Startup method of Francis turbine, startup program, and control device

Abstract

A startup method of a Francis turbine in an embodiment includes: a first step of controlling an opening of the guide vanes 5 in a micro time unit, and of changing the opening to a changed guide vane opening; a second step of deriving a swirling flow speed of the swirling flow at the changed guide vane opening; a third step of deriving a circumferential speed of the runner at the changed guide vane opening; a fourth step of deriving a relative 10 flow speed of the swirling flow based on the swirling flow speed and the circumferential speed; and a fifth step of comparing the relative flow speed and a predetermined relative flow speed threshold value, and of determining whether a rotational speed of the runner at the changed guide vane opening has reached a 15 predetermined speed when the relative flow speed is equal to or less than the predetermined relative flow speed threshold value. 20 25 20 02 28 13 J an 2 02 5 A B S T R A C T 2 0 2 5 2 0 0 2 2 8 1 3 J a n 2 0 2 5 A s t a r t u p m e t h o d o f a F r a n c i s t u r b i n e i n a n e m b o d i m e n t i n c l u d e s : a f i r s t s t e p o f c o n t r o l l i n g a n o p e n i n g o f t h e g u i d e v a n e s 5 i n a m i c r o t i m e u n i t , a n d o f c h a n g i n g t h e o p e n i n g t o a c h a n g e d g u i d e v a n e o p e n i n g ; a s e c o n d s t e p o f d e r i v i n g a s w i r l i n g f l o w s p e e d o f t h e s w i r l i n g f l o w a t t h e c h a n g e d g u i d e v a n e o p e n i n g ; a t h i r d s t e p o f d e r i v i n g a c i r c u m f e r e n t i a l s p e e d o f t h e r u n n e r a t t h e c h a n g e d g u i d e v a n e o p e n i n g ; a f o u r t h s t e p o f d e r i v i n g a r e l a t i v e 1 0 f l o w s p e e d o f t h e s w i r l i n g f l o w b a s e d o n t h e s w i r l i n g f l o w s p e e d a n d t h e c i r c u m f e r e n t i a l s p e e d ; a n d a f i f t h s t e p o f c o m p a r i n g t h e r e l a t i v e f l o w s p e e d a n d a p r e d e t e r m i n e d r e l a t i v e f l o w s p e e d t h r e s h o l d v a l u e , a n d o f d e t e r m i n i n g w h e t h e r a r o t a t i o n a l s p e e d o f t h e r u n n e r a t t h e c h a n g e d g u i d e v a n e o p e n i n g h a s r e a c h e d a 1 5 p r e d e t e r m i n e d s p e e d w h e n t h e r e l a t i v e f l o w s p e e d i s e q u a l t o o r l e s s t h a n t h e p r e d e t e r m i n e d r e l a t i v e f l o w s p e e d t h r e s h o l d v a l u e . A B S T R A C T 2 0 2 5 2 0 0 2 2 8 1 3 J a n 2 0 2 5 FIG. 7 7 / 97 / 9 4 5 R3 G R1 N 30 R2 11 20 6 FIG. 7 20 25 20 02 28 13 J an 2 02 5 < 1 1 6 R 3 N R 1 R 2 5 7 / 9 7 / 9 / FIG. 7 G 4 3 0 2 0 2 0 2 5 2 0 0 2 2 8 1 3 J a n 2 0 2 5 1 1 6 R 1 R 2 7 / 9 7 / 9 F I G . 7 4 3 0 2 0 2 5 2 0 0 2 2 8 1 3 J a n 2 0 2 5

Description

FIELD 5

[0001] Embodiments described herein relate generally to a startup method of a Francis turbine, a startup program, and a control device. 10                     BACKGROUND

[0002] A Francis turbine is a type of water turbine used in hydroelectric power generation. When a Francis turbine is operated, water from an upper reservoir is guided to a casing 15 through an inlet valve provided on an inlet pipe. The water sequentially passes through stay vanes and guide vanes to be guided to a runner, while its flow rate is regulated. When the runner is driven in rotation by the water flowing into the runner, a generator coupled to the runner via a main shaft is driven in 20 rotation together with the runner to generate power. Thereafter, the water flows out from the runner to be discharged to a lower reservoir or a tailrace through a draft tube.

[0003] In the rest state of the Francis turbine, the inlet valve and 25 the guide vanes are closed. When the Francis turbine is started up, the inlet valve provided on the inlet pipe is first opened to allow water to flow into the casing. Then, by opening the guide vanes up to a startup opening to allow the water to flow into the runner, the runner is driven in rotation and a rotational speed of 30 the runner is increased up to a rated rotational speed. 2025200228   13 Jan 2025

[0004] However, when the guide vanes are opened up to the startup opening upon startup of the operation of the Francis turbine, an annular flow path may be formed in the 5 circumferential direction of the runner, in particular, between the guide vanes and the runner. When the water having passed through the guide vanes flows rapidly through the annular flow path, a swirling flow at a high flow speed is generated around the runner. When the swirling flow collides with a runner blade, a 10 separation flow occurs around the runner blade. Particularly when a Francis turbine with a large head, the swirling flow may become faster and a stronger separation flow may occur.

[0005] Due to the generation of such a swirl flow and a separation 15 flow, a water pressure inside the runner is likely to decrease down to a saturated water vapor pressure or below. When an area whose water pressure is the saturated water vapor pressure or below increases inside the runner, cavitation may occur inside the runner. Then, shock load caused by large-scale collapse of the 20 cavitation may damage the runner.

[0006] In order to treat such a problem, it has been conventionally considered that a startup opening of the guide vanes is made small to suppress the speed of the swirling flow to weaken the 25 separation flow.

[0007] However, since this method maintains the small opening for a long time, it may take a time for the runner rotational speed to reach the rated rotational speed. 2025200228   13 Jan 2025 BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Fig. 1 is a structural view of a Francis turbine 1 according to this embodiment in a state where guide vanes are opened. 5          Fig. 2 is a structural view of the Francis turbine 1 according to this embodiment in a state where the guide vanes are closed. Fig. 3A is a view for explaining conventional startup of an operation of the Francis turbine 1, which is a time diagram showing an opening of the guide vanes 5. 10          Fig. 3B is a view for explaining the conventional startup of the operation of the Francis turbine 1, showing a water flow when the guide vanes 5 are opened at a startup opening. Fig. 4 is an explanatory view showing a control device C that controls a startup method 100 of the Francis turbine 1 in this 15 embodiment. Fig. 5 is a flowchart showing the startup method 100 of the Francis turbine 1 in this embodiment. Fig. 6 is a flowchart showing a derivation method 200 of a predetermined relative flow speed threshold value R0 in step 20  S105 of the startup method 100. Fig. 7 is an explanatory view of the startup method 100 of the Francis turbine 1 in this embodiment. Fig. 8 is an explanatory view showing a relationship between a guide vane opening G and a swirling flow speed R1 in 25 the startup method 100 of the Fransis turbine 1 in this embodiment. Fig. 9 is an explanatory view showing a relationship between a relative flow speed R3 and a stress N in the startup method 100 of the Fransis turbine 1 in this embodiment. 2025200228   13 Jan 2025 DETAILED DESCRIPTION

[0009] A startup method of a Francis turbine according to an embodiment is a startup method of a Francis turbine including 5 guide vanes capable of regulating a flow rate of water to be guided to a runner, including: a first step of controlling an opening of the guide vanes in a micro time unit, and of changing the opening to a changed guide vane opening; a second step of deriving a swirling flow speed of the swirling flow at the changed 10 guide vane opening; a third step of deriving a circumferential speed of the runner at the changed guide vane opening; a fourth step of deriving a relative flow speed of the swirling flow based on the swirling flow speed and the circumferential speed; and a fifth step of  comparing the relative flow  speed and  a 15 predetermined  relative flow speed threshold value, and  of determining whether a rotational speed of the runner at the changed guide vane opening has reached a predetermined speed when the relative flow speed is equal to or less than the predetermined relative flow speed threshold value. 20

[0010] A startup program of a Francis turbine according to an embodiment is a startup program of a Francis turbine including guide vanes capable of regulating a flow rate of water to be guided to a runner, including: a first command for controlling an 25 opening of the guide vanes in a micro time unit, and for changing the opening to a changed guide vane opening; a second command for deriving a swirling flow speed of the swirling flow at the changed guide vane opening; a third command for deriving a circumferential speed of the runner at the changed guide vane 30 opening; a fourth command for deriving a relative flow speed of 2025200228   13 Jan 2025 the swirling flow based on the swirling flow speed and the circumferential speed; and a fifth command for comparing the relative flow speed and a predetermined relative flow speed threshold value, and for determining whether a rotational speed 5 of the runner at the changed guide vane opening has reached a predetermined speed when the relative flow speed is equal to or less than the predetermined relative flow speed threshold value.

[0011] A control device of a Francis turbine according to an 10 embodiment is a control device of a Francis turbine including guide vanes capable of regulating a flow rate of water to be guided to a runner, including: an opening change unit that controls the guide vanes, and changes an opening of the guide vanes; a derivation unit that performs a calculation process or an 15 analysis process during control of the guide vanes; a memory unit that stores data from the derivation unit or an external unit; a comparison unit that compares respectively different data from among the data during control of the guide vanes; and an opening / closing command unit that receives determination of the 20 comparison unit, and issues a command for changing an opening of the guide vanes to the opening change unit.

[0012] A startup method of a Fransis turbine according to an embodiment, a startup program, and a control device are 25 described hereunder in detail below with reference to the drawings. The following embodiment is an example of the embodiment of the present disclosure by way of example, and is not intended to limit the scope of the disclosure. In the drawing referred to in the embodiment, the same reference numeral or a 30 similar reference numeral is used for the same part or a part with 2025200228   13 Jan 2025 the same function, and its description may be omitted. The size ratio in the drawings may differ from the actual one, and some of components may be omitted from the drawings.

[0013] 5         The Francis turbine 1 according to this embodiment is described first using Figs. 1 and 2. Fig. 1 is a structural view of the Francis turbine 1 according to this embodiment in a sate where guide vanes are opened.  Fig. 2 is a structural view of the Francis turbine 1 according to this embodiment in a state where 10 the guide vanes are closed. The Francis turbine 1 in Figs. 1 and 2 is connected to a generator (illustration omitted) via a main shaft A, and includes an inlet system 2, a casing 3, stay vanes 4, guide vanes 5, a runner 6, and a control device C. Hereunder, an axial direction around the main shaft A is referred to simply 15 as axial direction, and a circumferential direction and a radial direction around the main shaft A are referred to simply as circumferential direction and radial direction.

[0014] The inlet system 2 is configured to guide water from an 20 upper reservoir (illustration omitted) to the casing 3. The inlet system 2 has an inlet pipe 7, an inlet valve 8, a bypass pipe 9, and a bypass valve 10.

[0015] The inlet pipe 7 is connected, at its one end, to a water 25 pressure iron pipe (illustration omitted) extending from the upper reservoir, and is connected, at its other end, to the casing 3, to guide water flowing from the upper reservoir to the casing 3.

[0016] The inlet valve 8 is provided on the inlet pipe 7. A flow of 30 water through the inlet pipe 7 is opened or shut off by opening 2025200228   13 Jan 2025 or closing the valve. Specifically, during the rest of the Francis turbine 1, the inlet valve 8 is closed, and during the operation of the Fransis turbine 1, the inlet valve 8 is opened. The opening and closing of the inlet valve 8 may be controlled by the control 5 device C described later.

[0017] The bypass pipe 9 is connected, at its one end, to a part of the inlet pipe 7, which is upstream of the inlet valve 8, and is connected, at its other end, to a part of the inlet pipe 7, which is 10 downstream of the inlet valve 8, to guide water to the casing 3 by bypassing the inlet valve 8. The terms upstream / downstream herein refer to an upstream side / downstream side in a direction of a flow of water flowing from the upper reservoir toward the casing 3. 15

[0018] The bypass valve 10 is provided on the bypass pipe 9.  A flow of water through the bypass pipe 9 is opened or shut off by opening or closing the valve.  Specifically, during the rest of the Francis turbine 1, the bypass valve 10 is closed, and during the 20 operation of the Fransis turbine 1, the bypass valve 10 is opened. The opening and closing of the bypass valve 10 may be controlled by the control device C described later.

[0019] The casing 3 is formed in a spiral shape, and guides water 25 having flown from the inlet system 2 to the inside of the casing 3. A plurality of the guide vanes 4, a plurality of the guide vanes 5, and the runner 6 are provided inside the casing 3.

[0020] The stay vanes 4 are provided radially inside the casing 3 30 to guide the water having flown into the casing 3 to the guide 2025200228   13 Jan 2025 vanes 5 and the runner 6. Specifically, the stay vanes 4 are arranged radially inside the casing 3 at predetermined circumferential intervals therebetween, and are formed such that a flow path through which the water flows is formed therebetween. 5

[0021] The guide vanes 5 are arranged radially more inside than the stay vanes 4 to guide the water having flown from the stay vanes 4 to the runner 6. Specifically, the guide vanes 5 are radially more inside than the stay vanes 4 at predetermined 10 circumferential intervals therebetween, and are formed such that a flow path through which the water flows is formed therebetween. In addition, the guide vanes 5 are configured to be movable through a guide ring (illustration omitted) to be capable of changing its opening, in order to regulate a flow rate and a flow 15 speed of the water to be guided to the runner 6. An opening of the guide vanes 5 may be controlled by the control device C described later.

[0022] The runner 6 is arranged radially more inside than the 20 guide vanes 5, and is connected to the generator via the main shaft A. The runner 6 has a plurality of runner blades 11 which are arranged at predetermined circumferential intervals therebetween, and are configured such that a flow path through which the water flows is formed therebetween. In addition, the 25 runner 6 is configured to be circumferentially turned by the water having flown from the guide vanes 5 to be capable of converting energy of the water flowing into the runner 6 to rotational energy for rotating the generator via the main shaft A.

[0023] 30         The control device C is configured to be capable controlling 2025200228   13 Jan 2025 the aforementioned inlet valve 8, the bypass valve 10, the guide vanes 5, etc. Thus, for example, upon startup of the operation of the Francis turbine 1, the control device C controls openings of the inlet valve 8, the bypass valve 10, the guide vanes 5, etc., to 5 control steps of increasing a rotational speed of the runner Details of the control by the control device C will be described later.

[0024] According to the Francis turbine 1 in this embodiment, 10 during the rest of the Francis turbine 1, the inlet valve 8, the bypass valve 10, and the guide vanes 5 are closed. When the Francis turbine 1 is operated, the control device C controls to open the inlet valve 8 and the bypass valve 10 to then allow water from the upper reservoir to be guided into the casing 3 through 15 the inlet system 2. The water having guided into the casing 3 is guided to the guide vanes 5 through the stay vanes 4. The water having guided to the guide vanes 5 is guided to the runner 6, with its flow rate and flow speed being controlled by an opening of the guide vanes 5 under the control of the control device C. When 20 the water having flown into the runner 6 drives the runner 6 in rotation, the generator connected to the runner 6 via the main shaft A is rotated together with the runner 6 to generate power. Thereafter, the water having flown out from the runner 6 is discharged to a lower reservoir or a tailrace (illustration omitted) 25 through a draft tube (illustration omitted).

[0025] Next, a startup method 100 of the Fransis turbine 100 in this embodiment is described.

[0026] 30         In order to make clearer a difference between this 2025200228   13 Jan 2025 embodiment and the conventional one, a case in which the Francis turbine 1 according to this embodiment is started up by a conventional operation startup method is described as a comparative example, and then the startup method 100 of the 5 Francis turning 1 in this embodiment is described.

[0027] (Comparative Example) A conventional operation startup method of the Francis turbine 1 is described using Figs. 3A and 3B. Fig. 3A is a view 10 for explaining conventional startup of an operation of the Francis turbine 1, which is a time diagram showing an opening of the guide vanes 5. Fig. 3B is a view for explaining the conventional startup of the operation of the Francis turbine 1, showing a water flow when the guide vanes 5 are opened at a startup opening. 15

[0028] Upon startup of the conventional operation of the Francis turbine 1, the inlet valve 8 is opened to start to allow water to flow into the casing 3, and then, as shown in Fig. 3A, the guide vanes 5 are opened to a startup opening G1 from a time T1 to a 20 time T2 to increase a rotational speed of the runner 6. Thereafter, the rotational speed of the runner 6 is increased from a time T2 to a time T3 to reach a predetermined rotational speed. Then, the guide vanes 5 are closed to a no-load opening G2 from the time T3 to a time T4, and the rotational speed of the runner 25   6 is regulated to a rated rotational speed. The startup opening G1 herein means a predetermined opening at which a sufficient amount of water is supplied to the runner 6 to start up the Francis turbine 1. For example, the startup opening G1 may be an opening that is 10% or more and 20% or less of the maximum 30 opening of the guide vanes 5. In addition, the no-load opening 2025200228   13 Jan 2025 G2 herein means an opening that is less than the startup opening G1, and is an opening at which the generator is rotated at a rated rotational speed under no load. The no-load opening G2 may be an opening that is 5% or more and 15% or less of the maximum 5 opening of the guide vanes 5.

[0029] In this case, when the guide vanes 5 are opened to the startup opening G1, as shown in Fig. 3B, an annular flow path 20 is formed in the circumferential direction of the runner 6, in 10 particular, between the guide vanes 5 and the runner 6.  When the water having passed through the guide vanes 5 flows rapidly through the annular flow path 20, a swirling flow 30 at a high speed is generated. When the swirling flow 30 collides with the runner blade 11, a separation flow 4 occurs around the runner 15 blade 11. Due to the generation of such a swirling flow 30 and a separation flow 40, a water pressure inside the runner 6 is likely to decrease down to a saturated water vapor pressure or below. When an area whose water pressure is the saturated water vapor pressure or below increases inside the runner 6, cavitation may 20 occur inside the runner 6. Then, shock load caused by the cavitation may damage the runner 6.

[0030] (Startup Method of Francis Turbine 1 in Embodiment) The startup method 100 of the Fransis turbine 1 in this 25 embodiment is described using Figs. 4 to 9. Fig. 4 is an explanatory view showing the control device C that controls the startup method 100 of the Francis turbine 1 in this embodiment. Fig. 5 is a flowchart showing the startup method 100 of the Fransis turbine 1 in this embodiment. Fig. 6 is a flowchart 30 showing a derivation method 200 of a predetermined relative flow 2025200228   13 Jan 2025 speed threshold value R0 in step S105 of the startup method 100. Fig. 7 is an explanatory view of the startup method 100 of the Francis turbine 1 in this embodiment. Fig. 8 is an explanatory view showing a relationship between a guide vane opening G and 5 a swirl flow speed R1 in the startup method 100 of the Francis turbine 1 in this embodiment. Fig. 9 is an explanatory view showing a relationship between a relative flow speed R3 and a stress N in the startup method 100 of the Francis turbine 1 in this embodiment. 10

[0031] The control device C that controls the startup method 100 of the Fransis turbine 1 in this embodiment is described first using Fig. 4. As shown in Fig. 4, the control device C includes an opening change unit C1, a derivation unit C2, a measurement unit 15  C3, a memory unit C4, a comparison unit C5, and an opening / closing command unit C6.

[0032] The opening change unit C1 is an opening change unit that controls the guide vanes 5 of the Francis turbine 1 to change an 20 opening of the guide vanes 5. For example, the opening change unit C1 receives a command for changing an opening of the guide vanes 5 from the opening / closing command unit C6 described later and changes an opening of the guide vanes 5. Details of control of the startup method 100 will described later. 25

[0033] The derivation unit C2 is a derivation unit that performs a calculation process or an analysis process when needed during control of the guide vanes 5 of the Francis turbine 1 to derive a desired result. Details of control of the startup method 100 will 30 described later. 2025200228   13 Jan 2025

[0034] The measurement unit C3 is a measurement unit for measuring states of respective components of the Francis turbine 1. Details of control of the startup method 100 will described 5 later.

[0035] The memory unit C4 is a memory unit for storing data measured or derived by the control device C itself (derivation unit C2, measurement unit C3, etc.) or an external device. Details 10 of control of the startup method 100 will described later.

[0036] The comparison unit C5 is a comparison unit for comparing two respectively different data among data measured or derived by the control device C itself or an external device, etc., during 15 control of the guide vanes 5 of the Francis turbine 1. Details of control of the startup method 100 will described later.

[0037] The opening / closing command unit C6 is a command unit that receives determination by the comparison unit C5 and issues 20 a command for changing an opening of the guide vanes 5 of the Francis turbine 1 to the opening change unit C1. Details of control of the startup method 100 will described later.

[0038] Next, the startup method 100 of the Francis turbine 1 in 25 this embodiment is described using Fig. 5. The startup method 100 is a method for controlling an opening of the guide vanes 5 upon startup the operation of the Fransis turbine 1. The startup method 100 described below can be respectively applied to the Francis turbines 1 of respective available heads. In the following 30 description, the embodiment is described with reference to 2025200228   13 Jan 2025 reference numerals in Fig. 7 in order to facilitate understanding.

[0039] Process steps of the startup method 100 of the Francis turbine 1 in this embodiment are started when one or more 5 processors (illustration omitted) of the control device C executes a software program and / or a command set stored in a memory (illustration omitted).

[0040] Upon startup of the operation of the Fransis turbine 1, the 10 opening change unit C1 controls an opening of the guide vanes 5 in a micro time unit, and changes the guide vane opening G to a changed guide vane opening Gn’ (step S101, corresponding to first step). Specifically, the opening change unit C1 controls a predetermined opening speed of the guide vanes 5 in a micro 15 time unit, and changes it to the changed guide vane opening Gn’ which is a value obtained by adding an opening change amount, which is a product of the micro time unit and the opening speed, to the guide vane opening G at a certain time point. The micro time unit herein means a time unit which is previously set based 20 on precision when the guide vane opening is controlled. For example, at an initial change of the guide vane opening G, since the guide vane opening G is 0, a value obtained by adding an opening change amount, which is a product of the micro time unit and the opening speed, to 0 is set as the changed guide vane 25 opening G0’, and the opening of the guide vanes 5 is changed to the changed guide vane opening G0’.

[0041] Then, the derivation unit C2 derives a swirling flow speed R1 at the changed guide vane opening Gn’ which was changed in 30 step S101 (step S102, corresponding to second  step). 2025200228   13 Jan 2025 Specifically, the derivation unit C2 derives the swirling flow speed R1 of the swirling flow 30 corresponding to the changed guide vane opening Gn’ as shown in Fig. 8, based on a flow analysis using a calculation model having a flow path shape similar to that 5 of the Fransis turbine 1.

[0042] Then, the derivation unit C2 derives a circumferential speed R2 of a radially outside portion of the runner blade 11, based on a rotational speed of the runner 6 at the changed guide 10 vane opening Gn’ (step S103, corresponding to third step). Specifically, the derivation unit C2 predicts a rotational speed of the runner 6 at each time point at the changed guide vane opening Gn’ using a simulation result upon startup of the operation of the Francis turbine 1, and derives the circumferential 15 speed R2 of the radially outside portion of the runner blade 11 based on the predicted value.

[0043] How to derive the circumferential speed R2 is not limited to the aforementioned method. For example, upon startup of 20 the operation of the Francis turbine 1, the measurement unit C3 may measure a circumferential speed of the radially outside portion of the runner blade 11, and the measured value may be used as the circumferential speed R2.

[0044] 25         Then, the derivation unit C2 derives a relative flow speed R3 of the swirling flow 30 that collides with the runner blade 11 based on the swirling flow speed R1 derived in step S102 and the circumferential speed R2 derived in step S103 (step S104, corresponding to fourth step). 30

[0045] 2025200228   13 Jan 2025 Thereafter, the comparison unit C5 compares the relative flow speed R3 derived in step S104 and a predetermined relative flow speed threshold value R0 stoerd in the memory unit C4 (step S105). The predetermined relative flow speed threshold value 5 R0 refers to a threshold value of a reference stress for continuously operating the runner 6 until the assumed runner life is reached. The predetermined relative flow speed threshold value R0 is derived in advance before S101 is carried out. An example of deriving the predetermined relative flow speed 10 threshold value R0 will be described later. When the comparison unit C5 determines that the relative flow speed R3 is equal to or less than the relative flow speed threshold value R0 (Yes in step S105), whether a rotational speed of the runner 6 at the changed guide vane opening Gn’ at the comparison point has reached the 15 predetermined speed is continuously compared (step S106, corresponding to fifth step). The predetermined speed herein refers to a rotational speed of the runner which is a previously determined target value upon startup of the operation of the Fransis  turbine  1 using the  startup method 100 in this 20 embodiment. This target value is desirably equal to or less than a rated rotational speed of the runner 6. The rated rotational speed herein refers to a rotational speed of the runner 6 when a frequency of the generator of the Francis turbine 1 is in synch with a system frequency. The target value is determined as, for 25 example, 30% of the rated rotational speed, depending on operating conditions of the Francis turbine 1. However, the target value may be changeable by an operator to achieve more optimum operating conditions of the Francis turbine 1. When the companion unit C5 determines that the 30 rotational speed of the runner 6 at the changed guide vane 2025200228   13 Jan 2025 opening Gn’ has reached the predetermined speed (Yes in step S106), the comparison unit C5 determines to shift to a normal operation control (step S107, sixth step). Namely, in the startup stage of the Francis turbine 1, the startup method 100 is ended, 5 and then an opening of the guide vanes 5 is opened to an opening to bring a rotational speed of the runner 6 to reach the rated rotational speed by means of the normal operation control. The normal operation control herein refers to an operation control to bring a rotational speed of the runner 6 to reach the rated 10 rotational speed by opening the guide vanes at the startup opening G1 and thereafter opening them at the no-load opening G2, which was described in the Comparative Example.

[0046] On the other hand, when the comparison unit C5 15 determines that the relative flow speed R3 is not equal to or less than the predetermined relative flow speed threshold value R0 in step S105 (No in step S105), the opening / closing command unit C6 issues, to the opening change unit C1, a command to change the opening of the guide vanes 5 to a changed guide vane opening 20 Gn-1’ (guide vane closing command) that is less than the changed guide vane opening Gn’ (step S108, corresponding to seventh step). Then, the control returns to step S101, and the opening change unit C1 again changes an opening of the guide vanes 5 to the changed guide vane opening Gn-1’ which is a value obtained 25 by subtracting an opening change amount, which is a product of the micro time unit and the opening speed, from the changed guide vane opening Gn’. The respective steps after the control has returned to step S101 are the same as described above.

[0047] 30         When the comparison unit C5 determines that a rotational 2025200228   13 Jan 2025 speed of the runner 6 at the changed guide vane opening Gn’ does not reach the predetermined speed (No in step S106), the opening / closing command unit C6 issues, to the opening change unit C1, a command to change the opening of the guide vanes 5 5 to a changed guide vane opening Gn+1’ (guide vane opening command) that is more than the guide vane opening Gn’ (step S109, corresponding to eighth step). Then, the control returns to step S101, and the opening change unit C1 again changes an opening of the guide vanes 5 to the changed guide vane opening 10  Gn+1’, which is a value obtained by adding an opening change amount, which is a product of the micro time unit and the opening speed, to the changed guide vane opening Gn’. The respective steps after the control has returned to step S101 are the same as described above. 15

[0048] Next, an example of a deriving method 200 of the predetermined relative flow speed threshold value R0 in step S105 of the startup method 100 shown in Fig. 5 is described. The deriving method 200 of the predetermined relative flow 20 speed threshold value R0 is a step that is carried out in advance, for example, such as a test with water of the Francis turbine 1.

[0049] The measurement unit C3 first measures a stress N on a radially outside portion of the runner blade 11 of the runner 6 25 (step S201).

[0050] Then, the derivation unit C2 derives a predicted value of a swirling flow speed R1 of the swirling flow 30 at the guide vane opening G as shown in Fig. 8, based on a flow analysis using a 30 calculation model having a flow path shape similar to that of the 2025200228   13 Jan 2025 Fransis turbine 1 (step S202).

[0051] Then, the measurement unit C3 measures a rotational speed of the runner 6 at each guide vane opening G, and the 5 derivation unit C2 derives a circumferential speed R2 of the radially outside portion of the runner blade 11 from the measured value (step S203).

[0052] Then, the derivation unit C2 derives a relative speed R3 of 10 the swirling flow 30 that collides with the radially outside portion of the runner blade 11, based on the swirling flow speed R1 predicted in step S202 and the circumferential speed R2 derived in step S203 (step S204).

[0053] 15         Thereafter, the derivation unit C2 derives a relationship between the stress N and the relative flow speed R3 as shown in Fig. 9, based on the stress N measured in S201 and the relative flow speed R3 derived in step S204 (step S205).

[0054] 20         After these steps, the derivation unit C2 derives, as the relative flow speed threshold value R0, the relative flow speed R3 corresponding to a predetermined stress N0 from the relationship derived in step S205 (step S206). The predetermined stress N0 here refers to a stress N which is a starting point for fatigue 25 fracture of the runner blade 11, for example.

[0055] How to derive the predetermined relative flow speed threshold value R0 is not limited to the aforementioned method. For example, the derivation unit C2 may derive the 30 predetermined relative flow speed threshold value R0 based on a 2025200228   13 Jan 2025 stress analysis on the runner blade 11 when increase in pressure, which is derived from a flow analysis capable of simulating occurrence and collapse of cavitation, is applied to the runner blade 11. 5

[0056] Since the above startup method 100 of the Francis turbine 1 in this embodiment controls the guide vane opening G in a micro time unit based on a rotational speed of the runner 6, such that the relative flow speed R3 of the swirling flow speed R1 of the 10 swirling flow 30 and the circumferential speed R2 of the runner blade 11 does not exceed the predetermined relative flow speed threshold value R0 that is derived from a relationship between the relative flow speed R3 and the stress N of the runner blade 11, a rate of increase in rotational speed can be maximized until 15 the runner 6 reaches its rated rotational speed, while impact load associated with the separation flow 40 caused when the swirling flow 30 collides with the runner blade 11 can be maintained at a certain value or below.

[0057] 20         The aforementioned embodiment makes it possible that, upon startup of the operation of the Francis turbine, a rate of increase in rotational speed of the runner is maximized while impact load associated with the separation flow is maintained at a certain value or below, by controlling a guide vane opening 25 based on a rotational speed of the runner.

[0058] While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, 30 the novel methods and systems described herein may be 2025200228   13 Jan 2025 embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the methods and systems described herein may be made without departing from the spirit of the inventions. The accompanying claims and 5 their equivalents are intended to cover such forms or modifications as would fail within the scope and spirit of the invention.

Claims

1. A startup method of a Francis turbine including guidevanes capable of regulating a flow rate of water to be guided to 5 a runner, including:a first step of controlling an opening of the guide vanes ina micro time unit, and of changing the opening to a changed guide vane opening;a second step of deriving a swirling flow speed of the10 swirling flow at the changed guide vane opening;a third step of deriving a circumferential speed of the runner at the changed guide vane opening;a fourth step of deriving a relative flow speed of the swirling flow based on the swirling flow speed and the15 circumferential speed; anda fifth step of comparing the relative flow speed and a predetermined relative flow speed threshold value, and of determining whether a rotational speed of the runner at the changed guide vane opening has reached a predetermined speed20 when the relative flow speed is equal to or less than the predetermined relative flow speed threshold value.

2. The startup method of a Francis turbine according to claim1, wherein the derivation of the predetermined relative flow25 speed threshold value includes:a step of measuring a stress on the runner;a step of predicting a swirling flow speed of the swirling flow at each opening of the guide vanes based on a flow analysis using a calculation model having a flow path shape similar to that30 of the Fransis turbine;2025200228   13 Jan 2025a step of measuring a rotational speed of the runner at each opening of the guide vanes, and of deriving a circumferential speed of the runner;a step of deriving a relative speed of the swirling flow5 based on the swirling flow speed and the circumferential speed;a step of deriving a relationship between the stress and the relative flow speed based on the stress and the relative flow speed; anda step of deriving, as the predetermined relative flow 10 speed threshold value, the relative flow speed corresponding to a predetermined stress based on the relationship.

3. The startup method of a Francis turbine according to claim1, wherein the predetermined relative flow speed threshold value15 is derived by a stress analysis on the runner when increase in pressure, which is derived from a flow analysis simulating occurrence and collapse of cavitation, is applied to the runner.

4. The startup method of a Francis turbine according to claim20   1, wherein, in the second step, the swirling flow speed of theswirling flow at the changed guide vane opening is derived by a flow analysis using a calculation model having a flow path shape similar to that of the Fransis turbine.25   5.    The startup method of a Francis turbine according to claim1, wherein, in the third step, the circumferential speed of the runner at the changed guide vane opening is derived based on a rotational speed of the runner at the changed guide vane opening which is predicted by a simulation result upon startup of the30 Francis turbine.2025200228   13 Jan 20256.    The startup method of a Francis turbine according to claim1, wherein, in the third step, the circumferential speed of the runner at the changed guide vane opening is a circumferential 5 speed measured in the runner upon startup of the Francis turbine.

7. The startup method of a Francis turbine according to anyof claims 1 to 6, further including a sixth step of shifting to a normal operation control when a rotational speed of the runner is 10 determined to have reached a predetermined speed.

8. The startup method of a Francis turbine according to anyof claims 1 to 6, further including:a seventh step of issuing a command to change the 15 changed guide vane opening to a smaller opening when the relative flow speed is determined not to be equal to or less than the predetermined relative flow speed threshold value; andan eighth step of issuing a command to change the changed guide vane opening to a larger opening when a rotational 20 speed of the runner is determined not to reach a predetermined speed.

9. A startup program of a Francis turbine including guidevanes capable of regulating a flow rate of water to be guided to 25 a runner, including:a first command for controlling an opening of the guide vanes in a micro time unit, and for changing the opening to a changed guide vane opening;a second command for deriving a swirling flow speed of 30 the swirling flow at the changed guide vane opening;2025200228   13 Jan 2025a third command for deriving a circumferential speed of the runner at the changed guide vane opening;a fourth command for deriving a relative flow speed of the swirling flow based on the swirling flow speed and the5 circumferential speed; anda fifth command for comparing the relative flow speed and a predetermined relative flow speed threshold value, and for determining whether a rotational speed of the runner at the changed guide vane opening has reached a predetermined speed10 when the relative flow speed is equal to or less than the predetermined relative flow speed threshold value.

10. The startup program of a Fransis turbine according to claim9, wherein the derivation of the predetermined relative flow15 speed threshold value includes:a command for measuring a stress on the runner;a command for predicting a swirling flow speed of the swirling flow at each opening of the guide vanes based on a flow analysis using a calculation model having a flow path shape20 similar to that of the Fransis turbine;a command for measuring a rotational speed of the runner at each opening of the guide vanes, and for deriving a circumferential speed of the runner;a command for deriving a relative speed of the swirling25 flow based on the swirling flow speed and the circumferential speed;a command for deriving a relationship between the stress and the relative flow speed based on the stress and the relative flow speed; and30         a command for deriving, as the predetermined relative2025200228   13 Jan 2025flow speed threshold value, the relative flow speed corresponding to a predetermined stress based on the relationship.

11. The startup program of a Francis turbine according to claim 5  9, wherein the predetermined relative flow speed threshold valueis derived by a stress analysis on the runner when increase in pressure, which is derived from a flow analysis simulating occurrence and collapse of cavitation, is applied to the runner.10   12. The startup program of a Francis turbine according to claim9, wherein, in the second command, the swirling flow speed of the swirling flow at the changed guide vane opening is derived by a flow analysis using a calculation model having a flow path shape similar to that of the Fransis turbine.1513. The startup program of a Francis turbine according to claim 9, wherein, in the third command, the circumferential speed of the runner at the changed guide vane opening is derived based on a rotational speed of the runner at the changed guide vane 20 opening, which is predicted by a simulation result upon startup of the Francis turbine.

14. The startup program of a Francis turbine according to claim 9, wherein, in the third command, the circumferential speed of 25 the runner at the changed guide vane opening is a circumferential speed measured in the runner upon startup of the Francis turbine.

15. The startup program of a Francis turbine according to any of claims 9 to 14, further including a sixth command for shifting 30 to a normal operation control when a rotational speed of the2025200228   13 Jan 2025runner is determined to have reached a predetermined speed.

16. The startup program of a Francis turbine according to any of claims 9 to 14, further including:5        a seventh command for issuing a command to change thechanged guide vane opening to a smaller opening when the relative flow speed is determined not to be equal to or less than the predetermined relative flow speed threshold value; andan eighth command for issuing a command to change the10 changed guide vane opening to a larger opening when a rotational speed of the runner is determined not to reach a predetermined speed.

17. A control device of a Francis turbine including guide vanes15 capable of regulating a flow rate of water to be guided to a runner, including:an opening change unit that controls the guide vanes, and changes an opening of the guide vanes;a derivation unit that performs a calculation process or an20 analysis process during control of the guide vanes;a memory unit that stores data from the derivation unit or an external unit;a comparison unit that compares respectively different data from among the data during control of the guide vanes; and25         an opening / closing command unit that receivesdetermination of the comparison unit, and issues a command for changing an opening of the guide vanes to the opening change unit.

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