Energy Characteristics of Electric Drive of Oscillatory Motion at the Shock-Free Start

The peculiarity of operation of oscillatory electric drive with doubly-fed motor at realization of algorithm of shock-free start was considered. The method of evaluating of energy parameters of such motors operating at the resonance mode with yueTOM of quantitative and qualitative components of the process of energy conversion by an electric motor (doubly-fed motor) is proposed. The calculation of energy characteristics of electric drive of this type was made, the results of calculation show an increase of energy efficiency (an average, generalized efficiency coefficient nE increased by 10%), which confirms the practical significance of the research object.


Introduction
The modern concept of analysis and design of electric drives of oscillatory motion (EDOM) is based on the principles of energy and resource efficiency, and this is reflected in methods of analysis and synthesis. EDOM widely used in modern industry: from vibration systems for inspection of electrical equipment to the ventilation systems and human life [1][2][3][4]. Oscillations measured from a few microns to meters [1,5]. In each case it is necessary to consider the difference between these types of drives from industrial. For example, the nonsinusoidal supply voltage, the harmonic composition of the currents in the windings of the stator and rotor of the control motor, the double frequency in the electromagnetic torque. Consequently, the generally accepted criteria of efficiency of electric drives for this type of drive are not suitable, as it does not take into account their specificity.
It is therefore proposed to use the method of evaluating the energy characteristics of controlled EDOM on the base on serial asynchronous motor by scheme of doubly-fed motor (DFM). Its oscillatory mode is excited by periodic soft reverse [6]. A distinctive feature of this method is an account of harmonic content of supply voltage, and, as a consequence, of resulting electromagnetic torque, angular velocity of rotation and law of motion of movable element of motor of drive with allowance of distortion and asymmetry.
It is known that the highest power consumption at operating of any electric drive happens at its start due to the occurrence of inrush currents and torque, which may differ from the nominal value by several times. Therefore, we proposed a method of providing of shock-free start by current and torque of EDOM with DFM. According to [7,8] the phase correction of supply voltages reduces the magnitude of shock value of stator current on 30 % and the electromagnetic torque -in to 3 times.

Research object and method
The analysis of free components of inrush currents showed that the following condition is necessary to suppress the shock values of current of DFM [3]: The formation of supply voltage of windings of excitation (WE) and control (WC) of stator (S) and rotor (R) of executive engine (doubly-fed motor) occurs in the following laws, respectively: where U m -peak values of supply voltage of windings of stator and rotor; α, β, γ, φ -initial phases of voltage on motor windings (rad); ω 1 , ω 2 -angular supply frequencies of stator and rotor ω 2 =ω 1 +Ω, γ i -coefficients of signals.
Expressions for starting currents and torque shall not give here; we note only conditions of shockfree start by current and torque, based on the conditions of Table 1 (α i -attenuation coefficients of free components of stator and rotor currents of DFM, which were previously found as the roots of characteristic equations upon condition of retardation of shaft of executive motor) [3]. Table 1. Conditions for calculation of shock-free start by current and torque for EDOM.
Shock-free start of EDOM with DFM by current by torque Valuation of indicators of quality of designed system is produced by method of discrete synthesis at different frequency nutrition of DFM of EDOM. The energy quality indicators can be divided into two groups: first group determines the quality of process of electromechanical energy conversion of EDOM; the second group determines the comprehensive quantitative assessment of process of electromechanical energy conversion efficiency by motor and EDOM.
The consumption or generation of reactive power occurs at the work of electromechanical energy converters in dynamic modes except consumption of active power [6]. In this case, the total power consumption of motor is characterized by the power of distortion and asymmetry. Therefore power factor ( P K ), shear factor ( S K ), factor of distortion ( D K ) and asymmetry ( A K ) characterize the ratios between active and reactive powers and power of distortion and asymmetry. Feature of this approach to evaluating of energy characteristics allow evaluate the quality of energy consumption of EDOM.
Power factor P K is determined by the formula: where iAV iAV i T , Q , P -active power, average values of reactive and total power of distortion of i phase for the period.
The shear factor S K describes the relationship between active and reactive power of phase and it is determined by the formula: The distortion factor D K determines the degree of distortion of power consumption and it is calculated by the expression: The factor of asymmetry is calculated according to the expression: The generalized efficiency coefficient refers to the quantitative assessment criteria and it determines the useful portion of the consumed power diverted from the network: where P mec,a , Р mec,r , Р mec,d -active, reactive mechanical power and power of distortion of drive motor, respectively; S -total conditional power consumption of motor. The mechanical power of the electric motor in an oscillatory mode of operation includes power distortion Р mec,d , active P mec,a , and reactive Р mec,r components. Any of these components of mechanical power are involved in useful work depending on the target of drive and nature of load. The generalized efficiency coefficient considers the qualitative ( P K ) and quantitative (h) aspects of process. Therefore its maximum value is necessary to retain during operation of machine in the oscillatory mode (for providing of resonant mode).
This expression is used for determination of mechanical power of DFM at the feeding of windings of stator and rotor by currents of frequencies ω 1 and ω 2 at the first approximation: where 1 2 ω ω W − = -oscillation frequency of movable element of the executive motor; α, φ -initial phases of the first harmonic components of the motion law and electromagnetic torque of DFM.
Analytical expressions for determination of electromagnetic torque and angular speed of rotation were determined previously [7,9]. We give final versions for their determination. Electromagnetic torque of motor in expression (8) defined by formula: where R g -coefficient of damping load torque; C m -1 -coefficient of positional load torque; M c -torque of static load on the motor shaft, χ -coordinate of movable element of motor; J Σ -total inertia moment, which consists of the inertia moment of motor J m and load J l .
Instant consumption power of electric circuit AC at different frequency feeding is defined as where n takes on the values 1, 2, 3, 4, which correspond to the phase currents and voltages. Next we substitute the expressions (1) and the expressions for the currents of stator and rotor [7,8] in (9): ); Instant values of phase currents for specified functions of regulating are defined by the formula (10); for example, the expression of instant power of phase α s can be written in the form: [ ] (11) The total active and reactive power along the axes α and β are defined as ; ;  2 -modulator of frequency 2; 3 -phase -shifting device; 4 -linear autotransformer 2; 5 -autonomous voltage inverter 2; 6 -control winding of stator; 7 -excitation winding of rotor; 8 -autonomous voltage inverter 1; 9 -modulator of frequency 1; 10 -driving generator 1; 11control winding of rotor; 12 -linear autotransformer 1; 13 -current sensor 2; 14 -excitation winding of stator; 15 -speed sensor; 16 -current sensor 1; 17 -differentiator (integrator); 18 -sensor unit; 19 -personal computer.
EDOM (figure 1) consists of control system of stator and rotor of DFM realized on the basis of the asynchronous motor with slip-ring rotor, sensor unit (18) with system for converting analog signal to digital, IBM -compatible personal computer with built-in board with input-output data, providing feedback of speed and current. Control systems of stator and rotor of DFM consists of frequency converters with DC links, which specify the modulation frequency of linear autotransformers (4, 12), signal amplification unit and autonomous voltage inverters (5,8), switched -on from stator and rotor side with the carrier frequency f 1 = 50 Hz and the modulation frequency f 2 = 55 Hz.
The signals from the frequency modulators (2,9) are fed on autonomous voltage inverters (5,8) through the windings of stator and rotor respectively, signals U m come on them from driving generators (1,10). The signal from the phase-shifting device (3) comes to the input (5); this signal provides realization of algorithm of shock -free start of DFM in the composition of EDOM.
Electric machine of alternating current of type MTN -011-6U1with the following parameters was used as DFM: P n =1400 W, nominal voltage U n =220 V, nominal current of stator I n =3.35 А, η=76 %, cos φ н = 0.78, nominal frequency of rotation n n =1250 rev/min [8][9]. At calculation of energy indicators the following values for the components of the load were adopted (all values are given in relative units): at shock-free start by torque R g =1.35, C m  7)) are shown in Table 2. 4. Summary 1. Analysis of the energy characteristics of EDOM at the realization of shock -free start by current and torque has shown that the generalized efficiency coefficient η E increased by 10 % at the use of this method an average; power factor P K decreased by 0.4 relative units; shear factor S K decreased by 0.8 relative units; factor of distortion D K decreased by 0.035 relative units; factor of asymmetry A K decreased by 0.055 relative units. The harmonic composition of the supply voltage improves and affects on final consumption of active and reactive power.
2. The largest increase of the generalized efficiency coefficient η E (by 12 %) and the largest decrease of the factor of asymmetry (by 0.1 relative units) occur at the realization of shock -free start by torque. This suggests that the process of energy consumption occurs with the best of quantitative and qualitative indicators at the realization of algorithm of shock -free start by torque.
3. The dependences (3) -(7) allow one to accurately assess the energy characteristics of the electric drive of oscillatory motion (of any periodic movement) and to get an adequate result and to analyze the efficiency of the designed electric drives.