Mathematical Driving Model Based Evaluation of Losses Components in the Control Systems with Induction Motor Drive

Abstract -This paper is investigate the modelling of three phase ,two level inverter connected to three phase induction motor .This system divided to two parts , system control (inverter frequency ) and three phase induction motor . The modelling of this systems are built up by Method of Interconnected Subsystem decomposition of a that are coupled by means of dependent voltage and current sources. Such an approach ensured high adaptability in reliability of the work models in conjunction with worthy precision of calculation. The model reflected the mean coupling with basic properties of real machines and enables to calculate transient and steady-state responses as well as to evaluate components of energy losses in the system, adopting the programs (C++ and C builder) explore the optimization case from the systems ,when the varying leakage inductance in rotor windings, then the losses in both rotor and stator in induction motor have deferent variation so its impacted of the current displacement in rotor winding. Several of calculations are done for different numbers of pole to estimate suitable coefficient of load parameters.

sub scheme of the system with two-level inverter with induction motor drive.

II. MATHEMATICAL ANALYSIS FOR THREE PHASE TWO LEVEL INVERTER WITH INDUCTION MOTOR IM
The model of inverter connected to three-phase induction motor has handle real parameters (rated power 500KW and suppled voltage 380) etc. Computer models of The mathematical analysis system is dividing into sub circuit, interconnected dependent voltage , and current sources. As a result represented sub circuit shown in AB bridge rectified current shown in equation (7) below.
The current protection circuit shown in equation 8.
The currents in the bridge arms VSI shown in equation 9.
The input current of the transistor bridge VSI shown in equation 10.
The current of capacitor shown in equation 11.
Such the derivatives the load phase currents shown in equation 12.
These equations mentioned above present the mathematical inverter model behaver through operating system.

III. INDUCTION MOTOR WITH AN ARBITRARY NUMBER THREE-PHASE WINDINGS AND SQUIRREL CAGE. [10]
The mathematical expiration of the induction machines(IM) are mainly consisted with semiconductors ,converters (inverter frequency) in such systems phase voltages and currents of the stator winding machines may have significant alteration As the number of decrease-pate in energy losses in the rotor phase of the harmonic structure of higher spatial-decisive. The multiphase structure is particularly impact high speed machines, in which the weight and volume of active elements is relatively small. Then there is a problematic issue to reduce the surface energy losses in the rotor. That's cause increasing in the stator phase numbers windings to reduce the energy loss in the rotor of the higher harmonic components. The growth of numbers of phases reduced also the energy losses in the rotor side of the high rotation (3Ph) harmonics components. The other options are multiphase constructions could particularly active in high-speed machines, The machine windings are mutually phase-shifted by the ratio of 60 e. deg. to the number of windings. The zero point of the windings is withdrawn so the rotor is short-circuited and the asynchronous machine is configured similarly to the description of synchronous machines in separating it into a sub circuit interconnected through a dependent sources of voltage and current, as shown in fig.3. Directions of currents and voltages had taken in IM machine (for generator mode).The stator windings are presented in the following phase axes notation n -phase number (n = 1, 2, 3); m -number of winding (m = 1, .. M), M -the number of three-phase windings, U nm -phase voltage, I nm -phase currents. The sub circuit's stator windings as dependent sources considered EMF phase e nm )Due to the magnetic flux in the gap), and the mutual induction electromotive force along paths E snm scattering phases, Taken into account the phase inductance L and active resistance r 1 . E snm EMF and inductance L are determined using the following parameters: L -the inductance of the phase dispersion in a symmetric mode, all the windings, l s1 -inductance of phase scattering in a symmetric mode, a three-phase winding (otheropen), and l 0 -zero sequence inductance. The three-phase machines L = l. If the zero point of the three-phase windings is isolated, then l0 inductance can be taken as such, ls1. Rotary contours described in mutually perpendicular axes d and q, not under example, l s1 . Rotary outlines described in mutually perpendicular axes d and q, not under the rotor Vision. The rotor sub circuits loops on axes d and q as dependent sources incorporated currents I d and I q reaction anchor. It takes into account the magnetizing inductance l m , resistance circuit magnetization rm, rotor winding leakage inductance l s2 and active rotor winding resistance r 2 . On fig.3 direction indicated current and voltage sources, and the directions of the axes d and q axes α and β, the rotational direction of the rotor with the frequency ω, τ the angle of rotation of the rotor d axis relative to the axis α.
In which the weight and volume of actual elements is relatively small, and there is a problem of reducing the dissipating energy l in the rotor. The mathematical description of 3-phase machine with multi-phase IM machine . The following inductance is shown in equation 13.
The currents of armature reaction of the two orthogonal axes α and β shown in equations 24,25.  nominal value of magnetizing current. In accordance with (38) , the shaft torque due to mechanical losses is proportional to the square of the speed. And the torque due to losses in the steel, the magnetizing current is proportional to the second power and frequency1.3 degree rotation. Equation (38) can be converted to equation 39.

IV MODULATION SYSTEM CONTROL AND CALCULATION TRANSIENT AND STEADY STATE
REGION. The modeling system is interconnected sub circuit with induction motor to calculate transient and steady state by using software packages C++ Builder and visual C++ Language. Taking Effect of current displacement in the rotor winding of the rated power of motor is 500 kW and rated voltage 380V. Several calculations for the different numbers of pole in the rotor (3)(4)(5)  =12.45 NM To highlight mathematical divine of the system inverter frequency feeding induction motor to characteristics, calculation of rated operation regine of inverter frequency (control system) and induction motor was implemented for The frequency of the reference voltages of 1 kHz. The table (1) represents input data(parameter system ) and table 2 input data of control system The resistance of the rotor phase, pu R2 0.01738 43 The specified speed, pu. Oz 1.
Also the Table (2) represented input data for control system. The extent of the frequency corrections (0 to 1) at Voltage. KUd 0.5 13 The maximum allowable rectified voltage, V Ucmx 1500.
Consuming the parameters in Table (3) below of leakages inductance in rotor for induction motor relies improvement in the losses values  Figure 4 shows the flowchart programming for calculation and solution equation by using C++ and visual C++ [8].       ACKNOWLEDGMENT I sincerely acknowledge the support of received from Dr. M.S. Hasan and my family and all those whose helped me at dayala university during may writing possesses .