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Permanent-Magnet Synchronous Motor of Electric Vehicles Based on Digital. Signal Processor. Bochao Du, Shaopeng Wu, Member, IEEE, Shouliang Han, and ...
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Interturn Fault Diagnosis Strategy for Interior Permanent-Magnet Synchronous Motor of Electric Vehicles Based on Digital Signal Processor Bochao Du, Shaopeng Wu, Member, IEEE, Shouliang Han, and Shumei Cui Abstract—An interturn short-circuit fault diagnosis strategy for the interior permanent-magnet synchronous motor (IPMSM) of an electric vehicle (EV) was presented. Online and offline detection methods were integrated into the diagnostic strategy to optimize diagnostic performance based on work cycle of an EV. An iterative form was used to reduce the computational load in online detection. It can be embedded into the control program of an inverter using no additional hardware. To improve the diagnostic performance, high-frequency voltage excitation was employed to amplify the fault information in offline detection. Good performance for a variety of work cycles was achieved by the integration of the two detection methods. Experiments were presented to verify the proposed diagnosis strategy. Index Terms—Electric vehicle (EV), fault diagnosis, interior permanent magnet synchronous motor (IPMSM), interturn fault.

N OMENCLATURE α, δ βd1 , βd2 βq1 , βq2 η ω ωi ψf ψa , ψb , ψc ψ3h ψαi , ψβi ε

Parameters of the fal function. Parameters of the extended state observer (ESO) along the d-axis. Parameters of the ESO along the q-axis. Ratio between the number of shorted turns and the total turns per phase. Fundamental frequency of the motor. Frequency of the injected high-frequency voltage. Amplitude of the fundamental component of the phase flux linkage. Flux linkages of each phase. Amplitude of the third harmonic component of the phase flux linkage. Flux linkages caused by the injected high-frequency voltage in the αβ frame. Estimated error of the ESO.

Manuscript received July 3, 2015; revised August 25, 2015; accepted September 22, 2015. Date of publication November 2, 2015; date of current version February 8, 2016. This work was supported by the Chinese National Key Technology R&D Program under Project 2013BAG05B00. (Corresponding author: Shaopeng Wu.) The authors are with the Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150080, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2015.2496900

εd , εq εd1 a(t) ed , e q eαi , eβi eαn1 , eβn1 eαn2 , eβn2 eα , eβ edf , eqf

ia , ib , ic if iαi , iβi iαi , iβi iγd iγ , i δ iγ , iδ id , iq if i Indexoff Indexon k Laa , Lbb , Lcc Ld , Lq Mab , Mac , Mbc p Rf Rs ua , ub , uc un uαi , uβi

Estimated errors of the ESOs along the dq frame. Total disturbance of the ESO along the d-axis. Bounded external disturbance of the ESO along the d-axis. Fault information estimated by the ESO. High-frequency disturbances caused by a fault. Fault information after the first filter. Fault information after the second filter. Fault information estimated by the ESO in the αβ frame. Extra components of the back electromotive force (EMF) under fault conditions. Phase currents. Interturn short circuit current. Response currents caused by the injected high-frequency voltage in the αβ frame. High-frequency extra response currents caused by a fault. Direct component of high-frequency response current along γ-axis. High-frequency response currents in the γδ frame. High-frequency response currents in the γδ frame under fault conditions. Currents in the dq frame. Interturn short-circuit current caused by the injected high-frequency voltage. Index for offline detection. Index for online detection. Parameter of the second-order generalized integrator (SOGI). Stator self-inductances of each phase. Inductances in the dq frame. Mutual inductance between two phases. Differential operator. Interturn short-circuit resistance. Phase stator resistance. Phase voltages. Neutral point voltage. Injected high-frequency voltages.

0278-0046 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

DU et al.: INTERTURN FAULT DIAGNOSIS STRATEGY FOR IPMSM OF EV

ud , uq Vi w0 wd , wq sgn(·)

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Voltages in the dq frame. Amplitude of the injected high-frequency voltage. Maximum of the external disturbance. Estimated disturbances in the dq frame. Sign function. I. I NTRODUCTION

I

NTERIOR permanent-magnet synchronous motors (IPMSMs) are now widely applied to hybrid and pure electric vehicle (EV) power trains primarily on account of their high-efficiency and high-power density [1]. However, IPMSM reliability is not satisfactory mainly because the high-current density may lead to numerous failures. Meanwhile, vehicle motor safety requirements have been rapidly increasing. The applications of electric drive systems based on the IPMSM are restricted due to the contradiction. The interturn short-circuit fault (ISCF) is a common fault that has interested researchers for many years [2], [3]. In addition to improving the reliability of the motor in the aspect of motor design [4], fault diagnosis is also an active method to reduce the probability of an ISCF. In general, fault diagnosis technology can be classified into two types: online and offline diagnosis methods. Compared with offline diagnosis, online diagnosis has been paid more attention to owing to its instantaneity. In terms of existing online diagnostic technologies, electrical signature analysis is still preferred for its convenience, especially in small- and medium-sized systems, even though vibration analysis is a reliable online method for multifault diagnosis [5], [6]. Good results have been obtained from some analytical methods such as frequency analysis [7]–[9] and time-frequency analysis [10]–[15]. Moreover, many new technologies have been introduced, including model-based faultdiagnosis algorithms [16]–[18], parameter identification [19]– [21], novel search coils [22], high-frequency (HF) injection [23], and intelligent algorithms [24], [25]. In general, additional devices, high computational performance, and large quantities of data storage are required in the above-mentioned methods. However, there exist some special features in motor fault-diagnosis systems of EV [26]. First, it is easier to analyze electric signals than vibration signals which will be disturbed by the random mechanical vibrations in a vehicle. Second, motor-drive-integrated fault-diagnosis systems in which additional hardware is not needed are the most attractive for vehicle applications because of the limitations of space and cost. Depending on the above demands, the online detection algorithm should be sufficiently simple to be executed by industrial microprocessors in real time. Therefore, iterative algorithms that can be easily integrated into the control program were preferred [27]. In [27] and [28], an iterative method based on the reference frame theory was proposed to analyze current harmonics. However, the effect of the analysis of current harmonics was weakened in closed-loop current control [18]. In [18], an observer based on a closed-loop control was designed to estimate the back EMF. Subsequently, EMF was substituted for the current as an analytical object. Although this method is

Fig. 1. Diagnostic system structure.

suitable for closed-loop control, it cannot distinguish an ISCF from other faults such as demagnetization. However, the simplification of algorithm inevitably sacrifices diagnostic performance. To overcome this defect, offline detection is supplemented to improve diagnostic performance. Furthermore, the offline method has potential application value owing to the intermittent operation of the EV drive system. In general, offline diagnostic results are better than online diagnostic results because the disturbances are minimized when the motor stops. In [26], an offline diagnostic method for the induction machine of EVs was proposed to address the security needs of an urban work cycle. However, for high-speed work cycles with few stoppages, there are few opportunities of offline detection to act, and the online method is still needed. Therefore, a mixed diagnostic strategy in which online and offline detection are integrated is a promising scheme for EVs. In this study, a strategy for diagnosing IPMSM ISCFs was proposed. The integration of online and offline detection takes full advantage of the EV work cycle to optimize the diagnostic performance. The entire algorithm can be embedded into the inverter processor to create an integrated drive-diagnosis system in which additional hardware is not needed. For online diagnosis, a fault characteristic and the relevant detection are proposed. The fault characteristic is the third harmonic of the back EMF, which is used to distinguish ISCFs from other faults. Moreover, this characteristic can be enhanced by the magnetic reluctance, and therefore, it is suitable for IPMSMs. For detection, a second-order ESO [29], [30] and a SOGI [31] were employed to form the iteration algorithm. The iterative form can effectively relieve the computational load. In addition, offline detection with high diagnostic performance is used to improve the accuracy of the diagnostic system. HF voltage excitation was employed to amplify the fault information in the offline detection, thereby obtaining more accurate diagnostic results. This paper is organized as follows. Section II presents the structure of a fault-diagnosis system. Section III describes the fault characteristics derived from the IPMSM model with interturn faults. Section IV provides details about the online detection algorithm, and Section V introduces the offline detection algorithm. In Section VI, experimental results are presented to validate the proposed methods. Conclusions are drawn in Section VII.

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Fig. 2. NEDC work cycle.

II. FAULT D IAGNOSIS S YSTEM S TRUCTURE Fig. 1 shows the structure of the fault diagnosis system. Online detection is performed during motor operation, while offline detection is performed at intermittent stops. The sensors and inverter processor are shared by drive and detection modules; accordingly, addition hardware is not required in the diagnostic system. Fig. 2 shows the new European driving cycle (NEDC) and suitable situations for the two detection schemes. For low-speed work cycles (0–800 s), offline detection is superior owing to its better performance, and its defect of real-time monitoring is covered by the frequent stops to some extent. For high-speed work cycles (longer than 800 s), the diagnostic system mainly is dependent on online detection. In the high-speed region, credible diagnostic results can be obtained by online detection, and the system demand for real-time monitoring is satisfied. Based on each respective advantage, the performance of the diagnostic system is improved for the overall work cycle. III. FAULT C HARACTERISTICS Fig. 3 illustrates a model of an IPMSM in which an ISCF occurs in the a phase. Compared to the healthy winding, part of winding a is short circuited by the resistance, Rf . Rf is used to model the interturn short circuit loop in the windings. The broken winding a is divided into two parts: 1) the healthy part a1 and 2) the faulty part a2 . The electrical equations of the IPMSM with ISCFs are expressed as follows [13]: d [uabcf ] = [R][iabcf ] + ([Labcf ][iabcf ] + [ψabcf ]) dt [uabcf ] = [ua − un , ub − un , uc − un , 0]T [iabcf ] = [ia , ib , ic , if ]T , [ψabcf ] = [ψa , ψb , ψc , ηψa ]T ⎤ ⎡ ηRs Rs 0 0 ⎥ ⎢ 0 Rs 0 0 ⎥ [Rabcf ] = ⎢ ⎦ ⎣ 0 0 Rs 0 ηRs 0 0 ηRs + Rf ⎡ ⎤ LAA MAB MAC ηLAA ⎢ MAB LBB MBC ηMAB ⎥ ⎥ [Labcf ] = ⎢ ⎣ MAC MBC LCC ηMAC ⎦ ηLAA ηMAB ηMAC η 2 LAA ⎧ ⎨ ψa = ψf cos θ + ψ3h cos 3θ ψb = ψf cos(θ − 2π/3) + ψ3h cos 3θ ⎩ ψc = ψf cos(θ + 2π/3) + ψ3h cos 3θ.

(1)

Fig. 3. Faulty machine windings.

Note that the balance at the neutral point is broken. Hence, the neutral-point voltage is not yet zero. In this study, un corresponds to the neutral-point voltage. Otherwise, the third harmonic of the permanent magnet (PM) flux linkage is taken into account. To facilitate the analysis, a modified Park transformation must be applied to transform the abcf variables into dq0f variables. The transformation matrix is ⎤ cos θ cos(θ − 23 π) cos(θ + 23 π) 0 2 ⎢ − sin θ − sin(θ − 23 π) − sin(θ + 23 π) 0 ⎥ ⎥. T = ⎢ 1 1 0⎦ 3 ⎣ 12 2 2 3 0 0 0 2 ⎡

(2)

By applying (2) to (1), the result is [udq0f ] dT −1 d[Labcf ] −1 + T = T [Rabcf ]T −1 +[Labcf ] [idq0f ] dt dt d[idq0f ] d[ψdq0f ] dT −1 + T [Labcf ]T −1 + +T [ψdq0f ] dt dt dt [udq0f ] = [ud , uq , −un , 0]T , [idq0f ] = [id , iq , 0, if ]T [ψdq0f ] = [ψf , 0, ψ3h cos 3θ, ηψa ]T .

(3)

After the transformation, the voltage equation is expressed in (4), and the expression for un is presented in (5)

ud uq − ωψf



=

Rs + pLd −ωLq ωLd Rs + pLq



id iq



e + df eqf



DU et al.: INTERTURN FAULT DIAGNOSIS STRATEGY FOR IPMSM OF EV

 2 Rs cos θif + Ld p(cos θif ) + ωLq sin θif η −Rs sin θif − Lq p(sin θif ) + ωLd cos θif 3 (4) d 1 1 un = − ηRs if − ηL0 if + 3ωψ3h sin 3θ. (5) 3 3 dt

edf eqf



=

For comparison, the voltage equation of the IPMSM without faults is

   ud Rs + pLd −ωLq id = . (6) uq − ωψf ωLd Rs + pLq iq Indeed, the fault-related information exists in edf and eqf . Their analytical expressions should be obtained. According to (1), the interturn short-circuit current if is simplified to if = −

η(ua − un ) . η(1 − η)Rs + Rf

(7)

(8)

According to (5)–(8), the steady-state solution for if is expressed as k2 u d + k1 u q k2 u q − k1 u d cos θ + sin θ k12 + k22 k12 + k22 9ωk1 ψ3h 3ωk2 ψ3h sin 3θ − 2 cos 3θ + 2 2 9k1 + k2 9k1 + k22 1 2 Rf k1 = ηωL0 , k2 = Rs − ηRs + . 3 3 η if = −

edf eqf

For fault diagnosis of vector control systems, the effect of the closed-loop control should be considered. In closed-loop control, a harmonic component exists in both the input voltage and response current. Conventional current analysis does not account for information on the input voltage; therefore, the diagnostic performance is degraded. In this study, by applying the ESO and SOGI, an algorithm is designed to integrate the information on the input voltage and response current. The proposed algorithm has an iterative structure and can, therefore, be executed on a microprocessor for real-time application. A. Design of Online Detection

(9)

According to the above analysis, edf and eqf are expressed in (10), shown at the bottom of the page. There are the dc component Ed , positive-sequence second harmonic E2hp , negative-sequence second harmonic E2hn , and fourth harmonic

E4h . E2hp represents the third harmonic, which is eliminated by the symmetric structure of the three-phase system under healthy conditions. Hence, E2hp actually reflects the degree of asymmetry of the windings. Compared to conventional negative-sequence components, the superiority of E2hp is its immunity to stray asymmetry. Therefore, in this study, E2hp is used as the indicator of the ISCF. Furthermore, the first part of E2hp in (10) is the main contribution of this study. E2hp contains two parts, one caused by the fundamental component (the first term of the expression for E2hp ); the other caused by the third harmonic of the PM flux linkage (the second and third terms of the expression for E2hp ). Generally, the fundamental component is much greater than the third harmonic. Therefore, E2hp is more suitable for an IPMSM than a surface-mounted PMSM. For a surface-mounted PMSM, the first part of E2hp does not exist because Ld = Lq IV. O NLINE FAULT D IAGNOSIS

Assuming that the IPMSM operates in the steady state, the speed is constant, and the input voltage is ideally symmetric. This means that ud , uq , and frequency ω are constants. The voltage of phase α is expressed as ua = ud cos θ − uq sin θ.

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The ESO [30], [31] is a nonlinear observer that is used to estimate disturbances. In this study, an ESO was introduced to estimate the back EMF. The ESOs were designed as follows: ⎧ εd = ˆid − id ⎪ ⎪ ⎨ ˆ˙ id = L1d (ωLq iq − Rs id + ud ) − βd1 f al(εd ) + wd (11) ⎪ ⎪ ⎩ w˙ d = −βd2 f al(εd ) ed = −Ld wd



= Ed + E2hp + E2hn + E4h  

1 edf d Rs sin ϕ + ωLq cos ϕ Ed = = ηIf eqf d Rs cos ϕ − ωLd sin ϕ 3



  

ηIf 3h cos(2θ+ϕ) ηRs If 3h cos(2θ+ϕ3h ) sin(2θ+ϕ3h ) cos(2θ+ϕ2hp ) ηIf E2hp = V2hp ω(Ld −Lq ) ω(Ld +Lq ) + = − sin(2θ+ϕ) sin(2θ+ϕ2hp ) sin(2θ+ϕ3h ) − cos(2θ+ϕ3h ) 2 3 2



 

 1 ηIf Rs sin(2θ+ϕ) ηIf cos(2θ+ϕ) sin(2θ+ϕ3h ) sin(2θ+ϕ2hn ) E2hn = V2hn ω(Ld +Lq ) − ηIf 3h ω(Ld −Lq ) =− + − sin(2θ+ϕ) cos(2θ+ϕ2hn ) cos(2θ+ϕ3h ) cos(2θ+ϕ) 3 6 6

    3 5 1 ed4h sin(4θ+ϕ3h ) sin(4θ + ϕ3h ) −Rs cos(4θ + ϕ3h ) E4h = + ω(Ld + Lq ) + ω(Lq − Ld ) = − ηIf 3h eq4h Rs sin(4θ + ϕ3h ) cos(4θ + ϕ3h ) − cos(4θ + ϕ3h ) 3 2 2  k2 u d + k1 u q k2 u q − k1 u d z2 z1 = − , z2 = , If = z12 + z22 , ϕ = π − arctan k12 + k22 k12 + k22 z1  9ωk1 ψ3h 3ωk2 ψ3h z 4 z3 = − 2 , z4 = 2 , If 3h = z32 + z42 , ϕ3h = π − arctan (10) 9k1 + k22 9k1 + k22 z3

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The Bode diagrams of the SOGI are presented in Fig. 5 for ω = 100π rad/s and k = 0.1. An algorithm for separating the positive- and negativesequence quantities is then expressed as [32] Hd (s)Eα (s) + Hq (s)Eβ (s) 2 Hd (s)Eβ (s) − Hq (s)Eα (s) Eβn (s) = 2

Eαn (s) = Fig. 4. Equivalent block diagram of the SOGI.

⎧ ⎪ εq = ˆiq − iq ⎪ ⎪ ⎨ ˆ˙ iq = L1q (−ωLd id − Rs iq + uq ) − βq1 f al(εq ) + wq . ⎪ wq = −βq2 f al(εq ) ⎪ ⎪ ⎩ eq = Lq w q (12) where fal is a nonlinear function, expressed as  α |ε| sgn(ε) |ε| > δ f al(ε) = ε |ε| ≤ δ. δ 1−α

(13)

(14)

By applying the inverse Park transformation, E2hn in (10) is transformed into the third harmonic Eαβ3h , and E2hp is transformed into the negative-sequence component Eαβn . Subsequently, an algorithm based on the SOGI is applied to extract Eαβn . Fig. 4 shows the equivalent block diagram of the SOGI. A signal v and frequency ω are required as inputs. Two orthogonal sine waves are generated as outputs (vd and vq ). vd traces the fundamental component of the input signal, and vq is phase-shifted with respect to the input signal by 90◦ . The SOGI cannot only abstract negative quantities, but also filter higher harmonics [31]. The transfer function of a SOGI is kωs vd (s) = 2 v s + kωs + ω 2 kω 2 vq Hq (s) = (s) = 2 v s + kωs + ω 2

where Eαn (s) and Eβn (s) are the transfer functions of the negative sequence components, while Eα (s) and Eβ (s) are the transfer functions for eα and eβ . B. Fault Judgment and Frequency Error Analysis

Note that ed and eq are the observed components of the back EMF. ed ≈ 0 and eq ≈ −ωψf when the motor is healthy, and ed ≈ edf and eq ≈ −ωψf − eqf , when an ISCF occurs. The stability criteria for the ESO are presented in the Appendix. To extract E2hp from the estimated back EMF, an inverse Park transformation is applied as follows:  

 cos θ − sin θ ed eα = eβ eq sin θ cos θ = Eαβ + Eαβn + Eαβ3h + E 

 edf d cos θ + (eqf d + ωψf ) sin θ Eαβ = edf d sin θ − (eqf d + ωψf ) cos θ 

cos(θ + ϕ2hp ) Eαβn = V2hp , − sin(θ + ϕ2hp ) 

sin(3θ + ϕ2hn ) Eαβ3h = V2hn − cos(3θ + ϕ2hn ) 

e cos θ + eq4h sin θ E  = d4h . ed4h sin θ − eq4h cos θ

(16)

Generally, there is a small frequency error Δω between the practical and input frequencies of an SOGI. Δω typically originates from the low-pass filter (LPF) of the speed sample, which is employed to eliminate random noise. Suppose that the input signal of SOGI vin is



 cos ωt sin ωt vin = A+ + A− . (17) sin ωt cos ωt Assuming also that the input frequency of the SOGI is ω  , the stable output vout is  

cos(ωt + ϕerr ) sin(ωt + ϕerr ) + H− A− vout = H+ A+ sin(ωt + ϕerr ) cos(ωt + ϕerr ) 2 l1 l1 = ω  −ω 2 , l2 = kωω  , ϕerr = arctan , Δω = ω−ω  l2    kω Δω kω (ω + ω ) H+ =  2 , H− =  2 . (18) 2 l1 + l22 2 l1 + l22 From (18), a positive-sequence component still exists on account of Δω. To solve this problem, a cascade filter structure consisting of two separations was introduced. The filter structure is illustrated in Fig. 6, where eαn1 and eβn1 are the response signals after the first separation, and eαn2 and eβn2 are the final response signals after the second separation. Finally, the square of the amplitudes of the negative-sequence components is used as the fault index, which is expressed as 2 . Indexon = e2αn2 + e2βn2 ≈ V2hp

(19)

For fault judgment, a threshold value is applied to eliminate the effects of disturbances. If Indexon is beyond the threshold, the diagnostic system determines that a fault has occurred. Fig. 6 shows a schematic diagram of the online diagnosis. C. Parameter Variation Analysis

Hd (s) =

(15)

where k is the damping factor. If k is increased, the dynamic response becomes slower, and the filter performance improves.

V22hp is approximately expressed as 2 V2hp ≈

η2 ω2 2 [If (Ld − Lq )2 + If23h (Ld + Lq )2 4 + 2If If 3h (L2d − L2q ) sin(ϕ − ϕ3h )].

(20)

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Fig. 5. Bode diagrams of the SOGI (ω = 100π rad/s and k = 0.1).

From (20), V22hp is proportional to ω 2 . Therefore, the diagnostic sensitivity is degraded as ω decreases. Furthermore, If and If 3h are also smaller when ω is decreased. These two factors lead to the insensitivity of online detection at low speed. Another influence originates from the variations in Ld and Lq . Generally, Ld and Lq decrease as the stator core is saturated, especially under overloaded conditions. Based on (20), V2hp is weakened by the parameter variation, and this feature is adverse to ISCF detection. To alleviate this adverse feature, in this study, Ld and Lq were set as constants measured by the offline test; they are written as Ld,s and Lq,s , respectively. In practice, Ld,s and Lq,s are greater than the actual parameters during motor operation. The reasons for these settings are as follows. Under healthy conditions, the estimated back EMF can be expressed as     ud + ωLq,s iq − Rs,s id ed,est = (21) eq,est uq − ωLd,s id − Rs,s iq and the estimated error is    

ed,est ed ω(Lq,s −Lq )iq −(Rs,s −Rs )id ederr = − = . eqerr eq,est eq ω(Ld −Ld,s )id −(Rs,s −Rs )iq (22) Note that the estimated error is a dc component and can be completely filtered by the separation algorithm in (16). Therefore, a misdiagnosis cannot be caused by the parameter variation. Under faulty conditions, it is difficult to obtain an analytical expression for the estimated error in the closed-loop system. To simplify the problem, an analysis is presented for an open-loop system, and the conclusions can be extended to the closed loop system. In an open-loop system, if Rs is ignored, the estimated fault characteristic component is

 ηIf cos(2θ + ϕ) ω(Ld,s − Lq,s ) E2hp,est = sin(2θ + ϕ) 2

 ηIf 3h sin(2θ + ϕ3h ) − ω(Ld,s + Lq,s ) . − cos(2θ + ϕ3h ) 2 (23)

Fig. 6. Schematic diagram of online diagnosis.

As the current is increased, the stator core becomes saturated. Thus, the following relationship exists: Ld,s − Lq,s > Ld − Lq , Ld,s + Lq,s > Ld + Lq .

(24)

Therefore, it is concluded that |V2hp,est | > |V2hp | .

(25)

This means that the estimated error can amplify the fault characteristic, and it is beneficial for diagnosis. In the closed-loop system, the current harmonics are restrained by the proportional–integral (PI) regulator; moreover, the fault information is partially transferred to the input voltage. Therefore, the amplification caused by parameter variation is weakened. However, the amplification still exists. In conclusion, it is rational to employ constants as the ESO parameters.

V. O FFLINE FAULT D IAGNOSIS A. Design of Offline Detection An HF voltage signal is employed to monitor the motor conditions. The HF voltage signal is used to amplify the imbalance in the windings to increase the diagnostic accuracy. The expression for the HF signal is 

uαi uβi



= Vi

 cos ωi t . sin ωi t

(26)

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If the motor is healthy, the voltage equations for the IPMSM in the αβ frame are

  

 uαi Rs 0 iαi ψαi = +p uβi iβi ψβi 0 Rs   

L − ΔL cos 2θ −ΔL sin 2θ iαi ψαi = ψβi iβi −ΔL sin 2θ L + ΔL cos 2θ Lq − Ld Ld + L q , ΔL = . (27) L= 2 2

Fig. 7. Schematic diagram of offline diagnosis.

When an HF voltage is injected, the stator resistance Rs can be ignored. Hence, the response currents ignoring Rs are    iαi I cos(ωi t − π2 ) + I1 cos(2θr − ωi t + π2 ) = 0 I0 sin(ωi t − π2 ) + I1 sin(2θr − ωi t + π2 ) iβi

  L ΔL Vi Vi , I1 = . (28) I0 = L2 − ΔL2 ωi L2 − ΔL2 ωi If the motor is faulty, a modified Clarke transformation must be applied to transform the abcf variables into αβ0f variables, as in (2). This transformation matrix is ⎡ −1 −1 ⎤ 1 2 2 0 √ √ ⎢ 2 ⎢ 0 23 23 0 ⎥ ⎥ (29) T = ⎢1 1 1 ⎥. 3⎣2 2 2 0⎦ 0 0 0 32 By applying (29) to (1), the voltage equations of the IPMSM with ISCFs in the standstill state are      uαi + eαi  iαi L − ΔL cos 2θ −ΔL sin 2θ p  = −ΔL sin 2θ L + ΔL cos 2θ uβi + eβi iβi  

 [L − ΔL cos 2θ] 2 eαi  pif i . (30) =− η eβi  3 −[ΔL sin 2θ]

Fig. 8. Platform of 3 kW IPMSM control system based on DSP. (a) Drivers with dc-bus connection. (b) Load test platform. TABLE I IPMSM PARAMETERS

The expression for ua is ua = Vi cos ωi t.

(31)

According to (5), (7), and (31), the solution of if i is if i = − k5 =

k2 V i k5 V i cos ωi t − 2 sin ωi t k52 + k22 k5 + k22

1 ηωi L0 . 3

(32)

When substituting (32) into (30), current responses iαi and under faulty conditions are expressed as       ηk1 Vi 2 Vi iαi iαi 2 kηk 2 +k 2 cos ωi t + k 2 +k 2 sin ωi t 5 2 5 2 . = + 3 iβi iβi 0 (33)

iβi

To facilitate observation, a rotating coordinate frame γδ is introduced at angular speed ωi to convert the positive-sequence component into a dc quantity. This transformation is 

cos ωi t sin ωi t . (34) Ti = e−jωt = − sin ωi t cos ωi t

Moreover, the response currents in the γδ frame under healthy conditions are 







   I1 cos 2θr − 2ωi t + π2  = Ti = −I0 + I1 sin 2θr − 2ωi t + π2 iδ iβi (35) and the response currents under faulty conditions are 

iγ iδ





iαi



 iγ = iδ   ηk2 Vi ηk5 Vi 2 Vi + kηk 2 2 cos 2ωi t + k 2 +k 2 sin 2ωi t 1 k52 +k22 5 +k2 5 2 . + ηk5 Vi ηk2 Vi 5 Vi 3 − kηk 2 +k 2 + k 2 +k 2 cos 2ωi t − k 2 +k 2 sin 2ωi t 5

2

5

2

5

2

(36)

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Fig. 9. Waveform of the no-load phase back EMF and relevant Fourier analysis results.

In comparing (35) with (36), it is obvious that there is a dc component along the γ-axis when the motor is faulty, which is zero under healthy conditions. Therefore, the fault index of the ISCF is designed as Indexoff = iγd

(37)

where iγd is the dc component of iγ , which can be obtained by an LPF. A threshold is then applied to diagnose the fault. Fig. 7 shows the process of abstracting the fault index. B. Sensitivity Analysis If the ISCF is slight, Rf is large, or η is very small; thus, k2 >> k5 , and Indexoff is approximately simplified as Indexoff ≈

η 2 Vi . Rf

TABLE II ISCF S ITUATIONS

(38)

According to (38), Indexoff is independent of the motor parameters and only dependent on the fault parameters and Vi . The detection sensitivity can improved by increase in Vi . However, Vi cannot be increased without limit when accounting for the maximum phase current and eddy-current loss of PM. Moreover, the injection frequency is also an important factor. Based on (28), the amplitude of the HF response current is determined by Vi and ωi . If a higher frequency is adopted, a higher Vi can be injected. The injection frequency is limited by the switching frequency of the IGBT. In practice, the frequency of the injection signal is usually no more than 1/10 of the switching frequency. VI. E XPERIMENTAL R ESULTS In the experiment, an IPMSM was connected to a voltage source inverter. The experimental platform is shown in Fig. 8. The IPMSM parameters are listed in Table I. Fig. 9 shows the waveform of the no-load phase back EMF of the IPMSM at the rated speed (500 rpm) and the Fourier analysis results. The fundamental wave amplitude was 147.1 V, and the third-harmonic amplitude was 14.6 V. The motor had a neutral-point lead and an ISCF lead in the middle of one phase. The fault intensity was changed by connecting two leads with various values of Rf . Therefore, the fault severity η was fixed at 0.5. Four fault situations were

adopted to simulate the different intensities of the ISCF. Table II lists the relationship between the fault situation and the value of Rf . A TMS320F28335 Texas Instruments Processor was adopted to execute the torque control program and diagnostic algorithm. A drive motor was mechanically coupled with the IPMSM to control the speed. The PWM switching frequency was 10 kHz. A. Online Diagnostic Results In this experiment, a simple id = 0 control strategy was adopted. Three iq reference values 2, 5, and 10 A were set to represent light, medium, and full loads, respectively. Three fault situations were considered in the online diagnostic experiments: slight, medium, and serious fault situations. The parameters of the ESOs were chosen using a trial-anderror approach. In this case, βd1 = βq1 = 1000, βd2 = βq2 = 20, 000, α = 0.5, and δ = 0.01. The values of k for all SOGIs were fixed at 0.1. Moreover, according to the detection results under healthy conditions, indicator Indexon was less than 0.1 at most operational points. Considering the disturbances caused by the dynamic process, the threshold was determined to be 0.2. Fig. 10 shows the experimental results for the estimated output versus the input of the ESOs. Based on these results, the estimated output traced the input, whether or not an ISCF occurred. Fig. 11 shows a comparison of eαn1 , eβn1 , eαn2 , eβn2 , and Indexon for the medium fault situation. As shown, the positive-sequence components still exist in eαn1 and eβn1 after the first separation based on the SOGI. In comparison, eαn2 and eβn2 approximated ideal waveforms after the second separation and could be used to detect faults. According to these results, the integration of the ESO and SOGI was effective for extracting the fault signals. Fig. 12 shows the diagnostic results for various values of iq . The figures on the left-hand side show the values of Indexon , and on the right-hand side show the partially magnified graphs used to compare Indexon and the threshold. It is evident that the detection worked well for a serious fault situation. However, the

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Fig. 10. Output waveforms of the ESOs, iq = 10 A. (a) Waveform for id . (b) Waveform for iq .

detection performance was obviously degraded for the medium fault situation. The diagnostic results were suspect when the speed was low (less than 150 rpm). Finally, the online detection failed in most regions (less than 350 rpm) for a slight fault situation, and the diagnostic results in the high-speed region were only reliable. Based on these results, it was concluded that the detection performance became worse as the speed was decreased. This conclusion is basically consistent with the theoretical analysis in Section IV. The experimental results for 1.5 times the overload under medium fault conditions are shown in Fig. 13. Indexon became smaller in the overloaded region at various speeds. The phenomena were also in agreement with the analysis in Section IV, and the performance of online detection was degraded under overloaded conditions to some extent. For the extreme condition of Ld = Lq , the online detection performance was minimized. Fig. 14 shows the response of Indexon when a fault suddenly occurred. The system diagnosed the fault after its emergence in ∼200 ms. This response time can generally satisfy the diagnostic demand of small- and medium-sized power motors and prevent catastrophic events in a timely manner.

B. Offline Diagnostic Results In the offline detection experiments, Vi was fixed at 30 V, and the frequency was the only adjustable parameter. Four frequencies, 200, 300, 400, and 500 Hz, were used in the experiments. The experiments were performed in three states: very slight, slight, and medium fault situations. Fig. 15 illustrates the results of the offline diagnosis at various frequencies. As shown in this figure, the increasing tendency of Indexoff was independent of the frequency variation and approximately inversely proportional to Rf , and it was in agreement with (38). Moreover, Indexoff under healthy conditions was determined by ωi . When ωi was low, Rs could not be completely ignored and generated a small dc component in iγ . As ωi increased, the dc component approached zero. Finally, the performance for offline detection was excellent. The

increase in Indexoff was sufficiently large to diagnose the fault, even for the very slight fault situation. In comparing the experimental results for online and offline detection, it was obvious that offline detection was better than online detection. Offline detection worked well, even for a very slight fault situation. In contrast, online detection works well only for a serious fault situation. Therefore, offline detection was an effective supplement to the entire diagnostic system. C. Risk Analysis Based on the theoretical analysis and experimental results, online detection was insensitive in low-speed and overloaded regions. Therefore, it was necessary to estimate the risk over the entire work cycle. According to the experimental results, it was assumed that online detection became insensitive when the speed was less than one-third of the rated speed. Subsequently, a simple EV configuration was introduced: a driving motor with a rated speed of 3000 rpm was connected to a wheel by a fixed-ratio gearbox. A motor speed of 1000 rpm corresponded to a vehicle speed of 20 km/h. Based on this configuration, the statistical motor speed information for various vehicle speed regions is listed in Table III. As shown in Table III, the unreliable time for online detection was approximately 17% of the entire work cycle. The unreliable time was somewhat different owing to the configuration and work cycle change. Generally, the unreliable time ranged from 10% to 30%; thus, it seemed that the risk was high. However, some favorable factors could reduce the risk. First, the design principle of the EV configuration was to reduce the low-speed operation time to increase the efficiency of the driving system. This was undoubtedly beneficial for online detection. Second, there are generally frequent stoppages in low-speed operation; therefore, the diagnostic performance was improved by the operation of offline detection. Finally, when the ISCF became serious, the diagnostic capability of online detection was recovered to a certain extent. Otherwise, the duration of the overload is generally not longer than 2 min. This means that insensitivity in the overloaded region was not

DU et al.: INTERTURN FAULT DIAGNOSIS STRATEGY FOR IPMSM OF EV

Fig. 11. Waveforms of eαn1 , eβn1 , eαn2 , eβn2 , and Indexon . (a) Speed = 300 r/min, and iq = 10 A. (b) Speed = 500 r/min and iq = 10 A.

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Fig. 15. Offline detection results for various HFs. TABLE III NEDC S TATISTICS

VII. C ONCLUSION

Fig. 12. Online detection results for various values of iq . (a) iq = 2 A. (b) iq = 5 A. (c) iq = 10 A.

An ISCF diagnostic strategy in which online and offline detection were integrated into IPMSM-based variable-speed drive systems for EVs was herein proposed. The method accounts for the hardware restrictions and can be embedded into the control program for real-time applications with no additional hardware. Although the online method was not able to detect the fault at low speed, the computational load was effectively reduced by its iterative algorithm and satisfactory results were achieved in the high-speed region. In addition, the drawback at low speed was overcome by offline detection. A fault can be timely detected owing to the high sensitivity of the offline method, even if it was very slight. Based on the integration of the two detection schemes, good performance was shown in diagnostic systems for various work cycles, and safety of EV was ensured. A PPENDIX

Fig. 13. Indexon under overloaded conditions: Rf = 5 Ω.

Fig. 14. Response of Indexon at 400 rpm: iq = 5 A with Rf = 5 Ω.

very serious. Therefore, the risk was within a reasonable range, and the diagnostic strategy satisfied the demands of EV drive systems.

According to (6) and (11), the ESO error along the d-axis is ⎧ ε = ˆid − id ⎪ ⎪ ⎨ d ε˙d = εd1 − βd1 f al(εd ) (A1) ⎪ ε˙d1 = a(t) − w˙ d = a(t) − βd2 f al(εd ) ⎪ ⎩ |a(t)| ≤ w0 where a(t) is the bounded external disturbance that is not greater than w0 . This is caused by measurement and parameter errors. Generally, a(t) ≈ 0, when the motor is healthy and operates in the steady state. In this study, the ESO stability was mainly discussed under the condition that a(t) = 0, whereas the error analysis was performed if a(t) = 0. A linear transformation was applied. The expressions are  z1 = εd (A2) z2 = εd1 − βd1 f al(εd ).

DU et al.: INTERTURN FAULT DIAGNOSIS STRATEGY FOR IPMSM OF EV

(A1) then can be equivalently transformed as  z˙1 = z2 z˙2 = a(t) − βd2 f al(z1 ) − βd1 z2 f al (z1 ) where f al (z1 ) is the derivative of f al(z1 ), which is  α−1 α|ε| |ε| > δ f al (ε) = 1 |ε| ≤ δ. 1−α δ From (A4), it can be easily found that f al (ε) > 0. The Lyapunov function is constructed as  z1 z2 V = βd2 f al(z1 )dz1 + 2 . 2 0

(A3)

(A4)

(A5)

The derivative of V is then V˙ = z2 (a(t) − βd1 z2 f al (z1 )).

(A6)

V˙ = −βd1 z22 f al (z1 )) < 0.

(A7)

If a(t) = 0,

Therefore, the system in (A3) is Lyapunov stable. If a(t) = 0, the system is still stable if z2 satisfies |z2 | >

a(t) . βd1 f al (z1 )

(A8)

When the condition in (A8) is not satisfied, a system error occurs. Suppose that the system has reached the equilibrium point; then, z2 = 0 and z˙2 = 0. From (A3), z1 is satisfied as a(t) = βd2 f al(z1 ).

(A9)

Assuming also that |a(t)| = w0 , the stable state error range of the system in (A3) is w0 a(t) . (A10) , |z2 | ≤ |z1 | ≤ f al−1 βd2 βd1 f al (z1 ) R EFERENCES [1] P. Zheng, J. Zhao, R. Liu, C. Tong, and Q. Wu, “Magnetic characteristics investigation of an axial-axial flux compound-structure PMSM used for HEVs,” IEEE Trans. Magn., vol. 46, no. 6, pp. 2191–2194, Jun. 2010. [2] R. M. Tallam, T. G. Habetler, and R. G. Harley, “Stator winding turnfault detection for closed-loop induction motor drives,” IEEE Trans. Ind. Appl., vol. 39, no. 3, pp. 720–724, May/Jun. 2003. [3] H. Henao et al., “Trends in fault diagnosis for electrical machines: A review of diagnostic techniques,” IEEE Ind. Electron. Mag., vo. 8, no. 2, pp. 31–42, Jun. 2014. [4] A. M. EL-Refaie, “Fractional-slot concentrated-windings synchronous permanent magnet machines: Opportunities and challenges,” IEEE Trans. Ind. Appl., vol. 57, no. 1, pp. 107–121, Jan./Feb. 2010. [5] X. Jin, M. Zhao, T. W. S. Chow, and M. Pecht, “Motor bearing fault diagnosis using trace ratio linear discriminant analysis,” IEEE Trans. Ind. Electron., vol. 61, no. 5, pp. 2441–2451, May 2014. [6] V. Climente-Alarcon, J. A. Antonino-Daviu, F. Vedreno-Santos, and R. Puche-Panadero, “Vibration transient detection of broken rotor bars by PSH sidebands,” IEEE Trans. Ind. Appl., vol. 49, no. 6, pp. 2576–2582, Nov./Dec. 2013. [7] M. E. H. Benbouzid, M. Vieira, and C. Theys, “Induction motors’ faults detection and localization using stator current advanced signal processing techniques,” IEEE Trans. Power Electron., vol. 14, no. 1, pp. 14–22, Jan. 1999.

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[28] S. M. A. Cruz, H. A. Toliyat, and A. J. M. Cardoso, “DSP implementation of the multiple reference frames theory for the diagnosis of stator faults in a DTC induction motor drive,” IEEE Trans. Energy Convers., vol. 20, no. 2, pp. 329–335, Jun. 2005. [29] J. Li, H. Ren, and Y. Zhong, “Robust speed control of induction motor drives using first-order auto-disturbance rejection controllers,” IEEE Trans. Ind. Appl., vol. 51, no. 1, pp. 712–720, Jan./Feb. 2015. [30] J. Han, “From PID to active disturbance rejection control,” IEEE Trans. Ind. Electron., vol. 56, no. 3, pp. 900–906, Mar. 2009. [31] J. Matas, M. Castilla, L. G. de Vicuña, J. Miret, and J. C. Vasquez, “Virtual impedance loop for droop-controlled single-phase parallel inverters using a second-order general-integrator scheme,” IEEE Trans. Power Electron., vol. 25, no. 12, pp. 2993–3002, Dec. 2010. [32] J. A. Suul, A. Luna, P. Rodriguez, and T. Undeland, “Voltage-sensor-less synchronization to unbalanced grids by frequency-adaptive virtual flux estimation,” IEEE Trans. Ind. Electron., vol. 59, no. 7, pp. 2910–2923, Jul. 2012.

Bochao Du was born in Heilongjiang Province, China, in 1986. He received the B.S. and M.S. degrees from Harbin Institute of Technology, Harbin, China, in 2009 and 2011, respectively, where he is currently working toward the Ph.D. degree in electrical engineering. His research interests include motor fault diagnosis and fault-tolerance operation, motor parameter estimation, power electronics, and motor drivers.

Shaopeng Wu (M’11) was born in Heilongjiang Province, China, in 1983. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Harbin Institute of Technology (HIT), Harbin, China, in 2005, 2008, and 2011, respectively. Currently, he is a Lecturer with HIT. He was a Visiting Scholar at the Wisconsin Electric Machines and Power Electronics Consortium– (WEMPEC), University of Wisconsin-Madison, Madison, WI, USA, from 2013 to 2014. His research interests include the design and control of special electric machines, research on multiphysical couplings, related technologies in the electromagnetic launch field, and research on wireless power transfer. Dr. Wu was the recipient of the Peter J. Kemmey Memorial Scholarship at the 15th International EML Symposium, Brussels, Belgium, in 2010.

Shouliang Han received the B.S., M.S., and Ph.D. degrees in electrical engineering from Harbin Institute of Technology, Harbin, China, in 2005, 2007, and 2015, respectively. Currently, he is a Postdoctoral Researcher with the School of Electrical Engineering and Automation at Harbin Institute of Technology. His research interests include design, finite-element modeling, and analysis of electrical machines and drives, particularly special electrical drive systems in EVs and HEVs.

Shumei Cui was born in Heilongjiang Province, China, in 1964. She received the Ph.D. degree in electrical engineering from Harbin Institute of Technology (HIT), Harbin, China, in 1998. She has been a Professor with the Department of Electrical Engineering, HIT, where she is currently the Vice Dean of the Institute of Electromagnetic and Electronic Technology and the Dean of the Electric Vehicle Research Centre. Her research interests include design and control of micro and special electric machines, electric drive systems of electric vehicles, control and simulation of hybrid electric vehicles, and intelligent test and fault diagnostics of electric machines. Prof. Cui serves as the Vice Director of the Micro and Special Electric Machine Committee and the Chinese Institute of Electronics, and a member of the Electric Vehicle Committee and the National Automotive Standardization Technical Committee.