In literature, P_ij and P_ji have different formula. Intuitionally, they must be negative of each other. I am trying to test state estimation models for IEEE 14 bus, 30 bus systems.
The cause is the losses in the transmission line between i & j.
assume you have a dc source (V1) with two resistances the first one represent the transmission line Rt and the second represent the load Rl and its voltage V2.
the power from the dc source to load= V1 * ((V2-V1)/Rt) = P1
the power from the load resistance to the source = V2 * ((V1-V2)/Rt) =P2
P2 +P1= P(losses) !=0.
The Best Estimates formula incorporates both statistical variance and residual error. This may be the explanation for the difference in the formula.
Please do not hesitate to enhance my knowledge,
@Amlan Chakrabarti,
It is evident from the formula that P_ij and P_ji terms do not include statistical variance and residual error. These two errors have no role to play in the measurement function computation. These errors become relevant only when we find delta(x) using which we update the next_state.
Can you please elaborate your answer?
If you wish I can attach he snips of the formulae.
Thanks.
Varun,
Can you be more specific? Best Estimation vector elements does not give any formula for P_ij, P_ji. These have to be calculated from the Best Estimation vector elements. So, statistical variance and residual errors get into the estimation. A software package will not show you these details. I am not able to understand your requirement.
Regards,
@Amlan
I am not using any software package for the state estimation. I am implementing basic WLS estimator using Gauss-Markov approach for 3,5,14,30,57,... bus systems.
thanks.
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