Abstract:
Disclosed herein are an intelligent system and method for monitoring a generator reactive power limit using machine model parameters. The intelligent system and method for monitoring a generator reactive power limit using machine model parameters can calculate a maximum reactive power limit corresponding to over-excitation and a generator terminal voltage corresponding to under-excitation, estimate a correct field current even when system variable are changed, and monitor the generator reactive power limit by using machine model parameters and a one-machine infinite bus, to thereby supply a maximum or minimum reactive power to a power system within an allowable generator reactive power limit and prevent a generator trip caused by the reactive power limit and a power failure over a wide area.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an intelligent system and method for monitoring a generator reactive power limit using machine model parameters, and more particularly, to an intelligent system and method for monitoring a generator reactive power limit using machine model parameters, which can calculate a maximum reactive power limit corresponding to over-excitation and a generator terminal voltage corresponding to under-excitation, estimate a correct field current even when system variable are changed, and monitor the generator reactive power limit by using machine model parameters and a one-machine infinite bus, to thereby supply a maximum or minimum reactive power to a power system within allowable generator reactive power limit and prevent a generator trip caused by the reactive power limit and a power failure over a wide area. 
     2. Background of the Related Art 
     References for the present invention are as follows:
     [1] CWG &amp; MVWG, “Test Guidelines for Synchronous unit Dynamic Testing and Model Validation”, February, 1997, WSCC. www.wecc.biz;   [2] P. Kundur, Power System Stability and Control, PP. 101-102, 1994, McGraw-Hill;   [3] F. P. de Mello, L. N. Hannett, “Representation of Saturation in Synchronous Machines”, IEEE Transactions on Power Systems, Vol. PWRS-1, No. 4, November 1988, pp. 8-18;   [4] F. P. de Mello, J. R. Ribeiro, “Derivation of Synchronous Machine Parameters from Tests,”, IEEE PWR Apparatus and Systems, Vol. PAS-96, No. 4, July/August 1977;   [5] EPRI Report EL-1424, “Determination of Synchronous Machine Stability Constants,” Vol. 2, prepared by Ontario Hydro, December 1980;   [6] EPRI Report EL-1424, “Determination of Synchronous Machine Stability Constants,” Vol. 3, prepared by PTI, December 1980;   [7] Bharat Bhargava, “Synchronized Phasor Measurement System Project at Southern California Edison Co.”, IEEE PES SM 1999, pp. 18-22, 1999;   [8] Magnus Akke, “Phasor Measurement Applications in Scandinavia,” IEEE PES T&amp;D Conference and Exhibition 2002: Asia Pacific, pp. 480-484, 2002;   [9] Report, “Aug. 14, 2003 Outage Sequence of Events”, U.S./Canada Power Outage Task Force, Sep. 12, 2003;   [10] G. W. Stagg and A. H. Abiad, Computer Method in Power System Analysis McGraw-Hill, 1968;   [11] C. Lemaitre, J. P. Paul, J. M. Tesseron, Y. Harmand, and Y. S. Zhao, “An indicator of the Risk of voltage Profile Instability for Real-Time Control Applications,” IEEE Summer Meeting 1989, Paper 89Sm713-9 PWRS;   [12] V. Ajjarapu and C. Christy, “The Continuation Power Flow: A Tool for Steady State Voltage Stability Analysis,” IEEE PICA Conference Prodeedings, pp. 304-311, May 1991;   [13] N. Flatabo, R. Ognedal, and T. Carlsen, “Voltage Stability Condition in a Power Transmission System Calculated by Sensitivity Methods,” IEEE Trans.;   [14] C. Lemaitre, J. P. Paul, J. M. Tesseron, Y. Harmand, and Y. S. Zhao, “An indicator of the Risk of voltage Profile Instability for Real-Time Control Applications,” IEEE Summer Meeting 1989, Paper 89Sm713-9 PWRS; and   [15] TEST GUIDELINES FOR SYNCHRONOUS UNIT DYNAMIC TESTING AND MODEL VALIDATION, 1997, WSCC.   

     A generator reactive power limit is related to voltage stability of a power system. The voltage stability is detected using a method of monitoring a bus voltage of the power system (refer to references [11], [12], [13] and [14]). A large-scale power failure due to an over-excitation trip of a power plant has recently occurred (refer to reference [15]), and there is every possibility that a power failure occurs because of a trip caused by over-excitation or under-excitation of a power plant. Accordingly, a method of effectively monitoring the generator reactive power limit is required. However, conventional techniques cannot meet this requirement. 
     A conventional method of monitoring a generator reactive power limit analyzes and judges the current generator operating state by a field generator operator using a capability curve, an under-excitation limiter (UEL) limit, and an over-excitation limiter (OEL) limit provided by a generator manufacturer. This method is an approximate technique depending on the capability of the generator operator, and thus it is difficult to estimate a correct generator reactive power operation when power system variables are changed. That is, the conventional generator reactive power limit monitoring method has the following problems. 
     Firstly, it is impossible to calculate a reactive power limit with respect to an OEL generator field current limit and indicate the calculated result on a generator reactive power capability curve. In general, a method of monitoring the reactive power limit of a generator while the generator is operating uses a generator reactive capability curve illustrated in  FIG. 1 . The generator reactive capability curve illustrated in  FIG. 1  indicates an allowable reactive power at 500 MW generator power under 60 PSIG hydrogen pressure. A minimum reactive power limit according to under-excitation can be monitored by indicating an UEL limit on the generator reactive capability curve as illustrated in  FIG. 1 . In terms of monitoring of a maximum reactive power limit according to over-excitation, however, an OEL limit is set to a generator field current i fd , and thus it is difficult to calculate and indicate a reactive power limit with respect to the OEL generator field current limit. This is because the maximum reactive power limit is varied according to a generator output condition, a terminal voltage and a system voltage. Accordingly, a method of indicating the reactive power limit with respect to the OEL generator field current limit on the capability curve is required. 
     Secondly, it is impossible to calculate or estimate a terminal voltage corresponding to a reactive power limit with respect to an UEL and indicate the terminal voltage on the capability curve. An UEL limit corresponds to a ratio of a reactive power Qe to an active power Pe, and thus the UEL limit can be indicated on the capability curve as illustrated in  FIG. 1 . However, the terminal voltage of a generator is important in the actual operation of the generator. The conventional technique has difficulties in calculating or estimating the terminal voltage corresponding to the reactive power limit with respect to the UEL and indicating the terminal voltage on the capability curve. 
     Thirdly, it is impossible to estimate a variation in power system variables and indicate a maximum generator reactive power limit on the capability curve. A generator is not operated at a single operating point for ceaselessly generating large and small power system disturbances. For example, a generator terminal voltage, a generator active power, a generator reactive power and a network voltage change momentarily. If a generator operator can estimate these power system variables and prepare for a variation in the power system variables, power system reliability is improved. However, there is a limit in this manual method, and thus a method of estimating a variation in the power system variables according to a variation in generator power and automatically indicating the maximum generator reactive power limit on the capability curve is required. 
     Fourthly, a reactive power limit with respect to a generator over-voltage limit and a generator under-voltage limit cannot be calculated. The generator reactive power limit is affected by the generator over-voltage limit and the under-voltage limit as well as the OEL limit and the UEL limit. Generally, a generator over-voltage and a generator under-voltage are respectively 105% and 95% of a rated voltage. Accordingly, a method of calculating the reactive power limit with respect to the set generator over-voltage limit and the generator under-voltage limit is needed. 
     SUMMARY OF THE INVENTION 
     Accordingly, the present invention has been made in view of the above-mentioned problems occurring in the prior art, and it is a primary object of the present invention to provide an intelligent system and method for estimating and monitoring a correct generator reactive power limit using machine model parameters even when system variables such as a voltage and an active power are changed in a power plant. 
     Another object of the present invention is to provide an intelligent system and method for monitoring a generator reactive power limit using machine model parameters, which can estimate and monitor the generator reactive power limit to supply a maximum reactive power or a minimum reactive power to a power system within an allowable generator reactive power limit. 
     Yet another object of the present invention is to provide an intelligent system and method for monitoring a generator reactive power limit using machine model parameters to prevent a generator trip due to over-excitation and under-excitation and a large-scale power failure and supply a maximum reactive power to a power system. 
     To accomplish the above objects, according to one aspect of the present invention, there is provided an intelligent system for monitoring a generator reactive power limit using machine model parameter, which comprises: a real-time phasor measurement system for converting data measured from a three-phase power line connected to a generator through a current transformer and a potential transformer into phasors to calculate a terminal voltage, a terminal current, a reactive power and an active power in terms of root mean square (RMS) value; and a host computer for calculating the generator reactive power limit using the RMS data from the real-time phasor measurement system, a one-machine infinite bus, and the machine model parameters. 
     According to another aspect of the present invention, there is also provided an intelligent method for monitoring a generator reactive power limit using machine model parameters, which comprises: a first step of constructing machine model parameters and system data; a second step of reading measured data from a real-time phasor measurement system and storing the read data; a third step of executing a reactive power limit calculating method according to a system condition; and a fourth step of visualizing the calculated reactive power limit. 
     According to another aspect of the present invention, there is also provided a method for calculating a reactive power limit according to a system condition, which comprises: a first step of inputting an initial condition (P o , Q o , V to ) and a system equivalent impedance (X s ); a second step of carrying out at least one of calculation of a generator internal field current i fdo  and a load angle δ o  using machine model parameters, calculation of an infinite bus voltage V inf , calculation of a terminal voltage V to     —     OEL  with respect to an OEL field current limit i fdo     —     OEL , calculation of reactive power limits with respect to a maximum operation terminal voltage V to     —     max  and a minimum operation terminal voltage V to     —     min , calculation of a maximum limit reactive power value Q i     —     max  corresponding to an output power P i  (i=1, 2, . . . ), calculation of a terminal voltage V t     —     UEL  with respect to an UEL limit minimum reactive power Q UEL     —     lim , and calculation of a reactive power limit according to a variation in the infinite bus voltage V inf ; and a third step of checking whether the current operating point is included in a reactive power limit danger area, to perform warning of reactive power limit danger when the current operating point is included in the danger area, or finish the routine when the current operating point is not included in the danger area. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects, features and advantages of the present invention will be apparent from the following detailed description of the preferred embodiments of the invention in conjunction with the accompanying drawings, in which: 
         FIG. 1  illustrates a generator reactive capability curve according to a prior art; 
         FIG. 2  illustrates an intelligent system for monitoring a generator reactive power limit according to an embodiment of the present invention; 
         FIG. 3  is a flow chart of an intelligent method for monitoring a generator reactive power limit according to an embodiment of the present invention; 
         FIG. 4  is a flow chart of a phasor calculating method of a real-time phasor measurement system according to an embodiment of the present invention; 
         FIG. 5  is a flow chart of a reactive power limit calculating method according to an embodiment of the present invention; 
         FIG. 6  is a flow chart of a generator field current calculating method according to an embodiment of the present invention; 
         FIG. 7  illustrates a system for calculating an infinite bus voltage according to an embodiment of the present invention; and 
         FIG. 8  illustrates a generator reactive capability curve according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention will now be described more fully with reference to the accompanying drawings, in which exemplary embodiments of the invention are shown. The invention may, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein, rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the invention to those skilled in the art. 
       FIG. 2  illustrates an intelligent system for monitoring a generator reactive power limit according to an embodiment of the present invention. Referring to  FIG. 2 , electric power generated by a generator  1  is transmitted to a power system  2  through a three-phase power line, and a real-time phasor measurement system  5  corresponding to a target system measures a generator terminal current and a generator terminal voltage from the three-phase power line connected to the generator  1  through a current transformer  3  and a potential transformer  4 . The measured data is converted into phasors, and an RMS terminal voltage, an RMS terminal current, a reactive power and an active power are calculated and transmitted to a host computer  6  at a predetermined time interval. The host computer  6  estimates and calculates the generator reactive power limit using root mean square (RMS) data received from the real-time phasor measurement system  5 , a one-machine infinite bus and machine model parameters. According to circumstances, the host computer  6  visualizes and outputs a warning message. 
     The real-time phasor measurement system  5  converts measured waveform data into RMS values and calculates a frequency, an RMS active power and an RMS reactive power using the current and the voltage respectively measured by the current transformer  3  and the potential transformer  4 . The function of the real-time phasor measurement system  5  can be known from references [7] and [8]. 
     A one-machine infinite bus model used in the host computer  6  is a load flow calculation model and is used to initialize state variables of a generator. Numerical analysis of power system normal state is performed through a load flow calculating method. The load flow calculating method changes actual power variables to per unit values and calculates power flow in consideration of only positive sequence. The load flow calculating method can be known from reference [10]. Furthermore, the machine model parameters used in the host computer  6  are obtained using a model parameter inducing method through generator testing. The model parameter inducing method can be known from references [1] through [6]. 
     The one-machine infinite bus model calculates an infinite bus voltage V inf  using the measured data, that is, V t , P and Q. The infinite bus voltage V inf  is hardly changed in case of a large power system. An equivalent impedance used to calculate the infinite bus voltage V inf  corresponds to the sum of a generator step-up transformer impedance and a power transmission line impedance. 
     The machine model parameters are used to calculate an internal load angle and a field current of the generator using a measured initial condition P o , Q o  and V t . Verified machine model parameters include X d  (Vertical axis synchronous reactance), X q  (Horizontal axis synchronous reactance), X d ′ (Vertical axis transient reactance), X q ′ (Horizontal axis transient reactance), X″ (Initial transient reactance), X l  (Leakage reactance), S(1.0) (Saturation coefficient), and S(1.2) (Saturation coefficient). 
       FIG. 3  is a flow chart of an intelligent method for monitoring a generator reactive power limit according to an embodiment of the present invention.  FIG. 3  illustrates an intelligent generator reactive power limit calculating method carried in the host computer  6  of the intelligent generator reactive power limit calculating system illustrated in  FIG. 2 . 
     First of all, the host computer  6  is initialized in step S 301 , and then machine model parameters and system data are constructed in step S 302 . Subsequently, it is checked whether the real-time phasor measurement system  5  is operated in step S 303 . When the real-time phasor measurement system  5  is not operated in step S 304 , it is checked whether a start signal of the real-time phasor measurement system  5  is inputted in step S 305 . When the start signal is not inputted, steps S 304  and S 305  are repeated. When the start signal is inputted in step S 305 , the constructed data is transmitted to the real-time phasor measurement system  5  in step S 306 , and measured data is read from the real-time phasor measurement system  5  and stored in step S 307 . When the real-time phasor measurement system  5  is operated, the measured data is read from the real-time phasor measurement system  5  and stored in step S 307 . 
     Subsequently, it is checked whether the machine model parameters and the system data need to be changed in step S 308 . When it is required to change the machine model parameters and the system data, the machine model parameters and the system data are changed in step S 309 , and a reactive power limit calculating algorithm according to a system condition is performed in step S 310 . When there is no need to change the machine model parameters and the system data, the reactive power limit calculating algorithm according to the system condition is directly carried out in step S 310 . Then, a reactive power estimation value is visualized in step S 311 , and it is checked whether a stop signal is inputted or whether an error signal is generated in step S 312 . When the stop signal is not inputted or the error signal is not generated, it is checked whether data request is finished in step S 313 . When data request is not finished yet, step S 307  is performed. When data request is completed, resource deletion is carried out in step S 314 , and then step S 305  is performed. When the stop signal is inputted or the error signal is generated in step S 312 , the resource deletion is carried out in step S 314 , and then step S 305  is performed. 
       FIG. 4  is a flow chart of a phasor calculating method of the real-time phasor measurement system  5  according to an embodiment of the present invention. Hardware configuration of the real-time phasor measurement system  5  is carried out in step S 401 . Then, a voltage Vt and a current It are measured and a channel is read in step S 402 . Subsequently, a time stamp is read in step S 403 , phasors Pe, Qe and Vt are calculated in step S 404 , and measured data is transmitted to the host computer  6  in step S 405 . Then, it is checked whether the operation is finished or a stop signal is inputted in step S 406 , and an opened reference is closed in step S 407  when the stop signal is inputted. When the stop signal is not inputted, step S 402  is executed. 
       FIG. 5  is a flow chart of a reactive power limit calculating method according to an embodiment of the present invention.  FIG. 5  illustrates the step S 310  of  FIG. 3 . 
     Referring to  FIG. 5 , when a reactive power limit calculating process according to a system condition is started in step S 501 , an initial condition P o , Q o  and V to  and a system equivalent impedance X s  are inputted in step S 502 . Then, a generator internal field current i fdo  and a load angle δ o  are calculated using machine model parameters in step S 503 , and an infinite bus voltage V inf  is calculated in step S 504 . Subsequently, a terminal voltage V to     —     OEL  with respect to an OEL field current limit i fdo     —     OEL  is calculated in step S 505 , and reactive power limits with respect to a maximum operation terminal voltage V to     —     max  and a minimum operation terminal voltage V to     —     min  are calculated in step S 506 . Furthermore, a maximum limit reactive power value Q i     —     max  corresponding to an output power P i  (i=1, 2, . . . ) is calculated in step S 507 , a terminal voltage V t     —     UEL  with respect to an UEL limit minimum reactive power Q UEL     —     lim  is calculated in step S 508 , and a reactive power limit according to a variation in the infinite bus voltage V inf  is calculated in step S 509 . Then, it is checked whether the current operating point is included in a reactive power limit danger area in step S 510 , and warning of reactive power limit danger is performed in step S 511  when the current operating point is included in the danger area. When the current operating point is not included in the danger area, the process is ended in step S 512 . According to the reactive power limit calculating method illustrated in  FIG. 5 , the problems of the conventional generator reactive power limit monitoring method can be solved. 
     Specifically, the first problem of the conventional generator reactive power limit monitoring method is solved as follows. 
     The terminal voltage V to     —     OEL  with respect to the OEL field current limit i fdo     —     OEL  is estimated and calculated (S 505 ), and thus the reactive power limit Q o     —     OEL  with respect to the OEL generator field current limit can be indicated on the generator reactive power capability curve. The terminal voltage V to     —     OEL  with respect to the OEL field current limit i fdo     —     OEL  is estimated and calculated as follows. 
     When generator variables which are measured while the generator is operating include following variables, an infinite bus voltage V inf     —     o  (unknown value) is calculated using the following generator variables and Equation 1. This can be easily calculated because there are only a single equation and only a single unknown variable (infinite bus voltage). 
     [Generator Variables]
         P o  (MW): Current active power   Q o  (Mvar): Current reactive power
           V to  (kV): Terminal voltage of the currently operating generator   
           X s  System equivalent impedance (corresponding to the sum of a transformer impedance and a power transmission line impedance)       

     
       
         
           
             
               
                 
                   
                     
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     The maximum reactive power limit Q o     —     OEL  with respect to the OEL generator field current limit is obtained by calculating a terminal voltage that allows a calculated generator field current to correspond to a field current set in an OEL using an optimization technique corresponding to the least square method represented by Equation 2. Here, the field current is calculated through a generator modeling formula using machine model parameters. 
     
       
         
           
             
               
                 
                   
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     Here, i if     —     cal =f(x) denotes the calculated generator field current, and i fd     —     OEL  represents the OEL generator field current limit. 
     The second problem of the conventional reactive power limit monitoring method is solved as follows. 
     The terminal voltage V t     —     UEL  with respect to the reactive power limit Q UEL     —     lim  set to the UEL is calculated (S 508 ) using a known infinite bus voltage. That is, the terminal voltage corresponding to UEL reactive power can be calculated using the following variables and Equation 3. 
     [Variables] 
     P o  (MW): Current active power 
     Q UEL  (Mvar): Current minimum reactive power limit 
     V inf     —     o  (kV): Infinite bus voltage in the currently operating state 
     X s : System equivalent impedance (corresponding to the sum of a transformer impedance and a power transmission line impedance) 
     
       
         
           
             
               
                 
                   
                     
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     The third problem of the conventional reactive power limit monitoring method is solved as follows. 
     The maximum reactive power limit with respect to the field current at another power operating point (Pi) is calculated (S 507 ) by obtaining a terminal voltage that allows a calculated generator field current to correspond to a field current set to the OEL using an optimization technique corresponding to the least square method represented by Equation 4. Here, the infinite bus voltage is not easily changed. Accordingly, this calculating process is applied well to a large system. 
     
       
         
           
             
               
                 
                   
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     Here, i if     —     cal =f(x) denotes the calculated generator field current, P i  (i=1, 2, L) represents another generator active power operating point, and i fd     —     OEL  denotes the OEL generator field current limit. 
     The fourth problem of the conventional reactive power limit monitoring method is solved as follows. 
     The step (S 506 ) of calculating a generator reactive power Q max/min  with respect to a generator maximum over-voltage limit V max  and a generator minimum voltage limit V min  at a generator power operating point Po is carried out according to Equation 5. Here, an unknown value to be obtained is Q max/min . 
     
       
         
           
             
               
                 
                   
                     
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     Here, the generator field current is calculated using a generator field current calculating method illustrated in  FIG. 6  when an operating condition is (P o , Q max , V max ) or (P o , Q min , V min ). 
       FIG. 6  is a flow chart of a generator field current calculating method according to an embodiment of the present invention.  FIG. 6  illustrates the step S 503  of  FIG. 5 . 
     Referring to  FIG. 6 , when a generator field current calculating process is started in step S 601 , machine model parameters are inputted in step S 602 . Specifically, X d , X q , X d ′, X q ′, X″, X l , S(1.0) and S(1.2) are inputted in step S 603 . Then, an initial condition (P o , Q o , V to , V inf     —     o , X s ) is inputted in step S 604 . Subsequently, an internal phase difference angle δ is calculated in step S 605 , a stator current is split into a vertical axis current and a horizontal axis current in step S 606 , and a generator field current i fd     —     cal  is calculated in step S 607 . Then, it is determined whether an optimization technique is applied in step S 608 , and the process is finished in step S 612  when the optimization technique is not applied. When the optimization technique is applied, it is determined whether a difference between the OEL generator field current limit i fd     —     OEL  and the calculated generator field current i fd     —     cal  is smaller than a generator induced electromotive force ε in step S 609 . The process is finished in step S 612  when the difference is smaller than the generator induced electromotive force ε. When the difference is greater than the generator induced electromotive force ε, the optimization technique is executed in step S 610 , the terminal voltage V t  is changed in step S 611 , and the process returns to step S 605 . 
     Embodiments 
     Hereinafter, results obtained by applying the intelligent system and method for monitoring a generator reactive power limit using machine model parameters according to the present invention to 612 MVA large thermal generator (cylindrical) are described. A rated terminal voltage is 22 kV and a base field current is 1175 Amp. Machine model parameters to be used are verified machine model parameters which correspond to the following measured results. PSS/E power system simulation program is used. 
     —Verified Machine Model Parameters 
     Table 1 shows a terminal current, an active power, a reactive power, a field current and a load angle which are actually measured. Table 2 shows normal state machine model parameters extracted and verified according to generator testing. Table 3 shows calculation results according to the machine model parameters and measurement results. The field current and the load angle calculated according to the machine model parameters shown in Table 2 nearly correspond to the measured field current and the measured load angle as shown in  FIG. 3 . 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Measured normal state generator operation data 
               
             
          
           
               
                   
                 Terminal 
                 Active 
                 Reactive 
                 Field 
                 Load 
               
               
                 Measurement 
                 voltage 
                 power 
                 power 
                 current 
                 angle 
               
               
                 No. 
                 V t  (kV) 
                 P(MW) 
                 Q(Mvar) 
                 I fd (Amp) 
                 (Deg) 
               
               
                   
               
             
          
           
               
                 1 
                 21.215 
                 501.237 
                 0.071 
                 2491.382 
                 52.328 
               
               
                 2 
                 21.592 
                 500.015 
                 50.091 
                 2616.375 
                 47.954 
               
               
                 3 
                 21.994 
                 501.509 
                 100.064 
                 2753.834 
                 44.000 
               
               
                 4 
                 22.373 
                 506.149 
                 149.567 
                 2884.731 
                 40.663 
               
               
                 5 
                 22.578 
                 508.047 
                 200.943 
                 3057.293 
                 37.714 
               
               
                 6 
                 21.319 
                 375.248 
                 −1.591 
                 2064.243 
                 44.880 
               
               
                 7 
                 21.657 
                 372.550 
                 44.168 
                 2206.295 
                 40.368 
               
               
                 8 
                 22.078 
                 369.892 
                 94.060 
                 2339.160 
                 35.886 
               
               
                 9 
                 22.445 
                 375.047 
                 147.029 
                 2526.158 
                 32.658 
               
               
                 10 
                 21.436 
                 252.764 
                 −3.416 
                 1674.504 
                 34.401 
               
               
                 11 
                 21.850 
                 252.608 
                 50.239 
                 1859.203 
                 29.426 
               
               
                 12 
                 22.220 
                 253.414 
                 99.836 
                 2057.354 
                 25.945 
               
               
                 13 
                 22.511 
                 254.021 
                 148.460 
                 2256.161 
                 23.397 
               
               
                 14 
                 21.444 
                 115.430 
                 −6.982 
                 1327.740 
                 18.178 
               
               
                 15 
                 21.852 
                 110.961 
                 50.067 
                 1592.816 
                 14.276 
               
               
                 16 
                 22.236 
                 116.193 
                 100.272 
                 1819.835 
                 12.614 
               
               
                 17 
                 22.521 
                 120.691 
                 140.985 
                 2012.081 
                 11.759 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Verified machine model parameters 
               
             
          
           
               
                   
                 Model parameter 
                   
               
               
                 Parameter 
                 value 
                 Remark 
               
               
                   
               
               
                 Xd 
                 2.199 
                 Vertical axis synchronous reactance 
               
               
                 Xq 
                 1.587 
                 Horizontal axis synchronous reactance 
               
               
                 Xd′ 
                 0.257 
                 Vertical axis transient reactance 
               
               
                 Xq′ 
                 0.393 
                 Horizontal axis transient reactance 
               
               
                 X″ 
                 0.228 
                 Initial transient reactance 
               
               
                 X 1   
                 0.142 
                 Leakage reactance 
               
               
                 S(1.0) 
                 0.100 
                 Saturation coefficient 
               
               
                 S(1.2) 
                 0.238 
                 Saturation coefficient 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Comparison of calculated result according 
               
               
                 to machine model parameters with measured result 
               
             
          
           
               
                   
                   
                   
                   
                 Measured 
                 Calculated 
                   
               
               
                 Measurement 
                 Measured 
                 Calculated 
                   
                 load 
                 load 
                 Error 
               
               
                 No. 
                 I fd     —     mea (Amp) 
                 I fd     —     cal (Amp) 
                 % error 
                 angle(°) 
                 angle(°) 
                 (°) 
               
               
                   
               
             
          
           
               
                 1 
                 2491.382 
                 2513.681 
                 0.895 
                 52.328 
                 53.138 
                 −0.809 
               
               
                 2 
                 2616.375 
                 2622.347 
                 0.228 
                 47.954 
                 48.406 
                 −0.452 
               
               
                 3 
                 2753.834 
                 2759.153 
                 0.193 
                 44.000 
                 44.315 
                 −0.314 
               
               
                 4 
                 2884.731 
                 2919.412 
                 1.202 
                 40.663 
                 40.972 
                 −0.309 
               
               
                 5 
                 3057.293 
                 3090.257 
                 1.078 
                 37.714 
                 38.156 
                 −0.442 
               
               
                 6 
                 2064.243 
                 2036.754 
                 −1.332 
                 44.880 
                 44.842 
                 0.037 
               
               
                 7 
                 2206.295 
                 2167.094 
                 −1.777 
                 40.368 
                 40.299 
                 0.069 
               
               
                 8 
                 2339.160 
                 2328.513 
                 −0.455 
                 35.886 
                 35.958 
                 −0.072 
               
               
                 9 
                 2526.158 
                 2534.841 
                 0.344 
                 32.658 
                 32.786 
                 −0.129 
               
               
                 10 
                 1674.504 
                 1636.193 
                 −2.288 
                 34.401 
                 33.663 
                 0.738 
               
               
                 11 
                 1859.203 
                 1848.778 
                 −0.561 
                 29.426 
                 29.134 
                 0.292 
               
               
                 12 
                 2057.354 
                 2057.605 
                 0.012 
                 25.945 
                 25.913 
                 0.031 
               
               
                 13 
                 2256.161 
                 2264.613 
                 0.375 
                 23.397 
                 23.434 
                 −0.037 
               
               
                 14 
                 1327.740 
                 1306.323 
                 −1.613 
                 18.178 
                 17.081 
                 1.097 
               
               
                 15 
                 1592.816 
                 1578.149 
                 −0.921 
                 14.276 
                 13.775 
                 0.501 
               
               
                 16 
                 1819.835 
                 1831.137 
                 0.621 
                 12.614 
                 12.543 
                 0.071 
               
               
                 17 
                 2012.081 
                 2032.884 
                 1.034 
                 11.759 
                 11.792 
                 −0.033 
               
               
                   
               
             
          
         
       
     
     —Equivalent Impedance 
     A total impedance of a generator step-up transformer and a power transmission line is 0.20 Per unit at 612 MVA. 
     —OEL Limit (OEL Limit Illustrated in  FIG. 8 ) and UEL Limit (UEL Limit Illustrated in  FIG. 8 ) 
     An on-line OEL (AFFL) limit is 3,386 Amp, and an UEL limit is −218.9 Mvar at 0 MW, −233.8 Mvar at 183.6 MW, −253.9 Mvar at 367.2 MW, and −129.9 Mvar at 581.4 MW. 
     —Infinite Bus Voltage 
     It assumed that the initial condition of the currently operating generator is as follows.  FIG. 7  illustrates a one-machine infinite bus system. An infinite bus voltage satisfying the following initial condition, which is obtained using Equation 1 based on the one-machine infinite bus system illustrated in  FIG. 7 , is 0.973 Per Unit (rated voltage 22 kV). 
     [Generator Initial Condition] 
     Terminal voltage (V to ): 22.578 kV 
     Active power (P o ): 508.047 MW 
     Reactive power (Q o ) 200.943 Mvar 
     —Calculation of a Maximum Reactive Power Limit With Respect to the OEL Field Current 
     The OEL field current limit is 3,386 Amp. This value is converted to 2.88 (3386/1175) Per Unit. A terminal voltage or a maximum reactive power limit which allows a generator field current to become 2.88 Per Unit is calculated using an optimization technique. Here, known variables of a power system are as follows. 
     Infinite bus voltage (V inf ): 21.406 kV (0.973 Per Unit) 
     Active power (P o ): 508.047 MW 
     Field current (I fd     —     OEL ): 3,386 Amp (2.88 Per Unit) 
     An internal field current is calculated using given machine model parameters. A terminal voltage and a maximum reactive power limit which allow the field current to become 2.88 Per Unit are obtained using Equation 2 as follows. 
     Bus terminal voltage (V t ): 23.122 kV (1.051 Per Unit) 
     Maximum limit reactive power (Q OEL ): 289.0 Mvar 
     —Calculation of a Terminal Voltage with Respect to an UEL Limit 
     It is assumed that a reactive power limit according to an UEL (UEL Limit of  FIG. 8 ) at 508 MW on the reactive power capability curve illustrated in  FIG. 1  is −160 Mvar. A terminal voltage in this case is calculated as follows. 
     Currently known power variables are as follows. 
     Infinite bus voltage (V inf ): 21.406 kV (0.973 Per Unit) 
     Active power (P o ): 508.047 MW 
     Reactive power (Q UEL ): −160 Mvar 
     When the terminal voltage (V t     —     UEL ) is estimated using these power variables and Equation 3, 19.6944 kV (0.8952 Per Unit) is obtained. This value is indicated as −160 Mvar, 19.69 kV on the capability curve illustrated in  FIG. 8 . 
     —Calculation of a Maximum Reactive Power Limit According to an OEL for Another Generator Active Power 
     First of all, generator active power is increased by 50 MW and the maximum reactive power limit according to the OEL is calculated as follows. Currently known power system variables include an infinite bus voltage (V inf ) of 21.406 kV (0.973 Per Unit) and an active power (P 1 ) of 558.047 MW. Here, the OEL limit is 3386 Amp (2.88 Per Unit). When the reactive power limit is calculated using Equation 4, a bus terminal voltage (V t ) of 22.792 kV (1.036 Per Unit) and a maximum reactive power limit (Q OEL ) of 248.0 Mvar are obtained. 
     Then, the generator active power is decreased by 50 MW and the maximum reactive power limit is calculated as follows. Currently known power system variables include an infinite bus voltage (V inf ) of 21.406 kV (0.973 Per Unit) and an active power (P 2 ) of 458.047 MW. When the reactive power limit is calculated using Equation 4, a bus terminal voltage (V t ) of 23.386 kV (1.063 Per Unit) and a maximum reactive power limit (Q OEL ) of 321.87 Mvar are obtained. 
     Table 4 shows an OEL reactive power limit with respect to an active power. The OEL reactive power limit with respect to the active power, calculated as above, is indicated on the capability curve of  FIG. 8  as P 1 =458 MW, P o =508 MW, P 2 =558 MW and Operating Point. 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 OEL reactive power limit with respect to an active power 
               
             
          
           
               
                   
                 Q OEL  (Estimated limit 
                   
               
               
                 P (Active power) 
                 reactive power) 
                 Remark 
               
               
                   
               
               
                 P 1  = 458.047 MW 
                 321.9 Mvar 
                   
               
               
                 P o  = 508.047 MW 
                 289.0 Mvar 
                 Current operating point, 
               
               
                   
                   
                 200.943 Mvar 
               
               
                 P 2  = 558.047 MW 
                 248.0 Mvar 
               
               
                   
               
               
                 Calculation of a reactive power limit according to a generator over-voltage limit and a generacor under-voltage limit 
               
             
          
         
       
     
     A generator is normally operated 95% to 105% in order to prevent machine insulation of the generator and over-voltage and under-voltage of generator power. Reactive power limits at an over-voltage and an under-voltage of a generator terminal are calculated using Equation 5. Values which can be known from Equation 5 are as follows. 
     Infinite bus voltage (V inf ): 21.406 kV (0.973 Per Unit) 
     Active power (P o ): 508.047 MW 
     Over-voltage and under-voltage limits: V t     —     max =23.1 kV (1.05 Per Unit), V t     —     min =20.9 kV (0.95 Per Unit) 
     Maximum and minimum reactive power limits are calculated through Equation 4 using the aforementioned variables as follows. 
     Maximum reactive power limit: Q —max =285.63 Mvar 
     Minimum reactive power limit: Q —min =−19.0 Mvar 
     Accordingly, the intelligent system and method for monitoring a generator reactive power limit using machine model parameters have the following advantages. 
     First of all, an operator of a generator monitors a maximum reactive power limit according to an OEL, which is estimated at the current operation point, and thus a sudden accident can be prevented and a generator reactive power can be stably provided to a power system. 
     Secondly, the operator monitors a minimum terminal voltage limit according to an UEL, which is estimated at the current operation point, and thus a sudden accident can be prevented and a generator can absorb a reactive power of a power system. 
     Thirdly, an OEL reactive power limit according to a variation in a generator active power is estimated and monitored at the current generator active power operating point, and thus stability can be improved and a maximum generator reactive power can be supplied to the power system. 
     Fourthly, the operator estimates reactive power limits with respect to an OEL and an UEL in advance and operates a generator so that a generator trip caused by over-excitation or under-excitation can be prevented and reliability of supplying power to the power system can be improved. 
     Fifthly, since a generator trip caused by over-excitation or under-excitation can be prevented, a large-scale power failure due to the generator trip can be prevented. 
     While the present invention has been described with reference to the particular illustrative embodiments, it is not to be restricted by the embodiments hut only by the appended claims. It is to be appreciated that those skilled in the art can change or modify the embodiments without departing from the scope and spirit of the present invention.