RU2759558C1 - Method for forming the flux linkage of an asynchronous motor rotor as part of an electric drive with vector field-oriented control when operating in a limited voltage zone - Google Patents

Abstract

FIELD: electrical engineering.

SUBSTANCE: invention relates to the field of electrical engineering, in particular to a vector field-oriented control system for an electric drive based on an asynchronous motor with a short-circuited rotor. The method for forming the flux linkage of the rotor of an asynchronous motor with a short-circuited rotor as part of an electric drive with vector field-oriented control for static operation mode is that it provides the creation of a signal of a given moment M_ref, by means of which the dependence of the flux linkage of the rotor on the given moment M_ref is formed to determine the value of the flux linkage of the rotor at a given moment

. At the same time, the maximum

flux linkage is calculated, which, when the stator voltage reaches the given value

, limits the value of the rotor flux linkage

at a given moment and generates a flux linkage signal ψ_ref. Next, the boundary angular rotation frequency ω ^Pmax of the rotor is determined. If the angular frequency of the rotor is ω≤ω _Pmax, then a signal of a given flux linkage is formed, which corresponds to the flux linkage signal ψ_ref. As soon as the angular frequency exceeds the boundary value ω>ω_Pmax, a task signal is generated for the rotor flux linkage

in the power reduction zone, which is determined taking into account the value of the maximum stator voltage

. Next, the resulting signal of the specified flux linkage

of the asynchronous motor rotor is formed, the value of which at ω≤ω ^Pmax corresponds to the signal of the specified flux linkage ψ_ref for the limited voltage zone, and at ω>ω^Pmax, to the value of the signal of the rotor flux linkage task

in the power reduction zone.

EFFECT: increase in the energy performance of an asynchronous electric drive with vector field-oriented control when operating in the area of limiting the stator voltage and in the area of high engine speeds.

1 cl, 6 dwg, 1 tbl

Description

The present invention relates to the field of electrical engineering, in particular to a system of vector field-oriented control of an electric drive based on an asynchronous motor with a squirrel-cage rotor, and can be used in control systems for asynchronous electric drives of vehicles.

Asynchronous electric drives with vector control can be conditionally divided into two types. The first type includes electric drives of those mechanisms where the rotor flux linkage is maintained at a given constant, usually nominal level. The second type is electric drives, in which it is necessary to generate a rotor flux linkage signal according to a certain law in order to solve optimization problems according to any of the criteria.

So, for example, in traction electric drives of vehicles with vector control, the issue of energy efficiency is relevant, therefore, in the control algorithms for such drives, the rotor flux linkage (or flux-forming stator current) is formed so that maximum efficiency is ensured (Maximum Efficiency control strategy or ME) or minimum stator current at a given torque (control strategy Maximum Torque Per Ampere or MTPA).

However, optimality according to one criterion or another is achieved only in those modes until additional restrictions come into operation, associated, as a rule, with the conditions of the maximum allowable voltage or current.

It is known that the stator voltage of an induction motor depends quite strongly on other quantities, to the greatest extent on the flux linkage and electrical frequency, with the growth of which the voltage at the stator terminals also increases.

Usually, when the speed of rotation exceeds its nominal value, i.e. at the transition to the second zone, the stator voltage also rises above the nominal value. In this case, it is very important that it does not exceed the maximum permissible level, which is determined by the magnitude of the DC link voltage (DC link) and the voltage safety factor. Thus, the relationship between the stator line voltage and the DCB voltage is determined by expression (1).

where U _l - line voltage, U _DC - voltage in the DC link.

As a rule, the safety factor K _zap is about 0.15 ... 0.25 and is necessary to provide a margin for voltage regulation.

At present, open sources of information have considered in sufficient detail the issues of constructing systems of vector field-oriented control of an asynchronous electric drive. However, the emphasis is on the general case of the synthesis of speed control loops and flux linkage with one-zone or two-zone regulation [1, 2].

The issues of forming the laws of flux linkage control under vector control in the source [3] are considered in detail, including for optimization problems according to some of the criteria.

The book [4] describes a method for regulating the flux-forming component of the stator current, which in the static mode is proportional to the flux linkage of the rotor through the parameter of the mutual inductance of the stator and the rotor. In this case, regulation is carried out by introducing an EMF control loop of an induction motor, the structural diagram and recommendations for the synthesis of which are given in the source [4]. However, this method is associated with a number of assumptions that are valid only in a limited range of speeds.

That is why the problem of synthesizing such a method for controlling the flux linkage of the rotor (or the flux-forming component of the stator current) is urgent, in which the maintenance of the motor voltage in the entire range of the rotation frequency would be achieved.

The technical result, which the proposed technical solution is aimed at, is to increase the energy performance of an asynchronous electric drive with vector field-oriented control when operating in the area of limiting the stator voltage and in the zone of high rotational speeds of the electric motor.

одновременно осуществляют вычисление максимального потокосцепления

которым по достижению напряжением статора заданного значения

ограничивают значение потокосцепления

ротора при заданном моменте и формируют сигнал потокосцепления ψ_ref, далее определяют граничную угловую частоту вращения ω^Pmax ротора, причем если угловая частота ротора ω≤ω^Pmax, то формируют сигнал заданного потокосцепления, который соответствует сигналу потокосцепления ψ_ref, при этом, как только угловая частота превышает граничное значение ω>ω^Pmax, формируют сигнал задания по потокосцеплению

ротора в зоне снижения мощности, который определяют с учетом значения максимального напряжением статора

далее формируют результирующий сигнал заданного потокосцепления

ротора асинхронного двигателя, значение которого при ω≤ω^Pmax соответствует сигналу заданного потокосцепления ψ_ref для зоны ограниченного напряжения, а при ω>ω^Pmax значению сигнала задания по потокосцеплению

ротора в зоне снижения мощности. Совокупность всех указанных выше признаков направлена на повышение энергетических показателей работы асинхронного электропривода с векторным полеориентированным управлением при работе в области ограничения статорного напряжения и в зоне высоких частот вращения двигателя.The claimed technical result is achieved by creating a method for forming the rotor flux linkage of an induction motor with a squirrel-cage rotor as part of an electric drive with vector field-oriented control for a quasi-static mode of operation, which consists in creating a signal of a given moment M _ref , by means of which the dependence of the rotor flux linkage on a given moment M _ref to determine the value of the rotor flux linkage at a given torque

simultaneously calculate the maximum flux linkage

which upon reaching the stator voltage of the specified value

limit the value of flux linkage

rotor at a given torque and form a signal of flux linkage ψ _ref , then determine the boundary angular frequency of rotation ω ^{Pmax of the} rotor, and if the angular frequency of the rotor ω≤ω ^Pmax , then form a signal of a given flux linkage, which corresponds to the signal of flux linkage ψ _ref , while, as soon as the angular frequency exceeds the limit value ω> ω ^Pmax , form the signal of the flux linkage reference

rotor in the power reduction zone, which is determined taking into account the value of the maximum stator voltage

then the resulting signal of a given flux linkage is formed

rotor of an asynchronous motor, the value of which at ω≤ω ^Pmax corresponds to the signal of the specified flux linkage ψ _ref for the limited voltage zone, and at ω> ω ^{Pmax to the} value of the signal of the flux linkage reference

rotor in the power reduction zone. The combination of all the above features is aimed at increasing the energy performance of an asynchronous electric drive with vector field-oriented control when operating in the area of stator voltage limitation and in the area of high engine speeds.

Brief Description of Drawings

FIG. 1. Graphs of the dependence of the linear stator voltage on the current I _d at different speeds.

FIG. 2. Block diagram of a block for forming a given flux linkage during operation in the restricted area.

FIG. 3. The block for the formation of the torque-generating component of the stator current.

FIG. 4. Functional diagram of an asynchronous electric drive with vector control.

FIG. 5. Transient processes during the diesel locomotive acceleration up to 41 km / h.

FIG. 6. Illustration on the plane "I _d -I _q " of the choice of the operating point for different approaches to the formation of the flux-forming component of the stator current at a speed of 500 rpm.

The essence of the claimed method is to obtain an optimal electrical signal that allows the formation of the required flux linkage of the rotor of an induction motor under conditions of limited voltage.

To do this, an analytical expression should be obtained that relates the rotor flux linkage (or the flux-forming component of the stator current), the maximum stator voltage, the rotational speed and the given torque.

Let us use a mathematical description by the system of differential equations of an asynchronous motor with a squirrel-cage rotor for vector control problems. It is known that in this case the components of the stator voltage of the AM along the d, q axes are determined by the Park-Gorev system of equations in an orthogonal coordinate system oriented along the rotor flux linkage vector:

- коэффициент рассеяния, T_r=L_r/R_r - постоянная времени роторной цепи, Z_p - число пар полюсов, ω_эл=z_pω - электрическая угловая частота вращения ротора.where U _d , U _q , I _d , I _q are stator voltages and currents along the d and q axes, respectively, R _s , R _r , L _s , L _r are active resistances and total inductances of the stator and rotor, respectively, L _m is the mutual stator and rotor inductance,

is the scattering coefficient, T _r = L _r / R _r is the time constant of the rotor circuit, Z _p is the number of pole pairs, ω _el = z _p ω is the electric angular frequency of rotation of the rotor.

In a quasi-static operating mode, when the rates of change of currents and flux linkage are small, and the derivatives of these quantities can be neglected, the rotor flux linkage can be determined by expressing it from the third equation of system (2). Then the first two equations of system (2) are transformed to the form:

In system (3), the voltage drop across the active resistance of the stator can be neglected, since its value is much less than the value of the counter-EMF of rotation. In addition, the rotational speed of the rotor flux linkage vector described by the fourth equation of system (2) can be replaced by the electric rotor speed, since the value of the slip frequency is also relatively small. Then system (3) is transformed to the form:

In this case, the stator voltage amplitude, taking into account expression (4), will be calculated by the formula

In some sources, the stator voltage of an induction motor is simplified as the EMF of rotation from the product of the magnetic flux and the electrical frequency of rotation.

With regard to the issue under consideration, the above means that when assessing the stator voltage, only the second equation of system (4) will be taken into account, on the assumption that the first equation contains the dissipation coefficient as a factor, which, as a rule, is rather small in magnitude. In other words, in expression (5) U _d will make a significantly smaller contribution compared to U _q .

However, this approach is not fully correct, since with an increase in the rotational speed to maintain a given power, the current I _d should be reduced, and, accordingly, the current I _q should be increased. This will lead to the fact that the component of the stator voltage U _d will increase more and more, and U _{q will} decrease, therefore, it _{will be incorrect to neglect the contribution of U d} to the total stator voltage.

Let us carry out a comparative analysis of different methods for assessing the stator voltage on the example of a traction induction motor with vector control, using the parameters of its windings (Table 1).

Let us construct graphs of the dependence of the stator line voltage on the current I _d (Fig. 1) at a given mechanical power of 320 kW and speeds of 300, 400, 500, 600 min ^-1 for three cases of calculating the stator voltage:

1. Using a complete mathematical description of blood pressure in a static mode according to the system of equations (2);

2. Using expression (5);

3. Using only the second equation of system (4).

In these equations, the torque-generating component of the stator current is calculated from the expression of the torque in statics:

The moment in the formula (6) is calculated as M = P / ω.

From the analysis of the graph (Fig. 1), it follows that the calculation of the stress by expression (5) quite accurately approximates the real dependence described by system (2) in a static mode of operation.

If the voltage is calculated only according to the second equation of system (4), the accuracy of such a calculation decreases with increasing frequency, which can be seen from the given graphs.

Hence, it is more expedient to use expression (5) when synthesizing the IM vector control algorithm, which makes it possible to more accurately calculate the stator voltage in the entire frequency range.

So, using formula (5), we express I _d through all other quantities, which will allow us to obtain an expression for a given flow-forming stator current, which ensures the maintenance of a given maximum stator voltage:

However, equation (7) is not suitable for practical use, since it includes the current component I _q . In the works [5-6], a variant of the formation of the flow-forming current component is presented under the condition of limiting the total stator current. In this case, the I _q component is expressed as a given value from the total maximum current and the I _d component:

After that, expression (8) is substituted into (7):

This approach assumes that the drive operates not only at the maximum possible voltage, but also at the maximum current. This means that the ratio between the moment-forming and flow-forming current components at a given moment shifts towards an increase in I _q and a decrease in I _d . This is clearly shown in Appendix 1. In turn, this method of forming the current I _d causes a departure from the optimum in terms of efficiency or stator current.

Therefore, in order to obtain a ratio of the components I _d and I _q more close to the optimum, it is necessary to express I _q in expression (9) through the torque:

Substituting (10) into (5) and squaring both sides of equation (5), we get:

Moving all the terms in one direction, as well as performing some transformations, we get the biquadratic equation:

Equation (12) has four roots, two of which will be negative, therefore, having no practical meaning. The remaining two roots will be positive.

The smaller of the two remaining roots is also unsuitable in practice, since it causes too high stator currents, exceeding the maximum permissible currents of the power converter and the motor. Therefore, for problems of AM control, an expression should be used that is the largest positive root of equation (12), multiplying the right side by the inductance L _m :

This expression is applicable for the formation of the flux-forming component of the stator current, both in the second and third zones. However, in the third zone, the maximum possible realizable power decreases as the speed rises.

Obviously, the maximum power is reached in cases when the value of the "internal" root in the numerator becomes equal to zero in (13). When passing to the third zone, the flux linkage should be found by the expression, as shown in [5, 6]:

The cutoff frequency at which the IM will operate with maximum power at a limited voltage can be found by equating the radical expression of the internal root of expression (13) to zero, and then solving the resulting equation with respect to the frequency:

Below is an example of the implementation of the claimed method, taking into account the formation of a given rotor flux linkage.

The block diagram of the unit for forming a given flux linkage (BZP) during operation in the restricted zone is shown in Fig. 2.

The signal of the given moment M _{ref is} fed to the block of the primary formation of the given flux linkage 1, which contains the dependence of the optimal flux linkage of the rotor on the given moment in the first zone, which is formed either in a tabular form or in the form of an analytical expression. The use of this approach makes it possible to minimize the stator current or maximize the efficiency at a given torque in the zone where the stator voltage has not reached its limit. These issues are discussed in more detail in the sources [7-11].

по формуле (13), которое при достижении напряжением статора некоторого заданного значения, начинает ограничивать выходной сигнал

блока 1 посредством блока ограничения 3 для формирования сигнала потокосцепления ψ_ref с учетом ограничения.At the same time, block 2 calculates the maximum flux linkage

according to the formula (13), which, when the stator voltage reaches a certain specified value, begins to limit the output signal

block 1 by means of a limiting unit 3 to generate a flux linkage signal ψ _ref taking into account the limitation.

в зоне снижения мощности по формуле (13).By means of block 4, according to the formula (15), the cutoff frequency is calculated, upon reaching which it is necessary to reduce the power. For this, by means of the comparison unit 5, the fact of reaching the specified value by the frequency is determined. In this case, block 6 generates a signal for setting the rotor flux linkage

in the power reduction zone according to the formula (13).

So, in the range ω ω ^{Pmax, the} output logic signal of block 5 will be equal to "1", and by means of the multiplying unit 8, the corresponding signal of the specified flux linkage ψ _ref will be generated only for the limited voltage zone.

ротора в зоне снижения мощности, который определяют с учетом значения максимального напряжением статора

As soon as the frequency exceeds the limit value ω> ω ^Pmax , the output signal of block 5 becomes equal to "0" and by means of inverter 7 becomes equal to "1", further multiplying by means of multiplication block 9 by the output signal of block 6, i.e. form the signal of the flux linkage reference

rotor in the power reduction zone, which is determined taking into account the value of the maximum stator voltage

The output signals of blocks 8 and 9 are fed to the summation unit 10, the output of which is the resulting signal of a given flux linkage of the rotor of the induction motor.

Let us consider a variant of constructing an electric drive system with an asynchronous squirrel-cage motor, in which the proposed method of forming the rotor flux linkage is applied.

A functional diagram of such a system is shown in Fig. 4 and contains such basic elements as an asynchronous motor with a squirrel-cage rotor (IM), a power converter (SP), a speed sensor (DS), current sensors (DT), a DC link voltage (DC) voltage sensor, as well as a controller for which the function of implementing the vector control algorithm is assigned.

The input of the controller receives a signal of a given torque as a control action, as well as feedback signals from current, voltage and speed sensors. At the output of the controller, 6 control signals for the keys of the power converter are generated.

The structure of the vector control system includes the following blocks:

- block for forming pulse-width modulation (PWM);

- coordinate converters that implement the transition from a three-phase fixed coordinate system ABC to an orthogonal rotating coordinate system in the forward and backward directions (PK3-2, ABC-dq, nK2-3, dq-ABC);

- regulators of the flow-forming and torque-forming components of the stator current (RPT, RMT);

- block of compensation of cross-links (BCPS);

- rotor flux linkage regulator (RP);

- block for the formation and limitation of the set values of the torque and torque-generating current (BZMT);

- unit for identification of parameters of the rotor flux linkage vector (BIP);

- unit for setting the rotor flux linkage (BZP).

Note that such blocks as PWM, PK3-2, PK2-3, RPT, RMT, RP, BKPS (optional) constitute the basic (classical) structure when building vector control systems, and are always present in it. Such a basic structure is widely used today in electric drives of various mechanisms and is described in sufficient detail in the literature, for example, in [1, 2, 3, 4].

The BIP unit, which identifies the module and the angle of rotation of the rotor flux linkage vector, also appears more and more often in modern information sources in the structure of VU systems of electric drives as a mandatory element, since sensors for direct measurement of the rotor flux are not used in modern vector-controlled drives. This function is performed by flux link identifiers and observers based on one or another principle.

In this version, it is proposed to use the identifier based on the mathematical description of blood pressure in the d, q coordinate system, namely, on the basis of the system of equations (2). This identification method is described in the information source [2]. Any other identification method can also be used.

All other blocks are often optional. In this structure, they are designed to generate specified signals of torque, flux linkage and currents along the d and q axes, and their limitation. This structure is well suited for traction electric drive control.

In this structure, BZMT plays the role of a shaper and a limiter for setting the torque-generating current, as well as a limiter for a given torque for the maximum power in the second zone and for the maximum current. In this case, the limitation of the given moment is performed in accordance with the expressions:

Here, the limited torque-generating current is calculated using expression (8).

The block diagram of the block for generating and limiting the setpoint values of the torque and torque-generating current is shown in Fig. 3.

Block BZP performs the function of forming a given rotor flux linkage in accordance with the method described in this work. The above is the principle of its operation with reference to the block diagram (Fig. 2).

Next, let us analyze the transient processes in the electric drive when simulating the acceleration of the TEM-6m locomotive with software tools, which has an electromechanical transmission built on the basis of an asynchronous traction electric drive, taking into account the described method of forming the rotor flux linkage (Fig. 5).

In this case, the process of acceleration from zero to the TAD speed of 876 min ^-1 ) is shown. The graph (Fig. 5) can be divided into four areas.

In the first section of acceleration, an increase in the rotor flux linkage is observed, the current I _d is in limitation. TAD starts to move and starts acceleration at a maximum torque of 22.8 kN⋅m.

In the second section, the flux linkage decreases, since the unit for the formation of a given flux linkage comes into operation, depending on a given moment, providing maximum efficiency.

The third section of the diesel locomotive acceleration is characterized by the transition of the drive to the stator voltage limitation zone, which stops increasing when the level of 0.85U _DC = 637.5 V is reached, which is ensured by reducing the rotor flux linkage according to the law laid down in the algorithm. The graph also shows that the transition to the zone of limited voltage practically coincides in time with the entry into the second zone, or the zone of constancy of power.

The fourth section of acceleration is the operation of the drive in the third zone, or the zone of power reduction, which is necessary to maintain the voltage at a given level.

Note that the use of the proposed method for the formation of flux linkage makes it possible to provide a stable voltage margin over the entire range of speed variation (i.e., in the first, second, and third zones).

List of used sources of information:

1. Kozyaruk A.E. Modern and Perspective Algorithmic Support of Variable Frequency Electric Drives / A.E. Kozyaruk, V.V. Rudakov. - SPb .: Saint-Petersburg Electrotechnical Company, 2004 .-- 127 p.

2. Sokolovsky G.G. AC drives with frequency regulation: textbook. for universities. - M .: Academy, 2006 .-- 272 p.

3. Schreiner R.T. Mathematical modeling of AC electric drives with semiconductor frequency converters. - Yekaterinburg, Ural branch of the Russian Academy of Sciences, 2000 .-- 654 p.

4. Vinogradov A.B. Vector control of AC electric drives / Ivanovo State Power Engineering University named after V.I. Lenin ". Ivanovo, 2008 .-- 320 p.

5. Nguyen-Thac, K. et al. "Comparative analysis of the chosen field-weakening methods for the Direct Rotor Flux Oriented Control drive system." Archives of Electrical Engineering 61 (2012): 443-454.

6. S. Kim, S. Sul and M. Park, "Maximum torque control of an induction machine in the field weakening region," Conference Record of the 1993 IEEE Industry Applications Conference Twenty-Eighth IAS Annual Meeting, Toronto, Ontario, Canada , 1993, pp. 401-407 vol. 1.

7. C. Kwon, "An Adaptive Maximum Torque Per Amp Control Strategy," IEEE International Conference on Electric Machines and Drives, 2005., San Antonio, TX, 2005, pp. 783-788.

8. C. Kwon, "Performance of Adaptive MTPA Torque Per Amp Control at Multiple Operating Points for Induction Motor Drives," IECON 2018 - 44th Annual Conference of the IEEE Industrial Electronics Society, Washington, DC, 2018, pp. 637-641.

9. S. Kim, S. Sul and M. Park, "Maximum torque control of an induction machine in the field weakening region," Conference Record of the 1993 IEEE Industry Applications Conference Twenty-Eighth IAS Annual Meeting, Toronto, Ontario, Canada , 1993, pp. 401-407 vol. 1.

10. Sang-Hoon Kim and Seung-Ki Sul, "Maximum torque control of an induction machine in the field weakening region," in IEEE Transactions on Industry Applications, vol. 31, no. 4, pp. 787-794, July-Aug. 1995.

11. Lu Xianliang and Wu Hanguang, "Maximum efficiency control strategy for induction machine," ICEMS'2001. Proceedings of the Fifth International Conference on Electrical Machines and Systems (IEEE Cat.No.01EX501), Shenyang, China, 2001, pp. 98-101 vol. 1.

Claims (1)

A method of forming the rotor flux linkage of an induction motor with a squirrel-cage rotor as part of an electric drive with vector field-oriented control for a static operation mode, which consists in creating a signal of a given torque M _ref , by means of which the dependence of the rotor flux linkage on a given torque M _{ref is formed} to determine the value of the rotor flux linkage at a given moment

simultaneously calculate the maximum flux linkage

which upon reaching the stator voltage of the specified value

limit the value of flux linkage

rotor at a given torque and form a signal of flux linkage ψ _ref , then determine the boundary angular frequency of rotation ω ^{Pmax of the} rotor, and if the angular frequency of the rotor ω≤ω ^Pmax , then form a signal of a given flux linkage, which corresponds to the signal of flux linkage Ψ _ref , while, as soon as the angular frequency exceeds the limit value ω> ω ^Pmax , form the signal of the flux linkage reference

rotor in the power reduction zone, which is determined taking into account the value of the maximum stator voltage

then the resulting signal of the given flux linkage is formed

rotor of an induction motor, the value of which at ω≤ω ^Pmax corresponds to the signal of the given flux linkage ψ _ref for the zone of limited voltage, and when ω> ω ^Pmax - to the value of the signal of the flux linkage reference

rotor in the power reduction zone.

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