The circuit is powered up to I_INTERM_2. After a short plateau a powering failure is simulated by the power converter. After a minute the EE system is activated by a quench simulation in a current lead.
The aim of this test is to verify the correct functionality of the PC when a powering failure is generated.
The required analysis and signatures are listed below.
|Responsible|Type of analysis|Criterion|
|-----------|----------------|---------|
|PC|PC voltage check|PC voltage ~ -1.5 V ± 0.5 V, 1 s after the EE activation. The current decay time constant should be within 20% of Decay_Time_const. Smooth exponential waveform on the PC voltage and current during the whole decay|
|PC|Earth Current Analysis|The maximum earth current <50 mA during EE activation disregarding the peak at the opening of the EE system.|
|EE|Energy discharge|Maximum voltage on EE resistance ($R*I$±10%) and maximum temperature of the EE resistance (±10% from theoretical value)|
|EE|Energy discharge|Time delay on switch opening (300±50ms at odd point and 600±50ms at even point)|
source: Powering Procedure and Acceptance Criteria for the 13 kA Dipole Circuits, MP3 Procedure, <ahref="https://edms.cern.ch/document/874713">https://edms.cern.ch/document/874713</a>
%% Cell type:markdown id: tags:
# Analysis Assumptions
- We consider standard analysis scenarios, i.e., all signals can be queried. If a signal is missing, an analysis can raise a warning and continue or an error and abort the analysis.
- It is recommended to execute each cell one after another. However, since the signals are queried prior to analysis, any order of execution is allowed. In case an analysis cell is aborted, the following ones may not be executed (e.g. I\_MEAS not present).
# Plot Convention
- Scales are labeled with signal name followed by a comma and a unit in square brackets, e.g., I_MEAS, [A].
- If a reference signal is present, it is represented with a dashed line.
- If the main current is present, its axis is on the left. Remaining signals are attached to the axis on the right. The legend of these signals is located on the lower left and upper right, respectively.
- The grid comes from the left axis.
- The title contains timestamp, circuit name, and signal name allowing to re-access the signal.
- The plots assigned to the left scale have colors: blue (C0) and orange (C1). Plots presented on the right have colors red (C2) and green (C3).
- Each plot has an individual time-synchronization mentioned explicitly in the description.
- If an axis has a single signal, then the color of the label matches the signal's color. Otherwise, the label color is black.
## 4.2. Analysis of the Power Converter Main Current
This analysis module displays the main current of the power converter (I_MEAS) compared to the one obtained from the reference FPA (HWC PNO.b2 test with opening of EE systems and without magnet quench).
*ANALYSIS*:
- The evolution of the characteristic time $\tau$ of an exponential decay $f(t)$ is obtained as
Naturally, this formula only applies to exponential decayed characterised by a time constant. Nonetheless, for pseudo-exponential decays, this formula gives a notion of the change of the characteristic time $\tilde{\tau}$. For a circuit we compute the time-varying characteristic time as
- Check if the characteristic time of pseudo-exponential decay of I_MEAS from t=1 to 120 s is 90 s< Tau <110 s
*PLOT*:
- The main power converter current (analyzed and reference) on the left axis, I_MEAS
- The characteristic time calculated for the main current (reference and actual) on the right axis, -I_MEAS/dI_MEAS_dt
The actual characteristic time contains steps, which indicate a quenching magnet (decrease of circuit inductance); note that for the reference one the steps are not present. Timing of PIC abort, FGC timestamp, and the maximum current are reported next to the graph.
- t = 0 s corresponds to the respective (analyzed and reference) FGC timestamps.
## 4.3. Analysis of the Power Converter Main Current Smoothness
*ANALYSIS*:
- The current smoothness is evaluated on the basis of its second derivative. The derivative is calculated as a rolling division of current and time differences. The rolling window is fixed and equal to 10 points; with the sampling time equal to 0.1 s the time difference is equal to $dt=1 s$.
\begin{equation}
\frac{d i(t)}{dt} = \frac{i(t+dt)-i(t)}{dt}
\end{equation}
To obtain the second derivative of the current decay, the formula above is applied twice to the current profile from PM after the second EE opening (for t > 1 s).
*CRITERIA*
- Check if the second derivative of the current decay of I_MEAS from t = 1 s is -10 A/s^2< dI_MEAS/dt^2 < 10 A/s^2
*PLOT*:
- The second derivative of the main power converter current on the left axis, dI_MEAS/dt^2
- Green bar denotes the acceptance threshold for the second derivative of the main power converter current
- t = 0 s corresponds to the PM timestamp of the FGC
