Abstract:
A DC power transmission system of a voltage source converter using a pulse-interleaving auxiliary circuit is disclosed. 
     The converter system of the present invention comprises an IGBT converter for converting an AC power to a DC power or the DC power to the AC power; an open Y-Y transformer and a Y-Δ transformer for stepping up or stepping down the AC power having a predetermined magnitude; a capacitor for dividing a DC voltage; and a transformer and a half-bridge auxiliary circuit for overlapping a pulse type input voltage to increase a number of pulses of an output waveform. 
     In accordance with the present invention, the normal transformer is used instead of a tapped transformer to reduce the size thereof and to obtain an accurate transformer ratio, the 3-level half bridge is used instead of the H-bridge to reduce the switching loss in order to increase the number of pulses of the output waveform by superposing the voltage in the form of the pulse using the auxiliary transformer and the bridge circuit.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to a DC power transmission system, and in particular to a DC power transmission system using a voltage source converter with a pulse-interleaving auxiliary circuit comprising a transformer and a 3-level half bridge. 
         [0003]    2. Description of Prior Art 
         [0004]    Generally, an AC voltage and an AC current being outputted from a generator has a low voltage and a high current. The AC voltage and the AC current are subjected to a long distance power transmission in a form of a low current while maintaining a high voltage using a high voltage transformer or a ultra-high voltage transformer due to a conductor loss by the high current during the power transmission. However, the AC power transmission has a limitation in the long distance power transmission due to an inductance in the power transmission line and a capacitance between a power transmission line and a ground. In order to overcome the above-described limitation, a current source converter for converting AC to DC employing a thyristor having a large capacity was developed, thereby allowing a DC transmission. 
         [0005]    Of the above-described DC power transmission, a high-voltage DC (HVDC) transmission system that provides power by converting an AC power generated in a power plant to a DC power to be transmitted and converting back the DC power to the AC power at a receiving point has been widely used. The HVDC transmission system allows an economical power transmission through a step-up of a voltage, which is an advantage of a conventional AC power transmission technology and is also overcoming disadvantages of the conventional AC power transmission technology. 
         [0006]    The HVDC system employing thyristor, which has no turn-off capability at the gate, consumes reactive power from the interconnected AC system when it operates. A HVDC system using a voltage source converter, which employs semiconductor switches with gate turn-off capability such as GTO (Gate Turn-Off thyristor) or IGBT (Insulated Gate Bipolar Transistor), does not need reactive-power compensation. On the other hand, it has a capability to compensate the reactive power required in the interconnected AC system. 
         [0007]    A voltage source converter used in the HVDC transmission system includes a PWM converter wherein each of switching elements that constitute a single bridge is operated in a PWM mode and a multi-pulse converter that generates an output waveform by combining two or more bridges using transformers. 
         [0008]    While the PWM converter has a simple system configuration using the single bridge, a switching loss is large due to multiple switching of each of the switching elements per one AC cycle. Therefore, the PWM converter is not suitable for a large capacity system. 
         [0009]    Moreover, while the multi-pulse converter has a small switching loss due to a single switching per AC cycle, a number of pulses should be increased in order to reduce a harmonic level of the output waveform. Therefore, various schemes are used to increase the number of the pulses of the output waveform. The simplest scheme thereof is to increase a number of the bridges of the converter and a number of the transformers coupled to an AC output terminal to increase the number of the pulses. However, this scheme is disadvantageous in that a size of the system is large and a manufacturing cost is high due to the increase in the number of the bridges and the transformers. In order to overcome the disadvantage, an auxiliary transformer is employed between the transformer and the bridge to maintain the number of the main transformers while increasing the number of the pulses. However, a connection structure of the auxiliary transformer is complex so that a manufacturing process thereof is complicated and a reduction of the manufacturing cost is low. 
         [0010]    Therefore, a method wherein an auxiliary circuit is inserted at a DC stage to superpose a voltage in a form of the pulse on a voltage applied to a DC capacitor to generate the output waveform.  FIG. 1  is a diagram illustrating a conventional multi-pulse DC power transmission system disclosed in Korean Patent No. 10-034614. 
         [0011]    The system shown in  FIG. 1  comprises a multi-winding transformer  1  having a primary winding connected between a connection point of a ground terminal of a first converter  13  and an output terminal of a second converter  11  and a connection point of an output terminal of the first converter  13  and a ground terminal of the second converter  11  so that a difference of output voltages of the first converter  13  and the second converter  11 , first and second reactors  9  for rectifying first and second currents connected to one terminal of the multi-winding transformer  1  and output terminals of the second converter  11  and the first converter  13 , first and second DC dividing condensers  8 , and a plurality of thyristors  2  and  3  respectively connected to a second terminal of the multi-winding transformer  1  wherein one of the plurality of the thyristors become conductive by a rising edge pulse of a primary voltage thereof. The system is manufactured to operate identical to a 24-pulse thyristor HVDC system. 
         [0012]      FIG. 2  is a diagram illustrating another conventional 36-step converter using a DC auxiliary circuit. 
         [0013]    The conventional 36-step converter shown in  FIG. 2  is a 36-step converter including an auxiliary circuit consisting of a H-bridge and a tapped transformer, and a 12-step converter wherein a voltage generated by combining a voltage of a DC capacitor and a voltage formed by the H-bridge and the tapped transformer is provided to each 6-step bridge. An output voltage generated at each of the 6-step bridges is combined by a three-phase transformer so as to output an output waveform of 36-step. 
         [0014]    However, the conventional arts shown in  FIGS. 1 and 2  requires a special design and a manufacturing process compared to a normal transformer since the tapped transformer has the large size and a voltage ratio cannot be accurately matched. Moreover, when an inaccuracy of a winding ratio of the tapped transformer results in a lack of a symmetry of the output voltage waveform, thereby generating a harmonic. 
         [0015]    On the other hand, the HVDC system may be classified into a point-to-point system which is a DC link type consisting of a cable or an over-head line or a combination thereof, and a back-to-back system wherein the rectifier and an inverter are placed in a converter station. Since the back-to-back system is used to connect two AC systems having different frequencies or connecting a large scale wind power generation plant to a power system, the back-to-back system should be capable of independently controlling effective/reactive powers of the two connected AC systems and of controlling a bi-directional power flow. While a magnitude and a phase of an AC output voltage may be independently controlled and the effective/reactive powers may also be independently controlled when the voltage source converter operates in the PWM mode, the switching loss is generated when the PWM mode is applied in case of a large capacity voltage source system. 
       SUMMARY OF THE INVENTION 
       [0016]    It is an object of the present invention to provide a converter system wherein a normal transformer and a 3-level half bridge are used instead of a tapped transformer and a full bridge respectively, and a back-to-back converter system having the converter system applied thereto so that effective and reactive powers of an AC system interconnected to the system are independently controlled. 
         [0017]    In order to achieve the above-described objects of the present invention, there is provided a converter system comprising: an IGBT converter for converting an AC power to a DC power or the DC power to the AC power; an open Y-Y transformer and a Y-Δ transformer for stepping up or stepping down the AC power having a predetermined magnitude; a capacitor for dividing a DC voltage; and a transformer and a half-bridge auxiliary circuit for overlapping a pulse type input voltage to increase a number of pulses of an output waveform. 
         [0018]    The IGBT converter comprises a first converter connected to the Y-Y transformer and a second converter connected to the Y-Δ transformer, and wherein the capacitor comprises a first DC capacitor connected to a primary side terminal of a transformer of the half-bridge auxiliary circuit and an output terminal of the first converter, and a second DC capacitor connected to the primary side terminal of the transformer of the half-bridge auxiliary circuit and a ground terminal of the second converter. 
         [0019]    In addition, a half-bridge of the half-bridge auxiliary circuit comprises a 3-level half-bridge consisting of first through fourth switching element connected to the first DC capacitor and the second DC capacitor in parallel using an IGBT. 
         [0020]    Preferably, the transformer of the half-bridge auxiliary circuit comprises a primary side coil and a secondary side coil, the primary side coil being connected between a point where a ground terminal of the first converter and an output terminal of the second terminal are connected and a point where the output terminal of the first converter and the ground terminal of the second converter are connected, and the secondary side coil being connected to the half-bridge such that a difference of output voltages are provided, and wherein the half-bridge of the half-bridge auxiliary circuit comprises a first clamping diode and a second clamping diode, the first clamping diode being connected between a connection point of the first and the second switching elements and a connection point of a second terminal of the primary side coil and a first terminal of the secondary side coil, and the second clamping diode being connected between a connection point of the third and the fourth switching elements and the connection point of the second terminal of the primary side coil and the first terminal of the secondary side coil, whereby a 36-step waveform output voltage is obtained according to a level of a voltage inputted to the transformer of the half-bridge auxiliary circuit. 
         [0021]    In order to achieve the above-described objects of the present invention, there is provided a DC transmission system comprising a back-to-back converter wherein the back-to-back converter includes two of the 36-step converter systems, the two of the 36-step converter systems being connected to an AC voltage side in serial and connected to a DC voltage side in parallel. 
     
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0022]      FIG. 1  is a diagram illustrating a conventional multi-pulse DC power transmission system disclosed in Korean Patent No. 10-034614. 
           [0023]      FIG. 2  is a diagram illustrating a conventional 36-step converter using a DC auxiliary circuit. 
           [0024]      FIG. 3  is a schematic diagram illustrating a back-to-back system. 
           [0025]      FIG. 4  is a diagram illustrating a 36-step converter using a DC auxiliary circuit in accordance with the present invention. 
           [0026]      FIG. 5  is a graph illustrating a result of a simulation of an operation of a 36-step converter using a PSCAD/EMTDC software in accordance with the present invention. 
           [0027]      FIG. 6  is a graph illustrating a result of an experiment according to circuit parameters of table 1 using a DSP TMS320VC33 for a control of entire system and a generation of a gate pulse in order to verify an operation and a performance of a 36-step converter in accordance with the present invention. 
           [0028]      FIG. 7  is a diagram schematically illustrating a back-to-back HVDC system in accordance with the present invention. 
           [0029]      FIG. 8   a  illustrates a single-phase equivalent circuit of the back-to-back HVDC system of  FIG. 7  in accordance with the present invention, and  FIG. 8   b  illustrates a vector diagram illustrating a source voltage, an output voltage of each converter, and a resulting output voltage of the converter, when the upper and lower firing angles of a voltage source converter. 
           [0030]      FIG. 9  is a graph illustrating a variation of α 1  and α 2  with respect to P of table 2 as a function of Q. 
           [0031]      FIG. 10  is a block diagram illustrating a configuration of a controller of each converter. 
           [0032]      FIG. 11  is a graph illustrating a result of a simulation for verifying an operation of an entire system in accordance with the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0033]    The present invention will now be described in detail with reference to the accompanied drawings. 
         [0034]      FIG. 4  is a diagram illustrating a 36-step converter system using a DC auxiliary circuit in accordance with the present invention. 
         [0035]    The 36-step converter system shown in  FIG. 4  comprises a first converter  110  connected to a Y-Y transformer  160 , a second converter  120  connected to a Y-Δ transformer  170 , an injection transformer  130 , first and second DC capacitors  140  and  140 ′, and a 3-level half bridge circuit  150 . 
         [0036]    A ground terminal of the first converter  110  and an output terminal of the second converter  120  are connected to a first terminal of a primary winding of the injection transformer  130 , and a connecting point of the first and second DC capacitors  140  and  140 ′ serially connected between an output terminal of the first converter  110  and a ground terminal of the second converter  120  is connected to a second terminal of the primary winding of the injection transformer  130 . 
         [0037]    A first terminal of a secondary winding of the injection transformer  130  is simultaneously connected to the second terminal of the primary winding of the injection transformer  130  and the 3-level half bridge circuit  150 , and a second terminal of the secondary winding of the injection transformer  130  is connected to the 3-level half bridge circuit  150 . 
         [0038]    The 3-level half bridge circuit  150  comprises first through fourth switching elements S 1 , S 2 , S 1 ′ and S 2 ′, using an IGBT for instance, connected to the first and second DC capacitors in parallel, and a clamping diode D 1  connected between a connection point of the first and second switching elements S 1  and S 2  and a connection point of the second terminal of the primary winding and the first terminal of the secondary winding of the injection transformer  130 , and a clamping diode D 2  connected between a connection point of the third and fourth switching elements S 1 ′ and S 2 ′ and a connection point of the second terminal of the primary winding and the first terminal of the secondary winding of the injection transformer  130 . 
         [0039]    A characteristic of the converter described above will be described in detail below. 
         [0040]    When a bridge of the first and second converters  110  and  120  is assumed to be ideal, voltages of the first and second DC capacitors  140  and  140 ′ of upper and lower bridges are the same. Therefore, DC voltages of the first converter  110  connected to the Y-Y transformer  160  and the second converter  120  connected to the Y-Δ transformer  170  of  FIG. 4  may be expressed as equations 1 and 2 where V dc /2 is the voltage of the first and second DC capacitors  140  and  140 ′ and V aux  is an injection voltage of the 3-level half bridge circuit  150 . 
         [0000]        V   Y   =V   dc /2 +V   aux   [Equation 1] 
         [0000]        V   Δ   =V   dc /2 −V   aux   [Equation 2] 
         [0041]    An output AC voltage of each converter from above equations may be controlled simultaneously by the injection voltage V aux . On the other hand, the injection voltage V aux  is determined by a switching pattern of the 3-level half bridge circuit  150  and a winding ratio of the injection transformer  130 . Therefore, the injection voltage V aux  may have three levels of zero, k*V dc , −k*V dc , where k is the winding ratio of the injection transformer  130 . 
         [0042]    Two converter systems connected to the Y-Y transformer  160  and the Y-Δ transformer  170  shown in  FIG. 4  generate 12 steps by making a phase voltage of an AC side to have a phase difference of 30°, and the injection voltage V aux  forms a step corresponding to a frequency six times larger than a fundamental frequency since the 3-level half bridge circuit  150  operates at every 30°. The winding ratio k of the injection transformer  130  used in the 3-level half bridge circuit  150  should be determined such that a harmonic of an output voltage waveform is minimized. 
         [0043]      FIG. 5  is a graph illustrating a result of a simulation of an operation of a 36-step converter using a PSCAD/EMTDC software in accordance with the present invention. 
         [0044]      FIG. 5   a  illustrates a voltage injected through the transformer from the 3-level half bridge circuit  150 ,  FIG. 5   b  illustrates an A-phase voltage V YA  of an upper bridge of the first converter  110 , and  FIG. 5   c  illustrates an A-phase voltage V ΔA  of a lower bridge of the second converter  120 . In accordance with the present invention, a 36-step waveform shown in  FIG. 5   d  is obtained by combining a waveform of the upper bridge of  FIG. 5   b  and a waveform of the lower bridge of  FIG. 5   c.    
         [0045]    The multi-step output voltages V YA  and V ΔA  may be expresses as equations 3 and 4 using a Fourier series. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       V 
                       YA 
                     
                      
                     
                       ( 
                       
                         ω 
                          
                         
                             
                         
                          
                         t 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         1 
                       
                       ∞ 
                     
                      
                     
                         
                     
                      
                     
                       
                         4 
                         3 
                       
                        
                       
                         
                           cos 
                           2 
                         
                          
                         
                           ( 
                           
                             
                               n 
                                
                               
                                   
                               
                                
                               π 
                             
                             6 
                           
                           ) 
                         
                       
                        
                       
                         b 
                         n 
                       
                        
                       
                         V 
                         dc 
                       
                        
                       
                         sin 
                          
                         
                           ( 
                           
                             n 
                              
                             
                                 
                             
                              
                             ω 
                              
                             
                                 
                             
                              
                             t 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       
                         V 
                         
                           Δ 
                            
                           
                               
                           
                            
                           A 
                         
                       
                        
                       
                         ( 
                         
                           ω 
                            
                           
                               
                           
                            
                           t 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           1 
                         
                         ∞ 
                       
                        
                       
                           
                       
                        
                       
                         
                           2 
                           
                             3 
                           
                         
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 π 
                               
                               6 
                             
                             ) 
                           
                         
                          
                         
                           b 
                           n 
                         
                          
                         
                           V 
                           dc 
                         
                          
                         
                           sin 
                            
                           
                             ( 
                             
                               n 
                                
                               
                                   
                               
                                
                               ω 
                                
                               
                                   
                               
                                
                               t 
                             
                             ) 
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     
                       where 
                        
                       
                           
                       
                        
                       
                         b 
                         n 
                       
                     
                     = 
                     
                       
                         
                           [ 
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               n 
                             
                           
                           ] 
                         
                         
                           n 
                            
                           
                               
                           
                            
                           π 
                         
                       
                        
                       
                         { 
                         
                           1 
                           + 
                           
                             k 
                              
                             
                               [ 
                               
                                 
                                   8 
                                    
                                   
                                       
                                   
                                    
                                   sin 
                                    
                                   
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       π 
                                     
                                     6 
                                   
                                    
                                   sin 
                                    
                                   
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       π 
                                     
                                     12 
                                   
                                    
                                   cos 
                                    
                                   
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       π 
                                     
                                     36 
                                   
                                 
                                 - 
                                 1 
                               
                               ] 
                             
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
         [0046]    An AC voltage V A (ωt) of a primary winding of the transformer is a sum of V YA (ωt) and V ΔA (ωt). Therefore, a total RMS value of an output phase voltage is expressed as equation 5. 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     ARMS 
                   
                   = 
                   
                     
                       
                         V 
                         dc 
                       
                       9 
                     
                      
                     
                       
                         36 
                         + 
                         
                           15 
                            
                           
                             3 
                           
                         
                         + 
                         
                           
                             ( 
                             
                               24 
                               - 
                               
                                 12 
                                  
                                 
                                   3 
                                 
                               
                             
                             ) 
                           
                            
                           
                             k 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
         [0047]    A fundamental wave peak value is expressed as equation 6. 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     
                       A 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   = 
                   
                     
                       
                         4 
                          
                         
                             
                         
                          
                         
                           V 
                           dc 
                         
                       
                       π 
                     
                      
                     
                       [ 
                       
                         1 
                         + 
                         
                           
                             ( 
                             
                               
                                 4 
                                  
                                 
                                     
                                 
                                  
                                 cos 
                                  
                                 
                                   π 
                                   36 
                                 
                                  
                                 sin 
                                  
                                 
                                   π 
                                   12 
                                 
                               
                               - 
                               1 
                             
                             ) 
                           
                            
                           k 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
         [0048]    Therefore, a THD v  of the output phase voltage is expressed as equation 7. 
         [0000]    
       
         
           
             
               
                 
                   
                     THD 
                     v 
                   
                   = 
                   
                     
                       
                         
                           2 
                            
                           
                             V 
                             ARMS 
                             2 
                           
                         
                         
                           V 
                           
                             A 
                              
                             
                                 
                             
                              
                             1 
                           
                           2 
                         
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
         [0049]    The winding ratio k of the injection transformer is determined by 
         [0000]    
       
         
           
             k 
             = 
             
               
                 1.5 
                  
                 
                   ( 
                   
                     7 
                     + 
                     
                       4 
                        
                       
                         3 
                       
                     
                   
                   ) 
                 
                  
                 
                   ( 
                   
                     
                       4 
                        
                       
                           
                       
                        
                       cos 
                        
                       
                         π 
                         36 
                       
                        
                       sin 
                        
                       
                         π 
                         12 
                       
                     
                     - 
                     1 
                   
                   ) 
                 
               
               ≈ 
               0.6547 
             
           
         
       
     
         [0000]    at a minimum value of 5.09% of THD v , which is about 0.6547. 
         [0050]      FIG. 6  is a graph illustrating a result of an experiment according to circuit parameters of table 1 using a DSP TMS320VC33 for a control of entire system and a generation of a gate pulse in order to verify an operation and a performance of a 36-step converter in accordance with the present invention. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 Source Voltage 
                 3Φ 220 V 
               
               
                   
                 Frequency 
                 60 Hz 
               
               
                   
                 Source Inductance 
                 2 mH 
               
               
                   
                 Power Factor 
                 0.73 
               
               
                   
                 Load (R, L) 
                 20 Ω, 50 mH 
               
               
                   
                 Load Capacity 
                 2 kVA 
               
               
                   
                   
               
             
          
         
       
     
         [0051]      FIG. 6   a  illustrates a waveform of an injection voltage of the 3-level half bridge circuit  150 ,  FIG. 6   b  illustrates a waveform of the A-phase voltage V YA  of the upper bridge of the first converter  110 , and  FIG. 6   c  illustrates a waveform of the A-phase voltage V ΔA  of the lower bridge of the second converter  120 .  FIG. 6   d  illustrates a combination waveform of the waveform of the A-phase voltage V YA  of the upper bridge of the first converter  110  and the waveform of the A-phase voltage V ΔA  of the lower bridge of the second converter  120 . 
         [0052]    As shown in waveforms of  FIG. 6 , the entire voltage waveform is very similar to the wave forms of the simulation, and the entire waveform of the output voltage of the converter is close to a sinusoidal wave in spite of a small irregularity. 
         [0053]      FIG. 7  is a diagram schematically illustrating a back-to-back HVDC system in accordance with the present invention. 
         [0054]    As shown in  FIG. 7 , in accordance with the present invention, a back-to-back converter comprising two 36-step converter wherein the AC side thereof is connected in serial and a DC side thereof is connected in parallel. 
         [0055]      FIG. 8   a  illustrates a single-phase equivalent circuit of the back-to-back HVDC system of  FIG. 7  in accordance with the present invention. The back-to-back converter  200  independently controls effective/reactive powers of an interconnected AC system by operating a firing angle α 1  of an upper converter  210  and a firing angle α 2  of a lower converter  220  differently. 
         [0056]      FIG. 8   b  illustrates a vector diagram illustrating a source voltage, a voltage of each converter, and a total voltage of the converter when the upper and lower firing angles of the voltage source converter are different. As shown in  FIG. 8   b , when the firing angle α 1  of the upper converter  210  and the firing angle α 2  of the lower converter  220  are properly adjusted, an output voltage vector Vc of the converter forms a power angle δ with the source voltage Vs and a magnitude thereof may be adjusted. Therefore, the upper firing angle α 1  and the lower firing angle α 2  may be adjusted in order to independently control the effective/reactive powers of the interconnected AC system. 
         [0057]    Equation related to the firing angles α 1  and α 2  may be obtained using the vector diagram of the output voltage vector Vc and the power angle δ. 
         [0058]    Since V C =V 1 +V 2 =V∠α 1 +V∠α 2  in accordance with the vector diagram, and from 
         [0000]      V C =2V cos ρ  [Equation 8] 
         [0000]      ρ=α 1 −δ=δ−α 2 , where ρ denotes an angle between Vc and V 1  or Vc and V 2   [Equation 9] 
         [0059]    δ is express as equation 10. 
         [0000]    
       
         
           
             
               
                 
                   δ 
                   = 
                   
                     
                       
                         α 
                         1 
                       
                       + 
                       
                         α 
                         2` 
                       
                     
                     2 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
         [0060]    When a maximum value of Vc assumed to be 1.15 times the Vs, Vc may be expressed as equation 11. 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     C 
                   
                   = 
                   
                     1.15 
                      
                     
                       V 
                       S 
                     
                      
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             
                               α 
                               1 
                             
                             - 
                             
                               α 
                               2` 
                             
                           
                           2 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
         [0061]    The firing angles α 1  and α 2  of the converters  210  and  220 , which are expressed in equations 12 and 13, are obtained by combining equations 10 and 11 with respect to δ and Vc. 
         [0000]    
       
         
           
             
               
                 
                   
                     α 
                     1 
                   
                   = 
                   
                     δ 
                     + 
                     
                       
                         cos 
                         
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             V 
                             C 
                           
                           
                             1.15 
                              
                             
                               V 
                               S 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     12 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     α 
                     2 
                   
                   = 
                   
                     δ 
                     - 
                     
                       
                         cos 
                         
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             V 
                             C 
                           
                           
                             1.15 
                              
                             
                               V 
                               S 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     13 
                   
                   ] 
                 
               
             
           
         
       
     
         [0062]    The effective/reactive powers in the vector diagram of  FIG. 8   b  are expressed as equations 14 and 15. 
         [0000]    
       
         
           
             
               
                 
                   P 
                   = 
                   
                     
                       3 
                        
                       
                         V 
                         C 
                       
                        
                       
                         V 
                         S 
                       
                     
                     
                       X 
                       C 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     14 
                   
                   ] 
                 
               
             
             
               
                 
                   Q 
                   = 
                   
                     
                       3 
                        
                       
                         ( 
                         
                           
                             V 
                             S 
                             2 
                           
                           - 
                           
                             
                               V 
                               C 
                             
                              
                             
                               V 
                               S 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             δ 
                           
                         
                         ) 
                       
                     
                     
                       X 
                       C 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     15 
                   
                   ] 
                 
               
             
           
         
       
     
         [0063]    By combining equations 14 and 15 with respect to effective/reactive powers and using a solution formula of a second order equation, Vc and δ may be expressed as equations 16 and 17. 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     C 
                   
                   = 
                   
                     
                       
                         
                           
                             P 
                             2 
                           
                            
                           
                             X 
                             C 
                             2 
                           
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 3 
                                  
                                 
                                   V 
                                   S 
                                   2 
                                 
                               
                               - 
                               
                                 QX 
                                 C 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         9 
                          
                         
                           V 
                           S 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     16 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     δ 
                     = 
                     
                       
                         sin 
                         
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             PX 
                             C 
                           
                           
                             3 
                              
                             
                               V 
                               S 
                             
                              
                             
                               V 
                               C 
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     
                       where 
                        
                       
                           
                       
                        
                       a 
                     
                     = 
                     
                       
                         
                           
                             V 
                             S 
                           
                           
                             X 
                             C 
                           
                         
                          
                         
                             
                         
                          
                         and 
                          
                         
                             
                         
                          
                         b 
                       
                       = 
                       
                         1 
                         
                           X 
                           C 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     17 
                   
                   ] 
                 
               
             
           
         
       
     
         [0064]    Therefore, the firing angles α 1  and α 2  for given P and Q may be determined by obtaining values of Vc and δ using equations 16 and 17, and substituting the values into equations 12 and 13. 
         [0065]    Table 2 shows the values of Vc and δ with respect to P and Q when a line-to-line voltage is assumed to be 154 kV and a coupling inductance is assumed to be 15% at the base rating of 200 MVA.  FIG. 9  is a graph illustrating a variation of α 1  and α 2  with respect to P of table 2 as a function of Q. As shown in  FIG. 9 , as the reactive power Q shifts from inductive to capacitive value, the values of α 1  and α 2  moves close to 0o axis. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 50 MW 
                 100 MW 
                 150 MW 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 −150 
                 MVar 
                 1.114Vs ∠1.93° 
                 1.120Vs ∠3.84° 
                 1.129Vs ∠5.72° 
               
               
                 −75 
                 MVar 
                 1.058Vs ∠2.03° 
                 1.064Vs ∠4.04° 
                 1.074Vs ∠6.01° 
               
               
                 0 
                 MVar 
                 1.002Vs ∠2.14° 
                 1.008Vs ∠4.27° 
                 1.019Vs ∠6.34° 
               
               
                 75 
                 MVar 
                 0.946Vs ∠2.27° 
                 0.953Vs ∠4.52° 
                 0.964Vs ∠6.70° 
               
               
                 150 
                 MVar 
                 0.890Vs ∠2.42° 
                 0.897Vs ∠4.80° 
                 0.909Vs ∠7.11° 
               
               
                   
               
             
          
         
       
     
         [0066]    As described above, the back-to-back converter  200  consisting of two 36-step converter in accordance with the present invention allows the effective/reactive powers of the interconnected AC system to be controlled independently. 
         [0067]    A system operation characteristic and a performance analysis of a controller will now be described using PSCAD/EMTDC for the embodiment of  FIG. 7  in accordance with the present invention. 
         [0068]    A power circuit in accordance with the embodiment is embodied using circuit elements, switches and transformers. The controller, which is shown in  FIG. 10 , is embodied using a built-in controller module. Table 3 shows circuit parameters used in the simulation for the embodiment. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
             
             
               
                   
                 Source Voltage 
                 3Φ 154 kV, 60 Hz 
               
               
                   
                 Source Inductance 
                 15.7 mH 
               
               
                   
                 DC capacitor 
                 1500 uF 
               
               
                   
                 Phase transformer 
                 40 kV/20 kV(Y—Y) 
               
               
                   
                   
                 40 kV/34.64 kV(Y-Δ) 
               
               
                   
                 Auxiliary transformer 
                 32.7 kV/50 kV 
               
               
                   
                 System rating 
                 200 MVA 
               
               
                   
                   
               
             
          
         
       
     
         [0069]    A voltage source HVDC system operates by adjusting a magnitude of a terminal voltage applied to both terminals of the converter for controlling the firing angles, and changing a direction of power. That is, when the power is transmitted from the converter A  200  to the converter B  300  in  FIG. 7 , the converter A constantly performs a DC voltage control and a reactive power control. When the power is transmitted from the converter B  300  to the converter A  200 , an opposite control scheme is performed. Therefore, the controller of each converter has an identical configuration as shown in  FIG. 10 . 
         [0070]    When the converter A  200  transmits the power to the converter B  300 , a measured value of DC voltage v dc  follows a reference value v dc *. A reference value of an effective current I dA * is obtained from a measured value of an effective current I dB  in the converter B. Measured values of a reactive current I qA  and an effective current I dB  follow a reference value I qA * and I dB * through a control algorithm. An AC current controller has an identical configuration to that of the converter generally used in the controller. Reference values of a d-q transformed AC system voltage v dA * and v qA * are used to determine the values of V C  and δ. The values of α 1  and α 2  are obtained from V C  and δ using the relationship described in equations 12 and 13. 
         [0071]    Table 4 shows a simulation scenario used in an operation analysis of the back-to-back converter in accordance with the present invention. 
         [0000]    
       
         
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
             
             
               
                   
                   
               
               
                   
                 Mode 
               
             
          
           
               
                   
                 M1 
                 M2 
                 M3 
                 M4 
                 M5 
                 M6 
                 M7 
                 M8 
                 M9 
               
               
                   
                   
               
             
          
           
               
                 Time(sec) 
                 0.5~1.0 
                 1.0~1.5 
                 1.5~2.0 
                 2.0~2.5 
                 2.5~3.0 
                 3.0~3.5 
                 3.5~4.0 
                 4.0~4.5 
                 4.5~5.0 
               
             
          
           
               
                 Vdc*[kV] 
                 60 
               
             
          
           
               
                 idA*[A] 
                 Vdc control 
                 330 
                 660 
               
               
                 iqA*[A] 
                 0 
                 −500 
                 500 
               
             
          
           
               
                 idB*[A] 
                 0 
                 330 
                 330 
                 660 
                 660 
                 990 
                 990 
                 Vdc control 
               
               
                 iqB*[A] 
                 0 
                 −950 
                 950 
                 950 
                 −500 
                 −500 
                 500 
                 0 
               
             
          
           
               
                 PA[MW] 
                 0 
                 −50 
                 −50 
                 −100 
                 −100 
                 −150 
                 −150 
                 50 
                 100 
               
             
          
           
               
                 QA[Mvar] 
                 0 
                 −75 
                 75 
               
             
          
           
               
                 PB[MW] 
                 0 
                 50 
                 50 
                 100 
                 100 
                 150 
                 150 
                 −50 
                 −100 
               
             
          
           
               
                 QB[Mvar] 
                 0 
                 −150 
                 150 
                 150 
                 −75 
                 −75 
                 75 
                 0 
               
               
                   
               
             
          
         
       
     
         [0072]    The controller is in operation in 0.5 sec after the simulation starts. It is assumed that the direction of the power is from the system A  200  to the system B  300  between 0.5 sec and 4.0 sec, and the direction is changed from the system B  300  to the system A  200  at 4.0 sec. In addition, the reference values of effective and reactive power are varied according to each of the operation modes from M 1  to M 9  shown in Table 4 in order to analyze a control performance of the effective and reactive powers. 
         [0073]      FIGS. 11   a  through  11   g  illustrate a result of the simulation for verifying the operation of the entire system in accordance with the present invention. 
         [0074]    The controllers of the system A  200  and the system B  300  have the same structure, and the control parameters have same values with opposite sign.  FIG. 11   a  shows variations of the power angle δ, the upper firing angle α 1  and the lower firing angle α 2  of the output voltage of the converter A  200 , while  FIG. 11   b  shows variations of the power angle δ, the upper firing angle α 1  and the lower firing angle α 2  of the output voltage of the converter B  300 . The values of α 1  and α 2  correspond with those shown in  FIG. 9  and the value of δ corresponds to that shown in Table 2. 
         [0075]      FIG. 11   c  shows a variation of an RMS value of the output voltage and a superposed output voltage of the converter A  200 , and  FIG. 11   d  shows a variation of an RMS value of the output voltage and a superposed output voltage of the converter B  300 . The value of Vc, which is a vector sum of V 1  and V 2 , corresponds with that of Table 2.  FIG. 11   e  shows the control performance of a DC link voltage. The DC link voltage is initially charged to 60 kV so that the system may be in operation at 0.5 sec. A measured value of DC link voltage tracks a reference value of 60 kV without excessive transients.  FIG. 11   f  shows a variation of the effective and reactive powers transmitted from the converter B  300  to the AC system B. It is verified that the effective and reactive powers to the system B may be independently controlled.  FIG. 11   g  shows a variation of the effective and reactive powers transmitted from the AC system A to the converter A  200 . The value of the effective power is the same as that of  FIG. 11   f , while the reactive power has a different value since each controller carries out the independent control. Therefore, it may be verified that the DC transmission system in accordance with the present invention is capable of the independent control for the effective and reactive powers. 
         [0076]    While the DC transmission system in accordance with the present invention has been particularly shown and described with reference to the preferred embodiment thereof, it will be understood by those skilled in the art that various changes in form and details may be effected therein without departing from the spirit and scope of the invention. 
         [0077]    As described above, in accordance with the present invention, the normal transformer is used instead of a tapped transformer to reduce the size thereof and to obtain an accurate transformer ratio, the 3-level half bridge is used instead of the H-bridge to reduce the switching loss in order to increase the number of pulses of the output waveform by superposing the voltage in the form of the pulse using the auxiliary transformer and the bridge circuit. 
         [0078]    Moreover, the back-to-back converter system consisting of two 36-step converters allows the independent control of the effective and reactive powers of the connected AC systems.