Table 3 Summary of important equations used in different ASPAR schemes
From: A review of single phase adaptive auto-reclosing schemes for EHV transmission lines
Serial | Equation | Detail | Reference |
|---|---|---|---|
1 | varc(t) = Varc sgn [i(t)] \( \mathit{\operatorname{sgn}}\left[i(t)\right]=\left\{\begin{array}{c}+1, if\ i(t)\ge 0\\ {}-1, if\ i(t)<0\end{array}\right. \) | Static arc model | |
2 | \( \frac{d{g}_p}{dt}=\frac{1}{T_p}\left({G}_p-{g}_p\right) \) | Dynamic arc model | |
3 | \( THD\%=\frac{\sqrt{\sum \limits_{h=2}^5{V}_h^2}}{V_1}\ 100\% \) | Total harmonic distortion | |
4 | \( {\varepsilon}_k={X}_k-{\hat{X}}_k \) \( {TAES}_k=\frac{\sum \limits_{k=1}^{N_s}\left|{\varepsilon}_k\right|}{N_s} \) | Error and Time average error signal | [25] |
5 | \( {d}^1\left[n\right]=\sum \limits_{k=0}^{N-1}h(k)f\left(n-k\right) \) \( {a}^1\left[n\right]=\sum \limits_{k=0}^{N-1}g(k)f\left(n-k\right) \) | First level approximation in wavelet packet transform | [38] |
6 | \( {\varPsi}^r=\sum \limits_{k=1}^n\left({C}_{MP}^{r,k}{V}_{\overset{\acute{\mkern6mu}}{M}}^k+{C}_{NQ}^{r,k}{V}_{\overset{\acute{\mkern6mu}}{N}}^k+{D}_{MP}^{r,k}{I}_M^k+{D}_{NQ}^{r,k}{I}_N^k\right) \) | Index value calculation in synchrophasor based ASPAR scheme | [51] |
7 | Pk(1) =  max [(Pk − 1(1) + Vk(1) − Vdyn − k), 0] Pk(2) =  max [(Pk − 1(2) + Vk(2) − Vdyn − k), 0] | Basic ACUSUM algorithm for voltage amplitude detection | |
8 | \( {X}_k={\sum}_{n=0}^{N-1}{x}_n{e}^{-i2\pi kn/N}\ k=0,\dots ..,N-1 \) \( {X}_k={\sum}_{n=0}^{N-1}{x}_n{e}^{-\frac{2\pi i}{N} kn} \) | For calculating FFT and DFT of a signal |