KR100629824B1 - Pulse Width Modulation Method and Switching Signal Generator Using Carrier of Three Phase Four Leg Inverter - Google Patents

Abstract

In the pulse width modulation method using a carrier wave of a three-phase four-wire four-leg inverter including four legs and generating three output voltages from a power supply, the output voltage command values V _af , V _bf and V of each phase are provided. obtaining an offset voltage V _fn from _cf (a); (B) obtaining the pole voltages V _an , V _bn and V _cn of each phase from the output voltage command values V _af , V _bf and V _{cf of the} phases, and the offset voltage V _fn ; And (c) controlling the switches of each leg by comparing the pole voltages V _an , V _bn and V _cn , and the offset voltage V _fn with the carrier wave. will be.

Although the pulse width modulation method according to the present invention is easier to implement than the conventional spatial vector pulse width modulation method, the pulse width modulation method can obtain the same result as the conventional spatial vector pulse width modulation method.

Description

A Carrier-Based SVPWM Method for Three-Phase Four-Leg Inverter and a Switching Signal Generator}

1 shows a conventional three phase four wire four leg voltage source inverter,

2a shows a voltage vector on a spatial coordinate,

FIG. 2B is a projection of the voltage vector on the spatial coordinate of FIG. 2A onto the α-β plane,

3 illustrates a method of controlling a leg switch,

4 illustrates an inverter switching signal generator implementing the pulse width modulation method according to the present invention.

5 shows a first simulation result of the pulse width modulation method according to the present invention,

6 shows a second simulation result of the pulse width modulation method according to the present invention,

7 is a configuration diagram of an inverter system for experimenting with a pulse width modulation method according to the present invention;

8A to 8C show experimental results of the pulse width modulation method according to the present invention under experimental conditions in which the image voltage is removed.

9A to 9C show experimental results of the pulse width modulation method according to the present invention under the same conditions as the first simulation.

10a to 10c show the experimental results of the pulse width modulation method according to the present invention under the same conditions as the second simulation,

11A to 11D show a switching order for each tetrahedron (tetrahedron 1 to 4) existing in prism 1 among voltage space vectors, respectively.

12A to 12D show tetrahedral 1 to 4 in prism 1, respectively.

<Explanation of symbols for the main parts of the drawings>

11, 12, 13, 14: upper switch 21, 22, 23, 24: lower switch

30: Load 40: Offset Voltage Calculator

51, 52, 53: adder 61, 62, 63, 64: comparator

71: switching signal generator (DSP) 73: gate driver

74: DVS (Direct Voltage Sensing) Circuit

The present invention relates to a pulse width modulation method using a carrier wave of a three-phase four-wire four-leg power inverter.

A three-phase four-leg inverter has a function of independently generating any three outputs, for example, three-phase AC output voltages from a constant voltage source and supplying them to a load. A plurality of switching elements ("poles" or "legs") are provided. It will be referred to as). In the case of a three-phase three-leg inverter, three independent voltage combinations are known to be impossible.

As an inverter driving method, a sine wave pulse width modulation method and a space vector pulse width modulation method are known.

The sinusoidal pulse width modulation method is a method of controlling each pole using a triangular wave in a three-phase three-wire inverter composed of a plurality of poles that can operate independently of each other. However, the magnitude of the output voltage that can be synthesized is very limited compared to the space vector method. In addition, in the case of a three-phase four-leg inverter for applying a three-phase four-wire type, there is no command value to determine the switching state of the f-leg, and thus, application is difficult.

The space vector pulse width modulation method displays the voltage according to the switching state of each leg on a plane or space, and selects an appropriate switching state according to the voltage command value existing in the plane or space, thereby switching each leg. Means how to determine status. Since the space vector pulse width modulation method requires numerical calculation every switching period, it is implemented by a microprocessor performing numerical calculation and digital hardware for pulse width modulation implementation.

The three-phase four-wire four-leg inverter is a three-phase inverter composed of four legs. In FIG. 1, any three output voltages V _af ^* , V _bf ^* , and V _cf ^* may be supplied to the load 30. A typical three phase four wire four leg voltage source inverter is shown.

In the inverter of FIG. 1, since the total number of switches is 4 × 2, there are 2 ⁴ switching vectors V _af , V _bf , and V _cf. Table 1 below shows the switching vectors of the three-phase four-wire voltage source interconnector:

[Table 1] Switching Vector of 3-Phase 4-Wire Voltage Source Inverter

Here, p indicates that the state of the upper switch (11, 12, 13, 14) is ON, n indicates that the state of the upper switch (11, 12, 13, 14) is OFF, V _g = V _dc .

For example, if the upper switches 12, 13, 14 of the a-leg, b-leg and c-leg are ON, and the upper switch 11 of the f-leg is OFF, it is represented by a vector pppn. At this time, the upper switches 11, 12, 13, 14 and the lower switches 21, 22, 23, 24 of each leg operate complementarily. Of the total 16 voltage vectors, two voltage vectors (pppp) and (nnnn) are zero voltage vectors, and the remaining 14 voltage vectors are effective voltage vectors.

Each of the 16 voltage vectors is matched one-to-one on a dqo spatial coordinate (ie, αβγ coordinate system). This is summarized in Table 2 below:

Table 2. Spatial coordinates of each switching vector on dqo spatial coordinates

FIG. 2A shows the voltage vector on a dqo spatial coordinate (ie, αβγ coordinate system), and FIG. 2B shows a projection of the voltage vector on the spatial coordinate on the α-β plane.

Unlike three-phase three-wire, in the case of three-phase four-wire, there is an image split path through the f-leg, so the sum of each output voltage (V _af + V _bf + V _cf ) is not zero. Can be. In the case of the three-phase three-wire type, only the dq voltage is present, so that any voltage can be synthesized inside the hexagon of the plane (two degrees of freedom), that is, the hexagon of FIG. 2B. However, in the case of a three-phase four-wire system, the degree of freedom increases as one leg is added, so that the o voltage can be synthesized. In addition, a spatial coordinate (3 degrees of freedom) called dqo may be introduced. The o voltage is denoted by Vo, which is called an image voltage. The image voltage may be represented by (V _af + V _bf + V _cf ) / 3.

When instantaneously satisfying V _af + V _bf + V _cf = 0, the dq voltage (αβ voltage) converts the output voltages (V _af , V _bf , V _cf ) into two voltages V _d and V _q on the plane. It is one (two degrees of freedom, so there is no image). If V _af + V _bf + V _cf ≠ 0, there is an image voltage, and in this case, the output voltages (V _af , V _bf , V _cf ) are not only V _d and V _q components but also Vo voltage components. To include.

A method for synthesizing a desired voltage vector by selecting three effective voltage vectors from the sixteen voltage vectors of Table 2 has been studied. At this time, the harmonics should be minimized by applying the zero voltage vector for the same time at the beginning and the end of the constant switch period.

Richard Zhang, VH Prasad, D. Boroyevich, and Fred. C. Lee., "Three-dimensional Spase Vector Modulation for Four-Leg Voltage-Source Converters", IEEE Trans. Power Electron., Vol. 17, pp. 314-325, No. 3, May 2002, hereinafter referred to as "Zhang et al.", Are provided with voltage command values V _α , V _β and V _γ , The voltage command value can be represented as a vector on the αβγ spatial coordinate system.

(i) projecting the voltage command value onto the α-β coordinate plane to select one of six prisms;

(ii) discriminating the signs of V _af , V _{bf, and} V _cf for selecting adjacent effective voltage vectors, and selecting one tetrahedron out of four tetrahedra existing for each prism;

(iii) calculating the duty of three effective voltages according to the tetrahedron using 24 (6 × 4) matrices calculated in advance;

(iv) A method of modulating a space vector pulse width, the method comprising calculating the switching time of each arm in order to symmetrically align the zero voltage in a section where an effective voltage is applied.

The 24 matrices are shown in Table 3 below:

[Table 3] Matrix used in spatial vector pulse width modulation method

However, the method is very complicated to implement and requires many operations and tables. Therefore, there is a great need to develop a new pulse width modulation method that can replace the spatial vector pulse width modulation method as described above.

 Accordingly, the present inventors have studied to develop a pulse width modulation method of an easy-to-implement three-phase inverter. As a result, an offset voltage concept and a comparison method with a carrier can be used to easily implement pulse width modulation. Confirmed.

More specifically, the offset voltage V _fn is obtained from the output voltage command values V _af , V _bf and V _cf of each phase; _Obtaining pole voltages V _an , V _bn and V _cn of each phase from the output voltage command values V _af , V _bf and V _{cf of the} phases, and the offset voltage V _fn ; When the pulse width modulation is performed by comparing the respective pole voltages V _an , V _bn and V _cn , and the offset voltage V _fn with the control of the switch of each leg, the same result as the space vector pulse width modulation method described above is obtained. The present invention was confirmed to be easier to implement than the spatial vector pulse width modulation method described in "Zhang et al.".

Accordingly, an object of the present invention is to provide a pulse width modulation method of a three-phase four-wire four-leg inverter. It is also an object of the present invention to provide a switching signal generator for pulse width modulation of the inverter.

The present invention relates to a pulse width modulation method using a carrier wave of a three-phase four-wire four-leg inverter including four legs and independently generating three output voltages from a power supply.

_{Obtaining an} offset voltage V _fn from the output voltage command values V _af , V _bf and V _cf of each phase (a);

(B) obtaining the pole voltages V _an , V _bn and V _cn of each phase from the output voltage command values V _af , V _bf and V _{cf of the} phases, and the offset voltage V _fn ; And

(C) controlling the switches of each leg by comparing the pole voltages V _an , V _bn and V _cn , and the offset voltage V _fn with the carrier waves.

Hereinafter, a pulse width modulation method according to the present invention will be described in detail with reference to the drawings. However, the present invention is not limited by the following examples.

The three output voltage command values V _af , V _bf and V _cf of the inverter shown in FIG. 1 are the difference between the pole voltages V _an , V _bn , V _cn ) and the offset voltage V _fn . It can be expressed as:

[Equation 1]

V _af = V _an -V _fn

V _bf = V _bn -V _fn

V _cf = V _cn -V _fn

Equation (1) is the output voltage command value _{(V af, V bf, V} cf), an expression that represents the relationship between the pole voltage _{(V an, V bn, V} cn), and the offset voltage (V _fn), the V _af The values of, V _bf , and V _cf are set in advance as output voltage command values.
On the other hand, the offset voltage V _fn is determined as in Equation 2:

[Equation 2]

Wherein, V _max is V _{af, bf} V and V indicates the maximum value of _cf, V _min represents the minimum value of V _{af, bf} V and V _cf.

In addition, since the pole voltages V _an , V _bn and V _cn of each phase are the sums of the output voltages V _af , V _bf and V _{cf of} the respective phases corresponding to the offset voltage V _fn , respectively, can be obtained as shown in Equation 3 below. :

[Equation 3]

V _an = V _af + V _fn

V _bn = V _bf + V _fn

V _cn = V _cf + V _fn

The upper switches 14, 11, 12, of the switches of the legs a, b, c and f by comparing the pole voltages V _an , V _bn and V _cn and the offset voltage V _fn of each phase obtained by the method as described above with the carrier wave 13) and the lower switches 24, 21, 22, 23 can be controlled.

3 illustrates a method of generating switching signals of legs a and f.

As shown in Fig. 3, the switch 12 is turned on and the switch 22 is turned off in _a section T _{a in} which the pole voltage V _an is greater than the triangular wave which is the carrier wave. In other sections, switch 12 is turned off and switch 22 is turned on.

In addition, the switch 11 is turned on and the switch 21 is turned off in T _f , where the offset voltage V _fn is larger than the triangle wave. In other sections, switch 11 is turned off and switch 21 is turned on. The T _eff section indicates that the output voltage V _af is a valid voltage section other than zero.

The carriers used in FIG. 3 include peaks of + V _dc / 2 and -V _dc / 2 (where V _dc represents the magnitude of the DC voltage source), and the same period as the switching period (period = 2T _s). A triangular wave with) is used.

4 illustrates an inverter switching signal generator implementing the pulse width modulation method according to the present invention.

First offset voltage (V _fn) converter 40, each on the output voltage command value in V _af, obtains the offset voltage V _fn in accordance with the equation (2) from V and V _{bf cf.}

Thereafter, the adders 51, 52, and 53 add the output voltage command values V _af , V _bf and V _cf of the respective phases and the offset voltage V _fn to obtain the pole voltages V _an , V _bn and V _cn of each phase.

Thereafter, the comparators 61, 62, 63, and 64 compare the pole voltages V _an , V _bn and V _cn , and the offset voltage V _fn with a triangular wave to compare the switching signals S _a , S _b , S _c , S _f ) For example, the instantaneous values of the triangular waves are subtracted from the pole voltages V _an , V _bn and V _cn . If the value is positive, 1 is output, and if negative, 0 is output.

The switches 11, 12, 13, 14, 21, 22, 23, 24, and FIG. 1 of the three-phase inverter are controlled by the switching signals, respectively. For example, when the output value is 1, the corresponding upper switch is turned on and the lower switch is turned off. On the contrary, when the output value is 0, the corresponding upper switch is turned off, and the lower switch is turned on.

Hereinafter, the simulation experiment results for the pulse width modulation method according to the present invention will be described. Theoretically, the three output voltages V _af , V _bf and V _cf can be synthesized arbitrarily, but only a few cases where the application is frequent are simulated and tested. The parameters of the system used for simulation and experiment are shown in Table 4 below:

[Table 4] System Parameters

A. First Simulation Results

A simulation result according to the present invention under the output voltage command value condition given by Equation 4 is shown in FIG.

[Equation 4]

V _af = A _max cos (ωt) + V _omax

V _bf = A _max cos (ωt-2π / 3) + V _omax

V _cf = A _max cos (ωt + 2π / 3) + V _omax

In the above formula,

ω = 120π,

A _max = V _dc / ≒ 173.2 [V]

≒ 106.7[V]이다.V _omax = V _dc / 2-V _dc / 4

≒ 106.7 [V].

The above conditions assume that the maximum synthesized dq voltage (173.2V) under the constant V _dc (= 300V) voltage condition and the maximum imageable voltage (106.7V) that can be synthesized are output.

FIG. 5A shows the offset voltage V _fn , the pole voltage V _{an on a} , and the output voltage command value V _af on a, and (b) is generated when the synthesized voltage of the inverter is applied to the load. The load currents I _af , I _bf and I _cf of each phase are shown. The current was observed to have a DC offset by the Io component (Vomax / R).

B. Second Simulation Results

The simulation result according to the present invention under the output voltage command value condition given by Equation 5 (assuming that there is an offset voltage synchronized with phase a) is shown in FIG.

[Equation 5]

V _af = A _max cos (ωt) + V _omax cos (ωt)

V _bf = A _max cos (ωt-2π / 3) + V _omax cos (ωt)

V _cf = A _max cos (ωt + 2π / 3) + V _omax cos (ωt)

In the above formula,

ω = 120π,

≒ 173.2[V]A _max = V _dc /

≒ 173.2 [V]

≒ 106.7[V]이다.V _omax = V _dc / 2-V _dc / 4

≒ 106.7 [V].

The simulation is a case where an image voltage is applied as a sine wave and a dq voltage is given in the same manner as in the first simulation. 6 (a) shows the offset voltage V _fn , the pole voltage V _{an on a} , and the output voltage command value V _af on a, and (b) shows load currents I _af , I _bf and I of each phase. _cf is shown.

C. Experimental Results

After the inverter system shown in FIG. 7 was constructed, the three-phase inverter was pulse width modulated according to the method of the present invention. In the switching signal generator 71 as shown in FIG. 4, a switching signal is generated by the method according to the present invention, which is amplified by the gate driver 73 to turn the switch ON / OFF.

Since the actual output voltage is generated in the form of a pulse, the output voltages V _af , V _bf and V _cf were measured using a direct voltage sensing circuit (DVS) circuit 74.

The method of Zhang et al. Requires many operations and tables as described above, and therefore can be implemented only with digital circuits, not with analog circuits. In addition to complex computational operations, hardware memory space is also required. However, the pulse width modulation method according to the present invention can be implemented with a simple analog circuit, and can be easily implemented by using only DSP and simple digital logic as in the above experiment.

이 되도록 설정하여 영상분 전압을 제거하고, 상용 AC 전원의 주파수인 60Hz로 주파수를 설정하여 실험한 결과이다.8A to 8C show that the magnitude of the output voltage is V _dc /

This is the result of experiment by removing the image voltage and setting the frequency to 60Hz which is the frequency of commercial AC power.

8A shows output voltage command values V _af , V _bf , V _cf , and offset voltage V _fn of each phase, and FIG. 8B shows output voltages V _af ^* , V _bf ^* and V measured using a DVS circuit. ^* _cf the time limit will also, Figure 8c shows a current I _f of each on the load current I _{af, bf} I, I _cf, and f- leg.

From the figure, it can be seen that the actual measured output voltages V _af ^* , V _bf ^* and V _cf ^* coincide with the output voltage command values V _af , V _bf , and V _cf.

9A to 9C show the results of experiments under the same conditions as the first simulation in order to compare with the first simulation.

9A shows output voltage command values V _af , V _bf , V _cf , and offset voltage V _fn of each phase, and FIG. 9B shows output voltages V _af ^* , V _bf ^* and V measured using a DVS circuit. will illustrating ^* _cf, Figure 9c shows a current I _f of each on the load current I _{af, bf} I, I _cf, and f- leg.

From the figure, it can be seen that the actual measured output voltages V _af ^* , V _bf ^* and V _cf ^* coincide with the output voltage command values V _af , V _bf , and V _cf. In addition, it can be seen that the DC offset exists in the current.

10a to 10c show the results of experiments under the same conditions as the second simulation in order to compare with the second simulation.

10A shows output voltage command values V _af , V _bf , V _cf , and offset voltage V _fn of each phase, and FIG. 10B shows output voltages V _af ^* , V _bf ^* and V measured using a DVS circuit. _cf ^* , FIG. 10C shows the output voltage command value V _af for the a-leg, the actual measured output voltage V _af , the actual measured pole voltage V _an , and the load current I _af .

From the figure, it can be seen that the actual measured output voltages V _af ^* , V _bf ^* and V _cf ^* coincide with the output voltage command values V _af , V _bf , and V _cf.

As can be seen from the above simulation and experiment, the pulse width modulation method according to the present invention can be easily implemented, and any output voltage can be easily synthesized.

Hereinafter, when the pulse width modulation method according to the present invention is used, the same result as that of the spatial vector pulse width modulation method disclosed in the above-mentioned Zhang et al. Prove it.

The six prisms (prisms 1 to 6) present in FIGS. 2 and 3 are composed of two zero voltage vectors and four effective voltage vectors, respectively, and also according to the polarities of the output voltages V _af , V _bf and V _cf. Each can be divided into four tetrahedra. When a specific prism is selected, a duty ratio is calculated by selecting an effective voltage vector and a matrix according to Table 3 above. For example, when prism 1 is selected, the switching order for tetrahedral 1 to tetrahedral 4 existing therein is as shown in FIGS. 11A to 11D, respectively.

Assume that the reference voltage vector given by Equation 6 in the normal dqo reference coordinate system exists in the prism 1 region.

[Equation 6]

V _dqo = (V _d , V _q , V _o )

V _d , V _q , and V _o are represented by Equation 7a according to a cylindrical coordinate relationship, and the relationship between V _d , V _q , V _o and output voltages V _af , V _bf, and V _cf is represented by Equation 7b Can be represented as:

Equation 7a

[Equation 7b]

Therefore, the output voltages V _af , V _bf, and V _cf are expressed by R, Φ, and θ as follows:

[Equation 8]

In the region of prism 1, i.e., 0≤Φ≤π / 3 and -π / 2≤θ≤π / 2, an inequality of V _af ≧ V _bf ≧ V _cf holds.

The relationship between the output voltages V _af , V _bf and V _cf in the prisms 1 to 6 is shown in Table 5 below.

[Table 5] Relationship of output voltage V _af , V _bf and V _cf in each prism

In addition, each prism is divided into four tetrahedra as shown in Table 6 below.

[Table 6] Classification of tetrahedrons present in each prism

12A to 12D show tetrahedral 1 to 4 in prism 1, respectively.

For example, when the reference voltage vector is present in the tetrahedral 3 region of prism 1, the offset voltage determined and used according to Equation 2 according to the present invention is Vmin> 0.

[Equation 9]

In addition, the pole voltages V _an , V _bn and V _cn of each phase obtained from Equations 8 and 9 are represented by Equation 10 below:

[Equation 10]

According to the present invention, when the switch is controlled by comparing the pole voltage and the offset voltage with a carrier wave (triangle wave), the ON time of each switch is expressed by Equation 11 below:

[Equation 11]

On the other hand, according to the spatial vector pulse width modulation method disclosed in Zhang et al., The duty ratio of the switching vector in the tetrahedral 3 of prism 1 is equal to the following Equation 12, and the switching time is shown in Fig. 11C and the following Equation: Same as 13:

[Equation 12]

D _z = 1-D ₁ -D ₂ -D ₃

[Equation 13]

T _a = T _z / 2 + T ₃ + T ₂ + T ₁ = T _s (D _z / 2 + D ₃ + D ₂ + D ₁ )

T _b = T _z / 2 + T ₃ + T ₂ = T _s (D _z / 2 + D ₃ + D ₂ )

T _c = T _z / 2 + T ₃ = T _s (D _z / 2 + D ₃ )

T _f = T _z / 2 = T _s (D _z / 2)

Substituting Equation 7a into Equation 12, expressing the duty ratio as R, Φ, and θ, and substituting this into Equation 13, Equation 11 is obtained by using the offset voltage according to the present invention. You get the same result as The same result can be obtained for other tetrahedra and other prisms.

This means that the pulse width modulation method according to the present invention has the same result as the spatial vector pulse width modulation method known from the above-mentioned Zhang et al.

As described above, the pulse width modulation method according to the present invention is easier to implement than the space vector pulse width modulation method known from Zhang et al., But has the same results as the space vector pulse width modulation method. You can get it.

Claims (7)

In a pulse width modulation method using a carrier of a three-phase four-wire four-leg inverter that includes four legs and independently generates three output voltages from a power supply, _{Obtaining an} offset voltage V _fn from the output voltage command values V _af , V _bf and V _cf of each phase (a); (B) obtaining the pole voltages V _an , V _bn and V _cn of each phase from the output voltage command values V _af , V _bf and V _{cf of the} phases, and the offset voltage V _fn ; And (C) controlling the switch of each leg by comparing the pole voltages V _an , V _bn and V _cn , and the offset voltage V _fn with the carrier, and controlling the switch of each leg. Way. The method of claim 1, wherein the offset voltage V _fn of step (a) is obtained from the output voltage command values V _af , V _bf and V _cf of each phase by the following equation (2): [Equation 2]

Wherein, V _max is V _{af, bf} V and V indicates the maximum value of _cf, V _min represents the minimum value of V _{af, bf} V and V _cf. The method of claim 1, wherein the pole voltages V _an , V _bn and V _cn of each phase of the step (b) are respectively corresponding to the output voltage command values V _af , V _bf and V _{cf of} the respective phases according to Equation 3 below. And the offset voltage V _fn is a sum of: [Equation 3] V _an = V _af + V _fn V _bn = V _bf + V _fn V _cn = V _cf + V _fn 2. The switch control according to claim 1, wherein the switch control of each leg in the step (c) is performed by switching the corresponding leg in a section in which the pole voltage V _an , V _bn or V _cn , or the offset voltage V _fn is larger than the carrier. ON, and the switch is turned OFF in the other section. 5. The method of claim 4, wherein the carrier wave is a triangular wave. 5. A method according to claim 4, wherein the magnitudes of the positive and negative peak values of the carrier are each one half of the magnitude of the DC voltage source, the period being the same as the switching period. In the switching signal generator including four legs, for generating pulse width modulation using a carrier wave in a three-phase four-wire four-leg inverter that independently generates three output voltages from a power supply, An offset voltage calculator for obtaining an offset voltage V _fn from the output voltage command values V _af , V _bf, and V _cf of each phase; An adder for _summating the output voltage command values V _af , V _bf and V _cf of each phase and the offset voltage V _fn to obtain the pole voltages V _an , V _bn and V _cn of each phase; And And a comparator for comparing the pole voltages V _an , V _bn and V _cn , and the offset voltage V _fn with a triangular wave to generate a switching signal for each leg.

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