What is a Phasor?
Phasor is a quantity with magnitude and phase (with respect to a
reference) that is used to represent a sinusoidal signal
(figure below). Here the phase or phase angle is the
distance between the signal’s sinusoidal peak and a
specified reference and is expressed using an angular
measure. Here, the reference is a fixed point in time
(such as time = 0). The phasor magnitude is related to
the amplitude of the sinusoidal signal.
What is Phasor technology?
Phasor technology is considered to be one of the most
important measurement technologies in the future of
power systems due to its unique ability to sample analog
voltage and current waveform data in synchronism with a
GPS-clock and compute the corresponding 60 Hz phasor
component (i.e. complex numbers representing the
magnitude and phase angle of a 60 Hz sinusoidal
waveform) from widely dispersed locations (see figure).
This synchronized sampling process of the different
waveforms provides a common reference for the phasor
calculations at all the different locations.
Note: The phase angle differences between two sets of
phasor measurements (i.e. d1-d2)
is independent of the reference. Typically, one of the
phasor measurements is chosen as the “reference” and the
difference between all the other phase angle
measurements (also known as the absolute phase angle)
and this common “reference” angle is computed and
referred to as the relative phase angles with respect to
the chosen reference (see figure below).
Why are phase angle differences important?
Just as in DC circuits, power flows from high voltages
to low voltages, in an AC power system, power flows from
a higher voltage phase angle to a lower voltage phase
angle – the larger the phase angle difference between
the source and the sink, the greater the power flow
between those points implying larger the static stress
being exerted across that interface and closer the
proximity to instability.
The figure below shows the growing phase angle
difference between Cleveland and Michigan during the
August 14, 2003 blackout in the Eastern Interconnection.
What is unique about phasor technology? What makes it
superior to other technologies?
technology provides time synchronized sub-second
data (typically 20, 30 or 60 samples/second) which
is applicable for wide area monitoring; real time
dynamics and stability monitoring; dynamic system
ratings to operating power system closer to the
margin to reduce congestion costs and increasing
asset utilization; and improvements in state
estimation, protection, and controls.
Traditional SCADA/EMS systems are based on steady
state power flow analysis, and therefore cannot
observe the dynamic characteristics of the power
system – phasor technology is the “MRI of the power
system” industry providing the high sub-second
visibility required for observing dynamic behavior
and, therefore, overcoming the limitations of the
old “x-ray” quality visibility that traditional
SCADA-based systems offer.
precise timing of phasor data makes it useful beyond
the local bus where the measurement was taken, i.e.
the technology offers wide area visibility. This, in
turn, facilitates the capability for distributed
sensing and coordinated control action.
measurements directly provide the phase angles at
the high sub-second rate. These phase angles have
traditionally been obtained from state estimators
which are inherently slow (typically every 5
minutes) and susceptible to errors due to outdated
or inaccurate models required by the state
measurements improve post disturbance assessment
capability using high-resolution time-synchronized
data rates and low latency associated with phasor
acquisition systems provide the desired agility to
respond to abnormal conditions.
Why is time synchronization important?
Through the use of integral GPS receiver-clocks, PMUs
sample synchronously at selected locations throughout
the power system. This provides a system-wide snapshot
of the electrical system. The GPS not only provides time
tagging for all the measurements but also ensures that
all phase angle measurements are synchronized to the
same time as well.
Figure 6 shows how time skews in the measurement and
analysis process can induce errors in the phase angle
difference computations. Here, the phase angle
difference between two sets of measurements was
approximately 10 degrees. However, when one of these two
phase angle signals was skewed by 1 second and then the
phase angle difference was computed, then the resulting
answer incorrectly indicated a phase angle difference of
approximately 5 degrees between those two data sets.
Phasor calculations demand greater than 1 millisecond
What are the elements of a phasor network?
The simplest form of phasor network consists of TWO
nodes; one Phasor Measurement Unit (PMU) at node 1 that
communicates with one Phasor Data Concentrator (PDC) at
node 2. Typically, many PMUs located at various key
substations gather data in real-time and they are
connected to a PDC at the utility center where the data
is aggregated. A personal computer, connected to the
output of the PDC provides the users with software, such
as RTDMS that calculates and displays locally measured
frequencies, primary voltages, currents, MWs and MVARs
for system operators. Additionally, many PDCs belonging
to different utilities can also be connected to a common
central PDC (a.k.a., SuperPDC) to aggregate data across
the utilities to provide an Interconnection-wide
What is a Phasor Monitoring Unit (PMU)?
A PMU is an electronic device that uses state-of-the-art
digital signal processors that can measure 50/60Hz AC
waveforms (voltages and currents) typically at a rate of
48 samples per cycle (2880 samples per second). The
analog AC waveforms are digitized by an Analog to
Digital converter for each phase. A phase-lock
oscillator along with a Global Positioning System (GPS)
reference source provides the needed high-speed
synchronized sampling with 1 microsecond accuracy.
Additionally, digital signal processing techniques are
used to compute the voltage and current phasors
Line frequencies are also calculated by the PMU at each
site. This method of phasor measurement yields a high
degree of resolution and accuracy. The resultant time
tagged phasors can be transmitted to a local or remote
receiver at rates up to 60 samples per second.
Phasor Measurement Unit Block Diagram
Nuqui, “State Estimation and Voltage Security Monitoring
Using Synchronized Phasor Measurements”,
Doctorate Dissertation, Virginia Polytechnic Institute,
Blacksburg, VA, July 2, 2001.)
PMUs come in different sizes. Some of the larger ones
can measure up to 10 phasors plus frequency while others
only measure from one to three phasors plus frequency.
The approximate cost of the larger PMUs can range in the
$30 to $40 thousand of dollars while the smaller ones
cost considerably less.
What is involved in a PMU installation and connection?
Installation of a typical 10 Phasor PMU is a simple
process. A phasor will be either a 3 phase voltage or a
3 phase current. Each phasor will, therefore, require 3
separate electrical connections (one for each phase). We
are talking about 6 wires per phasor – 2 for each phase
of either voltage or current. The PMU will also measure
the line frequency from a specific voltage phasor
(typically a major bus assigned by the user).
Typically an electrical engineer designs the
installation and interconnection of a PMU at a
substation or at a generation plant. Substation
personnel will bolt equipment rack to the floor of the
substation following established seismic mounting
requirements. Then the PMU along with a modem and other
support equipment will be mounted on the equipment rack.
They will also install the Global Positioning Satellite
(GPS) antenna on the roof of the substation per
manufacturer instructions. The antenna signal cable will
be connected to the antenna and brought directly to the
PMU. Substation personnel will also install “shunts” in
all Current Transformer (CT) secondary circuits that are
to be measured. Potential Transformer (PT) connections
will not require the installation of any additional
equipment other than terminal blocks and fuses. They
will have to run wires from the CT shunts and the PTs to
either an interface cabinet or directly to the input
connections of the PMU (Figure 10). Note: Each phasor
(either Voltage or Current) will require three
connections – one for each phase.
In addition to the CT and PT connections the PMU will
also require the following connections:
- Power connection – typically from station batteries.
- Station ground connection.
- Global Positioning Satellite (GPS) antenna connection.
- Communication circuit connection (Modem if using
4-wire connection or Ethernet for network connection).
After all the connections are made, the PMU is
configured and tested. This task is typically performed
by a substation Test Technician.
The utility’s IT department will play a key role will
the phasor data connections phase of the PMU
installation. After the entire input channel
configuration and testing is completed, the PMU is
connected to the utility’s Phasor Data Concentrator
(PDC) via 4-wire Modem or Ethernet connection depending
on the bandwidth needs. They will also need to evaluate
the need to install additional communication equipment
in order to provide the necessary circuit connections
between the PDC at the master site and the PC
workstations at the client sites.
What is a Phasor Data Concentrator (PDC)?
A PDC forms a node in a system where phasor data from a
number of PMUs or PDCs is correlated and fed out as a
single stream to other applications. The PDC correlates
phasor data by time-tag to create a system wide
measurement set. The PDC provides additional functions
as well. It performs various quality checks on the
phasor data and inserts appropriate flags into the
correlated data stream. It checks disturbance flags and
records files of data for analysis. It also monitors the
overall measurement system and provides a display and
record of performance. It can provide a number of
specialized outputs, such as a direct interface to a
SCADA or EMS system.
What is a Super Phasor Data Concentrator (SuperPDC)?
Within a point-to-point phasor network architecture, the
SuperPDC is simply a central PDC that collects and
correlates phasor data from all remote PDCs and PMUs and
makes it available to a visualization software package
as described above (Figure 11). Typically, the SuperPDC
is also connected to a central database for long-term
archiving of the collected data
Will the SuperPDC be expected to archive the data or
just concentrate it and forward to the several
A SuperPDC should have the capability to do both if it
is fast enough. The obvious problem of locally storing
ALL the data would be the need to employ large disk
drives and have a system in place to regularly transfer
full disk phasor data to DVD for permanent storage. A
rate of 30 or 60 samples per second fills up a disk
drive very quickly.
What are some of the standard protocols used for phasor
The latest PMU/PDC protocol is the IEEE C37.118 that was
developed in the last few years and approved late 2005.
It will replace the IEEE 1344 synchrophasor protocol
which has been in use as the PMU standard since its
development in 1998. Before these standards were
developed, the defacto standard for PMU to PDC
communication has been the Macrodyne type 1 and type 2
protocols developed by Macrodyne Corporation. Some of
the PDC to PDC protocols include the PDC data exchange
format, the PDC stream, second level PDC using NTP time
and the PDC stream, second level PDC using native time.
These standards address issues like synchronization of
data sampling, data to phasor conversions, and formats
for timing input and phasor data output.
What kind of delays can be expected in the real time
A PDC receives data streams from PMUs and other PDCs and
correlates it in real-time into a single data stream
that is transmitted to a PC via an Ethernet port. They
propagation delays associated with communication links
from a PMU and PDC depend on the medium and the physical
distance separating these components. For a typical PMU
with 10-12 phasors, the associated delays for various
communication mediums are summarized below.
Associated Delays with Various Communication Links
(B. Naduvathuparambil, M.
C. Valenti, A. Feliachi, “Communication Delays in Wide
Area Measurement Systems”,
Proceedings of the Thirty-Fourth Southeastern Symposium
on System Theory, 18-19 March 2002, pp. 118-122.)
Associated Delay – one way (milliseconds)
Fiber-optic cables (50 Mbps – 1 Gbps)
Digital microwave links
Power line (PLC) (upto 4 Mbps)
Telephone lines (upto 56 kbps)
In addition, the fixed delay associated with processing,
concentrating, multiplexing, and transducers, and is
independent of the communication is 75 ms.
Finally, PDCs also have a maximum wait-time, typically
of 1-4 seconds, to allow for all the PMU data to come in
before aggregated data is outputted by the PDC. If the
data from all the PMUs reach the PDC within this
wait-time, it outputs the aggregated data right away.
However, in the extreme case that the data from one of
the PMUs is indefinitely delayed, then the PDC will wait
upto its pre-defined wait-time (i.e., 1-4 seconds)
before the data is outputted by the PDC. Hence, the PDC
can also introduce an additional delay equal to its
wait-time if one of the PMU channels stops transmitting
data to the PDC. In such circumstances, if there are
additional PDCs downstream in the point-to-point phasor
network architecture (such as the SuperPDC), then they
too will introduce a secondary delay equal to their
Phasor applications such as Real-Time Dynamics
Monitoring System™ (RTDMS) are designed to directly
integrate with the PDCs over the utility’s high speed
Local Area Network (100 Mbps) and display the data and
calculated individual engineering units such as MW,
MVAR, etc. within 1 second of receiving the data from
the PDC (Note: The Web based versions of the RTDMS
Clients, such as those deployed across the Eastern
Interconnection as part of the EIPP project, integrate
over secure internet connections rather than Local Area
Networks and can longer to display the information
within its visualization screens).
Bottom Line: The total delay from when the data is
captured by the PMU to it being visualized within the
RTDMS screens is typically a few seconds.
What type of data quality problems does one typically
encounter with such a system?
There are two main types of problems associated with
data validation: First, there is a data loss problem
associated with network problems such as bandwidth
limitations, collisions, misrouting, maintenance
outages, and equipment breakdown to name a few. There is
not much one can do about this other than to report it
to IT for review and repair. The other problem is
measurement data validation which has to do with
obtaining inaccurate information such as incorrect
resistor shunts as well as incorrect CT and PT rations.
This also includes larger inaccuracies, such as ±120°,
due to incorrect wiring errors or labeling
inconsistencies in what is called ‘Phase A’, ‘Phase B’
and ‘Phase C’ across utilities. The latter type will
take time to correct and may have to involve station
technicians at a particular site and even sometimes the
engineering department. If this data is also available
through the SCADA system the two values should be
compared in order to achieve some degree of validation.
Finally, each PMU vendor utilizes their own proprietary
phasor computation algorithms as well as pre and post
processing filters, each with their own unique design
characteristics. These and other factors can result in
adding constant offsets to the phase angle measurements
which may be more significant at off-nominal operating
frequencies. Figure 12 compares the phase angle offsets
of different PMUs over a wide frequency range about the
normal 60Hz operating frequency. As long as all the PMUs
within the phasor network are provided by the same
vendor, this is not an issue; otherwise these offset
errors should be corrected.
Figure courtesy of Ken
Martin, Bonneville Power Administration.