Patent Publication Number: US-9422866-B2

Title: Gas turbine controller and a method for controlling a gas turbine

Description:
RELATED APPLICATION 
     This application claims priority under 35 U.S.C. §119 to European application 11180563.6 filed in Europe on Sep. 8, 2011, the entire content of which are hereby incorporated by reference in their entirety. 
     FIELD 
     The disclosure relates to a gas turbine controller, such as a method for controlling operation of a gas turbine and to a gas turbine model with a controller configured to carry out such a method. 
     BACKGROUND INFORMATION 
     Modern gas turbines can operate with lean premix flames to meet emission specifications. To assure a stable combustion for all operating conditions, complex operating methods have been designed as for example known from EP0718470. 
     In addition to the low emissions, the market specification with regard to transient operation capabilities of gas turbines in utility use are becoming more and more stringent. Besides normal frequency support features, gas turbines in local electrical grids can be called for to maintain the grid frequency under various conditions, including emergencies, such as, loss of national grid connection or trip of a large consumer. Gas turbines should be capable of changing their power outputs very quickly in order to keep the generated power and the consumed power balanced in the local grid. 
     One prerequisite for fulfilling these transient operation specification involves combustion stability during rapid transients. However, lean premixing combustion, which is a known technology for dry NOx emission reduction, can have a relatively narrow flammability range. The flammability limits of a lean premix flame are for example much narrower than those of a diffusion flame; can be approximately one order of magnitude smaller. The flammability limits describe the stability of flames. In addition, water and steam injections are popular methods for power augmentation and for wet NOx reduction. They also affect combustion stability. 
     The flammability limits can easily be exceeded during fast transient operation if known operating methods are carried out based on measured values and with direct command to actuators and control valves. 
       FIG. 1  shows an example of a gas turbine control system in accordance with a known implementation.  FIG. 1  shows an example of a conventional gas turbine control system  30 , actuators  41 - 49  supply channels  21 , . . . ,  29  to a combustor  3 . The control system itself includes a controller  10 , and control lines  11 - 19 . Based on measured operating conditions, and operating targets the controller  10  determines the command mass flows for i fuel flows {dot over (m)} fuel,i   CMD , for j water/steam mass flow {dot over (m)} w/s,j   CMD , and for k air mass flows {dot over (m)} air,k   CMD . Based on these command mass flows the actuators for fuel supply  41 , . . . ,  43 , the actuators for water/steam supply  44 , . . . ,  47 , and the actuators for air supply change their position leading to a fuel gas mass flow at the actuators {dot over (m)} fuel,i   ACTUR , water/steam mass flow j at the actuators {dot over (m)} w/s,j   ACTUR , and air mass flow k at the actuator, i.e. VIGV {dot over (m)} air,k   ACTUR . 
     Ideally the mass flows entering the combustor  3  follow the commanded mass flow strictly. However this is not the case in a real engine because the fuel, water/steam and air supply channels have different shapes and volumes, and hence, possess different system dynamics. 
     Due to the different dynamics of the actuators, and of the fuel supply channels  21 , . . . ,  23 , the water/steam supply channels  24 , . . . ,  26 , and the air supply channels  27 , . . . ,  29 , changes in the actual i fuel mass flows {dot over (m)} fuel,i   CMBST , the actual j water/steam mass flows reaching the combustor inlet {dot over (m)} w/s,j   CMBST , and the actual k air mass flows {dot over (m)} air,k   CMBST  are not synchronized, even if the command signals are synchronized and therefore can lead to combustion instabilities. 
     SUMMARY 
     An exemplary method for operating a gas turbine during transient operation is disclosed, the gas turbine including a compressor with variable inlet guide vanes, a combustor, a turbine, a controller, measurement devices, actuators, inlet air supply channels and supply channels for fuel gas, and/or liquid fuel, and/or supply channels for water and/or steam, the method comprising: determining command values for an inlet air mass flow and at least one of fuel mass flow and water and/or steam mass flow, wherein at least one command value is dynamically compensated in at least one command value to compensate for differences in system dynamics of supply systems; and synchronizing changes in at least two of fuel mass flow, water, steam mass flow, and combustion air mass flow entering the combustor (e.g., fuel mass flow with at least one of water, steam mass flow and combustion air mass flow), so that a fuel to air ratio stays within a combustible limit. 
     An exemplary control system for controlling a gas turbine is disclosed, the gas turbine having a compressor with variable inlet guide vanes, a combustor, a turbine, a controller, measurement devices, actuators, and inlet air supply channels, and supply channels for at least one of fuel, water, and steam, wherein the controller determines command values for an inlet air mass flow and at least one of fuel mass flow, water mass flow steam mass flow, a dynamic compensator for the fuel supply; a dynamic compensator for at least one of the water and steam supply; and a dynamic compensator for the air supply to the combustor, the control system comprising: a processor configured to correct at least one command signal during transient operation to compensate for differences in the supply system dynamics to synchronize resulting changes in at least one of the fuel, water, steam, and combustion air mass flow, which enter the combustor, so that a fuel to air ratio stays within combustible limit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosure, its nature as well as its advantages, shall be described in more detail below with the aid of the accompanying drawings. Referring to the drawings: 
         FIG. 1  shows an example of a gas turbine control system in accordance with a known implementation; 
         FIG. 2  shows a gas turbine control system in accordance with an exemplary embodiment of the present disclosure; and 
         FIG. 3  shows in accordance with an exemplary embodiment of the present disclosure a gas turbine with a control system. 
     
    
    
     DETAILED DESCRIPTION 
     Exemplary embodiments of the present disclosure are directed to a method for operation of a gas turbine, which allows fast transient operation with synchronized changes in fuel, water/steam and airflows entering the combustor of a gas turbine. As a result speed of transient changes can be increased and flame stability can be maintained during these fast transients. Exemplary embodiments disclosed herein are further directed to a control system designed to carry out dynamic compensation and a gas turbine comprising such a controller. 
     The relation between the mass flow of fuel channel i at the actuator, {dot over (m)} fuel,i   ACTUR , and at the combustor inlet {dot over (m)} fuel,i   CMBST  can normally be expressed by a transfer function as follows:
 
 L ( {dot over (m)}   fuel,j   CMBST )= G   fuel,i ( s )· L ({dot over (m)} fuel,i   ACTUR )  equation 1
 
where L( ) denotes Laplace transform. G fuel,i (s) the transfer function that represents the system dynamics of fuel channel i. Their correlation depends on the shape and volume of fuel channel i.
 
     Corresponding correlations also exist for water/steam, and air supply channels
 
 L ( {dot over (m)}   W/S,j   CMBST )= G   W/S,j ( s )· L ( {dot over (m)}   W/S,j   ACTUR )  equation 2
 
 L ({dot over (m)} air,k   CMBST )= G   air,k ( s )· L ({dot over (m)} air,k   ACTUR )  equation 3
 
where, {dot over (m)} W/S,j   ACTUR  and {dot over (m)} W/S,j   CMBST  are the mass flows in the water/steam channel j at the actuator, and at the combustor inlet, respectively. {dot over (m)} air,k   ACTUR , and {dot over (m)} air,k   CMBST  are the mass flows of air channel k at the actuator, and at the combustor inlet, respectively. G w/s,j (s), and G air,k (s) are the transfer functions describing the system dynamics.
 
     Exemplary embodiments of the present disclosure are directed to the advantages achieved if at least one of the commanded mass flows is compensated for differences in dynamic behavior of the supply systems. 
     To compensate for differences in the dynamic behavior an exemplary method for operating a gas turbine during transient operation is disclosed herein. The method being performed in conjunction with gas turbines, which include a compressor with variable inlet guide vanes, a combustor, a turbine, a controller, measurement devices, actuators, and supply channels for inlet air, and at least for one of fuel gas, liquid fuel, water, and steam. 
     Besides pressure and temperature boundary conditions the flame stability can be determined by the mass flows, which enter a combustor. According to the proposed method a controller determines command values for the inlet air mass flow, and at least one command value for one of: the fuel gas mass flow, the liquid fuel mass flow, the water mass flow, and the steam mass flow. In order to synchronize the resulting changes in fuel, water, steam, and/or combustion air supply, which enter the combustion chamber, least one command value can be dynamically compensated. By compensating the system dynamics of the actuators, and/or supply channels the fuel to air ratio stays within the combustible limit. In the context of the present disclosure, a supply system includes supply channels, actuators, and control elements. 
     The dynamics of the different supply systems vary in speed. Speed can be limited to the speed of the slowest system. The speed of transient change depends among others on the ratio of the fuel distribution system&#39;s volume and the fuel gas volume flow. A fuel gas system, which comprises fuel gas channels with a large volume downstream of a control valve, has slow dynamics because changes in the valve position do not immediately affect the fuel gas flow into the combustor. For example, after an opening of the control valve the large volume of the fuel gas distribution system has to be further pressurized before the fuel flow into the combustor increases to the desired value. However, transient changes can be accelerated by a controlled signal acceleration. For example a control valve can be opened further than needed to reach a new operating point for a short period of time before reducing the valve opening back to the intended steady state position and a controlled fine-tuning. 
     In a further exemplary embodiment of the present disclosure changes in at least one command value can be accelerated. Specifically, in order to moderate the slow dynamics of the air, fuel gas, liquid fuel, water and/or steam supply systems changes in at least one command value are accelerated. The command value can be accelerated before or after the value is dynamically compensated in order to allow faster transient changes in operation. The acceleration and compensation can also be combined. 
     According to another exemplary embodiment of the disclosure at least one control signal from the controller is compensated before it is sent to the corresponding actuator. The compensation can be done in the control system itself. For this the controller can be virtually divided into a controller and a dynamic compensator. Alternatively, the control system includes a controller and a separate dynamic compensator. 
     Dynamic compensation can be based on a different algorithm. For example, an empirical compensation based on simulation or experiments can be implemented. The compensation specified for desired changes can be determined. The specified compensations can be stored in look up tables or approximated by polynomial functions. 
     A fast and numerically simple compensation can be carried out in the Laplace transformed frequency domain. According to an exemplary embodiment of the present disclosure, the dynamics of at least one of the air, fuel gas, liquid fuel, water, steam supply channels, actuators, and control elements are described with a transfer function. In this embodiment the dynamic compensation and/or acceleration of at least one command signal for the fuel gas, liquid fuel, water and/or steam supply system is approximated with transfer functions. 
     For example, the fuel command {dot over (m)} fuel,i   CMD  is compensated to a dynamically compensated fuel command {dot over (m)} fuel,i   COMP  as follows.
 
 L ( {dot over (m)}   fuel,i   COMP )= G   fuel,i   COMP ( s )· L ( {dot over (m)}   fuel,i   CMD )  equation 4
 
where G fuel,i   COMP  is the compensator for the fuel channel i. Similarly,
 
 L ( {dot over (m)}   w/s,j   COMP )= G   w/s,j   COMP ( s )· L ( {dot over (m)}   w/s,j   CMD )  equation 5
 
 L ( {dot over (m)}   air,k   COMP )= G   air,k   COMP ( s )· L ( {dot over (m)}   air,k   CMD )  equation 6
 
where G w/s,j   COMP  and G air,k   COMP  are the transfer functions describing the compensators for the water/steam channel j and the air channel k.
 
     Compared to the dynamics of the fuel channels the actuators can be fast and it can be assumed that they are perfectly calibrated. Then the following assumption can be used for simplification:
 
 {dot over (m)}   fuel,i   COMP   ={dot over (m)}   fuel,i   ACTUR   equation 7
 
 {dot over (m)}   w/s,j   COMP   ={dot over (m)}   w/s,j   ACTUR   equation 8
 
 {dot over (m)}   air,k   COMP   ={dot over (m)}   air,k   ACTUR   equation 9
 
     Replacing the actuator the compensated value by the actuator value according to equations 7 to 9 in equations 4 to 6 and applying the resulting equations for the actuator value to the correlations describing the supply system to the combustor (equations 1 to 3) one arrives at:
 
 L ( {dot over (m)}   fuel,i   CMBST )= G   fuel,i ( s )· G   fuel,i   COMP ( s )· L ( {dot over (m)}   fuel,i   CMD )  equation 10
 
 L ( {dot over (m)}   w/s,j   CMBST )= G   w/s,j ( s )· G   w/s,j   COMP ( s )· L ( {dot over (m)}   w/s,j   CMD )  equation 11
 
 L ( air,k   CMBST )= G   air,k ( s )· G   air,k   COMP ( s )· L ( {dot over (m)}   air,k   CMD )  equation 12
 
     In order to synchronize the changes in the different mass flows equations 10 to 12 show that the product of the transfer functions describing the supply system and the compensation functions have to be identical:
 
 G   fuel,i ( s )· G   fuel,i   COMP ( s )= G   w/s,j ( s )· G   w/s,j   COMP ( s )= G   air,k ( s )· G   air,k   COMP ( s )  equation 13
 
     This means that the transfer functions between the mass flow commands and the mass flows at the combustor inlet are the same for all channels. This leads to synchronized fuel, water/steam and air mass flows at the combustor inlet during transient operations: 
     
       
         
           
             
               
                 
                   
                     
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     The transfer functions can be synchronized according to this procedure for only two mass flows, for example air and fuel mass flow or in analogue way for any other mass flows. 
     In order accelerate the control, the compensators shall be designed to be phase lead, so that the delays caused by the fuel, water/steam and air supply channels can be moderated. 
     To simplify the compensation of command signals in a group of commands in another exemplary embodiment the command signal of the system with the slowest dynamics can be used without any compensation and the faster systems can be compensated to match the slow system. 
     Thus, for example if the fuel system is the slowest system, equation 10 without compensation becomes:
 
 L ( {dot over (m)}   fuel,i   CMBST )= G   fuel,i ( s )· L ( {dot over (m)}   fuel,i   CMD )  equation 15
 
or  G   fuel,i ( s )=· L ( {dot over (m)}   fuel,i   CMBST )/ L ( {dot over (m)}   fuel,i   CMD )  equation 16
 
     To obtain the compensation function for example for air one can insert equation 16 in equation 14 to obtain:
 
 G   fuel,i ( s )=· L ( {dot over (m)}   air,i   CMBST )/ L ( {dot over (m)}   air,i   CMD )  equation 17
 
and combing with equation 12 arrives at:
 
 G   fuel,i ( s )= G   air,k ( s )· G   air,k   COMP ( s )  equation 18
 
and finally at:
 
 G   air,k   COMP ( s )= G   fuel,i ( s )/ G   air,k ( s )  equation 19
 
     Analogously the compensation function for water/steam or any other mass flow command in the system can be derived. It should be understood that any other slowest system can be used to derive the compensation functions. 
     In general the compensation function G fast,k   COMP (s) of a channel with fast dynamics can be written as a function of the transfer function of the slowest channel G slow,i (s) and the fast channel G fast,k (s) according to equation 20:
 
 G   fast,k   COMP ( s )= G   slow,i ( s )/ G   fast,k ( s )  equation 20
 
     Thus, according to another exemplary embodiment described herein the dynamics of the slowest of the: air, fuel gas, liquid fuel, water, and steam supply systems remain dynamically uncompensated and are described with a transfer function. The dynamics of at least one of fuel gas, liquid fuel, water, and steam supply systems with faster dynamics are described with a transfer function and the dynamic compensation of at least one command signal for the air, fuel gas, liquid fuel, water and/or steam supply system carried out using the transfer functions. 
     According to an exemplary embodiment, in a system with one or many fuel gas supply channels with similar dynamics, the fuel gas cannels remain dynamically uncompensated and are described with a transfer function. The dynamics of the air supply system are described with transfer functions and are dynamically compensated. The dynamic compensation and/or acceleration of the command signal for air supply is calculated using the transfer functions. 
     In a further embodiment, in a system with several fuel gas supply systems with different dynamics, the dynamics of the slowest fuel gas system remains dynamically uncompensated. The dynamics of air supply and faster fuel gas, and/or liquid fuel supply systems are described with transfer functions. The command signal for air supply and faster fuel gas, and/or liquid fuel supply channels are dynamically compensated, wherein the dynamic compensation and/or an acceleration are derived from the transfer functions. 
     Other exemplary embodiments of the present disclosure are directed to a control system for a gas turbine, which is designed to carry out the exemplary methods already discussed. 
     The control system is designed to control a gas turbine including a compressor with variable inlet guide vanes, a combustor, a turbine, a controller, measurement devices, actuators, and inlet air supply channels, and supply channels for fuel gas, and/or liquid fuel, and/or water and/or steam. 
     The exemplary control system can be designed to determine the command values for an inlet air mass flow and at least one of: fuel gas mass flow, liquid fuel mass flow, water mass flow, steam mass flow. According to the disclosure the control system further includes a dynamic compensator for controlling at least one major mass flow entering the combustor, where the major mass flow includes air, fuel gas, and/or liquid fuel, and/or water, and/or steam mass flows. 
     During transient operation, at least one command signal is corrected in order to compensate for the different system dynamics of the different mass flow supply systems in order to synchronize the transient changes in fuel, water, steam, and combustion air mass flows, reaching the combustor. By synchronizing the transient changes the fuel to air ratio, or if applicable also the steam and/or water to fuel ratio, of the fluids reaching the combustor stay within the combustible limit. 
     According to an exemplary embodiment, the control system includes an accelerator to moderate the slow dynamics of the air, fuel gas, liquid fuel, water and/or steam supply systems before or after the value is dynamically compensated in order to allow faster transient changes in operation. The accelerator can also be combined with the dynamic compensator for fuel supply, the dynamic compensator for water or steam supply, and/or the dynamic compensator for air supply. 
     According to another exemplary embodiment the dynamic compensator for air supply system, includes a transfer function, which describes the dynamics of at least one of the: air, fuel gas, liquid fuel, water, and steam supply systems. 
     In a further embodiment, the control system for controlling a gas turbine has no dynamic compensator for the command signal for the slowest supply system of the combustor, but a dynamic compensator is provided for at least one supply system with faster dynamics. This means that the command signal is directly used for control of the slowest signal. More specifically, no dynamic compensator is provided for the slowest of air, fuel gas, liquid fuel, water and steam supply systems and at least one compensator is provided for at least one of: the fuel gas, liquid fuel, water, and steam supply systems with faster dynamics. 
     In another, more specific embodiment of the control system no dynamic compensator is provided for fuel gas channels and a dynamic compensator is provided for the air supply system. 
     In addition to the control system, exemplary embodiments of the present disclosure are directed to a gas turbine that includes an exemplary control system already discussed. 
     In the Laplace transformed domain the physical output variable can be expressed by Laplace transfer function. The parameters of these transfer functions can be identified by step response tests. These tests are either carried out on the real engine or by a detailed dynamic model. 
     The same or functionally identical elements can be provided with the same designations below. The values and dimensional specifications indicated below are only exemplary values and do not constitute any restriction of the disclosure to such express dimensions. 
       FIG. 2  shows a gas turbine control system in accordance with an exemplary embodiment of the present disclosure.  FIG. 2  is based on  FIG. 1  and shows a controller  10 , control lines  11 , . . . ,  19 , actuators  41 , . . . ,  49 , and supply channels  21 , . . . ,  29  to a combustor. In addition the control system  30  of  FIG. 2  includes dynamic compensators  31 , . . . ,  39 . The commanded fuel mass flows {dot over (m)} fuel,i   CMD  are compensated by the dynamic compensators for fuel supply  31 , . . . ,  33 , the commanded water/steam mass flows {dot over (m)} w/s,j   CMD  are compensated by the dynamic compensators for water/steam supply  34 , . . . ,  36 , and the commanded air mass flows {dot over (m)} air,i   CMD  are compensated by the dynamic compensators for air supply  37 , . . . ,  39 . 
     In the example of  FIGS. 1 and 3  the water and steam supply are presented as alternatives. However, this is in no way limiting and the disclosure can be implemented to gas turbines with water and steam injection as desired. 
       FIG. 3  shows in accordance with an exemplary embodiment of the present disclosure a gas turbine with a control system. The gas turbine  1  includes a controller  10 , dynamic compensators  31 ,  32 ,  37 , actuators  41 ,  42 ,  47 , control lines  11 ,  12 ,  17 , and supply channels  21 ,  22 ,  27  to a combustor  3 . 
     The gas turbine  1  of  FIG. 3  has two fuel gas supply channels  21 ,  22 , one to a main burner group and another one to a pilot burner group. The main burner group is a premix group and has much stricter rich and lean limits. It determines the combustors operation range. 
     In  FIG. 3  {dot over (m)} main   CMBST , {dot over (m)} pilot   CMBST  and {dot over (m)} air   CMBST  are the main fuel gas, pilot fuel gas and air mass flows at the combustor inlet. {dot over (m)} main   ACTUR  and {dot over (m)} pilot   ACTUR  are the fuel gas mass flows at the actuators  41 ,  42 , i.e. at the fuel gas control valves. The actuators for the air mass flow  47  are the variable inlet guide vanes (VIGV). The air mass flow at the actuator {dot over (m)} air   ACTUR  is the air mass flow at the compressor inlet. The controller  10  generates the mass flow commands for main fuel {dot over (m)} main   CMD , for pilot fuel {dot over (m)} pilot   CMD , and for airflow {dot over (m)} air   CMD . The mass flow commands are compensated for different dynamics in the dynamic compensators for fuel  31 ,  32 , and air  37  and the compensated commands {dot over (m)} main   COMP , {dot over (m)} pilot   COMP , and {dot over (m)} air   COMP  are sent to the actuators  41 ,  42 ,  47 . 
     A VIGV command θ VIGV   CMD  can be generated by the controller  10  instead CMD of an air mass flow command {dot over (m)} air   CMD . Furthermore, the fuel mass flow commands {dot over (m)} main   COMP  and {dot over (m)} pilot   COMP  can be converted into valve strokes. For the sake of simplification, the mass flows are still used hereafter instead of VIGV position and control valves strokes. 
     The fuel gas supply channels can have big volumes in their fuel distribution systems  8 ,  9 . Their system dynamics can be approximated by a first order delay with a transport delay according to: 
                     L   ⁡     (       m   .     main   CMBST     )       =           G   main     ⁡     (   s   )       ·     L   ⁡     (       m   .     main   ACTUR     )         =       1     1   +       t   main     ·   s         ⁢       ⅇ       -     L   main       ⁢   s       ·     L   ⁡     (       m   .     main   ACTUR     )                     equation   ⁢           ⁢   21                   L   ⁡     (       m   .     pilot   CMBST     )       =           G   pilot     ⁡     (   s   )       ·     L   ⁡     (       m   .     pilot   ACTUR     )         =       1     1   +       t   pilot     ·   s         ⁢       ⅇ       -     L   pilot       ⁢   s       ·     L   ⁡     (       m   .     pilot   ACTUR     )               ,           equation   ⁢           ⁢   22               
where L main  and L pilot  are transport delay times of the main gas channel  21  and pilot gas channel  22 , and t main  and t pilot  are delay time constants, which depend on fuel gas distribution system volumes.
 
     The compressor  2  supplies air to the combustor  3  and uses variable inlet guide vane (VIGV)  47  to control the mass flow. Its dynamics can be approximated by a second order delay with a transport delay according to: 
                       L   ⁡     (       m   .     air   CMBST     )       =           G   air     ⁡     (   s   )       ·     L   ⁡     (       m   .     air   ACTUR     )         =       1       (     1   +       t   VIGV     ·   s       )     ⁢     (     1   +       t   air     ·   s       )         ⁢       ⅇ       -     L   air       ⁢   s       ·     L   ⁡     (       m   .     air   ACTUR     )               ,             equation   ⁢           ⁢   23     ,               
where, L air  is the transport delay time of the compressor  2 . t VIGV  is the time constant of the VIGV servo and t air  the delay time constant, which depends on the compressor volume.
 
     In exemplary embodiments described herein, t main  and t pilot  can be much bigger than t VIGV  and t air , and L main  and L pilot  are longer than L air . Hence, the fuel gas channels  21 ,  22  have slower dynamics than the compressor  2 . 
     As for equations 7 and 9 the dynamics of the actuators  41 ,  42 , are fast compared to those of the fuel channels  21 ,  22  and it can be assumed that they are perfectly calibrated. Therefore, equations 7 and 9 can be applied. If no compensation is applied to the main fuel, and with the air channel (compressor  2 ) being the fast channel and the main fuel gas channel  21  being the slowest channel equations 21 and 23 can be used to obtain the transfer functions G main (s) and G air (s), and inserted in equation 20 to obtain the specified compensation function for the pilot gas: 
                         G   pilot   COMP     ⁡     (   s   )       =         G     fast   ,   k     COMP     ⁡     (   s   )       =           G     slow   ,   i       ⁡     (   s   )       /       G     fast   ,   k       ⁡     (   s   )         =         1   +       t   pilot     ·   s         1   +       t   main     ·   s         ⁢     ⅇ       -     (       L   main     -     L   pilot       )       ⁢   s               ,           equation   ⁢           ⁢   24               
and the specified compensation function for the air mass flow:
 
     
       
         
           
             
               
                 
                   
                     
                       
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                                   ) 
                                 
                               
                               ⁢ 
                               s 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   25 
                 
               
             
           
         
       
     
     To accelerate the system dynamics a compensator (1+t main ·s)/(1+t accel ·s) can be selected, where t accel  is a virtual time constant. It shall be smaller than the time constant of the slowest supply channel; in this case it is smaller than the time constant of the main fuel gas supply t main  in order to make the compensator phase lead. 
     By applying the compensator to equations 24 and 25 for the fast systems one obtains a compensation function for the accelerated pilot gas: 
                           G   ′     pilot   COMP     ⁡     (   s   )       =         1   +       t   pilot     ·   s         1   +       t   accel     ·   s         ⁢     ⅇ       -     (       L   main     -     L   pilot       )       ⁢   s           ,           equation   ⁢           ⁢   26               
and a compensation function for the accelerated air mass flow:
 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           G 
                           ′ 
                         
                         air 
                         COMP 
                       
                       ⁡ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               
                                 
                                   t 
                                   VIGV 
                                 
                                 · 
                                 s 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 1 
                                 + 
                                 
                                   t 
                                   air 
                                 
                               
                               ⁣ 
                               
                                 · 
                                 s 
                               
                             
                             ) 
                           
                         
                         
                           1 
                           + 
                           
                             
                               t 
                               accel 
                             
                             · 
                             s 
                           
                         
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           
                             - 
                             
                               ( 
                               
                                 
                                   L 
                                   main 
                                 
                                 - 
                                 
                                   L 
                                   air 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           s 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   27 
                 
               
             
           
         
       
     
     The resulting compensation function for the main fuel gas flow is unity times the compensator (1+t main ·s)/(1+t accel ·s) for acceleration: 
     
       
         
           
             
               
                 
                   
                     
                       
                         G 
                         ′ 
                       
                       main 
                       COMP 
                     
                     ⁡ 
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       + 
                       
                         
                           t 
                           main 
                         
                         · 
                         s 
                       
                     
                     
                       1 
                       + 
                       
                         
                           t 
                           accel 
                         
                         · 
                         s 
                       
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   28 
                 
               
             
           
         
       
     
     Again if the dynamics of the actuators are fast compared to those of the fuel channels and if it can be assumed that they are perfectly calibrated equations 7 and 9 can be applied and the compensated mass flows are equal to the actuator mass flows. Therefore, equations 26 and 27 can be applied to equations 21 and 22, respectively, as well as equation 28 to equation 23. All lead to the following accelerated overall transfer function G″(s): 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             G 
                             ″ 
                           
                           pilot 
                           CMBST 
                         
                         ⁡ 
                         
                           ( 
                           s 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           L 
                           ⁡ 
                           
                             ( 
                             
                               
                                 m 
                                 . 
                               
                               pilot 
                               CMBST 
                             
                             ) 
                           
                         
                         
                           L 
                           ⁡ 
                           
                             ( 
                             
                               
                                 m 
                                 . 
                               
                               pilot 
                               CMD 
                             
                             ) 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           
                             G 
                             ″ 
                           
                           air 
                           CMBST 
                         
                         ⁡ 
                         
                           ( 
                           s 
                           ) 
                         
                       
                       = 
                       
                         
                           
                             L 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   m 
                                   . 
                                 
                                 air 
                                 CMBST 
                               
                               ) 
                             
                           
                           
                             L 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   m 
                                   . 
                                 
                                 air 
                                 CMD 
                               
                               ) 
                             
                           
                         
                         = 
                         
                           
                             
                               
                                 
                                   G 
                                   ″ 
                                 
                                 main 
                                 CMBST 
                               
                               ⁡ 
                               
                                 ( 
                                 s 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                 L 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       m 
                                       . 
                                     
                                     main 
                                     CMBST 
                                   
                                   ) 
                                 
                               
                               
                                 L 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       m 
                                       . 
                                     
                                     main 
                                     CMD 
                                   
                                   ) 
                                 
                               
                             
                           
                           = 
                           
                             
                               1 
                               
                                 1 
                                 + 
                                 
                                   
                                     t 
                                     accel 
                                   
                                   · 
                                   s 
                                 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 
                                   - 
                                   
                                     L 
                                     main 
                                   
                                 
                                 ⁢ 
                                 s 
                               
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                   ⁢ 
                   29 
                 
               
             
           
         
       
     
     This means that the fuel gas and air mass flows at the combustor inlet can be synchronized and accelerated by implementing the compensators defined by equations 26 to 28. 
     In exemplary embodiments of the disclosure, the virtual time constant t accel  shall be carefully determined. On one hand, it shall be smaller than t main ; on the other hand, it shall not be too small. If the acceleration is to high, i.e. the time constant t accel  too small the whole closed loop control may become unstable. The ratio of acceleration time constant t accel  to the main time constant t main  is in the range of 0.2 to 0.8, for example. and preferably in the range of 0.4 to 0.6 to allow noticeable stable moderation of the dynamic system. 
     Thus, it will be appreciated by those skilled in the art that the present disclosure can be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The presently disclosed embodiments are therefore considered in all respects to be illustrative and not restricted. The scope of the disclosure is indicated by the appended claims rather than the foregoing description and all changes that come within the meaning and range and equivalence thereof are intended to be embraced therein. 
     DESIGNATIONS 
     
         
           1  gas turbine 
           2  compressor 
           3  combustor 
           4  turbine 
           5  generator 
           6  inlet air 
           7  exhaust gas 
           8  main fuel gas distribution system 
           9  pilot gas distribution system 
           10  Controller 
           11 , . . . ,  13  Control lines for fuel supply 
           14 , . . . ,  16  Control lines for water and/or steam supply 
           17 , . . . ,  19  Control lines for air supply 
           21 , . . . ,  23  Fuel supply channels 
           24 , . . . ,  26  Water and/or steam supply channels 
           27 , . . . ,  29  Air supply channels 
           30  Control system 
           31 , . . . ,  33  Dynamic compensator for fuel supply 
           34 , . . . ,  36  Dynamic compensator for water and/or steam supply 
           37 , . . . ,  39  Dynamic compensator for air supply 
           41 , . . . ,  43  Actuator for fuel supply 
           44 , . . . ,  46  Actuator for water and/or steam supply 
           47 , . . . ,  49  Actuator for air supply 
         {dot over (m)} main   CMBST  main fuel gas mass flow at the combustor inlet 
         {dot over (m)} pilot   CMBST  pilot gas mass flow at the combustor inlet 
         {dot over (m)} air   CMBST  air mass flow at the combustor inlet 
         {dot over (m)} fuel,i   CMBST  fuel mass flow i at the combustor inlet 
         {dot over (m)} w/s,j   CMBST  water/steam mass flow j at the combustor inlet 
         {dot over (m)} air,k   CMBST  air mass flow k at the combustor inlet 
         {dot over (m)} main   ACTUR  main fuel gas mass flows at the actuators 
         {dot over (m)} pilot   ACTUR  pilot fuel gas mass flows at the actuators 
         {dot over (m)} air   ACTUR  air mass flow at the actuator, i.e., VIGV 
         {dot over (m)} fuel,i   ACTUR  fuel mass flow i at the actuators 
         {dot over (m)} w/s,j   ACTUR  water/steam mass flow j at the actuators 
         {dot over (m)} air,k   ACTUR  air mass flow k at the actuator, i.e., VIGV 
         {dot over (m)} main   CMD  main fuel mass flow command generated by the controller  10   
         {dot over (m)} pilot   CMD  pilot fuel mass flow command generated by the controller  10   
         {dot over (m)} air   CMD  air mass flow command generated by the controller  10   
         {dot over (m)} fuel,i   CMD  fuel mass flow command i generated by the controller  10   
         {dot over (m)} w/s,j   CMD  water/steam mass flow command j generated by the controller  10   
         {dot over (m)} air,k   CMD  air mass flow k command generated by the controller  10   
         {dot over (m)} main   COMP  compensated main fuel mass flow command generated by dynamic compensator for main fuel supply  31   
         {dot over (m)} pilot   COMP  compensated pilot fuel mass flow command generated by dynamic compensator for pilot fuel supply  32   
         {dot over (m)} air   COMP  compensated air mass flow command generated by dynamic compensator for air supply  37   
         {dot over (m)} fuel,i   COMP  compensated fuel mass flow command i generated by dynamic compensator for fuel supply  31 , . . . ,  33   
         {dot over (m)} w/s,j   COMP  compensated water/steam mass flow command j generated by dynamic compensator for pilot fuel supply  34 , . . . ,  36   
         {dot over (m)} air,k   COMP  compensated air mass flow command k generated by dynamic compensator for air supply  37 , . . . ,  39   
         VIGV variable inlet guide vane 
         θ VIGV  virtual variable inlet guide vane position 
         θ VIGV,cmd  commanded variable inlet guide vane position 
         θ VIGV,real  variable inlet guide vane position