Stevenson J. Power system analysis
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656
CHAPTER 15 STATE ESTIMATION OF POWER SYSTEMS
of Eq. (1S.37) to nd that
R
(15.38)
Multiplying R by the bracketed matrix [I - R -
I
HG
-
I
HT] and then factoring
out R to the right from the result give
E[eeT] =
[
I - HG-
1H
T
R
-1
]
[
R
-
H
G
-1
H
T]
=
[I -
HG
-
1H
R
-1]
[
I
- HG 1
H
F
R
I]R
(
15.
39
)
The reader should show that the matrix [I - H
G
-
I
H
TR -
I
] multiplied by itself
remains unaltered (it is called an idempotent matrix), and so Eq.
(
15.39
)
simplies as follows:
(15.40)
The square matrix ee
T
takes the form of Eq. (1S.29) with typical entries given by
elj' Therefore, substituting for ej
=
(z
j
-i) in the diagonal
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