PMU Fundamentals

Here at OpenPMU HQ we get a lot of enquiries from students about the fundamentals of phasor measurement units and synchrophasor technology. On this page we'll try and answer the common questions.

What is a PMU?

A Phasor Measurement Unit (PMU) is an instrument which measures the voltage and/or current waveforms of the electrical power system. It is synchronised to a global time standard, Coordinated Universal Time (UTC).

First, the input waveforms, usually three-phases, are digitised. These digital samples represent the analogue input signals as numerical values, which are then operated on in the PMU to perform the measurements that the PMU makes. It measures and reports an amplitude and a phase angle; these two quantities are known as a phasor. As the waveforms were acquired in synchronism with a global time base, the estimated phasor is given a time code. The result is known as a synchrophasor.

The PMU measurements will additionally include the estimated frequency and rate-of-change-of-frequency of each waveform. In terms of naming, these are not considered part of the synchrophasor.

How are the waveforms measured?

The voltage and current waveforms applied to the terminals of the PMU are sampled using an analogue-to-digital converter (ADC). An ADC takes as an input which is continuously variable in amplitude and time and transforms it into a series of numerical data which can only change at discrete instances in time, and to discrete values. This process is known as sampling, and the series of numerical output data from the ADC are known as sampled values (SV).

The difference between the numerical value of the output of the ADC and the original waveform the numerical value asserts to represent is known as quantisation error. Quantisation error may be reduced by increasing the bit-depth of the ADC.

The required sampling rate is a subject of the Nyquist-Shannon sampling theorem. In brief, one must sample at 'at least twice' the frequency of the maximum frequency one wishes to recover. In practice, it is necessary to sample at significantly higher frequencies than the 'Nyquist rate'.

One must be conscious that the voltages and currents applied to the PMU terminals may have already been through one or more instrument transformers, the effects of which should be taken into account (i.e. frequency dependent amplitude / phase).

This section is an extremely simplistic overview of ADCs. Further reading should be considered, for example on filtering and aliasing.

How are phasors estimated?

This isn't a straight forward question to answer because there are numerous methodologies in use in practice, so what follows is a superficial overview of the general theory.

A phasor represents two of the parameters of a sinusoidal waveform, described below:

Where x(t) is the amplitude of the waveform at time t, X_m is the amplitude of the waveform, f is the frequency, and φ (phi) is the phase angle.

Phase has to be measured between two things: in the PMU, the phase is measured between the applied signal and a hypothetical reference signal whose frequency is exactly the nominal value of the power system (50 or 60 Hz) and whose cosine peaks at exactly the “tick” of the second of the UTC timebase.

The objective of the phasor estimator is to adjust the parameters X_m, f and φ until the resulting waveform is a good representation with respect to the acquired sampled values.

The PMU begins the process by filtering the incoming signal to remove much of the distortion that is expected to be present. This distortion could adversely affect the accuracy of the measurement. Then, the signal is considered over short intervals of time (known as “windows) over which the measurements are to be performed. The result is that a new measurement result is available several times every second. The exact rate of reporting results is set by a documentary standard, IEEE C37.118.1-2011.

A commonly employed measurement method is curve fitting. Depending on the implementation this may be described as 'least squares fitting' or 'linear regression'. At a high level, the method uses an iterative approach to adjust the estimated parameters (X_m, f, φ), whereby the adjustment is proportional to the error observed on the last iteration. The sampled values are compared with their corresponding points on the estimated waveform, and the error (or residuals) is determined. When the error is below a set threshold, or a maximum number of iterations occurs, the estimator stops and returns its result.

In most PMUs, the results from several measurement windows are combined to give a single value. This process may “smooth” the stream of results, but it means that the measurements are not independent.

When the estimated parameters (X_m, φ) are accompanied with the time at which the sampled values from which they are derived were acquired, the package of values is known as a synchrophasor.

What about Telecommunications?

This is where we move from the domain of measurement theory, to telecommunications engineering. We must first differentiate between 'presentation' of the synchrophasor data, and 'transport' of the data.

The IEEE Std. C37.118.2 primarily describes the presentation of synchrophasor data in a bit-mapped format, and allows for transport using serial links, or using Internet Protocol (IP) using either TCP/IP or UDP/IP. A Technical Report, IEC 61850-90-5, describes a similar approach to presentation, but goes into greater depth on transport within the IEC 61850 suite.

This area is fast moving, but it is important to consider the cyber security aspects of synchrophasor communications systems, especially as they become used in protection and control systems.

What about Time?

Most PMUs will use the GPS satellite constellation to achieve time synchronisation with the UTC time base. It's important to say that the PMU is synchronised to UTC, it is not synchronised to GPS. It uses GPS as a means to achieve synchronisation to UTC. Other Global Navigation Satellite Systems (GNSS) services, such as Galileo, and terrestrial time transfer methods exist and may be used by PMUs.

The Coordinated Universal Time (UTC) timebase includes 'leap seconds', which adjust UTC to keep it close to mean solar time (so that noon is when the sun is highest in the sky). This is complicated for databases and real-time systems to deal with. There is an argument that PMUs should use International Atomic Time (TAI).

Anything else?

It's really important to differentiate a PMU from a multifunction instrument, such as a disturbance recorder. Many disturbance recorders, protection relays, and other substation apparatus might include a PMU function and return synchrophasors, but the other functions of these devices (e.g. capturing waveforms during transients) are not functions of a PMU. It's an "all squares are rectangles, not all rectangles are squares" type definition.

How do I cite this?

The journal publication below has a good overview of the PMU fundamentals described here. You can get paper and the IEEE formatted citation via the link below.

The OpenPMU Platform for Open-Source Phasor Measurements
IEEE Transactions on Instrumentation and Measurement
D. M. Laverty, R. J. Best, P. Brogan, I. Al Khatib, L. Vanfretti and D. J. Morrow

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6463452

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