PPT第六章-储能元件

1、实际电容器实际电容器实际电容器实际电容器6-1 6-1 电容元件电容元件+ q- -q Us6-1 6-1 电容元件电容元件Ri0+ q- -q Us1. 1. 线性电容元件的定义及其图形符号线性电容元件的定义及其图形符号 0, 00, 0ququ Cuq uqC Cuq uqo0),(quf uqC Cuq Riu Cuq tuCtCutqiddd)d(dd3. 线性电容元件的线性电容元件的u-i关系关系(VCR)（约束方程）（约束方程）ttuCtid)(d)( Cuq )()( tGutiRRGttuCtid)(d)(i dtdu tuOt0dttiCtdu)(1)()()(0tutudu

2、ttdttiC0)(1 diCtututt 1)()(00ttuCtid)(d)( diCutut01)0()( , 00t令3. 线性电容元件的线性电容元件的u-i关系关系(VCR)（约束方程）（约束方程） )()( tCutqtuCidd diCtututt0 1)()(0 diCtututt 1)()(00ttuCtid)(d)()()(tRituui+R)()(tGutiCui diCtututt 1)()(003. 线性电容元件的线性电容元件的u-i关系关系(VCR)（约束方程）（约束方程）4.4.电容元件的功率和能量电容元件的功率和能量tuCuuipddttCpdtW0dtdtdu

3、uC tutuuduC0 tutuCu0221 )(21)(21)( 022tCutCutWCttuCtid)(d)(0)(21)(2CtCutW)(21)(21)(022tCutCutWC 1212222121tWtWtCutCuWCCC 01222CWtutu, 01222CWtutu,0)()(0 utu设设 )()( tCutq 4.4.电容元件的功率和能量电容元件的功率和能量0)(21)(2CtCutW 1212222121tWtWtCutCuWCCCttuCtid)(d)()(21)(2CtCutWCui )(21)(21)( 022tCutCutWC diCtututt 1)()

4、(00i0CuR6 6实际电容器的电路模型实际电容器的电路模型Cui+ q- -q UsCRL例题)(tusi电源电压电源电压的波形的波形s2 0s21 42s10 20 0)(Stttttttusttttttuti2 0s21A 1s 10A 10 0d)(d5 . 0)(SttuCtid)(d)(21t /s1i/A- -1O21t /s2Ous /Vs2 0s21)W 42(s 10 W 20 0)()()(tttttttitutps21t /s2Op/W- -2注意：分区间计算注意：分区间计算解解s2 0s21 42s10 20 0)(StttttttusttttttuCti2 0s2

5、1 1s 10 10 0d)(d)(S电容功率电容功率的波形的波形)(tusis2 0s21 )2(s 10 0 0)(25 . 0)(222CtttttttutWs)(21)(2CtCutWs2 0s21 V)42(s10 V 20 0)(Stttttttu0.5F)(tusCi21t /s2Op/W- -221t /s1oWC/Js2 0s21 1s 10 10 0)(ttttti 已知电容的电流已知电容的电流波形，求电容的电压波形，求电容的电压u。V 220d15 .01)0()(s 100 tttutu t ：42)22(2d) 1(5 . 01) 1 ()(1ttutut：s21 t

6、：ts2 tutu20d05 .01)2()(：0t0 05 . 01)()(dutut diCtututt0 1)()(021t /s1i/A- -1OCuiF5 . 0s2 0s21 V)42(s 10 V 20 0)(tttttttu6-2 6-2 电感元件电感元件1线性电感元件的定义及其图形符号线性电感元件的定义及其图形符号iuL )()( tLitLiuL 2 2. .线性电感元件的特性线性电感元件的特性韦安特性韦安特性iLLLioL0),(ifLiLo )()(tLitL 2 2. .线性电感元件的特性线性电感元件的特性韦安特性韦安特性iuLttiLttuL d)(d dd)(3线

7、性电感元件的线性电感元件的u-i关系关系（VCR）(约束方程约束方程) )()(tLitLttiLtu d)(d)( iu+ +- -LttuCtid)(d)(CuittiLtu d)(d)(6-2 6-2 电感元件电感元件u dtdi ,tiOiu+ +- -Lt06-2 6-2 电感元件电感元件ttiLtu d)(d)( )()(tLitL 0,0t令令 3线性电感元件的线性电感元件的u-i关系关系（VCR）(约束方程约束方程)iu+ +- -L )(1)()(00ttduLtiti )(1)0()(0tduLitittiLtud)(d)(ttiLtu d)(d)(iu+ +- -Liu+

8、 +- -L6-2 6-2 电感元件电感元件 3线性电感元件的线性电感元件的u-i关系关系（VCR）(约束方程约束方程) )(1)()(00ttduLtiti )(1)()(00ttduLtiti4. 电感元件的功率和能量电感元件的功率和能量itiLuipddttiLtu d)(d)()(21)(21)(022tLitLitWLttttttLLittiLitptW000) (21dddd)(2iu+ +- -L0)(21)(2tLitWL)()()(21)(21121222tWtWtLitLiWLLL 0,1222LWtiti 0,1222LWtiti)(21)(21)(022tLitLitW

9、L期间内期间内在在tt 04. 4. 电感元件的功率和能量电感元件的功率和能量iu+ +- -L 5. 5. 电感元件描述的电磁性质电感元件描述的电磁性质ttiLtu d)(d)()(21)(2tLitWL )(1)()(00ttduLtiti空心线圈空心线圈6. 6. 实际电感器（线圈）的模型实际电感器（线圈）的模型铁心线圈铁心线圈6. 6. 实际电感器（线圈）的模型实际电感器（线圈）的模型 6. 6. 实际电感器（线圈）的模型实际电感器（线圈）的模型LRLRCiu- -L)(21)(2CtCutW)(21)(2tLitWLttiLtu d)(d)( diCtututt01)()(0ttuC

10、tid)(d)( )()(tCutq )()(tLitL )(1)()(00ttduLtiti diCtututtkkk 001)()(一、电容元件的串联一、电容元件的串联ttnnidCCCtututu0)111()()()(2100201)()()()(21tutututunttnnttttidCtuidCtuidCtu0001)(1)(1)(0202101tteqdiCtutu0)(1)()(0u1uC2C1u2+- - -i- -+unCn- -nkkeqCC111)()()()(002010tutututunnkkeqCCCCC1111121iu+-CeqtteqdiCtutu0)(1

11、)()(0)()()()( :KVL21tutututunu1uC2C1u2+- - -i- -+unCn- -)()()()(002010tutututun 2121CCCCCeq21111CCCeq一、电容元件的串联一、电容元件的串联)()()( :02010tututu等效电容的初始电压等效电容的初始电压u1uC2C1u2+- - -i- -iu+-CeqtiCtud)(1)(11tiCtud)(1)(22uCCCuCCueq21211uCCCuCCueq21122 2121CCCCCeq diCtututtkkk0 1)()(0 diCututkkk 1)()(teqituCd)()(

12、 diCtutkk 1)(tteqidCtutu01)()(0u1uC2C1u2+- - -i- -teqdiCtu)(1)(niiii21ttuCtikkd)(d)(i2i1u+ +- -C1C2iinCndtduCdtduCdtduCn21dtduCdtduCCCeqn)(21 21neqCCCC)()()()(002010tutututundttduCtieq)()(iu+-Ceqi2i1u+ +- -C1C2i)()(2111tiCCCti)()(2122tiCCCti21 CCCeq二、电容元件的并联二、电容元件的并联21)()(d)(dCCtiCtittueqdttduCtieq)

13、()(ttuCtid)(d)(22ttuCtid)(d)(11neqLLLL21 iu+ +- -LeqdtdiLdtdiLdtdiLn21 )()()()( 002010titititinttiLtukk d)(d)(u1uL2L1u2+ + + +- - -Lnun+ +- - -nuuuu21dtdiLdtdiLLLeq)(n21dttdiLtueq)()( ttiLtud)(d)(11ttiLtud)(d)(2221 LLLequLLLu2111uLLLu2122dttdiLtueq)()( dttdiLtueq)()( u1uL2L1u2+ + + +- - -i- -ttnnttttudLtiudLtiudLti0001)(1)(1)(0202101)()()()(21titititinduLtitittkkk0)(1)()(0ttnnudLLLtititi0)111()()()(2100201duLtititteq0)(1)()(0u+ +L1L2i2i1LninikkeqLL11)()()()(002010titititinttequdLti01)(0neqLLLL111121)()()()(002010titititiniu+ +- -LeqduLtititteq0)(1)()(0 )(