21
.. ... mmmmm mmmm mmmmmmmf ff ffffff ffff ffffffffffffff ff fffff fffffff fff ffffffffff ff fff ffffff fff ffffffffff f ffffff ffffff fff ffffffffffff fffff fff ffffffffff f ffffffff fffff ffff f ffffff ffff ffffff ff fffffffffff ff fffff ffffff ff fffff fff ffffffffff fff ffffffffff f fffff ffffff ff fff fffffffffffffff ffffff ffff ff fffff f ffffffff fffff mm. .. mmmmm mm mm mm mmmmmmmf nffff ffffffffffff fff nff ffffffffff ff ffffffffffff ffffff fff ffffffffnf fff ffffff ff ffffffffff fffffff ff fffffffffff fff ffffff fff fffffnffff nffffff ffffffffffff fnffff fffff ff fnffffff fnfffffff ff fff fnffffffff )mmmm mmmmmmm ))f fff fffff ff fnffffffff fffff fnffffff ff fff ffff ff fffnffff ff fffffff fff ffffnffff fffffnfffff fff ffffff fff fff ffnf ff fnffffff nfffff ffffffffffff fff ffffffff ff fffff ff fnffff ffffnffff fffffnfffff ff fffffffff ffffff mmmmm mmmmmmm ))f fff fffff ff fnffffffff fffffff ff ffff fffffff fff ffffnffff fffffnfffff fff ffffff fff fff ffnf ff fffffff nffffffff ffffffffffff fff ffffffff ff fffff ff fnffff ffffnffff fffffnfffff ff fffffffff ffffff fffff ffffffffffff fff fff fff ffffff fffffnfffff fnfffff fff ffffnffffff ff ffff fffffff ff ffffff f nf ff ffffffff ff f fffff ffff ff fff ffff ffffff ff ffff fff ffffffff ffffff ffff f mm)m mmmmm )) fffnff ffffff fff nff fff fffffff ff fffffff f ffffnff nfff ffffff ff ffff ff fffffff ffnff f fffffffff ffffffff fffff ff f fffff fff fffffffff nff fff fff ffffnff ffffff fffffff ffffnff ffffff ffnnf ffffnff fffff ff ffffnff fffff

Elements of Power System Notes

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Page 1: Elements of Power System Notes

.. ... mmmmm mmmm mmmmmmmf ff ffffff ffff ffffffffffffff ff fffff fffffff fff ffffffffff ff

fff ffffff fff ffffffffff f ffff ff fff fff fff ffffffffffff fffff fff ffffffffff f ffffffff fffff� ��ffff f ffffff ffff ffffff ff fffffffffff ff fffff ffffff ff fffff fff ffffffffff fff ffffffffff f fffff fff fff ff fff fffffffffffffff ffffff ffff ff fffff f ffffffff fffff��

mm. .. mmmmm mm mm

mm mmm mmmm f nffff ffffffffffff fff nff ffffffffff ff ffffffffffff ffffff fff ffffffff nf fff ffffff ff ffffffffff fffffff ff ffffffff fff fff ffffff fff fffff nffff n ffffff ffffffffffff fnffff fffff ff fn ffffff f nfffffff ff fff fn ffffffff

)mmmm mmm mmmm ) )f fff fffff ff fn ffffffff fffff fnffffff ff fff ff ff ff fffnfff f ff fffffff fff ffffnffff fffffnfffff fff ffffff fff fff ffnf ff fnffffff nfffff ffffffffffff fff ffffffff ff fffff ff fnffff ffffnffff fffffnfffff ff ffffffff f ffffff

mm mmm mmm mmmm ) )f fff fffff ff fn ffffffff fffffff ff ffff fffffff fff ffffnffff fffffnfffff fff ffffff fff fff ffnf ff fffffff nffffffff ffffffffffff fff ffffffff ff fffff ff fnffff ffffnffff fffffnfffff ff ffffffff f ffffff fffff ffffffffffff ff f fff fff ffffff fffffnfffff fnfff ff fff ffffnffffff ff ffff fffffff ff f fffff f nf ff ffffffff ff f fffff ffff ff fff ffff ffffff ff ffff fff fffff fff ffffff ffff f

mm )m mmm mm ) ) fffnff fff fff fff nff fff fffffff ff fffffff f ffffnff nf ff ffffff ff ffff ff f ffffff ffnfff fff ffffff ffffffff fffff ff f fffff fff fffffffff nff fff fff ffffnff fff fff fff ffff ffffnff fff fff ffnnf ffffnff fff ff ff ffffnff fff ff

Page 2: Elements of Power System Notes

s mm m m s mm mmm m sm f fffffffff fff fffffff ff fn ffffffff ff fffffff f ffff ff fff ffffff fff fffffff fffffffffff ffffffff ffffffff fff fffffff ffff nf ff ff fff fff fffff ffff fff fff f f ff ffff ff f ff f fff ffffnff fff ff

) mm efff fnf ff ff fffff fffffffff ff fff ffff ffffff ff fff fff f ff f ffffffff fffffffffffff nf fff fff nff nf fff fff fff nfffff ff f ff ffffff ff ffnfffnff ffff fff fff ffff ffff ff ffff fnfffff ffffffff ffffffff ffffffff fffff ff nf ff ffffffffffff fff ffffff nf ff fffffffffffff ffffff nf ff ffff fffffffffffffffff fn ff nf ff fffffffffffff ffffffffff f fn ff nf ff ffffffffffff fn ff ffff ff fn ffffff nf ff ffffffffffff fff ff ff f ffff ffffff fff ff fffffff ff ffff nf ff ffffff

.... mm mmm mms mmm mm m m m mmm fff ffffffffffff ff ffffffff fffff ff ffffff ff ffff fffffff nf ff fff fffffffff ffffffff

m ) m m)mm m ) m mm mmmmm. ffff ff fff ffffffffffff ff ffffffff fffff f

f fffff fffff ffff

Page 3: Elements of Power System Notes

sm mmm m mmm mm m m m mmm f

f Jf r ff l fff ffffffffff ffffffffff ffffffffffff ffffffffff fffffffff ffff fff ffff ffffff ff ffffffff mm mmm m mm mm mmm mmmm mm pf

Page 4: Elements of Power System Notes

f Jf r ff l fff ffffffffff ffffffffff ffffffffff ffff fff ffffffff ffff fff ffffffffffff ffffff fffffffff mmmm m m m smms mmm mm m m m mmm. fff fff f f f fffnffffff ff fffff ffffff f fff ff ff nff fff fffffff fffff ff ffffff fff ffffffffffff ff fffff ff f f ff ff f fff nffff ffffffff fff fff ff fnff f fffff f ffff ffff ffffffffffff ffffff fffnfff ff

fff ffffffff ffff ff fffnffffff fff fff nfffff fff ffffffff ffff ff fffffffffffff ffffffffff ff fffff ffffffff fffffffnf

ffffffffff fffff ff f fffff ff fff ffffff ffffffffffff ffffff fffff fff f ffffffffffff fffffff ff f ffffffnfff ffff ffff fffff ff ffffff ffff fff ff fff ff ffff ff fff nffff ffffffff nf ff ffffff ffffff ff ffffff f fff ffffffff ffff ff fffnfffffff ffffffffffff ffffffffff fff fffff fff ffffff ff ffffff ffffffffffff ffffff ff fffffffffff f nffffff ff fffffffff

. s N s s f ff fff fffff f fff ffffff fnf ffff fff ffffffffffff ff ffffffff ffffff ffffff ffff f f ffffff ff nff fffffff f ffff fff fff fffff fffffff fff ffff f nff fff ffffffffffff nf ff fffffff ffffnffffffff fff ffffffff fffff ff fffffff ff ffffffffffff ffff

ffffff

i fff ffff ii fff ffff ffff ff fffff ffffff iii fffff ffff

. fffff fffff ffffff i fffff fffff fff ffff ii fffff fffff fff ffff ffff ff fffff ffffff iii fffff fffff fffff ffff

fff fffff ffffff i fff fffff ffnf ffff ii fff fffff fffff ffff

fffff fffff ffffff i fffff fffff fffff ffff ii fffff fffff ffnf ffff

fff fff f f f fffff ff fffffff ff fffff fffffffffffff ff ff fffffnff ff fff fffff fff fff ffffff ff nfffff ff nffff ffff fffff ff ffffffffff ff f ffff fff fff ffff ff fff nffff ffffffff ff fff ff fff ffff fffffffff fffffff ff f ffffff ffnffff fff fff ffffff fff ffffffffffff ff fffff ff ffff fff fffff fff ffnff ff fff nffff ffffffff ff nfff ff fffffnf ffffffffff fff ffnff ff fff nffff ffffffff ff nfff fffff fff ffff ff ffffffffff ffffff ffffffff fffffff

Page 5: Elements of Power System Notes

.. mpmmm m m ) m m mmmmm mm mmm ) mmsmm mm

ff fffffffff fff ffffff f fffnfff ff fff nffff ffffffff fffffffff fff ffffffff fffffff ff fffffffffffff fffffff fff ffffff ffff f fffnff ff ffff ffff ziz

f ffff fffff n fffff ffffffffff f ffff ffffff ff fff fffffff f ffffff f ff fffff fffff ff ffffffffff fffffff fff ffff fff fff ffff ffffff e fffff fff fff ffff ff ffff ffff f fff ff ffnf ffffff ffffff fff fff nffff ff fffff f ff fff ffff ff ffff ffff

mmm . . mm m s mm m ) m mmm sm

ff fff . ffff f fffffff fff ff fff fnffffff ff ffffff f ffff ff fff fffff ff fff fffnff ff ffffff f ffff ff fffff ff ff fff fff ff ffffffff ffffff fff fff fffff f ffffff ffffff fff nfffff

Vm nffff ff f ffffffffff ff ff f nfnff ffffffff ff ff f ffff ffffff ff fff ffff fff ffffffffff ffff fffff fffffff ffffffffff ffnff ff fff nffff ffffffff ff nfff ff ffff ffffff fffff f ff ff ff fff ffff nffffff iee

Page 6: Elements of Power System Notes

. mmm . . mm m s mm p mm mmm sm .

ff . . fffff fff fff ffff f ffffff ffff ff fffff ffffff fff ff ffnf ffffff ffffff fff fff nffff ff fffff ff Vm ff ffff ff ffnf ffffff ffffff fff nfffff ff .Vm

ff . .

e e e z l me m e i l e i e i i em i e e i e i

i e e e em i e e e e

Page 7: Elements of Power System Notes

.. smmm mmm . . mm.

ff f ffff f fffffff fffff fff fff fnffff ff f ff ff ff ffnffff ffff fffff ff ffffff ff fff fffffffff ff ff fffff ff ff ff fff fff ff ffffff f fff fnfffff ff fff ffnffff ffff ff fff ffnffff ffffff fff ff

mm. ..

ff fnffffff I .Vm

ff f fff ffff ff fffffff ff ffff fnfff ffff

e e e z l me m e i l e i e i i em i i e i e

i e e e em i e e e e

.. mmmmm psm m mmm m. . mm m s mm m ) m mmm sm .

ff . fffff f ffffff fffff . ffff f f ffffff ffff fff fff nffff ffffff fff ff ffnf ffffff ffffff fff nfffff ff Vm ff ffff f f f ffnf ff ffffff ffffff ffff ff Vm .� ffnffff fff fff fffff ffffff ff f fff �f

Page 8: Elements of Power System Notes

mm. ..

ff f fff ffff ff fffffff ff fff fff nffff

e e e z l me m e i l e i e i i em i � ime i e

e e em i e e e e e

.. mmmmm psm m mmm mm m s mm p mm mmm sm

ff . fffff f ffffff fffff f f ffffff ffff ff fffff ffffff fff fff fffff fffffff f nff ff ffffffff fffffff ff fffff ieee Vm ffffffffff fff ff ffnf ffffff ffffff

fff fff fffff ff .Vm fff f f f ffnf ff ffffff ffffff fff nfffff ff .Vm ffnffff fff fffff ffffff ff fff fff ff f fff �f�

Page 9: Elements of Power System Notes

ff .

e e e z l me m e i l e i e i i em i � ime i e

e e em i e e e e

.. mmmmm sm m . mmm mm fff ffffff fffff ffff ffffff ff f fffffff ff fffffffff ffff ffff f ffffff fff ffffff ffffffff ff fff fnffff ff ffnffff ffff ff ff ffff fff ff fffff ff fff fffff fff fff ff fffff ff ff ff fff fff ff ffffff f fff fnfffff ffffnff fff ffnffff ffff ff fff ffnffff ffffff fff f

Page 10: Elements of Power System Notes

mm. ..

f ffffff ffffff fff nfffff . Vm ffnf ff ffffff ffffff fff nfffff .Vm

ff fff f�f ff fff fff ff fff �f fffff ffnffff fff ffff ff fffffff ff ffnffff ffff ff f ffff ffff ff fff fnfff fffff ffnff ff fff nffff ffffffff ff nfff

e e e z l me m e i l e i e i i em i s � ime

e i e i i e e e em i e e e e

Page 11: Elements of Power System Notes

.. sm m )m mmm m. . mm f fffff ff ff . f fff ffnf fffff fff ff ff ffff fff ff f ff fff fff fffff fff ffff ff fff ff ffffff ff fff fff fff ffff fff ffffffff ffffffff ffff ffffff fff f fffff fff ff fff ff ffff fff ffffff fffff ffffffff ffff ffffffffffff fff ffff ff fff fffff fffff

mm. ..

f ffffff ffffff fnffff A ff B .Vm ffnf ff ffffff .Vm nffff fnfffff fff fffff iee f f fnffff A ff B . ffnffff f�f� ff fff fff ff f fff �f

ff f fff ffff ff fffffff ff fff fff nffff

Page 12: Elements of Power System Notes

e e e z l me m e i l e i e i em i � ime

i e e e em i e e e e

.. psm m . mmm mm. ff . fffff fff ffffff ffff f f ffffff fff ffff ff ffnffff ffff ff ff ff ffff fff nffffff ff fff fffff fff ffff fffff fffffff fff ff nf fffnff ffff ffff fffff ffnffff ffff fffff fffffffff fff ffff ff fff fffff fffff

fff ffffff ffffff fnffffff fff nffff ff ffnffff

mm. ..

ffnffff fff fnfffff ffffff ff f fffffffff fff ffff ff fffffff ff fff ffnffff ffff ffff f . fffff ffff ff ffffff ff fff fnffff

e e e z l me m e i l e i e i em i ss s � ime

i e e e em i e e e e

Page 13: Elements of Power System Notes

.. . sm m . mmm mm ffff ffffff ff ffffff nff fffffff f ffff fff ffffffffffff ff ffffffff fffff fff ffffff ffff ffffff fff f ffff ffffffff ff ffff ffffffff ff . fffff ffffff ffff ffff ffffffff ffffff fff ffnffff fffff ff ffffff

ff .

e e e z l me m e i l e i e i em i ss � ime

e i e i e e e em i e e e e

... . psm m . mmm mm ff ffff fffff ff ff ffnffff ffff ff ff ff ffff fff ffnffff fffff ff fffff ff ff . fff ffff ff fffffff ff fff ffnffff ffff ff fffffffff fff ffff ffff ff fff ffff fff nffff ff fff fff f fff ffffff f ffff fnfffff ffffnff fff ffnffff ffff ff fff ffnffff ffffff fff f ff f�f� ff fff fff ff fff �f

Page 14: Elements of Power System Notes

ff .

e e e z l me m e i l e i e i em i s � ime

e i e i e e e em i e e e e

.. s s ms

... m ) m

mm mm ) m m ) m mm mmmmm

fff ffff ffffffff nff fff nffff fffffffff fff f ff fff fffff fff fffffff ffnffffnff fffff ffff ffnffffnff fff fffff fffff ff ff ffnf ffffff fff ffffff ff f ffffffnfff ffffffff ffff ffff nfff fff fffff fff ff nfff ffffffffff ff ffffffffff ffffffffff ff fff fffff fff ffffff ff fff nfffff nff fff f fffff fffff fff fffffff ff fffff f ff ff ff ff ffffffff fff fff f fffff

Page 15: Elements of Power System Notes

ff fffff f fff nffffff fffff ff fffffffff fff fffffff ffff ff ffnf fffff fnffffff f ffffff ff fffff ffffffffff f .f f . fffff ffnff ff fffff fff fffffff fff fffff fnf ff ff ff f f nff fffff ff ff fff fffnffffnff ff fffff f fff nffffff fff ffffffnff f ffffff ff fffff fff ffffff ff ffffffff ff ffffffff fffffffff ff ffff ffffff fff fnf ffffffff .. pm m ) m

.. ppmm. fffff ff ff f fff ffffffff fff f fffff fffff fffff ff fff ffff ffffffffff fff nfff fff ff fffffff fffffff ffffffff ff ff ffffff nff ff fff fff ffff ffff ff fffff f fff nffff ffffnff fff ffffff ffffffff fff ffffffffff fff nfff fff ffffffff fff ff fffffffff fff fffffff ffffffff fffff fff ff

fffff fff ffff fnfffff ffffff iee f fff fnfffff ffffffff ffffffff ff ffffff fff nfff ff fffffffff ffff ff nfff fffff ffff fff f ff fff f fffffff fffffff fffffff fffffffff ffff ff fff nffff ff ff nfff ff fffff fff fff ffff ffffff f fff fff nffff ff fff fff f ff ff nff ffff fff ffff fffff ff nfff fffffffffnff nff ff ff fff ffff fffff ffnf fffff ff fff ff fff fn f ffff ffffff ff ff f fff ffffffff fff ffffffffffff ff fffff nffff ff ffffffff fffff fff fff nf ff fff ffffff ffff ff fff f ffff ffffff ff ff ffffff nff fff fffff fnffffff ff f fff fff ffff ff ff nff ffnffffnf ff fffff ff ffffff

. m)mmmm)m. fnffffnf ff fffff ff fffff ff fffffff ff ffffff nf ff fff fnff fffffff

fff nfff fff ff fffffff ffffffff fff ffffff f ffffffffff ff fff fff fffffffff ff fffff fffff ) ) fff fff nfff fff ff ffnffffnf ff m ffff ff ffffff fff fffffff fff nfff fff ff ffnffffnf

fffff ffff fff fff ffffffnfff ffffffffffff fffffffffff fff fffffffff ffff ff fff nffff fnff f ffffff ff ffnffffnf ffff ff ffffff ff fff ffff fffffffffff fff fffffff ff ffnffffnf fff nffff ff f fnf . fffff fff fffffff ff ffffff fff nffff fff ffffffff fffffff ff ffnffffnf f fffff f fffffff fnfffff ff fff fffffnff ff f ffffffffff fnffffffff ffffff fnff f ffffff fff fffffff fffff ffff ffffffff ffff fffff ff nffff fff nff ff ffffff ffffff ffff fffff nffff ff fffffff fff ) ) fff ffffffff fff fff ff ffnffffnf . ff ff ff fffff ffff ffff ff ffffff ff ff ffffffffff ff ffnffffnf fff nffff fff ffffff fff ffff fff ffffff ff f nf fffff ffffff fff nffff ff ffff fffffff fff fnffffffff fffnffnfff fff ffnffffnf fff fff f ff f ff ffffff ff ffff ff ffffff fff nffff ) ) fnffffnf fff nffff ffff ffffff ff fff ff ff fffffff ffffff ff fffff ffffff fffff ffff fff ff nfff ) v) nf ff fffff fffffff ffffffff ff ffffff ff fffffffff ff ffffff f fffffff ff ffnffffnff fff fff ff fffffff ff ffnffffnf fff nfffff ffff fffff fff fff fff ffffffffff ff fffff fff nfff ffff fffffff fffffffff ffffff fff f ffnffffnf fff ff f ff f ff ffffff ffffffffff ff ff ffff ff fff nff ff f fff nffff ffffffff ff ff ffffffnfffff fffffff ff ff nff ffnffffnf fff fff f fnfffff ffffffffffff fffff fff fff nffff ff f ff fffff ff fff ffff fffff f ff ff ffffffffff ff fff fffff ffff ff ffffffff ffffffffffff

Page 16: Elements of Power System Notes

.. mmm mm mm)mmmm)m. nf ff fff fffffff fffffffff ffnffffnf fff nfffff fff nff fffffff fff ffff fffff fff fffff nff fff ffffff fffff ff ff ff ffff nffnfff ff fff ffff fffffff ffffffffffff ff ff ff ff ffffffff fff fffffff fffffffff fff ffnffffnf fff nffff ff fffffffff ffff f ffff ff fff fffff fffff fffff fff fffffffff fff nffffffnf f fffff ff ffff ff eel e l mi i m ff ff f ff ffff ff ffnffffnf fff nffff fffff fffffffff ffff ffff ffnffffnf fff nffff ffffffff ff fffffff ffff ff fff fff f fffff fffff fnfffnf f f f fnf ff ff ffnffffnf fffff f fnfffff fffffff ff fff fffff ff ffnffffnf fffff ff fff ffff fff fffffff ff fff fff ffffff fff fffffffff ff fff fffff ff f nf fff f ff ffff ff f ff ff ff ff fff ffff fffffff ffffffff fff fff fff nffff ff fffff fffff ffff ffnffffnf fff nffff ff fff fff fffff ffff fnfffnf f f ff fffff ff ffnffffnf fff fffnff ff ffff fffffffff fff nffff ff ffff fffff ffff ff ff fffffff ffffffffff ff ffffffffff ffffffff fffff ffnffffnf fffff f fffff fff nf ff fnfffff fff fffff ffff ffnffffnf fff nfffff ff f fff fffffffff m mm mmm

) ) fff fffffffffffff ffff fffff fffffffff fff fffffff ffffffff nf ff fff ffff ffff ffff fff fffffffff fff nffff fffff ffffffffff fffff ffff ffnffffnf fff nfffff ffff fff nff fffffff fff ff fffff ffffff fffff fff f nff ) ) nf ff fffffff fff ffff fffff ffff ffnffffnf fff nffffff ffffff ff fffffff fffffff fff f

nff

mm mmm m mmm. ffff fff fff ffff fffffff ffffffff ffffffffff fff fffff fffff fff nfffff fff f nff fff f fffffff ffff fffff ff fff fffff ffff ffffffff f ffff ff f ffffffff ffff ffffffff nf ff ffffffff fff ffffff ffff ff f fff ffnf fff fnfff ff ff fnfff fffff fffff fffffffff ff fff ffff fffff fffffff nf ff ffff fff nfff fff ff ffff ffffffffff ff ffffff fnff fff nfffff fff fff fnfff ff fff ffffffffffff fffff fffff f ff f ffff fffffff fff fff ffff fff f nff ff f ffffff fff ffffffffffff f fffff fffff f ff f fffff fffffff fffff fff ff f ff fff ffffff fff nffff fffff ff ffff ffffffff fffff ffffffff ffnf f fff fffff ff ffnf nffnfff ff fff nff fffnff ff ffff ffffffffff ffffffff

.. m mm)m ppmm. fff fff nffff ffffffff fff ffff fffffff ff fffffff fffff ff ffffff ffffff ffff ff ffnf f f fffff ff m ff .m ff ffnf ff ffffff fffffffff fff fffffff ffffffff f f fnf m ff fff fff nfff fff ff ffff ff nff f m ffff ffff ff fnff ffffff ffffffffff ff ffnf ffffff fff nffff fff f nfffnf fff f fffffffffff ffff fffff fff fff nf

Page 17: Elements of Power System Notes

ff ffff ffff ff ff ffnff fnff fff nfffff ffff f ffffffffff ffff fff fffff ff fffff fffffff iee f fffff fff ffff ff ffffffffff fffffffff fff ffffffffffffff ffffff fffffffff fffff ffff fffff ff

ffffffff.f

... mm m

fff fffffffff fffffff nf ff nff nff fffff nffff ff ffffffff fnfffff f ff fff ffffff fffff fffffff ff fff fff nffff ffff nff fff ffff fffffff fffff ffffffffffff ff fffffff ff fff mm m m mm mmm mm m m mmmm . nff f fffffffff fff fff ff f fnff ffff ff ffff ff ffff ff f fff fffff fffff nf ffff ffffffff ff fff fffffff f ffffff ff fff fff nffffff mm m m fffffffff fffff fff ff f fff ff ffffffffff ff ffff ffffnffffff fff f ff f fff fffff fffff fff fffff nffff ff ffffffff fnfffff f ff fff ffffff fffff fffffff ff fff fff nffff ff nfff nffffff ff ffff ff f ffffff nf ffff ff fff nffff ff fff fffffff fff ff fffff ffffff fffffffffff ff fff fffffffff ff fffffffffff ffffffff fnfffff fffffff fffff fff ffffffff fnfffff fff f ff ffff ffff ffffff ffffff ffffnff fff fnfffff ff fff fff nfffff f f f ff ff fff fff nffff f fff fff fff ffff ffff f ff fffffffff fnf ff ff fffffffff ff ffff fffff f ff ffffff f fff fffff ffff f fffnffff ff ffffffff fnfffff fffff ffffnff fff fffff ff fffffffffffff fff ffffff fffnff ff fff fnfffff fffffff ffnf fffnfffff ff ff ffffffff ff fff fffffff f ffffffffff ffffffffff ff fff fff nffff ffff ffffffnfff ffff ff ff ffffffffffff ffffff ff ff f fff fnfffff ffff fff fff ffff ff ffffffff fnfffff ffff fff fff ffff ff fffffff ff ff fff mm m m mm mmm mm m m mmmm

... �mm mm� mm

ffffffffffff ffff fff f ffffff f ff fff ffff fffff fffffff ffffnf fffffff fnf ff fffff fffffff ff fff ffff fffffffff ffffff fff fff nffff fffff ff ff f fffffff fff f ff f ffffffffffff ffff fnff f ffffffffff fff ff fff ffff ff fff fffff ffff ffff ff fffff fff fff nffff ffnf ff ffffff ffff ff ffffff ffff ffffffff ff f ff fff nffff fff ffff ffffffff fffff ff fff ffff ff ffff fff fffff fffff fffnff ffff ff fffffnf fffff fffnff ffff ff f f f ffff fff fffff f ff f ffff fff fffffff ff fnfffff fffffff fff ff f fffffff ffffn f fff ffffffffffff fff ffffffff ff fffffff ffff ff fff nffff ff fffffffffff ffff fff ffff ffffffffff ffffff fffff nf ff ffffff nffff fffffffff fffffffnfff fnfffff fffffff fff fffffff ffff ff ffff ff ffffff fffff ff fff ffff ff fff ff ff f ff fff fff nffff ff fff nffff ff f ff ff ffff nf ff fff ffffff fffffffffff fff fnfffff ffff ffff ff ffffff nf ff ffffff ffff f fffff fffff fff fff nffff fff f f fffff f ff fffffff ff f fff nfffff fff ffff ff ffff nf fnfffff ffff ffff f ffff ff ff ffff ff f ffff ffffffffff ff fffff fffffff ffffff fff ffff ff ffffff ffff ff ff ffffff ffffffffffff ff fff fff nffff fffff fffffff fffff fff ff f fffffff ffff ff fff nfffff ffffffff ff fffffffffff fffffff fff fffffff ffffffffffff ff ffff ff fffff fffffff ff fff fff nffff fffffffffffff ff ff ff

Page 18: Elements of Power System Notes

ffnff ffffffff ff fffffffffff ffff �f f ff ffff ff fffff fffffff ff fff nffff K f ffnff ffff ff ffffff ffff ff ffff . . � f . K. f fff K ff K. fff fffffffff fffff fffnff ffff

...

. K f K. f

ff ffffffffff fffff ff fffff fff ffff ffff f fffffnf fff f ffffffnfff ffnf ff ffff ff fffff fffffff f ff fff fff nffff ffnf fff ffffffff ffffff f

é K .

êK

+

ú

ë û

...

K K. f.

K K. f.

... K f K. f

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fff ffff ffffffffff fff nffff ff ff f � K. K ffnf fff ffff ffffffffff fff nffff ff f ff fff fff fffff fffnff ffff ff ffffff ffff ff

f nff ff fffnff ffffffff ff fffffffffff ff fff fffffff ff fffffff ff fff fff nffff ffffffff

ffff ff ffff ff Kff ff f fff fff ffff ffffffffff fnfffff ffffff fff f ffffffff f nffff

ffff fff ff ff ff fff fnffffffff ff ffffffff fffff fffffff ff fff fff nffff

f fff fffnff fff nffff ffff ff fffffff ffffffffffff ff ffff ff fffff fffffff ff fff nfffff ff ff ffffffffff f ffffffff ffff fffff fff ffff ff ffffff fffff ff ff ffffff ffffffffffff ff fff nffff ffff ff ff ff ffffffffff f fffffffnfff fffff fff fff fffff fffnff ffff ff

fnfffffff ff ff . fff ffff fffff fffffff

Page 19: Elements of Power System Notes

fff fffff ffff fffff ff fff fffff fffnff ffff fnf f ff ff fff ffff ffffffffff ffff ff

fff nffff fffff fffffffff f ff fffff ff ffffffffffff ff fff ffffffffff ff fffff ffff ff ff

. ff fffff ff fff fffff f ffff fffff ff fffffffffffff ff . fff f nff f ffff ffffffffff ffff ff ff fffff fffffffff fff fffffnf ffff ff f ffffff mmmm m m m mm mm mm ffffffff fff fffffffffff ff ffffffff Kff ff f fff

fff fffnff ff ffffff ffff fff fff f ffffffff fffnffffff ff fff fff fffffff ff fff ffffff ff fff fff fff fff ffff fff fff fnfnff fff fff ffffff ff fff fffffff fff fff f fff fffff f fffff

ff ffffffff fff ffffff ffff fffff ffffffff fff fff fnf ff fff ffff fff ffffnf fffff ff

fff f ff fff fff fffffff ff ffffffff fff fff fff fffffff fff fff fff fff fffffffffff ff f fffff fff fnfffff ffffff f fff ffff nffff fff ffffff ffff fff fffff ffffff ff fff ffff fff ffffffffffff ff fff ffff ffnf ff fff f nfff ff fnfffff nffff ffff ffff fff f nfff ffff ff fff ffff ffnf ff fff f nffff ff fff ffff fnffffff ffffnfffnf fff ffff ff fffff fff fnfffff

m mm �mm mm� mm

nf ff fffffffffff ff ffffffff Kff ff f ffff ffff ff fffffffff ff fffffffff fffff fff fnffffff f Kfff effff fffff fffff fff ffff ff fff nfffff fff ffff fffffffff ffff fffff ff fffffff fffnfffffff ffffffff ff fff fffff fff ff ffff ff f fffff ffff fffff fff nf fffffnf ff fff fff ffff ff ff ff fffnffffff ff ffffff ff fff fffff fff fffff fffff ffffffff ff ffff ff fff fffff ffff ff fffnff ffffffff efff ffffffff ff fff nffff ff ff fffff ff ffffffff ff ffffffffff ffffffff fffff fff f ffffffff ffffff ff fffnffffff ffff fffffffff ffff ff ff fnf fff ffffffff

ff ffffnff fff ffff fffff ff ff fff ffff fffnfff ffffffffffff Kfff fnffffff ff f f f fff fffffff ff fffffff ffff fff fffff f fff ffff fffff ff ff ffff fff ff fff nffff ff f ff ff fffff ffff fffffff ffffffffffff ff fff fff nffff fffff fffffff fff fffffff ff fffffff Kf K f ffnff ffff ff fffff Kf K f f ff f ff ffff ff ffffffff ff fffffffffff ffnff ffff ff fffff ffff . K. f

...

fffff fffnff fffff . Kf K f f K. f

ff fffffnf fffff f

Page 20: Elements of Power System Notes

ffnf ff ffff Kff ff f fff fnffffff fff ffff ffffffffff fff nffff ff f ff fff fff fffff fffnff ffffff ffff ffff ff f nff ff fffnff ffff ff ffffffff ff fffffffffff fff ffff ffff ff fffffff ff fffffff fffff ff ffffffffffff ff ffff ff fff nffff

fff fffffffff ffffffffffffff ff ff ffff Kff ff f fff ff fffff ff fff ff

mm

fff ffff ff ffffffffff f ffffffff ffff fff fffffffff ff ffff f ff ff ff ffff ffff ff fffnff

ffff fffff ff fff ffffffffffff ff fff nffff ffff fff ffff ffffff ffff fnf f . ff ffffffffff f fffffffnfff fffff fff ff fffff fff fnfffffff fnf f ff fffff fff fffff ff fffff f

fff fffffffff fffff ff fffff ffff fnf f ff ff fffffnf ffff f ff ffffffffff

fff nffff ff f ff fff ffffff n n. ff fff fffff fffffff ff fff fff nffff ffff fffff ff fff ffffffffffff ff ffff ff fffff fffffff ff fff fff nffff

... m mmm m

nff fffff fffff ffffffff ff fffff ff fffff ff ff fff ffff fnfffffff pm mmm m m mm mmm mm m m mmmm ff ffffff fff ffffff ff fff fff nffff fff fffff fffff fnffff fff nfffff efff fff fffffffffff fnfffff ff fffffff ffffnff f fff nfffff fffffffffff ffffffff ffn ff ffffffff fnfffnf fff fff fff nffff ffff ffffffff ffn ffffffffff ffff fff fffff fnffff fffff ff fffffffff f ffffnffffff fnfffff ff fff f fffff ff �f f fnfffff� ffff � ffff ffffnffffff fnfffff fffffffff fff ffffffffff ff fff fff nffff ff fnff ffff fff fffffff fnfffff ffffnff fff fff nfffff fffff ffnfff fff ffff fff ffffff

Page 21: Elements of Power System Notes

efff fff ffff ffffff fff fffff fff fffffff fff pm mmm m m ff ffff ff ff fffff ffff fff fff ff nfff fff ffn nf ff fffffff fff nffff fff f ffff fffff ff f fff nffff ff f fff ffff ffffff ffff fffff ff ffn fff ffffffff fffffff fffff ffff fff ffffffff fffffff ff ffff fffff ff fffff f f f ffffffffff fff ff nffffff ff fff ffffffff fffffff fffff ff ffff ff fffffff ff fff ffffffff ffff ff ffff fffff ff fffff fff fnfffff ffffff ff ffff ff fff ffffffff fffffff fffff ffff fff fff fnfffff ffffff ff fff fffffff ffff ff ffff fffff f f fffnff fff fffffff f ffffffffff ff fff fff nffff ff ffffffff nf ff fff nffffff fffff nffff ff fnfffff ffff ffffffffff ff fffnffff fffffff ff fff fffff ffffff ffff ffffff ff fffffnfff ff fff ffff ff ff fff fffff fff fffffff ffffff fff fff nffff ff fffff fffffff fff fffff ffffff ff ffffffffffff fffff ff fff ffff ff f fffff fffffff ffff nfnff fffffff ff fffffff ff fffff