Abstract:
Critical stress in a gas turbine can be estimated using one or more readily measurable temperatures in the gas turbine. First and second critical temperatures can be estimated based on the at least one measurable temperature using heat conduction and convection equations. Subsequently, the critical stress can be estimated in real time according to a stress model prediction based on the difference between the critical temperatures, and possibly the rotational speed of the turbine, and some parameter, such as air pressure, that is indicative of air flow around the turbine component. Operation of the gas turbine can thus be controlled using the estimated critical temperatures.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    The present invention relates to gas turbine operation and, more particularly, to a system and method for controlling gas turbine operation in a closed-loop manner based on estimated stress levels at key locations within the turbine.  
           [0002]    Typical gas turbine operating control schedules are open-loop in nature, derived from extensive analysis of simulated thermal and mechanical stress levels in rotating components, and designed so that these nominal stresses are not exceeded during operation. As an example, a possible startup schedule for a gas turbine is shown in FIG. 1. The schedule includes turbine speed versus time and is used by the turbine speed controller as a reference. As the machine accelerates from startup, both mechanical and thermal stresses build up. Mechanical stresses are primarily due to aerodynamic reactions as well as rotational and centrifugal forces. Thermal stresses arise from differential thermal expansion within turbine metal parts. These thermal stresses result from sources of heat within the turbine that are not uniform, and hence different metal parts heat up at different rates. When two parts that are secured together expand at different rates, or even a single part that is massive enough that separate regions of the part expand at varying rates, mechanical deformation and severe stressing may result. Once these parts attain a substantially uniform temperature, however, the stress levels decrease.  
           [0003]    Since peak stress levels cannot be allowed to exceed limits dictated by material integrity as well as ultimate component life, it is important that the machine is operated in such a manner that the stress levels are kept below these limits at all times. In the case of machine startup, this is achieved by “holding” the turbine at certain predetermined points in its startup cycle to allow the heat to “soak” in. FIG. 1 shows two such hold points at 50% and 85% of full speed. Hold points and hold times are typically derived from extensive off-line analysis that attempt to predict stress patterns using accurate, but very high order finite-element models.  
           [0004]    To account for machine-to-machine variations as well as inaccuracies in the models, safety margins are built into the operating schedules. Better performance could be obtained from the machine in terms of quicker startups and the like if stresses could be measured or estimated on-line. Measuring such stress levels on rotating components, however, is prohibitively expensive.  
         BRIEF DESCRIPTION OF THE INVENTION  
         [0005]    In an exemplary embodiment of the present invention, a method of operating a gas turbine includes the steps of (a) measuring at least one measurable temperature (T MEAS ) in the gas turbine; (b) using heat conduction and convention equations to estimate a first critical temperature (T 1 ) and a second critical temperature (T 2 ) based on T MEAS ; and (c) controlling the gas turbine based on T 1  and T 2 .  
           [0006]    In another exemplary embodiment of the invention, a method of estimating critical stress in a gas turbine includes the steps of (a) measuring at least one measurable temperature (T MEAS ) in the gas turbine; (b) using heat conduction and convection equations to estimate a first critical temperature (T 1 ) and a second critical temperature (T 2 ) based on T MEAS ; and (c) estimating the critical stress in real time according to a stress model prediction based on the difference between T 1  and T 2 .  
           [0007]    In still another exemplary embodiment of the invention, a system is provided for estimating critical stress in a gas turbine. The system includes a probe that measures at least one measurable temperature (T MEAS ) in the gas turbine. A processor receives input from the probe and uses heat conduction and convection equations to estimate first and second critical temperatures based on T MEAS . The processor includes a memory storing a stress model prediction algorithm and estimates the critical stress in real time based on a difference between T 1  and T 2  using the stress model prediction algorithm. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0008]    [0008]FIG. 1 is a graph showing a possible startup schedule for a gas turbine;  
         [0009]    [0009]FIG. 2 is a schematic illustration of the system of the present invention;  
         [0010]    [0010]FIG. 3 is a graph showing a real-time stress model prediction compared with a stress level predicted by finite-element models; and  
         [0011]    [0011]FIG. 4 is a control schematic of the system of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0012]    With the system of the present invention, a simple on-line model is used to estimate stress at one or more key locations in the gas turbine, and this stress estimate is used to control the machine. As a first exemplary application of the invention, the typical startup schedule is modified to provide an estimate of stress and hence operate the machine in a regulated fashion.  
         [0013]    An important location in the compressor rotor where material stress limits operation has been identified using validated physics-based models. Extensive finite element analysis has also shown that this stress is strongly influenced by (1) the difference in temperature at two related points in the rotor, (2) the speed of the machine, and (3) the flow rate of air through the compressor, with the first factor being the most significant.  
         [0014]    [0014]FIG. 2 is a schematic illustration of the system of the present invention. The temperatures T 1  and T 2  are internal operating temperatures that are used to estimate stress values within the turbine. These internal temperatures, however, cannot be measured. The invention incorporates a model  10  that uses simple heat conduction and convection equations. In one example, the two temperatures are estimated by solving the following set of ordinary differential equations (using standard off the shelf software):  
                T   1            t       =       -       k   1          (       T   1     -     T     MEAS        (   1   )           )         -       k   2          (       T   1     -     T   2       )                          T   2            t       =       -       k   3          (       T   2     -     T   1       )         -       k   4          (       T   2     -     T     MEAS        (   2   )           )                               
 
         [0015]    The measured temperatures TMEAS 1  and TMEAS 2   12  are shown as the first part of the model  10  in FIG. 2, and for example are air temperature measurements obtained around the component where the stress is being estimated. The model  10  is dynamic in nature, i.e. the model evolves over time. The temperatures  12  are input into a low-order dynamic temperature estimator  14 , which is used to determine estimated values for T 1  and T 2 . The constants k 1 -k 4  are obtained from material properties such as coefficient of thermal conductivity, convective heat transfer coefficient, metal density, etc., as well as geometric properties such as length and thickness of the components. Subsequently, a non-linear static model or low-order non-linear stress estimator  22  inputs the determined temperatures T 1  and T 2 , machine speed  16 , pressure  18 , and temperature  20  measurements in the compressor to estimate stress.  
         [0016]    The following is an example of a static model that links the temperatures (T 1  and T 2 ), machine speed (S), and air pressure (P) to the peak stress (SEQ) at a particular critical location of the turbine:  
         SEQ= a   1 ( T   1 - T   2 )+ a   2   S   n   +a   3   P   m    
         [0017]    where a 1 , a 2 , a 3 , m and n are predetermined constants.  
         [0018]    This model can be obtained from physics-based principals or from nonlinear regression analysis. In one example, where the latter was used to obtain the model, the values in the equation were: a 1 =0.4; a 2 =0.005; a 3 =0.1; n=2; and m=0.5. These numbers can vary depending on the location of the critical stress point.  
         [0019]    [0019]FIG. 3 illustrates an example of how the real-time stress model prediction with the stress model  10  of FIG. 2 compares with the conventionally-determined stress level as predicted by the finite-element analysis model. The numerical values of stress have been normalized with respect to an arbitrary number and do not necessarily represent the stress level for the startup schedule in FIG. 1. The dotted line is the real-time stress model prediction (per the stress model  10  in FIG. 2), while the solid line represents the generally more accurate finite element analysis generated stress value. It can be seen from FIG. 3 that the real time stress model prediction almost identically matches the finite element analysis generated stress value.  
         [0020]    Once the stress values have been determined using the low-order non-linear stress estimator  22  discussed above, operation of the turbine can be controlled in real time. Limits on stress level for safe operation of a gas turbine have been previously determined. These limits can be used to automatically control the startup (or other operating condition) of the machine without an open-loop schedule. One possible control schematic is illustrated in FIG. 4. The model  10  continuously estimates the stress at the key location. If there is more than one location where the stress level is critical, similar models  10 A,  10 B can be developed to estimate these stresses using the stress model  10  discussed above with reference to FIG. 2.  
         [0021]    A maximum  24  of all these estimates is then compared against the limit, which is shown as being a constant in FIG. 4 but could be a function of other system parameters. A margin of safety is subtracted from this limit to accommodate modeling errors and other unknown variations. Reference number  26  designates the limit minus the margin of safety. While it is assumed in this detailed description that the limit is the same (whether constant or derived) for all locations, this does not necessarily have to be the case. Different limits can be incorporated for different locations. In this case, the differences between the stress levels and the individual limits (and corresponding safety margins) will be compared against each other to determine the maximum error.  
         [0022]    In operation, if the estimated stress exceeds the modified limit, a negative error signal e is generated that is multiplied by a gain k and subtracted from the measured machine acceleration. This new value is used, along with existing limiting values, to reduce the rate of increase in speed (i.e., the acceleration) of the turbine. This reduction in acceleration leads to a reduction in the differential temperature and thus to a lower value for stress. This continues until the stress is lower than the modified limit, whereby the error signal e now becomes positive. In this event, the measured acceleration is then modified in the positive direction, thus raising the existing limit and allowing the speed to increase faster (i.e., at a higher acceleration). A filter  28  is included in the feedback path to filter the acceleration signal. The choice of the constant a in the filter  28  as well as the gain k is determined by using standard control engineering practice to maintain adequate performance and stability margin. These constants will be different for differently constructed machines.  
         [0023]    In an alternative embodiment, other control methods can be implemented that function in essentially the same way but without the continuous control feature as described above. For example, a logical block could be added to the existing control algorithm that would receive the signal e (in FIG. 4) and hold the machine at the current speed whenever e is negative (to allow the stress to decrease) and allow it to accelerate along the normal startup schedule when e is positive.  
         [0024]    With this system, real time stress levels can be estimated at key locations within the turbine, and a gas turbine can be controlled in a closed-loop manner based on the estimated stress levels.  
         [0025]    While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiments, it is to be understood that the invention is not to be limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.