Multi-specialty coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica

Abstract

The invention belongs to the technical field of equipment simulation, and particularly relates to a multi-specialty coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica. Comprising the following steps that a supercritical carbon dioxide electromagnetic bearing compressor system is decomposed into a frequency converter, a motor, a shaft system and an impeller, and the relation between equipment is expressed in a structural diagram mode; modeling a frequency converter, a motor, a shaft system and an impeller; and defining data transmission among the component equipment through an input / output interface to form a signal closed loop of the whole system of the compressor so as to complete compressor system model integration. The method has the advantages that only specific physical phenomenon equations of the model need to be given, specific solving principles and solving steps do not need to be given, and when the model is solved, a software platform where the model is located can automatically compile and solve the model equations; the compressor system is subjected to multi-specialty modeling and solving under a unified framework, and the multi-specialty coupling simulation efficiency can be greatly improved.

Description

Technical Field

[0001] The invention belongs to the technical field of equipment simulation, and in particular relates to a multi-professional coupling modeling method of a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica. Background Art

[0002] The supercritical carbon dioxide electromagnetic bearing compressor system is the core equipment of the supercritical carbon dioxide Brayton cycle power generation system. Traditional system simulation and equipment simulation, system thermal hydraulic characteristics and equipment flow characteristics are all single-discipline simulations. Equipment-related control, electrical, electromagnetic, mechanical and other disciplines are also single-discipline simulations using different software. The coupling between different disciplines is generally based on loose coupling of software interfaces. Not only the problem of interface data transmission format must be solved, but also the problem of time synchronization must be considered. The simulation efficiency is low and easy to diverge. Digital twin technology modeling requires that the system and equipment simulation models can reflect the tight coupling characteristics between different disciplines. It is necessary to model and solve the multidisciplinary physical process of the simulation object under a unified framework and unified language specification. The present invention proposes a multi-discipline coupling modeling method for the electromagnetic bearing compressor system, which can simultaneously solve the controller equation and coordinate transformation equation of the inverter, the flow characteristic equation of the compressor, the voltage equation, magnetic flux equation, torque equation, motion equation of the motor, the displacement equation of the rotor, and the displacement control equation of the magnetic bearing, and simultaneously obtain the multi-discipline behavior characteristics of the compressor system, such as electrical, electromagnetic, pneumatic, control, and mechanical. Summary of the invention

[0003] The purpose of the present invention is to provide a multi-discipline coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica, which transforms the multi-discipline coupling mode based on a software interface into a modeling and solving method under a unified framework and unified language specification, thereby improving the multi-discipline coupling efficiency.

[0004] The technical solution of the present invention is as follows: a multi-disciplinary coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica, comprising the following steps:

[0005] S1: Decompose the supercritical carbon dioxide electromagnetic bearing compressor system into the inverter, motor, shaft system and impeller, and express the relationship between the equipment in the form of a structural diagram;

[0006] S2: Model the inverter based on Modelica language;

[0007] S3: Model the motor based on Modelica language;

[0008] S4: Model the axis system based on Modelica language;

[0009] S5: Model the impeller based on Modelica language;

[0010] S6: Based on the Modelica language, the data transmission between the components is defined through the input and output interfaces to form a signal closed loop of the entire compressor system and complete the compressor system model integration.

[0011] The frequency converter in S2 drives the motor by adjusting the frequency and voltage of the power supply, and includes a controller and an inverter, wherein the controller controls the motor speed and the inverter converts direct current into alternating current for output;

[0012] The inverter model is divided into three parts: speed regulator, current regulator and coordinate transformation module. The speed regulator and current regulator are PI controllers, and the coordinate transformation module includes Clark transformation, Park transformation, Clark inverse transformation and Park inverse transformation.

[0013] The Clark transformation is a module that completes the transformation from the three-phase stationary coordinate system abc to the two-phase stationary coordinate system αβ. The transformation formula is:

[0014]

[0015] The Park transformation is to transform the voltage or current value in the two-phase stationary coordinate system into the voltage or current value in the corresponding two-phase rotating coordinate system. The transformation formula is:

[0016]

[0017] The effect of the Clark inverse transform is opposite to that of the Clark transform, and the transform formula is:

[0018]

[0019] The effect of the Park inverse transform is opposite to that of the Park inverse transform, and its transformation formula is:

[0020]

[0021] In the above formula, u represents a parameter, such as voltage or current; in the following table, a, b, c represent the projection values ​​of the three coordinate axes a, b, c in the three-phase stationary coordinate system, the subscripts α and β represent the projection values ​​of the two coordinate axes α and β in the two-phase stationary coordinate system, and the subscripts d and q represent the projection values ​​of the two coordinate axes d and q in the two-phase rotating coordinate system.

[0022] The inverter is used to convert direct current into alternating current output. The alternating voltage converted by the three-phase inverter is three-phase, i.e., AC380V. The inverter is a device that amplifies the voltage, current, and power of the control signal of the IGBT switch device. The three-phase full-bridge inverter is composed of three bridge arms and six power transistors. The output of the inverter is located at the neutral point of the three groups of switches, and the voltage difference between the two gets the three electric currents required for the three-phase electricity. The three-phase bridge inverter controls the on and off sequence of the three groups of power transistors, and outputs three-phase electrical signals with equal amplitude and frequency.

[0023] The S3 includes a motor that converts electrical power into driving torque and is the power source of the compressor. The model of the motor includes a voltage equation, a magnetic flux equation, a torque equation and a motion equation.

[0024] The equation for the motor is as follows:

[0025] Voltage equation:

[0026] u sd =R s i sd +n p pψ sd -ωψ sq

[0027] u sq =R s i sq +n p ψ sq -ωψ sd

[0028] Magnetic flux equation:

[0029] ψ sa =L sa i sd +ψ f ψ sq =L sq +i sq

[0030] Torque equation:

[0031] T=n p *[L sd *i sq *i f -(L sd -L sq )*i sd *i sq ]

[0032] Equations of motion:

[0033]

[0034] In the formula, subscript s represents the stator, f represents the permanent magnet, subscript d represents the d-axis, and subscript q represents the q-axis. u represents voltage, V; R represents resistance, Ω; i represents current, A; ψ represents magnetic flux, Wb; ω represents angular velocity, rad / s; L represents inductance, H; T represents torque, Nm, T e Represents electromagnetic torque, T L Represents load torque; n p represents the number of magnetic pole pairs; J represents the moment of inertia, kg·m 2 .

[0035] The electromagnetic rotating shaft of the S4 compressor is composed of a magnetic floating rotor, a radial electromagnetic bearing and an axial electromagnetic bearing.

[0036] The magnetic levitation rotor uses the rotor dynamics equation to describe the speed change caused by the energy change of the magnetic levitation rotor.

[0037] The rotor dynamics equation is:

[0038]

[0039] Relationship between rotor power and speed:

[0040]

[0041] Where: m is the rotor mass, x c ,y c 、z c are the displacements of the rotor mass center in the X, Y, and Z directions, respectively, and f xa is the electromagnetic force of the radial bearing in the X direction, f xb b is the electromagnetic force of the radial bearing in the X direction, f ya is the electromagnetic force of the radial bearing in the Y direction, f yb b is the electromagnetic force of the radial bearing in the Y direction, f z is the electromagnetic force of the axial bearing in the Z direction, J d is the rotor diameter moment of inertia, J p is the rotor pole moment of inertia, ω is the rotor speed, θ x is the angular displacement of the rotor in the YoZ plane, θ y is the angular displacement of the rotor in the XoZ plane, l a and l b are the distances from a radial bearing and b radial bearing to the rotor mass center respectively;

[0042] The following relationship between rotor angular displacement and bearing displacement is obtained:

[0043]

[0044] In the formula, ya is the position of bearing a in the Y direction, y b is the position of bearing b in the Y direction, x a is the position of bearing a in the X direction, x b is the position of bearing b in the X direction;

[0045] Get the center of mass displacement (x c ,y c , z c ) and bearing displacement (x a ,y a , x b ,y b , z):

[0046]

[0047] Right now

[0048]

[0049] The angular velocity of the rotor is related to the rotational speed, namely:

[0050] ω=2πN

[0051] N is the rotor speed, rpm.

[0052] The radial magnetic bearing uses electromagnetic force to suspend the magnetic levitation rotor in space without mechanical friction and lubrication. The position sensor detects the shaft deviation signal of the rotor, transmits the signal to the controller, and controls the current in the electromagnet through the power amplifier, thereby generating a change in electromagnetic force to suspend the rotor at a specified position. The radial electromagnetic bearing consists of a radial magnetic bearing and a bearing control system. Given the control current, rotor offset air gap and electromagnetic coil structure parameters, the electromagnetic force of the radial bearing is calculated as:

[0053] Electromagnetic force calculation formula

[0054]

[0055] Where: μ0 is the vacuum magnetic permeability, A0 is the cross-sectional area of ​​the magnetic pole, N is the number of turns of the bearing electromagnetic coil, I is the current passing through the stator core, x is the air gap of the rotor,

[0056] For radial bearings, the magnetic levitation force in the X direction is

[0057]

[0058] In the formula, fx+ and fx- represent two opposite forces in the x direction, N; I0 represents the initial current in the coil, i.e. the bias current, A; Δi represents the change in current, i.e. the control current, A. This change can be positive or negative, depending on whether the current increases or decreases; x0 represents the initial x-coordinate position, m, which is the reference position of the object in the x direction. x represents the change in the position of the object in the x direction, m.

[0059] f x The linearization process is carried out using Taylor expansion at the equilibrium position to obtain

[0060]

[0061] Where: x0 is the air gap in the x direction when the rotor has no displacement deviation, x is the displacement of the rotor in the x direction, k i is the current coefficient, k x is the displacement coefficient, Δi x Represents the change in current in the x direction, A.

[0062] The suspension force of the radial bearing in the Y direction is

[0063]

[0064] Where: y0 is the air gap in the Y direction when the rotor has no displacement deviation, y is the displacement of the rotor in the Y direction, k i is the current coefficient, k y is the displacement coefficient, Δi y Represents the change in current in the y direction, A.

[0065] The axial magnetic bearing uses electromagnetic force to suspend the magnetic levitation rotor in space without mechanical friction and lubrication. The position sensor detects the shaft deviation signal of the rotor, transmits the signal to the controller, and controls the current in the electromagnet through the power amplifier, thereby generating a change in electromagnetic force to suspend the rotor at a specified position. The axial electromagnetic bearing consists of an axial magnetic bearing and a bearing control system. Given the control current, rotor offset air gap and electromagnetic coil structure parameters, the axial bearing electromagnetic force is calculated as follows:

[0066] The suspension force of the thrust bearing in the Z direction is obtained by linearization using Taylor expansion:

[0067]

[0068] Where z0 is the air gap in the Z direction when the rotor has no displacement deviation, z is the displacement of the rotor in the Z direction; k iis the current coefficient, k z is the displacement coefficient, Δi z Represents the change in current in the z direction, A.

[0069] The bearing control system electromagnetic bearing control system loop includes a rotor, a sensor, a controller and a power amplifier.

[0070] The sensor is a displacement sensor, which simulates the acquisition of displacement or position signals. The signals collected by the sensor are converted into data and then transmitted to other components through the output interface. The sensor collects the system or device status signals and transmits them to the sensor model through the defined interface.

[0071] Displacement sensor mechanism: s=f(s).

[0072] Where s represents displacement, m represents displacement, and f is a function that represents the mechanism by which the displacement sensor converts input signals into output signals.

[0073] The controller is a PID controller, which is converted into a PI controller and a PD controller. The input-output relationship of the PID is:

[0074] u=u p +u i +u d

[0075] Where u represents the output of the PID controller, and its unit depends on the type of control system; p Represents the output of the proportional control part, which is the ratio of the error signal (the difference between the set value and the actual value) and has the same unit as u; i It represents the output of the integral control part. It is the result of integrating the error signal over time. The integral action can eliminate the steady-state error. The unit is the same as u. d It represents the output of the differential control part. It is the ratio of the rate of change of the error signal. The differential action can predict the future trend of the error and make adjustments in advance. The unit is the same as u.

[0076] make Then the expression can be expressed as:

[0077]

[0078] Where u(t) is the controller output; e(t) is the input deviation; T i is the integration constant; T d is the differential time constant. K p Represents the proportional gain, which is a dimensionless coefficient used to adjust the system's response strength to errors.i Represents the integral gain, which is a dimensionless coefficient used to adjust the impact of the integral term on the controller output. d Represents the differential gain, which is a dimensionless coefficient used to adjust the effect of the differential term on the controller output

[0079] The transfer function of PID control is:

[0080]

[0081] In the formula, G(s) represents the transfer function of the system, which is the ratio of the output U(s) to the input E(s) in the Laplace transform domain. U(s) represents the output of the system, which is the Laplace transform of a certain variable in the control system. E(s) represents the input of the system, which is the Laplace transform of a certain reference signal or set value.

[0082] The power amplifier is equivalent to a gain coefficient, and the gain coefficient value is corrected by test data. The input is the controller output signal, and the output includes the magnetic bearing control current value.

[0083] In the above S5, the impeller speed ratio and flow ratio are known, and the compressor pressure ratio and efficiency are obtained by two-dimensional interpolation of the compressor characteristic curve. The working fluid outlet thermal parameters and the actual compressor power are obtained through the pressure ratio and isentropic adiabatic process.

[0084] The calculation process is as follows:

[0085] 1) According to the speed in the rotor characteristic data, the corresponding inputs at each speed are sorted in the order of flow rate, pressure ratio, and efficiency, and input into the model;

[0086] 2) According to the input speed N, the adjacent speed characteristic data is selected from the rotor characteristic data through an algorithm, and the flow rate, pressure ratio, and efficiency data at the current speed N are interpolated using a linear interpolation algorithm to obtain a two-dimensional array, where the first column is the flow rate, the second column is the pressure ratio, and the third column is the efficiency;

[0087] 3) According to the input flow value Wcor, substitute it into the flow, pressure ratio, and efficiency table, perform linear interpolation, and obtain the corresponding pressure ratio and efficiency;

[0088] The relationship between the converted flow rate and the actual flow rate at the inlet is:

[0089]

[0090] The speed ratio is

[0091]

[0092] The outlet pressure is

[0093] pout =p in ·π

[0094] Among them, W cor is the flow ratio, W C is the current flow rate, W C，d is the design flow rate, N cor_C is the speed ratio, N is the current speed, N d is the design speed, p in is the compressor inlet pressure, p out is the compressor outlet pressure, and π is the compressor pressure ratio.

[0095] The S6 includes the following:

[0096] 1) The input of the PID controller is the reference position and measured position data of the magnetic levitation rotor, and the PID outputs control signals to the power amplifier, including proportional, integral and differential control signals of increase or decrease;

[0097] 2) The power amplifier input is the PID controller output signal, and the output is the control current value of the magnetic bearing;

[0098] 3) The input of the magnetically levitated rotor is the control current signal output by the power amplifier, and the output is the force, displacement and angle data of the rotor;

[0099] 4) The rotor and impeller transmit the rotor speed, angle and torque data between the rotor and the motor;

[0100] 5) What is transmitted between the motor and the inverter is the speed.

[0101] The beneficial effects of the present invention are as follows: the present invention is based on the Modelica language, and only needs to provide the specific physical phenomenon equations of the model, without providing specific solution principles and solution steps. When the model is solved, the software platform where the model is located will automatically compile and solve the model equations; multi-professional modeling and solving of the compressor system under a unified framework can greatly improve the efficiency of multi-professional coupling simulation and provide a feasible path for the implementation of digital twin technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 It is the structural diagram of the multi-disciplinary model of the compressor unit;

[0104] Figure 2 Interpolation process for impeller characteristics;

[0105] Figure 3 This is the rotor force analysis diagram;

[0106] Figure 4 This is the circuit schematic diagram of the electromagnetic bearing control system;

[0107] Figure 5 This is the principle block diagram of the frequency converter controlling the speed;

[0108] Figure 6 It is a three-phase full-bridge inverter circuit for the frequency converter;

[0109] Figure 7 Integrate schematics for multi-discipline simulation models of compressor systems. DETAILED DESCRIPTION

[0110] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, the basic implementation principle of the present invention is described below in conjunction with the accompanying drawings. The specific implementation principle described herein is only used to explain the present invention and is not intended to limit the present invention. In the following description, many specific details are set forth in order to fully understand the present invention, but the present invention can also be implemented in other ways different from those within the scope of this description, and therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below. Based on the implementation principle of the present invention, all other implementation cases obtained by those skilled in the art without making creative work belong to the scope of protection of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments, as well as the steps in all disclosed methods or processes, except for mutually exclusive features or steps, can be combined, expanded and replaced in any way.

[0111] A multi-disciplinary coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica includes the following steps:

[0112] S1: Decompose the supercritical carbon dioxide electromagnetic bearing compressor system and represent the relationship between the equipment in the form of a structure diagram.

[0113] Specifically, the compressor system is decomposed into the inverter, motor, shaft system and impeller.

[0114] S2: Model the inverter of the compressor system based on the Modelica language.

[0115] The frequency converter drives the motor by adjusting the frequency and voltage of the power supply. It consists of a controller and an inverter. The controller controls the motor speed, and the inverter converts DC power into AC power output.

[0116] The inverter model is divided into three parts: speed regulator, current regulator and coordinate transformation module. Among them, the speed regulator and current regulator are conventional PI controllers, and the coordinate transformation module includes Clark transformation, Park transformation, Clark inverse transformation and Park inverse transformation.

[0117] Clark transformation is a module that completes the transformation from the three-phase stationary coordinate system abc to the two-phase stationary coordinate system αβ.

[0118] S3: Model the motor based on Modelica language.

[0119] The main function of the motor is to convert electrical power into driving torque, and it is the power source of the compressor. The motor body model uses the two-phase motion coordinate system DQ coordinate system as a reference. The mathematical model of the motor includes voltage equation, flux equation, torque equation and motion equation.

[0120] S4: Model the axis system based on Modelica language.

[0121] The electromagnetic shaft system of the compressor is composed of a magnetically floating rotor, a radial electromagnetic bearing and an axial electromagnetic bearing. During the rotation of the compressor rotor, the rotor dynamics equation is used to describe the speed change caused by the change in rotor energy. If the electromagnetic force is known, the displacement of the magnetically floating rotor can be calculated by the dynamics equation; if the power at both ends of the rotor is known, the speed of the rotor can be calculated by the relationship between power and speed.

[0122] The radial magnetic bearing uses electromagnetic force to suspend the magnetic rotor in space without mechanical friction and lubrication. The rotor shaft deviation signal is detected by the position sensor, and the signal is transmitted to the controller. The current in the electromagnet is controlled by the power amplifier, thereby generating changes in electromagnetic force to suspend the rotor at a specified position. The radial electromagnetic bearing consists of a radial magnetic bearing and a bearing control system. The radial magnetic bearing mainly balances the radial force of the rotor, which mainly reflects the relationship between the radial electromagnetic force and the bearing displacement and the change of the control current. The bearing control system loop consists of a rotor, a sensor, a controller and a power amplifier.

[0123] The axial magnetic bearing uses electromagnetic force to suspend the magnetic rotor in space without mechanical friction and lubrication. The rotor shaft deviation signal is detected by the position sensor, and the signal is transmitted to the controller. The current in the electromagnet is controlled by the power amplifier, thereby generating changes in electromagnetic force to suspend the rotor at a specified position. The axial electromagnetic bearing consists of an axial magnetic bearing and a bearing control system. The axial magnetic bearing mainly balances the force acting on the rotor in the axial direction, which mainly reflects the relationship between the axial electromagnetic force and the bearing displacement and the change in the control current. The electromagnetic bearing control system loop consists of a rotor, a sensor, a controller and a power amplifier.

[0124] S5: Model the impeller based on Modelica language.

[0125] Given the impeller speed ratio (actual operating speed / rated design speed) and flow ratio (actual working fluid flow / rated design flow), the compressor pressure ratio and efficiency are obtained through two-dimensional interpolation of the compressor characteristic curve. The working fluid outlet thermodynamic parameters and the actual compressor power are obtained through the pressure ratio and isentropic adiabatic process.

[0126] S6: Based on the Modelica language and according to the compressor system principle, the data transmission between the components is defined through the input and output interfaces to form a signal closed loop of the entire compressor system and complete the compressor system model integration.

[0127] Example:

[0128] The multi-disciplinary coupling modeling method of the supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica in this embodiment includes the following steps:

[0129] S1: Decompose the supercritical carbon dioxide electromagnetic bearing compressor system and represent the relationship between the equipment in the form of a structure diagram.

[0130] like Figure 1 As shown in the figure, the compressor system consists of a frequency converter, a motor, a shaft system and an impeller. The frequency converter provides the motor speed adjustment, and the motor converts the electric power into the shaft torque, which is transmitted through the shaft system to drive the impeller to do work and realize the compression and pressure increase of the working fluid.

[0131] S2: Based on the Modelica language, the inverter of the compressor system is modeled. The inverter drives the motor by adjusting the frequency and voltage of the power supply. It consists of a controller and an inverter. The controller controls the motor speed, and the inverter converts DC power into AC power output. Figure 5 The following is the inverter control logic diagram.

[0132] The inverter model is mainly divided into three parts: speed regulator, current regulator and coordinate transformation module. Among them, the speed regulator and current regulator are conventional PI controllers, and there are four coordinate transformations involved: Clark transformation, Park transformation, Clark inverse transformation and Park inverse transformation. Clark transformation is a transformation module that completes the transformation from the three-phase stationary coordinate system abc to the two-phase stationary coordinate system αβ.

[0133] Clark transformation is a module that completes the transformation from the three-phase stationary coordinate system abc to the two-phase stationary coordinate system αβ. The transformation formula is:

[0134]

[0135] Park transformation is to transform the voltage or current value in the two-phase stationary coordinate system into the voltage or current value in the corresponding two-phase rotating coordinate system. The transformation formula is:

[0136]

[0137] The effect of Clark inverse transform is opposite to Clark transform. Its transformation formula is:

[0138]

[0139] The function of Park's inverse transform is opposite to that of Park's inverse transform. Its transformation formula is:

[0140]

[0141] In the above formula, u represents a parameter, such as voltage or current; in the following table, a, b, c represent the projection values ​​of the three coordinate axes a, b, c in the three-phase stationary coordinate system, the subscripts α and β represent the projection values ​​of the two coordinate axes α and β in the two-phase stationary coordinate system, and the subscripts d and q represent the projection values ​​of the two coordinate axes d and q in the two-phase rotating coordinate system.

[0142] The function of the inverter is to convert direct current into alternating current output. The AC voltage converted by the three-phase inverter is three-phase, that is, AC380V. The inverter is a device that amplifies the control signals of switching devices such as IGBT into voltage, current and power. The circuit structure of the three-phase full-bridge inverter circuit is as follows Figure 6 As shown. The three-phase full-bridge inverter consists of three bridge arms and six power transistors. The output of the inverter is located at the neutral points of the three sets of switches. The voltage difference between the two sets can obtain the three voltages required for the three-phase electricity. By controlling the on and off sequence of the three sets of power transistors, the three-phase bridge inverter can output three-phase electrical signals with equal amplitude and frequency.

[0143] S3: Based on the Modelica language, the motor of the compressor system is modeled. The main function of the motor is to convert electrical power into driving torque, and it is the power source of the compressor. When modeling the motor body, the two-phase motion coordinate system DQ coordinate system is used as a reference. The mathematical model of the motor includes voltage equations, flux equations, torque equations and motion equations.

[0144] The equation for a permanent magnet synchronous motor is as follows:

[0145] Voltage equation:

[0146] u sd =R s i sd +n p pψ sd -ωψ sq

[0147] u sq =R s i s q+n pψ s q-ωψ sd

[0148] Magnetic flux equation:

[0149] ψ sa =L sa i sd +ψ f ψ sq =L sq +i sq

[0150] Torque equation:

[0151] T=n p *[L sd *i sq *i f -(L sd -L sq )*i sd *i sq ]

[0152] Equations of motion:

[0153]

[0154] In the formula, subscript s represents the stator, f represents the permanent magnet, subscript d represents the d-axis, and subscript q represents the q-axis. u represents voltage, V; R represents resistance, Ω; i represents current, A; ψ represents magnetic flux, Wb; ω represents angular velocity, rad / s; L represents inductance, H; T represents torque, Nm, T e Represents electromagnetic torque, T L Represents load torque; n p represents the number of magnetic pole pairs; J represents the moment of inertia, kg·m 2 .

[0155] S4: Based on the Modelica language, the shaft system of the compressor system is modeled. Taking the electromagnetic shaft as an example, the electromagnetic shaft system consists of a magnetically floating rotor, a radial electromagnetic bearing, and an axial electromagnetic bearing.

[0156] (1) Magnetic levitation rotor

[0157] During the rotation of the compressor rotor, the rotor dynamics equation is used to describe the speed change caused by the change in rotor energy. The dynamics equation knows the electromagnetic force, and the displacement of the magnetically floating rotor can be calculated; the power-speed relationship equation knows the power at both ends of the rotor, and the rotor speed can be calculated.

[0158] The rotor dynamics equation is:

[0159]

[0160] Relationship between rotor power and speed:

[0161]

[0162] Where: m is the rotor mass, kg; are the displacements of the rotor mass center in the X, Y, and Z directions, m; f xa is the electromagnetic force of the radial bearing in the X direction, N; f xb b is the electromagnetic force of the radial bearing in the X direction, N; f ya is the electromagnetic force of the radial bearing in the Y direction, N; f yb b is the electromagnetic force of the radial bearing in the Y direction, N; f z is the electromagnetic force of the axial bearing in the Z direction, N; J d is the rotor diameter moment of inertia, kg.m 2 ; J p is the rotor pole moment of inertia, kg.m 2 ;ω is the rotor speed, rad / s;θ x is the angular displacement of the rotor in the YoZ plane, rad; θ y is the angular displacement of the rotor in the XoZ plane, rad; l a and l b are the distances from radial bearing a and radial bearing b to the rotor mass center; g represents gravitational acceleration, kg.m 2 ; N is the speed, rpm; P a is the input power of the rotor, kW; P b is the output power of the rotor, kW.

[0163] Since the distance between the stator and the rotor is very small relative to the entire bearing, sinθ can be approximated as x =θ x 、sinθ y =θ y , so the following relationship between rotor angular displacement and bearing displacement is obtained:

[0164]

[0165] In the formula, y a is the position of bearing a in the Y direction; y b is the position of bearing b in the Y direction; x a is the position of bearing a in the X direction, x b is the position of bearing b in the X direction.

[0166] The center of mass displacement (x c ,y c , z c ) and bearing displacement (x a,y a , x b ,y b , z):

[0167]

[0168] Right now

[0169]

[0170] The angular velocity ω of the rotor is related to the rotational speed N, namely:

[0171] ω=2πN

[0172] N is the rotor speed, rpm.

[0173] (2) Radial bearings

[0174] The radial magnetic bearing uses electromagnetic force to suspend the magnetic rotor in space without mechanical friction and lubrication. The rotor shaft deviation signal is detected by the position sensor, and the signal is transmitted to the controller. The current in the electromagnet is controlled by the power amplifier, thereby generating changes in electromagnetic force to suspend the rotor at a specified position. The radial electromagnetic bearing consists of a radial magnetic bearing and a bearing control system. The radial magnetic bearing mainly balances the radial force of the rotor, which mainly reflects the relationship between the radial electromagnetic force and the bearing displacement and the change of the control current. The bearing control system loop consists of a rotor, a sensor, a controller and a power amplifier.

[0175] Given the control current, rotor offset air gap and electromagnetic coil structural parameters, the electromagnetic force of the radial bearing is calculated as:

[0176] Calculation formula of electromagnetic force F

[0177]

[0178] Where: μ0 is the vacuum magnetic permeability, H / m; A0 is the cross-sectional area of ​​the magnetic pole, m 2 ; N is the number of turns of the bearing electromagnetic coil; I is the current passing through the stator core, A; x is the air gap of the rotor, m.

[0179] like Figure 3 As shown in the rotor force analysis diagram, for the radial bearing, the magnetic levitation force in the X direction is

[0180]

[0181] In the formula, fx+ and fx- represent two opposite forces in the x direction, N; I0 represents the initial current in the coil, i.e. the bias current, A; Δi represents the change in current, i.e. the control current, A. This change can be positive or negative, depending on whether the current increases or decreases; x0 represents the initial x-coordinate position, m, which is the reference position of the object in the x direction. x represents the change in the position of the object in the x direction, m.

[0182] Compared with the bias current I0, the control current △i is much smaller. x Using Taylor expansion at the equilibrium position (i.e. x = 0) to obtain

[0183]

[0184] Where: x0 is the air gap in the x direction when the rotor has no displacement deviation, m; x is the displacement of the rotor in the x direction; k i is the current coefficient, k x is the displacement coefficient, Δi x Represents the change in current in the x direction, A.

[0185] Similarly, the suspension force of the radial bearing in the Y direction is

[0186]

[0187] Where: y0 is the air gap in the Y direction when the rotor has no displacement deviation, m; y is the displacement of the rotor in the Y direction; k i is the current coefficient, k y is the displacement coefficient, Δi y Represents the change in current in the y direction, A.

[0188] (3) Axial bearing

[0189] The axial magnetic bearing uses electromagnetic force to suspend the magnetic rotor in space without mechanical friction and lubrication. The rotor shaft deviation signal is detected by the position sensor, and the signal is transmitted to the controller. The current in the electromagnet is controlled by the power amplifier, thereby generating changes in electromagnetic force to suspend the rotor at a specified position. The axial electromagnetic bearing consists of an axial magnetic bearing and a bearing control system. The axial magnetic bearing mainly balances the force acting on the rotor in the axial direction, which mainly reflects the relationship between the axial electromagnetic force and the bearing displacement and the change in the control current. The electromagnetic bearing control system loop consists of a rotor, a sensor, a controller and a power amplifier.

[0190] Given the control current, rotor offset air gap and electromagnetic coil structural parameters, the axial bearing electromagnetic force is calculated as follows:

[0191] The basic principle of axial magnetic bearing is similar to that of radial magnetic bearing. Its electromagnetic force is only used to balance the external force in the axial direction. Similarly, using Taylor expansion for linearization, the thrust bearing's suspension force in the Z direction is:

[0192]

[0193] Where z0 is the air gap in the Z direction when the rotor has no displacement deviation, m; z is the displacement of the rotor in the Z direction; k i is the current coefficient, k z is the displacement coefficient, Δi z Represents the change in current in the z direction, A.

[0194] (4) Bearing control system

[0195] Whether the rotor can be suspended depends on the size of the electromagnetic force of the electromagnetic bearing. The electromagnetic force on the rotor is a nonlinear function of the electromagnet coil current and the rotor displacement. If the rotor deviates from the reference position and moves downward, the output voltage of the displacement sensor will decrease, and the deviation signal will be greater than zero. The output of the PID controller is processed by the differential circuit and sent to the pulse width modulator. At this time, the duty cycle of the pulse voltage of the upper coil is greater than the duty cycle of the pulse voltage of the lower coil, the suction of the upper coil increases, and the suction of the lower coil decreases, and the rotor moves upward; when the rotor deviates from the reference position and moves upward, the controller will output a voltage control signal to reduce the suction of the upper coil and increase the suction of the lower coil, so that the rotor moves to the reference position.

[0196] The control system loop of the electromagnetic bearing includes a rotor, a sensor, a controller, and a power amplifier. The control system model of the magnetic bearing can be constructed by the rotor model, the sensor model, the controller model, and the power amplifier model. Figure 4 . Among them, the rotor model is the characteristic curve of the compressor.

[0197] 1) Displacement sensor

[0198] The displacement sensor mainly simulates the acquisition of displacement or position signals. The signals collected by the sensor are converted into data and then transmitted to other components through the output interface for use. The sensor transmits the collected signals such as system or device status to the sensor model through the defined interface, processes them into a certain data type and then transmits them to the place where they are needed for use. Generally speaking, the data type selects real data, and the properties of the data are set according to the accuracy of the actual sensor, so that the collected signal matches the actual sensor usage process.

[0199] Displacement sensor mechanism: s = f(s)

[0200] Where s represents displacement, m represents displacement, and f is a function that represents the mechanism by which the displacement sensor converts input signals into output signals.

[0201] 2) PID controller

[0202] The controller of this project uses the rotor offset as the target value, the rotor displacement collected by the sensor as the feedback value, and outputs the appropriate current value to adjust the electromagnetic force to control the rotor offset.

[0203] The role of the proportional term is to make the system respond quickly, the role of the integral term is to eliminate static deviation, and the role of the differential term is to make advance adjustments. When the integral time is set to infinity, the role of the integral term is zero, and when the differential time is set to zero, the role of the differential term is zero. The PID controller can be converted into a PI controller and a PD controller by adjusting the size of the integral time and the differential time.

[0204] The input and output relationship of PID is:

[0205] u=u p +u i +u d

[0206] Where u represents the output of the PID controller, and its unit depends on the type of control system; p Represents the output of the proportional control part, which is the ratio of the error signal (the difference between the set value and the actual value) and has the same unit as u; i It represents the output of the integral control part. It is the result of integrating the error signal over time. The integral action can eliminate the steady-state error. The unit is the same as u. d It represents the output of the differential control part. It is the ratio of the rate of change of the error signal. The differential action can predict the future trend of the error and make adjustments in advance. The unit is the same as u.

[0207] make Then the expression can be expressed as:

[0208]

[0209] Where u(t) is the controller output; e(t) is the input deviation; T i is the integration constant; T d is the differential time constant. K p Represents the proportional gain, which is a dimensionless coefficient used to adjust the system's response strength to errors. i Represents the integral gain, which is a dimensionless coefficient used to adjust the impact of the integral term on the controller output. d Represents the differential gain, which is a dimensionless coefficient used to adjust the effect of the differential term on the controller output

[0210] The transfer function of PID control is:

[0211]

[0212] In the formula, G(s) represents the transfer function of the system, which is the ratio of the output U(s) to the input E(s) in the Laplace transform domain. U(s) represents the output of the system, which is the Laplace transform of a certain variable in the control system. E(s) represents the input of the system, which is the Laplace transform of a certain reference signal or set value.

[0213] When the displacement detection circuit and control circuit are determined, the control characteristics of the magnetic bearing are mainly determined by the parameters of the PID controller. By adjusting the parameters of the PID control, the system can meet the requirements of rapidity, accuracy and stability.

[0214] 3) Power amplifier

[0215] The power amplifier is an important part of the magnetic bearing system. It can convert the control signal into a current signal and act on the rotor through electromagnetic force. The performance of the power amplifier will affect the performance of the magnetic bearing. Here, the power amplifier is approximately equivalent to a gain coefficient, and the gain coefficient value is corrected by test data. The input is the controller output signal, and the output is the control current value of the magnetic bearing.

[0216] S5: Based on the Modelica language, the impeller of the compressor is modeled. Given the impeller speed ratio (actual working speed / rated design speed) and flow ratio (actual working fluid flow / rated design flow), the compressor pressure ratio and efficiency are obtained through two-dimensional interpolation of the compressor characteristic curve. Through the pressure ratio and isentropic adiabatic process, the working fluid outlet thermal parameters and the actual compressor power are obtained.

[0217] The curve calculation process is as follows Figure 2 The detailed calculation process is as follows:

[0218] 1) According to the speed in the rotor characteristic data, the corresponding inputs at each speed are sorted in the order of flow rate, pressure ratio, and efficiency, and input into the model;

[0219] 2) According to the input speed N, the adjacent speed characteristic data is selected from the rotor characteristic data through an algorithm, and the flow rate, pressure ratio, and efficiency data at the current speed N are interpolated using a linear interpolation algorithm to obtain a two-dimensional array, where the first column is the flow rate, the second column is the pressure ratio, and the third column is the efficiency;

[0220] 3) According to the input flow value Wcor, substitute it into the flow, pressure ratio, and efficiency table, perform linear interpolation, and obtain the corresponding pressure ratio and efficiency.

[0221] The relationship between the converted flow rate and the actual flow rate at the inlet is:

[0222]

[0223] The speed ratio is

[0224]

[0225] The outlet pressure is

[0226] p out =p in ·π

[0227] Among them, W cor is the flow ratio; W C is the current flow rate, kg / s; W C，d is the design flow rate, kg / s; N cor_C is the speed ratio; N is the current speed, rpm; N d is the design speed, rpm; p in is the compressor inlet pressure, MPa; p out is the compressor outlet pressure, MPa; π is the compressor pressure ratio. The compressor pressure ratio is interpolated according to the rotor characteristic curve.

[0228] S6: Based on the Modelica language and the compressor system principle, the data transmission between the components is defined through the input and output interfaces to form a signal closed loop of the entire compressor system and complete the compressor system model integration, such as Figure 7 The details are as follows:

[0229] 6) The input of the PID controller is the reference position and measured position data of the magnetic levitation rotor (x, y, z values, m), and the PID outputs control signals to the power amplifier, such as proportional, integral and differential control signals to increase or decrease;

[0230] 7) The power amplifier input is the PID controller output signal, and the output is the control current value (A) of the magnetic bearing;

[0231] 8) The input of the magnetically floating rotor is the control current signal (A) output by the power amplifier, and the output is the rotor force (N), displacement (m) and angle (radian) data;

[0232] 9) The rotor and impeller transmit the rotor speed (rpm), angle (radian) and torque (Nm) data between the rotor and the motor;

[0233] 10) What is transmitted between the motor and the inverter is the speed (rpm).

[0234] The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art shall not deviate from the spirit and scope of the present invention, and shall be within the scope of protection of the claims attached to the present invention.

Claims

1. A multi-disciplinary coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica, characterized in that: The following steps are involved: S1: Decompose the supercritical carbon dioxide electromagnetic bearing compressor system into the inverter, motor, shaft system and impeller, and express the relationship between the equipment in the form of a structural diagram; S2: Model the inverter based on Modelica language; S3: Model the motor based on Modelica language; S4: Model the axis system based on Modelica language; S5: Model the impeller based on Modelica language; S6: Based on the Modelica language, the data transmission between the components is defined through the input and output interfaces to form a signal closed loop of the entire compressor system and complete the compressor system model integration.

2. The multi-disciplinary coupling modeling method of a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 1, characterized in that: The frequency converter in S2 drives the motor by adjusting the frequency and voltage of the power supply, and includes a controller and an inverter, wherein the controller controls the motor speed and the inverter converts direct current into alternating current for output; The inverter model is divided into three parts: speed regulator, current regulator and coordinate transformation module. The speed regulator and current regulator are PI controllers, and the coordinate transformation module includes Clark transformation, Park transformation, Clark inverse transformation and Park inverse transformation.

3. A multi-disciplinary coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 2, characterized in that: The Clark transformation is a module that completes the transformation from the three-phase stationary coordinate system abc to the two-phase stationary coordinate system αβ. The transformation formula is:

4. A multi-disciplinary coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 2, characterized in that: The Park transformation is to transform the voltage or current value in the two-phase stationary coordinate system into the voltage or current value in the corresponding two-phase rotating coordinate system. The transformation formula is:

5. The multi-disciplinary coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 2, characterized in that: The effect of the Clark inverse transform is opposite to that of the Clark transform, and the transform formula is:

6. The multi-disciplinary coupling modeling method of a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 2, characterized in that: The effect of the Park inverse transform is opposite to that of the Park inverse transform, and its transformation formula is:

7. The multi-disciplinary coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 2, characterized in that: The inverter is used to convert direct current into alternating current output. The alternating voltage converted by the three-phase inverter is three-phase, i.e., AC380V. The inverter is a device that amplifies the voltage, current, and power of the control signal of the IGBT switch device. The three-phase full-bridge inverter is composed of three bridge arms and six power transistors. The output of the inverter is located at the neutral point of the three groups of switches, and the voltage difference between the two gets the three electric currents required for the three-phase electricity. The three-phase bridge inverter controls the on and off sequence of the three groups of power transistors, and outputs three-phase electrical signals with equal amplitude and frequency.

8. The multi-disciplinary coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 1, characterized in that: The S3 includes a motor that converts electrical power into driving torque and is the power source of the compressor. The model of the motor includes a voltage equation, a magnetic flux equation, a torque equation and a motion equation.

9. The multi-disciplinary coupling modeling method of a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 8, characterized in that: The equation for the motor is as follows: Voltage equation: you sd =R s I sd +pψ sd -oops sq you sq =R s I sq +pψ sq -oops sd Magnetic flux equation: ψ sd =L sd I sd +ψ f ;ψ sq =L sq +i sq Torque equation: T=p*[L sd *i sq *i f -(L sd -L sq )*i sd *i sq ] Equations of motion: In the formula, subscript s represents the stator, subscript d represents the d-axis, subscript q represents the q-axis, u represents voltage, R represents resistance, i represents current, ψ represents magnetic flux, ω represents angular velocity, L represents inductance, T represents torque, and p represents the number of magnetic pole pairs.

10. The multi-disciplinary coupling modeling method of supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 1, characterized in that: The electromagnetic rotating shaft of the S4 compressor is composed of a magnetic floating rotor, a radial electromagnetic bearing and an axial electromagnetic bearing.

11. The multi-disciplinary coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 10, characterized in that: The magnetic levitation rotor uses the rotor dynamics equation to describe the speed change caused by the energy change of the magnetic levitation rotor. The rotor dynamics equation is: Relationship between rotor power and speed: Where: m is the rotor mass, x c ,y c 、z c are the displacements of the rotor mass center in the X, Y, and Z directions, respectively, and f xa is the electromagnetic force of the radial bearing in the X direction, f xb b is the electromagnetic force of the radial bearing in the X direction, f ya is the electromagnetic force of the radial bearing in the Y direction, f yb b is the electromagnetic force of the radial bearing in the Y direction, f z is the electromagnetic force of the axial bearing in the Z direction, J d is the rotor diameter moment of inertia, J p is the rotor pole moment of inertia, ω is the rotor speed, θ x is the angular displacement of the rotor in the YoZ plane, θ y is the angular displacement of the rotor in the XoZ plane, l a and l b are the distances from a radial bearing and b radial bearing to the rotor mass center respectively; The following relationship between rotor angular displacement and bearing displacement is obtained: In the formula, y a is the position of bearing a in the Y direction, y b is the position of bearing b in the Y direction, x a is the position of bearing a in the X direction, x b is the position of bearing b in the X direction; Get the center of mass displacement (x c ,y c , z c ) and bearing displacement (x a ,y a , x b ,y b , z): Right now The angular velocity of the rotor is related to the rotational speed, namely: ω=2πn n is the rotation speed of the rotor.

12. The multi-disciplinary coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 10, characterized in that: The radial magnetic bearing uses electromagnetic force to suspend the magnetic levitation rotor in space without mechanical friction and lubrication. The position sensor detects the shaft deviation signal of the rotor, transmits the signal to the controller, and controls the current in the electromagnet through the power amplifier, thereby generating a change in electromagnetic force to suspend the rotor at a specified position. The radial electromagnetic bearing consists of a radial magnetic bearing and a bearing control system. Given the control current, rotor offset air gap and electromagnetic coil structure parameters, the electromagnetic force of the radial bearing is calculated as: Electromagnetic force calculation formula Where: μ0 is the vacuum magnetic permeability, A0 is the cross-sectional area of ​​the magnetic pole, N is the number of turns of the bearing electromagnetic coil, I is the current passing through the stator core, x is the air gap of the rotor, For radial bearings, the magnetic levitation force in the X direction is f x The linearization process is carried out using Taylor expansion at the equilibrium position to obtain Where: x0 is the air gap in the x direction when the rotor has no displacement deviation, x is the displacement of the rotor in the x direction, k i is the current coefficient, k x is the displacement coefficient, The suspension force of the radial bearing in the Y direction is Where: y0 is the air gap in the Y direction when the rotor has no displacement deviation, y is the displacement of the rotor in the Y direction, k i is the current coefficient, k y is the displacement coefficient, 13. The multi-disciplinary coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 10, characterized in that: The axial magnetic bearing uses electromagnetic force to suspend the magnetic levitation rotor in space without mechanical friction and lubrication. The position sensor detects the shaft deviation signal of the rotor, transmits the signal to the controller, and controls the current in the electromagnet through the power amplifier, thereby generating a change in electromagnetic force to suspend the rotor at a specified position. The axial electromagnetic bearing consists of an axial magnetic bearing and a bearing control system. Given the control current, rotor offset air gap and electromagnetic coil structure parameters, the axial bearing electromagnetic force is calculated as follows: The suspension force of the thrust bearing in the Z direction is obtained by linearization using Taylor expansion: Where z0 is the air gap in the Z direction when the rotor has no displacement deviation, z is the displacement of the rotor in the Z direction; k i is the current coefficient, k y is the displacement coefficient, 14. A multi-disciplinary coupling modeling method for a supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 11 or 12, characterized in that: The bearing control system electromagnetic bearing control system loop includes a rotor, a sensor, a controller and a power amplifier.

15. The multi-disciplinary coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 14, characterized in that: The sensor is a displacement sensor, which simulates the acquisition of displacement or position signals. The signals collected by the sensor are transmitted to other components for use through the output interface after data conversion. The sensor transmits the collected system or equipment status signals to the sensor model through the defined interface. The displacement sensor mechanism is: s=f(s).

16. The multi-disciplinary coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 14, characterized in that: The controller is a PID controller, which is converted into a PI controller and a PD controller. The input and output relationship of PID is: in=in p +in i +in d make and Then the expression can be expressed as: In the formula, u(t) is the controller output, e(t) is the input deviation value, K p Proportional coefficient, T i is the integration constant, T d is the differential time constant; The transfer function of PID control is:

17. The multi-disciplinary coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 14, characterized in that: The power amplifier is equivalent to a gain coefficient, and the gain coefficient value is corrected by test data. The input is the controller output signal, and the output includes the magnetic bearing control current value.

18. The multi-disciplinary coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 1, characterized in that: In the above S5, the impeller speed ratio and flow ratio are known, and the compressor pressure ratio and efficiency are obtained by two-dimensional interpolation of the compressor characteristic curve. The working fluid outlet thermal parameters and the actual compressor power are obtained through the pressure ratio and isentropic adiabatic process. The calculation process is as follows: 1) According to the speed in the rotor characteristic data, the corresponding inputs at each speed are sorted in the order of flow rate, pressure ratio, and efficiency, and input into the model; 2) According to the input speed N, the adjacent speed characteristic data is selected from the rotor characteristic data through an algorithm, and the flow rate, pressure ratio, and efficiency data at the current speed N are interpolated using a linear interpolation algorithm to obtain a two-dimensional array, where the first column is the flow rate, the second column is the pressure ratio, and the third column is the efficiency; 3) According to the input flow value Wcor, substitute it into the flow, pressure ratio, and efficiency table, perform linear interpolation, and obtain the corresponding pressure ratio and efficiency; The relationship between the converted flow rate and the actual flow rate at the inlet is: The speed ratio is The outlet pressure is p out =p in ·π Among them, W cor is the flow ratio, W C is the current flow rate, W C，d is the design flow rate, N cor_C is the speed ratio, N is the current speed, N d is the design speed, p in is the compressor inlet pressure, p out is the compressor outlet pressure, and π is the compressor pressure ratio.

19. The multi-disciplinary coupling modeling method for supercritical carbon dioxide electromagnetic bearing compressor system based on Modelica as claimed in claim 1, characterized in that: The S6 includes the following: 1) The input of the PID controller is the reference position and measured position data of the magnetic levitation rotor, and the PID outputs a control signal to the power amplifier, including the proportional, integral and differential control signals of increase or decrease; 2) The power amplifier input is the PID controller output signal, and the output is the control current value of the magnetic bearing; 3) The input of the magnetically levitated rotor is the control current signal output by the power amplifier, and the output is the force, displacement and angle data of the rotor; 4) The rotor and impeller transmit the rotor speed, angle and torque data between the rotor and the motor; 5) What is transmitted between the motor and the inverter is the speed.

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