Zero-Sequence Voltage Elimination for Dual-Fed Common DC-Link Open-End Winding PMSM High-Speed Starter–Generator—Part I: Modulation

In this paper, a dual-fed (DF) common dc-link topology open-end winding permanent magnet synchronous motor for aircraft high-speed starter–generator application is considered. While on one hand the common dc bus configuration significantly simplifies and reduces the costs of the topology, on the other hand it allows the zero-sequence current (ZSC) to flow freely in the system. High-speed machines are characterized by low phase inductance, which implies low zero-sequence impedance. A small time constant of the zero-sequence circuit produces a high-frequency, high-intensity ZSC ripple with the risk of harming the switching devices. This paper presents a novel hybrid space vector pulsewidth modulation that allows to instantaneously eliminate the zero-sequence voltage (ZSV) produced by the two voltage source converters (VSCs) by square wave modulating one of the two VSCs. The non-sinusoidal machine back electromotive force (EMF) has been considered and the effect of the converters’ dead time on the ZSV has been analyzed. The square-wave-modulated VSC uses insulated-gate bipolar transistor (IGBT) devices, whereas the other uses Silicon Carbide (SiC) technology. The proposed topology is tested through both simulations and experiments.


I. INTRODUCTION
The advantages of the OEW configuration for ac machines drives were already investigated in [1] showing how three-level inversion could be realized with two two-level inverters connected at each end of the machine. Furthermore the dual-fed OEW topology allows for increased fault-tolerant capability [2], [3], reduction of the dc-link voltage by half and redundant space-vector combinations. The dual-fed OEW configuration has found a wide range of applications such as wind power generation [4], [5], electric vehicles [6], [7], high power electric propulsion [8] and aircraft starter-generator systems [9]- [11]. Two isolated dc power supplies [12], one dc supply and a floating bridge [13] or a single dc supply [14] can be adopted for the dual-fed OEW. While on one hand the common dc bus configuration significantly simplifies and reduces the costs of the topology, on the other hand it allows the ZSC to flow freely in the system. As widely discussed in [4], [15] the causes of a circulating ZSC can be attributed to ZSV generated by the converters, third harmonic component of the back EMF, devices' DTs, device's voltage drops and coupling between the dq axes and the 0-axis when the machine second harmonics of the self and mutual inductance are not the same [16]. The magnitude of the ZSC depends on the equivalent ZSI which is generally low as reported in [17], [18].With a particularly low phase inductance, and consequently even smaller ZSI the equivalent zero sequence circuit is less able to filter out the high-frequency components of the switched voltage. In other words, a small time constant of the zero-sequence circuit produces a high frequency, high intensity current ripple with the risk of harming the switching devices. In this work an high speed machine characterized by a low phase inductance of 355µH is considered, which is significantly lower than the one considered in previous papers [19] [4] [20](respectively 8.5mH, 61.7mH and 17mH).
The more the machine inductance is low the more problems associated with the circulation of a ZSC are going to be enhanced leading to high intensity ZSC ripple. The ZSC reduces the overall system efficiency therefore many works focused on VSCs' modulations to reduce or eliminate the zerosequence component of the voltage supplied to the machine. In [17] a SVM that aims to set to zero the average ZSV produced by the two VSCs by zero vector time redistribution is proposed for an induction motor drive. In [19] a PMSM with perfectly sinusoidal back EMF is considered and a SVM where the average ZSV applied by the converters is zero is developed. In [16] a modulation which allows to provide a controllable ZSV component in order to synthesize the zerosequence controller output is proposed. Many works introduce modulations which allow to synthesize a reference ZSV in order to implement controllers that would allow to eliminate the ZSC flowing due to the machine's non-sinusoidal back-EMF. In [19] a PI regulator for the zero-axis in combination with a SVM where the average ZSV applied by the converters is zero is proposed. In order to better eliminate the sinusoidal ZSC a Proportional Resonant (PR) controller is implemented in [4], where the reference ZSV is synthesized by zero vector redistribution. Similarly, in [16] a frequency adaptive PR controller is used since the ZSC frequency changes according to the operating speed. In this paper a dual-fed common dclink topology OEW-PMSM for aircraft high speed Starter-Generator application is considered. SiC technology in combination with standard IGBT devices can be used to increase the system efficiency and drive the high speed machine as demonstrated in [10], [11]. The SiC devices can work at higher frequencies than the conventional IGBT with less switching losses. In this paper a modulation for the mixed technology dual-inverter is developed in order to exploit the different nature of the power devices and reduce the circulating ZSC. The focus of this work is to develop a modulation for the two VSCs that would allow to simultaneously exploit the different technologies and to eliminate the ZSV. Compared with previous works [16], [17], [19], the significantly lower ZSI does not allow to apply any ZSV. Therefore any type of zero-axis controller, such as PI or PR, cannot be implemented since a modulation that would produce a controllable ZSV cannot be used. The SVM proposed by the authors in [14] achieves instantaneous elimination of the ZSV applied by the two VSCs by square wave modulating one VSC and having the other working as an active filter in order to compensate for the distortion introduced by the first one and it is here experimentally validated. In addition the DT effect on the ZSV is considered and the analysis of its effect in conjunction with the modulation proposed is carried out. The square wave modulation allows for easy implementation of instantaneous elimination of the ZSV and allows to use different technologies for the two VSCs. Part I focuses on the analysis of the proposed modulation for instantaneous elimination of the ZSV produced by the dual-inverter. In Part II a novel strategy based on the VSCs' DT to eliminate the sinusoidal ZSC flowing due to the machine's back-EMF and achieve a satisfying phase current waveform is proposed based on the modulation presented in this paper.

II. OEW-PMSM MATHEMATICAL MODEL
The considered electrical system is a 3-phase, p-pole, PMSM [21] where the neutral point of the stator windings has been opened. The stator windings are identical sinusoidally distributed windings, displaced of 120 • with resistance R s . The magnetic axes of the stator windings are denoted by the as, bs and cs axes. The machine voltage and flux equations in the abc reference frame are reported in matrix form in (4) where the stator phase voltages V P M SM can be written as where V A and V B are the output voltages of the top an lower converter respectively. V aa , V bb and V cc are the OEW-PMSM phase voltages. I abc and λ abc are the phase currents and stator fluxes respectively. The rotor's permanent magnets flux linkage with the stator windings Λ r has been split in its fundamental Λ 1r and third harmonic component Λ 3r . Since a common dc-link topology has been chosen the zero-sequence circuit cannot be neglected, therefore the third harmonic back EMF has to be considered. R is a diagonal matrix with R s on the diagonal, L abc , Λ 1r and Λ 3r are reported in (1), (2) and (3) respectively. λ m is the peak flux linkage established by the rotor permanent magnets. k 3λ is defined as the ratio between the third harmonic flux and λ m . θ is the rotor angular position of the machine measured as the displacement of the quadrature axis (q) from the magnetic axis of phase as. The direct axis (d) is lagging of 90 • behind the q axis. Transforming the machine phase voltages equations (1) on the rotor synchronous reference frame the following system is obtained: ω e is the machine electrical speed, L q , L d and L 0 are the q, d and 0 axes inductances respectively. The relationship between L A , L B , L ls and the machine's inductances L q , L d and L 0 in the synchronous reference frame is reported in (9). The sum of the phase currents is no longer zero since a common dc-link DF OEW-PMSM topology has been chosen, therefore a ZSC i 0 is free to flow in the system.

A. Zero Sequence Equivalent Circuit
Whether the ZSC magnitude is acceptable it depends on the machine parameters (R s , L 0 and zero sequence back EMF) which could lead to high magnitude current ripple that could potentially harm the switching devices. The equivalent circuit of the zero-sequence axes can be derived from the third line of (6) and it is shown in Fig. 2, where V A 0 and V B 0 are generated by the VSCs and 3ω e λ m k 3λ cos(3θ) is generated by the third harmonic back EMF. The harmonic content of the machine flux often contains the third harmonic component therefore even if the VSCs' ZSV V A 0 − V B 0 would be cancelled the ZSC would still flow due to the third harmonic back EMF.

III. REFERENCE VOLTAGE GENERATION FOR THE DUAL-FED OEW-PMSM DRIVE
The duty cycles for the two VSCs are generated with the intention to keep instantaneously at zero the V P M SM 0 and to exploit the different nature of the two technologies used, IGBT and SiC devices. The voltage on the OEW-PMSM can be expressed as the difference between the VSC A voltage and the B one (4). The same relationship is used to generate the reference voltages for the two VSCs.  (FOC) and then used to obtain the reference signals for the A VSC as follows (11) shows that the A VSC reference voltages consist in three square-wave voltages of amplitude V dc 2 with the same phase displacement of the OEW-PMSM reference voltage signals. The reference signals for the B VSC are obtained from (10) The reference voltages split for the two VSCs as described in (10)-(12) consist of a square wave control of the IGBT converter allowing it to switch at the fundamental frequency set by the motor speed. By setting the VSC A to modulate in square-wave mode a simple and known profile for the converter's voltages is set. Therefore the same profile of V A 0 can be instantaneously synthesized by the VSC B in order to have V A 0 − V B 0 equal to zero. Fig. 3 shows the profiles of the normalised reference voltages over an electrical period. A SVM modulation that allows to satisfy at each sample time the conditions set by (12) and V P M SM 0 equal to zero has been developed and presented in Section IV. The six-step modulation of VSC A introduces elevated harmonic distortion therefore VSC B needs to switch at an higher frequency in order to compensate for it. Different technologies can be used for the two VSCs. The slow switching VSC A can be realised with IGBT devices while VSC B with SiC ones. The role of the SiC converter in this configuration can be interpreted as an active filter that eliminates the harmonic distortion introduced by the low switching IGBT one simultaneously providing the high switching frequency necessary to synthesize the fundamental of the machine. This separation of the reference signals V * P M SM between the two VSCs results in an increased efficiency of the overall architecture and allows exploitation of the different natures of the two converters [10], [11]. Considering the different switching frequencies of the two converters the IGBT is mainly responsible for the conduction losses while the SiC is responsible for the switching losses. E.g. if we consider a 3 pole pairs OEW-PMSM rotating at 3000 rpm the IGBT converter switching frequency would be 150 Hz.

IV. OEW-PMSM MODULATION STRATEGY FOR INSTANTANEOUS ZSV ELIMINATION A. Dual Inverter Voltage Vectors
From Fig. 1 the phase voltages of the OEW-PMSM as a function of the switching states can be written as: Where s h k indicates the switching state of the inverter leg and it can be equal to 1 if the switch device on the upper bridge turns on or 0 if the switch device turns off. It is therefore possible to identify the state of the inverter leg exclusively by the state of the upper switch. Subscript k indicates the phase while superscript h stands for the VSC A when equal to 1 or the VSC B when equal to 2. In the stationary αβ0 coordinate frame the VSCs phase voltages of (6) can be transformed on the stationary reference frame as (14).
It follows that there are 2 6 = 64 possible combinations of switching states: they are the possible realisations of 19 different space voltage vectors of which 18 are active vectors corresponding to the vertices of the black, blue and red hexagons of Fig. 4, and 1 zero vector located at the origin. It should be noted that this configuration provides a number of different space voltage vectors equal to the one of a three-level inverter. However, if the VSCs ZSV V A 0 −V B 0 wants to be kept to zero to avoid ZSC circulation, all the vectors that generate a non-zero V 0 cannot be used. The admissible switching states that can be used to synthesize the voltage control actions are the ones with zero V 0 component. The 64 switching states reduce to 20: they can produce 1 zero vector at the origin and 6 different active vectors corresponding to the vertexes of the red hexagon of Fig. 4.
The modulation index m is defined as WhereV * is the reference voltage vector. Always referring to Fig. 4 the maximum modulation indexes are 1 for the black hexagon, the red one and the blue one respectively. Working with space vectors with no ZSV corresponds to work on the red hexagon thus having a reduction of 13.4% compared to the maximum modulation index that this double converter configuration would allow. The dc-link utilisation is still higher if compared with a standard single VSI drive gaining 42.3%.

B. SVM for Instantaneous ZSV Elimination
In order to have zero V P M SM 0 applied on the machine the ZSVs produced by the two VSCs V A 0 and V B 0 must be instantaneously the same. An efficient solution to achieve zero V P M SM 0 is to choose a particular modulation for one of the two VSCs so that the ZSV can be easily described as a function of the converter reference voltage angle. I.e. if the VSC A is modulated in six-step mode its ZSV V A 0 has a well known profile. Fig. 5 shows the ZSV profile of a single VSC which is modulated in square wave mode. Table I shows the voltage components in the αβ0 reference system for the 8 switching states for a single VSC. Operating in square wave a VSC means applying only the 6 active vectors and jumping from one to the adjacent according to the verse of rotation of the machine. According to Table I the ZSV of the square wave modulated VSC V A 0 corresponds to a square wave that assumes the values ± 1 6 V dc with period 2π 3ωe . By adopting a conventional triangular wave PWM for the B converter the resulting V P M SM 0 on the OEW-PMSM would not be instantaneously equal to 0. In fact all the possible voltage state corresponding to the blue hexagon of Fig. 4 are used. A modulation for the B VSC is developed in order to instantaneously set V B 0 equal to V A 0 . The active vectors of the single inverter can be grouped in two sets, the ones that produce a negative ZSV (V A , V C and V E ) and the ones that produce a positive ZSV (V B , V D and V F ). According to which set belongs the active voltage vector that the squarewave modulated VSC A is applying the B one can only apply the three active voltage vectors which have the same ZSV component. The dwelling times for the three active vectors can be found similarly as done for a standard SVM. For the first set of vectors V A , V C and V E the following system can be written Similarly can be done for the set of vectors Where V is the module of the VSC's vectors in the αβ plane that correspond to 2V dc 3 and T s is the system sample time. By solving the system of equations (16) and (17) for respectively the dwelling times for the voltage vectors of the VSC B can be found. At each T s the square wave reference voltages are calculated according to (11), then it is checked if the reference voltage vector V * SW A belongs to the set of vectors that produce a positive or negative ZSV. According to which set it belongs either (16) or (17) are used to calculate the dwelling times for the voltage vectors of the B VSC. The three active voltage vectors are applied in ascending order from the one which has the shortest dwelling time to the longest. The three vectors can therefore be applied in 3! = 6 possible permutations. The three vectors will be identified as t min , t med and t max according to their dwelling time. Thanks to the modulation introduced the ZSV V P M SM 0 generated by the converters is instantaneously zero apart from the voltage distortion introduced by the DTs, therefore a ZSC PI controller is not needed. The elimination of the ZSV produced by the dual-inverter thanks to the proposed modulation can be achieved all over the operating points that fall inside the red hexagon of Fig. 4 and it is independent from the system parameters.

V. DEAD-TIME EFFECT ON OEW-PMSM ZSV
Failure of the switching devices and even of the whole inverter is possible if a DT is not added in the control scheme to ensure proper operation of the inverter. In this way the bridge shoot through can always be avoided eliminating additional losses or even thermal runaway. Usually several micro seconds are required for the DT which are no longer  ignorable in the inverter modelling. Even if the gate signal DT is always applied, the phase voltage distortion happens only in the two following cases: s j switches from 0 to 1 and i j > 0 or s j switches from 1 to 0 and i j < 0 where i is the phase current, s is the switching state of the leg top device and j stands for the j th inverter leg. Fig. 6 shows the three states of VSC B and their output phase voltages v a 0 , v b 0 and v c 0 in the case of i a > 0, i b > 0 and i c < 0. The set of vectors which produce a negative ZSV is considered, in particular the transition from V A to V C is analysed. Therefore the DT will cause a voltage distortion only on v b 0 . In fact when both the upper and lower devices are off the phase current will keep flowing through the lower diode keeping the voltage clamped to − V dc 2 . During the DT the ZSV V A 0 is − V dc 2 different from the ZSV produced by VSC A which is − V dc 6 . The result is a positive ZSV V 0 of V dc 3 on the machine that will cause a ZSC to circulate. It can be noticed that for the same switching V A to V C with i a < 0, i b < 0 and i c > 0 that the DT distortion on leg a due to a transition from 1 to 0 causes a negative ZSV of − V dc 3 on the machine. Similarly the same analysis can be done for the set of vectors t V B , t V D , t V F which produce a positive ZSV observing the same behaviour as the vectors

VI. SIMULATIONS RESULTS
Simulations of the proposed method have been analysed in Matlab-Simulink. The high speed starter-generator OEW-PMSM parameters are reported in Table II. The dc-link voltage is set to 540 V with the IGBT and SiC VSCs switching frequencies of 10 and 40 KHz respectively. The q and d axis current control is achieved by two simple PI regulators with gains selected in order to have an equivalent bandwidth of 1 KHz. The performances of the proposed topology when a standard PWM is used for both the converters are shown in Fig. 7. A common way to obtain the reference voltages for the two VSCs is to split the voltage reference into two vectors of same length but opposite phase. Therefore V * respectively as done in [17]. It can be noticed the high intensity ZSC ripple due to the ZSV applied by the VSCs which is superimposed to the third harmonic oscillation. A detail of the ZSC ripple and the ZSV are shown in Fig. 8, the ZSV is different from zero and it reaches peaks of V dc . In Fig. 9 the performances when the proposed SVPWM for instantaneous ZSV elimination are presented. Thanks to the modulation introduced the ZSV corresponds only to the distortion of ± V dc 3 introduced by the DT.  The proposed topology performances have been tested on an experimental set-up composed by an OEW-PMSM coupled with a DC motor as shown in Fig. 10. The recursive least square method [22] has been used to estimate both the electrical and mechanical parameters of the motor. The parameters of the OEW-PMSM used for experimental validation are reported in Table III. Even though the high speed machine of which previously discussed was still not available, the used set-up still shows the same problems on a smaller scale. The machine used is a 1.5 KW PMSM with a rated speed of 3000 rpm therefore characterized by much lower rated current than the high speed starter-generator. The low ZSI still causes high distortion on the machine phase currents, therefore it can be used effectively to experimentally validate the presented work. The control board specification can be found in [23]. The dc- link voltage is 80 V, the IGBT VSC is switched in square wave mode while the SiC VSC switching frequency is 40 KHz. The IGBT DT is set to 3µs while the SiC one to 1µs. Since the modulation proposed for the ZSV elimination is independent from the operating point of the machine, exclusively the inertial load case and a few operating speeds have been considered. Similarly as done in Fig. 7 the performances of the proposed system when two standard PWM are used for both converters are checked. Fig. 11 shows the distortion introduced by the ZSC on the phase current profile. Both the third harmonic back EMF component and the switching ZSV contribute can be identified on the ZSC. In fact the ZSC has a period that is three times the phase current and shows a high frequency intense ripple due to the fact that a standard PWM that allows to move on the whole blue hexagon of Fig. 4 is used. A detail of the ZSC and ZSV of Fig. 11 is reported in Fig. 12 showing a behaviour very similar to simulation results presented in Fig. 8. Fig. 13 shows the implementation of the proposed modulation. The VSC A, i.e. the IGBT one is square wave modulated while the VSC B, i.e. the SiC one is modulated according to (12) with a switching frequency of 40 KHz. The IGBT converter now switches at the machine fundamental frequency as it can be seen from Fig. 13 (a) where the phase current and the IGBT phase voltage are shown. The third harmonic component superimposed to the phase current due to the non-sinusoidal back EMF is still present. It can be noticed how the ZSV applied to the machine goes from 20 to -20 V which correspond to the voltage distortion introduced by the DT. Fig. 14 shows the experimental results obtained running the machine at 1600 rpm but applying a load torque instead of having only the inertial one. The higher waveform quality can be associated with the increased torque applied by the OEW-PMSM. ZSC is still present due to the third harmonic back-EMF of the machine therefore significantly reducing the phase current waveform quality. In Part II of this paper a novel DT Hysteresis control of the ZSC is discussed to eliminate the circulation of additional currents due to the non-sinusoidal machine back-EMF.

VIII. CONCLUSIONS
In this paper a dual-fed common dc link topology OEW-PMSM for aircraft high speed Starter-Generator application is considered. A novel hybrid SVPWM has been developed for the dual VSC in order to instantaneously eliminate the ZSV produced by the VSCs. The OEW-PMSM model has been presented considering the non-sinusoidal machine back EMF, furthermore analysis of the effect of the VSCs' DT on the ZSV has been carried out. Considering the new modulation proposed where one of the VSCs works in square wave mode, mixed technology is used for the two VSCs in order to obtain higher system efficiency and reduce the ZSC circulating  (a) Phase current ia. Xaxis: 5ms/div; Y-axis: 2 A/div (b) ZSC i 0 . X-axis: 5ms/div; Y-axis: 1 A/div (c) Phase voltage Vaa'. X-axis: 5ms/div; Y-axis: 50 V/div (d) ZSV V P M SM 0 . X-axis: 5ms/div; Y-axis: 50 V/div problem. The proposed techniques have been tested through simulations and verified experimentally. (a) Phase current ia (blue line) X-axis: 5ms/div; Y-axis: 5 A/div, V a0 (red line) X-axis: 5ms/div; Yaxis: 100 V/div. X-axis: 5ms/div; Y-axis: 5 A/div (b) ZSC i 0 . X-axis: 5ms/div; Y-axis: 0.5 A/div (c) Phase voltage Vaa'. X-axis: 5ms/div; Y-axis: 50 V/div (d) ZSV V P M SM 0