FOC and DTC comparison in PMSM for railway traction application

FOC and DTC comparison in PMSM for railway tractionapplicationMaitane Aguirre (*), Carlos Calleja (**), Amaia Lopez-de-Heredia (**), Javier Poza (*), AitorAranburu (***), Txomin Nieva (***)*Faculty of Engineering,University of Mondragon.Loramendi 420.500 Mondragon, SpainTel: +34 943 79 47 00Fax: +34 943 79 15 36 maguirre@ /enele**IKERLAN-IK4Technological Research CentrePº J.M. Arizmendiarrieta, 220.500 Mondragon, SpainTel: +34 943712400Fax: +34 943796944ccalleja@ikerlan.eswww.ikerlan.es***TRAINELEC S.L.Poligono Katategi20.271 Irura, SpainTel: +34 943 69 08 70Fax: +34 943 69 09 12aaranburu@AcknowledgementsThis work has been partially financed by the Basque government (PhD grant program).Keywords«Permanent magnet motor», «Traction application», «Rail vehicle», «Direct torque and flux control», «Vector control»AbstractThis paper presents a detailed comparison between two control strategies, field oriented control (FOC) and direct-torque control (DTC), in permanent-magnet synchronous machines (PMSM) for railway traction applications. The analysis is initially carried out in simulation, and some experimental results obtained from a 100 kW test bench are also included.IntroductionThroughout the history of the electric railway different dc and ac machines have been used for the same traction purpose. Until 1970 dc machines were the most common traction motors due to the simplicity of their control and the feasibility of implementation. Nevertheless, the development of semiconductor technology entailed the introduction of power converters into railway traction systems, which allowed the implementation of control algorithms for ac machines.Nowadays the squirrel-cage asynchronous machine (ASM) is the most widely used motor in railway applications, and it is considered a mature and robust technology. However, last trends aiming to complete new quality and environmental requirements have driven new research-works focused on efficiency improvement, volume reduction and noise minimization. This background and the high-performance permanent-magnet material development, make the permanent-magnet synchronous machine a very high-potential solution [1].PMSM machines provide high power density, high efficiency and small torque ripple. Nevertheless, they also present some drawbacks: only one motor can be connected to an inverter and additional contactors are required in order to isolate the motor from the inverter in case of failure, [2]. Regarding the control of the PMSM in railway traction applications, most of the publications show that the field oriented control is the most extended and preferred strategy among industrial applications [3], [4]. In spite of this fact, authors believed that the direct torque control strategy could also be a suitable solution for this kind of traction application.For this reason, the presented work wants to analyse both type of control and underline the advantages and drawbacks of each one considering specific traction operating constraints by numerical simulations and experimental results in a 100 kW PMSM test bench.Theoretical Considerations about the PMSM in railway traction applicationsBasic Equations of PMSMThe electrical behaviour of PMSM machines can be represented in a vector system by means of two-phase stationary (αβ) or rotating (dq) reference frame. Fig. 1 shows the PMSM vector diagram in arotating dq axis frame linked to the rotor in which the permanent-magnet field is oriented to d axis.Fig. 1: Vector diagram of a PMSM machine.Where, j represents the imaginary unit, V S and I S are the stator voltage and current respectively, R S is the stator resistance, L d and L q are the longitudinal and transversal inductances respectively, ФPM is the permanent-magnet flux, and ω and θ are the speed and position of the rotor with respect to the stator. The “uvw” frame represents a three-phase coordinate system linked to the stator and “αβ” and “dq” frames represent two-phase coordinate systems linked to the stator and the rotor respectively.The electric equations of stator voltage and flux corresponding to this representation are expressed as:⎪⎪⎩⎪⎪⎨⎧Φ++=Φ−+=Sd Sq Sq Sq s Sq Sq Sd Sd Sd s Sd dt di L i R V dtdi L i R V ωω, ( 1 )()()22Sq Sq SdSd PMS SqSq Sq SdSd PM Sd i L i L i L i L ++Φ=Φ⇒⎩⎨⎧=Φ+Φ=Φ ( 2 )The electromagnetic torque of a synchronous machine is directly imposed by the stator current vector, the amplitude (I S ) and phase (γ) or d and q axis components (I Sd , I Sq ):()()().232sin 21cos 232Sq Sd Sd Sq q S PM S Sd Sq S PM i i L L i p I L L I p T −−⋅=⎥⎦⎤⎢⎣⎡−−=ϕγγϕ( 3 )The electromagnetic torque expression is composed of two terms: a magnetic component and a reluctant component. Depending on the PMSM topology these torque components play a more or less important role; the bigger the saliency is the more important the reluctant torque component is. Hence, nonsalient machines (L d =L q ), like the surface PMSM (SPMSM), only present magnetic torque.Railway Application RequirementsRailway vehicles are the most widely used electric vehicles. Thanks to overhead or ground electrification systems, a heavy storage system is not required which improves the power-weight ratio.The railway traction system must be able to fulfil the dynamic requirements of the application assuring the functionality of the electric vehicle in the whole speed range and whole power demand under different environmental conditions.The Torque–Speed or Power-Speed characteristics of an electrical machine defines its operating area. Fig. 2 shows the different limits of the operating area of traction PMSM [5].Fig. 2: Torque-Speed characteristics of a PMSM machine.The first area corresponds to the constant-torque zone, where the torque remains constant and thevoltage increases with the speed. When the base speed (ωb ) is reached, the machine operates in the second area, called constant-power zone. In this area, the stator voltage cannot longer be increased due to the voltage supply limitation, so it remains constant to its maximum value. From equations ( 1 ) and ( 2 ) and neglecting the stator resistance R S , the stator voltage module can be expressed as:()()22Sq Sq SdSd PMS i L i L V ++Φ=ω.( 4 )In the second zone, the power is maintained constant instead of the torque by weakening the magnetic flux. In the case of PMSM machines, a magnetic flux opposite to the permanent magnet flux must be generated in order to weaken the magnetic field in the air gap. To achieved this, the stator current vector must be modified, by changing the vector phase γ or the direct component i Sd , as it can be concluded from equation ( 2 ). The equation ( 4 ) also shows that when the speed is increasing the stator voltage can be maintained constant by introducing a negative i Sd current.Regarding to the PMSM control, the implemented control strategy has to take into account the application requirements and limits: mechanical, electrical, signalling or quality constraints. Besides, the whole control algorithm must be designed in order to:• Be precise• Assure the stability and robustness of the system • Provide the required dynamic responses• Optimize the harmonic content of generated signals • Consider system limitations• Be feasible to implement and easy to tuneThe control algorithms analyzed through this work are going to be evaluated following these criteria, considering that the best solution is the one providing the best compromise between all these characteristics.PMSM Control StrategiesFor all the operation zone, constant-torque zone and constant-power zone, two control strategies are going to be presented: one based on the vector-control field oriented principles and the other based on direct-control techniques.Field Oriented ControlFirstly presented for induction machines by F. Blaschke [6] in 1971, FOC strategies transform machine three-phase variables into two-phase axes in order to obtain the same decoupling between flux and torque that exists naturally in dc machines.The presented control strategy is based on a rotor field oriented control (RFOC) and the stator three-phase current is transformed into dq components of a rotating reference frame. In this case, the d component of stator current controls the magnetic state of the machine (cf. equation ( 2 )), while the q component is in charge of generating the electromagnetic torque (cf. equation ( 3 )).Fig. 3 shows the bloc diagram of this control strategy, where both current control loops are implemented in the rotor flux reference frame using PI linear regulators with induced voltage compensation.Fig. 3: Bloc diagram of FOC control strategy in PMSM.In order to use efficiently the inverter output voltage, some authors have presented different solutionswhere the control strategy is changed in the field weakening zone from Cartesian coordinates to polarcoordinates [3], or from vector control to scalar control mode [4]. Those strategies also allow to easily control and limit the load angle.The FOC strategy requires a modulator which usually consists of a pulse-width modulation (PWM) based techniques. For high-power applications operating at high speeds the converter switching frequency is limited, meaning that at upper speeds the ratio between switching and fundamental frequencies will be small. This could cause undesired subharmonics and produce additional torque ripple and losses [7]. To avoid these drawbacks different type of modulation strategies have been proposed: a combination of asynchronous and synchronous space-vector modulation (SVM) [4] [8], programmed angles or selective harmonic elimination (SHE) techniques [9].Direct Torque ControlThe DTC, which was presented by I. Takahashi in 1986 for an induction machine [10], is based on the direct control of the torque and flux and involves non linear hysteresis controllers. The DTC generatesa sinusoidal stator flux, whereas the direct self control (DSC), presented in 1988 by M. Depenbrock[11], creates a trapezoidal flux.Direct-control strategies do not require the previously mentioned reference transformations to achieve a decoupled control of flux and torque. The currents of the machine are indirectly controlled through torque and flux control. Fig. 4 shows the general bloc diagram of the DTC control strategy:Fig. 4: Bloc diagram of DTC control strategy in PMSM.One of the advantages of DTC strategies is that they do not require a PWM based modulator. Instead, the low level control is composed of a switching table in which depending on the hysteresis controllers output a switching sequence is generated. Fig. 5 shows the power converter voltage vectors in a stationary αβ frame. By selecting the voltage vectors appropriately the flux trajectory and its speed can be controlled [10]. Hysteresis comparators can have different levels; usually the flux controller is a two-level comparator and the torque controller a three-level comparator [12].V3Fig. 5: Space vector diagram of inverter voltage vectors.Another advantage of the DTC is that it presents less dependency to the internal parameters of the machine in comparison with FOC strategy, [12]. In spite of its simplicity, DTC allows to obtain a good torque control in steady-state and transient operating conditions.On the other hand, DTC presents some drawbacks, such as the difficulty to control torque and flux at very low speeds, the variable switching frequency due to hysteresis controllers and current and torque ripples. However, for high-power applications with converter switching constraints, several improvements have been proposed in the literature: the use of sophisticated flux estimators to improve the low speed behaviour [13], improved switching tables with active null vector modulation strategies [14][15] or space vector modulation techniques [16] [17] that provide a constant switching frequency and reduce torque and flux ripples considerably.Simulation StudyOn the one hand, the steady-state and transient performances of both control strategies are going to be analyzed by numerical simulations. The steady-state performance can be compared evaluating the torque ripple and three-phase current waveform and harmonic spectrum. To compare the transient performance of both schemes, the response to a step variation of the torque command is analyzed, [12].On the other hand, both operation zones (constant-torque and constant-power zones) are going to be simulated to show both schemes functionality in the whole speed range. Fig. 6 and Fig. 7 show the steady-state and transient characteristics of FOC and DTC control schemes in constant-torque zone and in the Fig. 8 and Fig. 9 the constant-power zone is shown.f [Hz]I s H / I s F [%]e) Stator Phase Current Spectrumf [Hz]I s H / I s F [%]f) Stator Phase Current Spectrum 010203040506070t [ms]I S U [A ]c) Stator Phase Current010203040506070-200-1000100200t [ms]I S U [A ]d) Stator Phase Current 00.20.40.60.81300400500600700t [s]T E M [N m ]a) Electromagnetic Torque0.20.40.60.81300400500600700t [s]T E M [N m ]b) Electromagnetic TorqueFig. 6: Steady-state analysis at 600 rpm and 500 Nm. a) and b) Electromagnetic torque with FOC (a) and DTC (b ) control strategies. c)-f) Phase current temporal waveform and harmonic spectrum, with FOC (c-e) and DTC (d-f).Fig. 6 shows the torque and stator phase current waveforms at a constant speed of 600 rpm and a 500 Nm torque demand. Both strategies have an average switching frequency of 1 kHz.Regarding the torque, simulation results show that the DTC strategy presents a smaller ripple than the FOC strategy. Referring to the current waveform and its spectrum, in the FOC strategy harmonics are more centred on multiple frequencies of the switching frequency than in DTC in which current harmonics are more dispersed.The dynamics of both control strategies can be analyzed in Fig. 7 where the torque command varies in a step from 0 to 500 Nm at a speed of 800 rpm. In the torque and stator flux module responses can be seen that both control schemes present fast dynamics, but the DTC has a faster response with a settling time of about 2 ms and no significant overshoot. The torque dynamics of the corresponding FOC control is slower, with a settling time of about 5 ms and an overshoot of 10%. The torque step variation is also reflected in the flux waveform, because of the current rising.In Fig. 8 and Fig 9 the constant-power zone is illustrated by setting a 500 Nm torque demand and varying the speed from 1800 to 2250 rpm as it is represented in Fig 9.b and c. With the constant catenary voltage of Fig 9.a when the speed increases the stator voltage reaches to its maximum value and the flux is weakened (cf. equation ( 4 )). Therefore, the machine can no longer provide the required torque and as Fig. 8.a and b show the torque decreases with the increasing speed, keeping the power constant (see Fig 9.b and c).t [s]T E M [N m ]c) Electromagnetic Torquet [s]ψS M O D[W b ]a) Stator Flux modulus [Wb]t [s]T E M [N m ]d) Electromagnetic Torquet [s]ψS M O D[W b ]b) Stator Flux modulus [Wb]Fig. 7: Results of torque step variation (0 - 500 Nm) at 800 rpm in braking mode. a) and b) Stator flux response with FOC (a) and DTC (b) control strategies. c) and d) Electromagnetic torque response with FOC (c) and DTC (d ) control strategies.0100200300400500600t [s]T E M [N m ]a) Electromagnetic Torque0100200300400500600t [s]T E M [N m ]b) Electromagnetic TorqueFig. 8: Electromagnetic torque response to a speed variation (1800 – 2250 rpm) in constant-power zone with FOC (a) and DTC (b) control strategies.0255075100125150175P [k W ]t [s]b) Power and Rotor SpeedN [r p m]t [s]c) Power and Rotor SpeedP [k W]t [s]a) Catenary VoltageV [V ]Fig. 9: Results of a speed variation in constant-power zone. a) Catenary voltage. b) and c) Rotor speed variation and power with FOC (b) and DTC (c) control strategies.Experimental ResultsTo support the numerical simulations some experimental tests have been done using a prototype composed of a traction inverter (developed by IKERLAN-IK4 and TRAINELEC S.L) and a 100 kWcommercial PMSM (see Fig. 10).Fig. 10: Traction inverter and PMSM test bench: 4 pair of poles, maximum power of 100 kW, maximum torque of 500 Nm and maximum speed of 2300 rpm.Fig. 11 illustrates the steady-state performances of both control schemes at a constant speed of 600 rpm and constant torque of 500 Nm. Regarding the torque waveform, both strategies present a similar ripple. On the contrary, the phase current waveform and frequency spectrum show that both control schemes have different characteristics.As shown by numerical simulations in Fig. 6, the FOC strategy presents a current spectrum in which the harmonics are concentred at even multiples of the switching frequency, which cause a high-pitched acoustic noise. In contrast, the DTC current spectrum is dispersed causing a more irregular and low noise level, but presents more harmonic content at low frequencies.f [Hz]I s H / I s F [%]e) Stator Phase Current Spectrumf [Hz]I s H / I s F [%]f) Stator Phase Current Spectrum 010203040506070t [ms]I S U [A ]c) Stator Phase Current010203040506070-200-1000100200t [ms]I S U [A ]d) Stator Phase Current 00.20.40.60.81300400500600700t [s]T E M [N m ]a) Electromagnetic Torque 00.20.40.60.81300400500600700t [s]T E M [N m ]b) Electromagnetic TorqueFig. 11: Steady-state analysis at 600 rpm and 500 Nm. a) and b) Electromagnetic torque with FOC (a) and DTC (b ). c)-f) Phase current waveform and harmonic spectrum, with FOC (c-e) and DTC (d-f).In Fig. 12 flux and torque responses to a torque step variation of 500 Nm at 800 rpm are shown. We can see that experimental responses correspond to numerical simulation results of Fig. 7. Both strategies are designed to provide fast dynamics, but the DTC control presents a more direct response while the FOC control presents a longer torque and flux transient (see Fig. 12.e and f).0.170.180.190.20.210200400600t [s]T E M [N m ]e) Electromagnetic Torque0.170.180.190.20.21200400600t [s]T E M [N m ]f) Electromagnetic Torque0.511.5200400600t [s]T E M [N m ]c) Electromagnetic Torque0.511.50.40.450.50.550.60.650.7t [s]ψS M O D[W b ]a) Stator Flux modulus [Wb]00.511.50.40.450.50.550.60.650.7t [s]ψS M O D[W b ]b) Stator Flux modulus [Wb]00.511.5200400600t [s]T E M [N m ]d) Electromagnetic TorqueFig. 12: Results of torque step variation (0 - 500 Nm) at 800 rpm in braking mode. a) and b) Stator flux response with FOC (a) and DTC (b) control strategies. c) - f) Electromagnetic torque response with FOC (c and e) and DTC (d and f) control strategies.ComparisonTable I sums up the performances of both control strategies and includes the control complexity, meaning the need of switching between different modes to operate in the whole speed range and the ease of setting up the control parameters.Table I: Control characteristicsDynamic responseWaveform quality Complexity Control Setting upDTC Very Good More harmonic content at lower frequencies MediumNon linearcontrollers FOC Good More harmonic content athigher frequenciesMedium Linear controllersBoth control schemes show good dynamic responses, but DTC scheme, as it is a direct control presents faster responses. Regarding the waveform quality, the FOC control depends on the switching frequency. Therefore, choosing properly the switching frequency the signals quality may be better in FOC strategies than in DTC strategies because the DTC presents more harmonic content at low frequencies. In terms of control complexity, both strategies need to combine different control modes, and their complexity is considered to be similar. Both control algorithms are implemented in the same DSP and the computational time that they require is similar. To set up the DTC control, the parameters of hysteresis and non-linear controllers must be chosen, whereas the FOC control has PI linear controllers whose coefficients can be tuned depending on system parameters, settling time, maximum overshoot, etc.ConclusionIn this paper two different control strategies have been compared in order to determinate the main advantage and drawbacks of each control and be able to select the most suitable control for each railway traction application. Numerical simulations have been supported with experimental results which show that both strategies provide the required performance for a traction application.The DTC strategy might be chosen if the dynamic requirements are very restrictive or a simpler modulation technique needs to be implemented whereas the FOC scheme might be a better option when high waveform quality is demanded or an easier control setting up is preferred. References[1] R. H. Staunton, S. C. Nelson, P. J. Otaduy, J. M. McKeever, J. M. 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