Dynamic DC-Link Voltage Adjustment for Electric Vehicles Considering the Cross Saturation Effects

energies

Article Dynamic DC-link Voltage Adjustment for Electric Vehicles Considering the Cross Saturation Effects

Huimin Li, Shoudao Huang, Derong Luo *, Jian Gao and Peng Fan

College of Electrical and Information Engineering, Hunan University, Changsha 410082, China; [email protected] (H.L.); [email protected] (S.H.); [email protected] (J.G.); [email protected] (P.F.) * Correspondence: [email protected]; Tel.: +86-0731-8882-2461

Received: 4 July 2018; Accepted: 3 August 2018; Published: 7 August 2018

Abstract: The demands of remarkable reliability and high power density of traction systems are becoming more and more rigorous. The conflicting requirements imposed on the control strategy are higher accuracy and higher efficiency over the whole speed range. However, parameter variations caused by the cross coupling and magnetic saturation effect (omitted from the cross saturation effects in the following) are usually neglected in conventional control strategies, which could reduce the control precision. In order to fully consider the influence of parameter changes on the motor control and derive an approach that could realize the maximum efficiency during the whole speed range, this paper proposes a dynamic DC-link voltage adjustment strategy considering the cross coupling and magnetic saturation effects. The strategy can be categorized into three parts. Firstly, the torque request is transformed to the optimal current reference signal. Secondly, the differences between the setpoint and the real-time feedback signals of torque and voltage can be applied in the linearized function in the did,q coordinate. The solution guides the current vector into the optimal direction under the current and voltage limits to ensure the safety and reliability of the motor. Finally, last, the bus voltage can be modified according to the asked terminal voltage. A 10 kW prototype which instrumented a bidirectional DC-DC converter to regulating the bus voltage has been studied. The simulation and experiment results verify that the proposed control strategy can reduce the inverter losses in low speed region by offering the low bus voltage and track the actual maximum torque control trace more accurately, meanwhile, the flux weakening region can be delayed in high speed region by applying a high bus voltage. It helps the motor realize the high utilization rate of the DC-link voltage and guarantees the system reliability and robustness.

Keywords: dynamic DC-link voltage control; cross coupling effect; magnetic saturation effect; maximum efﬁciency

1. Introduction As the utilization rate of electrical vehicles (EVs) continues to grow, they have become an indispensable part in modern transportation development and electricity demand side management of the power grid. The characteristics of EVs, such as speed range and energy consumption per mile, could not only impact on their own output performance, but also inﬂuence the related distribution network construction, for example parking lot allocation and charging mechanism prediction [1–3]. Therefore the demands of high reliability and decent performance of EV especially in stringent working conditions have become serious. The interior permanent magnet synchronous machine (IPMSM), with the wider speed range, remarkable reliability and higher torque density than other type of permanent magnet synchronous motor, is a desirable candidate for EV applications [4,5]. In actual operation, EVs usually work under ﬂuctuating and complicated working conditions, thus the motors

Energies 2018, 11, 2046; doi:10.3390/en11082046 www.mdpi.com/journal/energies Energies 2018, 11, 2046 2 of 22 seldom run at their rated value and there will have unavoidable distortion of torque and current caused by frequent handoffs between constant torque and flux weakening region [6,7]. Thus, the optimal motor design under full speed range and the proper control strategy plays a crucial role to avert these excess and unnecessary losses. It is well known that the running state of IPMSMs can be divided into two parts—constant torque and the constant power operation [8–10]. In the constant torque region, numerous of optimal control strategies have been proposed to acquire the optimal torque output with the lowest motor loss, such as the maximum torque per amper (MTPA), id = 0 control, maximum efficiency per amper (MEPA), etc. [11–13]. When the speed is increased beyond the base speed, the control strategy must impose restriction on the terminal voltage to prevent the traction system from voltage overshoot and breakdown. Hence, it should introduce flux weakening control. Unfortunately, the torque output performance would be affected in this process [4,14]. In order to enlarge the range of the maximum torque operation, methods for boosting the DC-link voltage has been studied by many researchers. Reference [15] illustrated that the increased DC-link voltage is beneficial to elevating the turning speed. It could also enhance the overload capacity of motor indirectly. Reference [16] verified that boosting the DC-link voltage can enlarge the range of the constant torque operation and delay the introduction of the flux weakening control. References [17,18] showed the evidence that the losses the temperature rises caused by the flux weakening control can be delayed or diminished. Besides constant torque region enlargement, there is another way to discuss the influence of the DC-link voltage on the traction system. References [19,20] demonstrated that the switching losses of inverters are directly proportional to the bus voltage. Moreover, the DC bus is a connecting link between the inverter and the IPMSM, thus the rank of DC-link voltage is the foundation of control strategy design. Thus reveals the importance of the choice of the DC-link voltage grade to avoid excessive high voltage, which would not only reduce the bus voltage utilization rate, but also generate lots of harmonic waves and add to the total cost. However, insufficient voltage rank could lead to the over-modulation and then degrade the motor performance [16]. Therefore, the tradeoff of the proper bus voltage value to implement the maximum efficiency overall operation speed range becomes important. It should note that the DC-link voltage adjustment is dependent on the feedback of asked terminal voltage, which is composed of parameters such as speed-dependent back electromotive force, inductances and resistances [16,21]. In conventional control, these parameters are deemed to be constant during the operation. However, there are many factors could break this normal hypothesis, for example, the magnetic saturation, temperature, the cross coupling effect. They will play the pivotal roles to turn the motor parameters to nonlinear especially in heavy load condition [22]. Thus the accuracy and precision of control strategy applied the fixed parameters would discount. References [23,24] calculated out the influence of the cross coupling effect and magnetic saturation on inductance and flux linkage. References [23,25] concluded that the cross coupling effect could help the motor overcome the impact of saturation effect in high speed operation. References [22,25,26] pointed out the confirmation that the simulation result of control strategy considered these effects would more in line with the running state of actual motor. Albeit many researches and experimental works have been down, major parts of control strategies do not consider both cross coupling and magnetic saturation effect simultaneously. Reference [27] proposed an optimal current trajectory control strategy (the CTCS) that combined the variable parameters caused by the cross coupling and saturation effects. It implemented the seamless switching control from the constant torque mode to the flux weakening mode without pre-calculating the control reference to promote the accuracy and respond speed. The CTCS could realize the maximum output performance and dig out the potential of traction system within the electrical constrains. The influence of the cross coupling and saturation effect on motor running trajectory has been analyzed specifically. The conclusion showed that the CTCS can track the actual running state more properly and keep the robustness during variable working condition. Combining the CTCS, this paper proposes a dynamic DC-link voltage control taking the cross coupling effect and magnetic saturation into consideration. It is a discrete control strategy which takes Energies 2018, 11, 2046 3 of 22

Energies 2017, 10, x FOR PEER REVIEW 3 of 22 the asked terminal voltage of the motor as control reference to modify the bus voltage. The purpose of takes the asked terminal voltage of the motor as control reference to modify the bus voltage. The this bus voltage adjustment method is to realize the low DC-link voltage control in low load situation to purpose of this bus voltage adjustment method is to realize the low DC-link voltage control in low diminish the system losses and boost the bus voltage in high speed region to delay the flux weakening load situation to diminish the system losses and boost the bus voltage in high speed region to delay operation. The arrangement of this paper is as follows: Section2 introduces the working principle such the flux weakening operation. The arrangement of this paper is as follows: Section 2 introduces the as the mechanism of the cross saturation effects, the process of dynamic DC-link voltage adjustments. working principle such as the mechanism of the cross saturation effects, the process of dynamic Section3 displays the details of the simulation tests. A 10 kW IPMSM test rig is set meanwhile, DC-link voltage adjustments. Section 3 displays the details of the simulation tests. A 10 kW IPMSM relative experimental works are conducted to validate the accuracy of the strategy. Section4 presents test rig is set meanwhile, relative experimental works are conducted to validate the accuracy of the the conclusions of the paper. strategy. Section 4 presents the conclusions of the paper. 2. Working Principle 2. Working Principle 2.1. The Cross Saturation Effects 2.1. The Cross Saturation Effects The mathematic model of IPMSM and the electrical restriction boundary of inverters consist of theThe inductance mathematicLd andmodelLq ,of the IPMSM magnetic and fluxthe electrical linkage Ψ restrictionf, and the boundary stator resistance of invertersRs. Moreover, consist of differentthe inductance control L strategiesd and Lq, canthe bemagnetic traced backflux tolinkage finding Ψ af, decentand the current stator controlresistance reference, Rs. Moreover, and the solutiondifferent procedurecontrol strategies is determined can be traced by the back machine to finding parameters. a decent Therefore, current control a precise reference, parameter and date the andsolution its change procedure rules is can determined help to find by morethe machine accurate parameters. control results. Therefore, Under a conventional precise parameter conditions, date theand magnetic its change circuits rules incan the help direct-axis to find (mored-axis) accura and thete quadrature-axiscontrol results. Under (q-axis) conventional are presumed conditions, decoupled andthe themagnetic parameters circuits such in as the flux direct-axis linkage and (d inductance-axis) and aretheset quadrature-axis fixed by default. (q However,-axis) are aspresumed it shows indecoupled Figure1, theand flux the linkage parameters in d-axis such and asq -axisflux islink notage completely and inductance orthogonal. are Thereset fixed has overlappedby default. However, as it shows in Figure 1, the flux linkage in d-axis and q-axis is not completely orthogonal. path between two axis on the stator core which contribute to the mutual inductance Ldq and Lqd. ThisThere phenomenon has overlapped is called path thebetween cross couplingtwo axis effect.on the Bystator introduce core which the cross contribute coupling to inductance,the mutual theinductance flux linkage Ldq and model Lqd. canThis be phenomenon modified as: is called the cross coupling effect. By introduce the cross coupling inductance, the flux linkage model can be modified as: " # " #" # " # Ψ L L i Ψ d = ddLLqd d + f (1) Ψ Ψ ddfL ddL qd ii Ψ q=+dq qq q 0 (1) Ψ i qqLLdq qq 0 From Equation (1), Ldd and Lqq represent the self-inductances of d-axis and q-axis. Ldq and Lqd are the crossFrom coupling Equation inductances (1), Ldd and of Lqqd -axisrepresent and q the-axis self-inductances respectively. Ψ fofrefers d-axis to and the permanentq-axis. Ldq and magnetic Lqd are fluxthe cross linkage. couplingid, iq, Ψinductancesd, Ψq denote of the d-axis stator and current q-axis andrespectively. flux linkage Ψf refers component to the inpermanentdq coordinates. magnetic flux linkage.Thus, the id, electromagnetic iq, Ψd, Ψq denote torque the stator function current can and be rewrittenflux linkage as: component in dq coordinates. Thus, the electromagnetic torqueh function can be rewritten as: i = + − + 2 − 2 Te 1.5 p Ψf iq Ldd Lqqidiq Ldqiq2 Lqdid2 (2) 𝑇𝑒 = 1.5 𝑝 [𝛹𝑓𝑖𝑞 + 𝐿𝑑𝑑 −𝐿𝑞𝑞𝑖𝑑𝑖𝑞 +(𝐿𝑑𝑞𝑖𝑞 −𝐿𝑞𝑑𝑖𝑑)] (2)

22 22 T𝑇ecr𝑒𝑐𝑟==1.51.5 p 𝑝L 𝐿dq𝑑𝑞i𝑖q𝑞−−𝐿Lqd𝑞𝑑i𝑖d𝑑 (3)(3) where TTee means thethe electromagneticelectromagnetic torque.torque. TTecrecr representsrepresents the the torque torque introduced introduced by the cross coupling effect.

Figure 1. Results of magnet flux circuit with current while the Ψf is set to 0. (a) d-axis flux circuit Figure 1. Results of magnet flux circuit with current while the Ψf is set to 0. (a) d-axis flux circuit when when iq = 0; (b) q-axis magnet flux circuit when id = 0. iq = 0; (b) q-axis magnet flux circuit when id = 0.

In addition, the air gap between rotor and stator of the motor is uneven, and it is mainly distributed on the q-axis; meanwhile the direction of permanent magnetic flux is coincident with the

Energies 2018, 11, 2046 4 of 22

Energies 2017, 10, x FOR PEER REVIEW 4 of 22 EnergiesIn addition, 2017, 10, x the FOR air PEER gap REVIEW between rotor and stator of the motor is uneven, and it is mainly distributed4 of 22 ond-axis. the q -axis;It contributes meanwhile to a lower the directionpermeability of permanenton the q-axis. magnetic Consequently, flux isthe coincident amplitude withof fluctuation the d-axis. It contributesd-axis. It contributes to a lower to a permeability lower permeability on the onq-axis. the q-axis. Consequently, Consequently, the the amplitude amplitude of of fluctuation fluctuation of ofof the the flux flux linkage linkage on on q -axisq-axis with with the the stator stator current current is is more more obvious obvious than than it it on on d d-axis.-axis. This This variation variation of of the flux linkage on q-axis with the stator current is more obvious than it on d-axis. This variation thethe flux flux linkage linkage during during the the motor motor operation operation is is call calleded the the magnetic magnetic saturation saturation effect. effect. In In order order to to of the flux linkage during the motor operation is called the magnetic saturation effect. In order to evaluateevaluate the the effect effect of of operating operating states states on on the the flux flux linkage linkage and and inductance, inductance, a a 10 10 kW kW IPMSM IPMSM model model has has evaluate the effect of operating states on the flux linkage and inductance, a 10 kW IPMSM model has beenbeen made. made. Based Based on on the the calculation calculation model model in in [28] [28] the the inductance inductance as as function function of of stator stator current current can can be be been made. Based on the calculation model in [28] the inductance as function of stator current can be derived,derived, however, however, the the model, model, as as Equation Equation (4) (4) disp displayed,layed, should should be be modified modified according according to to Equation Equation derived,(1)(1) to to introduce however,introduce the thethe cross model,cross coupling coupling as Equation inductance inductance (4) displayed, into into account. account. should The The be finite modifiedfinite element element according analysis analysis to (FEA) Equation(FEA) has has (1) tobeen introducebeen conducted conducted the cross through through coupling the the ANSYS ANSYS inductance Maxwell Maxwell into software software account. (15.0.0.). (15.0.0.). The finite element analysis (FEA) has been conductedTheThe results through results are are the plotted plotted ANSYS in in Figures MaxwellFigures 2 2 and softwareand 3. 3. Figu Figu (15.0.0.).rere 2 2 displays displays the the flux flux linkage linkage varying varying with with dq dq-axis-axis current,current,The results and and Figure Figure are plotted 3 3 shows shows in the Figuresthe details details2 and of of inductances 3inductances. Figure2 displays dependent dependent the on on flux the the linkage armature armature varying currents: currents: with dq-axis current, and Figure3 shows the details of inductances dependent on the armature currents: 𝛹𝑑 𝑖𝑑,𝑖𝑞 − 𝛹𝑓 (0, 𝑖𝑞) ⎧ 𝛹𝑑 𝑖𝑑,𝑖𝑞 − 𝛹𝑓 (0, 𝑖𝑞)  ⎧𝐿𝑑 = 𝑖𝑞 =0 ⎪ 𝐿𝑑 =Ψd id, iq − Ψf 0, iq 𝑖𝑞 =0  ⎪ = 𝑖𝑑 =  Ld 𝑖𝑑 iq 0 (4)  id (4) ⎨ 𝛹𝑞𝑖𝑑,𝑖𝑞 (4) ⎨ 𝛹𝑞𝑖𝑑,𝑖𝑞 ⎪ 𝐿𝑞 = Ψq id, iq |𝑖𝑑 =0  ⎪ 𝐿𝑞 = |𝑖𝑑 =0 ⎩ Lq = 𝑖𝑞 |id = 0 ⎩ iq𝑖𝑞

Although id plays a predominant role in the d-axis flux linkage, its value slightly increases with AlthoughAlthoughid playsid plays a predominanta predominant role role in in the thed d-axis-axis fluxflux linkage,linkage, its its value value slightly slightly increases increases with with iq especially when the demagnetizing current is low, which thanks to the contribution of the cross iq especiallyiq especially when when the the demagnetizing demagnetizing current current isis low,low, whichwhich thanks to to the the contribution contribution of of the the cross cross coupling inductance. The variation range of flux and inductance in q-axis is more significant than in couplingcoupling inductance. inductance. The The variation variation range range of of flux flux and and inductanceinductance in q-axis-axis is is more more significant significant than than in in d-axis particularly when the armature current is high. Although the q-axis current determines Lq and d-axisd-axis particularly particularly when when the the armature armature current current is is high. high. Although Although thethe q-axis current current determines determines LLq andq and Ψq, their value also descends along with the increasing d-axis as shown in Figures 2b and 3b. Ψq,Ψ theirq, their value value also also descends descends along along with with the the increasing increasing dd-axis-axis as shown in in Figures Figures 2b2b and and 3b.3b.

0.4 0.4 0.4 0.3 0.4 0.3 0.3 0.2 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0 0 0 0 0 500 0 10 -10 0 5040 10 20 -20 -10 4030 -50 20 30 -30 -20 3020 -40 -50 30 40 -40 -30 2010 -20 -30 -40 40 50 -50 -40 i(A) 10 0 -10 -20 -30 -50 i(A)d q 0 -10 i(A)d 50 i(A) i(A)q i(A)d i(A)q d i(A)q

Figure 2. Flux linkages dependent on dq-axis current. (a) d-axis flux linkage; (b) q-axis flux linkage. FigureFigure 2. Flux2. Flux linkages linkages dependent dependent on ondq dq-axis-axis current. current. ((aa)) dd-axis-axis ﬂuxflux linkage; ( (bb)) qq-axis-axis flux ﬂux linkage. linkage.

8 8 6 20 6 20 4 15 4 15

2 () 10 q () () 2 10 LmH q () d

0 LmH

d 5 LmH 0 5 LmH 10 10 0 20 -10 0 0 0 2030 -20 -10 00 -10 0 3030 -30 -20 0 10 20 -20 -10 3040 -40 -30 10 20 30 -40 -30 -20 iAq () 4050 -50 -40 iAd () 30 40 50 -50 -30 iA() iAd () 40 -40 iA() q 50 -50 iAq () 50 -50 diA() iAq () d

Figure 3. Nonlinear parameters. (a) d-axis inductance as function of dq-axis current; (b) q-axis inductance FigureFigure 3. 3.Nonlinear Nonlinear parameters. parameters. (a) (da-axis) d-axis inductance inductance as function as function of dq-axis of current;dq-axis (b current;) q-axis inductance (b) q-axis as function of dq-axis current. inductanceas function as functionof dq-axis of current.dq-axis current.

According to the discussion above, the inductances are mainly regulated by their own axes AccordingAccording to to the the discussion discussion above, above, the the inductancesinductances are mainly regulated regulated by by their their own own axes axes current. The mutual interference from another axis current is small down to few millihenry. current.current. The The mutual mutual interference interference from from another another axis currentaxis current is small is downsmall todown few millihenry.to few millihenry. Therefore, Therefore,Therefore, the the planar planar details details of of inductance inductance variatio variationsns are are computed computed by by the the FEA FEA (ANSYS (ANSYS Maxwell Maxwell 15.0.0) 15.0.0)

Energies 2018, 11, 2046 5 of 22

EnergiesEnergies 20172017,, 1010,, xx FORFOR PEERPEER REVIEWREVIEW 55 ofof 2222 the planar details of inductance variations are computed by the FEA (ANSYS Maxwell 15.0.0) to toto confirmconfirm thethe specificspecific value.value. NoteNote thatthat thethe inflinfluenceuence ofof temperaturetemperature onon inductancesinductances andand permanentpermanent confirm the specific value. Note that the influence of temperature on inductances and permanent magneticmagnetic fluxflux isis absentabsent duedue toto thethe imperfectionimperfection ofof experimentalexperimental instrument.instrument. ItIt cancan bebe seenseen inin FigureFigure 4,4, thethe magnetic flux is absent due to the imperfection of experimental instrument. It can be seen in Figure4, distinctiondistinction of of LLdd isis as as small small as as almost almost 2 2 mH,mH, in in conseque consequencence it it is is deemeddeemed to to be be fixed fixed during during the the the distinction of Ld is as small as almost 2 mH, in consequence it is deemed to be fixed during the operation.operation. In In Figure Figure 4b, 4b, the the qq-axis-axis inductance inductance is is dependent dependent on on iiqq,, andand gives gives out out a a nonlinear nonlinear operation. In Figure4b, the q-axis inductance is dependent on i , and gives out a nonlinear characteristic. characteristic.characteristic. Comparing Comparing two two results, results, the the difference difference of of the theq mutual mutual inductance inductance with with twotwo axes axes is is Comparing two results, the difference of the mutual inductance with two axes is negligible, therefore, negligible,negligible, therefore,therefore, thethe mutualmutual inductanceinductance isis alsoalso regardedregarded asas constantconstant andand equal,equal, thatthat isis LLdqdq == LLqdqd.. the mutual inductance is also regarded as constant and equal, that is L = L . These phenomenon are TheseThese phenomenonphenomenon areare consequentconsequent fromfrom thethe crosscross couplingcoupling effecteffect andanddq thetheqd magneticmagnetic saturation.saturation. ToTo consequent from the cross coupling effect and the magnetic saturation. To simplify the calculation, simplifysimplify thethe calculation,calculation, LLqq isis linearizedlinearized asas follows:follows: Lq is linearized as follows:

L𝐿퐿𝑞q푞((i𝑖푖))===17.98 17.9817.98− −−0.149 0.149𝑖0.149iq(푖𝑞푞mH(mH)(mH) ) (5)((5)5)

10 20 LL 8 dd 15

LLqq LLqq --linear linear

d 6

d 10

L q Ldqdq q L (mH) L(mH) L (mH) L (mH) 5 4 LLqdqd 2 -100 -80 -60 -40 -20 0 0 20 40 60 80 100 i (A) i(A)idd (A) i(A)qq (a) (b)

FigureFigure 4.4. InductancesInductances asas functionfunction ofof itsits ownownown axisaxisaxis current.current.current. ((aa)) dd-axis-axis inductance;inductance; (((bb))) q q-axis-axis-axis inductance.inductance.inductance.

2.2. Dynamic DC-Link Control Strategy 2.2. Dynamic DC-Link Control Strategy FigureFigure 55 dislaysdislays thethe overviewoverview ofof thethe proposedproposed dynamicdynamic DC-linkDC-link voltagevoltage controlcontrol strategy.strategy. ItIt cancan Figure5 dislays the overview of the proposed dynamic DC-link voltage control strategy. It can bebe separatedseparated intointo threethree parts.parts. FirstFirst ofof all,all, thethe opoptimaltimal currentcurrent trajectorytrajectory controlcontrol algorithmalgorithm convertsconverts be separated into three parts. First of all, the optimal current trajectory control algorithm converts thethe torquetorque setpointsetpoint intointo thethe optimaloptimal currentcurrent referereferencence signal.signal. AccordingAccording toto thethe targettarget currentcurrent value,value, the torque setpoint into the optimal current reference signal. According to the target current value, thethe field-orientedfield-oriented control control calculat calculateses the the reference reference voltage voltage for for the the generation generation of of thethe SpaceSpace VectorVector the ﬁeld-oriented control calculates the reference voltage for the generation of the Space Vector Pulse PulsePulse WidthWidth ModulationModulation (SVPWM)(SVPWM) signal.signal. ThenThen itit alalsoso initiatesinitiates thethe busbus voltagevoltage adjustmentadjustment processprocess Width Modulation (SVPWM) signal. Then it also initiates the bus voltage adjustment process based basedbased onon comparingcomparing thethe askedasked referecereferece voltagevoltage andand real-timereal-time DC-linkDC-link voltage.voltage. ByBy introducingintroducing thethe on comparing the asked referece voltage and real-time DC-link voltage. By introducing the cross crosscross saturation saturation effects, effects, the the model model of of IPMSM IPMSM is is altered. altered. The The electromagnetic electromagnetic torque torque isis shiwn shiwn by by saturation effects, the model of IPMSM is altered. The electromagnetic torque is shiwn by Equation (2). EquationEquation (2).(2). TheThe ternimalternimal voltagevoltage needsneeds toto bebe rewrittenrewritten as:as: The ternimal voltage needs to be rewritten as: ( U=Ri-U = R i -ωωLii-L()( i) i -ωωLiLi Ud =dsdqqdRsid s− dωLq( qi)iq − qωLqd qddi qdd d  (6)((6)6) UU= =R Ri i+ + ωL Li i+ + ωLLi i+ + ωΨ  U=Ri+q qsqdddqqfqs q s qωωdLid d d +ωωLi+dq dqq qωΨωΨf f

id* ud* PI d,q Torque Current d,q demand vector iq* uq* Te* id.m adjustment PI α ,β MTPA a,b,c id iq uα uβ Optimal Current Rotor Trajectory control Udc Space Vector angle θ Ia,b,c PWM DC link voltage controller ud* uq* PWM q d L1 a T3 T4 Voltage b’ Source θ L2 C1 Inverter c’ udc ω c VD DC-link b T1 T2 a’

FigureFigure 5.5. TheThe overview overview ofof thethe dynamicdynamic DC-linkDC-link voltagevoltage controlcontrol strategy.strategy.

AA bidirectionalbidirectional DCDC converterconverter isis setset upup toto helphelp thethe DC-busDC-bus voltagevoltage keepingkeeping atat aa desireddesired value.value. TheThe DCDC sourcesource voltagevoltage amplitudeamplitude decidesdecides thethe lowerlower boundbound ofof thethe controlcontrol strategystrategy ((UUdcdc,min,min == 1.51.5UUDD),),

Energies 2018, 11, 2046 6 of 22

A bidirectional DC converter is set up to help the DC-bus voltage keeping at a desired value. The DC source voltage amplitude decides the lower bound of the control strategy (Udc,min = 1.5UD), while the upper limit (Udc,up) is limited at 700 V to protect the facilities from voltage overshoot. The inverter applying the space vector PWM control which has its theoretical maximum value, that is: √ Ulim = Udc/ 3 (7)

To discuss the beneﬁts of the dynamic bus voltage, the inverter loss model should be mentioned. Losses of the inverter can be categorized into conduction and switching loss. Based on [29], the conduction loss of half-bridge is as follows:

1 Z π 1 + M sin(x + ϕ) PCond, igbt = VCE|i| sin(x) dx 2π 0 2

1 Z 2π 1 + M sin(x + ϕ) PCond, f wdi = VEC|i sin(x)| dx 2π π 2 r 2 2 where |i| = 2/3 id + iq , it shows the amplitude of the line current. ϕ represents the power factor angle. VCE and VEC are voltage drop of Insulated Gate Bipolar Transistor (IGBT) and Freewheeling diode (FWDI) related to temperature and current which can be described minutely in datasheet. In this paper, VCE = VEC = 24 V. M denotes the modulation index of SVPWM. The switching loss of IGBT and the reverse recovery loss of FWDI can be derived from Equations (8) and (9): 1 Udc Psw,igbt = Eon + Eo f f (8) Ts Ure f

1 Udc Prr, f wdi = Err (9) Ts Ure f

Eon, Eoff denote the energy loss of IGBT for the turn-on and turn-off process, which are defined by the datasheet. Ts refers to the switching frequency and Err is energy for reverse recovery of FWDI. Udc and Uref represents the bus voltage and the reference DC bus voltage of the IGBT. The inverter current rating and power capacity is finite, therefore, in order to prevent the system from thermal induced failure and voltage overshoot, the current and voltage of motor should be restricted within a certain range: 2 2 2 id + iq ≤ Imax (10) u2 u2 + u2 ≤ dc (11) d q 3 It is clear that a lower bus voltage could reduce the switching loss of the inverter. However, the voltage limit of Equation (11) demonstrates that increasing the DC-link voltage could broaden the voltage range, in other words, it could delays the flux weakening operation. Thus, the tradeoff of a proper DC-link voltage according to the operating state could not only enhance the output efficiency, but also extend the speed modulation range. Figure6 illustrates the schematic process of the proposed DC-link voltage optimization. The bus voltage reference signal can be calculated dependent on the asked voltage reference ud* and uq*, as shown in Equation (12). The bus voltage controller generates the PWM signals to help the DC converter track the voltage setpoint:

r ∗ ∗2 ∗2 udc = 3 ud + uq + ∆u (12) where ∆u is safety margin to avoid the terminal voltage of IPMSM hitting the limit boundary. Energies 2018, 11, 2046 7 of 22 Energies 2017, 10, x FOR PEER REVIEW 7 of 22

*2+ *2 uudq 3

FigureFigure 6. 6. TheThe details details of of the the dynamic dynamic DC-link DC-link voltage voltage controller. controller.

2.2.1.2.2.1. DC-DC DC-DC Converter Converter Working Working Principle TheThe structure structure of of the the DC-DC DC-DC converter converter is is shown shown in in Figure Figure 5.5 .This This type type of ofconverter converter can can work work in twoin two modes, modes, the the boost boost mode mode and and the the buck buck mode. mode. In In the the boost boost mode, mode, it it energizes energizes the the bus bus voltage voltage based on the control reference. The IGBT of switching devices T1 and T2 and the diode of T3 and T4 based on the control reference. The IGBT of switching devices T1 and T2 and the diode of T3 and participate the conduction process in this mode. In the buck mode, the converter can collect the T4 participate the conduction process in this mode. In the buck mode, the converter can collect the redundantredundant energy fromfrom thethe load load to to the the DC DC source source and and implement implement the bidirectionalthe bidirectional function. function. The IGBTThe IGBT of T3 and T4 and the diode of T1 and T2 play dominant roles in this procedure. In this paper, of T3 and T4 and the diode of T1 and T2 play dominant roles in this procedure. In this paper, the DC the DC source UD is fixed and incapable of storing the dumped energy. Therefore the converter is source UD is fixed and incapable of storing the dumped energy. Therefore the converter is mainly mainlyworking working in the boostin the mode,boost mode, but if anbut energy if an energy storage storage source source is applied is applied to the to DC the sourceDC source such such as a assupercapacitor, a supercapacitor, the converter the converter can realize can realize bidirectional bidirectional energy flowenergy when flow the when electric the vehicles electric arevehicles under arespecial under working special conditions, working conditions, for example, for duringexample, acceleration during acceleration and regenerative and regenerative breaking. breaking. WhenWhen the converter is working atat thethe boostboost mode,mode, there there are are a a few few premises. premises. First, First, it it is is assumed assumed to tobe be the the continuous continuous conduction conduction mode, mode, CCM. CCM. The switchingThe switching devices devices use shifting use shifting phase parallelphase parallel control, control, and the duty cycle should 0.5 < d1 = d2 < 1. The capacitor of the converter is big enough to and the duty cycle should 0.5 < d1 = d2 < 1. The capacitor of the converter is big enough to neglect neglectits voltage its voltage ripple. Finally,ripple. theFinally, inductor the inductor currents arecurrents continuous. are continuous. They can beThey divided can be into divided four mode into fourtypes mode in one types switching in one period,switching as shownperiod, in as Figure shown7, in where Figured refers7, where to thed refers duty to cycle. the duty cycle. In mode 1, t0 < t < t1, the IGBT in T2 turns on, and the diode of T4 participates in the current flow. In mode 1, t0 < t < t1, the IGBT in T2 turns on, and the diode of T4 participates in the current flow. The inductance L2 and capacitor C1 provide the electricity for the load. The inductance L1 is charged The inductance L2 and capacitor C1 provide the electricity for the load. The inductance L1 is charged by the DC source UD, therefore its current could be enlarged as shown in Figure 7d. by the DC source UD, therefore its current could be enlarged as shown in Figure7d. In mode 2&4, t1 < t < t2 or t3 < t < t4, the switching device of T1 and T2 are in conducting state, the In mode 2&4, t1 < t < t2 or t3 < t < t4, the switching device of T1 and T2 are in conducting state, DC source energizes the inductance L1, L2 and enlarges its current, the voltage of capacitor C1 is in the DC source energizes the inductance L1, L2 and enlarges its current, the voltage of capacitor C1 is in holding state. holding state. In conclusion, the waveform of elements in the converter in each mode can be displayed as In conclusion, the waveform of elements in the converter in each mode can be displayed as Figure 7d. The state equation of the converter in steady state is as follows: Figure7d. The state equation of the converter in steady state is as follows: In mode 1: In mode 1:   diL1  L1 di = UD  dtL1 = LU1 D  didtL2 L2 = UD + Uc1 − Udc didt  L2 =+− LUUU21D cdc In modes 2 and 4:  dt  diL1  L = U In modes 2 and 4:  1 dt D  diL2  L2 di = UD LUdtL1 =  1 dt D  In mode 3: di  LUL2 = di2L1 D  L dt= U − U  1 dt D c1 In mode 3:  diL2  L2 = UD dt

Energies 2017, 10, x FOR PEER REVIEW 8 of 22

 di LUUL1 =−  11dt D c  di  L2 = LU2 D Energies 2018, 11, 2046  dt 8 of 22

FigureFigure 7. 7.TheThe working working principle principle of ofthe the DC-DC DC-DC converter: converter: (a) (thea) theequivalent equivalent circuit circuit of DC-DC of DC-DC converter converter in modein mode 1.; ( 1.;b) (theb) theequivalent equivalent circuit circuit of DC-DC of DC-DC converter converter in inmode mode 2&4; 2&4; (c) ( cthe) the equivalent equivalent circuit circuit of of DC-DCDC-DC converter converter in in mode mode 3; 3; (d (d) )The The main main waveform waveform of of the the circuit circuit in in the the boost boost mode. mode.

Based on the inductance “Volt-Second” equilibrium principle, the voltage gain M of the converter Based on the inductance “Volt-Second” equilibrium principle, the voltage gain M of the converter working at the boost mode can be derived: working at the boost mode can be derived:  u 2  M ==udc 2  M = dc = −  UdUD (1( − d ) )  D 1  uudc UUc1 == dc  c1 22 Note that the duty cycle is 0.5 < d < 1, the bus voltage can be enlarged at least four times higher Note that the duty cycle is 0.5 < d < 1, the bus voltage can be enlarged at least four times higher than the DC source voltage applying this type of converter. than the DC source voltage applying this type of converter. 2.2.2. Current Vector Adjustment 2.2.2. Current Vector Adjustment The process details of the current trajectory control strategy (the CTCS) have been analyzed in [27]. As forThe the process safety details concerns, of the thecurrent traction trajectory drive control must operate strategy within (the CT theCS) overlappinghave been analyzed area of in current [27]. Asrestrict for the circle safety and concerns, voltage limit the ellipse.traction These drive limits must couldoperate prevent within the the drive overlapping train from area breakdown of current and restrictinsulation circle failure and voltage due to overheat limit ellipse. and voltage These li overshoots,mits could especiallyprevent the when drive they train need from to be breakdown mounted in anda conﬁned insulation working failure space. due Theto overheat CTCS applies and avoltag geometricale overshoots, position especially method to when guide they the current need to vector be mountedtowards in the a idealconfined optimal working direction. space. It The takes CTCS the parameterapplies a geometrical variation into position consideration method andto guide conducts the currentseparating vector among towards each the step. ideal The optimal CTCS direction. operates It in takes the dq the-axis parameter incremental variation coordinate. into consideration The torque andand conducts terminal separating voltage has among to be each discretized step. The consequent CTCS operates to the in corresponding the dq-axis incremental position in coordinate. the current incremental plane. Through the distance between the torque setpoint line and original current vector as shown in Figure8, the target vector can be derived. Energies 2017, 10, x FOR PEER REVIEW 9 of 22

The torque and terminal voltage has to be discretized consequent to the corresponding position in the current incremental plane. Through the distance between the torque setpoint line and original Energies 2018, 11, 2046 9 of 22 current vector as shown in Figure 8, the target vector can be derived.

diq diq dTes dTes t u 0 did did did.m LT 0 LT LU (id0,iq0) (id0,iq0) LU dUs

dUs (a) (b)

Figure 8.8. GraphicalGraphicalillustration illustration of of the the optimal optimal current current vector vector modiﬁcation: modification: (a) voltage(a) voltage incremental incremental line inline the in outside the outside of current of current circle; circle; (b) The (b) intersectionThe intersection of torque of torque and voltage and voltage incremental incremental line in line the in right the handright hand side of side terminal of terminal current current vector. vector.

At ﬁrst,first, the difference of torque and voltage betweenbetween target setpoint and the value of the former iteration hashas toto bebe calculated:calculated: ∗ dTes = Te∗− Te0 (13) 𝑑𝑇 =𝑇 −𝑇 (13)

didm = idm − id0 (14) 𝑑𝑖𝑑𝑚 =𝑖𝑑𝑚 −𝑖𝑑0 (14) U𝑈dc 𝑇Ts dU = √ − U (15) 𝑑𝑈s =( −𝑈0) T (15) √33 𝑇c where: where: q = 2 + 2 U0 ud0 uq0 2 2 𝑈0 = 𝑢𝑑0 +𝑢𝑞0 Here ud0, uq0 are the feedback signals of PI controller of former iteration step. Tc is the time constant which is set at 2 ms. Ts is the sample period. From Equations (2) and (6), the current Here ud0, uq0 are the feedback signals of PI controller of former iteration step. Tc is the time value composed of the torque and the voltage which could be expressed as: y = f(id, iq). The partial constant which is set at 2 ms. Ts is the sample period. From Equations (2) and (6), the current value differential equation can help to ﬁnd out the torque and voltage incremental value dependent on composed of the torque and the voltage which could be expressed as: y = f(id, iq). The partial current differential signal (di , di ): differential equation can helpd toq find out the torque and voltage incremental value dependent on current differential signal (did, diq): ∂ f ∂ f dy = did + diq ∂id ∂iq 𝜕𝑓 𝜕𝑓 𝑑y = 𝑑𝑖 + 𝑑𝑖 It should note that the electromagnetic torque𝜕𝑖 and𝜕𝑖 the terminal voltage model (Equations (2) and (6)) has been adjusted consequent to the cross saturation effects. As it mentioned above, the CTCS It should note that the electromagnetic torque and the terminal voltage model (Equations (2) conducts in the d-q incremental plane, the differential equation can be regarded as linearized function and (6)) has been adjusted consequent to the cross saturation effects. As it mentioned above, the in these framework: CTCS conducts in the d-q incremental plane,γ dthe differential1 equation can be regarded as linearized diq = did − dTes (16) function in these framework: γq 1.5pγq where: 𝛾𝑑 1 𝑑𝑖𝑞 = 𝑑𝑖𝑑− 𝑑𝑇𝑒𝑠 (16) γd = Ld − Lq iq iq − 2Lqdid 𝛾𝑞 1.5𝑝𝛾𝑞 where: γq = Ψf + Ld − Lq iq id + 2Ldqiq

λ |U| 𝛾 = 𝐿𝑑 −𝐿d 𝑞(𝑖𝑞)𝑖𝑞 −2𝐿𝑞𝑑𝑖𝑑 𝑑 diq = did − dUs (17) λq λq where: λ = Rs − ωe L u + ωe L uq d dq d d Energies 2018, 11, 2046 10 of 22

λq = Rs + ωe Lqd uq − ωe Lqud

As shown in Figure8, the crosspoint of the torque incremental line (Equation (16)) and the voltage modiﬁcation line (Equation (17)) is the destination for the next iteration. The distance from the original point to the allowed voltage incremental line (LU) is the critical criterion to judge whether it beyond the current limit or not. Due to the overshoot of the voltage can lead some irresistible failure to whore system. Then the length from the origin spot to the target torque incremental line LT is computed:

id0γd + iq0γq + dUs LU = q 2 2 γd + γq

dTes LT = q 2 2 λd + (1.5pλq) Although the ideal modiﬁcation vector is the intersection of torque and voltage incremental line, there is a set of special situations. Firstly, when LU ≥ Imax, the voltage request amount exceeds the radius of the current restricted circle. The vector is the intersection of the current circle and the vertical line which from the origin point to the voltage adjustment line: " # " # " # did LU γd id0 = q − (18) diq 2 2 γq iq0 γd + γq

Then, if LU < Imax, meanwhile LT ≥ Imax, the modiﬁcation vector can be calculated through the vertical line from the origin position to the torque request line, the target vector is the crosspoint of the vertical line and the current limit circle: " # " # " # did Imax λd id0 = q − (19) diq 2 2 λq iq0 λd + λq

The results above are needed to judge its position on the voltage incremental line. It must locate at the left hand side of voltage line otherwise the system would loss the control of voltage and extends the error between the result point and the optimal current value idm:

γddid + γqdiq dUs Dsv = − q + q (20) 2 2 2 2 γd + γq γd + γq

If Dsv < 0, the adjustment vector should be crosspoint of current limit circle and the dUs line:

" # p 2 2 " # " # " # did Imax − LU −γq LU γd id0 = q + q − (21) diq 2 2 γd 2 2 γq iq0 γd + γq γd + rq

When the distance between the origin to torque and voltage incremental line are all smaller than the radius of the current limit, the vector can be calculated by introducing the optimal current variation target didm (as shown in Equation (14)):     " # did.m 0 did =  λd  +  dTes  (22) diq − did.m λq 1.5pλq Energies 2017, 10, x FOR PEER REVIEW 11 of 22

𝑑𝑖 𝑑𝑖. 0 = + (22) 𝑑𝑖 − 𝑑𝑖. .

Energies 2018The, 11criterion, 2046 Dsv is still available in this circumstance, if the value is negative, the result should11 of 22 be the intersection coordinate of Equations (16) and (17): λ −γ The criterion Dsv is still available in this1.5 circumstance,p qsdU qes if dT the value is negative, the result should di = be the intersection coordinate of Equationsdc (16) andλ (17):γ − λ γ 1.5p ()dq qd

1.5pλqdUs − γqdTes didc = λ1.5γp λ γq+−λ λγqγ 1.5 pdUdTqdd s dqd es dU di =− + s qc ()λγ− λγ γ γ 1.51.5pλpqγddUdqs + λ qddγqdT qes dUqs diqc = − + 1.5p λdγq − λqγd γq γq q q 𝐿= =𝑚𝑖𝑛( { (𝑑𝑖−−𝑖2 ))+𝑑𝑖 + −−𝑖2, 𝐼2 −𝐿𝑈− 2} Lcross min didc id0 diqc iq0, Imax LU

Finally,Finally, the the optimal optimal adjustment adjustment vector vector is is derived derived asas follows:follows:

" # 𝑑𝑖 𝐿" 𝛾# 𝐿𝑈 𝛾" 𝑖# " # did =Lcross γq + LU −γd id0 𝑑𝑖 −𝛾 𝛾 𝑖 = q + q − (23)(23) diq 2 𝛾2+𝛾− γd 𝛾2+𝛾 2 γq iq0 γd + γq γd + γq

ToTo simplify simplify the the resolving resolving process, process, the the ﬂow flow chart chart ofof thethe CTCSCTCS is displayed in in Figure Figure 9.9.

idm

, iid0 q0

FigureFigure 9. 9.Schematic Schematic overview overview of ofthe the proposedproposed dynamic DC-link DC-link voltage voltage control control strategy. strategy.

3. Experimental Results and Discussion This section investigates the influence of the dynamic DC-link voltage control and the cross saturation effects on motor performance. The control strategy is implemented in MATLAB (2010b) SIMULINK. There are three models studied in this paper, namely, Model I which took the entire cross coupling and the saturation effect into account, and it added the DC-link voltage adjustment according to the IPMSM terminal voltage as well. Model II which considered the cross saturation effects, but the DC-link voltage was kept fixed during the test. Model III which neglected the parameter variations Energies 2018, 11, 2046 12 of 22 and the cross coupling effect, meanwhile, it applied the dynamic DC-link voltage control strategy. The parameters change situation such as the inductance and flux vary with current are shown in Figures2 and3. Simulations are conducted using MATLAB/SIUMLINK, but due to this parameter variation, the IPMSM module in the Simulink becomes unavailable so that it should be replaced by the mathematical module. Table1 provides the specifications of the simulation model and the experimental prototype.

Table 1. Interior IPMSM speciﬁcaation.

Parameter Value Rated Power 10 kW Rated Torque 70 Nm Rated Speed 1500 rpm Number of pole pairs 3 d-axis inductance Ld 5.6419 mH Mutual inductance Ldq = Lqd 1.98 mH Stator resistance Rs 0.03165 Ω Magnetic ﬂux Ψf 0.6304 V·s

The first simulation was conducted to verify the motor performance at low torque restriction but with a high speed command situation under the proposed dynamic DC-link voltage control. Figure 10 illustrates the current trajectory when the torque is limited to 90 Nm and the motor speed climbs from 0 to 2800 rpm. This restricted torque value is obviously below the theoretical maximum torque, therefore, a decent flux weakening performance is required to deal with the ever-increasing motor speed. As shown in Figure 10, the cross saturation effects can create an upward bias for the constant torque line, it could raise a higher q-axis current component than it in the conventional motor model within the same torque range. Model II is the first to enter the deep flux weakening region. It shows the evidence that enhancing the DC-link voltage in high speed zone can extend the constant torque operation region. Figure 11 shows the DC-link voltage of three models under the proposed DC-link voltage adjustment strategy. Below 750 rpm, the bus voltage of Mode I and Mode III is controlled to the lower limit of 200 V, and the switching loss of inverter can obviously be reduced as shown in Figure 12. Figure 11 also demonstrates that the range of the low DC-link voltage area can be stretched by the cross saturation effects, thus the inverter loss of Model I is smaller than it in Model II. Above 750 rpm, the DC-link voltage grows with the increasing speed, and the discrepancy of inverter loss between Model II and Model I&III becomes smaller. When the speed is higher than 1500 rpm, the bus voltage of Models I and III reaches the top value and remains at 700 V according to the motor terminal voltage, it also means the voltage limit is higher than it in Model II. Therefore the motor could maintain the constantEnergies torque 2017, 10, drive x FOR PEER at high REVIEW speed without breaking the safety requirement of the voltage13 limits. of 22

60 MTPA MODEL I MODEL II MODEL III 40 MODEL I&II CONST.Tq.Line MODEL III CONST.Tq.Line (A) q I

0 -60 -40 -20 0 20 I (A) d

FigureFigure 10. 10.The The current current trajectory trajectory whenwhen torque command command is is restricted restricted at at9090 Nm. Nm. 800 600 (A)

dc 400

U MODEL I 200 MODEL II MODEL III 0 01234567 Time(s) Figure 11. Simulation results of the bus voltage when torque setpoint is 90 Nm.

300 100 80 200 60 MODEL I MODEL I 40 MODEL II 100 MODEL II MODEL III MODEL III Torque(Nm) 20

Inverter Loss(W) Inverter 0 0 01234567 01234567 Time(s) Time(s) (a) (b)

Figure 12. Simulation results of (a) inverter loss and (b) electromagnetic torque when torque setpoint is 90 Nm.

Figure 13 displays the DC-link voltage utilization rate when the torque is limited to 90 Nm. The maximum rates of Model I and Model II are the same. The high utilization area of Model I and Model III is larger than it in Model II. It concentrates on the low speed high torque region and the high speed region which nearly at 2500 rpm, but in Model II, it is just located in the high speed high torque region. The maximum rate of the bus voltage utilization in Model III is the lowest among three models. The utilization rate of the DC-link voltage can be slightly improved by the proposed scheme.

Energies 2017, 10, x FOR PEER REVIEW 13 of 22 Energies 2017, 10, x FOR PEER REVIEW 13 of 22

60 MTPA 60 MODELMTPA I MODEL III MODEL IIIII MODEL III 40 MODEL I&II CONST.Tq.Line 40 MODEL IIII&II CONST.Tq.Line CONST.Tq.Line

(A) MODEL III CONST.Tq.Line q I (A) q I 20 20

0 0 -60 -40 -20 0 20 -60 -40I -20(A) 0 20 Id(A) Energies 2018, 11, 2046 d 13 of 22 Figure 10. The current trajectory when torque command is restricted at 90 Nm. Figure 10. The current trajectory when torque command is restricted at 90 Nm. 800 800 600 600 (A) (A) dc 400 dc U 400 MODEL I U 200 MODEL III 200 MODEL IIIII 0 MODEL III 001234567 01234567 Time(s) Time(s) Figure 11. Simulation results of the bus voltage when torque setpoint is 90 Nm. Figure 11. SimulationSimulation results results of the bus voltage when torque setpoint is 90 Nm. 100 300 100 300 80 80 200 60 MODEL I 200 60 MODEL I MODEL I 40 MODEL II 100 MODEL III 40 MODEL IIIII

100 Torque(Nm) MODEL IIIII 20 MODEL III MODEL III Torque(Nm) 20

Inverter Loss(W) Inverter 0 0

Inverter Loss(W) Inverter 001234567 001234567 01234567Time(s) 01234567Time(s) Time(s) Time(s) (a) (b) (a) (b) Figure 12. Simulation results of (a) inverter loss and (b) electromagnetic torque when torque setpoint Figure 12. Simulation results of (a) inverter loss and (b) electromagnetic torque when torque setpoint isFigure 90 Nm. 12. Simulation results of (a) inverter loss and (b) electromagnetic torque when torque setpoint is 90 Nm. is 90 Nm. Figure 13 displays the DC-link voltage utilization rate when the torque is limited to 90 Nm. The Figure 13 displays the DC-link voltage utilization rate when the torque is limited to 90 Nm. The maximum rates of Model I and Model II are the same. The high utilization area of Model I and maximumFigure rates 13 displays of Model the I DC-linkand Model voltage II are utilization the same. rateThe whenhigh utilization the torque area is limited of Model to 90 I Nm.and Model III is larger than it in Model II. It concentrates on the low speed high torque region and the ModelThe maximum III is larger rates than of Modelit in Model I and II. Model It concentr II are theates same. on the The low high speed utilization high torque area ofregion Model and I andthe high speed region which nearly at 2500 rpm, but in Model II, it is just located in the high speed high highModel speed III is region larger thanwhich it innearly Model at II.2500 It concentratesrpm, but in Model on the lowII, it speedis just highlocated torque in the region high and speed the high torque region. The maximum rate of the bus voltage utilization in Model III is the lowest among torquespeed regionregion. which The maximum nearly at 2500 rate rpm, of the but bus in Model voltag II,e utilization it is just located in Model in the III high is the speed lowest high among torque three models. The utilization rate of the DC-link voltage can be slightly improved by the proposed threeregion. models. The maximum The utilization rate of therate bus of voltagethe DC-link utilization voltage in can Model be IIIslightly is the improved lowest among by the three proposed models. scheme. scheme.TheEnergies utilization 2017 , 10, x rateFOR PEER of the REVIEW DC-link voltage can be slightly improved by the proposed scheme. 14 of 22

100 100 100 0.1131 0.4150 0.6225 0.1038 0.4525 0.7919 0.56560.5656 0.3394 0.5656 0.7919 0.6788 0.000 0.4525 0.6788 0.7263 0.000

) 0.7263 80 0.2263 0.5656 80 0.1131 0.000 0.2075 0.6788 ) 80

m 0.7263 0.1131 ) 0.1131 0.3113 0.1038 m 0.7263 N m

( 0.2263

N 0.2075 0.2263 N ( 0.6225

e 60 ( 60 60 0.3394 0.3394 0.7919 0.3113 e u 0.2263 0.3394 e q u u r 0.4525 0.4525 0.4150 0.1131 0.4525 q 0.5188 q o r

0.5656 r

40 o 40 T 40 0.5656 0.5188 0.3394 o T

T 0.4525 0.6788 0.6788 0.6225 0.2263 0.7919 0.2075 20 20 0.7919 20 0.2075 0.7263 0.1131 0.1038 0.2263 0.1131 0.2075 0 0 0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Speed (rpm) Speed (rpm) Speed (rpm) (a) MODEL I (b) MODEL II (c ) MODEL III

Figure 1 13.3. The utilization rate of the dc bus voltage when torque setpoint is 90 Nm.Nm.

The second simulation was set to demonstrate the influence of the proposed DC-link voltage The second simulation was set to demonstrate the influence of the proposed DC-link voltage control strategy taking the cross saturation effects into account under an extreme condition. The control strategy taking the cross saturation effects into account under an extreme condition. The torque torque setpoint was given beyond the maximum value that can be reached, while the speed setpoint was given beyond the maximum value that can be reached, while the speed reference is set to reference is set to 3000 rpm. As shown in Figure 14, the cross saturation effects have an obvious 3000 rpm. As shown in Figure 14, the cross saturation effects have an obvious impact on the MTPA impact on the MTPA trajectory and the constant torque locus, thus the discrepancy of control trajectory and the constant torque locus, thus the discrepancy of control strategy applied the fixed strategy applied the fixed parameters will become significant. Figure 15 illustrates that the bus parameters will become significant. Figure 15 illustrates that the bus voltage variation trend of Model voltage variation trend of Model I and Model III is almost identical in this simulation. Even though I and Model III is almost identical in this simulation. Even though the DC-link voltage of Model the DC-link voltage of Model III is kept at almost 700 V, the terminal voltage still drops gradually III is kept at almost 700 V, the terminal voltage still drops gradually because of the saturation effect because of the saturation effect in q-axis. Figures 12 and 15 are show the evidence that models earn benefits from keeping the bus voltage as low as possible to reduce the inverter loss in low speed region, however, the disadvantage of high loss in high speed area becomes unconsidered in comparison with the advantage of the more extensive constant torque drive area. The difference between torque performances among three models is significant in the second simulation as shown in Figure 16. Note that the slope of Model II and Model III is almost equal, in other words, the turning speed from the constant torque to constant power operation can be increased through boosting the bus voltage, but the range of flux weakening is not changed obviously. However, the slope of Model I is larger than others, the reason is the d-axis current component increases in deep flux weakening operation so that the degree of saturation in q-axis could be relieved which profit from the introduction of the cross coupling inductance.

60 50

40 (A)

q 30 I

20 MTPA MODEL I MODEL II 10 MODEL III MODEL I&II Cons.Tq.Line 0 MODEL III Cons.Tq.Line -60 -40 -20 0 20 I (A) d Figure 14. The current trajectory when the torque setpoint is 190 Nm.

750 600

(V) 450 dc

U 300 MODEL I MODEL II 150 MODEL III 0 0 1 2 3 4 5 6 7 Time(s) Figure 15. Simulation result the bus voltage when torque command is limited at 190 Nm.

Energies 2017, 10, x FOR PEER REVIEW 14 of 22

Figure 13. The utilization rate of the dc bus voltage when torque setpoint is 90 Nm.

The second simulation was set to demonstrate the influence of the proposed DC-link voltage control strategy Figuretaking 13. the The crossutilization saturation rate of the effects dc bus voltageinto account when torque under setpoint an extremeis 90 Nm. condition. The torque setpoint was given beyond the maximum value that can be reached, while the speed The second simulation was set to demonstrate the influence of the proposed DC-link voltage referencecontrol is strategyset to 3000 taking rpm. the Ascross shown saturation in Figure effects 14, into the account cross saturationunder an extreme effects condition.have an obviousThe impacttorque on thesetpoint MTPA was trajectory given beyo andnd the maximumconstant torquevalue thatlocus, can thus be reached,the discrepancy while the ofspeed control strategyreference applied is set the to fixed3000 rpm.paramete As shownrs will in Figurebecome 14, significant. the cross saturation Figure 15effects illustrates have an that obvious the bus voltageimpact variation on the trend MTPA of trajectoryModel I and and Model the constant III is al torquemost identicallocus, thus in thethis discrepancysimulation. ofEven control though the DC-linkstrategy voltageapplied ofthe Model fixed parameteIII is keptrs atwill almost become 700 significant. V, the terminal Figure volt15 illustratesage still dropsthat the gradually bus voltage variation trend of Model I and Model III is almost identical in this simulation. Even though becauseEnergies of 2018the, 11saturation, 2046 effect in q-axis. Figures 12 and 15 are show the evidence that models14 of 22 earn benefitsthe DC-linkfrom keeping voltage theof Model bus voltage III is kept as atlow almost as possible 700 V, the to terminalreduce thevolt ageinverter still drops loss ingradually low speed region,because however, of the saturationthe disadvantage effect in q -axis.of high Figures loss 12 in and high 15 are speed show areathe evidence becomes that unconsidered models earn in inbenefitsq-axis. from Figures keeping 12 and the 15 bus are voltage show the as evidencelow as possible that models to reduce earn benefitsthe inverter from loss keeping in low the speed bus comparison with the advantage of the more extensive constant torque drive area. The difference voltageregion, ashowever, low as possible the disadvantage to reduce the of inverter high loss loss in in lowhigh speed speed region, area however,becomes theunconsidered disadvantage in between torque performances among three models is significant in the second simulation as shown ofcomparison high loss inwith high the speed advantage area becomes of the unconsideredmore extensive in comparisonconstant torque with drive the advantage area. The of difference the more in Figureextensivebetween 16. torque constantNote performancesthat torque thedrive slope among area. of TheModel three difference modelsII and between isModel significant torqueIII is in performancesalmost the second equal, simulation among in other three as words, modelsshown the turningisin significantFigure speed 16. from inNote the the that second constant the simulationslope torque of Model as to shown consII an intantd FigureModel power 16III. is Noteoperation almost that equal, the can slope inbe other ofincreased Model words, II through andthe boostingModelturning the III speedbus is almost voltage, from equal, the but inconstant otherthe range words, torque of the fluxto turning cons weakeningtant speed power from is notoperation the constantchanged can torque obviously.be increased to constant However, through power the slopeoperationboosting of Model the can I busis be larger increasedvoltage, than but through others, the range boosting the of reason flux the weakening busis the voltage, d-axis is butnot current thechanged range component obviously. of flux weakening increases However, is in notthe deep flux changedweakeningslope of obviously.Model operation I is However,larger so than that the others, the slope degree ofthe Model reason of Isaturation isis largerthe d-axis than in current others,q-axis thecouldcomponent reason be isrelieved increases the d-axis which in current deep profit fromcomponentflux the introductionweakening increases operation of in the deep cross so flux that coupling weakening the degree inductance. operation of saturation so that in theq-axis degree could of saturationbe relieved in whichq-axis couldprofit befrom relieved the introduction which profit offrom the cross the introduction coupling inductance. of the cross coupling inductance. 60 60 50 50 4040 (A) (A) q 30 q I 30 I

2020 MTPA MTPA MODEL MODEL II MODEL MODEL IIII 1010 MODEL MODEL IIIIII MODEL MODEL I&III&II Cons.Tq.Line MODEL III Cons.Tq.Line 0 0 MODEL III Cons.Tq.Line -60 -40 -20 0 20 -60 -40 -20I (A) 0 20 Id(A) d Figure 14. The current trajectory when the torque setpoint is 190 Nm. FigureFigure 14.14. TheThe current current trajectory trajectory when when the torquetorque setpoint setpoint is 190is 190 Nm. Nm. 750 750600

600(V) 450 dc (V) 450U 300 MODEL I dc MODEL II U 300150 MODEL MODEL III I 150 0 MODEL II 01234567 MODEL III 0 Time(s) 01234567 Figure 15. Simulation result the bus voltage whenTime(s) torque command is limited at 190 Nm.

EnergiesFigure 2017Figure, 10 15., x FOR Simulation 15. PEERSimulation REVIEW result result the the bus bus voltage voltage when when torquetorque command command is limitedis limited at 190 at 190 Nm. Nm.15 of 22

300 200 250 150 200 150 100 100 MODEL I 50 MODEL I 50 MODEL II Torque(Nm) MODEL II MODEL III MODEL III Inverter Loss(W) Inverter 0 0 01234567 01234567 Time(s) Time(s) (a) (b)

Figure 16. Simulation result of the (a) inverter loss and (b) electromagnetic torque when torque the Figure 16. Simulation result of the (a) inverter loss and (b) electromagnetic torque when torque the command is limited at 190 Nm. command is limited at 190 Nm.

The DC-link voltage utilization rate when the torque is restricted to 190 Nm is as shown in Figure 17. TheThe proposed DC-link control voltage strategy utilization helps rate the whensystem the to torqueacquire is the restricted largest high to 190 voltage Nm isutilization as shown rate in areaFigure among 17. The three proposed models. control It also strategy can be helps seen the that system the top to acquire rate value the largest and its high area voltage of Model utilization I and Model II are slightly higher than Model III, which indicates that the control strategy considering cross saturation could implement more effective utilization of the dc bus voltage.

0.5587 0.000 180 0.2100 200 0.000 0.7525 160 0.4470 0.6705 0.7350 0.000 0.1075 180 0.3352 0.1118 160 0.4200 0.5250 0.7350 0.1075 140 0.1050 0.6450 0.6300 0.000 160 0.2235 140 0.4300 0.2150 120 0.7823 0.2100 140 0.7823 120 0.3352 0.3150 120 0.3225 100 0.3150 0.3225 100 0.4470 0.4200 100 0.4300 80 80 0.5250 80 0.2150 0.5375 0.2235 0.5587 Torque Torque (Nm)

Torque (Nm) 60 60 0.6300

60 (Nm) Torque 0.5375 0.6450 0.6705 40 0.5587 0.1118 0.6705 40 0.4470 40 0.7350 0.7525 0.7823 20 20 20 0.2100 0.2150 0.2235 0.7823 0.1075 0.2235 0.1050 0 0 0.1118 0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Speed (rpm) Speed (rpm) Speed (rpm)

Figure 17. The DC bus voltage utilization rate when torque the command is limited at 190 Nm.

From the series of simulation works described above, it can be concluded that the proposed dynamic DC-link voltage adjustment scheme considering the cross saturation effects can expand the motor operation range over the entire speed region, precisely, not only the constant torque region in low speed but also the flux weakening range in high speed, therefore the control precision of algorithm and the motor output characteristic are can be enhanced. To testify the control strategy, a 10 kW IPMSM prototype has been established, as shown in Figure 18. The 12 kVA active front-end is a DC-DC converter, linked the DC source to realize the modification of the DC-link voltage (it packed with the inverter in the red box in Figure 18). The influence of temperature in the permanent magnet flux was neglected caused by the imperfect facility. The torque was detected by the HNJ-500 torque transducer. The switching and the sampling frequency of the system was 5 kHz. The current transducer is PEM CWT300LF (Power Electronic Measurements Ltd., Nottingham, UK) and the voltage transducer is PINTECH N1070A (PinTech, Guangzhou, China) to acquire the precision signals. There were two groups of experiments under two torque setpoints to show the difference between control strategies, while one model kept the constant DC-link voltage at 450 V.

Figure 18. Laboratory prototype of current trajectory control with sampling frequency f = 5 kHz.

Energies 2017, 10, x FOR PEER REVIEW 15 of 22 Energies 2017, 10, x FOR PEER REVIEW 15 of 22 300 200 300 200 250 150 250200 150 200150 100 150100 MODEL I 100 50 MODEL I MODEL II Torque(Nm) MODEL II 10050 MODEL I MODEL I MODEL III 50 MODEL III MODEL II Torque(Nm) MODEL II

Inverter Loss(W) Inverter 50 0 MODEL III 0 MODEL III Inverter Loss(W) Inverter 001234567 001234567 01234567Time(s) 01234567Time(s) Time(s) (a) (bTime(s)) (a) (b) Figure 16. Simulation result of the (a) inverter loss and (b) electromagnetic torque when torque the Figurecommand 16. isSimulation limited at result190 Nm. of the (a) inverter loss and (b) electromagnetic torque when torque the command is limited at 190 Nm. Energies 2018, 11, 2046 15 of 22 The DC-link voltage utilization rate when the torque is restricted to 190 Nm is as shown in Figure 17. TheThe proposed DC-link voltagecontrol utilizationstrategy helps rate thewhen system the torque to acquire is restricted the largest to 190 high Nm voltage is as shown utilization in Figure rate rate17.area The areaamong proposed among three three control models. models. strategy It also It alsohelps can can bethe beseen system seen that that to the acquire the top top rate the rate valuelargest value and high and its itsvoltage area area of ofutilization Model Model I andrate Modelarea among IIII areare slightlythree slightly models. higher higher thanIt thanalso Model canModel be III, seenIII, which whic that indicatesh theindicates top that rate that the value controlthe controland strategy its areastrategy considering of Model considering I cross and saturationModelcross saturation II are could slightly could implement higher implement more than effectivemoreModel effe III, utilizationctive whic utilizationh indicates of the of dc thethat bus dc voltage.the bus control voltage. strategy considering cross saturation could implement more effective utilization of the dc bus voltage.

0.5587 0.000 180 0.2100 200 0.000 0.7525 160 0.4470 0.6705 0.7350 0.000 180 0.1075 0.1118 160 0.4200 0.5250 0.7350 0.1075 0.33520.5587 0.000 180 0.2100 200 0.000 140 0.6300 0.1050 160 0.6450 0.7525 160 0.4470 0.6705 0.7350 0.000 0.000 0.1075 0.2235 140 180 0.4300 0.2150 0.3352 0.7823 0.1118 160 0.4200 0.5250 0.7350 0.2100 140 0.1075 140120 0.1050 0.6450 0.7823 120 0.6300 0.000 160 0.3225 0.22350.3352 140 0.3150 120 0.4300 0.2150 100 0.7823 0.3150 0.2100 140 0.3225 120 100 0.7823 0.4470 120 0.4200 100 0.4300 0.3352 0.3150 120 0.3225 10080 80 0.3150 0.3225 100 0.5250 80 0.2150 0.5375 0.2235 0.5587 0.4200 0.4300 Torque (Nm) 0.4470 Torque (Nm) 100 60 80 60 0.6300 60 0.6705 (Nm) Torque 80 80 0.5375 0.6450 0.5587 0.1118 0.6705 0.5250 0.2150 0.5375 400.2235 0.5587 40 Torque Torque (Nm) 0.7350

Torque (Nm) 60 40 0.4470 60 0.6300 60 0.5375 0.7525 0.6705 0.7823 (Nm) Torque 20 0.6450 20 0.5587 0.1118 0.6705 20 0.2100 40 0.2150 40 0.2235 0.7823 40 0.7350 0.1075 0.2235 0.4470 0.1050 0 0.7525 0.1118 0.7823 0 20 200 20 0.2100 0 5000.2150 1000 1500 2000 2500 0 5000.2235 1000 1500 20000.782 25003 0 500 1000 1500 2000 2500 0.1075 0.2235 0.1050 0 Speed (rpm) 0 0.1118 Speed (rpm) 0 Speed (rpm) 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Speed (rpm) Speed (rpm) Speed (rpm)

Figure 17. The DC bus voltage utilization rate when torque the command is limited at 190 Nm. Figure 17. The DC bus voltage utilization rate when torque the command is limited at 190 Nm. Figure 17. The DC bus voltage utilization rate when torque the command is limited at 190 Nm. From the series of simulation works described above, it can be concluded that the proposed dynamicFrom DC-link the seriesseries voltage ofof simulationsimulation adjustment works scheme describeddescribed consider above, ing the it cross can saturation bebe concludedconcluded effects thatthat can thethe expand proposedproposed the dynamicmotor operation DC-link DC-link rangevoltage over adjustment the entire scheme speed consider consideringregion, precisely,ing the cross not saturation only the constant effects can torque expand region the motorin low operationspeed but rangerange also overtheover flux thethe entireweakeningentire speed speed range region, region, in precisely, highprecisely, speed, not not onlytherefore only the the constant the constant control torque torque precision region region inof lowinalgorithm low speed speed butand alsobutthe alsomotor the flux the output weakeningflux weakeningcharacteristic range inrange highare canin speed, high be enhanced. thereforespeed, therefore the control the precision control ofprecision algorithm of andalgorithm theTo motortestify and outputthethe motorcontrol characteristic output strategy, characteristic area 10 can kW be IPMSM enhanced.are can beprototype enhanced. has been established, as shown in FigureTo 18. testifytestify The thethe12 kVA controlcontrol active strategy, front-end aa 1010 is kWkW a DC-DC IPMSMIPMSM converter, prototypeprototype linked hashas beenbeen the established,established,DC source to as realize shown the in Figuremodification 18.18. The The of 12 the 12 kVA kVADC-link active active voltage front-end front-end (it packedis isa DC-DC a DC-DCwith converter,the converter, inverter linked in linked the the red theDC box DCsource in source Figure to realize to 18). realize Thethe themodificationinfluence modification of temperatureof the of DC-link the DC-link in voltagethe voltagepermanent (it packed (it packedmagnet with with theflux inverter thewas inverter neglected in the in red thecaused box red in boxby Figure the in Figure imperfect 18). The18). Theinfluencefacility. influence The of temperaturetorque of temperature was indetected the inthe permanent permanentby the HNJ-magnet magnet500 fluxtorque flux was was transducer. neglected neglected causedThe caused switching by by the imperfect and the facility.sampling TheThe frequency torque torque was ofwas detectedthe detected system by was theby HNJ-5005the kHz. HNJ- Th torque500e current torque transducer. transducer transducer. The switchingis PEMThe switchingCWT300LF and the samplingand (Power the frequencysamplingElectronic frequencyMeasurements of the system of the wasLtd., system 5 Nottingham, kHz. was The 5 currentkHz. UK) Th and transducere current the voltage transducer is PEM transducer CWT300LF is PEM is CWT300LFPINTECH (Power Electronic N1070A(Power MeasurementsElectronic(PinTech, Guangzhou,Measurements Ltd., Nottingham, China) Ltd., to Nottingham, acquire UK) andthe precision theUK) voltage and signals.the transducer voltage There transducer were is PINTECH two groupsis PINTECH N1070A of experiments (PinTech,N1070A Guangzhou,(PinTech,under two Guangzhou, torque China) setpoints to acquireChina) to to theshow acquire precision the thedifference signals.precision between There signals. were control There two groupsstrategies,were two of experiments groupswhile one of experimentsmodel under kept two torqueunderthe constant two setpoints torque DC-link to setpoints show voltage the to differenceat show 450 V. the between difference control between strategies, control while strategies, one model while kept one themodel constant kept DC-linkthe constant voltage DC-link at 450 voltage V. at 450 V.

Figure 18. Laboratory prototype of current trajectory control with sampling frequency f = 5 kHz. Figure 18. Laboratory prototype of current trajectory control with sampling frequency f = 5 kHz. Figure 18. Laboratory prototype of current trajectory control with sampling frequency f = 5 kHz.

3.1. Torque Speed Characteristic It has been demonstrated elaborately in [27] that the CTCS can help the motor reach its high torque performance potential in low speed region under the low torque setpoint restriction, and in high speed operation, its output torque would be slightly influenced by the magnetic saturation effects. However, in this paper, Figure 19 shows the evidence that the boosted bus voltage can offset the side effect of the cross saturation on the torque performance to delay the flux-weakening operation. As it can be seen, Model II applying the fixed DC-link voltage should sacrifice the torque to ensure the terminal voltage does not exceed the safety boundary. Energies 2017, 10, x FOR PEER REVIEW 16 of 22 Energies 2017, 10, x FOR PEER REVIEW 16 of 22 3.1. Torque Speed Characteristic 3.1. Torque Speed Characteristic It has been demonstrated elaborately in [27] that the CTCS can help the motor reach its high It has been demonstrated elaborately in [27] that the CTCS can help the motor reach its high torque performance potential in low speed region under the low torque setpoint restriction, and in torque performance potential in low speed region under the low torque setpoint restriction, and in high speed operation, its output torque would be slightly influenced by the magnetic saturation high speed operation, its output torque would be slightly influenced by the magnetic saturation effects. However, in this paper, Figure 19 shows the evidence that the boosted bus voltage can offset effects. However, in this paper, Figure 19 shows the evidence that the boosted bus voltage can offset the side effect of the cross saturation on the torque performance to delay the flux-weakening the side effect of the cross saturation on the torque performance to delay the flux-weakening Energiesoperation.2018, 11, 2046As it can be seen, Model II applying the fixed DC-link voltage should sacrifice the torque16 of 22 operation. As it can be seen, Model II applying the fixed DC-link voltage should sacrifice the torque to ensure the terminal voltage does not exceed the safety boundary. to ensure the terminal voltage does not exceed the safety boundary. 100 100 80 80 60 60 40 MODEL I 40 MODEL III Torque (Nm) 20 MODEL IIIII

Torque (Nm) 20 0 MODEL III 0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 Speed (rpm) Speed (rpm) Figure 19. Torque-speed characteristic in different models under Te* = 90 Nm. FigureFigure 19. 19.Torque-speed Torque-speed characteristic characteristic in different models models under under TeT* e=* 90= Nm. 90 Nm. In order to discuss and verify elaborately the influence of the proposed dynamic bus voltage In order to discuss and verify elaborately the influence of the proposed dynamic bus voltage adjustmentIn order to strategy discuss on and the verifyoutput elaborately torque performa the influencence, the second of the test proposed shrinked dynamic the current bus limit voltage adjustment strategy on the output torque performance, the second test shrinked the current limit adjustmentand enhanced strategy the on torque the output command torque value, performance, therefore, theit is second easier testfor the shrinked motor theto enter current the limit flux and and enhanced the torque command value, therefore, it is easier for the motor to enter the flux enhancedweakening the torque operation command in the process value, therefore,of speed acce it isleration. easier forBelow the motorthe turning to enter speed, the the flux achieved weakening weakening operation in the process of speed acceleration. Below the turning speed, the achieved operationtorque inofthe Model process III is of slightly speed acceleration.higher than others Below. Due the turningto the restriction speed, the of achievedcurrent trajectory torque of and Model torque of Model III is slightly higher than others. Due to the restriction of current trajectory and III isoffset slightly of the higher MTPA than curve, others. the required Due to thedemagnetizing restriction ofcurrent current id of trajectory Model III and is the offset lowest of thewhich MTPA offset of the MTPA curve, the required demagnetizing current id of Model III is the lowest which could degrade the contribution of the relucti ance torque. Despite the small cross coupling curve,could the degrade required the demagnetizing contribution of current the reluctd ofance Model torque. III is theDespite lowest the whichsmall couldcross degradecoupling the inductance and parameter variation, the reflection of torque performance among three control contributioninductance of and the parameter reluctance variation, torque. Despitethe reflecti theon small of torque cross couplingperformance inductance among three and control parameter strategies is significant, as shown in Figure 20. The dynamic DC-link voltage control thinking about variation,strategies the is reflection significant, of as torque shown performance in Figure 20. among The dynamic three controlDC-link strategies voltage control is significant, thinking asabout shown the cross saturation effect can help the motor dig out its higher potential and earn the wider speed in Figurethe cross 20. saturation The dynamic effect DC-link can help voltage the motor control dig out thinking its higher about potential the cross and saturation earn the wider effect speed can help adjustment range is proved. the motoradjustment dig outrange its is higher proved. potential and earn the wider speed adjustment range is proved. 200 200 150 150 100 100 MODEL I

Torque (Nm) 50 MODEL III

Torque (Nm) 50 MODEL IIIII 0 MODEL III 0 500 1000 1500 2000 2500 500 1000Speed (rpm) 1500 2000 2500 Speed (rpm) Figure 20. Torque-speed characteristic in different models under Te* = 190 Nm. Figure 20. Torque-speed characteristic in different models under Te* = 190 Nm. Figure 20. Torque-speed characteristic in different models under Te* = 190 Nm. 3.2. Dynamic Performance of Dynamic Voltage Adjustment with Speed Reference Variation 3.2. Dynamic Performance of Dynamic Voltage Adjustment with Speed Reference Variation 3.2. DynamicThe test Performance prototype of is Dynamic controlled Voltage at speed Adjustment mode. For with the Speedfirst experiment, Reference Variation the reference speed is The test prototype is controlled at speed mode. For the first experiment, the reference speed is displayed in Figure 21. The rated speed of the motor is 1500 rpm and the torque value in the control displayedThe test prototypein Figure 21. is The controlled rated speed at speed of the mode.motor is For 1500 the rpm ﬁrst and experiment, the torque value the reference in the control speed is strategy is limited at 90 Nm, which below the theoretical maximum torque. Model I applies the displayedstrategy in is Figure limited 21 at. The90 Nm, rated which speed below of the the motor theoretical is 1500 maximum rpm and thetorque. torque Model value I applies in the controlthe proposed dynamic bus voltage algorithm, while Model II keeps the DC-Link voltage fixed during strategyproposed is limited dynamic at 90bus Nm, voltage which algorithm, below while the theoretical Model II keeps maximum the DC-Link torque. voltage Model fixed I appliesduring the the test. Both of them seek the parameter variation. proposedthe test. dynamic Both of them bus voltage seek the algorithm, parameter whilevariation. Model II keeps the DC-Link voltage ﬁxed during the test.Energies Both of2017 them, 10, x FOR seek PEER the REVIEW parameter variation. 17 of 22

3000 2500 2000 1500 1000 500 0 01234567 Reference Speed (rpm) Time (s) Figure 21. The reference speed variation with the DC-link voltage control strategy when torque is Figure 21. The reference speed variation with the DC-link voltage control strategy when torque is limited at 90 Nm. limited at 90 Nm. Figure 22 displays the responds of the current and terminal voltage amplitude of the two models. When the reference speed changes, both current and voltage obey the restriction well. The voltage limit of the Model I changes with the step climb of the speed. After 2 s, the speed increases beyond the nominal value, the voltage limit reaches its high boundary near 480 V. The amplitude of terminal voltage are almost the same when the speed is below 2000 rpm, however, after 4 s, the speed reference is stepped to 2500 rpm, the voltage of Model I is higher than that of Model II.

Figure 22. Results of current and voltage under the step change of the reference speed when the torque setpoint is 90 Nm. (a) actual current and the current limit of Model I; (b) actual current and the current limit of Model II; (c) actual voltage and the voltage limit of Model I; (d) actual voltage and the voltage limit of Model II.

Figure 23 compares the phase current and the bus voltage of the test. The DC-link voltage of the Model II is constant at 450 V. It can be seen that the bus voltage of Model I is lower than the fixed value when the motor speed is below the nominal value. The phase currents of the two models are nearly the same.

Energies 2017, 10, x FOR PEER REVIEW 17 of 22

3000 2500 2000 1500 1000 500 0 01234567 Reference Speed (rpm) Time (s) Energies 2018, 11, 2046 17 of 22 Figure 21. The reference speed variation with the DC-link voltage control strategy when torque is limited at 90 Nm. Figure 22 displays the responds of the current and terminal voltage amplitude of the two models. Figure 22 displays the responds of the current and terminal voltage amplitude of the two When the reference speed changes, both current and voltage obey the restriction well. The voltage models. When the reference speed changes, both current and voltage obey the restriction well. The limit of the Model I changes with the step climb of the speed. After 2 s, the speed increases beyond voltage limit of the Model I changes with the step climb of the speed. After 2 s, the speed increases the nominalbeyond the value, nominal the voltagevalue, the limit voltage reaches limit its reaches high boundaryits high boundary near 480 near V. 480 The V. amplitude The amplitude of terminal of voltageterminal are almost voltage the are same almost when thethe same speed when is belowthe speed 2000 is rpm,below however, 2000 rpm, after however, 4 s, the after speed 4 s, reference the is steppedspeed toreference 2500 rpm, is stepped the voltage to 2500 of rpm, Model the voltag I is highere of Model than I that is higher of Model than that II. of Model II.

FigureFigure 22. Results 22. Results of current of current and and voltage voltage under under the the step st changeep change of theof the reference reference speed speed when when the the torque setpointtorque is 90 setpoint Nm. ( ais) 90 actual Nm. current(a) actual and current the current and the limit current of Modellimit of I; Model (b) actual I; (b) currentactual current and the and current limitthe of Modelcurrent II; limit (c) actualof Model voltage II; (c) andactual the voltage voltage and limit the ofvoltage Model limit I; ( dof) actualModel voltageI; (d) actual and voltage the voltage limitand of Model the voltage II. limit of Model II.

Figure 23 compares the phase current and the bus voltage of the test. The DC-link voltage of the FigureModel II23 is compares constant at the 450 phase V. It can current be seen and that the the bus bus voltage voltage of of the Model test. I Theis lower DC-link than voltagethe fixed of the Modelvalue II is when constant the motor at 450 speed V. It can is below be seen the that nominal the bus value. voltage The phase of Model currents I is lowerof the thantwo models the ﬁxed are value whennearly the motor the same. speed is below the nominal value. The phase currents of the two models are nearly the same.Energies 2017, 10, x FOR PEER REVIEW 18 of 22

Figure 23. The phase current and the bus voltage of two models under Te* = 90 Nm.* (a) the phase current; Figure 23. The phase current and the bus voltage of two models under Te = 90 Nm. (a) the phase current;(b)the (b)the bus busvoltage. voltage. In order to discuss the performance of the proposed control strategy when the deeper flux weakening is required, the current limit value is shrunk and the step change amplitude of reference speed is higher than in the first test. Figure 24 reflects the speed reference variation situation.

3500 3000 2500 2000 1500 1000 500 0

Reference speed (rpm) 01234567 Time (s) Figure 24. The reference speed variation with the DC-link voltage control strategy when torque is limited at 190 Nm.

As the current limit shrinks, the turning speed and the theoretical maximum torque value are reduced, therefore, the threshold of the flux weakening control is lower than in the first test. Applying the fixed bus voltage (which is raised to 500 V to protect the test rig), as shown in Figure 25b,d, the fluctuation of the current and the voltage is obviously larger than it in the Model I. In the low speed area, below 2000 rpm, the voltage amplitude of two models is the same. When the motor accelerates above 2000 rpm, the proposed dynamic DC link voltage control algorithm adjusts the DC-DC converter to boost the bus voltage based on the real-time asked terminal voltage feedback. Note that, despite of the working condition and the torque restriction, the robustness of the control strategy can be observed in these two experiments. The bus voltage in the second test is higher than it in the first test, as shown in Figure 26b. It hits the high boundary at 700 V in high speed region. The phase currant is nearly consistent during the test as shown in Figure 26a.

Energies 2017, 10, x FOR PEER REVIEW 18 of 22

EnergiesFigure2018, 23.11, 2046The phase current and the bus voltage of two models under Te* = 90 Nm. (a) the phase current;18 of 22 (b)the bus voltage.

In order to discuss the performance of the proposed control strategy when the deeper flux flux weakening is required, the current limit value is shrunkshrunk and the step change amplitude of reference speed is higher than in the firstfirst test. Figure 24 reflectsreflects thethe speedspeed referencereference variationvariation situation.situation.

3500 3000 2500 2000 1500 1000 500 0

Reference speed (rpm) 01234567 Time (s) Figure 24. The reference speed variation with the DC-link voltage control strategy when torque is Figure 24. The reference speed variation with the DC-link voltage control strategy when torque is limited at 190 Nm. limited at 190 Nm.

As the current limit shrinks, the turning speed and the theoretical maximum torque value are reduced,Asthe therefore, current the limit threshold shrinks, of the the turning flux weakening speed and control the theoretical is lower than maximum in the first torque test. valueApplying are thereduced, fixed therefore,bus voltage the (which threshold is rais ofed the to flux 500 weakening V to protect control the test is lower rig), thanas shown in the in first Figure test. 25b,d, Applying the fluctuationthe fixed bus of the voltage current (which and the is raised voltage to is 500 obviously V to protect larger thethan test it in rig), the asModel shown I. in Figure 25b,d, Energiesthe fluctuationIn 2017 the, low10, x ofFORspeed the PEER currentarea, REVIEW below and the2000 voltage rpm, the is obviously voltage amplitude larger than of ittwo in themodels Model is the I. same.19 When of 22 the motor accelerates above 2000 rpm, the proposed dynamic DC link voltage control algorithm adjusts the DC-DC converter to boost the bus voltage based on the real-time asked terminal voltage feedback. Note that, despite of the working condition and the torque restriction, the robustness of the control strategy can be observed in these two experiments. The bus voltage in the second test is higher than it in the first test, as shown in Figure 26b. It hits the high boundary at 700 V in high speed region. The phase currant is nearly consistent during the test as shown in Figure 26a.

Figure 25. ResponseResponse of of current current and voltage amplitude to to the speed reference step variation when torque command isis 190190 Nm.Nm. ((aa)) actual actual current current and and the the current current limit limit of Modelof Model I; ( bI;) actual(b) actual current current and andthe currentthe current limit oflimit Model of Model II; (c) actual II; (c) voltage actual andvoltage the voltageand the limit voltage of Model limit I;of (d Model) actual I; voltage (d) actual and voltagethe voltage and limitthe voltage of Model limit II. of Model II.

In the low speed area, below 2000 rpm, the voltage amplitude of two models is the same. When the motor accelerates above 2000 rpm, the proposed dynamic DC link voltage control algorithm

Figure 26. The phase current and the bus voltage value of two models under Te* = 190 Nm. (a) the phase current; (b) the bus voltage.

4. Conclusions This paper proposes a dynamic DC-link voltage control strategy taking the cross coupling and magnetic saturation effect into consideration. The strategy is divided into three parts: the current reference vector generation, the optimal current vector direction adjustment and the bus voltage regulation. It is a discrete method that could combine and execute variable parameters in each iteration step. The first step translates the torque request into the ideal current reference. Then by estimating the position of linearized torque and voltage line in current incremental coordinates, the optimal current vector can be derived. At last, the bus voltage regulator takes the actual terminal voltage signal as control reference to modify the DC-link voltage. From the simulation and experimental results, the following conclusions can be proposed: In the low torque command and low speed region, the proposed control strategy is very accurate in tracking the MTPA trajectory without predefined parameters and reduces the inverter loss with low

Energies 2017, 10, x FOR PEER REVIEW 19 of 22

Energies 2018, 11, 2046 19 of 22 adjusts the DC-DC converter to boost the bus voltage based on the real-time asked terminal voltage feedback.Figure Note25. Response that, despite of current of the and working voltage condition amplitude and to the the speed torque reference restriction, step the variation robustness when of the controltorque strategy command can beis 190 observed Nm. (a in) actual these current two experiments. and the current The buslimit voltage of Model in theI; (b second) actual testcurrent is higher thanand it in the the current ﬁrst test, limit as shownof Model in II; Figure (c) actual 26b. Itvoltage hits the and high the boundaryvoltage limit at 700of Model V in high I; (d speed) actual region. Thevoltage phase currantand the isvoltage nearly limit consistent of Model during II. the test as shown in Figure 26a.

** FigureFigure 26. 26. TheThe phase phase current current and and the the bus bus voltage voltage value value of of two models under Tee == 190 190 Nm. Nm. (a (a) )the the phasephase current; current; ( (bb)) the the bus bus voltage. voltage.

4.4. Conclusions Conclusions ThisThis paper paper proposes proposes a a dynamic dynamic DC-link DC-link voltage voltage control control strategy strategy taking taking the the cross cross coupling coupling and and magneticmagnetic saturation saturation effect effect into into consideration. consideration. The The strategy strategy is is divided divided into into three three parts: parts: the the current current referencereference vector vector generation, generation, the the optimal optimal current current vector vector direction direction adjustment adjustment and and the the bus bus voltage voltage regulation.regulation. It isis aa discrete discrete method method that that could could combine combine and executeand execute variable variable parameters parameters in each iterationin each iterationstep. The step. first The step first translates step translates the torque the request torque into request the ideal into currentthe ideal reference. current reference. Then by estimating Then by estimatingthe position the of position linearized of linearized torque and torque voltage and line voltage in current line in incremental current incr coordinates,emental coordinates, the optimal the optimalcurrent current vector canvector be derived.can be derive At last,d. At the last, bus the voltage bus voltage regulator regulator takes the takes actual the actual terminal terminal voltage voltage signal signalas control as control reference reference to modify to mod theify the DC-link DC-link voltage. voltage. From From the the simulation simulation andand experimental results, results, thethe following following conclusions conclusions can can be be proposed: proposed: InIn the the low low torque torque command command and and low low speed speed region, region, the the proposed proposed control control strategy strategy is very is very accurate accurate in trackingin tracking the the MTPA MTPA trajectory trajectory without without predefined predefined parameters parameters and and reduces reduces the the inverter inverter loss loss with with low low bus voltage. When the speed climbs, the proposed scheme can obviously expand the constant torque operation region, the cross saturation effects have no evident influence on torque performance but it could extend the range of the low DC-link voltage area, which results in a low inverter loss from the global point of view compared with the fixed parameter model. In the high torque command situation, the range of the whole speed modification area is enlarged by the proposed control strategy, not only the constant torque region but also the flux weakening area. The system stability is guaranteed and the voltage ripple is reduced during the step change of the reference speed. To sum up: the proposed dynamic DC-link voltage control could not only realize the robustness and high reliability, but also ensures the optimal solution for the globe efficiency. The DC-link voltage utilization can also be improved. In the future, studies will be undertaken in energy feedback and regeneration mechanisms based on the proposed DC-link voltage control scheme by applying supercapacitors or batteries as the DC source with the bidirectional DC-DC converter.

Author Contributions: H.L., D.L. designed the proposed control strategy, H.L. and J.G. conducted experimental works, modeling and FEA simulation, S.H., D.L. and P.F. gave help of paper writing. Funding: This research received no external funding. Acknowledgments: This work was supported in part by the Education Ministry Joint Fund of China (51577052). Energies 2018, 11, 2046 20 of 22

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

Nomenclature

Ld, Lq d-axis and q-axis inductance Ψd, Ψq d-axis and q-axis ﬂux linkage Ψf Permanent magnetic ﬂux linkage Rs Stator resistance Ldd, Lqq d-axis and q-axis self-inductance Ldq, Lqd d-axis and q-axis mutual inductance id, iq Stator d-axis and q-axis current Ud, Uq Stator d-axis and q-axis voltage Udc DC-link voltage ϕ Power factor angle VCE, VEC Voltage drop of IGBT and FWDI base on the datasheet |i| Amplitude of the line current Eon, Eoff Energy loss of IGBT for turn-on and turn-off process PCond,igbt, PCond,fwdi Conduction loss of IGBT and FWDI Psw,igbt, Psw,fwdi Switching loss of IGBT and FWDI Te Electromagnetic torque Tecr Torque introduced by the cross coupling effect * Te Reference electromagnetic torque Ts Switching frequency Uref Reference DC bus voltage of the IGBT Err Energy for reverse recovery of FWDI. d Duty cycle UD DC source voltage M Voltage gain ∆u Safety margin to avoid the terminal voltage of IPMSM ud0, uq0 Feedback signals of PI controller of former iteration step Tc Time constant Imax Maximum current value LU Distance from the original point to the allowed voltage incremental line LT Length from the origin spot to the target torque incremental line

References

1. Amini, M.H.; Islam, A. Allocation of electric vehicles’ parking lots in distribution network. In Proceedings of the 10th Conference on Innovative Smart Grid Technologies (ISGT), Washington, DC, USA, 19–22 February 2014; pp. 1–5. 2. Zhang, L.; Liu, W.; Liu, Z. A Scope for the Research and Argument Activities on Electric Vehicle Development Mode in Demonstration City. In Proceedings of the 10th Conference on Innovative Smart Grid Technologies (ISGT), Washington, DC, USA, 19–22 February 2014; pp. 394–399. 3. Zhu, Z.; Lambotharan, S.; Chin, W.H.; Fan, Z. A Stochastic Optimization Approach to Aggregated Electric Vehicles Charging in Smart Grids. In Proceedings of the 10th Conference on Innovative Smart Grid Technologies (ISGT), Washington, DC, USA, 19–22 February 2014; pp. 51–56. 4. Huynh, T.A.; Hsieh, M.-F. Performance Analysis of Permanent Magnet Motors for Electric Vehicles (EV) Traction Considering Driving Cycles. Energies 2018, 11, 1385. [CrossRef] 5. Hirschmann, D.; Tissen, D.; Schroder, S.; Doncker, R.D. Reliability prediction for inverters in hybrid electrical vehicles. IEEE Trans. Power Electron. 2007, 22, 2511–2517. [CrossRef] 6. EL-Refaie, A.M.; Jahns, T.M.; Reddy, P.B.; McKeever, J.W. Modiﬁed Vector Control Algorithm for Increasing Partial-Load Efﬁciency of Fractional-Slot Concentrated-Winding Surface PM Machines. IEEE Trans. Ind. Appl. 2008, 44, 1543–1551. [CrossRef] Energies 2018, 11, 2046 21 of 22

7. Günther, S.; Ulbrich, S.; Hofmann, W. Driving Cycle-Based Design Optimization of Interior Permanent Magnet Synchronous Motor Drives for Electric Vehicle Application. In Proceedings of the International Symposium on Power Electronics, Electrical Drives, Automation and Motion, Ischia, Italy, 18–20 June 2014; pp. 25–30. 8. Jung, S.-Y.; Hong, J.; Nam, K. Current minimizing torque control of the IPMSM using Ferrari’s method. IEEE Trans. Power Electron. 2013, 28, 5603–5617. [CrossRef] 9. Morimoto, S.; Takeda, Y.; Hirasa, T.; Taniguchi, K. Expansion of operating limits for permanent magnet motor by current vector control considering inverter capacity. IEEE Trans. Ind. Appl. 1990, 26, 866–871. [CrossRef] 10. Xu, L.; Zhang, Y.; Guven, M. A New Method to Optimize Q-axis Voltage for Deep Flux Weakening Control of IPM Machines Based on Single Current Regulator. In Proceedings of the 2008 International Conference on Machines and Systems, Wuhan, China, 17–20 October 2008. 11. Mohamed, Y.R.; Lee, T.K. Adaptive self-tuning MTPA vector controller for IPMSM drive system. IEEE Trans. Energy Convers. 2006, 21, 636–644. [CrossRef] 12. Consoli, A.; Scelba, G.; Scarcella, G.; Cacciato, M. An Effective Energy-Saving Scalar Control for Industrial IPMSM Drives. IEEE Trans. Ind. Electron. 2013, 60, 3658–3669. [CrossRef] 13. Sousa, G.C.D.; Bose, B.K.; Cleland, J.G. Fuzzy Logic Based On-Line Efficiency Optimization Control of an Indirect Vector-Controlled Induction Motor Drive. IEEE Trans. Ind. Electron. 1995, 42, 192–198. [CrossRef] 14. Wang, X.; Xu, S.; Li, C.; Li, X. Field-Weakening Performance Improvement of the Yokeless and Segmented Armature Axial Flux Motor for Electric Vehicles. Energies 2017, 10, 1492. [CrossRef] 15. Chai, J.-Y.; Liaw, C.M. Development of a switch-reluctance motor drive with PFC front end. Energy Convers. 2009, 24, 271–280. 16. Lemmens, J.; Driesen, J. Dynamic DC-link Voltage Adaptation for Thermal Management of Traction Drives. In Proceedings of the IEEE Energy Conversion Congress and Exposition, Denver, CO, USA, 15–19 September 2013; pp. 180–187. 17. Yamamoto, K.; Shinohara, K.; Nagahama, T. Characteristics of permanent magnet synchronous motor driven by PWM inverter with voltage booster. IEEE Trans. Ind. Appl. 2004, 40, 1145–1152. [CrossRef] 18. Yamamoto, K.; Shinohara, K.; Makishima, H. Comparison between flux weakening and PWM inverter with voltage booster for permanent magnet synchronous motor drive. In Proceedings of the Power Conversion Conference-Osaka 2002, Osaka, Japan, 2–5 April 2002; pp. 161–166. 19. Sue, S.-M.; Liaw, J.-H.; Huang, Y.-S.; Liao, Y.-H. Design and Implementation of a Dynamic Voltage Boosting Drive for Permanent Magnet Synchronous Motors. In Proceedings of the 2010 International Power Electronics Conference (IPEC), Sapporo, Japan, 21–24 June 2010; pp. 1398–1402. 20. Okamura, E.S.M.; Sasaki, S. Development of Hybrid Electric Drive System Using a Boost Converter. In Proceedings of the 20th International Electric Vehicle Symposium and Exposition, Long Beach, CA, USA, 15–19 November 2003. 21. Choudhury, A.; Pillay, P.; Williamson, S.S. DC-Link Voltage Balancing for a Three-Level Electric Vehicle Traction Inverter Using an Innovative Switching Sequence Control Scheme. IEEE J. Emerging Sel. Top. Power Electron. 2014, 2, 296–307. [CrossRef] 22. Sun, T.; Wang, J.; Chen, X. Maximum Torque Per Ampere (MTPA) Control for Interior Permanent Magnet Synchronous Machine Drives Based on Virtual Signal Injection. IEEE Trans. Power Electron. 2015, 30, 5036–5045. [CrossRef] 23. Rabiei, A.; Thiringer, T.; Alatalo, M.; Grunditz, E.A. Improved Maximum Torque Per Ampere Algorithm Accounting for Core Saturation, Cross-Coupling Effect, and Temperature for a PMSM Intended for Vehicular Applications. IEEE Trans. Transp. Electrif. 2016, 2, 150–159. [CrossRef] 24. Li, Z.; Li, H. MTPA control of IPMSM system considering saturation and cross-coupling. In Proceedings of the 15th International Conference on Electrical Machines and Systems (ICEMS), Sapporo, Japan, 21–24 October 2012; pp. 1–5. 25. Hoang, K.D.; Aorith, H.K.A. Online control of IPMSM drives for traction applications considering machine parameter and inverter nonlinearities. IEEE Trans. Transp. Electrif. 2015, 1, 312–325. [CrossRef] 26. Lee, S.T.; Burres, T.A.; Tolbert, L.M. Power-factor and torque calculation with consideration of cross saturation of the interior permanent magnet synchronous motor with brushless field excitation. In Proceedings of the IEEE International Electric Machine and Drives Conference, Miami, FL, USA, 3–6 May 2009; pp. 317–322. Energies 2018, 11, 2046 22 of 22

27. Li, H.; Gao, J.; Huang, S.; Fan, P. A Novel Optimal Current Trajectory Control Strategy of IPMSM Considering the cross Saturation Effects. Energies 2017, 10, 1460. [CrossRef] 28. Chedot, L.; Friedrich, G. A cross saturation model for interior permanent magnet synchronous machine. Application to starter-generator. In Proceedings of the 39th IEEE IAS Annual Meeting, Seattle, WA, USA, 3–7 October 2004; pp. 1–6. 29. Demetriades, G.; de la Parra, H.; Andersson, E.; Olsson, H. A real-time thermal model of a permanent magnet synchronous motor. IEEE Trans. Power Electron. 2010, 25, 463–474. [CrossRef]

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).