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The first issue of the first volume of the illusion of February, Qingdao University Journal.
2 Using the article number Lagrangian Maxwell equation in the dynamic modeling of rotating electrical machine Cheng Lirong Electronic Technology Center of Qingdao University, Qingdao this paper briefly describes the Lagrangian Maxwell equation and its application in the dynamic analysis of rotating electrical machines, Through examples, the application of this method can make the modeling of complex problems simpler.
Key words Lagrangian Maxwell equation motor dynamic model picture classification number document identification code introduction computer simulation has become an indispensable important means in the research of rotating machine dynamic analysis, and the establishment of rotating machine dynamic mathematical model is the key to computer simulation research .
Using traditional methods for dynamic modeling,
It is more complicated and difficult to grasp.
If the Lagrangian Maxwell equation is used for dynamic modeling of rotating machines, it is quite simple.
Lagrangian Maxwell's equation is defined as a conservative system, and the generalized coordinates of the system are X. The generalized velocity of the two systems is the two Gorilla Lagrangian state function. For the functional system, the system starts and ends with the same start and end. When the position moves according to the same constraint, its true motion path will be described by the group differential equation that satisfies the variational condition, that is, when the extreme value is reached.
For electromechanical power systems, the differential equations are called Lagrangian Maxwell equations. The Lagrangian state function in the electromechanical dynamic system is defined as Cheng Lirong, male, Han nationality, Tianjin University of Electric Power and Automation Mainly engaged in motor design and simulation technology research.
He is currently a professor at the Electronic Technology Center of Qingdao University.
In the second volume of the Journal of Qingdao University, the sum of the magnetic energy and the kinetic energy and the kinetic energy are the sum of the electric field energy and the mechanical total energy including the gravitational potential energy.
The system has an electrical port and K mechanical ports, and N two according to the variational principle, for the complete constraint system with independent generalization coordinates, the functional port reaches the extreme value according to the variational condition 2), the electrical port and the mechanical port The equation of motion that is satisfied is the state of the sinking state of the electric state, and the generalized coordinates and the generalized velocity of the electric port of the pill. When the former takes the electric charge, the latter is the current when the former takes the flux linkage, and the latter is the voltage.
And the amount of the mechanical port is the angular displacement and angular velocity of the displacement and velocity respectively.
Only suitable for N-dimensional conservative electromechanical power systems.
In order to generalize the formula to the non-conservative system, that is, the actual system, the sum of the loss of each part of the loss function system and the port driving force can be introduced. At this time, the non-conservative force acting on any port is the final recognition of the hip. The partial derivative of the coordinates, so the formulae are all generalized.
As for the right end of the equation is zero, that is the reflection of the lossless passive nature of the conservative system.
When the 3) formula is extended to the actual system, according to the system equilibrium condition, the algebraic number of the non-conservative force acting on each port and the constant constant is equal to zero, that is, 3) is always equal to the type of the situation, and the 竺 戈 戈 竺 竺 竺 竺 竺 竺The formula is the Lagrangian Maxwell equation of the actual electromechanical power system.
The application premise is that the system must have complete constraints. Specifically, the generalized coordinates must be independent and independent. For the electromechanical power system with rotating electric machine as the research object, it is full except for the grid motor. The screen is fully constrained.
The general steps of using the Lagrangian Maxwell equation to establish a dynamic mathematical model of a rotating electrical machine are as follows: selecting generalized coordinates (2) using generalized coordinates and generalized velocity to write out the system's summation of the Lagrangian state function ( 3) Determining the loss function and the non-conservative excitation source acting on each port. The Lagrangian Maxwell equation is applied to the dynamic modeling of the rotating machine. The Lagrange Maxwell equation is used to write the motion equation of the port.
An example of a hidden pole motor with a counter is shown below.
The motor magnetic circuit is linear, and the resistance of the stator single-phase winding is the inductance of the external power supply voltage. The two-phase windings of the rotor are orthogonal and short-circuited respectively, and the resistance ruler is two feet and two feet. Inductance two into two.
The rotor rotor winding mutual inductance is a function of the angle between the winding and the winding, and the rotor moment of inertia is the rotational friction coefficient bounded by the load torque. It is necessary to write the motor motion equation.
In the figure, the motor has an electrical port and a mechanical port (the analysis variable is selected as shown in the following table. Table Variable Analysis Diagram Example Motor Schematic Analysis Variable Port Stator Winding Port Rotor Winding Port Rotor Winding Port Rotor Rotary Axis R Generalized Coordinates Generalized Velocity Loss The generalized force of the coefficient is determined by the above convention, and the Lagrangian function and the loss function of the motor are respectively combined, and the hair, the ten people and the ten thousand are combined with the force swallow, and the combination of the melon factory and the Lagrange Maxwell equation are substituted. Each port has two in turn. The production, the next child, the second lunch, the eight-year-old Pu'er, the moon, and the J-death exaggerate six or more acres is the required motion equation of the motor port.
It can be seen that the establishment process is very simple.
The second volume of the Journal of Qingdao University contains the term and the product of mutual inductance current.
......
In fact, the electromagnetic rotation of the motor is only taking the å…€ expression as an example to see the establishment process using the traditional method.
Without losing the generality, adopting the most universal system of torque formula and silk mouth 8 to swallow the guard due to gamma = gamma = a,
Eight Hanli four, cut-off state work 俪 铡 铡 0 edge of the site and the eve of the eight fires according to the formula can finally be called double million,
Conclusion For a simple rotating electrical system, based on practical experience, it is not difficult to establish a system analysis model by using the basic laws of electromagnetic mechanics kinematics.
However, when the system is more complicated, it is difficult and complicated to obtain various conditions including some extreme conditions that are difficult to be realized by the actual system. If the conventional method is used, it is difficult to establish a rotating motor system. The Lange Maxwell equation can make the problem a satisfactory solution and more general guiding significance.
Qi Chenglin Electromechanical Power System Analysis "Han Huazhong University of Science and Technology Press Gao Jingde, Wang Xiangxi, Li Fahai.
Analysis of AC motors and their systems [Beijing Tsinghua University Press, He Yikang.
Computer Simulation of AC Motor Hangzhou Zhejiang University Press, the application of the Lagrange Max City equation in the dynamic modeling of rotating electrical machines
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