SPACE VECTOR MODULATION FOR MATRIX CONVERTER AND CURRENT SOURCE CONVERTER

Abstract

A converter includes a transformer including primary windings and secondary windings, switches connected to the primary windings, an output inductor connected to the secondary windings, and a controller connected to the switches. The controller turns the switches on and off based on dwell times calculated using space vector modulation with a reference current {right arrow over (I)}.sub.ref whose magnitude changes with time.

Claims

1. A converter comprising: a transformer including primary windings and secondary windings; switches connected to the primary windings; an output inductor connected to the secondary windings; and a controller connected to the switches; wherein the controller turns the switches on and off based on dwell times calculated using space vector modulation with a reference current {right arrow over (I)}.sub.ref whose magnitude changes with time.

2. A converter of claim 1, wherein: the switches include six switches; the space vector modulation includes using six active switching states and three zero switching states; a current space is divided into six sectors by the six active switching states such that a vector with θ=0 is located halfway between two of the active switching states; and magnitudes of the six active switching states change with time.

3. A converter of claim 2, wherein: the controller turns the six switches on and off based on dwell times that are calculated based on an ampere-second balance equation:
{right arrow over (I)}.sub.refT.sub.s=∫.sub.0.sup.T.sup.α{right arrow over (I)}.sub.αdt+∫.sub.0.sup.T.sup.β{right arrow over (I)}.sub.βdt+∫.sub.0.sup.T.sup.0{right arrow over (I)}.sub.0dt where {right arrow over (I)}.sub.ref=I.sub.refe.sup.jθ, θ is an angle between the reference current {right arrow over (I)}.sub.ref and the vector with θ=0, T.sub.s is a sampling period, {right arrow over (I)}.sub.α, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0 are three nearest adjacent active vectors to {right arrow over (I)}.sub.ref, and T.sub.α,T.sub.β,T.sub.0 are dwell times of {right arrow over (I)}.sub.α, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0.

4. A converter of claim 3, wherein the controller turns the six switches on and off based on a vector sequence {right arrow over (I)}.sub.α, {right arrow over (I)}.sub.0, −{right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0, −.sub.α,{right arrow over (I)}.sub.0, during the sampling period T.sub.s.

5. A converter of claim 4, wherein the controller turns the six switches on and off based on a timing sequence T.sub.α/2, T.sub.0/4,T.sub.β/2,T.sub.0/4, T.sub.β/2, T.sub.0/4,T.sub.α/2,T.sub.0/4, during the sampling period T.sub.s.

6. A converter of claim 4, wherein: the controller calculates the dwell times using: $T_{\alpha }=\frac{-B+\sqrt{B^2+\mathrm{AC}.Math..Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}}{A}$ $T_{\beta }=\frac{-B+\sqrt{B^2+\mathrm{AC}.Math..Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}}{A}.Math.\frac{\sin \left(\pi .Math.\text{/}.Math.6+\theta \right)}{\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}$ $T_0=T_s-T_{\alpha }-T_{\beta }$ $\mathrm{where}$ $A=\left(4.Math.u_{1.Math.\alpha }.Math.\text{/}.Math.k-u_o\right)+\left(4.Math.u_{1.Math.\beta }.Math.\text{/}.Math.k-u_o\right).Math.\frac{\sin \left(\pi .Math.\text{/}.Math.6+\theta \right)}{\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}$ $B=4.Math.L_o.Math.I_{L.Math..Math.0}-3.Math.u_o.Math.T_s.Math.\text{/}.Math.2$ $C=8.Math.{\mathrm{kL}}_o.Math.I_{\mathrm{ref}}.Math.T_s$ u.sub.1α is a line-to-line voltage depending on the active switching state {right arrow over (I)}.sub.α, u.sub.1β is a line-to-line voltage depending on the active switching state {right arrow over (I)}.sub.β, k is a transformer turns ratio, u.sub.0 is an output voltage of the converter, θ is the angle between the reference current {right arrow over (I)}.sub.ref and the vector with θ=0, L.sub.o is an inductance of the output inductor, I.sub.L0 is the current through inductor L.sub.o at a beginning of the sampling period T.sub.s, T.sub.s. is the sampling period, and I.sub.ref is a magnitude of the vector {right arrow over (I)}.sub.ref.

7. A converter of claim 4, wherein: the controller calculates the dwell times using: $T_{\alpha }=2.Math.\sqrt{\frac{{\mathrm{kI}}_{\mathrm{ref}}.Math.L_o.Math.T_s.Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}{u_{1.Math..Math.\alpha }.Math.\text{/}.Math.k-u_o}}$ $T_{\beta }=2.Math.\sqrt{\frac{{\mathrm{kL}}_o.Math.I_{\mathrm{ref}}.Math.T_s.Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}{u_{1.Math..Math.\beta }.Math.\text{/}.Math.k-u_o}}$ where k is a transformer turns ratio, L.sub.o is an inductance of the output inductor, I.sub.ref is the magnitude of the vector {right arrow over (I)}.sub.ref, T.sub.s is the sampling period, θ is an angle between the reference current {right arrow over (I)}.sub.ref and the vector with θ=0, u.sub.1α is a line-to-line voltage depending on the active switching state {right arrow over (I)}.sub.α, u.sub.1β is a line-to-line voltage depending on the active switching state {right arrow over (I)}.sub.β, and u.sub.o is an output voltage of the converter.

8. A converter of claim 1, wherein the converter is one of a matrix rectifier, a current-source rectifier, and a current-source inverter.

9. A converter of claim 1, wherein the converter is operated in a continuous-conduction mode.

10. A converter of claim 1, wherein the converter is operated in a discontinuous-conduction mode.

11. A space-vector-modulation method for a converter including a transformer with primary windings and secondary windings, switches connected to the primary windings, and an output inductor connected to the secondary windings, the space-vector-modulation method comprising: turning the switches on and off based on dwell times calculated using space vector modulation with a reference current {right arrow over (I)}.sub.ref whose magnitude changes with time.

12. A method of claim 11, wherein: the switches include six switches; calculating the dwell times uses: six active switching states and three zero switching states; and a current space that is divided into six sectors by the six active switching states such that a vector with θ=0 is located halfway between two of the active switching states; and magnitudes of the six active switching states change with time.

13. A method of claim 12, wherein: turning the six switches on and off is based on dwell times that are calculated based on an ampere-second balance equation:
{right arrow over (I)}.sub.refT.sub.s=∫.sub.0.sup.T.sup.α{right arrow over (I)}.sub.αdt+∫.sub.0.sup.T.sup.β{right arrow over (I)}.sub.βdt+∫.sub.0.sup.T.sup.0{right arrow over (I)}.sub.0dt where {right arrow over (I)}.sub.ref=I.sub.refe.sup.jθ, θ is an angle between the reference current {right arrow over (I)}.sub.ref and the vector with θ=0, T.sub.s is a sampling period, {right arrow over (I)}.sub.α, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0 are three nearest adjacent active vectors to {right arrow over (I)}.sub.ref , and T.sub.α,T.sub.β,T.sub.0 are dwell times of {right arrow over (I)}.sub.α, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0.

14. A method of claim 13, wherein turning the six switches on and off is based on a vector sequence {right arrow over (I)}.sub.α, {right arrow over (I)}.sub.0, −{right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0, −{right arrow over (I)}.sub.α, {right arrow over (I)}.sub.0, during the sampling period T.sub.s.

15. A method of claim 14, wherein turning the six switches on and off is based on a timing sequence T.sub.α/2, T.sub.0/4,T.sub.β/2,T.sub.0/4, T.sub.β/2, T.sub.0/4,T/2,T.sub.0/4, during the sampling period T.sub.s.

16. A method of claim 14, wherein: the dwell times are calculated using: $T_{\alpha }=\frac{-B+\sqrt{B^2+\mathrm{AC}.Math..Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}}{A}$ $T_{\beta }=\frac{-B+\sqrt{B^2+\mathrm{AC}.Math..Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}}{A}.Math.\frac{\sin \left(\pi .Math.\text{/}.Math.6+\theta \right)}{\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}$ $T_0=T_s-T_{\alpha }-T_{\beta }$ $\mathrm{where}$ $A=\left(4.Math.u_{1.Math.\alpha }.Math.\text{/}.Math.k-u_o\right)+\left(4.Math.u_{1.Math.\beta }.Math.\text{/}.Math.k-u_o\right).Math.\frac{\sin \left(\pi .Math.\text{/}.Math.6+\theta \right)}{\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}$ $B=4.Math.L_o.Math.I_{L.Math..Math.0}-3.Math.u_o.Math.T_s.Math.\text{/}.Math.2$ $C=8.Math.{\mathrm{kL}}_o.Math.I_{\mathrm{ref}}.Math.T_s$ u.sub.1α is a line-to-line voltage depending on the active switching state {right arrow over (I)}.sub.α, u.sub.1β is a line-to-line voltage depending on the active switching state {right arrow over (I)}.sub.β, k is a transformer turns ratio, u.sub.o is an output voltage of the converter, θ is the angle between the reference current {right arrow over (I)}.sub.ref and the vector with θ=0, L.sub.o is an inductance of the output inductor, I.sub.L0 is the current through inductor L.sub.o at a beginning of the sampling period T.sub.s, T.sub.s is the sampling period, and I.sub.ref is a magnitude of the vector {right arrow over (I)}.sub.ref.

17. A method of claim 14, wherein: the controller calculates the dwell times using: $T_{\alpha }=2.Math.\sqrt{\frac{{\mathrm{kI}}_{\mathrm{ref}}.Math.L_o.Math.T_s.Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}{u_{1.Math..Math.\alpha }.Math.\text{/}.Math.k-u_o}}$ $T_{\beta }=2.Math.\sqrt{\frac{{\mathrm{kL}}_o.Math.I_{\mathrm{ref}}.Math.T_s.Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}{u_{1.Math..Math.\beta }.Math.\text{/}.Math.k-u_o}}$ where k is a transformer turns ratio, L.sub.o is an inductance of the output inductor, I.sub.ref is the magnitude of the vector {right arrow over (I)}.sub.ref, T.sub.s. is the sampling period, θ is an angle between the reference current {right arrow over (I)}.sub.ref and the vector with θ=0, u.sub.1α is a line-to-line voltage depending on the active switching state {right arrow over (I)}.sub.α, u.sub.1β is a line-to-line voltage depending on the active switching state {right arrow over (I)}.sub.β, and u.sub.o is an output voltage of the converter.

18. A method of claim 11, wherein the converter is one of a matrix rectifier, a current-source rectifier, and a current-source inverter.

19. A method of claim 11, further comprising operating the converter in a continuous-conduction mode.

20. A method of claim 11, further comprising operating the converter in a discontinuous-conduction mode.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0044] FIG. 1 is a circuit diagram of an isolated matrix rectifier.

[0045] FIG. 2 is a circuit diagram of a current-source rectifier.

[0046] FIG. 3 is a circuit diagram of a current-source inverter.

[0047] FIG. 4 shows a current-space vector hexagon.

[0048] FIG. 5 shoes the synthesis of reference current {right arrow over (I)}.sub.ref using I.sub.1 and I.sub.2 using known SVM.

[0049] FIGS. 6A and 6B show ideal and real DC current waveforms.

[0050] FIG. 7 shows the synthesis of reference current {right arrow over (I)}.sub.ref using I.sub.α and I.sub.β using SVM of a preferred embodiment of the present invention.

[0051] FIG. 8 shows the waveforms of the isolated matrix rectifier shown in FIG. 1.

[0052] FIGS. 9A, 9C, and 9E show waveforms of the isolated matrix rectifier shown in FIG. 1 in CCM using known SVM, and FIGS. 9B, 9D, and 9F show corresponding waveforms of the isolated matrix rectifier shown in FIG. 1 in CCM using SVM according to various preferred embodiments of the present invention.

[0053] FIGS. 10A, 10C, and 10E show waveforms of the isolated matrix rectifier shown in FIG. 1 in DCM using known SVM, and FIGS. 10B, 10D, and 10F show corresponding waveforms of the isolated matrix rectifier shown in FIG. 1 in DCM using SVM according to various preferred embodiments of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0054] Preferred embodiments of the present invention improve the known SVM. The improved SVM is capable of being used with both DCM and CCM operation, is capable of being used with smaller load-side inductors, and reduces line-side THD.

[0055] As with the known SVM, the improved SVM includes nine switching states, including six active switching states and three zero switching states as shown in FIG. 4, that are used to synthesize the reference current {right arrow over (I)}.sub.ref as shown in FIG. 7. However, in the improved SVM, the six active switching states, although stationary, are assumed to change with time. That is, the magnitude of the active switching states changes with time which is true in actual application.

[0056] The reference current {right arrow over (I)}.sub.ref preferably is synthesized by the three nearest vectors {right arrow over (I)}.sub.α, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0 as shown in FIG. 7, and the dwell time of each vector is T.sub.α,T.sub.β,T.sub.0. Here, (α, β) represent the subscript of the pair of active vectors in each sector such as (1,2) or (2,3) or (3,4) or (5,6) or (6,1). The dwell times preferably are calculated based on the principle of ampere-second balance. Because of current ripple, the inductor current is not constant, so the ampere-second balance of equation (9) becomes:

{right arrow over (I)}.sub.refT.sub.s=∫.sub.0.sup.T.sup.α{right arrow over (I)}.sub.αdt+∫.sub.0.sup.T.sup.β{right arrow over (I)}.sub.βdt+∫.sub.0.sup.T.sup.0{right arrow over (I)}.sub.0dt   (15)

[0057] Applying equation (15) to the isolated matrix rectifier shown in FIG. 1, provides the following analysis. The following assumptions are made in the following analysis: [0058] 1) Transformer T.sub.r is ideal; and [0059] 2) In one sampling period T.sub.s, phase voltages u.sub.a, u.sub.b, u.sub.c are constant.

[0060] Because of the isolation provided by the transformer, the output voltage of the matrix converter u.sub.1(t) must alternate between positive and negative with high frequency to maintain volt-sec balance. Thus, the preferred vector sequence in every sampling period T.sub.s is divided into eight segments as İ.sub.α, İ.sub.0, −{right arrow over (I)}.sub.β, İ.sub.0, {right arrow over (I)}.sub.β, İ.sub.0, −İ.sub.α, İ.sub.0, and the dwell time of each vector is respectively T.sub.α/2, T.sub.0/4, T .sub.β/2,T.sub.0/4, T.sub.β/2, T.sub.0/4,T.sub.α/2, T.sub.0/4. However, the sequence of the active vectors and zero vectors can be combined in different ways, and the dwell time for the zero vectors is not necessary to be divided equally. For example, the vector sequence could be six segments as {right arrow over (I)}.sub.α, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0, −{right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0, with dwell time T.sub.α/2, T.sub.β/2, T.sub.0/2, T.sub.α/2, T.sub.β/2, T.sub.0/2, respectively. Only the case with eight segments as {right arrow over (I)}.sub.α, {right arrow over (I)}.sub.0, −{right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0, {right arrow over (I)}.sub.β, {right arrow over (I)}.sub.0, −{right arrow over (I)}.sub.α, {right arrow over (I)}.sub.0, and the dwell time of each vector with T.sub.α/2, T.sub.0/4, T.sub.β/2,T.sub.0/4, T.sub.β/2, T.sub.0/4,T.sub.α/2, T.sub.0/4 is used as an example to show how the dwell times can be calculated to eliminate the effect of the current ripple on load side. FIG. 8 shows the waveforms of the matrix converter output voltage u.sub.1(t) the inductor current i.sub.L(t), the matrix converter output current i.sub.p(t), and the phase current i.sub.a(t). The inductor current i.sub.L(t) at the time t.sub.0, t.sub.1, t.sub.2, t.sub.3, t.sub.4, t.sub.5, t.sub.6, t.sub.7, t.sub.8, where t.sub.1 and (t.sub.7—t.sub.6)=T.sub.α/2, (t.sub.3−t.sub.2) and (t.sub.5−t.sub.4)=T.sub.β/2, and the dwell time of the zero vectors are all T.sub.0/4, can be described in equation (16):

[00009]$\begin{array}{cc}{I}_{\mathrm{Li}}=I_{\mathrm{Li}-1}+\frac{u_{\mathrm{Li}}}{L_o}.Math.\left(t_i-t_{i-1}\right).Math..Math.i=1,2,3,4,5,6,7,8& \left(16\right)\end{array}$

where the u.sub.Li is the voltage of load-side inductor between times t.sub.i−1 and t.sub.i and L.sub.o is the inductance of the load-side inductor L.sub.o. The instantaneous value of the load-side inductor current is provided by:

[00010]$\begin{array}{cc}{i}_L\left(t\right)=I_{\mathrm{Li}-1}+\frac{u_{\mathrm{Li}}}{L_o}.Math.\left(t-t_{i-1}\right).Math..Math.t_{i-1}<t<t_i& \left(17\right)\end{array}$

[0061] The output current i.sub.p of the matrix converter is provided by:

[00011]$\begin{array}{cc}{i}_p\left(t\right)=\{\begin{array}{cc}{i}_L\left(t\right).Math.\text{/}.Math.k.Math.& u_1>0\\ -i_L\left(t\right).Math.\text{/}.Math.k& u_1<0\end{array}={\mathrm{gi}}_L\left(t\right).Math.\text{/}.Math.k& \left(18\right)\end{array}$

where k is turns ratio of the transformer and the sign function g is defined by:

[00012]$\begin{array}{cc}g=\{\begin{array}{cc}1.Math.& u_1>0\\ -1& u_1<0\end{array},& \left(19\right)\end{array}$

Using equation (18), equation (7) for the active vectors becomes:

{right arrow over (I)}.sub.k2/√{square root over (3)}i.sub.p(t)e.sup.j((k−1)π/3−π/6) k−1,2,3,4,5,6   (20)

Substituting equations (17), (18), and (20) into the ampere-second balancing equation (15) provides:

[00013]$\begin{array}{cc}\begin{array}{c}{\stackrel{.Math.}{I}}_{\mathrm{ref}}.Math.T_s=.Math.{\int }_0^{t_1}.Math.{\stackrel{.Math.}{I}}_{\alpha +}.Math.\mathrm{dt}+{\int }_{t_2}^{t_3}.Math.{\stackrel{.Math.}{I}}_{\beta -}.Math..Math.\mathrm{dt}+{\int }_{t_4}^{t_5}.Math.{\stackrel{.Math.}{I}}_{\beta +}.Math.\mathrm{dt}+{\int }_{t_6}^{t_7}.Math.{\stackrel{.Math.}{I}}_{\alpha -}.Math.\mathrm{dt}\\ =.Math.{\int }_0^{T_{\alpha }.Math.\text{/}.Math.2}.Math.{\stackrel{.Math.}{I}}_{\alpha +}.Math.\mathrm{dt}+{\int }_0^{T_{\beta }.Math.\text{/}.Math.2}.Math.{\stackrel{.Math.}{I}}_{\beta -}.Math.\mathrm{dt}+{\int }_0^{T_{\beta }.Math.\text{/}.Math.2}.Math.{\stackrel{.Math.}{I}}_{\beta +}.Math.\mathrm{dt}+{\int }_0^{T_{\alpha }.Math.\text{/}.Math.2}.Math.{\stackrel{.Math.}{I}}_{\alpha -}.Math.\mathrm{dt}\\ =.Math.{\int }_0^{T_{\alpha }.Math.\text{/}.Math.2}.Math.\frac{2}{\sqrt{3}}.Math.\frac{1}{k}.Math.\left(I_{L.Math..Math.0}+\frac{u_{L.Math..Math.1}}{L_o}.Math.t\right).Math.e^{j\left(\mathrm{\alpha \pi }.Math.\text{/}.Math.3-\pi .Math.\text{/}.Math.6\right)}.Math.\mathrm{dt}+{\int }_0^{T_{\beta }.Math.\text{/}.Math.2}.Math.\frac{2}{\sqrt{3}}.Math.\frac{1}{k}.Math.\left(I_{L.Math..Math.2}+\frac{u_{L.Math..Math.3}}{L_o}.Math.t\right).Math.e^{j\left(\mathrm{\beta \pi }.Math.\text{/}.Math.3-\pi .Math.\text{/}.Math.6\right)}.Math.\mathrm{dt}+\\ .Math.{\int }_0^{T_{\beta }.Math.\text{/}.Math.2}.Math.\frac{2}{\sqrt{3}}.Math.\frac{1}{k}.Math.\left(I_{L.Math..Math.4}+\frac{u_{L.Math..Math.5}}{L_o}.Math.t\right).Math.e^{j\left(\mathrm{\beta \pi }.Math.\text{/}.Math.3-\pi .Math.\text{/}.Math.6\right)}.Math.\mathrm{dt}+{\int }_0^{T_{\alpha }.Math.\text{/}.Math.2}.Math.\frac{2}{\sqrt{3}}.Math.\frac{1}{k}.Math.\left(I_{L.Math..Math.6}+\frac{u_{L.Math..Math.7}}{L_o}.Math.t\right).Math.e^{j\left(\mathrm{\beta \pi }.Math.\text{/}.Math.3-\pi .Math.\text{/}.Math.6\right)}.Math.\mathrm{dt}\\ =.Math.{\int }_0^{T_{\alpha }.Math.\text{/}.Math.2}.Math.\frac{2}{\sqrt{3}}.Math.\frac{1}{k}.Math.\left(I_{L.Math..Math.0}+i_{L.Math..Math.6}+\frac{2.Math.u_{L.Math..Math.1}}{L_o}.Math.t\right).Math.e^{j\left(\mathrm{\alpha \pi }.Math.\text{/}.Math.3-\pi .Math.\text{/}.Math.6\right)}.Math.\mathrm{dt}+{\int }_0^{T_{\beta }.Math.\text{/}.Math.2}.Math.\frac{2}{\sqrt{3}}.Math.\frac{1}{k}.Math.\left(I_{L.Math..Math.2}+i_{L.Math..Math.4}+\frac{2.Math.u_{L.Math..Math.2}}{L_o}.Math.t\right).Math.e^{j\left(\mathrm{\beta \pi }.Math.\text{/}.Math.3-\pi .Math.\text{/}.Math.6\right)}.Math.\mathrm{dt}\\ =.Math.\frac{2}{\sqrt{3}}.Math.\frac{1}{k}.Math.\left(\left(I_{L.Math..Math.0}+I_{L.Math..Math.6}\right).Math.\frac{T_{\alpha }}{2}+\frac{u_{L.Math..Math.1}}{L_o}.Math.{\left(\frac{T_{\alpha }}{2}\right)}^2\right).Math.e^{j\left(\mathrm{\alpha \pi }.Math.\text{/}.Math.3-\pi .Math.\text{/}.Math.6\right)}+\frac{2}{\sqrt{3}}.Math.\frac{1}{k}.Math.\left(\left(I_{L.Math..Math.2}+I_{L.Math..Math.4}\right).Math.\frac{T_{\beta }}{2}+\frac{u_{L.Math..Math.2}}{L_o}.Math.{\left(\frac{T_{\beta }}{2}\right)}^2\right).Math.e^{j\left(\mathrm{\beta \pi }.Math.\text{/}.Math.3-\pi .Math.\text{/}.Math.6\right)}\end{array}& \left(21\right)\end{array}$

where (α, β) can be (1,2) or (2,3) or (3,4) or (5,6) or (6,1), depending on which sector {right arrow over (I)}.sub.ref is located in. For example, if {right arrow over (I)}.sub.ref is located in sector I, (α, β) will be (1,2).

[0062] Substituting {right arrow over (I)}.sub.ref=I.sub.refe.sup.jθ into equation (21), the dwell times can be calculated under the following three different cases.

[0063] Case 1: when the inductance L.sub.o>∞ or the inductance L.sub.o is so large that the current ripple can be ignored so that i.sub.L0=i.sub.L2=i.sub.L4=i.sub.L6−I.sub.L, then the dwell times are the same as the known SVM.

T.sub.α=mT.sub.s sin(π/6−θ)   (22)

T.sub.β=mT.sub.s sin(π/6+θ)   (23)

T.sub.0=T.sub.s−T.sub.α−T.sub.β  (24)

where the modulation index m is given by:

[00014]$\begin{array}{cc}m=k.Math.\frac{I_{\mathrm{ref}}}{I_L},& \left(25\right)\end{array}$

and θ is the angle between the reference current {right arrow over (I)}.sub.ref and the α-axis as shown in FIG. 7.

[0064] In this case, the improved SVM according to various preferred embodiments of the present invention is consistent with the known SVM.

[0065] Case 2: When the inductance L.sub.o is very small or the load is very light, then the load-side can be in DCM mode. The dwell times are calculated as:

[00015]$\begin{array}{cc}{T}_{\alpha }=2.Math.\sqrt{\frac{{\mathrm{kI}}_{\mathrm{ref}}.Math.L_o.Math.T_s.Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}{u_{1.Math..Math.\alpha }.Math.\text{/}.Math.k-u_o}}& \left(26\right)\\ T_{\beta }=2.Math.\sqrt{\frac{{\mathrm{kL}}_o.Math.I_{\mathrm{ref}}.Math.T_s.Math.\sin \left(\pi .Math.\text{/}.Math.6+\theta \right)}{{\beta }_{1.Math..Math.\beta }.Math.\text{/}.Math.k-u_o}}& \left(27\right)\\ T_0=T_s-T_{\alpha }-T_{\beta }& \left(28\right)\end{array}$

where k is the transformer turns ratio, L.sub.o is the inductance of the load-side inductor L.sub.0, {right arrow over (I)}.sub.ref is the magnitude of the vector {right arrow over (I)}.sub.ref and is determined by the controller, T.sub.s is the sampling period, θ is the angle between the reference current {right arrow over (I)}.sub.ref and the a-axis as shown in FIG. 7, u.sub.1α is measured by the controller and corresponds to a line-to-line voltage depending on the switching state, u.sub.1β is measured by the controller and corresponds to a line-to-line voltage depending on the switching state, and u.sub.o is the output voltage as measured by the controller. The line-to-line voltages u.sub.1α and u.sub.1β depend on the switching state. For example, in Sector I with active vectors {right arrow over (I)}.sub.1 and {right arrow over (I)}.sub.2, line-to-line voltages u.sub.1α and u.sub.1β are u.sub.ab and u.sub.ac, respectively.

[0066] Case 3: when in CCM operation and the current ripple cannot be ignored, then the dwell times are calculated as:

[00016]$\begin{array}{cc}{T}_{\alpha }=\frac{-B+\sqrt{B^2+\mathrm{AC}.Math..Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}}{A}& \left(29\right)\\ T_{\beta }=\frac{-B+\sqrt{B^2+\mathrm{AC}.Math..Math.\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}}{A}.Math.\frac{\sin \left(\pi .Math.\text{/}.Math.6+\theta \right)}{\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}& \left(30\right)\\ T_0=T_s-T_{\alpha }-T_{\beta }.Math..Math.\mathrm{where}& \left(31\right)\\ A=\left(4.Math.u_{1.Math.\alpha }.Math.\text{/}.Math.k-u_o\right)+\left(4.Math.u_{1.Math.\beta }.Math.\text{/}.Math.k-u_o\right).Math.\frac{\sin \left(\pi .Math.\text{/}.Math.6+\theta \right)}{\sin \left(\pi .Math.\text{/}.Math.6-\theta \right)}& \left(32\right)\\ B=2.Math.{\mathrm{nL}}_o.Math.I_{L.Math..Math.0}-3.Math.u_o.Math.T_s.Math.\text{/}.Math.2& \left(33\right)\\ C=2.Math.n^2.Math.{\mathrm{kLI}}_{\mathrm{ref}}.Math.T_s& \left(34\right)\end{array}$

where um is measured by the controller and corresponds to a line-to-line voltage depending on the switching state, u.sub.1β is measured by the controller and corresponds to a line-to-line voltage depending on the switching state, k is the transformer turns ratio, u.sub.o is the output voltage as measured by the controller, θ is the angle between the reference current {right arrow over (I)}.sub.ref and the α-axis as shown in FIG. 7, L.sub.o is the inductance of the load-side inductor L.sub.o, I.sub.L0 is the current through inductor L.sub.o as measured by the controller at the beginning of the sampling period T.sub.s, T.sub.s is the sampling period, and I.sub.ref is the magnitude of the vector {right arrow over (I)}.sub.ref and is determined by the controller. In one sampling period T.sub.s, the vector I.sub.α is divided to n equal parts. In this example, n is 2 because one sampling period includes I.sub.α and −I.sub.α. If n=2, then B and C are provided by:

B=4L.sub.oI.sub.L03u.sub.oT.sub.s/2   (35)

C=8kL.sub.oI.sub.refT.sub.s   (36)

[0067] FIGS. 9A, 9C, and 9E show waveforms of the isolated matrix rectifier shown in FIG. 1 in CCM using known SVM, and FIGS. 9B, 9D, and 9F show corresponding waveforms of the isolated matrix rectifier shown in FIG. 1 in CCM using SVM according to various preferred embodiments of the present invention. In FIGS. 9A and 9B, the load-side inductor current is continuous, so the isolated matrix rectifier is operating in CCM. FIGS. 9C and 9D show the waveforms in the time domain, and FIGS. 9E and 9F show the waveforms in the frequency domain. Comparing these figures demonstrates that the improved SVM according to various preferred embodiments of the present invention provide a line-side current with a better shaped waveform and with a smaller THD. The THD using the improved SVM was measured as 4.71% while the THD using the known SVM was measured as 7.59%, for example.

[0068] FIGS. 10A, 10C, and 10E show waveforms of the isolated matrix rectifier shown in FIG. 1 in DCM using known SVM, and FIGS. 1013, 10D, and 10F show corresponding waveforms of the isolated matrix rectifier shown in FIG. 1 in DCM using SVM according to various preferred embodiments of the present invention. In FIGS. 10A and 10, the load-side inductor current is discontinuous (i.e., the current is equal to zero), so the isolated matrix rectifier is operating in DCM. FIGS. 10C and 10D show the waveforms in time domain, and FIGS. 10E and 10F show the waveforms in the frequency domain. Comparing these figures demonstrates that the improved SVM according to various preferred embodiments of the present invention provide a line-side current with a better shaped waveform and with a smaller THD. The THD using the improved SVM was measured as 6.81% while the THD using known SVM was measured as 17.4%, for example.

[0069] Thus, the improved SVM according to various preferred embodiments of the present invention is capable of being used with the isolated matrix rectifier in FIG. 1 in both CCM and DCM operation. The line-side current THD is significantly reduced with the improved SVM compared to known SVM. The improved SVM is suitable for the compact and high-efficiency design with a wide-load range. The improved SVM can also be applied to current-source converter to improve the AC side current THD.

[0070] In the preferred embodiments of the present, to calculate the dwell times, the controller measures transformer primary current i.sub.p (or inductor current I.sub.L), line voltages u.sub.a, u.sub.b, u.sub.c, and output voltage u.sub.o. The controller can be any suitable controller, including, for example, a PI controller, a PID controller, etc. The controller can be implemented in an IC device or a microprocessor that is programmed to provide the functions discussed above.

[0071] The same techniques and principles applied to the isolated matric rectifier in FIG. 1 can also be applied to the current-source rectifier in FIG. 2 and to the current-source inverter in FIG. 3. These techniques and principles are not limited to the devices shown in FIGS. 1-3 and can be applied to other suitable devices, including, for example, non-isolated devices.

[0072] It should be understood that the foregoing description is only illustrative of the present invention. Various alternatives and modifications can be devised by those skilled in the art without departing from the present invention. Accordingly, the present invention is intended to embrace all such alternatives, modifications, and variances that fall within the scope of the appended claims.