Abstract:
A method for estimating grid properties of a power grid coupled to a generator at a point of common coupling is provided. First, a voltage V PCC  at the point of common coupling is measured. Second, a current I PCC  at the point of common coupling is measured. Third, the grid properties are estimated by a grid model using as input parameters the measured voltage V PCC  at the point of common coupling, the measured current I PCC  at the point of common coupling and the determined phase angle. Advantageously, the absolute phases of the voltage and the current at the point of common coupling are not necessary, which makes the present method less prone to errors due to measurement noise. Further, a device and a computer program product are provided.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority to and the benefit of European Application No. EP13176978 filed Jul. 18, 2013, incorporated by reference herein in its entirety. 
       FIELD OF INVENTION 
       [0002]    The present invention relates to a method and to a device for estimating grid properties of a power grid. Further, the present invention relates to a method and to an apparatus for controlling a generator coupled to a power grid as well as to a method and to an apparatus for operating a power grid. 
       BACKGROUND OF INVENTION 
       [0003]    The grid properties of an electric power grid particularly include the grid impedance and the grid voltage. For example, these grid properties may be estimated by a Thevenin equivalent model of the electric grid. 
         [0004]    Thevenin&#39;s theory holds, to illustrate in DC circuit theory terms, that any linear electric network, here the electric power grid, with voltage and current sources, like generators and solar plants, and resistances can be replaced at terminals, here the point of common coupling, by an equivalent voltage source, here the grid voltage, in series connection with an equivalent resistance, here the grid impedance. The equivalent voltage is the voltage obtained at the point of common coupling in an open circuit. The equivalent resistance, here the grid impedance, is the resistance obtained at the point of common coupling with all its independent current sources open-circuited and all its independent voltage sources short-circuited. 
         [0005]    Conventionally, the grid properties of a power grid are estimated by driving the system to different steady-state points where the current and the voltage are measured, both the amplitude and the absolute phase of both variables. One problem here is the imprecision of the measurements of the absolute phase changes between different operating points due to frequency variations. In such a case, it may be enough to have two operating points for identifying the grid model, but more points may be used to minimize the error due to measurement noise. On the other hand, the problem regarding the absolute phase changes remains. 
         [0006]    For example, K. O. H. Pedersen, A. H. Nielsen and N. K. Poulsen describe in the article “Short-circuit impedance measurement” methods for estimating the short-circuit impedance in the power grid for various voltage levels and situations. The short-circuit impedance is measured, preferably based on naturally occurring load changes in the grid. They show that such a measurement system faces different kinds of problems at different locations in the grid. This means that the best measurement methodology changes depending on the location in the grid. Three typical examples with different measurement programs at 400 kV, 132 kV and 400 V voltage level are discussed there. 
       SUMMARY OF INVENTION 
       [0007]    Accordingly, it is an object of the present invention to provide an improved estimation of the grid properties of a power grid coupled to a generator. 
         [0008]    According to a first aspect, a method for estimating grid properties of a power grid coupled to a generator at a point of common coupling PCC is provided. In a first step, a voltage V PCC  at the point of common coupling is measured. In a second step, a current I PCC  at the point of common coupling is measured. In a third step, the grid properties are estimated by a grid model using as input parameters the measured voltage V PCC  at the point of common coupling, the measured current I PCC  at the point of common coupling and the determined phase angle. 
         [0009]    In the present method, the grid properties are estimated based on the measured voltage V PCC , the measured current I PCC  and the determined phase angle between the voltage V PCC  and the current I PCC . Thus, the absolute phases of the voltage V PCC  and the current I PCC  are not necessary, which makes the present method less prone to errors due to measurement noise. In particular, the minimum number of operating points needed here is three, but more operating points may be used to mitigate the influence of noise. 
         [0010]    By means of the present method it is possible to formulate a grid estimation problem as a solution of a set of quadratic polynomial equations whose coefficients are functions of the amplitude of the voltage V PCC , the amplitude of the current I PCC  and the relative phase angle (or equivalently the magnitude of V PCC , the active power as well as the reactive power). Details for both are given in the following detailed description. 
         [0011]    In case of three operating points, the solution may also be found either analytically or numerically by applying appropriate equation solvers. 
         [0012]    According to an embodiment, the grid properties include a grid impedance Z G  and a grid voltage V G  of the power grid. 
         [0013]    Both, the estimated grid impedance and the estimated grid voltage may be of use for different technical applications. For example, the grid properties may be used for controlling a generator coupled to a power grid, wherein the generator is controlled in dependence on the estimated grid properties. Further, the estimated grid properties may be used to operate the power grid in dependence on said estimated grid properties. 
         [0014]    According to a further embodiment, the voltage V PCC  at the point of common coupling and the current I PCC  at the point of common coupling are measured at a fundamental frequency of the power grid. For example, the fundamental frequency is 50 Hz. 
         [0015]    According to a further embodiment, the method includes the following steps: 
         [0016]    a) measuring the voltage V PCC  at the point of common coupling PCC at N different working points of the power grid, N≧3, 
         [0017]    b) measuring the current I PCC  at the point of common coupling PCC at the N different working points, 
         [0018]    c) determining the phase angle α between the measured voltage V PCC  at the point of common coupling PCC and the measured current I PCC  at the point of common coupling PCC for each of the N different working points, and 
         [0019]    d) estimating the grid properties by the grid model using as input parameters the measured voltage V PCC  at the point of common coupling PCC, the measured current I PCC  at the point of common coupling PCC and the determined phase angle α for the N different working points. 
         [0020]    In particular, method steps a) to c) may be executed iteratively. The number of iterations is defined by N. Each iteration step of steps a) to c) provides a tuple of {V PCC , I PCC , α}. Based on said N tuples {V PCC , I PCC , α}, the grid properties are estimated in step d). 
         [0021]    In particular, step d) includes eliminating the absolute phases of the measured voltage V PCC  at the point of common coupling and the measured current I PCC  at the point of common coupling. 
         [0022]    Two examples for eliminating the absolute phases of the voltage V PCC  at the point of common coupling and the current I PCC  at the point of common coupling are given in the detailed description of  FIG. 3 . 
         [0023]    According to a further embodiment, the grid properties include a resistive part R of the grid impedance Z G , a reactive part X of the grid impedance Z G  and the grid voltage V G  of the power grid. 
         [0024]    According to a further embodiment, the resistive part R of the grid impedance Z G , the reactive part X of the grid impedance Z G  and the grid voltage V G  are determined by solving the following equation for three different working points: 
         [0000]      ( V   G ) 2   =|V   PCC ( i )| 2 +( R   2   +X   2 )·|I PCC ( i )| 2 −2·|V PCC ( i )|·|I PCC ( i )|·( R ·cos(α( i ))+ X ·sin(α( i ))) i= 1,2,3;
 
         [0025]    In the above equation, V PCC  indicates the measured voltage at the point of common coupling PCC, I PCC  indicates the measured current at the point of common coupling PCC, and a indicates the determined phase angle between the measured voltage V PCC  at the point of common coupling PCC and the measured current I PCC  at the point of common coupling PCC. 
         [0026]    In the above equation, no absolute phases of the voltage V PCC  at the point of common coupling and the current I PCC  at the point of common coupling are used. As a result, the present method is less prone to errors due to measurement noise. A detailed derivation of the above equation is given in the detailed description of the Figures. 
         [0027]    According to a further embodiment, the resistive part R of the grid impedance Z G , the reactive part X of the grid impedance Z G  and the grid voltage V G  are determined by solving the following equation for three different working points: 
         [0000]    
       
         
           
             
               
                 
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         [0028]    In the above equation, V PCC  indicates the voltage at the point of common coupling PCC, P indicates the active power injected at the point of common coupling PCC, and Q indicates the reactive power injected at the point of common coupling PCC. 
         [0029]    This equation is an equivalent formulation to the above equation. In the above equation, no absolute phases of the voltage V PCC  at the point of common coupling and the current I PCC  at the point of common coupling are used. As a result, the present method is less prone to errors due to measurement noise. A detailed revelation of above equation is given in the detailed description of the Figures. 
         [0030]    According to a further embodiment, the generator is a wind turbine coupled at the point of common coupling to a low-voltage power grid. 
         [0031]    Any embodiment of the first aspect may be combined with any embodiment of the first aspect to obtain another embodiment of the first aspect. 
         [0032]    According to a second aspect, the invention relates to a computer program product comprising a program code for executing the above discussed method for estimating grid properties of a power grid coupled to a generator at a point of common coupling when run on at least one computer. 
         [0033]    A computer program product, like a non-transitory computer-readable media, may be embodied as a memory card, USB stick, CD-ROM, DVD or as a file which may be downloaded from a server in a network. For example, this may be provided by transferring the respective file with the computer program product from a wireless communication network. 
         [0034]    According to a third aspect, a device for estimating grid properties of a power grid coupled to a generator at a point of common coupling is provided. The device includes a first sensor, a second sensor, a determiner, and a processor. The first sensor is configured to measure a voltage V PCC  at the point of common coupling. The second sensor is configured to measure a current I PCC  at the point of common coupling. The determiner is configured to determine a phase angle α between the measured voltage V PCC  at the point of common coupling and the measured current I PCC  at the point of common coupling. Further, the processor is configured to estimate the grid properties by a grid model using as input parameters the measured voltage V PCC  at the point of common coupling, the measured current I PCC  at the point of common coupling and the determined phase angle α. 
         [0035]    According to a fourth aspect, a method for controlling a generator coupled to a power grid by a point of common coupling is provided. In a first step, the grid properties of the power grid are estimated according to a method of above mentioned first aspect. In a second step, the generator is controlled in dependence on or based on the estimated grid properties. 
         [0036]    According to a fifth aspect, the invention relates to a computer program product comprising a program code for executing the above discussed method for controlling a generator coupled to a power grid by a point of common coupling when run on at least one computer. 
         [0037]    According to a sixth aspect, an apparatus for controlling a generator coupled to a power grid by a point of common coupling is provided. The apparatus includes a device for estimating grid properties of the power grid according to the above mentioned third aspect. Moreover, the apparatus includes a controller for controlling the generator in dependence on the estimated grid properties. 
         [0038]    According to a seventh aspect, a method for operating a power grid coupled to a generator by a point of common coupling is provided. In a first step, the grid properties of the power grid are estimated according to a method of above mentioned first aspect. In a second step, the power grid is operated in dependence on the estimated grid properties. In particular, the power grid is controlled based on the estimated grid properties. 
         [0039]    According to an eighth aspect, an apparatus for operating a power grid coupled to a generator at a point of common coupling is provided. The apparatus includes a device for estimating grid properties of the power grid according to the above mentioned third aspect. Moreover, the apparatus includes an operating entity for operating the power grid in dependence on the estimated grid properties. The operating entity may be a controller. This controller may be adapted to control the power grid based on the estimated grid properties. 
         [0040]    The respective means, e.g. the determiner, the processor or a controller, may be implemented in hardware and/or in software. If said means are implemented in hardware, it may be embodied as a device, e.g. as a computer or as a processor or as a part of a system, e.g. a computer system. If said means are implemented in software it may be embodied as a computer program product, as a function, as a routine, as a program code or as an executable object. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0041]    Further objects, features and advantages of the present invention will become apparent from the subsequent description and depending claims, taking in conjunction with the accompanying drawings, in which: 
           [0042]      FIG. 1  shows an equivalent model of a power grid coupled to a generator at a point of common coupling; 
           [0043]      FIG. 2  shows a first embodiment of a sequence of method steps for estimating grid properties of a power grid coupled to a generator; 
           [0044]      FIG. 3  shows a second embodiment of a sequence of method steps for estimating grid properties of a power grid coupled to a generator; 
           [0045]      FIG. 4  shows a schematic block diagram of an embodiment of a device for estimating grid properties of a power grid coupled to a generator; 
           [0046]      FIG. 5  shows an embodiment of a sequence of method steps for controlling a generator coupled to a power grid by a point of common coupling; 
           [0047]      FIG. 6  shows a schematic block diagram of an embodiment of an apparatus for controlling a generator coupled to a power grid; 
           [0048]      FIG. 7  shows an embodiment of a sequence of method steps for operating a power grid coupled to a generator; and 
           [0049]      FIG. 8  shows a schematic block diagram of an embodiment of an apparatus for operating a power grid coupled to a generator. 
       
    
    
     DETAILED DESCRIPTION OF INVENTION 
       [0050]    In the Figures, like reference numerals designate like or functionally equivalent elements, unless otherwise indicated. 
         [0051]    Further, in the Figures, the following symbols are used for discussing said embodiments for estimating grid properties of a power grid coupled to a generator at a point of common coupling: 
         [0000]    
       
         
               
               
               
               
             
               
             
               
               
               
               
             
               
             
               
               
               
               
             
               
             
               
               
               
               
             
               
             
               
               
               
               
             
               
             
               
               
               
               
             
               
             
               
               
               
               
             
               
             
           
               
                   
               
               
                   
                   
                   
                 Measured/ 
               
               
                   
                   
                   
                 Unknown/determined 
               
               
                 Symbol 
                 Definition 
                 Type 
                 from measurements 
               
               
                   
               
             
             
               
                 V G   
                 Grid voltage, used as 
                 real 
                 Unknown 
               
               
                   
                 reference for the phase 
               
               
                 Z G   
                 Grid impedance 
                 complex 
                 unknown 
               
               
                 R 
                 Resistive part of Z G   
                 real 
                 unknown 
               
               
                 X 
                 Reactive part of Z G   
                 real 
                 Unknown 
               
             
          
           
               
                 Z G  = R + j * X 
               
             
          
           
               
                 V PCC   
                 Voltage at the point of 
                 complex 
                 Partially unknown 
               
               
                   
                 common coupling 
               
               
                 |V PCC | 
                 Magnitude of V PCC   
                 real 
                 Measured 
               
               
                 θ 
                 Phase of V PCC  with respect 
                 Real 
                 unknown 
               
               
                   
                 to V G   
               
             
          
           
               
                 V PCC  = |V PCC |e j * θ   
               
             
          
           
               
                 I PCC   
                 Current injected at the 
                 complex 
                 partially unknown 
               
               
                   
                 point of common coupling 
               
               
                 |I PCC | 
                 Magnitude of I PCC   
                 real 
                 Measured 
               
               
                 φ 
                 Phase of I PCC  with respect 
                 real 
                 unknown 
               
               
                   
                 to V G   
               
             
          
           
               
                 I PCC  = |I PCC | e j * φ   
               
             
          
           
               
                 α 
                 Phase between voltage and 
                 real 
                 measured 
               
               
                   
                 current 
               
             
          
           
               
                 α = θ − φ 
               
             
          
           
               
                 P PCC   
                 Active power injected at 
                 real 
                 determined 
               
               
                   
                 PCC 
               
             
          
           
               
                 P PCC  = |U PCC | * |I PCC | * cos(α) 
               
             
          
           
               
                 Q PCC   
                 Reactive power injected at 
                 real 
                 determined 
               
               
                   
                 PCC 
               
             
          
           
               
                 Q PCC  = |U PCC | * |I PCC | * sin(α) 
               
             
          
           
               
                 S PCC   
                 Apparent power injected 
                 Complex 
                 determined 
               
               
                   
                 at PCC 
               
             
          
           
               
                 S PCC  = P PCC  + j * Q PCC  = U PCC  * conj(I PCC ) 
               
               
                   
               
             
          
         
       
     
         [0052]    In this regard,  FIG. 1  shows an equivalent model of a power grid  10  coupled to a generator  20  at a point of common coupling PCC. 
         [0053]    As illustrated in  FIG. 1 , the power grid  10  is modelled by its grid impedance Z G  and its grid voltage V PCC  at the point of common coupling PCC. At the point of common coupling PCC, the voltage V PCC  at the PCC, the current I PCC  injected at the PCC, the active power P PCC  injected at the PCC, and the reactive power Q PCC  injected at the PCC are depicted. 
         [0054]    Further,  FIG. 2  shows a first embodiment of a sequence of method steps for estimating grid properties Z G , V G  of the power grid  10  coupled to the generator  20  at the point of common coupling PCC as shown in  FIG. 1 . 
         [0055]    In particular, the power grid  10  is a low-voltage power grid, and the generator  20  is a wind turbine coupled to the low-voltage power grid  10  at the point of common coupling PCC. 
         [0056]    The method of  FIG. 2  comprises the steps  101 - 104 : 
         [0057]    In step  101 , the voltage V PCC  at the point of common coupling PCC is measured. In step  102 , the current I PCC  at the point of common coupling PCC is measured. 
         [0058]    In particular, the voltage V PCC  and the current I PCC  are measured at a fundamental frequency of the power grid  10 . For example, the fundamental frequency of the power grid  10  is 50 Hz. 
         [0059]    In step  103 , the phase angle α between the measured voltage V PCC  and the measured current I PCC  is determined. 
         [0060]    In step  104 , the grid properties Z G , V G  are estimated or determined by a grid model. The grid model uses the measured voltage V PCC , the measured current I PCC  and the determined phase angle α. The grid properties include the grid impedance Z G  and the grid voltage V G  of the power grid  10 . 
         [0061]      FIG. 3  shows a second embodiment of a sequence of method steps for estimating grid properties Z G , V G  of the power grid  10 . 
         [0062]    The method of  FIG. 3  includes the method steps  201 - 204 . In this regard, the method steps  201 - 203  are executed for at least three times at different working points of the system. For example, the system of  FIG. 1  including the power grid  10  and the generator  20  coupled at the point of common coupling PCC is driven to the at least three working points, where the voltage V PCC  is measured (step  201 ), the current I PCC  is measured (step  202 ) and the phase angle a between the measured V PCC  and the measured I PCC  is determined. 
         [0063]    As a result of method steps  201 - 203 , there are at least three tuples of {V PCC , I PCC , α}. Based on the tuples {V PCC , I PCC , α}, in step  204 , the grid properties Z G , V G  are estimated or determined by a grid model. The grid model uses as input tuples of V PCC , I PCC , and a determined at a minimum of three different working points. 
         [0064]    Within said step  204 , the absolute phases θ, φ of V PCC  and I PCC  are not used. In the following, this is explained for two different examples in which θ, φ are eliminated. In these two examples, the resistive part R of the grid impedance Z G , the reactive part X of the grid impedance Z G  and the grid voltage V G  are determined. 
         [0065]    According to a first example, with respect to  FIG. 1 , the resistive part R, the reactive part X and the grid voltage V G  may be determined by a first formulation with the voltage magnitude |V PCC |, the current magnitude |I PCC | and the phase a between the voltage V PCC  at the point of common coupling and the current I PCC  at the point of common coupling: 
         [0000]    
       
         
           
             
                 
             
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                                                 i 
                                                 ) 
                                               
                                             
                                           
                                           ] 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 - 
                                 
                                   
                                     Z 
                                     G 
                                   
                                   · 
                                   
                                      
                                     
                                       
                                         I 
                                         PCC 
                                       
                                        
                                       
                                         ( 
                                         i 
                                         ) 
                                       
                                     
                                      
                                   
                                 
                               
                               ) 
                             
                             * 
                           
                           = 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                                
                               
                                 
                                   V 
                                   PCC 
                                 
                                  
                                 
                                   ( 
                                   i 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           + 
                           
                             
                               
                                  
                                 
                                   Z 
                                   G 
                                 
                                  
                               
                               2 
                             
                             · 
                             
                               
                                  
                                 
                                   
                                     I 
                                     PCC 
                                   
                                    
                                   
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           
                             2 
                             · 
                             
                                
                               
                                 
                                   V 
                                   PCC 
                                 
                                  
                                 
                                   ( 
                                   i 
                                   ) 
                                 
                               
                                
                             
                             · 
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             
                                
                               
                                 
                                   I 
                                   PCC 
                                 
                                  
                                 
                                   ( 
                                   i 
                                   ) 
                                 
                               
                                
                             
                             · 
                             
                               Re 
                               ( 
                               
                                 
                                   Z 
                                   G 
                                   * 
                                 
                                 · 
                                 
                                   exp 
                                    
                                   
                                     ( 
                                     
                                       j 
                                        
                                       
                                         [ 
                                         
                                           
                                             ϕ 
                                              
                                             
                                               ( 
                                               i 
                                               ) 
                                             
                                           
                                           - 
                                           
                                             θ 
                                              
                                             
                                               ( 
                                               i 
                                               ) 
                                             
                                           
                                         
                                         ] 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               ) 
                             
                           
                           = 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                                
                               
                                 
                                   V 
                                   PCC 
                                 
                                  
                                 
                                   ( 
                                   i 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           + 
                           
                             
                               
                                  
                                 
                                   Z 
                                   G 
                                 
                                  
                               
                               2 
                             
                             · 
                             
                               
                                  
                                 
                                   
                                     I 
                                     PCC 
                                   
                                    
                                   
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           
                             2 
                             · 
                             
                                
                               
                                 
                                   V 
                                   PCC 
                                 
                                  
                                 
                                   ( 
                                   i 
                                   ) 
                                 
                               
                                
                             
                             · 
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                              
                             
                               
                                 I 
                                 PCC 
                               
                                
                               
                                 ( 
                                 i 
                                 ) 
                               
                             
                              
                           
                           · 
                           
                             ( 
                             
                               
                                 R 
                                 · 
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       α 
                                        
                                       
                                         ( 
                                         i 
                                         ) 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 X 
                                 · 
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       α 
                                        
                                       
                                         ( 
                                         i 
                                         ) 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
                  
                 
                   
 
                 
                 ⇒ 
                 
                   
                     ( 
                     
                       V 
                       G 
                     
                     ) 
                   
                   2 
                 
               
               = 
               
                 
                   
                      
                     
                       
                         V 
                         PCC 
                       
                        
                       
                         ( 
                         i 
                         ) 
                       
                     
                      
                   
                   2 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         R 
                         2 
                       
                       + 
                       
                         X 
                         2 
                       
                     
                     ) 
                   
                   · 
                   
                     
                        
                       
                         
                           I 
                           PCC 
                         
                          
                         
                           ( 
                           i 
                           ) 
                         
                       
                        
                     
                     2 
                   
                 
                 - 
                 
                   2 
                   · 
                   
                      
                     
                       
                         V 
                         PCC 
                       
                        
                       
                         ( 
                         i 
                         ) 
                       
                     
                      
                   
                   · 
                   
                      
                     
                       
                         I 
                         PCC 
                       
                        
                       
                         ( 
                         i 
                         ) 
                       
                     
                      
                   
                   · 
                   
                     ( 
                     
                       
                         R 
                         · 
                         
                           cos 
                            
                           
                             ( 
                             
                               α 
                                
                               
                                 ( 
                                 i 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         X 
                         · 
                         
                           sin 
                            
                           
                             ( 
                             
                               α 
                                
                               
                                 ( 
                                 i 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 i 
                 = 
                 1 
               
               , 
               2 
               , 
               
                 3 
                 ; 
                 
                   
                     α 
                      
                     
                       ( 
                       i 
                       ) 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         ϕ 
                          
                         
                           ( 
                           i 
                           ) 
                         
                       
                       - 
                       
                         θ 
                          
                         
                           ( 
                           i 
                           ) 
                         
                       
                     
                     ] 
                   
                 
               
             
           
         
       
     
         [0066]    According to a second example, and with respect to  FIG. 1 , R, X, V G  may be determined by a second formulation with the voltage magnitude |V PCC |, the reactive power P (or P PCC ) and the reactive power Q (or Q PCC ): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                             
                         
                          
                         
                           
                             
                               V 
                               PCC 
                             
                              
                             
                               ( 
                               i 
                               ) 
                             
                           
                           = 
                           
                             
                               
                                 V 
                                 G 
                               
                               + 
                               
                                 
                                   Z 
                                   G 
                                 
                                 · 
                                 
                                   
                                     I 
                                     PCC 
                                   
                                    
                                   
                                     ( 
                                     i 
                                     ) 
                                   
                                 
                               
                             
                             = 
                             
                               
                                 V 
                                 G 
                               
                               + 
                               
                                 
                                   Z 
                                   G 
                                 
                                 · 
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           S 
                                           PCC 
                                         
                                          
                                         
                                           ( 
                                           i 
                                           ) 
                                         
                                       
                                       
                                         
                                           V 
                                           PCC 
                                         
                                          
                                         
                                           ( 
                                           i 
                                           ) 
                                         
                                       
                                     
                                     ) 
                                   
                                   * 
                                 
                               
                             
                           
                         
                          
                         
                             
                         
                       
                     
                     
                       
                           
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               
                                 
                                    
                                   
                                     V 
                                     G 
                                   
                                    
                                 
                                 2 
                               
                               = 
                                 
                                
                               
                                 
                                   
                                     V 
                                     G 
                                   
                                   · 
                                   
                                     V 
                                     G 
                                     * 
                                   
                                 
                                 = 
                               
                             
                           
                         
                         
                           
                             
                               = 
                                 
                                
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         
                                           V 
                                           PCC 
                                         
                                          
                                         
                                           ( 
                                           i 
                                           ) 
                                         
                                       
                                       - 
                                       
                                         
                                           Z 
                                           G 
                                         
                                         · 
                                         
                                           
                                             ( 
                                             
                                               
                                                 
                                                   S 
                                                   PCC 
                                                 
                                                  
                                                 
                                                   ( 
                                                   i 
                                                   ) 
                                                 
                                               
                                               
                                                 
                                                   V 
                                                   PCC 
                                                 
                                                  
                                                 
                                                   ( 
                                                   i 
                                                   ) 
                                                 
                                               
                                             
                                             ) 
                                           
                                           * 
                                         
                                       
                                     
                                     ) 
                                   
                                   · 
                                   
                                     
                                       ( 
                                       
                                         
                                           V 
                                           PCC 
                                         
                                         - 
                                         
                                           
                                             Z 
                                             G 
                                           
                                           · 
                                           
                                             
                                               ( 
                                               
                                                 
                                                   
                                                     S 
                                                     PCC 
                                                   
                                                    
                                                   
                                                     ( 
                                                     i 
                                                     ) 
                                                   
                                                 
                                                 
                                                   
                                                     V 
                                                     PCC 
                                                   
                                                    
                                                   
                                                     ( 
                                                     i 
                                                     ) 
                                                   
                                                 
                                               
                                               ) 
                                             
                                             * 
                                           
                                         
                                       
                                       ) 
                                     
                                     * 
                                   
                                 
                                 = 
                               
                             
                           
                         
                         
                           
                             
                               = 
                                 
                                
                               
                                 
                                   
                                     
                                        
                                       
                                         
                                           V 
                                           PCC 
                                         
                                          
                                         
                                           ( 
                                           i 
                                           ) 
                                         
                                       
                                        
                                     
                                     2 
                                   
                                   + 
                                   
                                     
                                       
                                          
                                         
                                           Z 
                                           G 
                                         
                                          
                                       
                                       2 
                                     
                                      
                                     
                                       
                                         
                                            
                                           
                                             
                                               S 
                                               PCC 
                                             
                                              
                                             
                                               ( 
                                               i 
                                               ) 
                                             
                                           
                                            
                                         
                                         2 
                                       
                                       
                                         
                                            
                                           
                                             
                                               V 
                                               PCC 
                                             
                                              
                                             
                                               ( 
                                               i 
                                               ) 
                                             
                                           
                                            
                                         
                                         2 
                                       
                                     
                                   
                                   - 
                                   
                                     2 
                                     · 
                                     
                                       Re 
                                       ( 
                                       
                                         
                                           Z 
                                           G 
                                         
                                         · 
                                         
                                           
                                             ( 
                                             
                                               V 
                                               PCC 
                                             
                                             ) 
                                           
                                           * 
                                         
                                         · 
                                         
                                           
                                             ( 
                                             
                                               
                                                 
                                                   S 
                                                   PCC 
                                                 
                                                  
                                                 
                                                   ( 
                                                   i 
                                                   ) 
                                                 
                                               
                                               
                                                 
                                                   V 
                                                   PCC 
                                                 
                                                  
                                                 
                                                   ( 
                                                   i 
                                                   ) 
                                                 
                                               
                                             
                                             ) 
                                           
                                           * 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 = 
                               
                             
                           
                         
                         
                           
                             
                               = 
                                 
                                
                               
                                 
                                   
                                     
                                        
                                       
                                         
                                           V 
                                           PCC 
                                         
                                          
                                         
                                           ( 
                                           i 
                                           ) 
                                         
                                       
                                        
                                     
                                     2 
                                   
                                   + 
                                   
                                     
                                       
                                          
                                         
                                           Z 
                                           G 
                                         
                                          
                                       
                                       2 
                                     
                                      
                                     
                                       
                                         
                                            
                                           
                                             
                                               S 
                                               PCC 
                                             
                                              
                                             
                                               ( 
                                               i 
                                               ) 
                                             
                                           
                                            
                                         
                                         2 
                                       
                                       
                                         
                                            
                                           
                                             
                                               V 
                                               PCC 
                                             
                                              
                                             
                                               ( 
                                               i 
                                               ) 
                                             
                                           
                                            
                                         
                                         2 
                                       
                                     
                                   
                                   - 
                                   
                                     2 
                                     · 
                                     
                                       Re 
                                       ( 
                                       
                                         
                                           Z 
                                           G 
                                         
                                         · 
                                         
                                           
                                             S 
                                             PCC 
                                             * 
                                           
                                            
                                           
                                             ( 
                                             i 
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                      
                                     
                                       V 
                                       G 
                                     
                                      
                                   
                                   2 
                                 
                               
                             
                           
                         
                         
                           
                             
                               = 
                                 
                                
                               
                                 
                                   
                                      
                                     
                                       
                                         V 
                                         PCC 
                                       
                                        
                                       
                                         ( 
                                         i 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                 + 
                                 
                                   
                                     
                                        
                                       
                                         Z 
                                         G 
                                       
                                        
                                     
                                     2 
                                   
                                    
                                   
                                     
                                       
                                          
                                         
                                           
                                             S 
                                             PCC 
                                           
                                            
                                           
                                             ( 
                                             i 
                                             ) 
                                           
                                         
                                          
                                       
                                       2 
                                     
                                     
                                       
                                          
                                         
                                           
                                             V 
                                             PCC 
                                           
                                            
                                           
                                             ( 
                                             i 
                                             ) 
                                           
                                         
                                          
                                       
                                       2 
                                     
                                   
                                 
                                 - 
                                 
                                   2 
                                   · 
                                   
                                     Re 
                                      
                                     
                                       ( 
                                       
                                         
                                           Z 
                                           G 
                                         
                                         · 
                                         
                                           
                                             S 
                                             PCC 
                                             * 
                                           
                                            
                                           
                                             ( 
                                             i 
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                           
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               ⇒ 
                               
                                 
                                   ( 
                                   
                                     V 
                                     G 
                                   
                                   ) 
                                 
                                 2 
                               
                             
                             = 
                             
                               
                                 
                                   
                                      
                                     
                                       
                                         V 
                                         PCC 
                                       
                                        
                                       
                                         ( 
                                         i 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         R 
                                         2 
                                       
                                       + 
                                       
                                         X 
                                         2 
                                       
                                     
                                     ) 
                                   
                                   · 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             P 
                                             2 
                                           
                                            
                                           
                                             ( 
                                             i 
                                             ) 
                                           
                                         
                                         + 
                                         
                                           
                                             Q 
                                             2 
                                           
                                            
                                           
                                             ( 
                                             i 
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                     
                                       
                                          
                                         
                                           
                                             V 
                                             PCC 
                                           
                                            
                                           
                                             ( 
                                             i 
                                             ) 
                                           
                                         
                                          
                                       
                                       2 
                                     
                                   
                                 
                                 - 
                                 
                                     
                                 
                                  
                                 
                                   
                                     2 
                                     · 
                                     
                                       ( 
                                       
                                         
                                           R 
                                           * 
                                           
                                             P 
                                              
                                             
                                               ( 
                                               i 
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           X 
                                           * 
                                           
                                             Q 
                                              
                                             
                                               ( 
                                               i 
                                               ) 
                                             
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                    
                                   
                                       
                                   
                                    
                                   
                                     
 
                                   
                                    
                                   
                                       
                                   
                                    
                                   i 
                                 
                               
                               = 
                               1 
                             
                           
                           , 
                           2 
                           , 
                           3 
                         
                          
                         
                             
                         
                       
                     
                     
                       
                           
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
         [0067]    In  FIG. 4 , a schematic block diagram of an embodiment of a device  40  for estimating grid properties Z G , V G  of a power grid  10  coupled to a generator  20  at the point of common coupling is depicted (see  FIG. 1 ). 
         [0068]    The device  40  of  FIG. 4  comprises a first sensor  41 , a second sensor  42 , a determiner  43  and a processor  44 . The first sensor  41  may be coupled to the determiner  43  and the processor  44 . The second sensor  42  may be coupled to the determiner  43  and the processor  44 . The determiner  43  may be coupled to the processor  44 . 
         [0069]    The first sensor  41  is adapted to measure the voltage V PCC  and the point of common coupling PCC. The second ensor  42  is adapted to measure the current I PCC  at the point of common coupling PCC. The determiner  43  is adapted to determine the phase angle α between the measured voltage V PCC  at the point of common coupling PCC and the measured current I PCC  at the point of common coupling PCC. 
         [0070]    The processor  44  is adapted to estimate or to determine the grid properties Z G , V G  by a grid model, said grid model using as input parameters the measured voltage V PCC , the measured current I PCC  and the determined phase angle α. 
         [0071]      FIG. 5  shows an embodiment of a sequence of method steps for controlling a generator  20  coupled to a power grid  10  at a point of common coupling PCC. The method of  FIG. 5  comprises the steps  501  and  502 . 
         [0072]    In step  501 , the grid properties V G , Z G  of the power grid  10  are estimated. Embodiments for the estimation step  501  are given by  FIGS. 2 and 3 . 
         [0073]    In step  502 , the generator  20  is controlled or adjusted in dependence on the estimated grid properties Z G , V G . In particular, the generator  20  is controlled based on the estimated grid properties Z G , V G . 
         [0074]      FIG. 6  shows as schematic block diagram of an embodiment of an apparatus  60  for controlling a generator  20  coupled to a power grid  10  at a point of common coupling PCC. The apparatus  60  of  FIG. 6  comprises a device  40  for estimating grid properties Z G , V G  of the power grid  10 . An example for such a device  40  is depicted in  FIG. 4 . 
         [0075]    Further, the apparatus  60  of  FIG. 6  includes a controller  61  which is configured to control the generator  20  in dependence on the estimated grid properties Z G , V G . For controlling the generator  20 , the controller  61  may use a control signal C which is generated in dependence on the estimated grid properties Z G , V G . 
         [0076]      FIG. 7  shows an embodiment of a sequence of method steps for operating a power grid  10  coupled to a generator  20  at a point of common coupling PCC. 
         [0077]    In step  701 , the grid properties Z G , V G  of the power grid  10  are estimated by a method as described with reference to  FIG. 2  or  FIG. 3 . 
         [0078]    In step  702 , the power grid  10  is operated in dependence on the estimated grid properties Z G , V G . In particular, operating the power grid  10  may include diagnosis and maintenance of the power grid  10 . 
         [0079]      FIG. 8  shows a schematic block diagram of an embodiment of an apparatus  80  for operating a power grid  10  coupled to a generator  20 . The apparatus  80  of  FIG. 8  includes a device  40  for estimating the grid properties Z G , V G . An example for such a device is depicted in  FIG. 4 . 
         [0080]    Further, the apparatus  80  includes an operating entity  81  which is configured to operate the power grid  10  in dependence on the estimated grid properties Z G , V G . The operating entity  81  may be embodied as a controller or a processor. For controlling the power grid  10 , the controller may use a control signal S which may be generated based on the estimated grid properties V G , Z G . 
         [0081]    Although the present invention has been described in accordance with preferred embodiments, it is obvious for a person skilled in the art that modifications are possible in all embodiments.