Instrumentation & Measurement Magazine 23-2 - 27

parameter TVE is the module of the phasor relative estimation
error, FE is the FD estimation error, and RFE is the ROCOF estimation error. For both classes of performances in the above
Standard there are suggested the threshold values for the accuracy parameters under different steady-state, dynamic, and
transient conditions.
A dynamic model-based algorithm which provides accurate phasor measurements is the Taylor-based Weighted Least
Squares (TWLS) algorithm [17], [21]. By means of the TWLS algorithm firstly the phasor p(t) is expressed by Taylor's series
truncated to the 2nd-order terms, i.e.,
	

p ( t ) ≅ p0 + p1t + p2t 2	(4)

Then, the Taylor's coefficients p0, p1, and p2 are estimated by
means of the Weighted Least Squares (WLS) approach. Finally,
the phasor parameters are estimated as [17]:
	

aˆ1 = p0 and φˆ1 = angle { p0 } ,	(5)

{ } ,	(6)

	

Im p p
= 1
FD
2
2π
p0

	

 Im p p∗
Im p1 p0∗ ⋅ Re p1 p0∗
2 0
= 2
−
ROCOF
4
π p 2
p0
0


∗
1 0

{ }

{ } { }  .	(7)



In the literature there have been proposed both complex-valued [17] and real-valued [21] versions for the TWLS
algorithm, which have the same accuracy [21]. Unfortunately,
both of these versions require a high computational burden
mainly due to the calculation of the pseudoinverse matrix involved in the expression of the vector returned by the WLS
approach, and exhibit a low immunity to low order harmonics, especially the 2nd harmonic. To reduce the computational
burden in [21] the Taylor's series coefficients provided by the
real-valued TWLS algorithm have been expressed as a function of Discrete-Time Fourier Transform (DTFT) samples. To
reduce the contribution of the 2nd harmonic the TWLS algorithm should be applied to the waveform with the 2nd
harmonic removal. It is worth noting that in this case the TWLS
algorithm comply with the IEEE Standard C37.118.1-2011 for
both P-class and M-class of performances [21].

Educational Objectives
The goal of this application is to implement the low-complexity real-valued TWLS algorithm proposed in [21] in the
MATLAB environment and to apply it in the case of real-life
single phase power voltages. In addition, a GUI should be developed in the MATLAB environment in which the analyzed
waveform and its spectrum are visualized and the phasor
parameters estimates returned by both algorithms are presented. The above activities were split into two parts which
are performed by the EIS students in two laboratory experiments in the Processors and Acquisition Systems discipline.
April 2020	

Each laboratory experiment has a duration of two hours. In
the first part, the signal acquisition and the implementation
of the real-valued TWLS algorithm [21] are performed. In
the second part, the related GUI is implemented, and the developed phasor measurement system is applied to the single
phase voltages.
There are about 30 EIS students in the first year divided into
two subgroups. In the above laboratory each subgroup is divided into six small groups of two to three students each. The
students should have a good background in signal processing,
MATLAB and LabVIEW programming. At the end of the performed activities the students should gain abilities in:
◗◗ Parameter estimation;
◗◗ Data acquisition by means of an acquisition board
programmed in LabVIEW environment;
◗◗ Signal processing and GUIs development in MATLAB
environment;
◗◗ Phasor measurements.

Description of the Application
The reference frequency f0 used by the TWLS algorithm and
the second harmonic of the analyzed waveform are estimated
by means of the Interpolated Discrete Fourier Transform (IpDFT) algorithm based on the Maximum Sidelobe Decay (MSD)
windows [22], [23]. The above windows are used since they
have the highest sidelobe decay rate among all cosine class
windows [24], which ensures a high rejection of the spectral interference from the disturbance tones such as harmonics and
interharmonics. Also, by using these windows the IpDFT estimators are given by very simple expressions [22], [23].
The experimental setup is shown in Fig. 6a, while a GUI developed by students is presented in Fig. 6b and Fig. 6c.
The experimental setup contains the signal conditioning
circuit and a NI USB-6259 acquisition board. The signal conditioning circuit uses the Texas Instruments ISO 122U isolated
amplifier powered by DCH10515DN7 isolated bipolar dc to dc
converter. It ensures a division ratio between the input and the
output signals equal to 70:1. The signal is acquired and saved
into a file through an executable file obtained by using the LabVIEW environment, and accessed by means of the GUI. Also,
the acquired data are processed by using the GUI.

Lessons Learned
The performed application is very useful for students since
they learn how to develop a complete measurement system.
The problem sometimes encountered in the experiment
was that the TWLS algorithm was not finished until the end of
the first part of the experiment. In this case the finalization of
the algorithm was given as homework.

Conclusions and Future Work
In this paper four recently developed applications from the
Department of Measurements and Optical Electronics, University Politehnica of Timis¸oara, Romania, are presented.
They provide support for several I&M teaching activities.
Also, the related educational objectives and lessons learned

IEEE Instrumentation & Measurement Magazine	27



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