Patent Publication Number: US-10770978-B2

Title: DC power supply from a constant current source

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Patent Application No. 62/647,509 entitled “DC POWER SUPPLY FROM A CONSTANT CURRENT SOURCE” and filed on Mar. 23, 2018 for Hongjie Wang et al., which is incorporated herein by reference for all purposes. 
    
    
     FIELD 
     This invention relates to direct current (“DC”)-DC power supplies and more particularly relates to a DC-DC power supply fed by a constant current source and regulating output current. 
     BACKGROUND 
     Resonant converters are widely applied in various applications such as Uninterrupted Power Systems (“UPSs”), DC distribution systems and wireless power transfer (“WPT”) systems for high efficiency and low electromagnetic interference (“EMI”). In a variety of industrial applications, including LED drivers, battery charging and capacitor charging, output current regulated power supplies are often used. 
     Most of the research in the literature focuses on constant voltage input to resonant converters. However, LCL (inductor-capacitor-inductor) resonant network can be employed in a WPT system to generate a constant current running through the primary track, irresponsive to the change of the load. LCCL (inductor-capacitor-capacitor-inductor) resonant networks can provide a higher maximum track current compared to the LCL topology. The LCL-T resonant converter behaves as a current-source under certain operating condition. However, in some applications, such as underwater telecommunication and undersea observation system, a constant DC current distribution from the shore is preferred over DC voltage distribution for its robustness against cable impedance and faults. 
     SUMMARY 
     A power supply includes an active bridge section with input terminals that receive power from a constant current source where the active bridge section operates at a fixed switching frequency. The power supply includes a resonant section with a resonant inductor and a resonant capacitor. The resonant section is connected to an output of the active bridge section. The power supply includes an output rectifier that receives power from the resonant section and comprising output terminals for connection to a load and a controller that regulates output current to the load where the controller regulates output current to the load by controlling switching of the active bridge section. The fixed switching frequency of the active bridge section matches a resonant frequency of the resonant section. 
     Another embodiment of a power supply includes an active bridge section with input terminals that receive power from a constant current source, a resonant section with a resonant inductor and a resonant capacitor where the resonant section is connected to an output of the active bridge section and an output rectifier that receives power from the resonant section and with output terminals for connection to a load. The power supply includes a controller that regulates output current to the load. The power supply includes a bypass branch connected in parallel with the input terminals where the bypass branch shunts current from the constant current source through the bypass branch when the bypass branch is active, a resonant capacitor voltage clamping circuit that clamps voltage across the resonant capacitor to a voltage less than a maximum voltage rating of the resonant capacitor during a transient condition, and a current limiting circuit connected in series between an output terminal of the output rectifier and the load. The current limiting circuit increases a resistance across the current limiting circuit in response to output current to the load increasing above an output current limit. 
     A controller of a power supply includes an output current regulation feedback loop that regulates output current of the power supply to a load. The controller regulates output current to the load by controlling switching of an active bridge section of the power supply. The power supply includes a resonant section with a resonant inductor and a resonant capacitor. The resonant section is connected to an output of the active bridge section. The power supply includes the active bridge section with input terminals that receive power from to a constant current source. The active bridge section operates at a fixed switching frequency. The power supply includes an output rectifier that receives power from the resonant section and the output rectifier includes output terminals for connection to the load. The fixed switching frequency of the active bridge section matches a resonant frequency of the resonant section. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In order that the advantages of the invention will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings, in which: 
         FIG. 1  is a schematic block diagram illustrating one embodiment of a system with DC-DC converters and a constant current source; 
         FIG. 2  is a schematic block diagram illustrating one embodiment of a power supply that regulates output current and is fed by a constant current source; 
         FIG. 3A  is a schematic block diagram illustrating one embodiment of a series resonant converter (“SRC”) with a full-bridge switching section that regulates output current and is fed by a constant current source; 
         FIG. 3B  is a schematic block diagram illustrating one embodiment of a SRC with a half-bridge switching section and that regulates output current and is fed by a constant current source; 
         FIG. 4  is a schematic block diagram illustrating one embodiment of a SRC with a full-bridge switching section and that regulates output current and is fed by a constant current source and includes protection features; 
         FIG. 5  is an ideal waveform diagram demonstrating a phase shift angle; 
         FIG. 6  is a schematic block diagram illustrating an equivalent circuit diagram of the SRC topology; 
         FIG. 7  is a waveform diagram demonstrating minimum converter gain M I_min  versus normalized switching frequency F for different quality factor Q values with a transformer turns ratio of n=2; and 
         FIG. 8  is a schematic block diagram illustrating one embodiment of a SRC with a full-bridge switching section and that regulates output current and is fed by a constant current source and includes another embodiment of a resonant capacitor voltage clipping circuit. 
     
    
    
     DETAILED DESCRIPTION 
     Reference throughout this specification to “one embodiment,” “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment, but mean “one or more but not all embodiments” unless expressly specified otherwise. The terms “including,” “comprising,” “having,” and variations thereof mean “including but not limited to” unless expressly specified otherwise. An enumerated listing of items does not imply that any or all of the items are mutually exclusive and/or mutually inclusive, unless expressly specified otherwise. The terms “a,” “an,” and “the” also refer to “one or more” unless expressly specified otherwise. 
     Furthermore, the described features, structures, or characteristics of the invention may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided, such as examples of programming, software modules, user selections, network transactions, database queries, database structures, hardware modules, hardware circuits, hardware chips, etc., to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention. 
     A power supply includes an active bridge section with input terminals that receive power from a constant current source where the active bridge section operates at a fixed switching frequency. The power supply includes a resonant section with a resonant inductor and a resonant capacitor. The resonant section is connected to an output of the active bridge section. The power supply includes an output rectifier that receives power from the resonant section and includes output terminals for connection to a load and a controller that regulates output current to the load where the controller regulates output current to the load by controlling switching of the active bridge section. The fixed switching frequency of the active bridge section matches a resonant frequency of the resonant section. 
     In some embodiments, the controller regulates output current to the load as a function of current gain from the output current to current from the constant current source by controlling switching of the active bridge section as a single control variable over a range from a minimum load condition to a full load condition. In a further embodiment, the active bridge section is a full active bridge, the output rectifier is a diode half-bridge voltage doubler and the power supply includes a transformer between the resonant section and the output rectifier. The controller regulates the current gain as a function of a single control variable of a phase shift angle between switching in a first leg of the active bridge section and a second leg in the active bridge section. In a further embodiment, the controller regulates the current gain according to the equation: 
               M   I     =         I   out     I     =     1     2   ⁢   n   ⁢           ⁢     sin   ⁡     (     α   2     )                   
where M I  is the current gain, I out  is the output current, I is the current from the constant current source, n is a turns ratio of the transformer and α is the phase shift angle. In another further embodiment, the active bridge section is a half-bridge and the controller regulates the current gain as a function of a single control variable of a duty cycle of switches of the active bridge section.
 
     In some embodiments, the power supply includes a bypass branch connected in parallel with the input terminals, where the bypass branch shunts current from the constant current source through the bypass branch when the bypass branch is active. In other embodiments, the bypass branch includes a sensing resistor in series with a shunt switch that is a transistor. The controller operates the shunt switch in an active region of the transistor to shunt current from the constant current source in a range between zero current and a full current of the constant current source and the shunt switch is operable to shunt a portion of the current of the constant current source. 
     In some embodiments, the power supply includes a resonant capacitor voltage clamping circuit that clamps voltage across the resonant capacitor to a voltage less than a maximum voltage rating of the resonant capacitor during a transient condition. In other embodiments, the resonant capacitor voltage clamping circuit includes a diode full-bridge rectifier with an input of the diode full-bridge rectifier connected across the resonant capacitor and an output of the diode full-bridge rectifier connected in parallel with a clamping capacitor and connected in parallel with a bleeder resistor. During steady-state operation, voltage across the clamping capacitor is higher than a voltage rating of the resonant capacitor. 
     In some embodiments, the power supply includes a current limiting circuit connected in series between an output terminal of the output rectifier and the load where the current limiting circuit increases a resistance across the current limiting circuit in response to output current to the load increasing above an output current limit. In other embodiments, the current limiting circuit includes a current limiting switch in series with a sensing resistor. The current limiting switch is a transistor and voltage across the sensing resistor is connected to a control terminal of the transistor and a voltage level across the sensing resistor activates an active region of the transistor and a current increase in the sensing resistor increases a resistance across the transistor. 
     Another embodiment of a power supply includes an active bridge section with input terminals that receive power from a constant current source, a resonant section with a resonant inductor and a resonant capacitor where the resonant section is connected to an output of the active bridge section and an output rectifier that receives power from the resonant section and comprising output terminals for connection to a load. The power supply includes a controller that regulates output current to the load. The power supply includes a bypass branch connected in parallel with the input terminals where the bypass branch shunts current from the constant current source through the bypass branch when the bypass branch is active, a resonant capacitor voltage clamping circuit that clamps voltage across the resonant capacitor to a voltage less than a maximum voltage rating of the resonant capacitor during a transient condition, and a current limiting circuit connected in series between an output terminal of the output rectifier and the load. The current limiting circuit increases a resistance across the current limiting circuit in response to output current to the load increasing above an output current limit. 
     In some embodiments, the active bridge section operates at a fixed switching frequency and the controller regulates output current to the load by controlling switching of the active bridge section. The fixed switching frequency of the active bridge section matches a resonant frequency of the resonant section. In another embodiment, the controller regulates output current to the load as a function of current gain from the output current to current from the constant current source by controlling switching of the active bridge section as a single control variable over a range from a minimum load condition to a full load condition. In other embodiments, the active bridge section is a full active bridge, the output rectifier is a diode half-bridge voltage doubler and the power supply includes a transformer between the resonant section and the output rectifier. The controller regulates the current gain as a function of a single control variable of a phase shift angle between switching in a first leg of the active bridge section and a second leg in the active bridge section. 
     In some embodiments, the bypass branch includes a sensing resistor in series with a shunt switch that is a transistor and the controller operates the shunt switch in an active region of the transistor to shunt current from the constant current source in a range between zero current and a full current of the constant current source. The shunt switch is operable to shunt a portion of the current of the constant current source. In other embodiments, the resonant capacitor voltage clamping circuit includes a diode full-bridge rectifier with an input of the diode full-bridge rectifier connected across the resonant capacitor and an output of the diode full-bridge rectifier connected in parallel with a clamping capacitor and connected in parallel with a bleeder resistor. During steady-state operation voltage across the clamping capacitor is higher than a voltage rating of the resonant capacitor. In other embodiments, the current limiting circuit includes a current limiting switch in series with a sensing resistor, where the current limiting switch is a transistor. Voltage across the sensing resistor is connected to a control terminal of the transistor and a voltage level across the sensing resistor activates an active region of the transistor and a current increase in the sensing resistor increases a resistance across the transistor. 
     A controller of a power supply includes an output current regulation feedback loop that regulates output current of the power supply to a load. The controller regulates output current to the load by controlling switching of an active bridge section of the power supply. The power supply includes a resonant section with a resonant inductor and a resonant capacitor. The resonant section is connected to an output of the active bridge section. The power supply includes the active bridge section with input terminals that receive power from to a constant current source. The active bridge section operates at a fixed switching frequency. The power supply includes an output rectifier that receives power from the resonant section and the output rectifier includes output terminals for connection to the load. The fixed switching frequency of the active bridge section matches a resonant frequency of the resonant section. 
     In some embodiments, the power supply includes a bypass branch connected in parallel with the input terminals where the bypass branch shunts current from the constant current source through the bypass branch when the bypass branch is active. In other embodiments, the power supply includes a resonant capacitor voltage clamping circuit that clamps voltage across the resonant capacitor to a voltage less than a maximum voltage rating of the resonant capacitor during a transient condition, and a current limiting circuit connected in series between an output terminal of the output rectifier and the load. The current limiting circuit increases a resistance across the current limiting circuit in response to output current to the load increasing above an output current limit. The controller regulates output current to the load as a function of current gain from the output current to current from the constant current source by controlling switching of the active bridge section as a single control variable over a range from a minimum load condition to a full load condition. 
       FIG. 1  is a schematic block diagram illustrating one embodiment of a system  100  with DC-DC converters  102   a - n  (collectively or generically “ 102 ”) a constant current source  104 . In the embodiment, the constant current source  104  is direct current (“DC”) and is on a shore of an ocean or other body of salty or otherwise conductive water and a trunk cable feeds DC-DC converters  102 , which are series connected. Each DC-DC converter  102  feeds a load, such as a sensor, a light, a vehicle, a camera, and the like. 
     The constant current source  104  is grounded on land and the trunk cable is grounded by a seawater connection. An advantage of a system  100  with a constant current source  104  feeding converters  102  is robustness against voltage drop over a long distance of the trunk cable. In addition, the system  100  includes robustness against cable faults where seawater serves as the current return. Each DC-DC converter  102  has a constant input current with a regulated output current. Other systems in other situations also benefit from a constant current source feeding one or more DC-DC converters  102 . 
     In some embodiments, the converters  102  are series resonant converters or a similar topology and include an active bridge section with input terminals that receive power from a constant current source. In some embodiments, the active bridge section operates at a fixed switching frequency. The series resonant converter includes resonant section with a resonant inductor and a resonant capacitor where the resonant section is connected to an output of the active bridge section, and an output rectifier that receives power from the resonant section and includes output terminals for connection to a load. The series resonant converter includes, in some embodiments, a controller that regulates output current to the load. The controller regulates output current to the load by controlling switching of the active bridge section. In some embodiments, the fixed switching frequency of the active bridge section matches a resonant frequency of the resonant section. 
     Feeding the DC-DC converters  102  (or converters  102 ) with a constant current source creates challenges during startup and shutdown of the converters  102 . In addition, failures, transients, etc. may also cause problems for the converters  102 . For example, if switches of the converters  102  stop operating, input voltage across an input capacitor could rise dramatically. Other concerns with the converters  102  are also discussed below along with protection features. 
       FIG. 2  is a schematic block diagram illustrating one embodiment of a power supply  200  with that regulates output current and is fed by a constant current source I g . The SRC  200  includes an active bridge section  202  with input terminals that receive power from the constant current source I g  where the active bridge section  202  operates at a fixed switching frequency f s . In one example, the active bridge section  202  includes a full active bridge with a first switching leg with two switches Q 1  and Q 2  and a second switching leg with two additional switches Q 3  and Q 4  where the resonant section  204  connects to a connection point A between switches Q 1  and Q 2  of the first leg and connects to a connection point B between switches Q 3  and Q 4  of the second leg. In another example, the active bridge section  202  is a half-bridge with a single switching leg with two switches Q 1  and Q 2 . In other embodiments, the active bridge section  202  includes another active bridge topology. 
     The power supply  200  includes a resonant section  204  with a resonant inductor L r  and a resonant capacitor C c . The resonant section  204  is connected to an output of the active bridge section  202 . The power supply  202  includes an output rectifier  206  that receives power from the resonant section  204  and includes output terminals for connection to a load R L . In some embodiments, the output rectifier  206  is a diode half-bridge voltage doubler. In other embodiments, the output rectifier  206  is a diode half-bridge rectifier. In other embodiments, the output rectifier  206  is a diode full-bridge rectifier. In other embodiments, the output rectifier  206  includes an active rectifier topology with active switches. One of skill in the art will recognize other rectifier topologies for the output rectifier  206 . 
     The power supply  200  includes a controller  208  that regulates output current to the load R L  where the controller  208  regulates output current to the load by controlling switching of the active bridge section  202 . By regulating output current, the power supply  200  provides constant output current to the load R L . The fixed switching frequency f s  of the active bridge section  202  matches a resonant frequency f o  of the resonant section  204 , which provides a mechanism for simplified control. 
     In some embodiments, the power supply includes a transformer  210  between the resonant section  204  and the output rectifier  206  with a turns ratio of 1:n. Selection of the transformer turns ratio is useful in managing a current gain M I  of the power supply  200  and, in some embodiments, provides isolation between the input and the output of the power supply  200 . 
       FIG. 3A  is a schematic block diagram illustrating one embodiment of a series resonant converter (“SRC”)  300  with a full-bridge switching section that regulates output current and is fed by a constant current source I g . In the embodiment, the active bridge section  202  described above is a full-bridge switching section that includes four switches Q 1 -Q 4 . In some embodiments, each switch Q 1 -Q 4  is metal-oxide semiconductor field-effect transistor (“MOSFET”). In other embodiments, the switches Q 1 -Q 4  are other types of semiconductor switches or other types of switches capable of operating at the chosen switching frequency. The full-bridge switching section is in an H-bridge configuration with two switches Q 1 , Q 2  in a first switching leg and two switches Q 3 , Q 4  in a second switching leg. In some embodiments, the SRC  300  may also include an input capacitor C in  that helps to smooth voltage ripple on the input voltage V in  caused by switching of the switches Q 1 -Q 4  of the full-bridge switching section. 
     The SRC  300  includes a resonant section  204  with a resonant inductor L r  and a resonant capacitor C r  where the resonant section  204  is connected to an output of the active bridge section  202  at connection point A located between the switches Q 1 , Q 2  of the first switching leg and connection point B located between the switches Q 3 , Q 4  of the second switching leg. In the embodiment, the resonant inductor L r  is split into two parts, but may be a single inductor. The SRC  300  also includes an output rectifier  206  that receives power from the resonant section  204  and includes output terminals for connection to a load R load . In the depicted embodiment, the output rectifier  206  is a diode half-bridge voltage doubler that includes a first diode D 1 , and a second diode D 2 , a first capacitor C 1  and a second capacitor C 2  as depicted in  FIG. 3A . Typically, the output rectifier  206  also includes an output capacitor C out  that helps to smooth voltage ripple of the output voltage V out . 
     In some embodiments, the SRC  300  includes a controller  302  that regulates output current I out  to the load R load , where the controller  302  regulates output current I out  to the load R load  by controlling switching of the switches Q 1 -Q 4  of the active bridge section  202  by way of controlling a phase shift angle α, as explained below. In some embodiments, where the switching frequency of the active bridge section  202  is fixed, the fixed switching frequency f s  matches a resonant frequency f o  of the resonant section  204 , which provides benefits that are described below. 
       FIG. 3B  is a schematic block diagram illustrating one embodiment of a SRC  301  with a half-bridge switching section and that regulates output current I out  and is fed by a constant current source I g . The SRC  301  includes an active bridge section  202  that is a half-bridge switching section with two switches Q 1 , Q 2  in a single switching leg and includes input terminals that receive power from the constant current source I g . The resonant section  204  also includes a resonant inductor L r  and a resonant capacitor C r  connected to the active bridge section  202 . The output rectifier  206  also includes two diodes D 1  and D 2  in a different configuration than the SRC  300  of  FIG. 3A . In some embodiments, the switching frequency of the half-bridge switching section is fixed and the SRC  301  includes a controller  304  that regulates output current I out  to the load R load , where the controller  304  regulates output current I out  to the load R load  by controlling switching of the active bridge section  202  in the form of controlling a duty cycle of the switches Q 1 , Q 2 . In some embodiments, the active bridge section  202  includes a half-bridge as depicted in  FIG. 3B  and the controller  304  regulates the current gain as a function of a single control variable of a duty cycle of switches Q 1 , Q 2  of the active bridge section  202 . 
       FIG. 4  is a schematic block diagram illustrating one embodiment of a SRC  400  with a full-bridge switching section and that regulates output current I out  and is fed by a constant current source I g  and includes protection features. In the embodiment, the SRC  400  is substantially similar to the SRC  300  of  FIG. 3A , but includes a transformer T r  (e.g. transformer  210 ) that has a turns ratio of 1:n turns, along with protection features, which will be described below. The transformer T r , in some embodiments, provides isolation and a transformation of voltage and current that are useful in achieving a desired current gain. In some embodiments, the active bridge section  202  includes a full active bridge, the output rectifier  206  includes a diode half-bridge voltage doubler, as depicted in  FIG. 4 , and the SRC  400  includes a transformer T r  between the resonant section  204  and the output rectifier  206 . The controller  402  regulates the current gain as a function of a single control variable of a phase shift angle α between switching in a first leg of the active bridge section  202  and a second leg in the active bridge section  202 , as described below. 
     To appreciate advantages of the SRC  400  described above, the SRC  400  is analyzed using steady state analysis. The steady state analysis is presented for the SRC  400  with a constant current input I g , as shown by the circuit topology in  FIG. 4 , is based on a fundamental approximation, which assumes that power transferred from input to output is mostly carried by the fundamental components of the SRC  400 . As illustrated in  FIG. 4 , for the topology analyzed, the input is a constant current source, the SRC active bridge section  202  includes four MOSFETs Q 1 -Q 4 , the resonant section  204  includes the resonant inductor L r  and capacitor C r , and the output rectifier  206  is a diode half-bridge voltage doubler that includes diodes D 1  and D 2 . In addition, the 1:n power transformer T r  provides voltage conversion and isolation between input and output. In some embodiments, phase-shift modulation is employed as a driving scheme, with the definition of the phase shift angle α illustrated in  FIG. 5 . 
       FIG. 5  is an ideal waveform diagram demonstrating a phase shift angle α. The top waveform is the voltage at connection point A (v a ), the voltage at connection point B (v b ) and the voltage across the connection points v ab . The phase shift angle α is a difference between v a  and v b , which is used to control an amount of energy transferred from the source I g  to the load R load .  FIG. 6  is a schematic block diagram illustrating an equivalent circuit diagram  600  of the SRC topology. The equivalent circuit diagram  600  includes a constant current source with current I and an input capacitor C in  where input current I in  is measured after the input capacitor C in . 
     By applying the fundamental approximation and average approximation, the equivalent circuit of the SRC topology described herein can be derived as shown in  FIG. 6 . The equivalent resistor R ac , the input current I in  and the controlled voltage source vs 1  are expressed as: 
     
       
         
           
             
               
                 
                   
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     In equations (1-3), R L  is the load resistance, φ s  is the phase shift of i s1  with respect to v s1 , I s1  is the peak value of i s1 , and α is the input bridge phase shift angle, which ranges from 0° to 180°. 
     The resonant frequency, normalized switching frequency, characteristic impedance Z o  and the loaded quality factor Q of the resonant section  204  are defined as: 
     
       
         
           
             
               
                 
                   
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     Note that the input voltage V in  is not constant in the equivalent circuit show in  FIG. 6 . The input voltage V in  is determined by the constant input current I, phase shift angle α and load R L . For a lossless power converter, the output power is equal to the input power, which can be used to derive the input voltage expression. The input voltage can be expressed as: 
     
       
         
           
             
               
                 
                   
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     Based on equation (8) and the equivalent circuit illustrated in  FIG. 6 , the output current I out , output voltage V out  and output power P out  of an SRC  400  with constant input current I can be expressed in forms of normalized switching frequency F and the resonant tank quality factor Q as: 
     
       
         
           
             
               
                 
                   
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                           ⁡ 
                           
                             ( 
                             
                               α 
                               2 
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         1 
                         + 
                         
                           
                             
                               Q 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 F 
                                 - 
                                 
                                   1 
                                   F 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     V 
                     out 
                   
                   = 
                   
                     
                       
                         IR 
                         L 
                       
                       
                         2 
                         ⁢ 
                         n 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               α 
                               2 
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         1 
                         + 
                         
                           
                             
                               Q 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 F 
                                 - 
                                 
                                   1 
                                   F 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     P 
                     out 
                   
                   = 
                   
                     
                       
                         
                           I 
                           2 
                         
                         ⁢ 
                         
                           R 
                           L 
                         
                       
                       
                         4 
                         ⁢ 
                         
                           n 
                           2 
                         
                         ⁢ 
                         
                           
                             sin 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               α 
                               2 
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         + 
                         
                           
                             
                               Q 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 F 
                                 - 
                                 
                                   1 
                                   F 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Equations (8)-(11) are the steady state solutions for an SRC  400  with constant current input. From the steady state solutions, it can be seen that the SRC  400  with constant current input behaves quite differently from the constant voltage input case. 
     The current gain of the SRC  400  can be written as: 
                     M   I     =       I   out     I             (   12   )               
Substituting equation (9) into equation (12), the current gain can be written as:
 
     
       
         
           
             
               
                 
                   
                     M 
                     I 
                   
                   = 
                   
                     
                       
                         1 
                         + 
                         
                           
                             
                               Q 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 F 
                                 - 
                                 
                                   1 
                                   F 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                       
                     
                     
                       2 
                       ⁢ 
                       n 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             α 
                             2 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     From equation (13), the current gain M I  is a function of quality factor Q, normalized switching frequency F, transformer turns ratio n and the phase shift angle α. By close examination of equation (13), the current gain M I  becomes independent of Q (load) if the normalized switching F is equal to 1. When F is equal to 1, M I  can be expressed as: 
     
       
         
           
             
               
                 
                   
                     M 
                     I 
                   
                   = 
                   
                     
                       
                         I 
                         out 
                       
                       I 
                     
                     = 
                     
                       1 
                       
                         2 
                         ⁢ 
                         n 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               α 
                               2 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     From equation (14), the current gain M I  of the SRC  400  with constant current input only depends on the transformer turns ratio n and the SRC  400  input bridge phase shift angle α, and is independent of the load resistance R L , which means the SRC  400  has a current source output behavior. From equation (14), for the SRC  400  with constant current input I, maximum phase shift (180°) results in minimum current gain M I_min , while lower phase shift angle leads to a higher current gain. When the phase shift angle α equals to 180°, the minimum current gain M I_min  can be expressed as: 
     
       
         
           
             
               
                 
                   
                     M 
                     
                       I 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       _ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       m 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       i 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       n 
                     
                   
                   = 
                   
                     
                       
                         I 
                         out 
                       
                       I 
                     
                     = 
                     
                       1 
                       
                         2 
                         ⁢ 
                         n 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     From equation (15), the minimum current gain M I_min  of the SRC  400  with a constant current input I is determined by the transformer turns ratio n. As a result, the transformer turns ratio n, in some embodiments, is designed so that the minimum current gain M I_min  is lower than an objective, considering input current variation. As an example, the plots of minimum current gain M I_min  versus the normalized switching frequency F are illustrated in  FIG. 7  for different Q values with transformer turns ratio n=2. 
     With regard to component stress analysis and design considerations, the root-mean-square (“rms”) value of the resonant inductor current and resonant capacitor voltage can be expressed as: 
     
       
         
           
             
               
                 
                   
                     I 
                     
                       L 
                       , 
                       
                         rm 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                       
                     
                   
                   = 
                   
                     
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         I 
                       
                       
                         2 
                         ⁢ 
                         
                           2 
                         
                         ⁢ 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               α 
                               2 
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         1 
                         + 
                         
                           
                             
                               Q 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 F 
                                 - 
                                 
                                   1 
                                   F 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   
                     V 
                     
                       C 
                       , 
                       
                         rm 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                       
                     
                   
                   = 
                   
                     
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Z 
                           o 
                         
                         ⁢ 
                         I 
                       
                       
                         2 
                         ⁢ 
                         
                           2 
                         
                         ⁢ 
                         F 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               α 
                               2 
                             
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         1 
                         + 
                         
                           
                             
                               Q 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 F 
                                 - 
                                 
                                   1 
                                   F 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     As analyzed in above, the normalized switching frequency F is chosen to be one in order to obtain current source behavior at the output of the SRC  400  with constant current input I. As a result, the rms current of the resonant inductor L r  and voltage of the resonant capacitor C r  are independent from the load as well, which can be written as: 
     
       
         
           
             
               
                 
                   
                     I 
                     
                       L 
                       , 
                       
                         rm 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                       
                     
                   
                   = 
                   
                     
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       I 
                     
                     
                       2 
                       ⁢ 
                       
                         2 
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             α 
                             2 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   
                     V 
                     
                       C 
                       , 
                       
                         rm 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                       
                     
                   
                   = 
                   
                     
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Z 
                         o 
                       
                       ⁢ 
                       I 
                     
                     
                       2 
                       ⁢ 
                       
                         2 
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             α 
                             2 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     From equation (18), the rms current of the resonant inductor L r  only depends on DC input current I and the phase shift angle α. From equation (14), for a given current gain, the required phase shift angle α is determined by the transformer turns ratio n. So, the rms current of the resonant inductor is determined by the DC input current I and transformer turns ratio n for a given current gain. Since the resonant inductor rms current is independent from the load as well, it should be constant for the entire load range for a given design and DC input current I. 
     Equation (19) shows that the rms voltage of the resonant capacitor Cr depends on the characteristic impedance Z o  of the resonant section  204 , the input current I and the phase shift angle α. By looking at equations (18) and (19) carefully, the rms voltage of the resonant capacitor C r  is the rms current of the resonant inductor I L,rms  multiplied by the characteristic impedance Z o . Similar to the rms current of the resonant inductor I L,rms , the resonant capacitor rms voltage should be constant for the entire load range for a given design. 
     For a given application scenario, the SRC  400  with constant current input I and regulated output current I out  can be designed by applying equations (14), (18) and (19). The design procedure, in some embodiments, is summarized as follows:
         1. Calculate the possible current gain range based on the given input current range and desired output current.   2. Determine the transformer turns ratio n based on the minimum current gain M I_min  and equation (15) with the considerations of design margin and losses. Lower phase shift angle α means higher rms resonant inductor current, which means higher losses, so, in one embodiment, a proper margin is included in order to obtain higher efficiency.   3. Substituting equation (15) into equations (18) and (19), the rms values of the resonant inductor current and the resonant capacitor voltage are expressed as:       

     
       
         
           
             
               
                 
                   
                     I 
                     
                       L 
                       , 
                       
                         rm 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                       
                     
                   
                   = 
                   
                     
                       n 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         I 
                         out 
                       
                     
                     
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
             
               
                 
                   
                     V 
                     
                       C 
                       , 
                       
                         rm 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                       
                     
                   
                   = 
                   
                     
                       
                         n 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         m 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Z 
                           o 
                         
                         ⁢ 
                         
                           I 
                           out 
                         
                       
                       
                         2 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
         
         
           
             4. From equation (20), the resonant inductor rms current is determined once the transformer turns ratio n is selected. 
             5. Based on a desired voltage stress on the resonant capacitor C r , the designed transformer turns ratio n, the desired output current I out  and equation (21), the characteristic impedance Z o  of the resonant tank can be calculated. 
             6. The desired operating frequency of the SRC  400  generally is a known parameter for a design scenario. Based on the calculated characteristic impedance Z o , a desired switching frequency and equation (6), the value of either resonant inductor or resonant capacitor can be determined. 
             7. Based on the result from step  6  and equation (4), a value of the other resonant component can be calculated. 
           
         
       
    
     For the design of an SRC  400  with constant current input I and regulated output current I out , the minimum quality factor Q of the resonant tank is at full load. Lower voltage stress on the resonant capacitor C r  typically means lower characteristic impedance Z o , which results in lower quality factor Q at full load. Lower quality factor Q means higher harmonic components in the SRC  400 , which is not desired. 
     However, higher quality factor Q means lower resonant capacitance C r  for a given switching frequency. In practice, the transformer T r  used in the SRC  400  has a parasitic capacitance, especially for a high frequency, high isolation voltage transformer. In this case, high quality factor Q at full load may result in a condition that the transformer parasitic capacitance is comparable to the resonant capacitance, which is also not desirable. So, an SRC  400  with constant current input and regulated output current, in some embodiments, is designed according to the analysis and procedure presented herein along with other considerations such as load range and parasitic parameters of the employed transformer T r . 
     As discussed above, the SRC  400  with constant input current I behaves as a current source only when the SRC  400  operates at resonant frequency f o , so switching frequency control is not employed to control the output, otherwise the current source behavior will be lost. In addition,  FIG. 7  indicates that the current gain M I  is relatively flat for low quality factor Q in the vicinity of F=1. In addition, the quality factor Q is lower when the load resistance becomes higher. As a result, variation of switching frequency does not provide wide conversion range and output current regulation against large input current variations. Thus, constant frequency control has advantage. From equation (14), it can be seen that the current gain M I  can be controlled by the phase shift angle α of the active bridge section  202 , so phase shift modulation control can be applied to the SRC  400  with constant input current I. 
     If the circuit of SRC  400  with constant current input shown in  FIG. 4  is directly employed as the DC-DC converters  102  in  FIG. 1 , the entire system  100  has operational issues because the MOSFETs in the primary bridge are typically enhancement type MOSFETs which are normally open. Since the DC-DC converters  102  are connected in series, as shown in  FIG. 1 , open state of the MOSFETs means that the main trunk cable is open. One solution would be to provide an auxiliary supply separate from the trunk cable to supply power to the MOSFETs. However, in such a long distance, DC current distribution system for undersea and other applications, this solution is impractical with the consideration of cost, voltage drop and system reliability. Hence, auxiliary power for the DC-DC converters  102 , in some embodiments, is provided by the trunk cable, which requires a continuous current flow through the trunk cable in order to deliver auxiliary power to the DC-DC converters  102 . In this case, a closed circuit path for the trunk cable current is desirable at startup. 
     The SRC  400  in  FIG. 4  includes a bypass branch  404  connected in parallel with the input terminals where the bypass branch  404  shunts current I from the constant current source through the bypass branch  404  when the bypass branch  404  is active. In some embodiments, the bypass branch  404  includes a sensing resistor r s  in series with a shunt switch Q 5  that is a transistor, such as a MOSFET. The controller  402  operates the shunt switch Q 5  in an active region of the transistor to shunt current I from the constant current source in a range between zero current and a full current of the constant current source where the shunt switch Q 5  is operable to shunt a portion of the current I of the constant current source. 
     In the SRC  400  of  FIG. 4 , the MOSFET Q 5  is a depletion type MOSFET and r s  is the current sensing resistor in that branch. This bypass branch  404  in the SRC  400 , which is switch Q 5  in series with r s  and the submarine cable in the system  100  provide a continuous path for the main trunk current even before any SRC  400  in the system  100  is energized. The depletion type MOSFET Q 5 , in some embodiments, is selected to be capable of handling power dissipation during start-up and shut-down of SRC  400 . 
     In some embodiments, a three-step startup and shutdown technique is proposed for system operations. For the start-up, a first step is to turn on the shore power supply  104  and provide the desired distribution current to the rest of the system  100 , which is used to power all the auxiliary power supplies of each DC-DC converter  102  (e.g. SRC  400 ). When the auxiliary power supply  104  is on, a certain amount of time delay is employed before taking the next action in order to ensure that all the auxiliary power supplies in the system  100  are turned on. 
     A second step is to pass the trunk current from the bypass branch  404  to the input of the SRC  400 . In this step, the SRC  400  operates at 180° phase shift in open loop mode, which provides minimum output current I out  to the load R L . A bypass branch current controller in the controller  402  ramps down the current flow through the bypass branch  404  from full trunk current to zero. The ramp time and the load of the SRC  400  at 180° phase shift determines how much energy is dissipated in the bypass branch  404  during the start-up. The SRCs  400  in the system  100  can do this at the same time or in a sequence. The second step is completed once the full trunk current flows through the SRC  400  instead of the bypass branch  404 . 
     The third step is to enable the SRC  400  to start regulating its output current I out  and to close a feedback control loop of the SRC  400 . For the shut-down, the scenario is similar. The first step is to open the SRC feedback regulation, and then take the full trunk current from SRC input to the bypass branch  404  with a ramp by changing the current reference of the bypass branch current controller. The last step is to turn off the auxiliary power supplies of the SRCs  400  and then the shore power supply  104 . 
     In some embodiments, the SRC  400  includes a resonant capacitor voltage clamping circuit  406  that clamps voltage across the resonant capacitor C r  to a voltage less than a maximum voltage rating of the resonant capacitor C r  during a transient condition, such as an output short circuit condition where energy from the resonant capacitor C r  may be transferred to the output. 
     An SRC  400  with one embodiment of a resonant capacitor voltage clamping circuit  406  to protect the SRC  400  during fault transients is depicted in  FIG. 8 . In  FIG. 8 , the diodes D 3 , D 4 , D 5  and D 6  are used to clamp the voltage of the resonant capacitor C r  to the input voltage V in . However, by analyzing the voltage of resonant capacitor terminals to ground, the capacitor terminal voltages are expressed as Vin±0.5v Cr  when Q 1  and Q 3  are on, which is a general case for phase shift modulation control. In this embodiment, for phase shift modulation controlled SRC  400 , circulating currents between the resonant section  204  and the input filter are unavoidable. On the other hand, for the SRC  400  with constant current input, the voltage across the resonant capacitor C r  is higher than the input voltage V in  for certain load ranges, which means that the protection approach shown in  FIG. 8  may not be desirable in some embodiments because the resonant capacitor voltage clamping circuit of  FIG. 8  alters steady state operation. 
     In some embodiments, the SRC  400  of  FIG. 4  includes a resonant capacitor voltage clamping circuit  406  with a diode full-bridge rectifier, with diodes D 3 , D 4 , D 5  and D 6 , with an input of the diode full-bridge rectifier connected across the resonant capacitor C r  and an output of the diode full-bridge rectifier connected in parallel with a clamping capacitor C c  and connected in parallel with a bleeder resistor r c , where during steady-state operation voltage across the clamping capacitor C c  is higher than a voltage rating of the resonant capacitor C r . 
     The resonant capacitor voltage clamping circuit  406  of  FIG. 4  clamps the resonant capacitor voltage to the voltage of the floating clamping capacitor C c , which holds a peak voltage across the resonant capacitor C r  regardless of the relation between the resonant capacitor voltage and the input voltage V in . The bleed resistor R c  is in parallel with the clamping capacitor C c  and has a large enough value to not significantly affect efficiency, but will discharge the clamping capacitor C c  when the SRC  400  is not operating. During steady state, since the clamping capacitor C c  holds the resonant capacitor peak voltage, no significant current flows through the clamping diodes D 3 -D 6  except for a small current to feed the bleed resistor R c . 
     For the SRC  400  without a protection circuit, energy stored in the input capacitor C in  is transferred to the resonant section  204  during an output short circuit fault transient. With the resonant capacitor voltage clamping circuit  406  shown in  FIG. 4 , energy stored in the input capacitor C in  is transferred to the resonant section  204  and the clamping capacitor C c . In this case, during fault transients, voltage across the resonant capacitor C r  can be limited to protect the SRC  400 . 
     The energy stored on a capacitor is calculated from:
 
E=½CV 2   (22)
 
Hence the energy stored in the capacitors C in , C r , C c  of the SRC  400  before a fault can be expressed as:
 
E C     in   =½C in V in   2 , E C     r   =½C r V r   2 , E C     c   =½C c V c   2   (23)
 
where V in  is the DC input voltage, V Cr  is the peak voltage of the resonant capacitor C r , and V C  is the peak voltage of the clamping capacitor C c , which equals to V Cr .
 
     From the equations of (23), the total energy stored on the resonant capacitor C r  and the clamping capacitor C c  is:
 
 E   C     r     +E   C     c   =½( C   r   +C   c ) V   C     r     2   (24)
 
     During an output short circuit fault transient, the energy stored in the input capacitor C in  is transferred to the resonant section  204  and the clamping capacitor C c . Hence, the total energy E total  stored on C r  and C c  becomes:
 
 E   total   =E   C     r     +E   C     c     +E   C     in   =½( C   r   +C   c ) V   C     r     2 +½ C   in   V   in   2   (25)
 
     With the energy transferred from the input capacitor C in , the voltage across the resonant capacitor C r  and clamping capacitor C c  increases by: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     V 
                   
                   = 
                   
                     
                       
                         
                           V 
                           
                             C 
                             r 
                           
                           2 
                         
                         + 
                         
                           
                             
                               C 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 n 
                               
                             
                             ⁢ 
                             
                               V 
                               
                                 i 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 n 
                               
                               2 
                             
                           
                           
                             
                               C 
                               r 
                             
                             + 
                             
                               C 
                               c 
                             
                           
                         
                       
                     
                     - 
                     
                       V 
                       
                         C 
                         r 
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     From equation (26), the clamping capacitor C c  required for limiting the voltage across the resonant capacitor C r  to a certain voltage increment ΔV can be derived as: 
     
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       
                         
                           C 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             n 
                           
                         
                         ⁢ 
                         
                           V 
                           
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             n 
                           
                           2 
                         
                       
                       
                         
                           
                             ( 
                             
                               
                                 C 
                                 
                                   C 
                                   r 
                                 
                               
                               + 
                               
                                 Δ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 V 
                               
                             
                             ) 
                           
                           2 
                         
                         - 
                         
                           V 
                           
                             C 
                             r 
                           
                           2 
                         
                       
                     
                     - 
                     
                       C 
                       r 
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     For output short-circuit fault, the resulting large surge output current may damage the current sensing circuit if resistive current sensing is employed. From reliability aspect, it is preferred to have an output current limiting circuit for protection, especially for low output current, high output voltage applications. The proposed output current limiting circuit  408  in  FIG. 4 . In  FIG. 4 , switch Q 6  is a depletion type MOSFET and r 1  is a feedback resistor. As shown in  FIG. 4 , the negative voltage from r 1  is applied to the gate terminal of switch Q 6  to control the equivalent resistance presented by switch Q 6 , since switch Q 6  operates in the linear region. The proposed current limiting circuit  408  does not require any active drive or auxiliary circuits. The current limiting circuit does introduce additional power loss during normal operation because of the low output current that flows the high on-resistance of the depletion type MOSFET. In one embodiment of an SRC  400  used for experimentation, the current limiting circuit  408  introduces an additional 20Ω resistance that consumes 2 W during normal operation, which is negligible compared with 1 kW output power. 
     For the DC current distribution system  100 , the SRC  400  that has a fault should to be bypassed in order to keep the rest of the system  100  operating. Capacitance of the submarine cable, in some embodiments, is significantly high due to its parameters and length. Since the DC-DC converters  102  (e.g. SRCs  400 ) are connected in series, bypass of one module means discharging the cable capacitance in its forward current path. In this case, uncontrolled cable discharging may result in large current through other SRC  400  in the system  100 , and finally cause the entire system  100  shutdown. To help provide normal operation of the complete system  100 , a two-level fault response strategy is proposed. The first level is to disable the gate signals of the primary switches Q 1 -Q 4 , and the second level is to use the bypass branch  404  to control the discharging of the cable to make sure that the distribution current stay within the range. 
     The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.