Patent Publication Number: US-8538561-B2

Title: Method and system to estimate variables in an integrated gasification combined cycle (IGCC) plant

Description:
STATEMENT REGARDING FEDERALLY SPONSORED DEVELOPMENT 
     This invention was made with government support under Contract No. DE-FC26-07NT43094, awarded by the United States Department of Energy. Accordingly, the United States Government may have certain rights in this invention. 
    
    
     CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to U.S. patent application Ser. No. 13/053,731, titled “Model Predictive Control System And Method For Integrated Gasification Combined Cycle Power Generation”, filed concurrently herewith and herein incorporated by reference in its entirety. 
     FIELD 
     The present invention is generally related to integrated gasification combined cycle (IGCC) power generation, and, more particularly, to method and system to estimate variables in an IGCC power generation plant. 
     BACKGROUND 
     Integrated Gasification Combined Cycle (IGCC) technology continues progressing as an attractive technology for clean and efficient electric power generation, such as may be generated from abundant carbonaceous materials, e.g., coal and other relatively low-cost fuels. At the front end of IGCC is a process known as gasification, which is a partial oxidation process that transforms the fuel (e.g., coal) into a stream of combustible synthesis gas (syngas). IGCC is environmental-friendly because pollution-causing emissions (e.g., SO x , NO x , mercury, particulates, etc.) may be substantially removed from the syngas stream before combustion occurs. While IGCC technology intrinsically holds significant potential for clean and efficient power generation, there are opportunities yet to be exploited to improve IGCC power generation for enhanced reliability, availability, efficiency and flexibility. 
     It is known that present techniques for operation of an IGCC power plant tend to be based on simplistic control procedures, as may be conveyed to an operator by way of rigid and cumbersome operator guidelines, not necessarily designed to achieve any meaningful optimization strategy, such as may be due to limited online information for monitoring and controlling the IGCC plant. For example, a gasification section of the IGCC plant may be subject to a relatively harsh operating environment and as a result limited online sensors may be available for monitoring and control. 
     It is also known that model-based estimation implementations may be helpful to estimate plant variables. However, there are challenges that can arise since often modeling and/or sensing uncertainties may not be appropriately accounted for in such estimation implementations. 
     In view of the foregoing considerations, it would be desirable to formulate an estimation strategy where one may combine plant measurements, as may be obtained by way of a sensor suite, with model-based estimation for estimating plant variables, which are appropriately corrected for modeling and/or sensing uncertainties, without adding any substantial computational burden and while achieving substantial estimation accuracy. 
     BRIEF DESCRIPTION 
     Generally, at least some aspects of the present invention may be fulfilled by a system to estimate variables in an integrated gasification combined cycle (IGCC) power generation plant, the system may include a sensor suite coupled to sense signals indicative of respective plant input variables and plant output variables. The system may further include an extended Kalman filter (EKF) coupled to receive sensed plant input variables and comprising a dynamic model of the plant to generate at a discrete time a plurality of plant state estimates and a covariance matrix for the state estimates. A preemptive-constraining processor may be configured to preemptively constrain the state estimates and covariance matrix to be free of constraint violations. A measurement-correction processor may be configured to correct constrained state estimates and a constrained covariance matrix based on processing of sensed plant output variables. The measurement-correction processor is coupled to update the dynamic model with corrected state estimates and a corrected covariance matrix. The updated dynamic model may be configured to estimate values for at least one plant variable not originally sensed by the sensor suite. 
     At least some additional aspects of the present invention may be fulfilled by a method to estimate variables in an integrated gasification combined cycle (IGCC) power generation plant. The method may include the following actions: coupling a sensor suite to sense signals indicative of respective plant input variables and plant output variables; supplying sensed plant input variables to an extended Kalman filter (EKF), which comprises a dynamic model of the plant to generate at a discrete time a plurality of state estimates and a covariance matrix for the state estimates; preemptively constraining the state estimates and covariance matrix to be free of constraint violations; correcting constrained state estimates and a constrained covariance matrix based on processing of sensed plant output variables; updating the dynamic model with corrected state estimates and a corrected covariance matrix; and estimating with the updated dynamic model at least one plant variable not originally sensed by the sensor suite. 
     Still additional aspects of the present invention may be fulfilled by an non-transitory tangible computer-readable medium having computer-executable instructions, which when executed by a processor are configured to perform the following actions: measuring signals from a sensor suite, the signals indicative of respective plant input variables and plant output variables; supplying sensed plant input variables to an extended Kalman filter, which comprises a dynamic model of the plant to generate at a discrete time a plurality of state estimates and a covariance matrix for the state estimates; preemptively constraining the state estimates and covariance matrix to be free of constraint violations; correcting constrained state estimates and a constrained covariance matrix based on processing of sensed plant output variables; updating the dynamic model with corrected state estimates and a corrected covariance matrix; and estimating with the updated dynamic model at least one plant variable not originally sensed by the sensor suite. 
    
    
     
       DRAWINGS 
       These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
         FIG. 1  is a block diagram representation of an example estimation system embodying aspects of the present invention, as may be used to perform online estimation in an Integrated Gasification Combined Cycle (IGCC) power plant. 
         FIG. 2  is a simplified schematic model representation of an example gasification section of the IGCC plant, as may be simulated by a dynamic model, as may be part of the estimation system shown in  FIG. 1 . 
         FIG. 3  is a flow chart illustrating example processing actions in connection with a preemptively constrained extended Kalman filter (EKF), as may be part of the estimation system shown in  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     Aspects of the present invention may be applied in the context of an online sensing system for an Integrated Gasification Combined Cycle (IGCC) power generation plant. In one example embodiment one may combine measurements of plant variables, as may be obtained by way of a sensor suite, with model-based estimation (e.g., extended Kalman filter (EKF) estimation) for estimating plant variables, some of which may not have been originally measured by the sensor suite. 
     As will be appreciated by one skilled in the art, EKF estimation has proven to be a powerful computational tool to estimate the states of a dynamic plant. However, in traditional EKF implementations there are challenges that can arise since often model or signal uncertainties may not be appropriately accounted for in such EKF implementations. For example, constraints on plant states may be neglected because such constraints may not be readily accommodated by the processing architecture of traditional EKF implementations. The constraints may be based on real-world physical and/or operational considerations of the plant and therefore constraint violations may lead to inaccurate EKF estimation or could even lead to an erroneous assessment of the actual operating conditions of the plant. 
     The inventors of the present invention propose an innovative and elegant strategy or preemptively constraining the EKF so that without adding any substantial computational burden one may achieve a substantial improvement in the accuracy of the EKF estimates. As used herein, “preemptive constraining” refers to performing processing actions adapted to avoid constraint violations prior to performing a (Kalman filter) measurement update. 
       FIG. 1  is a block diagram representation of an example estimation system  10  embodying aspects of the present invention. In one example embodiment, system  10  may be used to estimate parameters in an integrated gasification combined cycle (IGCC) power generation plant  12 . A sensor suite  14  may be coupled to sense signals indicative of respective plant input variables  16 , such as fuel input (e.g., coal slurry), recycled CO 2 , oxygen feed, etc. Sensor suite  14  may be further coupled to sense signals indicative of respective plant output variables  18 , such as syngas composition and temperature, syngas flow rate, carbon conversion, etc. 
     Estimation system  10  may further include an extended Kalman filter (EKF)  20 , which comprises a preemptively-constrained EKF in accordance with aspects of the present invention. A dynamic model  22  of the plant is coupled to receive sensed (i.e., measured) plant input variables  16  and propagate at a discrete time a plurality of plant state estimates and a covariance matrix for the state estimates. It will be appreciated that at this stage of the Kalman cycle, the plant state estimates (e.g., a priori estimates) may be subject to sensing inaccuracies, such as bias and/or noise present in measurements from sensor suite  14  and/or modeling inaccuracies, which may be present in dynamic model  12 . 
     A preemptive-constraining processor  24  is configured to preemptively constrain the propagated state estimates and covariance matrix to be free of constraint limit violations. In one example embodiment, preemptive-constraining processor  24  generates constrained state estimates and a constrained covariance matrix. A measurement correction processor  26  is configured to correct the constrained state estimates and the constrained covariance matrix based on sensed plant output variables  18 . In one example embodiment, such a correction may involve comparing at least one sensed plant output variable with at least one corresponding model output variable. 
     Measurement correction processor  26  is coupled to update dynamic model  22  with corrected state estimates and a corrected covariance matrix. In one example embodiment, a corrected state estimate may comprise respective corrections for dynamic states of the plant, inputs (e.g., control inputs), output variables, such as may include virtual outputs (i.e., plant output variables not measured by sensor suite  14 ), biases for measured variables, and model parameters. In one example embodiment, updating the dynamic model may include defining a previously unknown model parameter and/or updating a model parameter which varies in time, such as gasifier kinetics, radiant syngas cooler (RSC) fouling etc.). In one example embodiment, the updated dynamic model may be configured to estimate values for at least one plant variable, which may not have been originally sensed by sensor suite  14  (i.e., virtual sensing). Although dynamic model  22 , preemptive constraining processor  24  and measurement correction processor  26  are illustrated in  FIG. 1  as separate processors (e.g., processing modules), it will be readily appreciated by one skilled in the art that such processors may be integrated in a common processor. 
       FIG. 2  is a simplified schematic model representation of an example gasification section  32 , as may be modeled by dynamic model  22 . As will be readily appreciated by one skilled in the art, example model components of gasification section  32  may include a gasifier model component  34 , a radiant syngas cooler (RSC) model component  36 , a RSC quench model component  38 , a high-pressure (HP) steam drum model component  40  and a scrubber model component  42 . Example input variables received by gasifier model component  34  may be indicative of fuel input (e.g., coal slurry), recycled CO 2 , and oxygen feed. Example model output variables supplied by gasifier model component  34  may be gasifier outlet syngas composition and temperature, ash flow and carbon conversion. 
     Example inputs received by RSC model component  36  may be the syngas output stream from gasifier model component  34 , and water/steam flow from HP steam drum model component  40  to, for example, calculate transient variation in the syngas temperature, a level of RSC tubing stress and the steam fraction in the water stream the RSC tubing. Quench model component  38  may receive as example inputs the respective syngas and ash/slag streams from the RSC outlet to, for example, calculate a quench outlet syngas stream flow rate, composition and enthalpy. RSC model component  36  may be coupled to HP steam drum model component  40  to, for example, calculate a water/steam circulation flow rate between the HP stream drum and the RSC piping. Scrubber model component  42  may receive from quench model component  38  the quench syngas output and then calculate a scrubbed syngas composition and temperature. It will be appreciated that the foregoing model representation of gasification section  32  should be construed in an example sense and not in a limiting sense being that aspects of the present invention are neither limited to any specific modeling implementation for the gasification section of the IGCC plant nor to any specific gasification design. 
     In one example embodiment, dynamic model  22  may comprise a reduced-order dynamic model of the gasification section suitable for online model prediction and optimization. In one example embodiment, a reduced-order model may be able to perform a simulation substantially faster (e.g., approximately at least a 1000 times faster) than a full-order model while maintaining a relatively high-level of accuracy. It will be appreciated that in a practical embodiment the faster simulation speed of the reduced-order model is desirable for real-time simulation and sensing and/or control design. 
       FIG. 3  is a flow chart illustrating example processing actions in connection with extended Kalman filter  20  ( FIG. 1 ) embodying aspects of the present invention. Block  50  represents an initialization action, such as may allow respective initialization of state estimates and a covariance matrix for the state estimates. Block  52  allows processing dynamic model  22  one time step, as may be allow respective updating of the state estimates and the state covariance matrix. Block  52  represents a pre-emptive constraining action, such as may allow a respective preemptive constraining of the state estimates and covariance matrix based on a sigma-point processing of the covariance matrix. Block  56  represents a measurement correction action, such as may involve use of sensed plant output variables to correct the constrained states and constrained covariance matrix. As will be appreciated by one skilled in the art, EKF is a recursive process and in one example embodiment, block  58  allows performing an updating action of dynamic model  22 , prior to iteratively proceeding to a next time step in block  52  and subsequent processing actions, such as constraining action  54  and measurement correcting action  56 . 
     Mathematical Underpinnings 
     The description below will focus on basic mathematical underpinnings of an extended Kalman filter (EKF) embodying aspects of the present invention. The description below is not meant to be a mathematical treatise on EKF since such information is readily available in the literature and our intent is just meant to appropriately highlight concepts embodying aspects of the present invention. 
     X k  represents a state vector (i.e., an overall state vector), which in one example embodiment may comprise dynamic plant states x k , inputs u k , biases b k  and model parameters p k , where k denotes a discrete sampling time. 
                     X   k     =     [           x   k               u   k               b   k               p   k           ]             Eq   .           ⁢   1               
Terminology
 
     P represents a covariance matrix for the state vector. Presuming an example size of the state vector is n x ×1, the size of the covariance matrix P would be n x ×n x . Matrix Q represents modeling uncertainty, such as may be due to modeling inaccuracies, Matrix R represents measurement uncertainty, such as may be due to sensor noise and/or bias, UB and LB respectively represent upper and lower bounds (e.g., constraint limits) for the state vector, EQ represents equality type of constraints for the state vector. 
     EKF Initialization
 
 X   0|0   ,P   0|0 ,Q,R,UB,LB,EQ
 
     As will be appreciated by one skilled in the art, the notation X 0|0  indicates an initial state vector and can be read as initial state estimates at an initialization time (e.g., time  0 ) based on measurements up to and including time  0 . In general, X k|k  can be read as “the estimate of X at time k based on measurements up to and including time k, (i.e., a posteriori estimate). Similarly, X k|k-1  can be read as “the estimate of X at time k based on measurements until time k−1, (i.e., a priori estimate). P 0|0  indicates an initial covariance matrix for the state vector. 
     EKF Propagation
 
 X   k|k-1   =F   Ts ( X   k-1|k-1   ,u   k-1|k-1   ,P   k-1|k-1 )  Eq. 2
 
     Eq. 2 indicates an example processing action of dynamic model  22  ( FIG. 1 ) to generate the a priori estimates for a current time step.
 
 Y   k   =g ( x   k|k-1   ,u   k|k-1   ,P   k|k-1 )  Eq. 3
 
     Eq. 3 indicates predicted outputs for the current time step.
 
 X   k   =AX   k-1  
 
 Y   k   =CX   k   Eq. 4
 
     Eq. 4 represents a linearization of dynamic model ( 22 ) to obtain respective state-space matrixes A and C.
 
 P   k|k-1   =AP   k-1|k-1   A   T   +Q   Eq. 5
 
     Eq. 5 indicates an updating processing action for the covariance matrix using the linearized form of the model and including model noise. It should be appreciated that in one example embodiment Eqs. 2-5 may be encompassed by block  52  ( FIG. 3 ). 
     In accordance with aspects of the present invention, the inventors of the present invention have developed an efficient computational algorithm for preemptively constraining the EFK prior to performing processing actions under the section titled “Performing Measurement Update”. 
     It is noted that traditional EKF estimation techniques do not perform the processing actions under the following section titled “Preemptive Constraining of EKF”. That is, traditional EKF estimation would continue to the processing actions under the section titled “Performing Measurement Update”, which will be recognized by one skilled in the art as the portion of the Kalman filter cycle where a measurement update adjusts the a priori estimate by an actual measurement at that time to generate the posteriori estimate. See for example the organic structure of Eq. 11. It will be appreciated that the measurement update involves computation of a Kalman gain K k , which is turn influenced by covariance estimates. See for example the organic structure of Eq. 12. Another step is to compute an a posteriori covariance matrix. See for example the organic structure of Eq. 13. It would be appreciated that constraint violations would detrimentally affect the accuracy of the foregoing computations. Thus, by performing the processing actions to be described below under the section titled “Preemptive Constraining of EKF”, one advantageously ensures that computation of the foregoing equations is respectful of any applicable constraints without introducing any substantial computational burden. 
     Preemptive Constraining of EKF 
     Determining Sigma-Points (SP)
 
 X=X   k|k-1 1 1×2n     x     Eq. 6
 
     Eq. 6 indicates a replicating action, where the state vector X k  obtained in the propagation step would be replicated 2n x  times.
 
    X   = X +[√{square root over ( n   x   P   k|k-1 )}−√{square root over ( n   x   P   k|k-1 )}]  Eq. 7
 
     Eq. 7 indicates adding and subtracting one or more standard deviations about a mean value of each state estimate to generate a sigma point matrix. 
     Applying Constraints
 
{tilde over ( X )}( i,j )=min(max(LB i   ,X ( i,j )),UB i )  Eq. 8
         for all i=1, . . . , n x  and j=1, . . . , 2n x          

     UB and LB respectively represent n x ×1 upper and lower bound vectors in Eq. 8 
     Determining Matrixes with Constrained Mean and Covariance Elements 
     
       
         
           
             
               
                 
                   
                     
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     Eq. 10 allows determining a constrained covariance matrix (e.g., analogous to unscented Kalman filter (UKF)). In one example embodiment, Eqs. 6-10 may be encompassed by block  54  ( FIG. 3 ). 
     Performing Measurement Update
 
 {hacek over (X)}   k|k   ={hacek over (X)}   k|k-1   +K   k ( Y   k   m   −Y   k )  Eq. 11
 
     Eq. 11 allows correcting the state vector based on the difference between predicted Y k  and measured Y k   m  outputs.
 
where  K   k   ={hacek over (P)}   k|k-1   C   T ( C{hacek over (P)}   k|k-1   C   T ) −1   Eq. 12
 
     K k  represents a Kalman gain computed with the constrained covariance matrix determined in Eq. 10.
 
 {hacek over (P)}   k|k =( I−K   k   C ) {hacek over (P)}   k|k−1 ( I−K   k   C ) T   +K   k   RK   k   T   Eq. 13
 
     Eq. 13 allows updating the state covariance matrix considering the effects of actual plant measurements. In one example embodiment, Eqs. 11-13 may be encompassed by block  56  ( FIG. 3 ). 
     Virtual Sensing
 
 Y   k   e   =g   e ( x   k|k   ,u   k|k   ,b   k|k   ,p   k|k )  Eq. 14
 
     As noted in the foregoing discussion, and mathematically represented by Eq. 14, originally unmeasured plant variable outputs—which may be desired for any of a variety of example purposes, such as plant control, monitoring and/or diagnostics—may be estimated by processing dynamic model  22  with the updated state vector. 
     It is contemplated that subsequent to “Performing Measurement Update” processing, depending on the needs of a given application, one could optionally perform a further constrain of the state estimates and matrix covariance by solving a constrained optimization (e.g., quadratic programming) problem using techniques, which would be available to one skilled in the art. For an example of a solution to such a constrained optimization, see paper titled “ Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering ” by Dan Simon and Donald L. Simon, ASME Conf. Proc. 2003, 485 (2003). 
     It will be appreciated that aspects of the inventive estimation system and method disclosed herein may be implemented by any appropriate processing system using any appropriate programming language or programming technique. The system can take the form of a hardware embodiment, a software embodiment or an embodiment comprising both hardware and software elements. In one embodiment, the system may be implemented by way of software (e.g., preemptively constrained EKF) and hardware (e.g., processor, sensors), which may include but is not limited to firmware, resident software, microcode, etc. Furthermore, parts of the system can take the form of a computer program product accessible from a computer-usable or computer-readable medium providing program code for use by or in connection with a computer or any instruction execution system. Examples of computer-readable media may include non-transitory tangible computer-readable media, such as a semiconductor or solid-state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disk and an optical disk. Current examples of optical disks include compact disk-read only memory (CD-ROM), compact disk-read/write (CD-R/W) and DVD. An interface display may be a tablet, flat panel display, PDA, or the like. 
     In one example embodiment, a processing system suitable for storing and/or executing program code may include in one example at least one processor coupled directly or indirectly to memory elements through a system bus. The memory elements can include local memory employed during actual execution of the program code, bulk storage, and cache memories which provide temporary storage of at least some program code in order to reduce the number of times code must be retrieved from bulk storage during execution. Input/output or I/O devices (including but not limited to keyboards, displays, pointing devices, etc.) can be coupled to the system either directly or through intervening I/O controllers. Network adapters may also be coupled to the system to enable the data processing system to become coupled to other data processing systems or remote printers or storage devices through intervening private or public networks. Modems, cable modem and Ethernet cards are just a few of the currently available types of network adapters. 
     While only certain features of the invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.