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Table 1 Feature extraction formulas used for the EDR

From: Data processing of high-rate low-voltage distribution grid recordings for smart grid monitoring and analysis

Value

Formula

Frequency

\( f=\frac{1}{T} \)

Average rectified value (ARV)

\( {X}_{\mathrm{ARV}}=\frac{1}{T}{\displaystyle \underset{t_0}{\overset{t_0+T}{\int }}}\left|x(t)\right|dt \)

Root mean square (RMS)

\( {X}_{\mathrm{RMS}}=\sqrt{\frac{1}{T}{\displaystyle \underset{t_0}{\overset{t_0+T}{\int }}}x{(t)}^2dt} \)

Offset

\( {X}_{\mathrm{offset}}=\frac{1}{T}{\displaystyle \underset{t_0}{\overset{t_0+T}{\int }}}x(t)dt \)

Maximum value

\( {X}_{\max }={ \max}_{\left\{{t}_0..{t}_0+T\right\}}\left(x(t)\right) \)

Minimum value

\( {X}_{\min }={ \min}_{\left\{{t}_0..{t}_0+T\right\}}\left(x(t)\right) \)

Amplitude

\( \widehat{X}=\frac{\left({X}_{\max }-{X}_{\min}\right)}{2} \)

Crest factor

\( C = \frac{X_{\max }}{X_{\mathrm{RMS}}} \)

Total harmonic distortion

\( \mathrm{T}\mathrm{H}\mathrm{D} = \frac{\sqrt{{\left({H}_2\right)}^2+{\left({H}_3\right)}^2+{\left({H}_4\right)}^2+\dots +{\left({H}_n\right)}^2\ }}{H_1} \)

Phase

\( \varphi =\frac{360}{T}*\left({t}_{\max }-{t}_0\right) \)

Harmonics 0 to 50

H i  = DFT8192| i = 0..50

Active power*

\( P=\frac{1}{T}{\displaystyle \underset{t_0}{\overset{t_0+T}{\int }}}V(t)*I(t)dt \)

Apparent power*

S = V RMS * I RMS

Reactive power*

\( Q=\sqrt{S^2-{P}^2} \)

  1. Values marked with an asterisk are only used for combined voltage and current configurations.