has always been a key aspect of power system state estimation. Generally speaking, the observability analysis function executes before the state estimation is done in order to determine the boundaries of the estimation problem.
There are many texts and much literature available on the subject, especially with regard to
, or non-linear
state estimation where SCADA serves as the data source. While the fundamental concepts are the same for the synchrophasor-only estimation problem, the observability analysis is somewhat different but also less complex.
With regard to PMU observability, every node in the network model can be classified into one of three states.
Note that this classification does not take into account measurement redundancy
- Directly Observed - A node can be directly observed when there is a voltage phasor measurement located at that node.
- Indirectly Observed - A node can be indirectly observed under several scenarios. First, a node which is connected to a directly or indirectly observed node through a negligible impedance (i.e. a circuit breaker or a switch) is also indirectly observed.
Second, a node which is connected to a directly observed node through a series impedance (i.e. a transmission line or a transformer with known or estimated tap ratio) where the directly observed node has a current phasor leaving the node is also indirectly
observed. Finally, a node can also be indirectly observed if it is connected to an indirectly observed node if that node is a zero injection node and one or less current phasors are absent from the measurement set (i.e. the zero injection bus case, commonly
used for PMU placement optimizations).
- Not Observed - A node is unobserved if it has been included in the network model and does not meet any of the criteria for the above to classifications.
This is reflected in Phasor Analytics
uses the concepts of a Substation
and Transmission Line
as little more than data containers for the network model. From an observability standpoint, the real network model is made up of
, and Two Terminal Devices
(i.e. Circuit Breakers
). Observability analysis could be performed on the network level, but because of the convenience of the substation and transmission line models, the observability analysis is performed at the substation and transmission
line level and where the network is resolved to a collection of observed busses. This collection and its contents represents the solution set for the observability analysis for the linear estimator
Substation Observability Analysis
The substation model is a set of collections of nodes, circuit breakers, switches, and transformers. Each node may be the parent of a voltage phasor measurement and each transformer may be the parent of a high side and low side current phasor measurement. To
perform the observability analysis, it is first necessary to represent the substation collections as a
. A graph is a very common data structure for representing networks; for more information see
. For the case of the substation, the collection of nodes make of the
of the graph and the circuit breakers, switches, and transformers make up the