22-12-2012, 04:35 PM
PMU Data Characterization and Application to Stability Monitoring
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Abstract:
This paper provides a methodology to
characterize the accuracy of PMU data (GPS-synchronized)
and the applicability of this data for monitoring system
stability. GPS-synchronized equipment (PMUs) is in general
higher precision equipment as compared to typical SCADA
systems. Conceptually, PMU data are time tagged with
precision better than 1 microsecond and magnitude accuracy
that is better than 0.1%. This potential performance is not
achieved in an actual field installation due to errors from
instrumentation channels and system imbalances. Presently,
PMU data precision from substation installed devices is
practically unknown. On the other hand, specific applications
of PMU data require specific accuracy of data. Applications
vary from simple system monitoring to wide area protection
and control to voltage instability prediction and transient
stability monitoring. The paper focuses on the last application,
i.e. transient stability monitoring. We propose an approach
that is based on the energy functions (Lyapunov indirect
method). Specifically, we provide a methodology for
determining the required data accuracy for the reliable real
time estimation of the energy function.
Introduction
Monitoring the operating state of the system and assessing its
stability in real time has been recognized as a task of
paramount importance and a tool to avert blackouts. It is also
recognized that when real time data are used to derive the real
time dynamic model of the system, it is possible to predict the
behavior of the system and therefore will enable preventive
action. This paper presents preliminary work in this area. The
paper is focused on the utilization of the available data for
extracting a real time dynamic model. The procedures
described are decentralized, i.e. the data are utilized at each
substation/generating substation of the system and they are
globally valid. It is shown that if GPS-synchronized data are
available at each substation this is possible. We describe the
technology of GPS-synchronized measurements first. The
utilization of this data for extracting the real time dynamic
model is described. This model is used to predict system
stability.
Method Description
The methodology is based on a detailed, integrated model of
the power system, instrumentation channel and data
acquisition system. The power system model is a detailed
three-phase, breaker oriented model and includes the
substation, the generating units and the interconnected
transmission lines. The instrumentation channel model
includes instrument transformers, control cables, attenuators,
burdens, and A/D converters. The modeling approach is
physically based, i.e. each model is represented with the exact
construction geometry and the electrical parameters are
extracted with appropriate computational procedures.
Generating Substation State Estimation
Instrumentation and other measurement data errors are filtered
with state estimation methods. We describe a dynamic state
estimation method. To introduce the method, consider the
single line diagram of the substation of Figure 2. The state of
the system is defined as the minimum number of independent
variables that completely define the state of the system. For
the substation of Figure 1 the state of the system consists of:
(a) the phasor voltages of phase A, B and C of the two buses
(transformer high side and low side), and (b) the generator
speed (frequency) and acceleration (frequency rate of change).
In summary, the state of the generating substation of Figure 2
is defined in terms of 6 complex variables and two real
variables.
The number of measurements for this system from GPSsynchronized
equipment, relays and standard SCADA system
is quite large. Typically, the direct voltage measurements
alone will have a redundancy of two to three, i.e. two to three
times the number of voltage states. The available current
measurements will generate a much larger redundancy
considering that there will be CTs at each breaker,
transformer, reactors, etc. For the system of Figure 2, and with
a typical instrumentation, there will be more than 120
measurement data. This represents a redundancy level of
850%.
Description of Measurement Model
This section presents the overall measurement model. This
model expresses each measurement as a function of the system
state. By appropriate selection of the power component
models, the relationship of the measurements to the states is
linear or at most quadratic. The measurement set consists of
the actual measurements (for example those that are defined in
table 1) and a set of pseudo measurements (see Appendix B).
The power system model consists of algebraic equations as
well as dynamic equations; see for example the generator
model in Appendix A. We convert the dynamical equations
into algebraic by use of the quadratic integration method. The
end result is that the power system model consists of algebraic
equations which are a combination of complex and real
equations. The state of the system has been defined in the
previous section. The model equations, i.e. the equations that
relate the state to the measurements are given below.
Conclusions
This paper presented methodologies for filtering available data
in substations (for example phasor data, relay data and
SCADA data) for the purpose of extracting a real time
dynamical model of the system. The real time dynamical
model is used for monitoring system stability and it is capable
to predict any instability that may arise.
The innovations presented here is that the entire filtering
process is confined to the substation, the instrumentation
channels are explicitly represented and the substation model is
a breaker-oriented three-phase model and generator dynamics
are included in the model. The methodology provides the
means for correcting errors from instrumentation channels.