Identification method for closed-loop optimization control system of deep peak regulation thermal power generating unit

Abstract

The invention mainly relates to the technical field of thermal power generating unit systems, in particular to a deep peak regulation thermal power generating unit closed-loop optimization control system identification method. Comprising the following steps: S100, establishing a space state model of a thermal power generating unit system; s200, linear quadratic controller parameters are designed according to the space state model of the thermal power generating unit system, an optimal control rule is calculated through a state feedback matrix, and a thermal power generating unit closed-loop system is formed; the control input, the control output and the system set value of the closed-loop system of the thermal power generating unit are obtained; s300, decomposing the closed-loop system of the thermal power generating unit into two open-loop subsystems; s400, obtaining a sensitivity function of the closed-loop system of the thermal power generating unit by performing subspace identification on the control input and the system set value of the closed-loop system of the thermal power generating unit, and constructing an intermediate signal without noise pollution through the sensitivity function of the closed-loop system of the thermal power generating unit; and S500, performing subspace identification on the intermediate signal and the control output of the closed-loop system of the thermal power generating unit to finally obtain consistent unbiased estimation of the system parameters of the thermal power generating unit.

Description

Technical Field

[0001] The present invention mainly relates to the technical field of thermal power unit systems, and specifically to a closed-loop optimization control system identification method for a deep peak-shaving thermal power unit. Background Art

[0002] With the transformation of energy structure, thermal power units will gradually become the main body of regulating power supply, characterized by deep peak regulation and frequent start-stop peak regulation. Deep peak regulation of thermal power units means that when the load of the power system fluctuates greatly, the thermal power units adjust their own loads to achieve fine regulation of the frequency of the power system. In the case of deep peak regulation, thermal power generating units often need to change their loads quickly to meet the needs of the power grid. In the process of load increase and decrease, the output power and heat load of the thermal power units will change, causing the temperature and pressure inside the combustion chamber to change accordingly, resulting in the inability of the thermal power units to continue to work at a stable working point. In order to achieve stable, safe and efficient operation of thermal power units under deep peak regulation and rapid load changes, accurate modeling of the thermal power unit control system is the prerequisite for all control and optimization.

[0003] The traditional modeling methods of thermal power units mainly include mechanism modeling and system identification modeling. The mechanism model can more comprehensively reflect the internal relationship between various parameters of the unit, and is suitable for studying the characteristics between various input and output of the unit and evaluating the performance of the control algorithm through simulation. However, for thermal power units with complex physical structures and obvious subsystem coupling characteristics, the use of mechanism modeling will result in many steps, complex modeling of nonlinear links, and poor model migration between units. In addition, mechanism modeling usually does not take environmental factors into consideration enough, and the actual process is affected by changes in coal quality and environmental interference, resulting in poor fitting between the simulation output of the mechanism model and the actual operation output data. Therefore, system parameter identification needs to be realized in the modeling process of the thermal power unit control system.

[0004] For the sake of safety and economy, the control of industrial processes of thermal power units is all closed-loop control, which brings challenges to the accurate identification of the system. The main difficulty is that after the system noise is fed back to the control system, it will act on the system input at the future moment, that is, there is a correlation between the noise data at the past moment and the input data at the future moment. Due to the correlation between noise and measurement data, it is difficult to eliminate the noise effect through simple regression calculation, which causes the identification deviation of the traditional open-loop identification method. In recent years, with the increase of actual closed-loop control industrial processes, system identification in a closed-loop environment has received more and more attention.

[0005] Subspace identification is an effective tool for modeling multivariable systems. It uses a simple error minimization criterion and then uses linear algebra tools to accurately identify the state space model. The only "parameter" required is the system order, which can effectively avoid numerical ill-conditioning, parameter overlap, and the minimum realization of the system. In particular, for data generated based on closed-loop industrial processes, the subspace identification method can be used to obtain a state space model that effectively represents the actual industrial production process. Therefore, the research on subspace identification methods for closed-loop systems has positive theoretical significance and important engineering application value. Summary of the invention

[0006] In order to solve the high reliability optimal control and parameter identification problems of a thermal power unit with rapid load change in all working conditions under online operation conditions, the present invention provides a closed-loop optimization control system identification method for a deep peak-shaving thermal power unit.

[0007] The present invention adopts the following technical solution: a method for identifying a closed-loop optimization control system of a deep peak-shaving thermal power unit, comprising: S100: Establishing a spatial state model of the thermal power unit system, selecting a coal quantity instruction and a turbine valve opening instruction as input quantities of the thermal power unit system, and selecting unit power and machine front pressure as system output quantities; S200: Design the parameters of the linear quadratic controller for the spatial state model of the thermal power unit system, calculate the optimal control law through the state feedback matrix, form a closed-loop system of the thermal power unit, and obtain the control input, control output and system setting value of the closed-loop system of the thermal power unit; S300: Decompose the closed-loop system of the thermal power unit into two open-loop subsystems; S400: obtaining a sensitivity function of the closed-loop system of the thermal power unit by performing subspace identification on the control input of the closed-loop system of the thermal power unit and the system setting value, and constructing an intermediate signal without noise pollution through the sensitivity function of the closed-loop system of the thermal power unit; S500: By performing subspace identification on the intermediate signal and the closed-loop system control output of the thermal power unit, a consistent and unbiased estimate of the system parameters of the thermal power unit is finally obtained.

[0008] In some embodiments, step S100 includes: S101: linearize the thermal power unit system with a small deviation at a certain operating point to transform it into a linear model of the unit load-pressure object; S102: According to the transfer function form of the unit load-pressure object shown in equation (1), a state space expression of the system is established.

[0009] In some embodiments, in step S101, the linear model of the unit load-pressure object is: in, The transfer function representing the change in pressure in front of the engine caused by the change in fuel, The transfer function representing the change in the turbine pressure caused by the change in the turbine valve opening command is: The transfer function representing the change in unit power caused by fuel change, The transfer function representing the change in unit power caused by the change in the turbine valve opening command; is the fuel quantity command, It is the steam turbine valve opening instruction; is the unit power, is the pressure before the machine; is the dynamic time of milling, is the boiler heat storage coefficient, is the turbine dynamic time, is the fuel command gain, is the superheater resistance coefficient, dimensionless, is the turbine gain; in the transfer function and is a constant, denoted by and .

[0010] In some embodiments, in step S102, the state space expression is: in, is the system state variable, represents the input variable, Represents an output variable.

[0011] In some embodiments, step S200 includes: S201: Design linear quadratic control for the state space model of the unit load-pressure object and introduce a quadratic objective function; Where X is the state vector, u is the system input, Q and R are given real symmetric weight matrices, and Q is positive semidefinite and R is positive definite; Assume that the linear feedback control rate of the thermal power unit system is , substituting the control rate into the system objective function, we get Given Q and R, the performance index of the system is J The minimum value is equivalent to the Riccati equation with a positive definite matrix solution P: , after obtaining the solution P, the control gain of the system Expressed as ; S202: For the thermal power unit system, we seek the control action u to minimize the quadratic objective function J. The solution to the steady-state LQR problem can be derived. The optimal control law is: u is the system input, R is a given real symmetric matrix, B is a parameter in the state space expression, P is the positive definite matrix solution of the Riccati equation, and X is the system state vector.

[0012] In step S300, The first open loop system is: The second open-loop system is: In the formula, The fuel quantity of the thermal power unit and the turbine valve opening command data, that is, the output data of the first open-loop system, is the unit power and front pressure data, is the fuel quantity of the thermal power unit and the setting value of the turbine regulating valve opening instruction, that is, the input data of the first open-loop system, G is the thermal power unit model, is the sensitivity function of the closed-loop system of the thermal power unit, , the feedback control L is designed LQ Controller.

[0013] In some embodiments, step S400 includes: S401: For the first open-loop subsystem model , converting it into a state space expression, the result is as follows: in, , are the closed-loop system control input and system setting value data vector at time t, is the state variable of the first open-loop subsystem at time t, is zero-mean white noise; is the sensitivity function of the closed-loop system of the thermal power unit Parameters; S402: Obtain the sensitivity function of the closed-loop system of the thermal power unit by performing subspace identification on the control input and system setting value of the closed-loop system of the thermal power unit ; S403: For the first open-loop subsystem identification result, give the same input , if the output value is the same as The trend is consistent and the error is small, which means that the sensitivity function of the closed-loop system of the thermal power unit is To meet the accuracy requirement, the sensitivity function Multiply it with the system setting value to get the intermediate signal without noise pollution.

[0014] Step S500 includes: S501: For the second open-loop subsystem , which is converted into a state space expression: in, , are the intermediate signal at time t and the output data vector of the closed-loop system control of the thermal power unit, is the state variable of the thermal power unit model at time t, is zero-mean white noise; The matrix is ​​the parameters of the thermal power unit system G; S502: Perform subspace identification on the intermediate signal and the closed-loop system control output of the thermal power unit to obtain the closed-loop system parameters of the thermal power unit model , are the consistent and unbiased parameter parameters of the thermal power unit model G.

[0015] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a method for identifying a closed-loop optimization control system of a deep peak-shaving thermal power unit. First, a linear model of the thermal power unit is obtained by small deviation linearization at any operating point, and the transfer function model of the unit load-pressure object is converted into a state space model of the system; secondly, a linear quadratic regulator is used to obtain the optimal control quantity, improve the dynamic characteristics of the thermal power unit, and obtain the thermal power unit system control input, control output data and system setting value data; then, the thermal power unit closed-loop system is decomposed into two open-loop subsystems through a two-stage method, and an intermediate signal without noise pollution is constructed to replace the actual control input, so as to eliminate the correlation between noise and control input; then, the two open-loop subsystems are identified respectively through a subspace identification method, and finally a consistent and unbiased estimate of the thermal power unit system parameters is obtained, thereby realizing accurate modeling of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of a closed-loop optimization control system identification method for a deep peak-shaving thermal power unit proposed by the present invention; Figure 2 It is a schematic diagram of the closed-loop system structure in the present invention; Figure 3 It is a schematic diagram of the structure of the two-stage method in the present invention; Figure 4 This is a flow chart of the neutron space identification method of the present invention; Figure 5 This is the input-output relationship diagram of the thermal power unit in the present invention. DETAILED DESCRIPTION

[0017] In order to facilitate the understanding of the present invention, the present invention will be described more comprehensively and meticulously below in conjunction with the accompanying drawings and preferred embodiments of the present invention, but the protection scope of the present invention is not limited to the following specific embodiments.

[0018] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0019] A method for identifying a closed-loop optimization control system of a deep peak-shaving thermal power unit, comprising: S100: Establishing a spatial state model of the thermal power unit system, selecting a coal quantity instruction and a turbine valve opening instruction as input quantities of the thermal power unit system, and selecting unit power and machine front pressure as system output quantities; Step S100 includes: S101: A common method for dealing with nonlinearity is to linearize the nonlinear model with small deviations at multiple operating points and use the basic theory of linear systems to analyze the object characteristics. To this end, the thermal power unit system is linearized with small deviations at a certain operating point to transform it into a linear model. The linear model of the unit load-pressure object can be described as: in, The transfer function representing the change in pressure in front of the engine caused by the change in fuel, The transfer function representing the change in the turbine pressure caused by the change in the turbine valve opening command is: The transfer function representing the change in unit power caused by fuel change, The transfer function representing the change in unit power caused by the change in the turbine valve opening command; is the fuel quantity command, It is the steam turbine valve opening instruction; is the unit power, is the pressure before the machine; is the dynamic time of milling, is the boiler heat storage coefficient, is the turbine dynamic time, is the fuel command gain, is the superheater resistance coefficient, dimensionless, is the turbine gain; in the transfer function and is a constant, denoted by and .

[0020] S102: According to the transfer function form of the unit load-pressure object shown in formula (1), the state space expression of the system is established: in, is the system state variable, represents the input variable, Represents an output variable.

[0021] The specific form of the coefficient matrices of its state space model is: .

[0022] S200: Design the linear quadratic controller parameters for the spatial state model of the thermal power unit system, calculate the optimal control law through the state feedback matrix, form a closed-loop system for the thermal power unit, and obtain the control input, control output and system setting value of the closed-loop system of the thermal power unit. The control input, control output data and system setting value data of the thermal power unit system are the actual data of the power plant and can be exported in the DCS system of the power plant.

[0023] Specifically, step S200 includes: S201: Design linear quadratic control for the state space model of the unit load-pressure object and introduce a quadratic objective function; Where X is the state vector, u is the system input, Q and R are given real symmetric weight matrices, and Q is positive semidefinite and R is positive definite; Assume that the linear feedback control rate of the thermal power unit system is , substituting the control rate into the system objective function, we get Given Q and R, the performance index of the system isJ The minimum value is equivalent to the Riccati equation with a positive definite matrix solution P: , after obtaining the solution P, the control gain of the system Expressed as ; S202: For the thermal power unit system, we seek the control action u to minimize the quadratic objective function J. The solution to the steady-state LQR problem can be derived. The optimal control law is: u is the system input, R is a given real symmetric matrix, B is a parameter in the state space expression, P is the positive definite matrix solution of the Riccati equation, and X is the system state vector.

[0024] S300: Decompose the closed-loop system of the thermal power unit into two open-loop subsystems, and construct an intermediate signal without noise pollution to replace the actual control input, so as to eliminate the correlation between noise and control input; refer to Figure 2 , the closed-loop system expression of the thermal power unit is as follows: Bundle Substitution We can get: refer to Figure 3 In the first stage, and Not relevant, and and can be measured, so we can As the first open-loop system, the set value data and process input data Identify the sensitivity function ; Furthermore, in the second stage, As a second open-loop system, firstly, according to the sensitivity function obtained in the first stage of identification Multiply it with the set value data to get the intermediate signal without noise pollution. and process output data The parameters of the thermal power unit are identified.

[0025] In the formula, The fuel quantity of the thermal power unit and the steam turbine valve opening instruction data are is the unit power and front pressure data, is the fuel quantity of the thermal power unit and the setting value of the turbine regulating valve opening instruction, G is the thermal power unit model, is the sensitivity function of the closed-loop system of the thermal power unit, , the feedback control L is designed LQ Controller.

[0026] LQR control is state feedback control, which belongs to closed-loop optimal control. After adding LQR state feedback control, the thermal power unit system becomes a thermal power unit closed-loop system.

[0027] S400: A sensitivity function of the closed-loop system of the thermal power plant is obtained by performing subspace identification on the control input and system setting value of the closed-loop system of the thermal power plant, and an intermediate signal without noise pollution is constructed through the sensitivity function of the closed-loop system of the thermal power plant.

[0028] Step S400 includes: S401: For the first open-loop subsystem model , converting it into a state space expression, the result is as follows: in, , are the closed-loop system control input and system setting value data vector at time t, is the state variable of the first open-loop subsystem at time t, is zero-mean white noise; is the sensitivity function of the closed-loop system of the thermal power unit Parameters; S402: Obtain the sensitivity function of the closed-loop system of the thermal power unit by performing subspace identification on the control input and system setting value of the closed-loop system of the thermal power unit ; First, the Hankel matrix is ​​constructed for the past and future data of the closed-loop system control input and system setting value of the thermal power unit, and the Hankel matrix row projection is obtained. , and then the projection singular value decomposition is performed to obtain the generalized observable matrix Kalman filter state Finally, and To determine the state matrix .

[0029] S403: For the first open-loop subsystem identification result, give the same input , if the output value is the same as The trend is consistent and the error is small, which means that the sensitivity function of the closed-loop system of the thermal power unit is To meet the accuracy requirement, the sensitivity function Multiply it with the system setting value to get the intermediate signal without noise pollution.

[0030] Step S300 is to convert the closed-loop system of the thermal power unit into two open-loop subsystems through a two-stage method, and obtain the system model of the thermal power unit through open-loop identification. Step S400 is to perform open-loop subspace identification on the two open-loop subsystems of the thermal power unit to obtain the state space equation.

[0031] S500: By performing subspace identification on the intermediate signal and the system output of the thermal power unit, a consistent and unbiased estimate of the system parameters of the thermal power unit is finally obtained.

[0032] S501: For the second open-loop subsystem , which is converted into a state space expression: in, , are the intermediate signal at time t and the output data vector of the closed-loop system control of the thermal power unit, is the state variable of the thermal power unit model at time t, is zero-mean white noise; The matrix is ​​the parameters of the thermal power unit system G; S502: Perform subspace identification on the intermediate signal and the closed-loop system control output of the thermal power unit to obtain the closed-loop system parameters of the thermal power unit model , are the consistent and unbiased parameter parameters of the thermal power unit model G.

[0033] The intermediate signal and the past and future data of the closed-loop control output of the thermal power unit are used to construct the Hankel matrix. The remaining identification process is the same as the identification process of the first open-loop subsystem, and finally the closed-loop system parameters of the thermal power unit are obtained. , are the consistent and unbiased parameter parameters of the thermal power unit model G.

[0034] Furthermore, the subspace identification step is as follows Figure 4 As shown, the following past and future data vectors and input and output Hankel matrices are defined, containing i blocks of rows and j blocks of columns: Among them, each element , are column vectors of input and output, respectively, where the subscript Indicates the past, Represents the future, matrix Depend on and constitute State Matrix and Also make a similar definition: Then the generalized data input and output matrix equations can be written in the following form, which play an important role in the subspace identification algorithm: The meaning of each part of the equation is as follows: Generalized observability matrix : Determine the low-dimensional block triangular Toeplitz matrix : Low-dimensional block triangular Toeplitz matrix : Inverse generalized observability matrix of {A,B} : Inverse generalized observability matrix of {A,K} : Solving the state matrix using subspace methods , both need to be derived from the generalized observable matrix and the Kalman filter state The main steps are as follows: The first step is to calculate the row space projection of a specific Hankel matrix, which can be obtained by mathematically using QR decomposition. The second step is to calculate the singular value decomposition of the projection to obtain the generalized observable matrix Kalman filter state The third step is to and To determine the state matrix .

[0035] First, we need to take Item, through , future input , find the future output The best prediction : Depend on The row space is and Orthogonal projection of Zhang Cheng's row space By means of oblique projection, we can obtain and : Defining the projection : It is equal to the generalized observable matrix and state sequence Non-stationary Kalman filter state estimation The product of .

[0036] available The second step of the subspace algorithm is to decompose the above equation into components and This is entirely possible, because if the number of columns j of the block Hankel matrix is ​​infinite, that is, , is a matrix of rank n, where n is the order of the system. However, in practice, due to the influence of noise and limited length data, is not necessarily a full rank matrix. n Before performing the singular value decomposition, Use and Perform left weighting and right weighting, we have: To maintain The rank of is unchanged, and It should be full rank. Observe the main singular value The order of the system can be estimated n From the above SVD decomposition, we can directly obtain the generalized observable matrix and the system state estimation sequence : The matrices A and C can be derived from the generalized observability matrix From the above formula, we can see that matrices A and C can be directly obtained by get After obtaining matrices A and C, we can solve matrices B and D: in For a full row rank matrix, For simplicity, we use M to represent the left side of the equation. Using L, the above formula can be written as: Obviously, the above equation is a linear equation system with B and D as variables, which can be solved by the least square method. Matrix to achieve accurate modeling of the system.

Claims

1. A method for identifying a closed-loop optimization control system for a deep peak-shaving thermal power unit, characterized in that: include: S100: Establishing a spatial state model of the thermal power unit system, selecting a coal quantity instruction and a turbine valve opening instruction as input quantities of the thermal power unit system, and selecting unit power and machine front pressure as system output quantities; S200: Design the linear quadratic controller parameters for the spatial state model of the thermal power unit system, calculate the optimal control law through the state feedback matrix, and form a closed-loop system for the thermal power unit; And obtain the control input, control output and system setting value of the closed-loop system of the thermal power unit; S300: Decompose the closed-loop system of the thermal power unit into two open-loop subsystems; S400: obtaining a sensitivity function of the closed-loop system of the thermal power unit by performing subspace identification on the control input of the closed-loop system of the thermal power unit and the system setting value, and constructing an intermediate signal without noise pollution through the sensitivity function of the closed-loop system of the thermal power unit; S500: By performing subspace identification on the intermediate signal and the closed-loop system control output of the thermal power unit, a consistent and unbiased estimate of the system parameters of the thermal power unit is finally obtained.

2. The method for identifying a closed-loop optimization control system for a deep peak-shaving thermal power unit according to claim 1 is characterized in that: The step S100 includes: S101: linearize the thermal power unit system with a small deviation at a certain operating point to transform it into a linear model of the unit load-pressure object; S102: According to the transfer function form of the unit load-pressure object shown in equation (1), a state space expression of the system is established.

3. The method for identifying a closed-loop optimization control system for a deep peak-shaving thermal power unit according to claim 2 is characterized in that: In step S101, the linear model of the unit load-pressure object is: in, The transfer function representing the change in pressure in front of the engine caused by the change in fuel, The transfer function representing the change in the turbine pressure caused by the change in the turbine valve opening command is: The transfer function representing the change in unit power caused by fuel change, The transfer function representing the change in unit power caused by the change in the turbine valve opening command; is the fuel quantity command, It is the steam turbine valve opening instruction; is the unit power, is the pressure before the machine; is the dynamic time of milling, is the boiler heat storage coefficient, is the turbine dynamic time, is the fuel command gain, is the superheater resistance coefficient, dimensionless, is the turbine gain; in the transfer function and is a constant, denoted by and .

4. The method for identifying a closed-loop optimization control system for a deep peak-shaving thermal power unit according to claim 3 is characterized in that: In step S102, the state space expression is: in, is the system state variable, represents the input variable, Represents an output variable.

5. The method for identifying a closed-loop optimization control system for a deep peak-shaving thermal power unit according to claim 4 is characterized in that: The step S200 includes: S201: Design linear quadratic control for the state space model of the unit load-pressure object and introduce a quadratic objective function; Where X is the state vector, u is the system input, Q and R are given real symmetric weight matrices, and Q is positive semidefinite and R is positive definite; Assume that the linear feedback control rate of the thermal power unit system is , substituting the control rate into the system objective function, we get Given Q and R, the performance index of the system is J The minimum value is equivalent to the Riccati equation with a positive definite matrix solution P: , after obtaining the solution P, the control gain of the system Expressed as ; S202: For the thermal power unit system, we seek the control action u to minimize the quadratic objective function J, and we can derive the solution to the steady-state LQR problem. The optimal control law is: u is the system input, R is a given real symmetric matrix, B is a parameter in the state space expression, P is the positive definite matrix solution of the Riccati equation, and X is the system state vector.

6. The method for identifying a closed-loop optimization control system for a deep peak-shaving thermal power unit according to claim 1, characterized in that: In step S300, The first open loop system is: The second open-loop system is: In the formula, The fuel quantity of the thermal power unit and the steam turbine valve opening instruction data, that is, the output data of the first open-loop system, is the unit power and front pressure data, is the fuel quantity of the thermal power unit and the setting value of the turbine regulating valve opening instruction, that is, the input data of the first open-loop system, G is the thermal power unit model, is the sensitivity function of the closed-loop system of the thermal power unit, and the feedback control L is designed LQ Controller.

7. The method for identifying a closed-loop optimization control system for a deep peak-shaving thermal power unit according to claim 6 is characterized in that: The step S400 includes: S401: For the first open-loop subsystem model , converting it into a state space expression, the result is as follows: in, , are the closed-loop system control input and system setting value data vector at time t, is the state variable of the first open-loop subsystem at time t, is zero-mean white noise; is the sensitivity function of the closed-loop system of the thermal power unit Parameters; S402: Obtain the sensitivity function of the closed-loop system of the thermal power plant by performing subspace identification on the control input and system setting value of the closed-loop system of the thermal power plant ; S403: For the first open-loop subsystem identification result, give the same input , if the output value is the same as The trend is consistent and the error is small, which means that the sensitivity function of the closed-loop system of the thermal power unit is To meet the accuracy requirement, the sensitivity function Multiply it with the system setting value to get the intermediate signal without noise pollution.

8. The method for identifying a closed-loop optimization control system for a deep peak-shaving thermal power unit according to claim 7, characterized in that: The step S500 includes: S501: For the second open-loop subsystem , which is converted into a state space expression: in, , are the intermediate signal at time t and the output data vector of the closed-loop system control of the thermal power unit, is the state variable of the thermal power unit model at time t, is zero-mean white noise; The matrix is ​​the parameters of the thermal power unit system G; S502: Perform subspace identification on the intermediate signal and the closed-loop system control output of the thermal power unit to obtain the closed-loop system parameters of the thermal power unit model , are the consistent and unbiased parameter parameters of the thermal power unit model G.

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