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> 13_030224_CLN_01.doc

***TO: DISTRIBUTION***

***FROM: C NEUMEYER***

***SUBJECT: ANALYSIS OF TF FAILURE***

*Summary*

On Friday, February 14, during the first plasma shot of the day (Shot#
110201), a Level 1 fault was annunciated in the TF system.

This was accompanied by a large bang heard on the test cell audio
system, and ensuing smoke seen on the test cell video system.

Multiple protective devices tripped, any one of which would result in
the Level 1 fault status:

-   TF power supply fault detector section overcurrent

-   TF Analog Coil Protection (ACP) overcurrent

-   TF Rochester Instrument System (RIS) overcurrent

-   TF ground fault (DBB4 relay)

The target level for the TF during this shot, and the operating limit in
effect for the run, was 53.4kA which produces Bt=4kG. The fault occurred
just prior to reaching flat top as the current passed the 50kA level.

Based on the observed evidence it is postulated that an open circuit
fault initiated the sequence of events. This was followed by a single
line to ground fault at or near the (+) terminal of the power supply,
then by another line to ground fault at the other (-) terminal of the
power supply. The double line to ground fault condition led to a spike
of fault current from the power supply which shunted the coil inner leg
assembly. Once the power supply tripped, the current spike decayed. This
was followed by a decay of the coil current as the coil released its
stored energy. However, the decay was not a simple exponential according
to the nominal L and R values of the coil circuit. Instead it was
modified by a series voltage drop of 125 volts and resistance of 500µΩ.
These extra series elements are attributed to an arc across the
postulated open circuit. The energy dissipated in the arc was of order
1.4MJ.

# Interpretation of Data

Comparison of the current waveform of shot 110201 with the prior 100%
test shot 110200 indicates no anomalies during the current rise prior to
the fault as shown in figure 1[^1]. In addition the writer has confirmed
that 110200 was essentially identical to the first 100% test shot of the
run period (109272 in early January) [^2].

![](media/image2.jpeg){width="5.997222222222222in"
height="4.594444444444444in"}

*Figure 1 -- Comparison of Fault Shot with Prior 100% Test Shot*

The current decay curve does not follow the normal exponential L/R
decay[^3] expected of the NSTX TF circuit after the power supplies go in
to bypass mode (V≈0). This is depicted in figure 2[^4] which shows an
overlay of 110201 with a shot earlier in the run (110107) which had an
abnormal termination. Also overlayed is a simple L/R decay where L=4.5mH
and R=8.5mΩ. These circuit values had previously been established by
calculation as well as measurement for use in estimating the follow-on
∫i^2^(t)dt from L/R decay.

![](media/image3.jpeg){width="5.991666666666666in"
height="4.647916666666666in"}

*Figure 2 -- Comparison of Decay Curves and Curve Fit*

The center stack rogowski coils, which are located at approx. z= +/-
1.4m and measure the total amp-turns passing down the TF inner leg
assembly do not show the current spike and other anomalies in the TF
waveform as measured at the power supply terminals as shown in figure
3[^5]. This figure shows the power supply current, rogowski current
(divided by number of turns) also shows a curve fit which is based on an
anomalous voltage drop and an additional resistance in series with the
normal TF circuit parameters. From this figure and the curve fit it is
evident that:

-   the large spike in power supply current flowed in parallel with the
    coil, not down the inner leg

-   the fault current decay in the coil exhibits an anomalous V=125
    volts and R=500µΩ in the series loop

-   the notches in the power supply current decay waveform are not
    evident in the inner leg coil decay waveform

-   the power supply current decay waveform is slightly offset from the
    coil current waveform during the decay

![](media/image4.jpeg){width="5.991666666666666in"
height="4.649305555555555in"}

*Figure 3 -- Comparison of Power Supply Current Measurement with Center
Stack Rogowski Measurement of Inner Leg Current per Turn and with Curve
Fit*

The differences between the CS rogowski waveform and the power supply
current appear to be coincident with the operation of the OH coil and
the plasma as shown in figure 4.

This indicates that a mutual coupling exists between power supply
circuit and the OH circuit, and/or between the power supply circuit,
including any fault current paths, and the plasma. One might expect to
see a response in the rogowski inner leg current measurement, based on
the idea that the poloidal component of Ip is linked to the TF. However,
this is not evident from the waveforms, indicating a coupling to the
external circuit only.

![](media/image5.pct){width="5.995138888888889in"
height="4.4215277777777775in"}

*Figure 4 -- TF, CS Rogowski, OH, and Ip Measurements*

*Postulated Sequence of Events*

An explanation of the sequence of events is presented in the following
paragraphs. This is aided by examination of the signals shown for the
duration of the shot in figure 5. Following is a description of the
signals:

[TF Sum]{.underline}: Current in power supply loop as measured by DC
current transducers (Halmars) in the four parallel power supply
branches, and then summed

[i_rogcscl1]{.underline}: Current flowing down inner leg assembly scaled
to amps per turn, as measured by center stack rogowski #1 in the lower
half plane.

[pc_tf_sds_vd1_1- pc_tf_sds_vd2_1]{.underline}: This is the difference
between the measured voltages to ground at the two terminals of the
power supply output at the Safety Disconnect Switches (SDS) in the power
supply building (FCPC). In other words, this is the voltage produced by
the power supply.

[pc_tf_sds_vd1_1, pc_tf_sds_vd2_1]{.underline}: The individual voltages
to ground at the SDS terminals

[pc_tf_gndcur]{.underline}: This is the current flowing through the
grounding resistors to the ground fault detector

![](media/image6.pct){width="5.991666666666666in"
height="4.129166666666666in"}

*Figure 5 -- Salient Signals Over Full Pulse Duration*

The following is a description of the postulated sequence of events.
Refer to figures 6 and 7 which give zoomed views of the signals shown in
figure 5.

[Prior to T1]{.underline}: TF current is rising, Power supply and
rogowski signals are identical. Commutations in power supply voltage are
evident. Power supply voltage has dropped from 1kV to around 750 volts
due to regulation under load. Voltages to ground at SDS are balanced at
+/-400V.

[T1]{.underline}: An open circuit occurs at a flag joint, arcing and
plasma ensue. Vd1 signal shows ground fault on (+) terminal as voltage
dips toward zero. Vd2 signal goes toward the full power supply voltage.
Ground fault current rises up.

[T2]{.underline}: Vd2 signal shows additional ground fault on (-)
terminal as voltage dips toward zero. Power supply voltage droops as
line-line short circuit condition has developed. Current in power supply
loop begins to increase rapidly, but inner leg current measured by
rogowski remains flat.

[T3]{.underline}: Power supplies have tripped, gone into suppress/bypass
mode and their output voltages (four branches operating on 15 degree
displaced sine waves) ride their respective sine waves toward zero.

[T4]{.underline}: Power supply current peaks at around 67kA.

[T5]{.underline}: Power supply voltage has reached zero, superimposed
power supply spike current begins L/R decay. Vd1 and Vd2 are both at
around 125V above ground, indicating that one ground fault still exists
and that the coil is developing a net back e.m.f. in response to an arc
voltage drop which is enhancing the current decay toward zero. Current
decay is rapid due to the arcing open circuit condition.

[T6]{.underline}: Superimposed power supply spike current is
extinguished. Line-line arc is extinguished. It does not reverse
direction (akin to the opening of a circuit breaker in an AC circuit).

[T7]{.underline}: Plasma disruption creates notch in power supply
current decay loop.

Timing of Events

  ----------------------- ----------------------- -----------------------
  Event                   Time                    Time Duration

  T1                      -0.1071                 0.0022

  T2                      -0.1049                 0.0034

  T3                      -0.1014                 0.0017

  T4                      -0.0998                 0.0070

  T5                      -0.0928                 0.0549

  T6                      -0.0379                 0.1453

  T7                      0.1074                  
  ----------------------- ----------------------- -----------------------

![](media/image7.pct){width="4.777083333333334in"
height="3.847916666666667in"}

*Figure 6 -- Zoomed over 80mS*

![](media/image7.pct){width="4.927777777777778in"
height="4.000694444444444in"}

*Figure 7 -- Zoomed over 20mS*

![](media/image8.pct){width="5.989583333333333in"
height="4.8902777777777775in"}

*Figure 8 -- Zoomed over 400mS*

*Correlation of Observations with Coil Layout*

The winding pattern shown in figure 9 along with the circuit diagram
shown in figure 10 can be used to postulate the physical location of the
faults.

Examination of the damage to the TF coil revealed that the bottom end
flag of turn 8A, which is the 3^rd^ turn in the winding sequence, was
ejected from its normal position in the hub assembly. Thus, in figure
10, coil section #1 probably consisted of turns 1-3, and section #2 of
turns 4-36, i.e. the open circuit fault probably occurred where, on the
bottom of the machine, the current exits turn 3 to go to the outer leg
corresponding to turn 4. No matter the location, an open circuit in the
loop would behave the same, but since turn 3 is so physically close to
the (+) and (-) terminals of the coil it seems quite likely that the
arcing and plasma generated by the open circuit would quickly result in
a single line to ground fault from the positive coil terminal to the
grounded hub assembly, followed by a second line to ground fault from
the negative terminal to the grounded hub assembly.

![](media/image7.pct){width="5.99375in" height="6.697222222222222in"}

*Figure 9 -- TF Winding Pattern*

*(Note: Darkened numbers indicate conductors which had coolant leaks)*

![](media/image7.pct){width="5.998611111111111in"
height="2.8881944444444443in"}

*Figure10 -- Simplified TF Circuit Schematic Showing Fault Locations*

*Circuit Simulation*

The postulated sequence of events was simulated using an electrical
circuit analysis program called PSCAD. The circuit model included the
known coil and power supply parameters along with the postulated
resistance and arc voltage drop associated with the open circuit fault.
The effect of mutual coupling with the OH and plasma was not included.
The results were in agreement with the observations, except for the
features attributed to the OH/plasma mutuals.

In addition, a feature was included in the modeling to simulate the
effect of a turn-to-turn short circuit. Using this modeling it was
confirmed that the observed waveforms do not correlate with those which
would be expected from turn-turn shorts.

*Energy Dissipation*

Based on the TF coil inductance of 4.5mH and an initial current of 50kA,
the total stored magnetic energy at the time of the fault was 6.4MJ.
However, taking the integral ∫\[(i(t)\*V~arc~+i^2^(t)\*R~fault~\] the
fault energy is calculated to be 1.4MJ. This amount of energy would be
sufficient to bring 3.3kG (7.2lbs) of copper to the melting point.

It is noted that, had the open circuit fault not caused ground fault(s)
or overcurrents, much more energy might have been dissipated, as the
power supply would have continued to attempt to produce the requested
current waveform.

cc:

E Baker

M Bell

W Blanchard

A Brooks

R Camp

J Chrzanowski

J Corl

L Dudek

T Egebo

D Gates

R Hatcher

R Hawryluk

P Heitzenroeder

A Ilic

M Kalish

S Kaye

J Levine

F Malinowski

J Malsbury

R Marsala

D McBride

T Meighan

J Menard

D Mueller

S Ramakrishnan

D O'Neill

M Ono

R Parsells

M Peng

J Schmidt

H Schneider

T Stevenson

E Synakowski

M Viola

A VonHalle

M Williams

I Zatz

[^1]: Obtained by overlay of the data after accounting for the
    difference in start time of the test shot and the plasma shot,
    relative to t=0

[^2]: Analysis of the total circuit resistance over a large number of
    shots has indicated a progressive trend of increasing resistance,
    however. See "TF Resistance Trend", M. Bell, 2/18/3

[^3]: One would expect I(t) = I~0~^-tR(t)/L^ where R(t) reflects the
    resistance variation with heating

[^4]: Obtained by overlay of the data so that the 50kA times are
    coincident.

[^5]: Obtained by scaling the CS rogowski signals by -0.0277427