**1. Introduction**

Permanent-magnet synchronous motors (PMSMs) have been widely applied in industrial fields [1–4] for the excellent features of high reliability, high efficiency, high torque density, good dynamic performance, etc. According to the structure of the permanent magnet of the rotor, the PMSM can be divided into interior permanent-magnet synchronous motor (IPMSM) and surface-mounted permanent-magnet synchronous motor (SPMSM). Compared with the SPMSM, the IPMSMs have attracted much attention in industrial fields recently due to their greatly improved overload capacity, power density and speed regulation range, which ascribes to the permanent magnet of the IPMSM is located inside the rotor.

To take advantage of these features, the information of rotor position acquired generally by the mechanical sensors, i.e., resolver or encoder, is necessarily required when the field-oriented control (FOC) scheme [5,6] is adopted. However, these mechanical sensors [7,8] mounted on the shaft of a PMSM bring several disadvantages such as extra cost, extra volume, low reliability, etc. In order to overcome these disadvantages, various kinds of position-sensorless control strategies that estimate the rotor position information without a mechanical sensor have been proposed in past decades [9–12]. Conventional sensorless control methods are mainly divided into two groups: (1) For medium- to high-speed operation, the schemes based on the estimation of back electromotive force (EMF), which contains the position information, (2) for low-speed operation, usually under 5% of the rated speed, the schemes based on the machine saliency injects an additional high-frequency (HF) signal to the PMSM which generates a response containing information of the rotor position.

This paper investigates the position-sensorless control strategy using the HF signal injection method in the low- and zero-speed operation, and according to the types of the injected HF signals, the signal can be mainly divided into rotating sinusoidal voltage injection (RSVI) [13], pulsating sinusoidal voltage injection (PSVI) [14], and pulsating square-wave voltage injection (PUVI) [15]. The first HF rotating sinusoidal voltage injection method was proposed by Lorenz R.D in the early time, and in this method, the balanced rotating voltage signals were injected into the stationary reference frame (SRF) and then the induced currents were extracted to obtain the rotor position information. However, this method injects an additional HF voltage into the SRF system, which will lead to the torque ripple caused by the fluctuation of q-axis current. Moreover, the saliency will be reduced under heavy load and the detection accuracy will be worse due to the magnetic saturation effect. For the improvement of the RSVI, pulsating sinusoidal voltage injection and pulsating square-wave voltage injection are proposed, which inject HF voltages in the estimated d-axis of the rotational reference frame (RRF) other than the SRF. To overcome these problems, a PSVI method [16] injects HF voltage into the estimated d-axis reference frame. Similar to RSVI method, the injection voltage frequency of PSVI method is usually about 1/10 of the carrier frequency. Therefore, this method should use low-pass filter (LPF) and band-pass filter (BPF) to separate the fundamental current component and HF currents, respectively, which decreases the control bandwidth and the dynamic performance. To improve the dynamic performance, reference [17] proposed the PUVI method, in which the HF square-wave injected into the estimated d-axis and increased the frequency of the injected signal as high as possible to the pulse width modulation (PWM) carrier frequency. Since the frequency of the injected HF square-wave voltage signal is much higher than the cut-off frequency of current loop, the LPFs in the current feedback loop can be omitted [18], which improves the response speed to some extent. Seung et al. [19] proposed a method that the frequency of the injected HF square-wave voltage signal is the same as the PWM switching frequency, in which two current samples were taken in a square-wave period and three arithmetic operations were performed to obtain the HF induced current signal. Besides, the dynamics of the position-sensorless control can be improved and the acoustic noise can be remarkably reduced. However, this method still needs to use a BPF for obtaining the feedback current signal. In [20], the fundamental current signal of the stator winding is obtained by arithmetic operation, without using a filter, but it is still necessary to sample the current twice in one square-wave period.

The conventional square-wave injection method has many advantages, such as low current noise, high bandwidth, and high steady state performance, etc. However, the voltage error caused by the nonlinearity of the inverter still needs to be taken seriously and solved. In addition, the magnetic polarity detection, which is one of the main problems to be improved, is essential for smooth startup and robust control of IPMSM. The conventional method [21] proposes to detect the initial position of the rotor by pulse voltage vector method, which injects a series of pulse voltage vectors with the same amplitude and different direction into the motor stator winding, and estimates the rotor pole position by comparing the magnitude of the response current based on the nonlinear saturation characteristics of the motor stator core. However, the current amplitude does not change much as the voltage vector approaches the rotor pole position. At the same time, the phase current measurement error and the inverter nonlinearity will affect the measurement accuracy [16].

In order to solve the problem of initial position detection in conventional sensorless control of IPMSM, a rotating voltage injection sensorless method of estimating the initial rotor position of a direct torque controlled IPMSM drive is proposed in [22], which injects a HF voltage to the windings and extracts the amplitude of the corresponding stator current components based on motor salient effect. However, this method still has some problems, such as obvious current sampling noise, influence by motor parameter variations, and special position interference. The improvement of the RSVI, PUVI, which has been proven to be the best injection type for the low- and zero-speed position sensorless control [23], can rarely be found for the initial rotor position detection in the sensorless control system. Xie et al. [24] proposed a PUVI method in which the two opposite voltage vectors were injected to reduce the effects of inverter voltage error on the position estimation accuracy. However, this method only studies the low-speed range, and does not conduct research and analysis on the zero-speed range, especially the lack of research on magnetic polarity detection, which is essential for smooth startup and robust control of IPMSM. In [25], the positive and negative test pulse voltages are injected into the estimated d-axis, and the positive direction of the magnetic polarity is judged by the time when the currents at different magnetic polarity are attenuated from the steady state value to 0. However, the position estimation is stopped in the process of polarity identification, which makes the structure of the code more complicated. This problem also exists in [26] and [27], and the interval of signal injection must be existed, resulting in long execution time and poor stability. Then, [28] uses the difference in current measured at zero time of each PWM period to determine the magnetic polarity. The advantage is that no additional injection voltage is required, and the convergence speed is fast. The disadvantage of this method is that the position estimation depends on the accuracy of the current. Once the current signal-to-noise ratio is too small, the rotor position cannot be accurately obtained. Based on the above references and the improvement points of this article, the comparison of Table 1 is obtained.


**Table 1.** List of the research contents covered by the articles.

Therefore, in view of the existing sensorless estimation methods for rotor position, a HF square-wave voltage injection scheme-based rotor position estimation of IPMSM in low-speed range and a new method of magnetic polarity detection in zero-speed range are proposed. Based on the principle analysis of d-axis magnetic circuit characteristics, a method for determining the direction of magnetic polarity of d-axis two-opposite DC voltage offset by uninterruptible square-wave injection is proposed, which is simple and can quickly converge by comparing the absolute value of the peak-to-peak value in the d-axis high-frequency current response. Therefore, the method of magnetic polarity identification proposed in this paper is not only suitable for the case where the motor is stationary, but also suitable for the free running condition of the motor. At the same time, the strategy injects a two-opposite HF square-wave voltage vectors into the estimated SRF, which considers the

effects of inverter voltage error on the rotor position estimation accuracy. With this approach, the LPF and the BPF are removed to simplify the signal process for estimating the rotor position and further improve control bandwidth.

This paper is organized as follows. First, the rotor position estimation strategy based on conventional HF square-wave voltage injection is analyzed in Section 2. In Section 3, the rotor position estimation strategy based on improved HF square-wave voltage injection and proposed magnetic polarity detection are investigated. Then, in Section 4, comprehensive simulation and experimental setup are introduced and experiments are provided to prove the effectiveness of the improved sensorless control strategy and proposed magnetic polarity detection method. Finally, Section 5 concludes this paper.
