182 Muntean et al. low speed, have been recently reported [11,12]. The initial angular position of the stator flux-linkage vector ψ s may be obtained from a low-resolution encoder. Subsequently, this encoder is not needed under the DTC scheme. Electromagnetic torque and stator flux-linkage magnitude errors, generated by compar- ison between estimated and reference values, are inputs to the respective flux and torque hysteresis regulators. The discretized outputs of these regulators are inputs to the optimum voltage switching selection table. It is used to properly choose the VSI-fed voltage vectors to regulate the stator flux and torque within their error bands. In the IPMSM DTC scheme of Fig. 3, the reference electromagnetic torque, m e,ref ,is obtained as the output of the rotor-speed controller from the outer loop, and is limited at a certain value, which guarantees the stator current not to exceed its maximum admissible value. In its turn, the reference value of the stator flux-linkage vector modulus, |ψ s,ref |,is generated in the proposed IPMSM DTC scheme as a function of the electromagnetic torque reference, i.e. |ψ s,ref |(m e,ref ), by maximizing the IPMSM torque over the wide-speed oper- ation range in the presence of current and voltage constraints. The stator-current limit, I s,lim , is an IPMSM thermal rating or a VSI maximum available current. The stator-voltage limit, U s,lim , is the VSI maximum available output voltage, depending on the DC-link voltage. Hence, the current and voltage constraints establish the following operating limits for the VSI-fed IPMSM: i s |=(i 2 sd +i 2 sq ) 1/2 ≤ I s,lim (9) |u s |=(u 2 sd + u 2 sq ) 1/2 ≤ U s,lim (10) In the speed operation range I from standstill up to the base rotor speed ω rb , current constraint of equation (9) is dominant, preventing the IPMSM overheating, whereas voltage constraint of equation (10) can be met, since the back-emf is rather low. Thus, the required function |ψ s,ref I |(m e,ref I ) forthe reference value of the stator flux-linkage magnitude inthe speed range I can be obtained by ensuring the IPMSM constant-torque operation in which the maximum torque-to-stator current ratio is achieved at the stator-current limit I s,lim , i.e. the motor is accelerated by the maximum available torque below the base speed; it results (i 2 sd, I +i 2 sq,I ) 1/2 = I s,lim (11) m e,maxI = (3p/4)|ψ PM |i sq, I {1 + [1 + (2ξL sq i sq, I /|ψ PM |) 2 ] 1/2 } (12) For the currents i sd, I and i sq, I , equation (5) can be written as |ψ s,ref I |=[(L sd i sd, I +|ψ PM |) 2 + (L sq i sq, I ) 2 ] 1/2 (13) Considering in equation (12) m e,max I = m e,ref I , solving equations (11) and (12) for the currents i sd, I and i sq, I , and then substituting in equation (13), one obtains the function |ψ s,ref I |(m e,ref I ) requested in the IPMSM DTC scheme over the speed range I, i.e. from standstill up to the base rotor speed ω rb . If one defines ω rb as the highest speed for the constant-torque operation mode with the maximum torque subject to the stator-current limit, and, at the same time, as the lowest speed for which the stator-voltage limit is reached, II-4. Wide-Speed Operation of Direct Torque-Controlled IPMSM 183 ω rb can be readily deduced from the steady-state IPMSM stator-voltage equations in the (d,q) coordinate system (neglecting the stator-resistance voltage drop): u sd =−ω r L sq i sq (14) u sq = ω r L sd i sd + ω r |ψ PM | (15) one obtains from equations (13)–(15) ω rb = U s,lim /[(L sd i sd, I +|ψ PM |) 2 + (L sq i sq, I ) 2 ] 1/2 (16) The IPMSM speed operation rangeII,justabove the base rotorspeed, is aflux-weakening constant-power region. The highest attainable IPMSM torque subject to both stator-current and -voltage limits of equations (9) and (10) yields m e,maxII = (3p/2)[|ψ PM |i sq, II − (L sq − L sd )i sd, II i sq, PM ] (17) where (i sd, II 2 +i sq, II 2 ) 1/2 = I s,lim (18) i sd, II = (|ψ PM |L sd −{(|ψ PM |L sd ) 2 + (L sq 2 − L sd 2 ) × [|ψ PM | 2 + (L sq I s,lim ) 2 − (U s,lim /ω r ) 2 ]} 1/2 )/ (L 2 sq − L 2 sd ) (19) Rewriting equation (13) for i sd,II and i sq,II , accounting in equation (17) m e,maxII = m e,refII , and eliminating the currents i sd,II and i sq,II between equations (13) and (17)–(19), one obtains the required function |ψ s,ref II |(m e,ref II ) for the IPMSM DTC scheme over the flux-weakening constant-power speed range II. Since for the considered IPMSM drive |ψ PM |/L sd < I s,lim , there is a high-speed flux- weakening region III, where IPMSM constant-power operation is no more achievable. However, the torque capability can be insured by the maximum torque-to-stator flux ratio subject to the stator-voltage limit alone. The rotor speed, at which IPMSM constant-power operation ceases, is termed as base power speed, ω rbp , and can be simply determined by ω rbp = U s,lim /(L sd I s,lim −|ψ PM |) (20) Beyond ω rbp , IPMSM flux-weakening operation is still available up to theoretically infinite speed. The IPMSM maximum available torque, m e,max III , as previously defined for the high- speed flux-weakening operation range III, is determined by introducing the upper-limit angle δ lim of equation (8) into equation (1) expressing the IPMSM torque, thus leading to m e,max III = (3p/2)|ψ s |(|ψ PM |−ξ|ψ s |{|ψ PM |/4ξ|ψ s |−[(|ψ PM |/4ξ|ψ s |) 2 + 1/2] 1/2 }) ×(1 −{|ψ PM |/4ξ|ψ s |−[(|ψ PM |/4ξ|ψ s |) 2 + 1/2] 1/2 } 2 )/ L sq (1 − ξ) (21) Equation (21) with m e,max III = m e,ref III , yields the required function |ψ s,ref III |(m e,ref III ) for the IPMSM DTC scheme over the high-speed flux-weakening operation range III. For the three IPMSM operation modes that have been previously identified over the wide-speed range (below and above the base speed) the specific reference relationships |ψ s,ref |(m e,ref ) can be computed off-line, and subsequently incorporated into the IPMSM DTC scheme as a simple look-up table. 184 Muntean et al. Table 1. Specifications of prototype IPMSM Number of pole-pairs, p 3 Stator phase resistance, R s 0.895 PM flux-linkage magnitude, |ψ PM | 0.2979 Wb d-axis stator self-inductance, L sd 12.16 mH q-axis stator self-inductance, L sq 21.3 mH Stator-current limit, I s,lim 6.75 A Stator-voltage limit, U s,lim 400 V Base rotor speed, ω rb 2,500 rpm Simulation results Extensive dynamic simulations using Matlab/Simulink software are carried out on a pro- totype IPMSM having the specifications given in Table 1 in order to validate and assess the performance of the proposed VSI-fed IPMSM DTC scheme over wide-speed operation range. Fig. 4 shows the simulated dynamic responses of DTC IPMSM speed, torque, and stator flux-linkage with respect to a step change in speed reference from 0 to 4,000 rpm under (a) (b) (c) (d) Figure 4. Dynamic simulation results for prototype IPMSM DTC over constant-torque and flux- weakening wide-speed operation ranges: (a) rotor-speed response; (b) torque response; (c) response of the stator flux-linkage magnitude; (d) locus of the stator flux-linkage vector. II-4. Wide-Speed Operation of Direct Torque-Controlled IPMSM 185 no-load conditionand subject to current and voltage constraints. It is seen from Fig. 4, that a smooth transition between the constant-torque and flux-weakening speed operation regions occurs when the rotor speed exceeds the base speed. With the proposed DTC scheme, IPMSM is accelerated by the maximum available torque in both constant-torque and flux- weakeningoperationmodesoverthewide-speedrangeinthepresenceofcurrentandvoltage constraints. Fig. 4(d) displays the dynamic locus of the stator flux-linkage vector, which is almost a circle in both constant-torque and flux-weakening wide-speed operation ranges. Conclusions An integrated approach to the proper design and DTC of VSI-fed IPMSMs requiring wide speed-torque envelope has been proposed. The relationship between the reference electromagnetic torque and stator flux-linkage has been derived to be used in IPMSM DTC insuring maximum-torque-per-stator-current operation below the base speed as well as constant-power flux-weakening and maximum- torque-per-stator-flux operations above the base speed. The simulated dynamic response in step speed command has confirmed the effectiveness of the proposed IPMSM DTC scheme over wide-speed operation range. References [1] S. Morimoto, M. Sanada, Takeda, Y. Wide-speed operation of interior permanent magnet synchronous motors with high-performance current regulator, IEEE Trans. Ind. Appl., Vol. 30, No. 4, pp. 920–926, 1994. [2] J M. Kim, S K. Sul, Speed control of interior permanent magnet synchronous motor drive for the flux weakening operation, IEEE Trans. Ind. Appl., Vol. 33, No.1, pp. 43–48, 1997. [3] M.N. Uddin, T.S. Radwan, M.A. Rahman, Performance of interior permanent magnet motor drive over wide speed range, IEEE Trans. Energy Convers., Vol. 17, No. 1, pp. 79–84, 2002. [4] M.F. Rahman, L. Zhong, K.W. Lim, A direct torque-controlled interior permanent magnet synchronous motor drive incorporating field weakening, IEEE Trans. Ind. Appl., Vol. 34, No. 6, pp. 1246–1253, 1998. [5] P. Vas, Sensorless Vector and Direct Torque Control, Oxford, UK: Oxford University Press, 1998, pp. 223–237 (Ch. 3). [6] J. Luukko, “Direct Torque Control of Permanent Magnet Synchronous Machines—Analysis and Implementation”, Ph.D. dissertation, Lappeenranta University of Technology, Finland, 2000, 172 p. [7] L. Qinghua, A.M. Khambadkone, A.Tripathi, M.A. Jabbar, “Torque Control of IPMSM Drives Using Direct Flux Control for Wide Speed Operation”, Proc. IEEE Int. Conf. Electr. Mach. Drives Conf. (IEMDC 2003), Vol. 1, Madison, Wisconsin, USA, June 1–4, 2003, pp. 188–193. [8] Y. Honda, T. Higaki, S. Morimoto, Y. Takeda, Rotor design optimization of a multi-layer interior permanent-magnet synchronous motor. IEE Proc. Electr. Power Appl., Vol.145, No. 2, pp. 119–124, 1998. [9] L. Qinghua, M.A. Jabbar, A.M. Khambadkone, “Design Optimization of a Wide-Speed Per- manent Magnet Synchronous Motor”, Proc.IEEInt. Conf. Power Electr. Mach. Drives (PEMD 2002), Bath, UK, April 16–18, 2002, pp. 404–408. [10] F.Rahman, R.Dutta, “A NewRotorofIPMMachineSuitableforWideSpeedRange”,Rec.29th Ann. Conf. IEEEInd. Electron. Soc. (IECON 2003),Roanoke, Virginia, USA, November 2–6, 2003, CD-ROM. 186 Muntean et al. [11] J.Luukko, M.Niemel¨a, J.Pyrh¨onen, Estimation oftheflux linkage in adirect-torque-controlled drive, IEEE Trans. Ind. Electron., Vol. 50, No. 2, pp. 283–287, 2003. [12] L. Tang, F. Rahman, M.E. Haque, “Low speed performance improvement of a direct torque- controlled interior permanent magnet synchronous machine drive”, Rec. 19th IEEE Ann. Appl. Power Electron. Conf. (APEC 2004), Anaheim, CA, USA, February 22–26, 2004, pp. 558–564. II-5. OPTIMAL SWITCHED RELUCTANCE MOTOR CONTROL STRATEGY FOR WIDE VOLTAGE RANGE OPERATION F. D’hulster 1 , K. Stockman 1 , I. Podoleanu 2 and R. Belmans 2 1 Hogeschool West-Vlaanderen, Dept. PIH, Graaf Karel de Goedelaan 5, B-8500 Kortrijk, Belgium frederik.dhulster@howest.be, kurt.stockman@howest.be 2 KU Leuven, Dept. ESAT, Div. ELECTA, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium isan.podoleanu@esat.kuleuven.ac.be, ronnie.belmans@esat.kuleuven.ac.be Abstract. This paper describes a technique to obtain optimaltorque control parameters of a switched reluctance motor (SRM). A relationship between dc-link voltage and rotor speed is used, reducing the number of control parameters. Using a nonlinear motor model, surfaces are created describing torque, torque ripple, and efficiency as function of rotor speed and the main control parameters. Next, optimization software generates optimal control parameter combinations out of these surfaces for equidistant torque-speed performance. The advantage of this technique is an offline optimization platform and the simplicity to create additional surfaces (e.g., acoustic noise, vibrations, ). Introduction Due to the ever increasing application demands put on switched reluctance motor drives, a flexible control strategy is gaining importance. Some applications demand a low acoustic noise or vibration level, others feature high efficiency. This paper deals with the design and implementation of an optimal control strategy for an 8/6 SRM, operating in a broad supply voltage range. Robust control must be applied for a dc-link voltage range of 115–325 V and a speed range of 0–2,000 rpm. At full motor load, a maximum torque control strategy must be used to obtain maximum mechanical power at the motor shaft. At medium load, different combinations of phase current and control angles are possible for a given reference torque. This degree of freedom enables optimization of the torque control parameters. A complete optimization of machine geometry—converter—control of a SRM is pro- posed in [1] using genetic algorithms (GA) as an optimization tool. In many applications, the use of standard motor designs is preferred rather than developing a motor geometry for every new application. The motor behavior as function of its torque control parameters is calculated only once and can serve as input for an offline optimization platform. Through a weighted sum of ob- jective functions, the control of a standard SRM can be optimized for different applications. Fig. 1 illustrates the flowchart of this procedure. First, the basic equations for the nonlinear SRM model are explained. Next, the main parameters (N) for the torque control are derived, taking into account the relation between S. Wiak, M. Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 187–200. C 2006 Springer. 188 D’hulster et al. FE magnetostatic 2D computation (Flux2D ® ) .GDF-file (Speed ® ) motor geometry material data End-effect correction [7] ),(.),(),( 2 qyqqy iiKi Deee = ),( 2 qy i D SRM lookup data generation ),( qy i e (B - C - D - E) ),( ),(),( ),( ),( ),( 0 qy q qy q q q qy q qy iE di iiW iTD i i C i B e i eco e e = ∂ ∂ = ∂ ∂ == ∂ ∂ = ∂ ∂ = Ú Current control 1) hysteresis / PWM 2) N° i-transducers BH-data Steinmetz parameters SRM optimization platform multiobjective weights w i optimal SRM torque control i ref,opt (T ref ,w) a ON,opt (T ref ,w) a DWELL,opt (T ref ,w) a FW,opt (T ref ,w) steady- state behaviour SRM behaviour maximum torque behaviour / control T max (w) i ref,m (w) a ON,m (w) a DWELL,m (w) objective functions (surfaces) (T m , T ripple ,h m ) =f(w , i ref , a ON a DWELL , a FW ) Figure 1. General flowchart of the optimal torque control of SRMs. II-5. Optimal Switched Reluctance Motor Control Strategy 189 the dc-link voltage and the rotor speed. Then, N-dimensional surfaces are created, repre- senting the SRM behavior as function of the torque control parameters. Finally, the optimal control parameters for the complete torque-speed range are determined using a genetic algorithm (GA) search tool or alternatively a “search for all” tool. SRM system equations and drive model The static behavior of a SRM can be explained by two equations, describing the current in a stator phase (1) and the instantaneous electromagnetic torque T , produced by a stator phase (2). Both equations depend on the partial derivatives of the flux-linkage ψ(i,θ). di dt = 1 ∂ψ ( i,θ ) ∂i u − Ri − ∂ψ ( i,θ ) ∂θ ω (1) T(i,θ) = ∂W co (i,θ) ∂θ i=cst = i 0 ∂ψ(i,θ) ∂θ · di (2) with: – ∂ψ(i,θ) ∂i = p i (i,θ): phase inductance [H] – ∂ψ(i,θ) ∂θ = p θ (i,θ): back-emf coefficient –ω: rotor speed (rad/s) –u: phase voltage (V) –i: phase current (A) – R: phase resistance (). This single-phase behavior, represented by four matrices as function of rotor position and phase current, is deducted from a magnetostatic finite element analysis (Fig. 2). The un- aligned rotor position is set to 30 ◦ and aligned to 60 ◦ . Fig. 3 shows the single-phase static behavior of the motor, further used in this paper. SRM control optimization is only possible using an accurate dynamic motor model, in- cluding saturation, iron lossestimation,and torque ripple calculation, combinedwitha drive model using the appropriate torque and current control (hysteresis or PWM). Both motor- ing and generating mode are supported, for different phase current sensing. Superposition of single-phase SRM-modeling, using lookup tables with 2D magnetostatic finite element Figure 2. Geometry and 2D finite element model (Flux2D R ). 190 D’hulster et al. Figure 3. Single-phase SRM lookup data. II-5. Optimal Switched Reluctance Motor Control Strategy 191 flux-linkage data, is described in [2]. This model is extended with iron loss calculation, based on the modified Steinmetz equation [3]. The Steinmetz parameters, describing the iron losses function for sinusoidal excitation are measured on a standard Epstein frame. Further in this paper, only motoring operation is considered. If ventilation and friction losses are neglected, efficiency and torque ripple for motoring operation are: η m = P m P m + P Cu + P Fe (3) T ripple = max(T ) −min(T) T m (4) with: – P m : mechanical power (W) – P Cu : Joule losses (W) – P Fe : iron losses (W) –T m : average torque (Nm). SRM torque control Unlike dc-machines or rotating field machines, in SRMs no direct link exists between torque and current, in this way complicating its control. This is linked to the fact that even in steady state the stored magnetic energy in the machine is not constant. A basic torque controller (Fig. 4) consists of lookup tables with the control parameters (turn-on angle a ON , dwell angle a DWELL = a OFF − a ON , freewheeling angle a FW , and reference current i ref ), i i * + current controller half bridge invertor 2/4 i-transducers 8/6 SRM i i commutation logic on off fw u specific current control parameters L H lookup tables θ on θ off θ fw T * optimization criterion resolver ω θ position/speed convertor from speed controller Figure 4. Basic SRM torque control structure. . flux-linkage has been derived to be used in IPMSM DTC insuring maximum-torque-per-stator-current operation below the base speed as well as constant-power flux-weakening and maximum- torque-per-stator-flux. (eds.), Recent Developments of Electrical Drives, 187 200 . C 200 6 Springer. 188 D’hulster et al. FE magnetostatic 2D computation (Flux2D ® ) .GDF-file (Speed ® ) motor geometry material data End-effect. constant-torque and flux- weakening wide-speed operation ranges: (a) rotor-speed response; (b) torque response; (c) response of the stator flux-linkage magnitude; (d) locus of the stator flux-linkage