TW201330480A - Self-balanced five-level inverter and method thereof - Google Patents

Abstract

The configuration and method for a five-level inverter are provided. The proposed inverter includes a first bridge arm having a first midpoint, a second bridge arm having a second midpoint, a first and a second capacitors connected to each other at a third midpoint, a first auxiliary circuit having a third bridge arm with a fourth midpoint connected to the third midpoint, a fourth bridge arm with a fifth midpoint connected to the first midpoint, and a first switch connected to the third and the fourth bridge arms in parallel, and a second auxiliary circuit having a fifth bridge arm with a sixth midpoint connected to the fourth midpoint, a sixth bridge arm with a seventh midpoint connected to the second midpoint, and a second switch connected to the fifth and the sixth bridge arms in parallel.

Description

Self-balanced fifth-order converter and method thereof

The invention relates to a self-balancing fifth-order converter, in particular to a fifth-order converter having a first and a second auxiliary circuit.

The traditional fifth-order converter has the disadvantage of unbalanced voltage of two input capacitors, and needs to use a DC capacitor with a relatively large capacitance value/inductance value and an output filter inductor, so that its volume is also large. In addition, the traditional fifth-order converter often has a skew of the output voltage waveform, resulting in a relatively high total harmonic distortion (THD) value. In addition, the chopping voltage on the input DC capacitors C ₁ and C ₂ is relatively large, which is a common problem to be improved in the conventional fifth-order converter.

As a result of the job, the inventor, in view of the lack of prior art, thought of and improved the idea of invention, and finally invented the "self-balancing fifth-order converter and its method" in this case.

The main purpose of this case is to provide a self-balancing fifth-order converter composed of a full-bridge converter and two sets of auxiliary circuits. The input capacitors are alternately discharged through two paths to avoid skewing of the output voltage. The THD of the output voltage waveform of the current device is lower than that of the conventional fifth-order converter, thereby improving the imbalance of the input capacitor voltage of the conventional fifth-order converter; the balanced converter can provide high power quality through the balance control. The power is supplied to the load, and a relatively small DC capacitor and output filter inductor are used, so the volume can also be reduced.

Another main object of the present invention is to provide a fifth-order converter comprising a first bridge arm having a first midpoint, a second bridge arm, a second midpoint, a first and a second capacitor Connected to a third midpoint, a first auxiliary circuit, including a third bridge arm, having a fourth midpoint connected to the third midpoint, and a fourth bridge arm having a connection to the third a fifth midpoint of a midpoint, and a first switch connected in parallel to the third and fourth bridge arms, and a second auxiliary circuit, including a fifth bridge arm, having a connection to the fourth A sixth midpoint of the point, a sixth bridge arm having a seventh midpoint connected to the second midpoint, and a second switch connected in parallel to the fifth and the sixth bridge arm.

The main purpose of the present invention is to provide a balanced discharge path for a fifth-order converter, comprising a first capacitor having a first voltage across, a second capacitor, a second voltage across, and a The switch module compares the two voltages such that when the two voltages are in a first comparison state, the first capacitor is discharged, and when the two voltages are in a second comparison state, the second The capacitor is discharged.

Another main object of the present invention is to provide a control method for a fifth-order converter, wherein the fifth-order converter includes a first capacitor having a first voltage across, and a second voltage-crossing a capacitor, and a switch module, comprising the steps of: comparing the two voltages; discharging the first capacitor when the first voltage is greater than the second voltage; and when the first voltage is not greater than The second capacitor is discharged during the second voltage across.

A further main object of the present invention is to provide a control method for a fifth-order converter, comprising the steps of: providing a DC input voltage V _bus , an AC output voltage v _o , and a first to fourth carrier V _Car1 ~ V _car4 and a reference signal V _ref ; when V _car1 > V _ref , v _o = V _bus ; when V _car1 < V _ref or V _car2 > V _ref , v _o = 0.5 V _bus ; when V _car2 < When V _ref or V _car3 > V _ref , v _o =0; when V _car3 < V _ref or V _car4 > V _ref , v _o =−0.5 V _bus ; and when V _car4 < V _ref , v _o =- V _bus .

The above described objects, features, and advantages of the present invention will become more apparent and understood.

The first figure shows the circuit diagram of the self-balanced fifth-order converter proposed by the present invention, which is based on a single-phase fifth-order converter architecture, and additionally adds two sets of auxiliary circuits (as shown in the first figure). . Due to the exchange operation of the first and second auxiliary circuits 11 and 12, the input DC capacitors C ₁ and C ₂ have different discharge paths, and the balance control is used to reduce the voltage chopping of the input DC capacitors C ₁ and C ₂ . Furthermore, the output voltage waveform skew phenomenon common to the conventional fifth-order converter is improved, so that the self-balanced fifth-order converter of the present invention can also improve the power quality of the output power.

As shown, four diodes and a switch consisting of two secondary circuits 11 (D1-D4 and S5) and 12 (D5-D8 to S6) are respectively connected to a first DC capacitor FIG C ₁ and C ₂ (receiving an input DC voltage V _bus) full-bridge converter (comprising a switch S ₁ -S _4, the inductance L _o of the output filter circuit and the output load capacitance C _o and L _o) between. According to the two auxiliary circuits 11 and 12, the output voltage of the fifth-order converter proposed by the present invention can be expressed as the following five types: + V _bus , +0.5 V _bus , 0, -0.5 V _bus , - V _bus .

The balance control method is as follows: When V _{C 1} > V _{C 2} , the PWM signal controls the switch S ₆ to generate 0.5 V _bus , and the switch S _{5 is} turned off. When V _{C 1} < V _{C 2} , the PWM signal drives S ₅ to transfer energy to the load, and the voltage of the DC capacitor C ₁ decreases. The voltage difference between the PWM signal and the DC capacitors C ₁ and C ₂ determines the drive signals of the switches S ₁ - S ₆ . The modulation signal of the fifth-order converter proposed by the present invention can be explained by the second figure. In the second figure, line A indicates the point at which the reference signal intersects the carrier signal, and line B indicates that the voltage difference between C ₁ and C ₂ (Δ V = V _{C 1} - V _{C 2} ) exceeds a small threshold δ , and the line C indicates that the reference signal moves from this area to the boundary of the next area.

As shown in the second figure, the four carriers and reference signals are defined as v _car1 , v _car2 , v _car3 , v _car4 and v _{ref , respectively} . The working principle of the fifth-order converter proposed by the present invention is described in Table 1, Table 2 and Table 3. Table 1 shows the switches that are turned on when V _{C 1} > V _{C 2} or V _{C 1} < V _{C 2} , and what is the output voltage. Table 2 shows the on or off states of all switches and their output voltages when V _{C 1} > V _{C 2} . Table 3 shows the on or off states of all switches and their output voltages when V _{C 1} < V _{C 2}

A comparison of conventional fifth-order converters (J. Selvaraj and NA Rahim, "Multilevel Inverter for Grid-Connected PV System Employing Digital PI Controller," IEEE Transactions on Industrial Electronics, vol. 56, no. 1, pp. 149-158, Jan. 2009.) and the voltage waveform diagram of the DC capacitors C1 and C2 of the fifth-order converter proposed by the present invention and the (pre-filtering) waveform pattern of the output voltage are respectively shown as the third diagram (a)- (b). Due to the balanced DC voltage designed by the fifth-order converter proposed by the present invention, the chopping voltage drop on the DC capacitors C ₁ and C ₂ is 3%, which is much less than 38% of the above-mentioned conventional fifth-order converter. Therefore, the waveform skew phenomenon before the output filtering of the AC side can be alleviated.

The fourth graphs (a)-(b) and fifth graphs (a)-(b) respectively show the filter output waveforms of the aforementioned conventional fifth-order current transformer and the fifth-order current transformer proposed by the present invention. As shown in the fourth (b) and fifth (b), the 110 μF DC capacitor output current THD of the present invention is 1.43%; the THD of the 110 μF DC capacitor output current of the present invention is 1.81%. Compared with the above-mentioned conventional fifth-order converters in the fourth (a) and fifth (a), using the same 110μF and 47μF DC capacitors, the THD of the output current is 5.73% and 13.2%, respectively. Compared with the conventional fifth-order converter THD described above, the THD of the converter proposed by the present invention has a significant improvement. The experimental results show that the proposed fifth-order converter of the present invention can provide higher output waveform power quality than the above-described conventional fifth-order converter.

Example:

A fifth-order converter comprising: a first bridge arm having a first midpoint; a second bridge arm having a second midpoint; a first and a second capacitor connected to each other a third intermediate point; a first auxiliary circuit comprising: a third bridge arm having a fourth midpoint connected to the third midpoint; and a fourth bridge arm having a first midpoint connected thereto a fifth midpoint; and a first switch connected in parallel to the third and the fourth bridge arm; and a second auxiliary circuit comprising: a fifth bridge arm having a first connection to the fourth midpoint a sixth midpoint; a sixth bridge arm having a seventh midpoint connected to the second midpoint; and a second switch connected in parallel to the fifth and the sixth bridge arm.

2. The fifth-order converter according to embodiment 1, further comprising a full-bridge converter, a third to a sixth switch, and each of the first anode and the second pole The first bridge and the second capacitor are a first and a second input DC capacitor, the full bridge converter includes the first bridge and the second bridge arm, and the first bridge arm includes a first bridge arm a third switch of the midpoint and the fourth switch, the second bridge arm including the fifth and the sixth switch connected to the second midpoint, the third bridge arm being connected to the fourth midpoint The first and the second diodes, the fourth bridge arm includes the third and the fourth diode connected to the fifth midpoint, and the fifth bridge arm is connected to the sixth midpoint The fifth and the second diodes, the sixth bridge arm includes the seventh and the second diode connected to the seventh midpoint, and the anode of the first diode is connected to the second a cathode of the diode, the anode of the third diode is connected to the cathode of the fourth diode, and the anode of the fifth diode is connected to the cathode of the sixth diode The anode of the seventh diode is connected to the cathode of the eighth diode, the cathode of the first diode is connected to the cathode of the third diode, and the anode of the second diode is connected In the anode of the fourth diode, the cathode of the fifth diode is connected to the cathode of the seventh diode, and the anode of the sixth diode is coupled to the eighth diode The anode.

3. The fifth-order current transformer of embodiment 1 or 2, wherein the first and the second input DC capacitors each have a first end and a second end, and the first to the sixth switches each have a first end, a second end and a control end, the first end of the first switch is connected to the cathode of the third diode, and the first end of the second switch is connected to the seventh a cathode of the pole body, the second end of the first switch is connected to the anode of the fourth diode, and the second end of the second switch is connected to the anode of the eighth diode, the The first end of the third switch is connected to the first end of the fifth switch and the first end of the first input DC capacitor, and the second end of the third switch is connected to the first end of the fourth switch The first midpoint, the second end of the fifth switch is connected to the first end of the sixth switch at the second midpoint, and the second end of the fourth switch is connected to the second end of the sixth switch And the second end of the second input DC capacitor, and each of the first to the sixth switches receives a driving signal to control one of the switches Turn on and off.

4. The fifth-order converter according to any one of the preceding embodiments, further comprising a first input and a second input, a first and a second output, and an output filter having an inductor and an output capacitor. The circuit, wherein the inductor and the output capacitor each have a first end and a second end, the first input end is connected to the first end of the first input DC capacitor, and the second end of the first input DC capacitor is connected The first end of the second input DC capacitor is connected to the second end of the second input DC capacitor, and the first end of the inductor is connected to the first midpoint. The first end of the output capacitor is connected to the second end of the inductor at the first output end, and the second end of the output capacitor is connected to the second output end at the second midpoint.

5. A balanced discharge path for a fifth-order converter, comprising: a first capacitor having a first voltage across a second; a second capacitor having a second voltage across the grid; and a switching module for comparing The two voltages are such that when the two voltages are in a first comparison state, the first capacitor is discharged, and when the two voltages are in a second comparison state, the second capacitor is discharged.

6. The discharge path of embodiment 5, wherein when the first voltage across the second voltage is greater than the second voltage, the two voltages are in the first comparison state, and when the first voltage is less than the second voltage When pressed, the two-span pressure is in the second comparison state.

7. The discharge path according to embodiment 5 or 6, wherein the fifth-order converter comprises: a first bridge arm having a first midpoint; a second bridge arm having a second midpoint; The first capacitor and the second capacitor are connected to each other at a third midpoint, and the switch module includes: a first auxiliary circuit, including: a third bridge arm, including: a fourth midpoint, connected to the a third midpoint; a first and a second diode connected to each other at the fourth midpoint; a fourth bridge arm comprising: a fifth midpoint connected to the first midpoint; a third And a fourth diode connected to the fifth midpoint; and a fifth switch connected in parallel to the third and the fourth bridge; and a second auxiliary circuit comprising: a fifth bridge The method includes: a sixth midpoint connected to the fourth midpoint; a fifth and a sixth diode connected to each other at the sixth midpoint; and a sixth bridge arm including: a seventh midpoint Connected to the second midpoint; a seventh and an eighth diode connected to each other at the seventh midpoint; and a sixth switch connected in parallel to the fifth and the Sixth bridge arm.

8. A control method for a fifth-order converter, wherein the fifth-order converter includes a first capacitor having a first voltage across, a second capacitor having a second voltage across the capacitor, and a switch The module includes the steps of: comparing the two voltages; discharging the first capacitor when the first voltage is greater than the second voltage; and when the first voltage is less than the second voltage The second capacitor is discharged.

A control method for a fifth-order current transformer, wherein the fifth-order current transformer is a fifth-order current transformer as shown in claim 2 of the patent application, comprising the steps of: providing a DC input voltage V _bus , an AC output voltage v _o , a first to fourth fourth carrier V _car1 - V _car4 and a reference signal V _ref ; when V _car1 > V _ref , v _o = V _bus ; when V _car1 < V _ref Or V _ca12 > V _ref , v _o =0.5 V _bus ; when V _car2 < V _ref or V _car3 > V _ref , v _o =0; when V _car3 < V _ref or V _car4 > V _ref , v _o =-0.5 V _bus ; and when V _car4 < V _ref , v _o =- V _bus .

10. The method of embodiment 9, wherein the first to the sixth switches are S1 - S6 , further comprising the steps of: providing a first input DC capacitor across the voltage V _C1 and a second One of the input DC capacitors is across voltage V _C2 ; when V _{C 1} > V _{C 2} and v _car1 > v _ref , S ₁ and S _{4 are} conducting and v _o is V _bus ; when V _{C 1} > V _{C 2} and v _car1 <when v _ref, S ₁ through the S ₆ guide and v _o is 0.5 V _bus; when V _{C 1} <V _{C 2} and v _car1> when v _ref, S ₁ and S ₄ is turned on and v _o is a V _Bus; when V _{When C 1} < V _{C 2} and v _car1 < v _ref , S ₄ and S _{5 are} turned on and v _o is 0.5 V _bus ; when V _{C 1} > V _{C 2} and v _car2 > v _ref , S ₁ and S _{6 are} turned on. And v _o is 0.5 V _bus ; when V _{C 1} > V _{C 2} and v _car2 < v _ref , S ₁ and S _{3 are} turned on and v _o is 0; when V _{C 1} < V _{C 2} and v _car2 > v _ref When S ₄ and S _{5 are} turned on and v _o is 0.5 V _bus ; when V _{C 1} < V _{C 2} and v _car2 < v _ref , S ₂ and S _{4 are} turned on and v _o is 0; when V _{C 1} > V _{When C2} and v _car3 > v _ref , S ₁ and S _{3 are} turned on and v _o is 0; when V _{C 1} > V _{C 2} and v _car3 < v _ref , S ₃ and S _{5 are} turned on and v _o is -0.5 V _Bus ; when V _{C 1} < V _{C 2} and v _car3 > v _ref , S ₂ and S _{4 are} turned on And v _o is 0; when V _{C 1} < V _{C 2} and v _car3 < v _ref , S ₂ and S _{6 are} turned on and v _o is -0.5 V _bus ; when V _{C 1} > V _{C 2} and v _car4 > v when _ref, S ₃ on and v _o is -0.5 V _bus and S ₅ guide; when V _{C 1>} V _{C 2} and _v car4 <when v _ref, S ₂ and S ₃ is turned on and v _o is - V _bus; when V _{When C 1} < V _{C 2} and v _car4 > v _ref , S ₂ and S _{6 are} turned on and v _o is -0.5 V _bus ; and when V _{C 1} < V _{C 2} and v _car4 < v _ref , S ₂ and S _{3 is} turned on and v _o is - V _bus .

In summary, the present invention provides a self-balancing fifth-order converter composed of a full-bridge converter and two sets of auxiliary circuits, which discharges input capacitors in two paths in turn to avoid skewing of the output voltage. The THD of the proposed output voltage waveform of the converter is less than that of the conventional fifth-order converter, thereby improving the imbalance of the input capacitor voltage of the conventional fifth-order converter; through the balance control, the proposed converter can provide High-power-quality power supplies loads, and uses relatively small DC capacitors and output filter inductors to reduce volume, so it is indeed progressive and novel.

Therefore, even though the present invention has been described in detail by the above-described embodiments, it can be modified by those skilled in the art, and is not intended to be protected as claimed.

11. . . First auxiliary circuit

12. . . Second auxiliary circuit

First: a circuit diagram showing a self-balancing fifth-order converter according to a preferred embodiment of the present invention;

Second: it shows a switch control waveform of a self-balancing fifth-order converter according to a preferred embodiment of the present invention;

FIG. 3(a) is a waveform diagram showing voltages of DC capacitors C1 and C2 of a self-balancing fifth-order converter according to a conventional fifth-order converter and a preferred embodiment of the present invention;

Third diagram (b): showing a (pre-filtering) waveform pattern comparing the output voltage of a conventional fifth-order converter with a self-balancing fifth-order converter according to a preferred embodiment of the present invention;

Figure 4 (a): shows the filtered output waveform and THD of a conventional fifth-order converter under 110μF DC capacitance;

FIG. 4(b) is a diagram showing a filtered output mode and THD of a self-balancing fifth-order converter under a 110 μF DC capacitor according to a preferred embodiment of the present invention;

Figure 5 (a): shows the filtered output waveform and THD of a conventional fifth-order converter at 47μF DC capacitance;

Fig. 5(b) is a diagram showing a filtered output mode and THD of a self-balancing fifth-order converter under a 47 μF DC capacitor in accordance with a preferred embodiment of the present invention.

11. . . First auxiliary circuit

12. . . Second auxiliary circuit

Claims (10)

A fifth-order converter includes: a first bridge arm having a first midpoint; a second bridge arm having a second midpoint; a first and a second capacitor connected to each other a first auxiliary circuit, comprising: a third bridge arm having a fourth midpoint connected to the third midpoint; and a fourth bridge arm having a fifth connected to the first midpoint a midpoint; and a first switch connected in parallel to the third and fourth bridge arms; and a second auxiliary circuit comprising: a fifth bridge arm having a sixth connection to the fourth midpoint a sixth bridge arm having a seventh midpoint connected to the second midpoint; and a second switch connected in parallel to the fifth and the sixth bridge arm. The fifth-order current transformer according to claim 1, further comprising a full-bridge converter, a third to a sixth switch, and each having an anode and a cathode, first to eighth, two a pole body, wherein the first and second capacitors are a first and a second input DC capacitor, the full bridge converter includes the first and second bridge arms, and the first bridge arm includes a connection The third and the fourth switch of the first midpoint, the second bridge arm includes the fifth and the sixth switch connected to the second midpoint, and the third bridge arm is connected to the fourth midpoint The first and the second diodes, the fourth bridge arm includes the third and the second diode connected to the fifth midpoint, and the fifth bridge arm is connected to the sixth midpoint The fifth and the sixth diode, the sixth bridge arm includes the seventh and the second diode connected to the seventh midpoint, and the anode of the first diode is connected to the first The cathode of the diode, the anode of the third diode is connected to the cathode of the fourth diode, and the anode of the fifth diode is connected to the cathode of the sixth diode The anode of the seventh diode is connected to the cathode of the eighth diode, the cathode of the first diode is connected to the cathode of the third diode, and the second diode The anode is coupled to the anode of the fourth diode, the cathode of the fifth diode is coupled to the cathode of the seventh diode, and the anode of the sixth diode is coupled to the anode The anode of the octapolar body. The fifth-order current transformer of claim 2, wherein the first and the second input DC capacitors each have a first end and a second end, and the first to the sixth switches each have a a first end, a second end and a control end, the first end of the first switch is connected to the cathode of the third diode, and the first end of the second switch is connected to the seventh pole The second end of the first switch is connected to the anode of the fourth diode, and the second end of the second switch is connected to the anode of the eighth diode, the third The first end of the switch is connected to the first end of the fifth switch and the first end of the first input DC capacitor, and the second end of the third switch is connected to the first end of the fourth switch a first midpoint, the second end of the fifth switch is connected to the first end of the sixth switch at the second midpoint, and the second end of the fourth switch is connected to the second end of the sixth switch And the second end of the second input DC capacitor, and each of the first to the sixth switches receives a driving signal to control each of the switches One is turned on and the other is turned off. The fifth-order current transformer of claim 3, further comprising a first input terminal and a second input terminal, a first output terminal and a second output terminal, and an output filter circuit having an inductor and an output capacitor. The first input end is connected to the first end of the first input DC capacitor, and the second end of the first input DC capacitor is connected to the first end. The first end of the second input DC capacitor is at the three midpoints, the second input is connected to the second end of the second input DC capacitor, and the first end of the inductor is connected to the first midpoint, the output The first end of the capacitor is connected to the second end of the inductor at the first output end, and the second end of the output capacitor is connected to the second output end at the second midpoint. A balanced discharge path for a fifth-order converter includes: a first capacitor having a first voltage across a second capacitor; a second capacitor having a second voltage across the capacitor; and a switch module comparing the two The voltage is across, such that when the two voltages are in a first comparison state, the first capacitor is discharged, and when the two voltages are in a second comparison state, the second capacitor is discharged. The discharge path of claim 5, wherein when the first voltage is greater than the second voltage, the two voltages are in the first comparison state, and when the first voltage is less than the second When the pressure is across, the two-span pressure is in the second comparison state. The discharge path of claim 6, wherein the fifth-order converter comprises: a first bridge arm having a first midpoint; a second bridge arm having a second midpoint; and the The first capacitor and the second capacitor are connected to each other at a third midpoint, and the switch module includes: a first auxiliary circuit, including: a third bridge arm, including: a fourth midpoint, connected to the first a third midpoint; a first and a second diode connected to each other at the fourth midpoint; a fourth bridge arm comprising: a fifth midpoint connected to the first midpoint; a third a fourth diode connected to the fifth midpoint; and a fifth switch connected in parallel to the third and the fourth bridge; and a second auxiliary circuit comprising: a fifth bridge arm, The method includes: a sixth midpoint connected to the fourth midpoint; a fifth and a sixth diode connected to each other at the sixth midpoint; and a sixth bridge arm including: a seventh midpoint, Connected to the second midpoint; a seventh and an eighth diode connected to each other at the seventh midpoint; and a sixth switch connected in parallel to the fifth With the sixth bridge arm. A control method for a fifth-order converter, wherein the fifth-order converter includes a first capacitor having a first voltage across, a second capacitor having a second voltage across, and a switch module The method includes the steps of: comparing the two voltages; discharging the first capacitor when the first voltage is greater than the second voltage; and when the first voltage is less than the second voltage The second capacitor is discharged. A control method for a fifth-order converter, wherein the fifth-order converter is a fifth-order converter as shown in the second item of the patent application, comprising the following steps: providing a DC input voltage V _bus An AC output voltage v _o , a first to fourth fourth carrier V _car1 - V _car4 and a reference signal V _ref ; when V _car1 > V _ref , v _o = V _bus ; when V _car1 < V _ref or V _{When car2} > V _ref , v _o =0.5 V _bus ; when V _car2 < V _ref or V _car3 > V _ref , v _o =0; when V _car3 < V _ref or V _car4 > V _ref , v _o =- 0.5 V _bus ; and when V _car4 < V _ref , v _o =- V _bus . The method of claim 9, wherein the first to the sixth switch are S1 - S6 , and further comprising the steps of: providing a first input DC capacitor across the voltage V _C1 and a first One of the two input DC capacitors is across voltage V _C2 ; when V _{C 1} > V _{C 2} and v _car1 > v _ref , S ₁ and S _{4 are} conducting and v _o is V _bus ; when V _{C 1} > V _{C 2} and v _{When car1} < v _ref , S ₁ and S _{6 are} turned on and v _o is 0.5 V _bus ; when V _{C 1} < V _{C 2} and v _car1 > v _ref , S ₁ and S _{4 are} turned on and v _o is V _bus ; When V _{C 1} < V _{C 2} and v _car1 < v _ref , S ₄ and S _{5 are} turned on and v _o is 0.5 V _bus ; when V _{C 1} > V _{C 2} and v _car2 > v _ref , S ₁ and S _{6 Turned} on and v _o is 0.5 V _bus ; when V _{C 1} > V _{C 2} and v _car2 < v _ref , S ₁ and S _{3 are} turned on and v _o is 0; when V _{C 1} < V _{C 2} and v _car2 > v _{When ref} , S ₄ and S _{5 are} turned on and v _o is 0.5 V _bus ; when V _{C 1} < V _{C 2} and v _car2 < v _ref , S ₂ and S _{4 are} turned on and v _o is 0; when V _{C 1} > When V _{C 2} and v _car3 > v _ref , S ₁ and S _{3 are} turned on and v _o is 0; when V _{C 1} > V _{C 2} and v _car3 < v _ref , S ₃ and S _{5 are} turned on and v _o is - 0.5 V _bus; when V _{C 1} <V _{C 2} and v _car3> v _ref when, S ₂ S ₄ is turned on and v _O is 0; when V _{C 1} <V _{C 2} and v _car3 <When v _ref, S ₂ and S ₆ is turned on and v _O is -0.5 V _bus; when V _{C 1>} V _{C 2} and v _{When car4} > v _ref , S ₃ and S _{5 are} turned on and v _o is -0.5 V _bus ; when V _{C 1} > V _{C 2} and v _car4 < v _ref , S ₂ and S _{3 are} turned on and v _o is - V _bus When V _{C 1} < V _{C 2} and v _car4 > v _ref , S ₂ and S _{6 are} turned on and v _o is -0.5 V _bus ; and when V _{C 1} < V _{C 2} and v _car4 < v _ref , S ₂ is turned on with S ₃ and v _o is - V _bus .