# Phasor Measurement Unit (PMU) technique

In their most organic form, basic Phasor Measurement Unit (PMU) in the smart grid are the sensing devices strategically placed in order to capture power system phasors using a common time source for synchronization. The process is usually done over wide geographical areas, through global positioning system enabled time-stamping. The data obtained from the device form the basis of all monitoring and control actions for wide-area measurement systems. The resulting measurement is known as a synchrophasor. With that said, it is safe to say that a PMU is the structured form of a wide-area measurement system.

A PMU can be a dedicated device, or the PMU function can be incorporated into a DFR (Digital Fault Recorder), PQA (Power Quality Analyzer) or other device.

## Phasor Measurement Technique.

Any pure sinusoidal signal can be presented as phasor with amplitude and phase angle, both representations are illustrated in the animation below:

The PMU output is just the phasor representation of the fundamental frequency.

In the 2011 edition of the C37.118.1 standard, both frequency and ROCOF (Rate Of Change Of Frequency) are introduced as parts of the synchrophasor measurements, and the error limits for frequency and ROCOF in all compliance tests are also defined. Frequency, f, can be derived from the difference between two consecutive phase angles, divide by the given reporting rate,

f = f_{nom} + ∆f

Where,

∆δ-phase angle differences between two consecutive samples

∆t-1/(reporting rate)

For example, 50 samples per second reporting rate yield a value of 20msec. is calculated between two consecutive samples, with adjustment made for wrapping around +180^{0} and -180^{0}. The result, is the offset from the nominals frequency. Therefore the result is added to the nominal frequency (50/60Hz) to get the actual frequency.

## Accuracy of synchrophasor data

Unlike typical scalars power parameters such RMS, Powers and Harmonics, synchrophasor outputs are vectors comprised from both magnitude and phase measurement. Therefore, the errors are consequence of the errors from either the magnitude or the phase, or both. To evaluate the total error of both in a single measured parameter the total vector error (TVE) was introduces in IEEE c37.118-2005 standard. TVE is defined as:

Where and are real and imaginary parts of the estimated (measured) synchrophasor.

## PMU performance classes

The IEEE C37.118.1-2011 introduced two performance classes as well as their corresponding dynamic performance requirements. The P class is mainly for protection and control purposes, which requires fast response, minimum filtering and minimum delay. The M class is mainly used for measurements in the presence of out-of-band signals, which requires greater precision and significant filtering, and allows slower response and longer delay. Some PMU devices can report both M class and P class simultaneously to different targets.

## PMU recorded data

The PMU reporting rate ranges between 10-60 samples per second evenly aligned to hour

(=> min & sec). Higher reporting rates of 100-240 samples per second are allowed and available with advance PMU devices.

In a typical reporting rate of 50 samples/second the amount of data required to record is enormous and requires a well-established communication and server’s infrastructures. While the PMU data is great for Wide Area Protection Systems (WAPS) and for monitor power system dynamics it is lack of information for power quality studies harmonics analysis and other SCADA required parameters.

## Synchrophasor data that includes none fundamental frequencies

According to Fourier series: any periodical signal can be express as sum of simple sine/cosine waves known as harmonics. Hence, extending the PMU technique to none fundamental frequencies will provide us the complete waveform signal in the spectrum domain.

The PQZIP compression algorithm extends the synchrophasor data to none fundamental frequencies. The algorithm evaluate the real and image component of every harmonics up-to the 511^{th} and store changes higher than TVE of 0.1%. This technique compress the data at 1000:1 compression ratio therefore, enable the recording of a continuous waveform signal at high sampling rate. A typical storage requirement for a complete waveform signal of 4 voltage and 4 current is 1GB/month. This means that no other recording device nor database is required since the waveform is the raw data for any given power parameter.

When coupled with Elspec PQSCADA Sapphire, a multi-vendors support power management software, ~5,000 power parameters at any given resolution are calculated for displaying and reporting purposes from the acquired waveform signals.