Pumped storage unit load shedding transition process algorithm based on adaptive time step length

Abstract

The invention discloses a pumped storage unit load shedding transition process algorithm based on adaptive time step size, which comprises the following steps: firstly, constructing a one-dimensional nonlinear model related to t, H, Q, y and omega, then solving a differential equation set in the model by adopting a fourth-order Runge-Kutta method, and realizing adaptive calculation of the time step size by controlling a local calculation error. When the local calculation error is greater than the allowable value, halving the time step length, and performing calculation again until the local calculation error is smaller than the allowable value; when the local calculation error is smaller than the allowable value, the time step length is doubled, and recalculation is conducted till the local calculation error is larger than the allowable value. According to the method, simulation of the multi-frequency characteristic of the water pressure is achieved through the self-adaption method for calculating the time step length, the water hammer pressure rising and pulsating pressure characteristics after load shedding of the pump turbine are rapidly and accurately calculated, the start-stop rule is optimized, and the requirement of engineering design can be well met.

Description

Technical Field

[0001] The present invention relates to the field of energy, and in particular to an algorithm for load rejection transient process of a pumped storage unit based on adaptive time step. Background Art

[0002] The construction of pumped-storage power plants is of great significance for promoting the development and utilization of nuclear power and renewable energy. To ensure the safe and reliable operation of pumped-storage power plants, load-shedding transient process calculations are required during the design phase. However, because the pump-turbines, key components of pumped-storage power plants, typically exhibit an inverse "S" characteristic, load shedding not only increases water hammer pressure but also generates significant pulsating pressure, leading to increased unit vibration and a serious threat to unit safety. Therefore, accurately predicting the water hammer and pulsating pressures of pumped-storage units after load shedding is particularly important.

[0003] The water pressure in the transition process after the pump-turbine load shedding exhibits multi-frequency characteristics, with a wide frequency distribution and a large amplitude. Existing transient process calculation methods based on the characteristic line method, such as the transient process calculation method considering the dynamic characteristics of the pump-turbine disclosed in the Chinese invention patent application with application number CN202310143281.5, obtain the mean pressure, i.e., the water hammer pressure, which cannot simulate the pulsating pressure; the method of using the model test pulsating pressure to predict the pulsating pressure of the real machine (empirical method), such as the journal Simulation of pulsating pressure in the transient process of pump-turbine load shedding (Yang Jiebin, Yang Jiandong, Wang Chao, Bao Haiyan; Simulation of pulsating pressure in the transient process of pump-turbine load shedding, Journal of Hydroelectric Engineering, 2014, 33(4) , 286-294), whether the results of a model test can be applied to all power stations needs further verification and revision, and its results can only be used as a reference; although the one-dimensional plus three-dimensional method can calculate the pulsating pressure, it also has some shortcomings. For example, the efficient calculation method and control system for the complex transient process of multiple pump-turbine units with successive load rejection disclosed in the Chinese invention patent application with application number CN202210214724.0 requires the use of a computer cluster or supercomputer, which has high computational costs. The calculation of one working condition takes several hours or even days, and the calculation cycle is long, which is difficult to meet the needs of engineering design. Therefore, it is urgent to develop a transient process algorithm that can accurately predict water hammer pressure and pulsating pressure while reducing computational costs and increasing computational speed. Summary of the Invention

[0004] In response to the above problems, the present invention provides a load rejection transition process algorithm for a pumped storage unit based on an adaptive time step. The algorithm adopts an adaptive calculation time step method to simulate the multi-frequency characteristics of water pressure, so as to quickly and accurately calculate the water hammer pressure increase and pulsating pressure characteristics after the pump turbine is rejected, optimize the start-up and shutdown rules, and meet the needs of engineering design.

[0005] The technical solutions of the present invention are as follows:

[0006] An algorithm for load rejection transient process of pumped storage units based on adaptive time step is first constructed. A one-dimensional nonlinear model for transient process calculation of pumped storage power station units is constructed, which is related to the time step t, water pressure H in the water diversion pipeline, flow Q, movable guide vane opening y, and unit angular velocity ω. Then, the fourth-order Runge-Kutta method (RK method) is used to solve the differential equations in the model. By controlling the local calculation error, time step adaptive calculation is achieved. When the local calculation error is greater than the allowable value, the time step is halved and the calculation is repeated until the local calculation error is less than the allowable value, and the calculation result is output. When the local calculation error is less than the allowable value, the time step is doubled and the calculation is repeated until the local calculation error is greater than the allowable value, and the calculation result is output.

[0007] In a further technical solution, constructing a one-dimensional nonlinear model specifically includes the following steps:

[0008] S11. Construct a piping system model based on the principles of fluid mechanics:

[0009]

[0010] Where H is the water pressure in the water supply pipe, m; Q is the flow rate, m 3 / s; V is the flow velocity, m / s; coefficient C = a 2 / gA, L = gA, R = f / 2DA; a is the propagation speed of water shock wave, m / s; g is the acceleration of gravity, m / s 2 ; A is the cross-sectional area of ​​the pipe, m 2 ; D is the pipe diameter, m; f is the friction coefficient;

[0011] S12. Construct a PID controller model. The unit frequency control is completed by the speed regulating device, which generally adopts the proportional-integral-differential control law (i.e. PID control). Its mathematical model is as follows:

[0012]

[0013] Where y is the opening of the movable guide vane, %; Δf is the unit frequency deviation signal, Hz; t is the time step, s; k p 、k i and k d They are the proportional coefficient of the proportional link, the integral time constant of the integral link, and the differential time constant of the differential link;

[0014] S13. Constructing the unit rotational motion model:

[0015]

[0016] Where J is the moment of inertia of the rotating part of the unit, kg˙m 2 ;ω is the angular velocity of the unit, rad / s; M t is the pump-turbine torque, N˙m, obtained by discrete interpolation of the comprehensive characteristics of the pump-turbine model; M g is the generator torque, N˙m, after load rejection M g =0;

[0017] S14. Integrate the above models (1)-(4) to construct a general calculation model related to the time step t, the water pressure H in the water supply pipeline, the flow rate Q, the movable guide vane opening y and the unit angular velocity ω:

[0018]

[0019] Where Y = (Q, H, y, ω) T ;

[0020] G=(g1(t,Y),g2(t,Y),g3(t,Y),g4(t,Y)) T ;

[0021] The above g1, g2, g3, and g4 correspond to models (1)-(4) respectively;

[0022] Initial value Y(t0)=Y0.

[0023] In a further technical solution, the transition process calculation process includes the following steps:

[0024] S21, input the initial time step Δt0, initial water pressure H0, initial flow Q0, initial opening y0, initial angular velocity ω0; set the time step range (Δt min ,Δt max ), calculation time range (t min ,t max ) and the allowable error ε, time step adaptive coefficient α = 1;

[0025] S22, from the minimum time t min , the calculation starts with the initial time step Δt0;

[0026] S23, solve the model (5) using the fourth-order Runge-Kutta method, and input the initial time t min , the initial time step Δt0 and the initial value Y i , find the intermediate variables M1, M2, M3, M4 and M5;

[0027] Where M1=G(t,Y i );

[0028]

[0029] S24. Calculate the value Y at the next moment based on the intermediate variables M1, M2, M3, M4, and M5. i+1 , and make further predictions

[0030] in,

[0031]

[0032] S25, by Y i+1 、 Find the difference And define the local error as:

[0033] S26. If the local error Δ>ε and αΔt>Δt min , then take the time step adaptive coefficient α=0.5, and set Y i+1 The value is taken as the initial value, and the process returns to step S23, and steps S23-S26 are repeated to calculate the value of the next time step; if Δ<ε and αΔt<Δt min , then take the time step adaptive coefficient α=2, and set Y i+1 The value is taken as the initial value, and the process returns to step S23, and steps S23-S26 are repeated to calculate the value of the next time step; if Δt>Δt max , then take the time step adaptive coefficient α=1, and set Y i+1 The value is used as the initial value, and the process returns to step S23, and steps S23-S26 are repeated to calculate the value of the next time step;

[0034] S27. Calculate until time t>t max until;

[0035] S28, end and output the result {Y i}.

[0036] The beneficial effects of the present invention are:

[0037] 1. The present invention constructs a high-precision nonlinear mathematical model for calculating the load rejection transient process of a pumped storage unit, which is used to calculate the fluctuation characteristics of various parameters after load rejection;

[0038] 2. Compared with the existing fixed time step transition process algorithm based on the characteristic line method, which can only calculate water hammer pressure but not pulsating pressure, the present invention proposes an algorithm based on the time step adaptive method to solve the nonlinear mathematical equations of the transition process, which can calculate both water hammer pressure and pulsating pressure;

[0039] 3. Compared with the existing one-dimensional plus three-dimensional calculation method, which has high calculation costs (requiring computer clusters or supercomputers) and long calculation cycles (usually calculating one working condition in days), the present invention can quickly calculate water hammer pressure and pulsation pressure, reducing calculation costs and shortening calculation cycles (calculating one working condition in minutes);

[0040] 4. The present invention can solve the changing characteristics of multi-frequency signals in the transition process, thereby improving the calculation accuracy of the transition process;

[0041] 5. The present invention can quickly calculate the water hammer pressure and pulsating pressure in the pipeline, and the results are basically consistent with the field test results, which can provide guidance for the design and operation of pumped storage power stations;

[0042] 6. The present invention can provide more effective services for nuclear power plants and the development and utilization of new energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a calculation flow chart of the transition process algorithm according to an embodiment of the present invention;

[0044] Figure 2 1 is a diagram showing the calculation results of the speed change of the pumped storage unit corresponding to different guide vane closing times after load rejection in an embodiment of the present invention;

[0045] Figure 3 1 is a graph showing the calculation results of the volute inlet water pressure change corresponding to different guide vane closing times after the pumped storage unit is loaded off in an embodiment of the present invention;

[0046] Figure 4 This is a diagram showing the calculation results of the volute inlet water pressure after load rejection when the shutdown time is 40.0s in an embodiment of the present invention;

[0047] Figure 5 yes Figure 4 The corresponding volute pulsation pressure spectrum;

[0048] Figure 6 This is a diagram showing the measured results of the volute inlet water pressure after load rejection when the shutdown time is 40.0s in an embodiment of the present invention;

[0049] Figure 7 yes Figure 6 The corresponding volute pulsation pressure spectrum. DETAILED DESCRIPTION

[0050] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0051] Example:

[0052] An algorithm for load rejection transient process of pumped storage units based on adaptive time step is first constructed. A one-dimensional nonlinear model for transient process calculation of pumped storage power station units is constructed, which is related to the time step t, water pressure H in the water diversion pipeline, flow Q, movable guide vane opening y, and unit angular velocity ω. Then, the fourth-order Runge-Kutta method (RK method) is used to solve the differential equations in the model. By controlling the local calculation error, time step adaptive calculation is achieved. When the local calculation error is greater than the allowable value, the time step is halved and the calculation is repeated until the local calculation error is less than the allowable value, and the calculation result is output. When the local calculation error is less than the allowable value, the time step is doubled and the calculation is repeated until the local calculation error is greater than the allowable value, and the calculation result is output.

[0053] The construction process of the one-dimensional nonlinear model of the present invention is as follows:

[0054] S11. Construct a piping system model based on the principles of fluid mechanics:

[0055]

[0056] Where H is the water pressure in the water supply pipe, m; Q is the flow rate, m 3 / s; V is the flow velocity, m / s; coefficient C = a 2 / gA, L = gA, R = f / 2DA; a is the propagation speed of water shock wave, m / s; g is the acceleration of gravity, m / s 2 ; A is the cross-sectional area of ​​the pipe, m 2 ; D is the pipe diameter, m; f is the friction coefficient;

[0057] S12. Construct a PID controller model. The unit frequency control is completed by the speed regulating device, which generally adopts the proportional-integral-differential control law (i.e. PID control). Its mathematical model is as follows:

[0058]

[0059] Where y is the opening of the movable guide vane, %; Δf is the unit frequency deviation signal, Hz; t is the time step, s; k p 、k i and k d They are the proportional coefficient of the proportional link, the integral time constant of the integral link, and the differential time constant of the differential link;

[0060] S13. Constructing the unit rotational motion model:

[0061]

[0062] Where J is the moment of inertia of the rotating part of the unit, kg˙m 2;ω is the angular velocity of the unit, rad / s; M t is the pump-turbine torque, N˙m, obtained by discrete interpolation of the comprehensive characteristics of the pump-turbine model; M g is the generator torque, N˙m, after load rejection M g =0;

[0063] S14. Integrate the above models (1)-(4) to construct a general calculation model related to the time step t, the water pressure H in the water supply pipeline, the flow rate Q, the movable guide vane opening y and the unit angular velocity ω:

[0064]

[0065] Where Y = (Q, H, y, ω) T ;

[0066] G=(g1(t,Y),g2(t,Y),g3(t,Y),g4(t,Y)) T ;

[0067] The above g1, g2, g3, and g4 correspond to models (1)-(4) respectively;

[0068] Initial value Y(t0)=Y0.

[0069] Based on the nonlinear calculation model constructed above, the transition process calculation process is as follows:

[0070] S21, input the initial time step Δt0, initial water pressure H0, initial flow Q0, initial opening y0, initial angular velocity ω0; set the time step range (Δt min ,Δt max ), calculation time range (t min ,t max ) and the allowable error ε, time step adaptive coefficient α = 1;

[0071] S22, from the minimum time t min , the calculation starts with the initial time step Δt0;

[0072] S23, solve the model (5) using the fourth-order Runge-Kutta method, and input the initial time t min , the initial time step Δt0 and the initial value Y i , find the intermediate variables M1, M2, M3, M4 and M5;

[0073] Where M1=G(t,Y i );

[0074]

[0075] S24. Calculate the value Y at the next moment based on the intermediate variables M1, M2, M3, M4, and M5. i+1 , and make further predictions

[0076] in,

[0077]

[0078] S25, by Y i+1 、 Find the difference And define the local error as:

[0079] S26. If the local error Δ>ε and αΔt>Δt min , then take the time step adaptive coefficient α=0.5, and set Y i+1 The value is taken as the initial value, and the process returns to step S23, and steps S23-S26 are repeated to calculate the value of the next time step; if Δ<ε and αΔt<Δt min , then take the time step adaptive coefficient α=2, and set Y i+1 The value is taken as the initial value, and the process returns to step S23, and steps S23-S26 are repeated to calculate the value of the next time step; if Δt>Δt max , then take the time step adaptive coefficient α=1, and set Y i+1 The value is used as the initial value, and the process returns to step S23, and steps S23-S26 are repeated to calculate the value of the next time step;

[0080] S27. Calculate until time t>t max until;

[0081] S28, end and output the result {Y i}.

[0082] This embodiment performs multiple calculations based on the above nonlinear calculation model and solution process, and finally plots the calculation results into a curve graph and analyzes them. Figure 2 and Figure 3 As shown in the figure, the calculation results of the unit speed change and the volute inlet water pressure change corresponding to different guide vane closing times after a pumped storage unit is loaded, it can be seen that when the guide vane closing time is 18.0s and 25.0s, the pump turbine enters the reverse pumping condition only once in the reverse "S" characteristic area (the second peak), and when the guide vane closing time is 35.0s, it enters the reverse pumping area twice (the second and third peaks). When the pump enters the reverse "S" area, pulsating pressure will be generated. In order to analyze the pulsating pressure characteristics, the volute inlet water pressure is further calculated when the guide vane closing time is 40.0s. The calculation results are shown in the figure below. Figure 4 and Figure 5As shown, and compared with the on-site pressure measurement of the volute of a pumped storage unit (measurement results see Figure 6 and Figure 7 ) for comparison. Field test results show the presence of a low-frequency pressure pulsation of 6.14 Hz, approximately 0.76 times the rotational frequency, within the rotational frequency multiple range of rotating stall. Simultaneously, a pressure pulsation of 168.96 Hz, approximately twice the blade rotational frequency, within the rotational frequency multiple range of static-dynamic interference, indicates that the pressure pulsation amplitude rapidly increases due to the increased static-dynamic interference between the turbine impeller and guide vanes. The pressure pulsation spectrum shows that the volute inlet pressure pulsation signal is primarily low-frequency, with higher-amplitude frequencies concentrated primarily between 0 and 42.73 Hz. Calculation results show that the pressure pulsation spectrum contains a low-frequency pressure pulsation of approximately 6.0 Hz, approximately 2 / 3 of the rotational frequency, within the rotational frequency multiple range of rotating stall. Furthermore, a pressure pulsation of 43.3-47.3 Hz exists, close to the unit's rated frequency of 50.0 Hz, which is generally consistent with the field measurement results.

[0083] The results show that the calculation results of the pulsating pressure in the range of 0Hz to 50Hz using the transition process algorithm of the present invention are basically consistent with the field test results, which are mainly low-frequency pulsations. Although the one-dimensional model cannot reproduce the high-frequency dynamic and static interference components, the proportion of the dynamic and static interference components is relatively small, indicating that this model is very effective. The research results can provide guidance for engineering design and unit operation.

[0084] The above-described embodiments merely represent specific implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A load rejection transient process algorithm for a pumped storage unit based on an adaptive time step, characterized in that: Firstly, a one-dimensional nonlinear model for calculating the transient process of a pumped storage power station unit related to the time step t, the water pressure H in the water diversion pipeline, the flow Q, the opening of the movable guide vane y and the angular velocity ω of the unit is constructed. Then, the fourth-order Runge-Kutta method is used to solve the differential equations in the model. By controlling the local calculation error, the time step adaptive calculation is realized. When the local calculation error is greater than the allowable value, the time step is halved and the calculation is repeated until the local calculation error is less than the allowable value, and the calculation result is output. When the local calculation error is less than the allowable value, the time step is doubled and the calculation is recalculated until the local calculation error is greater than the allowable value, and the calculation result is output.

2. The load rejection transient process algorithm of a pumped storage unit based on adaptive time step according to claim 1 is characterized in that: The construction of a one-dimensional nonlinear model specifically includes the following steps: S11. According to the principles of fluid mechanics, construct a pipeline system model: Where H is the water pressure in the water supply pipeline, m; Q is the flow rate, m 3 / s; V is the flow velocity, m / s; coefficient C = a 2 / gA, L = gA, R = f / 2DA; a is the propagation speed of water shock wave, m / s; g is the acceleration of gravity, m / s 2 ; A is the cross-sectional area of ​​the pipeline, m 2 ; D is the pipe diameter, m; f is the friction coefficient; S12. Construct PID controller model: Where y is the opening of the movable guide vane, %; Δf is the unit frequency deviation signal, Hz; t is the time step, s; k p , k i and k d They are the proportional coefficient of the proportional link, the integral time constant of the integral link and the differential time constant of the differential link respectively; S13. Constructing the unit rotational motion model: Where J is the moment of inertia of the rotating part of the unit, kg˙m 2 ;ω is the angular velocity of the unit, rad / s; M t is the pump-turbine torque, N˙m, obtained by discrete interpolation of the comprehensive characteristics of the pump-turbine model; M g is the generator torque, N˙m, after load rejection M g =0; S14. Integrate the above models (1)-(4) to construct a general calculation model related to the time step t, the water pressure H in the water diversion pipeline, the flow Q, the movable guide vane opening y and the unit angular velocity ω: Where, Y=(Q,H,y,ω) T ; G=(g1(t,Y),g2(t,Y),g3(t,Y),g4(t,Y)) T ; The above g1, g2, g3, and g4 correspond to models (1)-(4) respectively; Initial value Y(t0)=Y0.

3. The load rejection transient process algorithm of a pumped storage unit based on adaptive time step according to claim 2 is characterized in that: The transient process calculation process includes the following steps: S21, input the initial time step Δt0, initial water pressure H0, initial flow Q0, initial opening y0, initial angular velocity ω0; set the time step range (Δt min ,Δt max ), calculation time range (t min ,t max ) and the allowable error ε, time step adaptive coefficient α = 1; S22, from the minimum time t min , start calculation with the initial time step Δt0; S23, using the fourth-order Runge-Kutta method to solve model (5), input the initial time t min , the initial time step Δt0 and the initial value Y i , find the intermediate variables M1, M2, M3, M4 and M5; Where, M1=G(t,Y i ); S24, calculate the value Y at the next moment based on the intermediate variables M1, M2, M3, M4 and M5 i+1 , and make further predictions S25, by Y i+1 , Find the difference And define the local error as: S26, if the local error Δ>ε and αΔt>Δt min , then take the time step adaptive coefficient α = 0.5, and set Y i+1 The value is taken as the initial value, and the process returns to step S23, and steps S23-S26 are repeated to calculate the value of the next time step; if Δ<ε and αΔt<Δt min , then take the time step adaptive coefficient α = 2, and set Y i+1 The value is taken as the initial value, and the process returns to step S23, and steps S23-S26 are repeated to calculate the value of the next time step; if Δt>Δt max , then take the time step adaptive coefficient α = 1, and set Y i+1 The value is taken as the initial value, and the process returns to step S23, and steps S23-S26 are repeated to calculate the value of the next time step; S27, calculation until time t>t max until; S28, end and output the result {Y i }.

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