Three-phase Permanent Magnet Synchronous Machine Research Articles

A Position Error Correction Method for Sensorless Control of Dual Three-Phase Permanent Magnet Synchronous Machines

In this article, an online rotor position error correction method is proposed to eliminate the impact of parameter mismatch in sensorless control for dual three-phase (DTP) permanent magnet synchronous machines drives. The rotor position error production mechanism is first derived and shows that the error changes with the trend of current variation when there is a parameter mismatch. Based on this mechanism, by injecting sinusoidal current signals with low frequency and small amplitude into both sets of three-phase windings, the presence of parameter mismatch and its level can be revealed from the corresponding sinusoidal responses of the estimated speed of sensorless observers, which do not depend on the inertia of the machine. Since the amplitudes of these responses decrease as the parameter mismatch level reduces, with the help of the least mean square algorithm, the parameters can be adaptively adjusted to the actual values, and the position error can be thus corrected. Moreover, with the extra freedom of DTP machines, the detrimental effects on torque production due to current signal injections can be eliminated through adjusting the phase between the two injected signals. The effectiveness of the proposed method has been validated through simulation and experimental results.

Space-Vector-Optimized Predictive Control for Dual Three-Phase PMSM With Quick Current Response

This article proposes a scheme of space vector optimization for model predictive control (MPC) of dual three-phase permanent magnet synchronous machine (DTP-PMSM), which aims to restrain the current harmonics under the condition of low inductance. The multiphase electric motor possesses the characteristics of quick current variation rate by means of the low inductance. Especially incorporating with MPC schemes, its advantage of quick response shows promising prospects for various applications such as robotics, aerospace and medical devices. However, such a characteristic of low inductance requires shorter control period, which means that the traditional MPC cannot be implemented to suppress the current harmonics since the performance of the power switching devices and the digital controller limits the arbitrary increasing of the control frequency, which has nearly unexplored in previous studies. In order to address such an issue, this article presents the space-vector-optimized model predictive control (SVO-MPC) for the DTP-PMSMs with low inductance by presynthesizing space vectors to eliminate harmonics in the harmonic frame and optimizing the zero vector to deal with quick current response. As a result, the proposed SVO-MPC can remarkably improve the steady and dynamic control performance, while the traditional MPC almost fails at commonly-adopted control frequency. Finally, simulated and experimental results are both given to verify the feasibility of the proposed SVO-MPC for DTP-PMSMs with quick current response.

Mitigation of Interturn Short-Circuits in IPMSM by Using MTPCC Control Adaptive to Fault Severity

Incipient interturn short-circuits (ITSCs) in permanent-magnet synchronous machines (PMSMs) develop to direct short-circuit without proper mitigation. This article proposes an ITSC mitigation control for standard three-phase interior PMSMs (IPMSMs) driven by typical three-phase inverters, named as maximum torque per circulating current (MTPCC), to constrain the circulating current (CC) due to ITSC within acceptable limits so as to delay the insulation degradation between shorted turns, and to maximize output torque to support the postfault performance. In the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> current plane, it is shown that for a specific fault severity and machine speed, the operating points with the same CC form a circle, and for constant torque with ITSC is a hyperbola. ITSC is a fast-developing fault that implies the fault severity continues to increase with time, and the positions of the CC circle and torque hyperbola change with the increasing fault severity in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> current plane. The MTPCC control updates the mitigation operating point automatically, depending on the positions of the CC circle and torque hyperbola with respect to the circle of the machine's maximum current, to produce the maximum possible torque as the fault severity changes, which shows that it is adaptive to the variation of fault severity. The proposed mitigation control is validated through experiments.

Novel Machine Parameter Estimation Scheme Toward Accurate Maximum Torque Production for Dual Three-Phase PMSMs

This article proposes a hybrid signal injection-based maximum torque per ampere (MTPA) control for dual three-phase permanent magnet synchronous machines (PMSMs). The proposed method consists of a real dc current injection in the harmonic subspace and a virtual ac current injection in the fundamental subspace. The real dc current injection in the harmonic subspace does not impact the average torque production, and induced losses are small enough to be neglected. In the meantime, to guarantee the accuracy of the proposed MTPA method, a novel machine parameter estimation scheme considering voltage source inverter nonlinearity effects is proposed in this article, which can track the variation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q_{1}$ </tex-math></inline-formula> -axis inductance and resistance accurately. Therefore, the proposed method only requires command voltages and currents in the torque model, and the variations of machine parameters are compensated by the proposed parameter estimation scheme. As the command voltages have correspondence with the variations of machine parameters, the magnetic saturation and temperature effects have been taken into account. The proposed method is validated by simulations and experimental results under various torque, speed, and temperature conditions. Additionally, the accuracy of the proposed method is validated, and its performance is proven to be superior through comparison of the derived results with those obtained from various existing methods.

Multi-Virtual-Vector Model Predictive Current Control for Dual Three-Phase PMSM

This paper proposes a multi-virtual-vector model predictive control (MPC) for a dual three-phase permanent magnet synchronous machine (DTP-PMSM), which aims to regulate the currents in both fundamental and harmonic subspace. Apart from the fundamental α-β subspace, the harmonic subspace termed x-y is decoupled in multiphase PMSM according to vector space decomposition (VSD). Hence, the regulation of x-y currents is of paramount importance to improve control performance. In order to take into account both fundamental and harmonic subspaces, this paper presents a multi-virtual-vector model predictive control (MVV-MPC) scheme to significantly improve the steady performance without affecting the dynamic response. In this way, virtual vectors are pre-synthesized to eliminate the components in the x-y subspace and then a vector with adjustable phase and amplitude is composed of two effective virtual vectors and a zero vector. As a result, an enhanced current tracking ability is acquired due to the expanded output range of the voltage vector. Lastly, both simulation and experimental results are given to confirm the feasibility of the proposed MVV-MPC for DTP-PMSM.

Enhancement of Disturbance Rejection Capability in Dual Three-Phase PMSM System by Using Virtual Impedance

Dual three-phase permanent magnet synchronous machine systems usually suffer from small impedance to voltage disturbance such as inverter voltage errors and back EMF harmonics. This article proposes a virtual impedance technique to increase the machine equivalent impedance and, thus, enhance the disturbance rejection capability of the system. This enhancement can contribute to current harmonic suppression in a wide range of frequencies. In addition, the introduction of virtual impedance can also reduce the system sensitivity to parameter variation, which helps to suppress the dynamic current overshoot, pulsating, and cross-coupling effect caused by the parameter mismatch. Simulation and experimental results have verified the effectiveness of the proposed control strategy.

Current Injection-Based Simultaneous Stator Winding and PM Temperature Estimation for Dual Three-Phase PMSMs

This article proposes a current injection-based simultaneous stator winding and permanent magnet (PM) temperature tracking technique for dual three-phase permanent magnet synchronous machines (PMSMs). The estimation models involving winding and PM temperatures are derived for different control strategies with the cancelation of inductances. To improve the tracking performance, a Kalman filter is used for simultaneous winding and PM temperature estimation. Compared with the existing methods, the proposed simultaneous winding and PM temperature estimation technique is independent of the voltage-source nonlinearity effect and is applicable to various machine operating conditions. The main features of the proposed method are underscored by the cancelation of inductance and the elimination of the need for a lookup table. The test results on a laboratory dual three-phase PMSM are used to validate the proposed method under different speed and torque conditions.

Harmonic Current Suppression of Dual Three-Phase PMSM Based on Model Predictive Direct Torque Control

The traditional direct torque control (DTC) method will produce a larger harmonic current in the x, y subspace when applied to a dual three-phase permanent magnet synchronous machine (DTP-PMSM) because the voltage vector used for DTC is not equal to zero in the x, y harmonic subspace. To mitigate this problem, in this manuscript, a model predictive direct torque control (MPDTC) method is proposed to eliminate the harmonic current in DTP-PMSM. The spatial distribution characteristic DTP-PMSM voltage vector is analyzed; then, the table of vector group can be obtained according to DTC, and each vector group can be combined to obtain the zero-voltage vector in the x, y subspace. According to the cost function, MPDTC selects the vector group and obtains the optimal vector sequence combination to eliminate the harmonic current in the x, y subspace. Furthermore, the MPDTC achieves closed-loop control of harmonic currents in the x, y subspace. The MPDTC can also eliminate harmonic currents caused by other factors. The simulation results show that the method of MPDTC can effectively suppress the harmonic current of DTP-PMSM.

A Generalized Decomposition Model of Dual Three-Phase Permanent Magnet Synchronous Machines Considering Asymmetric Impedances and Compensation Capability

This article first proposes a generalized decomposition model for dual three-phase (3-ph) permanent magnet synchronous machines (PMSMs) with 0°, 30°, and 60° angle displacements between two sets of windings, allowing machines controlled in two-dimensional orthogonal αβ and xy subspaces. This model can decouple mutual inductances coupling phases from two sets, respectively. However, there often exist asymmetric impedances, due to inherent asymmetric machine parameters, cables with unequal lengths, manufacture tolerances, etc., in dual 3-ph PMSMs inevitably causing unbalanced phase currents and deteriorating the decoupling performance of the generalized machine model. Therefore, the generalized decomposition model incorporating asymmetric impedances is further developed, in which additional terms incurred by asymmetric impedances lead to the cross-coupling of αβ subspace and xy subspace. Through this model, the compensation capability of asymmetries is derived at a given dc link voltage. Then, a compensation strategy is illustrated to suppress unbalanced phase currents together with current harmonics caused by nonlinearities. Finally, experimental results testify the current balancing performance and simulation results further validate the machine model and the compensation capability.

Modelling and vector control of dual three‐phase PMSM with one‐phase open

This study proposes a generic mathematical modelling and decoupling fault-tolerant vector control for dual three-phase permanent magnet synchronous machine (PMSM) with one phase open based on the conventional dual three-phase voltage source inverters, accounting for the mutual coupling between two sets of three-phase windings and the second harmonic inductance. When the dual three-phase PMSM has one phase open, the permanent flux-linkages are asymmetric and there are second harmonic components in the conventional synchronous reference frame (dq-frame). Based on the proposed mathematical modelling, both permanent magnet flux-linkages and currents become DC values in the dq-frame, and therefore, the conventional proportional integral (PI) controller can be used to regulate the dq-axis currents. Then, a decoupling fault-tolerant vector control with/without a dedicated feed-forward compensation is proposed to validate the correctness of the proposed mathematical modelling. Experimental results on a prototype dual three-phase PMSM with one phase open show that the second harmonic dq-axis currents can be well suppressed simply by the conventional PI controller and dedicated feed-forward compensation. It also shows that the decoupling fault-tolerant control based on the proposed modelling and control method has excellent dynamic performance, which is equivalent to the vector space decomposition control for the healthy machine.

Switching-Table-Based Direct Torque Control of Dual Three-Phase PMSMs With Closed-Loop Current Harmonics Compensation

In this article, the new closed-loop current harmonics compensation strategy is introduced in the switching-table-based direct torque control (ST-DTC) of dual three-phase permanent magnet synchronous machines. The harmonic current distortion is the major problem of ST-DTC of multiphase machines and is typically caused by the lack of control in the auxiliary x-y subspace under the vector space decomposition model. The synthetic vectors to obtain average zero voltage in the x-y subspace can be a solution. However, this cannot compensate for current harmonics; for example, due to dead-time and back-electromotive force distortion, which is also mapped into the x-y subspace. Therefore, in this article, the x-y voltage references are obtained by the closed control loop that controls x-y currents to zero. To modulate the nonzero x-y voltage reference, the new modulation approach employing voltage vector groups in the x-y subspace together with the new switching table is developed and incorporated into ST-DTC. Meanwhile, the analysis of the two available sets of 12 voltage vector groups illustrates a tradeoff between linear range in the x-y subspace and the dc-link voltage utilization rate. Finally, the effectiveness of the proposed ST-DTC strategy is verified through experiments and simulation.

Compensation of Selective Current Harmonics for Switching-Table-Based Direct Torque Control of Dual Three-Phase PMSM Drives

Current harmonics are ubiquitous in dual three phase (DTP) permanent magnet synchronous machine (PMSM) drives. Due to back electromotive force (EMF) distortion, significant current harmonics are generated in the DTP-PMSM system. The influence of back EMF harmonics is investigated in this paper and a novel switching-table-based direct torque control method to compensate the selected current harmonics caused by the back EMF harmonics is proposed. It shows that by employing different optimal action time durations for voltage vectors in the z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> subspace and setting the synthetic voltage vectors to non-zero, the stator flux harmonics caused by the back EMF harmonics can be selectively compensated, as verified by experiments.

An Enhanced SVPWM Strategy Based on Vector Space Decomposition for Dual Three-Phase Machines Fed by Two DC-Source VSIs

This article presents an enhanced space vector pulse width modulation (SVPWM) strategy based on vector space decomposition (VSD) for the dual three-phase machines fed by two dc-source voltage source inverters (VSIs). Compared with existing methods that only account for balanced dc-link voltages, the proposed method considers unbalanced dc-link voltages in both the α-β and z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> planes. Two categories of medium voltage vectors are first defined in this article. An enhanced 12-sector SVPWM strategy that toggles two categories of medium voltage vectors in each fixed 30° sector is proposed. Moreover, the performance of the proposed method, including the modulation depth, the range of the dc-link voltage ratio, and the toggling point of the medium vector is analyzed. The proposed method can reduce the computational burden of the complicated sector classifications and it easily chooses suitable vectors to track the reference voltage with changes in the dc-link voltage ratio. The experimental results of the proposed SVPWM techniques are verified in a dual three-phase permanent magnet synchronous machine (PMSM) fed by two dc-source VSIs.

Model Predictive Torque Control for Dual Three-Phase PMSMs with Simplified Deadbeat Solution and Discrete Space-Vector Modulation

Unprecise voltage vectors applied in conventional model predictive control (MPC) would cause additional ripples in electromagnetic torque. To eliminate the problem, this article proposes an improved model predictive torque control (MPTC) based on deadbeat solution and discrete space-vector modulation (DSVM) for dual three-phase permanent magnet synchronous machines (PMSMs). First, deadbeat-direct torque and flux control (DB-DTFC) algorithm is applied and simplified, so that the computational burden can be reduced. Second, the virtual voltage vectors (VVVs) are adopted in dual three-phase voltage vector space to reduce voltage harmonics. Also, the DSVM is further proposed in this VVVs based vector space to generate more voltage vectors. After that, the simplified DB-DTFC and the DSVM scheme are artfully combined to select suitable voltage vector candidates for the MPTC, and the best one is then chosen to control the dual three-phase PMSMs. Finally, both simulation and experimental results are given to verify the effectiveness of the proposed method.

Modulation Strategies for Anisotropy-Based Position Estimation of PMSMs Using the Neutral Point Voltage

Information obtained about magnetic anisotropy via neutral point voltage measurements can be used to estimate the position of synchronous and induction machines at all speeds including standstill. Due to its usually high signal-to-noise ratio, this estimation method can be an attractive alternative to approaches that acquire anisotropy information via current measurements. The position estimation method looked at in this paper relies on anisotropy information in the form of position-dependent inductance ratios. These are obtained through measurement of the voltage between the machine's neutral point and an artificial neutral point during the application of different voltage vectors via a two-level switching inverter. We analyze the conditions placed on and the consequences of implementing necessary modifications to a standard space vector modulation. Five different modified modulation strategies are compared and investigated, including two newly proposed strategies which use only a minimal set of active and zero voltage vectors for measurement of the inductance ratios and therefore allow high utilization of available voltage and a high update rate of the estimated position. Experimental results for three low-power three-phase permanent magnet synchronous machines are presented which suggest that modulation strategies that use active measurement vectors in all three instead of only two axes of the machine are less susceptible to systematic deviations in the position estimation that presumably result from nonlinear machine properties. As part of the machine model, a normalizing inductance variation ratio is introduced, which simplifies expressions and supports the comparison of motors.

Collaborative Mid-Point Voltage Regulation in Low-Switching-Frequency MPC for Three-Level NPC Inverters Fed Dual Three-Phase PMSM Drives

In this paper, the control strategy is studied for the neutral-point-clamped three-level (NPC-3L) dual three-phase permanent-magnet synchronous machine (PMSM) drives at low-switching-frequency operation. The finite-control-set (FCS) model predictive control (MPC) scheme is investigated as the basic MPC scheme, where the average switching frequency is established as the cost function. With the high sampling frequency operation, the discretization with both forward and backward Euler methods is utilized so that the two sets of three-phase windings are controlled separately. To further decrease the switching frequency while maintaining the current and voltage control performance, a collaborative mid-point voltage regulation is proposed. The collaborative regulation strategy fully employs the additional control degree of freedom in the dual three-phase drives by setting the two NPC-3L inverters to select small vectors with opposite polarities. Therefore, the situation is avoided where the upper or the lower capacitor in the DC link provides load currents for the two sets of windings simultaneously. Simulation results of a 2.45MW dual three-phase drive and experimental results on a laboratory prototype have been presented to verify the validity of the proposed collaborative mid-point voltage regulation strategy.

Flux-Weakening Control of Dual Three-Phase PMSM Based on Vector Space Decomposition Control

This article proposes a flux-weakening (FW) control for dual three-phase permanent magnet synchronous machine (DTPMSM) based on vector space decomposition (VSD) control, where the output voltage in αβ subplane is employed for voltage feedback in the FW control loop. As the fundamental components are mapped to αβ subplane while the fifth and seventh harmonics are projected to harmonic z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> subplane, the FW current from this new control in αβ subplane is sixth harmonic-free regardless of the fifth and sixth harmonics being resulted from the nonsinusoidal back electromotive force (EMF) or inverter nonlinearity. The proposed control is compared with the conventional FW feedback control extended for DT-PMSM, where the FW control is applied to the two sets of three-phase windings separately. The experimental results show that the proposed FW control based on VSD is superior to the conventional FW control in terms of reduction in current unbalance and harmonic currents.

Dual Reference Frame Based Current Harmonic Minimization for Dual Three-Phase PMSM Considering Inverter Voltage Limit

This article proposes an optimized current harmonic minimization (CHM) approach for dual three-phase permanent magnet synchronous machines (PMSMs) with consideration of inverter voltage limit. The current harmonic model is derived to analyze the dominant current harmonic components in dual three-phase PMSM drives. Dual reference frame (DRF) model is proposed to convert the current harmonics into dc components in the new DRFs, and PI controllers are employed to control voltages to minimize the dc components. This article will prove that current harmonics can be minimized by using the DRF model. Since CHM requires additional voltages, inverter voltage limit must be considered especially at high speeds. Hence, inverter voltage limit is considered to derive the theoretical control strategy, in which minimal copper loss is selected as the design objective to reduce current harmonic with limited voltage. The proposed approach is supported by theoretical analysis and proof, and it does not require inverter voltage and machine parameters. Moreover, the proposed approach is compared with an existing method to show the performance improvement and evaluated with extensive tests on a laboratory prototype under both steady-state and transient conditions.

Force Fight and Its Elimination in a Prototype of a Redundant Direct-Drive Avionic Actuator

Nowadays, in aeronautical applications, rigorous reliability requirements are high constraints for embedded systems. Therefore, material redundancy is adopted to ensure safety whatever operation conditions may be. In the design of a direct-drive actuator for a specific application, redundancy is taken into account using a compound of four three-phase permanent magnet synchronous machines (PMSM). Each two electric machines are mounted in series sharing the same rotor with a common through shaft. The stators of each two electric machines are designed and manufactured as a six-phase machine. For each machine, power supply, sensors, and control loops are independent. In the characterization of the designed actuator and in the validation of its specific control in healthy operation mode and in faulty operation mode, taking into account the force fight phenomenon between the motor lanes, a specific test bench is developed. The aim of this paper is to highlight this phenomenon in faulty operation mode and to develop an easily implementable monitoring architecture, in order to eliminate it. Finally, with the proposed approach of monitoring, the force fight phenomenon is eliminated in faulty operation mode keeping the same performance as in healthy operation mode.

Fault-Tolerant Hybrid Current Control of Dual Three-Phase PMSM With One Phase Open

A fault-tolerant hybrid current control is proposed for dual three-phase permanent magnet synchronous machines (PMSMs) with one phase open in this article. The maximum torque control, minimum copper loss control, and single three-phase mode control are unified in the proposed method, which is a combination of single three-phase mode control and maximum torque control with different percentages. When the percentage of single three-phase mode control ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> ) varies from 0% to 100%, the hybrid current control transitions from maximum torque control ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k \,\,=0$ </tex-math></inline-formula> %) to minimum copper loss control ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k\,\,=50$ </tex-math></inline-formula> %) and then to single three-phase mode ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k =100$ </tex-math></inline-formula> %). Therefore, the hybrid current control can be switched among the aforementioned three control methods easily and smoothly. Meanwhile, it can be a mixed mode with a tradeoff between the maximum torque control and the minimum copper loss control, such as the minimum copper loss control for a given torque within the full torque range, which can be achieved by changing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> . The smoothness of transition among the maximum torque control, minimum copper loss control, and single three-phase mode control is verified by experimental results on a prototype machine.