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Spread Spectrum Time Domain Reflectometry for Complex Impedances:

Application to PV Arrays

Conference Paper · September 2018

DOI: 10.1109/AUTEST.2018.8532521

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Cynthia M. Furse Naveen Kumar Tumkur Jayakumar

University of Utah University of Utah
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 Spread Spectrum Time Domain Reflectometry
for Complex Impedances: Application to PV
Arrays
Cynthia Furse1,4, Fellow, IEEE, Naveen Kumar Tumkur Jayakumar1, Student Member, IEEE, Evan
Benoit1, Mashad Uddin Saleh1, Student Member, IEEE, Josiah LaCombe1, Michael Scarpulla1,
Member, IEEE, Joel Harley2, Samuel Kingston1, Brent Waddoups4, Chris Deline3
1
Department of Electrical Engineering, University of Utah, Salt Lake City, UT 84112
2
Department of Electrical Engineering, University of Florida, Gainesville, FL 32611
3
National Renewable Energy Laboratory, Golden, CO 80401
4
LiveWire Innovation, Salt Lake City, UT 84095
may be used on live electrical systems, [8] use pseudo-noise
Abstract—Spread spectrum time domain reflectometry (PN) codes and time correlation techniques. SSTDR hardware
(SSTDR) has previously been used for detection and location of has previously been applied to detect ground faults [9] and arc
intermittent faults on live electrical wiring. These intermittent faults [10] in PV arrays. This detection was based on very
faults can be open circuits, short circuits, or resistive changes, all
of which preserve the original shape of the SSTDR correlated simple algorithms, and both of these faults show up as effective
waveform. But things are very different when SSTDR encounters short circuits.
a complex impedance discontinuity such as a capacitor or In this paper, we evaluate the potential for SSTDR to locate
inductor. In this case, the reflection is a function of frequency, and measure the magnitude of a fault on a PV panel. This
changing the shape of the SSTDR signature. In this paper, we will requires analysis of the SSTDR signature. Previously, SSTDR
show the SSTDR response to single capacitors and inductors. We has been used to locate open and short circuits and resistive
will also explore how SSTDR responds to arrays of PV panels
(which are capacitive) connected by wires. We will show both loads. These are simple, as they change the magnitude of the
simulations and measurements. In some configurations, it is SSTDR signature, but not its shape. PV panels, on the other
relatively easy to see faults, although algorithms are still under hand, are capacitive. Capacitive loads, being frequency-
development. In other configurations, little change occurs, which dependent, change both the magnitude and shape of the SSTDR
makes it very difficult to create a system for testing for these faults. response, and are therefore somewhat more complex to
evaluate. In this paper, we will evaluate the SSTDR response to
Index Terms—Spread spectrum time domain reflectometry capacitive and inductive loads, as well as (capacitive) PV
(SSTDR), Photovoltaic (PV) arrays, Complex impedances, panels. This analysis provides the basis for future algorithm
Capacitance, Inductance
development work to locate and measure the complex load
impedances and correlate that to PV faults.
I. INTRODUCTION

E lectrical faults and degradation in photovoltaic (PV) arrays

can occur in either the modules themselves or within the
cabling that connects them [1, 2, 3]. These faults are difficult
II. SSTDR FOR RESISTIVE LOADS
The incident SSTDR signal is constructed by modulating
(multiplying) a square wave with a digital PN sequence
to detect and even more difficult to locate. Thermal imaging and generated from a linear feedback shift register, modulated by a
luminescence methods attached to cleaning robots or unmanned square wave. The modulation frequencies (fm) for the WILMA
aerial vehicles may be used, but these are cumbersome, W50A000F SSTDR device [11] used for our measurements
expensive, and likely to be used only intermittently [4, 5]. In range from 187.5kHz to 48MHz. For the measurement results
this paper, we propose a reflectometry approach that may be described in this paper, we select fm to be 48MHz due to its high
used continually on live, energized cables. resolution and accuracy. The SSTDR incident test signal is then
Reflectometry has been used to locate faults in many types launched down the transmission line where it interacts with the
of electrical systems. The time or phase delay between the impedance discontinuities in the system. At the boundaries of
incident and reflected signal gives the distance to the fault [8]. these discontinuities, the amount of signal reflected back to the
Several variations of reflectometry exist, based on the test SSTDR device can be calculated from the reflection coefficient:
signals utilized and methods of signal processing. Time domain
reflectometry (TDR) [6] utilizes impulse or step-edge signals, ܸ௥௘௙ ܼ௅ െ ܼ଴
and frequency domain reflectometry (FDR) [7] uses sinusoidal Ȟ= = (1)
ܸ௜௡௖ ܼ௅ + ܼ଴
signals. Sequence time domain reflectometry (STDR) and
spread spectrum time domain reflectometry (SSTDR), which

978-1-5386-5223-7/18/$31.00 ©2018 IEEE

where Vref is the reflected voltage, Vinc is the incident voltage, the end of the cable is between -1 and 0, while a termination
ZL is the impedance of the discontinuity (resistive, capacitive, with RL=R0 (157ȳ) corresponds to no reflection at the end of
inductive, open, short, etc.) at the frequency of interest, and Z0 the cable. We can see that resistive loads introduce a change in
is the characteristic impedance of the transmission line. The amplitude of the reflected signal, but do not change its basic
amount of signal transmitted across the boundaries of these shape.
impedance discontinuities can be calculated using the
transmission coefficient (T): III. SSTDR FOR COMPLEX LOADS
Resistive loads change the magnitude but not the shape of the
T = 1 + Ȟ (2) SSTDR signatures. Complex loads, on the other hand, change
both the magnitude and shape as we will see in this section. The
The reflected signal that enters the SSTDR device is then reflection coefficient as a function of frequency for a capacitor
cross-correlated with a delayed version of the incident signal. is governed by its characteristic impedance:
The resultant correlated waveform is integrated and sampled
using an analog-to-digital converter (ADC). For a frequency- 1
independent load, in this correlated waveform, the location of ܼ௅ = (3)
݆߱‫ܥ‬௅
each peak indicates the location of impedance discontinuities or
faults in the system [12]. The shape and magnitude of the peaks 7KLV LPSHGDQFH LV GHSHQGHQW RQ IUHTXHQF\ Ȧ  VR HDFK
indicate the type of impedance mismatch. Those with a negative frequency in the time-domain SSTDR signature will see a
reflection coefficient indicate impedance mismatches where the different impedance. This is what causes the signature shape to
load has a lower impedance value than the transmission line, change, in addition to the magnitude.
and the converse is true for positive reflections [13]. The time
domain signature is converted to distance by multiplying by the
velocity of propagation, which is calculated in the following
section and is generally approximately 2/3 the speed of light.
Fig. 1 shows the measured SSTDR responses for different load
impedances (ZL=1Mȳ, 1kȳ, 157ȳ, 10ȳ and SC) terminating
the end of a 40.5-foot-long 10AWG PV cable with a
characteristic impedance Z0 =157ȳ.

Fig.2. Experimental setup for measuring complex impedances

Fig.2 shows the experimental setup for measuring the

SSTDR response for different capacitors. In this configuration
we have used two 10 AWG PV cables (15-foot and 25-foot)
connected together using industry standard MC-4 connectors.
These cables are laid out in the form of a twin lead transmission
line with an average separation of 12mm. This cable is then
connected to the WILMA W50A000F SSTDR device [11] with
a load (ZL) at the end (Point-A). The transition from the 10
AWG PV cable to the load ZL was made possible by using a
connector made of two small 0.5-foot sections of PV cable and
a pair of MC-4 connectors shown in fig.3.

Fig.1. SSTDR signature for resistive loads

The first peak (at distance = 0) shows the SSTDR reflection

Fig.3. Connector used to connect load ZL to the PV leader cable
between the SSTDR test unit and the cable, Z0. The next
impedance discontinuity the signal encounters in is located at
The velocity of propagation (VOP) of the transmission line
the 15 feet point and is due to the first set of MC-4 connectors was determined by calculating the time delay of the signal to
where the leader cable connects to the test cable. The magnitude the open circuit (OC) load and back to the SSTDR through the
of this discontinuity is expected to be low. The junction consists PV leader cable. Utilizing this time delay and the known length
of 10 AWG PV cable to MC-4 connector and back to 10 AWG of the PV leader cable, the VOP was found to be 0.695 times
PV cable. The final impedance discontinuity that the signal the speed of light. The characteristic impedance (Z0) of the PV
encounters is at the 40.5 feet mark due to the load at point-A. leader cable was measured to be 157ȳ, from the reflection
For RL>R0 (1Mȳ and 1kȳ) the reflection at the end of the cable coefficient using the open circuit (OC) measurement and the
is between 0 and 1. For RL<R0 (10ȳ and SC) the reflection at known impedance of the SSTDR hardware. The OC
measurement along with measurements of several load
capacitors (ZL=50pF, 100pF, 330pF, 1μF) are shown in fig. 4,
where the end of the cable is marked with a vertical blue line,
indicating the location of the load.

Fig.5. SSTDR signatures for capacitive loads

Fig.4. SSTDR response for capacitive loads

Again, we see a significant reflection at distance=0 where the

SSTDR connects to the transmission line, a small reflection at
15’ where the MC4 connectors join the two transmission lines,
and then (at 45’) the reflections from the capacitive loads. The
capacitive loads result not only in a change to the amplitude of
the reflected signal, but they also introduce a shape change.
Based on (3), very small capacitors act very much like open
circuits (ZL approaches ’), and very large capacitors act like
short circuits (ZL approaches 0). But we can no longer use
simply the location of the peaks, nor their magnitude, to
determine the capacitance values, as we could with the resistive
loads shown in fig. 1. A more complicated algorithm will be
needed to do this.
The simulated SSTDR signatures for a wider range of
Fig.6. SSTDR signatures for inductive loads
capacitors is shown in fig. 5 for the setup shown in fig.2. These
can also be compared to capacitive measurements shown in fig.
4. Close agreement is seen between the measurements and the IV. SSTDR FOR PHOTOVOLTAIC PANELS
simulated SSTDR responses. The 1pF capacitor is seen to PV panels are a packaged assembly of solar cells connected
produce a nearly identical SSTDR signature as the OC with in series to obtain desired voltage at the output. A PV cell can
infinite resistance. be modelled using the lumped element model shown in fig.7,
Fig. 6 shows the simulated SSTDR signatures for inductive
loads (ZL=1nH, 300nH, 1μH, 2μH,100μH). Like capacitive
loads, inductive loads change both the magnitude and shape of
the reflected signal. This is to be expected, as the load
impedance is governed by the frequency-dependent impedance
of an inductor:

ܼ௅ = ݆߱‫ܮ‬௅ (4)

Larger inductors are closer to open circuits, and smaller to short Fig.7 Lumped element model of a PV module [14]
circuits. Fortunately, the shapes of inductor and capacitor
SSTDR responses are unique, and we can therefore expect to where, RS describes the losses due to front contacts, LS is the
be able to both locate and identify the magnitude of these load mutual inductance between the bus bars, RSH denotes ohmic
impedances. Like capacitors, inductors will require a more loss due to defects, Cdep represents the capacitance of the cell
advanced algorithm than resistors, but their unique signatures due to depletion region, Rdiff is the resistive part of the
will enable such an algorithm to be developed. admittance of PN-junction, and Cdiff is the reactive part of the
admittance of the PN-junction [13]. The Cdep dominates the loads, at least if they are within a mid-range of capacitors and
total capacitance of the module during reverse bias, and Cdiff inductors. For very large or very small values, the complex load
dominates in forward bias. A PV panel is just a series looks like a short or open circuit and cannot, then, be uniquely
connection of PV cells. Basically, the impedance of the PV defined. In this paper, we evaluated the SSTDR response to
panel can be modelled as a combination of resistors and capacitive and inductive loads, as well as (capacitive) PV
capacitors. panels. This analysis provides the basis for future algorithm
Each PV panel has two separate cables which can be used to development work to locate and measure the complex load
connect to successive panels through MC-4 connectors, impedances and correlate that to PV faults.
creating the measurement setup shown in fig. 8. The SSTDR
response for this test setup is as shown in fig.9. This panel has VI. ACKNOWLEDGMENT
a large capacitance and therefore appears nearly like a short This material is based upon work supported by the U.S.
circuit. Department of Energy’s Office of Energy Efficiency and
Renewable Energy (EERE) under Solar Energy Technologies
Office (SETO) Agreement Number DE-EE0008169

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