A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors

ISA Transactions xxx (xxxx) xxx

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A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors ∗

Xuan Wu a , Sheng Huang b , Ping Liu a , , Ting Wu a , Yunze He a , Xiaofei Zhang a , Kun Chen a , Qiuwei Wu b a b

College of Electrical and Information Engineering, Hunan University, Changsha 410082, China Department of Electrical Engineering, Technical University of Denmark, 2800 kgs. Lyngby, Denmark

highlights • • • •

A reliable initial rotor position detection method for sensorless control of the IPMSM is presented. No filters are needed for extracting the fundamental currents and the induced currents. The proposed method can improve the reliability of magnet polarity detection. The proposed method is suitable for standstill rotor application and free-running rotor application.

article

info

Article history: Received 15 November 2018 Received in revised form 26 June 2019 Accepted 2 July 2019 Available online xxxx Keywords: Interior permanent magnet synchronous motor (IPMSM) Sensorless Initial rotor position estimation Magnetic polarity detection High frequency pulse voltage injection

a b s t r a c t In this paper, a novel initial rotor position estimation method for reliable start-up of the IPMSM is presented. The proposed method combines the improved high frequency pulse signal injection with positive and negative d-axis current bias injection. Differing from the conventional initial rotor position detection scheme, the injection and the field-oriented control periods are separated in the proposed method. Therefore, the filters are not needed in the process of high-frequency response current and fundamental current extraction. The magnet polarity can be estimated by exciting the positive and negative d-axis currents. Afterwards, the peak values of d-axis current during the voltage injection period are accumulated to detect the rotor magnetic polarity. The proposed method can improve the reliability of the magnet polarity detection. Moreover, it is suitable for both the standstill rotor application and the free-running rotor application. The effectiveness of the proposed method is verified on a 1.5 kW IPMSM drive platform. © 2019 Published by Elsevier Ltd on behalf of ISA.

1. Introduction Permanent magnet synchronous motors (PMSMs) have been widely used in industrial applications with advantages, such as high efficiency, high energy density, etc. [1]. However, the real performance of the PMSMs is closely related to the motor control method. The field-oriented control (FOC) method is widely used in the area of motor control. The rotor position is required in PMSM when the FOC method is utilized [2–5]. Usually, a mechanical sensor, such as resolver and encoder, is adopted to detect the rotor position. Generally, the installation of position sensor reduces the system reliability and increases its cost. Therefore, sensorless control methods of PMSMs have been extensively studied during the past few years [6,7]. In PMSM drives, smooth start-up heavily relies on an accurate initial rotor position. When ∗ Corresponding author. E-mail addresses: [email protected] (X. Wu), [email protected] (P. Liu).

the initial position is abnormal, the starting for IPMSM will fail, or even reverse [8,9]. To obtain an accurate initial position, several saliency-based methods have been proposed for the interior-PMSM (IPMSM). For example, the high-frequency (HF) rotating signal injection method [10] and the HF pulsating carrier signal injection method [11]. In the HF rotating injection method, the voltage vector is injected into the αβ -axis [12]. Due to the use of the HF rotating signal, the dynamic performance is restricted within a narrow limit. Another estimation method is the pulsating carrier signal injection, which injects the pulsating signal into the d- or q-axis in the rotor reference frame [13]. The induced carrier current contains the position information, and it can be inputted into a phase-locked loop (PLL) to obtain the estimated position and speed. However, low pass filters (LPFs) are needed as feedback in FOC loops to extract fundamental current, which cause extra delay and the sacrifice of the control performance [14].

https://doi.org/10.1016/j.isatra.2019.07.012 0019-0578/© 2019 Published by Elsevier Ltd on behalf of ISA.

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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Since the inductance of IPMSM contains two cycles in a single electrical period, the rotor position obtained by above saliencybased methods fails to be distinguished whether it needs to add π elec-rad. Therefore, the identification of the magnet polarity is necessary [15]. To identify the magnetic polarity of the rotor, various methods have been employed [16–28], such as the short pulses injection method [16,17] and the secondary harmonics based method [20, 21]. In [16], the short pulses injection method is used for identifying the magnetic polarity. However, it is complicated to choose the pulses length and the amplitude, and only two single positive and negative peak values of induced current are used for the polarity detection. The estimation accuracy strongly depends on the current sampling precision of A/D converter, the difference between positive–negative current peak values is not always obvious enough to make a polarity judgment [17]. In addition, it is necessary to estimate the initial position of a free-running motor in some applied situation, which features that its rotating speed and direction is not clear [18]. For example, when the motor with large inertia is powered off abruptly, it takes some time for the rotor speed to decrease to zero. In the process of speed reducing, the motor may get a restart command suddenly. In such condition, the motor needs to fulfill the initial position estimation process. The short pulses injection is implemented when the position estimation process is suspended. It means that the short pulses injection leads to the inaccuracy position estimation when the motor operates in free-running mode [19]. The second harmonics detection method is suitable for the free-running operation of IPMSM [20]. However, the low signal-to-noise ratio (SNR) of secondary carrier current components has limited the precision of the rotor identification [21]. The zero sequence voltages injection method is reported in [22], the magnetic polarity identification is completed by modulating of the zero sequence carrier voltage amplitude. Therefore, the method not only enhances the SNR of position estimation, but also extenuates the distortion of the harmonic. However, the additional voltage sense circuit is requested to determine the zero sequence carrier voltage. A comprehensive initial position estimation method for IPMSM has been presented in [23], pulsating-voltage-vector injection method is used to obtain the estimated rotor position. In addition, a sinusoidal low-frequency d-axis current and a positive ramp qaxis current are combined to confirm rotor polarity. Although this combination method can make the position estimation correct, however, multiple filters are used to extract the HF current signal, which degrades the system performance owing to the time delay. Secondly, the magnetic polarity identification is not robust enough, and the method in [23] is only suitable for applying in the system which is allowed to rotate, such as pump-like or fan systems, the position estimation method in [23] has limited application range. To overcome these problems, a reliable initial position estimation method for the start-up of IPMSM drive is proposed in this paper. The proposed method combines the improved HF pulse signal injection method with two opposite current bias injection method. The voltage injection periods are separated from the FOC periods, therefore, the filters are not needed in the process of HF response currents and fundamental current extraction; the rotor position information is directly carried by the difference between the two current variations of d-axis. Moreover, the position estimation process is not affected by the inverter voltage error effects. For identifying the magnetic polarity, two opposite current bias are imposed into d-axis, and the d-axis current during the voltage injection period are accumulated. Then, the difference of the accumulated current is compared to confirm the rotor polarity. The proposed method is also suitable for free-running rotor applications. The effectiveness of proposed method has been verified on a 1.5-kW IPMSM drive platform by comparing with the method in [23].

Fig. 1. Signal processing for obtaining rotor position.

2. Analysis of conventional initial rotor position detection This section introduces the conventional initial position detection, which combines the pulsating carrier voltage injection method with the short pulses injected method. The PMSM can be modeled in the rotor reference frame as [13]:

⎧ ⎪ ⎨vd = Rid + Ld d id − ωr Lq iq dt

(1)

⎪ ⎩v = Ri + L d i + ω L i + ω ϕ q q q q r d d r m

dt where vd , vq and id , iq are the stator voltage and current; Ld and Lq are the d-, q-axis inductance; R is the stator resistance; ωr is the rotor electrical angular velocity; ϕm is the peak value of the rotor PM flux linkage. The injected HF pulsating carrier signal is,

⎡ ⎤ e ⎣vdc ⎦ e vqc

cos(wc t) 0

[ = Vc

] (2)

where Vc and wc are the amplitude, the angular speed of the injected HF pulsating carrier signal, respectively. The induced carrier current in the estimated dq-reference frame can be derived as [13], iedqc

=

Vc

{

2ωc

+

(

1 Ld

+

Vc2 d2 id 2ωc2 dλd 2

1 Lq

)+(

dλd (0) did

and

Ld

−

1 Lq

j2(˜ θr )

}

)e

sin ωc t

(ϕm ) sin2 ωc t cos2 (˜ θr )ej(θr ) ˜

where λd ≈ ϕm + Ld id + Ld =

1

d2λ d did 2

(3)

2

d 1 λd (0)id 2 2 did 2

is the d-axis flux linkage;

(0) < 0; ˜ θr = θr − θˆr is the rotor position

error, θr is the actual rotor position, and θˆr is the estimated rotor position. The rotor position information is contained in ˜ θr terms of (3), the q-axis carrier current component is more suitable for extracting the inductance saliency information. According to the heterodyning process in Fig. 1, the current response about rotor position information can be described as ipos =

Vc 1 1 ( − ) sin 2(˜ θr ) 2ωc Ld Lq

(4)

Note that when ipos is regulated to zero, ˜ θr can be either 0 or 180 electrical deg, and the rotor magnetic polarity may be the N-or S-poles. Therefore, additional rotor N/S pole identification process is necessary. As illustrated in Fig. 2, the conventional initial position estimation method is carried out in two steps [16,17]. Firstly, the rotor position is obtained by superimposing the pulsating carrier voltage on the estimated d-axis. Secondly, the rotor position estimation process is suspended, and the short pulse injects on the

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

X. Wu, S. Huang, P. Liu et al. / ISA Transactions xxx (xxxx) xxx

estimated d-axis, by comparing the peak values of d-axis response current to identify the magnet polarity. When the N/S pole identification process is implemented, the estimated rotor position will not update. Thus, the conventional initial position estimation method will cause the inaccuracy of the position estimation when the rotor operates in free running mode [18].

3

Referring to Fig. 3(a), when a single constant voltage vector V i = Vi is injected on the estimated d-axis, and the voltage signal injected on the estimated q-axis is zero. Then, it can be obtained that θˆm = 0. Thus, Eq. (11) can be expressed as, e

e

∆idq = ∆iαβ e−jθr = (c1 + c2 ej2(θr −θr ) )∆tV dq ˆ

ˆ

(12)

The voltage injection periods are separated from the FOC e period. In the FOC period, V dq = V FOC , where V FOC is the output

3. Proposed initial rotor position detection method

e

This section explains the proposed initial position estimation method, which means the combination of improved HF pulse voltage injection and two opposite current bias injection method. The improved HF pulse voltage method is adopted to obtain the initial rotor position without the correction of magnet polarity. Afterwards, the magnet polarity is distinguished by adopting the d-axis current bias.

voltage calculated from PI control. In the injection period, V dq = Vde = Vi when the voltage signal is applied to the estimated d-axis. Thus, Eq. (12) can be derived as,

3.1. Improved HF pulse voltage signal injection method

The imaginary part ∆ieq in (14) contains rotor position error ˜ θr , which can be used for rotor position estimation. However, the inverter nonlinear errors [24] will cause that the voltage vector cannot inject to the estimated d-axis accurately, which further result in an estimation error. Fig. 4 shows the sequence of the improved HF pulse voltage injection method. The position error, which is caused by inverter nonlinear effects, is compensated by applying two opposite voltage signals to the estimated d-axis. A control period includes three switching periods, which is composed of a FOC and a voltage injection period. In the injection period with two switching periods, two opposite pulse voltage signals (+Vde and −Vde ) are imposed to the d-axis, the single pulse voltage signal is injected once every two switching periods. For example, when the PWM switching frequency is 5 kHz, the injection frequency is 3.33 kHz. iedq (k) is the estimated d- and q-axis current at a certain time of k. In the position estimation process, the q-axis current is still used for rotor position detection. The q-axis current gained in turn is subtracted each other to obtain the current variable ∆ieqx , such as, ∆ieq0 , ∆ieq1 . ∆(∆ieq ) = ∆ieq1 − ∆ieq0 is the resultant current of

In the stationary αβ -reference frame, the vector representation of (1) can be described as

( ) d d ∗ ∗ v αβ = Riαβ + L∑ iαβ + L∆ iαβ ej2θr + j2ωr L∆ iαβ ej2θr dt

dt

+ jωr ϕm ejθr

(5) ∗ iαβ

where L∑ = (Ld + Lq )/2, L∆ = (Ld − Lq )/2, is the conjugate vector of iαβ . When the motor runs at low speed and standstill, ωr ≈ 0, and the resistive voltage drop is negligible. Thus, the equation of (5) can be approximated by, d d ∗ iαβ + L∆ iαβ ej2θr dt dt Consider that: d ∗ d v ∗αβ = L∑ iαβ + L∆ iαβ e−j2θr dt dt

v αβ = L∑

(6)

(7)

v ∗αβ

where is the conjugate vector of v αβ . In order to obtain the current differentiation tion eliminating the same factor d dt

iαβ =

1 L2Σ − L2∆

d ∗ i dt αβ

d i , dt αβ

the equa-

can be derived as:

(LΣ v αβ − L∆ v ∗αβ ej2θr )

(8)

v αβ = Vejθm is the fundamental equation for deriving e.g. the INFORM method [6], where θm is the voltage angle in the αβ reference frame. Then, Eq. (8) can be expressed as, d dt

iαβ = (

LΣ L2Σ − L2∆

Ve

jθm

−

L∆ L2Σ − L2∆

Ve

−jθm j2θr

e

)

Assuming that the period (e.g. a switching period) is extremely short, the current differentiation diαβ /dt of Eq. (9) can be approximated by ∆iαβ /∆t: (10)

where c1 = L /(L − L∆ ), c2 = −L∆ /(L − L∆ ). Referring to Fig. 3(a), dq-frame is the real dq-reference frame, which represents rotation angle of the real rotor position. de qe frame means estimated dq-reference frame, which is introduced when the rotor position is unknown in the sensorless control system. The de qe -frame has the phase difference of ˜ θr from dqframe. Then, the equation of (10) will be converted into the estimated dq-reference frame: ∑

e ∆idq

= ∆iαβ e

−jθˆr

2 ∑

2

= (c1 + c2 e

2 ∑

j2(θr −θˆr −θˆm )

e )∆tV dq

2

(11)

where θˆm = θm − θˆr is the phase difference between injected voltage vector and the estimated d-axis.

(13)

˜

Then, Eq. (13) can be further written as, e ∆idq

θr + jc2 ∆tVi sin 2˜ θr (14) = ∆ied + j∆ieq = c1 ∆tVi + c2 ∆tVi cos 2˜

the next and the moment, which contains the position estimation error. The following derivation details how the inverter voltage error is offset by the proposed method. Referring to Fig. 3(b) and Fig. 4, two voltage signals Vi and −Vi are applied to the de -axis. If the voltage errors ∆V will constant during the switching periods, the two real voltage signals can then be expressed as, e

(9)

∆iαβ = (c1 + c2 ej2(θr −θm ) )∆t · v αβ

e

∆idq = c1 ∆tVi + c2 ∆tVi ej2θr

V dq1 = Vi ejθm1 ≈ Vi − ∆V

(15)

e V dq2

(16)

ˆ

= Vi e

jθˆm2

≈ −Vi − ∆V

where subscripts 1 and 2 represent the first and the second injection period. Hence, by substituting (15) and (16) into (11), the current variations contained voltage errors in the estimated dq-reference are given:

∆idq1 = (c1 + c2 ej2(θr −θr −θm1 ) )∆t(Vi − ∆V )

e

ˆ

(17)

e ∆idq2

j2(θr −θˆr −θˆm2 )

(18)

= (c1 + c2 e

ˆ

)∆t(−Vi − ∆V )

As it can be observed from Fig. 3(b), θˆm1 = ∆θm1 , θˆm2 = −π + ∆θm1 , and ∆θm1 ≈ ∆θm2 . It is not difficult to find that: e

e

∆idq1 − ∆idq2 = 2c1 ∆tVi + 2c2 ej2(θr −θm1 ) ∆tVi ˜

ˆ

The imaginary part of current variations, be further derived as: e

e

e Im(∆idq1

(19)

−

Im(∆idq1 − ∆idq2 ) = ∆(∆ieq ) = 2c2 ∆tVi sin 2(˜ θr − θˆm1 )

e ∆idq2 ),

can

(20)

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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Fig. 2. Block diagram of the conventional initial position estimation method.

Fig. 3. Coordinate distribution of each axis. (a) One injected voltage vector scheme. (b) Two opposite voltage injection scheme.

Fig. 4. Sequence of improved HF pulse voltage signals injection method with opposite voltage injection.

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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5

In the situation that different DC d-axis currents Id∗ are given, imposing the injected HF pulse voltage signals with Vde = 60 V, then the amplitude of L′∑ and ied are measured. As shown in Fig. 8, the spline fitted curves are drawn based on the measured data points. The amplitude variation of ied in the left half of Fig. 8(b) is rather small than that in the right-half when opposite current biases are injected. Therefore, by comparing the amplitude of ied under two opposite current bias, the rotor magnet polarity can be detected. For guaranteeing ⏐ ⏐ the reliability of the method, ∑ ⏐⏐ e ⏐⏐ the accumulation form of the ⏐ied ⏐ can be considered, i.e. id (+I ∗ )

Fig. 5. Block diagram of the proposed signal processing.

and

d

∑ ⏐⏐ e ⏐⏐ id

(−Id∗ )

.

3.3. Implementation of the proposed initial position detection scheme

Fig. 6. Effects of magnetic saturation.

It is observed from (20) that the voltage error vectors have been contracted. Moreover, referring to Fig. 3(b), it is noted that the angle θˆm1 = ∆θm1 is very close to zero . Therefore,

∆(∆ieq )

= 2k sin(2˜ θr ) ≈ 4k˜ θr

(21)

where k = c2 ∆tVi is invariable. As illustrated in Fig. 5, the estimated rotor position θˆr and speed ω ˆ r can be extracted by applying a normal PLL. 3.2. Proposed magnetic polarity identification method by giving positive and negative d-axis current bias This section explains the proposed polarity detection method which applies two opposite current biases on the estimated daxis. The real part of the current variations terms in (14) can be rewritten as:

∆ied = c1 ∆tVi + c2 ∆tVi cos 2˜ θr

(22)

It should be noted that c2 ≪ c1 is observed from L∆
∆ied = c1 ∆tVi = ∆tVi •

L∑ (L2∑ − L2∆ )

≈ ∆tVi •

1 L′∑

(23)

where L′∑ is the equivalent incremental inductance of d-axis. Observing that if ∆t and Vi are constant, the magnitude of ∆ied will be inversely proportional to the L′∑ , which might reduce depending on the saturation situation. Figs. 6 and 7 show the magnetic saturation effect. Id∗ and −Id∗ represent positive- and negative-direction d-axis current bias, respectively. When Id∗ is used, the direction of ψs and ψm keep the same (Fig. 7(a)) so that the gap magnetic field is strengthen, lead to the increase of ied (as point B showed in Fig. 6); when −Id∗ is applied, ψs and ψm hold the opposite direction (Fig. 7(b)) so that the gap magnetic field is weaken, there is no d-axis current increment (as point A showed in Fig. 6). Therefore, in an artificial saturation condition, the difference of L′∑ , i.e., corresponding ∆ied represents the magnetic polarity.

Figs. 9 and 10 show the block diagram of the proposed initial position estimation method and the signal processing for position estimation method, respectively. During the implementation, two opposite pulse voltages are injected following the FOC switching period. A control period has three switching periods, the frequency of the injected pulse voltage signals is set as 2/3 of the PWM switching frequency. In step 1, the HF pulse voltage signals are injected to obtain the estimated position θˆr0 . In step 2, two opposite d-axis current bias are consequently set. Magnitudes of the induced d-axis currents are compared for identifying the magnet polarity. If the magnetic saturation effect is magnified, ⏐ ⏐ ⏐ e⏐ ⏐i ⏐ ∗ > ⏐ie ⏐ ∗ . Then, the correct initial rotor position is θˆr0 . In d (−I ) d (+I ) d

d

contrast, if ⏐ied ⏐(+I ∗ ) < ⏐ied ⏐(−I ∗ ) , the initial rotor position is θˆr0 + π .

⏐ ⏐

⏐ ⏐

d

d

The polarity detection is only implemented for one time, once the final rotor position θˆr is confirmed, it can be directly used for motor starting. 4. Initial rotor position detection capability analysis In this section, the capabilities analysis of the proposed initial position detection scheme is presented, including the comparison with the conventional position estimation method in freerunning situation, and the effects of cross-coupling magnetic saturation on position estimation accuracy. 4.1. Acquisition of position error and magnetic polarity in freerunning situation In the conventional initial position estimation method, the pulsating carrier injection and the short pulses injection are both implemented on the estimated d-axis. The two processes cannot be preceding simultaneously. Once the magnetic polarity identification starts, the rotor position estimation process stops. It means that the short pulses injection method is only valid in standstill, not in free-running situation. Different from the conventional method, the proposed magnetic polarity identification method is integrated with the HF pulse voltages injection method. During the rotor N/S pole identification, the HF pulse voltage vectors are still injected into d-axis. It means that the update for estimated rotor position is always carried out. Therefore, the proposed method is suitable for free-running rotor. In addition, the proposed nonzero d-axis biases injection method has higher SNR than the short pulses injection method. Thus, the proposed method has good reliability for magnetic polarity identification.

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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Fig. 7. Gap synthesizes magnetic field.

Fig. 8. Effects of both DC d-axis current iedl and HF pulse voltage signals Vde on the IPMSM. (a) Equivalent d-axis incremental inductance L′∑ . (b) Amplitude of d-axis current response ied . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 9. Block diagram of proposed position detection scheme.

4.2. Effect of cross-coupling magnetic saturation

Without taking the cross-saturation effect into account, L∑ and

Because the incremental self- and mutual-inductances in dqaxes vary with the dq-axes currents, the position estimation accuracy will be influenced by the cross-saturation effect [27]. Additionally, the position error rises up with the load current.

the high-frequency model can be modified as [27].

L∆ in (6) may cause a non-negligible position error. In the IPMSM,

[ ] [ vα L = T (θ r ) d vβ M

]

d M T −1 (θr ) • Lq dt

[ ] iα iβ

(24)

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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7

Fig. 10. Flowchart for proposed initial position estimation method.

where T (θr ) =

[

cos(θr ) sin(θr )

− sin(θr ) is the transformation macos(θr )

]

trix, M is the incremental mutual inductance related with the cross-saturation effect. The current in the stator frame can be deduced as [27],

⎡

d dt

[ ] iα iβ

1

1

⎢ L1 + L2 cos(2θr + θM ) =⎢ ⎣ 1 sin(2θr + θM ) L [ ]2 v • a vβ

1 L2 1 L1

−

sin(2θr + θM ) 1 L2

⎤ ⎥ ⎥ ⎦

cos(2θr + θM )

θM = tan−1 (−M /L∆ )

(25) (26)

where θM is the position error bias caused by the √cross-saturation

effect, L1 = (Ld Lq − M 2 )/LΣ , L2 = (Ld Lq − M 2 )/( L2∆ + M 2 ). 5. Experimental results

The proposed initial position detection method is verified on a 1.5 kW IPMSM drive platform, as shown in Fig. 11. The detailed parameters of IPMSM are listed in Table 1. The IPMSM has 4-pole, 12-slot construction, concentrated windings. The induction motor provides the load torque. The TMS320F2808 with 100 mHz, 32bit fixed-point DSP family, is used for implementing the control methods and providing the PWM signals for the inverter. The DSP also are responsible for the following functions: sampling of DC bus voltage and stator current, panel display and keyboard input, RS-232 and upper and lower machine CAN bus communication function, start overcurrent relay control, and energy consumption brake control, etc. The switching frequency is 5 kHz, the injected pulsating carrier voltage vector is 60 V/500 Hz, the injected HF pulse voltage signals is 60 V/3.33 kHz. In the proposed initial position method, the Id∗ is 2 A in the magnetic polarity identification process, and 0 A in other situations. The actual rotor speed and position are detected by the encoder PENON-K3808G. The obtained position and speed are used as the reference value, and they do not really participate in closed-loop control of the IPMSM drive. 5.1. Experimental results of the conventional magnetic polarity detection method based on the short pulse injection Fig. 12 shows d-axis response current waveforms with short pulses injection method. In order to verify the reliability of the

Table 1 IPMSM parameters. Parameters

Values

Parameters

Values

Rated Rated Rated Rated

1.5 380 2.7 3000

Rated torque (N m) Number of pole pairs d-axis inductance (mH) q-axis inductance (mH)

4.8 2 17.81 26.72

power (kW) voltage (V) current (A) speed (r/min)

short pulse injection method, the rotor is locked at 0◦ when the motor is standstill. The locked rotor position acts as a reference position, when compares with the estimated position. In Fig. 12(a), two opposite 200 V-1 ms pulses are injected, and the pulse interval is 50 ms. In Fig. 12(b), the peak value of positive current is higher than that of the negative. Therefore, the rotor polarity is N pole. On the contrary, when the peak value of negative current is higher than that of the positive in Fig. 12(c), the rotor polarity is S pole and a 180◦ compensation is necessary. However, the two peak values of d-axis current are too small, when the current sampling resolution is not enough, the system will hard to make correct identification.

5.2. Performance of the proposed initial position detection scheme at standstill The initial position estimation results of the proposed method is illustrated in Fig. 13, the current actual rotor position is 126◦ . After the step 1 illustrated in Fig. 13(a), the estimated rotor position θˆr0 is 308.3◦ . Then, in step 2, Id∗ and −Id∗ are consequently given. The d-axis response current ied is obtained and its peak values are accumulated for 15 times. As seen in Fig. 13(b), by come paring two corresponding accumulated values 180◦⏐ should ⏐ ∑ ⏐⏐ e ⏐⏐of id , a∑ ⏐ e⏐ be compensated for θˆr0 because of i < 15 d (+I ∗ ) 15 id (−I ∗ ) . d

d

d

d

Finally, the estimated position θˆr is 128.3◦ , and the position estimation error is 2.3◦ . Fig. 14 shows initial position detection results in the case that the actual rotor position is 54◦ . The estimated position θˆr0 is ob∗ tained by 55.5◦ , then the current Id∗ and As⏐ shown ⏐ given. ⏐ ∑−Id⏐⏐ eare ⏐ ∗ >∑ ⏐ie ⏐ ∗ . in Fig. 14(b), it can be found that i 15 d (+I ) 15 d (−I ) Therefore, the final estimated rotor position is still 55.5◦ , and the position estimation error is 1.5◦ .

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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Fig. 11. Experimental platform of 1.5 kW IPMSM drive system. (a) The whole experimental test. (b) The development board of TMS320F2808. (c) Hardware implementation diagram of the control system.

5.3. Performance of the proposed initial position detection scheme at free-running

◦ position convergence ⏐ e ⏐final estimated rotor position ∑ ⏐⏐ e ⏐⏐to 257.4 ∑ . The ◦ ⏐ ⏐ is 77.4 since 15 id (+I ∗ ) < 15 id (−I ∗ ) . d

Fig. 15(a) shows the initial position detection results of the proposed method in the case that an artificial rotor position step is applied during the magnetic polarity detection, i.e., freerunning situation. The actual initial rotor position is 90◦ , after the improved HF pulse voltage injection method is implemented, the estimated position θˆr0 is obtained by 88.6◦ . When a 60◦ position step is given, the estimated rotor position conver◦ ◦ gences ⏐ e ⏐ a 180 compensation is unnecessary since ∑ ⏐⏐ e ⏐⏐to 147.8 ∑ , and ⏐ ⏐ 15 id (+I ∗ ) > 15 id (−I ∗ ) . d

d

Fig. 16(a) shows experimental waveforms of another freerunning situation, where an artificial position falling step is applied during the negative d-axis DC bias excitation. The first actual rotor position is 120◦ , the estimated rotor position θˆr0 is 302.8◦ . Then, a 40◦ position falling step is given , the estimated rotor

d

5.4. Comparison with the initial position estimation method in [23] In this section, in order to demonstrate the effectiveness of the proposed method, a comparison between the proposed method and the method in [23] is given. According to the study carried in [23], the pulsating voltage frequency and amplitude are set as 500 Hz and 100 V, respectively. The injected sinusoidal d-axis current signal is amplitude of 3 A with frequency of 5 Hz, and the positive ramp q-axis current is 3 A and lasts 100 ms. Fig. 17 shows the current step responses results based on the proposed method and the pulsating-carrier-signal-injection method in [23]. The d-axis current step command is given, and the q-axis reference current is set to zero to ensure that the rotor will not rotate in the short period. The PI controllers of currentloop based on these two methods share a set of parameters. In

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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Fig. 12. Magnetic polarity detection with short pulses injection method. (a) Injection 200 V–1 ms pulses with a 50 ms interval. (b) d-axis current response when the rotor is at N pole. (c) d-axis current response when the rotor is at S pole.

Fig. 13. Initial position estimation at standstill (θr = 126◦ ). (a) Measured d-axis current and estimated rotor position. (b) Accumulated values of d-axis current peak.

Fig. 17(a), the d-axis current response is obtained from the proposed method. In order to avoid affecting the d-axis current step responses, it is worth to notice that two opposite voltage vectors are injected on the qe -axis and the closed-loop voltage signal of daxis participates in a FOC operation every three switching cycles. In Fig. 17(b), the proposed method has a faster d-axis current step response than the pulsating-carrier-signal-injection method in [23]. This is mainly due to the fact that the method in [23] uses

multiple filters to extract the current signal, which will reduce the bandwidth of the current control-loop. Fig. 18 gives the experimental results of the method in [23]. In order to compare the performance of the methods in initial position estimation, we use the same controller parameters. Moreover, the rotor position in Fig. 18(a) and (b) is set as the same as Figs. 13 and 14, which is initially locked at 126◦ and 54◦ . The whole position estimation process is performed in 450 ms. In Fig. 18(a), the pulsating-voltage-injection method is implemented, the rotor position is obtained as θˆr0 = 308.8◦ . The amplitude difference of the HF d-axis current response under positive- and negative-cycle of sinusoidal d-axis current is a negative number, which means that a 180◦ should be added on θˆr0 . Then, the estimated position is updated as 128.8◦ . The position estimation error is 2.8◦ with the sinusoidal d-axis current injection method performed. To confirm the correction of the rotor polarity, a positive ramp current with 100 ms is applied on the q-axis. The measured angular acceleration is positive, which shows the rotor polarity identification of the former method is correct. The final estimation error is 2.7◦ . In contrast to Fig. 18(b), the rotor position was estimated as θˆr0 = 55.2◦ . The magnetic polarity identification process is then performed in 200 ms. The amplitude difference of the HF d-axis current response between the positive- and negative-cycle of sinusoidal d-axis current is a positive number, which can be obtained when the rotor is at N pole. Thus, there is no angle needed to be compensated for θˆr0 . The final position estimation error is 3.2◦ . As illustrated in Fig. 18, compared with the proposed method, the position estimation accuracy of the method in [23] is roughly the same. However, the proposed method in polarity identification is more robust and has a wider applicative situation. The obtained d-axis response current is accumulated for magnetic polarity identification. Thus, the difference of accumulated valve is at least greater than 1 A as shown in Figs. 13 and 14. However, in the method proposed in [23], the polarity detection is implemented by utilizing a sinusoidal low-frequency current on d-axis. The amplitude difference of HF d-axis current response is

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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Fig. 14. Initial position estimation at standstill (θr = 54◦ ). (a) Measured d-axis current and estimated position. (b) Accumulated values of d-axis current peak.

Fig. 15. Initial position estimation at free-running situation (θr = 150◦ ). (a) Measured d-axis current and estimated position. (b) Accumulated values of d-axis current peak.

less than 0.4 A as shown in Fig. 18, which is easy to cause misjudgment in identifying magnetic polarity. Therefore, the positive ramp current, which is applied on the q-axis, needs to confirm whether the polarity estimation by sinusoidal low-frequency current injection method is correct. If the rotor polarity is incorrect, it will be detected again by sinusoidal low-frequency current injection method. So the method in [23] is more complicated to implement on. Although the combined rotor polarity estimation method can make a correct identification to magnetic polarity, it can only fit for the systems which allows to rotate, such as a

Fig. 16. Initial position estimation at free-running (θr = 80◦ ). (a) Measured d-axis current and estimated rotor position. (b) Accumulated values of d-axis current peak.

fan or pump-like systems. Thus, the position estimation method in [23] has limited application situations. In addition, the time of whole position estimation process in the proposed method and the method in [23] is 50 ms and 450 ms, respectively. The proposed method is shorter than the method in [23] with 400 ms. Moreover, it is much easier to implement the proposed method and the calculation of the position error is more straightforward. Because the difference of synthesizing current variation under two opposite voltage vector

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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injection directly contains the rotor position information. However, the magnetic polarity is identified by the combination of two steps in [23], and filters are needed to extract the dependent position error signal. 5.5. Starting performance of the proposed initial position detection scheme under different loads Fig. 19 shows the position estimation error at sensorless startup with different loads, from standstill to 300 rpm. There is no rotor reverse or shake phenomenon. The IPMSM is able to start with 200% of the maximum rated load. 5.6. Compensation of the inverter nonlinear error

Fig. 17. Current response with the proposed method and the method in [23]. (a) With the proposed method where the voltage signals are injected on qe -axis. (b) With the pulsating-carrier-signal-injection method in [23].

Fig. 20 illustrates the tracking results of actual rotor position with/without compensation of the inverter nonlinear error. For a more intuitive observation, Fig. 21 further demonstrates the position estimation error from 0◦ to 360◦ . In Fig. 21, without the compensation of the inverter nonlinear error, the average and maximum values of estimation error are 4.39◦ and 8.17◦ , respectively. After compensation, the average and maximum values of estimation error decrease to 3.12◦ and 6.31◦ , respectively. The better estimation accuracy can be obtained with the inverter nonlinear error compensation. Fig. 22 shows the startup results without/with compensation of the inverter nonlinear error, including the actual position θr , the estimated position θˆr , and the position estimation error ˜ θr . Experimental results show a better startup with the compensation.

Fig. 18. Initial position estimation process with the method in [23]. (a) When the actual position is 126◦ . (b) When the actual position is 54◦ .

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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Fig. 19. Experimental results of starting for IPMSM under different loads. (a) With 50% rated load. (b) With 100% rated load. (c) With 200% rated load.

Fig. 20. Tracking results of initial rotor position.

Fig. 21. Position estimation error with and without the proposed inverter nonlinear error compensation.

Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.

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Fig. 23. Cross-saturation effects and q-axis currents. Fig. 22. Startup test results with/without the inverter nonlinear error compensation. (a) Without compensation. (b) With compensation.

5.7. Compensation for the cross-saturation effects To eliminate the additional position error originating from the cross-saturation effect, many methods have been proposed to compensate the cross-saturation effect [28,29]. The position error can be compensated by using (26) and the pretested data in [29]. However, the predicted or measured incremental inductance characteristics may not constant with the changing in temperature. Through theoretical calculations and measured tests, the position error are roughly proportional to the q-axis current in the position sensored drive, i.e., θM ≈ KM • iq , where the compensation coefficient KM can be measured and then summarized from statistical data. Thus, with the utilization of KM , by regulating the q-axis current can compensate for the position error in the position sensored drive. Nevertheless, the crosssaturation effect further increases in the position sensorless drive, which is main source of position error. In this paper, the cross-saturation effects are compensated by a comprehensive test method, where the statistical results origin from both position sensored and sensorless drive. In the ′ sensorless drive, θM ≈ KM′ • iq . Then, the comprehensive error ′′ is θM ≈ KM′′ • iq , where KM′′ = (KM + KM′ )/2. Fig. 23 shows ′′ the compensatory angle θM based on iq in position sensored and sensorless drive, it can be found that the position error can be compensated online based on q-axis current. 6. Conclusions This paper has proposed a reliable initial position estimation method based on the combinations between the improved HF pulse signal injection method and two opposite current bias injection method. The crucial conclusions are summarized as follows. (1) Compared with available latest methods in reference, such as [23], the proposed improved HF pulse voltage signal injection method has an advantage of eliminating the filters, and also has a relatively high current control loop bandwidth. Moreover, the proposed method is more robust in magnetic polarity identification and has wider applicative situation.

(2) Compared with the conventional initial position detection method limited to standstill rotor mode, the proposed method can be suitable for free-running rotor application. (3) The inverter voltage error is offset by using two opposite pulse voltage signals in the improved HF pulse voltage signal injection method. (4) The effectiveness of the proposed initial position estimation method is verified through experimental results on a 1.5 kW IPMSM drive platform. Acknowledgments The authors are grateful to anonymous reviewers for their valuable comments and suggestions which help improve the quality of the paper. This work was supported by the Research Fund for the National Science Foundation of China (Grant no. 51707062) and the Key Research and Development Program of Hunan Province, China (2018GK2071). Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] Zheng Shiqi, Tang Xiaoqi, Song Bao, Lu Shaowu, Ye Bosheng. Stable adaptive PI control for permanent magnet synchronous motor drive based on improved JITL technique. ISA Trans 2013;52(5):539–49. [2] YingLuo, SiYiChen, YouGuoPi. PMSM sensorless control with separate control strategies and smooth switch from low speed to high speed. ISA Trans 2015;58:650–8. [3] Zhang BiTao, Pi YouGuo, Luo Ying. Fractional order sliding-mode control based on parameters auto-tuning for velocity control of permanent magnet synchronous motor. ISA Trans 2012;51(7):649–56. [4] Liu X, Zhang C, Li K, et al. Robust current control-based generalized predictive control with sliding mode disturbance compensation for PMSM drives. ISA Trans 2017;71(2):542–52. [5] Den Zhenhua, Shang Jing, Nian Xiaohong. Synchronization controller design of two coupling permanent magnet synchronous motors system with nonlinear constraints. ISA Trans 2018;1(1):1. [6] Robeischl E, Schroedl M. Optimized INFORM measurement sequence for sensorless PM synchronous motor drives with respect to minimum current distortion. IEEE Trans Ind Appl 2004;40(2):591–8.

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Please cite this article as: X. Wu, S. Huang, P. Liu et al., A reliable initial rotor position estimation method for sensorless control of interior permanent magnet synchronous motors. ISA Transactions (2019), https://doi.org/10.1016/j.isatra.2019.07.012.