電網(wǎng)絡(luò)課件-信號流圖

1、信號流圖概念：源點(diǎn)匯點(diǎn)X2X1X3a12a22a13a31a11a3333122213133132121111XaXaXaXXaXaXaXeg:信號流圖的變換x1x2a1+a2+.+anx1x2a1a2anx1x3ax2bx1x2ab串聯(lián)x1x2abbcx4x1x3ax2bcx4x1x3ax2bcx4abx1x2acx4bx1x2aa+bx1x2x1x2ax3bx4cdx1x2ax3bx4cd/bx1x2ax3bx4cd/c并聯(lián)支路移動節(jié)點(diǎn)吸收x1x2ax3bcx1x3abbcx1x2ax3bdcx1x3abbcadcdx1x2x3abcx3x1ab1-cx1xpy2m1px2xmy1ynm2

2、mmn1n2nny2y1ynx1xpm1x2xmm2mmn1n2nn1-p1-p1-p1-p1-p1-peg:x3a1x1x5x2x4a2a4a7a3a6a5消x3消x4節(jié)點(diǎn)移動x1x4a3x2x5a1a2a4a7a6a1a5a1a5 +a4x5a1a2a3a6a3+a7x2x1a1a5 +a4x5a1a2a3a7a6a3x2x1H= a1a2a3 +(a4+ a1a5 )(a6a3+a7)x1x2x3x4x5x6H1H2-G2-G1-G3求增益x6/ x121212132211211HHGGHHGHGHGHHH求增益u/ x2ux1x3x2難Mason公式kkPT各支路增益之積條前向通道增益

3、第kPk:3211lll回路增益二重互不接觸回路增益三重互不接觸回路增益益條前向通道去掉后的增即將第條前向通道的余子式第kkk,:x1x2x3x4x5x6H1H2-G2-G1-G3求增益x6/ x121212132211211HHGGHHGHGHGHHH求增益x6/ x1x1x2x3x4x5x6H1H2-G2-G1-G3求增益x6/ x1bdgfhbfhdgdgabhabcdeH1)1 (x1x2x3x4x5x6bd-g-fhace電網(wǎng)絡(luò)與信號流圖eg:畫出下圖的信號流圖對網(wǎng)絡(luò)有：)(00000)()()()()()(00000000000000000000000000)()()()()()(

4、13322113332222111332211sUsCsUsIsUsIsUsIRsCsCRRsCsCRRsCsUsIsUsIsUsIS)(00000)()()()()()(00000000000000000000000000)()()()()()(13322113332222111332211sUsCsUsIsUsIsUsIRsCsCRRsCsCRRsCsUsIsUsIsUsIS1sC1sC2sC3sC2sC3sC1R1R2R2R3RSU1I2I3I3U2U1U0UI00RUIIUUUU000sCRsCR1100010000R1GR10001R1R1sCsC0100sCsL1sCsCsC000

5、0sCsCR1s7s11s187n4n3n2n12v2v2222222211111同一網(wǎng)絡(luò)，變量選擇不同，則信號流圖不同。為了能快速選擇一組獨(dú)立而充分的流圖變量：1 選樹支電壓和連支電流為變量：電壓源支路樹支，電流源支路連支受控電壓源支路樹支，受控電流源支路連支受控源的控制支路： 壓控樹支，流控連支2 寫樹支電壓和連支電流的表達(dá)式（方程）：樹支電壓=f(連支電流),連支電流=g(樹支電壓)3以電源為起點(diǎn)，畫信號流圖eg:畫信號流圖)()(17sUsUs)(11)(123333IIsCIsCsU)()(5214444IIIRIRsU26)(rIsU樹支電壓連支電流6437111111)(UUUU

6、sLUsLsI643221)(UUURsI35)(gUsIoates流圖Mason公式反映了系統(tǒng)的因果關(guān)系，特別使用于控制系統(tǒng)，但是，對于電網(wǎng)絡(luò)中，網(wǎng)絡(luò)的方程為u，不很方便。oates流圖設(shè)方程為u，定義其對應(yīng)的有向圖為：u是輸入節(jié)點(diǎn)，Xnxxx,21是非輸入節(jié)點(diǎn)：0ija當(dāng)時，從ijijaxx 有一條支路，增益為到當(dāng)0ib時，從iibxu有一條支路，增益為到ux1x4x3-46x28-42106531-2-2-18eg:eg:SUsCsCUUUGGsCsCsCGsCsCsCGsCsCG01102132122221211111123SUsCsCUUUGGsCsCsCGsCsCsCGsCsCG0

7、1102132122221211111uSu1u2u311sC11sC1sC2sC2sCg11sCG 212sCsCG23sCgG1sC3310RUIss32154377577266566511111111111nnnUUUsLGRsCsCsLsCsCsLRRsLRRsLGeg:畫出其Coates流圖Coates流圖增益公式電網(wǎng)絡(luò)在復(fù)頻域中的方程為u，設(shè)AdetjnjjkkjnjjkkbuXubX111 1即為了能直接從電網(wǎng)絡(luò)中求增益，先介紹下面的概念1 冷圖（Gc)：cold graph從Coates流圖中去掉源節(jié)點(diǎn)及其所有流出支路后，得到的圖。從Coates流圖中去掉源節(jié)點(diǎn)及其所有流出支路

8、后，得到的圖。2 1-因子：符合下列條件的冷圖的子圖叫1-因子：包含Gc的所有節(jié)點(diǎn)每個節(jié)點(diǎn)僅含一條入支路，一條出支路。3 1-因子增益：1-因子中各回路的增益之積。冷圖為uSu1u2u311sC11sC1sC2sC2sCg11sCG 212sCsCG23sCgG1sCu1u2u31sC2sC2sCg11sCG 212sCsCG23sCgG1sC1-因子：u111sCG u2212sCsCGu323sCgGu2u32sC2sCu111sCG u1u2u31sC2sCgu1u21sC212sCsCGu323sCgG1sC單連接：若節(jié)點(diǎn)p和q滿足：p節(jié)點(diǎn)只有一條出支路，q節(jié)點(diǎn)只有一條入支路，其余節(jié)點(diǎn)

9、有且只有一條出支路和一條入支路，則p和q支路稱為單連接。單連接增益：單連接各支路的增益之積。eg：us到u3的單連接：uSu1u2u311sC1sC2sCuSu1u2u311sC2sC11sCG pbuXjnjjkk11單連接單連接的有向回路數(shù)因子因子回路數(shù)allnallnpA1111det11的單連接增益因子增益kxu 180046620210130280450104221xxxxeg:求X2ux1x4x3-46x28-42106531-2-2-18x1x4x3x2-42106531-2-2-18冷圖1-因子：因子：x1x4x3x26538x1x4x3x2-42-2-1x1x4x3x2101-288x1x4x3x2-43-2x1x4x3x225-18x1x4x3x2106-2-18)2(43126) 1()2(610131) 1()2(81013390461