Gas turbine control device, gas turbine control input determination method, and gas turbine control input determination program

WO2025046985A1PCT designated stage expired Publication Date: 2025-03-06MITSUBISHI HEAVY IND LTD
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Patent Information

Application Number
PCT/JP2024/015979
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2023-08-31
Filing Date
2024-04-24
Publication Date
2025-03-06

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Abstract

This gas turbine control device comprises: a prediction unit that predicts, using a prediction model, a future state quantity of a gas turbine corresponding to a control input to the gas turbine in a prediction horizon; an optimization unit that optimizes the control input in at least a part of the prediction horizon, using the prediction result; a storage unit that stores sensitivity information indicating sensitivity of the control input to a change speed of a state quantity for each of extracted steam flow rates from a compressor; and an update unit that reads, from the storage unit, the sensitivity information corresponding to the extracted steam flow rate assumed in the prediction horizon, and updates one or more coefficients of a prediction equation of the state quantity used in the prediction model, on the basis of the sensitivity information corresponding to the extracted steam flow rate.
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Description

Gas turbine control device, gas turbine control input determination method, and gas turbine control input determination program

[0001] This application claims priority to Japanese Patent Application No. 2023-141658, filed with the Japan Patent Office on August 31, 2023, the contents of which are incorporated herein by reference.

[0002] Patent Literature 1 discloses a gas turbine control device. This control device is configured to use a prediction model to predict future state variables of the gas turbine corresponding to control inputs to the gas turbine over a prediction horizon, and to optimize the control inputs based on the prediction results. Specifically, it describes optimizing a fuel flow command and an inlet guide vane opening control command, which are control inputs to the gas turbine, while updating sensitivity information of the prediction model in accordance with state variables such as the turbine inlet temperature.

[0003] Japanese Patent Application Laid-Open No. 2021-156260

[0004] Incidentally, gas turbines may be provided with an extraction pipe that returns a portion of the compressed air compressed by the compressor to the upstream side of the compressor, or a turbine bypass pipe that bypasses the turbine and supplies a portion of the compressed air compressed by the compressor to the exhaust side of the turbine. When a portion of the compressed air compressed by the compressor is extracted from the compressor using the extraction pipe or turbine bypass pipe, the amount of combustion air in the gas turbine changes depending on the extraction flow rate even if, for example, the fuel flow rate or the compressor intake flow rate is the same, and therefore the prediction accuracy of the prediction model in the control device described in Patent Document 1 decreases.

[0005] In view of the above circumstances, at least one embodiment of the present disclosure has an object to provide a gas turbine control device, a gas turbine control input determination method, and a gas turbine control input determination program that are capable of accurately predicting future state variables of a gas turbine and optimizing a control input even when the extraction air flow rate from a compressor changes.

[0006] In order to achieve the above object, a gas turbine control device according to at least one embodiment of the present disclosure is a gas turbine control device for controlling a gas turbine including a compressor, a combustor, and a turbine, and includes: a prediction unit configured to predict a future state variable of the gas turbine corresponding to a control input to the gas turbine in a prediction horizon using a prediction model; an optimization unit configured to optimize the control input in at least a part of the prediction horizon using a prediction result of the prediction unit; a memory unit for storing sensitivity information indicating, for each bleed air flow rate, the sensitivity of the control input to a rate of change of the state variable, where the flow rate of compressed air bled from the compressor is defined as the bleed air flow rate; and an update unit configured to read out the sensitivity information corresponding to the bleed air flow rate expected in the prediction horizon from the memory unit, and to update one or more coefficients of a prediction equation for the state variable used in the prediction model, based on the sensitivity information corresponding to the bleed air flow rate.

[0007] In order to achieve the above object, a gas turbine control input determination method according to at least one embodiment of the present disclosure includes: a prediction step in which a prediction model predicts a future state variable of the gas turbine corresponding to a control input to the gas turbine in a prediction horizon; an optimization step in which the control input in at least a part of the prediction horizon is optimized using a prediction result in the prediction step; a step in which, when a flow rate of compressed air extracted from a compressor of the gas turbine is defined as an extraction flow rate, a storage unit stores sensitivity information indicating a sensitivity of the control input to a rate of change of the state variable for each extraction flow rate; and a step in which the sensitivity information corresponding to the extraction flow rate expected in the prediction horizon is read from the storage unit, and one or more coefficients of a prediction equation for the state variable used in the prediction model are updated based on the sensitivity information corresponding to the extraction flow rate.

[0008] In order to achieve the above object, a gas turbine control input determination program according to at least one embodiment of the present disclosure causes a computer to execute the following steps: predicting a future state quantity of the gas turbine that corresponds to a control input to the gas turbine in a prediction horizon using a prediction model; optimizing the control input in at least a part of the prediction horizon using a prediction result of the prediction step; storing sensitivity information in a storage unit that indicates, for each bleed air flow rate, the sensitivity of the control input to a rate of change of the state quantity, where the flow rate of compressed air bled from a compressor of the gas turbine is defined as the bleed air flow rate; and reading out the sensitivity information corresponding to the bleed air flow rate expected in the prediction horizon from the storage unit, and updating one or more coefficients of a prediction equation for the state quantity used in the prediction model, based on the sensitivity information corresponding to the bleed air flow rate.

[0009] According to at least one embodiment of the present disclosure, there are provided a gas turbine control device, a gas turbine control input determination method, and a gas turbine control input determination program that are capable of accurately predicting future state variables of a gas turbine and achieving high control performance even when the extraction air flow rate from a compressor changes.

[0010] 1 is a diagram illustrating an example of a configuration of a gas turbine system 1 according to an embodiment. FIG. 1 is a diagram illustrating an example of a hardware configuration of a control device 100 illustrated in FIG. 1. FIG. 2 is a block diagram illustrating an example of a functional configuration of the control device 100 illustrated in FIGS. 1 and 2. FIG. 3 is a schematic diagram for explaining the principle of optimization performed by the control device 100 according to an embodiment. FIG. 4 is a diagram illustrating an example of a performance table stored in the control device 100 according to an embodiment. FIG. 5 is a graph illustrating an example of a relationship between a turbine inlet temperature T1T and a combustion efficiency η of a gas turbine 2 according to an embodiment. FIG. 6 is a block diagram for explaining an example of the function of the control device 100 described using FIGS. 1 to 6. FIG. 7 is a block diagram for explaining a modified example of the function of the control device 100. FIG. 8 is a block diagram for explaining another modified example of the function of the control device 100. FIG. 9 is a diagram for explaining an example of a method for correcting the target value trajectories of each of the gas turbine output power GTMW and the turbine inlet temperature T1T by a target value trajectory correction unit 180. FIG. 10 is a diagram for explaining an example of a method for correcting the target value trajectories of each of the gas turbine output power GTMW and the turbine inlet temperature T1T by a target value trajectory correction unit 180.

[0011] Several embodiments of the present disclosure will be described below with reference to the accompanying drawings. However, the dimensions, materials, shapes, relative arrangements, etc. of components described as embodiments or shown in the drawings are merely illustrative examples and are not intended to limit the scope of the invention. For example, expressions expressing relative or absolute arrangements, such as "in a certain direction," "along a certain direction," "parallel," "orthogonal," "center," "concentric," or "coaxial," not only strictly express such arrangements, but also express relative displacements with a tolerance or angle or distance to the extent that the same function is achieved. For example, expressions expressing the equality of things, such as "same," "equal," and "homogeneous," not only express strict equality, but also express tolerance or differences to the extent that the same function is achieved. For example, expressions expressing shapes such as a square or cylindrical shape not only express shapes such as a square or cylindrical shape in the strict geometric sense, but also express shapes including concave and convex portions, chamfered portions, etc., to the extent that the same effect is achieved. On the other hand, the expressions "comprise," "include," "have," "includes," or "have" of one element are not exclusive expressions that exclude the presence of other elements.

[0012] (Gas Turbine System) Fig. 1 is a diagram that schematically shows the configuration of a gas turbine system 1 according to one embodiment. As shown in Fig. 1, the gas turbine system 1 includes a gas turbine 2, a generator 7, and a control device 100 (gas turbine control device).

[0013] The gas turbine 2 is a gas turbine for generating electricity and includes a compressor 3, a combustor 4, and a turbine 5 as main components.

[0014] The compressor 3 is connected to the turbine 5 via a rotary shaft 8A. The compressor 3 is rotationally driven by the rotational energy of the turbine 5 to generate compressed air. The compressed air generated by the compressor 3 is supplied to the combustor 4. An air intake system 10 (e.g., an air intake duct equipped with a filter) and an inlet guide vane 9 attached to the air intake system 10 are provided on the inlet side of the compressor 3. The air flow rate G1, which is the intake air flow rate of the compressor 3, is controlled by adjusting the opening of the inlet guide vane 9 using an actuator 35. The opening of the inlet guide vane 9 is controlled based on an inlet guide vane opening control command IGVCSO from the control device 100. Specifically, the actuator 35 adjusts the opening of the inlet guide vane 9 based on the inlet guide vane opening control command IGVCSO from the control device 100. A flow meter 30 for measuring the air flow rate G1 and a thermometer 32 for measuring the compressor inlet temperature, i.e., the intake temperature of the compressor 3, are provided upstream of the inlet guide vane 9 in the intake equipment 10.

[0015] The combustor 4 is connected to a fuel supply line 12, and burns the fuel supplied from the fuel supply line 12 with compressed air supplied from the compressor 3 to generate combustion gas, which is a working fluid for the turbine 5. The combustion gas generated in the combustor 4 is sent from the combustor 4 to the downstream turbine 5. The flow rate of the fuel supplied to the combustor 4 is adjusted by a fuel flow control valve 14 provided in the fuel supply line 12. The opening of the fuel flow control valve 14 is controlled based on a fuel flow command CSO (fuel flow control valve opening control command) from the control device 100. A flow meter 13 is provided in the fuel supply line 12 to measure a fuel flow rate Gf, which is the flow rate of the fuel supplied to the combustor 4.

[0016] The turbine 5 is driven by the combustion gas generated in the combustor 4. The turbine 5 is connected to the generator 7 by a rotating shaft 8B, and the generator 7 generates electricity using the rotational energy of the turbine 5. The generator 7 is provided with a power meter 34 configured to measure a gas turbine output GTMW, which is the output of the gas turbine 2. The power meter 34 may measure the amount of electricity generated by the generator 7 as the gas turbine output GTMW.

[0017] As shown in FIG. 1 , the gas turbine 2 includes an extraction pipe 15 and a turbine bypass pipe 18. The extraction pipe 15 is configured to extract a portion of the compressed air compressed by the compressor 3 from the compressor 3 and return it to the upstream side of the compressor 3 (in the illustrated example, the upstream side of the inlet guide vane 9 in the air intake facility 10). The extraction pipe 15 is provided with a extraction valve 16 and a flow meter 17. The extraction valve 16 is a flow control valve that adjusts an extraction valve flow rate Gai, which is the flow rate of compressed air flowing through the extraction valve 16. The extraction valve flow rate Gai is the flow rate of compressed air extracted from the compressor 3 by the extraction pipe 15 (i.e., the flow rate of compressed air flowing through the extraction pipe 15). The opening of the extraction valve 16 is controlled based on an extraction valve opening control command AICSO (anti-icing command) from the control device 100. The flow meter 17 is configured to measure the extraction valve flow rate Gai.

[0018] The bleed valve 16 is also called an anti-icing valve because the intake temperature T1C of the compressor 3 can be increased by increasing the opening of the bleed valve 16. When anti-icing operation is performed, in which the gas turbine 2 is operated with the bleed valve 16 open, high-temperature, high-pressure air from the outlet of the compressor 3 is bled through the bleed pipe 15 and injected into the inlet of the compressor 3, thereby controlling the intake temperature T1C of the compressor 3 to a target temperature. The bleed valve flow rate Gai is controlled by the bleed valve position control command AICSO. However, the combustion air flow rate, which is the flow rate of air supplied to the combustor 4, is reduced by the bleed air from the compressor 3. Therefore, unless the inlet guide vane position control command IGVCSO is changed, the turbine inlet temperature T1T increases with the bleed air. Therefore, the control device 100 uses model predictive control, as will be described later, to control the intake-air temperature T1C to a target temperature while simultaneously controlling the inlet guide vane position control command IGVCSO, thereby achieving control of the desired gas turbine output GTMW, turbine inlet temperature T1T, and intake-air temperature T1C.

[0019] The turbine bypass pipe 18 is configured to supply a portion of the compressed air compressed by the compressor 3 to the downstream side of the turbine 5 (in the illustrated example, a turbine exhaust pipe 20 through which exhaust from the turbine 5 flows), bypassing the combustor 4 and the turbine 5. The turbine bypass pipe 18 is provided with a turbine bypass valve 22 and a flow meter 24. The turbine bypass valve 22 is a flow control valve that adjusts a turbine bypass valve flow rate Gtb, which is the flow rate of compressed air flowing through the turbine bypass valve 22. The turbine bypass valve flow rate Gtb is the flow rate of compressed air extracted from the compressor 3 by the turbine bypass pipe 18 (i.e., the flow rate of compressed air flowing through the turbine bypass pipe 18). The opening of the turbine bypass valve 22 is controlled based on a turbine bypass valve opening control command TBCSO from the control device 100. The flow meter 24 is configured to measure the turbine bypass valve flow rate Gtb.

[0020] Since the turbine inlet temperature T1T can be increased by increasing the opening degree of the turbine bypass valve 22, the turbine bypass valve 22 is used for the purpose of increasing the turbine inlet temperature T1T to improve efficiency and emissions when the gas turbine 2 is under low load, particularly when the opening degree of the inlet guide vane 9 is at or near the minimum opening degree. The control device 100 improves the controllability of the turbine inlet temperature T1T in the low load range of the gas turbine 2 by controlling the turbine bypass valve position control command TBCSO together with the inlet guide vane position control command IGVCSO using model predictive control, as will be described later.

[0021] In addition, a thermometer 26 is provided in the final stage of the turbine 5 to measure the blade path temperature TBP, which is the temperature of the combustion gas that has passed through the final stage blades, and a thermometer 28 is provided in the turbine exhaust piping 20 downstream of the thermometer 26 to measure the exhaust gas temperature TEX, which is the temperature of the turbine exhaust gas.

[0022] FIG. 2 is a diagram illustrating an example of the hardware configuration of the control device 100 shown in FIG. 1 . As shown in FIG. 2 , the control device 100 includes, for example, a processor 72, a random access memory (RAM) 74, a read-only memory (ROM) 76, a hard disk drive (HDD) 78, an input I / F 80, and an output I / F 82, which are connected to one another via a bus 84. The hardware configuration of the control device 100 is not limited to the above, and may be configured by a combination of a control circuit and a storage device. The control device 100 is also configured by a computer executing a program that realizes each function of the control device 100. The functions of each part of the control device 100 described below are realized, for example, by loading a program (e.g., a control input determination program described below) stored in the ROM 76 into the RAM 74 and executing it with the processor 72, as well as by reading and writing data from and to the RAM 74 and the ROM 76. The hardware constituting the control device 100 may be concentrated in one location, or may be distributed across multiple locations.

[0023] Fig. 3 is a block diagram showing an example of the functional configuration of the control device 100 shown in Fig. 1 and Fig. 2. As shown in Fig. 3, the control device 100 includes a prediction unit 110, an optimization unit 120, a storage unit 130, an update unit 140, a state quantity acquisition unit 150, a target value trajectory acquisition unit 160, and a table update unit 170.

[0024] The prediction unit 110 is configured to predict future state variables of the gas turbine 2 corresponding to control inputs to the gas turbine 2 over a prediction horizon, using a prediction model. The control inputs in this prediction model include a fuel flow rate command CSO, an inlet guide vane opening control command IGVCSO, a bleed valve opening control command AICSO, and a turbine bypass valve opening control command TBCSO. The state variables used in this prediction model include, for example, information indicating each of the fuel flow rate Gf, air flow rate G1, bleed valve flow rate Gai, turbine bypass valve flow rate Gtb, power output GTMW, turbine inlet temperature T1T, blade path temperature TBP, exhaust gas temperature TEX, and intake air temperature T1C of the gas turbine 2.

[0025] The optimization unit 120 is configured to optimize the control input in at least a part of the prediction horizon using the prediction result in the prediction unit 110. The optimization unit 120 inputs the control input in the prediction horizon to the prediction unit 110 to obtain the prediction result.

[0026] If the flow rate of compressed air extracted from the compressor 3 is defined as the extracted air flow rate, the storage unit 130 stores sensitivity information indicating the sensitivity of the control input to the rate of change of the state quantity for each extracted air flow rate. The storage unit 130 also stores constraints, a prediction model, and a control input determination program, which will be described later. The sensitivity information includes first sensitivity information and second sensitivity information, as will be described later. The sensitivity information may also be a performance table, which will be described later. In this embodiment, an example will be described in which the "extracted air flow rate" is the sum of the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb.

[0027] The update unit 140 reads out sensitivity information according to the bleed air flow rate assumed in the prediction horizon from the storage unit 130, and updates one or more coefficients of a prediction equation for the state quantity used in the prediction model based on the sensitivity information according to the bleed air flow rate. The sensitivity information according to the bleed air flow rate assumed in the prediction horizon may be sensitivity information corresponding to the current bleed air flow rate.

[0028] The state quantity acquisition unit 150 is configured to acquire state quantities of the gas turbine 2 from sensors or the like. The state quantity acquisition unit 150 acquires, for example, the fuel flow rate Gf measured by the flow meter 13, the air flow rate G1 measured by the flow meter 30, the extraction valve flow rate Gai measured by the flow meter 17, the turbine bypass valve flow rate Gtb measured by the flow meter 24, the gas turbine output GTMW measured by the power meter 34, the turbine inlet temperature T1T measured by the thermometer 36, the blade path temperature TBP measured by the thermometer 26, the exhaust gas temperature TEX measured by the thermometer 28, and the intake air temperature T1C acquired by the thermometer 32.

[0029] The target value trajectory acquisition unit 160 is configured to acquire the target value trajectories of the gas turbine output GTMW, the turbine inlet temperature T1T, and the intake air temperature T1C from among the above-mentioned state quantities.

[0030] The table update unit 170 is configured to update the performance table stored in the storage unit 130 based on performance data acquired during actual operation. For example, the initial performance table is created based on design information. Thereafter, the performance table is updated based on performance data acquired during actual operation.

[0031] (Prediction Model) The following describes the prediction model used by the prediction unit 110. In some embodiments, the prediction model may be configured to use a state space model described by a linear model, as described below.

[0032] First, the definitions of the terms in the prediction formula will be explained. x(k) is a state vector at the current time k. x(k) may be considered as a matrix with multiple state quantities as elements. u(k) is a control input vector at the current time k. y(k) is an observed output vector at the current time k. y(k) may be considered as a matrix with control quantities for some of the multiple state quantities as elements. z(k) is an evaluation output vector at the current time k. A, B, C y , C z are matrices that make up the state equation. Matrices A and B have elements that are one or more coefficients included in the prediction formula. When one or more coefficients are updated, matrices A and B are updated.

[0033] With these definitions, the following relational expressions can be considered to hold as functions of time. These expressions can be used as prediction expressions. x(k+1)=Ax(k)+Bu(k) (1) y(k)=C y x(k)...(2) z(k)=C z x(k)...(3)

[0034] In equation (1), x(k+1) is a future state vector. Note that the unit of time may be the control period. In other words, x(k+1) may be a future state vector expected when the current time k is advanced by one control period.

[0035] According to equation (1), it is possible to calculate a future state vector x(k+1) based on the state vector x(k) at the current time k, the control input vector u(k) at the current time k, and matrices A and B. By repeating such calculations, it is also possible to obtain a future state vector x(k+i) that is expected when the current time k is advanced by any control period i.

[0036] According to equation (2), the state vector x(k) and the matrix C y According to equation (3), the state vector x(k) and the matrix C zBased on this, it is possible to calculate the evaluation output vector z(k) at the current time k. Furthermore, by combining equations (1) to (3), it is also possible to calculate the observed output vector y(k+i) and the evaluation output vector z(k+i) corresponding to the future state quantity vector x(k+i).

[0037] Here, the difference from the equilibrium point (which may be close to the equilibrium point) of thermal equilibrium during operation of the gas turbine 2 may be considered to be the state quantity x. In this case, the state quantity vector x may be defined as a matrix having elements dGf, dG1, dGai, dGtb, dGTMW, dT1T, dTBP, dTEX, and dT1C, which are differences from the equilibrium point in the fuel flow rate Gf, the air flow rate G1, the bleed valve flow rate Gai, the turbine bypass valve flow rate Gtb, the power GTMW, the turbine inlet temperature T1T, the blade path temperature TBP, the exhaust gas temperature TEX, and the intake air temperature T1C. The control input u may be defined as a matrix having elements dCSO, dIGVCSO, dAICSO, and dTBCSO, which correspond to the state quantities (differences from the equilibrium point) of the fuel flow rate command CSO, the inlet guide vane opening control command IGVCSO, the bleed valve opening control command AICSO, and the turbine bypass valve opening control command TBCSO.

[0038] More specifically, dGf, dG1, dGai, dGtb, dGTMW, dT1T, dTBP, dTEX, and dT1C can be expressed by the following differential equation: For example, Gf-Gf 0 corresponds to the difference in fuel flow rate Gf from the equilibrium point, and dGf is d(Gf - Gf 0 ) dx / dt indicates the rate of change of the state quantity x. For example, d(Gf - Gf 0 ) / dt indicates the rate of change of the fuel flow rate Gf. The same can be said for other state quantities.

[0039] (Gf-Gf 0 ) + τ Gf ×d (Gf-Gf 0 ) / dt=K_Gf_CSO×(CSO-CSO 0 )...(4) (G1-G1 0 ) + τ G1 ×d (G1-G1 0) / dt=K_G1_IGVCSO×(IGVCSO-IGVCSOo)・・・(5) (Gai-Gai 0 )+τ Gai ×d(Gai-Gai 0 ) / dt=K_Gai_AICSO×(AICSO-AICSO 0 )・・・(6) (Gtb-Gtb 0 )+τ Gtb ×d(Gtb-Ttb 0 ) / dt=K_Gtb_TBCSO×(TBCSO-TBCSO 0 )・・・(7) (GTMW-GTMW 0 )+τ GTMW ×d(GTMW-GTMW 0 ) / dt=K_GTMW_Gf×(Gf-Gf 0 )+K_GTMW_G1×(G1-G1 0 )+K_GTMW_Gai×(Gai-Gai 0 )+K_GTMW_Gtb×(Gtb-Gtb 0 )・・・(8) (T1T-T1T 0 )+τ T1T ×d(T1T-T1T 0 ) / dt=K_T1T_Gf×(Gf-Gf 0 )+K_T1T_G1×(G1-G1 0 )+K_T1T_Gai×(Gai-Gai 0 )+K_T1T_Gtb×(Gtb-Gtb 0 )・・・(9) (TBP-TBP 0 )+τ TBP ×d(TBP-TBP 0 ) / dt=K_TBP_Gf×(Gf-Gf 0 )+K_TBP_G1×(G1-G1 0 )+K_TBP_Gai×(Gai-Gai 0 )+K_TBP_Gtb×(Gtb-Gtb 0 )・・・(10) (TEX-TEX 0 )+τ TEX ×d(TEX-TEX 0 ) / dt=K_TEX_Gf×(Gf-Gf 0 )+K_TEX_G1×(G1-G1 0) + K_TEX_Gai × (Gai - Gai 0 ) + K_TEX_Gtb × (Gtb - Gtb 0 )...(11) (T1C-T1C 0 ) + τ T1C ×d (T1C-T1C 0 ) / dt=K_T1C_Gai×(Gai-Gai 0 ) ... (12)

[0040] Equations (4) to (7) are first sensitivity information showing the relationship between the rate of change of the state quantity x and the control input u. These equations show the sensitivity of the control input u to the rate of change of the state quantity x. Equations (8) to (11) are second sensitivity information showing the relationship between the first state quantities Gf, G1, Gai, and Gtb and the rate of change of the second state quantities GTMW, T1T, TBP, and TEX. Equation (12) is second sensitivity information showing the relationship between the first state quantity Gai and the rate of change of the second state quantity T1C. τ Gf , τ G1 , τ Gai , τ Gtb , τ GTMW , τ T1T , τ TBP and τ TEX and τ T1C are the respective time constants.

[0041] These sensitivity information include sensitivity coefficients K_Gf_CSO, K_G1_IGVCSO, K_Gai_AICSO, K_Gtb_TBCSO, K_GTMW_Gf, K_GTMW_G1, K_GTMW_Gai, K_GTMW_Gtb, K_T1T_Gf, K_T1T_G1, K_T1T_Gai, K_T1T_Gtb, K_TBP_Gf, K_TBP_G1, K_TBP_Gai, K_TBP_Gtb, K_TEX_Gf, K_TEX_G1, K_TEX_Gai, K_TEX_Gtb, and K_T1C_Gai. For example, the sensitivity coefficient K_Gf_CSO is a coefficient that indicates the sensitivity of the fuel flow rate Gf to changes in the fuel flow command CSO. Similarly, the other sensitivity coefficients are coefficients that indicate the sensitivity of a previous parameter to changes in a subsequent parameter. As will be described later, the second sensitivity coefficients K_GTMW_Gf, K_T1T_Gf, K_TBP_Gf, and K_TEX_Gf among these sensitivity coefficients may be corrected taking into account the combustion efficiency η.

[0042] When equations (4) to (12) are rearranged into a matrix form, the state equation obtained by time-differentiating the state quantity vector x is expressed as the following equation (13). When the observation output vector y is expressed in a matrix form, it is expressed as the following equation (14). When the evaluation output vector z is expressed in a matrix form, it is expressed as the following equation (15).

[0043] (Optimization) An example of optimization by the optimization unit 120 will now be described in detail. FIG. 4 is a schematic diagram for explaining the principle of optimization performed by the control device 100 according to one embodiment. The upper graph in FIG. 4 shows the time progression of the controlled variables and the like, and the lower graph shows the time progression of the control input. The controlled variables are, for example, the output GTMW of the gas turbine 2, the turbine inlet temperature T1T, and the intake air temperature T1C. Note that the upper graph in FIG. 4 shows the time progression of the output GTMW as an example of the controlled variable.

[0044] In the upper graph of Figure 4, y(t) shown by a solid line indicates the observed output, and z(t) shown by a dotted line indicates the evaluation output. In other words, y(t) indicates the progress of the actual results up to the current time k, and z(t) indicates the progress of the predicted results in the future after the current time k (i.e., time k+i). r(k+i|k) indicates the operating line, i.e., the target value trajectory. This target value trajectory is acquired by the target value trajectory acquisition unit 160. It is preferable that the target value trajectory and the trajectory of the controlled variable are close to each other.

[0045] The horizontal axis is the time axis, and the time axis is common to the upper and lower graphs in Figure 4. On the time axis, the section from the evaluation start time k + Hw to time k + HP is the prediction horizon. The section from the current time k to time k + Hu is the control horizon. The control horizon is a shorter time than the prediction horizon.

[0046] 4, the solid line indicates the actual change in the control input u(t), and the dashed line indicates the change in the control input u(t) after the current time k. The change in the evaluation output z(t) in the upper graph is determined as the control amount predicted according to the control input u(t) after the current time k in the lower graph.

[0047] The optimization unit 120 determines the control input u(t) so that the value of the control input u(t) changes in the control horizon, and determines the control input u(t) so that the value of the control input u(t) in the section of the prediction horizon after the control horizon is constant. For example, as shown in Figure 4, the value of the control input u(t) changes in the section from the current time k to time k + Hu, whereas the value of the control input u(t) is constant in the section from time k + Hu to time k + Hp.

[0048] This constant value may be the value of the immediately preceding control input u(k+Hu). In other words, calculation of the constant value may be omitted. Note that the constant value may be the value of the control input u(t) calculated so that the evaluation output z(t) matches the reference r(k+i|k) indicating the desired value trajectory at the end of the prediction horizon (time k+Hp), as shown in FIG. 4 .

[0049] The optimization unit 120 inputs the control input in the determined prediction horizon to the prediction unit 110. As a result, the transition of the evaluation output z(t) is obtained. Note that the control input determined before input to the prediction unit 110 is not determined as the optimal control input, but is tentatively determined as a candidate for the optimal control input. In other words, the dashed line in the graph at the bottom of FIG. 4 indicates the control input u(t) during the optimization calculation.

[0050] For example, if the control input u(t) actually used is for one control cycle immediately after the current time (i.e., from current time k to time k+Hw), the prediction horizon is from one control cycle after the current time to 11 control cycles later, and the control horizon is five control cycles from the current time. In this case, calculated values ​​are set for the control inputs up to five moves ahead, and constant values ​​are set for the control inputs five moves ahead thereafter. Based on these control inputs, state variables and control variables for up to 11 moves ahead are predicted.

[0051] The optimization unit 120 may be configured to optimize the control input u(t) based on an evaluation function that depends on the deviation between the target value trajectory and the controlled variable (parameter). For example, the optimization unit 120 may determine the optimal control input u(t) by solving an optimization problem that minimizes the evaluation function while referring to the above-mentioned prediction result.

[0052] Here, the evaluation function may be a function including a first term indicating the error between the target value trajectory and the controlled variable in the prediction horizon, and a second term indicating the cumulative value of the change in the control input u(t) in the control horizon. For example, the evaluation function may be V shown in the following equation (16):

[0053] The evaluation function V shown in equation (16) is a weighting matrix that weights each l2 norm (distance). Q is a state weighting matrix, and R is a control weighting matrix. Specifically, Q is a matrix in which the weights for the gas turbine 2 output GTMW, the fuel-air ratio (i.e., turbine inlet temperature T1T), the blade path temperature TBP, the exhaust gas temperature TEX, and the intake air temperature T1C are arranged on the diagonal elements, with the other matrix elements set to zero. R is a matrix in which the weights for the fuel flow command CSO change, the weights for the inlet guide vane opening control command IGVCSO change, the weights for the bleed valve opening control command AICSO change, and the weights for the turbine bypass valve opening control command TBCSO change are arranged on the diagonal elements, with the other matrix elements set to zero. Q and R are parameters that affect controllability. Increasing Q relative to R improves control response but reduces stability. Conversely, increasing R relatively reduces control response but improves stability. The turbine bypass valve 22 is operated when the opening of the inlet guide vane 9 is at the minimum opening or an opening close to the optimum opening. Therefore, when the inlet guide vane 9 is not at the minimum opening or an opening close to the minimum opening, the control weight of the TBCSO may be set to be large so that the turbine bypass valve 22 does not operate.

[0054] The optimization unit 120 may be configured to optimize the control input u(t) based on constraints for constraining one or more of the rate of change of the control input u(t), the absolute value of the control input u(t), and the absolute value of the state quantity x. In this case, for example, the control input u(t) can be determined so as to satisfy the constraints on the operation of the gas turbine 2.

[0055] As a constraint condition for the rate of change of the control input u(t), for example, a constraint condition for satisfying −10 (% / sec)< rate of change of the fuel flow rate command CSO<10 (% / sec) may be set. As a constraint condition for the rate of change of the control input u(t), for example, a constraint condition for satisfying −10 (deg / sec)< rate of change of the inlet guide vane opening control command IGVCSO<10 (deg / sec) may be set.

[0056] As a constraint condition for the absolute value of the control input u(t), for example, a constraint condition for satisfying 0(%)<absolute value of fuel flow rate command CSO<100(%) may be set. As a constraint condition for the absolute value of the control input u(t), for example, a constraint condition for satisfying −8(deg)<absolute value of inlet guide vane opening control command IGVCSO<46(deg). As a constraint condition for the absolute value of the state quantity x, for example, a constraint condition for satisfying the condition that the turbine inlet temperature is less than 1650° C. may be set. These constraint conditions may be applied in combination.

[0057] The control device 100 may be configured to perform, for each control period, a process of predicting the state quantity x, a process of updating one or more coefficients included in the matrices A and B, and a process of optimizing the control input u(t). In other words, the control device 100 may perform these processes every time one control period elapses.

[0058] (Coefficient Update) Hereinafter, a specific example of updating the coefficients of the prediction equation by the update unit 140 will be described. As described above, the update unit 140 reads out sensitivity information corresponding to the bleed air flow rate expected in the prediction horizon (i.e., sensitivity information determined according to the bleed air valve flow rate Gai and the turbine bypass valve flow rate Gtb) from the storage unit 130, and updates one or more coefficients of the prediction equation for the state quantity used in the prediction model based on the sensitivity information corresponding to the bleed air flow rate.

[0059] The sensitivity information according to the bleed air flow rate assumed in the prediction horizon may be sensitivity information according to the current bleed air flow rate. The sensitivity information may be a performance table of the gas turbine 2. Fig. 5 is a diagram illustrating an example of the performance table stored in the control device 100 according to one embodiment.

[0060] For example, the performance table may be an information table in which information indicating the inlet guide vane position control command IGVCSO, information indicating the output GTMW of the gas turbine 2, information indicating the turbine inlet temperature T1T, information indicating the exhaust gas temperature TEX, information indicating the bleed valve flow rate Gai, information indicating the turbine bypass valve flow rate Gtb, the intake air temperature T1C, and the atmospheric temperature are associated with one another as state quantities. Here, if the sum of the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb is defined as the bleed air flow rate Gaitb, as shown in Fig. 5, the storage unit 130 may store an information table for each bleed air flow rate Gaitb, and multiple state quantities that are determined based on the bleed air flow rate Gaitb may be associated with one another in the information table.

[0061] In the example shown in Fig. 5, a plurality of state quantities are associated when the bleed air flow rate Gaitb is 10% of the air flow rate. In addition to the state quantities shown in Fig. 5, other state quantities (e.g., air flow rate G1, fuel flow rate Gf, etc.) may also be associated in the performance table. Although not shown in Fig. 5, the performance table allows the values ​​of other state quantities to be read when a certain state quantity is changed. In other words, the values ​​are arranged vertically in the table.

[0062] The performance table may be discrete data of numerical values ​​indicating each state quantity, as shown in Fig. 5. However, as the extracted air flow rate Gaitb, not only the discrete numerical values ​​shown in the performance table but also a linear interpolation value between the discrete numerical values ​​may be used. Furthermore, as described above, the performance table stored in the storage unit 130 may be updated by the table update unit 170 based on actual data during operation.

[0063] The performance table includes, for example, multiple sensitivity coefficients K_Gf_CSO, K_G1_IGVCSO, K_Gai_AICSO, K_Gtb_TBCSO, K_GTMW_Gf, K_GTMW_G1, K_GTMW_Gai, K_GTMW_Gtb, K_T1T_Gf, K_T1T_G1, K_T1T_Gai, K_T1T_Gtb, K_TBP_Gf, K_TBP_G1, K_TBP_Gai, K_TBP_Gtb, K_TEX_Gf, K_TEX_G1, K_TEX_Gai, K_TEX_Gtb, and K_T1C_Gai. As described above, the sensitivity coefficients indicate the sensitivity of a previous parameter to a change in a subsequent parameter indicated by a symbol. These sensitivity coefficients can be obtained by dividing the numerical values ​​in the performance table.

[0064] The update unit 140 can obtain one or more coefficients included in the prediction formula from such a performance table, i.e., sensitivity information. The update unit 140 can update the coefficients of the prediction formula (i.e., matrices A and B) using the obtained coefficients.

[0065] 6 is a graph showing an example of a relationship between the turbine inlet temperature T1T and the combustion efficiency η of the gas turbine 2 according to one embodiment. As shown in FIG. 6, the combustion efficiency η varies depending on the turbine inlet temperature T1T. The change in the combustion efficiency η significantly affects the sensitivity coefficient (second sensitivity coefficient) related to the fuel flow rate Gf.

[0066] Therefore, it is preferable that the updating unit 140 corrects a coefficient (second sensitivity coefficient) indicating the sensitivity of one or more state quantities among the power output GTMW, the turbine inlet temperature T1T, the blade path temperature TBP, and the exhaust gas temperature TEX to a change in the fuel flow rate Gf, based on the rate of change of the combustion efficiency η with respect to the turbine inlet temperature T1T. For example, the updating unit 140 may be configured to correct the second sensitivity coefficients K_GTMW_Gf, K_T1T_Gf, K_TBP_Gf, and K_TEX_Gf among the sensitivity coefficients included in the performance table, taking into account the combustion efficiency η of the gas turbine 2.

[0067] (Functions of the control device 100) The following describes the functions of the control device 100. Fig. 7 is a block diagram for explaining an example of the functions of the control device 100 described with reference to Figs.

[0068] First, the control device 100 acquires, as observed outputs, the fuel flow rate Gf measured by the flow meter 13, the air flow rate G1 measured by the flow meter 30, the bleed valve flow rate Gai measured by the flow meter 17, the turbine bypass valve flow rate Gtb measured by the flow meter 24, the gas turbine output GTMW measured by the power meter 34, the turbine inlet temperature T1T measured by the thermometer 36, the blade path temperature TBP measured by the thermometer 26, the exhaust gas temperature TEX measured by the thermometer 28, and the intake air temperature T1C measured by the thermometer 32. The state quantity acquisition unit 150 acquires state quantities of the fuel flow rate Gf, the air flow rate G1, the bleed valve flow rate Gai, the turbine bypass valve flow rate Gtb, the gas turbine output GTMW, the turbine inlet temperature T1T, the blade path temperature TBP, the exhaust gas temperature TEX, and the intake air temperature T1C from these observed outputs. Furthermore, the observed outputs may be used as input data for a disturbance observer in the optimization unit 120. The output data of the disturbance observer may be used in formulation in optimization (i.e., updating the coefficients of the prediction formula and calculating the evaluation function).

[0069] The control device 100 also acquires current target values ​​and final target values ​​for the gas turbine output GTMW, the turbine inlet temperature T1T, and the intake air temperature T1C. These values ​​may be based on values ​​set by a user. The target value trajectory acquisition unit 160 acquires target value trajectories for the gas turbine output GTMW, the turbine inlet temperature T1T, and the intake air temperature T1C by calculating the differences between the final target values ​​and the current target values ​​for each of the gas turbine output GTMW, the turbine inlet temperature T1T, and the intake air temperature T1C. The prediction unit 110 predicts future state quantities using a prediction model based on the state quantities acquired by the state quantity acquisition unit 150. At this time, the update unit 140 updates the coefficients of the prediction equation for the prediction model based on the sensitivity information stored in the storage unit 130. The update unit 140 also formulates an equation for the evaluation function V using the target value trajectory acquired by the target value trajectory acquisition unit 160 and the prediction model. The optimization unit 120 calculates an evaluation function V while acquiring the prediction results of the prediction model, and optimizes the control inputs so as to determine the control inputs (here, a combination of the above-mentioned four control commands, i.e., a combination of the fuel flow rate command CSO, the inlet guide vane position control command IGVCSO, the bleed valve position control command AICSO, and the turbine bypass valve position control command TBCSO) that minimize the evaluation function V as optimal control inputs. When the optimal control inputs are determined, the control inputs (i.e., CSO, IGVCSO, AICSO, and TBCSO) are output.

[0070] In this way, the control device 100 determines the optimal control input. Such a control input determination method may be executed based on a control input determination program. Furthermore, the control device 100 may be configured to control the gas turbine 2 in accordance with the control input optimized by the optimization unit 120.

[0071] The following describes the effects achieved by the above-described control device 100. The control device 100 can update one or more coefficients of the prediction formula in accordance with the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb. Therefore, even if the bleed valve flow rate Gai or the turbine bypass valve flow rate Gtb changes, it is possible to accurately predict the future state variables of the gas turbine 2 using a prediction model that uses coefficients in accordance with the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb, thereby making it possible to achieve high control performance.

[0072] Furthermore, by using not only the CSO and the IGVCSO but also the AICSO and the TBCSO as control inputs for bringing the gas turbine output GTMW and the turbine inlet temperature T1T closer to their target value trajectories, it is possible to calculate optimal control inputs even when the extraction valve 16 and the turbine bypass valve 22 are operating, thereby achieving high controllability.

[0073] Furthermore, when controlling the bleed valve 16, the CSO, IGVCSO, AICSO, and TBCSO can be optimized in consideration of the target value trajectory of the intake-air temperature T1C of the compressor 3 as well as the gas turbine output GTMW and the turbine inlet temperature T1T, and therefore the control accuracy of the intake-air temperature T1C can be improved.

[0074] Fig. 8 is a block diagram for explaining a modified example of the functions of the control device 100. In the following, among the functions of the control device 100 shown in Fig. 8, explanations of parts that overlap with the functions explained using Figs. 3 to 7 etc. will be omitted.

[0075] 8 , the control device 100 determines the bleed valve position control command AICSO and the turbine bypass valve position control command TBCSO by means other than the prediction model outside the model predictive control. The control device 100 may calculate the AICSO and the TBCSO by, for example, feedforward control or feedback control, separately from the model predictive control, and the calculation method of the AICSO and the TBCSO is not particularly limited.

[0076] 8 , the update unit 140 reads sensitivity information corresponding to the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb from the storage unit 130, based on the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb acquired as observation outputs by the control device 100, and updates one or more coefficients of a prediction equation for a state quantity used in the prediction model, based on the sensitivity information corresponding to the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb. The prediction unit 110 predicts the future state quantity using the prediction model including the updated coefficients, thereby taking the effects of AICSO and TBCSO into consideration. In this case, the state quantities input to the prediction model do not include the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb, and the state quantity acquisition unit 150 acquires, from the fuel flow rate Gf, air flow rate G1, bleed valve flow rate Gai, turbine bypass valve flow rate Gtb, gas turbine output GTMW, turbine inlet temperature T1T, blade path temperature TBP, exhaust gas temperature TEX, and intake temperature T1C acquired by the control device 100 as observation outputs, only the fuel flow rate Gf, air flow rate G1, gas turbine output GTMW, turbine inlet temperature T1T, blade path temperature TBP, and exhaust gas temperature TEX as state quantities to be input to the prediction model.

[0077] 8 , the target value trajectory obtaining unit 160 obtains the target value trajectories of the gas turbine output GTMW and the turbine inlet temperature T1T, but does not obtain the target value trajectory of the intake air temperature T1C. The updating unit 140 formulates an arithmetic expression for the evaluation function V using the target value trajectories obtained by the target value trajectory obtaining unit 160 and the updated prediction model.

[0078] The optimization unit 120 calculates an evaluation function V while acquiring the prediction result of the prediction model, and optimizes the control input so as to determine the control input (here, a combination of the fuel flow rate command CSO and the inlet guide vane opening control command IGVCSO) that minimizes the evaluation function V as the optimal control input. When the optimal control input is determined, the optimization unit 120 outputs the control input (CSO and IGVCSO).

[0079] In the embodiment described using Fig. 7 etc., equations (13) to (15) were shown as examples of prediction formulas for the prediction model, but in the embodiment shown in Fig. 8, as described above, the state quantities and control inputs used in the prediction model are different from those in the embodiment described using Fig. 7 etc. For this reason, in the embodiment shown in Fig. 8, the control device 100 may use, for example, the following equations (17) to (19) as prediction formulas for the prediction model.

[0080]

[0081]

[0082]

[0083] In this case, as shown in equation (17), the performance table serving as sensitivity information read from memory unit 130 may include K_Gf_CSO, K_G1_IGVCSO, K_GTMW_Gf, K_GTMW_G1, K_T1T_Gf, K_T1T_G1, K_TBP_Gf, K_TBP_G1, K_TEX_Gf and K_TEX_G1 as multiple sensitivity coefficients included in the prediction formula of the prediction model.

[0084] 8 , even if the bleed valve flow rate Gai or the turbine bypass valve flow rate Gtb changes, the future state variables of the gas turbine can be accurately predicted using a prediction model that uses coefficients according to the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb, and high control performance can be achieved. In particular, when the movement of the AICSO is relatively small compared to the movements of the other control commands (CSO and IGVCSO), the behavior of the other control commands within the prediction horizon can be ignored, and therefore high control performance can be expected.

[0085] Fig. 9 is a block diagram for explaining another modified example of the functions of the control device 100. In the following, among the functions of the control device 100 shown in Fig. 9, descriptions of parts that overlap with the functions explained using Fig. 8 etc. will be omitted.

[0086] In the embodiment shown in FIG. 9, the basic functions of the control device 100 are the same as those described using FIG. 8 etc., but differ from the embodiment shown in FIG. 8 in that the control device 100 further includes a target value trajectory correction unit 180 in addition to the units shown in FIG. 3.

[0087] 9 , the target value trajectory acquisition unit 160 acquires the target value trajectories of the gas turbine output GTMW and the turbine inlet temperature T1T, but does not acquire the target value trajectory of the intake air temperature T1C. The target value trajectory correction unit 180 acquires a bleed valve flow rate future prediction that indicates the transition of the predicted value of the bleed valve flow rate Gai over the prediction horizon, and a turbine bypass valve flow rate future prediction that indicates the transition of the predicted value of the turbine bypass valve flow rate Gtb over the prediction horizon. The bleed valve flow rate future prediction here may be, for example, the future predicted value of the bleed valve flow rate Gai, the future predicted value of the bleed valve position control command AICSO, or the future predicted value of the ratio of the bleed valve flow rate Gai to the air flow rate G1. Furthermore, the future prediction of the turbine bypass valve flow rate may be, for example, a future predicted value of the turbine bypass valve flow rate Gtb, a future predicted value of the turbine bypass valve position control command TBCSO, or a future predicted value of a turbine bypass ratio (hereinafter referred to as "TB ratio") which is the ratio of the turbine bypass valve flow rate Gtb to the air flow rate G1. The target value trajectory correction unit 180 corrects the target value trajectories of each of the gas turbine output GTMW and the turbine inlet temperature T1T over the prediction horizon, based on the acquired future prediction of the extraction valve flow rate and the future prediction of the turbine bypass valve flow rate.

[0088] 10 and 11 are diagrams for explaining an example of a method for correcting the target value trajectories of the gas turbine output GTMW and the turbine inlet temperature T1T by the target value trajectory correction unit 180.

[0089] As shown in FIG. 10, in the prediction horizon, when the gas turbine output GTMW is constant and the turbine bypass valve flow rate Gtb is constant (when the TB ratio is constant), the target value trajectory of the turbine inlet temperature T1T is also constant.

[0090] In contrast to this, as shown in FIG. 11 , in a case where the TB ratio indicated by the turbine bypass valve flow rate future prediction (the future prediction of the TB ratio in the example shown in the drawing) increases over time in the prediction horizon, the target value trajectory correction unit 180 may perform a correction by adding a positive value to the value of the target value trajectory of the gas turbine output GTMW acquired by the target value trajectory acquisition unit 160, and may perform a correction by adding a negative value to the value of the target value trajectory of the turbine inlet temperature T1T acquired by the target value trajectory acquisition unit 160.

[0091] In this case, the target value trajectory correction unit 180 may correct the target value trajectory of the gas turbine output GTMW based on, for example, the following equation (20): GTMWb(k+i)=GTMWa(k+i)−K_GTMW_Gtb×((Gtb(k+i)−Gtb(k)) (20)

[0092] Here, GTMWb(k+i) is the target value of the gas turbine output GTMW at a time advanced by an arbitrary i control periods from the current time k, and is the target value after correction by the target value trajectory correction unit 180. GTMWe(k+i) is the target value of the gas turbine output GTMW at a time advanced by an arbitrary i control periods from the current time k, and is the target value before correction by the target value trajectory correction unit 180 (i.e., the target value of the gas turbine output GTMW acquired by the target value trajectory acquisition unit 160). K_GTMW_Gtb is the above-mentioned sensitivity coefficient stored in the storage unit 130, and is a coefficient indicating the sensitivity of the gas turbine output to changes in the turbine bypass valve flow rate. Gtb(k+i) is the turbine bypass valve flow rate at a time advanced by an arbitrary i control periods from the current time k, in the future turbine bypass valve flow rate prediction. Gtb(k) is the turbine bypass valve flow rate at the current time k.

[0093] Furthermore, the target value trajectory correction unit 180 may correct the target value trajectory of the turbine inlet temperature T1T based on, for example, the following equation (21): T1Tb(k+i)=T1Ta(k+i)-K_T1T_Gtb×((Gtb(k+i)-Gtb(k)) (21)

[0094] Here, T1Tb(k+i) is the target value of the turbine inlet temperature T1T at a time advanced by an arbitrary i control periods from the current time k, and is the target value after correction by the target value trajectory correction unit 180. T1Ta(k+i) is the target value of the turbine inlet temperature T1T at a time advanced by an arbitrary i control periods from the current time k, and is the target value after correction by the target value trajectory correction unit 180. K_T1T_Gtb is the above-mentioned sensitivity coefficient stored in the storage unit 130, and is a coefficient indicating the sensitivity of the gas turbine output to changes in the turbine bypass valve flow rate. Gtb(k+i) is the turbine bypass valve flow rate at a time advanced by an arbitrary i control periods from the current time k, in the future turbine bypass valve flow rate prediction. Gtb(k) is the turbine bypass valve flow rate at the current time k.

[0095] In the embodiment described with reference to FIGS. 9 to 11 , the optimization unit 120 may optimize the control inputs CSO and IGVCSO based on an evaluation function V (see equation (16)) that depends on the deviation of each of the target value trajectories after correction by the target value trajectory correction unit 180 (i.e., each of the target value trajectories after correction of the gas turbine output and the target value trajectories after correction of the turbine inlet temperature) from the corresponding parameters (i.e., the deviation between the target value trajectory after correction of the gas turbine output and the predicted value of the gas turbine output in the prediction horizon, and the deviation between the target value trajectory after correction of the turbine inlet temperature and the predicted value of the turbine inlet temperature in the prediction horizon).

[0096] 9 to 11 , even if the bleed valve flow rate Gai or the turbine bypass valve flow rate Gtb changes, it is possible to accurately predict the future state variables of the gas turbine 2 using a prediction model that uses coefficients according to the bleed valve flow rate Gai and the turbine bypass valve flow rate Gtb, thereby making it possible to achieve high control performance. Furthermore, even if the fluctuations of the AICSO or TBCSO are relatively large, high control performance can be expected by correcting the target value trajectory of the gas turbine output and the target value trajectory of the turbine inlet temperature based on the future bleed valve flow rate prediction and the future turbine bypass valve flow rate prediction.

[0097] The present disclosure is not limited to the above-described embodiments, and includes modifications of the above-described embodiments and appropriate combinations of these modifications. For example, the gas turbine 2 shown in FIG. 1 includes the extraction pipe 15 and the turbine bypass pipe 18, but the gas turbine 2 may include only one of the extraction pipe 15 and the turbine bypass pipe 18. In other words, the gas turbine 2 may include only the extraction pipe 15 or only the turbine bypass pipe 18 out of the extraction pipe 15 and the turbine bypass pipe 18.

[0098] For example, in the embodiment described with reference to Figures 9 to 11, the target value trajectory correction unit 180 corrects each of the target value trajectory of the gas turbine output GTMW and the target value trajectory of the turbine inlet temperature T1T based on the future prediction of the bleed valve flow rate and the future prediction of the turbine bypass valve flow rate. However, the target value trajectory correction unit 180 may correct the target value trajectory of only one of the gas turbine output GTMW and the turbine inlet temperature T1T based on the future prediction of the bleed valve flow rate and the future prediction of the turbine bypass valve flow rate. That is, the target value trajectory correction unit 180 may correct the target value trajectory of only the gas turbine output GTMW out of the gas turbine output GTMW and the turbine inlet temperature T1T, or may correct the target value trajectory of only the turbine inlet temperature T1T, based on the future prediction of the bleed valve flow rate and the future prediction of the turbine bypass valve flow rate. In this case, the target value trajectory acquisition unit 160 may acquire only the target value trajectory to be corrected out of the target value trajectory of the gas turbine output GTMW and the target value trajectory of the turbine inlet temperature T1T.

[0099] The contents described in each of the above embodiments can be understood, for example, as follows.

[0100] [1] A gas turbine control device (e.g., the above-mentioned control device 100) according to at least one embodiment of the present disclosure is a gas turbine control device for controlling a gas turbine (e.g., the above-mentioned gas turbine 2) including a compressor (e.g., the above-mentioned compressor 3), a combustor (e.g., the above-mentioned combustor 4), and a turbine (e.g., the above-mentioned turbine 5), and includes: a prediction unit (e.g., the above-mentioned prediction unit 110) configured to predict a future state quantity of the gas turbine corresponding to a control input to the gas turbine in a prediction horizon using a prediction model; an optimization unit (e.g., the above-mentioned optimization unit 120) configured to optimize the control input in at least a part of the prediction horizon using a prediction result of the prediction unit; a storage unit (e.g., the above-mentioned storage unit 130) for storing sensitivity information indicating, when a flow rate of compressed air extracted from the compressor is defined as an extraction flow rate, the sensitivity of the control input to a rate of change of the state quantity for each extraction flow rate; an updating unit (for example, the above-described updating unit 140) configured to read out the sensitivity information corresponding to the bleed air flow rate assumed in the prediction horizon from the storage unit, and to update one or more coefficients of a prediction equation for the state quantity used in the prediction model based on the sensitivity information corresponding to the bleed air flow rate.

[0101] According to the gas turbine control device described in [1] above, one or more coefficients of the prediction formula can be updated in accordance with the bleed air flow rate from the compressor. Therefore, even if the bleed air flow rate from the compressor changes, the future state variables of the gas turbine can be accurately predicted using a prediction model that uses coefficients in accordance with the bleed air flow rate, thereby making it possible to achieve high control performance.

[0102] [2] In some embodiments, in the gas turbine control device described in [1] above, the gas turbine further includes a bleed piping (for example, the above-mentioned bleed piping 15) that returns a portion of the compressed air generated by the compressor to the upstream side of the compressor, and a bleed valve (for example, the above-mentioned bleed valve 16) that is provided on the bleed piping, wherein the bleed flow rate includes a bleed valve flow rate that is the flow rate of compressed air bled from the compressor by the bleed piping, and the update unit is configured to update one or more coefficients of a prediction equation for the state quantity used in the prediction model, based on the sensitivity information corresponding to the bleed valve flow rate.

[0103] According to the gas turbine control device described in [2] above, one or more coefficients of the prediction equation can be updated in accordance with the bleed valve flow rate (i.e., the flow rate of compressed air compressed by the compressor and returned to the upstream side of the compressor). Therefore, even if the bleed valve flow rate changes, it is possible to accurately predict the future state variables of the gas turbine, thereby realizing high control performance.

[0104] [3] In some embodiments, the gas turbine control device described in [2] above further comprises a target value trajectory acquisition unit (for example, the above-described target value trajectory acquisition unit 160) configured to acquire a target value trajectory of an output of the gas turbine, wherein the control input includes a bleed valve opening control command for controlling an opening of the bleed valve, and the optimization unit is configured to optimize the control input based on an evaluation function that depends on a deviation between the output of the gas turbine and the target value trajectory.

[0105] According to the gas turbine control device described in [3] above, by using a bleed valve position command as one of the control inputs for approximating the output of the gas turbine to the target value trajectory, it is possible to calculate an optimum control input for approximating the output of the gas turbine to the target value trajectory when the bleed valve is operating, and high controllability can be achieved.

[0106] [4] In some embodiments, in the gas turbine control device according to any one of the above [3], the target value trajectory acquisition unit is configured to acquire target value trajectories of each of an output of the gas turbine, a turbine inlet temperature, and an intake air temperature of the compressor, the state quantities include information indicating an output of the gas turbine, information indicating the turbine inlet temperature, information indicating an intake air temperature of the compressor, and information indicating the bleed valve flow rate, the control inputs include a fuel flow rate command for controlling the flow rate of fuel supplied to the combustor, an inlet guide vane opening control command for controlling an opening of an inlet guide vane of the compressor, and a bleed valve opening control command for controlling the opening of the bleed valve, and the optimization unit is configured to optimize the control inputs based on an evaluation function that depends on deviations of each of the output of the gas turbine, the turbine inlet temperature, and the intake air temperature of the compressor from the target value trajectories.

[0107] According to the gas turbine control device described in the above [4], when controlling the opening of the bleed valve, the fuel flow rate command, the air flow rate command, and the bleed valve opening command can be optimized in consideration of not only the output of the gas turbine and the turbine inlet temperature but also the target value trajectory of the intake air temperature of the compressor, and therefore the control accuracy of the intake air temperature can be improved.

[0108] [5] In some embodiments, in the gas turbine control device described in the above [2], the state quantity does not include information indicating the bleed valve flow rate, and the gas turbine control device is configured to determine a bleed valve position control command for controlling the opening of the bleed valve by a means different from the prediction model.

[0109] According to the gas turbine control device described in [5] above, even if the bleed air flow rate from the compressor changes, it is possible to accurately predict the future state variables of the gas turbine using a prediction model that uses coefficients according to the bleed air flow rate, thereby realizing high control performance. In particular, when the movement of the bleed valve position control command is relatively small compared to the movements of other control commands (for example, a fuel flow rate command and an inlet guide vane position control command), the behavior of the other control commands within the prediction horizon can be ignored, and high control performance can be expected.

[0110] [6] In some embodiments, the gas turbine control device according to any one of [2] or [5] above further comprises: a target value trajectory acquisition unit (for example, the above-described target value trajectory acquisition unit 160) configured to acquire a target value trajectory of at least one parameter of an output of the gas turbine and a turbine inlet temperature among the state quantities; and a target value trajectory correction unit (for example, the above-described target value trajectory correction unit 180) configured to acquire a bleed valve flow rate future prediction indicating a future predicted value related to the bleed valve flow rate, and to correct the target value trajectory of the at least one parameter based on the bleed valve flow rate future prediction, wherein the optimization unit is configured to optimize the control input based on an evaluation function that depends on a deviation between the target value trajectory corrected by the target value trajectory correction unit and the parameter.

[0111] According to the gas turbine control device described in [6] above, even when the fluctuation of the bleed valve position control command is relatively large, high control performance can be expected by correcting the target value trajectory of at least one of the parameters of the gas turbine output and the turbine inlet temperature based on the future prediction of the bleed valve flow rate.

[0112] [7] In some embodiments, in the gas turbine control device described in [1] or [2] above, the gas turbine further includes: a turbine bypass piping (for example, the above-mentioned turbine bypass piping 18) that bypasses the turbine and supplies a portion of the compressed air generated by the compressor to an exhaust side of the turbine; and a turbine bypass valve (for example, the above-mentioned turbine bypass valve 22) provided in the turbine bypass piping, wherein the extracted air flow rate includes a turbine bypass valve flow rate that is the flow rate of compressed air extracted from the compressor by the turbine bypass piping, and the updating unit is configured to update one or more coefficients of a prediction equation for the state quantity used in the prediction model, based on the sensitivity information corresponding to the turbine bypass valve flow rate.

[0113] According to the gas turbine control device described in [7] above, one or more coefficients of the prediction equation can be updated in accordance with the turbine bypass valve flow rate (i.e., the flow rate of compressed air that bypasses the combustor and turbine from the compressor and is supplied to the exhaust side of the turbine). Therefore, even if the turbine bypass valve flow rate changes, it is possible to accurately predict the future state variables of the gas turbine, thereby realizing high control performance.

[0114] [8] In some embodiments, the gas turbine control device described in [7] above further comprises a target value trajectory acquisition unit (e.g., the above-described target value trajectory acquisition unit 160) configured to acquire a target value trajectory of an output of the gas turbine, wherein the control input includes a turbine bypass valve opening control command for controlling an opening of the turbine bypass valve, and the optimization unit is configured to optimize the control input based on an evaluation function that depends on a deviation between the output of the gas turbine and the target value trajectory.

[0115] According to the gas turbine control device described in [8] above, by using a turbine bypass valve position command as one of the control inputs for bringing the output of the gas turbine closer to the target value trajectory, it is possible to calculate an optimal control input for bringing the output of the gas turbine closer to the target value trajectory when the turbine bypass valve is operating, and high controllability can be achieved.

[0116] [9] In some embodiments, in the gas turbine control device described in [8] above, the target value trajectory acquisition unit is configured to acquire target value trajectories for each of an output of the gas turbine and a turbine inlet temperature, the state quantities include information indicating an output of the gas turbine, information indicating the turbine inlet temperature, and information indicating the turbine bypass valve flow rate, the control inputs include a fuel flow rate command for controlling the flow rate of fuel supplied to the combustor, an inlet guide vane opening control command for controlling an opening of an inlet guide vane of the compressor, and a turbine bypass valve opening control command for controlling the opening of the turbine bypass valve, and the optimization unit is configured to optimize the control inputs based on an evaluation function that depends on deviations between the target value trajectories and each of the output of the gas turbine and the turbine inlet temperature.

[0117] According to the gas turbine control device described in [9] above, when controlling the aperture of the turbine bypass valve, the fuel flow rate command, the air flow rate command, and the turbine bypass valve aperture command can be optimized in consideration of the target value trajectories of the gas turbine output and the turbine inlet temperature, and therefore the control accuracy of the turbine inlet temperature can be improved.

[0118]

[10] In some embodiments, in the gas turbine control device described in [7] above, the state quantity does not include information indicating the turbine bypass valve flow rate, and the gas turbine control device is configured to determine a turbine bypass valve position control command for controlling the position of the turbine bypass valve by a means different from the prediction model.

[0119] According to the gas turbine control device described in

[10] above, even if the bleed air flow rate from the compressor changes, it is possible to accurately predict the future state variables of the gas turbine using a prediction model that uses coefficients according to the bleed air flow rate, thereby realizing high control performance. In particular, when the movement of the turbine bypass valve position control command is relatively small compared to the movements of other control commands (e.g., a fuel flow rate command and an inlet guide vane position control command), the behavior of the other control commands within the prediction horizon can be ignored, and high control performance can be expected.

[0120]

[11] In some embodiments, the gas turbine control device according to [7] or

[10] above further comprises: a target value trajectory acquisition unit (for example, the above-described target value trajectory acquisition unit 160) configured to acquire a target value trajectory of at least one parameter of an output of the gas turbine and a turbine inlet temperature from among the state quantities; and a target value trajectory correction unit (for example, the above-described target value trajectory correction unit 180) configured to acquire a turbine bypass valve flow rate future prediction indicating a future predicted value related to the turbine bypass valve flow rate, and to correct the target value trajectory of the at least one parameter based on the turbine bypass valve flow rate future prediction, wherein the optimization unit is configured to optimize the control input based on an evaluation function that depends on a deviation between the target value trajectory corrected by the target value trajectory correction unit and the parameter.

[0121] According to the gas turbine control device described in

[11] above, even when the fluctuation of the turbine bypass valve position control command is relatively large, high control performance can be expected by correcting the target value trajectory of at least one of the parameters of the gas turbine output and the turbine inlet temperature based on the future prediction of the turbine bypass valve flow rate.

[0122]

[12] In some embodiments, the gas turbine control device according to any one of [1] to

[11] above is configured to execute the process of predicting the state quantity, the process of updating the one or more coefficients, and the process of optimizing the control input for each control period.

[0123] According to the gas turbine control device described in

[11] above, the control input is reviewed for each control period, thereby improving prediction accuracy.

[0124]

[13] A gas turbine control input determination method according to at least one embodiment of the present disclosure includes: a prediction step in which a prediction model predicts a future state quantity of the gas turbine (e.g., the above-mentioned gas turbine 2) corresponding to a control input to the gas turbine in a prediction horizon; an optimization step in which the control input is optimized in at least a part of the prediction horizon by using a prediction result of the prediction step; a step in which, when a flow rate of compressed air extracted from a compressor of the gas turbine is defined as an extraction flow rate, a storage unit (e.g., the above-mentioned storage unit 130) stores sensitivity information indicating a sensitivity of the control input to a rate of change of the state quantity for each extraction flow rate; and a step in which, when a flow rate of compressed air extracted from a compressor of the gas turbine is defined as an extraction flow rate, the sensitivity information corresponding to the extraction flow rate is read from the storage unit, and one or more coefficients of a prediction equation for the state quantity used in the prediction model are updated based on the sensitivity information corresponding to the extraction flow rate.

[0125] According to the gas turbine control input determination method described in

[13] above, one or more coefficients of the prediction formula can be updated in accordance with the bleed air flow rate from the compressor. Therefore, even if the bleed air flow rate from the compressor changes, it is possible to accurately predict future state variables of the gas turbine using a prediction model that uses coefficients in accordance with the bleed air flow rate, thereby realizing high control performance.

[0126]

[14] A gas turbine control input determination program according to at least one embodiment of the present disclosure causes a computer to execute the following steps: predicting a future state quantity of the gas turbine corresponding to a control input to the gas turbine in a prediction horizon using a prediction model; optimizing the control input in at least a part of the prediction horizon using a prediction result of the prediction step; storing sensitivity information in a storage unit (for example, the above-mentioned storage unit 130) indicating the sensitivity of the control input to a rate of change of the state quantity, for each bleed air flow rate, where the flow rate of compressed air bled from a compressor of the gas turbine is defined as the bleed air flow rate; and reading out the sensitivity information corresponding to the bleed air flow rate expected in the prediction horizon from the storage unit, and updating one or more coefficients of a prediction equation for the state quantity used in the prediction model based on the sensitivity information corresponding to the bleed air flow rate.

[0127] According to the gas turbine control input determination program described in the above

[14] , one or more coefficients of the prediction formula can be updated in accordance with the bleed air flow rate from the compressor. Therefore, even if the bleed air flow rate from the compressor changes, it is possible to accurately predict future state variables of the gas turbine using a prediction model that uses coefficients in accordance with the bleed air flow rate, thereby realizing high control performance.

[0128] REFERENCE SIGNS LIST 1 Gas turbine system 2 Gas turbine 3 Compressor 4 Combustor 5 Turbine 7 Generator 8A, 8B Rotating shaft 9 Inlet guide vane 10 Intake equipment 12 Fuel supply line 13, 17, 24, 30 Flow meter 14 Fuel flow control valve 15 Bleed piping 16 Bleed valve 18 Turbine bypass piping 20 Turbine exhaust piping 22 Turbine bypass valve 26, 28, 32, 36 Thermometer 34 Output meter 35 Actuator 72 Processor 74 RAM 76 ROM 78 HDD 80 Input I / F 82 Output I / F 84 Bus 100 Control device 110 Prediction unit 120 Optimization unit 130 Storage unit 140 Update unit 150 State quantity acquisition unit 160 Target value trajectory acquisition unit 170 Table update unit 180 Target value trajectory correction unit

Claims

1. A gas turbine control device for controlling a gas turbine having a compressor, a combustor, and a turbine, comprising: a prediction unit configured to predict a future state quantity of the gas turbine corresponding to a control input to the gas turbine in a prediction horizon using a prediction model; an optimization unit configured to optimize the control input in at least a part of the prediction horizon using a prediction result of the prediction unit; a memory unit for storing sensitivity information indicating, for each bleed air flow rate, the sensitivity of the control input to a rate of change of the state quantity, where the flow rate of compressed air bled from the compressor is defined as an bleed air flow rate; and an update unit configured to read out from the memory unit the sensitivity information corresponding to the bleed air flow rate assumed in the prediction horizon, and update one or more coefficients of a prediction equation for the state quantity used in the prediction model, based on the sensitivity information corresponding to the bleed air flow rate.

2. The gas turbine control device according to claim 1, further comprising: an bleed piping for returning a portion of the compressed air generated by the compressor to the upstream side of the compressor; and an bleed valve provided in the bleed piping, wherein the bleed flow rate includes an bleed valve flow rate which is the flow rate of compressed air bled from the compressor by the bleed piping, and the update unit is configured to update one or more coefficients of a prediction equation for the state quantity used in the prediction model based on the sensitivity information corresponding to the bleed valve flow rate.

3. A gas turbine control device as described in claim 2, further comprising a target value trajectory acquisition unit configured to acquire a target value trajectory of an output of the gas turbine, wherein the control input includes an extraction valve opening control command for controlling an opening of the extraction valve, and the optimization unit is configured to optimize the control input based on an evaluation function that depends on a deviation between the output of the gas turbine and the target value trajectory.

4. A gas turbine control device as described in claim 3, wherein the target value trajectory acquisition unit is configured to acquire target value trajectories for each of the gas turbine output, turbine inlet temperature and intake air temperature of the compressor, the state quantities include information indicating the gas turbine output, information indicating the turbine inlet temperature, information indicating the compressor intake air temperature and information indicating the bleed valve flow rate, the control inputs include a fuel flow rate command for controlling the flow rate of fuel supplied to the combustor, an inlet guide vane opening control command for controlling the opening of an inlet guide vane of the compressor and an bleed valve opening control command for controlling the opening of the bleed valve, and the optimization unit is configured to optimize the control inputs based on an evaluation function that depends on a deviation between each of the gas turbine output, turbine inlet temperature and intake air temperature of the compressor and the target value trajectories.

5. A gas turbine control device as described in claim 2, wherein the state quantity does not include information indicating the bleed valve flow rate, and the gas turbine control device is configured to determine a bleed valve opening control command for controlling the opening of the bleed valve by a means other than the prediction model.

6. A gas turbine control device as claimed in claim 2 or 5, further comprising: a target value trajectory acquisition unit configured to acquire a target value trajectory of at least one parameter of an output of the gas turbine and a turbine inlet temperature among the state quantities; and a target value trajectory correction unit configured to acquire a future bleed valve flow rate prediction indicating a future predicted value of the bleed valve flow rate, and to correct the target value trajectory of the at least one parameter based on the future bleed valve flow rate prediction, wherein the optimization unit is configured to optimize the control input based on an evaluation function that depends on a deviation between the target value trajectory corrected by the target value trajectory correction unit and the parameter.

7. The gas turbine control device according to claim 1, further comprising: a turbine bypass piping that bypasses the turbine and supplies a portion of the compressed air generated by the compressor to an exhaust side of the turbine; and a turbine bypass valve provided in the turbine bypass piping, wherein the extraction flow rate includes a turbine bypass valve flow rate that is the flow rate of compressed air extracted from the compressor by the turbine bypass piping, and the update unit is configured to update one or more coefficients of a prediction equation for the state quantity used in the prediction model based on the sensitivity information corresponding to the turbine bypass valve flow rate.

8. A gas turbine control device as described in claim 7, further comprising a target value trajectory acquisition unit configured to acquire a target value trajectory of an output of the gas turbine, wherein the control input includes a turbine bypass valve opening control command for controlling an opening of the turbine bypass valve, and the optimization unit is configured to optimize the control input based on an evaluation function that depends on a deviation between the output of the gas turbine and the target value trajectory.

9. A gas turbine control device as described in claim 8, wherein the target value trajectory acquisition unit is configured to acquire target value trajectories for each of the gas turbine output and turbine inlet temperature, the state quantities include information indicating the gas turbine output, information indicating the turbine inlet temperature, and information indicating the turbine bypass valve flow rate, the control inputs include a fuel flow rate command for controlling the flow rate of fuel supplied to the combustor, an inlet guide vane opening control command for controlling the opening of an inlet guide vane of the compressor, and a turbine bypass valve opening control command for controlling the opening of the turbine bypass valve, and the optimization unit is configured to optimize the control inputs based on an evaluation function that depends on a deviation between each of the gas turbine output and turbine inlet temperature and the target value trajectory.

10. A gas turbine control device as described in claim 7, wherein the state quantity does not include information indicating the turbine bypass valve flow rate, and the gas turbine control device is configured to determine a turbine bypass valve opening control command for controlling the opening of the turbine bypass valve by a means other than the prediction model.

11. A gas turbine control device as claimed in claim 7 or 10, further comprising: a target value trajectory acquisition unit configured to acquire a target value trajectory of at least one parameter of the gas turbine output and turbine inlet temperature among the state quantities; and a target value trajectory correction unit configured to acquire a turbine bypass valve flow rate future prediction indicating a future predicted value of the turbine bypass valve flow rate, and to correct the target value trajectory of the at least one parameter based on the turbine bypass valve flow rate future prediction, wherein the optimization unit is configured to optimize the control input based on an evaluation function that depends on a deviation between the target value trajectory corrected by the target value trajectory correction unit and the parameter.

12. A gas turbine control device according to claim 1, configured to execute the process of predicting the state quantity, the process of updating the one or more coefficients, and the process of optimizing the control input every control period.

13. A gas turbine control input determination method comprising: a prediction step in which a prediction model predicts a future state quantity of the gas turbine corresponding to a control input to the gas turbine in a prediction horizon; an optimization step in which the control input in at least a part of the prediction horizon is optimized using a prediction result in the prediction step; a step in which, when the flow rate of compressed air extracted from a compressor of the gas turbine is defined as an extraction flow rate, a memory unit stores sensitivity information indicating the sensitivity of the control input to a rate of change of the state quantity for each extraction flow rate; and a step in which the sensitivity information corresponding to the extraction flow rate assumed in the prediction horizon is read from the memory unit, and one or more coefficients of a prediction equation for the state quantity used in the prediction model are updated based on the sensitivity information corresponding to the extraction flow rate.

14. A gas turbine control input determination program that causes a computer to execute the following steps: predicting a future state quantity of the gas turbine corresponding to a control input to the gas turbine in a prediction horizon using a prediction model; optimizing the control input in at least a part of the prediction horizon using a prediction result in the prediction step; storing in a memory unit sensitivity information indicating, for each bleed air flow rate, the sensitivity of the control input to the rate of change of the state quantity, where the flow rate of compressed air bled from a compressor of the gas turbine is defined as an bleed air flow rate; and reading out from the memory unit the sensitivity information corresponding to the bleed air flow rate assumed in the prediction horizon, and updating one or more coefficients of a prediction equation for the state quantity used in the prediction model based on the sensitivity information corresponding to the bleed air flow rate.

Citation Information

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