Extended Permanent Magnet Synchronous Motors Speed Range Based on the Active and Reactive Power Control of Inverters

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Article Extended Permanent Magnet Synchronous Motors Speed Range Based on the Active and Reactive Power Control of Inverters

Pham Quoc Khanh 1,* , Viet-Anh Truong 2 and Ho Pham Huy Anh 3

1 Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City (IUH), Ho Chi Minh City 70000, Vietnam 2 Faculty of Electrical and Electronics Engineering, University of Technology and Education, Ho Chi Minh City 70000, Vietnam; [email protected] 3 Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City 70000, Vietnam; [email protected] * Correspondence: [email protected]; Tel.: +84-934-093-716

Abstract: The paper proposes a new speed control method to improve control quality and expand the Permanent Magnet Synchronous Motors speed range. The Permanent Magnet Synchronous Motors (PMSM) speed range enlarging is based on the newly proposed power control principle between two voltage sources instead of winding current control as the conventional Field Oriented Control method. The power management between the inverter and PMSM motor allows the Flux-Weakening obstacle to be overcome entirely, leading to a significant extension of the motor speed to a constant power range. Based on motor power control, a new control method is proposed and allows for efficiently reducing current and torque ripple caused by the imbalance between the power supply of the inverter and the power required through the desired stator current. The proposed method permits for not only an enhanced PMSM speed range, but also a robust stability in PMSM speed control. The simulation results have demonstrated the efficiency and stability of the proposed control method. Citation: Khanh, P.Q.; Truong, V.-A.; Anh, H.P.H. Extended Permanent Keywords: permanent magnet synchronous motors (PMSM); active power control; reactive power Magnet Synchronous Motors Speed control; extended speed range; ripple torque reduction; flux-weakening (FW) Range Based on the Active and Reactive Power Control of Inverters. Energies 2021, 14, 3549. https:// doi.org/10.3390/en14123549 1. Introduction Academic Editor: Nicu Bizon Permanent Magnet Synchronous Motors (PMSM) are increasingly widely used in civil and industrial applications because of their high efficiency, high power density, low main- Received: 10 May 2021 tenance cost, and lower permanent magnet price. The vector control method’s popularity, Accepted: 9 June 2021 including Field Oriented Control (FOC) [1–6] and Direct Torque Control (DTC) [7–10], Published: 15 June 2021 stems from its advantages of simplicity in the control structure, ease of operation, reliability, and high efficiency [11,12]. Publisher’s Note: MDPI stays neutral There are two main parts of the operating speed range of PMSM operation, including with regard to jurisdictional claims in constant torque range and constant power range, as mentioned in Figure1. The speed published maps and institutional affil- control principle in the constant torque region (in which the PMSM rotor speed is below iations. the rated speed) is suitable for the vector control method when the operating voltage is lower than the inverter output voltage limit. When the PMSM speed exceeds the rated speed, the Back Electromotive Force (B-EMF) generated in the winding, caused by a permanent magnet flux on the rotating rotor in the lumen of the stator windings, can Copyright: © 2021 by the authors. increase beyond the limit of the voltage of the inverters. For motors that do not use Licensee MDPI, Basel, Switzerland. permanent magnets, such as induction motors, reducing the current rotor windings can This article is an open access article reduce the BEMF voltage [13–15]. Unfortunately, this way is not possible with rotor motors distributed under the terms and that use permanent magnets. Due to the limit of output voltage, the inverter cannot increase conditions of the Creative Commons the voltage to stabilize the stator current control. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Energies 2021, 14, 3549. https://doi.org/10.3390/en14123549 https://www.mdpi.com/journal/energies Energies 2021, 14, x FOR PEER REVIEW 2 of 17

permanent magnets. Due to the limit of output voltage, the inverter cannot increase the voltage to stabilize the stator current control. The input DC voltage is proportional to the maximum amplitude of the output voltage of the inverter. Therefore, in some studies, the expansion of the motor operating speed is achieved by increasing the inverter input voltage [16,17]. However, the step-up voltage method encounters the main limitation of expanding the power drive room for DC–DC voltage converter circuits, and only changes in a narrow speed range. In addition, inverters are designed to operate within a specific voltage limit. Increasing DC voltage to increase motor speed increases inverter costs in applications requiring a high-speed operation. To ensure that the active power is transmitted to the motor, the reactive power is drawn out of the inverter to ensure that a low voltage amplitude source can push power into a higher voltage source. Then, the d-axis current increases the negative amplitude Energies 2021, 14, 3549 during entering the FW region, which manifests reactive power inflowing from the PMSM2 of 16 to the inverter.

Constant Constant Power Torque Power Range decreasing Range Voltage Power

torque

Rated Speed speed

FigureFigure 1. 1. TheThe operating operating speed speed range range of of PMSM PMSM..

OnThe the input other DC hand, voltage during is proportional operation in to the maximumFW zone, the amplitude inverter of voltage the output cannot voltage ex- ceedof the the inverter. inverter Therefore, output voltage in some limit. studies, However, the expansion controlling of the stator motor current operating using speed cur- is rentachieved controllers by increasing will cause the the inverter estimated input controllervoltage [16 output,17]. However, voltage the to exceed step-up a voltage given boundary.method encounters This trouble the leads main to limitation an increase ofd expanding stator current the powerripple, driveresulting room in forincreasing DC–DC electromagneticvoltage converter torque circuits, ripple and and only reducing changes the in a efficiency narrow speed in reference range. In velocity addition, tracking. inverters are designedSeveral improvements to operate within have a specificbeen used voltage in PMSM limit. speed Increasing control DC in voltage FW to to improve increase controlmotor speedefficiency increases and reduce inverter current costs ripple in applications during voltage requiring limit a violation high-speed in the operation. FW zone. TheseTo methods ensure include that the the active Auto power-tuning is method transmitted [18–20] to, theFuzzy motor, Logic the Speed reactive Control power [21– is 25]drawn, Improved out of theUDE inverter-Based toFlux ensure-Weakening that a low Control voltage [26] amplitude, and Single source Current can push Regulator power into a higher voltage source. Then, the d-axis current increases the negative amplitude Control [27–30]. during entering the FW region, which manifests reactive power inflowing from the PMSM When entering the FW zone, the d-axis current is adjusted to increase negatively to the inverter. based on the PI controller, where input is the deviation between the maximum voltage On the other hand, during operation in the FW zone, the inverter voltage cannot amplitude supplied by the inverter and the voltage at the current controller output. As exceed the inverter output voltage limit. However, controlling the stator current using the voltage fluctuation is more extensive in the FW region, the d-axis current ripple also current controllers will cause the estimated controller output voltage to exceed a given increases. The fuzzy logic speed control method reduces the d-axis current ripple desired boundary. This trouble leads to an increased stator current ripple, resulting in increasing by replacing a PI controller with a Fuzzy PI controller. The Fuzzy PI current controller’s electromagnetic torque ripple and reducing the efficiency in reference velocity tracking. output voltage is less violated than the PI current controller, leading to a reduced ripple Several improvements have been used in PMSM speed control in FW to improve of the d-axis current component. However, this violation’s nature persists and adversely control efficiency and reduce current ripple during voltage limit violation in the FW zone. affects the control quality when the current controller output voltage estimated value still These methods include the Auto-tuning method [18–20], Fuzzy Logic Speed Control [21–25], exceedsImproved the UDE-Basedlimit voltage Flux-Weakening value of the inverter. Control [26], and Single Current Regulator Con- trol [27–30]. When entering the FW zone, the d-axis current is adjusted to increase negatively based on the PI controller, where input is the deviation between the maximum voltage amplitude supplied by the inverter and the voltage at the current controller output. As the voltage

ﬂuctuation is more extensive in the FW region, the d-axis current ripple also increases. The fuzzy logic speed control method reduces the d-axis current ripple desired by replacing a PI controller with a Fuzzy PI controller. The Fuzzy PI current controller’s output voltage is less violated than the PI current controller, leading to a reduced ripple of the d-axis current component. However, this violation’s nature persists and adversely affects the control quality when the current controller output voltage estimated value still exceeds the limit voltage value of the inverter. Single Current Regulator Control approach allows elimination of the output voltage violation when the voltage amplitude is kept at the rated value, as shown in [29]. However, the voltage angle change is based on a current error, without considering the inverter power balance and the load power caused by the wave. Results are demonstrated in [29], on the proposed solutions of Single Current Regulator Control method proposed in [27,31]. Energies 2021, 14, 3549 3 of 16

Research [29] can only minimize power imbalance by limiting voltage angle variation, but does not wholly address the power imbalance’s harmful effects. Another creative direction in minimizing current and torque ripple in the FW region aims to optimize the current controller parameters. The PSO algorithm is used in [32] to find suitable values when working conditions were changed. A Fuzzy-PI controller is used instead of the PI controller in the more refined determination of the d-axis reference current when the motor operates in the FW region. These innovative methods minimize output torque ripple, while reducing the reference current’s effect on the control voltage. However, these methods increase the complexity, and require an amount of computation in the speed control process of PMSM. The novelty and contributions of this paper are tri-fold. Firstly, this paper proposes the new PMSM speed control based on balancing the output inverter energy and the motor’s load energy. The proposed approach differs from the known solution because it does not use rated speed to switch from a constant torque region to an FW region. A change in reactive power leads to a change in rotor speed. Second, the energy transformation to the machine is done by sending energy between two voltage sources, the inverter output voltage and the BEMF of the motor. Eventually, a detailed analysis of the power transmission principle between the two voltage sources is discussed in the following section. Over the entire operating speed range of the PMSM, the increase (or decrease) of the rotor speed is accomplished by increasing (or decreasing) the active power of the inverter, which enables the roaming to operate without the need to switch different control methods between the two operating zones. Power control will minimize current and torque ripple, and the power supplied to the PMSM will also better monitored. This advantage is especially significant in mobile systems with batteries. The new control method allows efficient reduction of the electric current and torque ripples in the motor through direct control of the inverter output voltage. The remainder of this paper is structured as such: Part 2 presents the PMSM math model and the principle of transferring power from the inverter to the PMSM; Part 3 introduces the principle of controlling a PMSM motor’s speed based on the active power control; Part 4 shows the results obtained after the simulation modeling for the proposed algorithm with the Direct Current Calculation and Vector Current Control algorithms used in the comparison; Part 5 includes the conclusion.

2. Speed Control of PMSM Drive Systems 2.1. PMSM Model and Its Limitations According to [33], Equations (1) and (2) show the relationship between stator voltage, stator current, and rotor speed. The dq coordinate system is performed through the Park transformation, converting from the abc three-dimensional space to the dq two-dimensional space with almost constant values.

i v = R × i +L × d − Pp × ω × L × i (1) d S d d dt m q q

iq v = R i + L + Pp.ω .L .i + Pp.ω .λ (2) q S q q dt m d d m pm

where vd, vq, id and iq are the components voltage and current on the dq-axis, respectively. Ld and Lq are the stator coil inductance components in the dq coordinate system, λpm is the ﬂux linkage of the permanent magnet on the rotor, RS is the coil resistance, ω is the rotor speed, and Pp is the number of pole pairs. When analyzing the PMSM in the stationary state, the current variation is zero; the voltage Equations are rewritten in (3) and (4).

vd = RS × id − Pp × ωm × Lq × iq (3)

vq = RS × iq + Pp × ωm × Ld × id + Pp × ωm × λpm (4) Energies 2021, 14, 3549 4 of 16

Electromagnetic torque is determined by (5)

3 T = × Ppλ × i + L − L × i × i (5) e 2 pm q d q q d According to Newton’s Second Law for Rotation, the rotational acceleration of the rotor is determined by (6). dω 1 m = (T − T − Fω ) (6) dt J e L m where: J: The inertia of motor and load combined referred to the motor shaft. F: The combined viscous friction coefﬁcient of rotor and load. θ: Rotor angular position. TL: Shaft load torque. θm: Angular velocity of the rotor (mechanical speed) During operation, the stator voltage and current are limited below their rated values. The voltage limit is determined based on the motor insulation capacity and the maximum voltage amplitude generated by the inverter, determined by the dc bus voltage. Current limits are usually related to the motor heat dissipation, and the manufacturer provides its value. The Equations described the limits of voltage and current are expressed through (7) and (8), respectively: 2 2 2 2 vd + vq = vs ≤ vs,max (7) 2 2 2 2 id + iq = is ≤ is,max (8)

where vs represents the vector amplitude of the stator voltage, vs,max is the maximum output voltage of the inverter, is is the vector amplitude of the stator current, and is,max denotes the maximum output current of the inverter. When the PMSM motor speed exceeds the rated speed, it is possible to ignore the voltage drop on the stator coil since they are insigniﬁcant in comparison to the back EMF on the stator winding. On the other hand, in the steady-state, the ﬂux linkage is considered constant, resulting in the derivative of the current to zero (did/dt = 0; diq/dt = 0). Therefore, the stator voltage Equations in (1) and (2) are rewritten as follows:

vd = −ωeLqiq (9)

vq = ωeLdid + ωeλpm (10) Substitute (9) and (10) into (7), the stator voltage limit in the constant power region is described by (11). v2 2 + + λ 2 ≤ s,max Lqiq Ldid pm 2 (11) ωe The voltage and current restriction relationships of the IPMSM in the whole region are shown in Figure2, which indicates both of the voltage-limiting circle and current-limiting circle. Energies 2021, 14, x FOR PEER REVIEW 5 of 17 Energies 2021, 14, x FOR PEER REVIEW 5 of 17

The voltage and current restriction relationships of the IPMSM in the whole region Energies 2021, 14, 3549 The voltage and current restriction relationships of the IPMSM in the whole region5 of 16 areare shown shown in in Figure Figure 2 ,2 which, which indicates indicates both both of of the the voltage voltage-limiting-limiting circle circle and and current current- - limitinglimiting circle. circle.

voltagevoltage-limiting-limiting circlecircle CurrentCurrent-limiting-limiting circlecircle iq iq

id O id CC O

Figure 2. Operating regions of PMSM in dq component current plane. FigureFigure 2.2.Operating Operating regionsregions ofof PMSMPMSM inin dqdq componentcomponent currentcurrent plane. plane.

2.2.2.2.2.2. Principle PrinciplePrinciple of ofof Transferring TransferringTransferring Power Power Power from from from the the the Inverter Inverter Inverter to to to the the the Motor Motor Motor Consider the static state of the PMSM working with speed ω1 and electromagnetic ConsiderConsider thethe static state state of of the the PMSM PMSM working working with with speed speed ω1 ωand1 and electromagnetic electromag- torque Te1. the electromagnetic torque must balance with the load torque (friction torque netictorque torque Te1. the Te1 electromagnetic. the electromagnetic torque torque must balance must balance with the with load the torque load torque (friction (friction torque included) to keep the speed constant. At this time, the motor provides the power P1 (P1 = torqueincluded) included) to keep to the keep speed the constant. speed constant. At this Attime, this the time, motor the provides motor provides the power the powerP1 (P1 = ω1 × Te1). Ignore the energy conversion losses and the stator winding losses, and the PMSM Pω11(P × T1 e1=).ω Ignore1 × Te1 the). Ignoreenergy the conversion energy conversion losses and lossesthe stator and winding the stator losses, winding and losses, the PMSM and powerthepower PMSM consumption consumption power consumption is is equal equal to to the isthe equalinverter’s inverter’s to the electrical electrical inverter’s power. power. electrical power. The inverter needs to provide a power P2 (P2 = ω2 ×× Te2) in converting this operating TheThe inverterinverter needs needs to to provide provide a a power power P 2P(P2 (P2 =2 = ω2 2 × TTe2e2) in converting thisthis operatingoperating point to a new one with velocity ω2 and electromagnetic torque Te2. Thus, the working pointpoint toto aa new new one one with with velocity velocity ω2 2and and electromagnetic electromagnetic torque torque T Te2e2.. Thus,Thus, thethe working working conditionconditioncondition change changechange is isis to toto change changechange the thethe power powerpower supplied supplied supplied to to to the the the motor motor motor from from from the the the inverter. inverter. inverter. ChangingChangingChanging the the the rotor rotor rotor speed speed cannotcannot cannot bebe be instantaneousinstantaneous instantaneous but but but takes takes takes a a short ashort short time time time with with with a specifica aspe- spe- cificroute.cific route. route. During During During this this process, this process, process, the the inverter’s the inverte inverte powerr’sr’s power power can can changecan change change with with with the the principle the principle principle that that ifthat the if if thepowerthe power power increases, increases, increases, the the speed the speed speed will will increase,will increase increase and, and, viceand vice versa.vice versa. versa. WhenWhenWhen the thethe rotor rotor rotates rotates once, once, once, the the the permanent permanent permanent magnet’s magnet’s magnet’s magnetic magnetic magnetic field field field will will willsweep sweep sweep Pp Pp timesPptimes times the the number thenumber number of of coils coils of on coilson it. it. Thus,on Thus, it. the the Thus, BEMF BEMF the generated generated BEMF generated when when th the whenepermanent permanent the permanent magnet’s magnet’s magneticmagnet’s field magnetic turns fieldwith turns the speed with theωm speedinducedωm oninduced the stator on thecoil statoris determined coil is determined by Fara- magnetic field turns with the speed ωm induced on the stator coil is determined by Fara- by Faraday’s induction law (12). day’sday’s induction induction law law (12) (12). .

=E= Pp× ω m× λ pm (12) E PpE= Pp m m pm pm (12)(12)

WithWithWith the thethe synchronous synchronoussynchronous motor motormotor in inin the thethe stationary stationarystationary state, state,state, the thethe magnetic magneticmagnetic field fieldfield speed speedspeed equals equalsequals the rotor speed, ωe = ωm × Pp. The Equation (12) is rewritten according to the stator mag- thethe rotorrotor speed,speed, ωee == ωωm m× Pp.× Pp. The The Equation Equation (12) (12)is rewritten is rewritten according according to the to stator the stator mag- neticmagneticnetic field field rate, field rate, as rate, as shown shown as shown in in (8). (8). in (8). E =   E = e  pm (13) E = ωe ×eλpm pm (13)(13) WhenWhen two two altern alternatingating current current sources sources have have the the same same rotating rotating speed speed of of the the magnetic magnetic When two alternating current sources have the same rotating speed of the magnetic field,field, based based on on recommendations recommendations in in [33] [33], Figure, Figure 3 3represented represented the the equivalent equivalent circuit circuit of of thesefield, two based voltage on recommendations sources. in [33], Figure3 represented the equivalent circuit of thesethese twotwo voltagevoltage sources.sources.

RS LS RS LS IS IS

US E=ωe ⅹλpm US E=ωe ⅹλpm

Figure 3. Equivalent circuit of PMSM in steady-state [33].

Energies 2021, 14, x FOR PEER REVIEW 6 of 17

Energies 2021, 14, 3549 6 of 16

Figure 3. Equivalent circuit of PMSM in steady-state [33].

AccordingAccording to to Figure Figure 11, ,the the transparent transparent power power transmitted transmitted to to the the BEMF BEMF terminal terminal is is determineddetermined according according to to (14) (14) with with the the current current determined determined according according to to (15) (15)::

S= 3  E  IS (14) S = 3 × E × IS (14) U − E  00 | S| δ − | | 0 IS = US ∠ E ∠0 (15) IS = Z  (15) |ZSS|∠β FromFrom Equations Equations (14) (14) and and (15) (15),, we we get get

2 2 |UUEES|S×|E| |E| S =S3= 3∠ ((β  − δ)) −− 3 3 ∠ β (16(16)) |ZZZSSS| |ZS|

TheThe active active and and reactive reactive power power is derived is derived from from (16) (16)and anddetermined determined according according to (17) to and(17) (18) and respectively. (18) respectively.

2 |U UEE| ×|E| |E|2 P =P3= 3S S cos cos(β  − δ) −− 33 coscos  β (17) | | ( ) | | (17) ZSZZSSZS

2 2 |USUEE| ×|E| |E| Q =Q3= 3S sin sin(β  − δ) −− 33 sinsin  β (18) |ZS| ( ) |ZS| (18) ZZSS ◦ If resistance is neglected, then Zs = XL and β = 90 . At this time, Equations (17) and (18) ° areIf rewritten resistance as (19)is neglected, and (20), then respectively, Zs = XL asand follows. β = 90 . At this time, Equations (17) and (18) are rewritten as (19) and (20), respectively, as follows. |US| × |E| P = 3 UES  sin δ (19) P= 3XL sin (19) XL |E| Q = 3 E(|U | cos δ − |E|) (20) X S Q= 3L ( US cos  − E ) (20) X The active power P transmitted betweenL the two voltage sources is determined by theThe Equation active (21) power where P transmittedδ is an angular between deviation the two between voltage the sources phase of is invertersdetermined voltage by thevector Equation and phase(21) where of back δ is electromotive an angular deviation force vector between in the the stator phase winding, of inverters as shown voltage in vectorFigure and4. In phase order of to back stabilize electromotive PMSM operations force vector under in electric the stator motor winding, drive mode, as shownδ is kept in Figurewithin 4. (0; In πorder/2). to stabilize PMSM operations under electric motor drive mode, δ is kept |U | × |E| × sin δ within (0; π/2). P = 3 S (21) XL

θ δ id

Figure 4. Vector diagram of the voltages on the stator winding in the current plane in the dq axis. Figure 4. Vector diagram of the voltages on the stator winding in the current plane in the dq axis.

Energies 2021, 14, 3549 7 of 16

The two voltage sources’ impedance value is kept constant in the stationary state, with a constant rotor velocity according to (23), with a new inductance determined according to (10). The amplitude of BEMF is determined based on (13).

L = Ld = Lq (22)

(XL = ωe × L) (23) Combined with (13) and (23), the power applied to the motor from the inverter is determined according to (24).

|US| × λpm × sin δ P = 3 (24) L

During operation, L and λpm have slight changes due to magnetic saturation and magnet temperature. However, in comparison with US and δ, this change is not signiﬁcant and can be ignored. Therefore, we can consider that L and λpm are constants in the control process. We can calculate transmitted power based on (25) where constant k = 3 × λpm/L.

P = k × |US| × sin δ (25)

During operation, the inverter provides active power P to the motor. Reactive power Q does not participate in the transfer of energy from the stator to the rotor, but only serves as the power supply for the magnetization of the magnetic circuits. The reactive power Q only plays a speciﬁc role in the switching support, so the goal is to minimize the reactive power Q supplied to the BEMF source. The goal in motor control is zero reactive power QR at the BEMF end. Thus, the reactive power Q at the stator head only compensates for the magnetic circuit’s loss. The reactive power Q obtained at the BEMF input is determined according to (20). For Q = 0, then US must satisfy (26).

E U = (26) S cos δ When considering the internal resistance of the stator winding, the voltage drop across the winding is determined as follows: ∆U = IsZ = Id + jIq (RS + jXL) = IdRS − IqXL + j IqRS + IdXL (27) Due to IqRS + IdXL IdRS − IqXL , it leads to the voltage drop magnitude which is calculated by (28). |∆U| ' IqRS + IdXL (28) Combined (26) and (28), the inverter voltage amplitude is calculated according to (29).

E |U | = + I R + I ω L (29) S cos δ q S d e

Thus, the active power P to change the working point from the point with power P1 to the operation point with power P2 is determined by adjusting the inverter voltage range. The angle δ is calibrated to the new working point, so that the reactive power supplied to the BEMF is zero.

3. The Principle of Controlling the Speed of a PMSM Motor Is Based on the Power Control PQ The control diagram of the PMSM motor is shown in Figure5 below, based on the control principle analyzed above. Energies 2021, 14, x FOR PEER REVIEW 8 of 17

3. The Principle of Controlling the Speed of a PMSM Motor is Based on the Power Control PQ Energies 2021, 14, 3549 8 of 16 The control diagram of the PMSM motor is shown in Figure 5 below, based on the control principle analyzed above.

* * ωe P |US| v va PI_S PI_P v = U |sin(δ ) d dq d S v -> b vq M vc ωe P vq=|US|cos(δ ) abc

* * Encoder |US | Q δ θ θe PI_U PI_Q e ia ib

|US| Q id θe iq abc/dq

id P id V * d iq P=1.5(vdid+vqiq+2.v0i0) iq e  pm max |US | +iq R + i d  e L dt vd Q=1.5(vqid vdiq) Q ωe cos 0 ωe vq δ

FigureFigure 5. 5. TheThe PMSM PMSM speed speed control control principle principle is is based based on on the the active active and and reactive reactive power power control control of of the the inverters inverters..

• • TheThe active active power power is is adjusted adjusted through through the the speed speed PI PI controller controller (PI_S) (PI_S) from from the the actual actual speedspeed difference difference compared compared to to the the reference reference speed. speed. • • TheThe power power PI PI controller controller is is used used to to change change the the inverter inverter voltage voltage amplitude, amplitude, to to change change thethe power power supplied supplied to to the the inverter inverter according according to to the the reference reference power, power, • • ToTo ensure ensure that that reactive reactive power power Q Q is is not not fed fed to to the the BEMF BEMF source, source, the the inverter inverter voltage voltage mustmust be be kept kept at at a avalue value according according to to (18) (18) and and must must not not exceed exceed the the inverter inverter limit limit value value toto optimize optimize motor motor operation. operation. Inverter Inverter voltage voltage must must be be kept kept at at a adetermined determined value; value; somesome reactive reactive power power must be addedadded (or(or drawn)drawn) from from the the inverters. inverters. The The determination determina- tionof reactive of reactive power power Q is doneQ is done via a voltagevia a voltage controller controller with the with input the of input the error of the between error betweenthe reference the reference voltage andvoltage the actualand the voltage actual atvoltage the inverter at the inverter output. output. • • TheThe reactive reactive power power PI controller correctscorrects thethe voltage voltage angle angleδ betweenδ between U andU and E, respec-E, respectively,tively, to change to change the the reactive reactive power power to theto the reference reference value. value. The The BEMF BEMF vector vector angle an- gleis alwaysis always perpendicular perpendicular to the to direction the direction of the of d-axis the d current-axis current component, component, as shown as shownin Figure in Figure4; the voltage4; the voltage across across the inverters’ the inverters’ coordinate coordinate system system dq is determineddq is deter- minedaccording according to (19) to and (19) (20). and (20). vd = −|US| sin(δ) (30)

vvqdS= =−|U US| cos sin((δ)) (30(31))

4. Simulation Validation

4.1. Simulation IPMSM Speed Control ModelvqS= U cos( ) (31) The PMSM motor speed control model is built on the simulation software Mat- lab/Simulink used to evaluate the proposed control efﬁciency. Table1 shows the PMSM 4.motors’ Simulation parameters Validation used in the simulation; these parameters belong to the EMJ-04APB22 4.1.motor, Simulation which IPMSM Wang et Speed al. used Control in their Model study [34]. The Texas Instruments Company recommends the use of the EMJ-04APB22 motor in the quality assessment of controllers. The modelThe is PMSM built with motor three speed main blocks, control the model PMSM is motor built block, on the the simulation control unit, software and the Matlab/Simulinkinverter block Figure used6 toshows evaluate the simulation the proposed PMSM control model. efficiency. The Vector Table Current 1 shows Control the PM(VCC)SM motors’ method parameters [35] and the used Direct in Currentthe simulation; Calculation these (DCC) parameters method belong [36] wereto the used EMJ to- 04APB22evaluate motor, the proposed which controlWang et method’s al. used in effectiveness. their study The[34].simulation The Texas resultsInstruments under Com- differ- panyent operating recommends conditions the use are of satisfactorilythe EMJ-04APB22 introduced motor in in detail the quality in the followingassessment sections. of controllers. The model is built with three main blocks, the PMSM motor block, the control unit, and the inverter block Figure 6 shows the simulation PMSM model. The Vector Cur- rent Control (VCC) method [35] and the Direct Current Calculation (DCC) method [36]

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Table 1. PMSM parameters.

Parameter Symbol Value Unit Rated power 400 W Rated phase current Imax 2.7 Arms Rated speed ωrate 3000 RPM Rated torque Trate 1.27 N.m Number of poles P 4 Energies 2021, 14, x FOR PEER REVIEW pairs 9 of 17 Stator resistance R 2.35 Ω Stator inductance L = Ld= Lq 8.5 mH Flux linkage λpm 0.0615 Wb − were usedInertia to evaluate the proposed J control method’s167 effectiveness.× 10 6 The simulationKg.m2 results −6 underViscous different friction operating conditions F are satisfactorily106.9 introduced× 10 in detailN.m.s/rad in the follow- DC Bus Voltage V 200 V ing sections. dc

Figure 6. IPMSM control simulation model.

Table4.2. Simulation 1. PMSM parameters. Results The PMSM motor is used to test the proposed method’s control quality in constant Parameter Symbol Value Unit torque and constant power zones at various speeds. The speed variation between two operating zones,Rated as power well as within the same operating region of PMSM,400 is used toW evaluate the effectRated of extending phase current the operating speedImax range and minimizing2.7 the fluctuationsArms in electric torque, current, and associated flux of PMSM in the FW region of the proposed Rated speed ω 3000 RPM method. Figure7 shows the speed control results.rate The obtained results show that the control methodsRated can torque adhere well to the referenceTrate speed. 1.27 N.m TheNumber under-rated of poles speed pairs enlargement resultsP show that DCC and4 VCC control methods got lower overshootStator resistance than the proposed method.R The reason for this2.35 is that when controllingΩ the constant torque region, it is much more efficient to change the speed by changing the L=L =L current whenStator having inductance to indirectly control the speeddq by holding8.5 power inject to themH motor. Although theFlux response linkage is slower, the proposedλpm method is more0.0615 stable, with theWb speed’s ripple less than the other DCC and VCC ways. Inertia J 167 × 10−6 Kg.m2 The speed enlargement results in the FW region show that the two DCC and VCC Viscous friction F 106.9 × 10−6 N.m.s/rad methods also have a lower overshoot than the proposed method. However, these two methods’ speedDC Bus ripple Voltage is much higher, and thusVdc the quality of speed200 control is alsoV significantly reduced. The reason is that when entering the voltage limit area, the method of 4.2.current Simulation management Results and voltage correction through the current controller will no longer The PMSM motor is used to test the proposed method’s control quality in constant torque and constant power zones at various speeds. The speed variation between two operating zones, as well as within the same operating region of PMSM, is used to evaluate the effect of extending the operating speed range and minimizing the fluctuations in electric torque, current, and associated flux of PMSM in the FW region of the proposed method. Figure 7 shows the speed control results. The obtained results show that the control methods can adhere well to the reference speed. The under-rated speed enlargement results show that DCC and VCC control methods got lower overshoot than the proposed method. The reason for this is that when controlling the constant torque region, it is much more efficient to change the speed by changing the current when having to indirectly control the speed by holding power inject to the

Energies 2021, 14, x FOR PEER REVIEW 10 of 17

motor. Although the response is slower, the proposed method is more stable, with the speed’s ripple less than the other DCC and VCC ways. The speed enlargement results in the FW region show that the two DCC and VCC methods also have a lower overshoot than the proposed method. However, these two Energies 2021, 14, 3549 methods’ speed ripple is much higher, and thus the quality of speed control is also signif-10 of 16 icantly reduced. The reason is that when entering the voltage limit area, the method of current management and voltage correction through the current controller will no longer be as effective as inin thethe constantconstant torquetorque region.region. Then,Then, the proposedproposed methodmethod showsshows thethe advantages when the two control zones’ speed controlcontrol qualityquality isis thethe samesame andand stable.stable.

Figure 7. Comparative speed control results ofof PMSM.PMSM.

Figure 88aa showsshows thethe resultsresults ofof the the electromagnetic electromagnetic momentmoment ofof comparative comparative controlcontrol methods. The The simulation simulation results results show show that that all all three three approaches approaches give give a small a small ripple ripple in the in theconstant constant moment moment region. region. Electromagnetic Electromagnetic torque torque responds responds to changes to changes in the load in the torque load torqueand the and need the for need the engine’s for the engine’s acceleration acceleration or deceleration or deceleration speed. Figure speed. 8 Figureb shows8b electro- shows electromagneticmagnetic moment moment results resultsat a constant at a constant power power range. range. The electromagnetic The electromagnetic moment moment oscil- oscillationlation of VCC, of VCC, DCC DCCand the and proposed the proposed approach approach is (0.35 is– (0.35–0.6)0.6) N.m, ( N.m,0.38–0.5 (0.38–0.5)) N.m, (0.42 N.m,– (0.42–0.48)0.48) N.m, res N.mpectively., respectively. The result The result of the of flux the linkage ﬂux linkage ripple ripple percent percent is 26.3%, is 26.3%, 13.64%, 13.64%, and and6.67%, 6.67%, respectively. respectively. This means This means that the that VCC the and VCC DCC and methods’ DCC methods’ electromagnetic electromagnetic torque torquehas a more has asignificant more signiﬁcant ripple than ripple the than proposed the proposed method method while entering while entering the FW theregion. FW region.The results The demonstrate results demonstrate the proposed the proposed method’s method’s ability to ability minimize to minimize the electromagnetic the electro- magnetictorque ripple. torque The ripple. task of The reducing task of reducingelectromagnetic electromagnetic surges plays surges a crucial plays arole crucial in improv- role in improvinging not only not the only control the controlquality qualitybut also but the also electric the electricdrive system’s drive system’s stability. stability. The stator winding power loss is determined based on the stator current and stator resistance, as shown in (21). Figure9 shows the power loss simulation results. The results show that the proposed control method has the same effect of minimizing losses as the other comparative methods. These results show that the proposed control method effectively reduces power loss as the current-based control method, similar to the FOC control method.

2 Ploss = Is .Rs (32)

Figure 10a shows the flux linkage results. The flux linkage in the control method is greater than that of the flux linkage of the permanent magnet when operating in the constant torque region. The flux linkage decreases when entering the constant power region. Figure 10b shows the flux linkage results at a constant power range. It is important to note that flux linkage oscillation of VCC, DCC and the proposed approach is (0.038–0.045) Wb, (0.04–0.043) Wb, (0.04–0.041) Wb, respectively. This leads to the flux linkage ripple percent- age, at 18%, 7.5%, and 2.5%, respectively. Hence, the VCC and DCC methods’ flux linkage value has a more significant ripple than the proposed method. EnergiesEnergies2021 2021, 14, 14 3549, x FOR PEER REVIEW 11 of11 17 of 16

(a)

(b) Energies 2021, 14, x FOR PEER REVIEW 12 of 17 FigureFigure 8. Comparative8. Comparative Electromagnetic Electromagnetic Torque Torque resultsresults ofof PMSMPMSM in ( (aa)) full full simulation simulation time time range range and and (b () binterval) interval time time of of (3.2–3.5(3.2–3.5 s). s).

The stator winding power loss is determined based on the stator current and stator resistance, as shown in (21). Figure 9 shows the power loss simulation results. The results show that the proposed control method has the same effect of minimizing losses as the other comparative methods. These results show that the proposed control method effectively reduces power loss as the current-based control method, similar to the FOC control method.

2 Ploss= I s .R s (32)

Figure 9. Comparative power loss results of PMSM. Figure 9. Comparative power loss results of PMSM.

Figure 10a shows the flux linkage results. The flux linkage in the control method is greater than that of the flux linkage of the permanent magnet when operating in the constant torque region. The flux linkage decreases when entering the constant power region. Figure 10b shows the flux linkage results at a constant power range. It is important to note that flux linkage oscillation of VCC, DCC and the proposed approach is (0.038–0.045) Wb, (0.04–0.043) Wb, (0.04–0.041) Wb, respectively. This leads to the flux linkage ripple per- centage, at 18%, 7.5%, and 2.5%, respectively. Hence, the VCC and DCC methods’ flux linkage value has a more significant ripple than the proposed method.

(a)

Energies 2021, 14, x FOR PEER REVIEW 12 of 17

Figure 9. Comparative power loss results of PMSM.

Figure 10a shows the flux linkage results. The flux linkage in the control method is greater than that of the flux linkage of the permanent magnet when operating in the constant torque region. The flux linkage decreases when entering the constant power region. Figure 10b shows the flux linkage results at a constant power range. It is important to note that flux linkage oscillation of VCC, DCC and the proposed approach is (0.038–0.045) Wb, Energies 2021, 14, 3549 (0.04–0.043) Wb, (0.04–0.041) Wb, respectively. This leads to the flux linkage ripple12 ofper- 16 centage, at 18%, 7.5%, and 2.5%, respectively. Hence, the VCC and DCC methods’ flux linkage value has a more significant ripple than the proposed method.

Energies 2021, 14, x FOR PEER REVIEW 13 of 17

(a)

(b)

FigureFigure 10.10. Comparative Total Total Flux Flux linkage linkage results results of of PMSM PMSM in in(a) ( afull) full simulation simulation time time range range and and (b) interval (b) interval time time of (2.8 of– (2.8–3.73.7 s). s).

FigureFigure 11 11aa showsshows thethe resultingresulting statorstator currents currents controlled controlled by by different different methods. methods. TheThe similaritysimilarity ofof thethe currentscurrents withinwithin thethe constantconstant momentmoment rangerange cancan bebe seenseen immediately.immediately. However,However, when when entering entering the the FW FW region, region, the the quality quality of theof the stator stator current current has ahas big a difference.big differ- Zoomingence. Zooming in on these in on results these inresults Figure in 11Figureb from 11 3.2b from s to 3.53.2 s s shows to 3.5 thes shows difference the difference between thebetween comparative the comparative methods. Themethods. current The fluctuation current fluctuation of the VCC of method the VCC is the method most significantis the most (2.4–3.3)significant A, ( with2.4–3.3 a fluctuation) A, with a ratefluctuation of 15.8%. rate On of the 15.8%. contrary On the the contrary current instabilitythe current of insta- the proposedbility of the method proposed is the method smallest is the (2.6–2.8) smallest A, ( with2.6–2.8 a fluctuation) A, with a fluctuation rate of 3.7%. rate Hence, of 3.7%. a currentHence, ripplea current of the ripple proposed of the method proposed is significantly method is significantly smaller than smaller two other than comparative two other approachescomparative in approaches the FW mode. in the FW mode.

(a)

Energies 2021, 14, x FOR PEER REVIEW 13 of 17

(b) Figure 10. Comparative Total Flux linkage results of PMSM in (a) full simulation time range and (b) interval time of (2.8– 3.7 s).

Figure 11a shows the resulting stator currents controlled by different methods. The similarity of the currents within the constant moment range can be seen immediately. However, when entering the FW region, the quality of the stator current has a big difference. Zooming in on these results in Figure 11b from 3.2 s to 3.5 s shows the difference between the comparative methods. The current fluctuation of the VCC method is the most significant (2.4–3.3) A, with a fluctuation rate of 15.8%. On the contrary the current insta- bility of the proposed method is the smallest (2.6–2.8) A, with a fluctuation rate of 3.7%. Energies 2021, 14, 3549 Hence, a current ripple of the proposed method is significantly smaller than two 13other of 16 comparative approaches in the FW mode.

Energies 2021, 14, x FOR PEER REVIEW 14 of 17

(a)

(b)

Figure 11. Comparative current results of PMSM in (a) full simulation time range and ((b)) intervalinterval timetime ofof (3.2–3.5(3.2–3.5 s).s).

Figure 12 shows the voltage simulation results on the statorstator winding.winding. The recordedrecorded results show that the proposed method’s voltage is more stable than the DCC and VCC methods when operating in the FW region. In t thehe area of the constant moment, the ripple of the current and voltage amplitude is equivalent. Moreover Moreover,, it also shows the superiority of the proposed method in expanding the range of PMSM operating speeds in comparison with the DCC and VCC control methods.

Figure 12. Comparative Voltage results of PMSM.

5. Conclusions The paper proposes an advanced method to expand the PMSM speed range by controlling the inverter power instead of the conventional current control approach. Speed control based on power balance allows flexible control, no longer considering higher or lower rotor speed conditions along with switch control strategies. After comprehensive simulations, it is possible to state that the proposed control method is capable of stable operation from 300 to 5500 rpm, regardless of changing the PMSM speed control method

Energies 2021, 14, x FOR PEER REVIEW 14 of 17

(b) Figure 11. Comparative current results of PMSM in (a) full simulation time range and (b) interval time of (3.2–3.5 s).

Figure 12 shows the voltage simulation results on the stator winding. The recorded results show that the proposed method’s voltage is more stable than the DCC and VCC methods when operating in the FW region. In the area of the constant moment, the ripple of the current and voltage amplitude is equivalent. Moreover, it also shows the superiority Energies 2021, 14, 3549 of the proposed method in expanding the range of PMSM operating speeds in comparison14 of 16 with the DCC and VCC control methods.

Figure 12. Comparative Voltage results of PMSM. Figure 12. Comparative Voltage results of PMSM. 5. Conclusions 5. ConclusionsThe paper proposes an advanced method to expand the PMSM speed range by controllingThe paper the inverter proposes power an advanced instead of method the conventional to expand currentthe PMSM control speed approach. range by Speed con- controltrolling basedthe inverter on power power balance instead allows of the ﬂexible conventional control, current no longer control considering approach. higher Speed or lowercontrol rotor based speed on power conditions balance along allows with flexible switch control, control strategies.no longer considering After comprehensive higher or simulations,lower rotor speed it is possible conditions to state along that with the switch proposed control control strateg methodies. After is capable comprehensive of stable operationsimulations, from it is 300 possible to 5500 to rpm, state regardless that the proposed of changing control the PMSM method speed is capable control of method stable betweenoperation two from separate 300 to 5500 working rpm, stages:regardless the of constant changing power the PMSM region speed and constant control method torque region. By controlling the power injected into the PMSM, the proposed control method allows for reasonable control of the storage systems’ discharge power, necessary in mobile drive applications. The proposed control method contains the same number of control

loops, and does not need to provide any additional data compared to the two comparative control methods. In comparing simulation results with the two traditional DCC and VCC control methods, the proposed control method has proven to improve not only control quality and stability, but also to minimize electromagnetic torque and current ripples. The fact is that, during PMSM operation, the algorithm uses PMSM parameters to calculate the voltage to be supplied by the inverter, which leads to the requirement of accurately determining PMSM parameters. These limitations lead to the subsequent development direction of the research, to further improve the control efﬁciency of the proposed PMSM speed control algorithm.

Author Contributions: Conceptualization, P.Q.K. and V.-A.T.; methodology, P.Q.K.; software, P.Q.K.; validation, H.P.H.A.; formal analysis, P.Q.K. and V.-A.T.; investigation, H.P.H.A.; resources, P.Q.K.; data curation, P.Q.K.; writing—original draft preparation, P.Q.K.; writing—review and editing, H.P.H.A.; visualization, P.Q.K.; supervision, H.P.H.A.; project administration, H.P.H.A.; funding acquisition, H.P.H.A. This paper was a collaborative effort among all authors. All authors conceived the methodology, conducted the performance tests, and wrote the article. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: We acknowledge the support of the time and facilities of the Ho Chi Minh City University of Technology (HCMUT), VNU-HCM, for this study. Energies 2021, 14, 3549 15 of 16

Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature vd (vq) Stator voltage in d–q coordinate system id (iq) Stator current in d–q coordinate system Ld (Lq) stator inductance in dq coordinate system λpm Magnet flux linkage RS Stator resistance Ω rotor speed ωe magnetic field speed Pp number of pole pairs Te Electromagnetic torque J The inertia of motor and load combined reduced to the motor shaft. F The combined viscous friction coefficient of rotor and load. θ Rotor angular position TL Shaft load torque θm Angular velocity of the rotor (mechanical speed) P1,P2 Power at the inverter output E back electromotive force in the stator winding S transparent power transmitted to the back electromotive force terminal P Active power transmitted to the back electromotive force terminal Q Reactive power transmitted to the back electromotive force terminal |Us| Voltage amplitude at the inverter output ϕus the phase of inverters voltage vector ϕE the phase of back electromotive force in the stator winding δ angular deviation between ϕus and ϕE β Phase of winding impedance XL Winding impedance L winding inductance ∆U voltage drop across the winding

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