Control device, control method, and system

KR103013247B1Active Publication Date: 2026-09-01MITSUBISHI POWER LTD
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Patent Information

Application Number
KR1020247014533
Authority / Receiving Office
KR · KR
Patent Type
Patents
Current Assignee / Owner
Priority Date
2021-11-30
Filing Date
2022-09-27
Publication Date
2026-09-01
Estimated Expiration
2042-09-27

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Patent Text Reader

Abstract

The control device comprises an acquisition unit that acquires, as a first inlet pressure, the pressure value of the first steam on the first inlet side as viewed from the first control valve of a first turbine that rotates using the first steam supplied from the first inlet through the first control valve, and as a second inlet pressure, the pressure value of the second steam on the second inlet side as viewed from the second control valve of a second turbine that rotates on the same rotational axis as the first turbine using the second steam supplied from the second inlet through the second control valve, and a control unit that controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure.
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Description

Technology Field

[0001] The present disclosure relates to a control device, a control method, and a system. The present application claims priority based on Japanese Patent Application No. 2021-194470 filed on November 30, 2021, and incorporates the contents thereof herein. Background Technology

[0002] In the case of an extraction or mixed-pressure steam turbine, there is a problem of suppressing the thrust force applied to the rotor to within an allowable value (see, for example, Patent Document 1). Prior art literature

[0003] International Publication No. 2018 / 167907 The problem to be solved

[0004] The present disclosure is made to solve the above problem and aims to provide a control device, a control method, and a system capable of controlling the thrust force in a steam turbine within an allowable value. means of solving the problem

[0005] To solve the above problem, the control device according to the present disclosure comprises: an acquisition unit that acquires, as a first inlet pressure, the pressure value of the first steam on the first inlet side as viewed from the first control valve of a first turbine that rotates using the first steam supplied from the first inlet through the first control valve, and as a second inlet pressure, the pressure value of the second steam on the second inlet side as viewed from the second control valve of a second turbine that rotates on the same rotational axis as the first turbine using the second steam supplied from the second inlet through the second control valve; and a control unit that controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure.

[0006] A control method according to the present disclosure comprises the steps of: acquiring a pressure value of the first steam on the first inlet side as a first inlet pressure, viewed from the first control valve of a first turbine that rotates using the first steam supplied from the first inlet through the first control valve; acquiring a pressure value of the second steam on the second inlet side as a second inlet pressure, viewed from the second control valve of a second turbine that rotates on the same axis of rotation as the first turbine using the second steam supplied from the second inlet through the second control valve; and controlling the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure.

[0007] A system according to the present disclosure comprises a first control valve, a second control valve, a first turbine that rotates using first steam supplied from a first inlet through the first control valve, a second turbine that rotates on the same axis of rotation as the first turbine using second steam supplied from a second inlet through the second control valve, an acquisition unit that acquires a pressure value of the first steam on the first inlet side as a first inlet pressure as viewed from the first control valve, and acquires a pressure value of the second steam on the second inlet side as a second inlet pressure as viewed from the second control valve, and a control unit that controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure. Effects of the invention

[0008] According to the control device, control method, and system of the present disclosure, the thrust force in a steam turbine can be controlled within an allowable value. Brief explanation of the drawing

[0009] FIG. 1 is a schematic diagram of a system relating to a first embodiment of the present disclosure. FIG. 2 is a schematic diagram illustrating an example of operation of a control device according to a first embodiment of the present disclosure. FIG. 3 is a block diagram for explaining an example of the configuration of a control device according to a first embodiment of the present disclosure. FIG. 4 is a block diagram for explaining an example of the configuration of a control device according to a first embodiment of the present disclosure. FIG. 5 is a schematic diagram illustrating an example of operation of a control device according to a first embodiment of the present disclosure. FIG. 6 is a schematic diagram illustrating an example of operation of a control device according to a first embodiment of the present disclosure. FIG. 7 is a schematic diagram illustrating an example of operation of a control device according to a second embodiment of the present disclosure. FIG. 8 is a flowchart showing an example of operation of a control device according to a second embodiment of the present disclosure. FIG. 9 is a schematic diagram illustrating a control device according to a third embodiment of the present disclosure. FIG. 10 is a schematic block diagram showing the configuration of a computer according to at least one embodiment. Specific details for implementing the invention

[0010] Hereinafter, a control device, a control method, and a system relating to an embodiment of the present disclosure will be described with reference to the drawings. Additionally, in each drawing, the same reference numerals are used for identical or corresponding components, and descriptions are appropriately omitted.

[0011] <First Embodiment>

[0012] (System and control unit)

[0013] With reference to FIGS. 1 to 6, the configuration and operation examples of a system and control device according to the first embodiment of the present disclosure will be described. FIG. 1 is a schematic diagram of a system according to the first embodiment of the present disclosure. FIGS. 2 and FIGS. 5 to 6 are schematic diagrams for explaining operation examples of a control device according to the first embodiment of the present disclosure. FIGS. 3 and 4 are block diagrams for explaining configuration examples of a control device according to the first embodiment of the present disclosure.

[0014] FIG. 1 shows an example of a schematic diagram when a system according to the first embodiment of the present disclosure is applied to a gas turbine combined cycle power generation plant (GTCC). The system (1) shown in FIG. 1 comprises a gas turbine (10), a heat recovery boiler (20), a steam turbine (30), a generator (34), a condenser (35), and a control device (100). The steam turbine (30) comprises a high-pressure steam turbine (31), a medium-pressure steam turbine (32), and a low-pressure steam turbine (33), and a rotating shaft (36) for each turbine (31, 32 and 33). The generator (34) is driven by each turbine (10, 31, 32 and 33) to generate power. The condenser (35) returns the steam exhausted from the low-pressure steam turbine (33), etc., back into water.

[0015] The gas turbine (10) is equipped with a compressor (11), a combustor (12), a turbine (13), a fuel flow control valve (14), and a rotating shaft (15). The compressor (11) compresses outside air to produce compressed air. The combustor (12) mixes compressed air with fuel gas and combusts it to produce high-temperature combustion gas. The turbine (13) is driven by the combustion gas. The fuel flow control valve (14) controls the fuel flow supplied to the combustor (12). The rotating shaft (15) is the rotating shaft of the compressor (11) and the turbine (13). A fuel line is connected to the combustor (12) to supply fuel from a fuel source to the combustor (12). A fuel flow control valve (14) is provided in this fuel line. The exhaust port of the turbine (13) is connected to the heat recovery boiler (20) and the exhaust line (56).

[0016] The heat recovery boiler (20) is equipped with a high-pressure steam generating unit (21), a medium-pressure steam generating unit (22), a reheating unit (23), and a low-pressure steam generating unit (24). The heat recovery boiler (20) generates steam using the heat of exhaust gas exhausted from a gas turbine (10). The high-pressure steam generating unit (21) is equipped with a drum (21a) and a heat exchanger (21b) and generates high-pressure steam supplied to a high-pressure steam turbine (31). The medium-pressure steam generating unit (22) is equipped with a drum (22a) and a heat exchanger (22b) and generates medium-pressure steam supplied to a medium-pressure steam turbine (32). The reheating unit (23) heats the steam exhausted from the medium-pressure steam generating unit (22), etc. The low-pressure steam generating unit (24) is equipped with a drum (24a) and a heat exchanger (24b) and generates low-pressure steam to be supplied to a low-pressure steam turbine (33).

[0017] The steam inlet (311) of the high-pressure steam generator (21) and the high-pressure steam turbine (31) is connected to a high-pressure main steam line (41) that directs high-pressure steam to the high-pressure steam turbine (31) via a high-pressure steam stop valve (42) and a high-pressure main steam increase / decrease valve (43). The high-pressure main steam line (41) is connected to a medium-pressure main steam line (62) via a high-pressure steam turbine bypass valve (63). The steam outlet of the high-pressure steam turbine (31) is connected to a medium-pressure main steam line (44) via a backflow prevention valve (64) and is also connected to a condenser (35) via a ventilator valve (66). The medium-pressure main steam line (44) joins the medium-pressure main steam line (61) from the medium-pressure steam generator (22) at the steam inlet side of the reheating unit (23). The steam outlet side of the reheating section (23) is connected to the steam inlet (321) of the medium-pressure steam turbine (32) via the medium-pressure main steam line (62), the medium-pressure steam stop valve (45), and the medium-pressure main steam increase / decrease valve (46). The medium-pressure main steam line (62) is connected to the condenser (35) via the medium-pressure steam turbine bypass valve (65). The steam inlet (331) of the low-pressure steam turbine (33) is connected to the steam outlet of the medium-pressure steam turbine (32) via the medium-pressure turbine exhaust line (54), and is also connected to the low-pressure steam generation section (24) and the low-pressure main steam line (51) that guides low-pressure steam to the low-pressure steam turbine (33) via the low-pressure steam stop valve (52) and the low-pressure main steam increase / decrease valve (53). A condenser (35) is connected to the steam outlet of the low-pressure steam turbine (33). A feedwater line (55) is connected to the condenser (35) to guide the condensate to the heat recovery boiler (20).

[0018] The high-pressure main steam control valve (43) adjusts the amount of steam flowing into the high-pressure steam turbine (31) under the control of the control device (100). The medium-pressure main steam control valve (46) adjusts the amount of steam flowing into the medium-pressure steam turbine (32) under the control of the control device (100). The low-pressure main steam control valve (53) adjusts the amount of steam flowing into the low-pressure steam turbine (33) under the control of the control device (100). In addition, the high-pressure main steam control valve (43), the medium-pressure main steam control valve (46), and the low-pressure main steam control valve (53) adjust the valve opening based on the valve opening command value (hereinafter referred to as the valve opening command value) sent from the control device (100).

[0019] A pressure gauge (71) for measuring high-pressure steam is provided on the upstream side of the high-pressure main steam control valve (43). A pressure gauge (72) for measuring reduced-pressure steam is provided on the downstream side of the high-pressure main steam control valve (43). The pressure gauge (72) measures the pressure value of the high-pressure steam on the steam inlet (311) side as viewed from the high-pressure main steam control valve (43). A pressure gauge (73) for measuring medium-pressure main steam is provided on the upstream side of the medium-pressure main steam control valve (46). A pressure gauge (74) for measuring reduced-pressure medium-pressure steam is provided on the downstream side of the medium-pressure main steam control valve (46). The pressure gauge (74) measures the pressure value of the medium-pressure steam on the steam inlet (321) side as viewed from the medium-pressure main steam control valve (46). A pressure gauge (75) for measuring low-pressure main steam is provided on the upstream side of the low-pressure main steam control valve (53). A pressure gauge (76) for measuring reduced low-pressure steam is provided on the downstream side of the low-pressure main steam control valve (53). The pressure gauge (76) measures the pressure value of the low-pressure steam on the steam inlet (331) side as viewed from the low-pressure main steam control valve (53).

[0020] In addition, in the following description and drawings, the pressure value of the high-pressure steam on the steam inlet (311) side measured by the pressure gauge (72) is also referred to as the HPST inlet pressure. Also, the pressure value of the medium-pressure steam on the steam inlet (321) side measured by the pressure gauge (74) is also referred to as the IPST inlet pressure. Also, the high-pressure main steam control valve (43) is also referred to as the HPCV. Also, the medium-pressure main steam control valve (46) is also referred to as the IPCV. Furthermore, the high-pressure main steam control valve (43) and the medium-pressure main steam control valve (46) are also referred to as the HP governor valve and the IP governor valve, respectively. Also, HPST is an abbreviation for high-pressure steam turbine. IPST is an abbreviation for medium-pressure steam turbine. HPCV is an abbreviation for high-pressure steam control valve. IPCV is an abbreviation for medium-pressure steam control valve.

[0021] In addition, the system (1) is equipped with multiple sensors not shown that measure the temperature, pressure, flow rate, rotation speed, etc. of each part.

[0022] The control device (100) is composed of a computer and peripheral devices of the computer, and is a functionally configured combination of hardware such as a computer and software such as a program executed by the computer, and is equipped with an acquisition unit (101) and a control unit (102). The acquisition unit (101) acquires measurement values ​​of various sensors such as pressure gauges (71-76). The control unit (102) controls each part of the system (1) according to the acquisition results of the acquisition unit (101). In this embodiment, the control unit (102) adjusts the valve opening of the HPCV and the valve opening of the IPCV according to the HPST inlet pressure and the IPST inlet pressure, for example. Additionally, the control unit (102) receives various operation data or instruction data, and generates power using the generator (34) by controlling the output of the gas turbine (10), controlling the opening and closing of the high-pressure steam stop valve (42), controlling the valve opening of the high-pressure main steam increase / decrease valve (43), controlling the opening and closing of the medium-pressure steam stop valve (45), controlling the valve opening of the medium-pressure main steam increase / decrease valve (46), controlling the opening and closing of the low-pressure steam stop valve (52), and controlling the valve opening of the low-pressure main steam increase / decrease valve (53), etc. In addition, if a load cutoff occurs due to any abnormality, the control device (100) performs various controls at the time of load cutoff.

[0023] (Overview of Steam Turbine Control)

[0024] The GTCC generates power by converting feedwater in drums (21a, 22a and 24a) into steam using the thermal energy of the exhaust gas from the gas turbine (10) and passing it through the steam turbine (30). The steam turbine (30) is composed of a high-pressure (HP) steam turbine (31), a medium-pressure (IP) steam turbine (32), and a low-pressure (LP) steam turbine (33). In particular, if the pressure of the high-pressure steam turbine (31) and the medium-pressure steam turbine (32) is not balanced, thrust is compressed on the high-pressure side or the medium-pressure side, and in the worst case, this leads to thrust burnout and requires a huge cost for replacement. A sudden deviation in HPST inlet pressure and IPST inlet pressure occurs, for example, due to the closing operation of the ventilator valve (66) during the startup of the steam turbine (30) or the abnormal opening operation of the high-pressure steam turbine bypass valve (63) or the medium-pressure steam turbine bypass valve (65). Normally, the control device (100) monitors, for example, the main steam pressure (for example, the pressure upstream of the high-pressure main steam increase / decrease valve (43)) and performs pressure control to achieve a target steam pressure determined from the load of the gas turbine (10), etc. In this case, for example, when the medium-pressure main steam rises above the target value due to the closing operation of the ventilator valve (66), the high-pressure main steam increase / decrease valve (43) is opened to lower the main steam pressure. Then, steam exhausted from the steam outlet of the high-pressure steam turbine (31) passes through the medium-pressure main steam line (44 and 64) and reaches the steam inlet (321). In this state, the IPST inlet pressure rises, and thrust unbalance occurs.

[0025] Accordingly, in this embodiment, the control device (100) controls the valve opening of the HPCV and the valve opening of the IPCV by changing the upper limit value of the valve opening command value so that the balance between the HPST inlet pressure and the IPST inlet pressure falls within an allowable range. FIG. 2 shows an overview of the control according to the HPST inlet pressure and the IPST inlet pressure by the control device (100). FIG. 2 takes the HPST inlet pressure on the horizontal axis and the IPST inlet pressure on the vertical axis, and shows the corresponding relationship between the HPST inlet pressure and the IPST inlet pressure, where the thrust force applied to the rotation shaft (36) becomes appropriate, as a balance characteristic using a dashed line. In FIG. 2, the blank area A1 is the desired operating area, and the hatched areas A2 and A3 are the thrust unbalanced areas. In the upper area A2 of FIG. 2, the IPST inlet pressure is excessive, and in the lower area A3, the HPST inlet pressure is excessive. The control device (100) operates with a target operating balance (aiming for the balance characteristics in the drawing) by narrowing the IPCV in the upper IPST inlet pressure excess region A2 and narrowing the HPCV in the lower HPST inlet pressure excess region A3.

[0026] Additionally, region A1 shown in FIG. 2 is a range for the corresponding relationship between HPST inlet pressure and IPST inlet pressure based on the balance characteristic of the corresponding relationship between HPST inlet pressure and IPST inlet pressure, which ensures that the thrust force applied to the rotation shaft (36) is appropriate. In this case, region A1 (range) is a region sandwiched between the upper boundary line B_IPST and the lower boundary line B_HPST when represented by an orthogonal coordinate system with the horizontal axis representing HPST inlet pressure and the vertical axis representing IPST inlet pressure. Furthermore, the control device (100) adjusts the valve opening of the HPCV and the valve opening of the IPCV based on the HPST inlet pressure and the IPST inlet pressure, using region A1 (range) as a reference. At this time, the control device (100) adjusts the valve opening of the IPCV based on the upper boundary line B_IPST side of region A1 and adjusts the valve opening of the HPCV based on the lower boundary line B_HPST side.

[0027] In addition, the characteristics or regions shown in Fig. 2 may be represented with the IPST inlet pressure as the horizontal axis and the HPST inlet pressure as the vertical axis. In that case, the upper boundary line and the lower boundary line are reversed.

[0028] Hereinafter, with reference to FIGS. 3 and FIGS. 4, an example configuration of the control unit (102) is described. FIGS. 3 shows an example configuration of a calculation unit (200) that calculates a valve opening command value of an HPCV. FIGS. 4 shows an example configuration of a calculation unit (400) that calculates a valve opening command value of an IPCV. The control unit (102) shown in FIGS. 1 includes the calculation unit (200) shown in FIGS. 3 and the calculation unit (400) shown in FIGS. 4.

[0029] The calculation unit (200) shown in FIG. 3 includes a valve opening upper limit value calculation unit (210), a valve opening calculation unit (220), and a minimum value selector (230).

[0030] The valve opening calculation unit (220) includes a subtractor (221), a PI controller (proportional-integral controller) (222), and a maximum value selector (224). The subtractor (221) calculates the deviation of the HP main steam pressure from the target value by subtracting the high-pressure main steam pressure (HP main steam pressure) from the high-pressure main steam target pressure (HP main steam target pressure). The PI controller (222) calculates the valve opening command value of the HPCV by PI operation (proportional-integral operation) using the deviation calculated by the subtractor (221) as input. Additionally, the range of the valve opening command value is 0 to 100. Furthermore, the maximum value selector (224) outputs the larger value between "0" (223) and the calculated value of the PI controller (222). The maximum value selector (224) outputs the output value of the PI controller (222) when the output value of the PI controller (222) is 0 or greater. The HP main steam target pressure is determined, for example, from the load of the gas turbine (10) as described above. The HP main steam pressure is the upstream pressure of the high-pressure main steam increase / decrease valve (43) measured by the pressure gauge (71). The valve opening calculation unit (220) adjusts the HPCV valve opening command value so that the difference between the HP main steam target pressure and the HP main steam pressure is eliminated by feedback control. In addition, the control element is not limited to PI operation, but may be replaced with a control element using a PID operation (proportional-integral-derivative operation) or a model such as a machine learning model.

[0031] The valve opening upper limit value calculation unit (210) includes an HPST inlet pressure threshold value calculation unit (211), a subtractor (212), and a PI controller (213). The valve opening upper limit value calculation unit (210) calculates the upper limit value of the HPCV valve opening. The valve opening upper limit value calculated by the valve opening upper limit value calculation unit (210) and the HPCV valve opening command value calculated by the valve opening calculation unit (220) are input to a minimum value selector (230), and the smaller value is output. Accordingly, the HPCV valve opening command value output by the calculation unit (200) is limited to the valve opening upper limit value calculated by the valve opening upper limit value calculation unit (210).

[0032] The HPST inlet pressure threshold value calculation unit (211) calculates the HPST inlet pressure threshold value based on the respective measured values ​​of the IPST inlet pressure and the HPST inlet pressure, using the boundary line B_HPST, which is the reference for controlling the valve opening of the HPCV described with reference to FIG. 2. The HPST inlet pressure threshold value serves as a reference for determining whether or not to initiate upper limit control (PI control), and also serves as a target value for the HPST input pressure when controlling the upper limit. The HPST inlet pressure threshold value calculation unit (211), for example as shown in FIG. 5, calculates the HPST inlet pressure corresponding to the intersection point C10 with the boundary line B_HPST as the HPST inlet pressure threshold value when the IPST inlet pressure is PL1.

[0033] The subtractor (212) calculates the deviation of the HPST inlet pressure relative to the HPST inlet pressure threshold value by subtracting the HPST inlet pressure from the HPST inlet pressure threshold value. The PI controller (213) calculates the upper limit value of the HPCV valve opening by PI operation (proportional-integral operation) using the deviation calculated by the subtractor (212) as input. Additionally, the control element is not limited to PI operation and may be replaced with a control element using PID operation (proportional-integral-derivative operation) or a model such as a machine learning model.

[0034] As described above, the minimum value selector (230) inputs the valve opening upper limit value calculated by the valve opening upper limit value calculation unit (210) and the valve opening command value of the HPCV calculated by the valve opening upper limit value calculation unit (220), and outputs the smaller value.

[0035] The calculation unit (400) shown in FIG. 4 includes a valve opening upper limit value calculation unit (410), a valve opening calculation unit (420), and a minimum value selector (430).

[0036] The valve opening calculation unit (420) includes a subtractor (421), a PI controller (proportional-integral controller) (422), and a maximum value selector (424). The subtractor (421) calculates the deviation of the IP main steam pressure from the target value by subtracting the medium pressure main steam pressure (IP main steam pressure) from the medium pressure main steam target pressure (IP main steam target pressure). The PI controller (422) calculates the valve opening command value of the IPCV by PI operation using the deviation calculated by the subtractor (421) as input. Additionally, the range of the valve opening command value is 0 to 100. Furthermore, the maximum value selector (424) outputs the larger of "0" (423) and the calculated value of the PI controller (422). The maximum value selector (424) outputs the calculated value of the PI controller (422) when the calculated value of the PI controller (422) is 0 or greater. The IP main steam target pressure is determined, for example, from the load of the gas turbine (10). The IP main steam pressure is the upstream pressure of the medium pressure main steam increase / decrease valve (46) measured by the pressure gauge (73). The valve opening calculation unit (420) adjusts the IPCV valve opening command value by feedback control so that the difference between the IP main steam target pressure and the IP main steam pressure is eliminated. In addition, the control element is not limited to PI operation, but may be replaced with a control element using PID operation or a model such as a machine learning model.

[0037] The valve opening upper limit value calculation unit (410) includes an IPST inlet pressure threshold value calculation unit (411), a subtractor (412), and a PI controller (413). The valve opening upper limit value calculation unit (410) calculates the upper limit value of the IPCV valve opening. The valve opening upper limit value calculated by the valve opening upper limit value calculation unit (410) and the valve opening command value of the IPCV calculated by the valve opening calculation unit (420) are input to a minimum value selector (430), and the smaller value is output. Accordingly, the valve opening command value of the IPCV output by the calculation unit (400) is limited to the valve opening upper limit value calculated by the valve opening upper limit value calculation unit (410).

[0038] The IPST inlet pressure threshold value calculation unit (411) calculates the IPST inlet pressure threshold value based on the respective measured values ​​of the IPST inlet pressure and HPST inlet pressure, using the boundary line B_IPST, which is the reference for controlling the valve opening of the IPCV described with reference to FIG. 2. The IPST inlet pressure threshold value serves as a reference for determining whether or not to initiate upper limit control (PI control), and also serves as a target value for the IPST input pressure when controlling the upper limit. The IPST inlet pressure threshold value calculation unit (411), for example as shown in FIG. 6, calculates the IPST inlet pressure corresponding to the intersection point C20 with the boundary line B_IPST as the IPST inlet pressure threshold value when the HPST inlet pressure is PH1.

[0039] The subtractor (412) calculates the deviation of the IPST inlet pressure relative to the IPST inlet pressure threshold by subtracting the IPST inlet pressure from the IPST inlet pressure threshold. The PI controller (413) calculates the upper limit of the valve opening of the IPCV by using the deviation calculated by the subtractor (412) as input and by the PI operation (proportional-integral operation). In addition, the control element is not limited to the PI operation and may be replaced with a control element using a PID operation (proportional-integral-derivative operation) or a model such as a machine learning model.

[0040] As described above, the minimum value selector (430) inputs the valve opening upper limit value calculated by the valve opening upper limit value calculation unit (410) and the valve opening command value of the IPCV calculated by the valve opening upper limit value calculation unit (420), and outputs the smaller value.

[0041] (Actions / Effects)

[0042] As described above, according to the control device, control method, and system of the present disclosure, the valve opening of the HPCV and the valve opening of the IPCV can be adjusted so that the correspondence between the HPST inlet pressure and the IPST inlet pressure is appropriate, and thus the thrust force caused by the imbalance between the HPST inlet pressure and the IPST inlet pressure in the steam turbine (30) can be controlled within an allowable value.

[0043] In addition, according to the present embodiment, for example, when starting the steam turbine (30), even if the pressure in the system rises (or falls) transiently and the balance becomes unbalanced due to load cutoff, runback, load change, ventilator valve closing operation, or abnormal opening of the HP turbine bypass valve, the operation of the ST can continue with a normal thrust balance.

[0044] <Second Embodiment>

[0045] With reference to FIGS. 7 and 8, a control device according to a second embodiment of the present disclosure will be described. FIG. 7 is a schematic diagram illustrating an example of operation of a control device according to a second embodiment of the present disclosure. FIG. 8 is a flowchart showing an example of operation of a control device according to a second embodiment of the present disclosure.

[0046] The configuration of the system (1) according to the second embodiment is basically the same as the configuration of the system (1) according to the first embodiment. However, in the second embodiment, the operation of the control unit (102) provided by the control device (100) shown in FIG. 1 is partially different from that of the first embodiment.

[0047] Referring to FIG. 7, an example of the operation of the control unit (102) of the control device (100) of the second embodiment is described. In the second embodiment, the control unit (102) selects one of three different modes, (1) normal control, (2) back pressure control standby, and (3) back pressure control, and adjusts the upper limit value of the HPCV valve opening and the upper limit value of the IPCV valve opening. FIG. 7 shows an example of the time change of the upper limit value of the HPCV opening command value, the HPCV opening command value, and the HPST inlet pressure when the gas turbine (10) starts. In the example shown in FIG. 7, after starting, the mode changes in the order of (1) normal control, (2) back pressure control standby, and (3) back pressure control. In addition, the back pressure control is a control that adjusts the upper limit value based on the HPST inlet pressure, which is the pressure on the downstream side of the HPCV, and is identical to the upper limit control of the first embodiment. Control based on the pressure on the downstream side of the HPCV is referred to as back pressure control. Furthermore, regarding the control of the upper limit value of the IPCV opening command value, it is identical to the control of the upper limit value of the HPCV opening command value, and the control of the upper limit value of the HPCV opening command value will be explained below as an example.

[0048] (1) Normal control: When the steam turbine (30) starts, the amount of heat input to the heat recovery boiler (20) increases along with the load of the gas turbine (10), and the amount of steam increases accordingly. Therefore, during normal control, the target value of the HPCV valve opening command value increases as a function of, for example, the load of the gas turbine (10), and the HPCV opens gradually. When the HP side and IP side ST inlet pressures are within a preset normal range, the upper limit of the valve opening command value is kept constant at maximum opening.

[0049] (2) When waiting for back pressure control: When the HPST inlet pressure approaches the HPST inlet pressure threshold value set by the boundary line B_HPST shown in Fig. 5, and when the HPST inlet pressure exceeds the HPST inlet pressure threshold value, the upper limit of the valve opening is changed to the current valve opening + α1. By keeping the upper limit at the current valve opening + α1, it is possible to quickly close the valve when the HPST inlet pressure exceeds the allowable range.

[0050] (3) When controlling back pressure: When the pressure in the system changes rapidly and seems likely to go out of range due to an event such as the closing operation of the ventilator valve (66) or the abnormal opening of the high-pressure steam turbine bypass valve (63), the HPCV valve is closed according to the upper limit value output by the valve opening upper limit value calculation unit (210) in the same way as in the first embodiment, and the corresponding relationship between the HPST inlet pressure and the IPST inlet pressure can be brought into a normal range.

[0051] In the example shown in FIG. 7, normal control is performed at times t0 to t1. At time t1, the HPST input pressure becomes greater than or equal to the HPST input pressure threshold value not shown, and the back pressure control standby time is set. Then, at time t2, the HPST input pressure becomes greater than or equal to the HPST target pressure, and back pressure control is performed.

[0052] During normal control, the upper limit of the HPCV valve opening command value, indicated by the two-dot dashed line, remains constant at the maximum opening. Also, during normal control, the HPCV valve opening command value is set toward the HPST target pressure, indicated by the one-dot dashed line, and the HPST input pressure rises. During the back-pressure control standby, the upper limit of the HPCV valve opening command value is set to the current valve opening + α1%. Then, during back-pressure control, PI control of the upper limit value is initiated, and the HPCV valve opening is suppressed to the upper limit value. Furthermore, in the case of voltage control without back-pressure control, the HPCV valve opening continues to rise, for example, as indicated by the dashed line. Here, voltage control is control based on the pressure on the upstream side of the HPCV.

[0053] Next, with reference to FIG. 8, the flow of processing in the control unit (102) of the control device (100) of the second embodiment will be described. Also, in FIG. 8, HPCV is denoted as HP Governor Valve and IPCV is denoted as IP Governor Valve. The control unit (102) of the second embodiment performs in parallel the adjustment of the valve opening of the HPCV (HP Governor Valve) by processing steps S11 to S18 and the adjustment of the valve opening of the IPCV (IP Governor Valve) by processing steps S21 to S28.

[0054] When control is initiated, the control unit (102) calculates the HPST inlet pressure threshold value based on the IPST inlet pressure, using the boundary line B_HPST in the correspondence relationship between the HPST input pressure and the IPST input pressure shown in FIG. 5 as a reference (Step S11). Additionally, the processing of Step S11 is executed at predetermined time intervals. Next, the control unit (102) determines whether the HPST inlet pressure is greater than or equal to the HPST inlet pressure threshold value (Step S12). If the HPST inlet pressure is not greater than or equal to the HPST inlet pressure threshold value (Step S12: NO), the control unit (102) sets the upper limit of the valve opening to the maximum value, executes normal HP governor valve control (Step S13), and returns to Step S11. When the HPST inlet pressure is greater than or equal to the HPST inlet pressure threshold value (Step S12: YES), the control unit (102) sets the valve opening upper limit value to the current opening + α1, transitions to a standby state for HP governor valve back pressure control (Step S14), and determines whether the HPST inlet pressure is greater than or equal to the target pressure (Step S15).

[0055] If the HPST inlet pressure is not greater than or equal to the target pressure (Step S15: NO), the control unit (102) returns the process to Step S11. If the HPST inlet pressure is greater than or equal to the target pressure (Step S15: YES), the control unit (102) performs HP governor valve back pressure control (Step S16) and determines whether the HPST inlet pressure is less than the HPST inlet pressure threshold value (Step S17). If the HPST inlet pressure is not less than the HPST inlet pressure threshold value (Step S17: NO), the control unit (102) calculates the HPST inlet pressure threshold value (Step S18) and, after a predetermined time, performs the process of Step S16. If the HPST inlet pressure is less than the HPST inlet pressure threshold value (Step S17: YES), the control unit (102) returns the process to Step S11.

[0056] Additionally, when control is initiated, in parallel with the above processing, the control unit (102) calculates the IPST inlet pressure threshold value based on the HPST inlet pressure, using the boundary line B_IPST in the correspondence relationship between the HPST input pressure and the IPST input pressure shown in FIG. 6 as a reference (Step S21). Additionally, the processing of Step S21 is executed at a predetermined time interval. Next, the control unit (102) determines whether the IPST inlet pressure is greater than or equal to the IPST inlet pressure threshold value (Step S22). If the IPST inlet pressure is not greater than or equal to the IPST inlet pressure threshold value (Step S22: NO), the control unit (102) executes normal IP governor valve control with the valve opening upper limit value as the maximum value (Step S23) and returns to Step S21. When the IPST inlet pressure is greater than or equal to the IPST inlet pressure threshold value (Step S22: YES), the control unit (102) sets the valve opening upper limit value to the current opening + α2, transitions to the IP governor valve back pressure control standby state (Step S24), and determines whether the IPST inlet pressure is greater than or equal to the target pressure (Step S25). Additionally, α2 is a constant value on the IPST inlet pressure side corresponding to α1.

[0057] If the IPST inlet pressure is not greater than or equal to the target pressure (Step S25: NO), the control unit (102) returns the process to Step S21. If the IPST inlet pressure is greater than or equal to the target pressure (Step S25: YES), the control unit (102) executes IP governor valve back pressure control (Step S26) and determines whether the IPST inlet pressure is less than the IPST inlet pressure threshold value (Step S27). If the IPST inlet pressure is not less than the IPST inlet pressure threshold value (Step S27: NO), the control unit (102) calculates the IPST inlet pressure threshold value (Step S28) and, after a predetermined time, executes the process of Step S26. If the IPST inlet pressure is less than the IPST inlet pressure threshold value (Step S27: YES), the control unit (102) returns the process to Step S21.

[0058] As described above, according to the control device, control method, and system of the present disclosure, the valve opening of the HPCV and the valve opening of the IPCV can be adjusted so that the correspondence between the HPST inlet pressure and the IPST inlet pressure is appropriate, and thus the thrust force caused by the imbalance between the HPST inlet pressure and the IPST inlet pressure in the steam turbine (30) can be controlled within an allowable value.

[0059] In addition, according to the present embodiment, the control unit (102) adjusts the upper limit of the valve opening of the HPCV and the upper limit of the valve opening of the IPCV by selectively making each upper limit of the valve opening of the HPCV and the valve opening of the IPCV one of the maximum value of each valve opening, each value increased by a predetermined amount (α1 or α2) from each current value of the HPST inlet pressure and the IPST inlet pressure, or each value based on area A1. With this configuration, the valve can be quickly closed when the HPST inlet pressure or the IPST inlet pressure goes outside the allowable range.

[0060] <Third Embodiment>

[0061] Referring to FIG. 9, a control device according to a third embodiment of the present disclosure will be described. FIG. 9 is a schematic diagram for explaining a control device according to a third embodiment of the present disclosure.

[0062] The third embodiment presents a procedure for determining the thrust balance target range (region A1 in FIG. 2) shown in the first embodiment. In the third embodiment, region A1 (range) is determined in the following procedure.

[0063] (S1) Find multiple points C1 of combinations of HPST inlet pressure and IPST inlet pressure where the thrust forces of HPST and IPST are balanced.

[0064] (S2) From point C1 where the thrust force is balanced, the maximum range of thrust force that can be allowed when the ST inlet pressure on the HP side or IP side is deflected (HP side deflection, IP side deflection) is determined. In the example shown in FIG. 9, the range in which the HPST inlet pressure of the combination point C1 is deflected by ΔHP1 and ΔHP2, and the range in which the IPST inlet pressure of point C1 is deflected by ΔIP1 and ΔIP2 are determined. The range in which the HPST inlet pressure is deflected and the range in which the IPST inlet pressure is deflected are determined equally for each point C1. Then, a region A1a is determined that is sandwiched between the boundary line M_HPST and the boundary line M_IPST, indicated by dashed lines, so as not to exceed the range in which the HPST inlet pressure and the IPST inlet pressure of each point C1 are deflected.

[0065] (S3) The boundary line M_HPST and boundary line M_IPST of the HPST inlet pressure and IPST inlet pressure obtained in (S2) is subtracted from the constant γ (adjustment term) to become the boundary line B_HPST and boundary line B_IPST of region A1.

[0066] As described above, in this embodiment, the region A1 (range) described with reference to FIG. 2 corresponds to region A1a, where the thrust force when either the HPST inlet pressure or the IPST inlet pressure is deflected from the combination point C1 of the HPST inlet pressure and the IPST inlet pressure, where the thrust force from the HPST and the thrust force from the IPST are balanced, is less than or equal to the maximum allowable value. In addition, the control unit (102) controls the valve opening of the HPCV and the valve opening of the IPCV according to the HPST inlet pressure and the IPST inlet pressure, based on region A1 (range), which is the boundary of region A1a minus a predetermined constant γ into region A1a.

[0067] According to the present embodiment, it is possible to limit the thrust force to a restricted range.

[0068] (Other embodiments)

[0069] Although embodiments of the present disclosure have been described in detail with reference to the drawings, the specific configuration is not limited to these embodiments and includes design changes, etc., within the scope of not departing from the gist of the present disclosure.

[0070] Computer Configuration

[0071] FIG. 10 is a schematic block diagram showing the configuration of a computer according to at least one embodiment.

[0072] The computer (90) is equipped with a processor (91), main memory (92), storage (93), and an interface (94).

[0073] The above-described control device (100) is installed in a computer (90). The operation of each processing unit described above is stored in storage (93) in the form of a program. A processor (91) reads the program from storage (93), expands it into main memory (92), and executes the processing according to the program. Additionally, the processor (91) secures a memory area corresponding to each memory unit described above in main memory (92) according to the program.

[0074] The program may be intended to realize a part of the function to be performed by the computer (90). For example, the program may be designed to perform a function by combining it with another program already stored in storage, or by combining it with another program installed on another device. In addition, in other embodiments, the computer may be equipped with a custom LSI (Large Scale Integrated Circuit), such as a PLD (Programmable Logic Device), in addition to or instead of the above configuration. Examples of PLDs include PAL (Programmable Array Logic), GAL (Generic Array Logic), CPLD (Complex Programmable Logic Device), FPGA (Field Programmable Gate Array), etc. In this case, some or all of the function to be performed by the processor may be performed by the integrated circuit.

[0075] Examples of storage (93) include HDD (Hard Disk Drive), SSD (Solid State Drive), magnetic disk, magneto-optical disk, CD-ROM (Compact Disc Read Only Memory), DVD-ROM (Digital Versatile Disc Read Only Memory), semiconductor memory, etc. Storage (93) may be an internal medium directly connected to the bus of the computer (90), or an external medium connected to the computer (90) via an interface (94) or a communication line. Also, when this program is transmitted to the computer (90) via a communication line, the computer (90) that receives the transmission may expand the program into the main memory (92) and execute the above processing. In at least one embodiment, storage (93) is a non-temporary tangible storage medium.

[0076] <Appendix>

[0077] The control device (100) described in each embodiment is understood, for example, as follows.

[0078] (1) A control device (100) according to the first embodiment acquires the pressure value of the first steam on the first inlet side as the first inlet pressure by looking at the first control valve of a first turbine (high-pressure steam turbine (31)) that rotates using the first steam (high-pressure steam) supplied from the first inlet (steam inlet (311)) through the first control valve (high-pressure main steam increase / decrease valve (43)), and acquires the pressure value of the second steam on the second inlet side as the second inlet pressure by looking at the second control valve of a second turbine (medium-pressure steam turbine (32)) that rotates on the same rotation axis (36) as the first turbine using the second steam supplied from the second inlet (steam inlet (321)) through the second control valve (medium-pressure main steam increase / decrease valve (46)), and acquires the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure A control unit (102) for controlling is provided. According to the present embodiment and each of the following embodiments, the thrust force in the steam turbine can be controlled within an allowable value.

[0079] (2) The control device (100) of the second embodiment is the control device of (1), and the control unit (102) controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure based on a predetermined range (region A1) for the corresponding relationship (balance characteristic) of the first inlet pressure and the second inlet pressure, so that the thrust force applied to the rotating shaft (36) becomes appropriate. According to the present embodiment, since the valve opening of the first control valve and the valve opening of the second control valve can be controlled so that the corresponding relationship between the first inlet pressure and the second inlet pressure becomes appropriate, the thrust force caused by the imbalance between the first inlet pressure and the second inlet pressure in the steam turbine (30) can be controlled within an allowable value.

[0080] (3) The control device (100) of the third embodiment is the control device (100) of (2), and the control unit (102) controls the first control valve and the second control valve based on the upper boundary line (B_IPST) of the range when the range (area A1) is represented as an orthogonal coordinate with the horizontal axis being one side of the first inlet pressure and the second inlet pressure and the vertical axis being the other side of the first inlet pressure and the second inlet pressure.

[0081] (4) The control device (100) of the fourth embodiment is the control device (100) of (2) or (3), and the range (region A1) corresponds to region A1a, where the thrust force when either the first inlet pressure or the second inlet pressure is deflected from the combination (C1) of the first inlet pressure and the second inlet pressure in which the thrust force from the first turbine and the thrust force from the second turbine are balanced, is less than or equal to the maximum allowable value.

[0082] (5) The control device (100) of the fifth embodiment is the control device (100) of (4), and the control unit (102) sets the region A1, which is the region A1, by subtracting a predetermined constant γ from the boundary of the region A1a into the inner side of the region A1a, as the range (region A1), and controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure.

[0083] (6) The control device (100) of the sixth embodiment is the control device (100) of (2) to (5), and the control unit (102) controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure by adjusting the upper limit value of the valve opening of the first control valve and the upper limit value of the valve opening of the second control valve. According to the present embodiment, for example, the pressure upstream of the first control valve can be easily combined with the first control valve for feedback control of the pressure upstream of the second control valve or the second control valve for feedback control of the pressure upstream of the second control valve.

[0084] (7) The control device (100) of the seventh embodiment is the control device (100) of (6), and the control unit (102) adjusts the upper limit of the valve opening of the first control valve and the upper limit of the valve opening of the second control valve by selectively making the upper limit of the valve opening of the first control valve and the upper limit of the valve opening of the second control valve one of the maximum value of each valve opening, each value increased by a predetermined amount (α1, α2) from each current value of the first inlet pressure and the second inlet pressure, or each value based on the range (region A1). According to the present embodiment, the responsiveness of the control based on the upper limit can be improved.

[0085] Industrial applicability

[0086] According to each embodiment of the present invention, the thrust force in a steam turbine can be controlled within an allowable value. Explanation of the symbols

[0087] 1… system 10… gas turbine 11… Compressor 12… Combustion device 13… turbine 14… Fuel flow control valve 20… Array recovery boiler 21… High-pressure steam generator 22… Medium-pressure steam generator 23… Reheating section 24… Low-pressure steam generator 30… steam turbine 31… High-pressure steam turbine 32… medium-pressure steam turbine 33… Low-pressure steam turbine 34… Generator 35… Revenge 41… High-pressure main steam line 42… High-pressure steam stop valve 43… High-pressure main steam control valve 44, 61, 62… Medium-pressure main steam line 45… Medium-pressure steam stop valve 46… Medium-pressure main steam control valve 51… Low-pressure main steam line 52… Low-pressure steam stop valve 53… Low-pressure main steam control valve 54… Medium-pressure turbine exhaust line 55… water supply line 56… exhaust line 63… High-pressure steam turbine bypass valve 65… Medium-pressure steam turbine bypass valve 66… Ventilator valve 71, 72, 73, 74, 75, 76… pressure gauge 100… control device 101… Acquisition Department 102… Control unit

Claims

Claim 1 A acquiring unit that acquires, as a first inlet pressure, the pressure value of the first steam on the first inlet side as viewed from the first control valve of a first turbine that rotates using the first steam supplied from the first inlet through the first control valve, and as a second inlet pressure, the pressure value of the second steam on the second inlet side as viewed from the second control valve of a second turbine that rotates on the same rotational axis as the first turbine using the second steam supplied from the second inlet through the second control valve, and a control unit that controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure, wherein the control unit controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure based on a predetermined range for the corresponding relationship based on the corresponding relationship between the first inlet pressure and the second inlet pressure such that the thrust force applied to the rotational axis becomes appropriate, and the control unit, wherein the range is defined such that the horizontal axis is the first inlet pressure and the A control device that, when represented in an orthogonal coordinate system where one side of the second inlet pressure and the vertical axis are the other side of the first inlet pressure and the second inlet pressure, controls one side of the first control valve and the second control valve based on the upper boundary line side of the range, and controls the other side of the first control valve and the second control valve based on the lower boundary line side of the range. Claim 2 A control device according to claim 1, wherein the range corresponds to a region in which the thrust force is less than or equal to the maximum allowable value when either the first inlet pressure or the second inlet pressure is deflected from a combination of the first inlet pressure and the second inlet pressure in which the thrust force by the first turbine and the thrust force by the second turbine are balanced. Claim 3 In claim 2, the control unit is a control device that controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure, wherein the control unit has a range in which a predetermined constant is subtracted from the boundary of the region into the interior of the region. Claim 4 A control device according to any one of claims 1 to 3, wherein the control unit controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure by controlling the upper limit value of the valve opening of the first control valve and the upper limit value of the valve opening of the second control valve. Claim 5 A control device according to claim 4, wherein the control unit controls the upper limit value of the valve opening of the first control valve and the upper limit value of the valve opening of the second control valve by optionally making each upper limit value of the valve opening of the first control valve and the valve opening of the second control valve one of the maximum value of each valve opening, each value increased by a predetermined amount from each current value of the first inlet pressure and the second inlet pressure, or each value based on the range. Claim 6 delete Claim 7 A acquiring unit that acquires, as a first inlet pressure, the pressure value of the first steam on the first inlet side as viewed from the first control valve of a first turbine rotating using the first steam supplied from the first inlet through the first control valve, and as a second inlet pressure, the pressure value of the second steam on the second inlet side as viewed from the second control valve of a second turbine rotating on the same rotational axis as the first turbine using the second steam supplied from the second inlet through the second control valve, and a control unit that controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure, wherein the control unit controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure based on a predetermined range for the corresponding relationship based on the corresponding relationship between the first inlet pressure and the second inlet pressure such that the thrust force applied to the rotational axis becomes appropriate, and the control unit, wherein the upper limit value of the valve opening of the first control valve and A control device that controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure by adjusting the upper limit value of the valve opening of the second control valve, and the control unit controls the upper limit value of the valve opening of the first control valve and the upper limit value of the valve opening of the second control valve by selectively making each upper limit value of the valve opening of the first control valve and the valve opening of the second control valve one of the maximum value of each valve opening, each value increased by a predetermined amount from each current value of the first inlet pressure and the second inlet pressure, or each value based on the range. Claim 8 The method comprises a step of acquiring, as a first inlet pressure, the pressure value of the first steam on the first inlet side as viewed from the first control valve of a first turbine that rotates using the first steam supplied from the first inlet through the first control valve, and acquiring as a second inlet pressure the pressure value of the second steam on the second inlet side as viewed from the second control valve of a second turbine that rotates on the same rotational axis as the first turbine using the second steam supplied from the second inlet through the second control valve, and a step of adjusting the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure, wherein the adjusting step adjusts the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure based on a predetermined range for the corresponding relationship based on the corresponding relationship between the first inlet pressure and the second inlet pressure such that the thrust force applied to the rotational axis becomes appropriate, and wherein the adjusting step, wherein the range is the horizontal axis of the first A control method in which, when represented by an orthogonal coordinate system in which one side of the inlet pressure and the second inlet pressure is one side and the vertical axis is the other side of the first inlet pressure and the second inlet pressure, one side of the first control valve and the second control valve is controlled based on the upper boundary line side of the range, and the other side of the first control valve and the second control valve is controlled based on the lower boundary line side of the range. Claim 9 A first control valve and a second control valve; a first turbine that rotates using first steam supplied from a first inlet through the first control valve; a second turbine that rotates on the same rotation axis as the first turbine using second steam supplied from a second inlet through the second control valve; an acquisition unit that acquires the pressure value of the first steam on the first inlet side as a first inlet pressure as viewed from the first control valve, and acquires the pressure value of the second steam on the second inlet side as a second inlet pressure as viewed from the second control valve; and a control unit that controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure, wherein the control unit controls the valve opening of the first control valve and the valve opening of the second control valve according to the first inlet pressure and the second inlet pressure based on a predetermined range for the corresponding relationship based on the corresponding relationship between the first inlet pressure and the second inlet pressure, wherein the thrust force applied to the rotation axis becomes appropriate. A control unit is a system that, when the range is represented by an orthogonal coordinate system in which the horizontal axis is one side of the first inlet pressure and the second inlet pressure and the vertical axis is the other side of the first inlet pressure and the second inlet pressure, controls one side of the first control valve and the second control valve based on the upper boundary line side of the range and controls the other side of the first control valve and the second control valve based on the lower boundary line side of the range.

Citation Information

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