an A-phase mains voltage under a parallel connection with mains. As shown in the figure, under consideration of big inductance changes, a software of PSCAD/EMTDC is used for simulation with inductance parameters changed as following big current changes (simulation conditions are shown in Table 1) for showing waveforms of mains currents (i a , i b , i c ) of the mains side and mains voltages at A phase outputted from the three-phase MMC, where the current unit is kA, the voltage unit is 100V and the time unit is s. On using the traditional method of dq-axis conversion control, the mains currents (i a , i b , i c ) are severely affected by the big inductance changes with a total distortion of 17.2% as shown in  FIG. 6A . Yet, as shown in  FIG. 6B , on using the present invention, the mains currents (i a , i b , i c ) have good sine waves with a reduced total distortion of 1.4%, which proves that the present invention can effectively control mains currents and improve grid current harmonics under big inductance changes. 
     
       
         
               
               
               
             
               
               
               
               
             
               
               
               
             
               
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Parameter 
                 Value 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 submodule capacitance C 0   
                 5000 
                 μF 
               
             
          
           
               
                   
                 submodule number of arm N 
                 8 
               
             
          
           
               
                   
                 voltage amplitude of phase at  
                 3.266 
                 kV 
               
               
                   
                 AC side U m   
                   
                   
               
               
                   
                 voltage of DC side U dc   
                 2 
                 kV 
               
               
                   
                 Control cycle T 
                 0.0002 
                 s 
               
               
                   
                 Inductance-change range 
                 4-10 
                 mH 
               
             
          
           
               
                   
                 distortion of current harmonics  
                 17.2% 
               
               
                   
                 by dq-axis conversion control 
                   
               
               
                   
                 distortion of current harmonics  
                  1.4% 
               
               
                   
                 by D-Σ control 
               
               
                   
                   
               
             
          
         
       
     
     The present invention is a D-Σ control method suitable for MMC. The control method uses integration instead of two-step calculations of division and summation for obtaining common characteristic D-Σ equations in all areas. Inductance changes are considered in the characteristic equations for control, where converters are controlled by current sources so that the currents of the converters can be traced to sine-wave reference currents on having big inductance changes. The modulation method and the capacitor-voltage balancing method are SUPWM and sorted voltage-balancing method, respectively. A law of number change of submodules conducted by each arm is directly figured out through the control algorithm without complex sector judgments and table look-ups for relatively reducing computation and memory of the processor. 
     To sum up, the present invention is a method of current control of a three-phase MMC with inductance changes allowed, where inductance values following current changes are obtained; by building a table in a single chip, voltages corresponding to the current changes are calculated; with consideration of inductance changes during calculation, circuit gains are quickly adjusted to resolve mains current distortion owing to big inductance changes; the present invention does not need coordinate conversions, sector judgments and directly calculates a number of conducted submodules of each arm according to a characteristic equation; and the present invention has a simple process, a small amount of calculation and an easy digital control. 
     The preferred embodiment herein disclosed is not intended to unnecessarily limit the scope of the invention. Therefore, simple modifications or variations belonging to the equivalent of the scope of the claims and the instructions disclosed herein for a patent are all within the scope of the present invention.