Hydraulic turbine and water intake system model water flow inertia time constant correction system and method
By introducing the correction coefficient of the water flow time constant in the turbine and water diversion system models, the problem of deviation between the actual value of the water flow time constant and the design value is solved, the efficiency and accuracy of the stable calculation of the power system are improved, and the system oscillation caused by the water hammer effect is reduced.
Patent Information
- Application Number
- CN202111250794.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-10-26
- Publication Date
- 2025-06-24
- Estimated Expiration
- 2041-10-26
AI Technical Summary
There is a large deviation from the actual value of the inertia time constant of the water flow from the design value, resulting in a water hammer effect during the speed regulation of the water-power unit, which in turn causes ultra-low frequency oscillation of the system, seriously affecting the stable operation of the power system.
By introducing the correction coefficient of the inertia time constant of the water flow, the turbine and water diversion system models are improved, and simulation and verification are carried out based on the actual data of the operating unit. The correction coefficient is the relationship coefficient between the operating head and the unit flow.
It effectively solves the problem of deviation between the actual value of the inertia time constant of the water flow and the design value, improves the efficiency and accuracy of the stable calculation of the power system and reduces the system oscillation caused by the water hammer effect.
Smart Images

Figure CN113987967B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of hydroelectric generator unit regulation in a power grid, and in particular relates to a system and method for correcting the inertia time constant of a water turbine and a water diversion system model. Background Art
[0002] After the asynchronous interconnection of Yunnan Power Grid, the speed governor of large hydropower units caused a sudden change in the flow of the unit due to the rapid opening or closing of the unit guide vanes during the regulation process, which triggered the water hammer effect and caused the reverse regulation of active power. This phenomenon has a phase lag and provides negative damping to the system, which is easy to induce ultra-low frequency oscillation of the system and seriously deteriorate the stable operation of the system. In the power stability calculation, the main parameter characterizing the water hammer effect is the water flow inertia time constant (Tw) in the turbine and water diversion system model.
[0003] The water flow inertia time constant is defined as the water flow in the water pipe at the rated head H r Under the action, the flow rate increases from zero to the rated flow rate Q r The time required to calculate the inertia of the water flow in the water pipe can generally be obtained through the design parameters of the water diversion pipe. However, during the actual operation of the hydropower unit, the operating head is constantly changing, and the unit flow rate will also change with the change of the load condition point, resulting in the actual value of the water flow inertia time constant also constantly changing, which has a large deviation from the design value. In order to solve the problem of the deviation between the actual value and the design value of the water flow inertia time constant, and to meet the full-condition simulation of the stable calculation of the power system, it is necessary to improve the traditional turbine and water diversion system, and introduce the water flow inertia time constant correction coefficient. Summary of the invention
[0004] The present invention derives and provides a correction method for the water flow inertia time constant. By introducing a water flow inertia time constant correction coefficient, the problem of deviation between the actual value and the design value of the water flow inertia time constant is solved, thereby improving the efficiency and accuracy of full-operating condition simulation of power system stability calculation.
[0005] The present invention obtains the water flow inertia time constant correction coefficient by mathematical deduction, and measures the active power reverse regulation law of the hydropower unit under different operating heads and operating conditions through field tests. By adding the water flow inertia time constant correction coefficient to the turbine and water diversion system model and performing active power reverse regulation simulation, the simulation results prove the effectiveness and accuracy of the proposed water flow inertia time constant correction coefficient, which has practical value.
[0006] The technical solution of the present invention is as follows:
[0007] A water flow inertia time constant correction system in a hydraulic turbine and water diversion system model includes a collector and a processor; the processor performs the following processing based on the data collected by the collector:
[0008] For the same grid-connected operating unit, select several operating water heads, and select the same number of operating points at each operating water head. Conduct a step disturbance of the given guide vane, record the output curves of the operating water head, active power, and unit flow rate, and analyze the reverse regulation law of the active power;
[0009] Improve the traditional water turbine and water diversion system model, introduce the initial value of active power and the correction coefficient of the water flow inertia time constant that have a linear relationship with the reverse regulation of active power, and obtain the improved water turbine and water diversion system model:
[0010]
[0011] Among them: P represents the active power, MW; P i0 is the operating load condition, that is, the initial value of active power, MW; y represents the guide vane opening, %; f(y) represents the three-stage correction of the guide vane opening and active power at different water heads; Tw represents the water flow inertia time constant; s represents the Laplace operator;
[0012] Based on the improved water turbine and water diversion system model, combined with the designed value of the water flow inertia time constant of the operating unit, conduct a reverse regulation simulation check of the active power at different operating points under different operating water heads, and test the effectiveness and accuracy of the improved water turbine and water diversion system model and the water flow inertia time constant coefficient.
[0013] Furthermore, the correction coefficient of the water flow inertia time constant is the relationship coefficient between the operating water head and the unit flow rate. When the operating water head changes, the flow rate of the unit under rated load at different operating water heads is statistically analyzed, and then the correction coefficient of the water flow inertia time constant that changes with the operating water head can be obtained.
[0014] Furthermore, the correction coefficient of the water flow inertia time constant is:
[0015]
[0016] Among them: f(H t ) = Q i (i = 1, 2, 3...), representing the flow rate of the unit under rated load at different operating water heads; Q0 represents the rated flow rate of the water turbine, m 3 / s; H i represents the operating water head, m; H0 represents the rated water head, m.
[0017] Furthermore, the reverse regulation change law of the active power means that the reverse regulation of the active power caused by the water hammer effect increases with the increase of the load, and is approximately linearly related to the load. At the same load, the lower the water head, the greater the reverse regulation of the active power.
[0018] Further, when improving the traditional water turbine and water diversion system, a three-stage correction is performed on the guide vane opening and active power, and the measured three-stage active power and the corresponding guide vane openings are selected.
[0019] Further, the initial value of active power refers to the initial power when the unit operates at a certain operating point without reverse regulation of active power.
[0020] The present invention also relates to a method for correcting the water flow inertia time constant in a water turbine and water diversion system model, which is carried out as follows:
[0021] For the same grid-connected operating unit, several operating heads are selected, and the same several operating points are selected under each operating head. A step disturbance is given to the guide vane, and the output curves of the operating head, active power, and unit flow rate are recorded to analyze the law of reverse regulation of active power.
[0022] Improve the traditional water turbine and water diversion system model, introduce the initial value of active power and the correction coefficient of water flow inertia time constant that have a linear relationship with the reverse regulation of active power, and obtain the improved water turbine and water diversion system model:
[0023]
[0024] Among them: P represents active power, MW; P i0 is the operating load condition, that is, the initial value of active power, MW; y represents the guide vane opening, %; f(y) represents the three-stage correction of the guide vane opening and active power under different water heads; Tw represents the water flow inertia time constant; s represents the Laplace operator;
[0025] Based on the improved water turbine and water diversion system model, combined with the designed value of the water flow inertia time constant of the operating unit, the reverse regulation simulation check of active power is carried out for different operating points under different operating heads to test the effectiveness and accuracy of the improved water turbine and water diversion system model and the water flow inertia time constant coefficient.
[0026] Further, the correction coefficient of the water flow inertia time constant is:
[0027]
[0028] Among them: f(H i ) = Q i (i = 1, 2, 3...), represents the flow rate when the unit is under rated load under different operating heads; Q0 represents the rated flow rate of the water turbine, m 3 / s; H i represents the x operating head, m; H0 represents the rated head, m.
[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0030] 1. The correction coefficient of the water flow inertia time constant provided by the present invention fills a blank.
[0031] 2. By introducing the correction coefficient of the water flow inertia time constant, the present invention improves the traditional water turbine and water diversion system model, which has practical value.
[0032] 3. The present invention directly correlates the water turbine and water diversion system model with the correction coefficient of the water flow inertia time constant and the initial value of the active power. During simulation, it is not necessary to modify the designed value of the water flow inertia time constant, and the reverse adjustment of the active power under different operating water heads and multiple operating conditions can be realized. The test method is simple, the test value is accurate, and the efficiency and accuracy of the full-condition simulation of the power system stability calculation are improved. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] Figure 1 is the block diagram of the traditional water turbine and water diversion system model;
[0034] Figure 2 is the block diagram of the improved water turbine and water diversion system model;
[0035] Where: Q i is the unit flow rate at rated load under the operating water head, m 3 / s;
[0036] H i is the operating water head, m;
[0037] H1, H2, and H3 are the relationship curves between the guide vane opening and the active power under different operating water heads;
[0038] Figure 3 is the comparison diagram of the simulated and measured active powers under the condition of 600 MW at a water head of 108 m;
[0039] Figure 4 is the comparison diagram of the simulated and measured active powers under the condition of 480 MW at a water head of 108 m;
[0040] Figure 5 is the comparison diagram of the simulated and measured active powers under the condition of 240 MW at a water head of 108 m;
[0041] Figure 6 is the comparison diagram of the simulated and measured active powers under the condition of 600 MW at a water head of 113.8 m;
[0042] Figure 7 is the comparison diagram of the simulated and measured active powers under the condition of 480 MW at a water head of 113.8 m;
[0043] Figure 8 is the comparison diagram of the simulated and measured active powers under the condition of 240 MW at a water head of 113.8 m;
[0044] Figure 9 It is a comparison chart of the simulated and measured active power under the condition of 600MW at a water head of 117m;
[0045] Figure 10 It is a comparison chart of the simulated and measured active power under the condition of 480MW at a water head of 117m;
[0046] Figure 11 It is a comparison chart of the simulated and measured active power under the condition of 240MW at a water head of 117m. Specific implementation manners
[0047] Next, the technical solutions in the embodiments will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.
[0048] Unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application shall have the ordinary meaning understood by those of ordinary skill in the art in the relevant art. The "first", "second" and similar terms used in this embodiment do not denote any order, quantity or importance, but are only used to distinguish different components. The terms such as "including" or "comprising" mean that the elements or objects appearing before this term cover the elements or objects listed after this term and their equivalents, without excluding other elements or objects. The terms "installation", "connection" and "coupling" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection or an integral connection; it can be a direct connection or an indirect connection through an intermediate medium, and it can be the communication inside two elements. The terms "upper", "lower", "left", "right", "horizontal" and "vertical" are only used in terms of the orientation of the components in the accompanying drawings. These directional terms are relative concepts, and they are used for relative description and clarification, and they can change correspondingly according to the change of the orientation of the components placed in the accompanying drawings.
[0049] In the water turbine and water intake system model of this embodiment, the water flow inertia time constant correction system includes a collector and a processor; the processor processes the data collected by the collector as follows:
[0050] For the same grid-connected operation unit, select three operating water heads, select the same three operating points at each operating water head, perform a step disturbance of the guide vane setting, record the output curves of the operating water head, active power and unit flow rate, and analyze the reverse regulation law of the active power;
[0051] Improve the traditional water turbine and water diversion system model, introduce the initial value of active power and the correction coefficient of water flow inertia time constant with an inverse linear relationship with active power regulation, and obtain the improved water turbine and water diversion system model:
[0052]
[0053] Among them: P represents active power, MW; P i0 is the operating load condition, that is, the initial value of active power, MW; y represents the guide vane opening, %; f(y) represents the three-stage correction of the guide vane opening and active power under different water heads; Tw represents the water flow inertia time constant; s represents the Laplace operator;
[0054] Based on the improved water turbine and water diversion system model, combined with the designed value of the water flow inertia time constant of the operating unit, conduct active power inverse regulation simulation verification for different operating conditions at different operating water heads to test the effectiveness and accuracy of the improved water turbine and water diversion system model and the water flow inertia time constant coefficient.
[0055] In this embodiment, the mathematical derivation of the water flow inertia time constant correction coefficient is as follows:
[0056] 1) The water flow inertia time constant under rated water head and rated flow (rated load) is:
[0057]
[0058] In the formula: Q0 is the rated flow of the water turbine, m 3 / s; H0 is the rated water head, m; L is the length of each corresponding section of the water diversion pipeline, m; S is the cross-sectional area of each section of the water diversion pipeline, m; g is the acceleration due to gravity, m / s 2 .
[0059] 2) The water flow inertia time constant under different operating water heads and different loads is:
[0060]
[0061] In the formula: P i0 is the operating load condition (initial value of active power), MW; Q i is the unit flow rate at rated load under the operating water head, m 3 / s; Q0 is the rated flow of the water turbine, m 3 / s; H i is the operating water head, m; H0 is the rated water head, m; L is the length of each corresponding section of the water diversion pipeline, m; S is the cross-sectional area of each section of the water diversion pipeline, m; g is the acceleration due to gravity, m / s 2 .
[0062] 3) Statistically analyze the flow rate of the unit when it is under rated load at different operating water heads, i.e.:
[0063] f(H i ) = Q i (i = 1, 2, 3...)
[0064] From this, it can be obtained that:
[0065]
[0066] In summary, the correction coefficient of the water flow inertia time constant is:
[0067]
[0068] In this embodiment, the correction coefficient of the water flow inertia time constant is the relationship coefficient between the operating water head and the flow rate of the unit. When the operating water head changes, statistically analyze the flow rate of the unit when it is under rated load at different operating water heads, and then the correction coefficient of the water flow inertia time constant that varies with the operating water head can be obtained.
[0069] The reverse regulation variation law of the active power refers to that the reverse regulation of the active power caused by the water hammer effect increases with the increase of the load, and it is approximately linearly related to the load. At the same load, the lower the water head, the greater the reverse regulation of the active power.
[0070] The traditional water turbine and water diversion system model is as Figure 1 shown. The three-stage correction of the traditional water turbine and water diversion system shows a non-linear relationship between the guide vane opening and the active power of the hydropower unit. Three-stage correction processing is performed on the guide vane opening and the active power, and the measured three-stage active power and the corresponding guide vane openings are selected. The initial value of the active power refers to the initial power of the unit when it operates at a certain operating point without reverse regulation of the active power.
[0071] The improved water turbine and water diversion system model is as Figure 2 shown. It introduces the initial value of the active power and the correction coefficient of the water flow inertia time constant that are linearly related to the reverse regulation of the active power. The correction coefficient is the relationship coefficient between the operating water head and the flow rate of the unit when it is under rated load at different operating water heads.
[0072] It should be noted that it should be understood that the division of each module of the above device is only a logical function division. In actual implementation, it can be fully or partially integrated into a physical entity, or physically separated. And these modules can all be implemented in the form of software called by a processing element; they can also all be implemented in the form of hardware; or some modules can be implemented in the form of software called by a processing element, and some modules can be implemented in the form of hardware.
[0073] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a readable storage medium or transmitted from one readable storage medium to another. For example, the computer instructions can be transmitted from a website, computer, server, or data center to another website, computer, server, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.). The readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that includes one or more integrated available media. The available medium can be a magnetic medium (such as a floppy disk, hard disk, magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state disk (SSD)).
[0074] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.
[0075] The method for correcting the water flow inertia time constant in the water turbine and water diversion system model of this embodiment is carried out as follows:
[0076] For the same grid-connected operating unit, select several operating heads, select the same several operating points at each operating head, perform a step disturbance on the guide vane setting, record the output curves of the operating head, active power, and unit flow rate, and analyze the reverse regulation law of the active power;
[0077] Improve the traditional water turbine and water diversion system model, introduce the initial value of the active power and the correction coefficient of the water flow inertia time constant that have a linear relationship with the reverse regulation of the active power, and obtain the improved water turbine and water diversion system model:
[0078]
[0079] Wherein: P represents the active power, MW; P i0 is the operating load condition, i.e., the initial value of the active power, MW; y represents the guide vane opening, %; f(y) represents the three-stage correction of the guide vane opening and the active power at different water heads; Tw represents the water flow inertia time constant; s represents the Laplace operator.
[0080] Based on the improved water turbine and water diversion system model, combined with the designed value of the water flow inertia time constant of the operating unit, the active power reverse regulation simulation verification is carried out for different operating conditions at different operating water heads to test the effectiveness and accuracy of the improved water turbine and water diversion system model and the water flow inertia time constant coefficient.
[0081] As a specific correction example:
[0082] For a certain large-scale hydropower station, the type of the water turbine is vertical Francis turbine, the water diversion system adopts the single-pipe single-unit mode, the rated power is 600 MW, the rated water head is 111 m, and the rated flow rate is 597.95 m 3 / s, and the designed value of the water flow inertia time constant is 2 s.
[0083] At three operating water heads of 108 m, 113.8 m, and 117 m respectively, when the unit carries active powers of 240 MW, 480 MW, and 600 MW, a step amount of the guide vane given is applied to the governor, and the measured active power reverse regulation curve is obtained; the flow rates of the unit when carrying the rated load of 600 MW at the three water heads are statistically 601.32 m 3 / s, 561.72 m 3 / s, and 548.49 m 3 / s respectively. Substitute the water head and flow rate data into the Figure 2 shown model (f(H i ) = Q i (i = 1, 2, 3...)), then the three-stage correction model of the water flow inertia time constant coefficient can be obtained.
[0084] The correction coefficient of the water flow inertia time constant is:
[0085]
[0086] Wherein: f(H i ) = Q i (i = 1, 2, 3...), represents the flow rate of the unit when carrying the rated load at different operating water heads; Q0 represents the rated flow rate of the water turbine, m 3 / s; Hi represents the operating water head, m; H0 represents the rated water head, m.
[0087] Simulations were carried out at three operating heads of 108m, 113.8m, and 117m respectively using the improved turbine and water diversion system model and the measured water flow inertia time constant correction coefficient obtained above. The simulation parameter settings were as follows: the designed value of the water flow inertia time constant was 2s, and the initial values of the active power were 240MW, 480MW, and 600MW. Finally, the simulation active power reverse regulation curve was obtained.
[0088] Comparison between the simulation active power reverse regulation curve and the measured active power reverse regulation curve is as Figure 3 、 Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 、 Figure 11 shown;
[0089] The unit operating point parameters, the simulation and measured active power reverse regulation values, and the water flow inertia time constant correction coefficient results at the heads of 108m, 113.8m, and 117m are shown in Table 1.
[0090] Table 1: Comparison between simulation and measured results
[0091]
[0092] It can be seen from the above tests that at the same head, as the load increases, the water flow inertia time constant correction coefficient increases approximately linearly. The curves obtained by simulation using it are as Figure 3 、 Figure 4 、 Figure 5 shown. The simulation active power curve is very close to the measured curve, and the reverse regulation values of the active power are basically consistent; at different heads, the correction coefficient will change with the changes of the head and flow rate. The curves obtained by simulation using it are as Figure 3 、 Figure 6 、 Figure 9 shown, and the reverse regulation values of the active power are also basically consistent.
[0093] The above example verifies the correctness of the water flow inertia time constant correction coefficient derived in this patent; under different operating heads and operating conditions, when using the improved model with the correction coefficient added for simulation, the simulation results are all basically close to the measured results.
[0094] The improved model realizes the simulation of the dynamic change of the active power under different operating heads and conditions, better reflects the change law of the reverse regulation value, and improves the calculation accuracy of the power system stability compared with the traditional model.
Claims
1. A water turbine and a water flow inertia time constant correction system in a water diversion system model, characterized in that: It includes a collector and a processor; the processor processes the data collected by the collector as follows: For the same grid-connected operating unit, select several operating water heads, select the same number of operating points at each operating water head, conduct a step disturbance of the guide vane setting, record the output curves of the operating water head, active power, and unit flow rate, and analyze the reverse regulation law of the active power; Improve the traditional water turbine and water conveyance system model, introduce the initial value of the active power and the correction coefficient of the water flow inertia time constant that have a linear relationship with the reverse regulation of the active power, and obtain the improved water turbine and water conveyance system model: Where: P represents the active power, MW; P i0 is the operating load condition, i.e., the initial value of the active power, MW; y represents the guide vane opening, %; f(y) represents the three-stage correction of the guide vane opening and the active power at different water heads; Tw represents the water flow inertia time constant; s represents the Laplace operator; Based on the improved water turbine and water conveyance system model, combined with the designed value of the water flow inertia time constant of the operating unit, conduct a reverse regulation simulation check of the active power for different operating points at different operating water heads, and verify the effectiveness and accuracy of the improved water turbine and water conveyance system model and the water flow inertia time constant coefficient.
2. The system according to claim 1, wherein: The correction coefficient of the water flow inertia time constant is the relationship coefficient between the operating water head and the unit flow rate. When the operating water head changes, the flow rates of the unit under rated load at different operating water heads are statistically analyzed, and then the correction coefficient of the water flow inertia time constant that changes with the operating water head can be obtained.
3. The system according to claim 2, wherein: The correction coefficient of the water flow inertia time constant is: Where: f(H i ) = Q i , i = 1, 2, 3..., represents the flow rate of the unit with rated load under different operating heads; Q0 represents the rated flow rate of the water turbine, m 3 / s; H i represents the operating head, m; H0 represents the rated head, m.
4. The system according to claim 1, characterized in that: The reverse regulation change law of the active power means that the reverse regulation of the active power caused by the water hammer effect increases with the increase of the load, has an approximate linear relationship with the load, and the lower the water head at the same load, the greater the reverse regulation of the active power.
5. The system according to claim 1, characterized in that: The improvement of the traditional water turbine and water conveyance system is to perform three-stage correction processing on the guide vane opening and the active power, and select the measured three-stage active power and the corresponding guide vane openings.
6. The system according to claim 1, wherein: The initial value of the active power refers to the initial power of the unit when there is no reverse regulation of the active power during operation at a certain operating point.
7. A method for correcting the water flow inertia time constant in a water turbine and a water diversion system model, characterized in that: It is carried out as follows: For the same grid-connected operating unit, select several operating water heads, select the same number of operating points at each operating water head, conduct a step disturbance of the guide vane setting, record the output curves of the operating water head, active power, and unit flow rate, and analyze the reverse regulation law of the active power; Improve the traditional water turbine and water conveyance system model, introduce the initial value of the active power and the correction coefficient of the water flow inertia time constant that have a linear relationship with the reverse regulation of the active power, and obtain the improved water turbine and water conveyance system model: Where: P represents the active power, MW; P i0 is the operating load condition, i.e., the initial value of the active power, MW; y represents the guide vane opening, %; f(y) represents the three-stage correction of the guide vane opening and the active power at different water heads; Tw represents the water flow inertia time constant; s represents the Laplace operator; Based on the improved water turbine and water conveyance system model, combined with the designed value of the water flow inertia time constant of the operating unit, conduct a reverse regulation simulation check of the active power for different operating points at different operating water heads, and verify the effectiveness and accuracy of the improved water turbine and water conveyance system model and the water flow inertia time constant coefficient.
8. The method according to claim 7, characterized in that: The correction coefficient of the water flow inertia time constant is: Where: f(H i ) = Q i , i = 1, 2, 3..., represents the flow rate of the unit under rated load at different operating heads; Q0 represents the rated flow rate of the water turbine, m 3 / s; H i represents the operating head, m; H0 represents the rated head, m.
Citation Information
Patent Citations
Actual measurement method for water inertia time constant of diversion system of hydraulic turbine
CN104598726A
Water turbine for power system stability calculation and water diversion system parameter modeling and testing method
CN111507637A