CN116561986A - Pumped storage power station hydraulic oscillation analysis method, system and medium based on complex frequency domain equivalent circuit model - Google Patents
Pumped storage power station hydraulic oscillation analysis method, system and medium based on complex frequency domain equivalent circuit model Download PDFInfo
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Abstract
The invention discloses a pumped storage power station hydraulic oscillation analysis method, a system and a medium based on a complex frequency domain equivalent circuit model, which comprise the following steps: according to the runner structure of the pumped storage power station, primarily determining the number of water pipelines and various hydraulic boundary elements contained in a runner equivalent circuit model; establishing an equivalent circuit model of the long-distance water conveying pipeline; establishing an equivalent circuit model of each hydraulic boundary in the flow channel; according to the arrangement form of the power station flow channels, connecting the water pipes with equivalent circuits corresponding to the hydraulic boundaries among the pipes, and solving equivalent hydraulic impedance complex frequency expressions at the upstream or downstream boundaries of the pumped storage power station according to the serial-parallel principle in the circuit theory; and assigning a calculated complex frequency domain expression according to the upstream or downstream actual hydraulic impedance of the pumped storage power station, and solving each order of vibration modes of free oscillation of the research system. The invention can accurately and efficiently analyze the hydraulic oscillation of the pumped storage power station with a complex structure.
Description
Technical Field
The invention belongs to the technical field of hydropower station vibration analysis, and particularly relates to a pumped storage power station hydraulic oscillation analysis method, a system and a medium based on a complex frequency domain equivalent circuit model.
Background
Pumped storage power stations are important large-scale energy storage power sources in modern power systems, and play a key role in regulating power balance in a power grid. At present, the pumped storage power station in China is developing towards high water head and giant, the power station often has a very complex water delivery flow channel structure, and the hydraulic stability of the power station has important significance for the construction design and safe and stable operation of the power station. An important task for measuring the hydraulic stability of a pumped storage power station runner is to analyze the hydraulic oscillation characteristics of the power station runner and judge whether the natural frequency design of the power station is reasonable or not, and whether potential specific frequency resonance risks exist in the running process of a unit. Therefore, free oscillation analysis is required to be performed on the whole flow channel of the power station so as to acquire the vibration modes of free oscillation of each order of the flow channel of the power station. The mature analysis method in the engineering is usually used for carrying out free oscillation analysis of a system by constructing a continuous hydraulic impedance model of an integral runner of the power station and finally obtaining complex frequency domain vibration mode information comprising oscillation attenuation coefficients and eigenfrequencies of each order. However, since the continuous hydraulic impedance model is suitable for the pumped storage power station with a relatively simple flow channel structure, for the pumped storage power station with a complex structure, the analytical expression of the hydraulic impedance of the whole system is difficult to derive due to the reason that the order of the flow channel model is too high, the form of a hydraulic boundary equation is complex and the like. Therefore, a new complex frequency domain analysis method is needed to realize the accurate and efficient hydraulic oscillation analysis of the pumped storage power station with a complex structure.
Disclosure of Invention
The invention aims to overcome the defects of complicated hydraulic impedance deduction process and complex mathematical expression when a traditional continuous hydraulic impedance model models a pumped storage power station with a complex flow channel structure, and can perform high-efficiency hydraulic oscillation analysis on the pumped storage power station with the complex flow channel structure.
A pumped storage power station hydraulic oscillation analysis method based on a complex frequency domain equivalent circuit model comprises the following steps:
establishing an equivalent circuit model of the long-distance water conveying pipeline and an equivalent circuit model of each hydraulic boundary in the runner according to the number of the water conveying pipelines and various hydraulic boundary elements contained in the equivalent circuit model of the power station runner;
and obtaining the equivalent hydraulic impedance complex frequency at the upstream or downstream boundary of the pumped storage power station according to the equivalent circuit model, assigning a value to the equivalent hydraulic impedance complex frequency, and solving each order of vibration modes of free oscillation of the research system.
According to the hydraulic oscillation analysis method of the pumped storage power station based on the complex frequency domain equivalent circuit model, the number of water pipelines and various hydraulic boundary elements contained in the runner equivalent circuit model is determined according to the runner structure of the pumped storage power station, wherein the pipelines are divided into four sections, namely a diversion tunnel, a pressure steel pipe, a draft tube, an extension and a tail water tunnel; the hydraulic boundary comprises: the device comprises an upper reservoir, an upper pressure regulating chamber, a water pump turbine, a lower pressure regulating chamber and a lower reservoir.
In the method for analyzing the hydraulic oscillation of the pumped storage power station based on the complex frequency domain equivalent circuit model, the water flow characteristics of the water delivery pipeline are described by the san View equation group after linearization treatment; the long-distance water pipe is defined as formed by connecting multiple sections of pipe in series, and for a section of pipe with length delta x, the equivalent resistance R of the pipe is i ＝R ei Δx, equivalent inductance L i ＝L ei Δx and equivalent capacitance C i ＝C ei Δx; wherein R is ei ，L ei ，C ei The equivalent resistance, the equivalent inductance and the equivalent capacitance are respectively corresponding to the pipeline with unit length.
The hydraulic oscillation analysis of the pumped storage power station based on the complex frequency domain equivalent circuit modelMethod, a certain position x=x on a water pipe i Equivalent hydraulic impedance Z at equi Based on the following formula:
if x=x is known i+1 Hydraulic impedance at the point
If x=x is known i-1 Hydraulic impedance at the point
s is Laplacian, Z equi-1 、Z equi And Z equi+1 Respectively represent x=x i-1 、x＝x i And x=x i+1 Hydraulic impedance at; r is R i-1 、L i-1 And C i-1 Respectively represent x=x i-1 And x=x i Equivalent resistance, equivalent inductance and equivalent capacitance of the pipeline; r is R i 、L i And C i Respectively represent x=x i And x=x i+1 Equivalent resistance, equivalent inductance and equivalent capacitance of the pipeline.
In the method for analyzing hydraulic oscillation of pumped storage power station based on complex frequency domain equivalent circuit model, hydraulic loss at the joint of two sections of pipelines is defined by a variable parameter resistor R s Equivalent resistance value is related to flow passing through the node and pipeline sectional area, and the calculation formula is as follows:
wherein g is gravity acceleration, Q L For the pipeline flow on the left side of the node, A L And A R Representing the area of the left and right side ducts of the node, respectively.
In the method for analyzing hydraulic oscillation of pumped storage power station based on complex frequency domain equivalent circuit model, the pipeline is at the confluence nodeThe hydraulic loss can be equivalently regarded as three variable parameter resistors R connected in star shape on the respective branches T1 、R T2 And R is T3 The value of each equivalent resistance parameter is related to the flow of each branch and the sectional area of the pipeline, and the calculation formula is as follows:
wherein Q is b1 、Q b2 And Q m The flow rates of the branch pipe 1, the branch pipe 2 and the confluence main pipe are respectively shown; a is that b1 、A b2 And A m The cross-sectional areas of the branch pipe 1, the branch pipe 2, and the confluence main pipe are shown, respectively.
The method for analyzing the hydraulic oscillation of the pumped storage power station based on the complex frequency domain equivalent circuit model specifically solves the vibration modes of each order and specifically comprises the following steps of
Determining the number M of primary solutions, and determining the upper limit N of the hydraulic oscillation order to be calculated;
combining the known reservoir boundary condition with the calculated reservoir boundary hydraulic impedance complex frequency domain expression as an objective function;
randomly generating M real part value ranges sigma i ∈[-1,0]Range of values ω for the imaginary part i ∈[(i-1)ω 0 ,iω 0 ]Is complex of s i ＝σ i +j·ω i (i=1, 2,3, …, N) as the initial solution for newton's iteration, where ω 0 For angular frequency sampling interval, j is an imaginary unit;
each primary solution s i Substituting into the set objective function, applying Newton-Lapherson method to carry out iterative solution, and continuously updating s i Until a satisfactory objective function accuracy is obtained;
m solutions calculated by the Newton-Lapherson method are formed into a solution set, the solutions are arranged according to the magnitude of the imaginary part of the solutions from small to large, and the first N solutions which are different from each other are screened out to be used as the first N-order vibration modes of the system; the real part of each vibration mode is the attenuation coefficient of the order oscillation, and the imaginary part is the angular frequency of the order oscillation.
The equivalent circuit mode based on the complex frequency domainAccording to the known reservoir boundary conditions, if the upper reservoir boundary conditions are known, the hydraulic impedance of the upper reservoir corresponding to the complex frequency s is deduced from the lower reservoir along the flow channelConversely, if the boundary condition of the lower reservoir is known, deriving the hydraulic impedance of the lower reservoir along the flow passage from the upper reservoir>Wherein (1)>For the calculated complex frequency domain expression of the hydraulic impedance of the upstream boundary system,the hydraulic impedance complex frequency domain expression of the downstream water reservoir boundary system is calculated; and combining the known reservoir boundary condition with the calculated reservoir boundary hydraulic impedance complex frequency domain expression as an objective function.
A system, comprising
A first module: the method comprises the steps of setting up an equivalent circuit model of a long-distance water conveying pipeline and an equivalent circuit model of each hydraulic boundary in a runner according to the number of the water conveying pipeline and various hydraulic boundary elements contained in the equivalent circuit model of the power station runner;
a second module: and the system is configured to obtain and assign an equivalent hydraulic impedance complex frequency at the upstream or downstream boundary of the pumped storage power station according to an equivalent circuit model, and solve each order of vibration modes of free oscillation of the research system.
A medium storing a computer program capable of running the pumped storage power station hydraulic oscillation analysis method based on the complex frequency domain equivalent circuit model according to any one of claims 1 to 8.
Therefore, the invention has the following advantages: the hydraulic characteristics of the components such as the pipeline in the flow passage of the pumped storage power station, the pressure regulating chamber, the water pump turbine and the like are compared with those of the basic electric components such as resistance, inductance, capacitance and the like in the circuit. Therefore, the equivalent hydraulic impedance at any node of the integral flow channel of the pumped storage power station with the complex structure can be deduced through the series-parallel theory in the circuit theory, the calculated amount of the formula deduction is smaller than that of the traditional hydraulic impedance method, and the capability of processing complex pipeline structures such as bifurcation, loops and the like is strong.
Drawings
Fig. 1 is a schematic diagram of a hydraulic oscillation analysis flow of a pumped storage unit based on a complex frequency domain equivalent circuit model.
Fig. 2 is a multi-segment cascade equivalent circuit of a long-distance water pipe.
Fig. 3 is a schematic diagram of an impedance type surge chamber structure and its equivalent circuit.
Fig. 4 is an equivalent circuit at the junction of two sections of tubing.
Fig. 5 is a schematic illustration of a flow channel structure of a large pumped storage power station.
Fig. 6 is a circuit topology of the overall equivalent circuit of the pumped storage power station runner.
Fig. 7 shows the law of variation of the attenuation coefficient corresponding to the first five-order oscillation of the system.
Fig. 8 shows the angular frequency variation law corresponding to the first five-order oscillation of the system.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The invention discloses a hydraulic oscillation analysis method of a pumped storage unit based on a complex frequency domain equivalent circuit model, which is shown in figure 1 and comprises the following specific steps:
step 1: and primarily determining the number of water pipelines and various hydraulic boundary elements contained in the runner equivalent circuit model according to the runner structure of the pumped storage power station. In the example, the pipeline is divided into four sections, namely a diversion tunnel, a pressure steel pipe, a draft tube, an extension and tail water tunnel; the hydraulic boundary comprises: the device comprises an upper reservoir, an upper pressure regulating chamber, a water pump turbine, a lower pressure regulating chamber and a lower reservoir. In the embodiment, the structure of the power station runner is single-pipe single-machine arrangement, and pipeline confluence nodes are not involved, so that calculation of Rt is not involved.
Step 2: construction of equivalent circuit model of long-distance water delivery pipeline
Each water pipe in the system can be regarded as being formed by connecting a plurality of sections of pipe in series, and the hydraulic characteristic of the water pipe is reflected by a cascade centralized parameter equivalent circuit, as shown in fig. 2. For a section of length Deltax, its equivalent resistance R i ＝R ei Δx, equivalent inductance L i ＝L ei Δx and equivalent capacitance C i ＝C ei ·Δx。
Calculating a certain position x=x on the pipeline from different directions i Discrete hydraulic impedance atThe formulas of (a) are different, and the method of calculating from downstream to upstream is adopted in the embodiment, namely, calculating from right to left. Knowing x=x i+1 Hydraulic impedance at, then x=x i The hydraulic impedance at this point can be calculated by the following equation:
if the calculation is performed from upstream to downstream, i.e., from left to right. Then x=x is known i-1 Hydraulic impedance at, x=x i The hydraulic impedance at this point can be calculated by the following equation:
where s is the Laplacian,and->Respectively represent x=x i-1 、x＝x i And x=x i+1 Hydraulic impedance at; r is R i-1 、L i-1 And C i-1 Respectively represent x=x i-1 And x=x i Equivalent resistance of the pipeline between the twoAn effective inductance and an equivalent capacitance; r is R i 、L i And C i Respectively represent x=x i And x=x i+1 Equivalent resistance, equivalent inductance and equivalent capacitance of the pipeline.
Step 3: construction of equivalent circuit model of each hydraulic boundary in runner
(1) Hydraulic impedance model of water pump turbine
According to the full characteristic curve of the water pump turbine, the hydraulic impedance Z of the water pump turbine T Can be calculated by the following formula:
wherein,,represents a partial derivative operator; n and D 1 Respectively representing the rotating speed of the unit and the diameter of the rotating wheel; n is n 11 And Q 11 Respectively representing unit rotating speed and unit flow of the unit.
(2) Equivalent circuit model of upstream and downstream surge chamber
In this example, the upstream and downstream voltage regulating chambers of the power station all adopt impedance type voltage regulating chamber structures, and the equivalent circuit schematic diagram is shown in fig. 3, and can be regarded as a two-port circuit comprising series resistors and capacitors.
(3) Hydraulic impedance at pipeline joint
The hydraulic loss at the connection of the two sections of pipelines can be equivalent by a variable resistor, and the equivalent circuit diagram is shown in fig. 4. The equivalent resistance parameter is related to the flow and the pipeline sectional area, and the calculation formula is as follows:
wherein g is gravity acceleration, Q L For the pipeline flow on the left side of the node, A L And A R Representing the area of the left and right side ducts of the node, respectively.
Step 4: solving upstream or downstream of pumped storage power stationThe hydraulic impedance complex frequency expression at the downstream boundary. According to the flow channel structure of the pumped storage power station, connecting the equivalent circuits corresponding to the boundary nodes between each water pipe and the pipeline, and calculating the system hydraulic impedance at the upstream boundary of the power station by the circuit series connection and parallel connection principle in the circuit theoryOr the hydraulic impedance of the system at the boundary of the downstream water reservoir +.>
Step 5: and solving each order of vibration modes of free oscillation of the research system.
The invention uses a large pumped-storage power station as a research object of an implementation case, as shown in fig. 5.
In free-running analysis, the boundary conditions at both the upstream and downstream reservoirs were 0, were symmetrical, and were calculated from either direction, with the same result.
When free oscillation analysis is carried out, the actual hydraulic impedance at the upper and downstream boundaries of the pumped storage power station is zero, namely Z u ＝Z d =0, the pump turbine is in steady operation with fully opened guide vanes, i.e. Z T =0. The equivalent circuit topology of the whole pumped storage power station runner is shown in fig. 6. According to the theory of series and parallel circuits, the hydraulic impedance of the upstream boundary system can be calculated through the steps 2,3 and 4And substituted into the equation: />Further, complex frequencies s satisfying the boundary condition equation are obtained according to the Newton-Laportson method i (i=1, 2,3, …). The specific solving steps of each-order vibration modes of free oscillation of the research system are as follows:
step 5-1: determining the number M of primary solutions, and determining the upper limit N of the hydraulic oscillation order to be calculated;
step 5-2: according to the known boundary conditions of the reservoirIs defined as an objective function. Wherein (1)>Calculating the hydraulic impedance of the upstream boundary system;
step 5-3: randomly generating M real part value ranges sigma i ∈[-1,0]Range of values ω for the imaginary part i ∈[(i-1)ω 0 ,iω 0 ]Is complex of s i ＝σ i +j·ω i (i=1, 2,3, …, N) as the initial solution for newton's iteration, where ω 0 For angular frequency sampling interval, j is an imaginary unit;
step 5-4: each primary solution s i Substituting the obtained product into the objective function set in the step 2, and applying Newton-Laportson method to carry out iterative solution to continuously update s i Until a satisfactory objective function accuracy is obtained;
step 5-5: m solutions calculated by the Newton-Lapherson method are formed into a solution set, the solutions are arranged according to the magnitude of the imaginary part of the solutions from small to large, and the first N solutions which are different from each other are screened out to be used as the first N-order vibration modes of the system. The real part of each vibration mode is the attenuation coefficient of the vibration of the order, and the imaginary part is the angular frequency of the vibration of the order.
And selecting an analysis result of the traditional continuous hydraulic impedance model on the oscillation characteristics of the power station as a control group, and verifying the validity of the oscillation analysis method.
The free oscillation analysis of the pumped storage power station is carried out through a traditional continuous hydraulic impedance model and a discrete circuit equivalent model introduced by the invention, and the topology of the whole equivalent circuit of the system can be obtained according to the actual structure of the flow channel of the pumped storage power station as shown in figure 6. The results of the first ten-order oscillation modes (i.e. the attenuation coefficient and the characteristic frequency of the oscillation) of the system calculated by the two methods are shown in table 1. Further, the running states of different water pumps and turbines (namely the impedance Z of the water pump and turbine) are analyzed through numerical simulation T Different values) to take onThe damping coefficient and the oscillation frequency change rule corresponding to the first five-order oscillation of the system are shown in fig. 7 and 8 respectively. As can be seen from fig. 7 and 8: the damping coefficient of each order of oscillation follows substantially the Z-dependence T The increasing and gradually decreasing change rule shows that the larger impedance of the water pump turbine can improve the stability of the system; the oscillation frequency of each-order oscillation is insensitive to the change of the impedance of the water pump turbine, and the oscillation frequency is Z T The variation remains substantially unchanged.
TABLE 1 comparison of the results of the former ten-order oscillation modes of the system obtained by calculation of the two models
Through the cases, the equivalent model of the pumped storage power station complex frequency domain circuit built by the invention can effectively analyze the characteristics of free oscillation of each stage of the system, and compared with the traditional continuous hydraulic impedance analysis method, the calculation error is smaller, and the precision can reach the allowable range of engineering application.
The foregoing is merely illustrative of the preferred embodiments of the present invention and is not intended to limit the embodiments and scope of the present invention, and it should be appreciated by those skilled in the art that equivalent substitutions and obvious variations may be made using the teachings of the present invention, which are intended to be included within the scope of the present invention.
Claims (10)
1. A pumped storage power station hydraulic oscillation analysis method based on a complex frequency domain equivalent circuit model is characterized by comprising the following steps of:
establishing an equivalent circuit model of the long-distance water conveying pipeline and an equivalent circuit model of each hydraulic boundary in the runner according to the number of the water conveying pipelines and various hydraulic boundary elements contained in the equivalent circuit model of the power station runner;
and obtaining the equivalent hydraulic impedance complex frequency at the upstream or downstream boundary of the pumped storage power station according to the equivalent circuit model, assigning a value to the equivalent hydraulic impedance complex frequency, and solving each order of vibration modes of free oscillation of the research system.
2. The method for analyzing the hydraulic oscillation of the pumped storage power station based on the complex frequency domain equivalent circuit model according to claim 1, which is characterized in that the number of water pipelines and various hydraulic boundary elements contained in the runner equivalent circuit model is determined according to the runner structure of the pumped storage power station, wherein the pipelines are divided into four sections, namely a diversion tunnel, a pressure steel pipe, a draft tube, an extension and a tail water tunnel; the hydraulic boundary comprises: the device comprises an upper reservoir, an upper pressure regulating chamber, a water pump turbine, a lower pressure regulating chamber and a lower reservoir.
3. The method for analyzing the hydraulic oscillation of the pumped storage power station based on the complex frequency domain equivalent circuit model according to claim 1, wherein the water flow characteristics of the water delivery pipeline are described by a san-View equation group subjected to linearization treatment; the long-distance water pipe is defined as formed by connecting multiple sections of pipe in series, and for a section of pipe with length delta x, the equivalent resistance R of the pipe is i ＝R ei Δx, equivalent inductance L i ＝L ei Δx and equivalent capacitance C i ＝C ei Δx; wherein R is ei ，L ei ，C ei The equivalent resistance, the equivalent inductance and the equivalent capacitance are respectively corresponding to the pipeline with unit length.
4. The method for analyzing hydraulic oscillation of pumped storage power station based on complex frequency domain equivalent circuit model as claimed in claim 1, wherein a certain position x=x on a water transmission pipeline i Equivalent hydraulic impedance Z at equi Based on the following formula:
if x=x is known i+1 Hydraulic impedance at the point
If x=x is known i-1 Hydraulic impedance at the point
s is the laplace operator and,and->Respectively represent x=x i-1 、x＝x i And x=x i+1 Hydraulic impedance at; r is R i-1 、L i-1 And C i-1 Respectively represent x=x i-1 And x=x i Equivalent resistance, equivalent inductance and equivalent capacitance of the pipeline; r is R i 、L i And C i Respectively represent x=x i And x=x i+1 Equivalent resistance, equivalent inductance and equivalent capacitance of the pipeline.
5. The method for analyzing hydraulic oscillation of pumped storage power station based on complex frequency domain equivalent circuit model as defined in claim 1, wherein hydraulic loss at the joint of two sections of pipelines is defined by a variable parameter resistor R s Equivalent resistance value is related to flow passing through the node and pipeline sectional area, and the calculation formula is as follows:
wherein g is gravity acceleration, Q L For the pipeline flow on the left side of the node, A L And A R Representing the area of the left and right side ducts of the node, respectively.
6. The pumped storage power station hydraulic oscillation analysis method based on the complex frequency domain equivalent circuit model as claimed in claim 1, wherein the method is characterized in thatThe hydraulic loss at the pipeline confluence node can be equivalent to three variable parameter resistors R which are connected in star mode on the respective branches T1 、R T2 And R is T3 The value of each equivalent resistance parameter is related to the flow of each branch and the sectional area of the pipeline, and the calculation formula is as follows:
wherein Q is b1 、Q b2 And Q m The flow rates of the branch pipe 1, the branch pipe 2 and the confluence main pipe are respectively shown; a is that b1 、A b2 And A m The cross-sectional areas of the branch pipe 1, the branch pipe 2, and the confluence main pipe are shown, respectively.
7. The method for analyzing the hydraulic oscillation of the pumped storage power station based on the complex frequency domain equivalent circuit model according to claim 1, wherein the specific solving of each order of vibration modes comprises the following specific steps of
Determining the number M of primary solutions, and determining the upper limit N of the hydraulic oscillation order to be calculated;
combining the known reservoir boundary condition with the calculated reservoir boundary hydraulic impedance complex frequency domain expression as an objective function;
randomly generating M real part value ranges sigma i ∈[-1,0]Range of values ω for the imaginary part i ∈[(i-1)ω 0 ,iω 0 ]Is complex of s i ＝σ i +j·ω i (i=1, 2,3, …, N) as the initial solution for newton's iteration, where ω 0 For angular frequency sampling interval, j is an imaginary unit;
each primary solution s i Substituting into the set objective function, applying Newton-Lapherson method to carry out iterative solution, and continuously updating s i Until a satisfactory objective function accuracy is obtained;
m solutions calculated by the Newton-Lapherson method are formed into a solution set, the solutions are arranged according to the magnitude of the imaginary part of the solutions from small to large, and the first N solutions which are different from each other are screened out to be used as the first N-order vibration modes of the system; the real part of each vibration mode is the attenuation coefficient of the order oscillation, and the imaginary part is the angular frequency of the order oscillation.
8. The method for analyzing hydraulic oscillation of pumped storage power station based on complex frequency domain equivalent circuit model as set forth in claim 1, wherein the hydraulic impedance of the upper reservoir corresponding to complex frequency s is derived from the lower reservoir along the flow path if the upper reservoir boundary condition is known according to the known reservoir boundary conditionConversely, if the boundary condition of the lower reservoir is known, deriving the hydraulic impedance of the lower reservoir along the flow passage from the upper reservoir>Wherein (1)>For the calculated complex frequency domain expression of the hydraulic impedance of the upstream boundary system, < >>The hydraulic impedance complex frequency domain expression of the downstream water reservoir boundary system is calculated; and combining the known reservoir boundary condition with the calculated reservoir boundary hydraulic impedance complex frequency domain expression as an objective function.
9. A system, comprising
A first module: the method comprises the steps of setting up an equivalent circuit model of a long-distance water conveying pipeline and an equivalent circuit model of each hydraulic boundary in a runner according to the number of the water conveying pipeline and various hydraulic boundary elements contained in the equivalent circuit model of the power station runner;
a second module: and the system is configured to obtain and assign an equivalent hydraulic impedance complex frequency at the upstream or downstream boundary of the pumped storage power station according to an equivalent circuit model, and solve each order of vibration modes of free oscillation of the research system.
10. A medium, characterized in that a computer program is stored, said computer program being capable of running the method for analyzing hydraulic oscillations of a pumped storage power station based on a complex frequency domain equivalent circuit model according to any one of claims 1 to 8.
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| CN117572088A (en) * | 2023-10-30 | 2024-02-20 | 北京天兵科技有限公司 | Method, device, medium and equipment for calculating natural frequency of liquid oxygen delivery system |
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| CN105956350A (en) * | 2016-07-05 | 2016-09-21 | 华中科技大学 | Modeling method for water exchange system of pump storage group |
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| YANG ZHENG: "Discrete impedance method for the oscillation analysis of pumped-storage power plants", 《ENERGY REPORTS》, 27 February 2023 (2023-02-27), pages 3563 - 3575 * |
| YANG ZHENG: "Equivalent circuit modelling of large hydropower plants with complex tailrace system for ultra-low frequency oscillation analysis", 《APPLIED MATHEMATICAL MODELLING》, 20 October 2021 (2021-10-20), pages 176 - 194 * |
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| CN117572088A (en) * | 2023-10-30 | 2024-02-20 | 北京天兵科技有限公司 | Method, device, medium and equipment for calculating natural frequency of liquid oxygen delivery system |
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