Mathematical model of an asynchronous machine in real coordinates of state

A mathematical description of an asynchronous machine with unreduced parameters in the space of real phase coordinates is given. When studying an asynchronous motor in a dual power supply system with controlled converters in rotor and stator circuits, there is a need for an AM model without parameters, in which the processes in the stator and rotor circuits will correspond to reality in magnitude. In addition, such a model is necessary when analyzing the energy parameters of the whole electric drive controlled by the rotor. To observe real processes in the stator and rotor, the model should be designed in separate spatial coordinate systems. In reference books for AM with a wound rotor (WR), as a rule, the real parameters (resistances, currents and voltages) of the stator and rotor and the voltage reduction coefficient ( ke ) are given. Bringing currents and resistances (inductances) is carried out by coefficients ki=ke and kr=ke2 respectively. Let's consider the description of the machine without reduction of parameters. For the convenience of further consideration, let's introduce the general value of the mutual inductance. We obtain an equation for the electromagnetic moment in real coordinates. Let's design a model in the MATLAB dynamic modeling environment using vector-matrix representation. Matrix algebraic operations with vector variables are implemented by Matlab Fn blocks, which are the calls to userdefined functions described in the form of M-files. The content of Matlab Fn functions is considered. On the model, the processes of starting of an AM with a phase rotor of AK-52-6 type were. Shows the graphs of start-up transients. The processes in the obtained model coincided with the results of modeling of this engine in the model with the coordinates reduced to the rotor. Thus, the energy processes described by this model correspond to the processes to the model with the given parameters, and the processes of currents and flux linkages changing of the stator and rotor are real. The model designed in the MATLAB/Simulink dynamic modeling environment can be used to study double-powered asynchronous electric drives.

RESEARCH SENSITIVITY OF THE ROTOR FLUX LINKAGE OBSERVER TO CHANGE PARAMETERS OF THE ASYNCHRONOUS MACHINE

When changing the parameters of the control object to ensure the required quality of control, the tuning parameters of the control system must be changed. Investigation of the sensitivity of mathematical models helps to choose the right technical parameters of the regulators. Therefore, there is an urgent scientific task, which consists in the development of mathematical models for calculating the steady-state values ​​of the sensitivity functions of the coordinates of non-linear systems to changes in their parameters. When synthesizing observers of the rotor flux linkage, it is indicated that the signal for evaluating the rotor flux linkage is most sensitive to a change in the active resistance of the rotor of an induction machine. However, the numerical values ​​of the transmission coefficients between the coordinates of the observer and the increments of the parameters of the asynchronous machine during its operation are not given, which does not allow a comparative analysis of the degree of influence of changes in certain parameters of the asynchronous machine on the signals of the observer of the flux linkage. The task is to find and compare the numerical values ​​of the functions of the sensitivity of the coordinates of the observer of the rotor flux linkage to the change in the parameters of the asynchronous machine by joint analytical solution of the static equations of the observer's sensitivity model and the state model of the asynchronous machine. In this work, analytical expressions are obtained for the steady-state values ​​of the sensitivity functions of the coordinates of such a nonlinear object as an observer of the rotor flux linkage to a change in the parameters of an asynchronous machine. A comparative analysis of the values ​​of the transmission coefficients between the parameters and coordinates in the system asynchronous machine — observer of the rotor flux linkage for its various rotation speeds is carried out. The proposed technique makes it possible to find the numerical values ​​of the transmission coefficients and to compare the degree of influence of various parameters of the asynchronous machine on the coordinates of the flux linkage observer. Transient processes obtained in the course of solving the equations of the dynamics of an asynchronous electric drive with an observer of flux linkage complement the results of analytical calculations. The performed calculations are aimed at increasing the depth of analysis of the properties of the flux link observer, which helps to reasonably choose the structure of feedbacks when synthesizing a closed observer.

EXPERIMENTAL STUDY OF STATIC CHARACTERISTICS ASYNCHRONOUS MACHINE IN DYNAMIC BRAKING MODE WITH INDUCTION RESISTANCE IN THE ROTOR WINDING

The article discusses the results of a study of the static electromechanical characteristics of an asynchronous machine (AM) when prototypes of induction resistances (IR) with improved parameters are included in its rotor circuits. The dynamic braking (DB) of asynchronous machines, which is widespread in practice, provides for the dissipation of the kinetic energy of the rotating parts in the resistance boxes included in the rotor winding. In the process of stopping, to maintain a constant average braking torque AM, a bulky relay-contactor circuit for shunting rotor resistances is used. However, it is not possible to eliminate significant fluctuations in the electromagnetic torque in this way. To optimize the DB AM process, it is proposed to include a three-phase IR in the rotor winding instead of resistance boxes, the value of which automatically decreases along with the rotor current frequency. This approach allows you to abandon contact equipment and ensure smooth braking of the machine with fluctuations in the electromagnetic moment in narrower limits. The known IR designs are designed for starting modes of induction motors with a wound rotor, but they cannot ensure the constancy of the torque on the AM shaft in the DB mode. Therefore, the purpose of the study is to develop and experimentally confirm the effectiveness of simple control circuits of an induction machine in the specified mode with improved contactless induction rheostats in the rotor. The paper presents a diagram of a pilot plant and a figure explaining the design features of the IR. The studies were carried out for an asynchronous machine of the MTB-412-8 type, equipped with a thyristor exciter and a tachogenerator. The three phases of the AM rotor included ICs connected by a "star". The experiments were carried out in the direction of obtaining the necessary braking characteristics of the AM by varying the switching circuit of the stator phases and the value of the current supplying them. The figures show the mechanical characteristics of AM, obtained in the process of studying the influence on them of three typical circuits for switching on the phases of the stator winding and two values ​​of the fixed supply current. The research results show that the desired form of the mentioned AM characteristics is achieved only when using the stator phase switching in a function of the rotor speed and a constant supply current value.

Enhanced space vector modulated scalar control of induction motor

<p>A conventional vector control of the asynchronous machine makes an analogy of an equivalent separately excited DC machine. It offers a decoupled control of torque and flux which is perpendicular to each other hence one vector is not interfered by other parameters. So, torque and speed control is achieved in an isolated manner even though they are closely interlinked. This is implemented by aligning the rotor flux with the direct axis of the synchronously rotating reference frame. PI controllers play a key role to achieve the desired topology of the VFD. Three controllers are used in the system, flux, speed and torque controller. Tuning of flux controller is quite simple, but in case of speed and torque, it became quite tricky because the output of the speed controller is the reference signal of torque controller. Moreover, there is no distinct method to tune the controllers in the vector control system. Still, the entire high-performance dynamic response of the machine depends on the perfect tuning of those controllers. From the above analysis, it is understood that system identification is essential to tune the PI controllers. But being an asynchronous machine, to obtain system transfer function in a decoupled manner is very difficult. To overcome this problem, the proposed model will be Conventional sine PWM modulated switching pulses are used to implement variable frequency drives for induction motor. Space vector modulated PWM switching pulse is used to fire IGBT. In the case of sine, PWM modulated switching; DC bus voltage utilization is 50% whereas in space vector modulated inverter 57.73% DC Bus voltage utilization can be achieved. <strong></strong></p>

Simulation Model of an Asynchronous Machine with Wound Rotor in Matlab Simulink

The article presents a three-phase mathematical model of asynchronous machine with wound rotor based on differential equations. The equations are resolved with respect to the derivatives of flux linkages. The description of the computer program in the Matlab Simulink that implements the model and allows to simulate transients of the asynchronous motor is present. A simulation model of a three-phase asynchronous machine with wound rotor, which allows to investigate static and dynamic operating ranges when power converters are connected to the rotor circuit has been obtained. The results of approbation of the obtained simulation model in the Matlab Simulink environment and experimental research of asynchronous engine with wound rotor, driving into the asynchronous-valve cascade, are presented. The results of experimental studies of the asynchronous machine under sinusoidal voltage using a stand based on the asynchronous-valve cascade, and comparison of the oscillograms obtained with simulation results of the proposed model are presented. The comparison of experimental and calculated oscillograms of the current of the investigated asynchronous motor can be concluded on satisfactory accuracy of the proposed model and the possibility of its application for modeling and analysis of asynchronous electric drives.