Abstract:
Systems, methods, and devices relating to the extraction of parameters for a grid voltage. A multi-block hybrid PLL or hybrid observer receives grid voltage. The grid voltage is received by a harmonic/noise decomposer block which separates the harmonic/noise component of the incoming voltage from the clean voltage signal. The clean voltage signal is then output from the PLL/observer. The clean voltage signal is also sent to an amplitude estimator block which estimates the amplitude of the clean voltage signal. The harmonic/noise component of the input voltage signal is sent, along with the clean voltage signal, to a frequency estimator block. The frequency estimator block then determines the phase angle of the incoming signal as well as the frequency of the incoming voltage signal.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to systems, methods, and devices relating to grid-connected converters for use in a power grid. More specifically, the present invention relates to techniques used to extract grid voltage parameters for use in synchronizing grid connected power converters with the utility grid. 
       BACKGROUND OF THE INVENTION 
       [0002]    Distributed Generators (DGs) for power generation are becoming more prevalent due to their advantages over central power generation methods. By harvesting energy from renewable energy sources, DGs can provide a sustainable solution for future power generation. In order to accommodate a high number of DGs, the utility grid should be able to tolerate relatively high fluctuations in the frequency and amplitude of the grid voltage due to the dynamics the DGs impose on the utility grid. In order to accommodate these fluctuations, the standards for grid-connected power converters have rapidly been changing. The introduction of Rule 21 of “Test Protocols for Advanced Inverter Interoperability Functions” from Sandia National Laboratories for power converters with grid interconnection is one example of these changes. 
         [0003]    Grid-connected power converters must be synchronized with the grid voltage. Therefore, synchronization is an inevitable part of the control system for any grid-connected power converter. The grid synchronization block of the control system extracts the phase information of the grid voltage and synchronizes the power converter accordingly. It also extracts other attributes of the grid voltage such as amplitude whenever needed. 
         [0004]    The grid synchronization technique should be able to quickly extract the various parameters of the grid voltage even while in the presence of harmonics/noise. In particular, as the number of DGs coupled to the grid increase, there will be a significant amount of variations in the grid voltage. Thus, the synchronization technique must be able to properly synchronize with the grid despite the fluctuations and harmonics/noise in the grid voltage. 
         [0005]    Grid synchronizations based on the Adaptive Notch Filter (ANF) PLL and on the Second-Order Generalized Integrator (SOGI) PLL are the current state-of-the-art techniques used for grid synchronization. Both the ANF-based PLL and SOGI-based PLL each utilize two integrators in order to generate orthogonal signals. These orthogonal signals are then used to extract the phase/frequency information. Although these techniques provide a simple and practical solution for grid synchronization, they are susceptible to the harmonic content of the grid voltage. In order to mitigate the impact of harmonics, multiple modules need to be implemented for different harmonics. 
         [0006]      FIG. 1  shows the block diagram of the ANF-based PLL (Prior Art) while  FIG. 2  shows the block diagram of the SOGI-based PLL (Prior Art). According to  FIG. 1  and  FIG. 2 , both the ANF-based PLL and the SOGI-based PLL use two integrators (i.e., second order generalized integrator) to produce the orthogonal signals. Therefore, in terms of producing orthogonal signals, both methods have the same structure. However, the phase extraction technique from the orthogonal signals is different for the ANF-based PLL and the SOGI-based PLL. For the SOGI-based PLL, phase extraction is based on the dq-transformation (Park transformation) and PI controller for the SOGI-based PLL. For the ANF-based PLL, phase extraction is based on an adaptive algorithm. 
         [0007]    Neither the ANF-based PLL nor the SOGI-based PLL is able to precisely extract the attributes of the grid voltage in the presence of harmonics/noise and fluctuations. Therefore, grid-connected power converters require a more effective solution to be able to integrate into future DGs. 
         [0008]    Based on the above, there is therefore a need for systems and devices which mitigate if not avoid the shortcomings of the prior art. 
       SUMMARY OF INVENTION 
       [0009]    The present invention provides systems, methods, and devices relating to the extraction of parameters for a grid voltage. A multi-block hybrid PLL or hybrid observer receives grid voltage. The grid voltage is received by a harmonic/noise decomposer block which separates the harmonic/noise component of the incoming voltage from the clean voltage signal. The clean voltage signal is then output from the PLL/observer. The clean voltage signal is also sent to an amplitude estimator block which estimates the amplitude of the clean voltage signal. The harmonic/noise component of the input voltage signal is sent, along with the clean voltage signal, to a frequency estimator block. The frequency estimator block then determines the phase angle of the incoming signal as well as the frequency of the incoming voltage signal. 
         [0010]    In a first aspect, the present invention provides a system for determining parameters of an incoming signal, the system comprising:
       a harmonic/noise decomposer block for decomposing said incoming signal into a clean signal and a harmonic/noise component of said incoming signal;   a frequency estimator block for estimating a frequency and phase angle of said incoming signal, said frequency estimator block receiving said clean signal and said harmonic/noise component of said incoming signal;   an amplitude estimator block for estimating an amplitude of said incoming signal, said amplitude estimator block receiving said clean signal;       
 
         [0014]    wherein
       said decomposer block outputs said clean signal and said harmonic/noise component;   said frequency estimator block outputs said frequency and values related to said phase angle of said incoming signal;   said amplitude estimator block outputs said amplitude of said incoming signal.       
 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    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: 
           [0019]      FIG. 1  is a block diagram of an ANF-based PLL according to the prior art; 
           [0020]      FIG. 2  is a block diagram of a SOGI-based PLL according to the prior art; 
           [0021]      FIG. 3  is a block diagram of a hybrid observer according to one aspect of the present invention; 
           [0022]      FIG. 4  is a block diagram of a harmonic/noise decomposer block according to another aspect of the invention; 
           [0023]      FIG. 5  is a block diagram of a frequency estimator block according to another aspect of the invention; 
           [0024]      FIG. 6  is a block diagram of an amplitude estimator block according to another aspect of the invention; 
           [0025]      FIG. 7  are time domain waveforms of simulation results for the harmonic/noise decomposer; 
           [0026]      FIG. 8  are frequency domain waveforms of simulation results for the harmonic/noise decomposer; 
           [0027]      FIG. 9  are enlarged versions of frequency domain waveforms for simulation results for the harmonic/noise decomposer; 
           [0028]      FIG. 10  are waveforms showing the frequency tracking performance of the frequency estimator block; 
           [0029]      FIG. 11  is an enlarged version of sections of  FIG. 10 ; and 
           [0030]      FIG. 12  are waveforms of simulation results for the amplitude estimator block. 
       
    
    
     DETAILED DESCRIPTION 
       [0031]    Referring to  FIG. 3 , a block diagram of a hybrid observer according to one aspect of the present invention is illustrated. According to  FIG. 3 , the hybrid observer  10  includes three main blocks: a Harmonic/Noise Decomposer block  20 , a Frequency Estimator block  30 , and an Amplitude Estimator block  40 . In order to decouple the harmonics/noise from the grid voltage signal and to produce a clean sinusoidal signal, the Harmonic/Noise Decomposer block  20  is embedded in the hybrid observer  10 . After the signal is decomposed, the Frequency Estimator block  30  then extracts the phase information of the sinusoidal signal. Also, the Amplitude Estimator block  40  calculates the amplitude of the sinusoidal signal. 
         [0032]    The Harmonic/Noise Decomposer block  20  must decouple the harmonics/noise content of the grid voltage. The grid voltage is defined as: 
         [0000]      ν g ( t )= A  sin(ω t +φ)+ξ( t )  (1)
 
         [0000]    In Eqn. (1) the grid voltage consists of a sinusoidal term with the grid frequency and a term representing the harmonics/Noise content of the grid voltage, namely (t). Eqn. (1) can be rewritten as: 
         [0000]      ν g ( t )= x ( t )+ξ( t )  (2)
 
         [0000]    where x(t) is the sinusoidal signal with the grid frequency and ξ(t) is the harmonics/noise content of the grid voltage. 
         [0033]    In order to decouple the term ξ(t) from the grid voltage, the term ξ(t) must be estimated using the grid voltage ν g (t). To design a suitable estimator, the state variables of the system are defined as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                     g 
                     
                       State 
                        
                       
                           
                       
                        
                       
                         Vars 
                         . 
                       
                     
                   
                    
                   
                     : 
                   
                    
                   
                       
                   
                    
                   
                     { 
                     
                       
                         
                           
                             
                               x 
                               1 
                             
                             = 
                             
                               
                                 v 
                                 g 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               x 
                               2 
                             
                             = 
                             
                               
                                 1 
                                 ω 
                               
                                
                               
                                 
                                   x 
                                   . 
                                 
                                 1 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0034]    According to Eqn. (3), the dynamics of the system are given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     X 
                     g 
                     Dynamic 
                   
                    
                   
                     : 
                   
                    
                   
                       
                   
                    
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 x 
                                 . 
                               
                               1 
                             
                             = 
                             
                               ω 
                                
                               
                                   
                               
                                
                               
                                 x 
                                 2 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 x 
                                 . 
                               
                               2 
                             
                             = 
                             
                               
                                 
                                   - 
                                   ω 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   x 
                                   1 
                                 
                               
                               + 
                               ωξ 
                               + 
                               
                                 
                                   1 
                                   ω 
                                 
                                  
                                 
                                   ξ 
                                   ¨ 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0035]    In order to estimate the term ξ(t), the following mapping is introduced: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       Π 
                        
                       
                         : 
                       
                        
                       
                           
                       
                        
                       X 
                     
                      
                     
                       → 
                        
                     
                      
                     ϒ 
                   
                    
                   
                     
 
                   
                    
                   
                     
                        
                       = 
                       
                          
                         · 
                         χ 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                        
                       = 
                       
                         ( 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 - 
                                 1 
                               
                             
                             
                               1 
                             
                             
                               
                                 - 
                                 1 
                               
                             
                             
                               
                                 - 
                                 
                                   1 
                                   ω 
                                 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                             
                               0 
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       χ 
                       = 
                       
                         
                           ( 
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   x 
                                   2 
                                 
                               
                             
                             
                               
                                 ξ 
                               
                             
                             
                               
                                 
                                   ξ 
                                   . 
                                 
                               
                             
                           
                           ) 
                         
                         ∈ 
                         X 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                        
                       = 
                       
                         
                           ( 
                           
                             
                               
                                 
                                   ϑ 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   ϑ 
                                   2 
                                 
                               
                             
                             
                               
                                 
                                   ξ 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   ξ 
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                         ∈ 
                         ϒ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0036]    The mapping 
         [0000]    
       
         
           
             
               Π 
                
               
                 : 
               
                
               
                   
               
                
               X 
             
              
             
               → 
                
             
              
             ϒ 
           
         
       
     
         [0000]    is a diffeomorphism (i.e., since it is a bijection and invertible and its inverse is differentiable as well). Thus, X and Υ are diffeomorphic. It is worthwhile to mention that the importance of this mapping is to make the system observable for the term (t) (i.e., harmonic/noise content of the grid voltage). 
         [0037]    The dynamics of the system in Υ using the mapping 
         [0000]    
       
         
           
             
               Π 
                
               
                 : 
               
                
               
                   
               
                
               X 
             
              
             
               → 
                
             
              
             ϒ 
           
         
       
     
         [0000]    are given by: 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     g 
                     Dynamic 
                   
                    
                   
                     : 
                   
                    
                   
                       
                   
                    
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 ϑ 
                                 . 
                               
                               1 
                             
                             = 
                             
                               
                                 ωϑ 
                                 2 
                               
                               + 
                               
                                 ωϑ 
                                 1 
                               
                               + 
                               
                                 ωξ 
                                 1 
                               
                               + 
                               
                                 ξ 
                                 2 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 ϑ 
                                 . 
                               
                               2 
                             
                             = 
                             
                               
                                 
                                   - 
                                   2 
                                 
                                  
                                 
                                   ωϑ 
                                   1 
                                 
                               
                               - 
                               
                                 ωϑ 
                                 2 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 ξ 
                                 . 
                               
                               1 
                             
                             = 
                             
                               ξ 
                               2 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 ξ 
                                 . 
                               
                               2 
                             
                             = 
                             
                               ξ 
                               ¨ 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0038]    The observer for the system in in Υ is designed as: 
         [0000]                    Θ   g   Obs          :                     {                 ϑ   ^     .     1     =       ω          ϑ   ^     2       +     ωϑ   1     +     ω          ξ   ^     1       +       ξ   ^     2     +       μ   1            ϑ   ~     1                           ϑ   ^     .     2     =         -   2          ωϑ   1       -     ω          ϑ   ^     2       +       μ   2            ϑ   ~     1                           ξ   ^     .     1     =       ξ   ^     2                       ξ   ^     .     2     =       γ   1            ϑ   ~     1                         (   7   )               where θ 1 =θ 1 −θ 1 .
 
         [0039]      FIG. 4  shows the block diagram of the Harmonic/Noise Decomposer block, which is based on Eqn. (7). The outputs of this block are {circumflex over (ξ)} 1 , which is the estimation of the harmonics/noise, and {circumflex over (x)}, which is the grid voltage signal without the harmonics/noise content. It is important to mention that the diffeomorphism mapping 
         [0000]    
       
         
           
             
               Π 
                
               
                 : 
               
                
               
                   
               
                
               X 
             
              
             
               → 
                
             
              
             ϒ 
           
         
       
     
         [0000]    made it possible to precisely estimate the harmonics/noise content of the grid voltage signal. 
         [0040]    The other important aspect of the Harmonic/Noise Decomposer block  20  is the fact that it is not sensitive to the precise value of ω. Thus, the value of ω can be pre-set to a default value (e.g., 2π60 rad/s). Thus, regardless of the value of ω, the Harmonic/Noise Decomposer is able to precisely estimate the harmonic/noise content of the grid voltage signal. 
         [0041]    Referring to  FIG. 4 , one implementation of the decomposer block  20  has, as its input, the grid voltage (ν g )  110  while its outputs are {circumflex over (ξ)} 1    120 , which is the estimation of the harmonics/noise, and {circumflex over (x)}  130 , which is the grid voltage signal without the harmonics/noise content. The input  110  is received by three separate summation block  140 ,  150 ,  160 , and a multiplier block  170 . Summation block  140  adds the input  110  to the estimation output  120 . The result of this summation block  140  is then fed into another summation block  180  which adds the result to an interim variable {circumflex over (θ)} 2    190 . The result of summation block  180  is then multiplied by co by way of a multiplication block  200 . Summation block  210  then takes the result of multiplication block  200  and adds it to another interim variable {circumflex over (ξ)} 2 . The result of summation block  210  is then added to the term μ 1 {tilde over (θ)} 1  by way of summation block  220 . The result of summation block  220  is then passed through an integration block  230  to result in the interim variable {circumflex over (θ)} 1    240 . 
         [0042]    Returning to the input  110  to the decomposer  100 , this input is also received by summation block  150  that subtracts interim variable {circumflex over (θ)} 1    240  from the input  110 . The result is interim variable {tilde over (θ)} 1    250 . This interim variable  250  is multiplied using multiplier block  260  to result in the term μ 1 {tilde over (θ)} 1 . Similarly, this interim variable  250  is multiplied using multiplier block  270  to result in the term μ 2 {tilde over (θ)} 1 . 
         [0043]    As noted above, input  110  is received by multiplier block  170 . This multiplier block  170  multiplies the input  110  by the term 2ω and the result is fed into summation block  280 . Summation block  280  subtracts the result of multiplier block  170  from the negative of the result of multiplier block  290 . Block  290  multiplies the interim variable {circumflex over (θ)} 2    190  by the term co. The result of summation block  280  is then added by summation block  295  with the term μ 2 {tilde over (θ)} 1  and the result is fed into an integrator block  300 . The result is the interim variable {circumflex over (θ)} 2    190 . 
         [0044]    The result of summation block  150  is also multiplied by γ 1  using multiplier block  310 . The result of this block  310  is then passed through an integrator block  320  to result in interim variable {circumflex over (ξ)} 2 . This is passed through another integrator block  330  to result in output {circumflex over (ξ)} 1    120 . 
         [0045]    It should be noted that the other output {circumflex over (x)}  130  is achieved by subtracting output {circumflex over (ξ)} 1    120  from the input  110  by way of summation block  160 . 
         [0046]    The second block is the Frequency Estimator block  30 . The Frequency Estimator block  30  extracts the frequency/phase information from the resulting sinusoidal signal (i.e., the resulting output of the Harmonic/Noise Decomposer block). The output of the Harmonic/Noise Decomposer block  20  is given by: 
         [0000]      {circumflex over ( x )}( t )= A  sin(ω t +φ)  (8)
 
         [0047]    According to Eqn. (8), the dynamics of the system is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     Q 
                     Frq 
                     Dynamic 
                   
                    
                   
                     : 
                   
                    
                   
                       
                   
                    
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 q 
                                 . 
                               
                               1 
                             
                             = 
                             
                               q 
                               2 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 q 
                                 . 
                               
                               2 
                             
                             = 
                             
                               
                                 - 
                                 σ 
                               
                                
                               
                                   
                               
                                
                               
                                 q 
                                 1 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where q={circumflex over (x)}(t), q 2 ={dot over (q)} 1 , and θ=ω 2 . 
         [0048]    In order to estimate the parameter θ and, in turn, the frequency f, the following change of variables is used: 
         [0000]    
       
         
           
             
               
                 
                   
                     F 
                     Frq 
                     Mapping 
                   
                    
                   
                     : 
                   
                    
                   
                       
                   
                    
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 v 
                                 . 
                               
                               1 
                             
                             = 
                             
                               
                                 
                                   - 
                                   
                                     β 
                                     1 
                                   
                                 
                                  
                                 
                                   v 
                                   1 
                                 
                               
                               - 
                               
                                 v 
                                 2 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               v 
                               2 
                             
                             = 
                             
                               q 
                               1 
                             
                           
                         
                       
                       
                         
                           
                             
                               v 
                               3 
                             
                             = 
                             
                               
                                 q 
                                 2 
                               
                               - 
                               
                                 
                                   β 
                                   1 
                                 
                                  
                                 
                                   v 
                                   2 
                                 
                               
                               - 
                               
                                 σ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   v 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0049]    According to Eqn. (10), the system dynamics with the new state variables are given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     F 
                     Frq 
                     Dynamic 
                   
                   : 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 v 
                                 . 
                               
                               1 
                             
                             = 
                             
                               
                                 
                                   - 
                                   
                                     β 
                                     1 
                                   
                                 
                                  
                                 
                                   v 
                                   1 
                                 
                               
                               - 
                               
                                 v 
                                 2 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 v 
                                 . 
                               
                               2 
                             
                             = 
                             
                               
                                 v 
                                 3 
                               
                               + 
                               
                                 
                                   β 
                                   1 
                                 
                                  
                                 
                                   v 
                                   2 
                                 
                               
                               + 
                               
                                 σ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   v 
                                   1 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 v 
                                 . 
                               
                               3 
                             
                             = 
                             
                               
                                 
                                   - 
                                   
                                     β 
                                     1 
                                   
                                 
                                  
                                 
                                   v 
                                   3 
                                 
                               
                               - 
                               
                                 
                                   β 
                                   1 
                                   2 
                                 
                                  
                                 
                                   v 
                                   2 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0050]    The observer for the frequency is designed as: 
         [0000]                    Ψ   Frq   Obs     :     {               v   .     1     =         -     β   1            v   1       -     v   2                       v   .     2     =         v   ^     3     +       β   1          v   2       +       σ   ^                     v   1       +       β   2            v   ~     2                         v   .     3     =         -     β   1            v   3       -       β   1   2          v   2       +       β   3            v   ~     2                         σ   ^     .     =       γ   2          v   1            v   ~     2                       ϕ   ^     .     =       γ   3        cos                     θ   ^          (       v   2     -       A   ^                   sin                   θ   ^         )                       θ   ^     =       ∫         σ   ^               t         +     ϕ   ^                         (   12   )               where {tilde over (ν)} 2 =ν 2 −{circumflex over (ν)} 2 .
 
         [0051]      FIG. 5  shows the block diagram of the Frequency Estimator block, which is based on Eqn. (12). The outputs of this block is the phase information of the sinusoidal signal {circumflex over (x)}, namely {circumflex over (f)}, sin {circumflex over (θ)} and cos {circumflex over (θ)}. As should be clear, {circumflex over (f)} is the frequency of the signal and θ is the phase of the signal. 
         [0052]    From  FIG. 5 , one implementation of the Frequency Estimator block is illustrated. The estimator block  30  has, as input, the output {circumflex over (x)}  130  from the decomposer block and the output  400  of the amplitude estimator block  40 . As noted above, the outputs of this block  30  are the frequency {circumflex over (f)}  410  of the sinusoidal signal {circumflex over (x)}  130  and the phase related values sin {circumflex over (θ)}  420  and cos {circumflex over (θ)}  430 . 
         [0053]    Input  400  is multiplied with output  420  by way of multiplier block  440 . The result is then subtracted from input  130  by way of summation block  450 . The result of this summation block is then multiplied by γ 3  by way of multiplier block  460 . The result is then multiplied by output  430  by way of multiplier block  470 . The result of this block  470  is then passed through integrator block  480 . Integrator block  480  provides intermediate value {circumflex over (φ)}. This intermediate value is then added to the term {circumflex over (ω)}t (from integrator block  485 ) by way of summation block  490 . The result of summation block  490  is {circumflex over (θ)}. This value is then passed, in parallel, through sine block  500  and cosine block  510 . The result of sine block  500  is the output  420  and the result of cosine block  510  is the output  430 . 
         [0054]    It should be noted that estimator block  30  also produces three interim outputs {circumflex over (ν)} 1    520 , {circumflex over (ν)} 2    530 , and {circumflex over (ν)} 3    540  which are used in determining the outputs of the estimator block  30 . The interim output  520  is multiplied by multiplier block  550  by the value β 1 . The result is subtracted from the negative of the input  130  by summation block  560 . The result is then passed through integrator  570  to result in interim output  520 . 
         [0055]    The input  130  is received by multiplier block  580  which multiplies the input  130  by value β 1 . The result of this multiplier block is added to the interim output  540  by way of summation block  590 . The result of summation block  590  is then added, by summation block  600 , to the product of interim output  520  and {circumflex over (θ)}. This product is produced by multiplier  610 . The result of block  600  is then added to the value β 2 {tilde over (ν)} 2  by summation block  620 . The result is then passed through an integrator block  630  to result in the interim output  530 . 
         [0056]    It should be noted that input  130  is also received by summation block  640 . This summation block subtracts interim output  530  from input  130  to result in value {tilde over (ν)} 2 . This value is then multiplied, in parallel, using multiplier blocks  650 ,  660  to result in the values β 2 {tilde over (ν)} 2  and β 3 {tilde over (ν)} 2 . 
         [0057]    The input  130  is also received by multiplier block  670  which multiplies input  130  by β 1   2 . The result is then subtracted by summation block  680  from the negative of the result of multiplier block  690 . Multiplier block  690  multiplies the interim output  540  by the value β 1 . The result of summation block  680  is then added to the value β 3 {tilde over (ν)} 2  (from multiplier block  660 ) by way of summation block  695 . The result of this summation is passed through the integrator block  700 . The result is the interim output  540 . 
         [0058]    The input  130  is also received by multiplier block  710  which multiplies the input  130  by the result of summation block  640 . The result of this multiplier block  710  is then multiplied by multiplier block  720  by γ 2 . The resulting value is then integrated by integrating block  730 . The result of integrating block  730  is then passed through square root block  740  to produce {circumflex over (ω)}. This is then multiplied by 
         [0000]    
       
         
           
             1 
             
               2 
                
               π 
             
           
         
       
     
         [0000]    by the multiplier block  750 . This results in the output {circumflex over (f)}  410 . 
         [0059]    The third block is the Amplitude Estimator block  40 . In order to extract the amplitude, the output of the Harmonic/Noise Decomposer block  20  is used. This signal is a clean sinusoidal signal. Because of this, the harmonics/noise content has negligible impact on the amplitude estimation. In the present invention, the square value of the sinusoidal signal (i.e. the output of the Harmonic/Noise Decomposer block  20 ) is used to extract the amplitude of the sinusoidal signal. The output of the Harmonic/Noise Decomposer is given by: 
         [0000]      {circumflex over ( x )}( t )= A  sin(ω t +φ)  (13)
 
         [0060]    Thus a new variable is defined as: 
         [0000]        z ( t )=2 {circumflex over (x)}   2 ( t )=δ−δ cos(2ω t+ 2φ)  (14)
 
         [0000]    where δ=A 2 . 
         [0061]    According to Eqn. (14), the dynamics of the system is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     Z 
                     Amp 
                     Dynamic 
                   
                   : 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     z 
                                     . 
                                   
                                   1 
                                 
                                 = 
                                 
                                   2 
                                    
                                   ω 
                                    
                                   
                                       
                                   
                                    
                                   
                                     z 
                                     2 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     z 
                                     . 
                                   
                                   2 
                                 
                                 = 
                                 
                                   2 
                                    
                                   
                                     ω 
                                      
                                     
                                       ( 
                                       
                                         δ 
                                         - 
                                         
                                           z 
                                           1 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                          
                         
                             
                         
                          
                         where 
                          
                         
                           
 
                         
                          
                         
                           z 
                           1 
                         
                       
                       = 
                       
                         
                           z 
                            
                           
                               
                           
                            
                           and 
                            
                           
                               
                           
                            
                           
                             z 
                             2 
                           
                         
                         = 
                         
                           
                             1 
                             
                               2 
                                
                               ω 
                             
                           
                            
                           
                             
                               z 
                               1 
                             
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
         [0062]    In order to estimate the parameter δ and, in turn, the amplitude A, the following diffeomorphism mapping is used: 
         [0000]    
       
         
           
             
               
                 
                   
                     Ξ 
                     : 
                     
                       Z 
                        
                       
                         → 
                         A 
                       
                        
                       N 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       N 
                       = 
                       
                         Λ 
                         . 
                         Z 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       Λ 
                       = 
                       
                         ( 
                         
                           
                             
                               1 
                             
                             
                               0 
                             
                             
                               0 
                             
                           
                           
                             
                               
                                 - 
                                 1 
                               
                             
                             
                               1 
                             
                             
                               
                                 - 
                                 1 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                             
                               1 
                             
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       Z 
                       = 
                       
                         
                           ( 
                           
                             
                               
                                 
                                   z 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   z 
                                   2 
                                 
                               
                             
                             
                               
                                 δ 
                               
                             
                           
                           ) 
                         
                          
                         ε 
                          
                         
                             
                         
                          
                         Z 
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       N 
                       = 
                       
                         
                           ( 
                           
                             
                               
                                 
                                   η 
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   η 
                                   2 
                                 
                               
                             
                             
                               
                                 δ 
                               
                             
                           
                           ) 
                         
                          
                         ε 
                          
                         
                             
                         
                          
                         N 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0063]    According to Eqn. (16), N and Z are diffeomorphic with the mapping          . It is worthwhile to mention that the importance of this mapping is to make the system observable for the term δ and, in turn, A (i.e., the amplitude of the sinusoidal signal {circumflex over (x)}). 
         [0064]    The dynamics of the system in N using the mapping 
         [0000]    
       
         
           
             
               Ξ 
                
               
                 : 
               
                
               
                   
               
                
               Z 
             
              
             
               → 
               Λ 
             
              
             N 
           
         
       
     
         [0000]    is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     N 
                     g 
                     Dynamic 
                   
                   : 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 η 
                                 . 
                               
                               1 
                             
                             = 
                             
                               
                                 2 
                                  
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 
                                   η 
                                   2 
                                 
                               
                               + 
                               
                                 2 
                                  
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 
                                   η 
                                   1 
                                 
                               
                               + 
                               
                                 2 
                                  
                                 ωδ 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 η 
                                 . 
                               
                               2 
                             
                             = 
                             
                               
                                 
                                   - 
                                   4 
                                 
                                  
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 
                                   η 
                                   1 
                                 
                               
                               - 
                               
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 
                                   η 
                                   2 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               δ 
                               . 
                             
                             = 
                             
                               δ 
                               . 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0065]    The observer for the system in in N is designed as: 
         [0000]                    O   Amp   Obs     :     {                 η   ^     .     1     =       2      ω                     η   ^     2       +     2      ω                   η   1       +     2      ω        δ   ^       +       α   1            η   ~     1                           η   ^     .     2     =         -   4        ω                   η   1       -     2                 ω                       η     ^     2       +       α   2            η   ~     1                         δ   ^     .     =     2      ω                   γ   4            η   ~     1                         (   18   )               where {tilde over (η)} 1 =η 1 −{circumflex over (η)} 1 .
 
         [0066]      FIG. 6  shows the block diagram of the Amplitude Estimator block, which is based on Eqn. (18). The output of this block is the amplitude of the sinusoidal signal {circumflex over (x)}, namely {circumflex over (δ)} or, as shown in  FIG. 6 , Â. 
         [0067]    Referring to  FIG. 6 , the amplitude estimator block  40  has, as its input, the signal {circumflex over (x)}  130  from the decomposer block  20 . This input  130  is multiplied by itself (i.e. squared) by multiplier block  800  and the squared result is multiplied by multiplier block  810  by 2. The result of multiplier block  810  is then received by summation blocks  820 ,  830  and multiplier block  840 . 
         [0068]    The summation block  820  adds the result of multiplier block  810  to the value {circumflex over (δ)}. From block  820 , the result is then added by summation block  850  to the interim output {circumflex over (η)} 2    860 . The result from block  850  is then multiplied by multiplier block  870  with the value 2ω. From block  870 , the result is added by summation block  880  to the value α 1 {tilde over (η)} 1 . The result is passed through integrator block  890  to result in interim output {circumflex over (η)} 1    900 . 
         [0069]    As noted above, the result from multiplier block  810  is received by summation block  830 . Summation block  830  subtracts interim output  900  from this result from block  810 . The resulting value, {tilde over (η)} 1 , is then multiplied, in parallel, by multiplier blocks  910 ,  920  to result in the values α 1 {tilde over (η)} 1  and α 2 {tilde over (η)} 1 . 
         [0070]    Also as noted above, the result from multiplier block  810  is received by multiplier block  840 . This block  8540  multiplies the result from block  810  by  4   w  and the result is subtracted by summation block  930  from the negative of the result of multiplier block  940 . Block  940  multiplies the interim output  860  by 2ω. The result of block  930  is then added by summation block  950  to the value α 2 {tilde over (η)} 1  from multiplier block  920 . The result of block  950  then passed through integrator block  960  to result in the interim output  860 . 
         [0071]    The final branch of the block  40  has the result of summation block  830  being multiplied by 2ω by multiplier block  970 . The result of this block  970  is then multiplied by multiplier block  980  with value γ 3 . From this block  980 , the result is passed through integrator block  990 . A square root function is then applied to the result of this block  990  by square root block  1000  to result in output Â  400 . 
         [0072]    In order to evaluate the performance of the hybrid observer, a computer simulation has been conducted. In this simulation a polluted signal is given as the grid voltage.  FIG. 7 ,  FIG. 8 , and  FIG. 9  show the performance of the Harmonic/Noise Decomposer block. In this simulation, the pollution in the signal took the form and extent consisting of a 4% of the dc-component, a 4% of the 5 th  harmonic of a 60 Hz sinusoidal signal (i.e., 300 Hz) and a 4% of the 7 th  harmonic of a 60 Hz sinusoidal signal (i.e., 420 Hz) to a 100% of the fundamental component with the frequency of 59 Hz.  FIG. 7  shows that the Harmonic/Noise Decomposer block is able to isolate the harmonic/noise content of the signal and to extract the fundamental component in the presence of the harmonics and noise. It is important to note that the Harmonic/Noise Decomposer block is able to effectively estimate the dc-component as well as the harmonics. 
         [0073]      FIG. 8  shows the performance of the Harmonic/Noise Decomposer block in the frequency domain.  FIG. 8  confirms that the Harmonic/Noise Decomposer block can decouple the fundamental component from the harmonics/Noise.  FIG. 9  is an enlarged version of  FIG. 8  and shows that the Harmonic/Noise Decomposer block precisely estimates different components of the grid voltage signal. 
         [0074]      FIG. 10  and  FIG. 11  show the performance of the Frequency Estimator block.  FIG. 10  illustrates the frequency tracking performance of the Frequency Estimator block. In this figure, a step change from 59 Hz to 61 Hz is applied.  FIG. 10  shows that the Frequency Estimator block can precisely track the change in the frequency.  FIG. 11  is an enlarged version of  FIG. 10  and shows that the Frequency Estimator block is able to accurately estimate the frequency of the clean sinusoidal signal {circumflex over (x)}. 
         [0075]      FIG. 12  shows the performance of the Amplitude Estimator block.  FIG. 12  illustrates that the Amplitude Estimator block can precisely and quickly estimate the amplitude of the clean sinusoidal signal  2 . 
         [0076]    It should be noted that the systems and modules according to the present invention may be implemented using multiple methods. The present invention may be implemented using ASIC (application specific integrated circuit) technology or it may be implemented such that each block is implemented separately from the other blocks. Similarly, the present invention may be implemented using any suitable data processing device including a general data processor such as a general purpose computer. Alternatively, the present invention may be implemented using a dedicated data processing device specific for the use of the present invention. 
         [0077]    It should be noted that the functions and relationships detailed by Eqns. (7), (12), and (18) may be implemented using a general purpose computer using a suitable signal processing interface. The resulting values and/or signals can then be used in conjunction with a DG to synchronize grid-connected power converters with the grid. The values and/or signals from the general purpose computer can be used as input to a suitable interface with the power converter to thereby synchronize the power converter with the grid. 
         [0078]    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. 
         [0079]    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. 
         [0080]    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). 
         [0081]    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.