Hydraulic impedance calculation method considering motion characteristics of water turbine

Abstract

The invention relates to the field of water delivery and power generation systems of hydropower stations, in particular to a water turbine hydraulic impedance calculation method considering motion characteristics of a water turbine, which is characterized by comprising the following steps of: 1, reading various parameters of the water turbine; step 2, establishing a rotation equation of the water-turbine generator set; 3, establishing a stable operation condition output equation of the water turbine; and 4, deducing to obtain the relationship between the rotating torque and the working flow of the water turbine. Compared with an existing hydraulic impedance calculation method, the method can obtain the hydraulic impedance value considering the motion characteristics of the water turbine, the hydraulic impedance calculation formula considering the motion characteristics of the water turbine can improve the calculation precision, and the pressure change condition along the water delivery system can be more accurately simulated in numerical calculation.

Description

Technical Field

[0001] The invention relates to a water transmission and power generation system of a hydropower station, in particular to a hydraulic impedance calculation method taking into account the motion characteristics of a water turbine. Background Art

[0002] In recent decades, the structure of electric power energy has been gradually adjusted, and the proportion of intermittent renewable energy in the power grid has continued to increase, causing a great impact on the power grid. In order to adjust the parameters of the power grid, hydropower stations are required to deviate from the optimal operating conditions more frequently, and hydropower energy plays an irreplaceable role. In order to ensure the stable operation of the power system, the turbine undergoes many dynamic load imbalance states, and the flow state is complex during the process. At present, the operating stability of the mixed flow turbine under non-design conditions has become an issue that cannot be ignored. The adjustment of the unit's operating conditions will cause transient processes, and the unstable flow state in the flow channel may cause huge pressure oscillations and affect the stability of the unit and the safety of the power station. In recent years, the hydropower stations that have been built or are under construction are developing towards high head and large capacity. It is inevitable that they will operate under non-design conditions. Due to the disturbance in the flow channel, hydraulic resonance may occur, affecting the safety of the hydropower station. The hydraulic vibration research test method is costly, has safety hazards, is risky, and has great limitations.

[0003] As a key hydraulic component in a hydropower station, the calculation of hydraulic impedance of a turbine is closely related to the unit speed, flow, working head, and torque, and its dynamic characteristics play a vital role in the stability and safety of a hydropower station. In actual operation, if hydraulic vibration occurs in the system, the flow rate and pressure of the turbine runner will also change, and the equilibrium state of the turbine itself will be broken. The equilibrium state will be rebuilt during the transient process. However, in the current calculations related to hydraulic vibration characteristics, the turbine is regarded as a valve with a fixed orifice, ignoring the dynamic characteristics such as the unit speed and torque changes during the transient process. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the traditional hydraulic vibration analysis turbine mathematical model ignores the dynamic characteristics of the turbine, consider the motion characteristics of the turbine in the turbine hydraulic impedance model, better simulate the actual operation process of the unit, and propose a method for calculating the hydraulic impedance of the turbine considering the motion characteristics of the unit. To this end, the present invention adopts the following technical solutions:

[0005] A method for calculating hydraulic impedance of a water turbine taking into account the motion characteristics of the unit, the method comprising:

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

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

[0008]

[0009] Where I represents the additional 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, the unit is s; ω s is the turbine rotation angular acceleration, in rad / s; T z is the turbine shaft torque, in N·m; T g is the electromagnetic torque of the generator, the unit is N·m;

[0010] The form of the rotation angular velocity increment change during the transient process is:

[0011]

[0012] Among them, ω′ s represents the increment of turbine rotation angular acceleration, T T is the rotation torque increment of the turbine unit, in N·m; I is the additional rotation inertia of the rotating parts of the unit and the water body, in t·m 2 ; e is a natural constant; s is a complex number, s = σ + iω; t represents time;

[0013] Step 3: Establish the output equation of the turbine under stable operation conditions, expressed as:

[0014] P=Tω S =ηγ0QH (3)

[0015] Where P represents the turbine output in kW; T represents the instantaneous output torque of the turbine main shaft in N·m; ω s is the turbine rotation angular acceleration, the unit is rad / s; η is the turbine working efficiency; γ0 is the gravity of water, γ0=9.81kN / m 3 ; Q represents the instantaneous working flow of the turbine, the unit is m 3 / s; H represents the instantaneous working water head of the turbine, the unit is m;

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

[0017]

[0018]

[0019] Among them, η represents the working efficiency of the turbine; γ0 represents the gravity of water, γ0=9.81kN / m 3 ; Indicates the rated operating flow rate of the turbine, in m 3 / s; Indicates the rated operating head of the turbine, in m; H T Indicates the turbine node pressure amplitude, in m; Q T Indicates the turbine node flow amplitude, in m 3 / s;

[0020] Step 4: Based on the similarity law of turbine flow Similar to the turbine torque, The relationship between the rotation torque and the turbine working flow is derived and expressed as,

[0021]

[0022] Among them, Q 11 Indicates unit flow rate, the unit is m 3 / s; D1 represents the turbine diameter, in m; T 11 represents unit moment;

[0023] The improved turbine impedance expression 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 water turbine taking into account the motion characteristics of the unit, further, in step 2:

[0027] The characteristic is that in step 2:

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

[0029]

[0030] Where T′ represents the torque increment; ω′ s represents the increment of the turbine rotation angular acceleration; t represents time;

[0031] The rotation torque oscillation quantity is developed in the form of T′=T T e st Substituting into formula 2.1, integrating the time t on both sides of the equal sign, the incremental change of the rotational angular velocity during the transient process is:

[0032]

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

[0034] Step 3.1, the change of rotation torque and pressure oscillation are assumed to develop in a sinusoidal form. in, and are the output torque of the main shaft of the turbine and the angular velocity of the turbine under steady state; T T , Q T and H T The subscript T refers to the turbine node position, and represents the corresponding moment, flow and head at the node position;

[0035] Step 3.2, substitute the expressions of instantaneous rotation torque, instantaneous rotation angular velocity, instantaneous flow rate and instantaneous working water head in step 3.1 into the turbine output equation of formula (3),

[0036]

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

[0038]

[0039] Step 3.4, expand both sides of the equation (3.3), eliminate the average terms and high-order small terms on both sides of the equation, and obtain:

[0040]

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

[0042]

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

[0044]

[0045]

[0046] As described above, a method for calculating hydraulic impedance of a water turbine taking into account the motion characteristics of the unit, further, step 4 includes the following steps:

[0047] Step 4.1, expand the instantaneous torque and instantaneous flow in formula (4) into the form of the sum of the average term and the oscillation term, and obtain,

[0048]

[0049] in, It represents the average term of the turbine rotation torque, and its unit is N·m; ΔT represents the oscillation term of the turbine rotation torque, and its unit is N·m; ΔQ represents the oscillation term of the turbine operating flow, and its unit is m 3 / s.

[0050] Step 4.2, expand the flow term on the right side of the equation (4.1), because So the series converges, and as a first-order approximation, ignoring the higher-order small terms, we get,

[0051]

[0052] Step 4.3, eliminate the steady-state average term from formula (4.2) and 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 turbine impedance expression,

[0057]

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

[0059] 1. The hydraulic impedance calculation method proposed in the present invention takes into account the motion characteristics of the turbine, takes into account the change in the rotation speed of the unit during the hydraulic vibration process, and can simulate the mathematical model of the turbine unit more accurately.

[0060] 2. The hydraulic impedance calculation method proposed in the present invention taking into account the motion characteristics of the turbine can obtain the hydraulic impedance values ​​of the turbine under different disturbance frequencies and analyze the relationship between the hydraulic impedance of the turbine and the disturbance frequency.

[0061] 3. The hydraulic impedance calculation method proposed in the present invention taking into account the motion characteristics of the turbine can be used for hydraulic vibration analysis of the water transmission and power generation system to obtain the hydraulic vibration characteristics of the water transmission system taking into account the dynamic characteristics of the unit. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0063] Figure 1 This is the calculation result diagram of the hydraulic impedance of the turbine. DETAILED DESCRIPTION

[0064] In the actual hydraulic vibration process, if the flow rate of the turbine oscillates, the torque of the water flow on the runner will also change accordingly, the equilibrium state of the turbine will be broken, and it will be 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 working efficiency η; turbine main shaft output torque T, unit is N·m; turbine rotation angular velocity ω s , the unit is rad / s; the instantaneous working flow rate of the turbine Q, the unit is m 3 / s; instantaneous working water head of turbine H, in m; additional moment of inertia of rotating parts of unit and water body I, in t·m 2 ;

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

[0067]

[0068] Where I represents the additional 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, the unit is s; ω s is the turbine rotation angular acceleration, in rad / s; T z is the turbine shaft torque, in N·m; T g is the electromagnetic torque of the generator, the unit is N·m;

[0069] In the process of rotating mechanical motion, according to Newton's second law, the relationship between the rotating mechanical torque increment and the rotating angular velocity increment can be expressed as:

[0070]

[0071] The rotation torque oscillation quantity is developed in the form of T′=T T e st Substituting into equation (2.1), the terms on both sides of the equal sign are integrated with respect to time t, so that the increment change of the rotational angular velocity during the transient process is obtained as follows:

[0072]

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

[0074] P=Tω S =ηγ0QH (3)

[0075] Where P represents the turbine output in kW; T represents the instantaneous output torque of the turbine main shaft in N·m; ω s is the turbine rotation angular acceleration, the unit is rad / s; η is the turbine working efficiency; γ0 is the gravity of water, γ0=9.81kN / m 3 ; Q represents the instantaneous working flow of the turbine, the unit is m 3 / s; H represents the instantaneous working water head of the turbine, the unit is m;

[0076] According to the hydraulic vibration theory, the change of the rotation torque is assumed to develop in a sinusoidal form with the pressure oscillation. and are the output torque of the main shaft of the turbine and the angular velocity of the turbine under steady state; T T , Q T and H T The subscript T refers to the node position of the turbine, and represents the corresponding torque, flow and head at the node position respectively.

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

[0078]

[0079] The formula

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

[0081]

[0082] Expand both sides of the above equation to get:

[0083]

[0084] By eliminating the average terms and higher-order small terms on both sides of the equal sign, we get:

[0085]

[0086] Divide both sides by Q T ,get

[0087]

[0088] By rearranging formula (3.5), we can obtain

[0089]

[0090] Divide both sides by According to the definition of hydraulic impedance, the turbine impedance expression considering the changes in torque and speed during transient process is as follows:

[0091]

[0092] Based on the similarity law of turbine flow Based on the similarity law of turbine flow Similar to the turbine torque, the relationship between the rotation torque and the turbine working flow can be derived and expressed as,

[0093]

[0094] Expand the instantaneous torque and instantaneous flow in formula (4) into the sum of the average term and the oscillation term, and we get:

[0095]

[0096] Expand the flow term on the right side of the equal sign, because So the series converges, and as a first-order approximation, ignoring the higher-order small terms, we get,

[0097]

[0098] Eliminate the steady-state average term from formula (4.2) and we get:

[0099]

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

[0101]

[0102] Substituting expression (4.4) into formula (3.6.2), we get the improved turbine impedance expression:

[0103]

[0104] The proposed external pressure disturbance amplitude of the upstream continuous action is 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 hydraulic impedance modulus of the turbine is shown in Figure 1 .

Claims

1. A method for calculating hydraulic impedance considering the motion characteristics of a hydraulic turbine, characterized in that The steps include: Step 1: Read parameters, including: turbine working efficiency η; turbine main shaft output torque T, in N·m; turbine rotation angular velocity ω s , the unit is rad / s; the instantaneous working flow rate of the turbine Q, the unit is m 3 / s; instantaneous working water head of turbine H, in m; additional moment of inertia of rotating parts of unit and water body I, in t·m 2 ; Step 2: Establish the rotation equation of the hydro-generator set, expressed as: Where I represents the additional 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, the unit is s; ω s is the turbine rotation angular acceleration, in rad / s; T z is the turbine shaft torque, in N·m; T g is the electromagnetic torque of the generator, the unit is N·m; The form of the rotation angular velocity increment change during the transient process is: Among them, ω′ s represents the increment of turbine rotation angular acceleration, T T is the rotation torque increment of the turbine unit, in N·m; I is the additional rotation inertia of the rotating parts of the unit and the water body, in t·m 2 ; e is a natural constant; s is a complex number, s = σ + iω; t represents time; Step 3: Establish the output equation of the turbine under stable operation conditions, expressed as: P=Tω S =ηγ0QH (3) Where P represents the turbine output in kW; T represents the instantaneous output torque of the turbine main shaft in N·m; ω s is the turbine rotation angular acceleration, the unit is rad / s; η is the turbine working efficiency; γ0 is the gravity of water, γ0=9.81kN / m 3 ; Q represents the instantaneous working flow of the turbine, the unit is m 3 / s; H represents the instantaneous working water head of the turbine, the unit is m; The turbine impedance considering the changes in torque and speed during transient processes is: Among them, η represents the working efficiency of the turbine; γ0 represents the gravity of water, γ0=9.81kN / m 3 ; Indicates the rated operating flow rate of the turbine, in m 3 / s; Indicates the rated operating head of the turbine, in m; H T Indicates the turbine node pressure amplitude, in m; Q T Indicates the turbine node flow amplitude, in m 3 / s; Step 4: Based on the similarity law of turbine flow Similar to the turbine torque, The relationship between the rotation torque and the turbine working flow is derived and expressed as, Among them, Q 11 Indicates unit flow rate, the unit is m 3 / s; D1 represents the turbine diameter, in m; T 11 represents unit moment; The improved turbine impedance expression is: The hydraulic impedance of the turbine is calculated using formula (4.5).

2. A method for calculating hydraulic impedance taking into account the motion characteristics of a water turbine as claimed in claim 1, characterized in that In step 2: According to Newton's second law, the relationship between the rotational mechanical torque increment and the rotational angular velocity increment is expressed as: Where T′ represents the torque increment; ω s ′ represents the increment of the turbine rotation angular acceleration; t represents time; The rotation torque oscillation quantity is developed in the form of T′=T T e st Substituting into formula 2.1, integrating the time t on both sides of the equal sign, the incremental change of the rotational angular velocity during the transient process is:

3. A method for calculating hydraulic impedance taking into account the motion characteristics of a water turbine as claimed in claim 1, characterized in that Step three includes the following steps: Step 3.1, the change of rotation torque and pressure oscillation are assumed to develop in a sinusoidal form. in, and are the output torque of the main shaft of the turbine and the angular velocity of the turbine under steady state; T T , Q T and H T The subscript T refers to the turbine node position, and represents the corresponding moment, flow and head at the node position; Step 3.2, substitute the expressions of instantaneous rotation torque, instantaneous rotation angular velocity, instantaneous flow rate and instantaneous working water head in step 3.1 into the turbine output equation of formula (3), Step 3.3, substitute formula (2.2) into formula (3.2), expressed as: Step 3.4, expand both sides of the equation (3.3), eliminate the average terms and high-order small terms on both sides of the equation, and obtain: Step 3.5, divide both sides of formula (3.4) by Q T ,get Step 3.6: Rearrange the terms in formula (3.5) and divide both sides by The turbine impedance form considering the changes in torque and speed during transient processes is obtained.

4. A method for calculating hydraulic impedance taking into account the motion characteristics of a water turbine as claimed in claim 1, characterized in that Step 4 includes the following steps: Step 4.1, expand the instantaneous torque and instantaneous flow in formula (4) into the form of the sum of the average term and the oscillation term, and obtain, in, It represents the average term of the turbine rotation torque, and its unit is N·m; ΔT represents the oscillation term of the turbine rotation torque, and its unit is N·m; ΔQ represents the oscillation term of the turbine operating flow, and its unit is m 3 / s. Step 4.2, expand the flow term on the right side of the equation (4.1), because So the series converges, and as a first-order approximation, ignoring the higher-order small terms, we get, Step 4.3, eliminate the steady-state average term from formula (4.2) and obtain, Step 4.4, divide both sides of equation (4.3) by ΔQ to obtain Step 4.5, substitute the expression obtained from formula (4.4) into formula (3.6.2) to obtain the improved turbine impedance expression,

Images