Actively Calibrated Line Mountable Capacitive Voltage Transducer For Power Systems Applications

2.5 MB·

by  Raffi Sevlian

1
Actively Calibrated Line Mountable Capacitive
Voltage Transducer For Power Systems Applications
Raffi Avo Sevlian and Ram Rajagopal
Abstract—AclassofActivelyCalibratedLineMountedCapacitive a practical prototype. Section VI presents in detail the signal
Voltage Transducers (LMCVT) are introduced as a viable line processing methods required. Section VII presents experimental
mountable instrumentation option for deploying large numbers of
resultsprovingtheefficacyofthetechnology.Finally,SectionIX
voltage transducers onto the medium and high voltage systems.
addresses future challenges and opportunities for the proposed
Active Calibration is shown to reduce the error of line mounted
7
voltage measurements by an order of magnitude from previously sensing technology.
1
published techniques. The instrument physics and sensing method
0
2ispresentedandtheperformanceisevaluatedinalaboratorysetting. II. LINEMOUNTEDVOLTAGEMEASUREMENTMETHODS
Finally, a roadmap to a fully deployable prototype is shown.
This section reviews the main classes of line mounted voltage
n
a measurementmethodsandidentifiestheirbenefitsandlimitations.
J
I. INTRODUCTION
6 A. Electrostatic Field Measurement
2 Modern smart grid infrastructure envisions extensive deploy-
mentofrenewablegeneration,electricvehicles,storageandmany The electric field generated by an energized power line is

] measured inside the device at one or more points at varying
tother technologies. To enable these deployments, increased sens-
e distances from the line. The measured field is then used to
ingandenhancedsituationalawarenessisrequired.Indistribution
d reconstructthelinevoltagebasedonafixedmappingbetweenthe
systems, voltage and current are the main quantities which must
-
sbe monitored and deploying technologies to measure these in a measured field and line voltage. Much of the research on electric
n field based measurements has focused on the MEMs transducer
large scale can be prohibitively expensive. Therefore, there is
i
s.a need to develop inexpensive yet accurate sensor technology themselves,[2][3],[4][5].Thefundamentallimitationfortheline
mounted electrostatic sensors is the dependence on the physical
cfor the distribution system. This work presents a new sensing
i arrangement of the conductor and the ground which dictates the
stechnologywhichaimstodramaticallyreducethecostofaccurate
y observed electric field [6] [7], [8]. This can change over time,
voltage sensing for distribution system.
h but must be calibrated before sensor deployment typically in a
Thestateoftheartinvoltagemeasurementtechnologyiseither
p laboratory setting. When the physical environment changes over
[(1)expensivetodeployinlargenumbersor(2)suffersfromerrors
makinganypracticaluseimpossible.Accuratevoltagesensingin time, the inferred voltage level will deviate from the true value.
1
asubstationsettingreliesonVoltageTransformersorCapacitively
v B. Capacitive Voltage Measurement
Coupled Voltage Transducer (CCVT) [1] technology to step
0
3down the voltage. Inexpensive line mounted voltage relies on The term capacitive voltage measurements enumerate a num-
5(1) electrostatic field and (2) capacitively coupled measurements ber of different configurations of traditional and non-traditional
7which do not reach the required accuracy of metering quality voltage measurements:
0
sensing. 1 Line/Ground Mounted devices are electrically connected
.
1 This work proposes a solution to the limitations of line both to ground and the line. This method covers CCVTs
0
mounted voltage sensing. The main contributions of this work which are installed in high voltage substations.
7
are the following: (1) A detailed physics model of Line Mounted 2 Ground Mounted devices are connected to ground and
1
:Capacitive Voltage Transducers is presented with experimental capacitively coupled to the energized line. This method is
v
validation. (2) The active calibration methodology is detailed most often associated with ”Capacitively Coupled” mea-
i
Xalong with experiments showing its effectiveness of reducing the surement and is considered non-contact since it does not
rvoltagemagnitudeerrors.(3)Aresearchroadmaptoenableafull needelectricalconnectiontotheenergizedline.Themethod
a
deployable solution is given. has found uses in non-contact voltage instrumentation [2].
The paper is organized as follows. Section II reviews exist- However, issues with multiple interfering power lines and
ing line mounted voltage measurement approaches. Section III large distance between the ground and the conductors have
presents the basic line mounted capacitive voltage transducer. limited the accuracy. Some applications have been capable
SectionIVintroducestheactivecalibrationconceptanddiscusses of estimating the power line phase arrangements [9], even
some of it’s properties. Section V describes the development of with large sensor errors.
3 Line Mounted devices are connected to the energized line
R. Sevlian is with the Department of Electrical Engineering and the Stanford and capacitively coupled to earth ground. This method
SustainableSystemsLab,CA,94305.Email:[email protected].
requireselectricalconnectiontotheenergizedline,butdoes
R.RajagopaliswiththeStanfordSustainableSystemsLab,DepartmentofCivil
andEnvironmentalEngineering,StanfordUniversity,CA,94305.R.Rajagopalis notrequiregroundedconnection.Thepaperfocusesonthis
supportedbythePowellFoundationFellowship.Email:[email protected]. method since it is the only method that is line mountable,
This research was supported in part by the TomKat Center for Sustainable
easy to deploy but also (as will be shown) allows for an
Energy, the Precourt Institute for Energy Efficiency, and the Thomas V. Jones
StanfordGraduateFellowshipinScience&Engineering. active calibration procedure enabling high accuracy.
2
There has been some attention paid to line mounted capaci- A. Ideal Body Capacitive Probe Model
tively coupled voltage transducers for high voltage applications.
Two previously published patents: [10] and [11] introduce ’body
capacitive voltage measurement’ similar to those shown here. In r
[10], the authors state the use of a calibrated capacitor divider rprobe Capacitive Probe probe
circuit for determining the voltage on the line. The device is
a doughnut shaped conductive material with an identical charge r
Charge Sensor s
amplifier circuit presented in Section IV-A. In [11], the authors
introduce a ’body capacitive’ probe comprising of a fixed size
sphere which hangs on the power line. They present the sensing
AC High Voltage: vL(t) Transmission Line
circuitrytomeasuretheaccumulatedchargeonthedeviceaswell.
Like[10],thecalibrationoftheprobecapacitanceisdoneoffline.
In[12]and[13],theauthorsdevelopasimilarunderstandingof (a) (b)
the capacitive coupling and propose methods to track or mitigate Fig.1. 1(a)IdealLMCVTconsistingofabodycapacitiveprobeconnectedto
changes in probe capacitance. In [12], multiple conductors are anidealchargesensorconnectedtoACvoltagesource.1(b)IdealLMCVTwith
proximitytonearbyconductor.
usedtomitigatetheeffectofnearbyconductors.Theresultsshow
a nominal voltage magnitude error of 1−12% with 1-5 minute
Figure 1(a) introduces an ideal body capacitive probe. The
averaging periods. In [13] an algorithm is proposed to mitigate
probe is a conducting sphere of radius r . Although it is
the nearby conductors and determine the height of the device probe
impractical for a final device to be a round sphere, this model
from ground. A parametric model relating the unknown height
is used since it’s capacitance is simple to compute.
of the device from ground is used along with long time captures
Connected to the sphere is an ideal charge sensor which
to estimate the height of the device and the probe capacitance.
measures the charge that accumulates on the surface of the
Finally, the estimate of the probe capacitance is used to estimate
conductor. The model assumes that the voltage source and the
the line voltage.
sensor take infinitely small volume compared to the conducting
From these the prior and proposed LMCVT technology can be
sphere, therefore producing no electric field of its own. (the
classified in the following classes.
case of non-negligible voltage source is considered in III-B).
1 Offline Calibration estimates the voltage magnitude from a
Furthermore, there is no voltage drop between the ideal charge
fixed mapping function which is determined beforehand in
sensor and the conducting sphere.
laboratory testing [10], [11]. All electrostatic sensor based
Assumeattimet≤t thedeviceispreviouslybeinguncharged
methods will fall into this category as well, since they rely 0
and after t > t the device is connected to the voltage source.
on previously computed mapping function. 0
Calculating the accumulated charge on the sphere necessary
2 Online Passive Calibration tracks specific changes such as
to maintaining a voltage of V leads to Q = 4π(cid:15) r V .
the height of the device or proximity to conductors by L 0 probe L
This is the basic definition of the probe capacitance to ground,
processing multiple passive sources [12], [13]. The changes
where C = 4π(cid:15) r . The capacitance follows the standard
are tracked in an online manner so that the mapping func- 0 probe
relationship Q = CV which leads to a very simple voltage
tion changes over time, however the task is performed by L
transducer.IfthevalueofC isknownwithcertaintly,forexample
processing passive measurements. The commonality in both
bybuildingaprobewithasphericalshapeofknownradiusplaced
methodsisthatpassivecalibrationrequires(1)longcaptures
in free space, then measuring the waveform of Q(t) gives us the
(2) parametric models of disturbances and probe-to-ground
waveform for V (t).
capacitance. L
3 Online Active Calibration uses active voltage injection onto
the capacitive probe and then recover the perturbed value B. Ideal Probe with Power Line
(depending on the probe to ground capacitance). Careful The proximity of the capacitive probe to the charging power
signal design and signal processing techniques track in real line, or any other charged conductor will decrease the effective
time changes to the probe capacitance and estimate the line capacitance of the sphere. Consider Figure 1(b) with the capac-
voltage. itive transducer but now attached between the device and the
The third method is what is proposed here to enable low idealvoltagesourceisapowerline.Thecenteroftheconducting
cost high and medium voltage measurement technology. Unlike sphere is at a distance of r from the center of the power line.
s
passivetechniques,thismethoddoesnotrequireparametricmod- Assume a switch connecting the probe to the voltage source
els, and can compute the capacitance directly via pilot signaling is switched on at some time t At t ≤ t the cable is charged
0 0
mechanism. at V but disconnected from the probe. Given that the line is at
L
V there is a non-zero electric potential at various points in the
L
III. PHYSICALMODELOFLINEMOUNTEDCAPACITIVE system, V(r,φ,z).
VOLTAGETRANSDUCER Followingtheinfinitelengthpowerlineassumption,thevoltage
Various properties of a body capacitive probe are modeled profile will have rotational symmetry as well as uniformity along
throughthefirstprinciplesofthedevicesphysicaloperation.First the cable. Therefore, only V(r) needs to be considered. At the
the charge accumulation of an ideal conductor held at the high moment t > t only Q = C(V −V(r )) amount of electrons
0 L s
voltage while leads to the floating capacitor is introduced. Then, need to accumulate on the conductor surface in order to bring
the effective capacitance of the system is discussed as well as the device to line voltage V . The voltage at surface of the
L
interference effects on nearby conductors. conductor due to the accumulated charge is V −V(r ) while
L s
3
the contribution from the power line is V(r ) leading to both charge induced can be implemented in practice by an op-amp
s
the power line and the device being charged to V . This defines with feedback capacitor C .
L s
the effective capacitance C (cid:44) Q/V which holds regardless Assume the line voltage is v (t) = V cos(ωt + φ) and
p L L L
of power line proximity. Since Q = C(V −V(r )), the probe interference capacitance can be ignored, so C = 0 Calculate
L s I
capacitanceisnow:C =C(1−α(r))whereα(r )=V(r )/V the output of op-amp (and high end of the differential ADC),
p s s L
is invariant to the actual voltage level and is computed from VADC+(jω). Since it is a non-inverting operational amplifier
the system geometry. Therefore, introducing the power line and withfeedbackamplifierZ andinputimpedanceZ theoutput
F IN
voltage source only reduces the capacitance seen by the ideal voltage is
charge sensor. (cid:18) (cid:19)
Z
VADC+(jω)= 1+ F V+(jω) (4)
Z
IN
C. Ideal Probe with Coupling Interference Source (cid:18) (cid:19)
C
= 1+ p V (jω). (5)
C L
s
q Probe
1 c12 Interference Ideal Charge Sensor Here, assume that the operational amplifier is ideal. In practice
v1 v2 q2 CVoalptaacgiet ance/ ECfafpeacctiivtaen ce Cs a low M Ω resistor is put in parallel with the capacitor to
- maintaining the leakage current of the device. The low end of
c11 c22 CI Cp + v(t) +- ADC the differential ADC is VADC−(jω)=VL(jω).
So the differential voltage measured at the input of the analog
v(t)
I v(t) input is:
L
Line Voltage
V(jω)=VADC+(jω)−VADC−(jω)
(cid:18) (cid:19)
(a) (b) C
= p V (jω)
Fig. 2. 2(a) Body Capacitive probe as a multi conductor system. In a C L
s
distribution system, the distance between conductors is small enough whereby
c11+c12isanorderofmagnitudelargerthanc12.2(b)Circuitdiagramofpassive The addition of an interference source can be done via super-
LMCVT device with practical charge sensing capability, probe capacitance Cp position principle. Shorting the AC voltage source and the body
andinterferencecapacitanceCI. capacitor, leads to a negative feedback amplifier which results
Coupled measurements between nearby conductors is an im- in the final form: V(jω) = CCpsVL(jω)− CCIsVI(jω) or in time
domain:
portanteffectthatmustbeconsidered.Inacapacitivelinesensor,
C C
the predominant form of interference is from crosstalk between v(t)= pv (t)− Iv (t) (6)
the various lines. This work considers only a single interferer for Cs L Cs I
now,buttheresultscanbeextendedtomultipleinterferingpower
lines. Figure 2(a), shows the ideal body capacitor connected to B. Passively Calibrated LMCVT
thehighvoltagepowerline.Thisthreeconductorsystem,contains Giventhiscircuitmodel,apassiveLMCVTmerelysamplesthe
(1) the body capacitive probe v1, (2) earth environment which is signal in (6). The digital signal v[n] is then used to estimate the
grounded and (3) the interferer v2. probe capacitance and the line voltage. With offline calibration
In a multi conductor system, a capacitance matrix describes methods, Cˆ is assumed fixed and known. The line magnitude is
p
the electrostatic geometry [14], [15]. Given the arrangement in then recovered via: Vˆ =(C /Cˆ )Vˆ, where Vˆ is the magnitude
L s p
Figure 2(a) the full electrostatic environment is described by: of the digital waveform v[n]. Passive calibration techniques in
(cid:20) qq12 (cid:21)=(cid:20)c11−+c21c12 c22−+c12c12(cid:21)(cid:20) vv12 (cid:21) (1) [v1(2t)] aasndwe[1ll3a],sploronpgotsiemeuscinapgtumreosdetolinegstiamssautemCpˆtpioannsdofinnCaˆlplyaVˆnLd
as before.
Consider only the charge accumulation on probe q since q is
1 2
of no interest. Recall the effective capacitance C is due to both
p
C. Actively Calibrated LMCVT
the ground and the external environment. The cross term c is
12
the interference term C . This leads to Active calibration is an alternative method where one or more
I
out of band pilot signals close to 60 Hz be inserted between the
v (t)=(c +c )v (t)−c v (t) (2)
1 11 12 L 12 2 line voltage and the charge sensing stage. This can be performed
=CpvL(t)−CIvI(t). (3) with a general DSP platform, as in Figure 3. In this situation, the
device is energized at voltage level v (t), and the DAC output
L
IV. SENSINGMETHODOLOGY of pilot signal is v (t). The non-inverting terminal voltage in an
P
This section incorporates the physical model in Section III to active calibration system is v+(t) = vL(t)+vP(t) vs. v+(t) =
develop a circuit representation of a passive LMCVT device. vL(t) in the passive case.
Then the active calibration is introduced and it’s practically From (6), omitting the interfering power lines, the input of the
implemented is shown. differential measurement is
C
v(t)= p (v (t)+v (t)). (7)
A. Circuit Model of Body Capacitive Sensor C L P
s
The circuit equivalent of the body capacitive probe with both Since the line voltage and the pilot signal are at different
proximity effect and interference is shown in Figure 2(b). The frequencies,thereceivedlinevoltagesignal(C /C )v (t)canbe
p s L
ideal charge sensor used in Section III-A which measures the filtered,leavingonlytheterm(C /C )v (t).Thepilotsignalisa
p s P
4
LMCVT w/ Active Calibration conductorandtheremainingenvironment.Normally,someoffline
Interference Effective CS procedure is used to calibrate an inverse mapping VˆL =f−1(E),
Capacitance Capacitance
where f−1(·) is fixed. An active calibration must have a voltage
-
perturbation on the entire conductor, to measure a perturbed
+
vP(t) Amplifier output f(Vp) since the field depends on the changed conductor
C C v(t) interacting with the environment. In Figure 4(a), the perturbation
I P
DAC ADC voltage must be placed on the entire conductor.
Interference vP[n] v[n] Alternatively,forcapacitivecoupling,themeasuredQ=g(VL)
Signal vI(t) DSP depends on physical configuration of the capacitive material and
theremainingenvironment.Inthiscase,activecalibrationneedsto
only to inject a voltage perturbation onto the conductive material
Line Voltage vL(t) to measure a perturbed output g(Vp) since the accumulated
charge is caused by the conductive materials interaction with
the environment. This arrangement is feasible in a practical line
Fig.3. Equivalentcircuitdiagramrepresentingbasicvoltagemeasurement.The mounted circuit. In Figure 4(b), the perturbation voltage can be
body capacitor is shown as a shunt capacitance Cp to ground. The interference placed between the conductor and the floating capacitor.
sourceiscapacitivelycoupledwithvalueCI.Thechargesensingdeviceisbuilt
byafeedbackamplifierwithimpedanceCs.
V. DEVICEPROTOTYPE
known quantity, therefore, it is possible to use the known signal
to recover C . The practical implementation can be performed
p
in an onboard DSP platform. Active calibration eliminates the
need of performing offline calibration for ’typical arrangements’
of capacitive probes on transmission and distribution systems.
Intheory,asmalloutofbandpilotsignalcanestimatetheprobe
(a)
capacitanceatveryhighvoltages.Considera300KVhighvoltage
line, and an injected pilot signal of 10 V. Given the typical body
capacitance of C = 20pF, if the maximum desired the input
p
magnitude is ±5 V, then the feedback capacitor must be 600 nF.
Also, in this situation, the amplitude of the pilot in the ADC is
167 µV. This may be lower than the noise floor, but since the
geometry in high voltage lines changes so infrequently averaging
periods can be rather long. In comparison, for a distribution line Programmable GPS w/
with nominal voltage of 10 kV, the minimum pilot voltage is 5 Analog Front NI 9223 ADC Signal Generator PPS Output
NI cDAQ-9191 Charge Sense
Wireless MCU
mV which will be close to but higher than the noise floor. Enclosure w/ conductive material Circuit (bottom)
(b) (c)
Fig.5. 5(a)Currentprototypedesignedforfurtherdevelopmentandtesting.5(b)
D. Active Calibration and Line-Mounted Voltage Sensing
Internal electronics consists of analog front end board, data acquisition system,
andwirelesscommunication.5(c)Analogfrontendconsistsofawirelessmicro
controller communicating with a programmable signal generator which injects
CoCndouncdtuocr tor
the pilot signal into the system. Charge amplifier circuit to produce measurable
DeDviecvei ce POPMO M output,andGPSPPSsignalisoutputtedtotheNIwirelessADCsystemfortiming
synchronization.

v (vt)(t)
P P POPMO M v (vt)(t) Figure5(a)showsalinemountableprototypeforevaluatingthe
P P
actively calibrated LMCVT technology. The prototype includes a
v v(t)(t) v v(t)(t)
L L L L numberofcommercialofftheshelf(COTS)andcustomhardware
f(Vf(V)+)f+(Vf(V) ) g(Vg(V)+)g+(Vg(V) )
L L P P L L P P components (shown in Figure 5(b)):
ElEecletrcotsrotasttiact ic CaCpaapcaitciviteiv e 1) Analog front end for pilot injection and signal recovery.
(a) (b) 2) NI-9223ADCandNIcDAQ-9191willprovidea100KS/s,
Fig. 4. Comparison of ’active calibration’ mechanism in electrostatic field 12 bit ADC and wireless streaming.
measurements(4(a))andcapacitivelycoupledmeasurements(4(b)).Bothmethods 3) High density LiPo Batteries, which allow up to 5 Hrs of
includealinevoltagesourcevL(t),perturbationvoltagevP(t),deviceenclosure, continuous capture time.
pointofmeasurement(P.O.M.),andcontactconductor.
TheAnalogfrontendboardconsistsofthefollowingcomponents
LMCVT technology is the only line mounted measurement (shown in Figure 5(c)):
technique that lends itself to active calibration. To understand 1) PCB mountable GPS with Pulse Per Second (PPS) output;
why,considerboththeelectrostaticfieldtechniqueandcapacitive 2) Low bias current op-amp and feedback capacitor for out-
coupling method shown in Figure 4(a), 4(b). putting the appropriate scaled down voltage signal;
In the case of electrostatic field measurement, the Point of 3) Frequency Devices SPPOSC-02 Series Programmable Os-
Measurement (P.O.M) is a point inside the device. The measured cillator [16] which can be programmed to output pure and
value E = f(V ) depends on the physical configuration of the broadband pilot signals;
L
5
4) Bluetoothenabledmicrocontrollertocontrolprogrammable B. Sinusoid Estimation
oscillator;
A Non Linear Least Squares (NLLS) Estimation procedure
The device currently under development is shown in Figure 5(b) is applied to both v [n] and v [n]. This reduces to a standard
L B
and the analog front end in Figure 5(c). The modular design least squares signal estimator for the signal amplitude and phase,
allowstestingofthetechnologyandupgradesofeachcomponent. [17] and [18]. The method is applied on a vector of length
The signal generator [16] is capable of generating frequencies N, which is set by the sample rate and expected device output
from 400 Hz to 100 kHz from an internal DSP. rate. The nominal device output rate is f = 60S/s, which
frame
corresponds to a single cycle frame length. The general least
squares estimation problem is
VI. ACTIVECALIBRATION:ALGORITHMS
N
Thissectionprovidesahighlevelarchitectureviewofthetasks {θˆ,ωˆ}=argmin(cid:88)(f [n]−v[n])2. (8)
θ,ω
required for active calibration and detailed descriptions of each
θ,ω
n
task block.
Giventhesampledwaveformv[n]andthefittingfunctionf [n].
θ,ω
The fit function, f [n], is a sum of L sinusoids of various
A. Signal Processing Architecture θ,ω
unknown frequency (ω), amplitude (α ) and phase (θ), given by
l
L
nPPS fθ,ω[n]=(cid:88)αlsin(wln+φl). (9)
LPF vL[n] 60Hz Signal α[k] φ[k] VL[k] l=1
Estimator Line Voltage
v[n] v [n] Phasor φ[k] Assuming that the number of sinusoids can be determined from
B Pilot Capacitance prior knowledge or pre-processing step (FFT analysis), the prob-
BPF
Estimator Estimator CP[k] lem can be split into two separate subproblems: (1) ω known/θ
unknown (2) ω, θ unknown.
(fP,VP) Pilot Frequency Environment Change Bad Data Flag
Both can be solved by the same computational steps: if ω is
Selection β[k] Detection
known,θˆcanbecalculatedbythefollowingleastsquareanalysis.
Note the fit function can be rewritten as
Fig. 6. Data flow for the LMCVT device for enabling PMU functionality.
Sampled data v[n] is filtered: (1) with low pass filter (LPF) for line voltage L
(cid:88)
phasor estimation (2) band pass filtered (BPF) for each pilot signal. Variations f [n]= α cos(φ )sin(w n)+α sin(φ )sin(w n)
θ,ω l l l l l l
on (NLLS) sinusoid estimator are used in extracting recovered pilot magnitude (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125)
β1[k]...βM[k] and mains sinusoid phasor α[k], φ[k]. The pilot signals are l=1 γl ηl
uvsiaedbatdod(a1t)aeflsatgimvaiateenthveiropnrombeentcaalpcahcaintagnecepoCiˆnPtd[ke]tec(2ti)onin(v3a)liaddaateptisvieglnyalseotuptipluott , where θ =[γ1,η1,...,γL,ηL]T is unknown.
magnitudeandfrequenciesdependingonfrequencyavailability.Finally,β[k]and The inference problem in (8) is non-linear in α and φ , but
l l
α[k]areusedforoutputtingthefinalvoltagephasor.
linear in γ , η , where γ = α cos(φ ) and η = α sin(φ ). The
l l l l l l l l
matrixF(ω,θ)=[f [0],...,f [N]]T isconstructed,whichis
θ,ω θ,ω
Figure 6 illustrates the general signal processing workflow
equivalent to F(ω,θ)=M(ω)θ, with the matrix
devised to extract the line voltage from the received signal v[n].
 
For clarity, Appendix Table III shows the different signals used cos(w10) sin(w10) ... cos(wL0) sin(wL0)
. . . .
in the architecture diagram. M(ω)= . . . . 
 . . . . 
1 Line and Pilot Signal Estimation: This step estimates cos(w N) sin(w N) ... cos(w N) sin(w N)
1 1 L L
α[k],φ[k] the line magnitude/phase and β[k]...β [k], the
M
pilot magnitude in a single cycle basis. Signal α[k] is and v =[v[0],...,v[N]]T. Assuming fixed frequency, the ampli-
used to recover line voltage, and β [k]...β [k] is used tude/phase component can be determined via linear least squares
1 M
to recover the probe capacitance. analysis:θˆ(ω)=argmin(cid:107)v−M(ω)θ(cid:107)2.Theleastsquaresolution
2 FrequencySelector:Certainfrequencybandscanbeperiod- is the following: θˆ(θω) = (M(ω)TM(ω))−1M(ω)Tv. Finally
ically corrupted by interfering line sources. To ensure clear
giventheγ ,η values,thesinusoidamplitudeandphasecompute
l l
frequency access, the recovered signal must be deemed
by:
reliable, if not a reliable pilot frequency must be deter-
(cid:113)
mined. This block controls the M pilot frequencies and Amplitude = γ2+η2 (10)
l l l
magnitudes: f ,V .
p,m p,m Phase =tan−1(γ /η ). (11)
3 Probe Capacitance Estimator: Signals β [k]...β [k] are l l l
1 M
used to reconstruct the probe to ground capacitance Cp. This formulation allows us to separate the estimation of the mul-
Ideally environmental changes are infrequent (on order of tiple sinusoid parameters from the estimation of the frequency of
minutes or hours) so very accurate estimates can be made. theline/pilot/harmonics.Sincetheminimizationin(8)dependson
4 EnvironmentalChangeDetector:Therecoveredpilotsignal fixed pilot/harmonic frequencies ω, a second outer minimization
β[k] is used to detect changes to the environment so can be performed to track each frequency. In [18], the authors
that a portion of the system output is discarded. After presentanumberoftechniquestoquicklyestimatethefrequency
disturbances, the previous estimate data are discarded. of various harmonics. This level of computation is required
In the following sections we elaborate each of the subcompo- for tracking the pilot signal when it is surrounded by multiple
nents. Further work is needed to fully design optimal algorithms harmonics.ThishaspracticalreasonalsoduetoADCclockdrift:
for these subcomponents. actively tracking frequency improves the estimate output.
6
C. Capacitance Estimation 6 −20
Pilot Signal
Assuming non-interfering pilot frequency, and no- 4 4 −40
environmental changes, the capacitance of the system is 2 3.5 DB] −60
fiwxheedtheirnsinmgoledeorratmeulttiimpleescfraeleque(nmciineustaerse-huosuerds)inDtheepeenstdiminagtioonn,v[n]0 3 260 355 450 555 Magnitude [ −80
different estimation procedures can be deployed. Here only a −2 FFT −100
single pilot mechanism is discussd. −4 −120
Assume a constant C (t) = C over a short time horizon.
p p −60 500 1000 1500 2000−140 2800 3000 3200 3400 3600
In single pilot mode, the injected pilot signal is vP(t) = ADC Sample Hz
V cos(2πf t + φ ). From (6), the recovered signal can be (a) (b)
P 1 1
represented with the following linear equation: Fig.7. 7(a)ShowsatypicalcapturedtimeseriesfromtheLMCVTsystem.7(b)
Shows the frequency region around the 3.2 kHz pilot signal recovered on v(t).
β[k]= VPC +w[k] (12) Note prevalence of multiple harmonics of the main 60 Hz signal at amplitudes
C p closetothepilotamplitude.
s
for processing interval k = {1,...,K}. Here, w[k] is additive
noise with noise bandwidth coming from the bandpass filter in
thesystem.Figure7indicatesthatcaremustbetakeninextracting
Figure 6. Over a long timeframe, where the probe capacitance is
the pilot amplitude.
assumed fixed, and no environmental changes are detected.
The least square estimate of the probe capacitance is then: C. Line and Pilot Signal Estimation
(cid:32) K (cid:33)
Cˆ = Cs 1 (cid:88)β[k] . (13)
P VP K 0 1.01 LGMroCunVdT T−rDutehvice 1.004
1 1.003 C
Asimilarleastsquaremethodcanbedevisedformulti-frequency
pDi.loLtisnceheVmoleta,gbeutEisstinmoattieoxnplored here. Line Magnitude (rel.)01..901910 200 400 600 800 LG1Mr0o0Cu0nVdT T−rD1u2tehv0i0ce Line Magnitude (rel.)0011....9900990089112
Finally given the estimate of the probe capacitance, Cˆ [k], the
P 0.99 0.997 GT NC
line voltage can be estimated from 0 200 400 cyc6le0 i0ndex −8 0k0 1000 1200 0.996 T−6 T−7 T−8 T−9 T−10
Vˆ [k]= Cs α[k]. (14) (a) (b)
L CˆP[k] Fig. 8. 8(a) Normalized value of αk for the LMCVT device and COTS
resistor divider ground truth in restricted faraday cage setup (top subplot) and
Assuming that Cˆ [k] = Cˆ ,∀k. The estimation interval of α[k] openairexperiment(bottomsubplot).Timeseriesshowstabilityintheestimated
is set by the measpurementpoutput rate of the device. signalamplitude.8(b)BoxplotfortestT7,...,T10.Foreachtest,singlecycle
amplitudes shown in controlled, faraday cage (left) and outside, free floating
(right)environment.
VII. ACTIVECALIBRATION:EXPERIMENTS
Thecapturedwaveformv[n]islowpassfilteredtoremoveany
A. Experiment Setup
high frequency components. The NLLS procedure is applied on
The wall outlet voltage is connected to a variable transformer
v [n]undervarioustestvoltages.Figure8(a)showstherecovered
L
(variac)thentoastepuptransformersothatvarioustestvoltages
amplitudetimeseriesinasinglecyclecapturewindow.Inthecase
canbegenerated(seeappendixforfurtherdetails).Themaximum
of tracking the line frequency, since the line magnitude is orders
achievable voltage under this technique is 1.28 kV. This signal
of magnitude larger than any harmonics, v[n] can be low pass
hasasignificantamountharmonicdistortion.However,achieving
filtered and tracked with a single sinusoid M = 1 model. Note
high accuracy under this condition lends confidence of the pilot
that the pilot magnitude, β[k] is estimated identically as α[k],
mechanism working in an actual distribution and transmission
using (10).
lines where out of band noise is common.
Figure8(b)showboxplotsofthegroundtruth(GT),controlled
In the following sections, tests at various voltages are per-
(C) and free space (NC) relative voltage magnitude captures.
formed, indicated as {T ,T ,...T ,T }. This corresponds to
0 1 9 10 The experiments indicate that the received voltage magnitude are
variac positions of {0%, 10, ...90%, 100%} of the maximum
comparable in variation. This is very important since it indicated
voltage output. The multimeter ground truth values are V , for
L,t thatundernominalconditionsoffixedC ,thevariationbetweena
t={0,...,10}, and given in Table I, Column 1. p
traditionalgroundedinstrument(GT),fixedfloatingcapacitor(C),
andopenairfloatincapacitor(NC)arenearlyidentical.Asshown
B. Received Signal insectionVII-E,thelargestsourceoferroristheestimationerror
Figure 7, shows the typical voltage waveform v[n] in sample of the probe capacitance, and not the variation of the line signal.
and frequency domain. It is clear that the injected pilot signal is Thismakessensesince,themaximumvariationofthelinevoltage
observedinv[n],asshowninFigure7(a).However,lookinginthe α[k] is well within the ±1% limits for full capture variation.
frequency domain, Figure 7(b), the signal is close in magnitude
D. Capacitance Estimation
withrespecttothevariousharmonicsofthemainsvoltage.These
harmonics can be caused by (1) harmonic distortion from the Figure 9(b) shows the estimate of Cˆ under each experiment.
p
ADC(2)harmonicsofthe60Hzsignalthatisnormallypresentin Althoughthesignalslookveryclosetoeachother,anupwardbias
7
16.94 Columns 3 and 4 indicate the voltage estimation results when
17.2
16.92 thefullscalecapacitanceC(cid:63)isknown.Clearlythemeanbiasover
17.1 16.9 p
Pilot Amplitude [mV]11661..789 Capacitance [pF]11116666....88882468 ETsrutiem Cataep aCcaiptaancciteance ahltahlolcewktLeeosvMftesCrh,iiVsigthTriesrmdedusaicofyefiludvctueisorlotyntwtomheacultalltliihitmbarivesaetteecorlsoof.fsnsBeeeottdsotehov0ndi%citegh.ieotIavnolermtrdheauernltoeoixmtfhp1eeetr%reidrm.suTeeahnntitdoss
16.7 16.8 however, does not take away from the fact that in both cases, the
16.78
16.6 maximumvariationoveralltestsisquitesmall.Inbothcases,the
T−0 T−1 T−2 T−3 T−4 T−5 T−6 T−7 T−8 T−9T−10 T−0 T−1 T−2 T−3 T−4 T−5 T−6 T−7 T−8 T−9T−10
mean error is less than 1% in the higher voltage cases, where the
(a) (b)
effect of external interferers is minimal.
Fig.9. 9(a)Recoveredpilotmagnitudeβ[k]forK=60samples/secondoutput
rate. Note that pilot signal is fairly stable over the range of line voltages under Theseresultscanbecomparetothepassivecalibrationmethod
eachtest.9(b)Meanpilotamplitudeundereachtestscenarioisusedtoestimate published in [13]. This comparison is not exact since in [13], 5
theprobecapacitance.
minuteaveragesareusedandthetestvoltagelevelsrangingfrom
5 kV to 25 kV. Following Row 2 of Table IV (HV ) in [13], the
2
authors report µ(e) = 1.72%, r(e) = (0.1,14.8)%. In compari-
is evident (blue). A full scale estimate of the probe capacitance,
son,theresultsinTableI,Column3showsinglecycletestswhere
C(cid:63), is shown as well (horizontal-green).
p the mean error is µ(e) = 0.71%. Additionally, the maximum
α¯ =κV +e , (15) errorsare(excludingthelowestvoltagelevelr(e)=(0.03,1.79).
t L,t t
C(cid:63) =C κˆ (16) Comparing the variation of errors, [13] reports σ(e) = 4.2%,
p s
while the active calibration procedure attains σ(e) = 0.05%.
This is estimated as from the experimental data by solving Although, the mean error decreases by 60%, the maximum error
the following regression equation solving for κ in (15). Then decreasesby90%whilethestandarddeviationdecreasesby98%.
(16) calculates the true capacitance. Here, VL,t is the mean It should be noted that this comparison is overly conservative
voltage recorded on the digital multimeter ground truth and sincethereportedvaluesinTableIareforsinglecycleestimates,
α¯t = K1 (cid:80)kαt[k].Eachvariactestisanindependentobservation while [13] reports 5 minute averaged values.
of (15).
The error of a single cycle (K=1) estimate, using (13), is the F. Pilot Frequency Selector
(cid:16) (cid:17)
following: σ(Cˆp)= VCPs σW. For the 1.2 kV test environment, Since the line magnitude can be orders of magnitude larger
Cs = 10nF and VP = 10V, however additive variance is than the injected pilot signal, the presence of harmonics or
extremely small. To see why, the total additive noise on the spurious signal a the exact pilot frequency can be a source
signal is 3σ = 2mV and since the signal is bandpass filtered, of error. Care must be taken in deciding what frequency is
only a small portion of that initial noise will remain. Typically, chosen. An experiment is performed where two non-harmonic
σ(Cˆp) ≈ 3.8 × 10−4. So, the variation of the single cycle
caCˆspe, under moderate averaging intervals is fairly low. A more 1.03 2.5
Available Frequency
Occupied Frequency
important source of error is bias in the estimate, as discussed in 1.02 2.4
SEe.cTLtaiibonlneeVVIo,IIl-tsaEhg,oewleEsasdttsihmetoatpmieoronfsotRrmoesfautnlhtcseeearrttoari.ned in the experimentRelative Pilot Magnitude001...9908911 [mV][V]2212222....235250 200 400 600 800 100L0ine A12m0p0litud1e4 00
where the the line voltage magnitude is estimated via active
Pilot Amplitude
calibration. Table I, column 1, indicates the ground truth voltage 0.970 500 1000 1500 2000 2500 3000 3500 210 200 400 600 800 1000 1200 1400
cycle index − k cycle index − k
which is measured by a digital multimeter measurement of the (a) (b)
linesignal.Columns2and3indicatetheresultsofthepilotbased Fig. 10. 10(a) Experiment showing two frequencies used for pilot magnitude
estimation. The output of the device is a single cycle estimate estimation:f1=3.2kHzandf2=5kHz.Pilotf1 seesaninterferencesignal,
of the line voltage V [k]. From this the single cycle relative while f2 does not. The result is clear difference in the variation of each pilot
L amplitude:theclearfrequencyseesadditivelowvariancewhitenoise,whilethe
errors:e[k]= VL−VL[k] foreachtest,canbecomputed.Therefore, occupiedfrequencyexperienceshighvarianceautoregressiveprocess.
VL
following terms are reported on a single cycle basis:
1 error mean µ(e)= 1 (cid:80) e[k], pilot frequencies were chosen, 3.2 kHz and 5 kHz, and are
K k (cid:113) used for active calibration. In this case, the 3.2 kHz frequency
2 standard deviation σ(e)= 1 (cid:80) (e[k]−µ(e))2
K k contained energy from other sources, while the 5 kHz frequency
3 range: r(e)=(minke[k],maxke[k]) has none. These are referred to as available and occupied pilot
The results indicate that the current prototype is able to reach frequencies. In the reconstruction of the pilot frequency, there is
metering quality, in half of the test cases. The mean relative a very clear difference between the two signals shown in Figure
error over all the tests is 0.72%. This is because of the overall 10(a).Intheexperimenttheleastsquareestimatein(8),issolved
overestimate of the probe capacitance in each test as shown every 1/60 seconds. Using a sample rate of 55 kHz, this leads to
in Figure 9(b) indicating a positive bias. However, this may ∼ 917 samples for estimation, leading to high accuracy in the
be removed by a multi-frequency pilot mechanism or higher NLLS procedure.
frequency pilots where there is less harmonic distortion on the Observingthetwosituationsindicateacleardifferenceineach
signal. signal type. A clear channel frequency leads to constant receive
8
TABLEI
VOLTAGEESTIMATIONEXPERIMENTS.
Cˆ estimation via pilot C(cid:63) full scale estimate
p p
V Vˆ : mean/(range) [V] error : mean/sd/(range) [%] Vˆ : mean/(range) [V] error : mean/sd/(range) [%]
L L L
125.2 122.5 / (122.0 122.7) 2.19 / 0.0638 / (2.0 2.5) 123 (122 123) 1.61 / 0.0682 / (1.45 1.99)
250.5 250.1 / (249.6 250.5) 0.19 / 0.0749 / (0.03 0.37) 251 (250 251) -0.30 / 0.0748 / (-0.46 -0.12)
383.6 384.0 / (383.3 384.3) 0.19 / 0.0483 / (0.03 0.37) 386 (385 386) -0.72 / 0.0462 / (-0.80 -0.53)
499.2 502.6 / (501.7 503.1) 0.68 / 0.0467 / (-0.07 0.49) 506 (505 506) -1.39 / 0.0420 / (-1.48 -1.20)
631.4 629.3 / (626.9 629.8) 0.68 / 0.0457 / (-0.07 0.49) 634 (631 634) -0.40 / 0.0408 / (-0.49 -0.03)
763.6 752.8 / (749.9 753.3) 1.42 / 0.0406 / (1.35 1.79) 758 (755 758) 0.73 / 0.0435 / (0.65 1.10)
890.9 881.0 / (879.6 882.1) 1.11 / 0.0533 / (0.99 1.27) 888 (886 889) 0.30 / 0.0513 / (0.18 0.46)
1019.6 1011.5 / (1006.8 1013.0) 0.80 / 0.0716 / (0.64 1.25) 1020 (1015 1021) -0.06 / 0.0996 / (-0.22 0.38)
1146.9 1136.3 / (1130.8 1144.6) 0.92 / 0.0742 / (0.2 1.39) 1145 (1140 1154) 0.10 / 0.0751 / (-0.62 0.58)
1281.2 1270.1 / (1266.5 1272.1) 0.87 / 0.0696 / (0.71 1.14) 1282 (1278 1284) -0.07 / 0.0618 / (-0.23 0.20)
0.71 / 0.0589 / (0.52 1.01) -0.02 / 0.0593 /(-0.20 0.28)
pilot amplitude, assuming that the environment is fixed. In this Itisclearthatthechangedetectionproblemandthecapacitance
case,theerrorisofverylowvariance,uncorrelatedandgaussian. tracking problem can be solved separately. However, provided
On the other hand, when the pilot frequency is occupied, the better modeling of how probe capacitances behave in the real
received amplitude is highly correlated with a variance an order world,furtherjointoptimizationispossiblebutnotexploredhere.
ofmagnitudelargerthanintheclearchannelcase.Thereislikely
to be confusion between interfering signals at a chosen pilot, and
actual environmental changes that can lead to error if a single VIII. FUTUREWORKANDOPENPROBLEMS
pilot signal in a fixed frequency is used. If multiple frequencies,
In order to further improve the accuracy of such technology
or multiple pilots are used, this error can be averted.
and enable full deployment, the following future areas must be
explored:
G. Capacitance Change Detection 1) Interference Decoupling: In the case of multi-conductor
systems, there will be multiple coupled sources at similar
If the pilot frequency is clear of any interference sources, β[k]
voltagelevelsaswellasmeasurementsateachsource.Work
canbeusedtodetectchangesintheenvironment.Atlowenough
isneededtodesignmethodsandalgorithmswheremultiple
signal frequencies it can be assumed that all frequencies will
phasor measurements are used to decouple each voltage
see the same C (t). Any environmental disturbance affecting
P
source in this situation.
the 60 Hz line can be distinguished from actual voltage changes
2) Bias Correction via multi-Frequency Pilot Mechanism: As
since it will be seen on a clear pilot frequency. An experiment
shown in Section VII-D, the offset in received pilot magni-
illustrating this was performed (see Appendix for image). A
tude leads to an offset in the recovered probe capacitance
metallicpendulumwasbuiltandusedtobringagroundedsurface
as well as voltage estimate. A multi-frequency pilot can
repeatedly close to the shell of the device, as what would happen
potentially remove this bias and improve the estimated
in some fast changing environmental change on the line. A line
voltages, and should be explored.
voltage of 1.2 kV was applied on the main line, with a pilot
3) Adaptive Frequency Selection: Work on efficient frequency
signal of 10 V at 5 kHz. Again, a 1/60 second capture window
probing/selection algorithms must be done to ensure that
was chosen for processing. Although this can be varied, it’s
thepilotfrequenciesusedcanbeusedforprobeestimation.
implausiblethatchangesinthephysicalenvironmentwilloccurat
Figure 10(a), illustrates that simple time series testing can
a very high rate. Figure 10(b) shows clearly that disturbances on
detect such changes properly.
boththe60Hzlineand5kHzpilotsignalcanbedetecteddueto
4) Environmental Change Detection: Efficiently detecting en-
the sensitivity of the pilot signal. The frequency of the pendulum
given by 1 (cid:112)g ≈ 1.3Hz matches closely to the frequency of vironmental changes from the measured pilot signals to
2π l guaranteethatanychangeinα[k]isinfactfromlinevoltage
detectedoscillation.Theoutputofthedetectorwillbeabaddata
change.
quality flag indicating accuracy compromise of the system. Since
environmental disturbances do no constantly occur on a stable
transmissionlines,theimpactofmeasurementcontinuityislikely
IX. CONCLUSIONSANDFUTUREWORK
to be minor.
Thevarianceofthepilotestimateinafixedenvironmentwillbe This work presents a method of achieving high accuracy
crucial to the performance of any change point detector. There is line mountable capacitive voltage transducers for high voltage
a tradeoff in computational resources dedicated to more refined applications. The method relies on computing the probe-to-
pilot tracking; for example, (1) tracking and removing various ground capacitance in real time using out of band pilot signal
harmonics, adaptively tracking and estimating their frequencies injection. The concept is tested in experiments and a roadmap of
(3) length and bandwidth of bandpass filters. a functional prototype is given.
9
TABLEII
APPENDIX IDEALPLATECAPACITANCEEVALUATION.SIMULATION(S)AND
A. Low Voltage Test Environment EXPERIMENTAL(E)VALUESAREINCLOSEAGREEMENT.
Thetestenvironmentweuseisametallicmeshcageconnected
Plate # Dim. [in x in] C [pF] (S) C [pF] (E)
P P
to ground. Low voltage tests are performed are susceptible to 60
Hz interference at 120/240 V which is an order of magnitude 1 12x12 15.00 14.99
largerthanthelinevoltage.Thereforeametalliccageisusefulin 2 8x8 10.34 10.27
making an interference free environment. Consider prototyping a 3 4x4 4.78 4.88
system with V = 10 V. Unfortunately, all nearby interference 4 2x2 2.3 1.84
L
sources are scattered randomly in a real laboratory environment 5 1x1 1.2 0.38
with V =120 V.
I
0.14 P−1 0.9 Simulation
B. High Voltage Test Environment 0.12 PP−−23 0.85 Experiment
P−4 0.8
0.1 P−5
0.75
V−Out00..0068 a(r)00.6.75
0.6
0.04
0.55
0.02 0.5
00 2 4 6 8 10 12 14 0.451 1.5 2 2.5 3 3.5 4
V−Line Probe Location
(a) (b)
Fig.13. 13(a)Input/Outputvoltagerelationshipofbodycapacitiveprobe.Results
from plate test verifying the theoretical linear relationship from Eq. (6) . 13(b)
Simulationandexperimentalvaluesofα(r)atvariousdistancesfromthecharged
powerline.Resultsshowthevaluesarecloseleadingtoacceptanceofthemodel.
Variac Step Up
To Wall Outlet
Transformer
(a)
1) Placethevoltagesource(NIHardware)andchargesensing
Fig. 11. High voltage test setup used to generate a maximum of 1.2 kV in
device (metallic box) outside the grounded cage.
laboratorysetting.
2) Connect the plate to a shielded cable which becomes
Figure 11(a) shows the test setup used to generate a high unshielded at the entrance of the cage
voltage AC source. A variac connected to a step up transformer 3) Compute the total capacitance of the cable and plate body
cangenerateamoderatedACsignalforfullscalevoltagetesting. capacitance.Thisisdonebymeasuringthermsinput/output
voltage (Figure 13(a)). This leads to an experimental value
of C .
P
C. Verifying Probe Capacitance in Low Voltage Testing
4) Repeat step 3 with the cable alone. The difference in
capacitances being that of the plate alone.
Shielded Cable Bare Cable Grounded Cage
Table II shows that for larger plates, the simulated value
matches very closely to the electrostatic simulation. However the
simulationandexperimentdivergeforsmallerplates.Regardless,
the experiments validate the basic premise of the body capacitor
model.Figure13(a)showsalinearrelationbetweenV andV
L CAP
for each plate, validating the model.
D. Effective Capacitance
We show a method of verifying the proposed model for the
Instrumentation / Capacitive Plate effect of power line proximity to the body capacitance of a
AC Source
probe. Figure 14(a) shows a test setup inside the grounded cage.
(a)
Like the test in Section C the instrumentation is placed outside
Fig.12. 12(a)Experimentsetupforevaluatingthevoltageinput/outputrelation
andbodycapacitanceCP ofanidealrectangularplateinfixedenvironment. of the cage to prevent any unintentional charge to act on the
probe. However, there is an external field from the copper power
Here we demonstrate the basic body capacitive effect. First line in the experiment. The probes are copper wires set on at
given a set of sheet metal plates of various sizes, we compute fixed distances from the power line. This is done to minimize
the theoretical capacitance of the probe with no charged device measurement error in evaluating various distances.
in proximity of the of the charged plate. This is done in COM- A similar procedure is conducted as in Section C where the
SOL Multiphysics simulation environment using the electrostatic capacitance of the cable and the probe is computed first; then the
simulation package. capacitance of the cable alone. The difference of the two being
The test arrangement of this is shown in Figure 12(a). To the experimental effective capacitance under a charged (C ) and
p
experimentally evaluate the charged plate with an ideal voltage uncharged (C ) power line. An experimental value of α(r) =
P
sourcewithnoproximityeffectreducingtheeffectivecapacitance 1− Cp is computed, where C and C are computed at each
CP p P
we perform the following. distance. A theoretical α(r ) can be computed easily without
k
10
Grounding Cage Charged Power line
periodicdisturbancethatiseasilydetectablebythepilotsignaling
mechanism.
TABLEIII
r1 SIGNALPROCESSINGARCHITECTURE:VARIABLEDEFINITIONS
…
r
4
Variable Definition Typical Value
n ADC sample Index
Instrumentation /
F ADC Frame Rate 50 KS/s
AC Source Capacitive Probe ADC
F Device Output Rate 60 S/s
(a) frame
k Device output frame index
v[n] Differential Input sample
v [n],v [n] Low Pass/Band Pass Filter of v[n]
L B
α[k],φ[k] Mains Magnitude/Phase Estimate
M Number of pilot signals 1
f ,V Pilot Signal Frequency/Magnitude 3,5 KHz / 10 V
p,m p,m
β [k] Recovered Pilot magnitude
m
Cˆ [k] Probe Capacitance Estimate 16 pF
p
n GPS Pulse Per Second Output
PPS
Vˆ [k],φˆ[k] Voltage Phasor Estimate
L
(b)
Fig.14. 14(a)Experimentsetupforevaluatingtheproximityeffectontheprobe
capacitance.Setupsimilartotheplatetest,exceptwithwireprobeandacharged
cIsoon-dsuucrftaecde(aotfVvLol)tatgoesilmevuellatceomappouwteedrilninCeOthMeSdOevLicfeowrislplebceificcongneeocmteedtryto..14(b) REFERENCES
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