CN109951093A - A midpoint voltage control system and method based on hybrid parameters - Google Patents
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Abstract
本发明公开了一种基于混杂参数的中点电压控制系统及方法。该系统包括三电平并网逆变器、数字处理控制模块和驱动电路,其中数字处理控制模块包括采样单元、闭环控制单元、网侧信息计算单元、工况判断单元、混杂参数PI控制器单元和正弦脉宽调制单元。方法为:采样单元采集电网电压信号和网侧电流信号,经网侧信息计算单元处理后,将计算结果送入工况判断单元划分工况;混杂参数PI控制器单元根据工况切换相应的控制参数,并根据直流侧电容电压计算零序分量,然后将零序分量与三相调制信号相加,经过正弦脉宽调制单元处理,得到脉宽调制信号,驱动三电平并网逆变器开关管工作。本发明硬件成本低、控制准确、适用范围广,降低了入网电流的畸变率。
The invention discloses a midpoint voltage control system and method based on mixed parameters. The system includes a three-level grid-connected inverter, a digital processing control module and a drive circuit, wherein the digital processing control module includes a sampling unit, a closed-loop control unit, a grid-side information calculation unit, a working condition judgment unit, and a mixed parameter PI controller unit and sinusoidal PWM unit. The method is as follows: the sampling unit collects the grid voltage signal and the grid side current signal, and after being processed by the grid side information calculation unit, the calculation results are sent to the working condition judgment unit to divide the working conditions; the hybrid parameter PI controller unit switches the corresponding control according to the working conditions. parameters, and calculate the zero-sequence component according to the DC side capacitor voltage, then add the zero-sequence component to the three-phase modulation signal, and process it by the sinusoidal pulse width modulation unit to obtain the pulse width modulation signal, which drives the three-level grid-connected inverter switch. Tube work. The invention has low hardware cost, accurate control and wide application range, and reduces the distortion rate of the current entering the network.
Description
技术领域technical field
本发明属于电力电子变换技术中的控制技术领域,特别是一种基于混杂参数的中点电压控制系统及方法。The invention belongs to the technical field of control in power electronic conversion technology, in particular to a hybrid parameter-based midpoint voltage control system and method.
背景技术Background technique
NPC三电平并网逆变器由于其拓扑结构成熟、开关器件承受电压低、输出谐波含量少等优点,在中高功率场合得到了广泛的应用。但由于NPC三电平并网逆变器的固有特性,并网逆变器的直流侧会产生中点电压波动的问题。目前对于三电平并网逆变器直流侧中点电压波动的问题,主要有三种解决方法:(1)采用独立的直流电压源为直流侧电容供电;(2)外接中点平衡控制电路;(3)采用特定的中点电压控制方法。由于前两种方法会增加硬件成本,故一般不予考虑。The NPC three-level grid-connected inverter has been widely used in medium and high power applications due to its mature topology, low withstand voltage of switching devices, and low output harmonic content. However, due to the inherent characteristics of the NPC three-level grid-connected inverter, the DC side of the grid-connected inverter will have the problem of midpoint voltage fluctuation. At present, there are three main solutions to the problem of midpoint voltage fluctuation on the DC side of the three-level grid-connected inverter: (1) using an independent DC voltage source to supply power to the DC side capacitor; (2) externally connecting a neutral point balance control circuit; (3) Adopt a specific midpoint voltage control method. Since the first two methods will increase the hardware cost, they are generally not considered.
在理想电网条件下,现有的中点电压控制方法相对成熟,如基于零序分量注入的DPWM方法、基于冗余小矢量调整的SVPWM方法、基于混合调制的方法等。然而在实际情况中,电网故障会导致网侧三相电压不平衡,在三相电压不平衡的状态下,中点电压波动的幅值会增大,频率则由三相平衡时的三倍工频变为工频,且含有3、5、7次等奇次谐波分量,这给中点电压的控制带来了困难。Under ideal grid conditions, the existing mid-point voltage control methods are relatively mature, such as the DPWM method based on zero-sequence component injection, the SVPWM method based on redundant small vector adjustment, and the method based on hybrid modulation. However, in practical situations, grid faults will lead to unbalanced three-phase voltages on the grid side. In the state of unbalanced three-phase voltages, the amplitude of mid-point voltage fluctuations will increase, and the frequency will be three times that of three-phase balanced voltages. The frequency becomes the power frequency, and contains odd harmonic components such as the 3rd, 5th, and 7th order, which brings difficulties to the control of the midpoint voltage.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于提供一种能够在非理想电网条件下实现并网逆变器直流侧上、下电容电压的平衡,且在高不平衡度条件下有效地平衡中点电压的中点电压控制系统及方法。The purpose of the present invention is to provide a mid-point voltage control that can realize the balance of the upper and lower capacitor voltages on the DC side of the grid-connected inverter under non-ideal grid conditions, and effectively balance the mid-point voltage under the condition of high unbalance degree. system and method.
实现本发明目的的技术解决方案为:一种基于混杂参数的中点电压控制系统,包括三电平并网逆变器、数字处理控制模块和驱动电路,其中数字处理控制模块包括采样单元、闭环控制单元、网侧信息计算单元、工况判断单元、混杂参数PI控制器单元(HybridParameter PI,HP-PI)和正弦脉宽调制单元;The technical solution to achieve the purpose of the present invention is: a hybrid parameter-based midpoint voltage control system, comprising a three-level grid-connected inverter, a digital processing control module and a drive circuit, wherein the digital processing control module includes a sampling unit, a closed-loop Control unit, grid-side information calculation unit, working condition judgment unit, hybrid parameter PI controller unit (HybridParameter PI, HP-PI) and sinusoidal pulse width modulation unit;
所述采样单元分别采集三电平并网逆变器直流侧上、下电容电压信号、三电平并网逆变器交流侧的三相电压信号、三电平并网逆变器交流侧的三相电流信号,发送至闭环控制单元和网侧信息计算单元;网侧信息计算单元根据采样得到的电网电压信号及网侧电流信号,计算当前的不平衡度λ、功率因数角以及网侧电压负序分量相位角计算结果送至工况判断单元进行判断处理,将三电平并网逆变器的运行条件划分为不同的工况;混杂参数PI控制器单元根据不同的工况切换相应的控制参数,然后根据直流侧上、下电容电压计算零序分量u0;将零序分量与闭环控制单元得到的调制波信号相加,送至正弦脉宽调制单元,正弦脉宽调制单元的输出端经过驱动电路,接入三电平并网逆变器中每相桥臂的各个开关管。The sampling unit respectively collects the upper and lower capacitor voltage signals on the DC side of the three-level grid-connected inverter, the three-phase voltage signal on the AC side of the three-level grid-connected inverter, and the three-level grid-connected inverter AC side. The three-phase current signal is sent to the closed-loop control unit and the grid-side information calculation unit; the grid-side information calculation unit calculates the current unbalance degree λ and power factor angle according to the grid voltage signal and grid-side current signal obtained by sampling and the phase angle of the negative sequence component of the grid-side voltage The calculation results are sent to the working condition judgment unit for judgment processing, and the operating conditions of the three-level grid-connected inverter are divided into different working conditions; the hybrid parameter PI controller unit switches the corresponding control parameters according to different working conditions, and then according to The zero-sequence component u 0 is calculated from the upper and lower capacitor voltages on the DC side; the zero-sequence component is added to the modulated wave signal obtained by the closed-loop control unit, and sent to the sinusoidal pulse width modulation unit. The output end of the sinusoidal pulse width modulation unit passes through the drive circuit, Connect to each switch tube of each phase bridge arm in the three-level grid-connected inverter.
进一步地,所述数字处理控制模块采用TMS320F2808和EPM1270T芯片。Further, the digital processing control module adopts TMS320F2808 and EPM1270T chips.
一种基于混杂参数的中点电压控制方法,包括以下步骤:A hybrid parameter-based midpoint voltage control method, comprising the following steps:
步骤1、根据零序分量与平均中点电流之间的关系因子δ,将三电平并网逆变器的运行条件划分为两种不同的工况:Step 1. According to the relationship factor δ between the zero-sequence component and the average midpoint current, the operating conditions of the three-level grid-connected inverter are divided into two different working conditions:
当δ>0时,三电平并网逆变器工作于工况1;When δ>0, the three-level grid-connected inverter works in working condition 1;
当δ≤0时,三电平并网逆变器工作于工况2;When δ≤0, the three-level grid-connected inverter works in working condition 2;
步骤2、在不同工况下分别设计控制参数:Step 2. Design control parameters under different working conditions:
三电平并网逆变器工作于工况1时:When the three-level grid-connected inverter works in working condition 1:
定义δmax为工况1下关系因子δ的最大值,则比例系数kp为:Define δ max as the maximum value of relation factor δ under working condition 1, then the proportional coefficient k p is:
三电平并网逆变器工作于工况2时:When the three-level grid-connected inverter works in working condition 2:
定义δmin为工况2下关系因子δ的最小值,则比例系数kp为:Define δ min as the minimum value of the relationship factor δ under working condition 2, then the proportional coefficient k p is:
其中C为电容,fs为开关频率,关系因子δ为不平衡度λ、功率因数角及负序电压相位角的函数,采用拉格朗日乘子法分别计算关系因子最大值δmax和最小值δmin,最终得到相应的比例系数kp;Where C is the capacitance, f s is the switching frequency, the relation factor δ is the unbalance degree λ, the power factor angle and negative sequence voltage phase angle , the Lagrange multiplier method is used to calculate the maximum value δ max and the minimum value δ min of the relationship factor respectively, and finally the corresponding proportional coefficient k p is obtained;
步骤3、采样交流侧三相电压ea、eb、ec,交流侧三相电流ia、ib、ic,直流侧上电容电压UC1,直流侧下电容电压UC2;Step 3, sampling the three-phase voltages e a , eb , and ec on the AC side, the three-phase currents ia , ib , and ic on the AC side, the capacitor voltage U C1 on the DC side, and the capacitor voltage U C2 on the DC side;
步骤4、通过闭环控制单元得到三相调制波ua、ub、uc;Step 4. Obtain three-phase modulated waves u a , ub , and uc through the closed-loop control unit;
步骤5、通过网侧信息计算单元计算当前的不平衡度λ、功率因数角以及网侧电压负序分量相位角 Step 5. Calculate the current unbalance degree λ and power factor angle through the grid-side information calculation unit and the phase angle of the negative sequence component of the grid-side voltage
步骤6、工况判断单元根据步骤5的计算结果判断关系因子δ的符号,确定三电平并网逆变器所处的工况;Step 6, the working condition judgment unit judges the sign of the relationship factor δ according to the calculation result of step 5, and determines the working condition of the three-level grid-connected inverter;
步骤7、根据三电平并网逆变器所处的工况切换PI控制器的参数,然后根据直流侧电容电压计算零序分量u0;Step 7. Switch the parameters of the PI controller according to the working condition of the three-level grid-connected inverter, and then calculate the zero-sequence component u 0 according to the DC side capacitor voltage;
步骤8、将零序分量u0与步骤4得到的三相调制波相加,得到三相调制信号:Step 8. Add the zero-sequence component u 0 to the three-phase modulation wave obtained in step 4 to obtain a three-phase modulation signal:
步骤9、三相调制信号经正弦脉宽调制单元生成脉宽调制信号,通过驱动电路控制三电平并网逆变器开关管的工作。Step 9: The three-phase modulation signal is generated by the sinusoidal pulse width modulation unit to generate the pulse width modulation signal, and the operation of the switch tube of the three-level grid-connected inverter is controlled by the driving circuit.
进一步地,步骤1中所述的零序分量与平均中点电流之间的关系因子δ,具体如下:Further, the relationship factor δ between the zero-sequence component and the average midpoint current described in step 1 is as follows:
式中,Imp为网侧电流正序分量的幅值,λ为不平衡度,为功率因数角,为网侧电压负序分量相位角。In the formula, I mp is the amplitude of the positive sequence component of the grid-side current, λ is the unbalance degree, is the power factor angle, is the phase angle of the negative sequence component of the grid-side voltage.
进一步地,步骤2所述的在不同工况下分别设计控制参数,具体如下:Further, the control parameters are respectively designed under different working conditions as described in step 2, as follows:
三电平并网逆变器工作于工况1时:When the three-level grid-connected inverter works in working condition 1:
定义δmax为工况1下关系因子δ的最大值,则比例系数kp为:Define δ max as the maximum value of relation factor δ under working condition 1, then the proportional coefficient k p is:
使用拉格朗日乘子法求解关系因子的最大值δmax,定义拉格朗日函数:Use the Lagrangian multiplier method to find the maximum value of the relation factor, δ max , to define the Lagrangian function:
其中vi为拉格朗日乘子,i=1,2,3;为约束方程,表示为:where v i is the Lagrange multiplier, i=1,2,3; is the constraint equation, expressed as:
定义为拉格朗日函数关于变量λ、 的一阶梯度,由Karush-Kuhn-Tucher必要条件可知,函数最大值点应满足的一阶必要条件为:definition is the Lagrangian function Regarding the variable λ, The first-order gradient of , according to the Karush-Kuhn-Tucher necessary condition, the function The first-order necessary condition that the maximum point should satisfy is:
定义为拉格朗日函数关于变量λ、 的二阶梯度,函数最大值点应满足的二阶充分条件为:definition is the Lagrangian function Regarding the variable λ, The second-order gradient of , the function The second-order sufficient condition that the maximum point should satisfy is:
其中,表示为:in, Expressed as:
根据函数最大值点应满足的一阶必要条件和二阶充分条件,求得约束条件下的函数的最大值点,将最大值点代入函数即求得最大值δmax和比例系数kp;According to the function The first-order necessary condition and the second-order sufficient condition that the maximum point should satisfy, and the function under the constraint condition is obtained The maximum point of , substitute the maximum point into the function That is, the maximum value δ max and the proportional coefficient k p are obtained;
三电平并网逆变器工作于工况2时:When the three-level grid-connected inverter works in working condition 2:
定义δmin为工况2下关系因子δ的最小值,则比例系数kp为:Define δ min as the minimum value of the relationship factor δ under working condition 2, then the proportional coefficient k p is:
使用拉格朗日乘子法求解关系因子δ的最小值δmin,定义拉格朗日函数:Use the Lagrangian multiplier method to find the minimum value of the relation factor δ, δ min , to define the Lagrangian function:
式中表示为:in the formula Expressed as:
求得约束条件下函数的最小值点,将最小值点代入函数即求得最小值δmin和比例系数kp。find function under constraints The minimum point of , substitute the minimum point into the function That is, the minimum value δ min and the proportional coefficient k p are obtained.
本发明与现有技术相比,其显著优点在于:(1)根据不同的电网条件与输出功率因数切换自身的控制参数,能够在非理想电网下实现中点电压平衡控制;(2)能够在高不平衡度条件下有效地平衡中点电压,且控制系统简单,易于实现。Compared with the prior art, the present invention has the following significant advantages: (1) switching its own control parameters according to different power grid conditions and output power factors, so that the neutral point voltage balance control can be realized under non-ideal power grids; (2) it can The neutral point voltage is effectively balanced under the condition of high unbalance, and the control system is simple and easy to implement.
附图说明Description of drawings
图1是本发明基于混杂参数的中点电压控制系统的结构示意图。FIG. 1 is a schematic structural diagram of a hybrid parameter-based midpoint voltage control system of the present invention.
图2是本发明基于混杂参数的中点电压控制系统的控制框图。FIG. 2 is a control block diagram of the hybrid parameter-based midpoint voltage control system of the present invention.
图3是NPC三电平并网逆变器的主电路结构示意图。FIG. 3 is a schematic diagram of the main circuit structure of the NPC three-level grid-connected inverter.
图4是本发明实施例中不同不平衡度及功率因数角条件下的关系因子δ曲面图,其中(a)为当负序电压相位角时,不同不平衡度及功率因数角条件下的关系因子δ曲面图,(b)为当负序电压相位角时,不同不平衡度及功率因数角条件下的关系因子δ曲面图。4 is a surface diagram of the relationship factor δ under different unbalance and power factor angle conditions in the embodiment of the present invention, wherein (a) is the phase angle of the negative sequence voltage when When , the relationship factor δ surface diagram under different unbalance and power factor angle conditions, (b) is the phase angle of the negative sequence voltage when When , the relationship factor δ surface diagram under different unbalance and power factor angle conditions.
图5是本发明中混杂参数PI控制单元的参数选择流程图。FIG. 5 is a flow chart of parameter selection of the hybrid parameter PI control unit in the present invention.
图6是本发明实施例中不平衡度为0.1,功率因数为1时,在0.1s使用本发明的控制方法前后的直流侧上、下电容电压波形图。6 is a waveform diagram of the upper and lower capacitor voltages on the DC side before and after using the control method of the present invention for 0.1s when the unbalance degree is 0.1 and the power factor is 1 in the embodiment of the present invention.
图7是本发明实施例中不平衡度为0.1,功率因数为0.707时,在0.1s使用本发明的控制方法前后的直流侧上、下电容电压波形图。7 is a waveform diagram of the upper and lower capacitor voltages on the DC side before and after using the control method of the present invention for 0.1s when the unbalance degree is 0.1 and the power factor is 0.707 in the embodiment of the present invention.
图8是本发明实施例中不平衡度为0.2,功率因数为1时,在0.1s使用本发明的控制方法前后的直流侧上、下电容电压波形图。8 is a waveform diagram of the upper and lower capacitor voltages on the DC side before and after using the control method of the present invention for 0.1 s when the unbalance degree is 0.2 and the power factor is 1 in the embodiment of the present invention.
图9是本发明实施例中不平衡度为0.6,功率因数为0时,在0.1s使用本发明的控制方法前后的直流侧上、下电容电压波形图。9 is a waveform diagram of the upper and lower capacitor voltages on the DC side before and after using the control method of the present invention for 0.1s when the unbalance degree is 0.6 and the power factor is 0 in the embodiment of the present invention.
图10是本发明实施例中使用本发明的控制方法前后的网侧电流ib谐波分布对比图,其中(a)为不平衡度为0.1,功率因数为1时,使用本发明的控制方法前后的网侧电流ib谐波分布对比图,(b)为不平衡度为0.1,功率因数为0.707时,使用本发明的控制方法前后的网侧电流ib谐波分布对比图,(c)为不平衡度为0.2,功率因数为1时,使用本发明的控制方法前后的网侧电流ib谐波分布对比图,(d)为不平衡度为0.6,功率因数为0时,使用本发明的控制方法前后的网侧电流ib谐波分布对比图。10 is a comparison diagram of the harmonic distribution of grid-side current i b before and after using the control method of the present invention in the embodiment of the present invention, wherein (a) is when the unbalance degree is 0.1 and the power factor is 1, the control method of the present invention is used The comparison diagram of the harmonic distribution of grid side current i b before and after, (b) is when the unbalance degree is 0.1 and the power factor is 0.707, the comparison diagram of the harmonic distribution of grid side current i b before and after using the control method of the present invention, (c ) is the unbalance degree of 0.2, when the power factor is 1, the grid-side current i b harmonic distribution comparison diagram before and after using the control method of the present invention, (d) is that the unbalance degree is 0.6, when the power factor is 0, use Comparison diagram of the harmonic distribution of grid-side current i b before and after the control method of the present invention.
具体实施方式Detailed ways
下面结合附图和具体实施例对本发明作进一步详细说明。The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
结合图1,一种基于混杂参数的中点电压控制系统,包括三电平并网逆变器、数字处理控制模块和驱动电路,其中数字处理控制模块包括采样单元、闭环控制单元、网侧信息计算单元、工况判断单元、混杂参数PI控制器单元和正弦脉宽调制单元;With reference to Figure 1, a hybrid parameter-based midpoint voltage control system includes a three-level grid-connected inverter, a digital processing control module and a drive circuit, wherein the digital processing control module includes a sampling unit, a closed-loop control unit, and grid-side information Calculation unit, working condition judgment unit, mixed parameter PI controller unit and sinusoidal pulse width modulation unit;
所述采样单元分别采集三电平并网逆变器直流侧上、下电容电压信号、三电平并网逆变器交流侧的三相电压信号、三电平并网逆变器交流侧的三相电流信号,发送至闭环控制单元和网侧信息计算单元;网侧信息计算单元根据采样得到的电网电压信号及网侧电流信号,计算当前的不平衡度λ、功率因数角以及网侧电压负序分量相位角工况判断单元根据计算结果判断关系因子δ的符号,得到三电平并网逆变器所处的工况,此时,混杂参数PI控制器单元切换到对应的控制参数,然后根据直流侧上、下电容电压计算零序分量u0;将零序分量与闭环控制单元得到的调制波信号相加,发送至正弦脉宽调制单元,正弦脉宽调制单元的输出端经过驱动电路,接入三电平并网逆变器中每相桥臂的各个开关管。The sampling unit respectively collects the upper and lower capacitor voltage signals on the DC side of the three-level grid-connected inverter, the three-phase voltage signal on the AC side of the three-level grid-connected inverter, and the three-level grid-connected inverter AC side. The three-phase current signal is sent to the closed-loop control unit and the grid-side information calculation unit; the grid-side information calculation unit calculates the current unbalance degree λ and power factor angle according to the grid voltage signal and grid-side current signal obtained by sampling and the phase angle of the negative sequence component of the grid-side voltage The working condition judgment unit judges the sign of the relationship factor δ according to the calculation result, and obtains the working condition of the three-level grid-connected inverter. At this time, the hybrid parameter PI controller unit switches to the corresponding control parameter, and then according to the DC side , Calculate the zero-sequence component u 0 of the lower capacitor voltage; add the zero-sequence component and the modulated wave signal obtained by the closed-loop control unit, and send it to the sinusoidal pulse width modulation unit. Each switch tube of each phase bridge arm in the level grid-connected inverter.
作为一种具体示例,所述数字处理控制模块采用TMS320F2808和EPM1270T芯片。As a specific example, the digital processing control module adopts TMS320F2808 and EPM1270T chips.
一种基于混杂参数的中点电压控制方法,包括以下步骤:A hybrid parameter-based midpoint voltage control method, comprising the following steps:
步骤1、根据零序分量与平均中点电流之间的关系因子δ,将三电平并网逆变器的运行条件划分为两种不同的工况:Step 1. According to the relationship factor δ between the zero-sequence component and the average midpoint current, the operating conditions of the three-level grid-connected inverter are divided into two different working conditions:
当δ>0时,三电平并网逆变器工作于工况1;When δ>0, the three-level grid-connected inverter works in working condition 1;
当δ≤0时,三电平并网逆变器工作于工况2;When δ≤0, the three-level grid-connected inverter works in working condition 2;
δ为零序分量与平均中点电流之间的关系因子,δ可表示为:δ is the relationship factor between the zero-sequence component and the average midpoint current, and δ can be expressed as:
式中,Imp为网侧电流正序分量的幅值,λ为不平衡度,为功率因数角,为网侧电压负序分量相位角。In the formula, I mp is the amplitude of the positive sequence component of the grid-side current, λ is the unbalance degree, is the power factor angle, is the phase angle of the negative sequence component of the grid-side voltage.
步骤2、根据三电平并网逆变器所处的工况设计控制参数:Step 2. Design control parameters according to the working conditions of the three-level grid-connected inverter:
混杂参数PI控制器的传递函数为:The transfer function of the mixed parameter PI controller is:
其中,kp为比例系数,Ti为积分时间常数;Among them, k p is the proportional coefficient, and T i is the integral time constant;
结合图2,中点电压控制系统的开环传递函数为:Combined with Figure 2, the open-loop transfer function of the midpoint voltage control system is:
设定混杂参数PI控制器的拐点频率远大于其截止频率,在计算传递函数Gol(s)的截止频率的时候忽略时间常数Ti的影响,则截止频率ωc的表达式为:The corner frequency of the hybrid parameter PI controller is set to be much larger than its cutoff frequency, and the influence of the time constant T i is ignored when calculating the cutoff frequency of the transfer function G ol (s), the expression of the cutoff frequency ω c is:
在设计比例系数kp时,必须满足下列条件:When designing the proportional coefficient k p , the following conditions must be met:
工况1:δ>0Condition 1: δ>0
定义δmax为工况1下关系因子δ的最大值,根据kp设计时的条件,令比例增益kp为:Define δ max as the maximum value of the relationship factor δ under working condition 1. According to the conditions of k p design, let the proportional gain k p be:
其中关系因子δ为不平衡度λ、功率因数角及负序电压相位角的函数,记为δ(λ,),使用拉格朗日乘子法求解关系因子的最大值δmax,定义拉格朗日函数:The relationship factor δ is the unbalance degree λ, the power factor angle and negative sequence voltage phase angle The function of , denoted as δ(λ, ), use the Lagrangian multiplier method to find the maximum value of the relation factor δ max , and define the Lagrangian function:
其中vi为拉格朗日乘子,为约束方程,可表示为:where vi is the Lagrange multiplier, is the constraint equation, which can be expressed as:
定义为拉格朗日函数关于变量λ、 的一阶梯度,由Karush-Kuhn-Tucher必要条件可知,函数最大值点应满足的一阶必要条件为:definition is the Lagrangian function Regarding the variable λ, The first-order gradient of , according to the Karush-Kuhn-Tucher necessary condition, the function The first-order necessary condition that the maximum point should satisfy is:
定义为拉格朗日函数关于变量λ、 的二阶梯度,函数最大值点应满足的二阶充分条件为:definition is the Lagrangian function Regarding the variable λ, The second-order gradient of , the function The second-order sufficient condition that the maximum point should satisfy is:
其中,可表示为:in, can be expressed as:
可求得约束条件下函数的最大值点:The function under the constraints can be obtained The maximum point of :
将最大值点代入函数则最大值δmax为:Substitute the maximum point into the function Then the maximum value δmax is:
δmax=1.94 δmax = 1.94
当负序电压相位角时,不同不平衡度及功率因数角条件下的关系因子δ曲面图如图4(a)所示,最大值δmax的位置被标注在图4(a)中。When the negative sequence voltage phase angle When , the relationship factor δ surface graph under different unbalance and power factor angle conditions is shown in Fig. 4(a), and the position of the maximum value δmax is marked in Fig. 4(a).
工况2:δ≤0Working condition 2: δ≤0
定义δmin为工况2下关系因子δ的最小值,为满足设计条件,令比例增益kp为:Define δ min as the minimum value of the relationship factor δ under working condition 2, in order to meet the design conditions, let the proportional gain k p be:
使用拉格朗日乘子法求解关系因子δ的最小值δmin,定义拉格朗日函数:Use the Lagrangian multiplier method to find the minimum value of the relation factor δ, δ min , to define the Lagrangian function:
式中可表示为:in the formula can be expressed as:
求得约束条件下函数的最小值点:find function under constraints The minimum point of :
将最大值点代入函数则最小值δmin为:Substitute the maximum point into the function Then the minimum value δmin is:
δmin=-21.63δ min =-21.63
当负序电压相位角时,不同不平衡度及功率因数角条件下的关系因子δ曲面图如图4(b)所示,最小值δmin的位置被标注在图4(b)中。When the negative sequence voltage phase angle When , the relationship factor δ surface graph under different unbalance and power factor angle conditions is shown in Fig. 4(b), and the position of the minimum value δ min is marked in Fig. 4(b).
积分时间Ti为混杂参数PI控制器拐点频率的倒数,为保证混杂参数PI控制器的穿越频率不受其积分环节的影响,则混杂参数PI控制器的拐点频率应小于穿越频率ωc,而为了确保混杂参数PI控制器在并网逆变器的各个工况下有着较大的相位裕量,其拐点频率可选在1/10的穿越频率处,则积分时间常数Ti的表达式为:The integration time T i is the reciprocal of the inflection point frequency of the hybrid parameter PI controller. In order to ensure that the crossover frequency of the hybrid parameter PI controller is not affected by its integral link, the inflection point frequency of the hybrid parameter PI controller should be less than the crossover frequency ω c , while In order to ensure that the hybrid parameter PI controller has a large phase margin under various operating conditions of the grid-connected inverter, its inflection point frequency can be selected at 1/10 of the crossover frequency, the expression of the integral time constant T i is: :
则零序分量为:Then the zero sequence component is:
步骤3、采样交流侧三相电压ea、eb、ec,交流侧三相电流ia、ib、ic,直流侧上电容电压UC1,直流侧下电容电压UC2;Step 3, sampling the three-phase voltages e a , eb , and ec on the AC side, the three-phase currents ia , ib , and ic on the AC side, the capacitor voltage U C1 on the DC side, and the capacitor voltage U C2 on the DC side;
步骤4、通过闭环控制单元得到三相调制波ua、ub、uc;Step 4. Obtain three-phase modulated waves u a , ub , and uc through the closed-loop control unit;
步骤4.1、利用对称分量法对交流侧电压ea、eb、ec、交流侧电流ia、ib、ic进行正负序分解,因为本实施方案中NPC三电平并网逆变器采用三相三线制接法,故不考虑网侧电压、电流的零序分量,只考虑其正、负序分量;Step 4.1. Use the symmetrical component method to perform positive and negative sequence decomposition on the AC side voltages e a , eb , ec , and the AC side currents i a , ib , ic , because in this embodiment, the NPC three-level grid-connected inverter The device adopts three-phase three-wire connection method, so the zero-sequence components of grid-side voltage and current are not considered, only the positive and negative sequence components are considered;
步骤4.2、将三相静止坐标系下ea、eb、ec、ia、ib、ic的正、负序交流量转换为正、负序同步旋转坐标系下的直流量,正、负序同步旋转坐标系转换矩阵分别为:Step 4.2. Convert the positive and negative sequence AC quantities of e a , e b , ec , i a , ib , and ic in the three-phase stationary coordinate system to the direct current quantities in the positive and negative sequence synchronous rotating coordinate system, and the positive , Negative sequence synchronous rotation coordinate system transformation matrix are:
经过转换,得到正序同步旋转坐标系下电压、电流的d、q轴分量edp、eqp、idp、iqp,以及负序同步旋转坐标系下电压、电流的d、q轴分量edn、eqn、idn、iqn;After conversion, the d and q-axis components of the voltage and current in the positive-sequence synchronous rotating coordinate system, e dp , e qp , i dp , and i qp , and the d and q-axis components e of the voltage and current in the negative-sequence synchronous rotating coordinate system are obtained. dn , e qn , i dn , i qn ;
步骤4.3、在非理想电网条件下,并网逆变器的有功、无功瞬时功率会含有二倍工频的交流量,根据瞬时无功功率理论,其瞬时功率中的直流量及交流量为:Step 4.3. Under non-ideal grid conditions, the active and reactive instantaneous powers of the grid-connected inverter will contain AC quantities twice the power frequency. According to the theory of instantaneous reactive power, the DC and AC quantities in the instantaneous power are: :
其中,i* dp为正序d轴的电流给定,i* qp为正序q轴的电流给定,i* dn为负序d轴的电流给定,i* qn为负序q轴的电流给定,P0为瞬时有功功率的直流分量,Pc2、Ps2为瞬时有功功率的交流分量,Q0为瞬时无功功率的直流分量,Qc2、Qs2为瞬时无功功率的交流分量;Among them, i * dp is the current reference of the positive sequence d axis, i * qp is the current reference of the positive sequence q axis, i * dn is the current reference of the negative sequence d axis, and i * qn is the negative sequence q axis. Given current, P 0 is the DC component of the instantaneous active power, P c2 and P s2 are the AC components of the instantaneous active power, Q 0 is the DC component of the instantaneous reactive power, Q c2 and Q s2 are the AC components of the instantaneous reactive power weight;
当控制目标为消除有功功率波动量Pc2、Ps2时,可得到电流给定的表达式:When the control objective is to eliminate the active power fluctuations P c2 and P s2 , the current given expression can be obtained:
其中,E1、E2的表达式为:Among them, the expressions of E 1 and E 2 are:
步骤4.4、通过闭环控制单元,得到同步旋转坐标系下的4路调制波信号udp、uqp、udn、uqn,其控制方程如下:Step 4.4, through the closed-loop control unit, obtain four modulated wave signals udp , uqp , udn , and uqn in the synchronous rotating coordinate system, and the control equations are as follows:
步骤4.5、先将负序两相旋转坐标系下的调制波信号udn、uqn转换到三相静止坐标系下,再将三相静止坐标系下的负序分量转换到正序同步旋转坐标系下,转换矩阵分别为:Step 4.5. First convert the modulated wave signals u dn and u qn in the negative sequence two-phase rotating coordinate system to the three-phase stationary coordinate system, and then convert the negative sequence components in the three-phase stationary coordinate system into the positive-sequence synchronous rotating coordinate Under the system, the transformation matrices are:
经过转换,得到正序旋转坐标系下的负序分量,将同一坐标系下正、负序调制波分量相加,得到正序同步旋转坐标系下的调制波分量ud、uq;After conversion, the negative sequence components in the positive sequence rotating coordinate system are obtained, and the positive and negative sequence modulating wave components in the same coordinate system are added to obtain the modulating wave components ud and u q in the positive sequence synchronous rotating coordinate system;
步骤4.6、将同步旋转坐标系下的调制波信号转换为三相调制波信号ua、ub、uc,转换公式如下:Step 4.6, convert the modulated wave signal in the synchronous rotating coordinate system into three-phase modulated wave signals u a , ub , uc , the conversion formula is as follows:
步骤5、通过网侧信息计算单元计算当前的不平衡度λ、功率因数角以及网侧电压负序分量相位角 Step 5. Calculate the current unbalance degree λ and power factor angle through the grid-side information calculation unit and the phase angle of the negative sequence component of the grid-side voltage
步骤6、工况判断单元根据步骤5的计算结果判断关系因子δ的符号,确定三电平并网逆变器所处的工况;Step 6, the working condition judgment unit judges the sign of the relationship factor δ according to the calculation result of step 5, and determines the working condition of the three-level grid-connected inverter;
步骤7、根据三电平并网逆变器所处的工况切换混杂参数PI控制器的参数,然后根据直流侧电容电压计算零序分量u0;Step 7: Switch the parameters of the hybrid parameter PI controller according to the working condition of the three-level grid-connected inverter, and then calculate the zero-sequence component u 0 according to the DC side capacitor voltage;
步骤8、将零序分量u0与步骤4得到的三相调制波相加,得到三相调制信号:Step 8. Add the zero-sequence component u 0 to the three-phase modulation wave obtained in step 4 to obtain a three-phase modulation signal:
u'a=ua+u0 u' a =u a +u 0
u'b=ub+u0 u' b =u b +u 0
u'c=uc+u0 u' c =u c +u 0
步骤9、将加入零序分量后的调制波信号u'a、u'b、u'c送至正弦脉宽调制单元,生成脉宽调制信号,驱动电路控制三电平并网逆变器开关管的工作,实现中点电压平衡的控制。Step 9. Send the modulated wave signals u' a , u' b , and u' c after adding the zero-sequence component to the sinusoidal pulse width modulation unit to generate a pulse width modulation signal, and the drive circuit controls the switch of the three-level grid-connected inverter The work of the tube realizes the control of the neutral point voltage balance.
NPC三相三电平并网逆变器的调制规则为:如图3所示,以a相桥臂为例,在uaref的正半周,当uaref大于载波时,令Sa1、Sa2导通,a相桥臂输出高电平,当uaref小于载波时,令Sa2、Sa3导通,a相桥臂输出零电平;在uaref的负半周,当uaref小于载波时,令Sa3、Sa4导通,a相桥臂输出低电平,当uaref大于载波时,令Sa2、Sa3导通,a相桥臂输出零电平。b、c相桥臂的调制规则相同。The modulation rule of the NPC three-phase three-level grid-connected inverter is: as shown in Figure 3, taking the a-phase bridge arm as an example, in the positive half cycle of u aref , when u aref is greater than the carrier, let S a1 and S a2 Turn on, the a-phase bridge arm outputs a high level, when u aref is smaller than the carrier, make S a2 and S a3 turn on, and the a-phase bridge arm outputs zero level; in the negative half cycle of u aref , when u aref is smaller than the carrier , so that S a3 and S a4 are turned on, and the a-phase bridge arm outputs a low level. When u aref is greater than the carrier, S a2 and S a3 are turned on, and the a-phase bridge arm outputs zero level. The modulation rules of the b and c-phase bridge arms are the same.
图5为混杂参数控制器参数选择的流程图,其中与λ(k)分别为网侧电压负序分量相位角功率因数角与不平衡度λ在第k个工频周期的计算值,δ(k)表示关系因子δ在第k个工频周期的值,具体实施过程如下:Figure 5 is a flow chart of parameter selection of the hybrid parameter controller, in which and λ (k) are the phase angle of the negative sequence component of the grid-side voltage, respectively power factor angle With the calculated value of the unbalance degree λ in the kth power frequency cycle, δ (k) represents the value of the relationship factor δ in the kth power frequency cycle, and the specific implementation process is as follows:
S1、采样网侧三相电压和电流信号;S1. Sampling the three-phase voltage and current signals on the grid side;
S2、检测当前工频周期的负序分量相位角功率因数角与不平衡度λ(k);S2. Detect the phase angle of the negative sequence component of the current power frequency cycle power factor angle and unbalance degree λ (k) ;
S3、根据网侧信息判断当前工频周期关系因子δ(k)的符号,若则混杂参数PI控制器应用工况1下设计的控制参数,若则混杂参数PI控制器应用工况2下设计的控制参数。S3. Determine the sign of the current power frequency cycle relationship factor δ (k) according to the network side information, if Then the control parameters designed under the application condition 1 of the mixed parameter PI controller, if Then the control parameters designed under the application condition 2 of the mixed parameter PI controller.
实施例Example
本实施例搭建了基于数组信号处理器-复杂可编程逻辑器件(Digital SignalProcessor and Complex Programmable Logic Device,DSP-CPLD)控制架构的NPC三电平并网逆变器样机,直流电经直流母线电容后,由三电平逆变电路逆变输出三相电压,经LC滤波电路输出光滑的三相正弦电压。仿真过程中的电气参数设置如表1:In this embodiment, an NPC three-level grid-connected inverter prototype based on an array signal processor-complex programmable logic device (Digital Signal Processor and Complex Programmable Logic Device, DSP-CPLD) control architecture is built. The three-phase voltage is inverted and outputted by the three-level inverter circuit, and the smooth three-phase sinusoidal voltage is outputted by the LC filter circuit. The electrical parameter settings in the simulation process are shown in Table 1:
表1Table 1
图6为三电平并网逆变器网侧不平衡度为0.1,功率因数为1时的直流母线电容C1、C2瞬时电压Uc1、Uc2的仿真波形,在0.1s时刻使用本发明所述的控制方法。在未使用本发明中的控制方法之前,直流侧上、下电容的瞬时电压存在幅值约为40V的电压波动,在使用本发明中的控制方法之后,直流侧上、下电容电压的波动被限制在2V以内。Figure 6 shows the simulation waveforms of the instantaneous voltages U c1 and U c2 of the DC bus capacitors C 1 and C 2 when the grid-side unbalance is 0.1 and the power factor is 1 for the three-level grid-connected inverter. Invention of the control method. Before the control method of the present invention is used, the instantaneous voltage of the upper and lower capacitors on the DC side has voltage fluctuations with an amplitude of about 40V. After the control method of the present invention is used, the voltage fluctuations of the upper and lower capacitors on the DC side are Limited to 2V.
图7、图8和图9分别为不平衡度为0.1,功率因数为0.707时,不平衡度为0.2,功率因数为1时和不平衡度为0.6,功率因数为0时直流母线电容C1、C2瞬时电压Uc1、Uc2的仿真波形,其他条件不变,在0.1s时刻使用本发明所述的控制方法,直流侧上、下电容电压的波动被限制在2V以内。可以看出,在高不平衡度、低功率因数条件下,本发明中的控制方法仍有较为理想的效果。图10中的(a)、(b)、(c)、(d)分别是上述四种条件下使用中点控制方法之前及之后的网侧电流总谐波畸变率的对比,可以看出,本发明基于混杂参数的中点电压控制方法,有效的抑制了网侧电流中的3、5、7、9等奇次谐波,降低了电流的总谐波畸变率。Figure 7, Figure 8 and Figure 9 show that when the unbalance degree is 0.1, the power factor is 0.707, the unbalance degree is 0.2, when the power factor is 1 and the unbalance degree is 0.6, and the power factor is 0, the DC bus capacitor C 1 The simulation waveforms of the instantaneous voltages U c1 and U c2 of C 2 , other conditions remain unchanged, and the control method of the present invention is used at the moment of 0.1s, and the fluctuation of the upper and lower capacitor voltages on the DC side is limited within 2V. It can be seen that under the conditions of high unbalance and low power factor, the control method of the present invention still has a relatively ideal effect. (a), (b), (c), and (d) in Figure 10 are the comparison of the total harmonic distortion rate of the grid-side current before and after using the midpoint control method under the above four conditions. It can be seen that, The present invention effectively suppresses odd harmonics such as 3, 5, 7, and 9 in the grid-side current based on the hybrid parameter-based midpoint voltage control method, and reduces the total harmonic distortion rate of the current.
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