Abstract:
The scalable cascaded Z-source inverter is able to interface flexibly different distributed renewable energy sources or storages in wide voltage change range, such as wind power, solar power, battery, fuel cell, Ultra-capacitor and so on. The invention facilitates the AC 1 MHz frequency output; therefore high power density can be reached. Z-source network is integrated in each inverter module to wide system operation range, improve high system efficiency, and enhance high system reliability. The invention is applied for PV system to verify the performance.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority from U.S. Provisional Application No. 61/529,602 filed on Aug. 31, 2011, entitled “1 MHZ Scalable Cascaded Z-Source Inverter Using Gallium Nitride (GAN) Device”. 
    
    
     STATEMENT OF GOVERNMENT INTEREST 
     This invention was made with Government support under Grant No. 1124658 awarded by NSF (National Science Foundation) GOALI grant, entitled, “1 MHz, GaN-Based, Modular, Cascaded Z-Source Inverters for Scalable Grid-Interactive Photovoltaic (PV) Applications”. The Government has certain rights in the invention. 
    
    
     FIELD OF INVENTION 
     This invention relates to an inverter, more specifically, a scalable cascaded Z-source inverter. 
     BACKGROUND OF INVENTION 
     Department Of Energy requests $2.4 billion for renewable energy, efficiency in fiscal year 2011. The proposed budget boosts renewable energy sources and storages application and development, such as wind power, solar power, batteries, and fuel cells and so on. There is the widespread growth of distributed energy systems using these renewable energy sources and storages. More and more attention is paid to the high power density, high power efficiency, high power quality and high system reliability of the distributed energy systems. 
     The main reason that prevents the grid-connected photovoltaic (PV) systems from realizing its full market potential is the power losses due to the module mismatch, orientation mismatch, partial shading, and maximum power point tracking (MPPT) inefficiencies. The traditional cascaded dc-dc converter topology shown in  FIG. 1  can interface distributed PV modules and achieve MPPT for each PV module, therefore reduces the power loss. However, the configuration has dc-dc and dc-ac conversion stages, which decrease the overall system efficiency. Moreover, the switching frequency of dc-ac inverter is limited leading to the big size AC filter and large electrolyte capacitors, which restricts the system power quality and power density. Cascaded multilevel inverter topology such as H-bridge inverter, shown in  FIG. 2 , can interface distributed PV modules, achieve MPPT for each PV module and single stage energy conversion, support a higher equivalent pulse width modulation (PWM) frequency and a larger DC bus voltage. Nevertheless, the H-bridge inverter lacks boost function so that the inverter kVA requirement has to be increased twice with a PV voltage range of 1:2, which restricts the system power density. In addition, both configurations are not able to be immune to shoot-through faults. Therefore, the modular system meets a daunting challenge. 
     SUMMARY OF INVENTION 
     The present invention provides a scalable cascaded Z-source inverter configuration for dc-ac power conversion that can integrate distributed renewable energy sources and storages with wide voltage ranges. One embodiment of the invention in PV application is shown in  FIG. 3 . Single energy conversion and boost function can be achieved simultaneously. Independent MPPT for each Z-source inverter module can implement an efficient PV energy conversion. In another embodiment of the invention, the commercial low voltage GaN device is be used to facilitate modular structure due to its ultra-high frequency, small size AC filter and DC electrolyte capacitor, which reduces losses significantly and achieves high power efficiency. 
     The present invention is immune to shoot-through faults especially operating at high switching frequency and enhance the system reliability. A comprehensive Z-source network design is developed based on an innovative equivalent AC circuit model for the single phase PV system. Flexible and reliable control system integrated is developed to improve the PV energy harvesting capability. In particular, the invention is suitable for hybrid renewable energy sources and storages application in wide system operation range. High power density, high power efficiency, high power quality and high system reliability can be achieved. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a fuller understanding of the invention, reference should be made to the following detailed description, taken in connection with the accompanying drawings, in which: 
         FIG. 1  is an illustration of a grid connected PV system with cascaded DC-DC converters. 
         FIG. 2  is an illustration of a grid connected PV system with cascaded H-bridge inverters. 
         FIG. 3  is an illustration of the PV system configuration with the invented cascaded Z-source inverters. 
         FIG. 4  is an illustration of the PV system with four cascaded Z-source inverters at 1 kW. 
         FIG. 5  is an illustration of the Z-source inverter operation mode: (a) shoot-through state; (b) traditional zero state; (c) active state. 
         FIG. 6  is an illustration of the equivalent AC circuit model of Z-source inverter. 
         FIG. 7  is an illustration of the relationship between voltages ripples ΔV pv , ΔV ZC , ΔV dc  and C ZC . 
         FIG. 8  is an illustration of the input capacitor voltage ripple with different input capacitance and C ZC . 
         FIG. 9  is an illustration of the power loss distribution in each Z-source inverter module. 
         FIG. 10  is an illustration of the efficiency curves of each Z-source inverter module using diode and SR. 
         FIG. 11  is an illustration of the developed integrated control system for the PV systems. 
         FIG. 12  is an illustration of the PV power from four PV modules: (a) PV 1 ----P in1  and P in1   _   ref ; (a) PV 2 ----P in2  and P in2   _   ref ; (c) PV 3 ----P in3  and P in3   _   ref ; (d) PV 4 ----P in4  and P in4   _   ref . 
         FIG. 13  is an illustration of the real power from four PV modules and to grid: P in  and P out . 
         FIG. 14  is an illustration of the total inverter output voltage and grid current: V S  and i g . 
         FIG. 15  is an illustration of the voltage of Z-source inverter module1: (a) V PV1 ; (b) V ZC1 ; (C) V dc1 . 
         FIG. 16  is an illustration of Voltage and current ripple: (a) Zoomed V PV1 ; (b) Zoomed V ZC1 ; (C) Z-source inductor current i ZL1 . 
         FIG. 17  is the integration of PV system and control system 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     In the following detailed description of preferred embodiments, reference is made to the accompanying drawings, which form a part hereof, and within which are shown by way of illustration specific embodiments by which the invention may be practiced. It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the invention. 
     In one embodiment, the scalable cascaded Z-source inverter module can be applied for the 1 kW/120V single phase grid-connected PV system with 1 MHz frequency output, shown in  FIG. 4 . The 100V/25 A/7 mΩ GaN transistors recently introduced to the market by EPC Corporation are used in each Z-source inverter module (ZSIM). Each ZSIM is a standardized open-frame power module with 250 W. The input voltage of the PV module at maximum output power varies between 30V and 60V based on different PV manufactures. In order to generate 1 MHz operation frequency at output terminals, the switching frequency of each ZSIM is 125 kHz due to phase-shift PWM modulation method. The PV system facilitates to expand capacity to by series and paralleled inverter module. The system circuit parameters are shown in Table below. 
     
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Parameters 
                 Symbol 
                 Value 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Each 
                 DC link voltage 
                 V dc1 , V dc2  V dc3 , 
                 60 
                 V 
               
               
                 Z-source 
                   
                 V dc4   
                   
                   
               
               
                 inverter 
                 PV Voltage 
                 V PV1 , V PV2   
                 30-60  
                 V 
               
               
                 module 
                   
                 V PV3 , V PV4   
                   
                   
               
               
                 (ZSIM) 
                 Full PV power 
                 P in1 , P in2  P in3 , 
                 250  
                 W 
               
               
                   
                   
                 P in4   
                   
                   
               
               
                   
                 Switching frequency 
                 f SW   
                 125  
                 kHz 
               
               
                   
                 Z-source inductor 
                 L ZL   
                 18  
                 μH 
               
               
                   
                 Z-source capacitor 
                 C ZC   
                 15000  
                 μF 
               
               
                   
                 Input capacitor 
                 C in   
                 26  
                 μF 
               
               
                   
                 Cascaded inverter number 
                 n 
                 4 
                   
               
               
                 Grid 
                 Filter Inductor 
                 L f   
                 100  
                 μH 
               
               
                   
                 Rated RMS phase voltage 
                 V g   
                 120  
                 V 
               
               
                   
               
             
          
         
       
     
     The Z-source network design is critical for the system efficiency evaluation. The Z-source inductors are useful for reducing current ripple, as well Z-source capacitors and input capacitor can handle voltage ripple. The maximum current through the inductor occurs during maximum shoot-through duty cycle, which causes maximum ripple current. In the design, 40% current ripple through the inductors during maximum power operation is chosen. The inductance can be calculated by: 
                     L   ZL     =         V   ZC     ⁡     (     1   -   M     )         2   ⁢     f   sw     ⁢   Δ   ⁢           ⁢     I   ZL                 (   1   )               
Where V ZC =(V dc +V pv   _   low )/2 is the Z-source capacitor voltage, V dc  is the dc voltage after Z-source network, M=V peak /V tri  is modulation index, V tri  is the carrier peak value, f sw  is switching frequency, ΔI ZL  is the allowed maximum Z-source inductor current ripple.
 
     For the single phase inverter system, the instantaneous output power includes DC component and double fundamental frequency (DFF) components. The peak to peak value of the DFF power is twice DC power, which is PV power. From the energy conservation point of view, the DFF power should be absorbed by the input capacitor and Z-source capacitors, which causes DFF voltage ripple. Since the Z-source capacitor voltage V ZC  is much greater than input capacitor voltage V pv , Z-source capacitors should be used to deal with the DFF power. Otherwise, the total capacitance will increase resulting in low power density. In addition, input capacitor with big capacitance will cause the phase-shift between V ZC  and V pv  due to the equivalent LC filter on DC side, which will increase the burden of total capacitors to handle the DFF power. Therefore, the input capacitor is used for handling most high frequency voltage ripple. The maximum high frequency voltage ripple occurs during shoot-through period and PV module only delivers power to input capacitor. In order to achieve good voltage performance, high frequency voltage ripple is limited with 1%. The capacitance can be determined by: 
                     C   in     =           P   max     ⁡     (     1   -   M     )         2   ⁢     f   sw     ⁢     V   pv_low     ⁢   Δ   ⁢           ⁢     V   pv_hf         =         P   max     ⁡     (     1   -   M     )         2   ⁢     f   sw     ⁢     V   pv_low   2     ×   1   ⁢   %                 (   2   )               
Where ΔV pv   _   hf  is the allowed maximum input capacitor high frequency voltage ripple.
 
     The Z-source capacitor is used to handle the DFF voltage ripple and partly high frequency voltage ripple. In order to obtain suitable Z-source capacitance, the Z-source inverter operation mode is analyzed as shown in  FIG. 5 . The relationship between voltage, current and operation mode can be expressed by: 
                   {                   V   ZL     =         L   ZL     ⁢       ⅆ     i   ZL         ⅆ   t         =         D   st     ⁢     V   ZC       +       D   0     ⁢     (       V   pv     -     V   ZC       )       +                       D   1     ⁡     (       V   pv     -     V   ZC       )       =         D   nst     ⁢     V   pv       -       (       D   nst     -     D   st       )     ⁢     V   ZC                                   i   cin     =         C   in     ⁢       ⅆ     V   pv         ⅆ   t         =         D   st     ⁢     i   pv       +       D   0     ⁡     (       i   pv     -     2   ⁢     i   ZL         )       +                       D   1     ⁡     (       i   pv     -     2   ⁢     i   ZL       +     i   Lf       )       =       i   pv     -     2   ⁢     D   nst     ⁢     i   ZL       +       MI   g     ⁢     sin   2     ⁢   ω   ⁢           ⁢   t                                 i   ZC     =         C   ZC     ⁢       ⅆ     V   ZC         ⅆ   t         =         -     D   st       ⁢     i   ZL       +       D   0     ⁢     i   ZL       +                       D   1     ⁡     (       i   ZL     -     i   Lf       )       =         -     (       D   nst     -     D   st       )       ⁢     i   ZL       -       MI   g     ⁢     sin   2     ⁢   ω   ⁢           ⁢   t                             (   3   )               
Where D st  is the shoot-through duty ratio; D nst =D 0 +D 1  is the non-shoot-through duty ratio; D 0  is tradition zero duty ratio; D 1 =M sin ωt is active state duty ratio; i Lf =I g  sin ωt is the AC filter current; ω=2π×60; I g  is the peak value of the grid current.
 
     Among AC and DC components included in (3), AC components are useful for the Z-source capacitors design. They can be extracted from (4) and then converted as (5): 
                   {               L   ZL     ⁢       ⅆ       i   ~     ZL         ⅆ   t         =         D   nst     ⁢       V   •     pv       -       (       D   nst     -     D   st       )     ⁢       V   •     ZC                         C   in     ⁢       ⅆ       V   •     pv         ⅆ   t         =         i   ~     pv     -     2   ⁢     D   nst     ⁢       i   ~     ZL       -       1   2     ⁢     MI   g     ⁢   cos   ⁢           ⁢   2   ⁢   ω   ⁢           ⁢   t                       C   ZC     ⁢       ⅆ       V   •     ZC         ⅆ   t         =         (       D   nst     -     D   st       )     ⁢       i   ~     ZL       +       1   2     ⁢     MI   g     ⁢   cos   ⁢           ⁢   2   ⁢   ω   ⁢           ⁢   t                       (   4   )               {               (       D   nst         D   nst     -     D   st         )     ⁢       V   •     pv       =         V   •     ZC     +       (       L   ZL         D   nsht     -     D   st         )     ⁢       ⅆ       i   ~     ZL         ⅆ   t                                 (         D   nst     -     D   st         D   nst       )     [         (     1       D   nst     -     D   st         )     ⁢       i   ~     pv       -       (       D   st         D   nst     -     D   st         )     ⁢       i   ~     ZL       -       (       C   in         D   nst     -     D   st         )     ⁢       ⅆ       V   •     pv         ⅆ   t           ]     =                 2   ⁢       i   ~     ZL       -       1     D   nst       ⁢     (         -     1   2       ⁢     MI   g     ⁢   cos   ⁢           ⁢   2   ⁢   ω   ⁢           ⁢   t     +       D   st     ⁢       i   ~     ZL         )                             (       C   ZC       D   nst       )     ⁢       ⅆ       V   •     ZC         ⅆ   t         =         i   ~     ZL     -       (     1     D   nst       )     ⁢     (         -     1   2       ⁢     MI   g     ⁢   cos   ⁢           ⁢   2   ⁢   ω   ⁢           ⁢   t     +       D   st     ⁢       i   ~     ZL         )                         (   5   )               
Where D nst =M and D st =1−M in the worst case;
 
     
       
         
           
             
               
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     The equivalent AC circuit model is developed as shown in  FIG. 6 . Due to the DFF current ripple is absorbed by Z-source network, AC component of PV current can be ignored. The peak-peak voltage ripple on input capacitor ΔV pv , Z-source capacitor ΔV ZC  and DC link after Z-source network ΔV dc  can be calculated by (6). 
     
       
         
           
             
               
                 
                   
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     Based on (1), (2) and (6), the relationship between voltages ripples ΔV pv , ΔV ZC , ΔV dc  and C ZC  can be obtained in the  FIG. 7 .  FIG. 7  shows that the ΔV pv  is the highest. In order to achieve good voltage performance and maximum power point track (MPPT), ΔV pv  is limited with 1%.  FIG. 8  shows the relationship among C in , C ZC  and ΔV pv . It can be seen that Z-source capacitors can handle the DFF voltage ripple better than input capacitor. 
     There are four 100V GaN devices in each ZSIM. The power loss of each 250 W module is calculated around 10 watts so the maximum efficiency is around 96% at about half of rated output power when the input diode is used.  FIG. 9  shows the power loss distribution of the switching and conduction loss of GaN devices, input diode loss, the inductors and capacitors loss on Z-source network, and the input capacitor loss. Since the proposed topology allows each module to switch at only a fraction of the 1 MHz system frequency, distribution of power losses to a larger number of power devices leading to high efficiency at 1 MHz and air cooling becomes achievable. This architecture is particularly suitable for PV system where distributed PV arrays can be monitored, controlled, maintained, or replaced if necessary. If synchronous rectifier (SR) replaces the input diode to be in series with PV module, the efficiency of each Z-source inverter module is increased from 96% to 98.5%, shown in  FIG. 10 . 
     Another embodiment of the present invention is the control system, as shown in  FIG. 11 . Each ZSIM receives the voltage and current sensed from each PV module and sent to the MPPT control block. The MPPT control is used to generate the output voltage reference of the PV module. MPPT control can be achieved by different methods, such as perturb and observe (P&amp;O), incremental conductance (INC), ripple correlation control (RCC), etc. Therefore the output voltage of each PV module can be controlled accordingly to follow its own maximum power point (MPP). The PV module voltage control block generates a boost strip line o fabricate the PWM signal with boost function for each inverter module by shoot-through state. The controls of each ZSIM are independent so the MPPT of each module can be achieved even when PV modules receive different solar irradiation levels. The control system also includes the capacitor voltage control of each Z-source network and independent reactive power control. The Z-source capacitor voltage of each module is controlled to track the same reference by PI control with feedforwards so that the desired AC output voltage can be obtained. The output of capacitor voltage control contributes to the d-axis components of grid current. The reactive power control with PI controller is related to the q-axis components of grid current. Therefore, the desired gird current reference can be synthesized in the system control highlighted in dashed box in  FIG. 11 . In order to achieve the direct control of grid current, a proportional resonant (PR) is adopted to achieve the zero error. The output of the current control is added to the grid voltage feedforwards to generate the total inverter output voltage. However, considering the possible different real power and desired equal reactive power from each module, a real and reactive components extraction mechanism is developed to extract real and reactive power from each module. Due to the same AC current flowing through each module, the voltage distribution decides the power distribution. Therefore, the modulation index of each module can be generated based on the developed real and reactive components of output voltage. As a result, the objective voltage modulation of each inverter module is sent to PWM generation block, which will cooperate with the above boost strip line to generate the final PWM signal. If the number of inverter modules changes, the whole control remains the same except the minimum modification on “Grid current reference synthesis” and “Voltage modulation distribution” blocks. The control strategy provides a flexible and reliable operation to improve the system efficiency especially when PV modules operate under different solar irradiation levels. The same voltage on the dc-link after the Z-source network of each module can be guaranteed by the appropriate control to reduce the risk of low-frequency harmonic voltage on the total ac inverter output voltage spectrum. 
     The control system in the present invention may be extended to different cascaded PV inverter, such as traditional cascaded PV inverter without dc-dc converter, cascaded PV inverter with dc-dc converter. It is also flexible to be expanded to three phase cascaded inverter system. 
     The performance of the PV system with four cascaded ZSIM is verified in Matlab/Simulink+PSIM simulation platform.  FIGS. 12-16  show the simulation results when the designed Z-source network and developed control method were implemented on the PV system. As shown in  FIG. 12 , the temperature is 25° C. and solar irradiation is 1000 W/m 2  for four PV modules before 0.5 s. At 0.5 s, the solar irradiation over first three PV models (PV 1 , PV 2 , and PV 3 ) decreases to 700 W/m 2 , 800 W/m 2  and 900 W/m 2  respectively. The solar irradiation over fourth PV model (PV 4 ) keeps to 1000 W/m 2 . It is observed that the powers from PV 1  (P in1 ), PV 2  (P in2 ), and PV 3  (P in3 ) can be controlled to track their MMP smoothly and fast from 250 W to 165 W (P in1   _   ref ), 190 W (P in2   _   ref ), and 220 W (P in3   _   ref ) at 0.5 s in (a-c), respectively. And the power from PV 4  (P in4 ) always tracks the MPP of 250 W (P in4   _   ref ) regardless of the other PV power changes in (d).  FIG. 13  shows the input real power from four PV modules (P in ) and the power to grid (P out ). At 0.5 s, the P in  changes from 1000 kW to 825 W and P out  decreases from 985 W to 815 W. In the simulation, only conduction loss of each GaN device and the loss on AC line impedance are considered. The total output voltage of the cascaded inverter (V S ) and grid current (i g ) are shown in  FIG. 14 . Due to the small modulation index, there is only seven-level output voltage, not nine-level. The reactive power to grid is controlled to be zero. The grid current is almost in phase with the inverter output voltage if the reactive power on AC output filter is negligible.  FIGS. 12-14  show that the good performance and power quality of the PV system.  FIG. 15  shows the V pv1 , V ZC1 , and V dc1  of the first ZSIM. It can be seen that the V dc1  can be controlled to 60V during non-shoot-through period regardless of solar irradiation variation.  FIG. 16  shows ΔV pv1 , ΔV ZC1  and the high frequency current ripple through inductor (i LZ1 ) under different solar irradiation conditions for the first ZSIM. The current ripple is less than 40%, as well ΔV pv1  and ΔV ZC1  are less than 1%. The frequency of current ripple is 250 kHz due to phase-shift PWM method. 
     The integration of PV system and control system is shown in  FIG. 17 . The control system is a central control system. It collects voltage and current of each PV module, and capacitor voltage of each Z-source PV inverter module, grid voltage and grid current. With the appropriate control, it generates the objective PWM signal to each PV inverter module. The PWM signal can be transmitted by fiber-optical cable to improve the system reliability. One distributed control system can be also achieved by the control objective change. 
     It will be seen that the advantages set forth above, and those made apparent from the foregoing description, are efficiently attained. Further, since certain changes may be made in the above construction without departing from the scope of the invention, it is intended that all matters contained in the foregoing description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense. 
     It is also to be understood that the following claims are intended to cover all of the generic and specific features of the invention herein described, and all statements of the scope of the invention which, as a matter of language, might be said to fall there between.