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Title:
CORRECTION CURVE ESTIMATION FOR POWER PLANT COMPONENTS
Document Type and Number:
WIPO Patent Application WO/2019/123077
Kind Code:
A1
Abstract:
Techniques for estimating a correction curve (212, 214) for a component (104-110) of a power plant (102) are described. The correction curve (212, 214) indicates variation of a performance indicator of the component due to an operating parameter of the component (104-110). A function indicating dependence of the performance indicator on the operating parameter is defined. The function includes at least one coefficient. A plurality of values of the operating parameter and a plurality of values of the performance indicator corresponding to the plurality of values of the operating parameter are received. A value of the at least one coefficient is determined based on the plurality of values of the performance indicator and the plurality of values of the operating parameter. Thereafter, the correction curve (212, 214) is estimated based on the at least one coefficient and the plurality of values of the operating parameter.

Inventors:
SRINIVAS, Mekapati (3rd Line, 4th Cross Road House Number 6, Arundelpet 2, 522002, IN)
GUGALIYA, Jinendra (C1801 brigade metropolis mahadevapura, Bengaluru 8, 560048, IN)
BARABINO, Maurizio (Via Molo Giano, Porto, Genova, 16128, IT)
Application Number:
IB2018/059742
Publication Date:
June 27, 2019
Filing Date:
December 07, 2018
Export Citation:
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Assignee:
ABB SCHWEIZ AG (Brown Boveri Strasse 6, 5400 Baden, 5400, CH)
International Classes:
F02C9/56; F02C9/48
Domestic Patent References:
WO2008112823A12008-09-18
Foreign References:
US20080288198A12008-11-20
EP2770390A22014-08-27
Other References:
None
Download PDF:
Claims:
I/We claim:

1. A method for dynamically estimating a correction curve (212, 214) for a component (104-1 10) of a power plant (102) based on operating data of the component (104-1 10), to determine an operational status of the component (104-110), the component (104-1 10) being involved in production of one of steam and output electrical power and the correction curve (212, 214) indicating variation of the performance indicator of the component (104-1 10) due to the operating parameter, the method comprising:

defining a function indicating dependence of the performance indicator on the operating parameter, the function comprising at least one coefficient;

receiving a plurality of values of the operating parameter and a plurality of values of the performance indicator corresponding to the plurality of values of the operating parameter;

determining a value of the at least one coefficient based on the plurality of values of the performance indicator and the plurality of values of the operating parameter; and

estimating the correction curve (212, 214) based on the at least one coefficient and the plurality of values of the operating parameter, to determine the current operational statuses of the component (104-110) and the power plant (102).

2. The method as claimed in claim 1 , comprising calculating benchmark values for the performance indicator of the component (104-110) based on the correction curve (212, 214).

3. The method as claimed in claim 1 , wherein determining the value of the at least one coefficient comprises: formulating an optimization problem as a minimization of a difference between the plurality of values of the performance indicator and corresponding values of the performance indicator calculated using the function; and

solving the optimization problem.

4. The method as claimed in claim 3, wherein

the performance indicator varies based on a plurality of other operating parameters and variation of the performance indicator due to the plurality of other operating parameters are lumped in constant terms of the function, and

solving the optimization problem comprises forcing a sum of the constant terms to be equal to zero. 5. The method as claimed in claim 1 , wherein

the performance indicator depends on a second operating parameter,

the function indicates dependence of the performance indicator on the second operating parameter, and

the method comprises estimating a correction curve (212,

214) corresponding to the second operating parameter based on a plurality of values of the performance indicator corresponding to a plurality of values of second the operating parameter.

6. The method as claimed in claim 5, wherein

the component (104-110) is a gas turbine (104),

the performance indicator comprises heat rate and output power of the gas turbine (104), and

the operating parameter and the second operating parameter comprise ambient temperature and pressure drop at an inlet of a compressor of the gas turbine (104).

7. The method as claimed in claim 1 , comprising:

receiving an input of a hypothetical value of the operating parameter; and

determining a value of the performance indicator of the corresponding to the hypothetical value of the operating parameter based on the correction curve (212, 214).

8. A system (100) for dynamically estimating a correction curve (212, 214) for a component (104-1 10) of a power plant (102) based on operating data of the component (104-1 10), to determine an operational status of the component (104-1 10), the component (104-1 10) being involved in production of one of steam and output electrical power and the correction curve (212, 214) indicating variation of a performance indicator of the component (104-1 10) due to an operating parameter, the system (100) comprising:

a processor (1 16); and

a correction curve estimation engine (1 14) coupled to the processor (1 16) to:

receive a function indicating dependence of the performance indicator on the operating parameter, the function comprising a coefficient, a value of the coefficient being unknown; receive a plurality of values of the operating parameter and a plurality of values of the performance indicator corresponding to the plurality of values of the operating parameter;

determine a value of the coefficient based on the plurality of values of the performance indicator and the plurality of values of the operating parameter; and

compute a plurality of correction factors corresponding to the plurality of values of the operating parameter based on the coefficient for estimation of the correction curve (212, 214).

9. The system (100) as claimed in claim 8, wherein the correction curve estimation engine (1 14) is to plot the computed correction factors against the operating parameter to obtain the correction curve (212, 214).

10. The system (100) as claimed in claim 8, wherein, to determine the value of the coefficient, the correction curve estimation engine (1 14) is to:

formulate an optimization problem as a minimization of a difference between the plurality of values of the performance indicator and corresponding values of the performance indicator calculated using the function; and

solve the optimization problem.

Description:
CORRECTION CURVE ESTIMATION FOR POWER PLANT COMPONENTS

TECHNICAL FIELD

[0001 ] The present subject matter relates, in general, to power plants and, in particular, to estimating correction curves for components of power plants.

BACKGROUND

[0002] A power plant is an industrial facility for generation of electric power. Examples of power plants are steam turbine power plants, gas turbine power plants, and combined cycle power plants. A power plant may include several components, such as a gas turbine and a steam turbine. The performance of the components may vary based on various operating parameters. A correction curve indicates variation of the performance of a component based on variation of an operating parameter.

BRIEF DESCRIPTION OF DRAWINGS

[0003] The features, aspects, and advantages of the present subject matter will be better understood with regard to the following description, and accompanying figures. The use of the same reference number in different figures indicates similar or identical features and components.

[0004] Fig. 1 illustrates a system for analyzing performance parameters of a power plant, in accordance with an implementation of the present subject matter.

[0005] Fig. 2 illustrates generation of correction curves for components of the power plant, in accordance with an implementation of the present subject matter.

[0006] Fig. 3 illustrates a method for estimating correction curve for components of power plants, in accordance with an implementation of the present subject matter [0007] Fig. 4 illustrates a method for determining the value of at least one coefficient, in accordance with an implementation of the present subject matter.

[0008] Fig. 5 illustrates a method for performing benchmarking calculations for a component of a power plant, in accordance with an implementation of the present subject matter.

DETAILED DESCRIPTION

[0009] The present subject matter relates to systems and methods for estimating correction curves for components of a power plant.

[0010] Power plants are used for generation of electric power. A power plant can include several components. For example, a combined cycle power plant may include a gas turbine for generating output electric power from input natural gas and a steam turbine to generate output electric power from steam.

[001 1 ] The performance of a component of the power plant may be monitored using various performance indicators of the component. For example, the performance of a gas turbine may be monitored based on performance indicators like heat rate and output power of the gas turbine.

[0012] Typically, the performance indicators of the component vary based on various operating parameters of the component. For example, heat rate of a gas turbine may vary based on an ambient temperature of the gas turbine and a pressure drop at an inlet of a compressor of the gas turbine.

[0013] The variation of a performance indicator of a component with respect to an operating parameter may be monitored to analyze the performance of the component and the power plant at various operating conditions. For the monitoring, the variation of the performance indicator with respect to the operating parameter may be represented in the form of a correction curve. Each component may have several correction curves associated with it, where each correction curve represents variation of one of the performance indicators relative to one of the operating parameters. The variations of the performance indicators of the component relative to the operating parameters may be collectively referred to as an operational status of the component.

[0014] Generally, correction curves for a component are provided by manufacturers of the component at the time of installation of the component in the power plant. Therefore, the correction curves reflect the operational status of the component that existed at the time of its installation. However, the operational status of the component may change over a lifetime of the component. Consequently, the correction curves may become obsolete as the component ages. Further, the operational status of the component may also vary with changes to the power plant, such as addition, removal, or modification of another component in the power plant. Therefore, the correction curves may not reflect a current operational status of the component.

[0015] The present subject matter relates to systems and methods for estimating correction curves for components of a power plant. The systems and methods of the present subject matter can be used for dynamically estimating correction curves based on current values of operating parameters and performance indicators.

[0016] In an implementation of the present subject matter, to estimate correction curve of a component of a power plant, a function indicating dependence of a performance indicator the component on an operating parameter of the component is defined. The function includes at least one coefficient. The component may be involved in production of steam or output electrical power.

[0017] A plurality of values of the operating parameter and a plurality of values of the performance indicator corresponding to the plurality of values of the operating parameter are received. A value of the at least one coefficient is then determined based on the plurality of values of the performance indicator and the plurality of values of the operating parameter. The correction curve may then be estimated based on the at least one coefficient and the plurality of values of the operating parameter. The correction curve can be used to determine the current operational statuses of the component and of power plant.

[0018] With the systems and methods of the present subject matter, correction curves for components of the power plant can be dynamically estimated based on live data, i.e., current values of operating parameters and performance indicators. Thus, the correction curves accurately indicate the current operational status of the components. This reduces the dependence on manufacturer-provided correction curves for determining performance of the components. Further, the estimated correction curves can be used to accurately determine the impacts of changes in the operating parameters on the overall performance of the components and the power plants. For example, the correction curves can be used to perform“what-if” simulations of the components and the power plants.

[0019] The above and other features, aspects, and advantages of the subject matter will be better explained with regard to the following description, appended claims, and accompanying figures. Although various aspects of the subject matter are explained with a combined cycle power plant (CCPP) as an example, it is to be understood that the present subject matter can be applied to any other type of power plant, such as a fossil fuel fired power plant (FFPP).

[0020] Fig. 1 illustrates a system 100 for dynamically estimating a correction curve for a component of a power plant 102, in accordance with an implementation of the present subject matter. The system 100 may be implemented as any computing system which may be, but is not restricted to, a server, a workstation, a desktop computer, a laptop, and an application. The system 100 may also be a machine-readable instructions-based implementation or a hardware-based implementation, or a combination thereof. [0021 ] The power plant 102 includes a plurality of components. The components may be involved in production of either steam or output electrical power. For example, when the power plant 102 is a combined cycle power plant (CCPP) as illustrated in Fig. 1 , the components of the power plant 102 may include a gas turbine 104, a Fleat Recovery Steam Generator (FIRSG) 106, a steam turbine 108, and a heat exchanger 1 10.

[0022] As will be understood, natural gas may be provided as fuel to the gas turbine 104 for generation of high temperature and high pressure gases to generate electric power. Further, the heat of exhaust gas from the gas turbine 104 can be used by the FIRSG 106 to generate steam. The steam is provided to the steam turbine 108, which, then, generates electric power using the steam. The waste steam from the steam turbine 108 is then provided to the heat exchanger 1 10 for heat recovery from the waste steam.

[0023] As mentioned earlier, the system 100 can generate a correction curve, such as a correction curve 1 12, for a component, such as the gas turbine 104 or the steam turbine 108, of the power plant 102. The correction curve can indicate variation of a performance indicator of the component due to an operating parameter of the component. To generate the correction curve 1 12, the system 100 includes a correction curve estimation engine 1 14 and a processor 1 16. The system 100 may further include interface(s), memory, other engines, and system data, which are not shown in Fig. 1 .

[0024] The correction curve estimation engine 1 14 and other engines may be coupled to the processor 1 1 6. Further, the correction curve estimation engine 1 14 and other engines may be implemented in hardware, instructions executed by the processor 1 16, or by a combination thereof.

[0025] The system data may serve as a repository for storing data that may be fetched, processed, received, or created by the correction curve estimation engine 1 14, and other engines or received from connected computing systems and storage devices.

[0026] In an implementation, some or all of the correction curve estimation engine 1 14 and other engines may communicate with each other through a communication network (not shown in Fig. 1 ). The communication network may be a wireless or a wired network, or a combination thereof.

[0027] In operation, the correction curve estimation engine 1 14 can estimate a correction curve indicating variation of a performance indicator of a component due to an operating parameter of the component. For this, the correction curve estimation engine 1 14 may receive a function indicating dependence of the performance indicator on the operating parameter. The function includes a variable term having a coefficient, the value of which is unknown.

[0028] Then, the correction curve estimation engine 1 14 may receive a plurality of values of the operating parameter and a plurality of values of the performance indicator corresponding to the plurality of values of the operating parameter. For instance, the values of the performance indicator at a plurality of instants of time and the values of the operating parameter at the plurality of instants of time may be received.

[0029] Based on the plurality of values of the performance indicator and the plurality of values of the operating parameter, a value of the coefficient may be determined. Thereafter, a plurality of correction factors corresponding to the plurality of values of the operating parameter may be computed based on the coefficient. The plurality of correction factors may then be used for estimation of the correction curve. The estimation of the correction curve, in an implementation, will be explained with reference to Fig. 2.

[0030] Fig. 2 illustrates generation of correction curves for components of the power plant 102, in accordance with an implementation of the present subject matter. The corrections curves may be generated based on operating data of the components. Flere, operating data of a component refers to various data that are associated with the operation of the component. For example, the operating data may include values of the operating parameters and values of the performance indicators when the component is operating in the power plant 102. Thus, the present subject matter enables estimating correction curves for components during operation of components in the power plant 102. Therefore, the present subject matter enables estimating correction curves for the components dynamically, i.e., at any time during the operation of the components. This is in contrast to the conventional systems, in which the correction curves provided by manufacturers of components at the time of installation of the components are relied upon, and cannot be calculated upon installation in the power plant. Further, since the correction curves are estimated dynamically, the present subject matter can be used to determine the operational status of the components.

[0031 ] To estimate the correction curves for a component, correction curve estimation engine 1 14 receives various inputs 202 related to the component and the power plant 102. The inputs 202 may include various performance indicators 204, which are indices used for measuring performance of component. The performance indicators 204 may vary from one component to another. For example, for the gas turbine 104, the performance indicators 204 may include an output power generated and a heat rate, which is the amount of energy (in kCal) used for generating 1 kWh of output power. The inputs 202 may also include various operating parameters 206, which are parameters on which the performance indicators 204 depend. For example, for the gas turbine 104, the operating parameters 206 include an ambient temperature and a pressure drop at an inlet of a compressor of the gas turbine 104. The performance indicators 204 and operating parameters 206 may be obtained from operating personnel, such as an operator or an administrator, of the power plant 102. Alternatively, the performance indicators 204 and operating parameters 206 may be part of the system data and may be stored in a memory (not shown in Fig. 2) of the system 100. Accordingly, the performance indicators 204 and operating parameters 206 may be retrieved by the correction curve estimation engine 1 14 from the memory. [0032] The inputs 202 may further include reference values 208 for the operating parameters 206 and the performance indicators 204. The reference values 208 may be constant values or may depend on a load of the power plant 102. When a reference value is constant, it may be obtained from the operating personnel or the memory. When a reference value depends on the load of the power plant, it may be obtained by the correction curve estimation engine 1 14 using a mathematical function or a graph indicating dependence of the reference value on the load. The mathematical function or the graph may also be part of the system data.

[0033] The inputs 202 may further include operating data 210 of the component. As mentioned earlier, the operating data 210 refers to data associated with the operation of the component, and may include values of performance indicators and values of operating parameters of the component. Accordingly, for the gas turbine 104, the operating data 210 may include values of the ambient temperature and values of the pressure drop at the inlet of the compressor. Such values may be received at various instants of time during operation of the gas turbine 104. Further, the operating data 210 may include values of the output power values of the heat rate at the various instants of time. The values of the output power and the values of the heat rate may be received at the various instants of time, when the values of the operating parameters were received. Accordingly, the values of the performance indicators correspond to the values of the operating parameters. The operating data 210 may be received, for example, from a distributed control system (DCS) (not shown in Fig. 2) of the power plant 102.

[0034] In an example, upon receiving the inputs 202, the correction curve estimation engine 1 14 performs various pre-processing operations on the operating data 210. The pre-processing operations include performing a steady state detection to avoid the interference of state transition during estimation of the correction curves. The steady state detection may include extracting steady state operating data by removing transient data. [0035] The pre-processing operations may also include imputing missing data, cleaning noisy data, and removing outlier data. The imputing, cleaning, and outlier removal may be performed to prevent noise associated with the operating data 210 from affecting the correction curves to be estimated. The imputation may be performed using any known imputation technique, such as replacing missing values with mean value or a previous value. Further, the noise removal may be performed using any known noise removal technique, such as moving averages filter or Fast Fourier Transformation. The techniques for performing missing data imputation, noisy data cleaning, and outlier data removal are well-known in the art, and are not described herein for the sake of brevity.

[0036] Upon performing the pre-processing, the correction curve estimation engine 1 14 may estimate the correction curves for the component. The estimation of the correction curves will be explained with reference to heat rate for the gas turbine 104. Flowever, it is to be understood that the estimation can be used for other performance indicators and other components of the power plant 102 as well.

[0037] To perform the estimation, a function indicating the dependence of the heat rate on the operating parameters for the heat rate is defined. The defining of the function may be performed by the correction curve estimation engine 1 14. Alternatively, the function may be stored in the memory, and may be received by the correction curve estimation engine 1 14.

[0038] For defining the function, first, the value of the heat rate (FIR) may be represented as below:

HR = HRo + AHR (1), where FIRo denotes a reference value of the heat rate and AFIR represents the deviation of the heat rate from its reference value, FIRo. The value of the heat rate deviates from its reference value, FIRo, when the values of the operating parameters deviate from their respective reference values. Thus, AFIR is dependent on the operating parameters for the heat rate. As mentioned earlier, the operating parameters on which the heat rate depends on include ambient temperature and pressure drop at compressor inlet. Therefore, AHR may be represented as below:

AHR = f (T a , AP d , ...) (2), where T a denotes ambient temperature of the gas turbine 104 and APd denotes pressure drop at the inlet of the compressor of the gas turbine 104. Dividing equation (1 ) by HRo results in the below equation:

HR / HRo = (1 + AHR / HR 0 ) (3)

[0039] The left-hand side of equation (3) represents a correction factor (CF), which forms an ordinate of a correction curve. Substituting the value of CF in equation (1 ), equation (1 ) may be rewritten as follows:

HR = HR 0 + (CF-1) HR 0 (4)

[0040] The above equation is applicable when the heat rate depends on a single operating parameter. Flowever, in practice, the heat rate depends on several operating parameters. Accordingly, each operating parameter may have a corresponding correction factor. Therefore, equation (4) may be rewritten as follows:

HR = HRo + (CFi + CF 2 + ... CF,- i) HR 0 (5) where i is the number of operating parameters on which the heat rate depends and CFi is the correction factor corresponding to the i th operating parameter.

[0041 ] The correction factor corresponding to an operating parameter may be represented in the form of a mathematical function of the operating parameter. The type of the mathematical function, such as a linear function, polynomial function, exponential function, or logarithmic function, may be determined based on a prior knowledge of a relationship between AFIR and the operating parameter. For example, if it is known that the relationship between AHR and T a is a polynomial function of order 3, the correction factor corresponding to T a may be represented as follows:

CF1 = a(T a -Ta,o) 3 + b(Ta-Ta,o) 2 + c(T a -T a, o) + d (6) where CFi is the correction factor corresponding to T a , Ta,o is a reference value for T a , and a, b, c, and d are coefficients of the polynomial function representing the relationship between CFi and T a .

[0042] Similarly, if it is known that the relationship between AHR and APd is a polynomial function of order 3, the correction factor corresponding to APd may be represented as follows:

CF2 = G(AP ci AP ci,o) f(AP ci AP ci,o) 2 Q(AP ci AP ci,o) + h (7) where CF2 is the correction factor corresponding to APd, APd.o is a reference value for DR , and e, f, g, and h are coefficients of the polynomial function representing the relationship between CF2 and AP C\ .

[0043] When the variation of the heat rate due to T a alone is to be determined, by substituting the value of CFi from the equation (6) to the equation (5), the heat rate may be defined as a function of T a , as below:

HR = HRo + {a(T a -Ta,o) 3 + b(Ta-Ta,o) 2 + c(T a -T a, o) + d - 1} HRo (8) where HR denotes the value of heat rate to be calculated using equation (8), and may be referred to as a model-calculated value of heat rate. Equation (8) is the function that indicates the dependence of heat rate on the ambient temperature. This function includes coefficients a, b, c, and d, the values of which are unknown.

[0044] When the variation of the heat rate due to both T a and DRa is to be determined, the values of CFi and CF2 may be substituted in the equation (5), and the heat rate may be defined as below:

HR = HRo + { a(Ta~Ta,o ) 3 + b(Ta—Ta,o) 2 + c(Ta~Ta,o) + d + Q (AP ci - AP ci,0 ) 3 + f(AP Ci - APd,o) 2 + g(APci - APd,o) + h -2} HRo (9)

Equation (9) is the function that indicates the dependence of heat rate on the ambient temperature and the pressure drop and compressor inlet. This function includes coefficients a, b, c, d, e, f, g, and h.

[0045] Although equation (9) depicts the heat rate as a function of T a and DR alone, the heat rate may vary based on a plurality of other operating parameters as well. The plurality of other parameters may be collectively referred to as other operating parameters. The effects of the other operating parameters get captured in equation (9) in the constant terms on the right- hand side of equation (9). For instance, equation (9) may be rewritten as below:

HR— HRo + {cl(Ta— Ta,o) + b(Ta~Ta,o) 2 + C(Ta~Ta,o) q(AR ci AP ci,o) 2 + f(AP Ci - APd,o) 2 + g(AP Ci - AP Ci, o) + d + h -2} HRo (9)

[0046] Here, the terms a(T a -Ta,o) 3 , b(T a -Ta,o) 2 , and c(T a -T a, o) vary with T a and the terms e(APd - DRa,o) 3 , f(APd - DRa,o) 2 , and g(APd - DR ,o) vary with DR . However, the constant terms d, h, and 2 do not vary either with T a or with DR . Therefore, the variation of the heat rate due to the other operating parameters are present in d + h - 2. The presence of the variation of heat rate due to several operating parameters in the constant terms is referred to as lumping, as the effects of several operating parameters on the performance get“lumped” in the constant terms. The lumping of the variation of the performance indicators due to the other operating parameters in the constant terms can be used to obtain correction curves that accurately depict the variation of the heat rate due to the operating parameters of interest, i.e., T a and DR . This will be explained in greater detail in the subsequent paragraphs.

[0047] As will be understood, a function, such as the functions of equations (8) and (9), indicating dependence of any performance indicator on any operating parameter of any component of the power plant 102 may be defined in the manner as described above. Such functions will have at least one coefficient, such as the coefficients a, b, c, d, e, f, g, and h.

[0048] Upon defining the functions, the value of the at least one coefficient may be determined to estimate the correction curve for the component. The determination of the values of the coefficients will be explained with reference to the coefficients a, b, c, d, e, f, g, and h.

[0049] To determine the values of the coefficients a, b, c, d, e, f, g, and h, the operating data 210 may be used. For example, a plurality of values of T a collected at a plurality of instants of time, a plurality of values of DR collected at the plurality of instants of time, and a plurality of values of HR collected at the plurality of instants of time may be used.

[0050] In an implementation, using the values of the operating data, an optimization problem may be solved. The optimization problem may be formulated as a minimization of a difference (or error) between actual values of the heat rate and corresponding values of the heat rate that will be calculated using the function of equation (9). The optimization problem may be represented as below: where HR is the actual heat rate value, HR is the corresponding model- calculated heat rate value obtained from the function of equation (9), and‘n’ is the number of data points in the operating data 210. The actual values of heat rate may be the values of the heat rate at ‘n’ instants of time. Accordingly, the values of the model-calculated heat rate may also correspond to the‘n’ instants of time.

[0051 ] The above optimization problem may be solved using any of the known non-linear optimization techniques. For instance, based on the non linear nature of the optimization problem (convex or non-convex), an appropriate technique, such as local optimization solvers or global optimization solvers, may be used. The local optimization solvers may utilize methods, such as gradient descent method or Levenberg Marquardt method. The global optimization solvers may utilize methods, such as Branch and Bound or Genetic methods.

[0052] As mentioned earlier, the effects of the variation of the heat rate due to the other operating parameters get lumped in the constant term d + h - 2 in the equation (9). Therefore, to determine the variation of the heat rate due to T a and DR alone, the lumped effect may be forced to zero when solving the optimization problem. This may be achieved, for example, by imposing the below equality constraints when the optimization problem is solved:

d- 1 = 0 (1 1)

h - 1 = 0 (12)

[0053] Thus, using the present subject matter, variations of the performance indicators due to the operating parameters of interest can be accurately captured. Consequently, the correction curves estimated accurately indicate the variation of the performance indicator due to a particular operating parameter.

[0054] Although solving the optimization problem is explained with reference to equation (9), the solving can be performed for equation (8) also. In such a case, the other parameters include DR as well, and the variation of the heat rate due to the other operating parameters get lumped in the constant term d - 1. This constant term may then be forced to zero, using the equality constraint of equation (1 1 ). Also, it will be understood that the optimization problem can be solved for any operating parameter and any performance indicator, provided an equation similar to the equation (8) or (9) is available for that operating parameter.

[0055] The solving of the optimization problem provides the values of the coefficients a, b, c, d, e, f, g, and h. The coefficients can then be used by the correction curve estimation engine 1 14 to compute a plurality of values of the correction factors CFi and CF2. For example, by substituting the values of the coefficients a, b, c, and d in the equation (6), a plurality of values of the correction factor CF1 corresponding to a plurality of values of T a can be computed. Similarly, by substituting the values of the coefficients e, f, g, and h in the equation (7), the different values of the correction factor CF2 corresponding to a plurality of values of DR can be computed.

[0056] The correction curve estimation engine 1 14 can then obtain a correction curve 212 by plotting values of the correction factor CF1 against the corresponding values of T a . Similarly, the correction curve estimation engine 1 14 can plot the different values of the correction factor CF2 against the corresponding values of DR to obtain a correction curve 214.

[0057] In an implementation, the estimated correction curves can be used to perform“what-if” simulations for the component and the power plant 102. For this, the correction curve estimation engine 1 14 can receive a hypothetical value of the operating parameter, such as T a , of the component, such as the gas turbine 104, as an input. Based on the estimated correction curve, such as the correction curve 212, the value of the performance indicator corresponding to the hypothetical value of the operating parameter may be determined.

[0058] Figs. 3 and 4 illustrate methods 300 and 400 for estimating correction curves for components of power plants.

[0059] The order in which the methods 300 and 400 is described is not intended to be construed as a limitation, and any number of the described method blocks may be combined in any order to implement the methods 300-500, or an alternative method. Furthermore, the methods 300 and 400 may be implemented by processor(s) or computing device(s) through any suitable hardware, non-transitory machine-readable instructions, or a combination thereof.

[0060] It may be understood that steps of the methods 300 and 400 may be performed by programmed computing devices and may be executed based on instructions stored in a non-transitory computer readable medium. Although the methods 300 and 400 may be implemented in a variety of systems, the methods 300 and 400 is described in relation to the system 100, for ease of explanation. In an implementation, the steps of the methods 300 and 400 may be performed by the correction curve estimation engine 1 14.

[0061 ] Referring to method 300, at step 302, a function indicating dependence of a performance indicator of a component on an operating parameter of the component is defined. The component may be, for example, the gas turbine 104, FIRSG 106, or steam turbine 108. Accordingly, the operating parameter may be the ambient temperature or pressure drop at compressor inlet, and the performance indicator may be the heat rate or output power.

[0062] At step 304, a plurality of values of the operating parameter and a plurality of values of the performance indicator corresponding to the plurality of values of the operating parameter are received.

[0063] At step 306, a value of the at least one coefficient is determined based on the plurality of values of the performance indicator and the plurality of values of the operating parameter.

[0064] Finally, at step 308, the correction curve is estimated based on the at least one coefficient and the plurality of values of the operating parameter the correction curve may then be used to determine the current operational statuses of the component and the power plant.

[0065] In an implementation, the determination of the value of the at least one coefficient is performed by solving an optimization problem, as will be explained below.

[0066] Fig. 4 illustrates a method 400 for determining the value of the at least one coefficient, in accordance with an implementation of the present subject matter.

[0067] At step 402, an optimization problem is formulated as a minimization of a difference between the plurality of values of the performance indicator and corresponding values of the performance indicator.

[0068] At step 404, the optimization problem is then solved.

[0069] In some cases, the performance indicator of the component may vary due to a plurality of operating parameters other than the one for which the correction curve is estimated. Such operating parameters may be collectively referred to as a plurality of other operating parameters.

[0070] As explained earlier, the effects of the other operating parameters on the performance indicator get lumped in the constant terms of the function. To obtain correction curves that depict the variation of the performance indicator due to the operating parameter of interest, a sum of the constant terms may be forced to zero. For example, in equation (9), the constant terms in the function are d, h, and -2, and the sum of the constant terms, d + h - 2, is forced to zero. Since the variation of the performance indicator due to the plurality of other operating parameters is forced to zero, the estimated correction curve can accurately depict the variation of the performance indicator due to the operating parameter of interest.

[0071 ] In an implementation, the estimated correction curves can be used for calculating benchmark values for the performance indicators, such as the output power and the heat rate, of the components, such as the gas turbine 104. The calculation of the benchmark values may be referred to as performing benchmarking calculations, and will be explained with reference to Fig. 6.

[0072] Fig. 5 illustrates a method 500 for performing benchmarking calculations for a component of a power plant, in accordance with an implementation of the present subject matter.

[0073] It may be understood that steps of the method 500 may be performed by programmed computing devices and may be executed based on instructions stored in a non-transitory computer readable medium. Although the method 500 may be implemented in a variety of systems, the method 500 is described in relation to the system 100, for ease of explanation.

[0074] To perform the benchmarking calculations, a plurality of inputs may be received. The inputs include the operating parameters 206, the reference values 208, operating data 210, and a plurality of curves. The operating parameters 206 includes both controllable operating parameters 502 and non-controllable parameters 503. The operating data 210 may include actual values of operating parameters and actual values of performance indicators. The plurality of curves includes reference parameter curves (fRef) 504, power correction curves (fpcF) 505, heat rate (FIR) correction curves (fHRCF) 506, and heat rate versus power curve (fHRvp) 508. The reference parameter curves 504 (fRef) provide reference values for operating parameters as a function of load for the operating parameters for which the reference values vary with load. The power correction curves 505 and heat rate correction curves 506 may be the correction curves estimated using techniques of the methods 300-500, such as the correction curves 212 and 214. The heat rate versus power curve (fHRvp) 508 represents heat rate as a function of power.

[0075] At step 510, load of the component is calculated from the actual power and reference power using the below equation:

Load = 100 * (Actual Power (MW)/ Reference Power (MW)) (13) [0076] At step 512, reference values are calculated based on the load for the operating parameters whose reference values vary based on the load. For the calculation, the reference parameter curves 504 (fRef) and the load calculated in step 510 may be used.

ParRef (i) = fRefi(Load) ( 14)

where ParRef (i) is a reference parameter value for an i th operating parameter. For the operating parameters whose reference values do not vary based on load, the reference values may be directly obtained from the reference values 208.

[0077] At step 514, power deviation factors with respect to all controllable parameters (Parc) 502 are calculated from the correction curves using the below equation:

PDFc (i) = F(PCFc (Par(i))) (15)

[0078] Also, sum of all the power deviation factors are calculated with respect to the controllable parameters (Parc) 502.

Sumpoevc = åiL c PDF C (0 (16)

[0079] Further, power deviation factors with respect to all non- controllable parameters (Pa c) are calculated from the corresponding reference and actual power corrections.

PDFNC (i) =†PCF NC (Par(i)) (17) [0080] Then, sum of all the power deviation factors with respect to non- controllable parameters are calculated.

[0081 ] Thereafter, sum of all power deviation factors is calculated with respect to both controllable and non-controllable parameters

SumpDev = SumpDevC + SUHlpDevNC (19)

where:

PDFc (i) = Power deviation factor with respect i th to controllable parameter,

PDFNC (i) = Power deviation factor with respect to i th non-controllable parameter.

nParc = number of controllable parameters

nParisic = number of non-controllable parameters

nPar = nParC + nParNC.

[0082] At step 516, corrected power is calculated using the sum of power deviations and actual power.

Pcor = PAct / (1 + SumPDev/100) (20) where PAct is the actual power, which may be part of the operating data 210 and Pcor is the corrected power.

[0083] At step 518, power deviation with respect to all the parameters is calculated. Initially, power deviation is calculated with respect to all controllable parameters using corrected power (from Step 520) and power deviation factors for the controllable parameters (from Step 518).

^Poev l) = Pcor * PDF c (i)/W0 (21)

[0084] Subsequently, power deviation with respect to all non- controllable parameters is calculated using corrected power and the corresponding power deviation factors.

DR DevNC = Pcor* PDFNC(I)/100 (22) where: AP Dev c(0 = Power deviation with respect to controllable parameter i.

AP DeV Nc(0 = Power deviation with respect to non-controllable parameter i.

[0085] At step 520, optimal power is calculated using the reference power and power deviations from non-controllable parameters. Initially, sum of power deviations is calculated from non-controllable parameters.

SumPDevNC = å PDF NC (0 (23)

[0086] Subsequently, the optimal power is calculated from reference power (obtained from the reference values 208) and the sum of power deviations from all non-controllable parameters.

Popt = P Ref* SumPDevNC (24)

where Popt is the optimal power and SumPDevNC is the sum of power deviations.

[0087] At step 522, the expected power is calculated using the optimal power and power deviations from controllable parameters. Initially, sum of power deviations from all controllable parameters is calculated.

Sumpoevc = å? = C PDF C (i) (25)

[0088] Subsequently, the expected power is calculated from the optimal power (step 520) and the sum of power deviations from all controllable parameters.

PEXP = PRef* SumpDevC (26) where PEX P is the expected power.

[0089] At step 524, actual heat rate is calculated from the following equation:

HR Act = (3.6 * Fpuei * FuelLHv)/ P Ac t (27) where:

HRAct = Actual Heat Rate in kJ/kWh,

FFuei = Flow of fuel in kg/s, FuelLHv = Calorific value of fuel in kJ/kg, and

PAct = Actual power in MW.

[0090] At step 526, reference heat rate is calculated from the heat Rate versus power curve 508 using corrected power (calculated in step 516)

HR Ref = fhiRvP (P Cor) (28)

where:

Poor = Corrected Power

HR Ref = Reference Heat Rate

f H R V p = Function representing the heat rate versus power curve 508, where input argument is the power while output is the Heat Rate.

[0091 ] At step 528, Heat Rate deviation factors are calculated with respect to all controllable parameters (Parc)

HRDFc (i) = f HRCFc (Par(i)) (29)

[0092] Then, sum of all the Heat Rate deviation factors with respect to controllable parameters is calculated.

SumHRDevc = åf = c HRDF C (i) (30)

[0093] Subsequently, Heat rate deviation factors with respect to all non-controllable parameters (Pamc) are calculated from the corresponding reference and actual Heat Rate corrections.

HRDFNC (i) = F HRCFNC (Par(i)) (31)

[0094] Further, sum of all the Heat Rate deviation factors is calculated with respect to non-controllable parameters.

[0095] Thereafter, sum of all the Heat Rate deviation factors is calculated with respect to both controllable and non-controllable parameters.

SurriHRDev = SumHRDevc + Su fTlHRDevNC (33) where: HRDFc(i) = Heat Rate deviation factor with respect to i th controllable parameter

H RDFNC(I) = Heat Rate deviation factor with respect to i th non-controllable parameter

nParc = number of controllable parameters

nParNc = number of non-controllable parameters

nPar = nParc + nParisic

[0096] At step 530, corrected Heat Rate is calculated using actual Heat Rate and sum of Heat Rate deviations (from Step 528) using the below equation:

HRcor = HRAct / (1+ SurriHRDev/100) (34) where HRAct is the actual Heat Rate (from Step 524) and HRcor is the corrected Heat Rate.

[0097] At step 532, Heat Rate deviation is calculated with respect to all the parameters. Initially, Heat Rate deviation is calculated with respect to all controllable parameters using corrected Heat Rate (from Step 530) and Heat Rate deviation factors for all controllable parameters (from Step 528).

AHR DevC (i) = HRcor * HRDF c (i)/100 (35)

[0098] Subsequently, Heat Rate deviation is calculated with respect to all non-controllable parameters using corrected Heat Rate and the corresponding Heat Rate deviation factors for all non-controllable parameters.

AHR DevNC = HRcor * HRDFNC(I)/100 (36) where:

AHR DevC (i) = Heat Rate deviation with respect to i th controllable parameter, and

AHR DevNC (i) = Heat Rate deviation with respect to i th non-controllable parameter. [0099] At step 534, the optimal Heat Rate is calculated using the reference Heat Rate and Heat Rate deviation factors from non-controllable parameters. Initially, sum of Heat Rate deviation factors from non- controllable parameters is calculated.

[00100] Subsequently, the optimal Heat Rate is calculated from the reference Heat Rate (from step 526) and the sum of Heat Rate deviation factors from all non-controllable parameters.

HRopt = HRRef * SumHRDevNC (38)

where HRopt is the optimal power.

[00101 ] At step 536, the expected Heat Rate is calculated using the optimal Heat Rate and Heat Rate deviation factors from controllable parameters. Initially, sum of Heat Rate deviation factors is calculated from controllable parameters as below:

[00102] Subsequently, the expected power is calculated from the optimal Heat Rate (from step 534) and sum of Heat Rate deviation factors from all controllable parameters as below:

HRExp = HRRef * SumHRDevC (40)

where H REX P = Expected power.

[00103] Thus, by performing the above steps, power benchmarks 546 and heat rate benchmarks 548 are obtained. The power benchmarks 546 include the corrected power (Poor), optimal power (Popt), expected power (PEXP), and the power deviations. Further, the heat rate benchmarks 548 include corrected heat rate (HRcor), optimal heat rate (HRopt), expected heat rate (HRE XP ), and heat rate deviations.

[00104] In some implementations, the functions fRet, fpcF and fHRCF are polynomial functions of 2 nd order as given below.

f = p * x 2 + q * x + r (41) In some other implementations, the polynomial equations may be of 3rd order.

[00105] In case of reference parameter curves, the polynomial functions take load as the input argument. For instance,

Par Ref = f Ref (load ) (42)

[00106] In some cases, there will be multiple reference curves for the same parameter. For instance, there may be multiple reference curves for the pressure drop at compressor inlet for different ambient temperatures.

[00107] The present subject matter enables estimating dynamically correction curves for components of the power plant based on live data. Thus, the correction curves accurately indicate the current operational status of the components and the power plant. Further, the estimated correction curves can be used to accurately determine the impacts of changes in the operating parameters on the overall performance of the components and the power plants. For example, the correction curves can be used to perform“what-if” simulations of the components and the power plants.

[00108] Although the present subject matter has been described with reference to specific embodiments, this description is not meant to be construed in a limiting sense. Various modifications of the disclosed embodiments, as well as alternate embodiments of the subject matter, will become apparent to persons skilled in the art upon reference to the description of the subject matter.