CN106712054A

CN106712054A - Modular multilevel-based STATCOM device for inhibiting ripples of capacitive voltage

Info

Publication number: CN106712054A
Application number: CN201710150668.8A
Authority: CN
Inventors: 刘万勋; 魏胜民; 余晓鹏; 田春筝; 毛玉宾; 刘永民; 黄景慧; 王洋; 于琳琳; 张丽华; 司瑞华; 马杰; 李甜甜; 王世谦; 程昱明; 孙思培; 袁鹏; 杜习超; 王圆圆; 贾鹏
Original assignee: State Grid Corp of China SGCC; Economic and Technological Research Institute of State Grid Henan Electric Power Co Ltd
Current assignee: State Grid Corp of China SGCC; Economic and Technological Research Institute of State Grid Henan Electric Power Co Ltd
Priority date: 2017-03-14
Filing date: 2017-03-14
Publication date: 2017-05-24
Anticipated expiration: 2037-03-14
Also published as: CN106712054B

Abstract

The invention provides a modular multilevel-based STATCOM device for inhibiting ripples of capacitive voltage. The STATCOM device comprises an STATCOM system which is directly connected to a common node through a connection inductor in parallel, wherein the STATCOM system comprises a bridge arm phase A, a bridge arm phase B, a bridge arm phase C and a bridge arm phase D. On the basis of an MMC topology, the DC bus voltage of the MMC is eliminated, the hidden danger of a short circuit of a common bus of a DC side is eliminated and the security of the device is improved; the low-frequency ripples of capacitive voltage of an upper bridge arm and a lower bridge arm of each bridge arm phase are inhibited by using a low-voltage and low-capacity capacitor, so that use of lower capacitance of a sub-module is facilitated, the cost of a system is reduced and the volume of the device is reduced. The bride arm phases of switching devices are replaced with buffer inductors, the quantities of the capacitors and the switching devices are reduced to 3/4 of those of a conventional structure, so that the cost and the volume of the device are significantly reduced and the loss of the system is reduced. The application of the bridge arm phase is not limited to the application scene of reactive power compensation and an existing bridge arm phase adopting cascaded H-bridge multilevel topological devices can be replaced.

Description

A kind of STATCOM device for suppressing capacitance voltage pulsation based on modular multilevel

Technical field

The present invention relates to power electronics flexible transmission equipment technical field, and in particular to a kind of based on modular multilevel suppression The STATCOM device of capacitance voltage pulsation processed.

Background technology

The presence of a large amount of imbalance industrial loads such as industrial ac arc furnace, electric railway and single-phase Large Copacity load, And power electronic equipment is widely used, to power system substantial amounts of reactive current and negative-sequence current are brought, not only increased Loss, and harm power equipment.In this context, because Power Electronic Technique can participate in maintaining power system stability fortune Row and trend distribution, are increasingly becoming the important technical of power system compensation and regulation.

STATCOM (Static Synchronous Compensator:STATCOM) it is power electronic equipment Participate in one of main application of power network regulation.STATCOM is seen as a controllable independent voltage source, can enter depending on application scenario Row reactive power compensation, access point voltage-regulation, harmonics restraint etc., to improve the quality of power supply of public access point (PCC), improve The stability of system.As user steps up to quality of power supply requirement, STATCOM start to receive more and more attention and Research.

Based on the STATCOM systems of traditional two level PWMs working method, cannot be answered by pressure-resistant limitation of single power device Mesohigh field is used, is limited by individual devices switching frequency, its output end generally requires the passive filter ability of heaviness Access power network.And modular multilevel is to realize the technology that high-power is converted with low voltage power devices, its modularization sets Meter, using low tension switch device, output waveform quality be good etc., many merits are considered as being especially suitable for applying high-power in middle high-pressure The quality of power supply regulation and control occasion.Its general principle is connected using multiple mutually isostructural basic transformation device units, realize etc. The staircase output voltage of number level approaches sinusoidal voltage waveform, and in industrial circle successful Application.

STATCOM based on modular multilevel (referred to as " MMC ") has been obtained for widely paying close attention to and grinding in academia Study carefully, and a kind of Transformerless STATCOM topological structures based on MMC of Authorization Notice No. CN201774259U, and based on module Change reactive-load compensation (MMC-STATCOM) method of Multilevel Inverters, provided in being the A of CN 105226687 in application notification number A kind of energy-storage system topological structure and its control strategy generated electricity suitable for large-scale photovoltaic, the topological structure includes connected benefit Repay device and A, B, C three phase network circuit；The compensation device is the dress that STATCOM functions are combined with energy-storage system function phase Put.The topological structure is easy to be extended to high-power field, simultaneously because its switching frequency is low, it is small to be lost, with energy storage device With reference to the capacity of energy-storage system can be reduced, so as to reduce the cost and volume of device.But, based on modular multilevel STATCOM still suffers from some intrinsic problems to be needed boundary's concern and gives to solve, first, public direct-current in the STATCOM based on MMC There is the high voltage of power network grade in bus, once dc-side short-circuit, will cause huge short circuit current, burn device；Secondly, work Journey experience have shown that, substantial amounts of submodule electric capacity occupies the big quantity space of device in MMC, so as to increased the volume of device, together When also increase system cost, the capacitance for reducing submodule capacitor can significantly reduce the electric capacity of capacitor, so as to significantly subtract The volume of few device, reducing apparatus cost；In addition, when STATCOM is used for having the unbalanced system of neutral dot system, and need When repaying out-of-balance current, extra zero sequence passage makes one bridge arm of increase of MMC, the also proportional increasing of the cost and volume of device Plus.

The content of the invention

In view of this, the present invention for reduction MMC submodule electric capacity volume, is eliminated for the STATCOMM systems based on MMC HVDC side voltage, how increased number of devices when reducing compensation out-of-balance current, the invention provides a kind of new idle Compensation device, the present invention mutually eliminates DC bus-bar voltage using new bridge arm, and electric capacity is connected by increasing between upper and lower bridge arm Come the low frequency pulsating for forming energy channel to suppress submodule capacitor voltage, using two buffer inductances and of low-voltage-grade Individual passive resonant circuit constitutes zero-sequence current passage.

In order to solve the above technical problems, the technical solution used in the present invention is：

A kind of STATCOM device for suppressing capacitance voltage pulsation based on modular multilevel, including directly by connecting electricity Sense is connected in parallel on the STATCOM systems of common node, and the STATCOM systems include bridge arm phase A, bridge arm phase B, bridge arm phase C and bridge Arm phase D；

The bridge arm phase A, bridge arm phase B, bridge arm phase C are made up of switching device, are connected with A, B, C of power network respectively, form nothing The compensation passage of work(electric current and negative-sequence current,

The bridge arm phase D is made up of two inductance, is connected with the neutral point of power network, forms zero sequence current compensation passage, to realize Total current compensation under power network or laod unbalance.

The STATCOM systems, the reactive current compensated according to needed for ip-iq methods are calculated, negative-sequence current and zero sequence electricity The command value of stream, then transducer port voltages of the MMC as corresponding to instruction current output compensation electric current is calculated, using phase-shifting carrier wave The required port output voltage of modulation strategy synthesis.

The DC side of the STATCOM systems does not include energy storage Support Capacitor.

The bridge arm phase A, the bridge arm phase B in the STATCOM systems is identical with the structure of the bridge arm phase C, and Bridge arm phase A, bridge arm phase B and bridge arm phase C are composed in series by upper bridge arm and lower bridge arm；

The upper bridge arm forms upper/lower terminal mouthful circuit, the lower bridge arm and institute by multiple half-bridge submodules successively head and the tail series connection The structure for stating bridge arm is identical, and the lower port of the lower port connection upper bridge arm of the lower bridge arm collectively constitutes a bridge arm Phase, i.e. the structure of the upper bridge arm rotates 180 degree as lower bridge arm and upper bridge arm drop-over.

The upper bridge arm and lower bridge arm include 2N submodule respectively.

One identical buffer inductance of each series connection in the tie point both sides of the upper bridge arm and lower bridge arm.

The half-bridge submodule is connected by two full control switching devices, and two terminal circuits formed after series connection are in parallel with electric capacity, Two full-controlled devices distinguish one diode of inverse parallel.

The bridge arm phase D is connected by two buffer inductances and forms two-port circuit, buffer inductance and bridge arm phase A, bridge arm phase Buffer inductance in B, bridge arm phase C is identical.

The bridge arm phase A, bridge arm phase B, bridge arm phase C, bridge arm phase D one end are connected by positive common DC bus P, and its is another One end is connected by negative common DC bus N.

The bridge arm phase A, bridge arm phase B, the midpoint exit of bridge arm phase C are connected with power network, used as the passage of compensation electric current, bridge arm The midpoint of phase D is connected by a communication channel with neutral point of electric network.

The communication channel is made up of passive element.

Electrical potential difference between the common DC bus P and common DC bus N of the STATCOM systems is zero, the STATCOM systems Electrical potential difference in system between common DC bus P and common DC bus N be zero principle it is as follows：

The upper bridge arm of each bridge arm phase and lower bridge arm resultant voltage are expressed as：

Wherein, V_CIt is all submodule capacitor voltage sums of bridge arm, ω₀It is power frequency angular frequency,

Then the voltage of common DC bus P and N is uPN：

u_PN=u_U+u_L=0 (3)

Wherein, uU, uL are respectively the resultant voltage of bridge arm and lower bridge arm.

The bridge arm is divided into upper and lower two sub- bridge arms, and every sub- bridge arm includes N number of submodule, the upper bridge of bridge arm phase Upper and lower sub- bridge arm midpoint forms energy channel with the upper and lower sub- bridge arm midpoint of lower bridge arm by being connected capacitance connection in arm.

The connection electric capacity is subjected only to high frequency voltage, is not subject to the DC voltage and power-frequency voltage of power network grade, i.e. voltage class And capacity is smaller.

The bridge arm of the connection electric capacity can mutually realize that the pulsation of submodule capacitor voltage suppresses, and it is as follows that it suppresses principle：

One equivalent circuit of bridge arm phase is as shown in Fig. 2 omit power frequency composition and flip-flop, an equivalent circuit for bridge arm phase Fig. 3 is equivalent to, in figure 3, only retaining can generate the amount of active power, then Fig. 3 is further simplified as Fig. 4, Fig. 4 medium-high frequencies The voltage of component, electric current are expressed as

u_U1=u_e+U_hcos(ωt)

u_U2=-u_e-U_hcos(ωt)

u_L1=-u_e+U_hcos(ωt)

u_L2=+u_e-U_hcos(ωt) (4)

Wherein, uU1 is the upper sub- bridge arm resultant voltage of upper bridge arm, and uU2 is the lower sub- bridge arm resultant voltage of upper bridge arm；

uL₁It is the upper sub- bridge arm resultant voltage of lower bridge arm, uL₂It is the lower sub- bridge arm resultant voltage of lower bridge arm；Ue is swashing for ih Encourage, ue is high frequency content, its angular frequency is ω.

4 sub- bridge arm currents of each bridge arm phase are

i_U1=I_h cos(ωt)

i_U2=-I_h cos(ωt)

i_L1=-I_h cos(ωt)

i_L2=I_h cos(ωt) (5)

Wherein, iU₁It is the electric current of the upper sub- bridge arm of upper bridge arm, iU₂It is the electric current of the lower sub- bridge arm of upper bridge arm；

iL₁It is the electric current of the upper sub- bridge arm of lower bridge arm, iL₂It is the electric current of the lower sub- bridge arm of lower bridge arm；

Then the power of each sub- bridge arm is：

It is of ac per the first three items in formula, does not produce active, last per formula is to there is a term of works, also, upper bridge arm have Work(and lower bridge arm it is active in opposite direction, be used to suppress low frequency pulsating power in opposite direction in upper and lower bridge arm electric capacity.

Described ih is a controlled free degree, controls the amplitude and phase of ih so as to control upper and lower bridge arm Power Exchange Direction and size.

The beneficial effect that the present invention reaches is：

1. the present invention is topological based on MMC, but eliminates the DC bus-bar voltage of MMC, eliminates the short circuit of DC side common bus Hidden danger, improves the security of device, and remains the modularization feature of MMC.

2. engineering is actual proves, substantial amounts of floating capacitance occupies the huge space of device in MMC devices, and its cost is also even high In its corresponding half-bridge module, the present invention is by accounting for a leading suppression for pulsating volage composition, directly reducing floating The voltage class that electric capacity is born, is easy to select less floating capacitance, reduces system cost, reduces device volume；

3. the new bridge arm phase structure of the present invention eliminates the grid level voltages at two ends, is made up of switching device therefore, it is possible to use Bridge arm mutually substitute the conventional bridge arm phase being made up of switching device, electric capacity and switching device number are reduced to the 3/4 of conventional structure, from And installation cost and volume are significantly reduced, additionally, it is conventional 3/4 that the drive circuit of device is also accordingly less, improve system Reliability, decrease system loss；

4. in the suppressing method of capacitance voltage low frequency pulsating, increased hardware component is almost minimum, and suppressing method is to compensation electric current Without influence；

5. the application of phase bridge arm of the invention is not limited solely to the application scenario of reactive-load compensation, can substitute existing using cascade The phase bridge arm of many level topology apparatus of H bridges, such as cascaded H-bridges star topology, cascaded H-bridges star topology, preposition rectification circuit.

Brief description of the drawings

The present invention is further described with reference to the accompanying drawings and examples.

Fig. 1 is STATCOM systems proposed by the present invention；

Fig. 2 is single-phase fully equivalent circuit diagram of the invention；

Fig. 3 is the single-phase high frequency component equivalent circuit diagram of omission power frequency of the invention and flip-flop；

Fig. 4 is further to be omitted on the basis of Fig. 3 with the single-phase active high fdrequency component formed after active unrelated composition etc. Effect circuit diagram；

In figure：

The 1 upper bridge arm for representing each bridge arm phase；The 2 lower bridge arms for representing each bridge arm phase；

Represent bridge arm on the son of each bridge arm；Bridge arm under 4 sons for representing each bridge arm；

5 bridge arm buffer inductances；

The connection electric capacity of 6 upper and lower bridge arms；

Connection inductance between 7 converters and power network.

Specific embodiment

To make the purpose, technical scheme and advantage of the embodiment of the present invention clearer, below in conjunction with the embodiment of the present invention Accompanying drawing 1-4, the technical scheme to the embodiment of the present invention is clearly and completely described.Obviously, described embodiment is this A part of embodiment of invention, rather than whole embodiments.Based on described embodiments of the invention, the common skill in this area The every other embodiment that art personnel are obtained, belongs to the scope of protection of the invention.

Embodiment

A kind of STATCOM systems for suppressing capacitance voltage pulsation based on modular multilevel, the STATCOM systems are directly led to Connection inductance in parallel is crossed in common node, without transformer, the STATCOM systems include 4 bridge arm phases, wherein, bridge arm phase A, Bridge arm phase B, bridge arm phase C are made up of switching device, and bridge arm phase D is made up of two inductance.

The bridge arm phase A, bridge arm phase B, bridge arm phase C structure it is identical, each bridge arm is by upper bridge arm 1, lower bridge arm 2 two Bridge arm is composed in series, and upper bridge arm is connected by multiple half-bridge submodules successively head and the tail, forms upper/lower terminal mouthful circuit, lower bridge arm and The structure of upper bridge arm is identical, as lower bridge arm after upper bridge arm two-port circuit rotation 180 degree, then with upper bridge arm drop-over, and composition The new bridge arm phase of the present invention, this is different from conventional MMC structures；Respectively one identical of series connection is delayed on the both sides of upper and lower bridge arm tie point Rush inductance 5.Each bridge arm includes 2N submodule, and each half-bridge submodule is connected by two full control switching devices, shape after series connection Into two terminal circuits it is in parallel with electric capacity, two full-controlled devices distinguish one diode of inverse parallel.

Bridge arm phase D forms two-port circuit by two series connection of buffer inductance 5.

The bridge arm phase A, bridge arm phase B, bridge arm phase C and bridge arm phase D one end are connected by positive common DC bus P, it The other end connected by negative common DC bus N；Bridge arm phase A, bridge arm phase B, the midpoint of bridge arm phase C, as exit, Connect respectively one and connect A, B, C phase being connected to the grid after inductance 7, reactive current, negative-sequence current for compensation network；Bridge arm The exit at D midpoints hinders DC circuit (preferably LC industrial frequency resonances circuit) by a passive logical exchange of connecting, and is connected to the grid Neutral point, be used to form zero sequence current compensation passage.

Upper and lower bridge arm forms energy channel by connecting electric capacity 6, to suppress low frequency pulsating in upper and lower bridge arm submodule electric capacity, tool Body connection method is：Bridge arm is divided into upper and lower two sub- bridge arms, and every sub- bridge arm includes N number of submodule, bridge arm in bridge arm phase Upper and lower sub- bridge arm midpoint sub- bridge arm midpoint upper and lower with lower bridge arm by being connected capacitance connection.The connection capacitance and voltage Smaller grade, according to requirement of engineering, can use single electric capacity, it is also possible to the cascade string constituted using multiple electric capacity.

The computational methods of the STATCOM system balances instruction are with prior art without essence difference.

Additionally, bridge arm of the invention can mutually substitute the bridge arm phase of many level of existing cascaded H-bridges, so as to reach only with half-bridge Module only synthesizes the purpose of output AC voltage.

Used as another embodiment of the invention, the common DC bus P and public direct-current of the STATCOM systems are female Electrical potential difference between line N is zero, and the electrical potential difference in the STATCOM systems between common DC bus P and common DC bus N is zero Principle it is as follows：

Then the voltage of common DC bus P and N is uPN：

u_PN=u_U+u_L=0 (3)

The bridge arm is divided into upper and lower two sub- bridge arms, and every sub- bridge arm includes N number of submodule, in the upper bridge arm of bridge arm phase The upper and lower sub- bridge arm midpoint of upper and lower sub- bridge arm midpoint and lower bridge arm forms energy channel by being connected capacitance connection.

The connection electric capacity is subjected only to high frequency voltage, is not subject to the DC voltage and power-frequency voltage of power network grade, i.e. voltage Grade and capacity are smaller.

One equivalent circuit of bridge arm phase as shown in Fig. 2 omit power frequency composition and flip-flop, bridge arm phase it is equivalent Circuit equivalent is Fig. 3, and in figure 3, only retaining can generate the amount of active power, then Fig. 3 is further simplified as Fig. 4, in Fig. 4 The voltage of high fdrequency component, electric current are expressed as

u_U1=u_e+U_hcos(ωt)

u_U2=-u_e-U_hcos(ωt)

u_L1=-u_e+U_hcos(ωt)

u_L2=+u_e-U_hcos(ωt) (4)

UL1 is the upper sub- bridge arm resultant voltage of lower bridge arm, and uL2 is the lower sub- bridge arm resultant voltage of lower bridge arm；Ue is the excitation of ih, Ue is high frequency content, and its angular frequency is ω.

4 sub- bridge arm currents of each bridge arm phase are

i_U1=I_hcos(ωt)

i_U2=-I_hcos(ωt)

i_L1=-I_hcos(ωt)

i_L2=I_hcos(ωt) (5)

Wherein, iU1 is the electric current of the upper sub- bridge arm of upper bridge arm, and iU2 is the electric current of the lower sub- bridge arm of upper bridge arm；

IL1 is the electric current of the upper sub- bridge arm of lower bridge arm, and iL2 is the electric current of the lower sub- bridge arm of lower bridge arm；

Then the power of each sub- bridge arm is：

The beneficial effect that the present invention reaches is：

Embodiment described above, the only present invention are applied to the embodiment of STATCOM, and those skilled in the art will be understood that this Invent the half-bridge submodule and belong to preferred structure of the invention, the present invention is not limited to the bridge arm being made up of half-bridge circuit, Single level monopole type construction module including other many level or multi-form, is related to the topological structure of such phase bridge arm all should Cover in the present invention.

Claims

It is 1. a kind of that the STATCOM device that capacitance voltage is pulsed is suppressed based on modular multilevel, it is characterised in that：Including directly leading to STATCOM system of the connection inductance in parallel in common node is crossed, the STATCOM systems include bridge arm phase A, bridge arm phase B, bridge arm Phase C and bridge arm phase D；

The bridge arm phase A, bridge arm phase B, bridge arm phase C are made up of switching device, are connected with A, B, C of power network respectively, form nothing The compensation passage of work(electric current and negative-sequence current；

The bridge arm phase D is made up of two inductance, is connected with the neutral point of power network, forms zero sequence current compensation passage, to realize Total current compensation under power network or laod unbalance；

The STATCOM systems, the reactive current compensated according to needed for ip-iq methods are calculated, negative-sequence current and zero-sequence current Command value, then transducer port voltages of the MMC as corresponding to instruction current output compensation electric current is calculated, modulated using phase-shifting carrier wave The required port output voltage of strategy synthesis.
2. as claimed in claim 1 to suppress the STATCOM device that capacitance voltage is pulsed based on modular multilevel, its feature exists In：The DC side of the STATCOM systems does not include energy storage Support Capacitor.
3. as claimed in claim 1 to suppress the STATCOM device that capacitance voltage is pulsed based on modular multilevel, its feature exists In：The bridge arm phase A, the bridge arm phase B in the STATCOM systems is identical with the structure of the bridge arm phase C, and bridge arm phase A, bridge arm phase B and bridge arm phase C are composed in series by upper bridge arm and lower bridge arm.
4. as claimed in claim 3 to suppress the STATCOM device that capacitance voltage is pulsed based on modular multilevel, its feature exists In：The upper bridge arm forms upper/lower terminal mouthful circuit by multiple half-bridge submodules successively head and the tail series connection, the lower bridge arm and described The structure of upper bridge arm is identical, and the lower port of the lower port connection upper bridge arm of the lower bridge arm collectively constitutes a bridge arm Phase, i.e. the structure of the upper bridge arm rotates 180 degree as lower bridge arm and upper bridge arm drop-over.
5. as claimed in claim 4 to suppress the STATCOM device that capacitance voltage is pulsed based on modular multilevel, its feature exists In：The upper bridge arm and lower bridge arm include 2N submodule respectively, and N is nonnegative integer；The connection of the upper bridge arm and lower bridge arm One identical buffer inductance of each series connection in point both sides.
6. as claimed in claim 4 to suppress the STATCOM device that capacitance voltage is pulsed based on modular multilevel, its feature exists In：The half-bridge submodule is connected by two full control switching devices, and two terminal circuits formed after series connection are in parallel with electric capacity, and two complete Control device difference one diode of inverse parallel.
7. as claimed in claim 5 to suppress the STATCOM device that capacitance voltage is pulsed based on modular multilevel, its feature exists In：The bridge arm phase D is connected by two buffer inductances and forms two-port circuit, buffer inductance and bridge arm phase A, bridge arm phase B, bridge arm Buffer inductance in phase C is identical.
8. as claimed in claim 1 to suppress the STATCOM device that capacitance voltage is pulsed based on modular multilevel, its feature exists In：The bridge arm phase A, bridge arm phase B, bridge arm phase C, bridge arm phase D one end are connected by positive common DC bus P, its other end Connected by the common DC bus N for bearing；The bridge arm phase A, bridge arm phase B, the midpoint exit of bridge arm phase C are connected with power network, Used as the passage of compensation electric current, the midpoint of bridge arm phase D is connected by a communication channel with neutral point of electric network；The communication channel It is made up of passive element.
9. as claimed in claim 8 to suppress the STATCOM device that capacitance voltage is pulsed based on modular multilevel, its feature exists In：Electrical potential difference between the common DC bus P and common DC bus N of the STATCOM systems is zero；Each bridge arm phase it is upper Bridge arm and lower bridge arm resultant voltage are expressed as：

$u_{U . x} = \frac{c o s (ω_{0} t) + 1}{2} V_{C} - - - (1)$

$u_{L . x} = \frac{- c o s (ω_{0} t) - 1}{2} V_{C} - - - (2)$

Wherein, V_CIt is all submodule capacitor voltage sums of bridge arm, ω₀It is power frequency angular frequency,

Then the voltage of common DC bus P and N is uPN：

u_PN=u_U+u_L=0 (3)

Wherein, uU, uL are respectively the resultant voltage of bridge arm and lower bridge arm；

The bridge arm is divided into upper and lower two sub- bridge arms, and every sub- bridge arm includes N number of submodule, in the upper bridge arm of bridge arm phase The upper and lower sub- bridge arm midpoint of upper and lower sub- bridge arm midpoint and lower bridge arm forms energy channel by being connected capacitance connection.
10. it is as claimed in claim 1 that the STATCOM device that capacitance voltage is pulsed, its feature are suppressed based on modular multilevel It is：The voltage of high fdrequency component, electric current are expressed as

u_U1=u_e+U_hcos(ωt)

u_U2=-u_e-U_hcos(ωt)

u_L1=-u_e+U_hcos(ωt)

u_L2=+u_e-U_hcos(ωt) (4)

Wherein, uU₁It is the upper sub- bridge arm resultant voltage of upper bridge arm, uU₂It is the lower sub- bridge arm resultant voltage of upper bridge arm；

uL₁It is the upper sub- bridge arm resultant voltage of lower bridge arm, uL₂It is the lower sub- bridge arm resultant voltage of lower bridge arm；Ue is the excitation of ih, Ue is high frequency content, and its angular frequency is ω；

4 sub- bridge arm currents of each bridge arm phase are

i_U1=I_hcos(ωt)

i_U2=-I_hcos(ωt)

i_L1=-I_hcos(ωt)

i_L2=I_hcos(ωt) (5)

Wherein, iU₁It is the electric current of the upper sub- bridge arm of upper bridge arm, iU₂It is the electric current of the lower sub- bridge arm of upper bridge arm；iL₁It is lower bridge arm The electric current of upper sub- bridge arm, iL₂It is the electric current of the lower sub- bridge arm of lower bridge arm；

Then the power of each sub- bridge arm is：

$p_{U 1} = u_{e} i_{h} + \frac{1}{2} U_{h} I_{h} c o s (2 ω t) + \frac{1}{2} U_{h} I_{h}$

$p_{U 2} = u_{e} i_{h} + \frac{1}{2} U_{h} I_{h} c o s (2 ω t) + \frac{1}{2} U_{h} I_{h}$

$p_{L 1} = u_{e} i_{h} - \frac{1}{2} U_{h} I_{h} c o s (2 ω t) - \frac{1}{2} U_{h} I_{h}$

$p_{L 2} = u_{e} i_{h} - \frac{1}{2} U_{h} I_{h} c o s (2 ω t) - \frac{1}{2} U_{h} I_{h} - - - (6)$ ；

Described ih is a controlled free degree, controls the amplitude and phase of ih so as to control the direction of upper and lower bridge arm Power Exchange And size.