Unified fault and stability analysis system and method considering unbalanced topologies
For systems subject to unbalanced faults, analytical model building for stability assessment is a challenging task. This application presents a straightforward modeling approach. A generalized dynamic circuit representation is achieved by use of the Laplace transform variables. The voltage and current relationship at the fault location is translated into the relationship of three subsystems. The final circuit model is an interconnected sequence network with impedances in the Laplace domain. This circuit can be directly converted from a steady-state sequence network.
1 . A method comprising:
deriving a first circuit diagram representing a steady state sequence network by a computing device;
receiving an indication of an unbalanced condition in the steady state sequence network by the computing device;
in response to the indication of the unbalanced condition, converting the first circuit diagram to a second circuit diagram comprising impedances in the Laplace domain by the computing device;
performing a system analysis of the second circuit diagram using the unbalanced condition to determine if the unbalanced condition may result in a loss of stability for a power grid by the computing device; and
in response to determining that the unbalanced condition may result in a loss of stability, generating an alert that the unbalanced condition may result in the loss of stability by the computing device.
2 . The method of claim 1 , wherein the unbalanced condition is caused by a fault in the power grid.
3 . The method of claim 2 , wherein the fault is a balanced or unbalanced fault.
4 . The method of claim 1 , wherein the steady state sequence network represents the power grid.
5 . The method of claim 4 , wherein the power grid comprises generators and a transmission network.
6 . The method of claim 1 , wherein the unbalanced condition is associated with an unbalanced fault in an otherwise balanced and symmetrical three-phase transmission system.
7 . The method of claim 1 , wherein converting the first circuit diagram to the second circuit diagram comprises representing the steady-state circuit diagram as a special case in a frequency domain, and expanding the representation to an entire frequency domain by identifying quantities associated with a nominal frequency and replacing a variable jω with a Laplace transform variable s, where w is the nominal frequency or a synchronous frequency of the first circuit diagram.
8 . A system comprising:
one or more processors; and
a computer-readable medium with computer-executable instructions that when executed by the one or more processors cause the one or more processors to:
derive a first circuit diagram representing a steady state sequence network;
receive an indication of an unbalanced condition in the steady state sequence network;
in response to the indication of the unbalanced condition, convert the first circuit diagram to a second circuit diagram comprising impedances in the Laplace domain;
perform a system analysis of the of the second circuit diagram using the unbalanced condition to determine if the unbalanced condition may result in a loss of stability for a power grid; and
in response to determining that the unbalanced condition may result in a loss of stability, generate an alert that the unbalanced condition may result in the loss of stability.
9 . The system of claim 8 , wherein the unbalanced condition is caused by a fault in the power grid.
10 . The system of claim 9 , wherein the fault is a balanced or unbalanced fault.
11 . The system of claim 8 , wherein the steady state sequence network represents the power grid.
12 . The system of claim 11 , wherein the power grid comprises generators and a transmission network.
13 . The system of claim 8 , wherein the unbalanced condition is associated with an unbalanced fault in an otherwise balanced and symmetrical three-phase transmission system.
14 . The system of claim 8 , wherein converting the first circuit diagram to the second circuit diagram comprises representing the steady-state circuit diagram as a special case in a frequency domain, and expanding the representation to an entire frequency domain by identifying quantities associated with a nominal frequency and replacing a variable jω with a Laplace transform variable s, where w is the nominal frequency or a synchronous frequency of the first circuit diagram.
15 . A non-transitory computer-readable medium with computer-executable instructions that when executed by one or more processors cause the one or more processors to:
derive a first circuit diagram representing a steady state sequence network;
receive an indication of an unbalanced condition in the steady state sequence network;
in response to the indication of the unbalanced condition, convert the first circuit diagram to a second circuit diagram comprising impedances in the Laplace domain;
perform a system analysis of the second circuit diagram using the unbalanced condition to determine if the unbalanced condition may result in a loss of stability for a power grid; and
in response to determining that the unbalanced condition may result in a loss of stability, generate an alert that the unbalanced condition may result in the loss of stability.
16 . The non-transitory computer-readable medium of claim 15 , wherein the unbalanced condition is caused by a fault in the power grid.
17 . The non-transitory computer-readable medium of claim 16 , wherein the fault is a balanced or unbalanced fault.
18 . The non-transitory computer-readable medium of claim 15 , wherein the steady state sequence network represents the power grid.
19 . The non-transitory computer-readable medium of claim 18 , wherein the power grid comprises generators and a transmission network.
20 . The non-transitory computer-readable medium of claim 15 , wherein the unbalanced condition is associated with an unbalanced fault in an otherwise balanced and symmetrical three-phase transmission system.