Page 304 - Mathematical Models and Algorithms for Power System Optimization

296 Chapter 8

speed of the assumed power angle in a local equilibrium state, when each local part of the
system meets these relations:

δ i tðÞ ¼ δ ei tðÞ
_ _ ½ 1, N 1Š (8.7)
δ i tðÞ ¼ δ ei tðÞ
the overall system will be in a steady operation state again.
It must be pointed out that δ ei is assumed as the local power equilibrium state, and in fact is of no
actual physical meaning but rather just an abstract virtual variable.

The concept of the power angle δ ei for the assumed local equilibrium state is introduced here,
which can be used as the respective stability reference for the local dynamic power angles of the
power system. Because its time-varying characteristic, δ ei could serve as the stability reference
for δ i only in a transient dynamic sense, and the criterion is valid only in a local sense.
In line with the assumption when introducing δ ei concept, δ ei could be obviously obtained
from the time-varying data set {E i ,P mi ,P Li ,Q Li ,U j ,α j ,u j } for local system i,wherethe
0
control variable u i is with non-zero value only when imposing local stability control, and it
is of zero value in other time. If the initial value of the time-varying data set is known and
can be replaced in a real-time manner, δ ei will be uniquely determined. The equivalent
circuit for obtaining the power angle δ ei for the assumed local equilibrium state is shown
in Fig. 8.3.

Fig. 8.3

Circuit for defining assumed local equilibrium state.
As is known from common sense in the power system, the process of calculating δ ei is to derive
theinstantpowerflowsolutionofthelocalnetworkasshowninFig.8.3.Thevirtualinstantquantity
of U ei and α ei could be derived as well while calculating δ ei . U ei ∠α ei can be deemed as the instant
local equilibrium reference for the generator terminal voltage U i ∠α i . U ei , α ei and δ ei together
constitutethetime-varyingdataset{δ ei ,U ei ,α ei }belongingtotheassumedlocalpowerequilibrium
state, so the time-varying data set is regarded as the instant stability balance reference vector
T T
[δ ei ,U ei ,α ei ] fortheactuallocaloperationparametervector[δ i ,U i ,α i ] ofthepowersystem.Iftheir