1 / 22 Lecture 8: Sensorless Synchronous Motor Drives ELEC-E8402 Control of Electric Drives and Power Converters (5 ECTS) Marko Hinkkanen Spring 2017
2 / 22 Learning Outcomes After this lecture and exercises you will be able to: Explain the voltage-model estimator Explain the basic principles of high-frequency signal-injection methods
3 / 22 Rotor-Position Estimation Methods Fundamental-excitation-based methods Voltage model, reduced-order observer, or full-order observer Rely on the mathematical model of the motor Sensitive to parameter errors at low speeds Signal-injection methods Pulsating excitation signal in estimated rotor coordinates (or rotating excitation signal in stator coordinates) Rely on magnetic anisotropy, Ld L q is necessary Dynamic performance may be poor Cause additional losses and noise Combined methods A PM-SyRM will be used as an example motor in this lecture, but methods are quite similar for other AC motors as well.
4 / 22 Outline Fundamental-Excitation-Based Methods Signal-Injection Method Combined Method
Typical Sensorless Control System Fast current-control loop Position observer is often implemented in estimated rotor coordinates Dead-time effect and power-device voltage drops are compensated for in the PWM Torque and speed controllers are similar to those in sensored drives i s,ref ˆω m ˆϑ m Current controller Position observer u s,ref i s dq abc dq abc PWM U dc i a, i b, i c M The inverter nonlinearities can be approximately compensated for as u a,ref = u a,ref + u sign(ia), where u a,ref is the compensated voltage reference and u is the compensation magnitude (typically a few volts). The compensation is used for the b- and c-phases as well. 5 / 22
6 / 22 Voltage Model in Stator Coordinates Stator flux estimator Flux estimate dˆψ s s = u s s dt ˆR s i s s ˆψ s s = (u s s ˆR s i s s)dt ˆψ s s = ˆψ α + j ˆψ β = ˆψ s e j ˆϑ Flux angle estimate ( ) ˆϑ = arctan ˆψ β / ˆψ α Rotor speed in steady state ˆω m = d ˆϑ dt How to obtain the rotor angle ˆϑ m?
7 / 22 Properties of the Voltage Model Estimation-error dynamics are marginally stable (pure integration) Flux estimate will drift away from the origin due to any offsets in measurements Very sensitive to ˆR s and inverter nonlinearities at low speeds Good accuracy at higher speeds despite the parameter errors (but pure integration has been remedied) Can be improved with suitable feedback observer Can be implemented in estimated rotor coordinates
8 / 22 Real-Time Simulation of Motor Equations State estimator in estimated rotor coordinates dˆψ s dt = u s ˆR s î s jˆω m ˆψ s Stator current components î d = ( ˆψ d ˆψ f )/ˆL d î q = ˆψ q /ˆL q Current vector Rotor position estimator d ˆϑ m dt = ˆω m How to obtain the speed estimate? Could we improve this open-loop flux estimator? î s = îd + jîq
9 / 22 Speed-Adaptive Observer Adjustable model dˆψ s dt = u s ˆR s î s jˆω m ˆψs + k 1 (i d îd) + k 2 (i q îq) Stator current components î d = ( ˆψ d ˆψ f )/ˆL d Angle estimator d ˆϑ m dt Speed-adaptation law = ˆω m ˆω m = k p (i q îq) + k i (i q îq)dt î q = ˆψ q /ˆL q Stator current vector î s = îd + jîq drives îq i q to zero Also the d-component could be used in speed adaptation
10 / 22 Outline Fundamental-Excitation-Based Methods Signal-Injection Method Combined Method
11 / 22 Currents in the d and q Directions i s i s i s = i d + j0 ψ s = L d i d + ψ f i s = 0 + ji q ψ s = jl q i q + ψ f
12 / 22 Position Estimation Error Actual rotor coordinates are marked with the superscript r Controller operates in estimated rotor coordinates (no superscript) Some estimation error exists ϑ m = ϑ m ˆϑ m This leads to control errors q (estimated) q r (actual) d (estimated) ϑ m d r (actual) i r s = i s e j ϑ m ψ r s = ψ s e j ϑ m
13 / 22 Signal Injection: Alternating Excitation Signal Subscript i refers to injected high-frequency components Excitation voltage u di = u i cos(ω i t) is injected in the d-axis u s,ref = u s,ref + u di Typical excitation frequencies ω i /(2π) = 500... 1 000 Hz Injected flux-linkage components in estimated rotor coordinates ψ di = u i ω i sin(ω i t) ψ qi = 0 where R s = 0 and ω m = 0 is assumed Injected flux components in actual rotor coordinates ψ r di = u i ω i sin(ω i t) cos ϑ m ψ r qi = u i ω i sin(ω i t) sin ϑ m
14 / 22 Resulting current components in actual rotor coordinates i r di = ψr di /L d i r qi = ψr qi /L q Component in the estimated q-direction i qi = i r di sin ϑ m + i r qi cos ϑ m = u i 2ω i L q L d L d L q sin(2 ϑ m ) sin(ω i t) i qi is an amplitude modulation of the carrier signal by the envelope sin(2 ϑ m ) Demodulation i qi sin(ω i t) = u i L q L d sin(2 ϑ m )[1 sin(2ω i t)] 4ω i L d L q Low-pass filtering ɛ = LPF { i qi sin(ω i t) } = u i 4ω i L q L d L d L q sin(2 ϑ m ) Error signal ɛ is roughly proportional to the position estimation error
15 / 22 Outline Fundamental-Excitation-Based Methods Signal-Injection Method Combined Method
16 / 22 Sensorless Control System With Signal Injection u di U dc Excitation voltage u di is nonzero only at low speeds i s,ref Current controller u s,ref dq abc PWM Speed-adaptive observer is augmented to exploit information from signal injection ˆω m ˆϑ m Adaptive observer ɛ i s dq abc Error signal i a, i b, i c M
17 / 22 Speed-Adaptive Observer Augmented With Signal Injection Error signal calculation Adaptive observer (augmented with error signal) Delay and cross-saturation compensations are omitted in the figure for simplicity i s u s Adjustable model î s ĩ s ĩ d ĩ q ˆω m ˆϑm i s i d i q LPF ɛ ɛ ω ɛ sin(ω i t)
18 / 22 Experimental Results: 6.7-kW SyRM SyRM drive is operated in the torque-control mode Torque reference is reversed Speed reference of the load machine is kept at 0
19 / 22 SyRM drive is operated in the speed-control mode Speed reference is kept at 0 Load-torque steps: 0 T N T N T N 0
20 / 22 Sensorless Control: Problems and Properties Sources of errors in the position estimation Parameter errors: ˆRs is important at low speeds Accuracy of the stator voltage (inverter nonlinearities) Sustained operation at zero stator frequency is not possible (under the load torque) unless signal injection is applied Most demanding applications still need a speed or position sensor
21 / 22 Other Control Challenges High saliency ratio and low PM flux High stator frequency, which increases sensitivity to Time delays Discretization Parameter variations Magnetic saturation Effect of temperature variations on the stator resistance and PM flux Skin effect (in form-wounded stator windings) Identification of the motor parameters Self-commissioning during the drive start-up Finite-element analysis?
22 / 22 Further Reading F. Blaabjerg et al., Improved modulation techniques for PWM-VSI drives, IEEE Trans. Ind. Electron., vol. 44, 1997. M. Corley and R.D. Lorenz, Rotor position and velocity estimation for a salient-pole permanent magnet synchronous machine at standstill and high speeds, IEEE Trans. Ind. Applicat., vol. 43, 1998. M. Hinkkanen et al. A combined position and stator-resistance observer for salient PMSM drives: design and stability analysis, IEEE Trans. Pow. Electron., vol. 27, 2012. T. Tuovinen and M. Hinkkanen, Adaptive full-order observer with high-frequency signal injection for synchronous reluctance motor drives, IEEE J. Emerg. Sel. Topics Power Electron., vol. 2, 2014.