Analytical modelling and parametric sensitivity analysis for the PMSM steady‐state performance prediction

Abstract

Inaccuracy in the permanent magnet synchronous motor (PMSM) steady-state performance calculation corresponds to the parameter error and model imprecision. Accurate determination of the PMSM parameters may encounter various complications because of its rotor structure and drive design. Therefore PMSM performance calculation is generally vulnerable to inaccuracy because of the parameter error. This article studies the effect of parameter error on the inaccuracy of the performance calculations. Several methods for determining the PMSM armature resistance, flux linkage constant and d-and q-axis inductances with varying level of accuracy are proposed. The presented methods are applied to a laboratory PMSM and the sensitivity of the PMSM output power to the equivalent circuit parameters is analysed based on the experimental results. In addition, this study contributes to accurate performance estimations of the PMSM by developing a precise model that incorporates the saturation saliency and core losses. The accuracy of the proposed model is compared with the conventional dq-axis model and its higher accuracy is validated through experimental results. NomenclatureR a , L l armature resistance and leakage inductance N, p number of turns per phase and number of pole pairs L s armature stack effective length h M height of the permanent magnets g, g q air-gap length in d-and q-axis τ pole pitch a number of parallel paths σ electric conductivity s a conductor cross-sectional area λ f , E f flux linkage constant and excitation voltage k w stator winding coefficient B r remnant magnet flux density μ rrec relative recoil permeability μ 0 magnetic permeability of free space L d , L q d-and q-axis synchronous inductances λ ls per-slot leakage permeance s number of stator slots V DC-150% DC voltage corresponding to 150% of the rated current V DC-100% DC voltage corresponding to rated current I DC-150% DC current corresponding to 150% of the rated current I DC-100% DC current corresponding to rated current i(t), v(t) armature instantaneous current and voltage t time I DC PMSM steady-state DC current R CKT circuit resistance in the DC standstill test τ d , τ q time constants for d-and q-axis inductance measurements I a , V aphase 'a' current and voltage L aa phase 'a' self-inductance M ac mutual inductance between 'a' and 'c' phases ω s , ω r angular frequency of rotor and stator V t , I t stator terminal voltage and current a 0 , a 1 coefficients of L aa fitted curve b 0 , b 1 coefficients of M ac fitted curve θ, δ phase and torque angle S g r sensitivity of γ to ρ γ ex , γ cal experimental and calculated performance factor ρ act , ρ det actual value and determined value of the parameter E id , E iq d-and q-axis internal voltage R c , R ce , R ch core, eddy-current and hysteresis loss resistances L md , L mq d-and q-axis magnetising inductances I d , I q d-and q-axis currents V d , V q d-and q-axis voltages L md , L mq d-and q-axis inductances including the core loss

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