8电力系统稳定分析

PowerSystemStabilityAnalysis201234561•••f(x)f(x0)+f'(x0)(x-x0)2•••••I&ifEqEq0⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧+=+=--=-=-=′ΣIjXUIjXUEPPPdtdTdtdEETdtEdqqtqDemJqqedq&&&&&wwwd00)1()(1dLTqdXXXXX++==ΣΣPm=P0PD=0dsinΣ=dqEXUEPqifEq=Xadif=const.⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧=°∠=+=-=-=-=ΣΣconst.,00.1sin)1(00qdqdqEmJEUIjXUEXUEPPPdtdTdtdq&&&&dwwwdj⎪⎪⎩⎪⎪⎨⎧==00dtddtdwd⎪⎩⎪⎨⎧==Σ0sin1PXUEdqdw⎪⎩⎪⎨⎧==⎪⎩⎪⎨⎧==Σ-Σ-UEXPbUEXPaqdbbqdaa0101sin1)(,sin1)(pdwdwdDddDddDd°\madqEPPXUEPq=Δ+=Σ0)sin(dd0dtdTJwwwdwa1,0=wwdtdda0,0dtdPPqEwa''w10,0dtdPPqEwwa'...ww1w1ddaada+Dd90°⎪⎪⎩⎪⎪⎨⎧Δ+=Σ0)sin(0dtdPXUEPadqEqwdda1,0=wwdtdd0,0dtdPPqEwa'1,0=wwdtda''...(Dd0)da+Dda''w=1dw1dw1bdbb(Dd0)db+Ddb'db+Dd90°0)sin(PXUEPbdqEqΔ+=Σdd10=wwdtdwbbdw1dbbdb+Dd(Dd0)b''db+Dd90°0)sin(PXUEPbdqEqΔ+=Σdd10=wwdtdwbabdw1ab:Dd0PEDPE0dDd0PEDPE0dDd0PEDPE0dDd0PEDPE0dDPE=PE-P00ΔΔdEP0ΔΔdEP)()()(20dddddddddΔ+Δ⋅=-=-=Δ=OddPorPPPPPbaqqqqorEbaEEEE0→ΔdddddPPqEE→ΔΔdddPSqqEE=dcosΣ=dqEXUESq0,90=°=qESdPmax%10000max×-=PPPKpKpP0PmaxKPEqUXdSP0⎪⎩⎪⎨⎧==Σ-UEXPaqdaa01sin1)(dw⎪⎪⎩⎪⎪⎨⎧Δ+-=Δ+-Δ+=Δ+Σ)sin()()1()(00ddwwwwwddadqajaaXUEPdtdTdtd⎪⎪⎩⎪⎪⎨⎧Δ⋅-≈Δ+-=ΔΔ=ΔΣΣddddwwwdadqadqjXUEXUEPdtdTdtdcos)sin(00⎪⎪⎩⎪⎪⎨⎧Δ⋅-=ΔΔ⋅=ΔddwwwdjaETSdtddtdq)(0⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=0)(00jaETSAqdw0)(aEqSd0)(02=+jaETSqwdljaEjaETSjTSjqq0201)(,)(wdlwdl-==0)(aEqSd⎪⎩⎪⎨⎧-==Σ-UEXPbqdbb01sin1)(pdw⎪⎪⎩⎪⎪⎨⎧Δ⋅-=ΔΔ=ΔΣddwwwdbdqjXUEdtdTdtdcos00)(bEqSd0)(02=+jbETSqwdljbEjbETSTSqq0201)(,0)(wdlwdl--=-=0)(bEqSdl3••••w»w⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧+=+=--=-=-=′ΣIjXUIjXUEPPPdtdTdtdEETdtEdqqtqDemJqqedq&&&&&wwwd00)1()(1)()(qdLTqdXXXXXX++=ΣΣPe»0E¢dsinΣ′′=deXUEP⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧′′=′+=′+=′--=-=ΣΣdwwwdsin)1(0deddtDemJXUEPIXjUIXjUEPPPdtdTdtd&&&&&dLTdXXXX′++=′Σ4•••••212TLTdIXXXXX+++′=ddsinsinIMIIPXUEP=′=XDE′&ddsinsinIIMIIIIPXUEP=′=XDE′&21TLTdIIIXXXXX+++′=ddsinsinIIIMIIIIIIPXUEP=′=⎪⎪⎩⎪⎪⎨⎧-=-=)(1)1(0ImJPPTdtddtdwwwd1))(,)(())(,)((effffcfXttttttt==≤--++wdwd⎪⎪⎩⎪⎪⎨⎧-=-=)(1)1(0IImJPPTdtddtdwwwd⎪⎪⎩⎪⎪⎨⎧-=-=)(1)1(0IIImJPPTdtddtdwwwd1))(,)(())(,)((Xttttttccccc==--++wdwd2eX10)1,())0(),0((0efXtt==≤≤dwd1eX2ex1exctxda=d0w=1Pm=P00,0==dtddtdwdPm=P0baPIPIId0bw=1Pm=P0DP=P0PII0bacbdcdPIIctcdcw1w­cedcw1PIIdcPIIIDP=P0PIII0w¯w1dPIIIfbacdcedfef(d=dfw=1)w1fd=dfw=1DP=P0PIII0w¯w1dPIII…kkbacdcedfididfkdcdfdhdddddd®dDP=P0PII∫-==cdPPSSIIabcdddd0)(0dcdidfd0d®dDP=P0PIII∫-==fcdPPSSIIIedgfddd)(0bfSS=∫∫-≤-hccdPPdPPIIIIIdddddd)()(000∫-=hcdPPSIIIddd)(0maxdddddcdcrtcr∫∫-=-hcrcrdPPdPPIIIIIdddddd)()(000∫∫-=-hcrcrdPPdPPIIIMIIMdddddddd)sin()sin(000)()cos(cos)cos(cos)(0000hcrhcrIIIMcrIIMcrPPPPdddddddd-⋅+-⋅=-⋅+-⋅dcrIIMIIIMIIMhIIIMhcrPPPPP--+-=-0001coscos)(cosdddddIIMIIIMIIMhIIIMhcrPPPPP--+-=000coscos)(cosdddddIIIMhhhIIIMPPPP010sin)2(0sin--=⇒=-pdpdddcrtcr1,,0)(1)1(000===⎪⎪⎩⎪⎪⎨⎧-=-=wddwwwdtPPTdtddtdIIj⎪⎪⎩⎪⎪⎨⎧===-=-=0,,0)sin()(0000022dtdtPPTPPTtddIIMjIIjddddwwdd(t)w(t)dcrtcrSSbacdcedfididfgd0dc¯Pe­P0¯20.76.2555.13.058.062.0=°∠=′=′==JdqdTEXXX&1.0=TX5.1=LX5.1=LX°∠=00.1U&11Eq0.76.2555.144.03.02=°∠=′==′JdTEXX&1.01=TX1.02=TX35.11=LX35.11=LX104LLXX=104LLXX=‘°∠=00.1U&