Simple Voltage Modulation Technique for Quasi Six

Simple Voltage Modulation Technique for Quasi Six-Phase Series Connected Two-Motor Drive System Atif Iqbal Senior Member IEEE Electrical & Computer Engineering, Texas A&M University at Qatar, Doha

M. Arif Khan

Sk. Moin Ahmed

H. Abu-Rub

Deptt. of Electrical Engineering, K.I.E.T., Ghaziabad, 201206, India,

Student Member IEEE Electrical & Computer Engineering, Texas A&M University at Qatar, Doha, Qatar [email protected]

Senior Member IEEE Electrical & Computer Engineering, Texas A&M University at Qatar, Doha [email protected]

[email protected]

[email protected]

Abstract: Several proposals on multi-phase multi-motor drive systems are given in the literature. This paper focuses on one such configuration with stator windings of two quasi six-phase machines (two set of stator windings with 30˚ phase displacement) connected in series and supplied from a single sixphase voltage source inverter, forming two-motor drive structure. A simple voltage modulation technique is described for six-phase voltage source inverter feeding such motor drive configuration. The proposed modulation is based on the sampled reference voltages and effective time concept. In the proposed technique the actual switching times for each inverter legs are obtained directly in simple form. The execution time in real time application can be reduced significantly compared to the conventional space vector pulse width modulation (SVPWM). Simulation and experimental results are provided to validate the proposed theory. Index Terms – Six-phase, PWM, Space vector, Time equivalent SVPWM.

I. INTRODUCTION Adjustable speed multi-phase motor drive systems have gained popularity in recent time due to some inherent advantages that they offer compared to three-phase drive systems. Some of the offered advantages are reduced torque pulsation, reduced rotor current harmonics, reduced volume of machine for the same power output and reduced converter per leg rating [1-6]. The application areas of multi-phase drive systems are in high power medium voltage range, such as ship propulsion, electric and hybrid electric vehicles, more electric aircraft applications and safety critical applications where higher redundancy are required [6]. One of the interesting applications of the multi-phase machines are in the two-motor drive system where each machine is with open-end stator and their windings are connected in series and supplied from a single inverter. The open-end of the second machine are tied together to form the neutral. It is a general concept where stator windings of n numbers of machines can be connected in series with appropriate phase transposition and each machine can be controlled independently while feeding them from a single multi-phase voltage source inverter, the detail analysis of such configuration is given in [7-9]. A specific case of fivephase two-motor drive is elaborated in [10-13], six-phase twomotor drive is presented in [14-16] where a symmetrical sixphase machine (60˚ phase displacement with single neutral point) connected in series with a three-phase machine is described, six-phase two-motor drive is illustrated in [17-18], where two quasi six-phase machines are connected in series. Similar to series connection of multi-phase machines, parallel connection are also possible with independent control of each

machine and supplied from one inverter. Such configurations are presented in [19-20]. The series-connected multi-motor drive increases the copper losses of both machines and thus lowers the efficiency. However, it is suggested that for special applications where the load requirement is such that all the motors are not fully loaded simultaneously, this technique is beneficial. One such application is identified as Winder drive [9]. The inverter feeding such multi-motor drive system requires appropriate PWM control. Carrier-based and space vector PWM are once again considered as the best control practices for use in such applications [21-24]. A comprehensive relationship between carrier-based PWM and space vector PWM for five-phase voltage source inverter is presented in [25] and the analytical solution of current ripple for using space vector PWM are reported in [26]. Recently space vector PWM technique is presented for five-phase three-level neutral point clamped inverter feeding series-connected five-phase two motor drive system [27] and independence of control is shown. Nevertheless, it is important to emphasize here that implementation of space vector PWM in multi-phase system is much more computational intensive because of the presence of large number of space vectors. On the other hand carrierbased PWM does not fully utilize the available dc bus [28]. Thus this paper emphasis on the development of simple voltage modulation technique where the dc bus utilization is equal to that of the space vector PWM and the implementation is as simple as carrier-based PWM scheme. Hence the proposed PWM scheme combines the advantages of the two popular PWM schemes. Another aspect to be highlighted here is that the developed PWM scheme is independent of the machine types being used for the series connection. Moreover, since the PWM control of inverter for multi-motor drive configuration is independent of the connection type i.e. series or parallel, the technique developed in this paper is applicable to both topologies. In this paper, simple voltage modulation scheme is described from the concept of “effective voltage” similar to the one used in [29] and later on applied to multi-level threephase inverter in [30]. The same scheme is extended in this paper for application to six-phase inverter feeding two seriesconnected six-phase machines. The actual switching time for each inverter legs are deduced directly in a simple form in the proposed PWM scheme. The real time implementation of this scheme is extremely simple and the computational burden is minimal for the DSP.

Simulation and experimental approach is used to validate the concept. II. THE DRIVE STRUCTURE The drive structure investigated in this paper consists of two quasi six-phase (any type), motors a six-phase voltage source inverter and two vector controllers. The two quasi six-phase machines have open-end stator windings. The input of first machine is connected to the six-phase voltage source inverter, the output is connected to the input of the second machine and the output winding end of the second machine is shorted to form two star points. The stator windings of the two machines are required to be connected with appropriate transposition to obtain independent control of the two machines [16-19]. The basic principle is to make the d-q component of one machine to act as x-y component to other machine and vice versa. Further, it is to be noted that the type of machines is irrelevant from control point in this case since the inverter has to generate two frequency output corresponding to the operating fundamental frequencies of each machine. The block schematic of the control structure is depicted in Fig. 1. There are two possibilities of connecting the stator windings of the machines to obtain their independent control, one is given in Table 1. The other possibility is available in [7] whose connectivity matrix is given in Table 2. The controller structure remains the same except the method of summing up the voltages and currents which are as per the rules defined by Table 1 and Table 2. III. INVERTER CONTROL METHODS The inverter control technique depends upon the machines requirements as current controlled or voltage controlled. For current controlled motor drive the simplest approach is hysteresis or alternatively ramp comparison or carrier-based control. To enhance the modulation index in such schemes, harmonic injection approach is used [33]. Multi-phase harmonic injection scheme is also applied for multi-phase inverters and it is seen that with increasing number of phases, the increase in the modulation index is reduced [34]. The maximum achievable output for carrier based scheme is 0.5Vdc and for the harmonic injection scheme it is 0.5785Vdc for a six-phase VSI [17]. ω1

id i q *

vs1

ω1*

Table 2. Connectivity matrix for the quasi six-phase drive scheme 2 M1 M2

A 1 1

*

vs2

i

ω1

i

dq xy

Fig. 1 Series-connection of two quasi six-phase machines scheme 1. Table 1. Connectivity matrix for the quasi six-phase drive Scheme 1 M1 M2

B 2 6

C 3 4

D 4 5

E 5 4

F 6 6

IV. PROPOSED TIME EQUIVALENT SPACE VECTOR PWM SCHEME The proposed modulation called here, “Time Equivalent Space Vector PWM (TESVPWM)” utilizes simply the sampled reference voltages to generate the gating time directly for which each inverter leg to yield sinusoidal output. This method is an extension of the technique developed for a threephase VSI [29, 30]. The major advantage offered by the proposed scheme is its flexible nature as relocation of “effective time” within the switching period results in various types of PWM schemes. Additionally, the computation time is greatly reduced as the sector identification and reference of lookup table is not used in the proposed algorithm contrary to the conventional SVPWM techniques. The SVPWM technique especially becomes too complex for two-motor drive and the proposed technique greatly simplifies the implementation algorithm. In the proposed algorithm the reference voltages are sampled at fixed time interval equal to the switching time of the inverter. The sampled amplitudes are converted to equivalent time signals. The time signals thus obtained are imaginary quantities as they will be negative for negative reference voltage amplitudes. Thus a time offset is added to these signals to obtain the real gating time of each inverter leg. This offset addition centers the active switching vectors within the switching interval offering high performance PWM similar to SVPWM. The algorithm is given below, where Vx; x=a,b,c,d,e,,f,; are the sampled amplitudes of reference phase voltages during sampling interval and Ts is the inverter switching period. Tx; x=a,b,c,d,e,f; is referred as time equivalents of the sampled amplitudes of reference phase voltages. Tmax and Tmin are the maximum and minimum values of Tx during sampling interval. To is the time duration for which the zero vectors is applied in the switching interval. Toffset is the offset time when added to time equivalent becomes gating time signal or the inverter leg switching time Tgx;x=a,b,c,d,e,f .

ω *2

A 1 5

C 3 2

Algorithm of the proposed TESVPWM: (a) Sample the reference voltages Va , Vb, Vc, Vd, Ve & Vf in every switching period Ts. (b) Determine the equivalent times T1,T2, T3,T4, T5 & T6 given by expression, where x= a,b,c,d,e and f;

v*s ,α*

ω2 ix i y

B 2 3

D 4 1

E 5 2

F 6 3

Txs = V xs × ω2

Ts Vdc

;

(c) Determine Toffset ;

Toffset =

TS Tmax + Tmin − 2 Vdc

(d) Then the inverter leg switching times are obtained as T gx = T x + Toffset ; x = a,b,c,d,e and f. Fig. 2 shows the principal of Time Equivalent method for asymmetrical six-phase case, if one cycle of modulating signal

is divided into ten equal parts (sectors) and sampling is done in the first part. Then on the basis of mathematical analysis the equivalent switching waveform is shown in Fig. 3. From the switching waveform of Fig. 3, for first part the corresponding space vectors applied are 32,34,50,54 and 55 for the implementation of modulation scheme [18]. Although the proposed PWM technique does not directly act upon the space vector, but it means here the implied space vectors that are imposed as a result of the modulation approach. The implied space vectors used in all the sectors and their order of switching are given in Table 3. The complete space vector model of a quasi six-phase voltage source inverter is presented in [31] and these vectors mappings (Table 3) can be seen there.

IV SIMULATION RESULTS Simulation results are provided in Fig. 4. The reference leg voltages shown in Fig.4 (a) and the equivalent offset time signals are calculated according to algorithm are shown in Fig. 4 (b). The harmonic spectrum for phase ‘a’ voltage is shown in Fig. 4 (c) and Fig. 4 (d), shows the harmonic spectrum for phase ‘a’ voltage in d-axis. Fig. 4(e) shows the harmonic spectrum phase ‘a’ voltage in x-axis and filtered output voltage is shown in Fig. 4(f). Two input reference is given such as to operate one machine rated speed (50 Hz) and another at half rated speed (25 Hz) keeping equal v/f ratio. Consequently, the inverter outputs two fundamental frequencies voltages one at 25 Hz and other at 50 Hz. This is illustrated from the frequency domain characteristics of Fig. 4c, 4d and 4e. The phase voltage shows two fundamental frequency output. In the transformed domain the d-axis voltage appears at 25 Hz fundamental and in the x-axis domain it appears at 50 Hz fundamental. The independence of control of the two series connected machine is thus evident. The maximum modulation index obtained here is 1.15 i.e. 0.575VDC. This is an increase of 15% in the modulation index. The reference asymmetric six-phase voltage is provided with amplitude equals to ± 0.5 VDC and VDC is kept unity. The enhancement in the modulation index is achieved due to common mode voltage addition in the reference voltage. The switching frequency is chosen equal to 5 KHz for the simulation purpose.

Fig. 3 switching waveforms for sector 1 for scheme 1

-4

Vf

Tf

Vd

Vb

Td

Ve

Tb

Vc

Tmax= Ta

Va

Te

x 10

1

0

II

III

IV

V

VI

IX X

VII VIII

Tmin= Tc

I

-1

Teffective 0.042

0.044

0.046

0.048

0.05

0.052

0.054

0.056

0.058

0.06

Ts

Pole A Toffset Pole E Tmin

0.04

Pole B Pole D Pole F Pole C

Fig. 2 Principal of TESVPWM for sector 1 for scheme 1

(a)

Reference leg voltage (d) Harmonic spectrum for phase ‘a’ voltage in d axis

(b) .Equivalent offset time signals

(e) Harmonic spectrum for phase ‘a’ voltage in x-axis

(c) Harmonic spectrum for phase ‘a’ voltage Table 3 Vectors used for SVPWM in different sectors Sector Vectors Sector No. No. 1 32,34,50.54.55 6 2 32,48,52,54,55 7 3 32,36,52,60,61 8 4 32,40,44,60,61 9 5 8,12,44,45,61 10

Vectors 8,9,11,29,31 8,9,11,15,31 2,10,11,27,31 2,3,19,23,31 2,18,19,51,55

(f) Filtered output voltage Fig 4 Simulation results of TESVPWM scheme for scheme 1

V. EXPERIMENTAL INVESTIGATION A prototype six-phase voltage source inverter is built in the laboratory and experimental investigation is done to implement the proposed scheme for quasi-six phase VSI to

produce two independent fundamental frequencies at the output. The DC link voltage is set to 100 V. The Texas instrument DSP TMS320F2812 is used to implement the proposed modulation scheme. Fig. 5 shows the experimental results of a DSP based quasi-six phase VSI output. Fig 5(a) shows the switching waveforms of the PWM signals and 5 (b) shows the filtered PWM signals. Fig 5 (c) shows the output of the PWM inverter and 5 (d) shows the harmonic spectrum of the phase ‘a’ voltage. For the experimental investigation the voltage magnitudes for both outputs is kept equal 100 volts and the frequency is kept at 25 Hz. Therefore the v/f values for both the schemes are kept at 4. The gate drive signals for the four legs are shown in Fig. 5a (due to limited number of oscilloscope channels). The filtered PWM signal which is actually the leg voltage, is illustrated in Fig. 5b which matches closely to the simulation waveform of Fig. 4a. The output filtered phase voltages are given in Fig. 5c. Finally the frequency domain curve of phase ‘a’ output voltage is depicted in Fig. 5d which shows one fundamental output as the two components overlap each other. By transforming this signal into d-q and x-y axes can prove the two equal magnitude components at 25 Hz fundamental. Thus this validates the proposed PWM technique for quasi six-phase series-connected machines fed by a single quasi six-phase inverter.

(c) Filtered output phase voltages of the PWM inverter

(d) Harmonic spectrum of phase ‘a’ voltage Fig. 5 experimental results for the quasi six-phase series connected two motor drive system for scheme 1

VI

(a) switching waveforms

(b)Filtered PWM signal

CONCLUSIONS

In this paper a simple voltage modulation technique is presented and is designated as time equivalent SVPWM. In the proposed method, reference space vector is sampled at a regular interval to determine the inverter switching vectors and their time durations in a sampling interval. These equivalent times are then converted to the actual gating time of each leg. In comparison with the present convention SVPWM schemes, in the proposed scheme, there is no need to look for sectors, vectors, lookup tables and no need to calculate the time of application for switching vectors. The proposed method offers a simple approach to realise the complex SVPWM algorithm. The output obtainable has the same quality as that of the conventional SVPWM. The proposed TESVPWM offers major advantages in real time DSP implementation due its computational efficiency. The Matlab/Simulink implementation and their simulation results are provided. The experimental results validate the simulation approach.

VII.

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Acknowledgment: Authors gratefully acknowledge the support provided by the council of scientific and industrial research (CSIR), New Delhi, India for this work under the research grant no. 22(0420)/07/EMR-II