CN113987802B - Calculation method and system for characteristic coefficients of water pump turbine - Google Patents
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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 multiple iterative calculations on the obtained characteristic coefficient of the water pump and the water 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
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-electricity mutual coupling complex nonlinear system, and has the function of adjusting the frequency and the load of the unit.
The pump turbine is core equipment of a pumped storage unit regulating 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 water turbine runs, wherein the rotating wheel rotates clockwise, and the water pump runs 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 characteristic coefficient of the pump turbine at the current moment t is set, and the characteristic coefficient comprises the following steps: characteristic coefficient e of torque pair guide vane opening y(t) Characteristic coefficient e of torque to rotating speed x(t) Moment to head coefficient of characteristics e h(t) Flow versus guide vane opening characteristic coefficient e qy(t) Flow rate vs. speed characteristic coefficient e qx(t) Coefficient of flow vs. head characteristic e qh(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 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 moment t1 relative to the current moment t is a set time step length;
(3) Solving at a unit rotating speed: according to the relative value y of the opening deviation of the guide vane at 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 moment t1 is obtained by the conversion relation between the unit parameters of the pump turbine and the working parameters of the real machine 11(t1) (ii) a The working parameters of the real machine comprise flow Q, moment M and guide vanesOpening degree Y, rotating speed n and working water head H;
(4) Solving equivalent unit rotating speed: unit rotation speed x according to the next time t1 11(t1) Calculating the equivalent unit rotation speed X at the next time t1 from the equivalent full characteristic curve 11(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 x 11 Conversion to equivalent unit speed X 11 Keeping the ordinate unchanged;
wherein x is 11r Is rated unit speed, Q 11 Is a unit flow rate, Q 11r For rated unit flow rate, M 11 Is unit moment, M 11r Is rated unit moment, alpha 1 、v 1 Is an intermediate variable, e is the base of the natural logarithm function;
(5) And flow torque solving: according to the equivalent unit rotating speed X of the next moment t1 11(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 t1 11 And unit moment M 11 ；
(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, 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 the equivalent unit rotating speeds of the first working condition point and the second working condition point are the same, and the 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 working parameters of the real machine and the relative value y of the guide vane opening deviation at the next moment t1 (t1) Water head deviation relative value h (t1) Unit speed x 11(t1) Unit flow rate Q 11 And unit moment M 11 Calculating 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: respectively using the relative values y of the guide vane opening deviation 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 characteristic coefficient of the pump turbine at the current time t by using the value of the characteristic coefficient of the pump turbine 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; and the stable characteristic coefficient is the characteristic coefficient of the pump turbine at the next moment t1 when the steady-state working condition is reached.
Preferably, the nonlinear state space equation of the pumped storage group in the state variable solving step is as follows:
wherein the content of the first and second substances,
is the derivative of the relative value of the flow deviation at the present time t>
Is a derivative of the relative value of the speed deviation at the present time t->
Is the derivative of the relative value of the opening deviation of the guide vane at the current time T, T wt0 Is the water hammer inertia time constant, h t0 For head loss, H 0 At waterhead conditions, T J Is the unit inertia time constant, K p To proportional gain, K i Is 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:
the unit rotation speed x at the next time t1 in the unit rotation speed solving step 11(t1) Comprises the following steps:
wherein D is the diameter of the runner, n 0 To stabilize the rotation speed.
Preferably, the flow Q of any one of the four operating points in the operating point solving step i Moment M i Opening degree Y of guide vane i Rotational speed n i And an operating head H i The following equations (A4) to (A8) are used:
M i ＝M 11i(t1) D 3 H i (A5)
Y i ＝Y max (1+y i(t1) ) (A7)
H i ＝(1+h i(t1) )H r (A8)
wherein Q is 11i(t1) Unit flow rate of the operating point, M 11i(t1) Is the unit moment of the operating point, x 11i(t1) Is the unit speed of the operating point, Y max Maximum opening of the guide vanes, H r Is the rated working head.
Preferably, the stability characteristic coefficients in the stability characteristic coefficient solving step are respectively:
wherein e is y(t1) Characteristic coefficient of torque versus opening degree of guide vane, e, for the next time t1 x(t1) Characteristic coefficient of torque vs. rotation speed for the next time t1, e h(t1) Coefficient of torque vs. head characteristic at the next time t1, e qy(t1) Flow versus guide vane opening characteristic coefficient, e, for the next time t1 qx(t1) A flow rate vs. rotation speed characteristic coefficient, e, for the next time t1 qh(t1) Is the characteristic coefficient of the flow to the water head at the next moment t 1; m r At rated torque, Q r At a rated flow rate, n r At a rated speed, Y 1 Opening degree of guide vane, Q, being a first operating point 1 Flow at a first operating point, M 1 Moment of the first operating point, Y 2 Opening of guide vanes, Q, being a second operating point 2 Flow at the second operating point, M 2 Moment of the second operating point, n 3 Rotational speed at the third operating point, H 3 Head of water at the third operating point, Q 3 Flow at the third operating point, M 3 Moment of the third operating point, n 4 Is the rotational speed of the fourth operating point, H 4 Head of the fourth operating point, Q 4 Is the flow rate of the fourth operating point, M 4 The moment at the fourth operating point.
The invention provides a computing system of pump turbine characteristic coefficient, comprising:
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 characteristic coefficient of the pump turbine at the current moment t is set, and the characteristic coefficient comprises the following steps: characteristic coefficient e of opening degree of guide vane by torque pair y(t) Characteristic coefficient e of torque to rotating speed x(t) Coefficient of torque vs. head characteristic e h(t) Flow versus guide vane opening characteristic coefficient e qy(t) Flow rate vs. speed characteristic coefficient e qx(t) Coefficient of flow vs. head characteristic e qh(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 pump turbine into the nonlinear state space equation of the pumped storage unit by using EuropeThe equation is solved by a pulling method to obtain the relative value q of the flow deviation at the 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) ；
The step length of the next moment t1 relative to the current moment t is a set time step length;
a unit rotating speed solving module: the relative value y of the deviation of the opening degree 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 machine 11(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 said next instant t1 11(t1) Calculating the equivalent unit rotation speed X at the next time t1 from the equivalent full characteristic curve 11(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 x 11 Conversion to equivalent unit speed X 11 Keeping the ordinate unchanged;
the flow moment solving module: for an equivalent unit speed X according to the next instant t1 11(t1) Interpolating the equivalent full-feature curve using a linear grid interpolation methodThe value is obtained to obtain the unit flow Q of the next time t1 11 And unit moment M 11 ；
The operating point solving module comprises: and the value is taken within a 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 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 working parameters of the real machine and the relative value y of the opening deviation of the guide vane at the next moment t1 (t1) Water head deviation relative value h (t1) Unit speed x 11(t1) Unit flow rate Q 11 And unit moment M 11 Calculating 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 carrying out approximate calculation in the equivalent full characteristic curve 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 to obtain the characteristic coefficient of the water pump turbine at the next moment t 1;
a stable characteristic coefficient solving module: a relative value y of the deviation of the opening degree of the guide vane 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 characteristic coefficient of the pump turbine at the current time t by using the value of the characteristic coefficient of the pump turbine 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 of the state variable solving module, the unit rotating speed solving module, the equivalent unit rotating speed solving module, the flow torque solving module, the operating point solving module and the characteristic coefficient solving module until the pump turbine reaches a steady-state operating condition to obtain a stable characteristic systemCounting; and the stable characteristic coefficient is the characteristic coefficient of the water pump turbine at the next moment 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:
and 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:
the unit rotating speed x of the next moment t1 in the unit rotating speed solving module 11(t1) Comprises the following steps:
preferably, the flow Q of any one of the four operating points in the operating point solving module i Moment M i Opening degree Y of guide vane i Rotational speed n i And an operating head H i The following equations (B4) to (B8) are obtained:
M i ＝M 11i(t1) D 3 H i (B5)
Y i ＝Y max (1+y i(t1) ) (B7)
H i ＝(1+h i(t1) )H r (B8)。
preferably, the stability characteristic coefficients in the stability characteristic coefficient solving module are respectively:
the invention provides a computing device of pump turbine characteristic coefficients, 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.
Compared with the prior art, the technical scheme provided by the invention has the advantages that the full characteristic curve of the 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 multiple iterative calculations on the obtained characteristic coefficient of the water pump and the water 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 an artificial set ideal six-coefficient; 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 regulating system, and can obviously improve the precision of the numerical modeling simulation calculation of the full water head range of the pumped storage unit regulating 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) 0.01, relative value y of deviation of opening degree of 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 opening y(t) 1, characteristic coefficient of torque to rotation speed e x(t) Has a torque to head characteristic coefficient e of-1 h(t) 1.5, flow vs. guide vane opening characteristic coefficient e qy(t) 1, flow rate vs. rotation speed characteristic coefficient e qx(t) Is 0 and a flow vs. head characteristic coefficient e qh(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) Flow deviation relative value q (t) Substituting the characteristic coefficient of the 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:
wherein, T wt0 ＝10，h t0 ＝2(m)，T J ＝10，K p ＝0.2，K i ＝0.1。
Flow deviation relative value q at next time t1 (t1) Relative value x of rotational speed deviation (t1) Guide, guideRelative value y of leaf opening deviation (t1) And head deviation relative value h (t1) Respectively as follows:
(3) Solving at a unit rotating speed: according to the relative value y of the opening deviation of the guide vane at the next moment t1 (t1) Relative value x of rotational speed deviation (t1) Flow deviation relative value q (t1) And head deviation relative value h (t1) The unit rotating speed x of the next moment t1 is obtained by the conversion relation between the unit parameters of the pump turbine and the working parameters of the real machine 11(t1) ：
Wherein D =3.57m.
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 according to the next time t1 11(t1) Calculating the equivalent unit rotation speed X at the next time t1 from the equivalent full characteristic curve 11(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 x 11 Conversion to equivalent unit speed X 11 Keeping the ordinate unchanged;
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. All the characteristics of various normal operation conditions and transition conditions of the pump turbine are called full characteristics, the full characteristics can be represented by four-quadrant characteristic curves, including a flow characteristic curve and a torque characteristic curve, the flow characteristic curve and the torque characteristic curve both take unit rotating speed as abscissa and respectively take unit flow or unit torque as 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 pump turbine full characteristic curve, so that the equivalent full characteristic curve after conversion 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 pump turbine full characteristic curve is solved.
(5) And flow torque solving: equivalent unit rotating speed X according to the next time t1 11(t1) The linear grid interpolation method is used for carrying out interpolation calculation on the equivalent full-characteristic curve to obtain the unit flow Q of the next moment t1 11 And unit moment M 11 。
The linear grid interpolation method is used for expressing linear interpolation based on numerical values of 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, wherein the four working condition points are respectively as follows: 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 working parameters of the real machine and the relative value y of the opening deviation of the guide vane at the next moment t1 (t1) Water head deviation relative value h (t1) Unit speed x 11(t1) Unit flow rate Q 11 And unit moment M 11 And solving 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 points i Moment M i Opening degree Y of guide vane i Rotational speed n i And an operating head H i The following equations (A4) to (A8) are obtained:
M i ＝M 11i(t1) D 3 H i (A5)
Y i ＝Y max (1+y i(t1) ) (A7)
H i ＝(1+h i(t1) )H r (A8)
wherein H r ＝195(m)，Y max ＝43.01(cm)。
(7) And solving the characteristic coefficients: 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 differential instead of differential method, and the characteristic coefficient of the water pump turbine at the next moment t1 is obtained:
wherein M is r ＝1.2×10 6 (N·m)，Q r ＝176.1(m 3 /s)。
(8) And a stable characteristic coefficient solving step:
using the relative values y of the opening deviation of the guide vanes 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 characteristic coefficient of the pump turbine at the current moment t by using the value of the characteristic coefficient of the pump turbine at the next moment 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 rotating speed deviation relative value p The steady state working condition is less than or equal to 0.001; the stable characteristic coefficient is the characteristic coefficient of the pump turbine at the next moment t1 when the steady-state working condition is reached.
Head condition H 0 188m for low regime, 195mMedium regime, 215m high regime; 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:
coefficient of stability table
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 moment t as the moment when the 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) Flow deviation relative value 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 torque pair guide vane opening y(t) Characteristic coefficient e of torque to rotating speed x(t) Moment to head coefficient of characteristics e h(t) Flow versus guide vane opening characteristic coefficient e qy(t) Flow rate vs. speed characteristic coefficient e qx(t) Coefficient of flow vs. head characteristic e qh(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 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 moment t1 relative to the current moment t is a set time step length;
the nonlinear state space equation of the pumped storage unit is as follows:
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:
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 moment t1 is obtained by the conversion relation between the unit parameters of the pump turbine and the working parameters of the real machine 11(t1) ：
The unit parameters of the water pump turbine comprise unit rotating speed, unit flow and unit moment; the working parameters of the real machine comprise flow, moment, guide vane opening, rotating speed and working water head.
Equivalent unit rotating speed solving module: for a unit speed x according to the next instant t1 11(t1) Calculating the equivalent unit rotation speed X at the next time t1 from the equivalent full characteristic curve 11(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 x 11 Conversion to equivalent unit speed X 11 Keeping the ordinate unchanged;
the flow moment solving module: for equivalent unit speed X according to the next instant t1 11(t1) The linear grid interpolation method is used for carrying out interpolation calculation on the equivalent full-characteristic curve to obtain the unit flow Q of the next moment t1 11 And unit moment M 11 ；
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 the equivalent unit rotating speeds of the first working condition point and the second working condition point are the same, and the guide vane opening degrees of the third working condition point and the fourth working condition point are the same;
then according to the unit of pump turbineThe conversion relation between the parameters and the working parameters of the real machine, and the relative value y of the deviation of the opening degree of the guide vane at the next moment t1 (t1) Water head deviation relative value h (t1) Unit speed x 11(t1) Unit flow rate Q 11 And unit moment M 11 Calculating 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 points i Moment M i Opening degree Y of guide vane i Rotational speed n i And an operating head H i The following equations (B4) to (B8) are obtained:
M i ＝M 11i(t1) D 3 H i (B5)
Y i ＝Y max (1+y i(t1) ) (B7)
H i ＝(1+h i(t1) )H r (B8)。
the characteristic coefficient solving module is used for: the method is used for carrying out 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 an 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: for using the relative value y of the deviation of the opening 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 characteristic coefficient of the pump turbine at the current moment t by using the value of the characteristic coefficient of the pump turbine at the next moment t 1; pushing the current time t backwards according to a set time step, and repeatedly and sequentially executing the operations of 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 and the water turbine reach 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 moment t1 when the steady-state working condition is reached.
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) Initialization stepThe method comprises the following steps: 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 pair y(t) Characteristic coefficient e of torque to rotating speed x(t) Coefficient of torque vs. head characteristic e h(t) Flow versus guide vane opening characteristic coefficient e qy(t) Flow rate vs. speed characteristic coefficient e qx(t) Coefficient of flow vs. head characteristic e qh(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) Flow deviation relative value q (t) Substituting the characteristic coefficient of the 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 moment t1 relative to the current moment t is a set time step length;
(3) And a unit rotating speed solving step: according to the relative value y of the opening deviation of the guide vane at 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 machine 11(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 rotation speed x according to the next time t1 11(t1) Calculating the equivalent unit rotation speed X at the next time t1 from the equivalent full characteristic curve 11(t1) ；
The construction method of the equivalent full characteristic curve comprises the following steps: according to the formulas (A1) - (A3), the water turbine is arranged in the full characteristic curve of the pump turbineThe abscissa is given by unit speed x 11 Conversion to equivalent unit speed X 11 Keeping the ordinate unchanged;
wherein x is 11r Is rated unit speed, Q 11 Is unit flow rate, Q 11r For rated unit flow rate, M 11 Is unit moment, M 11r Is rated unit moment, alpha 1 、v 1 Is an intermediate variable, e is the base of the natural logarithm function;
(5) And flow torque solving: according to the equivalent unit rotating speed X of the next time t1 11(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 t1 11 And unit moment M 11 ；
(6) And (3) solving the working condition points: taking values in 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 working parameters of the real machine and the relative value y of the guide vane opening deviation at the next moment t1 (t1) Water head deviation relative value h (t1) Unit speed x 11(t1) Unit flow rate Q 11 And unit moment M 11 To find each operating mode at the next time t1Flow, moment, guide vane opening, rotating speed and working water head of the point;
(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: respectively using the relative values y of the guide vane opening deviation 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 moment t by using the value of the pump turbine characteristic coefficient at the next moment t 1; pushing the current time t backwards according to the set time step, and repeating the steps from 2 to 7 until the pump turbine reaches a steady working condition to obtain a steady characteristic coefficient; and the stable characteristic coefficient is the characteristic coefficient of the water pump turbine at the next moment 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:
wherein the content of the first and second substances,
is the derivative of the relative value of the flow deviation at the current time t @>
For relative deviation of speed of rotation at present time tDerivative,. Or>
Is the derivative of the relative value of the deviation of the opening of the guide vane at the current time T, T wt0 Is the water hammer inertia time constant, h t0 For head loss, H 0 At waterhead conditions, T J Is the unit inertia time constant, K p To proportional gain, K i Is 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:
the unit rotation speed x at the next time t1 in the unit rotation speed solving step 11(t1) Comprises the following steps:
wherein D is the diameter of the runner, n 0 To stabilize the rotation speed.
3. The method for calculating the characteristic coefficient of the pump turbine according to claim 1, wherein the flow Q of any one of the four operating points in the operating point solving step i Moment M i Opening degree Y of guide vane i Rotational speed n i And an operating head H i The following equations (A4) to (A8) are obtained:
M i ＝M 11i(t1) D 3 H i (A5)
Y i ＝Y max (1+y i(t1) ) (A7)
H i ＝(1+h i(t1) )H r (A8)
wherein Q is 11i(t1) Unit flow rate of the operating point, M 11i(t1) Is the unit moment of the operating point, x 11i(t1) Is the unit speed of the operating point, Y max Maximum opening of the guide vanes, H r Is 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:
wherein e is y(t1) Characteristic coefficient of torque versus opening degree of guide vane, e, for the next time t1 x(t1) The characteristic coefficient of torque vs. rotation speed, e, for the next time t1 h(t1) Coefficient of moment versus head characteristic at the next time t1, e qy(t1) Is a characteristic coefficient of flow versus guide vane opening at the next time t1, e qx(t1) A flow rate vs. rotation speed characteristic coefficient, e, for the next time t1 qh(t1) The flow rate vs. head characteristic coefficient at the next time t 1; m r At rated torque, Q r At a rated flow rate, n r At a rated rotational speed, Y 1 Opening of guide vane, Q, at a first operating point 1 Flow at a first operating point, M 1 Moment of the first operating point, Y 2 Opening of guide vanes, Q, being a second operating point 2 Flow at the second operating point, M 2 Moment of the second operating point, n 3 Rotational speed at the third operating point, H 3 Head of water at the third operating point, Q 3 Flow at the third operating point, M 3 Moment of the third operating point, n 4 Is the rotation speed of the fourth operating point, H 4 Head of the fourth operating point, Q 4 Is the flow rate of the fourth operating point, M 4 The moment at the fourth operating point.
5. A calculation system for pump turbine characteristic coefficients is characterized by comprising:
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 pair y(t) Torque to rotational speed characteristic coefficient e x(t) Coefficient of torque vs. head characteristic e h(t) Flow versus guide vane opening characteristic coefficient e qy(t) Flow rate vs. speed characteristic coefficient e qx(t) Coefficient of flow vs. head characteristice qh(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 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 moment t1 relative to the current moment t is a set time step length;
a unit rotating speed solving module: the relative value y of the deviation of the opening degree 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 machine 11(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 said next instant t1 11(t1) Calculating the equivalent unit rotation speed X at the next time t1 from the equivalent full characteristic curve 11(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 x 11 Converted into equivalent unit rotation speed X 11 Keeping the ordinate unchanged;
the flow moment solving module: for an equivalent unit speed X according to the next instant t1 11(t1) Performing interpolation calculation on the equivalent full-characteristic curve by using a linear grid interpolation method to obtain the unit flow Q of the next time t1 11 And unit moment M 11 ；
The operating point solving module comprises: and the value is taken within a 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 device comprises a first working condition point, a second working condition point, a third working condition point and a fourth working condition point, wherein the equivalent unit rotating speeds of the first working condition point and the second working condition point are the same, and the 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 working parameters of the real machine and the relative value y of the guide vane opening deviation at the next moment t1 (t1) Water head deviation relative value h (t1) Unit speed x 11(t1) Unit flow rate Q 11 And unit moment M 11 Calculating 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 carrying out approximate calculation in the equivalent full characteristic curve 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 to obtain the characteristic coefficient of the water pump turbine at the next moment t 1;
a stability characteristic coefficient solving module: a relative value y of the deviation of the opening degree of the guide vane 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 with the value of the pump turbine characteristic coefficient at the next time t1(ii) a 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; and the stable characteristic coefficient is the characteristic coefficient of the water pump turbine at the next moment 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:
and 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:
the unit rotating speed x of the next moment t1 in the unit rotating speed solving module 11(t1) Comprises the following steps:
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 points i Moment M i Opening degree Y of guide vane i Rotational speed n i And an operating head H i The following equations (B4) to (B8) are obtained:
M i ＝M 11i(t1) D 3 H i (B5)
Y i ＝Y max (1+y i(t1) ) (B7)
H i ＝(1+h i(t1) )H r (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:
9. a computing device for characteristic coefficients of a 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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