Ключевые слова: электропривод с расщепленными фазами, сдвоенная инверторная система, широтно-импульсная модуляция, синхронизация фазного напряжения.

Multiphase, and, in particular, dual three-phase (six-phase) induction motor drives are a subject of increasing interest in the last years due to some advantages compared with conventional three-phase adjustable speed drives [1]-[5]. Ones of the perspective applications of the six-phase (split-phase) drives are now traction drive systems, in particular, hybrid electric vehicle drives, powered from fuel cell and battery [5].

Fig. 1 presents topology of the electrical vehicle system on the base of the split-phase (six-phase) induction motor supplied by two inverters with two different DC links: 1) Battery DC link with the V_dc1 voltage, and 2) Fuel Cell DC link with the V_dc2 voltage [5]. There are symmetrical and asymmetrical topologies of split-phase (dual three-phase) converters and drives. In particular, in the case of symmetrical dual three-phase systems the induction machine has two sets of winding spatially shifted by 60 electrical degrees with isolated neutral points [6]-[8].

Fig. 1. The topology of the electrical vehicle system

To provide increased efficiency of symmetrical six-phase drives, novel space-vector-based control and modulation strategies have been proposed and developed for these systems with the single DC-link [6]-[8]. It is known, that for drives with increased power rating it is necessary to synchronize voltage waveforms of power converters for elimination of undesirable sub-harmonics of voltage and current [9],[10]. So, this paper presents results of dissemination of novel method of synchronized PWM to symmetrical traction system with two DC voltage sources with different voltages.

Basic properties of synchronized schemes of space-vector modulation

In order to avoid asynchronism of conventional versions of voltage space-vector modulation, novel methods of synchronized PWM can be used for control of each inverter in symmetrical six-phase systems [11].

Figs. 2-3 present switching state sequences of standard three-phase voltage source inverter inside the interval 0⁰-90⁰. It illustrates schematically basic continuous (CPWM, Fig. 2) and discontinuous (DPWM, Fig. 3) versions of space-vector pulsewidth modulation, which are used typically in adjustable speed drive systems. The upper traces in Figs. 2-3 are switching state sequences (in accordance with conventional designation [11]), then - control signals for the cathode switches of the phases a, b, c (x, y, z) of each inverter. The lower traces in Figs. 2-3 show the corresponding quarter-wave of the line output voltage of inverters. Signals represent total switch-on durations during switching sub-interval, signals are generated on the borders (Fig. 2) or in the centres (Fig. 3) of the corresponding. Widths of notches represent duration of zero sequences.

Special signals ( in Fig. 2, in Fig. 3) with the neighbouring ( in Fig. 2, in Fig. 3) are formed in the clock-points (0⁰, 60⁰, 120⁰..) of the output curve of inverters with synchronous PWM. They are reduced simultaneously till close to zero value at the boundary frequencies between control sub-zones.

Fig. 2. Switching state sequences of standard three-phase voltage source inverter inside the interval 0⁰-90⁰

This control principle provides continuous adjustment of the voltage waveforms of inverters, with smooth pulses-ratio changing.

Fig. 3. Switching state sequences of standard three-phase voltage source inverter inside the interval 0⁰-90⁰

Equations (1)-(8) present a set of control functions for determination of parameters of signals of inverters with synchronized PWM in absolute values (seconds) for scalar V/F control mode of the system during the whole control range including the zone of overmodulation [11]:

For j = 2,...i-1:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

, (8)

where: - total switch-on duration inside switching interval;

- minor parts of the total switch-on durations;

- duration of notches;

- switching interval (sub-cycle);

m = F/F_m - modulation index;

F_i and F_i-1 - boundary frequencies between control sub-zones (index i is equal to the number of notches inside a half of the 60⁰-clock-intervals, including the notch on the border of the clock-intervals);

until , and after ;

- coefficient of synchronization;

the first coefficient of overmodulation until ,

and between and ;

the second coefficient of overmodulation until ,

and in the zone between and ;

K₃ = 0 for CPWM, and K₃ = 0.25 for DPWM.

Synchronized pwm in symmetrical six-phase traction system with two dc voltage sources

motor drive voltage synchronized modulation

Control of symmetrical six-phase induction machine drives is based on the 60⁰-phase-shift of control and output signals of two inverters [6]-[8]. In accordance with the theory of vector space decomposition, the basic six-dimensional space (as, bs, cs, xs, ys, zs) of a dual-three phase induction machine with isolated neutral points can be transformed into two orthogonal two-dimensional subspaces (sa, sb) and (m1, m2) [1]. Voltage components V_sa and V_m1 in these subspaces, and also the phase voltage V_as = V_sa + V_m1, are calculated for symmetrical six-phase system with two isolated neutrals as [7]:

V_sa = 0.333(V_a - 0.5V_b - 0.5V_c + 0.5V_x - V_y + 0.5V_z) (9)

V_m1 = 0.333(V_a - 0.5V_b -0.5V_c - 0.5V_x + V_y - 0.5V_z) (10)

V_as = V_sa + V_m1 = V_a - 0.333(V_a + V_b + V_c) (11)

where V_a, V_b, V_c, V_x, V_y, V_z are the corresponding pole voltages of each three-phase inverter.

In this case, the V_sa component, which produces useful rotating MMF k-th order voltage harmonics (, m=1,2,3,.), is the useful component. But the V_m1 component, which generates loss-producing harmonics (, m=1,3,5,..), is the undesirable voltage component.

In order to provide equivalence of the output fundamental voltages of two inverters (with the same fundamental frequency) during scalar V/F control of the system, it is necessary to provide linear correlations between its modulation indices and magnitudes of the DC voltages:

m₁ V_dc1 = m₂ V_dc2 (12)

Figs. 4 - 6 present the pole (V_a and V_x), and phase V_as and V_xs voltages, and also the useful V_sa component of the phase voltage, of two inverters (with spectral characteristic of the V_sa voltage) of the six-phase system (Fig. 1) with two DC sources, where V_dc1 = 0.75V_dc2.

Fig. 4 shows basic signals of the drive system with continuous synchronized PWM (CPWM). Fig. 5 presents the corresponding signals for the six-phase drive with discontinuous PWM with the 30⁰-non-switching intervals (DPWM). Fig. 6 shows basic voltage waveforms for the system with combined CPWM+DPWM control.

The switching and fundamental frequencies of each inverter are, respectively, equal to 900 Hz and 35 Hz (modulation indices of two inverters in accordance with (12) are equal correspondingly to m₁ = 0.75 and m₂ = 0.56).

Fig. 4. Basic signals of the drive system with continuous synchronized PWM (CPWM)

Fig. 5. Signals for the six-phase drive with discontinuous PWM with the 30⁰-non-switching intervals (DPWM)

Fig. 6. Basic voltage waveforms for the system with combined CPWM+DPWM control

The motor phase voltages V_as and V_xs of the six-phase vehicle drives with both continuous and discontinuous synchronized PWM have symmetry during the whole control range (see Figs. 4 - 6), and its spectra do not include even harmonics and sub-harmonics, which is especially important for high power/high current systems.

Fig. 7 presents calculation results of Weighted Total Harmonic Distortion factor (WTHD) for the useful component V_sa of the phase voltage (averaged values of ) of symmetrical dual three-phase traction system with continuous (CPWM), discontinuous (DPWM), and combined (CPWM+DPWM) schemes of synchronized modulation. DC-link voltages are V_dc1 = 0.75V_dc2 in this case. In accordance with (12), modulation indices for the first and the second inverters have to be in linear dependence m₂=0.75m₁. The average switching frequency of each three-phase inverter is 900 Hz, control mode corresponds here to standard V/F control during the whole undermodulation zone.

Fig. 7. Calculation results of Weighted Total Harmonic Distortion factor

The spectral characteristics, presented in Fig. 7, show, that algorithms of combined CPWM+DPWM synchronized PWM provide better spectral composition of the useful component of the phase voltage of symmetrical dual three-phase systems (in comparison with two identical (CPWM or DPWM) schemes of modulation for control of two inverters) during the whole linear control range.