Electric Motors for Variable-Speed Drive of Lock Valves

Improving the operational reliability of nuclear power plants, combined heat and power plants (CHP), as well as oil and gas pipelines is a priority task in the development of a variablespeed drive for lock valves used at these facilities. The paper analyzes technical requirements for such devices; the motor has been selected, its electrical equilibrium and moment equations have been obtained; recommendations for the selection of the kinematic drive scheme have been formulated. Based on the theoretical data obtained, a prototype has been developed, manufactured and tested.


Introduction
Developing, designing and producing adjustable lock valves play an important role in ensuring human life.Thus, the annual global demand for valves of only one type, highpressure steam with setup diameters from 20 to 350 mm used at nuclear power facilities and heat and power plants, amounts to tens million pieces per year, and the cost of some samples can exceed $ 50,000.
Various researchers have dealt with the design problems of new electrical machines with an increased starting torque.Work [1] presents a modified method of predicted torque control of induction machines.This method allows reducing the torque ripple at the moment of starting a highly loaded AC electric motor.The modified predictive torque control results in a more stable starting behavior of the electric motor in relation to torque ripple control methods compared to conventional direct torque control.Field control (FOC) and direct torque control (DTC) methods are reported to be the two most commonly used control methods for induction machine (IM) drives operating under severe starting conditions.But the data for the method are already technically outdated enough [2,3].DTC and FOC methods associated with direct self-control of the starting torque were introduced into the industry at the end of the 80s of the last century [4][5][6].
Commercial use in manufacturing lock valve drives was developed in the mid-90s of the last century [7].The presented methods did not allow ensuring completely the stable operation of the electric motor in the low-speed range, and did not allow getting rid completely of the torque ripples at the start.There are also known methods of variable load control and space-vector modulation (SVM), which provide more stable operation of an AC motor at low speed discussed in [8].Improvements to the DTC method can be found in [9], but even all the improvements do not allow controlling efficiently the lock valve drive without the use of a gearbox.In parallel with the methods considered above, MPC methods based on the use of power electronics were developed.They are considered in works [10][11][12][13][14].There are various options of the MPC implementation, for example, FCS-MPC used for motor start control, but it requires significant computational power of the control system due to the fact that it is necessary to calculate the weighting factors for all possible transients.Many researchers have improved this method with a combination of modern control methods to increase the MPC reliability [15][16][17].It also provides the information of the empirical procedure for obtaining suitable weighting factors [18].Direct use of the considered methods is impossible to control the drive without a gear valve, since at the start it is possible that the stem will be stationary due to the slagging of the cone.In this situation, the current protection must be triggered in order to prevent the failure of the electric motor.The value of the phase current should change in a small range in all the operating modes of the electric drive, from idle to short circuit.It is also desirable to remove the current and thermal protection from the electric circuit of the drive and not to introduce into the control system a time limit for working out a given movement.This requires a different drive control principle and a completely different design.So in [19] there is the information of induction machines that have a strongly nonlinear characteristic; it also presents the results of research carried out on a 50 HP asynchronous motor driven by a three-phase inverter, which provides high-quality speed and torque control.The IM torque control IM using FOC has been considered quite often in past studies; in [20] various methods of slip control are presented for different modes of starting an electric motor at different loads.There is also the information of the adaptive control of the sliding mode [21].Work [17] proposes simplified models for convenient fixation of transient processes of an AC electric motor, which can be used in the design of induction machines, but this model is rather simplified and has lost its relevance at the present time [22].There are studies presented in [23] related to duty cycle modulation, direct torque control, brushless machines with double feed.For brushless double feed machine (BDFM), traditional direct torque control (DTC) has many problems such as a large output torque ripple and undefined inverter switching frequency.The presented control method has several advantages over traditional direct torque control, while reducing the ripple flux linkage.There are also proposed measures to optimize direct torque control.The SVM -DTC algorithm [4] can effectively reduce the torque ripple, but it requires large calculations and additional parameters, which cannot be used for lock valves due to the increased cost of the control system.There is some information of the methods of monitoring the magnetic fields of permanent magnet synchronous machines using a Texas Instruments F28343 200 MHz microcontroller [25].There are similar works related to the regulation of electric machines with permanent magnets, which provide an algorithm for finding the optimal current vector [26], analytical solutions [27] and the search for methods to minimize losses [28,29].There are research results in the aspect close to this work, where the reversible dependence of the speed and the time of an asynchronous machine at start-up without load and with load is considered, based on the induction parameters.There is presented an equivalent circuit of the machine and a description of the torque equation method.Analytical expressions of the speed dependence on the time of an asynchronous machine with a direct start are considered.
The process of starting an electric motor with a large starting torque is a rather serious scientific and practical problem [31,32].IM starting methods are based on the use of soft starters [33] or by shunting the stator and rotor windings, which are quite outdated [34], as well as on the use of power electronic devices [35].In work [36], there is presented the calculation of the permanent magnet synchronous machine parameters, taking into account characteristics of the load.
Let's list the main requirements that must be taken into account when designing drives for lock valves [37]: • a high degree of protection from the environment.As a rule, motors and control systems are designed with protection not less than IP54 (closed, protected design allowing the presence of water jets at any point on the outer surface of a technical object); • significant excess of the maximum torque at start, in comparison with the nominal value with free movement of the stem.So, examining a high-pressure steam valve with a setup diameter of 20 mm, it was found that in the nominal mode, the torque of 5-10 Nm is required (depending on the equipment wear), and when the "slagged" stem is torn off in the closed state, the torque increases to 80 Nm; • low speed of the drive output shaft at the level of 10 -20 rpm, which should exclude the possibility of hydrodynamic shock.Therefore, in drives that do not provide for speed variation and operating in the "start-stop" mode, it is necessary to use gearboxes with a large gear ratio.Traditionally, in such valves, asynchronous motors are most often used.They are designed for an output shaft speed of 1000 and 1500 rpm.Therefore, for them, the minimum value of the reduction factor is 50 units, and this is a rather complex and expensive technical object; • there are practically no requirements regarding the limitations of the dimensions and weight of the electric actuator of lock valves; • difficult access to many objects of the lock valves.This feature is most significantly manifested in heating plants, as well as in the areas of oil and gas pipelines remote from settlements; • high reliability of protection of motor windings from overheating and maximum permissible currents.
The analysis of the above-mentioned data inevitably leads to the need of solving the problem in which two mutually exclusive requirements are laid: the first one is taking into account the peculiarities of operation.It is necessary to simplify the control system as much as possible, since the elements of power electronics are most susceptible to the effect of the environment and are the "weak link" of the entire drive.The second one consists in that if you design a drive that does not include the possibility of speed regulation, then in the starting mode the current in the windings will increase 5 -8 times.
This means that if within a short time interval the torque on the shaft does not decrease to the nominal value, the current protection must be triggered.In such a situation, when there is not enough time to start the movement of the stem, there is a need for repeated (or multiple) switching on the drive, and, in extreme cases, the use of human physical strength [38][39][40].Thus, the ideal solution to this problem is the use a motor in the drive with the following characteristics: • when connected to an industrial network of alternating current 50 Hz (or 60 Hz), the shaft rotation frequency will be 10 -120 rpm, which will either get rid of the gearbox in the drive kinematic diagram, or eliminate the problem of developing a complex mechanical transmission; • the value of the specific moment (the ratio of the moment to the mass of the drive) is comparable to that of a drive containing an asynchronous motor and a gearbox [41]; • there are no moving contacts due to the presence of a collector, slip rings, etc.This condition is most significant when it comes to the explosion-proof version of the drive; • the value of the phase current varies in a small range for all modes of operation, from no-load to short-circuit.If this condition is met, then it becomes possible to remove the current and thermal protection from the drive and not to introduce into the control system a time limit for the specified movement.
This set of requirements is most satisfied by inductor motors with electromagnetic speed reduction.For example, if we take an inductor machine with a distributed winding on the stator and a ring magnet on the rotor, then the excitation field for it will be determined as where 0 m B is the constant component of magnetic induction due to the flow of magnets; Here: unchanged dimensions, electrical losses, the number of pole pairs and the current density will be equal to: which is in complete agreement with earlier estimates, for example, in [42,43].Now let us compare the capabilities of two inductor machines with excitation from ring permanent magnets, provided that one of the machines has a distributed winding on the stator, and the other one has a winding with a toothed pitch [44,45].To simplify the analysis, we represent the excitation field and MMF in the form of idealized discrete Rademacher functions, as it was done in [42].If we do not touch upon the design features of the magnetic system and assume that the fundamental harmonic of the field is the same as in the previously considered cases, then: Here s z is the number of elementary teeth located on the inner surface of the large teeth, in the grooves between which the winding is laid; Using the previously obtained expressions [46,47], we find the ratio of the moments of an inductor motor with a distributed winding on rotor and a synchronous machine with permanent magnets on the rotor: where s z , based on the recommendations for selecting the geometry of the notched- groove zone [48], takes values from three to six.Thus, in the linear formulation of the problem, the torque of the inductor motor is (4.6 -6) times higher than that of a synchronous machine with magnets!This gives grounds to assert that the proposed engine has solid technical advantages over other types of electrical machines and can be considered as the basic option when designing a lock valve drive with a coaxial planetary gear.

Mathematical model
The most famous representative of electric machines with an axial flow is a twophase stepper motor with electromagnetic speed reduction made according to [45].The motor contains a toothed two-pack rotor and a stator.An annular magnet is located between the packages of the rotor and produces a unipolar magnetic flux within each half of the machine.There are eight large teeth on the stator, on the inner surface of which there are elementary teeth with a toothed division close to or equal to the tooth division on the rotor.The coils belonging to phase A are placed on large stator teeth, the geometric angle between which is 90 degrees.The other 4 teeth with coils belong to phase B. In the considered design, several negative factors can be distinguished.
1. To develop a large unipolar flux, it is necessary to increase to the limit the ratio of the bore diameter to the inner diameter of the rotor.Otherwise, it is necessary to reduce the length of each stator (rotor) package or to develop a multi-package structure.However, such a step will entail relative increasing the non-working zones (between packets) and, as a consequence, decreasing the specific moment.
2. To close the unipolar flux along the stator, a massive ferromagnetic housing is required.(To eliminate this negative factor, the French company SAGEM makes the stator packages not lined but limits the maximum rotational speed to 18 -20 rpm).
3. With a small cross-section of the groove, it is impossible to develop armature flux of the required magnitude, since it closes along a long path (a quarter of the circumference) with high magnetic resistance.Additional decreasing is due to the branching of magnetic field lines in the area where there are no currents (2, 4, 6, 8 -Figure 1), which is clearly demonstrated by the problem of graphic -analytical calculation of the field.each of which has large teeth with coils belonging to the same phase.The coils are in aiding connection in order to reinforce mutually each other's magnetic fluxes.Permanent magnets are located between the segments developing a radial field of excitation of the same polarity within the segment.Thus, if one coil amplifies, the other weakens the resulting field.
In contrast to the two-phase analogue considered above, here, due to the magnetic isolation of the segments, the armature field is weakened only due to the scattering fluxes and, as calculations show, it turns out to be 10-15 % greater than the field under the large teeth 1, 5 (Figure 3 ).Another positive feature of the motor is that the excitation flow and the armature flow are closed in different parts by a yoke and come together only in the "right places": the air gap and the large tooth.For example, the excitation flux from the top magnet in Figure 4 closes along large teeth 1, 12 and the areas with a yoke between them, and the anchor flow closes only along large teeth 1, 2 and the areas with a yoke between them.This allows minimizing the height of the rotor yoke and designing the motor with a large internal bore in the shaft required for the valve stem to pass.

Figure 2. Electric motor design
It is also important that there is no unipolar flux (magnetic circuit) in the machine under consideration, which greatly simplifies the design of the motor.We also note the main feature of the proposed technical solution: the absence of a rotating magnetic field, which at first glance contradicts the fundamental provisions of the general theory of electrical machines.This "paradox" is explained as follows.Let's select in the motor large teeth (segments), within which the field of excitation has the same direction: 1, 2 -phase A; 5, 6 -phase C; 9, 10 -phase B. Suppose that with a fixed position of the rotor, magnetic conductivity of the air gap within each large tooth is determined as shown in Figure 3 and is provided with a different distance between adjacent elementary teeth located on different large teeth.In this case, it can be assumed that within each large tooth, "its own rotor" rotates with the such a machine into six parts and rearrange its individual fragments accordingly, then the mathematical analogue of a real motor will look as shown in Figure 4.
Figure 3 Figure 4 Air gap magnetic conductivity within each large tooth with a fixed rotor position

Control algorithm
Figure 5 shows a possible algorithm of controlling an electric drive using a voltage inverter (VI), in which the torque of the electric motor operating at maximum speed is regulated.The algorithm is based on the ideas of work [43].
To ensure the required ratio between the fundamental and higher time harmonics of the current, negative feedbacks on the motor currents are used.In this case, in the rotating coordinate system, a signal is set by the first and fifth harmonics, and the assignment for the 5th harmonic is determined by the ratio ) (t  is the instantaneous value of the phase of the VI output voltage that is set using the rotor position sensor (RPS).The shape of the assignment total signals along the orthogonal axes is shown in Figure 6.
The signals of the third harmonic form a zero sequence and therefore are formed in the "A-B-C" axes according to the relation where ( ) To obtain astatic regulation of the fundamental harmonic of the electric motor currents, PI controllers are used with transfer characteristics of the form: The transfer characteristic itself in the torque control channel (TR) in the general case has the form . ) ( The nature of the dependence of these coefficients on the magnitude of the M ~moment is shown in Figure 5.
As a result of using the proposed algorithms, the shape of the resulting current in the motor phases will have the form close to that shown in Figure 7.
The above studies made it possible to design and to manufacture a high-torque inductor-type electric motor intended for operation as a part of a controlled electric drive.
The criterion of optimality in the calculation was proposed the function The forced formation of the third and fifth time harmonics, alongside with organization of a no-current pause near the point of transition of the function i(t) through zero (about 60 degrees), made it possible at the same current amplitude to increase the torque by 37 % with simultaneous decreasing of losses by 18 %.

Analysis
When analyzing the models shown in Figures 3, 4 2. The electrical machine shown in Figure 4 has all the disadvantages of a two-phase stepper motor and undoubtedly loses in its technical characteristics to the motor shown in Figure 3, but in the linear formulation of the problem it turns out to be identical to it.
The equations for own and mutual inductances for the mathematical model (Figure 4) are similar to those derived earlier in [47].
To derive the equations of stress and moment, we will use the modified Rademacher functions, the basic concepts of which, as well as the methods of calculating inductances with their help, are set forth in [50].After carrying out the necessary mathematical operations, the expressions for own and mutual (with respect to the "excitation winding") inductances will be obtained in the following form: Here: m = 3, 5, 7 ... is the number of phases; k = 1, 2, 3, … is a positive integer.
Having performed transformations using the method of symmetric components and assuming for the steady-state mode of operation that the operator p is equal to zero, and

Results
The above studies made it possible to design and to manufacture a high-torque inductor-type electric motor intended for operation as part of shut-off valves (Figure 8).The max / → Р М function was proposed as the optimality criterion in the calculation, where P is the electrical losses in the windings, and the constraints are the dimensions of the electric machine.
This study can be developed in the direction of simplifying the circuit, which will provide a minimum number of elements.This will lead to the use of the maximum torque, and the solution will be to bring the control system with a circuit on the limit switches.
Below there are the main parameters of the electric mechanism that includes an inductor motor and a planetary mechanical transmission:

Preprints
(www.preprints.org)| NOT PEER-REVIEWED | Posted: 12 October 2021 doi:10.20944/preprints202110.0189.v1 the coefficient of the magnetic conductivity of the air gap pulsation; 2 z is the number of rotor teeth;  is the number of periods of changing magnetic conductivity equal to the number of pole pairs  = p ;  is the angle along the inner surface of the stator; the angle of rotation of the rotor; p  is the angular frequency of rotation.In the linear formulation of the problem, substituting (1) into the energy equation and differentiating the result by the angle of rotation of the rotor, we obtain the expression for the moment stator inner diameter and active length; 0  is the initial value of the angle of rotation of the rotor.The number of rotor teeth and the number of pole pairs in an inductor machine with axial excitation, having an electromagnetic speed reduction, is related by the ratio: Then the ratio of the maximum moments of an inductor machine with an axial flux and a classical synchronous machine with permanent magnets on the rotor with Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 12 October 2021 doi:10.20944/preprints202110.0189.v1 between the maximum possible and accepted in the design of the s z value.

Figure 1 .
Figure 1.Graphic-analytical calculation of the field.

p z  2 frequency.
It presents a ferromagnetic segment located with the eccentricity relative to the stator and having "its own initial phase".If we mentally cut Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 12 October 2021 doi:10.20944/preprints202110.0189.v1

RectifierFigure 5 .
Figure 5. Algorithm of controlling an electric drive using a voltage inverter (VI)

Figure 6 .
Figure 6.The shape of the assignment total signals along the orthogonal axes Here ensure the dependence of the orthogonal components of the electric motor current on the magnitude of the torque, the

Figure 7 .
Figure 7.The shape of the resulting current in the motor phases

1 .
, the following conclusions can be drawn: Rotating waves of MMF and magnetic conductivity ) , (    in Figure 3 are replaced by pulsating waves acting within each phase in Figure 3.At this, the spatial and time characteristics tooth remain unchanged. ),(15) are derived for the case when instead of permanent magnets, a winding with the 0 w number of turns develops a radial excitation flux.If the machine uses magnets, then flux linkage is considered as

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 12 October 2021 doi:10.20944/preprints202110.0189.v1
If positive voltage is applied to phase A, then under two diametrically located large teeth, the unipolar field is enhanced, and under large teeth that are offset by the angle of 90 degrees, it is weakened.With an appropriate selection of the number of elementary teeth on the stator and rotor 1