Tie-Line Control

Tie-line is used to control frequency for the power station and power transfer from one station to an another station in interconnected system. It is also to avoid overload in the system as a result from accidental power exchange.

Formula derivation
Lets look at this example,



dpt = power transfered to
Pa  = a constant for frequency power for station A
Pb  = a constant for frequency power for station B

-Station B experienced imbalance power of dpb
-Cause station A to transfer power at dpt

To synchronize the frequency value, station A has frequency drop at;
dFa = -dpt / Pa

and Station B experienced frequency drop at;
dFb = -(dpb - dpt) / Pb


( The negative sign for frequency magnitude to show the frequency drop on both station )

But the change of both stations are the same.


          dFA                          =         dFb
      -dpt / Pa                        =        -(dpb-dpt) / Pb
       dpt / Pa                        =        (dpb / Pb) - (dpt / Pb)
dpt (1 / Pa + 1 / Pb )           =        dpb / Pb
dpt [ (Pa + Pb) / PaPb ]      =        dpb / Pb

To summarize the equation:

dpt = [(PaPb) / (Pb + Pa)] x (dpb / Pb)


dpt = [Pa / (Pb + Pa)] x dpb

If the Tie-Line is open, station A will release power dpt and the frequency considered as fA, and station B has the additional load dpt and frequency as fB;

fA = fs + (dpt / Pa)
fB = fs - (dpt / Pb)


fA will be larger than fB because station A has released load while station B has additional load.

where,

fA - fB = [f + (dpt / Pa)] - [f - (dpt / Pb)]
            = (dpt / Pa) + (dpt / Pb)
            = dpt [(1/Pa) + (1/Pb)]
            = dpt [(Pb + Pa) / PaPb]


(Pb + Pa) / PaPb = dpt / (fA-fB)

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