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An Efficient Braking Algorithm for Interior Permanent Magnet Synchronous Motors

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An Efficient Braking Algorithm for Interior Permanent Magnet Synchronous Motors 13th INTERNATIONAL SYMPOSIUM on POWER ELECTRONICS - Ee 2005 XIII Međunarodni simpozijum Energetska elektronika – Ee 2005 NOVI SAD, SERBIA & MONTENEGRO, November 2nd - 4th, 2005 AN EFFICIENT BRAKING ALGORITHM FOR INTERIOR PERMANENT MAGNET SYNCHRONOUS MOTORS Vladan R. Jevremović, Borislav Jeftenić* SR Drives Ltd – Emerson Motor Technologies, Harrogate, United Kingdom Faculty of Electrical Engineering, University of Belgrade, Serbia & Montenegro* Abstract: This paper presents an efficient braking permanent magnet and reluctance torque has been algorithm for a permanent magnet synchronous motor proposed. drives with a diode front end rectifier. Regenerative braking energy is dissipated in stator windings which act 2. EFFICIENT BRAKING CRITERIA as a braking resistor, without adding any additional Braking methods within electrical motor drives can braking choppers and electronic control circuits. be classified into three main groups – inertial, soft and Application of this braking algorithm results in maximum active braking. power losses in stator windings and relatively high a) Inertial, passive braking (coast down) is achieved braking torque, all within inverter current and voltage simply by turning off the inverter. The whole braking capabilities. Also, this algorithm determines braking process relies on rotor inertia, mechanical load, viscous dynamics by regulating voltage on a DC link capacitor and ventilating friction. This braking method has no well bellow critical limit. practical value when being used at high motor speeds, Key Words: Braking/Permanent Magnet Synchronous Motor due to very long stopping time. Also, this way of braking is recommended for low speeds only. In case of high 1. INTRODUCTION speeds, where field weakening algorithm is used (with Permanent magnet synchronous motor drives can notoriously high direct axis currents), electromotive operate in all four quadrants of torque-speed force can be relatively high (several kV). In case of high characteristics. Beside the work in motoring and current trip situation, it is required from stator windings generating mode, braking mode is particularly interesting to be shorted, in order to protect stator stack. This on the for speed regulated drives. Nowadays large number of other hand, interrupts braking process and makes it less commercially available electric drives come with diode efficient. front end rectifiers (due to their low price), which have b) Soft braking (ramp down) represents a controlled irreversible nature; hence it is not possible to drive deceleration of motor. With this type of braking, speed recuperative energy back to the mains. Instead, this control loop normally follows linearly falling reference energy largely contributes to the raise of voltage on a DC signal (speed ramp) and generates limited braking link capacitor. A common way of solving this problem is torque. Gradient of speed ramp is most commonly to add switching and passive element (braking transistor limited by raise of DC link capacitor voltage due to and resistor) in parallel with DC link capacitor, though appearance of recuperative braking energy. The value of creating a braking chopper. Chopper maintains voltage stator current in the case of soft braking is not on a DC link capacitor and dissipates regenerated necessarily the highest possible and therefore it is not braking energy. However, this device also increases possible to dissipate complete braking energy, nor give drive complexity and price and decreases reliability; maximum braking torque. This braking method gives therefore it is worthy considering different methods for good results for mid and low speed ranges, but still it is braking, which employ main motor operating features not the most efficient method. instead of using additional electronics. Holtz [1] c) Active braking provides maximum braking torque, presented and efficient braking scheme for induction by having maximum dissipated power (losses) in motor motor drive with diode front end rectifier. Paper [2] deals stator windings. To achieve maximum losses in stator with efficient braking methods for surface permanent copper, stator current has to be highest possible, which is magnet synchronous motors. In this paper, in order to normally constrained by inverter capabilities. This is the maximize braking torque without adding any braking most efficient and the fastest braking method which resistors, a braking algorithm suitable for interior results with the shortest stopping time. permanent magnet synchronous motors that employ both 1 In order to get optimal torque during active braking This curve, when represented in d-q plane has form of an sequence, it is pertinent to define three criteria that have ellipse with the centre in (0, -pψmωr/2Rs). To maximize to be met: braking power, q-axis current must be maximized, whilst 1) DC link capacitor voltage has to be limited to a at the same time, both d and q-axis current must meet maximum allowable value that prevents capacitor inverter current and voltage boundaries (second destruction (dielectric breakthrough). criterion). The d-axis and q-axis voltages vsd and vsq are 2) Maximization of stator current within voltage and limited by the maximum available output voltage of the current inverter limits has to result in quickest dissipation inverter Vsmax. Since maximum available inverter voltage of generated energy. is a function of instantaneous DC bus voltage and 3) Braking torque has to be maximized in order to assuming that inverter can operate also in reduce motor braking (stopping) time. overmodulation, voltage limit imposed through stator currents isd and isq can be formulated as (limiting curve is 3. ACTIVE BRAKING WITHIN VECTOR an ellipse in d-q plane with the centre in (-ψm/Lsd, 0)): CONTROLLED IPMSM DRIVE 2 2 2 Lsd ψ m 2 Vs max In case of vector controlled interior permanent + + ≤ (6) isd isq magnet synchronous motor (IPMSM) drive, definition of Lsq Lsd pω r Lsq active braking scheme is effectively a definition of In order to avoid overmodulation region, a common reference current trajectories in d-q reference frame. practice is to adopt that maximum available output Starting point for definition of these trajectories is a voltage equals fundamental voltage harmonic (which is mathematical model of interior permanent magnet 2V /π for wye and 3V /π for delta connected stator). synchronous motor in d-q synchronously rotating dc dc Current limit of inverter in d-q reference frame can be reference frame [3]: defined as: vsd Rs + sLsd − ωe Lsq isd 0 = + (1) 2 + 2 ≤ (7) + isd isq I s max vsq ω e Lsd Rs sLsq isq ω eψ m where Ismax is a peak inverter current, and the whole = 3 + − limiting curve represents a circle in d-q plane. Te pisq ψ m Lsd Lsq isd (2) 2 [ ( ) ] During braking from high speed, power limit and voltage where vsd and vsq are d and q-axis stator voltages, isd and limits (5) and (6) are applied simultaneously on reference isq are d and q-axis stator currents, Rs is stator phase values of isd and isq currents. The voltage boundary resistance, Lsd and Lsq are d and q-axis stator angular speed for which current under the voltage limit synchronous inductances, ψm is flux linkage of rotor reaches that of the current limit (7), is given by permanent magnets, ωr is rotor mechanical speed, p is = Vs max number of rotor pole pairs, = p is rotor electrical ω rv (8) ωe ωr p(L I + ) speed and Te is electromagnetic torque. sd sw max ψ m Power generated during braking can be defined with Bellow speed ωrv, reference stator currents are governed following expression by power and current limits (5) and (7). The trajectory of 3 stator current space vector during optimized active = ≈ (3) Pg Teω r pψ misqω r braking is shown in Fig. 1. 2 q Reluctance component of electromagnetic torque can be I neglected in this case, assuming that ZDAC (Zero D-Axis swmax Current) control strategy is being used. Also, in the case current limit of IPMSM motors, inductance Lsq is generally greater than Lsd resulting in negative reluctance torque for positive values of isd current. Due to very high value of voltage limit braking currents, stator core (iron) losses are negligible Iswmax in comparison with stator copper losses (PFe ≈ 0). The copper losses in stator windings can be expressed as -ψm / Lsd 0 d 3 2 2 P = R i + i (4) P1(ωrv) power limit Cu 2 s ( sd sq ) DC link capacitor voltage is highly dependant on the difference between generated and dissipated power in stator windings, and by simultaneous regulation of both P ( ) powers it is possible to meet first criterion (limitation of 2 ωri DC link capacitor voltage). Available d and q-axis currents have to meet a power limit condition, which Fig. 1 Trajectory of stator current space vector during dictates that dissipated power (4) has to be greater or braking ≥ equal than regenerated (braking) power (3) (PCu Pg): 2 2 During operation in area limited by power and current, p p stator current vector is shifted towards q-axis, finally 2 + + ψ mω r ≥ ψ mω r isd isq (5) having zero direct component and maximum negative 2Rs 2Rs quadrature component currents (isd = 0, isq = -Iswmax) at maximum voltage on a DC link capacitor is 500V. rotor angular speed IPMSM drive operates at 20 kHz switching frequency, using SVPWM symmetrical switching pattern. Current = Rs ω ri I sw max (9) regulation loop works at 10 kHz and speed regulation pψ m loop works at 500Hz. Also, PI current loop bandwidth is Bellow speed ωri, regenerated power is lower than tuned at 500Hz and PI speed loop bandwidth is tuned at maximum dissipated power in stator windings. Reference 20Hz. To improve current regulation dynamics, both current trajectories for d and q-axis currents can be magnetic decoupling and electromotive force feed derived as functions of rotor angular speed ωr with forward compensations have been included in current different equations for different speed regions (defined regulation scheme.
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