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1 On-line MTPA control strategy for DTC synchronous reluctance motor drives Silverio Bolognani, Member, IEEE, Luca Peretti, Mauro Zigliotto, Member, IEEE Abstract—This paper presents a on-line procedure for the including their non-linearity, as self- and mutual inductances, automatic search of the maximum-torque-per-ampere operating and possibly the iron losses. It is quite intuitive that the more region for a synchronous reluctance motor (SynchRM). The precise the machine model, the more effective the MTPA algorithm is based on a signal-injection method with a random- based perturbation pattern applied to a common direct-torque- implementation. While often computationally not intensive, controlled drive. Among motor parameters, only the stator those approaches definitely requires both a measurement batch resistance is required to perform the automatic procedure. on the motor and an off-line data pre-processing. Simulations and experimental results are presented in the paper, In [6], again, a conventional FOC algorithm is merged demonstrating the benefits of the proposed algorithm. The with a MTPA strategy. The problems are incidental to the solution is easily extended to any AC drive. minimization procedure, which calculates the MTPA point Index Terms—AC motor drives, Reluctance motor drives, temporarily overriding the speed controller. The approach may Losses, Optimisation methods. fail if the initial working point is far away from MTPA, since a little current angle deviation may cause a relatively I. INTRODUCTION high change in torque. Alike the former methods, the torque calculation needs the knowledge of the motor inductances, and Recent environmental and energetic issues call for best ef- no information about the convergence speed has been found ficiency solutions for electrical drives. Actually, high-dynamic in the paper. drives are still required, but besides speed, increased efficiency Another interesting solution is proposed in [7]. The paper of the whole drive system could make the difference for a keen focuses on the MTPA control of an interior permanent-magnet customer. Maximum-torque-per-ampere (MTPA) strategies are synchronous machine. Both current and voltage limitations are a smart answer to the call for efficiency. In principle, the target considered to derive proper equations for the current references of MTPA strategies is to deliver the electromagnetic torque in a standard FOC drive. The solution is promising since it can with the lowest current magnitude. In this way, copper losses work during transients, but there is again the need of a precise are minimised and the overall system efficiency is increased, knowledge of both the d and the q axis inductances. at least as long as copper losses are dominant. The latest solution for an automatic MTPA search in FOC Modern AC drives usually implement either field oriented drives is presented in [8]. The MTPA is sought by varying the control (FOC) or direct torque control (DTC). In the following, current vector angle of a common FOC algorithm, looking a short review of MTPA applied to those technique will be for the changes in the current magnitude reference signal presented. generated by the speed PI controller. While attractive because One of the first examples of automatic MTPA search of the simplicity of the MTPA detector, a drawback is repre- algorithm is presented in [1], in which a FOC algorithm is sented by the injected perturbation signal waveform, which integrated with an automatic procedure aimed to minimize the is sinusoidal. This can constitute a problem with sensitive input power. The major drawback is that the d axis current loads, in particular when the sinusoid frequency is close to a id is perturbed with a step-like signal, and the convergence is mechanical resonance. On the other hand, the great advantage very low (in the order of minutes). of this solution is that the signal injection skips the need of an Another solution, which minimizes the input power, is accurate drive model. The parameters are still necessary, but presented in [2]. The drawback, there, is that steady-state is for the FOC implementation, and not for the MTPA itself. never reached, since the method foresees a continuous, slow A more recent combination of [8] and [1], which proves current chattering around the minimum loss operating point. the industry interest in signal injection-based procedure, was In addition, the algorithm suffers in presence of noisy input presented in [9]. power signals. To the Authors’ knowledge, and opposite to the aforemen- Other solutions, as [3], [4], and [5] implement MTPA tioned FOC schemes, the DTC-based AC drives have been strategies that need the knowledge of machine parameters, scarcely investigated from the MTPA point of view. This is probably due to the fact that the DTC drives extremely fast Manuscript received ...; revised ... S. Bolognani is with the University of Padova, Department of Electri- dynamics fits for to servo applications, in which the focus cal Engineering, Via Gradenigo 6/A, 35131 Padova, Italy (e-mail: silve- remains on transient behaviour. But there are other emerging [email protected]). applications, as in mining and steel industry, in which the L. Peretti and M. Zigliotto are with the University of Padova, Department of Technique and Management of Industrial Systems, Stradella San Nicola 3, energy saving issue is going to play a major rule. DTC technol- 36100 Vicenza, Italy (e-mail: [luca.peretti], [mauro.zigliotto]@unipd.it). ogy is quite mature, and in most conventional schemes a fast, 2 robust and reliable torque production is obtained by stating a Electromechanical torque and load equations complete the proper flux-linkage angle, as proposed by [10]. Nevertheless, system model: as claimed by the Authors themselves, the drive operates at 3 constant flux-linkage magnitude at all loads, resulting in a τ = p (λ i − λ i ) 2 d q q d probable lack of efficiency at light loads. dω (3) τ = J m + Bω + τ There are few examples of efficiency-optimization solutions dt m L for DTC schemes. One of them is [11], which deals with In (3), λ and λ are respectively the d and q components of steady-state efficiency optimization in DTC control of perma- d q the flux linkage space vector, i and i are respectively the nent magnet synchronous motors. The best-efficiency stator d q d and q components of the stator phase current space vector, flux linkage reference is found from an off-line procedure τ is the load torque, J is the load inertia, B is the viscous which aims to minimise electrical losses in the motor for a L friction. wide operating range. On-line computational effort is limited For DTC purposes, the first of (3) should be expressed in to the access of a look-up table (LUT) which stores the flux terms of flux linkage magnitude |λ| and flux linkage angle δ linkage reference as function of the torque and speed value. with respect to the dq reference frame [15]. Fig. 1 reports the As for many FOC-based solutions, the method requires the nomenclature in case of a motor with one pole pair (p = 1). knowledge of inductances and resistances (stator and core loss) Substituting i = λ /L and i = λ /L , where L and L of the motor. Further developments of this work were reported d d d q q q d q are the direct and quadrature inductances (which in general are in [12], where it is recognized that the best-efficiency stator function of i and i ), and λ = |λ| cos(δ) and λ = |λ| sin(δ) flux linkage value is not the optimum one for the fastest torque d q d q in the first of (3), leads to: response. The paper presents a solution which combines itself to the best-efficiency LUT, and selects a proper flux linkage 3 1 1 2 τ = p − |λ| sin(2δ) (4) reference for fast torque transients only during start-ups. 4 Lq Ld The proposed work aims to get an energy-optimised drive, by combining the simplicity, speed and robustness of DTC control (in its original form, thus without voltage space vec- tor modulation) with a parameter-insensitive, injection-based MTPA strategy. The signal injection is operated in the flux magnitude reference signal of the DTC drive, either at steady state or during the constant-torque transients, and by observing the changes in the measured stator current magnitude. A random-number-generation pattern is chosen as perturbation signal instead of a pure sinusoidal signal. One positive side- effect of the approach is that the formulation is general Fig. 1. SynchRM’s synchronous reference frame. enough to allow its extension to permanent magnet motors, and induction motors drives as well. Expression (4) represents the base equation of a DTC The paper is organised as follows. In Sect. II, some basics algorithm for SynchRMs. The torque is changed either by on the SynchRM and the DTC approach will be discussed. varying the flux linkage magnitude |λ| or the flux linkage Sect. III is devoted to the MTPA strategy and the details angle δ with respect to the reference frame dq. A fast torque of the procedure. Sect. IV presents some simulation results, change is obtained by a variation of δ [15], while a |λ| while Sect. V shows the experimental results. A conclusive variation is normally used to change the motor operating discussion ends the paper. region (flux weakening, for example) or to reach particular working conditions (MTPA, for example). Fig. 2 reports the II. DTC FOR SYNCHRONOUS RELUCTANCE MOTORS - general block schematic of a DTC algorithm for SynchRMs, BASIC CONCEPTS including speed control and completed with a MTPA detector The space vector equation that describes the motor dynam- block for flux linkage reference generation.

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