Page 101 - Decision Making Applications in Modern Power Systems

68 Decision Making Applications in Modern Power Systems

are inserted in the output data stream. The output from the PDC can be used
to provide visualizations, which enhance the situational awareness of power
system operator.

3.2 Risk assessment and uncertainty analysis of wide area
synchrophasor measurement system
The failure of a PMU or its communication network results in the loss of
observability of a certain portion of the electrical network. Thus it is impor-
tant to assess the impact that the failure of the PMU or its communication
network has on the monitoring capability of the WASMS. This impact is
measured in terms of risk, which is defined as the loss incurred due to the
probable failure of a system [13,14].
Consider an individual event k, whose risk r k is measured as the product
of the probability of failure (p k ) with the severity of failure (s k ) and is given
by the following equation:

r k 5 p k 3 s k ð3:1Þ
The composite risk O when a system involves N distinct events is the
sum of the risk pertaining to the individual events and is given by the follow-
ing equation:
N
X
O 5 r k ð3:2Þ
k51
In the framework of risk assessment for WASMS, the severity of loss
is taken as the number of buses that become unobservable due to the fail-
ure of a PMU or its communication network, while the probability of fail-
ure depends on the failure rates and repair rates of the constituent
components of a system. The uncertainties involved with these parameters
pose a formidable challenge for the accurate determination of the risk.
Hence, uncertainty analysis must be incorporated into the risk assessment
of the WASMS.

3.2.1 Basics of estimating the probability of failure

Reliability analysis is an important aspect of system design. It provides the
probabilistic estimate of the system’s capability to function for the desig-
nated time period under certain operating conditions [15]. The mathematical
representation of reliability (R) is given by the following equation:
Ð t
2 λðtÞdt
RðtÞ 5 e 0 ð3:3Þ
where λ(t) is the system’s failure rate and t represents the time.