CN113987802A - Calculation method and system for characteristic coefficients of water pump turbine - Google Patents

Calculation method and system for characteristic coefficients of water pump turbine Download PDF

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CN113987802A
CN113987802A CN202111264435.3A CN202111264435A CN113987802A CN 113987802 A CN113987802 A CN 113987802A CN 202111264435 A CN202111264435 A CN 202111264435A CN 113987802 A CN113987802 A CN 113987802A
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许颜贺
赵坤杰
周建中
张勇传
刘颉
李思樊
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Huazhong University of Science and Technology
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Abstract

The invention discloses a method and a system for calculating characteristic coefficients of a water pump turbine, wherein the method comprises the following steps: the full characteristic curve of the water pump turbine is subjected to numerical value conversion, so that the converted equivalent full characteristic curve only corresponds to one unit flow rate at the same unit rotating speed; then, based on the equivalent full characteristic curve, interpolating by using a linear grid interpolation method to obtain the moment and the flow of the corresponding working condition point; finally, approximate calculation is carried out by adopting a method of replacing differential by difference, and the characteristic coefficient of the water pump turbine at the next moment is obtained; and carrying out repeated iterative calculation on the obtained characteristic coefficient of the water pump turbine to obtain a stable characteristic coefficient. The stability characteristic coefficient of the invention is obtained after a plurality of iterative calculations, and the corresponding stability characteristic coefficient can be calculated according to different water head working conditions. The stability characteristic coefficient of the invention can obviously improve the accuracy of numerical modeling simulation calculation of the full water head range of the regulating system of the pumped storage unit.

Description

Calculation method and system for characteristic coefficients of water pump turbine
Technical Field
The invention belongs to the technical field of simulation modeling of an electric power system, and particularly relates to a method and a system for calculating characteristic coefficients of a water pump turbine.
Background
The pumped storage unit plays roles of peak regulation, valley filling and phase regulation in a power grid, is an important tool for power grid operation scheduling, and has great significance for guaranteeing the safety and power supply quality of the power grid, coordinating the operation scheduling of thermal power, nuclear power and wind power in the power grid and improving the quality and economic benefit of the power grid.
The pumped storage unit adjusting system is an important component of a pumped storage unit, is a water-machine-electric mutual coupling complex nonlinear system, and has the function of adjusting the frequency and the load of the unit.
The pump turbine is the core equipment of a pumped storage unit adjusting system, can be used as a water pump and a water turbine, is also called as a reversible turbine, and can be used as a water pump when the rotating wheel rotates clockwise and a water pump when the rotating wheel rotates anticlockwise.
Under the condition of small fluctuation, in the numerical modeling simulation calculation of the full water head range of the pumped storage unit adjusting system, the dynamic characteristic of the pump turbine is usually expressed by adopting the characteristic coefficient of the pump turbine under the steady-state condition. The steady-state operating condition is a state that the peak value of the time chart of the relative value of the rotating speed deviation is smaller than a specified value. The characteristic coefficient of the pump turbine obtained under the steady-state working condition is generally considered as the optimal characteristic coefficient, and the method is most suitable for numerical modeling simulation calculation of the full water head range of the pumped storage unit regulating system.
The characteristic coefficients of the water pump turbine are six in total, and specifically include: the characteristic coefficient of the opening of the guide vane by the moment, the characteristic coefficient of the rotating speed by the moment, the characteristic coefficient of the water head by the moment, the characteristic coefficient of the opening of the guide vane by the flow, the characteristic coefficient of the rotating speed by the flow and the characteristic coefficient of the water head by the flow.
The water head working conditions of the pump-turbine are divided into three types, namely low, medium and high, and the same characteristic coefficients of the pump-turbine are used under the three types of water head working conditions in the prior art and are fixed ideal six coefficients set manually; however, the artificially set ideal six coefficients are far from the characteristic coefficients of the water pump turbine under the steady-state working condition, so that the accuracy of numerical modeling simulation calculation of the full water head range of the regulating system of the pumped storage unit can be greatly reduced by adopting the artificially set ideal six coefficients.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method and a system for calculating characteristic coefficients of a water pump turbine, and aims to solve the problem that the accuracy of numerical modeling simulation calculation of the full water head range of a regulating system of a pumped storage unit is reduced by an ideal six-coefficient set manually.
In order to achieve the purpose, the invention provides a method for calculating the characteristic coefficient of a pump turbine, which comprises the following steps:
(1) an initialization step: setting the current time t as the time when the water pump turbine is subjected to frequency disturbance excitation in a stable state; setting a relative value y of the opening deviation of the guide vane at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)(ii) a The water pump turbine characteristic coefficient of the current time t is set, and the method comprises the following steps: characteristic coefficient e of opening degree of guide vane by torque pairy(t)Characteristic coefficient e of torque to rotating speedx(t)Coefficient of torque vs. head characteristic eh(t)Flow versus guide vane opening characteristic coefficient eqy(t)Flow rate vs. speed characteristic coefficient eqx(t)Coefficient of flow vs. head characteristic eqh(t)；
(2) And (3) solving the state variable: the relative value y of the guide vane opening deviation at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)Substituting the characteristic coefficient of the water pump turbine into a nonlinear state space equation of the pumped storage unit, and solving the equation by using an Euler method to obtain a relative value q of flow deviation at the next moment t1(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)；
The step length of the next time t1 relative to the current time t is a set time step length;
(3) solving at a unit rotating speed: according to the relative value y of the guide vane opening deviation at the next time t1(t1)Relative value x of rotational speed deviation(t1)Relative value of flow deviation q(t1)And head deviation relative value h(t1)The unit rotating speed x of the next time t1 is obtained from the conversion relation between the unit parameters of the pump turbine and the working parameters of the real machine11(t1)(ii) a The real machine working parameters comprise flow Q, moment M, guide vane opening Y, rotating speed n and working water head H;
(4) equivalent unit rotating speed solving: unit speed x according to the next time t111(t1)The equivalent unit speed X at the next time t1 is obtained from the equivalent full characteristic curve11(t1)；
The construction method of the equivalent full characteristic curve comprises the following steps: according to the formulas (A1) - (A3), the abscissa in the full characteristic curve of the pump turbine is defined by the unit rotating speed x11Conversion to equivalent unit speed X11Keeping the ordinate unchanged;
Figure BDA0003326526570000031
Figure BDA0003326526570000032
Figure BDA0003326526570000033
wherein x is11rIs rated unit speed, Q11Is unit flow rate, Q11rFor rated unit flow rate, M11Is unit moment, M11rIs rated unit moment, alpha1、v1Is an intermediate variable, e is the base of the natural logarithm function;
(5) and flow torque solving:equivalent unit rotation speed X according to the next moment t111(t1)Performing interpolation solving on the equivalent full-characteristic curve by using a linear grid interpolation method to obtain the unit flow Q of the next moment t111And unit moment M11；
(6) And (3) solving the working condition points: taking values in the set range of the working condition points at the next moment t1 in the equivalent full characteristic curve to obtain four working condition points, which are respectively: the device comprises a first working condition point, a second working condition point, a third working condition point and a fourth working condition point, wherein equivalent unit rotating speeds of the first working condition point and the second working condition point are the same, and guide vane opening degrees of the third working condition point and the fourth working condition point are the same;
according to the conversion relation between the unit parameters of the pump turbine and the operating parameters of the real machine and the relative value y of the opening deviation of the guide vane at the next time t1(t1)Water head deviation relative value h(t1)Unit speed x11(t1)Unit flow rate Q11And unit moment M11Obtaining the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point at the next moment t 1;
(7) and (3) solving the characteristic coefficient: in the equivalent full characteristic curve, according to the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point, approximate calculation is carried out by adopting a difference instead of differentiation method, and the characteristic coefficient of the water pump turbine at the next moment t1 is obtained;
(8) and a stable characteristic coefficient solving step: using the relative value y of the opening deviation of the guide vane at the next time t1(t1)Relative value x of rotational speed deviation(t1)Relative value q of flow deviation of(t1)Update the relative value y of the guide vane opening deviation at the current time t(t)Relative value x of rotational speed deviation(t)And the relative value q of the flow deviation(t)Updating the value of the pump turbine characteristic coefficient at the current time t by using the value of the pump turbine characteristic coefficient at the next time t 1; pushing the current time t backwards according to the set time step length, and repeating the steps 2 to 7 until the water pump turbine reaches a steady-state working condition to obtain a steady characteristic coefficient; the stable characteristic coefficient is the water pump at the next moment t1 when the steady-state working condition is reachedCharacteristic coefficient of the water turbine.
Preferably, the nonlinear state space equation of the pumped storage group in the state variable solving step is as follows:
Figure BDA0003326526570000041
wherein the content of the first and second substances,
Figure BDA0003326526570000042
as a derivative of the relative value of the flow deviation at the present time t,
Figure BDA0003326526570000043
as a derivative of the relative value of the rotational speed deviation at the present moment t,
Figure BDA0003326526570000044
is the derivative of the relative value of the opening deviation of the guide vane at the current time T, Twt0Is the water hammer inertia time constant, ht0For head loss, H0At waterhead conditions, TJIs the unit inertia time constant, KpTo proportional gain, KiIs the integral gain;
a flow deviation relative value q at the next time t1 in the state variable solving step(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)Respectively as follows:
Figure BDA0003326526570000051
the unit rotation speed x at the next time t1 in the unit rotation speed solving step11(t1)Comprises the following steps:
Figure BDA0003326526570000052
wherein D is the diameter of the runner, n0To stabilize the rotation speed.
Preferably, the flow Q of any one of the four operating points in the operating point solving stepiMoment MiOpening degree Y of guide vaneiRotational speed niAnd an operating head HiThe following equations (A4) to (A8) were obtained:
Figure BDA0003326526570000053
Mi＝M11i(t1)D3Hi (A5)
Figure BDA0003326526570000054
Yi＝Ymax(1+yi(t1)) (A7)
Hi＝(1+hi(t1))Hr (A8)
wherein Q is11i(t1)Unit flow rate of the operating point, M11i(t1)Is the unit moment of the operating point, x11i(t1)Is the unit speed of the operating point, YmaxMaximum opening of the guide vanes, HrIs the rated working head.
Preferably, the stability characteristic coefficients in the stability characteristic coefficient solving step are respectively:
Figure BDA0003326526570000055
Figure BDA0003326526570000061
Figure BDA0003326526570000062
Figure BDA0003326526570000063
Figure BDA0003326526570000064
Figure BDA0003326526570000065
wherein e isy(t1)Characteristic coefficient of torque versus opening degree of guide vane, e, for the next time t1x(t1)The torque-to-speed characteristic coefficient, e, for the next time t1h(t1)Coefficient of moment versus head characteristic, e, for the next time t1qy(t1)Flow versus guide vane opening characteristic coefficient, e, for the next time t1qx(t1)The flow rate vs. rotation speed characteristic coefficient e at the next time t1qh(t1)The flow rate vs. head characteristic coefficient at the next time t 1; mrAt rated torque, QrAt a rated flow rate, nrAt a rated rotational speed, Y1Opening degree of guide vane, Q, being a first operating point1Flow at a first operating point, M1Moment of the first operating point, Y2Opening of guide vanes, Q, being a second operating point2Flow at the second operating point, M2Moment of the second operating point, n3Rotational speed at the third operating point, H3Head of water at the third operating point, Q3Flow at the third operating point, M3Moment of the third operating point, n4Is the rotation speed of the fourth operating point, H4Head of the fourth operating point, Q4Is the flow rate of the fourth operating point, M4The moment at the fourth operating point.
The invention provides a computing system of characteristic coefficients of a water pump turbine, which comprises:
an initialization module: the method is used for setting the current time t as the time when the water pump turbine is excited by frequency disturbance in a stable state; setting a relative value y of the opening deviation of the guide vane at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)(ii) a The water pump turbine characteristic coefficient of the current time t is set, and the method comprises the following steps: moment of forceCoefficient of opening characteristic e of guide vaney(t)Characteristic coefficient e of torque to rotating speedx(t)Coefficient of torque vs. head characteristic eh(t)Flow versus guide vane opening characteristic coefficient eqy(t)Flow rate vs. speed characteristic coefficient eqx(t)Coefficient of flow vs. head characteristic eqh(t)；
A state variable solving module: the relative value y of the deviation of the opening degree of the guide vane at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)Substituting the characteristic coefficient of the water pump turbine into a nonlinear state space equation of the pumped storage unit, and solving the equation by using an Euler method to obtain a relative value q of flow deviation at the next moment t1(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)；
The step length of the next time t1 relative to the current time t is a set time step length;
a unit rotating speed solving module: for the relative value y of the deviation of the opening degree of the guide vane according to the next time t1(t1)Relative value x of rotational speed deviation(t1)Relative value of flow deviation q(t1)And head deviation relative value h(t1)The unit rotating speed x of the next time t1 is obtained from the conversion relation between the unit parameters of the pump turbine and the working parameters of the real machine11(t1)(ii) a The real machine working parameters comprise flow Q, moment M, guide vane opening Y, rotating speed n and working water head H;
equivalent unit rotating speed solving module: for a unit speed x according to the next instant t111(t1)The equivalent unit speed X at the next time t1 is obtained from the equivalent full characteristic curve11(t1)；
The construction method of the equivalent full characteristic curve comprises the following steps: according to the formulas (B1) - (B3), the abscissa in the full characteristic curve of the pump turbine is defined by the unit rotating speed x11Conversion to equivalent unit speed X11Keeping the ordinate unchanged;
Figure BDA0003326526570000081
Figure BDA0003326526570000082
Figure BDA0003326526570000083
the flow moment solving module: for an equivalent unit speed X according to said next moment t111(t1)Performing interpolation solving on the equivalent full-characteristic curve by using a linear grid interpolation method to obtain the unit flow Q of the next moment t111And unit moment M11；
The operating point solving module comprises: and obtaining values within a set range of the working condition points at the next moment t1 in the equivalent full characteristic curve to obtain four working condition points, wherein the four working condition points are respectively as follows: the device comprises a first working condition point, a second working condition point, a third working condition point and a fourth working condition point, wherein equivalent unit rotating speeds of the first working condition point and the second working condition point are the same, and guide vane opening degrees of the third working condition point and the fourth working condition point are the same;
according to the conversion relation between the unit parameters of the pump turbine and the operating parameters of the real machine and the relative value y of the opening deviation of the guide vane at the next time t1(t1)Water head deviation relative value h(t1)Unit speed x11(t1)Unit flow rate Q11And unit moment M11Obtaining the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point at the next moment t 1;
the characteristic coefficient solving module is used for: the method is used for performing approximate calculation by adopting a difference instead of differentiation method according to the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point in the equivalent full characteristic curve to obtain the characteristic coefficient of the water pump turbine at the next moment t 1;
a stability characteristic coefficient solving module: the relative values y of the opening deviation of the guide vanes for using the next time t1 respectively(t1)Relative value x of rotational speed deviation(t1)Relative value q of flow deviation of(t1)Value of (d) updates the guide vane opening at the current time tRelative value of deviation y(t)Relative value x of rotational speed deviation(t)And the relative value q of the flow deviation(t)Updating the value of the pump turbine characteristic coefficient at the current time t by using the value of the pump turbine characteristic coefficient at the next time t 1; pushing the current time t backwards according to the set time step, and repeatedly and sequentially executing the operations in the state variable solving module, the unit rotating speed solving module, the equivalent unit rotating speed solving module, the flow moment solving module, the working condition point solving module and the characteristic coefficient solving module until the water pump turbine reaches a steady-state working condition to obtain a stable characteristic coefficient; the stable characteristic coefficient is the characteristic coefficient of the pump turbine at the next time t1 when the steady-state working condition is reached.
Preferably, the nonlinear state space equation of the pumped storage group in the state variable solution module is as follows:
Figure BDA0003326526570000091
the flow deviation relative value q at the next moment t1 in the state variable solving module(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)Respectively as follows:
Figure BDA0003326526570000092
the unit rotation speed x of the next time t1 in the unit rotation speed solving module11(t1)Comprises the following steps:
Figure BDA0003326526570000093
preferably, the flow Q of any one of the four operating points in the operating point solving moduleiMoment MiOpening degree Y of guide vaneiRotational speed niAnd an operating head HiAccording to formulas (B4) - (B8)Obtaining:
Figure BDA0003326526570000094
Mi＝M11i(t1)D3Hi (B5)
Figure BDA0003326526570000101
Yi＝Ymax(1+yi(t1)) (B7)
Hi＝(1+hi(t1))Hr (B8)。
preferably, the stability characteristic coefficients in the stability characteristic coefficient solving module are respectively:
Figure BDA0003326526570000102
Figure BDA0003326526570000103
Figure BDA0003326526570000104
Figure BDA0003326526570000105
Figure BDA0003326526570000106
Figure BDA0003326526570000107
the invention provides a computing device for characteristic coefficients of a water pump turbine, which is characterized by comprising a memory and a processor; the memory for storing a computer program; the processor is used for realizing the calculation method of the characteristic coefficient of the pump turbine when executing the computer program.
The present invention provides a computer-readable storage medium, characterized in that the storage medium has stored thereon a computer program which, when executed by a processor, implements the method for calculating the pump turbine characteristic coefficient as described above.
Through the technical scheme, compared with the prior art, the method carries out numerical value conversion on the full characteristic curve of the water pump turbine, so that the converted equivalent full characteristic curve only corresponds to one unit flow rate at the same unit rotating speed; then, based on the equivalent full characteristic curve, interpolating by using a linear grid interpolation method to obtain the moment and the flow of the corresponding working condition point; finally, approximate calculation is carried out by adopting a method of replacing differential by difference, and the characteristic coefficient of the water pump turbine at the next moment is obtained; and carrying out repeated iterative calculation on the obtained characteristic coefficient of the water pump turbine to obtain a stable characteristic coefficient. The stability characteristic coefficient of the invention is obtained after repeated iterative computation, and is more real and more accurate than the artificial set ideal six coefficients; the method can calculate the corresponding six stable coefficients according to different water head working conditions, and compared with the prior art that the same characteristic coefficients of the water pump turbine are used under three water head working conditions, the method has the advantages that the stable characteristic coefficients are more detailed and more comprehensive; the stability characteristic coefficient of the invention is more suitable for numerical modeling simulation calculation of the full water head range of the pumped storage unit adjusting system, and can obviously improve the precision of the numerical modeling simulation calculation of the full water head range of the pumped storage unit adjusting system.
Drawings
Fig. 1 is a flowchart of a method for calculating a characteristic coefficient of a pump turbine according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The method for calculating the characteristic coefficient of the pump turbine provided by the embodiment of the invention, as shown in fig. 1, comprises the following steps: the method comprises the steps of initialization, state variable solving, unit rotating speed solving, equivalent unit rotating speed solving, flow moment solving, working condition point solving, characteristic coefficient solving and stable characteristic coefficient solving.
(1) An initialization step:
and setting the current time t as the time when the water pump turbine is excited by frequency disturbance in a stable state, specifically the time when the frequency disturbance of the pumped storage unit adjusting system is 0.01.
Respectively setting the relative value q of the flow deviation at the current time t(t)Is 0, the relative value x of the rotational speed deviation(t)Is 0.01, and the relative value y of the deviation of the opening degree of the guide vane(t)Is 0.
Setting the characteristic coefficient of the water pump turbine at the current time t: setting characteristic coefficient e of torque pair guide vane openingy(t)1, coefficient of torque vs. rotation speed characteristic ex(t)Has a torque to head characteristic coefficient e of-1h(t)1.5, flow vs. guide vane opening characteristic coefficient eqy(t)1, flow rate vs. rotation speed characteristic coefficient eqx(t)Is 0 and a flow vs. head characteristic coefficient eqh(t)Is 0.5.
(2) And (3) solving the state variable: the relative value y of the deviation of the opening degree of the guide vane at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)Substituting the characteristic coefficient of the water pump turbine into a nonlinear state space equation of the pumped storage unit, and solving the equation by using an Euler method to obtain a relative value q of flow deviation at the next moment t1(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)(ii) a The step length of the next time t1 relative to the current time t is a set time step length, and the time step length of the embodiment is 1 second;
the Eulerian method is a method of solving the approximate solution of the variation problem by using the broken line slope instead of the tangent slope.
The nonlinear state space equation of the pumped storage unit is as follows:
Figure BDA0003326526570000121
wherein, Twt0＝10，ht0＝2(m)，TJ＝10，Kp＝0.2，Ki＝0.1。
Flow deviation relative value q at next time t1(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)Respectively as follows:
Figure BDA0003326526570000131
(3) solving at a unit rotating speed: the relative value y of the deviation of the opening degree of the guide vane according to the next time t1(t1)Relative value x of rotational speed deviation(t1)Relative value of flow deviation q(t1)And head deviation relative value h(t1)The unit rotating speed x of the next time t1 is obtained from the conversion relation between the unit parameters of the pump turbine and the working parameters of the real machine11(t1)：
Figure BDA0003326526570000132
Wherein D is 3.57 m.
The unit parameters of the water pump turbine comprise unit rotating speed, unit flow and unit moment; the real machine working parameters comprise flow, moment, guide vane opening, rotating speed and working water head.
(4) Equivalent unit rotating speed solving: unit speed x at the next time t111(t1)The equivalent unit speed X at the next time t1 is obtained from the equivalent full characteristic curve11(t1)。
The construction method of the equivalent full characteristic curve comprises the following steps: according to the formulas (A1) - (A3), the water pump turbine is arranged in the full characteristic curveThe abscissa is given by unit speed x11Conversion to equivalent unit speed X11Keeping the ordinate unchanged;
Figure BDA0003326526570000133
Figure BDA0003326526570000134
Figure BDA0003326526570000141
the full characteristic curve of the pump turbine is the basic basis for calculation of the hydraulic transition process of the pumped storage power station. The full characteristics of various normal operation conditions and transition conditions of the pump turbine are called full characteristics, and the full characteristics can be represented by four-quadrant characteristic curves, including a flow characteristic curve and a torque characteristic curve, wherein the flow characteristic curve and the torque characteristic curve take a unit rotating speed as an abscissa and respectively take a unit flow or a unit torque as an ordinate. The full characteristic curve reflects five working condition areas of the water pump, the water pump brake, the water turbine brake and the reverse water pump which can appear under the normal operation working condition and the transition working condition of the water pump and the water turbine, and the five working condition areas are respectively positioned in four quadrants.
Due to the reversible design of the pump turbine, the S characteristic region of the full characteristic curve of the pump turbine has interpolation problem, and the method is specifically shown in the way that the pump turbine can correspond to three different unit flows at the same unit rotating speed when operating in the S characteristic region; the interpolation problem can cause the pumped storage unit to frequently switch among the working condition of the water turbine, the braking working condition and the working condition of the reverse pump, so that the characteristic coefficient of the water turbine of the water pump under the steady-state working condition can not be obtained.
The embodiment carries out numerical value conversion on the full characteristic curve of the pump turbine, so that the converted equivalent full characteristic curve only corresponds to one unit flow rate at the same unit rotating speed, and the interpolation problem existing in the S characteristic region of the full characteristic curve of the pump turbine is solved.
(5) And flow torque solving: equivalent unit speed X according to the next moment t111(t1)The equivalent full-characteristic curve is interpolated and solved by using a linear grid interpolation method to obtain the unit flow Q of the next moment t111And unit moment M11。
The linear grid interpolation method represents linear interpolation based on numerical values at grid points of adjacent points in each dimension.
(6) And (3) solving the working condition points:
taking values in the set range of the working condition point at the next moment t1 in the equivalent full characteristic curve to obtain four working condition points, which are respectively: the guide vane opening degree of the third working condition point is the same as that of the fourth working condition point.
According to the conversion relation between the unit parameters of the pump turbine and the operating parameters of the real machine and the relative value y of the deviation of the opening degree of the guide vane at the next time t1(t1)Water head deviation relative value h(t1)Unit speed x11(t1)Unit flow rate Q11And unit moment M11And obtaining the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point at the next moment t 1. Flow Q of any one of four operating pointsiMoment MiOpening degree Y of guide vaneiRotational speed niAnd an operating head HiThe following equations (A4) to (A8) were obtained:
Figure BDA0003326526570000151
Mi＝M11i(t1)D3Hi (A5)
Figure BDA0003326526570000152
Yi＝Ymax(1+yi(t1)) (A7)
Hi＝(1+hi(t1))Hr (A8)
wherein Hr＝195(m)，Ymax＝43.01(cm)。
(7) And (3) solving the characteristic coefficient: in the equivalent full characteristic curve, according to the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point, approximate calculation is carried out by adopting a difference instead of differentiation method, and the characteristic coefficient of the water pump turbine at the next moment t1 is obtained:
Figure BDA0003326526570000153
Figure BDA0003326526570000154
Figure BDA0003326526570000155
Figure BDA0003326526570000161
Figure BDA0003326526570000162
Figure BDA0003326526570000163
wherein M isr＝1.2×106(N·m)，Qr＝176.1(m3/s)。
(8) And a stable characteristic coefficient solving step:
using the vane opening deviation relative values y at the next time t1(t1)Relative value x of rotational speed deviation(t1)Relative value q of flow deviation of(t1)Update the relative value y of the guide vane opening deviation at the current time t(t)Relative value x of rotational speed deviation(t)And the relative value q of the flow deviation(t)Updating the value of the pump turbine characteristic coefficient at the current time t by using the value of the pump turbine characteristic coefficient at the next time t 1; and (4) pushing the current time t backwards according to the set time step length, and repeating the steps from the step 2 to the step 7 until the water pump turbine reaches the steady-state working condition to obtain a stable characteristic coefficient.
Wherein, the peak value x of the timing chart when the relative value of the rotating speed deviationpThe steady state working condition is that the working condition is less than or equal to 0.001; the steady characteristic coefficient is the pump turbine characteristic coefficient at the next time t1 when the steady state condition is reached.
Head condition H0188m for low operating mode, 195m for medium operating mode, and 215m for high operating mode; the stability characteristic coefficients under three water head working conditions of low, medium and high are respectively calculated, and the result is shown in a stability characteristic coefficient table:
stability coefficient table
Figure BDA0003326526570000164
Figure BDA0003326526570000171
According to the stability characteristic coefficient table, the difference of the stability characteristic coefficients of the pump turbine is large under different water head working conditions. The stability characteristic coefficient of the embodiment is obtained after multiple iterative computations, and is more real and more accurate than an ideal six-coefficient set artificially; the corresponding six stable coefficients can be calculated according to different water head working conditions, and compared with the prior art that the same characteristic coefficients of the water pump turbine are used under three water head working conditions, the stable characteristic coefficients of the embodiment are more detailed and comprehensive; the stability characteristic coefficient of the embodiment is more suitable for numerical modeling simulation calculation of the full water head range of the pumped storage unit adjusting system, and the precision of the numerical modeling simulation calculation of the full water head range of the pumped storage unit adjusting system can be obviously improved.
The embodiment of the invention provides a computing system for characteristic coefficients of a pump turbine, which comprises: the device comprises an initialization module, a state variable solving module, a unit rotating speed solving module, an equivalent unit rotating speed solving module, a flow moment solving module, a working condition point solving module, a characteristic coefficient solving module and a stable characteristic coefficient solving module.
An initialization module: the method is used for setting the current time t as the time when the water pump turbine is excited by frequency disturbance in a stable state; setting a relative value y of the opening deviation of the guide vane at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)(ii) a The water pump turbine characteristic coefficient of the current time t is set, and the method comprises the following steps: characteristic coefficient e of opening degree of guide vane by torque pairy(t)Characteristic coefficient e of torque to rotating speedx(t)Coefficient of torque vs. head characteristic eh(t)Flow versus guide vane opening characteristic coefficient eqy(t)Flow rate vs. speed characteristic coefficient eqx(t)Coefficient of flow vs. head characteristic eqh(t)。
A state variable solving module: for calculating the relative value y of the deviation of the opening degree of the guide vane at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)Substituting the characteristic coefficient of the water pump turbine into a nonlinear state space equation of the pumped storage unit, and solving the equation by using an Euler method to obtain a relative value q of flow deviation at the next moment t1(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)；
The step length of the next time t1 relative to the current time t is a set time step length;
the nonlinear state space equation of the pumped storage unit is as follows:
Figure BDA0003326526570000181
flow deviation relative value q at next time t1(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)Respectively as follows:
Figure BDA0003326526570000182
a unit rotating speed solving module: for the relative value y of the deviation of the opening of the guide vane according to the next moment t1(t1)Relative value x of rotational speed deviation(t1)Relative value of flow deviation q(t1)And head deviation relative value h(t1)The unit rotating speed x of the next time t1 is obtained from the conversion relation between the unit parameters of the pump turbine and the working parameters of the real machine11(t1)：
Figure BDA0003326526570000183
The unit parameters of the water pump turbine comprise unit rotating speed, unit flow and unit moment; the real machine working parameters comprise flow, moment, guide vane opening, rotating speed and working water head.
Equivalent unit rotating speed solving module: for a specific speed x according to the next time t111(t1)The equivalent unit speed X at the next time t1 is obtained from the equivalent full characteristic curve11(t1)；
The construction method of the equivalent full characteristic curve comprises the following steps: according to the formulas (B1) - (B3), the abscissa in the full characteristic curve of the pump turbine is defined by the unit rotating speed x11Conversion to equivalent unit speed X11Keeping the ordinate unchanged;
Figure BDA0003326526570000191
Figure BDA0003326526570000192
Figure BDA0003326526570000193
the flow moment solving module: for an equivalent unit speed X according to the next instant t111(t1)Using linear netsThe equivalent full characteristic curve is subjected to interpolation calculation by a lattice interpolation method to obtain the unit flow Q of the next moment t111And unit moment M11；
The operating point solving module comprises: the method is used for taking values in the set range of the working condition points at the next moment t1 in the equivalent full characteristic curve to obtain four working condition points, which are respectively: the device comprises a first working condition point, a second working condition point, a third working condition point and a fourth working condition point, wherein equivalent unit rotating speeds of the first working condition point and the second working condition point are the same, and guide vane opening degrees of the third working condition point and the fourth working condition point are the same;
then according to the conversion relation between the unit parameters of the pump turbine and the real machine working parameters and the relative value y of the guide vane opening deviation at the next time t1(t1)Water head deviation relative value h(t1)Unit speed x11(t1)Unit flow rate Q11And unit moment M11Obtaining the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point at the next moment t 1;
flow Q of any one of four operating pointsiMoment MiOpening degree Y of guide vaneiRotational speed niAnd an operating head HiThe following equations (B4) to (B8) were obtained:
Figure BDA0003326526570000194
Mi＝M11i(t1)D3Hi (B5)
Figure BDA0003326526570000195
Yi＝Ymax(1+yi(t1)) (B7)
Hi＝(1+hi(t1))Hr (B8)。
the characteristic coefficient solving module is used for: in the equivalent full characteristic curve, according to the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point, approximate calculation is carried out by adopting a difference instead of differentiation method, and the characteristic coefficient of the water pump turbine at the next moment t1 is obtained:
Figure BDA0003326526570000201
Figure BDA0003326526570000202
Figure BDA0003326526570000203
Figure BDA0003326526570000204
Figure BDA0003326526570000205
Figure BDA0003326526570000206
a stability characteristic coefficient solving module: for using the relative value y of the opening deviation of the guide vane at the next time t1(t1)Relative value x of rotational speed deviation(t1)Relative value q of flow deviation of(t1)Update the relative value y of the guide vane opening deviation at the current time t(t)Relative value x of rotational speed deviation(t)And the relative value q of the flow deviation(t)Updating the value of the pump turbine characteristic coefficient at the current time t by using the value of the pump turbine characteristic coefficient at the next time t 1; pushing the current time t backwards according to a set time step, and repeatedly and sequentially executing the operations in the state variable solving module, the unit rotating speed solving module, the equivalent unit rotating speed solving module, the flow moment solving module, the working condition point solving module and the characteristic coefficient solving module until the water pump turbine reaches a steady-state working condition to obtain a stable characteristic coefficient; stable coefficient of characteristics for reaching steady state conditionsThe pump turbine characteristic coefficient at the next time t 1.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A calculation method for characteristic coefficients of a water pump turbine is characterized by comprising the following steps:
(1) an initialization step: setting the current time t as the time when the water pump turbine is subjected to frequency disturbance excitation in a stable state; setting a relative value y of the opening deviation of the guide vane at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)(ii) a The water pump turbine characteristic coefficient of the current time t is set, and the method comprises the following steps: characteristic coefficient e of opening degree of guide vane by torque pairy(t)Characteristic coefficient e of torque to rotating speedx(t)Coefficient of torque vs. head characteristic eh(t)Flow versus guide vane opening characteristic coefficient eqy(t)Flow rate vs. speed characteristic coefficient eqx(t)Coefficient of flow vs. head characteristic eqh(t)；
(2) And (3) solving the state variable: the relative value y of the guide vane opening deviation at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)Substituting the characteristic coefficient of the water pump turbine into a nonlinear state space equation of the pumped storage unit, and solving the equation by using an Euler method to obtain a relative value q of flow deviation at the next moment t1(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)；
The step length of the next time t1 relative to the current time t is a set time step length;
(3) solving at a unit rotating speed: according to the relative value y of the guide vane opening deviation at the next time t1(t1)Relative value x of rotational speed deviation(t1)Relative value of flow deviation q(t1)And head deviation relative value h(t1)The unit rotating speed x of the next time t1 is obtained from the conversion relation between the unit parameters of the pump turbine and the working parameters of the real machine11(t1)(ii) a The real machine working parameters comprise flow Q, moment M, guide vane opening Y, rotating speed n and working water head H;
(4) equivalent unit rotating speed solving: unit speed x according to the next time t111(t1)The equivalent unit speed X at the next time t1 is obtained from the equivalent full characteristic curve11(t1)；
The construction method of the equivalent full characteristic curve comprises the following steps: according to the formulas (A1) - (A3), the abscissa in the full characteristic curve of the pump turbine is defined by the unit rotating speed x11Conversion to equivalent unit speed X11Keeping the ordinate unchanged;
Figure FDA0003326526560000021
Figure FDA0003326526560000022
Figure FDA0003326526560000023
wherein x is11rIs rated unit speed, Q11Is unit flow rate, Q11rFor rated unit flow rate, M11Is unit moment, M11rIs rated unit moment, alpha1、v1Is an intermediate variable, e is the base of the natural logarithm function;
(5) and flow torque solving: equivalent unit rotation speed X according to the next moment t111(t1)Performing interpolation solving on the equivalent full-characteristic curve by using a linear grid interpolation method to obtain the unit flow Q of the next moment t111And unit moment M11；
(6) And (3) solving the working condition points: taking values in the set range of the working condition points at the next moment t1 in the equivalent full characteristic curve to obtain four working condition points, which are respectively: the device comprises a first working condition point, a second working condition point, a third working condition point and a fourth working condition point, wherein equivalent unit rotating speeds of the first working condition point and the second working condition point are the same, and guide vane opening degrees of the third working condition point and the fourth working condition point are the same;
according to the conversion relation between the unit parameters of the pump turbine and the operating parameters of the real machine and the relative value y of the opening deviation of the guide vane at the next time t1(t1)Water head deviation relative value h(t1)Unit speed x11(t1)Unit flow rate Q11And unit moment M11Obtaining the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point at the next moment t 1;
(7) and (3) solving the characteristic coefficient: in the equivalent full characteristic curve, according to the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point, approximate calculation is carried out by adopting a difference instead of differentiation method, and the characteristic coefficient of the water pump turbine at the next moment t1 is obtained;
(8) and a stable characteristic coefficient solving step: using the relative value y of the opening deviation of the guide vane at the next time t1(t1)Relative value x of rotational speed deviation(t1)Relative value q of flow deviation of(t1)Update the relative value y of the guide vane opening deviation at the current time t(t)Relative value x of rotational speed deviation(t)And the relative value q of the flow deviation(t)Updating the value of the pump turbine characteristic coefficient at the current time t by using the value of the pump turbine characteristic coefficient at the next time t 1; pushing the current time t backwards according to the set time step length, and repeating the steps 2 to 7 until the water pump turbine reaches a steady-state working condition to obtain a steady characteristic coefficient; the stable characteristic coefficient is the characteristic coefficient of the pump turbine at the next time t1 when the steady-state working condition is reached.
2. The calculation method of pump turbine characteristic coefficients according to claim 1,
the nonlinear state space equation of the pumped storage unit in the state variable solving step is as follows:
Figure FDA0003326526560000031
wherein the content of the first and second substances,
Figure FDA0003326526560000032
as a derivative of the relative value of the flow deviation at the present time t,
Figure FDA0003326526560000033
as a derivative of the relative value of the rotational speed deviation at the present moment t,
Figure FDA0003326526560000034
is the derivative of the relative value of the deviation of the opening of the guide vane at the current time T, Twt0Is the water hammer inertia time constant, ht0For head loss, H0At waterhead conditions, TJIs the unit inertia time constant, KpTo proportional gain, KiIs the integral gain;
a flow deviation relative value q at the next time t1 in the state variable solving step(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)Respectively as follows:
Figure FDA0003326526560000035
the unit rotation speed x at the next time t1 in the unit rotation speed solving step11(t1)Comprises the following steps:
Figure FDA0003326526560000041
wherein D is the diameter of the runner, n0To stabilize the rotation speed.
3. Calculation of pump turbine characteristic coefficients according to claim 1The method is characterized in that the flow Q of any one of the four working condition points in the working condition point solving stepiMoment MiOpening degree Y of guide vaneiRotational speed niAnd an operating head HiThe following equations (A4) to (A8) were obtained:
Figure FDA0003326526560000042
Mi＝M11i(t1)D3Hi (A5)
Figure FDA0003326526560000043
Yi＝Ymax(1+yi(t1)) (A7)
Hi＝(1+hi(t1))Hr (A8)
wherein Q is11i(t1)Unit flow rate of the operating point, M11i(t1)Is the unit moment of the operating point, x11i(t1)Is the unit speed of the operating point, YmaxMaximum opening of the guide vanes, HrIs the rated working head.
4. The calculation method of the characteristic coefficients of the pump turbine according to claim 1, wherein the stability characteristic coefficients in the stability characteristic coefficient solving step are respectively:
Figure FDA0003326526560000044
Figure FDA0003326526560000045
Figure FDA0003326526560000051
Figure FDA0003326526560000052
Figure FDA0003326526560000053
Figure FDA0003326526560000054
wherein e isy(t1)Characteristic coefficient of torque versus opening degree of guide vane, e, for the next time t1x(t1)The torque-to-speed characteristic coefficient, e, for the next time t1h(t1)Coefficient of moment versus head characteristic, e, for the next time t1qy(t1)Flow versus guide vane opening characteristic coefficient, e, for the next time t1qx(t1)The flow rate vs. rotation speed characteristic coefficient e at the next time t1qh(t1)The flow rate vs. head characteristic coefficient at the next time t 1; mrAt rated torque, QrAt a rated flow rate, nrAt a rated rotational speed, Y1Opening degree of guide vane, Q, being a first operating point1Flow at a first operating point, M1Moment of the first operating point, Y2Opening of guide vanes, Q, being a second operating point2Flow at the second operating point, M2Moment of the second operating point, n3Rotational speed at the third operating point, H3Head of water at the third operating point, Q3Flow at the third operating point, M3Moment of the third operating point, n4Is the rotation speed of the fourth operating point, H4Head of the fourth operating point, Q4Is the flow rate of the fourth operating point, M4The moment at the fourth operating point.
5. A calculation system for pump turbine characteristic coefficients is characterized by comprising:
initialA conversion module: the method is used for setting the current time t as the time when the water pump turbine is excited by frequency disturbance in a stable state; setting a relative value y of the opening deviation of the guide vane at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)(ii) a The water pump turbine characteristic coefficient of the current time t is set, and the method comprises the following steps: characteristic coefficient e of opening degree of guide vane by torque pairy(t)Characteristic coefficient e of torque to rotating speedx(t)Coefficient of torque vs. head characteristic eh(t)Flow versus guide vane opening characteristic coefficient eqy(t)Flow rate vs. speed characteristic coefficient eqx(t)Coefficient of flow vs. head characteristic eqh(t)；
A state variable solving module: the relative value y of the deviation of the opening degree of the guide vane at the current time t(t)Relative value x of rotational speed deviation(t)Relative value of flow deviation q(t)Substituting the characteristic coefficient of the water pump turbine into a nonlinear state space equation of the pumped storage unit, and solving the equation by using an Euler method to obtain a relative value q of flow deviation at the next moment t1(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)；
The step length of the next time t1 relative to the current time t is a set time step length;
a unit rotating speed solving module: for the relative value y of the deviation of the opening degree of the guide vane according to the next time t1(t1)Relative value x of rotational speed deviation(t1)Relative value of flow deviation q(t1)And head deviation relative value h(t1)The unit rotating speed x of the next time t1 is obtained from the conversion relation between the unit parameters of the pump turbine and the working parameters of the real machine11(t1)(ii) a The real machine working parameters comprise flow Q, moment M, guide vane opening Y, rotating speed n and working water head H;
equivalent unit rotating speed solving module: for a unit speed x according to the next instant t111(t1)The equivalent unit speed X at the next time t1 is obtained from the equivalent full characteristic curve11(t1)；
The construction method of the equivalent full characteristic curve comprises the following steps: according to formulas (B1) - (B3), the water is pumped to the water wheelThe abscissa of the machine full characteristic curve is defined by unit rotation speed x11Conversion to equivalent unit speed X11Keeping the ordinate unchanged;
Figure FDA0003326526560000061
Figure FDA0003326526560000062
Figure FDA0003326526560000063
the flow moment solving module: for an equivalent unit speed X according to said next moment t111(t1)Performing interpolation solving on the equivalent full-characteristic curve by using a linear grid interpolation method to obtain the unit flow Q of the next moment t111And unit moment M11；
The operating point solving module comprises: and obtaining values within a set range of the working condition points at the next moment t1 in the equivalent full characteristic curve to obtain four working condition points, wherein the four working condition points are respectively as follows: the device comprises a first working condition point, a second working condition point, a third working condition point and a fourth working condition point, wherein equivalent unit rotating speeds of the first working condition point and the second working condition point are the same, and guide vane opening degrees of the third working condition point and the fourth working condition point are the same;
according to the conversion relation between the unit parameters of the pump turbine and the operating parameters of the real machine and the relative value y of the opening deviation of the guide vane at the next time t1(t1)Water head deviation relative value h(t1)Unit speed x11(t1)Unit flow rate Q11And unit moment M11Obtaining the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point at the next moment t 1;
the characteristic coefficient solving module is used for: the method is used for performing approximate calculation by adopting a difference instead of differentiation method according to the flow, the moment, the guide vane opening, the rotating speed and the working water head of each working condition point in the equivalent full characteristic curve to obtain the characteristic coefficient of the water pump turbine at the next moment t 1;
a stability characteristic coefficient solving module: the relative values y of the opening deviation of the guide vanes for using the next time t1 respectively(t1)Relative value x of rotational speed deviation(t1)Relative value q of flow deviation of(t1)Update the relative value y of the guide vane opening deviation at the current time t(t)Relative value x of rotational speed deviation(t)And the relative value q of the flow deviation(t)Updating the value of the pump turbine characteristic coefficient at the current time t by using the value of the pump turbine characteristic coefficient at the next time t 1; pushing the current time t backwards according to the set time step, and repeatedly and sequentially executing the operations in the state variable solving module, the unit rotating speed solving module, the equivalent unit rotating speed solving module, the flow moment solving module, the working condition point solving module and the characteristic coefficient solving module until the water pump turbine reaches a steady-state working condition to obtain a stable characteristic coefficient; the stable characteristic coefficient is the characteristic coefficient of the pump turbine at the next time t1 when the steady-state working condition is reached.
6. The calculation system of pump turbine characteristic coefficients according to claim 5,
the nonlinear state space equation of the pumped storage unit in the state variable solving module is as follows:
Figure FDA0003326526560000081
the flow deviation relative value q at the next moment t1 in the state variable solving module(t1)Relative value x of rotational speed deviation(t1)And a relative value y of the opening deviation of the guide vane(t1)And head deviation relative value h(t1)Respectively as follows:
Figure FDA0003326526560000082
the unit rotation speed x of the next time t1 in the unit rotation speed solving module11(t1)Comprises the following steps:
Figure FDA0003326526560000083
7. the calculation system for pump turbine characteristic coefficients according to claim 5, wherein the operating point solving module is configured to solve the flow Q of any one of the four operating pointsiMoment MiOpening degree Y of guide vaneiRotational speed niAnd an operating head HiThe following equations (B4) to (B8) were obtained:
Figure FDA0003326526560000084
Mi＝M11i(t1)D3Hi (B5)
Figure FDA0003326526560000085
Yi＝Ymax(1+yi(t1)) (B7)
Hi＝(1+hi(t1))Hr (B8)。
8. the calculation system for pump turbine characteristic coefficients according to claim 5, wherein the stability characteristic coefficients in the stability characteristic coefficient solving module are respectively:
Figure FDA0003326526560000091
Figure FDA0003326526560000092
Figure FDA0003326526560000093
Figure FDA0003326526560000094
Figure FDA0003326526560000095
Figure FDA0003326526560000096
9. a computing device for characteristic coefficients of a water pump turbine is characterized by comprising a memory and a processor; the memory for storing a computer program; the processor, when executing the computer program, is configured to implement the method for calculating pump turbine characteristic coefficients according to any one of claims 1 to 4.
10. A computer-readable storage medium, characterized in that the storage medium has stored thereon a computer program which, when executed by a processor, implements the method of calculating pump turbine characteristic coefficients according to any one of claims 1 to 4.
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