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The Current Harmonics Elimination Control Strategy for Six-Leg Three-Phase Permanent Magnet Synchronous Motor Drives Jonq-Chin Hwang and Hsiao-Tse Wei

Abstract—This paper focuses on the analysis and development of low-current harmonics for a six-leg, three-phase inverter for permanent-magnet synchronous motor (PMSM) drives. Each phase of the PMSM is operating independently, the low-order harmonics appear in the back electromotive forces (EMFs) and currents. In this case, the standard vector control cannot handle the current harmonics. This harmonic enhances the current and causes the torque ripple. This paper presents a zero-axis current estimator auxiliary vector control method to compensate for three multiples of the voltage harmonic. This method can eliminate the zero-axis current. A prototype PMSM system was built using the TMS302F28335 digital signal processor. And the computer simulation and control method were completed. When the system operated at half load, the total harmonic distortion of current decreased from 20.89% to 4.42%. At full load, the total harmonic distortion of current decreased from 8.43% to 1.71%. Index Terms—Current harmonics elimination, six-leg, threephase permanent magnet synchronous motor, zero-sequence harmonic.

δ F q h , δF d h δah , δbh , δch ea , eb , ec εF Fm h fˆr ia , ib , ic ˆi0 m i0α i0β Ls Rs θr θˆ0 va , vb , vc v0∗

NOMENCLATURE Phase shifts of qd-axis signal from the hth harmonic. Phase shifts of each phase from the hth harmonic. Three-phase back EMFs of the motor. Imbalanced value projecting to the qd-axis. hth harmonic of the peak value. Angular frequency of the rotor. Three-phase currents of the stator. Peak current of zero-axis. Instantaneous sinusoidal current of zero-axis. Instantaneous cosine current of zero-axis. Equivalent inductance. Equivalent resistance of the stator. Angle of the rotor. Angle of instantaneous zero-axis current. Three-phase voltages of the stator. Commanded zero- axis voltage.

Manuscript received November 27, 2012; revised March 23, 2013 and May 25, 2013; accepted July 16, 2013. Date of current version January 29, 2014. Recommended for publication by Associate Editor J. Hur. The authors are with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan (e-mail: [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/TPEL.2013.2275194

I. INTRODUCTION HREE-PHASE motors generally use a three-leg inverter for the power circuit. When a phase of a motor breaks down, the system cannot form a circuit, and stops running. Many topologies have been proposed so far to improve the fault tolerance and stability of the motor. The topologies mentioned previously are as follows. 1). Delta connected three-phase motor: The Δ-connected topology is applicable to situations where the high rotational speed is required [1], [2]. With this topology, the hardware cost will not increase. Moreover, it still can run at single-phase open-circuit fault. However, the fault tolerance is relatively low. Moreover, the current flowing through the windings will interfere with each other. 2). The three-phase motor with redundant leg inverter: Generally speaking, there are two types of redundant leg inverter topologies. For the first type, the neutral point is connected to the redundant leg [3]. If one of the legs is faulted, the current can still flow through the neutral point to form a circulation. However, each phase voltage, phase current, line voltage, and line current will affect each other. For the second type, just like a Y-connected motor, the motor will not be able to operate normally since the neutral point is not connected to the windings [4], [5]. 3). Multiphase motors: Multi-phase motors have high fault-tolerance since it has more phases in terms of more circuit loops. Five-phase motors are illustrated from [6]–[8]. There still exists a circuit loop even if one group of MOSFETs and one motor windings are faulted. However, other windings still affect each other. As for six-phase motors, the topology can be seen as two groups of three-phase motor. Therefore, only one group of three-phase motor needs to be isolated in order for the system continuously to operate under faulted condition. Note that only half of the power will be outputted under faulted condition [9], [10]. The system proposed in this paper uses a six-leg, three-phase inverter for a PMSM [11], [12]. Connecting each winding to two separately controlled legs yields three dc–ac inverters. Accordingly, the potential difference of both ends of the dc power supply is the phase voltage. Assuming identical dc link is adopted in both types of inverters, the rotational speed of motor of the six√ leg, three-phase inverter is 3 times higher than the rotational speed of motor of the three-leg, three-phase inverter. In other words, the power density of the system can also be increased. Since there exists no neutral point in the topology of six-leg, three-phase system, both zero-axis current and zero-sequence harmonic cannot be coupled at the neutral point. Therefore, the zero-sequence harmonic will circulate through respective circuits, increasing the torque ripple. As a result, this paper

T

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HWANG AND WEI: CURRENT HARMONICS ELIMINATION CONTROL STRATEGY

focuses on developing a control strategy of eliminating harmonics in the six-leg, thee-phase topology under normal condition. Since the torque is influenced by both current and back EMF, the torque ripple is then produced due to the harmonic components of the current and the back EMF. Harmonics suppression is able to reduce the torque ripple and peak currents in terms of improving the system performance [13]. Harmonics causes include motor design, control strategy, dead-time, and other factors. In this paper, the control strategy which eliminates harmonics and reduced the torque ripple is categorized as follows. 1) Dead-time compensation [11], [14]–[17]: The purpose of dead-time compensation is to analyze the voltage distortion due to dead-time effects by using mathematical approaches such as the fast Fourier transform, so that the harmonic component of such voltage distortion can be obtained and eliminated by injecting equal-but-opposite harmonics. There are two approaches that can be implemented in software. The first approach is to perform the fast Fourier transform analysis with software and then rewrite the current command, so that it contains calculated harmonic components. The second approach is to analyze the harmonics with mathematical concepts and then write the related equations in the program. For the first approach, complicated calculation has to be done. For the second approach, outside interferences resulted from the operation of the system cannot be avoided. However, this approach is capable of calculating the harmonics due to dead-time effects precisely and minimizing the influence of dead-time effects. 2) Back EMF compensation and data records. From [18]–[22], they all share the same feature which requires data of torque or back EMF variances after a full rotation of the motor. Such variance will be injected into the command signal. This approach allows the user to create a table which is filled in experimental data and then write the program based on the data recorded. The program execution time is fast and no extra controller is required. However, this approach does not improve the resistance of outside interferences in terms of eliminating harmonics effectively. 3) Low harmonics voltage space vector pulse width modulation (VSVPWM) of multiphase [7], [8]: This approach expands the zero-sequence signal into a z1–z2 (x-axis and y-axis for zero domain) space and then combines the zero-sequence signal with qd-axis space vector so that the total sum of the zero-sequence signal becomes zero in the z1–z2 space. By doing so, the system is able to operate on the traditional vector control structure due to the improvement of the switch combinations of the VSVPWM. However, the switching control is more complicated and more switches are needed to eliminate the harmonic components. 4) Phase-shift-based synchronous modulation: Two sets of VSVPWM can be used in the six-leg, three-phase topology [12]. Make one set of VSVPWM phase shift so that zero-sequence harmonic can be eliminated after combining both sets of VSVPWM. This approach is easy to implement and no extra controller is required. However, the instantaneous interferences cannot be avoided while the system is operating. The method of calculation and control strategy for the processing of the current harmonics are complex, numerous, and difficult to achieve. Most controllers are proportional integral

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Fig. 1. System of six-leg, three-phase inverter for a permanent magnet synchronous motor.

controllers. This type of controller cannot deal with sinusoidal signals effectively. The implementation system is also prone to divergence, so the output signal contains harmonics caused by the controller. The harmonics of the current vary with different loads, requiring accurate calculation of real-time harmonic changes to avoid a large compensation that enhances the harmonic. Unbalanced contents and harmonics synthesis to the zeroaxis signal, which creates the zero-axis signal based on the third-harmonic distortion sinusoidal signal, increases the difficulty of handling harmonics. To deal with unbalanced loads, a power system must separate unbalanced contents (including harmonics). Using active or passive filters to compensate for this imbalance can eliminate the system harmonics [23]–[26]. This paper considers the six-leg, three-phase inverter unbalanced load, and uses the zero-axis current estimator to obtain the zero-axis instantaneous peak current and angle. The ac signal of the zero-axis is converted to approximate the dc signal. The zero-axis current regulator eliminates the zero-axis current. Then, it is possible to combine the zero-axis current regulator with vector control and this system can be implemented accordingly. This control method is simple and easy to implement. Fig. 1 shows the system of six-leg, three-phase inverter for a PMSM. The neutral point of winding of the three-phase motor is open, causing the voltage across the winding to be equal to the dc bus voltage. This paper discusses the harmonic of system and its torque ripple effect on the motor, and analyzes the control strategy using MATLAB/Simulink computer simulation software. A prototype and control strategy of system for PMSM were built based on a digital signal processor TMS302F28335. And the computer simulation and control method were completed to validate the feasibility of the control strategy.

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⎡

II. CURRENT HARMONICS AND TORQUE RIPPLE OF A PERMANENT SYNCHRONOUS MOTOR

−1

Tqrd0

The voltage equations of a three-phase PMSM can be expressed by d νa = Rs ia + Ls ia + ea dt d νb = Rs ib + Ls ib + eb dt d νc = Rs ic + Ls ic + ec dt

∞

(2)

fabc = Tqrd0 fqrd0 .

(3)

Fm h cos(hθr + δah )

fb = Fm 0 + Fm 1 cos(θr − 120 + δb1 ) Fm h cos[h(θr − 120◦ ) + δbh ]

(5)

h=2,3,...

fc = Fm 0 + Fm 1 cos(θr + 120◦ + δc1 ) ∞

Fm h cos[h(θr + 120◦ ) + δch ]

(6)

h=2,3,...

where fa , fb , and fc can be expressed as back EMFs or currents. Fm 0 is the dc component. Fm h is from the hth harmonic of the peak value. δah , δbh , and δch are the phase shifts of each phase from the hth harmonic. And θr is the angle of the rotor. Consider the coordinate transformation projection abc-axis to qd0-axis. The transformation matrix and inverse transform matrix are ⎡ ⎤ cos θr cos(θr − 120◦ ) cos(θr + 120◦ ) 2 Tqrd0 = ⎣ sin θr sin(θr − 120◦ ) sin(θr + 120◦ ) ⎦ (7) 3 1 1 1 2

2

(9) (10)

Each axis of the fundamental frequency and harmonics can be combined by superposition theorem. Therefore, it is possible to isolate the signal as positive, negative, and zero-sequence harmonics and other unbalanced coupling. This can be simplified to fqr = Fm 1 −

∞

Fm h cos[(h + 1)θr + δF q h ]+

h=3n −1 n =1,2,3,...

∞ h=3n +1 n =1,2,3,...

× Fm h cos[(h − 1)θr + δF q h ] +

∞

εF q h (hθr )

(11)

h> 1

fdr

∞

=0+

∞

Fm h sin[(h + 1)θr + δF d h ] −

h=3n −1 n =1,2,3,...

h=3n +1 n =1,2,3,...

× Fm h sin[(h − 1)θr + δF d h ] +

∞

εF d h (hθr )

(12)

h> 1

f0r = Fm 3 cos(3θr + δF 0 3 ) +

∞

Fm h cos[hθr + δF 0 h ]

h=3n n =2,3,4,...

+

∞

εF 0 h (hθr )

(13)

h> 1

◦

+

(8)

−1

(4) ∞

⎤ 1 1⎦. 1

Define the qd0-axis and abc-axis associated equations as fqrd0 = Tqrd0 fabc

h=2,3,...

+

sin θr sin(θr − 120◦ ) sin(θr + 120◦ )

(1)

where Rs is the equivalent resistance of the stator. Ls is the equivalent inductance of the stator. va , vb , and vc are the threephase voltages of the stator. ia , ib , and ic are the three-phase currents of the stator. ea , eb , and ec are the three-phase back EMFs of the motor. Even back EMF harmonics of the motor, caused by back EMF and the rotor flux symmetry, cancel each other out. Under the Y-connected motor, zero-sequence harmonics are negligible because they are coupled at the two ends of each phase [27]. Thus, it is only necessary to consider the odd harmonics of the positive sequence and negative sequence. Because the neutral point of the six-leg, three-phase inverter for a PMSM is open, the zero-sequence harmonics of the back EMFs still exist. Current harmonics are affected by magnet coercivity, the magnetization curve, and magnetic saturation. When the neutral point is open, the zero-sequence currents cannot be coupled, and flow in their respective circuits. Therefore, we need to consider the zero-sequence harmonic of each phase current. The relationship between back EMF and current of six-leg, three-phase inverter for a PMSM is as follows: fa = Fm 0 +Fm 1 cos(θr +δa1 ) +

cos θr = ⎣ cos(θr − 120◦ ) cos(θr + 120◦ )

2

where fqr is q-axis signal. fdr is d-axis signal. And δF q h , δF d h are the phase shifts of qd-axis signal from the hth harmonic. εF is an imbalanced value projecting to the qd-axis. The second terms in (11) and (12) are negative sequence harmonics. The third terms in (11) and (12) are positive sequence harmonics. The last term is an imbalanced value projecting to the qd-axis is a function that varies with angles. f0r is the zero-axis signal. The maximum amplitude in the zero-axis signal is the third harmonic. The third harmonic can be viewed as the fundamental wave of the zero-axis. The second term in (13) represents triple frequency harmonic content in addition to the outside of the third harmonic. The last term is the imbalanced value projecting to the zero-axis is a function that varies with angles. When the space vector has zero-sequence harmonic, the rotation trajectory is a 3-D surface whose radius is a combination of fqr , fdr , and f0r . By ignoring the influence of positive and negative sequence harmonics, the instantaneous radius of this surface varies with respect to rotor position. This equation from instantaneous radius of the surface is 2 2 (14) fm = fqr 2 + fdr + f0r .

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Fig. 3. Fig. 2. (Green Line) Only the currents or back EMFs exhibit third harmonics in the system and its torque response. (Blue Line) Currents or back EMFs both exhibit third harmonic in the system and its torque response. The third-harmonic of back EMF content is 10%. The third harmonic of the current content is 20%. The base is T e = 3 E2 ωmmI m .

The electromagnetic power and torque of the PMSM can be obtained using the back EMFs and currents Pe = ea ia + eb ib + ec ic Te =

Pe ωm

(15) (16)

where ωm is the mechanical angular velocity. Both equations show that the electromagnetic power affects the electromagnetic torque. Therefore, the power ripple causes vibration during motor operation. When back EMFs and currents have no harmonics, then the torque is constant. However, a motor that is running certainly has positive, negative, and zero-sequences harmonics and other unbalanced couplings. This paper analyzes how the torque response is affected by the zero-sequence harmonic and then eliminates the torque ripple. The zero-sequence harmonic is primarily affected by the third harmonic. Therefore, the third harmonic is the main object of analysis. While only the currents or back EMFs exhibit third harmonics in the system, the green line in Fig. 2 shows every degree of the torque variation. By observing the torque variation, the torque is not affected only if the back EMFs contains third harmonic. If the back EMFs and currents have a third harmonic, then both of them affect each other and produce the torque ripple. The blue line in Fig. 2 shows the analysis of the torque variation. In this case, the torque improves slightly. Frequency sextupling sinusoidal ripple appear in a cycle of electrical degree. Harmonics increase the injection peak current of the system, which in turn increases the copper loss of the motor, and reduces system efficiency. III. CURRENT HARMONICS ELIMINATION STRATEGY OF A SIX-LEG, THREE-PHASE INVERTER FOR A PERMANENT MAGNET SYNCHRONOUS MOTOR This section combines the proposed control strategy with standard vector control and applies this strategy to a six-leg, three-phase inverter for a PMSM. A zero-axis current regulator must be added to the standard vector control strategy to eliminate the zero-sequence harmonic. The zero-axis feedback signal is a sinusoidal signal whose fundamental frequency is identical to the frequency of the third harmonic. But using proportional integral controller to handle sinusoidal signal will cause this signal delay or phase shift. The optimal parameters of the

Peak current and angle of the zero-axis current estimator.

proportional integral controller are set at the ultimate oscillation. This oscillation is exactly the reciprocal signal of the fundamental signal of the third harmonic and thus cancelling out with each other. However, this control strategy working at a variable speed is not easy to design and must consider many variables. Therefore, the effect is not so obvious. This paper proposes a zero-axis current estimator which helps improve the control strategy. This zero-axis current estimator which consists of an all-pass filter, calculation of peak values of zero-axis signal, and calculation of angles of zero-axis is illustrated in Fig 3. This approach separates the zero-axis signal into a dc signal. It is simple to design the control parameters using this method. It can get the maximum utility to address step signal and step interference. First, ignore other signals outside the zero-axis of the basic wave. The signal of the first-order digital filter is staggered 90◦ . This digital filter transfer function is APF(S) =

u−s . s+u

(17)

This filter is retarded, allowing the signal to be 90◦ behind. u is 6π fˆr . This main zero-axis current is the third-harmonic signal. fˆr is the angular frequency of the rotor. The signal before and after the digital filter is as follows: i0α = I0 m sin(3θr + δ0 )

(18)

i0β = I0 m cos(3θr + δ0 ).

(19)

The peak value of zero-axis current can be analyzed from the aforementioned two equations ˆi0 m = ir0α2 + ir 2 . (20) 0β The angle of instantaneous zero-axis current is i0 −1 sin(3θr + δF 0 ) ˆ ˆ θ0 = 3θr + δ0 = tan = tan−1 α . cos(3θr + δF 0 ) i0 β (21) By using superposition theorem to sort out the zero-sequence fundamental signal outputted from the first-order filter and other signals, the equation can be rewritten as ˜0 (θˆ0 )] i0 = [ˆi0 m + ε˜0 (θˆ0 )] cos[θˆ0 + σ

(22)

Where ε˜0 is a function of instantaneous peak value which varies with respect to zero-axis angles and it can be also considered a instantaneous disturbance of peak values. σ ˜0 is a function of angles which varies with respect to zero-axis angle and can be also considered an instantaneous disturbance of an angle.

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Reorganizing the aforementioned equation makes it possible to design a new zero-axis current regulator v0∗m = G0 ◦ Δi0 m

(23)

where G0 means a zero-axis current regulator. “ ◦” means the operand of proportional controller and integral controller, and Δi0 m is the error of zero-axis peak current. The zero-axis current regulator includes a proportional controller and integral controller. The mathematical model is as follows: ki i 0 (24) G0 = kp i 0 + s kp i 0 is parameter of proportional controller for zero-axis. ki i 0 is parameter of integral controller for zero-axis. The design approach is kp

i0

= L0 ωc

ki

i0

=

Rs kp L0

i0 i0

(25) (26)

where ωc i 0 is the target bandwidth of the controller. L0 is the equivalent inductance of zero-axis, this L0 equal Ls + 2Lm . And Lm is the mutual inductance of stator. In this paper, the controller design adopts the method of pole-zero cancellation. The controller bandwidth is chosen to be 700 Hz. Moreover, the system is simulated by using MATLAB/Simulink, so that the response of the system can be observed. When the performance of the system is being evaluated, the system then can be tuned based on the parameters obtained from the simulations. The instantaneous zero-axis voltage signal can be computed from the output of zero-axis current regulator and the instantaneous angle from zero-axis current estimator v0∗ = v0∗m cos θˆ0 .

Fig. 4.

Proposed current harmonics elimination control strategy.

also falls to 0.04%. The remaining odd harmonics coupled to zero-axis are reduced as well. Fig. 5(d) shows the torque response, showing that the torque ripple amplitude ranging from 0.975 to 1.019 decreases to 0.983 to 1.0085 pu. Fig. 5(e) shows the zero-axis current response, showing that the current range from ± 0.183 pu decreases to ± 0.04 pu. The required peak current for the system decreases from 1.045 to 1.006 pu and gradually stabilizes. These results show that the proposed control strategy reduces the current harmonic distortion, suppresses torque ripple, and improves system efficiency.

(27)

Finally, the block diagram of the current harmonics elimination control strategy can be implemented by combining the vector control and zero-axis current regulator with the zero-axis current estimator. The block diagram of the current harmonics elimination control strategy is shown in Fig. 4. This paper uses computer simulations to verify the performance of the proposed current harmonics elimination control strategy. This computer simulations employed ideal conditions, and did not consider the nonideal and nonlinear effects (deadtime exhibited the most severe influences on the nonlinear distortion) occurring in actual system operations. Fig. 5 shows the steady state and its current response of six-leg, three-phase inverter with PMSM before and after using the current harmonics elimination control strategy. During the full-load operation, the third-harmonic increases the peak current which is higher than the rated current before adopting the current harmonics elimination control strategy. The left half of Fig. 5(a) shows the current in phase a before using the current harmonics elimination control strategy. The maximum harmonic distortion is the third harmonic at 20.44%. The ninth-harmonic distortion is 2.83%. The right half of Fig. 5(a) shows the current in phase a after using the current harmonics elimination control strategy. The peak current falls to rated current and its third-harmonic distortion decreases to 0.37%. The ninth-harmonic distortion

IV. EXPERIMENTAL RESULTS The experiments in this paper illustrate the harmonics elimination performance of the proposed control strategy. Figs. 6 and 7 show the experimental test before and after using the current harmonics elimination control strategy. Figs. 6(a) and 7(a) show the steady-state current in phase a of the system operating at full load. Before using the current harmonics elimination control strategy, the zero-sequence harmonic produces a peak current of more than 1 pu. The RMS value of the current Irm s−b is 1.00403 pu. After using the current harmonics elimination control strategy, the peak current falls to 1 pu. The RMS value of the current (Irm s−a ) is 1.0012 pu. The copper loss is reduced approximately by 0.78% at full load after the harmonics elimination strategy is adopted. Figs. 6(b) and 7(b) show the steady-state current in phase b of the system operating at full load. Figs. 6(c) and 7(c) show the steady-state current in phase c of the system operating at full load. Figs. 6(d) and 7(d) show the total harmonic distortion of the current in phase a. Before using the current harmonics elimination control strategy, the maximum harmonic distortion is the third harmonic at 4.324%. The ninth-harmonic distortion is 1.36%. After using the current harmonics elimination control strategy, the third-harmonic distortion decreases 0.83%. The ninth-harmonic distortion also falls to 0.39%. All the other coupled to zero-axis harmonics

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Fig. 5. Response before and after the simulation using the current harmonics elimination control strategy. (a) Current in phase a. (b) Total harmonic distortion of the current in phase a before using the current harmonics elimination control strategy. (c) Total harmonic distortion of the current in phase a after using the current harmonics elimination control strategy. (d) Electromagnetic torque. (e) Zero-axis current. (f) Required peak current for the system.

also decrease. Figs. 6(e) and 7(e) show the torque response. Before using the current harmonics elimination control strategy, the torque remains at approximately 1 pu and ripple range is approximately 0.06 pu. After using the current harmonics elimination control strategy, the torque is still approximately 1 pu and ripple range decreases to approximately 0.03 pu. Figs. 6(f)

Fig. 6. Experimental results of running at full load before using the current harmonics elimination control strategy. (a) Current in phase a. (b) Current in phase b. (c) Current in phase c. (d) Total harmonic distortion of the current in phase a before using the current harmonics elimination control strategy. (e) Electromagnetic torque. (f) Zero-axis current. (g) Required peak current for the system.

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Fig. 8. Experimental results of the system when an open fault occurred in the winding of phase c. (a) Three-phase currents of the stator. (b) Total harmonic distortion of the steady-state current in phase a after the phase c fault. (c) Zero-axis current. (d) Electromagnetic torque. (e) Mchanical angular velocity.

Fig. 7. Experimental results of running at full load after using the current harmonics elimination control strategy. (a) Current in phase a. (b) Current in phase b. (c) Current in phase c. (d) Total harmonic distortion of the current in phase a after using the current harmonics elimination control strategy. (e) Electromagnetic torque. (f) Zero-axis current. (g) Required peak current for the system.

and 7(f) show the zero-axis current from ± 0.05 pu decreases to ± 0.037 pu. Figs. 6(g) and 7(g) show the required peak current for the system fall from 1.142 pu to approximately 1.045 pu. The fault control in this paper directly excised the winding of phase c. Prior to the fault, this paper used a current harmonics elimination control strategy. After the fault occurred, the zero-axis current was affected by a three-phase imbalance. Thus, after the fault, the control strategy replaced the current harmonics elimination control strategy of this paper with general vector control. Fig. 8 indicates the actual test result of the

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TABLE I COMPARISON OF COMPUTER SIMULATION ANALYSIS AND EXPERIMENTAL RESULTS

system when an open fault occurred in the winding of phase c. Fig. 8(a) shows the three-phase current signals. After the fault, the current in phase c was zero. This type of three-phase imbalance generated a smaller current in phase a than in phase b. Because the mechanical angular velocity and the torque command were unchanged, the two-phase current must increase to share the energy of phase c. The steady-state peak current in phase a was approximately 1.122 pu, and the steady-state peak current in phase b was approximately 1.43 pu. Fig. 8(b) shows the analysis on the total harmonic distortion of the steady-state current after the phase c fault. The total harmonic distortion was 9.88%. Fig. 8(c) shows the zero-axis current signal. This steady-state current was approximately ± 0.393 pu. Fig. 8(d) shows the electromagnetic torque. After the phase c fault, the torque produces a fixed-frequency ripple. The ripple range after reaching a steady state was approximately 0.914 to 1.075 pu. Fig. 8(e) shows the mechanical angular velocity of the motor. After the fault, the mechanical angular velocity was affected by the torque and power ripples, causing the mechanical angular velocity to produce vibrations. The ripple range after achieving steady state was approximately between 0.962 and 1.073 pu. After the phase c fault also produced torque ripples, leading to vibration and noise in the motor. The experiments in this paper show that these control strategy help to reduce the harmonic distortion of zero-axis current, inhibit torque ripple, and reduce the peak current required for system. Therefore, these strategy increase system efficiency. Table I presents a summary of simulation analysis and experimental results. Finally, the six-leg, three-phase inverter for PMSM can still operate normally under fault condition by turning OFF the power MOSFETs corresponding to faulted windings. The torque and rotational speed are stable and it is clearly that this topology has high reliability.

V. CONCLUSION This paper discusses the reasons for harmonic generation with a six-leg, three-phase inverter for a PMSM. When the windings of each phase are independent, zero-sequence harmonic appear in both the back EMFs and currents. This mutual influence produces torque ripple, generating noise, and vibration when the motor is running. This paper combines vector control with zero-axis current regulator and zero-axis current estimator. The zero-axis current estimator calculates the instantaneous peak current of zero-axis and the instantaneous angle of zero-axis in real time. The calculated results obtained previously then can be used as the operating principle of the zero-axis current regulator. The major contributions of this paper are as follows: 1) The controller is easy to design: The fundamental frequency of the zero-sequence harmonic is the third harmonic. In this paper, the zero-sequence harmonic is decomposed into dc signal which allow the proportional integral controller to trace the command signal more effectively. By doing so, designing the parameters is much easier. 2) The adaptability of the system is high: Since the controller calculates the instantaneous peak current of zero-axis based on the instantaneous current feedback signal, it is capable of resisting interference or variances. 3) Harmonics suppression: A small amount of imbalanced component such as small differences of back EMF or current phase and amplitude between each phase will be projected to the zero-axis which leads to increasing the harmonics in the zero sequence. Such a small amount of imbalanced component is included in the instantaneous peak values of the current. Therefore, other harmonic components and imbalanced coupling can be cancelled out as well with zero-axis current regulator. 4) High fault-tolerance: When a winding experienced an open fault in a motor based on a six-leg, three-phase PMSM system framework, it can still operate with stability, retain control, and vibrate slightly.

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Finally, the feasibility of the control strategy is validated by using MATLAB/Simulink. Also, a digital signal processing device, TMS28335, is used as the control core to implement a six-leg, three-phase motor. REFERENCES [1] A. Sayed-Ahmed and N. A. O. Demerdash, “Fault-tolerant operation of delta-connected scalar- and vector-controlled AC motor drives,” IEEE Trans. Power Electron., vol. 27, no. 6, pp. 3041–3049, Jun. 2012. [2] A. Sayed-Ahmed, B. Mirafzal, and N. A. O. Demerdash, “Fault-tolerant technique for Δ-connected AC-motor drives,” IEEE Trans. Energy Convers., vol. 26, no. 2, pp. 646–653, Jun. 2011. [3] S. Bolognani, M. Zordan, and M. Zigliotto, “Experimental fault-tolerant control of a PMSM drive,” IEEE Trans. Ind. Electron., vol. 47, no. 1, pp. 1134–1141, Oct. 2000. [4] R. R. Errabelli and P. Mutschler, “Fault-tolerant voltage source inverter for permanent magnet drives,” IEEE Trans. Power Electron., vol. 27, no. 2, pp. 500–508, Feb. 2012. [5] Q. T. An, L. Z. Sun, K. Zhao, and Z. Sun, “Switching function modelbased fast-diagnostic method of open-switch faults in inverters without sensors,” IEEE Trans. Power Electron., vol. 26, no. 1, pp. 119–126, Jan. 2011. [6] A. Mohammadpour and L. Parsa, “A unified fault-tolerant current control approach for five-phase PM motors with trapezoidal back EMF under different stator winding connections,” IEEE Trans. Power Electron., vol. 28, no. 7, pp. 3517–3527, Jul. 2013. [7] F. Yu, X. F. Zhang, M. Z. Qiao, and C. D. Du, “The direct torque control of multiphase permanent magnet synchronous motor based on low harmonic space vector PWM,” in Proc. IEEE Int. Conf. Ind. Technol., 2008, pp. 1–5. [8] S. Xue, X. H. Wen, and Z. Feng, “Multiphase permanent magnet motor drive system based on a novel multiphase SVPWM,” in Proc. Int. Power Electron. Motion Control Conf., 2006, pp. 1–5. [9] T. J. Wang, F. Fang, X. S. Wu, and X. Y. Jiang, “Novel filter for stator harmonic currents reduction in six-step converter fed multiphase induction motor drives,” IEEE Trans. Power Electron., vol. 28, no. 1, pp. 498–506, Jan. 2013. [10] F. J. Lin, Y. J. Hung, J. C. Hwang, and M. T. Tsai, “Fault-tolerant control of a six-phase motor drive system using a Takagi–Sugeno–Kang type fuzzy neural network with asymmetric membership function,” IEEE Trans. Power Electron., vol. 28, no. 7, pp. 3357–3572, Jul. 2013. [11] C. B. Bae, Y. K. Kim, J. M. Kim, and H. C. Kim, “Vector control and harmonic ripple reduction with independent multi-phase PMSM,” in Proc. Int. Power Electron. Conf., 2010, pp. 1056–1063. [12] V. Oleschuk, A. Sizov, B. K. Bose, and A. M. Stankovic, “Phase-shiftbased synchronous modulation of dual inverters for an open-end winding motor drive with elimination of zero-sequence currents,” in Proc. Int. Conf. Power Electron. Drives Syst., 2005, vol. 1, pp. 325–330. [13] L. H. Hoang, P. Robert, and F. Rene, “Minimization of torque ripple in brushless DC motor drives,” IEEE Trans. Ind. Appl., vol. IA-22, no. 4, pp. 748–755, Jul. 1986. [14] N. Urasaki, T. Senjyu, K. Uezato, and T. Funabashi, “An adaptive deadtime compensation strategy for voltage source inverter fed motor drives,” IEEE Trans. Power Electron., vol. 20, no. 5, pp. 1150–1160, Sep. 2005. [15] S. Y. Kim and S. Y. Park, “Compensation of dead-time effects based on adaptive harmonic filtering in the vector-controlled ac motor drives,” IEEE Trans. Ind. Electron., vol. 54, no. 3, pp. 1768–1777, Jun. 2007. [16] A. R. Munoz and T. A. Lipo, “On-line dead-time compensation technique for open-loop PWM-VSI drives,” IEEE Trans. Power Electron., vol. 14, no. 4, pp. 683–689, Jul. 1999. [17] D. Leggate and R. Kerkman, “Pulse based dead-time compensator for PWM voltage inverters,” in Proc. IEEE Ind. Electron. Society Conf. Rec., 1995, pp. 474–481.

[18] P. Mattavelli, L. Tubiana, and M. Zigliotto, “Torque-ripple reduction in PM synchronous motor drives using repetitive current control,” IEEE Trans. Power Electron., vol. 20, no. 6, pp. 1423–1431, Nov. 2005. [19] H. Zhu, X. Xiao, and Y. D. Li, “Permanent magnet synchronous motor current ripple reduction with harmonic back EMF compensation,” in Proc. Int. Conf. Elect. Mach. Syst., 2010, pp. 1094–1097. [20] T. Nakai and H. Fujimoto, “Harmonic current suppression method of SPM motor based on repetitive perfect tracking control with speed variation,” in Proc. Annu. Conf. IEEE Ind. Electron., 2008, pp. 1210–1215. [21] N. Nakao and K. Akatsu, “A new control method for torque ripple compensation of permanent magnet motors,” in Proc. Int. Power Electron. Conf., 2010, pp. 1421–1427. [22] G. H. Lee, S. I. Kim, J. P. Hong, and J. H. Bahn, “Torque ripple reduction of interior permanent magnet synchronous motor using harmonic injected current,” IEEE Trans. Magn., vol. 44, no. 6, pp. 1582–1585, Jun. 2008. [23] R. L. De Araujo Ribeiro, C. C. De Azevedo, and R. M. De Sousa, “A robust adaptive control strategy of active power filters for power-factor correction, harmonic compensation, and balancing of nonlinear loads,” IEEE Trans. Power Electron., vol. 27, no. 2, pp. 718–730, Feb. 2012. [24] F. Bertling and S. Soter, “Improving grid voltage quality by decentral injection of current harmonics,” in Proc. IEEE Conf. Ind. Electron. Soc., 2005, pp. 2535–2537. [25] S. S. Kim, “Harmonic reference current generation for unbalanced nonlinear loads,” in Proc. IEEE Power Electron. Spec. Conf., 2003, vol. 2, pp. 773–778. [26] S. Kim, “Active zero-sequence cancellation technique in unbalanced commercial building power system,” in Proc. IEEE Appl. Power Electron. Conf. Exp., 2004, vol. 1, pp. 185–190. [27] D. Hanselman, Brushless Permanemt Magnet Motor Design, 2nd ed. Lebanon, Ohio: Magna Physics Pub, 2006.

Jonq-Chin Hwang received the B.S., M.S., and Ph.D. degrees in electrical engineering from National Taiwan University of Science and Technology, Taipei, Taiwan, in 1986, 1988, and 1997, respectively. He has been a member of the faculty at the National Taiwan University of Science and Technology, where he is currently an Associate Professor in the Department of Electrical Engineering. His teaching and research interests include electric machines, power electronics, ac motor control, and DSP-based control systems.

Hsiao-Tse Wei was born in Taipei, Taiwan, in 1982. He received the B.S. degree in electrical engineering from the China University of Science and Technology, Taipei, Taiwan, and the M.S. degree in electrical engineering from the National Taiwan University of Science and Technology, Taipei, Taiwan, in 2007 and 2009, respectively, where he is currently working toward the Ph.D. degree in electrical engineering His research interests include fault-tolerant control, harmonics elimination, ac motor control, and DSP-based control systems.

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 6, JUNE 2014

The Current Harmonics Elimination Control Strategy for Six-Leg Three-Phase Permanent Magnet Synchronous Motor Drives Jonq-Chin Hwang and Hsiao-Tse Wei

Abstract—This paper focuses on the analysis and development of low-current harmonics for a six-leg, three-phase inverter for permanent-magnet synchronous motor (PMSM) drives. Each phase of the PMSM is operating independently, the low-order harmonics appear in the back electromotive forces (EMFs) and currents. In this case, the standard vector control cannot handle the current harmonics. This harmonic enhances the current and causes the torque ripple. This paper presents a zero-axis current estimator auxiliary vector control method to compensate for three multiples of the voltage harmonic. This method can eliminate the zero-axis current. A prototype PMSM system was built using the TMS302F28335 digital signal processor. And the computer simulation and control method were completed. When the system operated at half load, the total harmonic distortion of current decreased from 20.89% to 4.42%. At full load, the total harmonic distortion of current decreased from 8.43% to 1.71%. Index Terms—Current harmonics elimination, six-leg, threephase permanent magnet synchronous motor, zero-sequence harmonic.

δ F q h , δF d h δah , δbh , δch ea , eb , ec εF Fm h fˆr ia , ib , ic ˆi0 m i0α i0β Ls Rs θr θˆ0 va , vb , vc v0∗

NOMENCLATURE Phase shifts of qd-axis signal from the hth harmonic. Phase shifts of each phase from the hth harmonic. Three-phase back EMFs of the motor. Imbalanced value projecting to the qd-axis. hth harmonic of the peak value. Angular frequency of the rotor. Three-phase currents of the stator. Peak current of zero-axis. Instantaneous sinusoidal current of zero-axis. Instantaneous cosine current of zero-axis. Equivalent inductance. Equivalent resistance of the stator. Angle of the rotor. Angle of instantaneous zero-axis current. Three-phase voltages of the stator. Commanded zero- axis voltage.

Manuscript received November 27, 2012; revised March 23, 2013 and May 25, 2013; accepted July 16, 2013. Date of current version January 29, 2014. Recommended for publication by Associate Editor J. Hur. The authors are with the Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan (e-mail: [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/TPEL.2013.2275194

I. INTRODUCTION HREE-PHASE motors generally use a three-leg inverter for the power circuit. When a phase of a motor breaks down, the system cannot form a circuit, and stops running. Many topologies have been proposed so far to improve the fault tolerance and stability of the motor. The topologies mentioned previously are as follows. 1). Delta connected three-phase motor: The Δ-connected topology is applicable to situations where the high rotational speed is required [1], [2]. With this topology, the hardware cost will not increase. Moreover, it still can run at single-phase open-circuit fault. However, the fault tolerance is relatively low. Moreover, the current flowing through the windings will interfere with each other. 2). The three-phase motor with redundant leg inverter: Generally speaking, there are two types of redundant leg inverter topologies. For the first type, the neutral point is connected to the redundant leg [3]. If one of the legs is faulted, the current can still flow through the neutral point to form a circulation. However, each phase voltage, phase current, line voltage, and line current will affect each other. For the second type, just like a Y-connected motor, the motor will not be able to operate normally since the neutral point is not connected to the windings [4], [5]. 3). Multiphase motors: Multi-phase motors have high fault-tolerance since it has more phases in terms of more circuit loops. Five-phase motors are illustrated from [6]–[8]. There still exists a circuit loop even if one group of MOSFETs and one motor windings are faulted. However, other windings still affect each other. As for six-phase motors, the topology can be seen as two groups of three-phase motor. Therefore, only one group of three-phase motor needs to be isolated in order for the system continuously to operate under faulted condition. Note that only half of the power will be outputted under faulted condition [9], [10]. The system proposed in this paper uses a six-leg, three-phase inverter for a PMSM [11], [12]. Connecting each winding to two separately controlled legs yields three dc–ac inverters. Accordingly, the potential difference of both ends of the dc power supply is the phase voltage. Assuming identical dc link is adopted in both types of inverters, the rotational speed of motor of the six√ leg, three-phase inverter is 3 times higher than the rotational speed of motor of the three-leg, three-phase inverter. In other words, the power density of the system can also be increased. Since there exists no neutral point in the topology of six-leg, three-phase system, both zero-axis current and zero-sequence harmonic cannot be coupled at the neutral point. Therefore, the zero-sequence harmonic will circulate through respective circuits, increasing the torque ripple. As a result, this paper

T

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HWANG AND WEI: CURRENT HARMONICS ELIMINATION CONTROL STRATEGY

focuses on developing a control strategy of eliminating harmonics in the six-leg, thee-phase topology under normal condition. Since the torque is influenced by both current and back EMF, the torque ripple is then produced due to the harmonic components of the current and the back EMF. Harmonics suppression is able to reduce the torque ripple and peak currents in terms of improving the system performance [13]. Harmonics causes include motor design, control strategy, dead-time, and other factors. In this paper, the control strategy which eliminates harmonics and reduced the torque ripple is categorized as follows. 1) Dead-time compensation [11], [14]–[17]: The purpose of dead-time compensation is to analyze the voltage distortion due to dead-time effects by using mathematical approaches such as the fast Fourier transform, so that the harmonic component of such voltage distortion can be obtained and eliminated by injecting equal-but-opposite harmonics. There are two approaches that can be implemented in software. The first approach is to perform the fast Fourier transform analysis with software and then rewrite the current command, so that it contains calculated harmonic components. The second approach is to analyze the harmonics with mathematical concepts and then write the related equations in the program. For the first approach, complicated calculation has to be done. For the second approach, outside interferences resulted from the operation of the system cannot be avoided. However, this approach is capable of calculating the harmonics due to dead-time effects precisely and minimizing the influence of dead-time effects. 2) Back EMF compensation and data records. From [18]–[22], they all share the same feature which requires data of torque or back EMF variances after a full rotation of the motor. Such variance will be injected into the command signal. This approach allows the user to create a table which is filled in experimental data and then write the program based on the data recorded. The program execution time is fast and no extra controller is required. However, this approach does not improve the resistance of outside interferences in terms of eliminating harmonics effectively. 3) Low harmonics voltage space vector pulse width modulation (VSVPWM) of multiphase [7], [8]: This approach expands the zero-sequence signal into a z1–z2 (x-axis and y-axis for zero domain) space and then combines the zero-sequence signal with qd-axis space vector so that the total sum of the zero-sequence signal becomes zero in the z1–z2 space. By doing so, the system is able to operate on the traditional vector control structure due to the improvement of the switch combinations of the VSVPWM. However, the switching control is more complicated and more switches are needed to eliminate the harmonic components. 4) Phase-shift-based synchronous modulation: Two sets of VSVPWM can be used in the six-leg, three-phase topology [12]. Make one set of VSVPWM phase shift so that zero-sequence harmonic can be eliminated after combining both sets of VSVPWM. This approach is easy to implement and no extra controller is required. However, the instantaneous interferences cannot be avoided while the system is operating. The method of calculation and control strategy for the processing of the current harmonics are complex, numerous, and difficult to achieve. Most controllers are proportional integral

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Fig. 1. System of six-leg, three-phase inverter for a permanent magnet synchronous motor.

controllers. This type of controller cannot deal with sinusoidal signals effectively. The implementation system is also prone to divergence, so the output signal contains harmonics caused by the controller. The harmonics of the current vary with different loads, requiring accurate calculation of real-time harmonic changes to avoid a large compensation that enhances the harmonic. Unbalanced contents and harmonics synthesis to the zeroaxis signal, which creates the zero-axis signal based on the third-harmonic distortion sinusoidal signal, increases the difficulty of handling harmonics. To deal with unbalanced loads, a power system must separate unbalanced contents (including harmonics). Using active or passive filters to compensate for this imbalance can eliminate the system harmonics [23]–[26]. This paper considers the six-leg, three-phase inverter unbalanced load, and uses the zero-axis current estimator to obtain the zero-axis instantaneous peak current and angle. The ac signal of the zero-axis is converted to approximate the dc signal. The zero-axis current regulator eliminates the zero-axis current. Then, it is possible to combine the zero-axis current regulator with vector control and this system can be implemented accordingly. This control method is simple and easy to implement. Fig. 1 shows the system of six-leg, three-phase inverter for a PMSM. The neutral point of winding of the three-phase motor is open, causing the voltage across the winding to be equal to the dc bus voltage. This paper discusses the harmonic of system and its torque ripple effect on the motor, and analyzes the control strategy using MATLAB/Simulink computer simulation software. A prototype and control strategy of system for PMSM were built based on a digital signal processor TMS302F28335. And the computer simulation and control method were completed to validate the feasibility of the control strategy.

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⎡

II. CURRENT HARMONICS AND TORQUE RIPPLE OF A PERMANENT SYNCHRONOUS MOTOR

−1

Tqrd0

The voltage equations of a three-phase PMSM can be expressed by d νa = Rs ia + Ls ia + ea dt d νb = Rs ib + Ls ib + eb dt d νc = Rs ic + Ls ic + ec dt

∞

(2)

fabc = Tqrd0 fqrd0 .

(3)

Fm h cos(hθr + δah )

fb = Fm 0 + Fm 1 cos(θr − 120 + δb1 ) Fm h cos[h(θr − 120◦ ) + δbh ]

(5)

h=2,3,...

fc = Fm 0 + Fm 1 cos(θr + 120◦ + δc1 ) ∞

Fm h cos[h(θr + 120◦ ) + δch ]

(6)

h=2,3,...

where fa , fb , and fc can be expressed as back EMFs or currents. Fm 0 is the dc component. Fm h is from the hth harmonic of the peak value. δah , δbh , and δch are the phase shifts of each phase from the hth harmonic. And θr is the angle of the rotor. Consider the coordinate transformation projection abc-axis to qd0-axis. The transformation matrix and inverse transform matrix are ⎡ ⎤ cos θr cos(θr − 120◦ ) cos(θr + 120◦ ) 2 Tqrd0 = ⎣ sin θr sin(θr − 120◦ ) sin(θr + 120◦ ) ⎦ (7) 3 1 1 1 2

2

(9) (10)

Each axis of the fundamental frequency and harmonics can be combined by superposition theorem. Therefore, it is possible to isolate the signal as positive, negative, and zero-sequence harmonics and other unbalanced coupling. This can be simplified to fqr = Fm 1 −

∞

Fm h cos[(h + 1)θr + δF q h ]+

h=3n −1 n =1,2,3,...

∞ h=3n +1 n =1,2,3,...

× Fm h cos[(h − 1)θr + δF q h ] +

∞

εF q h (hθr )

(11)

h> 1

fdr

∞

=0+

∞

Fm h sin[(h + 1)θr + δF d h ] −

h=3n −1 n =1,2,3,...

h=3n +1 n =1,2,3,...

× Fm h sin[(h − 1)θr + δF d h ] +

∞

εF d h (hθr )

(12)

h> 1

f0r = Fm 3 cos(3θr + δF 0 3 ) +

∞

Fm h cos[hθr + δF 0 h ]

h=3n n =2,3,4,...

+

∞

εF 0 h (hθr )

(13)

h> 1

◦

+

(8)

−1

(4) ∞

⎤ 1 1⎦. 1

Define the qd0-axis and abc-axis associated equations as fqrd0 = Tqrd0 fabc

h=2,3,...

+

sin θr sin(θr − 120◦ ) sin(θr + 120◦ )

(1)

where Rs is the equivalent resistance of the stator. Ls is the equivalent inductance of the stator. va , vb , and vc are the threephase voltages of the stator. ia , ib , and ic are the three-phase currents of the stator. ea , eb , and ec are the three-phase back EMFs of the motor. Even back EMF harmonics of the motor, caused by back EMF and the rotor flux symmetry, cancel each other out. Under the Y-connected motor, zero-sequence harmonics are negligible because they are coupled at the two ends of each phase [27]. Thus, it is only necessary to consider the odd harmonics of the positive sequence and negative sequence. Because the neutral point of the six-leg, three-phase inverter for a PMSM is open, the zero-sequence harmonics of the back EMFs still exist. Current harmonics are affected by magnet coercivity, the magnetization curve, and magnetic saturation. When the neutral point is open, the zero-sequence currents cannot be coupled, and flow in their respective circuits. Therefore, we need to consider the zero-sequence harmonic of each phase current. The relationship between back EMF and current of six-leg, three-phase inverter for a PMSM is as follows: fa = Fm 0 +Fm 1 cos(θr +δa1 ) +

cos θr = ⎣ cos(θr − 120◦ ) cos(θr + 120◦ )

2

where fqr is q-axis signal. fdr is d-axis signal. And δF q h , δF d h are the phase shifts of qd-axis signal from the hth harmonic. εF is an imbalanced value projecting to the qd-axis. The second terms in (11) and (12) are negative sequence harmonics. The third terms in (11) and (12) are positive sequence harmonics. The last term is an imbalanced value projecting to the qd-axis is a function that varies with angles. f0r is the zero-axis signal. The maximum amplitude in the zero-axis signal is the third harmonic. The third harmonic can be viewed as the fundamental wave of the zero-axis. The second term in (13) represents triple frequency harmonic content in addition to the outside of the third harmonic. The last term is the imbalanced value projecting to the zero-axis is a function that varies with angles. When the space vector has zero-sequence harmonic, the rotation trajectory is a 3-D surface whose radius is a combination of fqr , fdr , and f0r . By ignoring the influence of positive and negative sequence harmonics, the instantaneous radius of this surface varies with respect to rotor position. This equation from instantaneous radius of the surface is 2 2 (14) fm = fqr 2 + fdr + f0r .

HWANG AND WEI: CURRENT HARMONICS ELIMINATION CONTROL STRATEGY

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Fig. 3. Fig. 2. (Green Line) Only the currents or back EMFs exhibit third harmonics in the system and its torque response. (Blue Line) Currents or back EMFs both exhibit third harmonic in the system and its torque response. The third-harmonic of back EMF content is 10%. The third harmonic of the current content is 20%. The base is T e = 3 E2 ωmmI m .

The electromagnetic power and torque of the PMSM can be obtained using the back EMFs and currents Pe = ea ia + eb ib + ec ic Te =

Pe ωm

(15) (16)

where ωm is the mechanical angular velocity. Both equations show that the electromagnetic power affects the electromagnetic torque. Therefore, the power ripple causes vibration during motor operation. When back EMFs and currents have no harmonics, then the torque is constant. However, a motor that is running certainly has positive, negative, and zero-sequences harmonics and other unbalanced couplings. This paper analyzes how the torque response is affected by the zero-sequence harmonic and then eliminates the torque ripple. The zero-sequence harmonic is primarily affected by the third harmonic. Therefore, the third harmonic is the main object of analysis. While only the currents or back EMFs exhibit third harmonics in the system, the green line in Fig. 2 shows every degree of the torque variation. By observing the torque variation, the torque is not affected only if the back EMFs contains third harmonic. If the back EMFs and currents have a third harmonic, then both of them affect each other and produce the torque ripple. The blue line in Fig. 2 shows the analysis of the torque variation. In this case, the torque improves slightly. Frequency sextupling sinusoidal ripple appear in a cycle of electrical degree. Harmonics increase the injection peak current of the system, which in turn increases the copper loss of the motor, and reduces system efficiency. III. CURRENT HARMONICS ELIMINATION STRATEGY OF A SIX-LEG, THREE-PHASE INVERTER FOR A PERMANENT MAGNET SYNCHRONOUS MOTOR This section combines the proposed control strategy with standard vector control and applies this strategy to a six-leg, three-phase inverter for a PMSM. A zero-axis current regulator must be added to the standard vector control strategy to eliminate the zero-sequence harmonic. The zero-axis feedback signal is a sinusoidal signal whose fundamental frequency is identical to the frequency of the third harmonic. But using proportional integral controller to handle sinusoidal signal will cause this signal delay or phase shift. The optimal parameters of the

Peak current and angle of the zero-axis current estimator.

proportional integral controller are set at the ultimate oscillation. This oscillation is exactly the reciprocal signal of the fundamental signal of the third harmonic and thus cancelling out with each other. However, this control strategy working at a variable speed is not easy to design and must consider many variables. Therefore, the effect is not so obvious. This paper proposes a zero-axis current estimator which helps improve the control strategy. This zero-axis current estimator which consists of an all-pass filter, calculation of peak values of zero-axis signal, and calculation of angles of zero-axis is illustrated in Fig 3. This approach separates the zero-axis signal into a dc signal. It is simple to design the control parameters using this method. It can get the maximum utility to address step signal and step interference. First, ignore other signals outside the zero-axis of the basic wave. The signal of the first-order digital filter is staggered 90◦ . This digital filter transfer function is APF(S) =

u−s . s+u

(17)

This filter is retarded, allowing the signal to be 90◦ behind. u is 6π fˆr . This main zero-axis current is the third-harmonic signal. fˆr is the angular frequency of the rotor. The signal before and after the digital filter is as follows: i0α = I0 m sin(3θr + δ0 )

(18)

i0β = I0 m cos(3θr + δ0 ).

(19)

The peak value of zero-axis current can be analyzed from the aforementioned two equations ˆi0 m = ir0α2 + ir 2 . (20) 0β The angle of instantaneous zero-axis current is i0 −1 sin(3θr + δF 0 ) ˆ ˆ θ0 = 3θr + δ0 = tan = tan−1 α . cos(3θr + δF 0 ) i0 β (21) By using superposition theorem to sort out the zero-sequence fundamental signal outputted from the first-order filter and other signals, the equation can be rewritten as ˜0 (θˆ0 )] i0 = [ˆi0 m + ε˜0 (θˆ0 )] cos[θˆ0 + σ

(22)

Where ε˜0 is a function of instantaneous peak value which varies with respect to zero-axis angles and it can be also considered a instantaneous disturbance of peak values. σ ˜0 is a function of angles which varies with respect to zero-axis angle and can be also considered an instantaneous disturbance of an angle.

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 6, JUNE 2014

Reorganizing the aforementioned equation makes it possible to design a new zero-axis current regulator v0∗m = G0 ◦ Δi0 m

(23)

where G0 means a zero-axis current regulator. “ ◦” means the operand of proportional controller and integral controller, and Δi0 m is the error of zero-axis peak current. The zero-axis current regulator includes a proportional controller and integral controller. The mathematical model is as follows: ki i 0 (24) G0 = kp i 0 + s kp i 0 is parameter of proportional controller for zero-axis. ki i 0 is parameter of integral controller for zero-axis. The design approach is kp

i0

= L0 ωc

ki

i0

=

Rs kp L0

i0 i0

(25) (26)

where ωc i 0 is the target bandwidth of the controller. L0 is the equivalent inductance of zero-axis, this L0 equal Ls + 2Lm . And Lm is the mutual inductance of stator. In this paper, the controller design adopts the method of pole-zero cancellation. The controller bandwidth is chosen to be 700 Hz. Moreover, the system is simulated by using MATLAB/Simulink, so that the response of the system can be observed. When the performance of the system is being evaluated, the system then can be tuned based on the parameters obtained from the simulations. The instantaneous zero-axis voltage signal can be computed from the output of zero-axis current regulator and the instantaneous angle from zero-axis current estimator v0∗ = v0∗m cos θˆ0 .

Fig. 4.

Proposed current harmonics elimination control strategy.

also falls to 0.04%. The remaining odd harmonics coupled to zero-axis are reduced as well. Fig. 5(d) shows the torque response, showing that the torque ripple amplitude ranging from 0.975 to 1.019 decreases to 0.983 to 1.0085 pu. Fig. 5(e) shows the zero-axis current response, showing that the current range from ± 0.183 pu decreases to ± 0.04 pu. The required peak current for the system decreases from 1.045 to 1.006 pu and gradually stabilizes. These results show that the proposed control strategy reduces the current harmonic distortion, suppresses torque ripple, and improves system efficiency.

(27)

Finally, the block diagram of the current harmonics elimination control strategy can be implemented by combining the vector control and zero-axis current regulator with the zero-axis current estimator. The block diagram of the current harmonics elimination control strategy is shown in Fig. 4. This paper uses computer simulations to verify the performance of the proposed current harmonics elimination control strategy. This computer simulations employed ideal conditions, and did not consider the nonideal and nonlinear effects (deadtime exhibited the most severe influences on the nonlinear distortion) occurring in actual system operations. Fig. 5 shows the steady state and its current response of six-leg, three-phase inverter with PMSM before and after using the current harmonics elimination control strategy. During the full-load operation, the third-harmonic increases the peak current which is higher than the rated current before adopting the current harmonics elimination control strategy. The left half of Fig. 5(a) shows the current in phase a before using the current harmonics elimination control strategy. The maximum harmonic distortion is the third harmonic at 20.44%. The ninth-harmonic distortion is 2.83%. The right half of Fig. 5(a) shows the current in phase a after using the current harmonics elimination control strategy. The peak current falls to rated current and its third-harmonic distortion decreases to 0.37%. The ninth-harmonic distortion

IV. EXPERIMENTAL RESULTS The experiments in this paper illustrate the harmonics elimination performance of the proposed control strategy. Figs. 6 and 7 show the experimental test before and after using the current harmonics elimination control strategy. Figs. 6(a) and 7(a) show the steady-state current in phase a of the system operating at full load. Before using the current harmonics elimination control strategy, the zero-sequence harmonic produces a peak current of more than 1 pu. The RMS value of the current Irm s−b is 1.00403 pu. After using the current harmonics elimination control strategy, the peak current falls to 1 pu. The RMS value of the current (Irm s−a ) is 1.0012 pu. The copper loss is reduced approximately by 0.78% at full load after the harmonics elimination strategy is adopted. Figs. 6(b) and 7(b) show the steady-state current in phase b of the system operating at full load. Figs. 6(c) and 7(c) show the steady-state current in phase c of the system operating at full load. Figs. 6(d) and 7(d) show the total harmonic distortion of the current in phase a. Before using the current harmonics elimination control strategy, the maximum harmonic distortion is the third harmonic at 4.324%. The ninth-harmonic distortion is 1.36%. After using the current harmonics elimination control strategy, the third-harmonic distortion decreases 0.83%. The ninth-harmonic distortion also falls to 0.39%. All the other coupled to zero-axis harmonics

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Fig. 5. Response before and after the simulation using the current harmonics elimination control strategy. (a) Current in phase a. (b) Total harmonic distortion of the current in phase a before using the current harmonics elimination control strategy. (c) Total harmonic distortion of the current in phase a after using the current harmonics elimination control strategy. (d) Electromagnetic torque. (e) Zero-axis current. (f) Required peak current for the system.

also decrease. Figs. 6(e) and 7(e) show the torque response. Before using the current harmonics elimination control strategy, the torque remains at approximately 1 pu and ripple range is approximately 0.06 pu. After using the current harmonics elimination control strategy, the torque is still approximately 1 pu and ripple range decreases to approximately 0.03 pu. Figs. 6(f)

Fig. 6. Experimental results of running at full load before using the current harmonics elimination control strategy. (a) Current in phase a. (b) Current in phase b. (c) Current in phase c. (d) Total harmonic distortion of the current in phase a before using the current harmonics elimination control strategy. (e) Electromagnetic torque. (f) Zero-axis current. (g) Required peak current for the system.

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Fig. 8. Experimental results of the system when an open fault occurred in the winding of phase c. (a) Three-phase currents of the stator. (b) Total harmonic distortion of the steady-state current in phase a after the phase c fault. (c) Zero-axis current. (d) Electromagnetic torque. (e) Mchanical angular velocity.

Fig. 7. Experimental results of running at full load after using the current harmonics elimination control strategy. (a) Current in phase a. (b) Current in phase b. (c) Current in phase c. (d) Total harmonic distortion of the current in phase a after using the current harmonics elimination control strategy. (e) Electromagnetic torque. (f) Zero-axis current. (g) Required peak current for the system.

and 7(f) show the zero-axis current from ± 0.05 pu decreases to ± 0.037 pu. Figs. 6(g) and 7(g) show the required peak current for the system fall from 1.142 pu to approximately 1.045 pu. The fault control in this paper directly excised the winding of phase c. Prior to the fault, this paper used a current harmonics elimination control strategy. After the fault occurred, the zero-axis current was affected by a three-phase imbalance. Thus, after the fault, the control strategy replaced the current harmonics elimination control strategy of this paper with general vector control. Fig. 8 indicates the actual test result of the

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TABLE I COMPARISON OF COMPUTER SIMULATION ANALYSIS AND EXPERIMENTAL RESULTS

system when an open fault occurred in the winding of phase c. Fig. 8(a) shows the three-phase current signals. After the fault, the current in phase c was zero. This type of three-phase imbalance generated a smaller current in phase a than in phase b. Because the mechanical angular velocity and the torque command were unchanged, the two-phase current must increase to share the energy of phase c. The steady-state peak current in phase a was approximately 1.122 pu, and the steady-state peak current in phase b was approximately 1.43 pu. Fig. 8(b) shows the analysis on the total harmonic distortion of the steady-state current after the phase c fault. The total harmonic distortion was 9.88%. Fig. 8(c) shows the zero-axis current signal. This steady-state current was approximately ± 0.393 pu. Fig. 8(d) shows the electromagnetic torque. After the phase c fault, the torque produces a fixed-frequency ripple. The ripple range after reaching a steady state was approximately 0.914 to 1.075 pu. Fig. 8(e) shows the mechanical angular velocity of the motor. After the fault, the mechanical angular velocity was affected by the torque and power ripples, causing the mechanical angular velocity to produce vibrations. The ripple range after achieving steady state was approximately between 0.962 and 1.073 pu. After the phase c fault also produced torque ripples, leading to vibration and noise in the motor. The experiments in this paper show that these control strategy help to reduce the harmonic distortion of zero-axis current, inhibit torque ripple, and reduce the peak current required for system. Therefore, these strategy increase system efficiency. Table I presents a summary of simulation analysis and experimental results. Finally, the six-leg, three-phase inverter for PMSM can still operate normally under fault condition by turning OFF the power MOSFETs corresponding to faulted windings. The torque and rotational speed are stable and it is clearly that this topology has high reliability.

V. CONCLUSION This paper discusses the reasons for harmonic generation with a six-leg, three-phase inverter for a PMSM. When the windings of each phase are independent, zero-sequence harmonic appear in both the back EMFs and currents. This mutual influence produces torque ripple, generating noise, and vibration when the motor is running. This paper combines vector control with zero-axis current regulator and zero-axis current estimator. The zero-axis current estimator calculates the instantaneous peak current of zero-axis and the instantaneous angle of zero-axis in real time. The calculated results obtained previously then can be used as the operating principle of the zero-axis current regulator. The major contributions of this paper are as follows: 1) The controller is easy to design: The fundamental frequency of the zero-sequence harmonic is the third harmonic. In this paper, the zero-sequence harmonic is decomposed into dc signal which allow the proportional integral controller to trace the command signal more effectively. By doing so, designing the parameters is much easier. 2) The adaptability of the system is high: Since the controller calculates the instantaneous peak current of zero-axis based on the instantaneous current feedback signal, it is capable of resisting interference or variances. 3) Harmonics suppression: A small amount of imbalanced component such as small differences of back EMF or current phase and amplitude between each phase will be projected to the zero-axis which leads to increasing the harmonics in the zero sequence. Such a small amount of imbalanced component is included in the instantaneous peak values of the current. Therefore, other harmonic components and imbalanced coupling can be cancelled out as well with zero-axis current regulator. 4) High fault-tolerance: When a winding experienced an open fault in a motor based on a six-leg, three-phase PMSM system framework, it can still operate with stability, retain control, and vibrate slightly.

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Finally, the feasibility of the control strategy is validated by using MATLAB/Simulink. Also, a digital signal processing device, TMS28335, is used as the control core to implement a six-leg, three-phase motor. REFERENCES [1] A. Sayed-Ahmed and N. A. O. Demerdash, “Fault-tolerant operation of delta-connected scalar- and vector-controlled AC motor drives,” IEEE Trans. Power Electron., vol. 27, no. 6, pp. 3041–3049, Jun. 2012. [2] A. Sayed-Ahmed, B. Mirafzal, and N. A. O. Demerdash, “Fault-tolerant technique for Δ-connected AC-motor drives,” IEEE Trans. Energy Convers., vol. 26, no. 2, pp. 646–653, Jun. 2011. [3] S. Bolognani, M. Zordan, and M. Zigliotto, “Experimental fault-tolerant control of a PMSM drive,” IEEE Trans. Ind. Electron., vol. 47, no. 1, pp. 1134–1141, Oct. 2000. [4] R. R. Errabelli and P. Mutschler, “Fault-tolerant voltage source inverter for permanent magnet drives,” IEEE Trans. Power Electron., vol. 27, no. 2, pp. 500–508, Feb. 2012. [5] Q. T. An, L. Z. Sun, K. Zhao, and Z. Sun, “Switching function modelbased fast-diagnostic method of open-switch faults in inverters without sensors,” IEEE Trans. Power Electron., vol. 26, no. 1, pp. 119–126, Jan. 2011. [6] A. Mohammadpour and L. Parsa, “A unified fault-tolerant current control approach for five-phase PM motors with trapezoidal back EMF under different stator winding connections,” IEEE Trans. Power Electron., vol. 28, no. 7, pp. 3517–3527, Jul. 2013. [7] F. Yu, X. F. Zhang, M. Z. Qiao, and C. D. Du, “The direct torque control of multiphase permanent magnet synchronous motor based on low harmonic space vector PWM,” in Proc. IEEE Int. Conf. Ind. Technol., 2008, pp. 1–5. [8] S. Xue, X. H. Wen, and Z. Feng, “Multiphase permanent magnet motor drive system based on a novel multiphase SVPWM,” in Proc. Int. Power Electron. Motion Control Conf., 2006, pp. 1–5. [9] T. J. Wang, F. Fang, X. S. Wu, and X. Y. Jiang, “Novel filter for stator harmonic currents reduction in six-step converter fed multiphase induction motor drives,” IEEE Trans. Power Electron., vol. 28, no. 1, pp. 498–506, Jan. 2013. [10] F. J. Lin, Y. J. Hung, J. C. Hwang, and M. T. Tsai, “Fault-tolerant control of a six-phase motor drive system using a Takagi–Sugeno–Kang type fuzzy neural network with asymmetric membership function,” IEEE Trans. Power Electron., vol. 28, no. 7, pp. 3357–3572, Jul. 2013. [11] C. B. Bae, Y. K. Kim, J. M. Kim, and H. C. Kim, “Vector control and harmonic ripple reduction with independent multi-phase PMSM,” in Proc. Int. Power Electron. Conf., 2010, pp. 1056–1063. [12] V. Oleschuk, A. Sizov, B. K. Bose, and A. M. Stankovic, “Phase-shiftbased synchronous modulation of dual inverters for an open-end winding motor drive with elimination of zero-sequence currents,” in Proc. Int. Conf. Power Electron. Drives Syst., 2005, vol. 1, pp. 325–330. [13] L. H. Hoang, P. Robert, and F. Rene, “Minimization of torque ripple in brushless DC motor drives,” IEEE Trans. Ind. Appl., vol. IA-22, no. 4, pp. 748–755, Jul. 1986. [14] N. Urasaki, T. Senjyu, K. Uezato, and T. Funabashi, “An adaptive deadtime compensation strategy for voltage source inverter fed motor drives,” IEEE Trans. Power Electron., vol. 20, no. 5, pp. 1150–1160, Sep. 2005. [15] S. Y. Kim and S. Y. Park, “Compensation of dead-time effects based on adaptive harmonic filtering in the vector-controlled ac motor drives,” IEEE Trans. Ind. Electron., vol. 54, no. 3, pp. 1768–1777, Jun. 2007. [16] A. R. Munoz and T. A. Lipo, “On-line dead-time compensation technique for open-loop PWM-VSI drives,” IEEE Trans. Power Electron., vol. 14, no. 4, pp. 683–689, Jul. 1999. [17] D. Leggate and R. Kerkman, “Pulse based dead-time compensator for PWM voltage inverters,” in Proc. IEEE Ind. Electron. Society Conf. Rec., 1995, pp. 474–481.

[18] P. Mattavelli, L. Tubiana, and M. Zigliotto, “Torque-ripple reduction in PM synchronous motor drives using repetitive current control,” IEEE Trans. Power Electron., vol. 20, no. 6, pp. 1423–1431, Nov. 2005. [19] H. Zhu, X. Xiao, and Y. D. Li, “Permanent magnet synchronous motor current ripple reduction with harmonic back EMF compensation,” in Proc. Int. Conf. Elect. Mach. Syst., 2010, pp. 1094–1097. [20] T. Nakai and H. Fujimoto, “Harmonic current suppression method of SPM motor based on repetitive perfect tracking control with speed variation,” in Proc. Annu. Conf. IEEE Ind. Electron., 2008, pp. 1210–1215. [21] N. Nakao and K. Akatsu, “A new control method for torque ripple compensation of permanent magnet motors,” in Proc. Int. Power Electron. Conf., 2010, pp. 1421–1427. [22] G. H. Lee, S. I. Kim, J. P. Hong, and J. H. Bahn, “Torque ripple reduction of interior permanent magnet synchronous motor using harmonic injected current,” IEEE Trans. Magn., vol. 44, no. 6, pp. 1582–1585, Jun. 2008. [23] R. L. De Araujo Ribeiro, C. C. De Azevedo, and R. M. De Sousa, “A robust adaptive control strategy of active power filters for power-factor correction, harmonic compensation, and balancing of nonlinear loads,” IEEE Trans. Power Electron., vol. 27, no. 2, pp. 718–730, Feb. 2012. [24] F. Bertling and S. Soter, “Improving grid voltage quality by decentral injection of current harmonics,” in Proc. IEEE Conf. Ind. Electron. Soc., 2005, pp. 2535–2537. [25] S. S. Kim, “Harmonic reference current generation for unbalanced nonlinear loads,” in Proc. IEEE Power Electron. Spec. Conf., 2003, vol. 2, pp. 773–778. [26] S. Kim, “Active zero-sequence cancellation technique in unbalanced commercial building power system,” in Proc. IEEE Appl. Power Electron. Conf. Exp., 2004, vol. 1, pp. 185–190. [27] D. Hanselman, Brushless Permanemt Magnet Motor Design, 2nd ed. Lebanon, Ohio: Magna Physics Pub, 2006.

Jonq-Chin Hwang received the B.S., M.S., and Ph.D. degrees in electrical engineering from National Taiwan University of Science and Technology, Taipei, Taiwan, in 1986, 1988, and 1997, respectively. He has been a member of the faculty at the National Taiwan University of Science and Technology, where he is currently an Associate Professor in the Department of Electrical Engineering. His teaching and research interests include electric machines, power electronics, ac motor control, and DSP-based control systems.

Hsiao-Tse Wei was born in Taipei, Taiwan, in 1982. He received the B.S. degree in electrical engineering from the China University of Science and Technology, Taipei, Taiwan, and the M.S. degree in electrical engineering from the National Taiwan University of Science and Technology, Taipei, Taiwan, in 2007 and 2009, respectively, where he is currently working toward the Ph.D. degree in electrical engineering His research interests include fault-tolerant control, harmonics elimination, ac motor control, and DSP-based control systems.