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Role of microphasor measurement unit Chapter | 7 185

2. Small line length: The distances in distribution system are smaller than
transmission system. Hence, both phase angle as well as magnitude dif-
ference of electrical quantities between nodes are much smaller leading
to small power flows. The phase angle difference in a distribution system
is typically in the range of tenths to hundredths of a degree unlike trans-
mission system where the difference is in the range of degrees.
Moreover, the difference is much smaller than nonrandom measurement
errors and measurement noise. This calls for higher precision measure-
ment in a µPMU.
3. Noise corruption: The signals in a distribution system are heavily cor-
rupted with noise. This noise occurs due to the proximity of numerous
devices connected closely in the distribution system. These devices
include loads, transformer, capacitor banks, and switchgear that intro-
duce harmonics and transients. Thus the signals obtained in the distribu-
tion system need to be accurately denoised through appropriate
methods.

7.3 Synchrophasor technology
Synchrophasor technology refers to calculation of phasor from measured
data samples using a standard common time reference. This technology was
first introduced in PMU [16]. The PMUs used it to measure voltage, current,
etc. at different locations of the transmission system but with a common
time reference.
To understand the underlying philosophy of phasor generation, consider
an ideal sinusoidal signal as in Eq. (7.2), where ω is the frequency of the sig-
nal (in radians per second), θ is the phase angle (in rad), and X max is the
maximum magnitude of the signal [16].

xðtÞ 5 X max cosðωt 1 θÞ ð7:2Þ
Expressing the cosine term in exponent form, Eq. (7.2) can be written as
follows:
iωt iθ
xtðÞ 5 ReðX max e iðωt1θÞ Þ 5 Re½ e X max e Š ð7:3Þ
Ignoring the term e i(ωt) , Eq. (7.3) can be represented by a complex num-
ber X p as in the following equation, X p being the phasor representation:

X max iθ
X p 5 p ffiffiffi e 5 X rms ½cosθ 1 isinθŠ ð7:4Þ
2
An ideal sinusoid signal along with its phasor representation is depicted
in Fig. 7.3A and B, respectively [16]. The phase angle of the phasor depends
on the instant at which t 5 0. It is the angle between the axis t 5 0 and the
instant at which the signal reaches its maximum. The length of the phasor is