Techniques for processing power system network information
Techniques and apparatus for parameter error detection in a power system based on state estimation are described. In one embodiment, for example, an efficient process may be used to derive and compute only the necessary subset of the gain matrix and covariance matrix, thus avoiding the computation and storage of large dense matrices. The described efficient process can be applied either to single-scan or multiple-scan schemes. Other embodiments are described.
1. An apparatus, comprising:
at least one memory; and
logic coupled to the at least one memory, the logic to:
determine a state estimation solution for a scan q of a plurality of buses of an electrical power system, the electrical power system comprising one of an electrical utility power system or an industrial power system,
determine a plurality of Lagrange multipliers for the scan q based on the state estimation,
determine a necessary subset (Ω′ nec (q) ) of non-zero terms of a covariance matrix of a measurement residual vector associated with the Lagrange multipliers,
determine a necessary subset of an inverse gain matrix ([G (q) ] −1 ) nec based on the necessary subset Ω′ nec (q) , and
determine test values of a covariance of a normalized set of the Lagrange multipliers based on the necessary subset Ω′ nec (q) and calculating only non-zero terms of the inverse gain matrix ([G (q) ] −1 ) nec ,
compare the test values to a threshold to determine at least one gross error in a plurality of parameters of the electrical power system, and
modify operation of at least one component of the electrical power system based on the at least one gross error.
2. The apparatus of claim 1 , the electrical power system comprising greater than 500 buses.
3. The apparatus of claim 1 , the electrical power system comprising at least 14,000 buses.
4. The apparatus of claim 1 , the necessary subset Ω′ nec (q) is determined according to the following:
Ω′ nec (q) ={Ω′ nec (q) ( k,l )| H p (q) ( i,l )≠0; H p (q) ( i,k )≠0; i= 1,2, . . . , u},
where H p is a measurement Jacobian with respect to a parameter vector p associated with the state estimation.
5. The apparatus of claim 1 , the necessary subset of the inverse gain matrix ([G (q) ] −1 ) nec is determined according to the following:
(
[
G
(
q
)
]
-
1
)
nec
=
{
G
(
q
)
]
-
1
(
k
,
l
)
H
(
q
)
(
i
,
l
)
≠
0
;
H
(
q
)
(
j
,
k
)
≠
0
Ω
′
(
q
)
(
i
,
j
)
ϵΩ
nec
′
(
q
)
}
.
6. The apparatus of claim 1 , a number of necessary entries per parameter in the inverse gain matrix [G (q) ] −1 is independent of a size of the electrical power system.
7. A computer-implemented method, comprising, by a processor of a computing device communicatively coupled to an electrical power system:
determining a state estimation solution for a scan q of the electrical power system, the electrical power system comprising one of an electrical utility power system or an industrial power system;
determining a plurality of Lagrange multipliers for the scan q based on the state estimation;
determining a necessary subset (Ω′ nec (q) ) of non-zero terms of a covariance matrix of a measurement residual vector associated with the Lagrange multipliers;
determining a necessary subset of an inverse gain matrix ([G (q) ] −1 ) nec based on the necessary subset Ω′ nec (q) ;
determining test values of a covariance of a normalized set of the Lagrange multipliers based on the necessary subset Ω′ nec (q) and calculating only non-zero terms of the inverse gain matrix ([G (q) ] 1 ) nec ;
comparing the test values to a threshold to determine at least one gross error in a plurality of parameters of the electrical power system; and
modify operation of at least one component of the electrical power system based on the at least one gross error.
8. The computer-implemented method of claim 7 , the electrical power system comprising greater than 500 buses.
9. The computer-implemented method of claim 7 , the electrical power system comprising at least 14,000 buses.
10. The computer-implemented method of claim 7 , the necessary subset Ω′ nec (q) is determined according to the following:
Ω′ nec (q) ={Ω′ nec (q) ( k,l )| H p (q) ( i,l )≠0; H p (q) ( i,k )≠0; i= 1,2, . . . , u},
where H p is a measurement Jacobian with respect to a parameter vector p associated with the state estimation.
11. The computer-implemented method of claim 7 , the necessary subset of the inverse gain matrix ([G (q) ] −1 ) nec is determined according to the following:
(
[
G
(
q
)
]
-
1
)
nec
=
{
G
(
q
)
]
-
1
(
k
,
l
)
H
(
q
)
(
i
,
l
)
≠
0
;
H
(
q
)
(
j
,
k
)
≠
0
Ω
′
(
q
)
(
i
,
j
)
ϵΩ
nec
′
(
q
)
}
.
12. The computer-implemented method of claim 7 , a number of necessary entries per parameter in the inverse gain matrix [G (q) ] −1 is independent of a size of the electrical power system.
13. A non-transitory computer-readable storage medium that stores computer-executable instructions for execution by processing circuitry of a computing device communicatively coupled to an electrical power system, the computer-executable instructions, when executed, to cause the computing device to:
determine a state estimation solution for a scan q of the electrical power system, the electrical power system comprising one of an electrical utility power system or an industrial power system;
determine a plurality of Lagrange multipliers for the scan q based on the state estimation;
determine a necessary subset (Ω′ nec (q) ) of non-zero terms of a covariance matrix of a measurement residual vector associated with the Lagrange multipliers;
determine a necessary subset of an inverse gain matrix ([G (q) ] −1 ) nec based on the necessary subset Ω′ nec (q) ;
determine test values of a covariance of a normalized set of the Lagrange multipliers based on the necessary subset Ω′ nec (q) and calculating only non-zero terms of the inverse gain matrix ([G (q) ] 1 ) nec ;
compare the test values to a threshold to determine at least one gross error in a plurality of parameters of the electrical power system; and
modify operation of at least one component of the electrical power system based on the at least one gross error.
14. The non-transitory computer-readable storage medium of claim 13 , the electrical power system comprising greater than 500 buses.
15. The non-transitory computer-readable storage medium of claim 13 , the electrical power system comprising at least 14,000 buses.
16. The non-transitory computer-readable storage medium of claim 13 , the necessary subset Ω′ nec (q) is determined according to the following:
Ω′ nec (q) ={Ω′ nec (q) ( k,l )| H p (q) ( i,l )≠0; H p (q) ( i,k )≠0; i= 1,2, . . . , u},
where H p is a measurement Jacobian with respect to a parameter vector p associated with the state estimation.
17. The non-transitory computer-readable storage medium of claim 13 , the necessary subset of the inverse gain matrix ([G (q) ] −1 ) nec is determined according to the following:
(
[
G
(
q
)
]
-
1
)
nec
=
{
G
(
q
)
]
-
1
(
k
,
l
)
H
(
q
)
(
i
,
l
)
≠
0
;
H
(
q
)
(
j
,
k
)
≠
0
Ω
′
(
q
)
(
i
,
j
)
ϵΩ
nec
′
(
q
)
}
.
18. The non-transitory computer-readable storage medium of claim 13 , a number of necessary entries per parameter in the inverse gain matrix [G (q) ] −1 is independent of a size of the electrical power system.