Controlling a Switched Reluctance Motor with a Conventional Three-Phase Bridge Instead of Asymmetric H-Bridges

energies

Article Controlling a Switched Reluctance Motor with a Conventional Three-Phase Bridge Instead of Asymmetric H-Bridges

Haitao Sun 1,* , Ali Farzan Moghaddam 1, Abdalla Hussein Mohamed 1,2, Mohamed Nabil Ibrahim 1,3,4 , Peter Sergeant 1,3 and Alex Van den Bossche 1 1 Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Gent University, 9052 Gent, Belgium; [email protected] (A.F.M.); [email protected] (A.H.M.); [email protected] (M.N.I.); [email protected] (P.S.); [email protected] (A.V.d.B.) 2 Department of Electrical Power and Machines, Cairo University, Giza 12613, Egypt 3 Core Lab EEDT-MP, Flanders Make, The Strategic Research Centre for the Manufacturing Industry, Gaston Geenslaan 8, 3001 Leuven, Belgium 4 Electrical Engineering Department, Kafrelshiekh University, Kafrelshiekh 33511, Egypt * Correspondence: [email protected]; Tel.: +32-465-32-38-37

Received: 30 October 2018; Accepted: 20 November 2018; Published: 22 November 2018

Abstract: This paper proposes a new driving method for switched reluctance motors (SRMs) using the standard full-bridge inverter. In spite of changing the internal structure of an SRM, the proposed method uses an extra ring structure circuit to make it possible for the inverter to drive the SRM. Next to the standard converter, a controllable DC source is needed. With theoretical analysis and calculation, the reference value of the circulating current in the ring structure was determined and the new method was proven via simulation. A comparison was made with the conventional method for driving an SRM: the asymmetric H-bridges. Also, the current studies were then made to conﬁrm that the SRM could be controlled without lowering the performance of the machine. Experimental veriﬁcation was also made under different conditions, as well as comparison with the simulation results.

Keywords: current control; bridge circuits; switched reluctance motor; ring structure; circulating current

1. Introduction Switched reluctance motors (SRMs) are usually controlled via asymmetric H-bridges. The conventional power converter topology for a switched reluctance motor can be found in Figure1. Though it is a commonly used driving circuit for SRMs, six diode transistor legs are required in the traditional topology with a minimum number of eight contacts (two for supplies and six for outputs); there are also some disadvantages: one switch is always in the current conduction path, thus increasing the losses in the converter, requiring a larger heat sink for cooling, and causing a reduction of the system efﬁciency: two switches are always in series with the motor winding, which increases the conduction loss [1]. Apart from the technical drawbacks, there is also a cost issue: asymmetric H-bridges are usually not mass produced and are, therefore, more expensive than standard full bridge converters. Figure2 describes a conventional full bridge inverter, which is standard for driving induction motor and synchronous motors (permanent magnetic (PM) or excited). This type of converter, can reach high voltages with low harmonics without the use of transformers or series-connected synchronized switching devices [2]; it can also easily provide the high power required for a large electric drive [3]. With a multilevel topology, the synthesized output waveform of the full bridge inverter has more steps, which produces a staircase wave that approaches a desired waveform; and the harmonic distortion

Energies 2018, 11, 3242; doi:10.3390/en11123242 www.mdpi.com/journal/energies EnergiesEnergiesEnergies2018, 201811 2018, 3242, 11, 11, x, xFOR FOR PEER PEER REVIEW REVIEW 2 2of of 15 152 of 15

electricelectric drive drive [3]. [3]. With With a a multilevel multilevel topology, topology, th thee synthesized synthesized output output waveform waveform of of the the full full bridge bridge of theinverterinverter output has has wave more more decreases, steps, steps, which which approaching produces produces a a stairc zerostaircase asase thewave wave number that that approaches approaches of levels a increases.a desired desired waveform; waveform; The voltage and and that can bethethe spanned harmonic harmonic by distortion distortion summing of of multiplethe the output output voltage wave wave decrea levelsdecreases, alsoses, approaching approaching increases [ 3zero ],zero as as aas result,the the number number the multilevel of of levels levels full increases. The voltage that can be spanned by summing multiple voltage levels also increases [3], as bridgeincreases. inverter The is a voltage structure that that can hasbe spanned no voltage by summing sharing problemsmultiple voltage for series levels of also connected increases devices [3], as are aa result, result, the the multilevel multilevel full full bridge bridge inverter inverter is is a a structure structure that that has has no no voltage voltage sharing sharing problems problems for for encountered [3]. It can also obtain improved power quality, lower switching losses, and higher voltage seriesseries of of connected connected devices devices are are encountered encountered [3]. [3]. It It can can also also obtain obtain improved improved power power quality, quality, lower lower capabilityswitchingswitching [4]; losses, andlosses, a betterand and higher higher electromagnetic voltage voltage capability capability compatibility [4]; [4]; and and a a better isbetter also electromagnetic electromagnetic obtained by acompatibility compatibility design which is is also hasalso less parasiticobtainedobtained inductances by by a a design design [4 ].which which has has less less parasitic parasitic inductances inductances [4]. [4].

Q1Q1 Q3Q3 Q5Q5

Q2Q2 Q4Q4 Q6Q6

FigureFigureFigure 1. Standard 1. 1. Standard Standard asymmetric asymmetric asymmetric H-bridge H-bridge H-bridge topologytopology topology fo forfor rswitched switched reluctance reluctance reluctance motors motors motors (SRMs). (SRMs). (SRMs).

Q1Q1 Q3Q3 Q5Q5

Q2Q2 Q4Q4 Q6Q6

FigureFigureFigure 2. Conventional 2. 2. Conventional Conventional three-phase three-phase three-phase full full full bridgebridge bridge for for brushless brushlessbrushless direct direct direct curre curre currentntnt motors motors motors (BLDCs). (BLDCs). (BLDCs).

It is commonlyItIt is is commonly commonly known known known that that that a standarda a standard standard inverter inverter inverter cannot cannot cannot be be used used used for for for driving driving driving SRMs, SRMs, SRMs, because because because of of the the of the uniqueuniqueunique operating operating operating principles principles principles of of SRMs:of SRMs: SRMs: the the the varyingvarying varying magnetic magnetic reluctance reluctance of of ofthe the the machine machine machine creates creates creates a a force force a force that attemptsthatthat attempts attempts to align to to align align the rotorthe the rotor rotor pole pole pole with with with the the nearestthe nearest nearest stator stator stator pole. pole. pole. In In In order order order to to to maintain maintain maintain rotation,rotation, rotation, the the sign signsign of of all all the the winding winding currents currents should should be be kept kept the the same, same, though though it it does does not not matter matter to to choose choose a a of all the winding currents should be kept the same, though it does not matter to choose a positive or positivepositive or or negative negative value value for for the the current. current. negative value for the current. InIn order order to to improve improve the the perfor performancemance of of the the SRM SRM converter converter topology, topology, many many researchers researchers have have Intriedtried order toto find tofind improve the the solutionsolution the performance to to drivedrive anan SRM ofSRM the byby SRM a a standardstandard converter inverter inverter topology, [5–12].[5–12]. many All All the researchersthe existingexisting novelhavenovel tried to finddesignsdesigns the solution cancan bebe to divideddivided drive an intointo SRM twotwo by groups:groups: a standard changichangi inverterngng thethe [5 structurestructure–12]. All or theor topologytopology existing of novelof thethe designsSRMSRM andand can be dividedchangingchanging into two the the excitationgroups: excitation changing method. method. The The the following following structure paragrap paragrap or topologyhshs give give of an an the overview overview SRM and of of the changingthe literature literature the first first excitation for for method.changingchanging The followingthe the structure, structure, paragraphs and and then then for givefor changing changing an overview the the excitation. excitation. of the literature first for changing the structure, and thenThe forThe changingauthors authors in in the Reference Reference excitation. [5] [5] present present a a solution solution in in the the first first group. group. They They designed designed a a mutually mutually Thecoupledcoupled authors SRM. SRM. inBy By Referencechanging changing the the [5 ]structure structure present of aof the solutionthe ph phasease windings, inwindings, the first two two group. phases phases Theycan can be be designed conducted conducted a at mutuallyat the the coupledsamesame SRM. time. time. ByThus, Thus, changing the the bipolar bipolar the excitationstructure excitation can ofcan theproduce produce phase positive positive windings, electromagnetic electromagnetic two phases torque torque can be for for conducted this this type type of of at the SRMSRM withwith modifiedmodified windings,windings, andand aa standardstandard ththree-phaseree-phase inverterinverter cancan generategenerate thethe bipolarbipolar same time. Thus, the bipolar excitation can produce positive electromagnetic torque for this type of excitation.excitation. Actually, Actually, the the machine machine becomes becomes a a synchron synchronousous reluctance reluctance machine, machine, the the main main idea idea for for its its SRM with modified windings, and a standard three-phase inverter can generate the bipolar excitation. operationoperation is is a a rotating rotating magnetic magnetic field, field, which which does does not not exist exist in in a a conventional conventional SRM. SRM. Actually, theAA novel machinenovel dual-channeldual-channel becomes aSRMSRM synchronous waswas designeddesigned reluctance inin ReferenceReference machine, [6],[6], the whichwhich main changes ideachanges for the itsthe operation windingwinding is a rotatingconfigurationconfiguration magnetic of field,of the the whichSRM SRM so so does that that not the the existmagnetic magnetic in a conventionalpolarity polarity on on the the SRM. stator stator poles poles is is different different from from the the A novel dual-channel SRM was designed in Reference [6], which changes the winding configuration of the SRM so that the magnetic polarity on the stator poles is different from the conventional SRM. By using two three-phase standard inverters, the new SRM can be driven, which corresponds also in fact to three single-phase H bridges. Energies 2018, 11, 3242 3 of 15

For the second group—changing the excitation—References [7,8] present a four-phase SRM converter with a different topology, with an extra DC-link current sensor and a single-current sampling resistance, resulting in four transistor-diode legs, but with a compromise of efficiency. The new design can contribute to fault diagnosing and decreasing the cost of SRM controller, and the main ideas were still the improvement of conventional asymmetric H-bridges. Reference [9] proposed a novel single-stage power factor corrected drive for SRMs, which combines a DC link capacitor used as direct current (DC) source and a diode used for driving the motor into one power stage with conventional asymmetric H-bridges. It has a simple structure and a low cost. In fact, it is still an improvement on the conventional power converter for SRMs. Another topology is described in Reference [10]. The novel excitation method in this paper can drive the bipolar SRM with a three-phase H-bridge inverter. For each phase, during the working period, there should be 12 transistor drivers working for it at the same time, instead of six for the conventional asymmetric H-bridge solution. This causes a more complex solution, as four switches must be controlled per phase, but the advantage is the torque ripple and iron loss are significantly reduced with sinusoidal bipolar excitation, albeit with reduced torque capability, and if metal-oxide-semiconductor field-effect transistors (MOSFETs) are used, the on-state voltage of which (0.25 V) can be less than a diode drop (0.7 V). Reference [11] describes a delta-connected three-phase synchronous reluctance motor that can be driven by a standard three-phase inverter. In this inverter, three voltage pulses are applied in phase in all three stator windings in a stationary condition, by turning on and turning off the different switches. Because of the difference between an SRM and a synchronous reluctance motor, it still cannot prove that the conventional SRM can be driven by a standard inverter. The authors of Reference [12] use an SRM converter that combines two three-phase insulated gate bipolar transistor (IGBT) inverters and a one-leg IGBT power module. This power converter is used to drive an 8/6 SRM. In fact, it is still a variant of asymmetric H-bridges by changing the position of the corresponding used devises in the circuit. In conclusion, apart from the methods of the first group that need to change the structure of SRMs, the three existing methods of the second group that changes the excitation method all use at least two standard inverters, excite one phase with at least four switches or add some other components to build a variant of the conventional asymmetrical half-bridge converter. In this paper, a circulating current control method is proposed. It is a new drive topology that combines a conventional off-the-shelf, three-phase SRM with a conventional three-phase full transistor bridge structure. By using the ring structure and controlling the circulating current via a DC source, the standard inverter can be applied in the SRM driving system. The proposed idea in this paper does not need to change the structure of the SRM, which means that it can be applied in any SRM. The converter does not need more legs than the number of phases, it is also not a variant of the conventional asymmetrical half-bridge converter.

2. Theoretical Analysis of the Proposed Topology with a Conventional Three-Phase Bridge and Circulating Currents

2.1. Topology We consider a conventional SRM with three phases, e.g., a 6/4 SRM or a 12/8 SRM. The three phase windings are connected in series to form a ring structure. Many more variants are described in the corresponding patent [13]. The ring is closed via an additional DC source. This source is a means for generating a circulating current. The injected currents Ia, Ib, and Ic are produced by the conventional three-phase converter. In order to apply the additional DC power supply into the circuit, the combination of a controlled half bridge and a DC-DC buck circuit is chosen to be the alternative of the controlled voltage source. The concept of the ring structure can be found in Figure3. EnergiesEnergies2018, 11 2018, 3242, 11, x FOR PEER REVIEW 4 of 154 of 15 Energies 2018, 11, x FOR PEER REVIEW 4 of 15

I1 Ia I1 Ia I2 Ib I2 Ib I3 Ic I3 Ic

FigureFigure 3. Concept 3. Concept of of the the ring ring structure structure to generate circulating circulating current. current. Figure 3. Concept of the ring structure to generate circulating current. The fullThe topologyfull topology proposed proposed is is shown shown in in Figure Figure4 4.. WithWith thethe additional additional ring ring structure, structure, the thebasic basic currentThe fullin each topology winding proposed can be isincreased, shown in which Figure means 4. With the the “zero additional point” of ring the structure,winding currentthe basic can current in each winding can be increased, which means the “zero point” of the winding current can be currentbe increased in each towinding a higher can value be increased, (9.5 A with which load means of 19.3 the N·m, “zero WP2 point” and ofWP5 the describedwinding current in Figure can 5). · increasedbeThus, increased to it a is higher topossible a higher value to valuekeep (9.5 A(9.5the with Asign with load of loadthe of 19.3 cuofrrent 19.3 N m, N·m,in WP2the WP2 winding and and WP5 WP5 positive, described described even in inwith FigureFigure the5 5).).full Thus, it isThus, possibletransistor it is to possiblebridge. keep the to sign keep of the sign current of the in thecurrent winding in the positive, winding even positive, with theeven full with transistor the full bridge. transistor bridge.

SRM C1 Q7 SRM Q1 Q3 Q5 C1 Q7 Q1 Q3 Q5 Circulating Leg I1 CirculatingCurrent Ia LegCurrent I1 Ia Current Current RC1 C3 (IRC2) 2 (I ) I b I (IRC1) C3 (IRC2) I2 Ib I3 Ic I3 Ic

C2 Q8 Q2 Q4 Q6 C2 Q8 Q2 Q4 Q6

Figure 4. Full topology of the conventional three phase bridge with additional power supply (C1–C3: FigureEnergies 4. 2018Full, 11 topology, x FOR PEER of REVIEW the conventional three phase bridge with additional power supply (C1–C3:5 of 15 Figurecapacitors; 4. Full Q1–Q8: topology IGBTs; of the I 1conventional–I3: winding currents;three phase Ia–I bridgec: leg currents). with additional power supply (C1–C3: capacitors; Q1–Q8: IGBTs; I1–I3: winding currents; Ia–Ic: leg currents). capacitors; Q1–Q8: IGBTs; I1–I3: winding currents; Ia–Ic: leg currents). 2.2. Operating Principle 2.2. Operating Principle The principle for operating this system is based on the fact that, for each phase winding, the totalThe current principle flowing for operating through thisthe systemphase windingis based onis thethe sumfact that,of the for circulating each phase current winding, and the an totalindividual current AC flowing current through from the the power phase switches. winding is the sum of the circulating current and an individualThe changeAC current of the from current the power can be switches. explained via the well-known flux linkage-current diagram of an TheSRM change as is shown of the in current Figure can 5. be explained via the well-known flux linkage-current diagram of an SRMSuppose as is shown we use in Figurean asymmetric 5. H-bridge, then we would change the current from 0 A to 16.8 A in unalignedSuppose we position, use an asymmetricand from 16.8 H-bridge, A back thento 0 Awe in would aligned change position. the currentThis trajectory from 0 A is toshown 16.8 A by inworking unaligned points position, WP1 andto WP6 from in 16.8Figure A back5, and to the 0 A en inclosed aligned surface position. is an Thisindication trajectory for theis shown energy. by workingWith points the WP1proposed to WP6 topology, in Figure we 5, setand a theconstant enclosed DC surface circulating is an currentindication with for a the reference energy. value (referenceWith the current proposed for topology,the circul atingwe set current). a constant To DCkeep circulating the explanation current easywith ato reference understand, value we (referenceassume the current full bridge for the circuit circul createsating current).three 120° To phase keep shifted the explanation sinusoidal currenteasy to waveforms,understand, which we assumehaveFigure each theFigure 5. fulla Thezero bridge5. fluxThevalue flux linkage-currentcircuit as linkage-current average, creates and three diagram diagraman 120°instantaneous of phaseof a a practical practical shifted sum SRM sinusoidal equal collected collected to zero. current from from experimentation. experimentation.waveforms, which have eachWhen a zero the valueleg current as average, from andthe inverteran instantaneous increases sum from equal a negative to zero. value to zero at unaligned 2.2. Operatingposition,WhenWhen Principlethe the legworking working current point frompoint of theSRMhits inverter WP2, will move whereincreases from the from windingWP1 a tonegative WP2.current Invalue equalsthis tointerval, zerothe circulatingat theunaligned winding DC position,current, the the working current inpoint the ofinverter SRM willleg ismove zero. fromThen WP1the leg to currentWP2. In keeps this interval,increasing, the causing winding the Thecurrent principle is the fordifference operating between this system the DC is circul basedating on thecurrent fact and that, the for AC each current phase in winding, the winding the total currentcomingworking is from thepoint differencethe to transistor move between from legs. WP2the DCto WP3.circul atingNow, current the winding and the current AC current is the in sum the ofwinding the DC current flowing through the phase winding is the sum of the circulating current and an individual AC comingcirculating from currentthe transistor and the legs. leg current from the inverter. current fromWhen the the power position switches. of the rotor teeth moved from the unaligned to the aligned position, the Theworking change point of moves the current from WP3 can beto WP4. explained Consequently, via the well-knownwith the decreasing flux linkage-current leg current, the working diagram of an SRM as is shown in Figure5. point moves from WP4 to WP5, the point where the inverter current turns to zero. The inverter Supposecurrent becomes we use annegative asymmetric again, and H-bridge, the leg thencurrent we keeps would decreasing, change the the current working from point 0A moves to 16.8 A in unalignedfrom WP5 position, to WP6. andFinally, from the 16.8 teeth A position back to move 0 A ins from aligned the aligned position. to the This unaligned, trajectory so is that shown the by workinginitial points position WP1 WP1 toWP6 is reached. in Figure 5, and the enclosed surface is an indication for the energy. With this novel topology, the stator windings can generate a back electromotive force (EMF), which makes it possible that the SRM shares the same operation principle with the synchronous reluctance machines. The SRM can also be controlled by trapezoidal wave generated by the inverter, as the result, the pulse width of every phase winding will be fixed with 120 degree. Based on the topology, the control method for the SRM can be regarded as a double closed loop control method. As is described in Figure 4, the inner loop is the control of the circulating current (defined later in (3)), of which the reference value for the circulating is IRC2, as shown in the figure; the external loop is the control of the leg current, of which the reference value is IRC1. With a given reference circulating current (IRC2), the control strategy for SRM can be the same as for brushless direct current motor (BLDC) [14]. Only the position signals and the inverter leg currents will be needed for the loop feedback, it will be unnecessary to obtain the winding current signals. According to the law of Kirchhoff [15], the total current in each winding is the vector sum of the trapezoidal currents from every bridge leg and the circulating current from the ring structure. For the AC current, pulse width modulation (PWM) can be used.

2.3. Range of the DC Current In order to calculate the minimum value for the DC current in the ring structure, we start from Figure 3. =+ III21a , (1)

=− III31c , (2)

++  +−  I123II3 III 1ac II == = , (3) ring current RC 2 33

Energies 2018, 11, 3242 5 of 15

With the proposed topology, we set a constant DC circulating current with a reference value (reference current for the circulating current). To keep the explanation easy to understand, we assume the full bridge circuit creates three 120◦ phase shifted sinusoidal current waveforms, which have each a zero value as average, and an instantaneous sum equal to zero. When the leg current from the inverter increases from a negative value to zero at unaligned position, the working point of SRM will move from WP1 to WP2. In this interval, the winding current is the difference between the DC circulating current and the AC current in the winding coming from the transistor legs. When the working point hits WP2, where the winding current equals the circulating DC current, the current in the inverter leg is zero. Then the leg current keeps increasing, causing the working point to move from WP2 to WP3. Now, the winding current is the sum of the DC circulating current and the leg current from the inverter. When the position of the rotor teeth moved from the unaligned to the aligned position, the working point moves from WP3 to WP4. Consequently, with the decreasing leg current, the working point moves from WP4 to WP5, the point where the inverter current turns to zero. The inverter current becomes negative again, and the leg current keeps decreasing, the working point moves from WP5 to WP6. Finally, the teeth position moves from the aligned to the unaligned, so that the initial position WP1 is reached. With this novel topology, the stator windings can generate a back electromotive force (EMF), which makes it possible that the SRM shares the same operation principle with the synchronous reluctance machines. The SRM can also be controlled by trapezoidal wave generated by the inverter, as the result, the pulse width of every phase winding will be fixed with 120 degree. Based on the topology, the control method for the SRM can be regarded as a double closed loop control method. As is described in Figure4, the inner loop is the control of the circulating current (defined later in (3)), of which the reference value for the circulating is IRC2, as shown in the figure; the external loop is the control of the leg current, of which the reference value is IRC1. With a given reference circulating current (IRC2), the control strategy for SRM can be the same as for brushless direct current motor (BLDC) [14]. Only the position signals and the inverter leg currents will be needed for the loop feedback, it will be unnecessary to obtain the winding current signals. According to the law of Kirchhoff [15], the total current in each winding is the vector sum of the trapezoidal currents from every bridge leg and the circulating current from the ring structure. For the AC current, pulse width modulation (PWM) can be used.

2.3. Range of the DC Current In order to calculate the minimum value for the DC current in the ring structure, we start from Figure3. → → → I2 = I1 + Ia, (1) → → → I3 = I1 − Ic, (2) → → → → → → → → I + I + I 3I + I − I I = I = 1 2 3 = 1 a c , (3) ringcurrent RC2 3 3 where IRC2 is the reference current for the DC circulating current (as is shown in Figure4). I1, I2, I3 are the winding currents in the different phases. In order to control the leg currents (Ia, Ib, Ic) in the full bridge topology (as is shown in Figure4), there should be a reference value for the alternating leg currents, which is deﬁned as IRC1. Based on the relationship among the leg currents and the winding currents (delta connection). For the fundamental: → ◦ If Ia = IRC1∠0 , → ◦ → ◦ Then Ic = IRC1∠ − 120 , I1 = I1∠150 , Energies 2018, 11, x FOR PEER REVIEW 6 of 15

where IRC2 is the reference current for the DC circulating current (as is shown in Figure 4). I1, I2, I3 are the winding currents in the different phases. In order to control the leg currents (Ia, Ib, Ic) in the full bridge topology (as is shown in Figure 4), there should be a reference value for the alternating leg currents, which is defined as IRC1. Based on the relationship among the leg currents and the winding currents (delta connection). For the fundamental: Energies 2018, 11, 3242 6 of 15  =∠° If IIaRC1 0 ,  =∠−°  =∠ ° Then IIcRC1 120 , II11150 , √ → ◦3III∠+∠−∠− 150°°◦ 0 120◦ ° 3 I ∠+ 150 °◦ 3 I ∠ 30 °◦ 3I1∠150 ==+1111IRC1∠0RC− IRC1∠ RC− 120 3I1∠150 + RC 13IRC1∠30 I = I RC 2 = , ,(4) (4) RC2 3 333

→ ◦ √ ◦ = =∠+°° + ∠ 3IRC2 3IIRC321I1∠ 3150 1503 3I IRC RC 1∠ 3030, ,(5) (5)

The amplitudeThe amplitude values values of ofIRC IRC1 1and and IIRCRC22 areare fixed, ﬁxed, and and the the phase phase angles angles of IRC of1 andIRC 1I1 andare fixed.I1 are ﬁxed. In orderIn order to make to make sure sure that that the the winding winding currentcurrent works works within within the the working working area, area, as can as be can found be found in Figurein Figure5, the 5, maximumthe maximum value value of of winding winding current current isis inin WP3 and and WP4, WP4, which which is described is described as Imax as, Imax, then the winding current will rise from 0A to Imax, and back from Imax to 0 A, as is shown in Figure 6. then the winding current will rise from 0A to Imax, and back from Imax to 0 A, as is shown in Figure6.

1 IRC1 3I RC IRC2

90.0° 60.0°

30.0° 2 0A 3I RC

Figure 6. The vector illustration of currents (for the fundamental). Figure 6. The vector illustration of currents (for the fundamental). According to the parameters shown in Figure6, According to the parameters shown in Figure 6, ≤≤ 0 II1max, (6) 0 ≤ I1 ≤ Imax, (6) √ 33 II= =×× , 3IRC1 RC1maxImax 3,(7) (7) √ |3IRC2| = 3I==max = 3IRC1, (8) 33IIRCRC2max1 3 I, (8) The results show that with the well-calculated I and I , the winding current can be limited The results show that with the well-calculated IRCRC22 and IRCRC1, the1 winding current can be limited withinwithin the workingthe working area. area.

3. Comparison3. Comparison of Asymmetricof Asymmetric H-Bridges H-Bridges with with CirculatingCirculating Current Current Concept Concept for forA 6/4 A SRM 6/4 SRM A three-phaseA three-phase SRM SRM is chosenis chosen as as the the device device underunder test. test. The The flux flux linkage-current linkage-current diagram diagram of this of this machinemachine has beenhas been described described in Figure in Figure5. The 5. machineThe machine is a 6/4 is a SRM 6/4 SRM with 120with mm 120 outermm outer stator stator diameter and 80diameter mm stack and length.80 mm Itsstack rated length. voltage Its rated is 200 voltage V, rated is 200 power V, rated 5 kW, power rated 5 torque kW, rated 19.3 torque N·mand 19.3 rated speedN·m 1750 and rpm. rated Both speed in the1750 simulation rpm. Both andin the in simulati the experimentalon and in the setup, experimental three current setup, sensors three current are chosen sensors are chosen for the feedback of the current signals, two of them measuring the leg currents Ia for the feedback of the current signals, two of them measuring the leg currents Ia and Ic in the inverter and Ic in the inverter legs, and the third one measuring the winding current I1 in the ring structure, as legs, and the third one measuring the winding current I in the ring structure, as described in (3). described in (3). Three hall sensors are implemented for the1 position and speed signal, mechanically Three hall sensors are implemented for the position and speed signal, mechanically positioned at 0◦, 120◦ and −120◦, in a 6/4 SRM also resulting in electrical phase shifts of 0◦, 120◦ and −120◦. As can be seen in Figure6, based on (6)–(8), the reference value for the circulating current can be well defined, the reference current for the leg currents in the inverter can also be defined by the reference speed [16]. We compare the two types of control methods at a reference speed of 1000 rpm, and a load of 6 N·m. For the conventional method, the turn-on angle is 45 degree and the turn-off angle is 75 degree [17]. With the constant load of 6 N·m, and the reference speed of 1000 rpm, Figure7a describes the winding currents from the SRM driven by the conventional method, where we choose a turn-on angle of 45 degree and a turn-off angle of 75 degree (the optimization angles for driving three-phase SRM). Energies 2018, 11, x FOR PEER REVIEW 7 of 15

positioned at 0°, 120° and −120°, in a 6/4 SRM also resulting in electrical phase shifts of 0°, 120° and −120°. As can be seen in Figure 6, based on (6)–(8), the reference value for the circulating current can be well defined, the reference current for the leg currents in the inverter can also be defined by the reference speed [16]. We compare the two types of control methods at a reference speed of 1000 rpm, and a load of 6 N·m. For the conventional method, the turn-on angle is 45 degree and the turn-off angle is 75 degree [17]. Energies[17].2018 , 11, 3242 7 of 15 With the constant load of 6 N·m, and the reference speed of 1000 rpm, Figure 7a describes the winding currents from the SRM driven by the conventional method, where we choose a turn-on angle of 45 degree and a turn-off angle of 75 degree (the optimization angles for driving three-phase It canangle be found of 45 thatdegree all and excitation a turn-off pulses angle are of 75 similar degree to (the ﬂat optimization top waves [ 18angles], this for is driving because three-phase with the ﬁxed SRM). It can be found that all excitation pulses are similar to flat top waves [18], this is because with turn-onSRM). and It turn-off can be found degrees, that all the excitation speed is pulses controlled are similar by the to current flat top hysteresiswaves [18], method.this is because with the fixed turn-on and turn-off degrees, the speed is controlled by the current hysteresis method. At the same time, Figure7b shows the winding current waveforms from the SRM driven by the At the same time, Figure 7b shows the winding current waveforms from the SRM driven by the new method, where the excitation pulses of the new topology are more similar to trapezoidal waves. new method, where the excitation pulses of the new topology are more similar to trapezoidal waves. This isThis because is because the trapezoidalthe trapezoidal driving driving current current is is generated generated from from thethe full bridge circuit, circuit, the the function function of the circulatingof the circulating current current is only is toonly increase to increase the “zerothe “zero level” level” of of the the winding winding current. current. FigureFigure8 shows 8 shows that that for for the the different different topologies, both both of the of thepeak-to-peak peak-to-peak torque torque ripples ripplesare less are less thanthan 55 NN·m.·m. This means that that the the new new driving driving me methodthod can can keep keep the the torque torque performance performance of the of the conventionallyconventionally driven driven SRM. SRM.

(a) (b)

FigureFigure 7. (a )7. the (a) windingthe winding current current waveform waveform of of SRM SRM drivendriven by by asymmetric asymmetric H-bridge; H-bridge; (b) (theb) winding the winding currentcurrent waveform waveform of SRM of SRM driven driven by by new new topology. topology.

Figure 8. The comparison of the torque between two driving methods. FigureFigure 8. The 8. The comparison comparison of of the the torquetorque between two two driving driving methods. methods.

4. Current Studies

The waveforms of different currents at steady state can describe their different roles in the SRM [19], which are all tested under the condition of 200 V DC voltage, reference speed of 1000 rpm and load of 6 N·m. The waveform of the circulating current in steady state is shown in Figure9. Note that this current cannot be directly measured as such and it has to be calculated. Also note that it is not perfect DC. Because of the inductive energy storage in the windings and the delta structure, the circulating current contains a ripple of mainly triple harmonics, that repeats every 120◦. Energies 2018, 11, x FOR PEER REVIEW 8 of 15

Energies4. Current 2018, Studies11, x FOR PEER REVIEW 8 of 15

4. CurrentThe waveforms Studies of different currents at steady state can describe their different roles in the SRM [19], which are all tested under the condition of 200 V DC voltage, reference speed of 1000 rpm and load Theof 6 waveformsN·m. of different currents at steady state can describe their different roles in the SRM [19], whichThe waveform are all tested of the under circulating the condition current of in 200 steady V DC state voltage, is shown reference in Figure speed 9.of Note1000 rpmthat andthis loadcurrent of 6 cannot N·m. be directly measured as such and it has to be calculated. Also note that it is not perfect DC. TheBecause waveform of the inductiveof the circulating energy storage current in in the steady windings state and is shown the delta in structure,Figure 9. Notethe circulating that this currentcurrent cannotcontains be a directly ripple of measured mainly triple as such harmonics, and it has that to be repeats calculated. every Also 120°. note that it is not perfect DC. Because of the inductive energy storage in the windings and the delta structure, the circulating Energiescurrent2018 contains, 11, 3242 a ripple of mainly triple harmonics, that repeats every 120°. 8 of 15

Figure 9. The simulated waveform of the circulating currents.

As is described inFigureFigure Figure 9.9. 3The and simulated (1)–(3), waveformwaveformthe circulating ofof thethe circulatingcurrentcirculating is currents.thecurrents. average current in the ring structure. From Figure 9, with a reference value of 5.5 A, it can be found that the circulating current As is described in Figure3 and (1)–(3), the circulating current is the average current in the ring is keptAs isrelatively described stable, in Figure which 3 and can (1)–(3), generate the circtheulating stable currentcompensatory is the average current current for the in windingthe ring structure.structure.currents. From From FigureFigure9 ,9, with with a a reference reference value value of of 5.5 5.5 A, A, it canit can be be found found that that the the circulating circulating current current is keptis kept relativelyThe relatively curves stable, of stable,the which current which can in generate eachcan phasegenerate the of stable thethe full compensatorystable bridge compensatory are shown current in forcurrent Figure the winding 10.for the currents. winding currents.The curves of the current in each phase of the full bridge are shown in Figure 10. The curves of the current in each phase of the full bridge are shown in Figure 10.

FigureFigure 10.10. TheThe simulatedsimulated waveformwaveform ofof thethe inverterinverter currents.currents.

AsAs cancan bebe foundfound inFigurein FigureFigure 10. The 1010,, simulated thethe legleg current currentwaveform waveformswaveforms of the inverter ofof thecurrents.the three-phasethree-phase bridgebridge havehave aa trapezoidaltrapezoidal shapeshape butbut areare notnot symmetrical,symmetrical, whichwhich isis becausebecause thethe ringring structurestructure triestries toto guaranteeguarantee thethe windingwindingAs can currentscurrents be found toto bebe positive,inpositive, Figure while while10, the thethe leg inductancesinduct currentances waveforms areare changing,changing, of the whichwhich three-phase causecause asymmetryasymmetry bridge have inin thethe a invertertrapezoidalinverter currents.currents. shape but are not symmetrical, which is because the ring structure tries to guarantee the windingFromFrom currents FigureFigure 10 to10,, be combined combined positive, with withwhile Figures Fi thegure induct7 7b and andances9, itFigure can are be changing,9, found it can thatbe which found because cause that of becauseasymmetry (5), the windingof (5), in thethe currentinverterwinding is currents. thecurrent vector is sumthe vector of circulating sum of currentcirculating and current leg current and from leg current the inverter. from Itthe is alsoinverter. worth It notingis also thatworth becauseFrom noting Figure of that the 10, triplebecause combined harmonics of thewith intriple Fi thegure circulatingharmonics 7b and Figure current,in the 9, thecirculatingit can waveforms be found current, ofthat three-phase becausethe waveforms of winding (5), the of currentswindingthree-phase werecurrent winding not is totally the currents vector similar. sumwere of not circulating totally similar. current and leg current from the inverter. It is also worth noting that because of the triple harmonics in the circulating current, the waveforms of 5. Inﬂuence of the Speed and the Load three-phase winding currents were not totally similar. By using the simulation tools, the characteristics of the SRM can be analyzed. The performance of the SRM is mainly manifested in its speed and torque characteristics [20], and based on the operation principle described above, these characteristics are determined by the winding currents. Figure 11 describes the relationship between the speed and torque of the SRM driven by the conventional method and new method. Energies 2018, 11, x FOR PEER REVIEW 9 of 15

5. Influence of the Speed and the Load By using the simulation tools, the characteristics of the SRM can be analyzed. The performance of the SRM is mainly manifested in its speed and torque characteristics [20], and based on the operation principle described above, these characteristics are determined by the winding currents. Figure 11 describes the relationship between the speed and torque of the SRM driven by the Energiesconventional2018, 11, 3242method and new method. 9 of 15 torque (Nm)

(a) (b)

FigureFigure 11.11.( a(a)) Speed/torque Speed/torque curvecurve ofof thethe SRMSRM drivendriven by by the the conventional conventional method; method; ( b(b) speed/torque) speed/torque curvecurve ofof the the SRM SRM driven driven by by the the new new method. method.

AsAs cancan bebe foundfound inin FigureFigure 11 11a,b,a,b, withwith thethe torquetorque ratingrating 19.319.3 NN·m,·m, thethe speedspeed cancan rangerange fromfrom 5050 toto 10001000 rpm, rpm, because because 60T·N P = , (9) π60TN P =2 , (9) 2π where P is the power of the SRM, T is the torque of the SRM, and N is the speed of the SRM. whereWith P is the the constant power of torque the SRM, of 19.3 T is N ·them, fromtorque 50 of to the 1000 SRM, rpm, and the N SRM is the works speed in of the the constant SRM. torque area,With because the in constant this area, torque the power of 19.3 of N·m, the SRM from does 50 to not 1000 achieve rpm, itsthe highest SRM works value (powerin the constant rating), thetorque speed area, can because increase in with this thearea, constant the power load. of The the powerSRM does of the not SRM achieve increases its highest with the value increasing (power speed,rating), after the thespeed point can of increaseN = 1000 with rpm, the the constant highest powerload. The is achieved, power of and the then SRM keeps increases constant with with the theincreasing increasing speed, speed, after as thethe result,point theof N torque = 1000 decreases rpm, the [ 21highest]. power is achieved, and then keeps constantFrom with the comparisonthe increasing between speed, theas the two result, control the methods, torque decreases it can be found[21]. that for a speciﬁc SRM, its relationshipFrom the comparison between speed between and torque the two does control not changemethods, even it can driven be found by different that for methods, a specific it SRM, also provesits relationship that thenew between method speed does and not torque change does the not characteristics change even of driven the SRM. by different methods, it also provesFigure that 12 the shows new method the relationship does not betweenchange the the characteristics speed and winding of the currentSRM. of the SRM driven by the conventionalFigure 12 shows method the andrelationship new method, between with the a constant speed and load winding of 6 N· m.current of the SRM driven by the conventionalFrom Figure 12 methoda,b, it can and be new found method, that the with trends a constant of the winding load of current6 N·m. based on increasing speed of bothFrom the twoFigure methods 12a,b, areit can similar: be found with that a constant the trends load, of the the winding winding current current increases, based on and increasing then the speedspeed decreases.of both the This two is methods because withare similar: the decreasing with a constant winding load, current the andwinding constant current excitation increases, voltage, and thethen back the EMF speed in thedecreases. armature This decreases, is because which with leads the to the decreasing increase of winding armature current current, and and thenconstant the torqueexcitation increases, voltage, as the the back result, EMF the speedin the ofarmature the SRM de increasescreases, which [22]. leads to the increase of armature current,In fact, and no then phase the leadtorque has increases, been implemented as the result, in this the article.speed of Actually, the SRM at increases the same time,[22]. in order to keep theIn fact, higher no speed,phase lead the frequencyhas been implemented of the winding in current this article. will alsoActually, increase at the [23 ].same time, in order to keepFrom the Figure higher 12 speed, it can alsothe frequency be found thatof the with winding the same current speed, will the also value increase of the [23]. winding current in the newFrom method Figure is 12 less it thancan also the onebe found in the that conventional with the same method. speed, This the is value because of ofthe the winding change current of the onin andthe new off angles, method the is on-time less than of the windingone in the in conventional the new method method. increases, This theis because amplitude of the of its change current of hasthe toon be and decreased. off angles, the on-time of the winding in the new method increases, the amplitude of its currentFigure has 13 to describesbe decreased. the relationship between the winding current and torque of the SRM driven by theFigure conventional 13 describes method the andrelationship new method, between with th ae constantwinding referencecurrent and speed torque of 1000 of the rpm. SRM driven by the conventional method and new method, with a constant reference speed of 1000 rpm.

Energies 2018, 11, x FOR PEER REVIEW 10 of 15

Energies 2018, 11, x FOR PEER REVIEW 10 of 15 Energies 2018, 11, 3242 10 of 15

1600 1400 1600 1200 1400 1000 1200 800 1000

speed (rpm) 600 800 400

speed (rpm) 600 200 400 0 200 6.4 6.6 6.8 7 7.2 current (A) 0 6.4 6.6 6.8 7 7.2 current(a) (A) (b)

Figure 12. (a) Speed/winding(a) current curve of the SRM driven by the conventional(b) method; (b) speed/winding current curve of the SRM driven by the new method. FigureFigure 12. 12.(a) ( Speed/windinga) Speed/winding current current curve curve of of the the SRM SRM drivendriven byby thethe conventionalconventional method; method; (b (b) ) speed/windingspeed/winding current current curve curve of of the th SRMe SRM driven driven by by the the new new method. method.

(a) (b)

FigureFigure 13. 13.(a )(a Winding) Winding( current/torquea )current/torque curvecurve of the SRM driven driven by by the the conventional conventional(b) method; method; (b) ( b) windingwinding current/torque current/torque curve curve of of the the SRM SRM drivendriven by the new method. method. Figure 13. (a) Winding current/torque curve of the SRM driven by the conventional method; (b) TheThewinding similar similar current/torque waveforms waveforms of curve of the the windingof winding the SRM current currentdriven by basedbase thed new on increasingmethod. increasing torque torque with with different different control control methodsmethods are are described described in Figurein Figure 13a,b, 13a,b, it can it becan found be found that withthat with the constant the constant speed, speed, the winding the winding current The similar waveforms of the winding current based on increasing torque with different control increases,current thenincreases, the torque then the increases torque increases as well. Theas well reason. The isreason that withis that the with increasing the increasing load, theload, output the methods are described in Figure 13a,b, it can be found that with the constant speed, the winding poweroutput of thepower SRM of increases,the SRM increases, if the excitation if the excitati voltageon keepsvoltage constant, keeps constant, the winding the winding current current will increase, will current increases, then the torque increases as well. The reason is that with the increasing load, the as theincrease, result, as the the torque result, ofthe the torque SRM of also the increasesSRM also [increases24]. [24]. output power of the SRM increases, if the excitation voltage keeps constant, the winding current will It is also worth noting that with the same torque, the values of the winding current in the two increase,It is also as worth the result, noting the that torque with of thethe sameSRM also torque, increases the values [24]. of the winding current in the two control methods are different, of which the reason is the different topologies of the two driving control methodsIt is alsoare worth different, noting of that which with the the reason same torq is theue, different the values topologies of the winding of the two current driving in the circuits. two circuits. In the winding of the SRM driven by the conventional method, only one phase winding is In thecontrol winding methods of the are SRM different, driven byof thewhich conventional the reason method, is the different only one topologies phase winding of the is two turned driving on at turned on at the same time (Figure 7a), for the winding of the SRM driven by the new method, the samecircuits. time In (Figurethe winding7a), for of thethe windingSRM driven of the by SRMthe conventional driven by the method, new method, only one however, phase winding there are is however, there are at least two phase windings turned on at the same time (Figure 7b), and both of at leastturned two on phase at the windings same time turned (Figure on at7a), the for same the winding time (Figure of the7b), SRM and driven bothof by them the new can generatemethod, them can generate torque for the SRM. torquehowever, for the there SRM. are at least two phase windings turned on at the same time (Figure 7b), and both of Figure 14 shows the relationship between the speed and the circulating current of the SRM themFigure can 14 generate shows the torque relationship for the SRM. between the speed and the circulating current of the SRM driven driven by the new method, with a constant load of 6 N·m. by the newFigure method, 14 shows with athe constant relationship load ofbetween 6 N·m. the speed and the circulating current of the SRM driven by the new method, with a constant load of 6 N·m.

EnergiesEnergies 20182018,, 1111,, x 3242 FOR PEER REVIEW 1111 of of 15 15

Figure 14. Speed/circulatingSpeed/circulating current current curve curve of of the the SRM SRM driven driven by by the the new new method. method.

WithWith a a reference reference value of 5.5 5.5 A, A, it it can can be be found found from from Figure Figure 1414 thatthat the the circulating circulating current current keeps keeps relativelyrelatively constant constant even even with with the the increasing increasing speed. speed. It It is is also also worth worth noting noting that that the the SRM SRM works works in in the the constantconstant power power area area when when the speed achieves 1300 rpm with a load of 6 N·m. N·m. It It also also proves proves that that for for a a specificspeciﬁc SRM, thethe circulatingcirculating current current keeps keeps relatively relatively constant, constant, which which does does not changenot change with thewith speed the speedor load. or load. ByBy making making the the analysis analysis among among the the winding winding current, current, circulating circulating current, current, torque torque and and speed speed of of the the SRMSRM driven by thethe newnew method,method, it it can can be be found found that that even even with with the the new new driving driving method, method, the the SRM SRM can cankeep keep its ownits own mechanical mechanical properties, properties, where where the the ring ri structureng structure will will not not have have a bad a bad inﬂuence. influence. For For an anSRM, SRM, it canit can be be easy easy to maketo make a prediction a prediction of itsof its performance performance with with the the new new driving driving method, method, based based on onthe the existed existed characteristics characteristics of theof the SRM. SRM.

6.6. Validation Validation TheThe experimentalexperimental system system consists consists of aof switched a switch reluctanceed reluctance motor withmotor the with characteristics the characteristics described describedin Section 3in and Section Figure 3 5and, a breakingFigure 5, machinea breaking with mach torqueine sensors,with torque a conventional sensors, a conventional inverter box, inverter current box,sensors, current position sensors, sensors, position a 200 sensors, V DC power a 200 supply,V DC power a DC-DC supply, buck a circuit,DC-DC a buck DSPACE circuit, 1103 a controllerDSPACE 1103board, controller and the PCboard, with and DSPACE the PC 1103 with blocks DSPACE installed. 1103 The blocks experiment installed. system The experiment is shown in system is shownThe in windingsFigure 15. inside the SRM were connected in series. According to (3), there should be at least threeThe current windings sensors inside in thethe experimentSRM were connected system, two in series. of them According are used to to (3), measure there should the leg be currents at least threein the current three-phase sensors inverter, in the experiment the rest was system, used to two measure of them the are winding used to current. measure With the theleg feedbackcurrents in of theposition three-phase signals inverter, and the current the rest signals, was used the SRMto me couldasure bethe controlled winding bycurrent. regulating With the the current feedback in theof positioninverter signals [25] and and the the current current in thesignals, DC-DC the buckSRM circuit.could be controlled by regulating the current in the inverterThe [25] reference and the speed current of in the the SRM DC-DC was buck set to circuit. 1000 rpm, and the load was set to 6 N·m. Both of the simulationThe reference results speed and of experimentalthe SRM was resultsset to 1000 of the rpm, leg and current the andload windingwas set to current 6 N·m. are Both shown of the in simulationFigure 16. Figureresults and15. experimental results of the leg current and winding current are shown in Figure 16. From the comparison between simulation and validation in Figure 16, it can be found that for both of theFrom leg currentthe comparison and the winding between current, simulation the measuredand validation results in match Figure well 16, withit can the be simulatedfound that ones. for both ofFigure the leg 17 currentshows theand simulation the winding result current, and th experimentale measured results result ofmatch the leg well current with the and simulated winding ones.current, where the reference speed is increased to 1300 rpm, and the load is kept at 6 N·m. FigureBased on17 Figureshows 11the, with simulation a load of re 6sult N·m and and experimental a speed of 1300 result rpm, ofthe the SRM leg current works in and the winding constant current,power area, where so the in comparison reference speed with is Figure increased 16, from to 1300 Figure rpm, 17 and, a good the load agreement is kept at with 6 N·m. the theoretical analysisBased can on still Figure be observed 11, with for a bothload ofof the6 N·m measured and a resultsspeed andof 1300 simulated rpm, the results, SRM which works shows in the a constanthigher frequency power area, and so slope in comparison limited current with waveforms Figure 16, thanfrom in Figure Figure 17, 16 .a good agreement with the theoreticalFigure analysis 18 shows can the still simulation be observed result for and both experimental of the measured result ofresults the leg and current simulated and winding results, whichcurrent, shows where a higher the reference frequency speed and is keptslope with limited 1000 current rpm, and waveforms the load than is increased in Figure to 16. 8 N ·m. FigureBased on18 theshows analysis the simulation in Section5 ,re withsult theand increasing experimental load, result the amplitude of the leg of current the excitation and winding current current,will also where increase. the reference In comparison speed is with kept Figure with 101600, from rpm, Figure and the 18 load, it can is increased be found to that 8 N·m. both of the simulated results and measured results have the same trend with the theoretical prediction.

Energies 2018, 11, 3242 12 of 15

From Figures 16–18, it is also worth mentioning that the minor error between the results of simulation and validation, of which the inﬂuencing factors are electromagnetic noise from the cables and sensors, as well as the measuring error and accuracy, these contribute to the discrepancy and the ripple in the measured results. The validation proves that the new control method can be applied in the practical system; theEnergies theoretical 2018, 11 analysis, x FOR PEER and REVIEW the parametric studies can be veriﬁed with the experiment, and12 of the15 Energiesresults 2018 of, 11 the, x FOR validation PEER REVIEW show the same trend as the simulation results even with different12 of 15 speed and load.

DSPACE 1103 DSPACE 1103 Power supply Power supply

DC-DC buck circuit DC-DC buck circuit

Three phase inverter SRM Three phase inverter SRM

Figure 15. The setup of the SRM control system. Figure 15. The setup of the SRM control system. Figure 15. The setup of the SRM control system.

(a) (b) (b) FigureFigure 16. (16.a) The(a) legThe(a) currentleg current in the in inverter the inverter at a speed at a speed of 1000 of rpm 1000 and rpm load and of load 6 N· m;of (6b N·m;) the winding(b) the Figurecurrentwinding 16. in ( thea) currentThe inverter leg in current atthe a inverter speed in the of at 1000inverter a speed rpm ofat and 1000a speed load rpm ofof and 61000 N load·m. rpm of 6and N·m. load of 6 N·m; (b) the winding current in the inverter at a speed of 1000 rpm and load of 6 N·m.

Energies 2018, 11, x FOR PEER REVIEW 13 of 15

Energies 2018, 11, x FOR PEER REVIEW 13 of 15 Energies 2018, 11, 3242 13 of 15 current (A) current (A)

(a) (b)

Figure 17. (a) The leg(a )current in the inverter with speed of 1300 rpm and (loadb) of 6 N·m; (b) the winding current in the inverter with speed of 1300 rpm and load of 6 N·m. FigureFigure 17. 17.(a) ( Thea) The leg currentleg current in the in inverterthe inverter with with speed speed of 1300 of rpm1300 andrpm load and ofload 6 N ·ofm; 6 (bN·m;) the ( windingb) the currentwinding in the current inverter in the with inverter speed with of 1300 speed rpm of 1300 and loadrpm ofand 6 Nload·m. of 6 N·m.

(a) (b)

FigureFigure 18. 18.(a) The(a) The leg currentleg(a) current in the in inverterthe inverter with with speed speed of 1000 of rpm1000 andrpm load and of (loadb 8) N ·ofm; 8 ( bN·m;) the ( windingb) the currentwinding in the current inverter in the with inverter speed with of 1000 speed rpm of and1000 loadrpm ofand 8 Nload·m. of 8 N·m. Figure 18. (a) The leg current in the inverter with speed of 1000 rpm and load of 8 N·m; (b) the 7. ConclusionswindingBased on current the analysis in the inverter in Section with speed 5, with of 1000 the rpmincreasing and load load, of 8 N·m. the amplitude of the excitation current will also increase. In comparison with Figure 16, from Figure 18, it can be found that both of A newBased type on the of controlanalysis method in Section for 5, SRM with has the been increasing proposed, load, instead the amplitude of asymmetric of the excitation H-bridges, a conventionalthe simulated three-phase results and bridgemeasured was results used tohave drive the thesame SRM trend by with using the a theoretical ring topology. prediction. currentFrom will Figures also increase. 16–18, Init comparisonis also worth with mentioning Figure 16, that from the Figure mino 18,r error it can between be found the that results both of Based on the phase windings connected in a series, the theoretical analysis of the proposed thesimulation simulated and results validation, and measured of which theresults influencing have the factors same trend are electromagnetic with the theoretical noise prediction. from the cables topology was made. A vector operation between the inverter current and the winding current was and sensors,From Figures as well 16–18, as the itmeasuring is also worth error mentioningand accuracy, that these the contribute minor error to thebetween discrepancy the results and the of made to obtain the formula, with which the reference value of the circulating current can be obtained, simulationripple in the and measured validation, results. of which the influencing factors are electromagnetic noise from the cables based on the parameters of the SRM. and sensors,The validation as well asproves the measuring that the new error control and ac methodcuracy, thesecan be contribute applied in to the the practicaldiscrepancy system; and the rippletheoreticalWith in the the analysis simulation measured and results. tool,the parametric the comparisons studies betweencan be verified different with driving the experiment, methods and were the also results made, basedof the onThe validation the validation analysis show proves of the winding same that thetrend currents new as controlthe and simu torque methodlation waveforms, results can be even applied aswith well in different the as practical the speed waveforms system; and load. ofthe the windingtheoretical current, analysis the circulatingand the parametric current, studies and the can inverter be verified leg current, with the and experiment, it explained and how the results the new methodof7. Conclusionsthe drovevalidation the SRMshow with the same the standard trend as the inverter simulation and trapezoidal results even currents. with different speed and load. The validation was also made to be compared with the simulation results. All the practical results A new type of control method for SRM has been proposed, instead of asymmetric H-bridges, a showed7. Conclusions similar trends with the simulation results with different speeds and loads (Figures 16–18). conventional three-phase bridge was used to drive the SRM by using a ring topology. AsABased the new result, ontype the of the phasecontrol new windings topologymethod forconnected for SRM driving has in been ana seri SRM proposed,es, canthe theoretical be instead applied of analysisasymmetric for an off-the-shelfof the H-bridges, proposed SRM. a It provesconventionaltopology that was it isthree-phase made. possible A vector to bridge drive operation was an SRM used between byto drive using the the a standardinverter SRM by current full-bridgeusing a and ring inverterthe topology. winding and current an additional was DC-source.madeBased to Byobtain on controlling the the phase formula, thewindings inverter with connectedwhich currents the andin reference a addingseries, valuethe a circulating theoretical of the circulating current, analysis an of current SRM the proposed can can also bebe controlledtopologyobtained, with wasbased waveformsmade. on the A parametersvector that canoperation beof the used betweenSRM. for driving the inverter a BLDC current but not and limited the winding to these. current At the was same time,made the newto obtain topology the formula, also has thewith versatility which the for reference different value type ofof SRMs. the circulating current can be obtained, based on the parameters of the SRM.

Energies 2018, 11, 3242 14 of 15

Author Contributions: Conceptualization, H.S. and A.V.d.B.; Data curation, H.S., A.F.M. and A.H.M.; Formal analysis, H.S.; Funding acquisition, H.S. and P.S.; Investigation, H.S., M.N.I. and A.V.d.B.; Methodology, H.S.; Project administration, P.S.; Resources, H.S. and A.V.d.B.; Software, H.S. and A.F.M.; Supervision, P.S. and A.V.d.B.; Validation, H.S., A.F.M., A.H.M., P.S. and A.V.d.B.; Visualization, H.S.; Writing—original draft, H.S.; Writing—review & editing, H.S., P.S. and A.V.d.B. Funding: This research was funded by CHINA SCHOLARSHIP COUNCIL, grant number 201606930007. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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