A hydraulic impedance calculation method considering the motion characteristics of a water turbine

Abstract

The present application relates to the field of water power station water delivery power generation system, specifically a kind of water turbine hydraulic impedance calculation method considering the motion characteristics of water turbine, it is characterized in that, step includes: step one, reads the parameters of water turbine;Step two, establish water turbine generator set rotation equation;Step three, establish water turbine stable operation condition output equation;Step four, derive the relationship between the rotational torque and the working flow of water turbine.Relative to the existing hydraulic impedance calculation method, the hydraulic impedance value considering the motion characteristics of water turbine can be obtained by this method, the hydraulic impedance calculation formula considering the motion characteristics of water turbine can improve the calculation accuracy, and the pressure change along the line of water delivery system can be simulated more accurately in numerical calculation.

Description

Technical Field

[0001] This invention relates to a hydropower station water conveyance and power generation system, specifically a method for calculating hydraulic impedance considering the motion characteristics of a water turbine. Background Technology

[0002] In recent decades, the power energy structure has been gradually adjusted, with the proportion of intermittent renewable energy in the power grid continuously increasing, causing significant impacts on the grid. To regulate grid parameters, hydropower stations are required to operate more frequently outside their optimal conditions, making hydropower an irreplaceable energy source. To ensure stable power system operation, turbines experience numerous dynamic load imbalances, resulting in complex flow patterns. Currently, the operational stability of mixed-flow turbines under off-design conditions has become a significant issue. Adjustments to unit operating conditions can cause transient processes, and unstable flow patterns within the flow channel can lead to substantial pressure oscillations, affecting unit stability and power station safety. Hydropower stations already built or under construction in recent years are trending towards higher head and larger capacity, inevitably operating under off-design conditions. Disturbances within the flow channel can lead to hydraulic resonance, impacting power station safety. Hydraulic vibration research and testing methods are costly, pose safety hazards, and carry significant risks, thus presenting considerable limitations.

[0003] As a crucial hydraulic component in a hydropower station, the calculation of the hydraulic impedance of a turbine is closely related to the unit's speed, flow rate, operating head, and torque. Its dynamic characteristics play a vital role in the stability and safety of the hydropower station. During actual operation, if hydraulic vibration occurs within the system, the flow rate and operating pressure of the turbine runner will change accordingly, disrupting the turbine's equilibrium state. This equilibrium state will be re-established during the transient process. However, current calculations related to hydraulic vibration characteristics treat the turbine as a valve with a fixed orifice, neglecting the dynamic characteristics such as changes in unit speed and torque during transient processes. Summary of the Invention

[0004] The purpose of this invention is to address the problem that traditional hydraulic vibration analysis models of turbines neglect the dynamic characteristics of the turbine. This invention considers the turbine's motion characteristics in the turbine's hydraulic impedance model, better simulating the actual operation of the unit, and proposes a method for calculating the hydraulic impedance of a turbine that considers the unit's motion characteristics. To this end, this invention adopts the following technical solution:

[0005] A method for calculating the hydraulic impedance of a hydro turbine considering the motion characteristics of the unit, the method comprising:

[0006] Step 1: Read the parameters, including: turbine operating efficiency η; turbine main shaft output torque T, in N·m; turbine rotational angular velocity ω. s The unit is rad / s; the instantaneous operating flow rate of the water turbine is Q, and the unit is m³ / s. 3 / s; Instantaneous operating head of the turbine, H, in meters; Moment of inertia I of the rotating parts of the unit and the water body, in t·m. 2 ;

[0007] Step 2: Establish the rotation equation of the hydro-generator unit, expressed as:

[0008]

[0009] Where I represents the moment of inertia of the rotating parts of the unit and the water body, and the unit is t·m. 2 ; d represents the differential operator; t represents time, in seconds; ω s T is the angular acceleration of the turbine, measured in rad / s. z T is the shaft torque of the water turbine, measured in N·m. g This represents the electromagnetic torque of the generator, measured in N·m.

[0010] The form of change in rotational angular velocity increment during a transient process:

[0011]

[0012] Where, ω′ s T represents the increment of the turbine's rotational angular acceleration. T I represents the increment of the rotational torque of the turbine unit, in N·m; I represents the moment of inertia added to the rotating parts of the unit and the water body, in t·m. 2 e is the natural constant; s is a complex number, s = σ + iω; t represents time;

[0013] Step 3: Establish the power output equation for the turbine under stable operating conditions, expressed as:

[0014] P=Tω S =ηγ0QH (3)

[0015] Where P represents the turbine output power, in kW; T represents the instantaneous output rotational torque of the turbine main shaft, in N·m; ω s η represents the angular acceleration of the turbine, measured in rad / s; η represents the turbine's efficiency; γ0 represents the specific weight of water, γ0 = 9.81 kN / m³. 3 Q represents the instantaneous operating flow rate of the water turbine, measured in cubic meters per second (m³). 3 / s; H represents the instantaneous operating head of the water turbine, in meters (m);

[0016] The turbine impedance form considering the changes in torque and speed during transient processes is as follows:

[0017]

[0018]

[0019] Where η represents the turbine's efficiency; γ0 represents the specific weight of water, γ0 = 9.81 kN / m³. 3 ; This indicates the rated operating flow rate of the water turbine, in cubic meters per second (m³). 3 / s; H represents the rated operating head of the water turbine, measured in meters (m). T Q represents the nodal pressure amplitude of the water turbine, in meters (m). T This represents the flow rate amplitude at the turbine node, measured in meters (m). 3 / s;

[0020] Step 4: Based on the similarity law of turbine flow rates Similar to the torque of a water turbine, The relationship between the rotational torque and the turbine's operating flow rate is derived and expressed as follows:

[0021]

[0022] Among them, Q 11 This represents the unit flow rate, with units of m. 3 / s; D1 represents the turbine diameter, in meters (m); T 11 Indicates unit torque;

[0023] The improved expression for the turbine impedance is:

[0024]

[0025] The hydraulic impedance of the turbine is calculated using formula (4.5).

[0026] As described above, in the method for calculating the hydraulic impedance of a turbine considering the motion characteristics of the unit, further, in step two:

[0027] The feature lies in step two:

[0028] According to Newton's second law, the relationship between the increment of torque and the increment of angular velocity in a rotating machine is expressed as follows:

[0029]

[0030] Where T′ represents the torque increment; ω′ s The increment of the turbine's angular acceleration is represented by t; time is represented by t.

[0031] The oscillation of rotational torque is developed into the form T′=T T e st Substituting into Equation 2.1, and integrating both sides of the equation with respect to time t, we obtain the form of the change in the rotational angular velocity increment during the transient process:

[0032]

[0033] As described above, the method for calculating the hydraulic impedance of a turbine considering the motion characteristics of the unit further includes the following steps in step three:

[0034] Step 3.1: The changes in rotational torque and pressure oscillations are assumed to develop in a sinusoidal manner. in, and These are the turbine main shaft output torque and turbine rotational angular velocity under steady-state conditions, respectively; T T Q T and H T The subscript T refers to the turbine node position, representing the corresponding torque, flow rate, and head at that node position;

[0035] Step 3.2, substitute the expressions for instantaneous rotational torque, instantaneous rotational angular velocity, instantaneous flow rate, and instantaneous working head from Step 3.1 into formula (3) the turbine output equation.

[0036]

[0037] Step 3.3, substitute formula (2.2) into formula (3.2), which is expressed as:

[0038]

[0039] Step 3.4: Expand both sides of equation (3.3), eliminate the average term and higher-order terms on both sides, and obtain:

[0040]

[0041] Step 3.5: Divide both sides of formula (3.4) by Q. T ,get

[0042]

[0043] Step 3.6: Rearrange formula (3.5) by dividing both sides by... The turbine impedance form considering torque and speed changes during transient processes is obtained.

[0044]

[0045]

[0046] As described above, the method for calculating the hydraulic impedance of a turbine considering the motion characteristics of the unit further includes the following steps in step four:

[0047] Step 4.1, expand the instantaneous torque and instantaneous flow rate in formula (4) into the sum of average and oscillatory terms, to obtain,

[0048]

[0049] in, ΔT represents the average rotating torque of the turbine, in N·m; ΔT represents the oscillating torque of the turbine, in N·m; ΔQ represents the oscillating flow rate of the turbine, in m³ / s. 3 / s.

[0050] Step 4.2, expand the flow term on the right side of equation (4.1), since... Therefore, the series converges. Taking a first-order approximation and ignoring higher-order terms, we obtain:

[0051]

[0052] Step 4.3, eliminate the steady-state average term from formula (4.2) to obtain,

[0053]

[0054] Step 4.4, divide both sides of equation (4.3) by ΔQ to obtain...

[0055]

[0056] Step 4.5: Substitute the expression obtained from formula (4.4) into formula (3.6.2) to obtain the improved expression for the turbine impedance.

[0057]

[0058] The beneficial effects of this invention are as follows:

[0059] 1. The present invention proposes a method for calculating hydraulic impedance considering the motion characteristics of a water turbine, which takes into account the change in unit speed during hydraulic vibration, and can more accurately simulate the mathematical model of the water turbine unit.

[0060] 2. The present invention proposes a method for calculating hydraulic impedance considering the motion characteristics of a water turbine, which can obtain the hydraulic impedance values ​​of a water turbine under different disturbance frequencies and analyze the relationship between the hydraulic impedance of the water turbine and the disturbance frequency.

[0061] 3. The hydraulic impedance calculation method considering the motion characteristics of the turbine proposed in this invention can be used for hydraulic vibration analysis of water conveyance power generation system to obtain the hydraulic vibration characteristics of water conveyance system considering the dynamic characteristics of the unit. Attached Figure Description

[0062] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0063] Figure 1 The diagram shows the calculation results of the hydraulic impedance of the turbine. Detailed Implementation

[0064] In actual hydraulic vibration processes, if the turbine experiences oscillations due to excessive flow, the torque exerted by the water flow on the runner will also change accordingly, disrupting the turbine's equilibrium state and placing it in a transient process. Therefore, the dynamic characteristics of the turbine are introduced into the hydraulic impedance model. The specific steps are as follows.

[0065] Read parameters including: turbine operating efficiency η; turbine main shaft output torque T, in N·m; turbine rotational angular velocity ω. s The unit is rad / s; the instantaneous operating flow rate of the water turbine is Q, and the unit is m³ / s. 3 / s; Instantaneous operating head of the turbine, H, in meters; Moment of inertia I of the rotating parts of the unit and the water body, in t·m. 2 ;

[0066] The rotation equation of the hydro-generator unit can be expressed as:

[0067]

[0068] Where I represents the moment of inertia of the rotating parts of the unit and the water body, and the unit is t·m. 2 ; d represents the differential operator; t represents time, in seconds; ω s T is the angular acceleration of the turbine, measured in rad / s. z T is the shaft torque of the water turbine, measured in N·m. g This represents the electromagnetic torque of the generator, measured in N·m.

[0069] During the motion of rotating machinery, according to Newton's second law, the relationship between the increment of the rotating machinery's torque and the increment of its rotational angular velocity can be expressed as follows:

[0070]

[0071] The oscillation of rotational torque is developed into the form T′=T T e st Substituting into equation (2.1), and integrating the terms on both sides of the equation with respect to time t, we obtain the following form of the change in the rotational angular velocity increment during the transient process:

[0072]

[0073] Based on the working principle of a water turbine, under stable operating conditions, the power output of a water turbine can be expressed as follows:

[0074] P=Tω S =ηγ0QH (3)

[0075] Where P represents the turbine output power, in kW; T represents the instantaneous output rotational torque of the turbine main shaft, in N·m; ω s η represents the angular acceleration of the turbine, measured in rad / s; η represents the turbine's efficiency; γ0 represents the specific weight of water, γ0 = 9.81 kN / m³. 3 Q represents the instantaneous operating flow rate of the water turbine, measured in cubic meters per second (m³). 3 / s; H represents the instantaneous operating head of the water turbine, in meters (m);

[0076] Based on the theory of hydraulic vibration, it is proposed that the change in rotational torque develops in a sinusoidal manner, similar to the pressure oscillation. and These are the turbine main shaft output torque and turbine rotational angular velocity under steady-state conditions, respectively; T T Q T and H T The subscript T refers to the turbine node position, representing the corresponding torque, flow rate, and head at that node position.

[0077] Expanding the instantaneous rotational torque, instantaneous rotational angular velocity, instantaneous flow rate, and instantaneous working head in formula (3), we obtain:

[0078]

[0079] Formula

[0080] (2.2) Substituting into formula (3.2), we have,

[0081]

[0082] Expanding both sides of the above equation, we get:

[0083]

[0084] By eliminating the average term and higher-order terms from both sides of the equation, we obtain:

[0085]

[0086] Divide both sides by Q T ,get

[0087]

[0088] Rearranging and simplifying formula (3.5) yields the following:

[0089]

[0090] Divide both sides by Based on the definition of hydraulic impedance, the expression for the turbine impedance considering the changes in torque and speed during transient processes is as follows.

[0091]

[0092] Based on the similarity law of water turbine flow Similar to the relationship between the torque of a water turbine, the relationship between the rotational torque and the operating flow rate of the water turbine can be derived, expressed as follows:

[0093]

[0094] Expanding the instantaneous torque and instantaneous flow rate in formula (4) into the sum of average and oscillatory terms, we get:

[0095]

[0096] Expanding the flow term on the right side of the equals sign, since... Therefore, the series converges. Taking a first-order approximation and ignoring higher-order terms, we obtain:

[0097]

[0098] Eliminating the steady-state average term from formula (4.2) yields:

[0099]

[0100] Dividing both sides of the equation by ΔQ, we get

[0101]

[0102] Substituting expression (4.4) into formula (3.6.2), we obtain the improved expression for the turbine impedance.

[0103]

[0104] The amplitude of the upstream continuous external pressure disturbance is set at K = 0.01, and the frequency range of the forcing function is selected from 0.001 to 20 rad / s. Under the action of the forcing function, the magnitude of the turbine hydraulic impedance modulus is shown below. Figure 1 .

Claims

1. A method for calculating hydraulic impedance considering the motion characteristics of a hydraulic turbine, characterized by The steps include: Step 1: Read the parameters, including: turbine operating efficiency η; turbine main shaft output torque T, in N·m; turbine rotational angular velocity ω. s The unit is rad / s; the instantaneous operating flow rate of the water turbine is Q, and the unit is m³ / s. 3 / s; Instantaneous operating head of the turbine, H, in meters; Moment of inertia I of the rotating parts of the unit and the water body, in t·m. 2 ; Step two, the establishment of the rotating equation of the hydroelectric generating set, expressed as: wherein I represents the added moment of inertia of the rotating part of the unit and the water body, in t-m 2 ; d represents the differential operator; t represents time, in s; ω s represents the rotational angular acceleration of the water turbine, in rad / s; T z represents the water turbine shaft torque, in N-m; T g represents the generator electromagnetic torque, in N-m; The form of the increment of the rotational angular velocity in the transient process: where ω′ s represents the water turbine rotation angle acceleration increment, T T is the water turbine set rotation torque increment, with the unit of N·m; I is the additional moment of inertia of the rotating part of the set and water body, with the unit of t·m 2 ; e is a natural constant; s is a complex number, s=σ+iω; t represents time; Step three, the establishment of the output equation of the hydroelectric generating set in the stable operation condition, expressed as: P = Tω S = ηg0QH (3) where P represents the output of the water turbine, in kW; T represents the instantaneous output rotational torque of the main shaft of the water turbine, in N-m; ω s represents the rotational speed of the main shaft of the water turbine, in rad / s; η represents the working efficiency of the water turbine; γ0represents the specific weight of water, γ0= 9.81 kN / m 3 ; Q represents the instantaneous working flow of the water turbine, in m 3 / s; and H represents the instantaneous working head of the water turbine, in m. The impedance form of the hydroelectric generating set considering the changes of the torque and the rotational speed in the transient process is: wherein η represents the water turbine working efficiency; γ0represents the specific gravity of water, γ0= 9.81 kN / m 3 ; represents the water turbine rated working flow, with the unit of m 3 / s; represents the water turbine rated working head, with the unit of m; H T represents the water turbine node pressure amplitude, with the unit of m; Q T represents the water turbine node flow amplitude, with the unit of m 3 / s; Step four, based on the hydraulic turbine flow similarity law and the hydraulic turbine torque similarity relationship, The relationship between the rotational torque and the hydraulic turbine working flow is derived, expressed as, where Q 11 represents the unit flow rate, with units of m 3 / s; D1 represents the turbine diameter, with units of m; T 11 represents the unit torque; The improved impedance expression of the hydroelectric generating set is: The hydraulic impedance of the hydroelectric generating set is calculated according to the formula (4.5).

2. The method for calculating hydraulic impedance considering the motion characteristics of a hydraulic turbine according to claim 1, characterized in that In step two: According to the second law of Newton, the relationship between the increment of the rotational mechanical torque and the increment of the rotational angular velocity is expressed as: where T' represents the moment increment; ω s ' represents the water turbine rotational angular acceleration increment; t represents time; The rotational torque oscillation development form T' = T T e st Substituting formula 2.1, integrating both sides with respect to time t, the rotational angular velocity increment change form during the transient process:

3. The method of claim 1, wherein the water power impedance is calculated considering the motion characteristics of the hydraulic turbine. Step three includes the following steps: Step 3.1, the development of the variation of the rotational torque and the pressure oscillation in the form of a sine, wherein, and T and ω are the output rotational torque of the main shaft of the water turbine and the rotational angular velocity of the water turbine in the steady state, respectively; T Q and H T and H T The subscript T in the middle and lower part indicates the node position of the water turbine, which respectively represents the corresponding torque, flow and water head of the node position. Step 3.2, the expression forms of the instantaneous rotational torque, the instantaneous rotational angular velocity, the instantaneous flow and the instantaneous working water head in step 3.1 are substituted into the output equation of the hydroelectric generating set in formula (3), Step 3.3, formula (2.2) is substituted into formula (3.2), expressed as: Step 3.4, the both sides of formula (3.3) are expanded, and the average terms and the high-order small terms on both sides of the equal sign are eliminated, to obtain: Step 3.

5. Divide both sides of equation (3.4) by Q T to obtain Step 3.

6. Rearranging equation (3.5) by moving terms to the left-hand side and dividing both sides by The impedance form of hydraulic turbine is obtained considering the change of torque and speed during transient process.

4. The method of claim 1, wherein the water power impedance is calculated considering the motion characteristics of the hydraulic turbine. Step four includes the following steps: Step 4.1, the instantaneous torque and the instantaneous flow in formula (4) are expanded into the sum of the average terms and the oscillation terms, to obtain, wherein, represents the water turbine rotating torque average term, the unit is N-m; ΔT represents the water turbine rotating torque oscillation term, the unit is N-m; ΔQ represents the water turbine operating flow oscillation term, the unit is m 3 / s; Step 4.2, expand the flow term on the right side of equation (4.1), since Therefore, the series converges, and a first order approximation is made, neglecting the small higher order terms, to give Step 4.3, the steady average term in formula (4.2) is eliminated, to obtain, Step 4.4, step formula (4.3) is divided by ΔQ on both sides of the equal sign, to obtain Step 4.5, the expression obtained from formula (4.4) is substituted into formula (3.6.2), to obtain the improved impedance expression of the hydroelectric generating set,

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