The paper introduces the results of mathematical simulation of the operating modes of an asynchronous motor when powered by a sinusoidal voltage source and a width-modulated voltage pulse source. The study shows the possibilities of increasing the energy efficiency of an asynchronous electric drive. Findings of research show the feasibility of studying the switching of the motor power source from a pulse width-modulated voltage to a sinusoidal voltage source in the nominal operating mode in order to increase the energy efficiency of the electric drive

Приведены результаты математического моделирования режимов работы асинхронного двигателя при питании от источника синусоидального напряжения и от импульсного источника широтно-модулированного напряжения. Отмечены возможности повышения энергоэффективности асинхронного электропривода. Обоснован вывод о целесообразности исследования переключения источника питания двигателя с импульсного широтно-модулированного напряжения на источник синусоидального напряжения в номинальном режиме работы с целью повышения энергоэффективности электропривода

A modern frequency-controlled asynchronous electric drive (FCAD) is widely used both in the products of military equipment (ME) and in those converted for civilian use (CE). Products of the first category must comply with severe requirements to operating conditions (in accordance with the set of state military standards “Klimat-6” and “Moroz-7”). In the ME products, electric drive often functions under conditions of a thermally loaded enclosure, which complicates the task of reducing heat emission and providing heat dissipation. The requirements for ensuring warranty performance of the driving/working mechanism are conditioned, in particular, by FCAD energy efficiency improvement. Such a task is dependent, first of all, on the degree of minimisation of losses in the drive components, as such losses result in efficiency deterioration and increased power consumption. Proceeding from this, improving FCAD energy efficiency is a vital task in these circumstances.

The object of this study is a frequency- controlled AC electric drive whose power circuit employs a three-phase asynchronous motor (AM) with a squirrel-cage rotor powered from frequency converter (FC) of a power controller with pulse- width modulation (PWM).

The purpose of the work is to investigate feasibility of improving energy efficiency of FCAD used in electro-hydraulic transmission of a self-propelled hoisting machine. The paper is a continuation of works [

One of the options for solving the task is refinement of the existing electric motor types and semiconductor converters and development of new ones, with improved energy characteristics.

In the field of electric machine-building, national industry has mastered production of several general-purpose asynchronous motor series (AI, 5A) with higher efficiency and power factors. For example, “RUSELPROM” JSC has developed special crane motors of 5MTK and 7MTK series for a frequency-controlled electric drive. The improved stator winding manufacturing technologies and the magnetic core design ensure reliable operation of electric motors when powered from autonomous voltage inverters (AVI) and a possibility for rotation frequency control in a wide range.

Today’s achievements in the development of microprocessor control facilities make it possible to solve highly complex practical tasks, such as identification of parameters, assessment of state variables, adaptive and optimal control. One of important trends in variable-speed electric drive theory and practice remains that of developing electric drives that would support technological processes with minimum energy consumption.

Practically feasible domains of FCAD functioning are determined also by the variable- frequency control law and the quality of its implementation in the regulating system. At the present time there exist different AM control types,

implemented in FC on the basis of scalar and vector control systems. In its turn, vector control is divided into two basic types: with direct rotor field orientation (with rotor position sensor, speed sensor, magnetic flux sensor in the air gap) and with indirect rotor field orientation (sensorless).

Accordingly, vector control with indirect rotor field orientation allows to do without speed sensor (as well as other sensor types), but this option has the following specific disadvantages:

The use of speed sensor to a certain extent decreases FCAD reliability due to the influences of a wide-range complex of physical-chemical and climatic factors, e. g. under conditions of a confined thermally loaded space with vibrating and/or heat emitting equipment. Moreover, speed sensors (encoders) are the least reliable elements in a crane electric drive, with their failure occurring ever so often [

At the same time, selection of AM for operation in a variable-speed drive is a key factor influencing the reliability of drive/working mechanism operation. This paper considers a new traction motor (RF patent No. 184734 for a utility model is granted) with the following specifications: nominal power PN = 15 kW; nominal phase voltage UN = 127 V; nominal phase current IN = 50.38 А; supply voltage frequency fN = 400 Hz; efficiency factor = 0.8651; power factor cos φN= 0.8351; number of pole pairs zp = 4; relative sliding s = 0,0269; rotor rotation speed Ω2 = 611.42 rad/s. The motor is manufactured for heavy-duty operation under conditions of exposure to various adverse factors. To increase motor reliability, its design also features a cooling circuit with cooling channels passing through rotor in the axial direction. The adopted solutions allow to improve the internal air circulation and thus enhance the heat transfer circuit.

AM power supply from FC does not improve FCAD energy efficiency figures in a direct way. On the contrary, losses of an electric motor supplied from inverter with voltage PWM is higher than those of a motor supplied from the mains. This is conditioned both by decrease of the active voltage in the nominal mode and increased electrical and magnetic losses due to the influence of the switching component of current and stator field higher harmonics [

Hence, FCAD operation is accompanied by a number of negative factors: occurrence of supply voltage higher harmonics, which cause pulse overvoltages in the stator winding; high losses reducing efficiency factor and AM usable power and causing increased heating; extra inertial moments increasing vibration and noise.

In this respect, for quantitative estimation, it is proposed to undertake a comparative mathematical simulation of a particular AM powered from the mains and from FC. The simulation consists in modelling of the mode of AM direct start and achieving the ideal idling speed (Ω0N = 628.3 rad/s), followed by active load surge Mc = 24,6 N⋅m; herewith, the speed decreases to Ω2 = 611.4 rad/s (relative value of rotor nominal speed ω2 = 1 - s = 0,9731).

A number of experiments were performed on the AM mathematical model with power supplied from the mains (Fig. 1), while reading off the values of shaft rotation speed and effective values of currents and electrical losses in the stator and rotor windings. The results are given in Table 1.

For presenting a quantitative estimation of the values of electrical losses in the stator and rotor windings, as well as for establishing the causes and their specific effect on power losses in the motor, mathematical simulation of the modes of start by underfrequency relay was performed, followed by load surge on the AM shaft, with power supplied from a pulse width-modulated voltage source.

Table 1

Values of currents and electrical losses of motor supplied from the mains

Parameter Мс = 6.15 N⋅m(= 0.25 Мном) Мс = 12.3 N⋅m(= 0.5 Мном) Мс = 18.45 N⋅m(= 0.75 Мном) Мс = 24.6 N⋅m (= Мном) Shaft rotation speed, rad/s 624.4 620.4 616.3 611.4 Stator current effective value, A 24.0 30.57 39.3 49.2 Electrical losses in stator winding, W 71.29 115.6 191.2 300 Rotor current effective value, A 10.6 21.25 32.1 43.13 Electrical losses in rotor winding, W 24.14 97.6 222.4 401.8

Table 2

Summary table of stator current effective values

Conditions Stator current effective value, A Experiment Mathematical model n = 125,66 рад/c (0,2 Ω2), Мс = 12 Н-м (0,5 Мном) 46 45 n = 125,66 рад/c (0,2 Ω2), Мс = 6 Н-м (0,25) 32.6 n = 235.62 rad/s (0.375 ад, Мс = 10 N.m (0.41 Мном) 37 37 n = 611,4 рад/c (Ω2), Мс = 12 Н-м (0,5 Мном) 39 39

Given in Table 2 are the effective values of stator current, obtained experimentally and with the use of a mathematical model of the motor, read off under certain specified conditions, with power supplied from FC.

The data given in Table 2 confirm compliance of the mathematical model of a squirrel-cage asynchronous motor with the experiment results.

The mathematical simulation was performed using the values of active resistances of the AM windings for a temperature of 150 °С provided by the manufacturer, Sarapul Electric Generator Plant (“SEGZ” JSC): stator - R1 = 0.0412 a; rotor - R2 = 0.0743 a. In the FC - AM control system, the scalar variable-frequency control law is implemented (shown as the red line in Fig. 2). The blue line designates the law of proportional variable-frequency control. The minimum voltage on low frequencies Uboost = 29 В (= 0,16 U6). PWM carrier frequency - 4 kHz.

A number of experiments were performed on the AM mathematical model with power supplied from FC with scalar control system (Fig. 3), with reading off the values of shaft rotation speed and effective values of currents and electrical losses in the stator and rotor windings. The simulation results are given in Table 3.

Table 3

Values of currents and electrical losses of motor supplied from FC

Parameter Мс = 6,15 Н-м (= 0,25 Мном) Мс = 12,3 Н-м (= 0,5 Мном) Мс = 18,45 Н-м (= 0,75 Мном) Мс = 24,6 Н-м (= М ном) Shaft rotation speed, rad/s 624.3 620.2 615.8 611.4 Stator current effective value, A 27.80 33.8 42.26 523 Electrical losses in stator winding, W 95.33 141.4 221.0 338 Rotor current effective value, A 17.40 25.7 35.70 46.6 Electrical losses in rotor winding, W 65.30 142.5 275.0 468

For convenience of comparing the results of mathematical simulation of motor operating modes when supplied from different voltage sources, Fig. 4 shows the dependencies of the currents of stator I1 and rotor I2, windings, electrical losses in the stator ΔРэл1 and rotor ΔРэл2 windings on the moment of load on the AM shaft when supplied from the mains (solid lines) and from an autonomous voltage inverter, AVI (dashed lines).

With AM supplied from a PWM source, at nominal load, stator current would increase by 6.3 %, and rotor current by 8.1 % (see Fig. 4). An increase in the currents of motor windings leads to respective increase in the electrical losses of stator winding by 12.7 %, and rotor winding by 16.5 % as compared with the simulation results of AM modes when supplied from a sinusoidal voltage source.

An increase in AM power losses when supplied from a pulse width-modulated voltage source can be explained by the presence of higher harmonics in the voltage supplied to the stator windings, voltage drop on the power semiconductor devices of the FC, and voltage decrease on the motor, conditioned by the PWM use. Let us consider the following factors.

Due to the presence of higher harmonics, the effective value of stator current (ΙΣ) appears to be too great, which can be described by the following formula:

where I(1) - effective value of the fundamental harmonic;

KВГТ - stator current harmonic distortion factor.

In particular, for nominal load and PWM carrier frequency equal to 4 kHz, stator current harmonic distortion factor KВГТ= 0.254 (calculated in the MATLAB Simulink package by the method of [

Much greater effect is produced by current higher harmonics on the value of losses in the motor. Relative to sinusoidal power supply, electrical losses in the motor increase by 15 %, and total losses - by 4.6 %.

Moreover, non-sinusoidal power supply leads to increased losses not only in copper, but also in steel. In particular, the increase of losses from eddy currents can be approximately estimated using a similar formula:

UΣ = U(1) (1+ KВГТ2) (2)

where U(1) - effective value of the fundamental harmonic;

KВГТ = 0,701 - stator voltage harmonic distortion factor at nominal load (calculated in the MATLAB Simulink package by the method of [

In the detailed MATLAB Simulink mathematical model of FCAD [

It follows from this that the factor of losses increase caused by eddy currents equals to 1 + KВГТ2 = 1+ 0,7012 = 1,491. Hence, unlike the electrical losses, losses in steel from eddy currents increase, approximately, 1.5-fold, which will result in an increase of total losses by ca. 7.5 %.

Summing up the increase of electrical losses and losses in steel, as well as considering increased additional losses, a degree of total losses increase at nominal load on the AM shaft can be approximately estimated as 12 % relative to the losses under sinusoidal power supply, i. e. nominal losses.

To establish a quantitative estimate of the influence of voltage level in the direct current segment on the values of current in stator and rotor windings, and, as a consequence, the values of electrical losses in the motor windings, a number of experiments were performed on a mathematical model consisting of a DC voltage source, AVI, and AM.

Because of negative effects of the AVI, such as ‘dead’ time and voltage loss on the power switches in straight and reverse direction, as well as non-ideal software compensation of those effects, the required voltage level often cannot be reached.

Therefore, at the nominal frequency, the levels of driving phase voltages generated by the AVI will be by 5...10 % less than the nominal value.

Voltage of the direct current segment is maintained at a constant level Ud = 311В from a high-power DC voltage source. Such voltage level in the direct current segment corresponds to that available on the clamps of filter capacitor bank installed downstream of a three-phase rectifier, implemented according to the Larionov circuit, supplied to the input of which is effective three- phase line voltage of 220 V. The frequency of the fundamental (first) harmonic of the output voltage is 400 Hz.

The results of mathematical simulation of FCAD operating modes under varying values of load on the motor shaft and different voltages in the direct current segment are summarised in the form of plots and presented in Fig. 5 and 6.

The plots of the winding currents of stator I1 and rotor I2 (see Fig. 5) are of non-linear character, with the values of currents increasing along with the increase of load on the AM shaft. Besides, the values of currents of the stator and rotor windings increase with the decrease of voltage in the FC direct current segment.

An increase of currents leads to the increase of respective electrical losses, which is shown in the plot families of electrical losses in stator winding ∆Рэл1 and rotor winding ∆Рэл2, given in Fig. 6.

The plots of electrical losses have a non-linear parabolic character. With an increase of load on the AM shaft, the electrical losses increase accordingly. In addition to that, the values of electrical losses in the stator and rotor windings increase along with the decrease of DC segment voltage.

Voltage decrease on the motor, conditioned by the use of PWM, is associated with natural (physical) voltage limitation, which can be obtained at the output of FC supplying the motor. The maximum permissible voltage value can also be additionally restricted by the electrical strength of motor winding insulation. Moreover, with a decrease of feed voltage frequency, the values of all reactive resistances of the AM equivalent circuit decrease proportionally, while the values of active resistances remain unchanged. Therefore, in the small-frequency domain, the share of stator winding active resistance in the motor impedance rises. Accordingly rising is the share of voltage drop on the active resistance of stator winding and its influence on the magnetising circuit voltage at a fixed stator voltage and variation of load on the AM shaft.

In this way, the analysis of electrical losses in the AM stator and rotor windings for the cases of using sources of sinusoidal voltage and pulse width-modulated voltage as motor power supply source demonstrated advisability of motor power supply source switchover from PWM feed to a sinusoidal voltage source in the nominal operating mode.

Proceeding from this, it is proposed to modify the circuit of motor connection from frequency converter to the supply mains by using a bypass, i. e., make a provision for motor power supply switchover from pulse width-modulated voltage source to sinusoidal voltage source. Fig. 7 shows two options of schematic diagrams of FC with asynchronous motor connection to the supply mains.

A conventional connection diagram (see Fig. 7, а) does not provide for a possibility of asynchronous motor direct connection to the supply mains. Conventionally shown in the diagram are the FC and contactors K1 and K2, without respective control windings. With power supplied to the FC, the controller sends a closing command to contactor K2 for pre-charging of the capacitor

bank. After that, contactor K2 opens, while contactor K1 closes, thus connecting FC to the supply mains.

One of the possible options of a schematic diagram of FC with asynchronous motor connection to the supply mains, with a possibility to switch over the voltage source feeding the motor, is given in Fig. 7 (b). As compared with the conventional arrangement, this diagram of FC with asynchronous motor connection to the supply mains is supplemented by two three-phase contactors, which perform switchover of voltage source feeding the motor from pulse width-modulated voltage to sinusoidal voltage, in accordance with the control signal state (i. e., a redundant/bypass power supply circuit is added).

Also shown in Fig. 7 (a, b) is current-limiting resistor R, which is necessary for the procedure of capacitor bank pre-charging.

Let us consider an algorithm of AM feeding source switchover from pulse width-modulated voltage to sinusoidal voltage, and vice versa, when running in the modes of electric motor acceleration and slow-down.

The initial state: all contactors are open, zero voltage in the FC direct current segment. With power supplied to the FC, the controller sends a closing command to contactor K2 for pre-charging of the capacitor bank. After that, contactor K2 opens, while contactor K1 closes, thus connecting FC to the supply mains. In this state, the motor accelerates to the nominal speed at a specified pace. After the motor has reached the nominal speed, contactor K3 opens and contactor K4 closes. Thereon the motor is running under power supply from a sinusoidal voltage source.

Before entering the mode of electrical braking, contactor K4 opens and contactor K3 closes. The AM is slowing down at a specified pace. When reaching zero speed, controller changes over to the start waiting mode.

It is important to point out that application of the option being considered, along with an improved drive power efficiency, implements a higher reliability of the drive, since its performance is supported in the event of FC failure.

Hence, in accordance with the policy of industrial and technological development of the integrated structure of “Almaz - Antey” Air and Space Defence Corporation for the period until 2026, one of the crucial tasks is implementation of the intellectual activity results and mastering of the output of innovative industrial products, which determines the relevance of the scientific research works described above.

Based on the results of mathematical simulation in the MATLAB Simulink software package, modernisation of power controller is performed for improving power efficiency of FCAD and drive mechanism as a whole.

The authors declare that there are no conflicts of interest present.