Analysis of the influence of non-sinusoidal and unbalanced network modes on induction motors

The parameters of electrical network modes do not correspond the requirements GOST 32144-2013 of Russian and the National technical regulation of Vietnam. In real operating conditions in electrical networks in non-sinusoidal and unbalanced modes there are harmonic components of voltages and currents as well as voltages and currents of negative sequence. They cause additional losses of active power, which leads to additional heating and causes premature aging of the insulation, and as the result, the reduction in the service life of induction motors. Currently, we see that the process of formation of intelligent electrical power systems is underway. Systems for continuous monitoring of power quality indices and parameters of electrical systems modes are being developed. These systems can be supplemented with programs for calculating characteristics that issue the warning when the unfavorable influence of the parameters of non-sinusoidal and unbalanced modes is detected on various electrical equipment of both electrical power systems and consumers of electrical energy. The paper provides an overview of the characteristics used to analyze, assess and predict the influence of poor power quality associated with non-sinusoidal and unbalanced of currents and voltages on induction motors. A computer program was developed to calculate these characteristics. The program was used to study the influence of non-sinusoidal and unbalanced modes on the induction motors of the coal sorting plant of the Vietnamese company “Cua Ong-Vinacomin”.


Introduction
The study of the influence of the parameters of nonsinusoidal and unbalanced modes on induction motors has been engaged in for a long time, since induction motors are the most used electrical equipment [1][2][3][4][5][6][7][8][9][10][11].A special standard specifies the operating conditions for induction motors with unbalanced voltages [12].They continue to fail due to damage despite many years of ongoing research on the influence of poor power quality on induction motors.For example, in April 2017, due to the poor power quality the induction motor failed at the "Alexandrovsky Mine" enrichment plant in the Trans-Baikal Territory [13].Another 17 induction motors failed at water supply facilities and in the boiler house in the Trans-Baikal Territory in December 2017 [14].Nonsinusoidal and unbalanced modes occur very often in electrical networks in Russia [15].Poor power quality exists in coal mining areas in Vietnam [16].This paper provides the overview of the characteristics used in special works to analyze, assess and predict the influence of poor power quality associated with non-sinusoidal and unbalanced of currents and voltages on induction motors.The computer program "Predicting the influence of nonsinusoidal unbalanced voltage on an induction motor" based on Microsoft Excel and Matlab was developed to calculate these characteristics.The program was used to study the influence of non-sinusoidal and unbalanced voltages on induction motors of the coal sorting plant of the Vietnamese company "Cua Ong-Vinacomin".At present, intelligent electrical power systems are being created equipped with systems for continuous monitoring of mode parameters and power quality indices.They can be supplemented with programs for calculating characteristics that signal the influence of non-sinusoidal and unbalanced voltages and currents on the electrical equipment of electrical power systems and consumers of electrical energy.

Additional losses of active power in the induction motor in non-sinusoidal and unbalanced network modes
Non-sinusoidal and unbalanced voltages applied to the stator winding of the induction motor cause nonsinusoidal and unbalanced currents in the motor windings.They cause additional losses of active power.Fig. 1 presents the diagram of additional active power losses at non-sinusoidal and unbalanced voltages in the motor.

Assessment of the influence of nonsinusoidal voltage on the induction motor
The non-sinusoidal voltage leads to the increase in the active resistance to harmonic currents since at increased There are also additional losses that are caused by the action of harmonics of magnetomotive forces, pulsation of magnetic induction in the teeth.These additional losses are taken equal to 1% of the rated power, are taken into account and added to the losses in the rotor winding [3].Additional resistive losses (PR-NS) are calculated according to [2,4,6] where KRthe resistive loss coefficient in sinusoidal mode.The resistive loss coefficient is calculated by the expression ( ) ( ) PR-Sthe resistive losses in the windings of both the stator and the rotor of the induction motor in sinusoidal mode, which are calculated according to [17]

Assessment of the influence of unbalanced voltage on the induction motor
In [1,3,5] it is noted that the resistance of the negative sequence of induction motors is 5-8 times less than the resistance of the positive sequence.Therefore, the voltage unbalance of 1% already creates the unbalance of currents in the windings of 7-9%.It is also indicated that at the value of the negative sequence voltage equal to 4% of the nominal, the service life of the induction motor is halved.When negative sequence currents flow, additional active power losses occur.Negative sequence currents cause additional heating, reduce the useful torque and available power of the induction motor.To assess the influence of unbalanced voltage on the induction motor, the parameters presented below are used.When calculating additional active power losses [PAL-UB] in unbalanced mode, it is assumed that they are proportional to the losses in the stator winding at the rated current of the fundamental frequency and do not depend on the motor load [3].Additional power losses are determined by the expression where PST-Sthe active power losses in the stator winding in symmetrical mode at the rated current of the fundamental frequency; KILthe locked-rotor current ratio at rated voltage; K2Uthe negative sequence voltage unbalance coefficient.
Losses of active power in the stator winding at nominal conditions are determined in [17] as ) where INthe rated phase current of the stator of the motor; RST-S -the resistance of the stator at rated power mode.
The real service life of the induction motor in unbalanced mode is defined in [3] as (14) The above characteristics are calculated using the computer program and are presented below.

The results of the analysis of the measured indices of the power quality in the power supply system of the coal sorting plant of the company "Cua Ong-Vinacomin"
Below are the results of measurements of indices of the power quality associated with non-sinusoidal and unbalanced modes, which affect the operation of induction motors.Tables 1-3 present the results of the analysis of the measured total harmonic distortion (KU), the indices of the n-th harmonic component of the voltage (KU(n)), the indices of the n-th harmonic component of the current (KI(n)), the negative sequence voltage unbalance index (K2U).The standard values for the indices are set at [19,20].The value of the measured KU(n)) should not exceed 3%, and KI(n) 12%.Values that do not meet regulatory requirements are shown in bold in the tables.It can be seen from the tables that the voltage is nonsinusoidal at the node for connecting the electrical network of the plant to the supply network, since KU is more than two times higher than the standard value.The indeces KU(n) and KI(n) are also significant.The K2U value is much less than the standard value, therefore the voltage unbalance is insignificant.

Prediction of the influence of nonsinusoidal and unbalance voltages on induction motors of the coal sorting plant
At the coal sorting plant, 58 induction motors with a capacity from 4 to 185 kW are in operation.As an example, 2 induction motors with the power of 45 and 110 kW are taken for calculation.Table 4 presents their technical characteristics [21].The table shows: PN, UN, ηN,, sNthe rated power, the voltage, the efficiency, the slip; bthe coefficient characterizing the insulation of the induction motor; KILthe locked-rotor current ratio at rated voltage; R´ST-S, Х´ST-Sthe resistance and the inductance of the stator winding; R´RO-S, Х´RO-Sthe resistance and the inductance of the rotor winding; ТSSLthe standard service life of the motor.
The calculation of characteristics that assess the influence of non-sinusoidal and unbalanced voltages on the induction motor was carried out using the program "Predicting the influence of non-sinusoidal unbalanced voltages on an induction motor".The screenshot of Sheet 1 of the program, which shows the modules of the program, is shown in Fig. 2. Table 5 shows the characteristics that assess the influence of non-sinusoidal voltage on induction motors.The calculation results show that with the constant operation of the induction motor with a power of 45 kW at a nonsinusoidal voltage with the indices given in tables the actual service life can be reduced by almost 9 years.The service life of a 110 kW motor can be shortened by more than 3 years.The screenshot of the program showing the calculating the reduction in the service life of the induction motor with the power of 110 kW is shown in Fig. 3.The screenshot of the program sheet, which presents the results of calculating the characteristics that assess the influence of unbalanced voltage on the induction motor with a power of 110 kW, is shown in Fig. 4.The calculated characteristics for two motors are given in Table 6.The calculation results show that since the voltage unbalance is negligible, the potential reduction in service life of induction motors is less than one year.

Conclusion
The calculation results show that non-sinusoidal and unbalanced voltages reduce the service life of induction motors.Their premature failure will lead to economic damage.Currently, the process of formation of intelligent electrical power systems is underway.Systems for continuous monitoring of indices of the power quality and parameters of the mode of electrical networks are being developed.They could be supplemented with programs for calculating characteristics that predict the influence of non-sinusoidal and unbalance modes on various electrical equipment, which would facilitate a prompt response to negative changes in the parameters in order to provide reliable, high quality, cost-effective power supply to consumers. The induction motor windings in unbalanced mode, С; bthe coefficient characterizing the insulation of the induction motor[18], С -1 .The temperature rise of the windings in unbalanced mode is defined in[3] as losses in the induction motor in unbalanced mode.Change in the coefficient of efficiency caused by unbalanced voltage

Fig. 3 .
Fig. 3. Sheet of the program for calculating the service life decrease of the induction motor.

Fig. 4 .
Fig. 4. Sheet of the program for calculating the characteristics of influence of unbalanced voltage on the induction motor.
in bearings and friction of the rotor against air.Mechanical losses are neglected as they have little influence on motor heating.

Table 4 .
Technical characteristics of induction motors.

Table 5 .
Calculated characteristics at non-sinusoidal voltage.

Table 6 .
Calculated characteristics at unbalanced voltage.
research was carried out under State Assignment Project (No. FWEU-2021-0001) of the Fundamental Research Program of Russian Federation 2021-2030.