System state estimation with asynchronous measurements
The present disclosure provides techniques for estimating network states using asynchronous measurements by leveraging network inertia. For example, a device configured in accordance with the techniques of the present disclosure may receive electrical parameter values corresponding to at least one first location within a power network and determine, based on the electrical parameter values and a previous estimated state of the power network, an estimated value of unknown electrical parameters that correspond to a second location within the power network. The device may further cause at least one device within the power network to modify operation based on the estimated value of the unknown electrical parameters. The leveraging of network inertia may obviate the need for probabilistic models or pseudo-measurements.
1. A device comprising:
at least one processor configured to:
receive at least one electrical parameter value corresponding to at least one first location within a power network;
determine, based on the at least one electrical parameter value and a previous estimated state of the power network, an estimated value of at least one unknown electrical parameter, wherein the at least one unknown electrical parameter corresponds to a second location within the power network; and
cause at least one device within the power network to modify operation based on the estimated value of the at least one unknown electrical parameter, wherein:
determining the estimated value of the at least one unknown electrical parameter comprising determining
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k
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γ
Λ
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,
{circumflex over (x)}(k) is a matrix representation of a current estimated state of the power network and contains the estimated value of the at least one unknown electrical parameter,
Λ( k )=γ(Φ k T S ( k ) T N k −1 S ( k )Φ k +γI ) −1 ,
{circumflex over (x)}(k−1) is a matrix representation of the previous estimated state of the power network,
γ is an inertia parameter that represents how much the current estimated state of the power network can change from the previous estimated state of the power network,
Φ k is a matrix housing a linearization of power flow equations which represents how power flows in the power network,
S(k) is a selection matrix that selects from Φ k based on received electrical parameter values,
N k is a matrix housing values that indicate accuracy of received electrical parameter values,
I is an identity matrix, and
y(k) is a vector containing the at least one electrical parameter value.
2. The device of claim 1 , wherein determining the estimated value of the at least one unknown electrical parameter is based further on a linearization of power flow equations which represents how power flows in the power network.
3. The device of claim 1 , wherein determining the estimated value of the at least one unknown electrical parameter is further based on a respective at least one weighting value that represents the accuracy of the at least one electrical parameter value.
4. The device of claim 1 , wherein determining the estimated value of the at least one unknown electrical parameter comprises determining respective active and reactive power values for nodes in the power network.
5. The device of claim 1 , wherein receiving the at least one electrical parameter value comprises receiving a voltage magnitude, a real power value, and a reactive power value, each corresponding to the at least one first location.
6. The device of claim 5 , wherein receiving the at least one electrical parameter value further comprises receiving a voltage angle corresponding to the at least one first location.
7. The device of claim 1 , wherein causing the at least one device within the power network to modify operation based on the estimated value of the at least one unknown electrical parameter comprises outputting the estimated value of the at least one unknown electrical parameter.
8. A method comprising:
receiving, by a power network management system comprising at least one processor, at least one electrical parameter value corresponding to at least one first location within a power network;
determining, by the power network management system, based on the at least one electrical parameter value and a previous estimated state of the power network, an estimated value of at least one unknown electrical parameter, wherein the at least one unknown electrical parameter corresponds to a second location within the power network; and
causing, by the power network management system, at least one device within the power network to modify operation based on the estimated value of the at least one unknown electrical parameter, wherein:
determining the estimated value of the at least one unknown electrical parameter comprising determining
x
^
(
k
)
=
Λ
(
k
)
x
^
(
k
-
1
)
+
1
γ
Λ
(
k
)
Φ
k
⊤
S
(
k
)
⊤
N
k
-
1
y
(
k
)
,
{circumflex over (x)}(k) is a matrix representation of a current estimated state of the power network and contains the estimated value of the at least one unknown electrical parameter,
Λ( k )=γ(Φ k T S ( k ) T N k −1 S ( k )Φ k +γI ) −1 ,
{circumflex over (x)}(k−1) is a matrix representation of the previous estimated state of the power network,
γ is an inertia parameter that represents how much the current estimated state of the power network can change from the previous estimated state of the power network,
Φ k is a matrix housing a linearization of power flow equations which represents how power flows in the power network,
S(k) is a selection matrix that selects from Φ k based on received electrical parameter values,
N k is a matrix housing values that indicate accuracy of received electrical parameter values,
I is an identity matrix, and
y(k) is a vector containing the at least one electrical parameter value.
9. The method of claim 8 , wherein determining the estimated value of the at least one unknown electrical parameter is based further on a linearization of power flow equations which represents how power flows in the power network.
10. The method of claim 8 , wherein determining the estimated value of the at least one unknown electrical parameter is further based on a respective at least one weighting value that represents the accuracy of the at least one electrical parameter value.
11. The method of claim 8 , wherein determining the estimated value of the at least one unknown electrical parameter comprises determining respective active and reactive power values for nodes in the power network.
12. The method of claim 8 , wherein receiving the at least one electrical parameter value comprises receiving a voltage magnitude, a real power value, and a reactive power value, each corresponding to the at least one first location.
13. The method of claim 12 , wherein receiving the at least one electrical parameter value further comprises receiving a voltage angle corresponding to the at least one first location.
14. The method of claim 8 , wherein causing the at least one device within the power network to modify operation based on the estimated value of the at least one unknown electrical parameter comprises outputting the estimated value of the at least one unknown electrical parameter.