Basic Calculation Reference (OPT-POWER-BASIC)¶

Table 6 Legend¶
Symbol	Equation	Description
$SR$	–	Samplerate
$NP$	–	Number of Power Phases
$N$	$\frac{SR}{f_{fund}}$	Number of Samples
$T_{int}$	–	Integration Time, Time of Visualisation

Voltage (U)¶

U_tRMS¶

This is the Power Group average true RMS Voltage

$\begin{aligned} U_{tRMS} &= \frac{1}{NP} \sum_{i=1}^{NP} U[i]_{tRMS} & Unit: \mathbf{V} \end{aligned}$

U[i]_tRMS¶

This is the Power Phase number i True RMS Voltage

$\begin{aligned} U[i]_{tRMS} &= \sqrt{\frac{1}{N} \sum_{n=0}^{N} u_i[n]^2} & Unit: \mathbf{V} \end{aligned}$

U[ij]_tRMS¶

This is the Line-Line ij True RMS Voltage. This channel is only available in 3-Phase Power Configurations.

$\begin{aligned} U[ij]_{tRMS} &= \sqrt{\frac{1}{N} \sum_{n=0}^{N} \left( u_i[n]-u_j[n] \right) ^2} & Unit: \mathbf{V} \end{aligned}$

U[i]_tAVG¶

This is the Power Phase number i Average Voltage

$\begin{aligned} U[i]_{tAVG} &= \frac{1}{N} \sum_{n=0}^{N} u_i[n] & Unit: \mathbf{V} \end{aligned}$

U[i]_tPP¶

This is the Power Phase number i Peak-Peak Voltage

$\begin{aligned} U[i]_{tPP} &= \max_{0 \rightarrow N} u_i[n] - \min_{0 \rightarrow N} u_i[n] & Unit: \mathbf{V} \end{aligned}$

U_fundRMS¶

This is the Power Group average fundamental effective Voltage

$\begin{aligned} U_{fundRMS} &= \frac{1}{NP} \sum_{i=1}^{NP} U[i]_{fundRMS} & Unit: \mathbf{V} \end{aligned}$

U[i]_fundRMS¶

This is the Power Phase number i Fundamental Effective Voltage.

$\begin{aligned} U[i]_{fundRMS} &= \sqrt{Re\left\lbrace \underline{U}[i]_{fund} \right\rbrace ^2 + Im \left\lbrace \underline{U}[i]_{fund}\right\rbrace ^2 } & Unit: \mathbf{V} \end{aligned}$

U[ij]_fundRMS¶

This is the Line-Line ij Fundamental Effective Voltage.

$\begin{aligned} U[ij]_{fundRMS} &= \sqrt{Re\left\lbrace \underline{U}[i]_{fund} - \underline{U}[j]_{fund} \right\rbrace ^2 + Im \left\lbrace \underline{U}[i]_{fund} - \underline{U}[j]_{fund}\right\rbrace ^2 } & Unit: \mathbf{V} \end{aligned}$

U[i]_fundPHI¶

This is the Power Phase number i Fundamental Voltage Phase Angle.

$\begin{aligned} U[i]_{fundPHI} &= arctan2 \left( Im\left\lbrace \underline{U}[i]_{fund} \right\rbrace , Re \left\lbrace \underline{U}[i]_{fund}\right\rbrace \right) & Unit: \mathbf{deg} (^\circ) \end{aligned}$

U[ij]_fundPHI¶

This is the Line-Line ij Fundamental Voltage Phase Angle.

$\begin{aligned} U[i]_{fundPHI} &= arctan2 \left( Im\left\lbrace \underline{U}[i]_{fund} - \underline{U}[j]_{fund} \right\rbrace , Re \left\lbrace \underline{U}[i]_{fund} - \underline{U}[j]_{fund}\right\rbrace \right) & Unit: \mathbf{deg} (^\circ) \end{aligned}$

U_fundRMS_SYM+¶

This is the Power Group Fundamental Voltage Positive Sequence Magnitude. This channel is only available in 3-Phase Power Group.

$\begin{aligned} a &= e^{j \frac{2 \pi}{NP}} \\ \underline{U}^+ &= \frac{1}{NP} \sum_{i=1}^{NP} U[i]_{fundRMS} \cdot e^{j \cdot U[i]_{fundPHI}} \cdot a^{(i-1)} \end{aligned}$

$\begin{aligned} U_{fundRMS\_SYM+} &= \sqrt{Re\left\lbrace \underline{U}^+ \right\rbrace ^2 + Im\left\lbrace \underline{U}^+ \right\rbrace ^2} & Unit: \mathbf{V} \end{aligned}$

U_fundRMS_SYM-¶

This is the Power Group Fundamental Voltage Negative Sequence Magnitude. This channel is only available with a minimum of two phases configured.

$\begin{aligned} a &= e^{j \frac{2 \pi}{NP}} \\ \underline{U}^- &=\frac{1}{NP} \sum_{i=1}^{NP} U[i]_{fundRMS} \cdot e^{j \cdot U[i]_{fundPHI}} \cdot a^{(NP+1-i)} \end{aligned}$

$\begin{aligned} U_{fundRMS\_SYM-} &= \sqrt{Re\left\lbrace \underline{U}^- \right\rbrace ^2 + Im\left\lbrace \underline{U}^- \right\rbrace ^2} & Unit: \mathbf{V} \end{aligned}$

U_fundRMS_SYM0¶

This is the Power Group Fundamental Voltage Zero Sequence Magnitude. This channel is only available in 3-Phase Power Group.

$\begin{aligned} a &= e^{j \frac{2 \pi}{NP}} \\ \underline{U}^0 &=\frac{1}{NP} \sum_{i=1}^{NP} U[i]_{fundRMS} \cdot e^{j \cdot U[i]_{fundPHI}} \end{aligned}$

$\begin{aligned} U_{fundRMS\_SYM0} &= \sqrt{Re\left\lbrace \underline{U}^0 \right\rbrace ^2 + Im\left\lbrace \underline{U}^0 \right\rbrace ^2} & Unit: \mathbf{V} \end{aligned}$

U_fundRMS_SYM¶

This is the Power Group Fundamental Voltage Symmetry.

$\begin{aligned} U_{fundRMS\_SYM} &= \frac{U_{fundRMS\_SYM+} - U_{fundRMS\_SYM-}}{U_{fundRMS\_SYM+} + U_{fundRMS\_SYM-}} & Unit: \mathbf{None} \end{aligned}$

U_fund_UNBAL+¶

This is the Power Group Fundamental Voltage Positive Sequence Unbalance.

$\begin{aligned} U_{fund\_UNBAL+} &= \frac{U_{fundRMS} - U_{fundRMS\_SYM+}}{U_{fundRMS}} \cdot 100\% & Unit: \mathbf{\%} \end{aligned}$

U_fund_UNBAL-¶

This is the Power Group Fundamental Voltage Negative Sequence Unbalance.

$\begin{aligned} U_{fund\_UNBAL-} &= \frac{U_{fundRMS\_SYM-}}{U_{fundRMS\_SYM+}} \cdot 100\% & Unit: \mathbf{\%} \end{aligned}$

U_fund_UNBAL0¶

This is the Power Group Fundamental Voltage Zero Sequence Unbalance.

$\begin{aligned} U_{fund\_UNBAL0} &= \frac{U_{fundRMS\_SYM0}}{U_{fundRMS\_SYM+}} \cdot 100\% & Unit: \mathbf{\%} \end{aligned}$

U_fundCOS_SYM+¶

The Real part of the fourier coefficients of the signal is. (F-1 in FGW-TG3 Annex F)

$\begin{aligned} U[i]_{fund\_cos} & = \frac{2}{N} \sum_{n=-N-1}^{0} u_i[n] \cdot cos(2\cdot\pi \cdot F_{fund} \cdot \frac{n}{SR}) & Unit: \mathbf{V} \end{aligned}$

The Imaginary part of the fourier coefficients of the signal is. (F-2 in FGW-TG3 Annex F)

$\begin{aligned} U[i]_{fund\_sin} & = \frac{2}{N} \sum_{n=-N-1}^{0} u_i[n] \cdot sin(2\cdot\pi \cdot F_{fund} \cdot \frac{n}{SR}) & Unit: \mathbf{V} \end{aligned}$

Using both fourier coefficients, this is the real vector component of the Positive Voltage Sequence.

$\begin{aligned} U_{fundCOS\_SYM+} = &\frac{1}{6} \left( 2 \cdot U1_{fund\_cos} - U2_{fund\_cos} - U3_{fund\_cos} - \right. \nonumber \\ & \left. \sqrt{3} \left(U3_{fund\_sin} - U2_{fund\_sin} \right) \right) & Unit: \mathbf{V} \end{aligned}$

U_fundSIN_SYM+¶

This is the imaginary vector component of the Positive Voltage Sequence.

$\begin{aligned} U_{fundSIN\_SYM+} = &\frac{1}{6} \left( 2 \cdot U1_{fund\_sin} - U2_{fund\_sin} - U3_{fund\_sin} - \right. \nonumber \\ & \left. \sqrt{3} \left(U2_{fund\_cos} - U3_{fund\_cos} \right) \right) & Unit: \mathbf{V} \end{aligned}$

U_fundPHI_SYM+¶

This is the phase angle of the Positive Voltage Sequence.

$\begin{aligned} U_{fundPHI\_SYM+} & = arctan2(U_{fundSIN\_SYM+} , U_{fundCOS\_SYM+}) & Unit: \mathbf{deg}(^\circ) \end{aligned}$

U_fundCOS_SYM-¶

This is the real vector component of the Negative Voltage Sequence.

$\begin{aligned} U_{fundCOS\_SYM-} = &\frac{1}{6} \left( 2 \cdot U1_{fund\_cos} - U2_{fund\_cos} - U3_{fund\_cos} - \right. \nonumber \\ & \left. \sqrt{3} \left(U2_{fund\_sin} - U3_{fund\_sin} \right) \right) & Unit: \mathbf{V} \end{aligned}$

U_fundSIN_SYM-¶

This is the imaginary vector component of the Negative Voltage Sequence.

$\begin{aligned} U_{fundSIN\_SYM-} = &\frac{1}{6} \left( 2 \cdot U1_{fund\_sin} - U2_{fund\_sin} - U3_{fund\_sin} - \right. \nonumber \\ & \left. \sqrt{3} \left(U3_{fund\_cos} - U2_{fund\_cos} \right) \right) & Unit: \mathbf{V} \end{aligned}$

U_fundPHI_SYM-¶

This is the phase angle of the Negative Voltage Sequence.

$\begin{aligned} U_{fundPHI\_SYM-} & = arctan2(U_{fundSIN\_SYM-} , U_{fundCOS\_SYM-}) & Unit: \mathbf{deg}(^\circ) \end{aligned}$

U_fundCOS_SYM0¶

Using the fourier coefficients, this is the real vector component of the Zero Voltage Sequence.

$\begin{aligned} U_{fundCOS\_SYM0} &= \frac{1}{3 \cdot \sqrt{2} } \left( U1_{fund\_cos} + U2_{fund\_cos} + U3_{fund\_cos}\right) & Unit: \mathbf{V} \end{aligned}$

U_fundSIN_SYM0¶

Using the fourier coefficients, this is the imaginary vector component of the Zero Voltage Sequence.

$\begin{aligned} U_{fundSIN\_SYM0} &= \frac{-1}{3 \cdot \sqrt{2} } \left( U1_{fund\_sin} + U2_{fund\_sin} + U3_{fund\_sin}\right) & Unit: \mathbf{V} \end{aligned}$

Current (I)¶

I_tRMS¶

This is the Power Group average true RMS Current

$\begin{aligned} I_{tRMS} &= \frac{1}{NP} \sum_{i=1}^{NP} I[i]_{tRMS} & Unit: \mathbf{A} \end{aligned}$

I[i]_tRMS¶

This is the Power Phase number i True RMS Current

$\begin{aligned} I[i]_{tRMS} &= \sqrt{\frac{1}{N} \sum_{n=0}^{N} i_i[n]^2} & Unit: \mathbf{A} \end{aligned}$

I[i]_tAVG¶

This is the Power Phase number i Average Current

$\begin{aligned} I[i]_{tAVG} &= \frac{1}{N} \sum_{n=0}^{N} i_i[n] & Unit: \mathbf{A} \end{aligned}$

I[i]_tPP¶

This is the Power Phase number i Peak-Peak Current

$\begin{aligned} I[i]_{tPP} &= \max_{0 \rightarrow N} i_i[n] - \min_{0 \rightarrow N} i_i[n] & Unit: \mathbf{A} \end{aligned}$

I_fundRMS¶

This is the Power Group average fundamental effective Current

$\begin{aligned} I_{fundRMS} &= \frac{1}{NP} \sum_{i=1}^{NP} I[i]_{fundRMS} & Unit: \mathbf{A} \end{aligned}$

I[i]_fundRMS¶

This is the Power Phase number i Fundamental Effective Current.

$\begin{aligned} I[i]_{fundRMS} &= \sqrt{Re\left\lbrace I[i]_{fund} \right\rbrace ^2 + Im \left\lbrace I[i]_{fund}\right\rbrace ^2 } & Unit: \mathbf{A} \end{aligned}$

I[i]_fundPHI¶

This is the Power Phase number i Fundamental Current Phase Angle.

$\begin{aligned} I[i]_{fundPHI} &= arctan2 \left( Im\left\lbrace I[i]_{fund} \right\rbrace , Re \left\lbrace I[i]_{fund}\right\rbrace \right) & Unit: \mathbf{deg} (^\circ) \end{aligned}$

I_fundRMS_SYM+¶

This is the Power Group Fundamental Current Positive Sequence Magnitude. This channel is only available in 3-Phase Power Group.

$\begin{aligned} a &= e^{j \frac{2 \pi}{NP}} \\ \underline{I}^+ &= \frac{1}{NP} \sum_{i=1}^{NP} I[i]_{fundRMS} \cdot e^{j \cdot I[i]_{fundPHI}} \cdot a^{(i-1)} \end{aligned}$

$\begin{aligned} I_{fundRMS\_SYM+} &= \sqrt{Re\left\lbrace \underline{I}^+ \right\rbrace ^2 + Im\left\lbrace \underline{I}^+ \right\rbrace ^2} & Unit: \mathbf{A} \end{aligned}$

I_fundRMS_SYM-¶

This is the Power Group Fundamental Current Negative Sequence Magnitude. This channel is only available in 3-Phase Power Group.

$\begin{aligned} a &= e^{j \frac{2 \pi}{NP}} \\ \underline{I}^- &=\frac{1}{NP} \sum_{i=1}^{NP} I[i]_{fundRMS} \cdot e^{j \cdot I[i]_{fundPHI}} \cdot a^{(NP+1-i)} \end{aligned}$

$\begin{aligned} I_{fundRMS\_SYM-} &= \sqrt{Re\left\lbrace \underline{I}^- \right\rbrace ^2 + Im\left\lbrace \underline{I}^- \right\rbrace ^2} & Unit: \mathbf{A} \end{aligned}$

I_fundRMS_SYM0¶

This is the Power Group Fundamental Current Zero Sequence Magnitude. This channel is only available in 3-Phase Power Group.

$\begin{aligned} a &= e^{j \frac{2 \pi}{NP}} \\ \underline{I}^0 &=\frac{1}{NP} \sum_{i=1}^{NP} I[i]_{fundRMS} \cdot e^{j \cdot I[i]_{fundPHI}} \end{aligned}$

$\begin{aligned} I_{fundRMS\_SYM0} &= \sqrt{Re\left\lbrace \underline{I}^0 \right\rbrace ^2 + Im\left\lbrace \underline{I}^0 \right\rbrace ^2} & Unit: \mathbf{A} \end{aligned}$

I_fundRMS_SYM¶

This is the Power Group Fundamental Current Symmetry.

$\begin{aligned} I_{fundRMS\_SYM} &= \frac{I_{fundRMS\_SYM+} - I_{fundRMS\_SYM-}}{I_{fundRMS\_SYM+} + I_{fundRMS\_SYM-}} & Unit: \mathbf{None} \end{aligned}$

I_fund_UNBAL+¶

This is the Power Group Fundamental Current Positive Sequence Unbalance.

$\begin{aligned} I_{fund\_UNBAL+} &= \frac{I_{fundRMS} - I_{fundRMS\_SYM+}}{I_{fundRMS}} \cdot 100\% & Unit: \mathbf{\%} \end{aligned}$

I_fund_UNBAL-¶

This is the Power Group Fundamental Current Negative Sequence Unbalance.

$\begin{aligned} I_{fund\_UNBAL-} &= \frac{I_{fundRMS\_SYM-}}{I_{fundRMS\_SYM+}} \cdot 100\% & Unit: \mathbf{\%} \end{aligned}$

I_fund_UNBAL0¶

This is the Power Group Fundamental Current Zero Sequence Unbalance.

$\begin{aligned} I_{fund\_UNBAL0} &= \frac{I_{fundRMS\_SYM0}}{I_{fundRMS\_SYM+}} \cdot 100\% & Unit: \mathbf{\%} \end{aligned}$

I_fundCOS_SYM+¶

The Real part of the fourier coefficients of the signal is. (F-1 in FGW-TG3 Annex F)

$\begin{aligned} I[i]_{fund\_cos} & = \frac{2}{N} \sum_{n=-N-1}^{0} i_i[n] \cdot cos(2\cdot\pi \cdot F_{fund} \cdot \frac{n}{SR}) & Unit: \mathbf{A} \end{aligned}$

The Imaginary part of the fourier coefficients of the signal is. (F-2 in FGW-TG3 Annex F)

$\begin{aligned} I[i]_{fund\_sin} & = \frac{2}{N} \sum_{n=-N-1}^{0} i_i[n] \cdot sin(2\cdot\pi \cdot F_{fund} \cdot \frac{n}{SR}) & Unit: \mathbf{A} \end{aligned}$

Using both fourier coefficients, this is the real vector component of the Positive Voltage Sequence.

$\begin{aligned} I_{fundCOS\_SYM+} = &\frac{1}{6} \left( 2 \cdot I1_{fund\_cos} - I2_{fund\_cos} - I3_{fund\_cos} - \right. \nonumber \\ & \left. \sqrt{3} \left(I3_{fund\_sin} - I2_{fund\_sin} \right) \right) & Unit: \mathbf{A} \end{aligned}$

I_fundSIN_SYM+¶

This is the imaginary vector component of the Positive Voltage Sequence.

$\begin{aligned} I_{fundSIN\_SYM+} = &\frac{1}{6} \left( 2 \cdot I1_{fund\_sin} - I2_{fund\_sin} - I3_{fund\_sin} - \right. \nonumber \\ & \left. \sqrt{3} \left(I2_{fund\_cos} - I3_{fund\_cos} \right) \right) & Unit: \mathbf{A} \end{aligned}$

I_fundCOS_SYM-¶

This is the real vector component of the Negative Voltage Sequence.

$\begin{aligned} I_{fundCOS\_SYM-} = &\frac{1}{6} \left( 2 \cdot I1_{fund\_cos} - I2_{fund\_cos} - I3_{fund\_cos} - \right. \nonumber \\ & \left. \sqrt{3} \left(I2_{fund\_sin} - I3_{fund\_sin} \right) \right) & Unit: \mathbf{A} \end{aligned}$

I_fundSIN_SYM-¶

This is the imaginary vector component of the Negative Voltage Sequence.

$\begin{aligned} I_{fundSIN\_SYM-} = &\frac{1}{6} \left( 2 \cdot I1_{fund\_sin} - I2_{fund\_sin} - I3_{fund\_sin} - \right. \nonumber \\ & \left. \sqrt{3} \left(I3_{fund\_cos} - I2_{fund\_cos} \right) \right) & Unit: \mathbf{A} \end{aligned}$

I_fundCOS_SYM0¶

Using the fourier coefficients, this is the real vector component of the Zero Voltage Sequence.

$\begin{aligned} I_{fundCOS\_SYM0} &= \frac{1}{3 \cdot \sqrt{2} } \left( I1_{fund\_cos} + I2_{fund\_cos} + I3_{fund\_cos}\right) & Unit: \mathbf{A} \end{aligned}$

I_fundSIN_SYM0¶

Using the fourier coefficients, this is the imaginary vector component of the Zero Voltage Sequence.

$\begin{aligned} I_{fundSIN\_SYM0} &= \frac{-1}{3 \cdot \sqrt{2} } \left( I1_{fund\_sin} + I2_{fund\_sin} + I3_{fund\_sin}\right) & Unit: \mathbf{A} \end{aligned}$

Active Power (P)¶

P_t¶

This is the Power Group Overall active Power.

$\begin{aligned} P_{t} &= \sum_{i=1}^{NP} P[i]_{t} & Unit: \mathbf{W} \end{aligned}$

P[i]_t¶

This is the Power Phase number i active Power.

$\begin{aligned} P[i]_{t} &= \frac{1}{N} \sum_{n=0}^{N} u_i[n] \cdot i_i[n] & Unit: \mathbf{W} \end{aligned}$

P_fund¶

This is the Power Group Overall fundamental active Power.

$\begin{aligned} P_{fund} &= \sum_{i=1}^{NP} P[i]_{fund} & Unit: \mathbf{W} \end{aligned}$

P[i]_fund¶

This is the Power Phase number i fundamental active Power.

$\begin{aligned} P[i]_{fund} &= U[i]_{fundRMS} \cdot I[i]_{fundRMS} \cdot cos \left( P[i]_{fundPHI} \right) & Unit: \mathbf{W} \end{aligned}$

P[i]_fundPHI¶

This is the Power Phase number i fundamental Power Phase Angle.

$\begin{aligned} P[i]_{fundPHI} &= U[i]_{fundPHI} - I[i]_{fundPHI} & Unit: \mathbf{deg} (^\circ) \end{aligned}$

Reactive Power (Q)¶

Q_t¶

This is the Power Group Overall reactive Power.

$\begin{aligned} Q_{t} &= s \cdot \sqrt{S_t^2 - P_t^2} \hspace{3em} s = \begin{cases} 1 & \quad \text{if } Q_{fund} > 0\\ -1 & \quad \text{if } Q_{fund} <= 0\\ \end{cases} & Unit: \mathbf{var} \end{aligned}$

Q[i]_t¶

This is the Power Phase number i reactive Power.

$\begin{aligned} Q[i]_{t} &= s \cdot \sqrt{S[i]_t^2 - P[i]_t^2} \hspace{3em} s = \begin{cases} 1 & \quad \text{if } Q_{fund} > 0\\ -1 & \quad \text{if } Q_{fund} <= 0\\ \end{cases} & Unit: \mathbf{var} \end{aligned}$

Q_fund¶

This is the Power Group Overall fundamental reactive Power.

$\begin{aligned} Q_{fund} &= \sum_{i=1}^{NP} Q[i]_{fund} & Unit: \mathbf{var} \end{aligned}$

Q[i]_fund¶

This is the Power Phase number i fundamental reactive Power.

$\begin{aligned} Q[i]_{fund} &= U[i]_{fundRMS} \cdot I[i]_{fundRMS} \cdot sin \left( P[i]_{fundPHI} \right) & Unit: \mathbf{var} \end{aligned}$

Apparent Power (S)¶

S_t¶

This is the Power Group Overall apparent Power.

$\begin{aligned} S_{t} &= \sum_{i=1}^{NP} S[i]_{t} & Unit: \mathbf{VA} \end{aligned}$

S[i]_t¶

This is the Power Phase number i apparent Power.

$\begin{aligned} S[i]_{t} &= U[i]_{tRMS} \cdot I[i]_{tRMS} & Unit: \mathbf{VA} \end{aligned}$

S_fund¶

This is the Power Group Overall fundamental apparent Power.

$\begin{aligned} S_{fund} &= \sum_{i=1}^{NP} S[i]_{fund} & Unit: \mathbf{VA} \end{aligned}$

S[i]_fund¶

This is the Power Phase number i fundamental apparent Power.

$\begin{aligned} S[i]_{fund} &= U[i]_{fundRMS} \cdot I[i]_{fundRMS} & Unit: \mathbf{VA} \end{aligned}$

Power Factor (PF)¶

PF_t¶

This is the Power Group Overall Power Factor

$\begin{aligned} PF_t &= \frac{P_t}{S_t} & Unit: \mathbf{None} \end{aligned}$

PF[i]_t¶

This is the Power Phase number i Power Factor.

$\begin{aligned} PF[i]_t &= \frac{P[i]_t}{S[i]_t} & Unit: \mathbf{None} \end{aligned}$

PF_fund¶

This is the Power Group Overall fundamental Power Factor.

$\begin{aligned} PF_{fund} &= \frac{P_{fund}}{S_{fund}} & Unit: \mathbf{None} \end{aligned}$

PF[i]_fund¶

This is the Power Phase number i fundamental Power Factor.

$\begin{aligned} PF[i]_{fund} &= \frac{P[i]_{fund}}{S[i]_{fund}} & Unit: \mathbf{None} \end{aligned}$

Energy (W)¶

W_t¶

This is the Power Group Overall active Energy.

$\begin{aligned} W_{t} &= \sum_{i=1}^{NP} W[i]_{t} & Unit: \mathbf{Wh} \end{aligned}$

W[i]_t¶

This is the Power Phase number i active Energy.

$\begin{aligned} W[i]_{t} &= \sum_{k=0}^{T_{int}} P[i]_{t,k} \cdot \frac{N}{SR} \cdot \frac{1}{3600} & Unit: \mathbf{Wh} \end{aligned}$

W_t+¶

This is the Power Group Overall positive aggregated active Energy.

$\begin{aligned} W_{t+} &= \sum_{i=1}^{NP} W[i]_{t+} & Unit: \mathbf{Wh} \end{aligned}$

W[i]_t+¶

This is the Power Phase number i positive aggregated active Energy.

$\begin{aligned} W[i]_{t+} &= \sum_{k=0}^{T_{int}} \frac{N}{SR} \cdot \frac{1}{3600} \begin{cases} P[i]_{t,k} & \quad \text{if } P[i]_{t,k} > 0\\ 0 & \quad \text{if } P[i]_{t,k} <= 0\\ \end{cases} & Unit: \mathbf{Wh} \end{aligned}$

W_t-¶

This is the Power Group Overall negative aggregated active Energy.

$\begin{aligned} W_{t-} &= \sum_{i=1}^{NP} W[i]_{t-} & Unit: \mathbf{Wh} \end{aligned}$

W[i]_t-¶

This is the Power Phase number i negative aggregated active Energy.

$\begin{aligned} W[i]_{t-} &= \sum_{k=0}^{T_{int}} \frac{N}{SR} \cdot \frac{1}{3600} \begin{cases} 0 & \quad \text{if } P[i]_{t,k} > 0\\ P[i]_{t,k} & \quad \text{if } P[i]_{t,k} <= 0\\ \end{cases} & Unit: \mathbf{Wh} \end{aligned}$

W_fund¶

This is the Power Group Overall fundamental active Energy.

$\begin{aligned} W_{fund} &= \sum_{i=1}^{NP} W[i]_{fund} & Unit: \mathbf{Wh} \end{aligned}$

W[i]_fund¶

This is the Power Phase number i fundamental active Energy.

$\begin{aligned} W[i]_{fund} &= \sum_{k=0}^{T_{int}} P[i]_{fund,k} \cdot \frac{N}{SR} \cdot \frac{1}{3600} & Unit: \mathbf{Wh} \end{aligned}$

W_fund+¶

This is the Power Group Overall positive aggregated active Energy.

$\begin{aligned} W_{fund+} &= \sum_{i=1}^{NP} W[i]_{fund+} & Unit: \mathbf{Wh} \end{aligned}$

W[i]_fund+¶

This is the Power Phase number i fundamental positive aggregated active Energy.

$\begin{aligned} W[i]_{fund+} &= \sum_{k=0}^{T_{int}} \frac{N}{SR} \cdot \frac{1}{3600} \begin{cases} P[i]_{fund,k} & \quad \text{if } P[i]_{fund,k} > 0\\ 0 & \quad \text{if } P[i]_{fund,k} <= 0\\ \end{cases} & Unit: \mathbf{Wh} \end{aligned}$

W_fund-¶

This is the Power Group Overall fundamental negative aggregated active Energy.

$\begin{aligned} W_{fund-} &= \sum_{i=1}^{NP} W[i]_{fund-} & Unit: \mathbf{Wh} \end{aligned}$

W[i]_fund-¶

This is the Power Phase number i fundamental negative aggregated active Energy.

$\begin{aligned} W[i]_{fund-} &= \sum_{k=0}^{T_{int}} \frac{N}{SR} \cdot \frac{1}{3600} \begin{cases} 0 & \quad \text{if } P[i]_{fund,k} > 0\\ P[i]_{fund,k} & \quad \text{if } P[i]_{fund,k} <= 0\\ \end{cases} & Unit: \mathbf{Wh} \end{aligned}$

C¶

This is the Power Group Overall accumulated electrical capacity.

$\begin{aligned} Q &= \sum_{i=1}^{NP} C[i] & Unit: \mathbf{Ah} \end{aligned}$

C[i]¶

This is the Power Phase number i accumulated electrical capacity.

$\begin{aligned} Q[i] &= \sum_{k=0}^{T_{int}} I[i]_{tAVG,k} \cdot \frac{N_{k}}{SR} \cdot \frac{1}{3600} & Unit: \mathbf{Ah} \end{aligned}$

C_+¶

This is the Power Group Overall positive accumulated electrical capacity.

$\begin{aligned} C_{t+} &= \sum_{i=1}^{NP} C[i]_{+} & Unit: \mathbf{Ah} \end{aligned}$

C[i]_+¶

This is the Power Phase number i positive accumulated electrical capacity.

$\begin{aligned} C[i]_{+} &= \sum_{k=0}^{T_{int}} \cdot \frac{N}{SR} \cdot \frac{1}{3600} \cdot \begin{cases} I[i]_{tAVG,k} & \quad \text{if } I[i]_{tAVG,k} > 0\\ 0 & \quad \text{if } I[i]_{tAVG,k} <= 0\\ \end{cases} & Unit: \mathbf{Ah} \end{aligned}$

C-¶

This is the Power Group Overall negative accumulated electrical capacity.

$\begin{aligned} C_{t-} &= \sum_{i=1}^{NP} C[i]_{-} & Unit: \mathbf{Ah} \end{aligned}$

C[i]_-¶

This is the Power Phase number i negative accumulated electrical capacity.

$\begin{aligned} C[i]_{-} &= \sum_{k=0}^{T_{int}} \cdot \frac{N}{SR} \cdot \frac{1}{3600} \cdot \begin{cases} 0 & \quad \text{if } I[i]_{tAVG,k} > 0\\ -I[i]_{tAVG,k} & \quad \text{if } I[i]_{tAVG,k} <= 0\\ \end{cases} & Unit: \mathbf{Ah} \end{aligned}$

C_RMS¶

This is the Power Group Overall accumulated current effective values.

$\begin{aligned} C\_{RMS} &= \sum_{i=1}^{NP} C[i]\_{RMS} & Unit: \mathbf{Ah} \end{aligned}$

C[i]_RMS¶

This is the Power Phase number i accumulated accumulated current effective values.

$\begin{aligned} C[i]\_{RMS} &= \sum_{k=0}^{T_{int}} I[i]_{tRMS,k} \cdot \frac{N_{k}}{SR} \cdot \frac{1}{3600} & Unit: \mathbf{Ah} \end{aligned}$

Additional Channels¶

F_fund¶

This is the fundamental frequency channel. See Sync Channel Mode for more information. $T_{fund}$ is the period duration of the fundamental signal estimated by the Zero Crossing Detect

$\begin{aligned} F_{fund} &= \frac{1}{T_{fund}} & Unit: \mathbf{Hz} \end{aligned}$