CN108933543B - 一种背靠背mmc结构中逆变器的预充电控制方法 - Google Patents

一种背靠背mmc结构中逆变器的预充电控制方法 Download PDF

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CN108933543B
CN108933543B CN201811023967.6A CN201811023967A CN108933543B CN 108933543 B CN108933543 B CN 108933543B CN 201811023967 A CN201811023967 A CN 201811023967A CN 108933543 B CN108933543 B CN 108933543B
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王兴贵
齐刚
马平
王海亮
杨维满
李晓英
郭群
郭永吉
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Lanzhou University of Technology
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483Converters with outputs that each can have more than two voltages levels
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M5/00Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases
    • H02M5/40Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc
    • H02M5/42Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters
    • H02M5/44Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac
    • H02M5/453Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M5/458Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H02M5/4585Conversion of ac power input into ac power output, e.g. for change of voltage, for change of frequency, for change of number of phases with intermediate conversion into dc by static converters using discharge tubes or semiconductor devices to convert the intermediate dc into ac using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only having a rectifier with controlled elements
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02MAPPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483Converters with outputs that each can have more than two voltages levels
    • H02M7/4835Converters with outputs that each can have more than two voltages levels comprising two or more cells, each including a switchable capacitor, the capacitors having a nominal charge voltage which corresponds to a given fraction of the input voltage, and the capacitors being selectively connected in series to determine the instantaneous output voltage

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Abstract

一种背靠背MMC结构中逆变器的预充电控制方法,首先进行第一充电阶段,控制充电电流对MMC逆变器所有子模块电容充电,并计算出充电电流作用的时间。然后进行第二充电阶段,根据第一充电阶段结束时刻,控制IGBT的关断与开通,对首先投入的子模块电容充电,切除剩余子模块。最后以首先投入充电的子模块电容充电结束时刻控制IGBT的通断,投入剩余子模块的同时切除首先投入充电的子模块,可计算出整个预充电所需时间。从而实现通过控制充电电流对MMC逆变器预充电,并保证安全充电的同时使得充电时间最短,以时间节点控制子模块的充电状态,节省了子模块电容电压检测装置。

Description

一种背靠背MMC结构中逆变器的预充电控制方法
技术领域
本发明涉及MMC(模块化多电平变换器)技术领域,具体涉及一种背靠背MMC结构中逆变器的预充电控制方法。
背景技术
MMC与传统的多电平变流器相比,MMC具有开关损耗小,输出波形质量高,故障处理能力强,易于扩容,可四象限运行等特点。MMC系统中包含大量悬浮的子模块电容,在启动前所有子模块电容均无电压。启动MMC时,首先要采取相应的控制方法对子模块电容充电,将子模块电容充电至稳定运行时的电压要求。背靠背MMC由MMC整流器和MMC 逆变器构成,已经有许多公开文献详细介绍了通过交流侧对MMC整流器的预充电控制方法,而对MMC逆变器预充电控制策略的研究比较少。背靠背MMC结构中可以通过MMC整流器对MMC逆变器充电,在充电过程中必须抑制充电电流的冲击,因此发明了一种背靠背 MMC结构中逆变器的预充电控制方法。
发明内容
本发明的目的是通过控制充电电流只对背靠背MMC结构中的逆变器预充电,解决充电电流的冲击问题,并实现在安全充电的同时使得充电时间最短。
本发明一种背靠背MMC结构中逆变器的预充电控制方法,其特征在于,其步骤为:预充电控制方法分为两个阶段;在第一充电阶段,对MMC逆变器所有子模块电容充电;在第二充电阶段,首先对投入的n个子模块充电,切除剩余的n个子模块;计算出首先投入子模块充电时间,根据时间节点将首先投入的子模块切除,对剩余子模块充电;MMC逆变器各相结构相同,以a相为例,流过a相桥臂电流为ia=Id/3;在充电过程中,MMC逆变器桥臂存在杂散电感Ls,包括桥臂电感,充电电流的突变会产生过电压;在部分充电时间段内,充电电流变化产生的过电压ΔU=Lsdia/dt,为保证充电系统的安全,将ΔU控制在10%Udc以内,Udc为背靠背MMC稳定运行时直流母线电压;在安全充电的同时使得充电时间最短,充电电流变化速率k=10%Udc/Ls;第一充电阶段分为三个步骤:
步骤一:在0-t1时间段内,控制充电电流Id=Id1,即:
Id1=kt(0≤t≤t1) (公式一)
式中t1为第一充电阶段Id上升至Im时刻,Im为功率器件所能承受的最大电流;计算得:
Figure GDA0002290479710000011
步骤二:在t1-t2时间段内,以最大电流Im对电容充电,充电电流Id=Im(t1<t<t2),t2为第一充电阶段Id从Im开始下降时刻;
步骤三:在t2-t3时间段内,充电电流Id=Id2,即:
Id2=-k(t3-t)(t2≤t≤t3) (公式三)
式中t3为第一充电阶段结束时刻;第一充电阶段结束时,子模块电容电压为u1=Udc/2n;
在第一充电阶段,子模块电容电压为:
Figure GDA0002290479710000021
计算得:
Figure GDA0002290479710000022
Figure GDA0002290479710000023
在t3时刻进入第二充电阶段,第二充电阶段分为以下步骤:
步骤一:第二充电阶段,需要控制IGBT的通断状态,首先每相投入n个子模块,切除剩余子模块;在t3时刻Id为0,在延迟Δtd后开始控制电流变化,Δtd应大于IGBT的开关时间;
步骤二:在t4时刻对首先投入的子模块电容充电,由公式六可知:
Figure GDA0002290479710000024
在t4-t5时间段内,t5为Id上升至Im时刻,充电电流Id=Id3,为:
Id3=k(t-t4) (t4≤t≤t5) (公式八)
由公式七、八可得:
Figure GDA0002290479710000025
步骤三:在t5-t6时间段内,以最大电流Im对电容充电,充电电流Id=Im(t5<t<t6),t6为Id从 Im开始下降时刻;
步骤四:在t6-t7时间段内,充电电流Id=Id4,为:
Id4=-k(t7-t) (t6≤t≤t7) (公式十)
式中t7为首先投入的子模块充电结束时刻;在第二充电阶段,首先投入子模块电容电压达到UC=Udc/n,首先投入充电的子模块电容电压变化为:
Figure GDA0002290479710000026
计算得:
Figure GDA0002290479710000027
Figure GDA0002290479710000028
步骤五:在t7时刻首先投入的子模块电容电压达到UC,此时Id为0,在Δtd内把首先投入的子模块切除,将剩余的子模块投入充电状态;
步骤六:在t8时刻开始对剩余子模块电容充电,可得
Figure GDA0002290479710000029
在t8-t9时间段内,t9为Id上升至Im时刻,充电电流Id=Id5,为:
Id5=k(t-t8) (t8≤t≤t9) (公式十五)
计算得:
Figure GDA00022904797100000210
步骤七:在t9-t10时间段内,以最大电流Im对电容充电,充电电流Id=Im(t9<t<t10),t10为Id从Im开始下降时刻;
步骤八:在t10-t11时间段内,充电电流Id=Id6,为:
Id6=-k(t11-t) (t10≤t≤t11) (公式十七)
式中t11为剩余投入的子模块充电结束时刻;在第二充电阶段,剩余投入子模块电容电压达到UC,剩余充电子模块电容电压变化为:
Figure GDA0002290479710000031
计算得
Figure GDA0002290479710000032
Figure GDA0002290479710000033
在t11时刻,保证安全充电的同时,所有子模块电容电压以最短的时间达到UC,此时整个预充电过程结束。
本发明的有益之处是:通过控制充电电流的变化对MMC逆变器子模块预充电,有效地解决了充电过程中充电电流的冲击问题。计算出各充电阶段所需的时间,以时间节点控制子模块的充电状态,不需要子模块电容电压检测装置,减小了设备成本。在充电过程中,流经子模块的电流均相同,不需要考虑充电时子模块电容均压问题。
附图说明
图1是背靠背MMC拓扑结构,图2为充电电流和子模块电容电压变化趋势。
具体实施方式
如图1所示,本发明所述背靠背MMC结构中的逆变器由三个相单元构成,每相由上、下桥臂构成,每个桥臂由n个SM(子模块)和一个桥臂电感L串联构成,子模块电容容值为C。背靠背MMC稳定运行时,直流母线电压为Udc,子模块电容电压UC=Udc/n。将MMC整流器等效为可控电流源,输出电流为Id
本发明是一种背靠背MMC结构中逆变器的预充电控制方法,其步骤为:MMC逆变器子模块的预充电方法分为两个阶段,如图2所示,在第一充电阶段,对MMC逆变器所有子模块电容充电。在第二充电阶段,首先对投入的n个子模块充电,切除剩余的n个子模块;计算出首先投入子模块充电时间,根据时间节点将首先投入的子模块切除,对剩余子模块充电。MMC逆变器各相结构相同,以a相为例,流过a相桥臂电流为ia=Id/3。在充电过程中, MMC逆变器桥臂存在杂散电感Ls(包括桥臂电感),充电电流的突变会产生过电压。在部分充电时间段内,充电电流变化产生的过电压DU=Lsdia/dt,为保证充电系统的安全,将DU控制在10%Udc以内。在安全充电的同时使得充电时间最短,充电电流变化速率k=10%Udc/Ls
第一充电阶段分为三个步骤:
步骤一:在0-t1时间段内,控制充电电流Id=Id1,即:
Id1=kt (0≤t≤t1) (公式一)
式中t1为第一充电阶段Id上升至Im时刻,Im为功率器件所能承受的最大电流;计算得:
Figure GDA0002290479710000041
步骤二:在t1-t2时间段内,以最大电流Im对电容充电,充电电流Id=Im(t1<t<t2),t2为第一充电阶段Id从Im开始下降时刻;
步骤三:在t2-t3时间段内,充电电流Id=Id2,即:
Id2=-k(t3-t) (t2≤t≤t3) (公式三)
式中t3为第一充电阶段结束时刻;第一充电阶段结束时,子模块电容电压为u1=Udc/2n;
在第一充电阶段,子模块电容电压为:
Figure GDA0002290479710000042
计算得:
Figure GDA0002290479710000043
Figure GDA0002290479710000044
在t3时刻进入第二充电阶段,第二充电阶段分为以下步骤:
步骤一:第二充电阶段,需要控制IGBT的通断状态,首先每相投入n个子模块,切除剩余子模块;在t3时刻Id为0,在延迟Δtd后开始控制电流变化,Δtd应大于IGBT的开关时间;
步骤二:在t4时刻对首先投入的子模块电容充电,由公式六可知:
Figure GDA0002290479710000045
在t4-t5时间段内,t5为Id上升至Im时刻,充电电流Id=Id3,为:
Id3=k(t-t4) (t4≤t≤t5) (公式八)
由公式七、八可得:
Figure GDA0002290479710000046
步骤三:在t5-t6时间段内,以最大电流Im对电容充电,充电电流Id=Im(t5<t<t6),t6为Id从 Im开始下降时刻;
步骤四:在t6-t7时间段内,充电电流Id=Id4,为:
Id4=-k(t7-t) (t6≤t≤t7) (公式十)
式中t7为首先投入的子模块充电结束时刻;在第二充电阶段,首先投入子模块电容电压达到UC,首先投入充电的子模块电容电压变化为:
Figure GDA0002290479710000047
计算得:
Figure GDA0002290479710000048
Figure GDA0002290479710000049
步骤五:在t7时刻首先投入的子模块电容电压达到UC,此时Id为0,在Δtd内把首先投入的子模块切除,将剩余的子模块投入充电状态;
步骤六:在t8时刻开始对剩余子模块电容充电,可得
Figure GDA0002290479710000051
在t8-t9时间段内,t9为Id上升至Im时刻,充电电流Id=Id5,为:
Id5=k(t-t8) (t8≤t≤t9) (公式十五)
计算得:
Figure GDA0002290479710000052
步骤七:在t9-t10时间段内,以最大电流Im对电容充电,充电电流Id=Im(t9<t<t10),t10为Id从Im开始下降时刻;
步骤八:在t10-t11时间段内,充电电流Id=Id6,为:
Id6=-k(t11-t) (t10≤t≤t11) (公式十七)
式中t11为剩余投入的子模块充电结束时刻;在第二充电阶段,剩余投入子模块电容电压达到UC,剩余充电子模块电容电压变化为:
Figure GDA0002290479710000053
Figure GDA0002290479710000054
Figure GDA0002290479710000055
Figure GDA0002290479710000056
在t11时刻,保证安全充电的同时,所有子模块电容电压以最短的时间达到Uc,此时整个预充电过程结束。
如图1所示,本发明所述背靠背MMC结构中的逆变器由三个相单元构成,每相由上、下桥臂构成,每个桥臂由n个SM和一个桥臂电感L串联构成,子模块电容容值为C。背靠背MMC稳定运行时,直流母线电压为Udc,子模块电容电压UC=Udc/n。将MMC整流器等效为可控电流源,输出电流为Id
如图2所示,本发明的预充电控制方法分为两个阶段,在第一充电阶段,对MMC逆变器所有子模块电容充电。在第二充电阶段,首先对每相投入的n个子模块充电,切除剩余子模块;计算出首先投入子模块充电时间,根据时间节点切除首先投入的子模块,对剩余子模块充电。
MMC逆变器各相结构相同,以a相为例,流过a相桥臂电流为ia=Id/3。在充电过程中,MMC逆变器桥臂电感远大于线路中的杂散电感Ls≈2L,充电电流的突变会产生过电压。在部分充电时间段内,充电电流变化产生的过电压Δ U =Lsdia/dt,为保证充电系统的安全,将Δ U 控制在10%Udc以内。在安全充电的同时使得充电时间最短,充电电流变化速率k=10%Udc/Ls
在预充电过程中,MMC逆变器所有子模块的V1都处于关断状态,控制V2的关断与开通,可以控制子模块是否投入充电状态。第一充电阶段,所有子模块的V2处于关断状态,第一充电阶段分为三个步骤:
步骤一:在0-t1时间段内,控制充电电流Id=Id1,即:
Id1=kt (0≤t≤t1) (公式二十一)
式中t1为第一充电阶段Id上升至Im时刻,Im为功率器件所能承受的最大电流;计算得:
Figure GDA0002290479710000061
步骤二:在t1-t2时间段内,以最大电流Im对电容充电,充电电流Id=Im(t1<t<t2),t2为第一充电阶段Id从Im开始下降时刻;
步骤三:在t2-t3时间段内,充电电流Id=Id2,即:
Id2=-k(t3-t) (t2≤t≤t3) (公式二十三)
式中t3为第一充电阶段结束时刻;第一充电阶段结束时,子模块电容电压为u1=Udc/2n;
在第一充电阶段,子模块电容电压为:
Figure GDA0002290479710000062
计算得:
Figure GDA0002290479710000063
Figure GDA0002290479710000064
在t3时刻进入第二充电阶段,第二充电阶段分为以下步骤:
步骤一:在t3时刻进入第二充电阶段,在t3时刻Id为0,在延迟Δtd后开始控制电流变化,Δtd的取值为2倍IGBT的开关时间。首先每相投入n个子模块充电,在Δtd内开通剩余子模块的V2,将剩余子模块切除。
步骤二:在t4时刻开始对首先投入的子模块电容充电,可知:
Figure GDA0002290479710000065
在t4-t5时间段内,t5为Id上升至Im时刻,充电电流Id=Id3,为:
Id3=k(t-t4) (公式二十八)
式中t4≤t≤t5,可得
Figure GDA0002290479710000066
步骤三:在t5-t6时间段内,以最大电流Im对电容充电,充电电流Id=Im(t5<t<t6),t6为Id从 Im开始下降时刻;
步骤四:在t6-t7时间段内,充电电流Id=Id4,为:
Id4=-k(t7-t) (t6≤t≤t7) (公式三十)
式中t7为首先投入的子模块充电结束时刻;在第二充电阶段,首先投入子模块电容电压达到UC=Udc/n,首先投入充电的子模块电容电压变化为:
Figure GDA0002290479710000071
计算得:
Figure GDA0002290479710000072
Figure GDA0002290479710000073
步骤五:在t7时刻首先投入的子模块电容电压达到UC,此时Id为0,在Δtd内开通首先投入的子模块的V2,把首先投入的子模块切除,并关断剩余子模块的V2,将剩余子模块投入充电状态。
步骤六:在t8时刻开始对剩余子模块电容充电,可得
Figure GDA0002290479710000074
在t8-t9时间段内,t9为Id上升至Im时刻,充电电流Id=Id5,为:
Id5=k(t-t8) (t8≤t≤t9) (公式三十五)
计算得:
Figure GDA0002290479710000075
步骤七:在t9-t10时间段内,以最大电流Im对电容充电,充电电流Id=Im(t9<t<t10),t10为Id从Im开始下降时刻;
步骤八:在t10-t11时间段内,充电电流Id=Id6,为:
Id6=-k(t11-t) (t10≤t≤t11) (公式三十七)
式中t11为剩余投入的子模块充电结束时刻;在第二充电阶段,剩余投入子模块电容电压达到UC,剩余充电子模块电容电压变化为:
Figure GDA0002290479710000076
计算得
Figure GDA0002290479710000077
Figure GDA0002290479710000078
在t11时刻,保证安全充电的同时,所有子模块电容电压以最短的时间达到UC,此时整个预充电过程结束。
由以上步骤可以实现,通过控制充电电流对背靠背MMC结构中逆变器预充电,充电过程中以时间节点控制子模块的关断与开通,在安全充电的同时使得子模块电容电压在最短时间内达到运行的要求。

Claims (1)

1.一种背靠背MMC结构中逆变器的预充电控制方法,其特征在于,其步骤为:预充电控制方法分为两个阶段;在第一充电阶段,对MMC逆变器所有子模块电容充电;在第二充电阶段,首先对投入的n个子模块充电,切除剩余的n个子模块;计算出首先投入子模块充电时间,根据时间节点将首先投入的子模块切除,对剩余子模块充电;MMC逆变器各相结构相同,以a相为例,流过a相桥臂的电流为ia=Id/3;在充电过程中,MMC逆变器桥臂存在杂散电感Ls,包括桥臂电感,充电电流的突变会产生过电压;在部分充电时间段内,充电电流变化产生的过电压ΔU=Lsdia/dt,为保证充电系统的安全,将ΔU控制在10%Udc以内,Udc为背靠背MMC稳定运行时直流母线电压;在安全充电的同时使得充电时间最短,充电电流变化速率k=10%Udc/Ls;第一充电阶段分为三个步骤:
步骤一:在0-t1时间段内,控制充电电流Id=Id1,即:
Id1=kt(0≤t≤t1) (公式一)
式中t1为第一充电阶段Id上升至Im时刻,Im为功率器件所能承受的最大电流;计算得:
Figure FDA0002290479700000011
步骤二:在t1-t2时间段内,以最大电流Im对电容充电,充电电流Id=Im(t1<t<t2),t2为第一充电阶段Id从Im开始下降时刻;
步骤三:在t2-t3时间段内,充电电流Id=Id2,即:
Id2=-k(t3-t)(t2≤t≤t3) (公式三)
式中t3为第一充电阶段结束时刻;第一充电阶段结束时,子模块电容电压为u1=Udc/2n;
在第一充电阶段,子模块电容电压为:
Figure FDA0002290479700000012
计算得:
Figure FDA0002290479700000013
Figure FDA0002290479700000014
在t3时刻进入第二充电阶段,第二充电阶段分为以下步骤:
步骤一:第二充电阶段,需要控制IGBT的通断状态,首先每相投入n个子模块,切除剩余子模块;在t3时刻Id为0,在延迟Δtd后开始控制电流变化,Δtd应大于IGBT的开关时间;
步骤二:在t4时刻对首先投入的子模块电容充电,由公式六可知:
Figure FDA0002290479700000015
在t4-t5时间段内,t5为Id上升至Im时刻,充电电流Id=Id3,为:
Id3=k(t-t4)(t4≤t≤t5) (公式八)
由公式七、八可得:
Figure FDA0002290479700000016
步骤三:在t5-t6时间段内,以最大电流Im对电容充电,充电电流Id=Im(t5<t<t6),t6为Id从Im开始下降时刻;
步骤四:在t6-t7时间段内,充电电流Id=Id4,为:
Id4=-k(t7-t)(t6≤t≤t7) (公式十)
式中t7为首先投入的子模块充电结束时刻;在第二充电阶段,首先投入子模块电容电压达到UC=Udc/n,首先投入充电的子模块电容电压变化为:
Figure FDA0002290479700000021
计算得:
Figure FDA0002290479700000022
Figure FDA0002290479700000023
步骤五:在t7时刻首先投入的子模块电容电压达到UC,此时Id为0,在Δtd内把首先投入的子模块切除,将剩余的子模块投入充电状态;
步骤六:在t8时刻开始对剩余子模块电容充电,可得
Figure FDA0002290479700000024
在t8-t9时间段内,t9为Id上升至Im时刻,充电电流Id=Id5,为:
Id5=k(t-t8)(t8≤t≤t9) (公式十五)
计算得:
Figure FDA0002290479700000025
步骤七:在t9-t10时间段内,以最大电流Im对电容充电,充电电流Id=Im(t9<t<t10),t10为Id从Im开始下降时刻;
步骤八:在t10-t11时间段内,充电电流Id=Id6,为:
Id6=-k(t11-t)(t10≤t≤t11) (公式十七)
式中t11为剩余投入的子模块充电结束时刻;在第二充电阶段,剩余投入子模块电容电压达到UC,剩余充电子模块电容电压变化为:
Figure FDA0002290479700000026
计算得
Figure FDA0002290479700000027
Figure FDA0002290479700000028
在t11时刻,保证安全充电的同时,所有子模块电容电压以最短的时间达到UC,此时整个预充电过程结束。
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