Abstract:
Systems, methods, and devices for controlling a DC-bus voltage for a power conditioning system. A control system regulates the DC value of the DC-bus voltage. The control system uses an adaptive DC-value estimator/observer to estimate this DC-value. Instead of having to determine the DC-value of a signal with a low frequency ripple without compromising the signal&#39;s dynamic response, a suitably precise estimate for that DC-value is used.

Description:
TECHNICAL FIELD 
     The present invention relates to control systems for grid-connected DC/AC converters. More specifically, the present invention relates to systems and methods for use in controlling the DC-bus voltage in grid connected DC/AC converters. 
     BACKGROUND OF THE INVENTION 
     Renewable energy is the key to future global sustainability, and many endeavours are being made to harvest renewable energy in an efficient and profitable manner. Environmental concerns and diminishing fossil fuel reserves increase the urgency of transitioning towards clean renewable energies. This explains the exponential growth of wind turbine (WT) and photovoltaic (PV) usage in the past few years. However, the variable nature of the power produced by WTs and PVs makes their controllability a challenge. Furthermore, when connecting renewable energies to the grid, increasingly stringent grid connection standards must be met. These standards emphasize the importance of fast control, the quality of the injected power into the grid, and robustness. Two main issues must be addressed in order to bring grid-connected renewable energies into the mainstream: cost and controllability. 
     A typical power conditioning system for renewable energy applications has two stages, and therefore requires two separate control schemes. The first stage is called the input-side converter, and is typically an AC/DC rectifier for WTs (see  FIG. 1A ) or a DC/DC converter for PVs (see  FIG. 1B ). The second stage is called the grid-side converter, and is typically a DC/AC inverter for most systems. The main task of the input-side converter is to achieve Maximum Power Point Tracking (MPPT) and extract maximum power from WTs or PVs. The main task of the grid-side converter is to ensure that all of the power extracted by the first stage is transferred to the grid quickly. To achieve this, the voltage across the capacitor between the two stages, also called the DC-bus capacitor, must be regulated. Although the second stage converter should also perform other important tasks, such as injecting high quality current to the grid, islanding detection, synchronization, reactive power compensation, and other ancillary services, regulating the DC-bus voltage is vitally important in order to guarantee the reliable operation of the power conditioning system. 
     The DC-bus capacitor acts as an energy storage capacitor and provides the flexibility to alternate the instantaneous power in between the two stages, giving the system the ability to absorb sudden changes in power coming from the input-side converter. More importantly, in single-phase power conditioning systems, the DC-bus capacitor is used to decouple the power ripple by providing a low frequency current. The main challenge regarding the DC-bus voltage loop controller for grid-connected single-phase inverters is the presence of the low frequency ripple in the DC-bus capacitor voltage (this ripple is also present in three-phase unbalanced systems). In a conventional DC-bus voltage control scheme, a very low bandwidth PI controller is usually used to regulate the DC-bus voltage. The PI controller should have a very low bandwidth in order to prevent the low frequency ripple from propagating to the control loop through the DC-bus voltage feedback. Because of this, the conventional DC-bus voltage controller produces a very sluggish and poor transient response. This not only affects the performance of the DC/AC converter, but also forces the designer to over-design the converter in order to have reliable performance against the overshoots/undershoots that occur during transients. 
     Based on the above, there is therefore a need for developments which mitigate if not overcome the shortcomings of the prior art. 
     SUMMARY OF INVENTION 
     The present invention provides systems, methods, and devices for controlling a DC-bus voltage for a power conditioning system. A control system regulates the DC value of the DC-bus voltage. The control system uses an adaptive DC-value estimator/observer to estimate this DC-value. Instead of having to determine the DC-value of a signal with a low frequency ripple without compromising the signal&#39;s dynamic response, a suitably precise estimate for that DC-value is used. 
     In a first aspect, the present invention provides a control system for use in controlling a converter, the control system comprising:
         a voltage controller for controlling a voltage of said converter;   a current controller for controlling a current of said converter;   an observer/estimator for estimating a DC-bus voltage of said converter;   wherein   an estimate of said DC-bus voltage is subtracted from a measured DC-bus voltage of said converter;   said current controller produces a value used to control a timing of opening and closing of switches in said converter.       

     In a second aspect, the present invention provides a component for estimating a DC-bus voltage of a converter, the component being represented by: 
     
       
         
           
             
               Σ 
               
                 v 
                 BUS 
               
             
             ⁢ 
             
               : 
             
             ⁢ 
             
                 
             
             ⁢ 
             
               { 
               
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             
                               η 
                               ^ 
                             
                             . 
                           
                           1 
                         
                         = 
                         
                           
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ω 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     
                                       η 
                                       ^ 
                                     
                                     2 
                                   
                                   + 
                                   
                                     η 
                                     1 
                                   
                                   + 
                                   
                                     
                                       V 
                                       ^ 
                                     
                                     DC 
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               ξ 
                               1 
                             
                             ⁢ 
                             
                               
                                 η 
                                 ~ 
                               
                               1 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             
                               η 
                               ^ 
                             
                             . 
                           
                           2 
                         
                         = 
                         
                           
                             
                               - 
                               4 
                             
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               η 
                               1 
                             
                           
                           - 
                           
                             2 
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 η 
                                 ^ 
                               
                               2 
                             
                           
                           + 
                           
                             
                               ξ 
                               2 
                             
                             ⁢ 
                             
                               
                                 η 
                                 ~ 
                               
                               1 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             
                               V 
                               ^ 
                             
                             . 
                           
                           DC 
                         
                         = 
                         
                           2 
                           ⁢ 
                           μ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               η 
                               ~ 
                             
                             1 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     where ξ 1 ε             + , ξ 2 =2ω, {tilde over (η)} 1 =η 1 −{circumflex over (η)} 1 , and {tilde over (η)} 2 =η 2 −{circumflex over (η)} 2 .
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The embodiments of the present invention will now be described by reference to the following figures, in which identical reference numerals in different figures indicate identical elements and in which: 
         FIG. 1A  is a circuit diagram for an AC/DC rectifier for wind turbines according to the prior art; 
         FIG. 1B  is a circuit diagram for a DC/DC converter for photovoltaic solar farms according to the prior art; 
         FIG. 2  is a schematic of a grid connected DC/AC converter with an LCL-filter; 
         FIG. 3  is a block diagram of a voltage control system for a single-phase grid-connected DC/AC converter; 
         FIG. 4  is a block diagram of a DC-value observer/estimator according to one aspect of the invention; 
         FIG. 5  is a block diagram of a closed-loop control system with a DC value observer according to one aspect of the invention; 
         FIG. 6  illustrates the transient response of the observer/estimator for a step change in the DC-bus voltage; 
         FIG. 7  shows the trajectory for η 1  and η 2  when the step change in  FIG. 6  is applied; 
         FIG. 8  shows the trajectory of the control system for the transient in  FIG. 7 ; 
         FIG. 9  illustrates the performance of the closed loop control system in  FIG. 5  for positive step changes; 
         FIG. 10  illustrates the performance of the closed loop control system in  FIG. 5  for negative step changes; and 
         FIG. 11  shows experimental waveforms from an experimental prototype of one aspect of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     The present invention relates to a DC-bus voltage controller which performs the DC-bus voltage regulation for a renewable energy power conditioning system. The present invention provides a new DC-bus voltage controller which is able to improve the transient response of the DC-bus voltage control loop significantly and provides a robust and reliable solution for multiple applications. The control scheme of the present invention is based on estimating the DC value of the DC-bus voltage through a specific adaptive filter. The structure of the filter provides a very fast and robust estimation for the DC value of the DC-bus voltage. The DC-extraction technique is able to precisely estimate the DC value in the presence of a double frequency ripple on top of the the DC-bus voltage. 
     Referring to  FIG. 2 , a schematic of a grid-connected DC/AC converter with an LCL-filter is shown. LCL-filters are widely used at the output of the DC/AC in order to filter out the high frequency components produced by switching and to thereby deliver a high quality current to the utility grid. LCL-filters provide better attenuation than comparably sized L-filters (i.e., attenuation for LCL-filters is at −60 dB/dec while attenuaton for L-filters is at −20 dB/dec). 
     Between the two stages of a power conditioning system, there is a DC-bus which is supported by a fairly large capacitor depending on the system specifications. This capacitor acts as an energy storage capacitor and provides the flexibility of alternating the instantaneous energy in the power conditioning system. Erratic behaviour of the renewable energy sources demand a fairly robust control system in order to smoothly control the power flow between the two stages of the power conditioning system. 
       FIG. 3  shows a typical block diagram of a voltage control system for a single-phase grid-connected DC/AC converter. In  FIG. 3 , the voltage control system  10  has a reference voltage  20  as input to the system  10 . An adder  30  substracts the reference voltage  20  from the DC-bus voltage (v BUS )  40  of the converter. The output of the adder  30  is then sent to a voltage controller  50 . The result of the voltage controller  50  is a reference current (I ref )  60  which is sent to a multiplier  70 . The multiplier  70  multiplies the reference current  60  with a signal  80  (sin(cot)) from a PLL  90 . The output  100  (i ref ) of the multiplier  70  is sent to another adder  110 . The adder  110  subtracts a current output  120  (i g ) of the converter from this output  100  of the multiplier  70 . The output  120  of the adder  110  is then sent to a current controller  130 . As another input to the current controller  130 , a value  135  (K·X) from a multiplier block  140 . The output of the current controller is a value  150  (inverter output voltage duty cycle d) that is fed into a DC/AC converter  160 . The converter  160  outputs a value  170  for a system state variable (X) that is fed into multiplier  140 . As well, the converter outputs a signal  180  (grid voltage v g ) that is fed into PLL  90 . 
     According to  FIG. 3 , an external voltage control loop regulates the DC-bus voltage of the converter. The voltage controller determines the amplitude of the current to be injected to the grid such that the power balance between the first-stage and second-stage is satisfied, or equivalently, that the DC-bus voltage is maintained at a constant. Because the voltage controller deals with DC signals, PI regulators are usually used to implement this controller. The main issue with this control approach is that a significant amount of double frequency ripple is present on the DC-bus voltage due to the inevitable power ripple inherent in single-phase power conditioning systems (this ripple is also present in three-phase unbalanced systems). This double frequency ripple is produced by the output power and reflected back on to the DC-bus voltage. The low frequency component is superimposed on top of the DC-bus voltage component. Since the power ripple is imposed on the DC-bus voltage, this causes challenges for the DC-bus voltage controller. The double frequency ripple will propagate to the current loop if the DC-bus voltage controller does not remove it. Removal of the double frequency ripple from the DC-bus voltage can have repercussions. In order for the PI controller to remove the double frequency ripple, its bandwidth must be lowered significantly. This will result in a very sluggish transient performance and an inability to deal with sudden changes in the input power. Thus, when there is a sudden transient, the voltage across the DC-bus capacitor will fluctuate considerably. As a result, the DC-bus capacitor and converter switches will need to be overrated so that they can perform reliably and do not burn out. This not only causes an increase in system costs but also results in very poor transient performance and marginal stability. 
     The voltage loop controller is designed to regulate the DC value of the DC-bus voltage. Extracting the DC-value of a signal with a low frequency ripple without compromising the dynamic response is very challenging, especially since low pass filters with low bandwidth introduce a large delay into the filtered signal. The present invention, in one aspect, provides a novel fast DC value extraction without compromising the dynamics. The DC-bus voltage has a DC value with a superimposed double-frequency ripple. Therefore, the DC-bus voltage is represented by:
 
 v   BUS   =V   DC   +V   ripple  sin(2ω t )  (1)
 
     The objective is to extract V DC  from v BUS  without introducing a delay to the signal. From Eqn. (1), the following equations are derived: 
     
       
         
           
             
               
                 
                   
                     
                       v 
                       . 
                     
                     BUS 
                   
                   = 
                   
                     2 
                     ⁢ 
                     ω 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       V 
                       ripple 
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         
                           2 
                           ⁢ 
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           t 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             v 
                             ¨ 
                           
                           BUS 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             - 
                             4 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ω 
                             2 
                           
                           ⁢ 
                           
                             V 
                             ripple 
                           
                           ⁢ 
                           
                             sin 
                             ⁡ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             - 
                             4 
                           
                           ⁢ 
                           
                             
                               ω 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   v 
                                   BUS 
                                 
                                 - 
                                 
                                   V 
                                   DC 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     From the above, the following equation describes the dynamics of the DC-bus voltage:
 
 {umlaut over (v)}   BUS +4ω 2   v   BUS −4ω 2   V   DC =0  (4)
 
     Eqn. (4) represents a second order system and can be presented in the standard form as follows: 
     
       
         
           
             
               
                 
                   
                     Σ 
                     
                       v 
                       BUS 
                     
                   
                   ⁢ 
                   
                     : 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                               
                             ⁢ 
                             
                               
                                 
                                   x 
                                   . 
                                 
                                 1 
                               
                               = 
                               
                                 2 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   x 
                                   2 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                             ⁢ 
                             
                               
                                 
                                   x 
                                   . 
                                 
                                 2 
                               
                               = 
                               
                                 
                                   - 
                                   2 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ω 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         x 
                                         1 
                                       
                                       - 
                                       
                                         V 
                                         DC 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     where x 1 =v BUS  and 
     
       
         
           
             
               x 
               2 
             
             = 
             
               
                 1 
                 
                   2 
                   ⁢ 
                   ω 
                 
               
               ⁢ 
               
                 
                   
                     x 
                     . 
                   
                   1 
                 
                 . 
               
             
           
         
       
     
     The objective is to estimate V DC  from the dynamics given in Eqn. (5). Since V DC  is in the second equation of Eqn. (5) and x 2  is not measurable, a change of variables need to be performed. The change of variable used in this invention is given by:
 
η 1   =x   1   (6)
 
η 2   =x   2   −x   1   −V   DC   (7)
 
     The system dynamics with the new variables are given by: 
     
       
         
           
             
               
                 
                   
                     Σ 
                     
                       v 
                       BUS 
                     
                   
                   ⁢ 
                   
                     : 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                               
                             ⁢ 
                             
                               
                                 
                                   η 
                                   . 
                                 
                                 1 
                               
                               = 
                               
                                 2 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       η 
                                       2 
                                     
                                     + 
                                     
                                       η 
                                       1 
                                     
                                     + 
                                     
                                       V 
                                       DC 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                             ⁢ 
                             
                               
                                 
                                   η 
                                   . 
                                 
                                 2 
                               
                               = 
                               
                                 
                                   
                                     - 
                                     4 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ωη 
                                     1 
                                   
                                 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   ω 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     η 
                                     2 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Eqn. (8) is in the proper form for designing the observer which will perform the estimation. The change of variables, using Eqns. (6)-(7), makes it possible to design the observer as the desired parameter, V DC , now appears in the measurable variable dynamics {circumflex over (η)} 1 . The adaptive observer for V DC  can thus be designed as: 
     
       
         
           
             
               
                 
                   
                     
                       Σ 
                       ^ 
                     
                     
                       v 
                       BUS 
                     
                   
                   ⁢ 
                   
                     : 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                               
                             ⁢ 
                             
                               
                                 
                                   
                                     η 
                                     ^ 
                                   
                                   . 
                                 
                                 1 
                               
                               = 
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ω 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           
                                             η 
                                             ^ 
                                           
                                           2 
                                         
                                         + 
                                         
                                           η 
                                           1 
                                         
                                         + 
                                         
                                           
                                             V 
                                             ^ 
                                           
                                           DC 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     ξ 
                                     1 
                                   
                                   ⁢ 
                                   
                                     
                                       η 
                                       ~ 
                                     
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                             ⁢ 
                             
                               
                                 
                                   
                                     η 
                                     ^ 
                                   
                                   . 
                                 
                                 2 
                               
                               = 
                               
                                 
                                   
                                     - 
                                     4 
                                   
                                   ⁢ 
                                   ω 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     η 
                                     1 
                                   
                                 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   ω 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     
                                       η 
                                       ^ 
                                     
                                     2 
                                   
                                 
                                 + 
                                 
                                   
                                     ξ 
                                     2 
                                   
                                   ⁢ 
                                   
                                     
                                       η 
                                       ~ 
                                     
                                     1 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                               
                             ⁢ 
                             
                               
                                 
                                   
                                     V 
                                     ^ 
                                   
                                   . 
                                 
                                 DC 
                               
                               = 
                               
                                 2 
                                 ⁢ 
                                 μ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     η 
                                     ~ 
                                   
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
         
         
           
             where, ξ 1 ε           + , ξ 2 =2ω, {tilde over (η)} 1 =η 1 −{circumflex over (η)} 1 , and {tilde over (η)} 2 =η 2 −{circumflex over (η)} 2 . 
           
         
       
    
     The error dynamics for this adaptive observer is derived as: 
     
       
         
           
             
               
                 
                   
                     
                       Σ 
                       ~ 
                     
                     
                       v 
                       BUS 
                     
                   
                   ⁢ 
                   
                     : 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 
                                   η 
                                   ~ 
                                 
                                 . 
                               
                               1 
                             
                             = 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                   ω 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           η 
                                           ~ 
                                         
                                         2 
                                       
                                       + 
                                       
                                         
                                           V 
                                           ~ 
                                         
                                         DC 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               - 
                               
                                 
                                   ξ 
                                   1 
                                 
                                 ⁢ 
                                 
                                   
                                     η 
                                     ~ 
                                   
                                   1 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   η 
                                   ~ 
                                 
                                 . 
                               
                               2 
                             
                             = 
                             
                               
                                 
                                   - 
                                   2 
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                   
                                     η 
                                     ~ 
                                   
                                   2 
                                 
                               
                               - 
                               
                                 
                                   ξ 
                                   2 
                                 
                                 ⁢ 
                                 
                                   
                                     η 
                                     ~ 
                                   
                                   1 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   V 
                                   ~ 
                                 
                                 . 
                               
                               DC 
                             
                             = 
                             
                               
                                 - 
                                 2 
                               
                               ⁢ 
                               μω 
                               ⁢ 
                               
                                 
                                   η 
                                   ~ 
                                 
                                 1 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
         
         
           
             where {tilde over (V)} DC =V DC −{circumflex over (V)} DC . 
           
         
       
    
     The existence and boundedness of the solution of Eqn. (10) are guaranteed by using the following Lyapunov function: 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         
                           η 
                           ~ 
                         
                         1 
                         2 
                       
                     
                     + 
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         
                           η 
                           ~ 
                         
                         2 
                         2 
                       
                     
                     + 
                     
                       
                         1 
                         
                           2 
                           ⁢ 
                           μ 
                         
                       
                       ⁢ 
                       
                         
                           V 
                           ~ 
                         
                         DC 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The derivative of the Lyapunov function is given by: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           V 
                           . 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               
                                 η 
                                 ~ 
                               
                               1 
                             
                             ⁢ 
                             
                               
                                 
                                   η 
                                   ~ 
                                 
                                 . 
                               
                               1 
                             
                           
                           + 
                           
                             
                               
                                 η 
                                 ~ 
                               
                               2 
                             
                             ⁢ 
                             
                               
                                 
                                   η 
                                   ~ 
                                 
                                 . 
                               
                               2 
                             
                           
                           + 
                           
                             
                               
                                 V 
                                 ~ 
                               
                               DC 
                             
                             ⁢ 
                             
                               
                                 
                                   V 
                                   ~ 
                                 
                                 . 
                               
                               DC 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               - 
                               
                                 ξ 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 η 
                                 ~ 
                               
                               1 
                               2 
                             
                           
                           - 
                           
                             2 
                             ⁢ 
                             ω 
                             ⁢ 
                             
                               
                                 
                                   
                                       
                                   
                                   ⁢ 
                                   η 
                                 
                                 ~ 
                               
                               2 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     According to Eqn. (12), the derivative of the Lyapunov function is negative semi-definite (i.e. it is not negative definite). Eqn. (12) only guarantees that the error signals {tilde over (η)} 1  and {tilde over (η)} 2  converge to zero. However, only the boundedness of {tilde over (V)} DC  is guaranteed, not the asymptotic convergence. The particular structure of the adaptive observer provides the necessary and sufficient condition to prove the asymptotic convergence of {tilde over (V)} DC . The asymptotic convergence is proven by using the persistency of excitation theorem. This theorem states that if the update law {dot over ({circumflex over (V)})} DC  is persistently excited, the global asymptotic stability is concluded for the estimation errors. In particular, in order to have persistency of excitation, the following condition must be satisfied for two positive real values T and k:
 
∫ t   t+T   {circumflex over (V)}   DC   2 (τ) dτ≧k&gt; 0  (13)
 
     Because there is inherently a double-frequency ripple present at the DC-bus voltage, the update law {dot over ({circumflex over (V)})} DC =2μω{tilde over (η)} 1  is constantly being excited. In particular, by choosing T=1/(2ω t ) (i.e. half a line cycle) and convergence of {circumflex over (η)} 1  to an arbitrary dc value with a double frequency ripple given by: 
                            V   ripple          peak     =       P   in       2   ⁢     ω   line     ⁢     C   BUS     ⁢     V   BUS                 (   14   )               
the condition for the theorem is satisfied. Thus, the update law in the adaptive observer is persistently excited. The persistency of excitation theorem proves the globally exponentially stable equilibrium point (0,0,0) for ({tilde over (η)} 1 , {tilde over (η)} 2 , {tilde over (η)} DC ).
 
     From the above, it has rigorously been shown how the proposed observer precisely estimates the DC value of the DC-bus voltage. Intuitively, the observer operates based on the energy of the estimation errors. The natural double frequency ripple in the system persistently excites the system. This persistent excitation provides energy for the estimated parameter, V DC  to converge to its actual value. 
     The adaptive observer described by Eqn. (9) is able to estimate the DC value of DC-bus voltage very quickly. The block diagram of the DC-value observer is shown in  FIG. 4 . Using this observer to extract the DC value of the DC-bus voltage allows the voltage controller to have a very high bandwidth. Since the double frequency ripple becomes completely isolated from the control loop, the bandwidth of the voltage loop controller can be significantly increased when compared to the bandwidth for a conventional voltage control loop. 
     Referring to  FIG. 4 , the inputs to the observer  200  are the DC-bus voltage  210  (v BUS ) of the converter  160 , the value  220  (2ω), and the value  225  (4ω). The output voltage  210  is sent to a first adder  230 , a second adder  240 , and a multiplier  250 . The adder  230  subtracts an output  260  ({circumflex over (η)} 1 ) of the observer from the DC-bus voltage  210 . The adder  240  adds another output  270  ({circumflex over (V)} DC ) to the DC-bus voltage  210 . This output  270  is an estimated DC voltage used by the controller. The multiplier  250  multiplies the value  225  with the DC-bus voltage  210 . The output of this multiplier  250  is then subtracted with the output of another multiplier  280  by way of adder  285 . This multiplier  280  multiplies the value  220  with another output  290  (({circumflex over (η)} 2 ). The output of adder  285  is added by adder  300  to the result of multiplier  310 . Multiplier  310  multiplies value  220  with the result of adder  230 . The result of adder  300  is then integrated by integrator  320  to result in output  290 . 
     Continuing the reference to  FIG. 4 , the result of adder  240  is received by another adder  330 . Adder  330  adds the result of adder  240  to the output  290  of the observer  200 . The result of adder  330  is multiplied by multiplier  340  with value  220 . The result of multiplier  340  is then added to the result of adder  230  by adder  350 . The output of this adder  350  is then integrated by integrator  360 . The result of integrator  360  is the output  260 . 
     At the top of  FIG. 4 , the value  220  is multiplied by multiplier  370  to the result of adder  230 . The result of multiplier  370  is then integrated by integrator  380  to result in output  270 . 
     The arrangement, shown in  FIG. 5 , represents the block diagram of the closed-loop control system with the DC value observer. The DC-value Estimator block (shown in detail in  FIG. 4 ) implements Eqn. (9). 
     Referring to  FIG. 5 , the control system in  FIG. 5  is similar to the control system in  FIG. 3  with the addition of a DC-value estimator  400 . For ease of reference, reference numerals in  FIG. 3  for similar elements are used in  FIG. 5 . The DC-value estimator  400  (also referred to as an observer) receives a value  410  (ω) from PLL  90 . Along with this, the DC-value estimator  400  also receives DC-bus voltage (v BUS )  40  of the converter  160 . The result of the DC-value estimator  400  is subtracted from the input  420  V DC  by way of adder  30 . 
       FIG. 6  shows the transient response of the adaptive observer for a step change in the DC-bus voltage. This figure demonstrates a very fast estimation of the DC component of the DC-bus voltage.  FIG. 7  shows the trajectory of η 1  and η 2  when the step change is applied. According to  FIG. 7 , the system is steered from a first DC voltage level to the second DC voltage level when the step change is applied.  FIG. 8  shows the trajectory of the system for this transient. The steady-state limit cycles for two DC voltage levels are evident in  FIG. 8 . 
     The performance of the closed-loop control system is illustrated in  FIG. 9  and  FIG. 10  for positive and negative step changes respectively. According to  FIG. 9  and  FIG. 10 , the observer provides a very fast and accurate estimation of the DC value of the DC-bus voltage. Therefore, a very fast transient response is achievable with the closed-loop control system. 
       FIG. 11  shows the experimental waveforms obtained from an experimental prototype. The experimental prototype is a 1 kW grid-connected photovoltaic (PV) micro-inverter. a 50% step load change is applied to the system by increasing the converter input power (through the PV simulator). This figure shows a smooth and stable transient response of the proposed voltage loop control system. 
     It should be noted that the observer of the invention may also be implemented as a suitably programmed ASIC to provide the requisite control signals for the power semiconductors in the PFC converter. 
     The embodiments of the invention may be executed by a computer processor or similar device programmed in the manner of method steps, or may be executed by an electronic system which is provided with means for executing these steps. Similarly, an electronic memory means such as computer diskettes, CD-ROMs, Random Access Memory (RAM), Read Only Memory (ROM) or similar computer software storage media known in the art, may be programmed to execute such method steps. As well, electronic signals representing these method steps may also be transmitted via a communication network. 
     Embodiments of the invention may be implemented in any conventional computer programming language. For example, preferred embodiments may be implemented in a procedural programming language (e.g.“C”) or an object-oriented language (e.g.“C++”, “java”, “PHP”, “PYTHON” or “C#”). Alternative embodiments of the invention may be implemented as pre-programmed hardware elements, other related components, or as a combination of hardware and software components. 
     Embodiments can be implemented as a computer program product for use with a computer system. Such implementations may include a series of computer instructions fixed either on a tangible medium, such as a computer readable medium (e.g., a diskette, CD-ROM, ROM, or fixed disk) or transmittable to a computer system, via a modem or other interface device, such as a communications adapter connected to a network over a medium. The medium may be either a tangible medium (e.g., optical or electrical communications lines) or a medium implemented with wireless techniques (e.g., microwave, infrared or other transmission techniques). The series of computer instructions embodies all or part of the functionality previously described herein. Those skilled in the art should appreciate that such computer instructions can be written in a number of programming languages for use with many computer architectures or operating systems. Furthermore, such instructions may be stored in any memory device, such as semiconductor, magnetic, optical or other memory devices, and may be transmitted using any communications technology, such as optical, infrared, microwave, or other transmission technologies. It is expected that such a computer program product may be distributed as a removable medium with accompanying printed or electronic documentation (e.g., shrink-wrapped software), preloaded with a computer system (e.g., on system ROM or fixed disk), or distributed from a server over a network (e.g., the Internet or World Wide Web). Of course, some embodiments of the invention may be implemented as a combination of both software (e.g., a computer program product) and hardware. Still other embodiments of the invention may be implemented as entirely hardware, or entirely software (e.g., a computer program product). 
     A person understanding this invention may now conceive of alternative structures and embodiments or variations of the above all of which are intended to fall within the scope of the invention as defined in the claims that follow.