Rolling Computation (OPT-POWER-EXP)¶

This chapter describes the Rolling Computation feature. It is designed for analysing fast changes in power grid connected applications e.g. renewable energy testing. In advance to the “normal” calculation, which is performed each single fundamental period, the computation in default setting is done every 1ms over the period of one fundamental cycle.

Fig. 53 Detail Settings in OXYGEN Power Group¶

Details Tab for Settings of the rolling computation
Enable/Disable Rolling Calculation
Selector for nominal frequency fallback (50 Hz / 60 Hz)
Input field for frequency threshold.

If a frequency is detected within the nominal frequency $\pm$ threshold %, the rolling window size is the actual period duration. Otherwise, e.g. in the case of a voltage interruption, where no frequency can be measured, the window size is the inverse nominal frequency (0–95 %).
Update rate (0.1–20 ms)
Window length (0.5 cycles / 1 cycles)

Attention

The following graph shows the details of the operation principle. It is similar to a moving average calculation, but with a variable window size, which depends on the actual measured fundamental frequency. If the calculate window size exceeds the maximum allowed size, which is given by (1/Nominal Frequency)*(1 + Frequency Threshold/100), the window size is set to 1/Nominal Frequency.

Channel Reference (Basic)¶

Some of the shown intermediate results or variables are not available in the software today. They are marked with a *.

Table 13 Legend¶
Symbol	Equatiom	Description
$\mathrm{SR}$	–	Samplerate
$\mathrm{NP}$	–	Number of Power Phases
$\mathrm{N}$	$\frac{SR}{f_{fund}}$	Number of Samples

U[i]_tRMS_rc¶

This is the Power Phase number i True RMS Voltage, updated every 1ms.

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

U[ij]_tRMS_rc¶

This is the Line-Line ij True RMS Voltage, updated every 1ms. This channel is only available in 3-Phase Power Configurations.

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

I[i]_tRMS_rc¶

This is the Power Phase number i True RMS Current, updated every 1ms.

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

P_t_rc¶

This is the Power Group Overall active Power, updated every 1ms.

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

P[i]_t_rc¶

This is the Power Phase number i active Power, updated every 1ms.

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

P_fund_rc¶

This is the Power Group Overall fundamental active Power, updated every 1ms.

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

P[i]_fund_rc¶

This is the Power Phase number i fundamental active Power, updated every 1 ms.

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

$U[i]_{fundRMS\_rc} , P[i]_{fundPHI\_rc}$ are internal channels, not available for users.

Q_t_rc¶

This is the Power Group Overall reactive Power, updated every 1ms.

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

Q[i]_t_rc¶

This is the Power Phase number i reactive Power, updated every 1 ms.

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

Q_fund_rc¶

This is the Power Group Overall fundamental reactive Power, updated every 1ms.

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

Q[i]_fund_rc¶

This is the Power Phase number i fundamental reactive Power, updated every 1ms.

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

S_t_rc¶

This is the Power Group Overall apparent Power, updated every 1ms.

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

S[i]_t_rc¶

This is the Power Phase number i apparent Power, updated every 1ms.

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

S_fund_rc¶

This is the Power Group Overall fundamental apparent Power, updated every 1ms.

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

S[i]_fund_rc¶

This is the Power Phase number i fundamental apparent Power, updated every 1ms.

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

U_DC_rc¶

This is the DC Voltage in case the DC Power Analysis is enabled in the Efficiency tab, updated every 1ms.

$\begin{aligned} U_{DC\_rc} &= \frac{1}{N} \sum_{n=0}^{N} u_{DC}[n] & Unit: \mathbf{V} \end{aligned}$

I_DC_rc¶

This is the DC Current in case the DC Power Analysis is enabled in the Efficiency tab, updated every 1ms.

$\begin{aligned} I_{DC\_rc} &= \frac{1}{N} \sum_{n=0}^{N} i_{DC}[n] & Unit: \mathbf{A} \end{aligned}$

P_DC_rc¶

This is the DC Power in case the DC Power Analysis is enabled in the Efficiency tab, updated every 1ms.

$\begin{aligned} P_{DC\_rc} &= \frac{1}{N} \sum_{n=0}^{N} u_{DC}[n] \cdot i_{DC}[n] & Unit: \mathbf{W} \end{aligned}$

Channel Reference (Symmetrical Components)¶

This section describes the equations for symmetrical components according to FGW-TG3 Annex F and IEC 61400-21 Annex C.

U[i]_fund_cos_rc¶

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

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

U[i]_fund_sin_rc¶

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

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

U_fundCOS_SYM+_rc¶

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

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

U_fundSIN_SYM+_rc¶

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

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

U_fundPHI_SYM+_rc¶

This is the phase angle of the Positive Voltage Sequence.

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

U_fundCOS_SYM-_rc¶

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

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

U_fundSIN_SYM-_rc¶

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

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

U_fundPHI_SYM-_rc¶

This is the phase angle of the Negative Voltage Sequence.

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

U_fundCOS_SYM0_rc¶

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

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

U_fundSIN_SYM0_rc¶

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

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

U_fund_SYM+_rc¶

This is the RMS value of the Phase-Phase (Line-Line) voltages positive sequence system.

$\begin{aligned} U_{fund\_SYM+\_rc} &= \sqrt{\frac{3}{2} \left( U_{fundCOS\_SYM+\_rc}^2 + U_{fundSIN\_SYM+\_rc}^2 \right)} & Unit: \mathbf{V} \end{aligned}$

U_fund_SYM-_rc¶

This is the RMS value of the Phase-Phase (Line-Line) voltages negative sequence system.

$\begin{aligned} U_{fund\_SYM-\_rc} &= \sqrt{\frac{3}{2} \left( U_{fundCOS\_SYM-\_rc}^2 + U_{fundSIN\_SYM-\_rc}^2 \right)} & Unit: \mathbf{V} \end{aligned}$

U_fund_SYM0_rc¶

This is the RMS value of the Phase-Phase (Line-Line) voltages zero sequence system.

$\begin{aligned} U_{fund\_SYM0\_rc} &= \sqrt{3 \cdot \left( U_{fundCOS\_SYM0\_rc}^2 + U_{fundSIN\_SYM0\_rc}^2 \right)} & Unit: \mathbf{V} \end{aligned}$

I[i]_fund_cos_rc¶

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

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

I[i]_fund_sin_rc¶

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

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

I_fundCOS_SYM+_rc¶

This is the real vector component of the Positive Current Sequence.

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

I_fundSIN_SYM+_rc¶

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

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

I_fundCOS_SYM-_rc¶

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

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

I_fundSIN_SYM-_rc¶

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

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

I_fundCOS_SYM0_rc¶

This is the real vector component of the Zero Current Sequence.

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

I_fundSIN_SYM0_rc¶

This is the real vector component of the Zero Current Sequence.

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

P_fund_SYM+_rc¶

$\begin{aligned} P_{fund\_SYM+\_rc} = \frac{3}{2} \cdot & \left( U_{fundCOS\_SYM+\_rc} \cdot I_{fundCOS\_SYM+\_rc} \right. & \nonumber \\ & \left. + U_{fundSIN\_SYM+\_rc} \cdot I_{fundSIN\_SYM+\_rc} \right) & Unit: \mathbf{W} \end{aligned}$

P_fund_SYM-_rc¶

$\begin{aligned} P_{fund\_SYM-\_rc} = \frac{3}{2} \cdot & \left( U_{fundCOS\_SYM-\_rc} \cdot I_{fundCOS\_SYM-\_rc} \right. & \nonumber \\ & \left. + U_{fundSIN\_SYM-\_rc} \cdot I_{fundSIN\_SYM-\_rc} \right) & Unit: \mathbf{W} \end{aligned}$

P_fund_SYM0_rc¶

$\begin{aligned} P_{fund\_SYM0\_rc} = 3 \cdot & \left( U_{fundCOS\_SYM0\_rc} \cdot I_{fundCOS\_SYM0\_rc} \right. & \nonumber \\ & \left. + U_{fundSIN\_SYM0\_rc} \cdot I_{fundSIN\_SYM0\_rc} \right) & Unit: \mathbf{W} \end{aligned}$

Q_fund_SYM+_rc¶

$\begin{aligned} Q_{fund\_SYM+\_rc} = \frac{3}{2} \cdot & \left( U_{fundCOS\_SYM+\_rc} \cdot I_{fundSIN\_SYM+\_rc} \right. & \nonumber \\ & \left. - U_{fundSIN\_SYM+\_rc} \cdot I_{fundCOS\_SYM+\_rc} \right) & Unit: \mathbf{var} \end{aligned}$

Q_fund_SYM-_rc¶

$\begin{aligned} Q_{fund\_SYM-\_rc} = \frac{3}{2} \cdot & \left( U_{fundCOS\_SYM-\_rc} \cdot I_{fundSIN\_SYM-\_rc} \right. & \nonumber \\ & \left. - U_{fundSIN\_SYM-\_rc} \cdot I_{fundCOS\_SYM-\_rc} \right) & Unit: \mathbf{var} \end{aligned}$

Q_fund_SYM0_rc¶

$\begin{aligned} Q_{fund\_SYM0\_rc} = 3 \cdot & \left( U_{fundSIN\_SYM0\_rc} \cdot I_{fundCOS\_SYM0\_rc} \right. & \nonumber \\ & \left. - U_{fundCOS\_SYM0\_rc} \cdot I_{fundSIN\_SYM0\_rc} \right) & Unit: \mathbf{var} \end{aligned}$

S_fund_SYM+_rc¶

$\begin{aligned} S_{fund\_SYM+\_rc} & = \sqrt{P_{fund\_SYM+\_rc}^2 + Q_{fund\_SYM+\_rc}^2} & Unit: \mathbf{VA} \end{aligned}$

S_fund_SYM-_rc¶

$\begin{aligned} S_{fund\_SYM-\_rc} & = \sqrt{P_{fund\_SYM-\_rc}^2 + Q_{fund\_SYM-\_rc}^2} & Unit: \mathbf{VA} \end{aligned}$

S_fund_SYM0_rc¶

$\begin{aligned} S_{fund\_SYM0\_rc} & = \sqrt{P_{fund\_SYM0\_rc}^2 + Q_{fund\_SYM0\_rc}^2} & Unit: \mathbf{VA} \end{aligned}$

I_fund_P_SYM+_rc¶

$\begin{aligned} I_{fund\_P\_SYM+\_rc} &= \frac{P_{fund\_SYM+\_rc}}{\sqrt{3} \cdot U_{fund\_SYM+\_rc}} & Unit: \mathbf{A} \end{aligned}$

I_fund_P_SYM-_rc¶

$\begin{aligned} I_{fund\_P\_SYM-\_rc} &= \frac{P_{fund\_SYM-\_rc}}{\sqrt{3} \cdot U_{fund\_SYM-\_rc}} & Unit: \mathbf{A} \end{aligned}$

I_fund_P_SYM0_rc¶

$\begin{aligned} I_{fund\_P\_SYM0\_rc} &= \frac{P_{fund\_SYM0\_rc}}{\sqrt{3} \cdot U_{fund\_SYM0\_rc}} & Unit: \mathbf{A} \end{aligned}$

I_fund_Q_SYM+_rc¶

$\begin{aligned} I_{fund\_Q\_SYM+\_rc} &= \frac{Q_{fund\_SYM+\_rc}}{\sqrt{3} \cdot U_{fund\_SYM+\_rc}} & Unit: \mathbf{A} \end{aligned}$

I_fund_Q_SYM-_rc¶

$\begin{aligned} I_{fund\_Q\_SYM-\_rc} &= \frac{Q_{fund\_SYM-\_rc}}{\sqrt{3} \cdot U_{fund\_SYM-\_rc}} & Unit: \mathbf{A} \end{aligned}$

I_fund_Q_SYM0_rc¶

$\begin{aligned} I_{fund\_Q\_SYM0\_rc} &= \frac{Q_{fund\_SYM0\_rc}}{\sqrt{3} \cdot U_{fund\_SYM0\_rc}} & Unit: \mathbf{A} \end{aligned}$

PF_fund_SYM+_rc¶

$\begin{aligned} PF_{fund\_SYM+\_rc} &= \frac{P_{fund\_SYM+\_rc}}{\sqrt{P_{fund\_SYM+\_rc}^2 + Q_{fund\_SYM+\_rc}^2}} & Unit: \mathbf{-} \end{aligned}$

PF_fund_SYM-_rc¶

$\begin{aligned} PF_{fund\_SYM-\_rc} &= \frac{P_{fund\_SYM-\_rc}}{\sqrt{P_{fund\_SYM-\_rc}^2 + Q_{fund\_SYM-\_rc}^2}} & Unit: \mathbf{-} \end{aligned}$

PF_fund_SYM0_rc¶

$\begin{aligned} PF_{fund\_SYM0\_rc} &= \frac{P_{fund\_SYM0\_rc}}{\sqrt{P_{fund\_SYM0\_rc}^2 + Q_{fund\_SYM0\_rc}^2}} & Unit: \mathbf{-} \end{aligned}$