CN104601028A - Neutral-point voltage control system and method for parameter on-line tuning - Google Patents

Abstract

The invention discloses a neutral-point voltage control system for parameter on-line tuning and a neutral-point voltage control method for parameter on-line tuning. The neutral-point voltage control system comprises a three-level inverter and a digital processing control module, wherein the digital processing control module comprises a sampling unit, a digital phase-locked loop unit, an output loop-closed control unit, a PI parameter online tuning unit, a neutral-point voltage PI control unit and an SVPWM (Space Vector Pulse Width Modulation) vector control unit; the output end of the SVPWM vector control unit is connected with each phase bridge arm of the three-level inverter through a driving circuit. The direct-current bias of the neutral-point voltage and the neutral-point voltage fluctuation can be restrained by the system and the method, so that the neutral-point voltage balance control can be realized.

Description

Mid-point voltage control system and method for on-line parameter setting

technical field

The invention belongs to the field of control technology in power electronic conversion technology, in particular to a midpoint voltage control system and method for parameter online setting.

Background technique

With the rapid development of power electronic devices, high-voltage and high-power power electronic devices and AC speed control systems have been widely used in steelmaking and rolling industrial systems, electrochemical industrial systems, railway ship power systems and other fields. These power electronic devices have the characteristics of high control requirements, high power, high voltage level, and complex systems. Two-level inverters have many limitations such as high switching loss, high electromagnetic interference, and high voltage stress on the switch tubes, making it difficult for two-level inverters to meet these applications. Compared with the two-level inverter, the multi-level inverter has more output levels, and the obtained ladder wave platform has more orders, so the closer it is to the standard sine wave, the less its harmonic components, and the multi-level inverter The emergence of the device provides a possibility of both high performance and large capacity for the realization of high-voltage and high-power systems, and its circuit topology and control methods have become a research hotspot today.

The topology of multilevel inverters can be roughly divided into three categories: neutral point clamping type, cascaded type, and flying capacitor type, among which the most widely used one is the neutral point clamping type inverter. Taking the three-level inverter as an example, the three-level neutral-point clamped inverter can be divided into a diode-clamped (NPC) inverter and a T-type inverter. Ideally, the DC bus voltage in these two topologies is equally divided by the upper and lower DC bus capacitors; however, in practical applications, due to various reasons, the voltage division of the upper and lower DC bus capacitors is unbalanced, that is, the midpoint voltage is unbalanced, and its manifestations can be Divided into: (1) midpoint voltage DC bias; (2) midpoint voltage fluctuation. The unbalanced midpoint voltage will lead to poor output waveform quality, unsafe operation of power switch tubes, and even affect the normal operation of the system in severe cases. Therefore, the neutral point voltage balance control problem has always been the research focus of the three-level inverter.

In response to this problem, domestic and foreign scholars have proposed many methods to solve the midpoint voltage balance problem. The commonly used methods are mainly divided into methods of changing hardware topology and software implementation methods of adjusting control algorithms. The methods to change the hardware topology are: (1) Multiple DC source method; replace the DC bus voltage dividing capacitor with DC source; (2) Additional hardware circuit method. The advantage of the hardware method is that the control effect is not affected by the working conditions and load changes of the inverter, but it will increase the hardware cost. Therefore, the most researched neutral point voltage balance control method is the software implementation method based on the control algorithm, for example: (1) Research on neutral point voltage balance based on space vector modulation; (2) Research on neutral point voltage balance based on carrier modulation . The realization of the first method is mainly to achieve neutral point voltage balance by redistributing the action time of redundant positive and negative small vectors. The realization of the second method is mainly to achieve midpoint voltage balance by adding zero-sequence components in the modulation wave. For example: Literature 1 (Gong Bo, Cheng Shanmei, Qin Yi. Carrier-based three-level neutral point voltage balance control strategy [J]. Journal of Electrotechnical Society, 2013, 28(6): 172-177.) and patent 1 ( Cheng Shanmei, Gong Bo, Ning Bowen, Liu Jiang. A mid-point voltage control method for NPC type three-level inverter based on carrier amplitude shift: China, CN201210140269.0.2012-09-19.) A carrier-based The variable-amplitude SPWM control scheme eliminates the DC offset of the midpoint voltage by sampling the midpoint voltage to change the carrier amplitude in real time. However, the object of this method is the average value of the unbalanced component of the midpoint voltage in a power frequency cycle. Fluctuations in the midpoint voltage have no control effect.

Contents of the invention

The object of the present invention is to provide a control system and method for mid-point voltage with simple control method and easy digital realization of parameter online setting.

The technical solution to realize the object of the present invention is: a midpoint voltage control system with parameter online setting, including a three-level inverter and a digital processing control module, wherein:

The digital processing control module includes a sampling unit, a digital phase-locked loop unit, an output closed-loop control unit, a PI parameter online tuning unit, a midpoint voltage PI control unit and a SVPWM vector control unit;

The sampling unit respectively collects the DC bus voltage and DC bus midpoint voltage signal of the three-level inverter, the three-phase voltage signal output by the three-level inverter, and the three-phase current signal output by the three-level inverter;

The output terminal of the SVPWM vector control unit is connected to each switch tube of each phase bridge arm of the three-level inverter through the drive circuit;

In each switching cycle, the sampling unit of the digital processing control module collects the DC bus voltage and DC bus midpoint voltage signal of the three-level inverter, the three-phase voltage signal output by the three-level inverter, and the three-level The three-phase current signal output by the inverter is processed by the output closed-loop control unit to obtain the three-phase reference phase voltage signal;

The phase voltage and phase current signals output by the inverter collected by the sampling unit are passed through the digital phase-locked loop unit to obtain the phase angle difference between the phase voltage and phase current, that is, the power factor angle

The power factor angle obtained by the digital phase-locked loop unit The three-phase current signal obtained by the sampling unit is processed by the PI parameter online setting unit to obtain the PI parameter;

The PI parameters obtained by the PI parameter online tuning unit, the DC bus voltage obtained by the sampling unit and the midpoint voltage signal of the DC bus, and the output closed-loop control unit process the three-phase reference phase voltage signals V _a , V _b , V _c through the midpoint voltage PI The control unit obtains new three-phase reference phase voltage signals V _a ', V _b ', V _c ', and the three-phase reference phase voltage signals are processed by the SVPWM vector control unit to obtain pulse width modulation control signals;

The pulse width modulation signal is controlled by the drive circuit to control the normal operation of the three-level inverter, and effectively suppresses the DC bias of the midpoint voltage and the fluctuation of the midpoint voltage, thereby controlling the balance of the midpoint voltage.

According to the improvement of the present invention, a kind of midpoint voltage control method based on online setting of parameters of the above-mentioned midpoint voltage control system is also proposed. In each power frequency cycle, the method is based on the current three-phase current amplitude and power factor angle during the online setting. The PI parameters of the point voltage PI controller, the DC bus voltage obtained by the sampling unit and the midpoint voltage signal of the DC bus are corrected by the midpoint voltage PI controller to obtain the adjustment amount of the three-phase reference phase voltage and adjust the three-phase reference phase voltage signal in real time. In order to achieve the purpose of adjusting the midpoint voltage, the following steps are included:

Step 1. In each switching cycle, the sampling unit of the digital processing control module separately collects the DC bus voltage and DC bus midpoint voltage signal of the three-level inverter, the three-phase voltage signal output by the three-level inverter, The three-phase current signal output by the three-level inverter;

Step 2, the output closed-loop control unit performs proportional integral differential adjustment according to the signal collected in step 1 and the reference reference signal, and outputs three-phase reference phase voltage signals V _a , V _b , V _c ;

Step 3. The digital phase-locked loop unit processes the phase voltage and phase current signals collected in step 1 to obtain the phase angle difference between the phase voltage and phase current, that is, the power factor angle

Step 4, the PI parameter online tuning unit processes the three-phase current signal collected in step 1 and the power factor angle signal obtained in step 3 to obtain the PI parameter of the midpoint voltage PI control unit;

Step 5. The midpoint voltage PI control unit performs a check on the DC bus voltage and DC bus midpoint voltage signal collected in step 1, the three-phase reference phase voltage signals V _a , V _b , and V _c obtained in step 2, and the The obtained PI parameters are processed, and the dynamic adjustment value is superimposed on the three-phase reference phase voltage signal to obtain new three-phase reference phase voltage signals V _a ', V _b ', V _c ';

Step 6. The SVPWM vector control unit performs vector calculation on the new three-phase reference phase voltage signals V _a ', V _b ', and V _c ' obtained in step 5, and obtains a voltage that can suppress the midpoint voltage DC bias and midpoint voltage fluctuations The pulse width modulation control signal;

Step 7. The drive circuit distributes the pulse width modulation control signal obtained in step 6 to each switching tube of each phase bridge arm of the three-level inverter to control the working state of the three-level inverter while suppressing the DC bias of the midpoint voltage and midpoint voltage fluctuations, thereby adjusting the midpoint voltage balance.

Compared with the prior art, the present invention has significant advantages in that:

(1) The dynamic response of this control method is fast; when the working conditions such as load mutation or power mutation change, the PI parameter online tuning unit can adjust the appropriate PI parameters in real time according to the current system working conditions, so as to effectively control the neutral point voltage balance ;

(2) When the midpoint voltage is unbalanced, the control method can quickly eliminate the DC bias component of the midpoint voltage and effectively suppress the fluctuation of the midpoint voltage;

(3) The control method reduces the output voltage and current harmonics, improves the quality of the output waveform, and the control method is simple, has good real-time performance, and is convenient for digital realization.

Description of drawings

Fig. 1 is a structural diagram of a mid-point voltage control system with parameter online tuning in the present invention.

Figures 2a-2b are the topological structure diagrams of NPC type and T type three-level inverters respectively.

Fig. 3 is a distribution map of SVPWM space vector.

Figure 4 is the A-phase equivalent modulation wave of the SVPWM modulation method.

Fig. 5 is a graph showing the variation of the DC bus capacitor voltage difference before and after the control after the per-unit processing.

Fig. 6 is a simplified block diagram of midpoint voltage PI control.

Fig. 7 is a flow chart of the mid-point voltage control method for parameter online setting proposed by the present invention.

Fig. 8 is a waveform diagram of DC-side bus capacitor voltages V _c1 and V _c2 under the control method of the present invention in the embodiment, where (a) is a resistive load, and (b) is a resistive-inductive load.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

The mid-point voltage control system and method for parameter online adjustment of the present invention collects the DC bus voltage and the mid-point voltage signal of the DC bus in real time to obtain the adjustment values of the three-phase reference phase voltages V _a , V _b , and V _c through the PI controller; superposition adjustment The measured new three-phase reference phase voltage V _a ', V _b ', V _c ' undergoes SVPWM vector control operation to obtain a pulse width modulation control signal that can suppress the midpoint voltage DC bias and the midpoint voltage fluctuation, thus Realize the balanced control of the midpoint voltage.

In conjunction with Fig. 1, the mid-point voltage control system for parameter online tuning of the present invention includes a three-level inverter and a digital processing control module, and the digital processing control module includes a sampling unit, a digital phase-locked loop unit, an output closed-loop control unit, and a PI parameter An online setting unit, a midpoint voltage PI control unit, and a SVPWM vector control unit; the sampling unit respectively collects the DC bus voltage of the three-level inverter, the midpoint voltage signal of the DC bus, and the three-phase output of the three-level inverter. The voltage signal, the three-phase current signal output by the three-level inverter, and the output terminal of the SVPWM vector control unit are connected to each switch tube of each phase bridge arm of the three-level inverter through a driving circuit.

In each switching cycle, the sampling unit of the digital processing control module collects the DC bus voltage and the midpoint voltage signal of the DC bus of the three-level inverter, the three-phase voltage signal output by the three-level inverter, and the three-level The three-phase current signal output by the inverter is processed by the output closed-loop control unit to obtain the three-phase reference phase voltage signal; the phase voltage output by the inverter and the phase current signal output by the inverter collected by the sampling unit are passed through the digital phase-locked loop The unit obtains the phase angle difference of phase voltage and phase current, that is, the power factor angle The power factor angle obtained by the digital phase-locked loop unit The three-phase current signal obtained by the sampling unit is processed by the PI parameter online setting unit to obtain the PI parameter; the PI parameter obtained by the PI parameter online setting unit, the DC bus voltage obtained by the sampling unit and the midpoint voltage signal of the DC bus, and the output closed-loop control unit are processed to obtain The three-phase reference phase voltage signals V _a , V _b , V _c get new three-phase reference phase voltage signals V _a ', V _b ', V _c ' through the midpoint voltage PI control unit, and the three-phase reference phase voltage signals are passed through The SVPWM vector control unit processes the pulse width modulation control signal. The pulse width modulation signal is controlled by the drive circuit to control the normal operation of the three-level inverter, and effectively suppresses the DC bias of the midpoint voltage and the fluctuation of the midpoint voltage, thereby controlling the balance of the midpoint voltage.

Preferably, the digital processing control module is an STM32F407 chip.

Combining with Fig. 1 and Fig. 7, the present disclosure also proposes a midpoint voltage control method for parameter online setting, which adjusts the midpoint voltage PI online according to the current three-phase current amplitude and power factor angle in each power frequency cycle The PI parameters of the controller, the DC bus voltage obtained by the sampling unit and the midpoint voltage signal of the DC bus are corrected by the midpoint voltage PI controller to obtain the adjustment amount of the three-phase reference phase voltage and adjust the three-phase reference phase voltage signal in real time to achieve regulation The purpose of the midpoint voltage involves the following steps:

Step 1. In each switching cycle, the sampling unit of the digital processing control module separately collects the DC bus voltage and DC bus midpoint voltage signal of the three-level inverter, the three-phase voltage signal output by the three-level inverter, The three-phase current signal output by the three-level inverter;

Step 2, the output closed-loop control unit performs proportional integral differential adjustment according to the signal collected in step 1 and the reference reference signal, and outputs three-phase reference phase voltage signals V _a , V _b , V _c ;

Step 3. The digital phase-locked loop unit processes the phase voltage and phase current signals collected in step 1 to obtain the phase angle difference between the phase voltage and phase current, that is, the power factor angle

Step 4, the PI parameter online tuning unit processes the three-phase current signal collected in step 1 and the power factor angle signal obtained in step 3 to obtain the PI parameter of the midpoint voltage PI control unit, the specific steps are:

(4.1) Determine the current amplitude I _m according to the three-phase current output by the inverter in step 1;

(4.2) According to the power factor angle obtained by the current amplitude _Im and step 3 Determine the PI parameters of the current switching cycle: proportional coefficient k _p(N) and integral time constant T _(N) , as follows:

In the formula: m is the modulation ratio; C is the capacitance value of the DC side; ω _c is the cut-off frequency, and ω _c is generally selected at 0.1 times the switching frequency f _s . After determining the cut-off frequency, the value of the proportional coefficient k _p can be determined according to the above formula. The integral time constant T of the PI controller is the reciprocal of the corner frequency ω _s . In order to ensure sufficient phase margin at the cut-off frequency ω _c , the corner frequency ω _s is smaller than the possible minimum value of the cut-off frequency ω _c .

The corner frequency ω _s and the cut-off frequency ω _c can be reasonably selected according to actual needs.

(4.3) Compare whether the PI parameters k _p(N) and T _(N) of the current switching cycle are equal to the PI parameters k _p(N-1) and T _(N-1) of the previous switching cycle. If they are not equal, execute Step (4.4); if equal, execute step (4.5);

(4.4) Assign new values k _p(N) , T _(N) to PI parameters k _p , T.

(4.5) PI parameters k _p and T remain unchanged.

Step 5. The midpoint voltage PI control unit performs a check on the DC bus voltage and DC bus midpoint voltage signal collected in step 1, the three-phase reference phase voltage signals V _a , V _b , and V _c obtained in step 2, and the The obtained PI parameters are processed, and the dynamic adjustment value is superimposed on the three-phase reference phase voltage signal to obtain new three-phase reference phase voltage signals V _a ', V _b ', V _c '; the determination process of the adjustment value △ V is as follows :

$\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}$

In the formula, △V _c is the voltage difference between the two bus capacitors on the DC side.

Step 6. The SVPWM vector control unit performs vector calculation on the new three-phase reference phase voltage signals V _a ', V _b ', and V _c ' obtained in step 5, and obtains a voltage that can suppress the midpoint voltage DC bias and midpoint voltage fluctuations The pulse width modulation control signal;

Step 7. The drive circuit distributes the pulse width modulation control signal obtained in step 6 to each switching tube of each phase bridge arm of the three-level inverter to control the working state of the three-level inverter while suppressing the DC bias of the midpoint voltage and midpoint voltage fluctuations, thereby adjusting the midpoint voltage balance.

Taking T-type and NPC-type three-level inverters as examples, the implementation process of the present invention will be described in detail below.

(1) Analysis of the principle of midpoint voltage unbalance under the traditional SVPWM modulation method

2a-2b are T-type and NPC-type three-level inverter topologies, each phase bridge arm has four switch tubes S _x1 , S _x2 , S _x3 , S _x4 (x=a,b,c). The letters "P", "0" and "N" respectively represent the three working states of the switching tubes S _x1 , S _x2 , S _x3 , and S _x4 of each phase of the bridge arm of the inverter and the output voltages of the three bridge arms. Ideally, see Table 1 for the detailed correspondence between the bridge arm output voltage and the switch state.

Table 1 Three-level inverter bridge arm output level and switch state reference table

In the table, "√" indicates that the switch tube is turned on, "×" indicates that the switch tube is turned off, and V _dc indicates the DC bus voltage. Each phase has three working states, so there are 27 (3 ³ ) working states for three phases. If one working state corresponds to one vector in the SVPWM space vector distribution diagram, then 27 working states correspond to 27 vectors. SVPWM space vector distribution map shown in Figure 3. Observing Figure 3, we can see that the 27 vectors can be divided into four categories according to the modulus length: 6 large vectors with a modulus length of 2V _dc /3; 6 modulus lengths of 12 small vectors whose modulus length is V _dc /3; 3 zero vectors whose modulus length is zero. Among the 27 vectors, only the midpoint of the DC bus is connected to the load when the medium vector and the small vector act. At this time, the midpoint current is the load current of a certain phase connected to the midpoint. The instantaneous expression of the midpoint current is:

i _o ＝(1-|S _a |)i _a +(1-|S _b |)i _b +(1-|S _c |)i _c (1)

In the formula, S _x (x=a, b, c) is a function of the three working states of the inverter:

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

1 represents the "P" state, 0 represents the "0" state, and -1 represents the "N" state. The average value of the midpoint current during the switching cycle is usually taken as its instantaneous value:

i _o ＝D _ao i _a +D _bo i _b +D _co i _c (3)

Among them, D _ao , D _bo , and D _co are the duty ratios of the three-phase load connected to the midpoint within a switching period T _s .

As shown in Figures 2a and 2b, taking the direction of the midpoint current flow as the positive direction, the relationship between the voltage difference △ _Vc of the two bus capacitors on the DC side and the midpoint current is:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula, C is the capacitance of DC bus capacitors C ₁ and C ₂ , T _s is the switching cycle, V _c1 is the instantaneous voltage of the capacitor between the positive pole and the midpoint of the DC bus, and V _c2 is the distance between the midpoint and the negative pole of the DC bus. The instantaneous voltage across the capacitor. Therefore, when the midpoint voltage is balanced, ΔV _c =0. Putting formula (3) into formula (4), the expression of △V _c can be obtained as:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; ao</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; bo</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; co</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, i _a , i _b , and i _c are the three-phase output load currents of the inverter, which can be expressed as:

In formula (6), _Im is the magnitude of the load current, is the load power factor angle, ω is the power frequency angle frequency. When using the SVPWM modulation method, in order to be able to analyze the specific expressions of D _ao , D _bo , and D _co from the angle of the modulation wave, the SVPWM modulation is equivalent to the carrier modulation method that adds a specific zero-sequence component to the standard sine modulation wave. For phase A, the equivalent modulation wave expression of SVPWM is:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\\ \mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; )</span>& \frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; )</span>& \frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; \&le;</span>\frac{\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In formula (7), m is the modulation ratio. The graph of V _a is shown in Figure 4, which is a standard saddle wave. It is not difficult to write the expression for the duty cycle D _ao of the load of phase A connected to the midpoint within a switching period T _s , as shown in equation (8), and the expressions of the other two phases are only different from phase A in terms of phase 2π/3.

${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; ao</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; )</span>& \frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; )</span>& \frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}<span\; class="notranslate">\; ,</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; \&omega;t</span>}<span\; class="notranslate">\; \&le;</span>\frac{\mathrm{<span\; class="notranslate">\; 11</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 6</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Take m=0.8, Treat T _s , C , and I _m as per units, and substitute the expressions of D _ao , D _bo , and D _co into formula (5) to make a trend diagram of the difference △V _c of the two bus capacitor voltages on the DC side as a function of ωt , as shown in Figure 5, ΔV _c fluctuates at 3 times the power frequency.

(2) Analysis of the principle of midpoint voltage control under the control method of the present invention

The difference between the capacitance voltage difference and the reference value passes through the PI controller and is superimposed on the three-limit reference phase voltage signal as an adjustment value to obtain a PWM wave with midpoint voltage control capability. The simplified block diagram of the midpoint voltage PI control is shown in Figure 6 Show.

G(s) in the figure is the transfer function of the PI controller, and the expression is:

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; s\; T</span>}}{\mathrm{<span\; class="notranslate">\; s\; T</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Gc(s) in the figure is the transfer function of the system. It can be known from Kirchhoff’s current law and the relationship between the voltage difference ΔV _c of the DC bus capacitor and the midpoint current i _o . The expression of the transfer function G _C (s) in Fig. 6 The formula is:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; C</span>}\frac{\mathrm{<span\; class="notranslate">\; d\&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Where I _o is the average value of the midpoint current in a power frequency cycle:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&omega;t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Substituting formula (6) and formula (7) into formula (11), we can see that the expression of I _o is:

Substituting into formula (10) the expression of the transfer function G _C (s) is:

The open-loop transfer function of the system after correction by the PI controller is:

The cutoff frequency ω _c of G _open (s) is given by Partially determined, the expression for the cut-off frequency ω _c is:

The cut-off frequency ω _c is generally selected at 0.1 times the switching frequency f _s , if m=0.8, Treating T _s , C and I _m as per units, it is not difficult to obtain the proportional parameter k _p =0.91 of the PI controller from formula (15). The integral time constant T of the PI controller is the reciprocal of the corner frequency ω _s . In order to ensure sufficient phase margin at the cut-off frequency ω _c , the corner frequency ω _s must be smaller than the possible minimum value of the cut-off frequency ω _c . Therefore, in this paper, the corner frequency ω _s =2π·50rad/s, so the integral time constant T=0.02s. The PI parameter online tuning unit judges whether the working state of the system changes every power frequency cycle, and updates the parameters of the PI controller if it changes, so as to ensure that the midpoint voltage control effect is optimal under different working states of the system.

The difference △V _c of the two bus capacitor voltages on the DC side is adjusted by the PI controller to obtain the adjustment value △V:

$\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

The adjustment value △V is superimposed on the three-phase reference phase voltages V _a , V _b , V _c in formula (7) to obtain new three-phase reference phase voltages V _a ', V _b ', V _c ':

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

The duty cycle of the three-phase "0" state after correction is:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; ao</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; bo</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; co</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

Substituting the three-phase "0" state duty cycle D' _ao , D' _bo , and D' _co after PI correction into formula (5) to obtain the difference △V' of the DC bus capacitor voltage within one switching period T _S after correction _c :

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; ao</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; bo</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; co</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

Take m=0.8, Treat T _s , C, and I _m as per units, and the proportional coefficient k _p =0.91. After correction, the trend diagram of △V' _c changing with ωt is shown in Figure 5. It can be seen from the figure that after PI correction, the magnitude of △V' _c is close to zero, so the fluctuation amplitude of the midpoint voltage is almost zero.

It should be noted that during the adjustment process, the new three-phase reference phase voltages V _a ', V _b ', and V _c ' in equation (17) need to meet the following constraints

|V _x '|≤1(x＝a,b,c) (20)

The flow chart of the mid-point voltage control method for parameter online setting proposed by the present invention is shown in FIG. 7 . The specific implementation process is as follows:

(1) Sampling the DC bus voltage and DC bus midpoint voltage signal of the three-level inverter, the three-phase voltage signal output by the three-level inverter, and the three-phase current signal output by the three-level inverter, and enter ( 2);

(2) The output closed-loop control unit performs proportional integral differential adjustment according to the signal collected in (1) and the reference reference signal, outputs three-phase reference phase voltage signals V _a , V _b , V _c , and enters (3);

(3) The midpoint voltage PI control unit performs PI calculation on the DC bus capacitance voltage difference △V _c to obtain the adjustment value △V of the three-phase reference phase voltage signals V _a , V _b , and V _c :

$\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}$

V _a , V _b , V _c superimpose the adjustment value △V to get a new three-phase reference phase voltage signal V _a ', V _b ', V _c ', enter (4);

(4) The SVPWM vector control unit determines the vector sequence of the seven-segment vector symmetrical output form and the three-phase voltage signal in the current switching cycle according to the new three-phase reference phase voltage signals V _a ', V _b ', and V _c ' obtained in (3). The control signal of the switch tube of each phase bridge arm of the flat inverter is distributed to each switch tube of each phase bridge arm of the three-level inverter through the drive circuit to control the working state and midpoint voltage balance of the three-level inverter.

The PI parameters _kp and T in step (3) are realized in the PI parameter online tuning unit, and the specific implementation process is as follows:

(3.1) Sampling the A-phase voltage and three-phase current signals output by the three-level inverter to determine the current amplitude I _m and the power factor angle enter(3.2);

(3.2) Determine the PI parameters of the current switching cycle: proportional coefficient k _p(N) and integral time constant T _(N) , as follows:

In the formula: m is the modulation ratio; C is the capacitance value of the DC side; ω _c is the cut-off frequency, and ω _c is generally selected at 0.1 times the switching frequency f _s . After determining the cut-off frequency, the value of the proportional coefficient k _p can be determined according to the above formula. The integral time constant T of the PI controller is the reciprocal of the corner frequency ω _s . In order to ensure sufficient phase margin at the cut-off frequency ω _c , the corner frequency ω _s must be smaller than the possible minimum value of the cut-off frequency ω _c . Reasonable selection according to actual needs;

(3.3) Judging whether the PI parameters k _p(N) and T _(N) of the current switching cycle are equal to the PI parameters k _p(N-1) and T _(N-1) of the previous switching cycle, if not, execute Step (3.4); if equal, execute step (3.5);

(3.4) Assign new values _{kp (N)} and T _(N) to PI parameters kp and T;

(3.5) PI parameters k _p and T remain unchanged.

In summary, under the traditional SVPWM modulation method, the midpoint voltage has a fluctuation of 3 times the power frequency frequency, and a midpoint voltage control system and method for parameter online tuning proposed by the present invention can select a suitable PI controller under different working conditions The parameters of the midpoint voltage DC bias and midpoint voltage fluctuation are controlled to achieve midpoint voltage balance.

In order to verify the feasibility and effectiveness of a mid-point voltage control method with parameter online tuning proposed by the present invention, a three-level inverter circuit was built by using the Simulink tool in MATLAB. The electrical parameter settings during the simulation are as follows:

Figures 8a-8b show the simulation waveforms of the voltages V _c1 and V _c2 of the DC bus capacitors C ₁ and C ₂ under the above electrical parameter settings. In order to verify the control effect of the method proposed by the present invention when there is a serious imbalance, that is, when the upper and lower capacitor voltages differ greatly. The upper bus capacitor C ₁ is connected in parallel with a 2150Ω resistor, so that the equivalent impedance of the upper and lower capacitors is inconsistent and there is a DC bias and fluctuation in the midpoint voltage. It can be seen from Figure 8 that when the traditional SVPWM modulation method is used before 0.3s, the midpoint voltage deviates seriously from the reference value due to the inconsistency of the circuit parameters, fluctuates at three times the power frequency and contains a large DC offset. 0.3s switching to the midpoint voltage control method of the online parameter setting proposed by the present invention. Figure 8a shows the resistive load. After about 5ms of adjustment time, the DC bias of the midpoint voltage can be eliminated and the stability of the midpoint voltage fluctuation can be suppressed. State; Figure 8b shows the steady state of eliminating midpoint voltage DC bias and suppressing midpoint voltage fluctuations after about 5 ms of adjustment time under the condition of resistive inductive load. The simulation verifies that the control effect of the mid-point voltage control method of parameter online setting proposed by the present invention is remarkable.

In summary, the mid-point voltage control system and method for parameter online setting of the present invention are applied to three-level inverters, and the control method is set online according to the current three-phase current amplitude and power factor angle in each power frequency cycle For the parameters of the PI controller, if the working state of the system changes, the parameters of the PI controller are updated, so as to ensure that the midpoint voltage control effect is optimal under different working states of the system. The error signal between the difference of the DC bus capacitor voltage collected in each switching cycle and the reference value is passed through the PI controller to obtain the adjustment value for superimposing to the three-phase reference voltage, and the midpoint voltage balance is controlled in real time. The control method has fast dynamic response, and can effectively suppress the DC bias and fluctuation of the DC bus midpoint voltage of the three-level inverter under different load conditions, and overcomes the disadvantage of large output inductor current ripple; the control method has the characteristics of output waveform harmonic It has the advantages of low wave content, good real-time performance, simple control method, and easy digital realization.

Claims (6)

1. A mid-point voltage control system for parameter online tuning, characterized in that it comprises a three-level inverter and a digital processing control module, wherein: The digital processing control module includes a sampling unit, a digital phase-locked loop unit, an output closed-loop control unit, a PI parameter online tuning unit, a midpoint voltage PI control unit and a SVPWM vector control unit; The sampling unit respectively collects the DC bus voltage and DC bus midpoint voltage signal of the three-level inverter, the three-phase voltage signal output by the three-level inverter, and the three-phase current signal output by the three-level inverter; The output terminal of the SVPWM vector control unit is connected to each switch tube of each phase bridge arm of the three-level inverter through the drive circuit; In each switching cycle, the sampling unit of the digital processing control module respectively collects the DC bus voltage and DC bus midpoint voltage signal of the three-level inverter, the three-phase voltage signal output by the three-level inverter, and the three-phase voltage signal output by the three-level inverter. The three-phase current signal output by the level inverter is processed by the output closed-loop control unit to obtain the three-phase reference phase voltage signal; The phase voltage output by the three-level inverter and the phase current signal output by the three-level inverter collected by the sampling unit are obtained by the digital phase-locked loop unit to obtain the phase angle difference between the phase voltage and the phase current, that is, the power factor angle The power factor angle obtained by the digital phase-locked loop unit The three-phase current signal obtained by the sampling unit is processed by the PI parameter online setting unit to obtain the PI parameter; The PI parameter obtained by the PI parameter online tuning unit, the DC bus voltage obtained by the sampling unit and the midpoint voltage signal of the DC bus are processed by the output closed-loop control unit to obtain three-phase reference phase voltage signals V _a , V _b , and V _c through the midpoint The voltage PI control unit obtains new three-phase reference phase voltage signals V' _a , V' _b , V' _c , and the three-phase reference phase voltage signals are processed by the SVPWM vector control unit to obtain pulse width modulation control signals; The pulse width modulation signal is controlled by the drive circuit to control the normal operation of the three-level inverter, so as to realize the suppression of the DC bias of the midpoint voltage and the fluctuation of the midpoint voltage, thereby controlling the balance of the midpoint voltage. 2. the mid-point voltage control system of parameter online tuning according to claim 1, is characterized in that, described digital processing control module is STM32F407 chip. 3. a midpoint voltage control method based on the parameter online tuning of the midpoint voltage control system of the parameter online tuning according to claim 1, it is characterized in that, the method outputs according to the three-level inverter in each power frequency cycle The three-phase current amplitude, power factor angle Information, the PI parameters of the midpoint voltage PI controller are set online, the DC bus voltage and the DC bus midpoint voltage are collected in each switching cycle, and the adjustment amount of the three-phase reference phase voltage is obtained in real time after being corrected by the midpoint voltage PI controller Adjust the three-phase reference phase voltage signal to achieve the purpose of adjusting the neutral point voltage balance. The specific implementation includes the following steps: Step 1. In each switching cycle, the sampling unit of the digital processing control module separately collects the DC bus voltage and DC bus midpoint voltage signal of the three-level inverter, the three-phase voltage signal output by the three-level inverter, The three-phase current signal output by the three-level inverter; Step 2, the output closed-loop control unit performs proportional integral differential adjustment according to the signal collected in step 1 and the reference reference signal, and outputs three-phase reference phase voltage signals V _a , V _b , V _c ; Step 3, the digital phase-locked loop unit processes the phase voltage and phase current signals collected in step 1 to obtain the phase angle difference between the phase voltage and the phase current, that is, the power factor angle; Step 4, the PI parameter online tuning unit processes the three-phase current signal collected in step 1 and the power factor angle signal obtained in step 3 to obtain the PI parameter of the midpoint voltage PI control unit; Step 5. The midpoint voltage PI control unit performs a check on the DC bus voltage and DC bus midpoint voltage signal collected in step 1, the three-phase reference phase voltage signals V _a , V _b , and V _c obtained in step 2, and the The obtained PI parameters are processed, and the dynamic adjustment value is superimposed on the three-phase reference phase voltage signal to obtain new three-phase reference phase voltage signals V' _a , V' _b , V'_c; Step 6. The SVPWM vector control unit performs vector calculation on the new three-phase reference phase voltage signals V' _a , V' _b , and V' _c obtained in step 5, and obtains The pulse width modulation control signal; and Step 7. The drive circuit distributes the pulse width modulation control signal obtained in step 6 to each switching tube of each phase bridge arm of the three-level inverter to control the working state of the three-level inverter while suppressing the DC bias of the midpoint voltage and midpoint voltage fluctuations, thereby adjusting the midpoint voltage balance. 4. according to the mid-point voltage control method of parameter online tuning described in claim 3, it is characterized in that, the PI parameter online tuning unit described in step 4 is to the three-phase current signal that gathers in step 1 and step 3 obtains The power factor angle signal is processed to obtain PI parameters, and the specific steps are: (4.1) Determine the current amplitude I _m according to the three-phase current output by the inverter in step 1; (4.2) According to the power factor angle obtained by the current amplitude _Im and step 3 Determine the PI parameters of the current switching cycle: proportional coefficient k _{p (N)} , integral time constant T _(N) ; (4.3) Compare whether the PI parameters k _p(N) and T _(N) of the current switching cycle are equal to the PI parameters k _p(N-1) and T _(N-1) of the previous switching cycle. If they are not equal, execute Step (4.4); if equal, execute step (4.5); (4.4) Assign new values _{kp (N)} and T _(N) to PI parameters kp and T; (4.5) Keep the PI parameters k _p and T unchanged. 5. the mid-point voltage control method of parameter on-line tuning according to claim 4, is characterized in that, described in (4.2) according to the power factor angle of current amplitude _Im and step 3 gained Determine the PI parameters for the current switching cycle, as follows: In the formula: m is the modulation ratio; C is the capacitance value of the DC side; ω _c is the cut-off frequency, ω _c is selected at 0.1 times the switching frequency f _s , k _p is the proportional coefficient, and the integral time constant T of the PI controller is the reciprocal of the corner frequency ω _s , in order to ensure sufficient phase margin at the cut-off frequency ω _c , the corner frequency ω _s is smaller than the possible minimum value of the cut-off frequency ω _c . 6. according to the midpoint voltage control method of parameter online setting according to claim 3, it is characterized in that, the midpoint voltage PI control unit described in the step 5 collects the DC bus voltage and the DC bus midpoint voltage signal in the step 1 , the three-phase reference phase voltage signals V _a , V _b , V _c obtained in step 2 and the PI parameters obtained in step 4 are processed, and the dynamic adjustment value ΔV is superimposed on the three-phase reference phase voltage signal to obtain a new three-phase Phase reference phase voltage signals V′ _a , V′ _b , V′ _c , the determination process of the adjustment value ΔV is as follows: $\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}$ In the formula, ΔV _c is the voltage difference between the two bus capacitors on the DC side.