Phasor technology and the Phasor Measurement Unit (PMU) [2] is a valuable measurement technology in the power system for monitoring the condition of transmission and distribution networks. The phasor of the 50 Hz signal component is obtained based on the digitally sampled analog voltage waveform that is synchronized with the clocking signal from the GPS receiver in distributed locations as shown in Figure 2 . The accuracy of a phasor estimate from a PMU is measured in terms of the Total Vector Error (TVE). The TVE for an operational PMU under steady-state conditions should not exceed the 1% or 0.01 pu mark. For purposes of determining the phase angle error of the PMU, an alternating Current (AC) signals can be represented by;

$x\left(t\right)=X_m\text{cos}\left(\omega t+\varnothing \right)$ (1)

where $X_m$is the signal’s peak value and $\omega =2\pi f$ is the angular frequency and $\varnothing$ is the initial phase-angle.

The signal’s phasor representation can be written as:

$X=\frac{X_m}{\sqrt{2}}{e}^{i\varnothing }=\frac{X_m}{\sqrt{2}}\left(\cos \varnothing +i\sin \varnothing \right)=X_r+i{X}_i$ (2)

where $\frac{X_m}{\sqrt{2}}$ is the RMS value, $X_r$ is the real part and $i{X}_i$ is the imaginary part of the signal [10] .

When the signal is in this form the amplitude and phase can be calculate by using the following equations [11] ;

$X_{amp}=\sqrt{{\left(X_{rms}\cos \varnothing \right)}^2+{\left(X_{rms}i\sin \varnothing \right)}^2}=\sqrt{X_r^2+i{X}_i^2}$ (3)

$\varnothing \left(t\right)={\tan }^{-1}\frac{\sin \varnothing }{\cos \varnothing }={\tan }^{-1}\frac{X_i}{X_r}$ (4)

Assuming no magnitude errors in the synchro-phasor estimate, then a 1% TVE corresponds to a phase angle error of ${0.573}^0$. In terms of time, this is about 31.8 µs at the system frequency of 50 Hz [5] . In order to achieve a TVE of below 1% or timing errors of less than 31.8 µs in a 50 Hz system, only GPS, IRIG-B and IEEE 1588 PTP is recommended in synchro-phasor applications [5] . For constant amplitude signals, the phase angle error in degrees is given by:

$\text{Phase}\text{angle}(˚)=\left(\frac{\text{Time}\text{error}\left(s\right)}{\text{Period}\left(s\right)}\right)\times 360$ (5)

The input data of the PMU are a component obtained from the electrical signals from the power systems; these are 3-phase voltages and currents. From the perspective of transmission systems, voltages and currents signals are obtained from the substation equipment—the secondary of the Voltage Transformer (VT) and a Current Transformer (CT). The input signals to the signal acquisition and condition module is stepped-down to match the low-power dissipation components of the module. The three phase voltages of the VT are applied to the PMU. Most of the microcontroller ADC take voltages of up to only 3.3 V [12] . The data acquisition module is responsible for obtaining voltage or current waveforms data for the test. The Data Acquisition and Conditioning Module (DAM) can be implemented in the form of either Hardware or Software. Sampling of the three phase signals will be initiated by the Microprocessor after receiving 1 pulse per second (1 PPS) signal from the GPS module [13] .

The three-phase signal acquisition and conditioning module is separated into two sections: The Line voltage measurement interface and Line frequency measurement interface.

The Phase Estimation Module (PEM) is one of the major component of the PMU implementation. It is responsible for applied voltage phase angle processing by means of the phase estimation algorithm that runs on it. The algorithm can be of two types; Static State Estimation or Dynamic State Estimation.

In Static State Estimation (SSE), estimates are obtained from the present state measurements made at the system buses at a more significant interval of time, ranging from few seconds to minutes [14] . To reduce the complexity of computation associated with static state estimation, the estimates are updated only in a few minutes. This brings about a limitation of the SSE – that it cannot be used as a real–time monitoring tool of the power system [15] . The estimates obtained in SSE are not real time and simply illustrates the quasi-static representation of the power system.

In Dynamic State Estimation (DSE), time-synchronized data from PMUs is used to provide exact and real-time state of a power system. As a consequence, an erroneous or a missing synchronization may affect not only the reporting time reference and thus the correct aggregation with other PMU measurements, but also the estimated quantities, particularly the phase angle and its derivatives [7] . That is, if the state vector at an instant of time “t” is known, then the dynamic state estimation model can be used to predict the state vector of the power system at the next time instant, “t +1” [6] . One such promising alternative is soft synchronized sampling. This approach corrects timing errors between two consecutive PPS signals using interpolation techniques, eliminating the need for frequent adjustments of the ADC [8] . The disadvantages of DSE and SSE are highlighted in Table 1 below.

Accurate time synchronization is required to offer the time-stamp of the signals taken and managed by the PMU. If a reliable GPS signal is available, the Analogue-to-digital converter (ADC) is used to convert the voltage waveform into numerical values sampled at controlled intervals by an independent local oscillator. In this case, the sampling clock is not locked to the GPS signal. The PMU should perform all the measurements and report the results at a constant reporting rate, expressed in terms of frames per second [16] . Devices based on synchrophasor technology must handle measurements at least at the mandatory reporting rates of 10, 25, and 50 frames per second [13] . However, the sampling data appears to be in synchronism with GPS signal because of the running function on the microprocessor controlling the ADC. Inherently, a clock drift occurs in this approach. Therefore, interpolation of sample points to fit specified time values is recorded and utilized by the phasor estimation algorithm to correct for sampling clock drift.

The Data Acquisition can also be constructed such that internally generated sampling clock is synchronized with the GPS signal. This ensures that the ADC samples the waveforms at predetermined instances thereby ensuring that there is no sampling clock drift.

The communication interface module provides the external communication functions of the device. When the proposed PMU was implemented, a reference implementation of IEEE C37.118.2, but the Open PMU project prefers a more open communication module with security built into its design.

Microprocessor after receiving 1 pulse per second (1 PPS) signal from the GPS module [17] .

The three-phase signal acquisition and conditioning module is separated into two sections: The Line voltage measurement interface and Line frequency measurement interface.

DAM implementation is achieved by means of an analogue-to-digital converter (ADC) which is normally connected to an external time source. This approach has the advantage of high process speed compared to the software implementation method.

In this application, a virtual sampling procedure in a numerical environment is used, e.g., MATLAB/Simulink, PSSE/Python, or LabVIEW.