CN104038096A - Novel space vector pulse width modulation method of five-phase inverter - Google Patents

Abstract

The invention relates to a novel space vector pulse width modulation method of a five-phase inverter. The space vector pulse width modulation method comprises constructing five-dimensional reference voltage vectors; and optimizing conducting times of five bridge arm power tubes of the inverter, which has the steps of: sequencing the conducting times of the five bridge arm power tubes, defining action times of two zero vectors of the inverter and calculating the action times of optimized zero vectors, calculating the conducting times of the five optimized bridge arm power tubes of the inverter, and outputting a switch control signal. By reassigning the action times of the zero vectors, modulation range is expanded, and the utilization rate of DC bus voltage is effectively improved.

Description

The new space vector width pulse modulation method of a kind of Five-phase inverter

Affiliated technical field

The present invention relates to a kind of Five-phase inverter space vector PWM modulation algorithm, particularly, belong to motor driven systems research field.

Background technology

Along with the development of modern power electronics technology, for the alternating current machine by inverter power supply, the number of phases of stator can be regarded a new design parameter.Compare with conventional three phase electric machine, polyphase machine has many advantages.For example, it can meet low-pressure high-power occasion by increasing number of motor phases.Increasing of number of motor phases also makes the number of times of the space harmonics that impact is larger increase and amplitude decline, thereby makes torque pulsation less.Polyphase machine still can fall energetic start up and operation when stator phase shortage, is applicable to the field of high reliability.Polyphase machine drove the development in field also to promote accordingly the development of polyphase inverter pulse-width modulation (PWM) strategy in the last few years.

In traditional five-phase induction motor drive system, the sinusoidal voltage of inverter output single-frequency, output voltage only comprises fundametal compoment.Research shows, on first-harmonic basis, meets the harmonic current of certain proportion and phase relation by injection, can effectively improve motor output torque and electric efficiency, and makes motor have under the low speed good dynamic response and loaded starting ability.Now, need inverter except first-harmonic, can also output frequency, the controlled harmonic wave of amplitude.On the other hand, at the polyphase machine of some, by suitable phase sequence transformation rule, be together in series, in many motors tandem drive system of a polyphase inverter power supply, also require independent, the controlled multi-frequency voltage of inverter output.

In order to meet this requirement, must study the modulation strategy of polyphase inverter.Some scholars divide plane sector from sine space vector PWM (SVPWM), select effective vector to set out, in a switch periods, utilize respectively the reference vector of synthetic two the d-q planes of four effective vectors, then by merging subcycle, the centre position to switch periods of mobile each phase switching pulse, is finally converted to the synthetic multidimensional reference vector of four effective vectors.Some scholars, by dividing multidimensional sector, set up the mode of question blank under line, utilize suction parameter to enter question blank and select effective vector and calculate action time.It is more that these algorithms exist sector division, and vector selection is complicated, and sector table takies the problem of a large amount of internal memories, and be difficult for to the problem of more heterogeneous number popularization.

Summary of the invention

The object of the invention is the problems referred to above for existing Five-phase inverter space vector pulse width modulation (SVPWM) method, a kind of Five-phase inverter SVPWM method is proposed, according to given reference voltage, control the on off state of 5 branch power pipes of Five-phase inverter.The method definition space phasor1 is used for synthesizing the reference voltage of two planes as one group of fundamental space vector, avoided the difficult problem that sector is divided and vector is selected, introduce convenient calculating of zero sequence time, utilize Zero voltage vector as a free parameter, by redistributing zero vector action time, expand modulation range, effectively raised the utilance of DC bus-bar voltage.

The new space vector width pulse modulation method of Five-phase inverter, comprising:

(1) with inverter DC bus-bar voltage V _dcfor voltage base value, establish be respectively the d after five phase system coordinate transforms ₁-q ₁and d ₃-q ₃the perunit value of the space vector of voltage in plane, ${\stackrel{\‾}{v}}_{1\_\mathrm{ref}}=v_{d1\_\mathrm{ref}}+{\mathrm{jv}}_{q1\_\mathrm{ref}},$ ${\stackrel{\‾}{v}}_{3\_\mathrm{ref}}=v_{d3\_\mathrm{ref}}+{\mathrm{jv}}_{q3\_\mathrm{ref}},$ Wherein, v _d1-refthe perunit value of the component of voltage on d1 axle, v _q1-refthe perunit value of the component of voltage on q1 axle, v _d3-refthe perunit value of the component of voltage on d3 axle, v _q3-refthe perunit value of the component of voltage on q3 axle, independently first-harmonic and harmonic component in corresponding inverter output voltage, is provided by upper level control unit respectively;

(2) the reference voltage vector v in given zero sequence plane _{0_ref}, first establish v _{0_ref}=0.5;

(3) the reference voltage vector U of structure five dimensions _ref=(v _{d1_ref}, v _{q1_ref}, v _{d3_ref}, v _{q3_ref}, v _{0_ref}) ^t

(4) establish T _a, T _b, T _c, T _d, T _efor the ON time initial value of power tube on five brachium pontis of inverter, T _sfor the switch periods of inverter power pipe, T _a, T _b, T _c, T _d, T _ecan be expressed as

$T_a=T_s(v_{d_{1\_}\mathrm{ref}}+v_{d_{3\_}\mathrm{ref}}+v_{0\_\mathrm{ref}})$

$T_b=T_s(v_{d_{1\_}\mathrm{ref}}\cos 2/5\mathrm{\π}+v_{q_{1\_}\mathrm{ref}}\sin 2/5\mathrm{\π}+v_{d_{3\_}\mathrm{ref}}\cos 6/5\mathrm{\π}+v_{q_{3\_}\mathrm{ref}}\sin 6/5\mathrm{\π}+v_{0\_\mathrm{ref}})$

$T_c=T_s(v_{d_{1\_}\mathrm{ref}}\cos 4/5\mathrm{\π}+v_{q_{1\_}\mathrm{ref}}\sin 4/5\mathrm{\π}+v_{d_{3\_}\mathrm{ref}}\cos 2/5\mathrm{\π}+v_{q_{3\_}\mathrm{ref}}\sin 2/5\mathrm{\π}+v_{0\_\mathrm{ref}})$

$T_d=T_s(v_{d_{1\_}\mathrm{ref}}\cos 6/5\mathrm{\π}+v_{q_{1\_}\mathrm{ref}}\sin 6/5\mathrm{\π}+v_{d_{3\_}\mathrm{ref}}\cos 8/5\mathrm{\π}+v_{q_{3\_}\mathrm{ref}}\sin 8/5\mathrm{\π}+v_{0\_\mathrm{ref}})$

$T_e=T_s(v_{d_{1\_}\mathrm{ref}}\cos 8/5\mathrm{\π}+v_{q_{1\_}\mathrm{ref}}\sin 8/5\mathrm{\π}+v_{d_{3\_}\mathrm{ref}}\cos 4/5\mathrm{\π}+v_{q_{3\_}\mathrm{ref}}\sin 4/5\mathrm{\π}+v_{0\_\mathrm{ref}})$

(5) optimize the ON time of five brachium pontis power tubes of inverter, concrete steps are as follows:

A. the ON time of five brachium pontis power tubes is sorted, establishing maximum is T ₁ ^p, minimum value is T ₅ ^p;

B. be respectively T the action time that defines two zero vectors of inverter ₀, T ₃₁, obtain

T ₀＝T _s-T ₁ ^P，T ₃₁＝T ₅ ^P；

C. definition of T ' ₀, T ' ₃₁action time for the zero vector after optimizing, be expressed as

T’ ₀＝T’ ₃₁＝1/2(Ts-T ₁ ^P+T ₅ ^P)；

D. definition of T _a', T _b', T _c', T _d', T _e' for the ON time of power tube on five brachium pontis of inverter after optimizing, can be expressed as

T _i'＝T _i-T ₅ ^p+T' ₃₁，i＝a、b、c、d、e；

(6) output switch control signal, above-mentioned time is corresponding the duty ratio of each phase switch respectively, and it is compared to the required pwm signal of rear generation Five-phase inverter with triangular carrier signal respectively.

Technique effect of the present invention is as follows:

1, the five phase SVPWM methods that the present invention provides are from the essence of space vector, when synthesized reference vector from new angle Selection space vector, utilize the concept of phasor1 directly by the synthetic service time of transferring to each phase of space vector, realized a kind of brand-new Five-phase inverter space vector pulse width modulation.

2, this kind of implementation saved sectorization, selects the trouble of vector, saved processor memory, optimized operation time.

3, obtain each space phasor1 after action time, then using zero vector as free parameter, it is being redistributed to action time, modulation effect is greatly improved, expanding modulation range, improving DC bus-bar voltage utilance.

Accompanying drawing explanation

Fig. 1 five phase voltage source inventer topological structures.

The space voltage vector of Fig. 2 Five-phase inverter distributes, and is (a) that the space vector of d1-q1 plane distributes, and (b) space vector of d3-q3 plane distributes.

Fig. 3 five distributions of Phase Space vector in decoupling zero plane, (a) are the distribution of space phasor1 in d1-q1 plane, are (b) distribution of space phasor1 in d3-q3 plane, are (c) distribution of space phasor1 on zero sequence space.

Phasor1 pulse of placing placed in the middle in switch periods of Fig. 4.

Being respectively conducted the time after Fig. 5 zero vector mean allocation.

Embodiment

In order to make those skilled in the art person understand better the application's scheme, below in conjunction with accompanying drawing, the application is described in further detail.

The canonical topology structure of Five-phase inverter as shown in Figure 1.DC bus-bar voltage is V _dc, each brachium pontis has upper and lower two switching devices, and five phase loads are Y-connection.The switch function that defines each phase is s _k(k=a, b, c, d, e), s when upper brachium pontis switching device is opened _k=1, s when lower brachium pontis switching device is opened _k=0.Each constantly, upper and lower bridge arm only has a switching device conducting, five phase brachium pontis switches can form 32 kinds of switching modes, corresponding 32 space voltage vectors respectively, when each phase load under certain switching mode has flow of power, corresponding space vector is referred to as effective voltage vector, otherwise is called zero vector, and switching mode is two kinds of situations of (11111) and (00000).

Below the proposition process from novel multi-vitamin SVPMW modulator approach and specific implementation two aspects are described further.

1. the proposition of Five-phase inverter space vector width pulse modulation method of the present invention

1) the space synthesis mode of definition Five-phase inverter space vector

According to principle of coordinate transformation, the d of 30 non-zero vectors of Five-phase inverter after decoupling zero ₁-q ₁, d ₃-q ₃the distribution of plane as shown in Figure 2.Voltage vector correspondence in two planes independently first-harmonic and the harmonic component in Five-phase inverter output voltage, can, by selecting different nonzero voltage space vectors to combine and control action time of each voltage vector, just can change frequency and the amplitude of Five-phase inverter output voltage.

Corresponding 5 voltage vectors in switch function (10000), (01000), (00100), (00010), (00001) in definition Fig. 2 are space phasor1, wherein U _a ⁽¹⁾, U _b ⁽¹⁾, U _c ⁽¹⁾, U _d ⁽¹⁾, U _e ⁽¹⁾be respectively switch function (10000), (01000), (00100), (00010), (00001) corresponding at d ₁-q ₁voltage vector perunit value in plane, amplitude is 0.4, U _a ⁽³⁾, U _b ⁽³⁾, U _c ⁽³⁾, U _d ⁽³⁾, U _e ⁽³⁾be respectively switch function (10000), (01000), (00100), (00010), (00001) corresponding at d ₃-q ₃voltage vector perunit value in plane, amplitude is 0.4, can be found out d by vector composition principle ₁-q ₁, d ₃-q ₃in plane, other space vectors all can be synthetic by these five phasor1s.Space phasor1 is at decoupling zero plane d ₁-q ₁, d ₃-q ₃spatial distribution as shown in Fig. 3 (a), Fig. 3 (b).

With inverter DC bus-bar voltage V _dcfor voltage base value, the voltage reference value of establishing inverter output is with be the d after five phase system coordinate transforms ₁-q ₁and d ₃-q ₃the perunit value of the space vector of voltage in plane, wherein, v _d1-refthe perunit value of the component of voltage on d1 axle, v _q1-refthe perunit value of the component of voltage on q1 axle, v _d3-refthe perunit value of the component of voltage on d3 axle, v _q3-refit is the perunit value of the component of voltage on q3 axle. distinguish in fact independently first-harmonic and harmonic component in corresponding inverter output voltage, by upper level control unit, provided.The reference voltage vector that utilizes synthetic two planes of space phasor1, can be expressed as:

$\begin{array}{c}{T}_s{\stackrel{\‾}{v}}_{1\_\mathrm{ref}}=T_a{U_a}^{\left(1\right)}+T_b{U_b}^{\left(1\right)}+T_c{U_c}^{\left(1\right)}+T_d{U_d}^{\left(1\right)}+T_e{U_e}^{\left(1\right)}\\ T_s{\stackrel{\‾}{v}}_{3\_\mathrm{ref}}=T_a{U_a}^{\left(3\right)}+T_b{U_b}^{\left(3\right)}+T_c{U_c}^{\left(3\right)}+T_d{U_d}^{\left(3\right)}+T_e{U_e}^{\left(3\right)}\end{array}---\left(1\right)$

In formula, T _a, T _b, T _c, T _d, T _efor the ON time of power tube on five brachium pontis of inverter, T _sswitch periods for inverter power pipe.

In formula (1), equation group has comprised 4 equations, 5 unknown numbers.Obviously, in order to solve, also need increase condition the action time of each space phasor1.Except d ₁-q ₁component, d ₃-q ₃, after five phase system coordinate transforms, there is zero-sequence component in component.Zero-sequence component is an isolated system, can not affect inverter phase voltage output, can process separately, but can affect the modulation ratio of inverter, and be a variable that needs are optimized in inverter PWM modulation strategy.The pass of zero-sequence component and five Phase Space vectors is

T _sv ₀＝T _aU _a ⁽⁰⁾+T _bU _b ⁽⁰⁾+T _cU _c ⁽⁰⁾+T _dU _d ⁽⁰⁾+T _eU _e ⁽⁰⁾ (2)

In formula, U _a ⁽⁰⁾, U _b ⁽⁰⁾, U _c ⁽⁰⁾, U _d ⁽⁰⁾, U _e ⁽⁰⁾be respectively switch function (10000), (01000), (00100), (00010), (00001) corresponding voltage vector perunit value in zero sequence plane, amplitude is 0.2, and spatial distribution is as shown in Fig. 3 (c).

2) determine zero sequence free parameter initial value v _{0_ref}

According to the modulation relation of space vector, in each switch periods, every phase switch service time must be greater than 0 and be less than switch periods, in above formula, is comprising an automatic constraints 0≤T _i≤ T _s(i=a, b, c, d, e).Can determine residual voltage v according to this constraints ₀scope.Definition m ₁, m ₃be respectively Five-phase inverter at d ₁-q ₁plane and d ₃-q ₃the index of modulation in plane, i.e. the ratio of reference voltage vector amplitude and DC bus-bar voltage, therefore have

v _d1＝m ₁cosθ ₁,v _q1＝m ₁sinθ ₁,v _d3＝m ₃cosθ ₃,v _q3＝m ₃sinθ ₃ (3)

In formula, θ ₁, θ ₃be respectively d ₁-q ₁plane and d ₃-q ₃the angle of voltage vector and d axle in plane.

Can obtain voltage zero-sequence component v ₀scope:

max{m ₁cos(θ ₁-kφ)+m ₃(θ ₃-3kφ)}≤v ₀≤min{1-m ₁cos(θ ₁-kφ)-m ₃(θ ₃-3kφ)} (4)

In formula, k=0,1 ... 4, φ=2/5 π.

In order to obtain the value of time resolution expression formula, need to determine v ₀value.Easily obtain v ₀one to reduce the scope be m ₁+ m ₃≤ v ₀≤ 1-m ₁-m ₃.When getting v ₀=0.5 o'clock, this inequality is permanent to be set up, therefore desirable v _0-ref=0.5.Modulation range is now

m ₁+m ₃<0.5 (5)

3) calculate phasor1 action time

Introduce after zero-sequence component, for the solving just to change into and separate one group of five yuan of equation of each phasor1 action time, can be expressed as:

$T_s{\stackrel{\&OverBar;}{v}}_{1\_\mathrm{ref}}=T_a{U_a}^{\left(1\right)}+T_b{U_b}^{\left(1\right)}+T_c{U_c}^{\left(1\right)}+T_d{U_d}^{\left(1\right)}+T_e{U_e}^{\left(1\right)}$

$T_s{\stackrel{\&OverBar;}{v}}_{3\_\mathrm{ref}}=T_a{U_a}^{\left(2\right)}+T_b{U_b}^{\left(2\right)}+T_c{U_c}^{\left(2\right)}+T_d{U_d}^{\left(2\right)}+T_e{U_e}^{\left(2\right)}---\left(6\right)$

T _sv _{0_ref}＝T _aU _a ⁽⁰⁾+T _bU _b ⁽⁰⁾+T _cU _c ⁽⁰⁾+T _dU _d ⁽⁰⁾+T _eU _e ⁽⁰⁾

Can obtain reference voltage vector in the pass of the mean value of a switch periods and space phasor1 action time is:

$T_s\left(\begin{array}{c}{v}_{d1\_\mathrm{ref}}\\ v_{q1\_\mathrm{ref}}\\ v_{d3\_\mathrm{ref}}\\ v_{q3\_\mathrm{ref}}\\ v_{0\_\mathrm{ref}}\end{array}\right)=\frac{2}{5}\left(\begin{array}{ccccc}1& \cos 2/5\mathrm{\&pi;}& \cos 4/5\mathrm{\&pi;}& \cos 6/5\mathrm{\&pi;}& \cos 8/5\mathrm{\&pi;}\\ 0& \sin 2/5\mathrm{\&pi;}& \sin 4/5\mathrm{\&pi;}& \sin 6/5\mathrm{\&pi;}& \sin 8/5\mathrm{\&pi;}\\ 1& \cos 6/5\mathrm{\&pi;}& \cos 2/5\mathrm{\&pi;}& \cos 8/5\mathrm{\&pi;}& \cos 4/5\mathrm{\&pi;}\\ 0& \sin 6/5\mathrm{\&pi;}& \sin 2/5\mathrm{\&pi;}& \sin 8/5\mathrm{\&pi;}& \sin 4/5\mathrm{\&pi;}\\ 1/2& 1/2& 1/2& 1/2& 1/2\end{array}\right)\left(\begin{array}{c}{T}_a\\ T_b\\ T_c\\ T_d\\ T_e\end{array}\right)---\left(7\right)$

The analytical expression that solves each phase switch conduction time is:

T _a＝T _s(v _{d1_ref}+v _{d3_ref}+v _{0_ref})

T _b＝T _s(v _{d1_ref}cos2/5π+v _{q1_ref}sin2/5π+v _{d3_ref}cos6/5π+v _{q3_ref}sin6/5π+v _{0_ref})

T _c＝T _s(v _{d1_ref}cos4/5π+v _{q1_ref}sin4/5π+v _{d3_ref}cos2/5π+v _{q3_ref}sin2/5π+v _{0_ref}) (8)

T _d＝T _s(v _{d1_ref}cos6/5π+v _{q1_ref}sin6/5π+v _{d3_ref}cos8/5π+v _{q3_ref}sin8/5π+v _{0_ref})

T _e＝T _s(v _{d1_ref}cos8/5π+v _{q1_ref}sin8/5π+v _{d3_ref}cos4/5π+v _{q3_ref}sin4/5π+v _{0_ref})

4) optimize phasor1 action time

In switch periods during placed in the middle placement, be equivalent to four useful space voltage vectors and two zero vectors act on successively the action time of space phasor1.As shown in Figure 4.Suppose five space phasor1s action time size order be arranged as T ₁ ^pt ₅ ^p, establishing maximum is T ₁ ^p, minimum value is T ₅ ^p, can be expressed as the action time of two zero vectors:

T ₀＝T _s-T ₁ ^P (9)

T ₃₁＝T ₅ ^P (10)

Knownly in effectively vector sequence of operation and time, determine that, in situation, do not affect output effect the action time of zero vector, if the action time of mean allocation zero vector, the T ' action time of the zero vector after definition is optimized ₀, T ' ₃₁, can be expressed as

T’ ₀＝T’ ₃₁＝1/2(T ₀+T ₃₁) (11)

That is, zero vector (00000) equated with the action time of (11111).

Definition of T _a', T _b', T _c', T _d', T _e' be the ON time of power tube on five brachium pontis of inverter after optimizing, can be obtained by the relation of optimizing power tube ON time on the first five brachium pontis:

T _i'＝T _i-T ₅ ^p+T' ₃₁ i＝a、b、c、d、e (12)

Now respectively be conducted the time as shown in Figure 5, in fact do not change as seen selected space vector of voltage.

Now constraints weaken for

T ₁ ^P-T ₅ ^P<Ts (13)

Because the constraints limit of space phasor1 action time the scope of reference voltage, therefore, after constraints dies down, the modulation range of reference voltage increases thereupon.

2. implementation

In order to prove the validity of the modulation algorithm of proposition, based on DSP28335, build system platform and verify.The agent structure of system platform is divided into inverter major loop and control loop two parts.The H bridge circuit consisting of MOSFET forms the main body of five phase voltage source inventers, and the output of Five-phase inverter is connected with five phase RL loads of Y-connection.Control loop is used for realizing novel without sector SVPWM modulation algorithm, and the gate pole trigger impulse of formation control switching device is with the operation of control inverter.Control loop adopts DSP28335 development board to form pwm signal.Select IR2110 to drive chip to form the power device that driving loop is used for controlling main circuit.

The main body of SVPWM modulation algorithm of the present invention is to realize in the EPWM of DSP28335 module, the value that time base period register is set in EPWM module can obtain the carrier cycle needing, count mode is set for increase and decrease counting, time base counter is started from scratch, increase until reach periodic quantity, then start to reduce until reach zero, using that this repeats to obtain triangular wave as carrier wave.

Modulation algorithm calculates size action time of each phase space vector according to given reference voltage level, programming realizes the mean allocation of zero sequence space vector then, then each phase space vector is readjusted action time, finally determines the conducting of each phase constantly.

Direct voltage can be as required and load rating power given, and switch periods is made as 500 microseconds.When debugging, given different frequency and voltage magnitude are verified modulation effect and scope respectively.Voltage magnitude can be by changing index of modulation m ₁, m ₃value change, two frequencies can be adjusted respectively by changing the size of two count values in interrupt cycle, the size correspondence of count value the cycle of output voltage.

Work as m ₁given, m ₃be 0 o'clock, the modulation result obtaining is sinusoidal voltage output; When count value corresponding to f1 equals count value corresponding to the f3 of three times, the modulation result obtaining is the Voltage-output that contains triple-frequency harmonics; When the f1 count value corresponding with f3 is irrelevant, the modulation result obtaining is independent frequency Voltage-output.

Claims (1)

1. the new space vector width pulse modulation method of Five-phase inverter, comprising:

(1) with inverter DC bus-bar voltage V _dcfor voltage base value, establish be respectively the d after five phase system coordinate transforms ₁-q ₁and d ₃-q ₃the perunit value of the space vector of voltage in plane, ${\stackrel{\&OverBar;}{v}}_{1\_\mathrm{ref}}=v_{d1\_\mathrm{ref}}+{\mathrm{jv}}_{q1\_\mathrm{ref}},{\stackrel{\&OverBar;}{v}}_{3\_\mathrm{ref}}=v_{d3\_\mathrm{ref}}+{\mathrm{jv}}_{q3\_\mathrm{ref}},$ Wherein, v _d1-refthe perunit value of the component of voltage on d1 axle, v _q1-refthe perunit value of the component of voltage on q1 axle, v _d3-refthe perunit value of the component of voltage on d3 axle, v _q3-refthe perunit value of the component of voltage on q3 axle, independently first-harmonic and harmonic component in the corresponding inverter output voltage of difference;

(2) the reference voltage vector v in given zero sequence plane _{0_ref}, first establish v _{0_ref}=0.5;

(3) the reference voltage vector U of structure five dimensions _ref=(v _{d1_ref}, v _{q1_ref}, v _{d3_ref}, v _{q3_ref}, v _{0_ref}) ^t

(4) establish T _a, T _b, T _c, T _d, T _efor the ON time initial value of power tube on five brachium pontis of inverter, TS is the switch periods of inverter power pipe, T _a, T _b, T _c, T _d, T _ecan be expressed as

$T_a=T_s(v_{d_1\_\mathrm{ref}}+v_{d_3\_\mathrm{ref}}+v_{0\_\mathrm{ref}})$

$T_b=T_s(v_{d_1\_\mathrm{ref}}\cos 2/5\mathrm{\&pi;}+v_{q_1\_\mathrm{ref}}\sin 2/5\mathrm{\&pi;}+v_{d_3\_\mathrm{ref}}\cos 6/5\mathrm{\&pi;}+v_{q_3\_\mathrm{ref}}\sin 6/5\mathrm{\&pi;}+v_{0\_\mathrm{ref}})$

$T_c=T_s(v_{d_1\_\mathrm{ref}}\cos 4/5\mathrm{\&pi;}+v_{q_1\_\mathrm{ref}}\sin 4/5\mathrm{\&pi;}+v_{d_3\_\mathrm{ref}}\cos 2/5\mathrm{\&pi;}+v_{q_3\_\mathrm{ref}}\sin 2/5\mathrm{\&pi;}+v_{0\_\mathrm{ref}})$

$T_d=T_s(v_{d_1\_\mathrm{ref}}\cos 6/5\mathrm{\&pi;}+v_{q_1\_\mathrm{ref}}\sin 6/5\mathrm{\&pi;}+v_{d_3\_\mathrm{ref}}\cos 8/5\mathrm{\&pi;}+v_{q_3\_\mathrm{ref}}\sin 8/5\mathrm{\&pi;}+v_{0\_\mathrm{ref}})$

$T_e=T_s(v_{d_1\_\mathrm{ref}}\cos 8/5\mathrm{\&pi;}+v_{q_1\_\mathrm{ref}}\sin 8/5\mathrm{\&pi;}+v_{d_3\_\mathrm{ref}}\cos 4/5\mathrm{\&pi;}+v_{q_3\_\mathrm{ref}}\sin 4/5\mathrm{\&pi;}+v_{0\_\mathrm{ref}})$

(5) optimize the ON time of five brachium pontis power tubes of inverter, concrete steps are as follows:

A. the ON time of five brachium pontis power tubes is sorted, establishing maximum is T ₁ ^p, minimum value is T ₅ ^p;

B. be respectively T the action time that defines two zero vectors of inverter ₀, T ₃₁, obtain

T ₀=T _s-T ₁ ^P，T ₃₁=T ₅ ^P；

C. definition of T ' ₀, T ' ₃₁action time for the zero vector after optimizing, be expressed as

T’ ₀=T’ ₃₁=1/2(Ts-T ₁ ^P+T ₅ ^P)；

D. definition of T _a', T _b', T _c', T _d', T _e' for the ON time of power tube on five brachium pontis of inverter after optimizing, can be expressed as

T _i'＝T _i-T ₅ ^p+T' ₃₁，i=a、b、c、d、e；

(6) output switch control signal, above-mentioned time is corresponding the duty ratio of each phase switch respectively, and it is compared to the required pwm signal of rear generation Five-phase inverter with triangular carrier signal respectively.