Single phase controlling method and three phase inverting device using the same

Abstract

A three phase inverting device includes a three phase inverter module and a three phase filter module. The three phase inverter module includes a plurality of switches, each two switches are connected for forming a bridge arm, an input end of each of the bridge arm are coupled for forming a DC end, the DC end is connected to a DC load. The three phase filter module is connected to the three phase inverter module, wherein the three phase filter module includes a plurality of inductances and a plurality of capacitances, the inductances are connected at one side of the capacitances, a portion of the capacitances are connected to a output end of each of the bridge arm of the three phase inverter module, a portion of the inductances are connected to an AC end.

Description

RELATED APPLICATIONS

This application claims priority to Taiwan Application Serial Number 108100101, filed Jan. 2, 2019, which is herein incorporated by reference.

BACKGROUND

Technical Field

The present disclosure relates to a controlling method and an inverting device using the same. More particularly, the present disclosure relates to a single phase controlling method and a three phase inverting device using the same.

Description of Related Art

The demand on the renewable energy is increasing owing to the issue of the global warming becomes more serious. An inverter parallel system has become a mainstream owing to the continuously developed technologies of the renewable energy (e.g. a solar power generation system). The power of the inverter parallel system can be enhanced by connecting a plurality of inverter modules in parallel and is increased with the quantity of the inverter modules. Furthermore, when one of the inverter modules is failed, the other inverter modules can be used as a substitute, thereby achieving a high reliability of the system. The requirement on the voltage and current resistance is also lower in this kind of inverter parallel system. When comparing a three phase inverter with three single phase inverters, the three phase inverter has a constant instantaneous power, and a low voltage ripple can be obtained using a low capacitance value. Furthermore, smaller quantity of the switch can be used, thereby reducing power loss and the circuit manufacturing cost.

It is important to increase a current sharing in a single phase and reduce circulating currents between each phase of the inverter parallel system. The common methods for achieving the current sharing include a centralized controlling method, a client-server controlling method, a circular track controlling method, a distributed logic controlling method and a wireless automatic controlling method, etc. The common methods for reducing the circulating currents include a hardware reducing method, a synchronous controlling method and a switch modulating method, etc. However, since the three phases are coupled with each other, the methods for controlling the current sharing and the circulating currents are complicated, thus leading to resource consumption. Therefore, there is a need to develop a method that can effectively control the current-sharing and the circulating currents.

SUMMARY

According to one aspect of the present disclosure, a single phase controlling method is provided. The single phase controlling method is applied to a three phase inverting device, the three phase inverting device includes a three phase switch, the single phase controlling method includes: inputting a DC current into a DC end of the three phase inverting device; performing a de-coupling procedure to calculate a switching duty ratio using an average value of a voltage between the DC end and a ground of an AC end of the three phase inverting device and generating an electric output of a single phase circuit in accordance with the average value of the voltage and the switching duty ratio; performing a dividing procedure to divide the electric output of the single phase circuit into two current variations of an inverting end of the three phase inverting device, wherein the two current variations are corresponded to an excitation state and a demagnetization state respectively; and performing an integrating procedure to integrate the two current variations corresponded to the excitation state and the demagnetization state for obtaining another switching duty ratio on a next duty of the three phase switch.

According to another aspect of the present disclosure, a three phase inverting device is provided. The three phase inverting device includes a three phase inverter module and a three phase filter module. The three phase inverter module includes a plurality of switches, each two of the switches are connected for forming a bridge arm, an input end of each of the bridge arm are coupled for forming a DC end, the DC end is connected to a DC load. The three phase filter module is connected to the three phase inverter module, wherein the three phase filter module includes a plurality of inductances and a plurality of capacitances, the inductances are connected at one side of the capacitances, a portion of the capacitances are connected to a output end of each of the bridge arm of the three phase inverter module, a portion of the inductances are connected to an AC end.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure can be more fully understood by reading the following detailed description of the embodiment, with reference made to the accompanying drawings as follows:

FIG. 1 is a flow chart showing a single phase controlling method according to one embodiment of the present disclosure.

FIG. 2 is a schematic view showing a circuit of a three phase inverting device using the single phase controlling method of FIG. 1.

FIG. 3 is a schematic view showing a switching state of a three phase switch of FIG. 2.

FIG. 4 is schematic view showing a single phase circuit of the three phase inverting device of FIG. 2.

FIG. 5 is schematic view showing that the three phase inverting devices of FIG. 2 are connected in parallel for forming an inverter parallel system.

FIG. 6 is a schematic view showing a comparison of three phase currents in an AC end and an inverter end when a supply mains is in four different power factors and in a strong power grid.

FIG. 7 is a schematic view showing a comparison of three phase currents in an AC end and an inverter end when a supply mains is in four different power factors and in a weak power grid.

DETAILED DESCRIPTION

FIG. 1 is a flow chart showing a single phase controlling method according to one embodiment of the present disclosure. The single phase controlling method of the present disclosure is applied in a three phase inverting device. The three phase inverting device includes a three phase switch. The single phase controlling method of the present disclosure includes: a step S101 for inputting a DC current into a DC end of the three phase inverting device; a step S102 for performing a de-coupling procedure to calculate a switching duty ratio using an average value of a voltage between the DC end and a ground of an AC end of the three phase inverting device and generating an electric output of a single phase circuit in accordance with the average value of the voltage and the switching duty ratio; a step S103 for performing a dividing procedure to divide the electric output of the single phase circuit into two current variations of an inverting end of the three phase inverting device, wherein the two current variations are corresponded to an excitation state and a demagnetization state respectively; a step S104 for performing an integrating procedure to integrate the two current variations corresponded to the excitation state and the demagnetization state for obtaining another switching duty ratio on a next duty of the three phase switch. In the aforementioned single phase controlling method, the de-coupling procedure, the dividing procedure and the integrating procedure can be performed through a controller. Furthermore, a converter parallel system can be obtained through connecting a plurality of the three phase inverting devices in parallel. The operation mechanism of the single phase controlling method of the present disclosure is then described.

For clearly understanding the present disclosure, the following table lists the definitions of the symbols of the circuit of the present disclosure.

symbol          definition
VnO             a voltage between a virtual ground n and a
                ground of an inverter
uRO             a voltage of R phase relative to a ground 0
                of an inverter between switches on the upper
                arm and the lower arm
uSO             a voltage of S phase relative to a ground 0
                of an inverter between switches on the upper
                arm and the lower arm
uTO             a voltage of T phase relative to a ground 0
                of an inverter between switches on the upper
                arm and the lower arm
ΔiiR            a current variation of R phase at an inverter
                end of the inductance Li
ΔiiS            a current variation of S phase at an inverter
                end of the inductance Li
ΔiiT            a current variation of T phase at an inverter
                end of the inductance Li
ΔiCR            a current variation of a capacitance of R phase
                of a LCL filter
ΔiCS            a current variation of a capacitance of S phase
                of a LCL filter
ΔiCT            a current variation of a capacitance of T phase
                of a LCL filter
ΔiCgR           a current variation of a capacitance of R phase
                of a LCL filter
ΔiCgS           a current variation of a capacitance of S phase
                of a LCL filter
ΔiCgT           a current variation of a capacitance of T phase
                of a LCL filter
LiR             an inductance Li value of R phase at a switch
                end of a LCL filter
LiS             an inductance Li value of S phase at a switch
                end of a LCL filter
LiT             an inductance Li value of T phase at a switch
                end of a LCL filter
LgR             an inductance Lg value of R phase at an AC end
                of a LCL filter
LgS             an inductance Lg value of S phase at an AC end
                of a LCL filter
LgT             an inductance Lg value of T phase at an AC end
                of a LCL filter
T               a time of a cycle
VRpn            a voltage of R phase relative to a virtual ground
                n in an AC end
VSpn            a voltage of S phase relative to a virtual ground
                n in an AC end
VTpn            a voltage of T phase relative to a virtual ground
                n in an AC end
ΔiCg            a current variation of a capacitance of a LCL
                filter
iCg(t)          a current of a capacitance of a LCL filter at an
                instant cycle
iCg(t − TS)     a current of a capacitance of a LCL filter at
                previous cycle
Cg              a capacitance of a LCL filter LCL
Vcgn(t)         a voltage between two sides of the capacitance
                of LCL filter at an instant cycle
Vcgn(t − TS)    a voltage between two sides of the capacitance
                of LCL filter at previous cycle
Vcgn(t − 2TS)   a voltage between two sides of the capacitance
                of LCL filter at a cycle before the previous cycle
TS0             a time of S0 sate during a cycle
TS1             a time of S1 sate during a cycle
TS2             a time of S2 sate during a cycle
TS7             a time of S7 sate during a cycle
S0              a state showing that the switches of three phases
                are non-conductive
S1              a state showing that only the switch of R phase
                is conductive
S2              a state showing that only the switches of R and S
                phases are conductive
S7              a state showing that three phases are conductive
DR              a switching duty ratio of the switch of R phase R
DS              a switching duty ratio of the switch of S phase S
DT              a switching duty ratio of the switch of T phase T
VnO             an average voltage between a virtual ground n
                and the ground O of the inverter
VnOS0           a voltage between the virtual ground n and the
                ground 0 of the inverter at S0 state
VnOS1           a voltage between the virtual ground n and the
                ground 0 of the inverter at S1 state
VnOS2           a voltage between the virtual ground n and the
                ground 0 of the inverter at S2 state
VnOS7           a voltage between the virtual ground n and the
                ground 0 of the inverter at S7 state
VRcn(t)         a voltage of R phase between two sides of the
                capacitance of the LCL filter at an instant cycle
VRcn(t − TS)    a voltage of R phase between two sides of the
                capacitance of the LCL filter at an previous cycle
VRcn(t − 2TS)   a voltage of R phase between two sides of the
                capacitance of the LCL filter at a cycle before the
                previous cycle
VScn(t)         a voltage of S phase between two sides of the
                capacitance of the LCL filter at an instant cycle
VScn(t − TS)    a voltage of S phase between two sides of the
                capacitance of the LCL filter at an previous cycle
VScn(t − 2TS)   a voltage of S phase between two sides of the
                capacitance of the LCL filter at a cycle before the
                previous cycle
VTcn(t)         a voltage of T phase between two sides of the
                capacitance of the LCL filter at an instant cycle
VTcn(t − TS)    a voltage of T phase between two sides of
                the capacitance of the LCL filter at a previous cycle
VTcn(t − 2TS)   a voltage of T phase between two sides of the
                capacitance of the LCL filter at a cycle before the
                previous cycle
DRST            a switching duty ratio of the three phase switch
LiRST           a capacitance Li value at the AC end of the three
                phase LCL filter
LgRST           an inductance Lg value at the AC end of the three
                phase LCL filter
ΔiiRST          a current variation of the inductance Li at the inverter
                end of the three phase LCL filter
VRSTpn          a voltage relative to the virtual ground n at the AC
                end
VRSTcN (t)      a voltage of the capacitance relative to the ground
                N of the AC end of the three phase LCL filter at
                an instant cycle
VRSTcN(t − TS)  a voltage of the capacitance relative to the ground
                N of the AC end of the three phase LCL filter at a
                previous cycle
VRSTcN(t − 2TS) a voltage of the capacitance relative to the ground
                N of the AC end of the three phase LCL filter at a
                cycle before the previous cycle
CgRST           a capacitance value of the three phases of the LCL
                filter
LgRST           an inductance Lg value at the AC end of the three
                phase LCL filter
X               an extra term of the duty ratio of the R phase
                switch R
Y               an extra term of the duty ratio of the S phase
                switch S
Z               an extra term of the duty ratio of the T phase
                switch T
Lik             an inductance Li value at the AC end of any phase
                of the three phase LCL filter
Δiik,mag        a current variation of the inductance Li at the
                excitation sate at the inverter end of the LCL filter
dt              a time variation
Lgk             an inductance Lg value at the AC end of any phase
                of the three phase LCL filter
ΔiCk,mag        a current variation at the excitation state of any phase
                of the three phase LCL filter
Vkpn            a voltage at the AC end relative to the virtual ground
                n of any phase of the three phases
Δiik,dem        a current variation of the inductance Li at the
                demagnetization state at the inverter end
ΔiCk,dem        a current variation at the demagnetization state of
                any phase of the three phases of the capacitance of
                the LCL filter
Δiik            a current variation of the inductance Li of any phase
                of the three phases at the inverter end of the LCL
                filter
ΔiCk            a current variation of the capacitance of any phase
                of the three phases at the inverter end of the LCL
                filter
Δiik(n + 1)     a current variation of the inductance Li of any phase
                of the three phases the LCL filter at an instant cycle
igk,ref(n + 1)  a reference current of the inductance Lg of the LCL
                filter at a next cycle
igk,ref(n)      a reference current of the inductance Lg of the LCL
                filter at an instant cycle
ii(n)           a current of the inductance Li of single phase of the
                LCL filter at an instant cycle
iik(n)          a current of the inductance Li of any phase of the
                three phases at an instant cycle
i*gk,ref(n + 1) a term used for substituting a portion of Δiik(n + 1)
Lge(i)          an evaluation value of the inductance Lg at the AC
                end of the LCL filter LCL
Lie(i)          an evaluation value of the inductance Li at the inverter
                end of the LCL filter LCL
LTe(i)          a summation of Lge(i) and Lie(i)
dGC(n + 1)      a duty ration at a next cycle
vkpn(n)         a voltage relative to the virtual ground n of any phase
                of the three phases
vdc(n)          a DC voltage of the inverter end at an instant cycle
ick(n)          a current of the capacitance of any phase of the three
                phases of the LCL filter at an instant cycle
ick(n − 1)      a current of the capacitance of any phase of the three
                phases of the LCL filter at an previous cycle
vkcn(n)         a voltage relative to the virtual ground n of the
                capacitance of any phase of the three phases of the
                LCL filter at an instant cycle
vkcn(n − 1)     a voltage relative to the virtual ground n of the
                capacitance of any phase of the three phases of the
                LCL filter at an previous cycle
vkcn(n − 2)     a voltage relative to the virtual ground n of the
                capacitance of any phase of the three phases of
                the LCL filter at a cycle before the previous cycle
VRN             a voltage of R phase which relative to a ground N
                of a supply mains at the AC end
VSN             a voltage of S phase which relative to a ground N
                of a supply mains at the AC end
VTN             a voltage of T phase which relative to a ground N
                of a supply mains at the AC end
Ll              an equivalent inductance at the AC end
SCR             a short circuit ratio of the power grid of the supply
                mains
IIR             a current of the equivalent inductance of R phase
                at the AC end
IIS             a current of the equivalent inductance of S phase
                at the AC end
IIT             a current of the equivalent inductance of T phase
                at the AC end
IgR1            a current of the inductance Lg of R phase of the
                LCL filter of the first inverter in the inverter
                parallel system
IgS1            a current of the inductance Lg of S phase of the
                LCL filter of the first inverter in the inverter
                parallel system
IgT1            a current of the inductance Lg of T phase of the
                LCL filter of the first inverter in the inverter
                parallel system
IgR2            a current of the inductance Lg of R phase of the
                LCL filter of the second inverter in the inverter
                parallel system
IgS2            a current of the inductance Lg of S phase of the
                LCL filter of the second inverter in the inverter
                parallel system
IgT2            a current of the inductance Lg of T phase of the
                LCL filter of the second inverter in the inverter
                parallel system
IgR3            a current of the inductance Lg of R phase of the
                LCL filter of the third inverter in the inverter
                parallel system
IgS3            a current of the inductance of S phase of the
                LCL filter of the third inverter in the inverter
                parallel system
IgT3            a current of the inductance Lg of T phase of the
                LCL filter of the third inverter in the inverter
                parallel system

FIG. 2 is a schematic view showing a circuit of a three phase inverting device using the single phase controlling method of FIG. 1. In FIG. 2, the three phase inverting device includes a three phase inverter module 110 and a three phase filter module 120. In the embodiment, the switches S1-S6 of the three phase inverter module 110 are arranged to form a full-bridge inverter circuit, however, it is also possible to use a half-bridge inverter circuit or other type of the inverter circuit, there is no limitations. The three phase filter module 120 includes inductances L1-L6 and capacitances C1-C3, thereby forming a three phase LCL filter. The three phase inverter module 110 includes a DC end DCT, and three phases are represented by symbols R, S ant T respectively. The switch S1 and the switch S2 are connected to form a bridge arm B1; the switch S3 and the switch S4 are connected to form a bridge arm B2; and the switch S5 and the switch S6 are connected to form a bridge arm B3. An input end of each of the bridge arms B1-B3 are connected as the DC end DCT, which connects to a front end of a DC load (e.g. solar cell) for receiving or outputting a DC voltage VDC. An output end of each of the bridge arms B1-B3 is connected to one end of each of the inductances L1, L3 and L5. The other end of each of the inductances L1, L3 and L5 is connected to each of the capacitances C1-C3. One end of each of the inductances L2, L4 and L6 is connected to each of the capacitances C1-C3. The other end of each of the inductances L2, L4 and L6 is connected to a three phase power of an AC end ACT (e.g. supply mains or other AC power source).

Each of the switches S1-S6 can be controlled independently by a controlling signal so that a conductive state of each of the switches S1-S6 can be controlled. The switches S1, S3 and S5 are located in an upper arm of the bridge arms B1-B3. The switches S2, S4 and S6 are located in a lower arm of the bridge arms B1-B3. The switches in the same arm will be conducted with each other alternatively in accordance with the signal received (e.g. the switches S1 and S2 are conducted with each other alternatively; the switches S3 and S4 are conducted with each other alternatively; and the switches S5 and S6 are conducted with each other alternatively). Therefore, voltages u_ROu_SO and u_TO are generated on the output end of the bridge arms B1-B3 in accordance with the DC voltage V_DC. The inductances L1-L6 can store or release energy in accordance with voltage variations of the voltages u_RO u_So and u_TO. The capacitances C1-C3 have filtering effect. Therefore, an electric power can be transformed between the DC end DCT and the AC end ACT of the three phase inverting device.

The operation mechanism of the single phase controlling method of the present disclosure is then described in the following paragraphs.

Assuming that V_nO represents a voltage of the three phases which are all connected to a ground n and a ground O, the V_nO can be represented by the following equations (1), (2) and (3) in accordance with a Kirchhoff's law:

$\begin{array}{cc}{V}_{\mathrm{nO}}=u_{\mathrm{RO}}-\frac{\Delta i_{\mathrm{iR}}{L}_{\mathrm{iR}}}{T}-\frac{\left(\Delta i_{\mathrm{iR}}-\Delta i_{\mathrm{CR}}\right)L_{\mathrm{gR}}}{T}-V_{\mathrm{Rpn}},& \left(1\right)\\ V_{\mathrm{nO}}=u_{\mathrm{SO}}-\frac{\Delta i_{\mathrm{iS}}{L}_{\mathrm{iS}}}{T}-\frac{\left(\Delta i_{\mathrm{iS}}-\Delta i_{\mathrm{CS}}\right)L_{\mathrm{gS}}}{T}-V_{\mathrm{Spn}},& \left(2\right)\\ V_{\mathrm{nO}}=u_{\mathrm{TO}}-\frac{\Delta i_{\mathrm{iT}}{L}_{\mathrm{iT}}}{T}-\frac{\left(\Delta i_{\mathrm{iT}}-\Delta i_{\mathrm{CT}}\right)L_{\mathrm{gT}}}{T}-V_{\mathrm{Tpn}}.& \left(3\right)\end{array}$

The equations (1), (2) and (3) can be combined to equation (4), and Δi_Cg can be replaced by a voltage of a capacitance, which is shown in equation (5):

$\begin{array}{cc}\begin{array}{c}{V}_{\mathrm{nO}}=\frac{u_{\mathrm{RO}}+u_{\mathrm{SO}}+u_{\mathrm{TO}}}{3}-\frac{\frac{\Delta i_{\mathrm{iR}}{L}_{\mathrm{iR}}}{T_S}+\frac{\Delta i_{\mathrm{iS}}{L}_{\mathrm{iS}}}{T_S}+\frac{\Delta i_{\mathrm{iT}}{L}_{\mathrm{iT}}}{T_S}}{3}-\\ \frac{V_{\mathrm{Rpn}}+V_{\mathrm{Spn}}+V_{\mathrm{Tpn}}}{3}-\\ \frac{\begin{array}{c}\frac{\left(\Delta i_{\mathrm{iR}}-\Delta i_{\mathrm{CgR}}\right)L_{\mathrm{gR}}}{T_S}+\frac{\left(\Delta i_{\mathrm{iS}}-\Delta i_{\mathrm{CgS}}\right)L_{\mathrm{gS}}}{T_S}+\\ \frac{\left(\Delta i_{\mathrm{iT}}-\Delta i_{\mathrm{CgT}}\right)L_{\mathrm{gT}}}{T_S}\end{array}}{3},\end{array}& \left(4\right)\\ \begin{array}{c}\Delta i_{\mathrm{Cg}}=i_{\mathrm{Cg}}\left(t\right)-i_{\mathrm{Cg}}\left(t-T_S\right)\\ =C_g(\frac{V_{\mathrm{cgn}}\left(t\right)-V_{\mathrm{cgn}}\left(t-T_S\right)}{T_S}-\\ \frac{V_{\mathrm{cgn}}\left(t-T_S\right)-V_{\mathrm{cgn}}\left(t-2T_S\right)}{T_S})\\ =C_g\frac{V_{\mathrm{cgn}}\left(t\right)-2V_{\mathrm{cgn}}\left(t-T_S\right)+V_{\mathrm{cgn}}\left(t-T_S\right)}{T_S}.\end{array}& \left(5\right)\end{array}$

As shown in FIG. 3, when the three phase switches switching signals, a cycle can be divided into six regions, seven states S0, S1, S2, S3, S4, S5, S6 and S7 can be presented in each of the regions, and four states SO, S1, S2 and S7 can be presented in some regions. Therefore, the occupied time T can be shown with a duty ratio of the three phase switches and voltages u_RO, u_SO and u_TO, in the following TABLE 1.

	TABLE 1
		URO	USO	UTO	T
	S0	0	0	0	TSO = (1 − DR)T
	S1	VDC	0	0	TS1 = (DR − DS)T
	S2	VDC	VDC	0	TS2 = (DS − DT)T
	S7	VDC	VDC	VDC	TS7 = (DT − 0)T

Accordingly, V_nO can be represented by the following equation (6):

$\begin{array}{cc}\begin{array}{c}\stackrel{\_}{V_{\mathrm{nO}}}=\frac{T_{S0}{V}_{\mathrm{nOS}0}+T_{S1}{V}_{\mathrm{nOS}1}+T_{S2}{V}_{\mathrm{nOS}2}+T_{S7}{V}_{\mathrm{nOS}7}}{T_S}\\ =\left(1-D_R\right)V_{\mathrm{nOS}0}+\left(D_R-D_S\right)V_{\mathrm{nOS}1}+\\ \left(D_S-D_T\right)V_{\mathrm{nOS}2}+D_T{V}_{\mathrm{nOS}7}.\end{array}& \left(6\right)\end{array}$

V_nOS0, V_nOS1, V_nOS2 and V_nOS7 can be represented by the following equations (7), (8), (9) and (10):

$\begin{array}{cc}{V}_{\mathrm{nOS}0}=-\frac{\Delta i_{\mathrm{iR}}{L}_{\mathrm{iR}}+\Delta i_{\mathrm{iS}}{L}_{\mathrm{iS}}+\Delta i_{\mathrm{iT}}{L}_{\mathrm{iT}}}{3T_S}-\frac{V_{\mathrm{Rpn}}+V_{\mathrm{Spn}}+V_{\mathrm{Tpn}}}{3}-\frac{\left(\Delta i_{\mathrm{iR}}-\Delta i_{\mathrm{CgR}}\right)L_{\mathrm{gR}}+\left(\Delta i_{\mathrm{iS}}-\Delta i_{\mathrm{CgS}}\right)L_{\mathrm{gS}}+\left(\Delta i_{\mathrm{iT}}-\Delta i_{\mathrm{CgT}}\right)L_{\mathrm{gT}}}{3T_S},& \left(7\right)\\ V_{\mathrm{nOS}1}=\frac{V_{\mathrm{DC}}}{3}-\frac{\Delta i_{\mathrm{iR}}{L}_{\mathrm{iR}}+\Delta i_{\mathrm{iS}}{L}_{\mathrm{iS}}+\Delta i_{\mathrm{iT}}{L}_{\mathrm{iT}}}{3T_S}-\frac{V_{\mathrm{Rpn}}+V_{\mathrm{Spn}}+V_{\mathrm{Tpn}}}{3}-\frac{\left(\Delta i_{\mathrm{iR}}-\Delta i_{\mathrm{CgR}}\right)L_{\mathrm{gR}}+\left(\Delta i_{\mathrm{iS}}-\Delta i_{\mathrm{CgS}}\right)L_{\mathrm{gS}}+\left(\Delta i_{\mathrm{iT}}-\Delta i_{\mathrm{CgT}}\right)L_{\mathrm{gT}}}{3T_S},& \left(8\right)\\ V_{\mathrm{nOS}2}=\frac{2V_{\mathrm{DC}}}{3}-\frac{\Delta i_{\mathrm{iR}}{L}_{\mathrm{iR}}+\Delta i_{\mathrm{iS}}{L}_{\mathrm{iS}}+\Delta i_{\mathrm{iT}}{L}_{\mathrm{iT}}}{3T_S}-\frac{V_{\mathrm{Rpn}}+V_{\mathrm{Spn}}+V_{\mathrm{Tpn}}}{3}-\frac{\left(\Delta i_{\mathrm{iR}}-\Delta i_{\mathrm{CgR}}\right)L_{\mathrm{gR}}+\left(\Delta i_{\mathrm{iS}}-\Delta i_{\mathrm{CgS}}\right)L_{\mathrm{gS}}+\left(\Delta i_{\mathrm{iT}}-\Delta i_{\mathrm{CgT}}\right)L_{\mathrm{gT}}}{3T_S},& \left(9\right)\\ V_{\mathrm{nOS}7}=V_{\mathrm{DC}}-\frac{\Delta i_{\mathrm{iR}}{L}_{\mathrm{iR}}+\Delta i_{\mathrm{iS}}{L}_{\mathrm{iS}}+\Delta i_{\mathrm{iT}}{L}_{\mathrm{iT}}}{3T_S}-\frac{V_{\mathrm{Rpn}}+V_{\mathrm{Spn}}+V_{\mathrm{Tpn}}}{3}-\frac{\left(\Delta i_{\mathrm{iR}}-\Delta i_{\mathrm{CgR}}\right)L_{\mathrm{gR}}+\left(\Delta i_{\mathrm{iS}}-\Delta i_{\mathrm{CgS}}\right)L_{\mathrm{gS}}+\left(\Delta i_{\mathrm{iT}}-\Delta i_{\mathrm{CgT}}\right)L_{\mathrm{gT}}}{3T_S}.& \left(10\right)\end{array}$

Therefore, V_nO can be represented by the following equation (11)

$\begin{array}{cc}\stackrel{\_}{V_{\mathrm{nO}}}=\frac{V_{\mathrm{DC}}}{3}\left(D_R+D_S+D_T\right)-\frac{V_{\mathrm{Rpn}}+V_{\mathrm{Spn}}+V_{\mathrm{Tpn}}}{3}-\frac{\Delta i_{\mathrm{iR}}\left(L_{\mathrm{iR}}+L_{\mathrm{gR}}\right)+\Delta i_{\mathrm{iS}}\left(L_{\mathrm{iS}}+L_{\mathrm{gS}}\right)+\Delta i_{\mathrm{iT}}\left(L_{\mathrm{iT}}+L_{\mathrm{gT}}\right)}{3T_S}-\frac{\left[V_{\mathrm{Rcn}}\left(t\right)-2V_{\mathrm{Rcn}}\left(t-T_S\right)+V_{\mathrm{Rcn}}\left(t-2T_S\right)\right]C_{\mathrm{gR}}{L}_{\mathrm{gR}}}{3T_S^2}-\frac{\left[V_{\mathrm{Scn}}\left(t\right)-2V_{\mathrm{Scn}}\left(t-T_S\right)+V_{\mathrm{Scn}}\left(t-2T_S\right)\right]C_{\mathrm{gS}}{L}_{\mathrm{gS}}}{3T_S^2}-\frac{\left[V_{\mathrm{Tcn}}\left(t\right)-2V_{\mathrm{Tcn}}\left(t-T_S\right)+V_{\mathrm{Tcn}}\left(t-2T_S\right)\right]C_{\mathrm{gT}}{L}_{\mathrm{gT}}}{3T_S^2}.& \left(11\right)\end{array}$

Thus, a switching duty ratio of the three phase switch can be represented by the following equation (12):

$\begin{array}{cc}{D}_{\mathrm{RST}}=\frac{\left(L_{\mathrm{iRST}}+L_{\mathrm{gRST}}\right)\Delta i_{\mathrm{iRST}}}{V_{\mathrm{DC}}{T}_S}+\frac{V_{\mathrm{RSTpn}}}{V_{\mathrm{DC}}}+\frac{\left[V_{\mathrm{RSTcN}}\left(t\right)-2V_{\mathrm{RSTcN}}\left(t-T_S\right)+V_{\mathrm{RSTcN}}\left(t-2T_S\right)\right]C_{\mathrm{gRST}}{L}_{\mathrm{gRST}}}{V_{\mathrm{DC}}{T}_S^2}+\frac{\stackrel{\_}{V_{\mathrm{nO}}}}{V_{\mathrm{DC}}}.& \left(12\right)\end{array}$

An aspect of the present disclosure is to use a single phase to control three phases. Therefore, it is needed to prove that the duty ratio of each of the three phases R, S and T is the same, thereby completing the de-coupling procedure. From the above equation (12), it is known that

$\frac{\left(L_{\mathrm{iRST}}+L_{\mathrm{gRST}}\right)\Delta i_{\mathrm{iRST}}}{V_{\mathrm{DC}}{T}_S},\frac{V_{\mathrm{RSTpn}}}{V_{\mathrm{DC}}}\mathrm{and}$ $\frac{\left[V_{\mathrm{RSTcN}}\left(t\right)-2V_{\mathrm{RSTcN}}\left(t-T_S\right)+V_{\mathrm{RSTcN}}\left(t-2T_S\right)\right]C_{\mathrm{gRST}}{L}_{\mathrm{gRST}}}{V_{\mathrm{DC}}{T}_S^2}$ can be independently presented in each of the three phases R, S and T respectively; however, in the V_nO shown in the equation (11), the three phases R, S and T are coupled with each other and cannot be divided into a single phase equation. Therefore, it is assumed that in the duty ratio of each of the three phases R, S and T, in addition to the three terms mentioned above, there is an unknown part. Therefore, when dividing the duty ratio of the three phases into the duty ratio of the single phase, assuming that the unknown part of the duty ratio of the R phase can be combined into an extra term X (the number of the equations in X is not limited); the unknown part of the duty ratio of the S phase can be combined into an extra term Y (the number of the equations in Y is not limited); the unknown part of the duty ratio of the T phase can be combined into an extra term Z (the number of the equations in Y is not limited). The duty ratio of each of the three phases can be represented by the following equations (13), (14) and (15):

$\begin{array}{cc}{D}_R=\frac{\left(L_{\mathrm{iR}}+L_{\mathrm{gR}}\right)\Delta i_{\mathrm{iR}}}{V_{\mathrm{DC}}{T}_S}+\frac{V_{\mathrm{Rpn}}}{V_{\mathrm{DC}}}+\frac{\left[V_{\mathrm{RcN}}\left(t\right)-2V_{\mathrm{RcN}}\left(t-T_S\right)+V_{\mathrm{RcN}}\left(t-2T_S\right)\right]C_{\mathrm{gR}}{L}_{\mathrm{gR}}}{V_{\mathrm{DC}}{T}_S^2}+X,& \left(13\right)\\ D_S=\frac{\left(L_{\mathrm{iS}}+L_{\mathrm{gS}}\right)\Delta i_{\mathrm{iS}}}{V_{\mathrm{DC}}{T}_S}+\frac{V_{\mathrm{Spn}}}{V_{\mathrm{DC}}}+\frac{\left[V_{\mathrm{ScN}}\left(t\right)-2V_{\mathrm{ScN}}\left(t-T_S\right)+V_{\mathrm{ScN}}\left(t-2T_S\right)\right]C_{\mathrm{gS}}{L}_{\mathrm{gS}}}{V_{\mathrm{DC}}{T}_S^2}+Y,& \left(14\right)\\ D_T=\frac{\left(L_{\mathrm{iT}}+L_{\mathrm{gT}}\right)\Delta i_{\mathrm{iT}}}{V_{\mathrm{DC}}{T}_S}+\frac{V_{\mathrm{Tpn}}}{V_{\mathrm{DC}}}+\frac{\left[V_{\mathrm{TcN}}\left(t\right)-2V_{\mathrm{TcN}}\left(t-T_S\right)+V_{\mathrm{TcN}}\left(t-2T_S\right)\right]C_{\mathrm{gT}}{L}_{\mathrm{gT}}}{V_{\mathrm{DC}}{T}_S^2}+Z.& \left(15\right)\end{array}$

Substituting the equations (13), (14) and (15) to the equation (11), an equation (16) can be derived as follows:

$\begin{array}{cc}\stackrel{\_}{V_{\mathrm{nO}}}=\frac{V_{\mathrm{DC}}}{3}\left(X+Y+Z\right).& \left(16\right)\end{array}$

Assuming that the terms X, Y and Z are equal, V_nO can be represented by the equation (17):V_nO=V_DCX=V_DCY=V_DCZ  (17).

Therefore, the duty ratio of the three phase switch returns back to the equation (12), showing that the three phases can be de-coupled to three single phases. Therefore, an operation of the three phases can be controlled by controlling three independent single phases being de-coupled.

The dividing procedure as shown in FIG. 3, in an excitation state, an equation (18) can be derived in accordance with a Kirchhoff's law, and an equation (19) can be used to represent an excitation current variation Δi_ik,mag of the inverter end, where k represents any one of the three phases R, S and T, the equations (18) and (19) are as follows:

$\begin{array}{cc}{V}_{\mathrm{dc}}=L_{\mathrm{ik}}\frac{\Delta i_{\mathrm{ik},\mathrm{mag}}}{dt}+L_{\mathrm{gk}}\frac{\Delta i_{\mathrm{ik},\mathrm{mag}}-\Delta i_{\mathrm{Ck},\mathrm{mag}}}{dt}+V_{\mathrm{kpn}},& \left(18\right)\\ \Delta i_{\mathrm{ik},\mathrm{mag}}=\frac{\left(V_{\mathrm{dc}}-V_{\mathrm{kpn}}\right)dt}{L_{\mathrm{ik}}+L_{\mathrm{gk}}}+\Delta i_{\mathrm{Ck},\mathrm{mag}}\frac{L_{\mathrm{gk}}}{L_{\mathrm{ik}}+L_{\mathrm{gk}}}.& \left(19\right)\end{array}$ where dt=dTs.

In a demagnetization state, an equation (20) can also be derived in accordance with a Kirchhoff's law, and an equation (21) can be used to represent a demagnetization current variation Δi_ik,dem of the inverter end, the equations (20) and (21) are as follows:

$\begin{array}{cc}{V}_{\mathrm{dc}}=L_{\mathrm{ik}}\frac{-\Delta i_{\mathrm{ik},\mathrm{dem}}}{dt}+L_{\mathrm{gk}}\frac{-\Delta i_{\mathrm{ik},\mathrm{dem}}+\Delta i_{\mathrm{Ck},\mathrm{dem}}}{dt}+V_{\mathrm{kpn}},& \left(20\right)\\ \Delta i_{\mathrm{ik},\mathrm{dem}}=\frac{-\left(V_{\mathrm{dc}}-V_{\mathrm{kpn}}\right)dt}{L_{\mathrm{ik}}+L_{\mathrm{gk}}}+\Delta i_{\mathrm{Ck},\mathrm{dem}}\frac{L_{\mathrm{gk}}}{L_{\mathrm{ik}}+L_{\mathrm{gk}}}.& \left(21\right)\end{array}$ where dt=(1−d)Ts.

In the integrating procedure, when combining the excitation current Δi_ik,mag in the equation (19) and the demagnetization current Δi_ik,dem in the equation (21), an equation (22) can be obtained as follows:

$\begin{array}{cc}\Delta i_{\mathrm{ik}}=\Delta i_{\mathrm{ik},\mathrm{mag}}+\Delta i_{\mathrm{ik},\mathrm{dem}}=\frac{2V_{\mathrm{dc}}{T}_S}{L_{\mathrm{ik}}+L_{\mathrm{gk}}}d-\frac{\left(V_{\mathrm{dc}}+V_{\mathrm{kpn}}\right)T_S}{L_{\mathrm{ik}}+L_{\mathrm{gk}}}+\frac{L_{\mathrm{gk}}}{L_{\mathrm{ik}}+L_{\mathrm{gk}}}\Delta i_{\mathrm{Ck}}.& \left(22\right)\end{array}$

The current in the converter end in the next cycle can be represented as an equation (23), which can be viewed as a summation of a difference between a reference current in the instant cycle and the reference current in the next cycle and a difference between the reference current in the instant cycle and the current in the converter end, the equation (23) is as follows:Δi_ik(n+1)={i_gk,ref(n+1)−i_gk,ref(n)}+{i_gk,ref(n)−i_i(n)}=i_gk,ref(n+1)−i_ik(n)  (23)

The switching duty ratio in the next cycle can be obtained using the equations (22) and (23), which is represented as an equation (24), in which i*_gk,ref(n+1) can be represented by an equation (25), and the equation (25) can be rewritten to an equation (26):

$\begin{array}{cc}{d}_{\mathrm{GC}}\left(n+1\right)=\frac{1}{2}+\frac{v_{\mathrm{kpn}}\left(n\right)}{2v_{\mathrm{dc}}\left(n\right)}+L_{\mathrm{Te}}\left(i\right)\frac{i_{\mathrm{gk},\mathrm{ref}}^{*}\left(n+1\right)-i_{\mathrm{ik}}\left(n\right)}{2v_{\mathrm{dc}}\left(n\right)T_S},& \left(24\right)\\ i_{\mathrm{gk},\mathrm{ref}}^{*}\left(n+1\right)=i_{\mathrm{gk},\mathrm{ref}}\left(n+1\right)+\frac{L_{\mathrm{ge}}\left(i\right)}{L_{\mathrm{Te}}\left(i\right)}\left(i_{\mathrm{ck}}\left(n\right)-i_{\mathrm{ck}}\left(n-1\right)\right),& \left(25\right)\\ i_{\mathrm{gk},\mathrm{ref}}^{*}\left(n+1\right)=i_{\mathrm{gk},\mathrm{ref}}\left(n+1\right)+\frac{L_{\mathrm{ge}}\left(i\right)}{L_{\mathrm{Te}}\left(i\right)}\frac{C_g\left(v_{\mathrm{kcn}}\left(n\right)-2v_{\mathrm{kcn}}\left(n-1\right)+v_{\mathrm{kcn}}\left(n-2\right)\right)}{T_S}.& \left(26\right)\end{array}$

FIG. 5 is schematic view showing that the three phase inverting devices of FIG. 2 are connected in parallel for forming an inverter parallel system. In the embodiment, the DC end of each of the three phase inverting device are connected in parallel for receiving and outputting the current voltage V_DC, and an output end of the three phase filter module 120 are connected in parallel, therefore a three phase power can be provided to an AC circuit in the back end, or the three phase power can be received through the AC circuit for inverting. In this kind of client-server architecture, one of the three phase inverting devices is functioned as a server and takes charge of a modulation of an output voltage, the other of the three phase inverting devices is functioned as a client and takes charge of tracing current commands send by the main three phase inverting device. Therefore, a current-sharing control can be achieved, and each of the three phase inverting devices has an equivalent power output. Furthermore, in a conventional inverter parallel system, the value of the output current of each of the inverters is inconsistent, thus unbalanced currents are generated in the system, so called circulating currents. In the inverter parallel system of the present disclosure, the single phase controlling method is applied to each of the three phase inverting devices. The circuit of each phase of the three phase inverting device is treated as an independent single circuit, and the current command of each of the three phase inverting devices is traced independently. Therefore, the circulating current between each of the three phase inverting devices can be dramatically reduced. The effects of the single phase controlling method of the present disclosure applied to the aforementioned inverter parallel system are then described in the following paragraphs.

In an example, the three phase inverting device of the present disclosure is applied in an AC end (e.g., a supply mains). The parameter settings in a simulation circuit are shown in TABLE 2.

TABLE 2
DC current inputted from the inverter end 400 V
AC voltage of the AC end         220 V
switching frequency of the switch 20 kHz
power                            30 kVA
inductance Lik of the filter     1.5 mH
capacitance Cgk of the filter    10 μH
inductance Lgk of the filter     0.5 mH
effective inductance Llk of the transmission line 0~146.2 μH

For evaluating the efficiency of the single phase controlling method of the present disclosure, five times of harmonic wave and seven times of harmonic wave are inputted to the system, as shown in TABLE 3. The AC voltage of the AC end is set to an unbalance state, as shown in TABLE 4.

TABLE 3
harmonic wave
five times  5% of 220 Vrms
seven times 5% of 220 Vrms

TABLE 4
unbalance state of the
supply mains
VRN 220                                              2                                                              ⁢                                          sin                      ⁡                                              (                                                  2                          ⁢                                                                                                          ⁢                          π60                          ⁢                                                                                                          ⁢                          t                                                )
VSN 242                                              2                                                              ⁢                                          sin                      ⁡                                              (                                                                              2                            ⁢                                                                                                                  ⁢                            π60                            ⁢                                                                                                                  ⁢                            t                                                    -                                                      120                            ⁢                            °                                                                          )
VTN 176                                              2                                                              ⁢                                          sin                      ⁡                                              (                                                                              2                            ⁢                                                                                                                  ⁢                            π60                            ⁢                                                                                                                  ⁢                            t                                                    +                                                      120                            ⁢                            °                                                                          )

FIG. 6 is a schematic view showing a comparison of three phase currents in an AC end and an inverter end when a supply mains is in four different power factors and in a strong power grid. The strong power grid indicates that (L1=0, SCR=∞). The current and the THD (Total Harmonic Distortion) of FIG. 6 are shown in TABLE 5. In TABLE 5, it is shown that the single phase controlling method of the present disclosure is performed under the strong power grid. When the power factor is 1 or −1, the THD is smaller than 0.93%. When the power factor is 0, and the current lags the voltage, the THD is smaller than 0.92%. When the power factor is 0, and the current leads the voltage, the THD is smaller than 0.95%.

TABLE 5
		PF = 1	PF = −1	PF = 0 (lgs)	PF = 0 (leds)
		THD	current	THD	current	THD	current	THD	current
AC end	IIR	0.92%	111.6	A	0.92%	111.3	A	0.90%	113.4	A	0.93%	109.5	A
	IIS	0.92%	111.3	A	0.92%	111.6	A	0.90%	113.5	A	0.94%	109.4	A
	IIT	0.92%	111.4	A	0.92%	111.5	A	0.90%	113.2	A	0.93%	109.7	A
Inverter	IgR1	0.92%	37.2	A	0.92%	37.1	A	0.91%	37.8	A	0.94%	36.49	A
1	IgS1	0.92%	37.11	A	0.92%	37.2	A	0.90%	37.83	A	0.94%	36.46	A
	IgT1	0.93%	37.13	A	0.92%	37.17	A	0.91%	37.73	A	0.94%	36.56	A
Inverter	IgR2	0.92%	37.2	A	0.92%	37.1	A	0.91%	37.8	A	0.94%	36.49	A
2	IgS2	0.92%	37.11	A	0.92%	37.2	A	0.91%	37.83	A	0.94%	36.46	A
	IgT2	0.92%	37.13	A	0.92%	37.17	A	0.90%	37.73	A	0.94%	36.56	A
Inverter	IgR3	0.92%	37.2	A	0.92%	37.1	A	0.91%	37.8	A	0.94%	36.49	A
3	IgS3	0.92%	37.11	A	0.92%	37.2	A	0.91%	37.83	A	0.94%	36.46	A
	IgT3	0.92%	37.13	A	0.92%	37.17	A	0.91%	37.73	A	0.94%	36.56	A

FIG. 7 is a schematic view showing a comparison of three phase currents in an AC end and an inverter end when a supply mains is in four different power factors and in a weak power grid. The strong power grid indicates that (L1=146.2 μH, SCR=10). The current and the THD (Total Harmonic Distortion) of FIG. 7 are shown in TABLE 6. In TABLE 6, it is shown that the single phase controlling method of the present disclosure is performed under the strong power grid. When the power factor is 1 or −1, the THD is smaller than 0.96%. When the power factor is 0, and the current lags the voltage, the THD is smaller than 0.94%. When the power factor is 0, and the current leads the voltage, the THD is smaller than 0.98%.

TABLE 6
		PF = 1	PF = −1	PF = 0 (lgs)	PF = 0 (leds)
		THD	current	THD	current	THD	current	THD	current
AC end	IIR	0.94%	111.7	A	0.94%	111.4	A	0.93%	113.5	A	0.96%	109.5	A
	IIS	0.94%	111.4	A	0.94%	111.7	A	0.92%	113.6	A	0.96%	109.4	A
	IIT	0.94%	111.5	A	0.94%	111.6	A	0.93%	113.3	A	0.96%	109.7	A
Inverter	IgR1	0.94%	37.23	A	0.94%	37.12	A	0.93%	37.83	A	0.97%	36.52	A
1	IgS1	0.95%	37.13	A	0.95%	37.22	A	0.93%	37.86	A	0.97%	36.48	A
	IgT1	0.94%	37.15	A	0.94%	37.2	A	0.93%	37.76	A	0.97%	36.58	A
Inverter	IgR2	0.94%	37.23	A	0.94%	37.12	A	0.93%	37.83	A	0.96%	36.52	A
2	IgS2	0.95%	37.13	A	0.94%	37.22	A	0.92%	37.86	A	0.96%	36.48	A
	IgT2	0.95%	37.15	A	0.94%	37.2	A	0.93%	37.76	A	0.96%	36.58	A
Inverter	IgR3	0.95%	37.23	A	0.94%	37.12	A	0.93%	37.83	A	0.96%	36.52	A
3	IgS3	0.94%	37.13	A	0.94%	37.22	A	0.92%	37.86	A	0.96%	36.48	A
	IgT3	0.95%	37.15	A	0.94%	37.2	A	0.93%	37.76	A	0.96%	36.58	A

In sum, the three phase inverting device of the present disclosure can be controlled using a single phase after performing the de-coupling procedure, and complicated procedures (e.g. a abc to dq step) can be omitted when using the dividing procedure and the integrating procedure. Furthermore, through the evaluation result, it is shown that the current of each of the three phases can be precisely controlled, thereby achieving automatic current-sharing in a single phase, and the circulating current can also be reduced. Therefore, the inverting procedures can be dramatically simplified.

Although the present disclosure has been described in considerable detail with reference to certain embodiments thereof, other embodiments are possible. Therefore, the spirit and scope of the appended claims should not be limited to the description of the embodiments contained herein.

It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the present disclosure without departing from the scope or spirit of the disclosure. In view of the foregoing, it is intended that the present disclosure cover modifications and variations of this disclosure provided they fall within the scope of the following claims.

Claims

1. A single phase controlling method applied to a three phase inverting device, the three phase inverting device includes a three phase switch, the single phase controlling method comprising: inputting a DC current into a DC end of the three phase inverting device;performing a de-coupling procedure to calculate a switching duty ratio using an average value of a voltage between the DC end and a ground of an AC end of the three phase inverting device and generating an electric output of a single phase circuit in accordance with the average value of the voltage and the switching duty ratio;performing a dividing procedure to divide the electric output of the single phase circuit into two current variations of an inverting end of the three phase inverting device, wherein the two current variations are corresponded to an excitation state and a demagnetization state respectively; andperforming an integrating procedure to integrate the two current variations corresponded to the excitation state and the demagnetization state for obtaining another switching duty ratio on a next duty of the three phase switch.

2. The single phase controlling method of claim 1, wherein the three phase inverting device includes a three phase inverting module and a three phase filter module coupled with the three phase inverting module, and the three phase inverting module comprises a plurality of the three phase switches.

3. The single phase controlling method of claim 2, further comprising: performing the de-coupling procedure, the dividing procedure and the integrating procedure through a controller.

4. The single phase controlling method of claim 1, further comprising: connecting a plurality of the three phase inverting devices in parallel for forming an inverter parallel system.

5. The single phase controlling method of claim 2, wherein the switching duty ratio of the three phase switch is represented as the following equation:

6. A three phase inverting device using the single phase controlling method of claim 1, comprising: a three phase inverter module, wherein the three phase inverter module comprises a plurality of switches, each two of the switches are connected for forming a bridge arm, an input end of each of the bridge arm are coupled for forming a DC end, the DC end is connected to a DC load; anda three phase filter module connected to the three phase inverter module, wherein the three phase filter module comprises a plurality of inductances and a plurality of capacitances, the inductances are connected at one side of the capacitances, a portion of the capacitances are connected to a output end of each of the bridge arm of the three phase inverter module, a portion of the inductances are connected to an AC end.