energies

Article
An Online Measurement Method for Insulator
Creepage Distance on Transmission Lines
Jing Huang, Kejian Liu, Dan Zeng and Zhijiang Zhang *
Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory
of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and
Data Science, Shanghai University, 99 Shangda Road, Shanghai 200444, China; 18818217918@163.com (J.H.);
liukejian07@163.com (K.L.); dzeng@t.shu.edu.cn (D.Z.)
* Correspondence: zjzhang@i.shu.edu.cn; Tel.: +86-136-7191-2787




Received: 10 June 2018; Accepted: 30 June 2018; Published: 6 July 2018


Abstract: Insulators play a crucial role in ensuring the normal operation of the power system, and
the creepage distance is an important electrical parameter of insulators. Most available solutions
focus mainly on offline measurement methods, and online measurement for insulator creepage
distance on transmission lines remains a challenging task. To address this issue and to further
improve the corresponding work efficiency, an online measurement method for insulator creepage
distance is presented in this paper. Considering the glass material of the insulator and the long
measuring distance, this method recognizes the insulator type indirectly by calculating the structural
parameters of the insulators based on their geometric features, and then obtaining the creepage
distance. Accordingly, a measurement system, which mainly includes an electronic total station and a
camera with a telephoto lens, is designed in this paper. Moreover, this paper also proposes an error
analysis model aimed at reducing the errors caused by the layout of this system. In the conducted
experiments, this proposed method effectively obtains the creepage distance and the error correction
model can further improve the measurement accuracy of structural parameters.

Keywords: insulators; creepage distance; features; error correction

1. Introduction
Electrical power systems are expanding daily all over world, so situations of unscheduled
power supply interruptions can cause problems ranging from simple inconveniences up to significant
losses [1]. As a basic part of the power system, insulators play an important role in transmission
lines. Several factors affect the performance of outdoor insulators, pollution probably being the most
significant one. Contamination of insulators can cause flashovers in distribution lines as well as
outages [1–4]. Therefore, electric power departments must conduct regular inspections and timely
maintenance on electric transmission lines. The traditional inspection on electric transmission lines
mainly depends on manpower inspection, which implies high labor intensity and low inspection
efficiency [5]. In recent years, much work has been dedicated to address the above issues. For example,
various types of robots are used to inspect power transmission lines. Power line robots (PLRs) have
been developed throughout the world for inspection or maintenance tasks [6], but this emerging type of
outdoor mobile robot do not use LIDAR to detect obstacles. Lately the Hokuyo UTM-30LX laser range
finder has been used in power line robots to detect obstacles in their paths and has good performance
when encountering the challenging, outdoor, power line environmental conditions [7]. For power
transmission lines (PTLs) located in coastal and mountainous areas, inspection by aircraft is expensive
and can be dangerous under bad weather conditions. Therefore, various types of maintenance robots
for PTLs have been developed. In [8], state-of-the-art maintenance robots for power transmission lines,

Energies 2018, 11, 1781; doi:10.3390/en11071781 www.mdpi.com/journal/energies

Energies 2018, 11, 1781 2 of 18

including PTL maintenance robots that have been developed by eight major research institutions, were
summarized and tested. Moreover, due to the importance of smart sensing and power line tracking in
a smart grid system, inspection robots are also used to detect illegal electricity usage by remote current
measurement on overhead power lines [9]. For the possibility of remote detection of defective devices
on power transmission lines, an inspection robot with cameras which combine ultraviolet, infrared
and visual imaging techniques has been applied to execute the navigation and inspection tasks on
500 KV power transmission lines [10]. However, these robots do not support the inspection of other
power line components and surrounding objects.
Besides manually inspecting power lines, which is still the main method, using unmanned aerial
vehicles (UAVs) for performing automatic inspection of overhead power lines instead of foot patrols is
an attractive option, since doing so is safer and offers considerable cost savings [11]. Some researchers
have started to use unmanned helicopters to inspect power lines, such as an applied inspection robot
called Smart Copter based on an Unmanned Autonomous Helicopter (UAH) [12]; a low-altitude
unmanned aerial vehicle (UAV) remote-sensing platform, equipped with an optical digital camera,
which is used to inspect power line corridors and locate obstacles within the power line corridor
with accuracy [13]. Detecting and localizing the insulators automatically are very important for
intelligent inspection tasks, which are the prerequisites for fault diagnoses. Images of transmission
lines can also be acquired by using cameras or video cassette recorders (VCRs) carried on an UAV.
After obtaining these aerial photographs, many methods have been proposed to detect and locate the
insulators in the images with the difficulty of complex background and low image resolution [14–20].
In [14], an improved segmentation Fuzzy C-Means algorithm (FCM) is proposed to accurately segment
insulators from the image. In [15], a method based on the Histogram Oriented Gradient which could
precisely extract the insulators from the images and is suitable for many practical applications such as
insulator fault diagnosis, insulator contamination grade determination and so on was described.
Alternatively, many researchers have further analysed the insulators in the images. In [19], an
intelligent discriminant diagnosis method for porcelain fuselage insulators in transmission lines
which is based on a convolutional neural network (CNN) model is presented. In [20], a multi-saliency
aggregation-based porcelain insulator flashover fault detection approach is proposed to identify the
damaged area based on the color features of the damaged areas on the insulator surface in a color
model. However, these methods are limited to the insulator image information, and ignore the typical
structural parameters of insulators.
Because the electrical parameters of insulator are of great significance in preventing flashover
of electric transmission lines [21], among which creepage distance is a very important parameter
index [22–24], the measurement of the insulator creepage distance is meaningful. The creepage distance
is the shortest path between two conductive media measured along the surface of nonconductive
media [25]. The traditional approach is to measure the shortest distance between two electrodes
of a test piece along the insulator surface using a non-stretch tape (or wire), but this method is not
suitable for large-scale investigation of insulation creepage distance and has the disadvantage of
being time-consuming and causing outages. Much work has been dedicated to address the above
issue. In [26], auto CAD software has been used with the relationships between the curve and the
geometric equations of the insulator to calculate creepage distance and surface area; however, this
approach introduces man-made effects and still requires an offline state. The shape of the insulator
shed is arc-shaped, so the upper and lower surface area of the shed can’t be simply made by the
plane circle. In order to accurately measure the arc section of the outer skirt of the umbrella skirt,
which is the creepage distance, a sensor is used to acquire the insulator image with a laser strip and
obtain the creepage distance of the insulator in combination with the line structure light and visual
photogrammetry methods [27], but it is relatively complicated to obtain a complete laser stripe image
using a multi-pitch angle. In recent years, 3D reconstruction technology has been widely used in
inspecting power transmission lines. Comprehensive 3D point cloud data can be obtained by 3D laser
scanning and 3D modeling can also be performed by professional software. Then the creepage distance
Energies 2018, 11, 1781 3 of 18

Energies 2018, 11, x FOR PEER REVIEW 3 of 19

of the insulator is calculated based on the model [28–30]. However, this method requires fixed targets
fixed targets
around around
measured measured
insulators and isinsulators and to
not applicable is glass
not applicable to glass
insulators due to theinsulators due
detrimental to the
effects of
detrimental effects of the glass on the laser. Therefore, how to realize the online measurement of
the glass on the laser. Therefore, how to realize the online measurement of the glass insulator creepage the
glass insulator
distance creepage
has recently distance
become has recently
a challenging become a challenging problem.
problem.

2. Overview
2. Overview
The creepage
The creepagedistance
distanceisisan animportant
importantparameter
parameterofofthe the insulator
insulator that
that affects
affects thethe safe
safe operation
operation of
of transmission
transmission lines.
lines. It refers
It refers totothethe shortestdistance
shortest distancebetween
betweentwo twoelectrodes
electrodesalong
alongthetheouter
outer surface
surface
of the
of the insulating
insulating member
member under under aanormal
normaloperating
operating voltage.
voltage. TheThe creepage
creepage distance
distance measurement
measurement
mainly includes offline and online measurements. Generally, offline methods are adopted, however,
mainly includes offline and online measurements. Generally, offline methods are adopted, however,
those methods
those methods are are not
not applicable
applicable in in practical
practical situations
situations because
because of of the
the power-off
power-off and
and low
low efficiency.
efficiency.
On the
On the other
other hand,
hand, there
there areare certain
certain difficulties
difficulties with
with online
online measurements,
measurements, mainly mainly reflected
reflected in in the
the
following three
following three aspects:
aspects: (1) (1) most
most of of the
the currently
currently used
used insulators
insulators on on transmission
transmission lines
lines are
are glass
glass
materials;(2)
materials; (2)insulators
insulatorslocated
locatedininthe the high-voltage
high-voltage transmission
transmission lineline tower
tower are are
at a at a large
large distance;
distance; and
and (3) non-contact measurements
(3) non-contact measurements are required. are required.
Different insulator
Different insulator types
types generally
generally present
present different
different electrical
electrical parameters.
parameters. In In Figure
Figure 1,1, the
the first
first
row shows four different insulator types and the second row describes
row shows four different insulator types and the second row describes the corresponding section the corresponding section
outlines. The
outlines. The red
red path
path describes
describes the the creepage
creepage distance
distance ofof the
the insulator.
insulator. Because
Because the
the insulator
insulator type
type has
has
in one-to-one
in one-to-one correspondence
correspondence with with thethe creepage
creepage distance,
distance, andand the
the structural
structural parameters
parameters of of different
different
insulator types are also different, the insulator type can be obtained by
insulator types are also different, the insulator type can be obtained by calculating the structural calculating the structural
parameters of
parameters of the
the insulator
insulator and and then
then thethecreepage
creepagedistance
distanceisisdetermined.
determined.

Figure 1. Profile of different insulators.

Figure 1. Profile of different insulators.

In
In this
this paper,
paper, anan online
online measurement
measurement method method of of insulator
insulator creepage
creepage distance
distance is is proposed,
proposed, which
which
indirectly
indirectlyobtains
obtainsthetheinsulator
insulatortype
typebybycalculating
calculating the structural
the structuralparameters
parameters of the insulators
of the based
insulators on
based
their geometric features and then obtains the creepage distance. The idea behind
on their geometric features and then obtains the creepage distance. The idea behind the proposed the proposed solution
is depictedisindepicted
solution Figure 2. inFirstly, the electric
Figure 2. Firstly,power theengineers
electric set up a engineers
power non-contactset measurement system
up a non-contact
consisting
measurement of ansystem
electronic total station
consisting of anand a camera
electronic module.
total stationTheandcamera module
a camera is usedThe
module. to capture
camera
images
moduleof is the insulators
used to capture and the electronic
images total station
of the insulators and theacquires the depth
electronic distance
total station of the the
acquires insulator
depth
through
distance laser
of theranging.
insulatorNext,
throughthelaser
contours of umbrella
ranging. Next, theskirts
contoursare of
extracted
umbrella inskirts
the image and then
are extracted in
the
the absolute
image and dimensions
then the of the insulator’s
absolute dimensions structural
of the parameters are obtained
insulator’s structural based on are
parameters geometrical
obtained
feature
based on of area ratio andfeature
geometrical geometrical
of areafeature
ratio of
and radius. Finally, feature
geometrical a structural parameter
of radius. processing
Finally, step
a structural
is performed
parameter to matchstep
processing the is
type and then
performed to determine
match the type the creepage
and then distance.
determineHowever,
the creepage because the
distance.
glass has detrimental effects on the laser, the existing laser ranging method
However, because the glass has detrimental effects on the laser, the existing laser ranging method has a large measurement
error
has aandlargemay even cause error
measurement the failure
and mayof the measurement.
even Therefore,
cause the failure of thethe measured depth
measurement. distance
Therefore, the
from the system
measured depthtodistance
the metal umbrella
from handle
the system toisthe
used to approximately
metal umbrella handle replace the distance
is used from the
to approximately
system
replace to thethe glass umbrella
distance from theskirt
systemof each
to thelayer.
glassSimultaneously,
umbrella skirt of theeach
errors caused
layer. by the layoutthe
Simultaneously, of
the measurement
errors caused bysystem are also
the layout of corrected to improvesystem
the measurement the measurement accuracy to
are also corrected of the insulator
improve the
measurement accuracy of the insulator structural parameters, thereby achieving accurate recognition
of the insulator types and acquisition of the creepage distance.
Energies 2018, 11, 1781 4 of 18

structural parameters, thereby achieving accurate recognition of the insulator types and acquisition of
Energies 2018, 11, x FOR PEER REVIEW 4 of 19
the creepage distance.

Target saliency-
The camera area ratio feature
module Contours of
Capturing the Structural parameters
umbrella skirts
image
Energies 2018, 11, x FOR PEER of insulator
REVIEW processing
4 of 19
extraction
Target saliency-
Measurement radius feature
system design
Target saliency-
The camera
Acquiring the
area ratio feature
module
Electronical depth distance
Capturing the
Contours of
umbrella skirts Structural parameters
Determine the
total station image of insulator processing
extraction creepage distance
Target saliency-
Measurement radius feature
system design
Acquiring
Correcting the the
errors
caused depth
Electronical by the distance
geometric Determine the
total station layout creepage distance

Figure 2. Correcting
Flowchart
2. Flowchart of the theproposed
errors insulator creepage
creepage distance
distance measurement
measurement approach.
approach.
Figure causedofbythe
the proposed
geometric insulator
layout

3. Methods
3. Methods
Figure 2. Flowchart of the proposed insulator creepage distance measurement approach.
3.1. Design
3.1. Design of
of the
the Measurement
Measurement System
System
3. Methods
Based on
Based on the proposed
proposed solution,
solution, the the electric
electric power
power engineerengineer needs needs to to establish
establish aa measurement
measurement
3.1. Designtheof the Measurement System
system. As
system. As shown
shown in in Figure
Figure 3, 3, the
the system
system includes
includes three three parts:
parts: (a) (a) the
the measured
measured insulator;
insulator; (b)(b) the
the
electronic Based
total on the proposed
station with a solution,
laser the electric power
transmitter; and (c) engineer
the needs module.
camera to establishThe a measurement
measured insulator
electronic total station with a laser transmitter; and (c) the camera module. The measured insulator
whosesystem.
whose umbrella
umbrella
As shown
skirts in
skirts are
are
Figure
made
made
3, of
theglass
system
of glass
includeson
is placed
is placed three parts: (a) the measured
aa transmission
transmission line at insulator;
at aa large
large (b) the Since the
distance.
electronic total station with a laser transmitter; and on (c) the camera module. line The measured distance.
insulator Since the
measurement distance
measurement distanceisisfar farthe the visual
visual method leads
method to ato a large error indepth the depth measurement
whose umbrella skirts are made of glass is placedleads large
on a transmission error
line atina the
large distance.measurement
Since the of the
of the insulator.
insulator. Therefore,
measurement Therefore,
the electronic
distance the electronic
is far the visualtotal total
station
method station
is used
leads to a large is used
to obtain to
error inthe obtain the depth
depthmeasurement
the depth distance
distance ofofthe of the
theinsulator.
insulator.
Because Because
insulator.
the transparentthe transparent
Therefore, theglass
electronic glassstation
total
umbrella umbrella
is used
skirts skirts
scatterto obtainscatter
limitsthethe limits
depth thelight,
distance
laser laser light,
of the causing
insulator.
causing from
from large
large Because
measurement the transparent
measurement errorserrors
up to up glass umbrellaof
to failures
failures skirts scatter limitsthe
measurement,
of measurement, the depth thedepth
laser light,
distance iscausing
distance from largeby hitting
is measured
measured by hitting the
the measurement
laser on the errorshandle
metal up to failures
of the of measurement,
insulator, which theisdepth distance
regarded as isthe
measured
distance by from
hittingthethesystem to
laser on the metal handle of the insulator, which is regarded as the distance
laser on the metal handle of the insulator, which is regarded as the distance from the system to each
from the system to each
each umbrella
umbrella skirt,
skirt,skirt,
andand and
thethethe
error error caused by this replacement has been verified to be negligible in the
the
umbrella errorcaused
caused by thisreplacement
by this replacement has has
beenbeen
verified verified to be negligible
to be negligible in the in
following
following experiment.
experiment.
following experiment. At
AtAt the
the same
thesame time,
same time, the camera
thecamera
time, the camera module
module
module is used
is used
is used to capture
to capture
to capture a clear image
a clearofimage
a clear image the of the
of the
measured
measured insulator
measured insulator
insulator from
fromfromaa large
large distance
a largedistance
distance andandobtain
and obtain
obtain the
thethe two-dimensional
two-dimensional
two-dimensional parameters parameters ofthe
theinsulator.
of the insulator.
parameters of insulator.

Figure 3.
Figure 3. Illustration
Illustration of of
thethe
measurement system.
measurement system.

Figure 3. Illustration of the measurement system.

Energies 2018, 11, 1781 5 of 18

3.2. Saliency Geometry Features of the Insulator

The insulator type can be obtained through calculating the structural parameters of the insulator.
These structural parameters should meet the characteristics of easy capture and good distinction.
The method proposed in this paper uses the salient geometric features of the insulator to obtain the
structural parameters. The feature of the radius is used to preliminarily distinguish insulator types
and the feature of the area ratio of umbrella skirts can further distinguish similar insulators. Thus, the
type of insulator can be determined.

3.2.1. The Radius Feature of the Target

Figure 4 shows a projection sketch map of an insulator with three layers. According to the
invariant theory of projective properties, a circle in 3D space is generally projected to an ellipse in an
image. In particular, the long axis of the ellipse equals the diameter of the circle. Since all the umbrella
skirts of an insulator are concentric circles, their plane projections are also all concentric ellipses.
Moreover, the long shaft of each concentric ellipse is as long as the diameter of the corresponding
umbrella skirt.
In this measurement model as shown in Figure 3, XL YL ZL is the coordinate system of the electronic
total station, and the depth distance denoted as s1 from the system to the insulator can be obtained
in this coordinate system; In computer vision [31], Xc Yc Zc is called the camera’s coordinate system,
and the intersection of the optical axis and the image plane is O1 . Setting f as the focal length of the
lens, illustrated explanations are made as follows: O1 Oc is the distance from the image plane to the
projective centre and is denoted m; POc is the distance from the point P to the projective centre and is
denoted n. Thus, according to the Gaussian imaging formula, Equation (1) is satisfied:

1 1 1
= + . (1)
f m n

The electronic total station and the camera are on the same horizontal line, and the distance
between them is small compared with the measured depth distance, so the object distance n is replaced
with the measured depth distance s1 . Thus, the following equation is obtained:

f s1
m= . (2)
s1 − f

Since n >> f, the small hole imaging model can be used here. Thus, the relationship between the
radius r in the image and the actual radius R is established, where r = r 0 · N, r 0 is the pixel value of the
22.3
insulator radius on the image and N = 1056 (mm/pixels) which is the size conversion of pixels and
physical distances:
R n
= . (3)
r m
Thus the solution of the real radius R could be described using Equation (4). The serial number of
insulator layers from outside to inside recorded as i is less than or equal to four, i.e., i ≤ 4. The same
definition is adopted in the rest of this paper:

s1 − f
R= r. (4)
f

The evolution of the real radius R with respect to depth distance s1 is given by:

∂R r
= . (5)
∂s1 f

Since f is much larger than r and s1 has little effect on R, the depth distance from the system to the
metal handle can be used to represent the depth distance of each umbrella skirt in theory.
Energies 2018, 11, x FOR PEER REVIEW 6 of 19

EnergiesSince
2018, 11,
f is1781
much larger than r and 𝑠1 has little effect on R, the depth distance from the system
6 of 18
to
the metal handle can be used to represent the depth distance of each umbrella skirt in theory.
Furthermore, the error caused by this replacement is considered and discussed in Figure 5. For
Furthermore, the error caused by this replacement is considered and discussed in Figure 5.
example, consider an insulator where the measured distance from the system to the metal handle O
For example, consider an insulator where the measured distance from the system to the metal handle
is 44.501 m, the radius r of the 2th layer in the image is 5.4788 mm, and the distance recorded as t from
O is 44.501 m, the radius r of the 2th layer in the image is 5.4788 mm, and the distance recorded as t
the 2th layer of the umbrella skirts to the metal handle O is changing within 40 mm. From Table 1, it
from the 2th layer of the umbrella skirts to the metal handle O is changing within 40 mm. From Table 1,
can be seen that the error of the measured radius caused by the replacement is less than 0.1 mm, and
it can be seen that the error of the measured radius caused by the replacement is less than 0.1 mm, and
the statistical error is 0.042 mm calculated from 40 sets of data. Therefore, the error introduced by the
the statistical error is 0.042 mm calculated from 40 sets of data. Therefore, the error introduced by the
approximate substitution has a very small influence on the measured values of our system and can
approximate substitution has a very small influence on the measured values of our system and can be
be ignored here.
ignored here.

r1
r2 Projective
r3 center

R3
R2
Imaging Plane
R1

Figure 4. Projection of an insulator with three layers.

Figure 4. Projection of an insulator with three layers.

Table 1. Radius error caused by the replacement.

Table 1. Radius error caused by the replacement.

t (mm)
t (mm) 4 4 8 8 1212 16
16 20
20 24
24 28
28 3232 3636 40 40
Error (mm)
Error (mm) 0.0084 0.0169 0.0253 0.0337 0.0421 0.0506 0.0590 0.0674 0.0759 0.0843
0.0084 0.0169 0.0253 0.0337 0.0421 0.0506 0.0590 0.0674 0.0759 0.0843

Because an ellipse has five degrees of freedom, the position and shape of an ellipse can be
Because an ellipse has five degrees of freedom, the position and shape of an ellipse can be
determined solely by five parameters. The implicit equation of ellipse is written as follows:
determined solely by five parameters. The implicit equation of ellipse is written as follows:
F ( x, y)  a1 x 2  a2 xy  a3 y 2  a4 x  a5 y  a6  0. (6)
F ( x, y) = a1 x2 + a2 xy + a3 y2 + a4 x + a5 y + a6 = 0. (6)
Using the least squares method based on the algebraic distance to fit the ellipse, the engineers
select
Usingfive evenly
the leastdistributed points on
squares method the ion
based th layer of the umbrellas in the image, which are denoted
the algebraic distance to fit the ellipse, the engineers
as (x ij, yij ) j = [1, 2, 3, 4, 5]. Due to some errors, the above equation does not necessarily have a solution
select five evenly distributed points on the ith layer of the umbrellas in the image, which are denoted
matching
as (xij , yij ) jthe
= [1,actual
2, 3, 4,measured
5]. Due topoints. In thisthe
some errors, case, the best
above approximation
equation theoremshave
does not necessarily are introduced
a solution
to explore the existence of an approximate solution. The specific solution
matching the actual measured points. In this case, the best approximation theorems are introduced process has been described
in [32,33]. Thus, the long shaft of ellipse can be computed with the following
to explore the existence of an approximate solution. The specific solution process has been described equation:
in [32,33]. Thus, the long shaft of ellipse can be computed with the following equation:
4 2a
a  2r=  √ 6 .
i 1
−4 2a6 
 
(7)
a = 2ri = n (a  a ) F  (a 2 a 2  a 2  2a a  a 2 ) 2  o 1 .
1 2
(7)
 1 3 2 6 1 1 3 3 1 2
( a1+ a3 ) F − ( a2 2 a6 2 + a1 2 − 2a1 a3 + a3 2 ) 2

3.2.2.
3.2.2.The
TheArea
AreaRatio
RatioFeature
Featureof
ofthe
theTarget
Target
As
Asshown
shownin inFigure
Figure5,5,AB,
AB,CD,
CD,andandEF
EFare arethe
theumbrella
umbrellaskirts
skirtsof
ofone
oneinsulator,
insulator,and
andAB,
AB,CD,
CD,and
and
GH
GH are the umbrella skirts of another insulator. The two insulators differ only in the thicknessof
are the umbrella skirts of another insulator. The two insulators differ only in the thickness ofthe
the
00 00
third layer, both of which are projected as E F on the plane of the metal handle O
third layer, both of which are projected as E″F″ on the plane of the metal handle O and both have and both have the
same measured
the same radiusradius
measured values. In thisIn
values. case,
thisthey
case,will be will
they misrecognized as the same
be misrecognized insulator
as the if only theif
same insulator
radius feature
only the is feature
radius used. Toisaddress
used. Tothe shortcomings
address of the radius
the shortcomings feature,
of the radius this paper this
feature, further proposes
paper further
the feature of the area ratio, namely, the area ratio between each layer of the fitted umbrella skirts in
the image.
Energies 2018, 11, x FOR PEER REVIEW 7 of 19
Energies 2018, 11, x FOR PEER REVIEW 7 of 19

proposes
Energies the
2018, feature
11,feature
1781 of the area ratio, namely, the area ratio between each layer of the fitted umbrella
7 of 18
proposes the of the area ratio, namely, the area ratio between each layer of the fitted umbrella
skirts in the image.
skirts in the image.
According to the dependency and definite proportion of line projections, collinear line segments
According to
According to the
the dependency
dependency and definite
and definite proportion
proportion of line
of line projections, collinear line
projections,incollinear line segments
segments
will retain the same length ratio before and after projection. As illustrated Figure 6, a concentric
will
will retain the
retain the same
same length
length ratio before
ratio denoted and
before and after
after projection. As illustrated in Figure 6, a concentric
projection. As illustrated in Figure 6, a concentric
hemisphere has a line segment, O1-A 1-B1 passing through its centre, and its corresponding
hemisphere
hemisphere has a line segment, denoted O 1-A1-B1 passing through its centre, and its corresponding
projection onhasthea 2D
lineimaging
segment, is denoted
denoted O -A21-B
O12-A -B21. passing through its centre, and its corresponding
projection on
projection on the
the 2D
2D imaging
imaging isis denoted
denoted OO2-A
-A2-B-B2..
2 2 2

A
A
C
C
projective E
projective E G
center G
center
O
O 3 2 1
3 2 1
F
F H
H
D
D aa
B
B
t
t
Imaging plane Umbrella skirts of
Imaging plane Umbrella skirts of
insulator
insulator

Figure 5. Example
Figure 5. Example of
of two
two similar
similar insulators.
insulators.
Figure 5. Example of two similar insulators.

R2
O1 R1 R2
O1 R1 A1 B1
A1 B1

a2
O2 a1 a2 A2 B2
O2 a1 A2 B2
b1
b1 b
2
b2

Figure 6.
Figure 6. Projection
Projection of
of aa spatial
spatial circle
circle on
on imaging
imaging plane.
plane.
Figure 6. Projection of a spatial circle on imaging plane.

Thus, the following

Thus, following equation isis satisfied:
satisfied:
Thus, the
the following equation
equation is satisfied:
a R1 b1
a1 a11 =RR bb11 .
11  (8)
a2 R2= b2. .
= = (8)
a2 a2 RR 22 bb22
Furthermore, the area ratio is defined as follows:
Furthermore, the area ratio is defined
defined asas follows:
follows:
R R1 a1b1
 RR11R
area ratio πR a1bb1 .
1 = πa (9)
areaarea =  1R
ratio
ratio R21R2== a12b12 ..
a 22bb22 (9)
πR2 R2 R22 πa

Therefore, the engineer can directly calculate the area ratio in the image with the long and short
shafts of the ellipse to obtain the actual area ratio of the umbrella skirt. In Figure 5, the projections to
Energies 2018, 11, 1781 8 of 18

the imaging plane from EF and GH are regarded as E0 F0 and G0 H0 , respectively; thus, their area ratios
are different and can be used to distinguish these two similar types.

3.3. Correction of the Errors Caused by the Geometric Layout

In the above established measurement system, as shown in Figure 3, the distance s1 measured by
the electronic total station is considered the depth distance from the projective centre to the insulator in
the camera model; this distance is an approximate substitution based on ignoring the distance between
the electronic total station and the camera. However, in this section, the paper will consider the
above distance and will analyse the error caused by the geometric layout of this system; subsequently,
an error correction model is established to improve the measurement accuracy of the radius values.
As shown in Figure 6, the electronic total station and the camera are fixed separately on screws OL
and OR , and the distance between OL and OR is denoted as d, which leads to the error; the correction
calculation equation is also given in this section.
In Figure 7, the coordinate system for the electronic total station OL -XL YL ZL is established.
Moreover, the distance of OL OR is 320 mm, and point P is one point on the metal handle of the
insulator. The distance from P to OL is s1 , and θ denotes the angle between POL and OL OR ; this angle
can also be obtained by the electronic total station directly. Moreover, the point Oc is the projective
centre, P1 is the projected point of P in the imaging plane, and the distance between OR and the
imaging plane written as c is 4.88 mm. In this established model, the corrected distance from the point
P to the projective centre can be calculated as follows:
1
n = (S1 2 + d2 − 2dS1 cos θ ) 2 + c + m. (10)

Substitute this into Equation (1), the following equation set is established:
( 1
n = (S1 2 + d2 − 2dS1 cos θ ) 2 + c + m
1 1 1
. (11)
f = m + n

Assume that A = S12 + d2 − 2dS1 cos θ + c, and then solve Equation (10) to obtain m:

n o1
(2 f − A) + ( A − 2 f )2 + 4A f
2

m= (12)
2
Therefore, in this model, the calculation equation of the measured radius is given by:
 

 

 2A 
Ri = 1+ h i 1 ri (13)
 2 2

 (2 f − A) + ( A − 2 f ) + 4A f  
Energies 2018,
2018, 11,
11, 1781
x FOR PEER REVIEW 9 of 18
19

screw d c

Figure
Figure 7. Correction model
7. Correction model of
of error
error caused
caused by
by geometric
geometric layout.
layout.

3.4. Structural Parameters Processing

ki 𝑖 𝑘 k0
measured area
The measured arearatio
ratioof
ofthe
theellipse
ellipseand
andthe
thestandard
standardvalue
valueare
aredefined
defined Sij 𝑆=
asas 𝑖𝑗 = and0 𝑆𝑖𝑗 k=
k 𝑘and Sij =
i
0,
j 𝑗 j
′
𝑘𝑖
respectively (i and j arej are
serial numbers of umbrella skirts i < j,i <k jj,, k𝑘0j represent
andand the ellipse area and
𝑘𝑗′
, respectively (i and serial numbers of umbrella skirts 𝑗 , 𝑘𝑗 represent the ellipse area
standard area of jth layer). Moreover, R j and RS j are the measured radius and the standard value of
andjstandard
the area of jth layer).
layer, respectively, and Moreover, 𝑅𝑗 the
N represents 𝑅𝑆𝑗number
andtotal are the measured
of umbrella radius andThus,
skirts. the standard value
the matching
th
of theEjthislayer,
error respectively,
calculated and N represents the
as the root-mean-square total
error numberTherefore,
(RMSE). of umbrella theskirts. Thus,
problem is the matching
transformed
error
to E is calculated
seeking as the
the insulator root-mean-square
type with the minimum errormatching
(RMSE). Therefore,
error. Thenthe theproblem
creepage is distance
transformed to
of the
seeking the insulator
insulator is determined: type with the minimum matching error. Then the creepage distance of the
insulator is determined:
 N N −1 N
 12
2 0 2 1
 j∑ (NR j − Rs j ) + ∑N 1 ∑N (Sij − Sij ) 
 =1 ( R  R ) 2 i 2
E=   j sj
0.5( N 2 +

=1 j = i +1
)i 1
i 1Nj 
( S ij  S ' 2
ij ) 
 (14)
E  
j 1
(14)
 
 0.5( N 2  N ) 
 

4. Experimental Results and Discussion 

Several experiments are conducted to evaluate the performance of the proposed online
4. Experimental
measurement Results
system. and
First Discussion
of all, the experimental schedules are managed, and the experimental setup
is described in detail; secondly, the
Several experiments are conducted pose stability of the measurement
to evaluate is verified
the performance of in
theTest_1, comparative
proposed online
testing for the error
measurement correction
system. First ofmodel is established
all, the experimentalin Test_2, and are
schedules the results
managed, of insulator
and thetype matching
experimental
and
setupcreepage distance
is described are described
in detail; secondly,inthe Test_3;
pose Finally,
stabilitythe
of practical performance
the measurement of the in
is verified proposed
Test_1,
system is evaluated
comparative testing outdoors.
for the error correction model is established in Test_2, and the results of insulator
type matching and creepage distance are described in Test_3; Finally, the practical performance of
4.1. Experimental Setup
the proposed system is evaluated outdoors.
The proposed measurement system is illustrated in Figure 8. The workflow is listed as follows:
Energies 2018,
Energies 2018, 11,
11, xx FOR
FOR PEER
PEER REVIEW
REVIEW 10 of
10 of 19
19

Energies 2018, 11, 1781 10 of 18

4.1. Experimental
4.1. Experimental Setup
Setup
The proposed
The proposed measurement
measurement systemsystem is is illustrated
illustrated inin Figure
Figure 8.
8. The
The workflow
workflow is is listed
listed as
as follows:
follows:
(1) Data collection: Construct the measurement system as shown in Figure 8. Next, adjust the
(1) Data
(1) Data collection:
collection:
electronic Construct
Construct
total station the the
the
to make measurement
measurement
laser preciselysystem
system as metal
as
hit the shown
shown in Figure
in
handle Figure 8.insulator
of the8. Next, adjust
Next, adjust
and thenthe
the
electronic
electronic total station
total station
capture a clear image of to make
to the
make the laser
the laser
distant precisely
precisely
insulator on the hit the metal
hittransmissionhandle
the metal handle of
linesof the insulator
the insulator
using the camera and
and then
thena
with
capture
capture
telephoto aa clear
clear image of
lens. image of the
the distant
distant insulator
insulator onon the
the transmission
transmission lines
lines using
using the
the camera
camera with
with aa
telephoto
(2) telephoto lens.
lens.
Solving parameters: Combine the measured depth distance of the insulator and the captured
(2) Solving
(2) Solving parameters:
image toparameters: Combine
calculate theCombine
structural the
the measuredofdepth
measured
parameters depth distance of
distance
the insulator. of the
the insulator
insulator andand the
the captured
captured
image
(3) image
Creepageto calculate
to calculate the
distance the structural parameters
structural
measurement: parameters
Post-process of these
of the insulator.
the insulator.
parameters, obtain the matching result that
(3) Creepage
(3) Creepage distance
distance
is the expected measurement:
measurement:
insulator Post-process
type, andPost-process
then gain the these
these parameters,
finalparameters, obtain the
obtain
creepage distance. the matching
matching result
result that
that
is the expected insulator type, and then gain the final creepage
is the expected insulator type, and then gain the final creepage distance. distance.

Figure
Figure 8. Composition of
8. Composition of the
the measurement
measurement system.
system.
system.

4.2. Several
4.2. Several Experiments
Experiments

4.2.1. Test_1:
Test_1: Pose
4.2.1. Test_1: Pose Stability
Stability Testing
Stability Testing
Testing
The
The experiment
The experimentof
experiment oftest_1
of test_1isis
test_1 isaimed
aimedatat
aimed atverifying
verifyingthe
verifying thepose
the posestability
pose ofof
stability
stability the
of the
themeasurement.
measurement.
measurement. AsAs
Asshown
shown
shownin
Figure
in 9, an
in Figure
Figure insulator
9, an
9, an insulator
insulatorwith sixsix
with
with sixslight postural
slight
slight posturalchanges
postural changesisis
changes isplaced
placedatat
placed ataaafixed
fixeddistance,
fixed distance, which
distance, which simulates
which simulates
the
the slight pose difference of the same insulator on an actual transmission line. In this experiment, the
slight pose difference
difference of
of the same
same insulator
insulator on an
an actual
actual transmission
transmission line.
line. In this experiment, the
measurement
measurementsystem
measurement systemisis
system isused
usedtoto
used toobtain
obtainthe
obtain the
thestructural parameters
structural
structural parameters
parameters of the insulator
of the
of the in different
insulator
insulator poses,
in different
in different and
poses,
poses,
experimental
and experimental
and results
experimental are analysed
results
results are analysed
are and discussed
analysed in thein
and discussed
and discussed infollowing paragraphs.
the following
the following paragraphs.
paragraphs.

(a) Pose
(a) Pose 11 (b) Pose
(b) Pose 22 (c) Pose
(c) Pose 33

(d) Pose
(d) Pose 44 (e) Pose
(e) Pose 55 (f) Pose
(f) Pose 66

Figure 9.
Figure 9. An
An insulator with
with six different
different poses.
poses.
Figure 9. An insulator
insulator with six
six different poses.
Energies 2018, 11, 1781 11 of 18
Energies 2018, 11, x FOR PEER REVIEW 11 of 19

InFigure
In Figure10,
10,the
theabscissa
abscissaindicates
indicatesthe
thedifferent
differentstructural
structuralparameters
parametersof ofthe
theinsulator,
insulator,and andthe
the
ordinate shows the relative error between the measured structural parameters value
ordinate shows the relative error between the measured structural parameters value and the standard and the standard
value. Different
value. Different colours
colours represent
represent the
the above
above six
sixdifferent
differentposes.
poses. From
From the
thediagram,
diagram,the thefollowing
following
analyses can be obtained:
analyses can be obtained:
(1)About
(1) AboutR1 R1andandR2,
R2,points
pointsononthe
thepolylines
polylinesareareclose,
close,while
whilepoints
pointsarearerelatively
relativelydispersed
dispersed
regardingR3.
regarding R3.Because
BecauseR3 R3represents
representsthetheradius
radiusofofthe
theinnermost
innermostlayerlayerofofthe
theinsulator,
insulator,andandin inthe
thecase
case
of the same measurement error, the smaller the radius is, the more obvious the
of the same measurement error, the smaller the radius is, the more obvious the relative error is. relative error is.
(2)The
(2) Thearea
area ratios
ratios of insulators
of the the insulators generally
generally range range
from 0from
to 10; 0however,
to 10; however,
relative torelative to the
the measured
insulator radiuses which usually range from 40 mm to 200 mm, the measurement error is moreis
measured insulator radiuses which usually range from 40 mm to 200 mm, the measurement error
more obviously
obviously reflectedreflected in thethat
in the figure figure
thesethat these
points points representing
representing the area
the area ratios ratiosdispersed
are more are more
dispersedwith
compared compared with radiuses.
radiuses.
(3) Based on the
(3) Based on the actual actual measurement
measurement requirements,
requirements, the measurement
the measurement error the
error is within is within
allowablethe
allowable range, so the polylines approximately coincide together, indicating
range, so the polylines approximately coincide together, indicating that the measured results tend to that the measured
results
be stabletend
whento the
be stable whenhave
insulators the insulators havechanges.
slight postural slight postural changes.

3.0
2.8
2.6
2.4
2.2
2.0
Relative error(%)

1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
pose1 pose2
0.2
pose3 pose4
0.0 pose5 pose6
-0.2
R1 R2 R3 S12 S13 S23
Parameters

Figure10.
Figure 10.Relative
Relativeerrors
errorsgraph
graphof
ofthe
theinsulator
insulatorwith
withdifferent
differentposes.
poses.

4.2.2.Test_2:
4.2.2. Test_2:Comparative
ComparativeTesting
Testingwith
withError
ErrorCorrection
Correction
Theexperiment
The experiment of oftest_2
test_2isisto
toverify
verifythetheeffectiveness
effectivenessof ofthe
theerror
errorcorrection
correctionmodel,model,multiple
multiple
insulators at different distances are measured by the measurement system
insulators at different distances are measured by the measurement system and the error correction and the error correction
modelisisused
model usedtotocorrect
correctthethemeasured
measuredvalues.
values. InInFigure
Figure11,
11,diagrams
diagrams(a–d)
(a–d)arearecomparison
comparisoncharts charts
before and after the error correction of the radius in the different skirt layers, where the subscriptsa
before and after the error correction of the radius in the different skirt layers, where the subscripts
aand
andbbrepresent
represent the the radius-measured
radius-measured value value after
after and before the
and before the correction,
correction, respectively
respectively and and the
the
subscriptssdenotes
subscript denotesthe thestandard
standardvalues.
values.Moreover,
Moreover,the thered
redline
linerepresents
representsthethemeasured
measuredradius radiusbefore
before
the error correction, the blue line represents the measured radius after the
the error correction, the blue line represents the measured radius after the error correction, and theerror correction, and the
standard value is displayed by
standard value is displayed by the grey line. the grey line.
Fromthe
From thefigure,
figure,ititcan
canbebeseen
seenthat
thatthe
thered
redline
linehashasgreater
greaterdeviation
deviationfrom
fromthethegrey
greyline
lineandandthese
these
errors are introduced by the geometric layout of the measurement system.
errors are introduced by the geometric layout of the measurement system. Then the RMSE is used Then the RMSE is used
hereto
here toevaluate
evaluate the the deviation
deviation between
between the the measured
measured values
valuesand
andthethestandard
standardvalues.
values.The The RMSE
RMSE of
R 1𝑏 , R 2𝑏 , R 3𝑏 , and R 4𝑏 are 6.646 mm, 4.568 mm, 3.464 mm, and 2.495 mm,
of R1b , R2b , R3b , and R4b are 6.646 mm, 4.568 mm, 3.464 mm, and 2.495 mm, respectively; whereas respectively; whereas the
blue lineline
appears to overlap with thethe
grey line. Similarly, thethe
RMSE R1𝑎
of of , R , ,RR3𝑎 ,, and
2𝑎2a R are are
the blue appears to overlap with grey line. Similarly, RMSE R1a ,R 3a and R4𝑎 4a
0.849mm,
0.849 mm,1.046
1.046mm, mm,0.830
0.830mm,mm,andand0.827
0.827 mm,
mm, respectively,
respectively,indicating
indicatingthat
thatthe
theerror
errorcorrection
correctionmodelmodel
can effectively reduce the deviation to a
can effectively reduce the deviation to a certain degree. certain degree.
Therefore, these above experimental results show that the error correction model can effectively
improve the measurement accuracy of the insulator structure parameters, thereby further improving
the accuracy of pattern matching.
Energies 2018, 11, 1781 12 of 18

Therefore, these above experimental results show that the error correction model can effectively
improve the measurement accuracy of the insulator structure parameters, thereby further improving
the accuracy of pattern matching.
Energies 2018, 11, x FOR PEER REVIEW 12 of 19

160

155

150

145

140
R1 (mm)

135

130

125

120 R
1b 𝑅1𝑎
𝑅1𝑎
𝑅1𝑎
R
1s
115 R
1a

110
5 10 15 20 25 30 35 40 45 50 55
Serial Number of Measured Insulators

(a) Radius diagram of the first layer

125

120

115

110

105
R2 (mm)

100

95

90
R
85 2b
R
2s
80 R
2a

75
5 10 15 20 25 30 35 40 45 50 55
Serial Number of Measured Insulators

(b) Radius diagram of the second layer

90

85

80

75
R3 (mm)

70

65

60
R
3b
R
55 3s
R
3a

50
5 10 15 20 25 30 35 40 45 50 55
Serial Number of Measured Insulators

(c) Radius diagram of the third layer

Energies 2018,11,
Energies2018,
Energies 2018, 11,1781
11, xxFOR
FORPEER
PEERREVIEW
REVIEW 13
13of
13 of18
of 19
19

80
80

75
75

70
70

65
65

60
60

(mm)
R4 (mm)
55
55
R4
50
50

45
45

40
40 RR
4b4b
RR
4a4a
35
35 RR
4s4s

30
30
55 10
10 15
15 20
20 25
25 30
30 35
35 40
40 45
45 50
50 55
55
Number
NumberofofMeasured
MeasuredInsulators
Insulators

(d)
(d)Radius
Radiusdiagram
diagramof
ofthe
thefourth
fourthlayer
layer

Figure 11.
Figure11.
Figure Radius
11.Radius comparison
Radiuscomparison diagrams.
comparisondiagrams.
diagrams.

4.2.3. Test_3:
4.2.3.Test_3:
4.2.3. Creepage
Test_3:Creepage Distance
CreepageDistance Determination
DistanceDetermination
Determination
The creepage
Thecreepage
The distance
creepagedistance determination
distancedetermination
determinationis isisan
an important
animportant
importantpart part
partofof proposed
ofproposed method.
proposedmethod. After
method.After obtaining
Afterobtaining
obtaining
the structural parameters of the insulator, the matching error between the measured insulator and and
the
the structural
structural parameters
parameters of
of the
the insulator,
insulator, the
the matching
matching error
error between
between the
the measured
measured insulator
insulator and
the
the
the standard
standard insulator
insulator is
is calculated
calculated by
by screening
screening the
the insulator
insulator types
types
standard insulator is calculated by screening the insulator types in the database. Here, the insulator in
in the
the database.
database. Here,
Here, the
the
insulator
insulator
labelled labelled
A10labelled
is takenA10
A10asisis
ataken
takenas
measured asaameasured
measuredand
insulator insulator
insulator and
searched searched
andthesearched
database the database
theto seek theto
database to seek
seekthe
correct the correct
correct
matching
matching
matching type.
type. In
In Figure
Figure 12,
12, the
the abscissa
abscissa indicates
indicates the
the standard
standard insulators
insulators
type. In Figure 12, the abscissa indicates the standard insulators in the database, and the ordinate in
in the
the database,
database, and
and the
the
ordinate
shows theshows
ordinate shows
matching the
thematching
matching
error between error
errorthebetween
between
queried the
the queried
queriedand
insulator insulator
insulator and
andthe
the galleried galleried
galleriedinsulators.
theinsulators. insulators.
In
In the
the experimental
experimental results,
results, insulators
insulators with
with different
different structures
structures
In the experimental results, insulators with different structures have obvious differences have
have obvious
obvious differences
differencesin in
in
matching
matching errors.
errors. In
In the
the figure,
figure, the
the matching
matching error
error ranges
ranges from
from
matching errors. In the figure, the matching error ranges from 0.6108 mm to 15.901 mm. The minimum 0.6108
0.6108 mm
mm to
to 15.901
15.901 mm.
mm. The
The
minimum
minimumerror
matching matching
matching
is 0.6108errormmisis
error and0.6108
0.6108 mm
mm and
its matching and its
typeits matching
ismatching
A10, whichtype
typeis isis A10,
the A10, which
correct one, is
which is the
the correct
thatone,
correct
indicating one,
the
indicating
indicating that
that the
the insulator
insulator
insulator style matching is effective. style
style matching
matching is
is effective.
effective.

20
20
Matching
MatchingError
Error
18
18
15.9016
15.9016 15.901
15.901
16
16

14
14
Error(mm)
Matching Error(mm)

12
12

10
10
Matching

88 7.4262 7.6991
7.4262 7.6991
6.8396
6.8396 6.8632
6.8632
6.1817
6.1817 6.129
6.129
66

44
1.9488
1.9488
22
0.6108
0.6108

00
A1
A1 A2
A2 A3
A3 A4
A4 A5
A5 A6
A6 A7
A7 A8
A8 A9
A9 A10
A10
Serial
Serialnumber
numberofofInsulators
Insulators

Figure 12. The matching errors between the query insulator and gallery insulators.
Figure
Figure12.
12.The
Thematching
matchingerrors
errorsbetween
betweenthe
thequery
queryinsulator
insulatorand
andgallery
galleryinsulators.
insulators.
Energies 2018, 11, 1781 14 of 18

Table 2 enumerates the matching errors between the targeted insulators and the searched
insulators, and the creepage distances of the corresponding insulator types are also displayed;
Q denotes the queried insulator types, G denotes the galleried insulator types, and E denotes the
matching error. T denotes the matching types; Y/N shows its correctness, where Y denotes correct,
and N denotes incorrect. The value in bold is the minimum.

Table 2. Matching results of insulators.

G
E (mm) D
A1 A2 A3 A4 A5 A6 A7 A8 T Y/N
(mm)
Q
A1 0.339 8.279 2.312 9.040 2.434 4.376 2.939 9.036 A1 Y 380
A2 9.003 0.905 8.208 17.083 7.466 6.727 7.988 17.083 A2 Y 400
A3 2.561 7.278 0.527 9.609 0.605 2.899 0.791 9.609 A3 Y 450
A4 9.824 17.541 10.341 0.849 10.867 11.632 10.327 1.508 A4 Y 570
A5 2.540 6.458 1.340 10.554 0.480 2.372 1.286 9.822 A5 Y 460
A6 3.808 6.579 2.994 10.039 2.263 0.536 2.097 10.041 A6 Y 410
A7 3.049 7.008 1.283 9.715 0.842 2.157 0.506 9.716 A7 Y 450
A8 8.580 16.351 9.109 0.792 9.644 10.496 9.126 0.325 A8 Y 550

From the table, each queried insulator can be matched to the correct type based on the minimum
matching error and the corresponding creepage distance is determined. On the one hand, the matching
error of the insulator with similar structures is relatively close, but it can also be matched to the correct
type by seeking the minimum matching error. On the other hand, insulators with similar creepage
distances but different types are also different. For example, the difference in creepage distance
between A2 and A6 is only 10 mm, but the matching error is obviously different in Table 2, indicating
that their structural parameters are very different. Therefore, the experimental results show that
the proposed measurement method is effective and can distinguish types and obtain corresponding
creepage distances even if the insulators with similar creepage distances.

4.3. Outdoor Testing

The outdoor testing is aimed at verifying the practicality of the measurement system and
effectiveness of the proposed measurement method on multiple transmission lines. A large number
of outdoor transmission lines in Huizhou of Guangdong, Shanghai and so on are tested using the
measurement system; selected images are shown in Figure 13. Moreover, corresponding experimental
results are clearly displayed in Tables 3–5. In Tables 3 and 4, N is the serial number of the insulators
shown in Figure 13, s1 and θ are the distance and the angle measured by the electronic total station, the
measured value is denoted as M, and the standard value is denoted as S. The measured values of the
structural parameters, including the radius and the area ratio, along with its standard values, are listed
in the table.
In Table 3, (a–d) represent the four types of insulators with different angles and at far distances
ranging from 30 m to 60 m, which have different structural parameters reflecting the differences in
the type. The measurement system is used to measure the structural parameters of the insulators
and experimental results show that the deviations between the measured radius and the standard
value of each layer of the insulators are within 2 mm, which indicates that the measuring system can
effectively achieve the accurate measurement of the structural parameters of the insulators on different
transmission lines.
Energies 2018, 11, 1781 15 of 18
Energies 2018, 11, x FOR PEER REVIEW 15 of 19

(a) (b)

(c) (d)
Figure 13. Examples of insulators on high tension lines; (a) the first type of the insulators; (b) the
Figure 13. Examples of insulators on high tension lines; (a) the first type of the insulators; (b) the
second type of the insulators; (c) the third type of the insulators; (d) the fourth type of the insulators;
second type of the insulators; (c) the third type of the insulators; (d) the fourth type of the insulators;
Table 3. Measured and standard values of radius.
Table 3. Measured and standard values of radius.
R1 (mm) R2 (mm) R3 (mm) R4 (mm)
N Θ (°)
(mm) M S M S M S M S
.5 .5 .5 R1 (mm) R2 (mm) R3 (mm) R4 (mm)
N (a) S1 40.49
(mm) Θ (◦ ) 133.02
69.65 134.3 100.77 199.9 68.69 70.0 NULL NULL
M S M S M S M S
(b) 47.59 82.08 136.12 136.7 93.06 93.8 61.99 61.5 NULL NULL
(a) (c) 40.49
58.13 69.65
70.63 133.02 156.3
157.29 134.3 124.52
100.77 125.0
199.9 94.29
68.69 94.470.0 63.96
NULL 64.6NULL
(b) (d) 47.59
31.43 82.08
92.23 136.12 136.3
137.06 136.7 98.64
93.06 99.793.8 62.4761.99 62.061.5 NULL
NULLNULL NULL
(c) 58.13 70.63 157.29 156.3 124.52 125.0 94.29 94.4 63.96 64.6
(d) 31.43 92.23 137.06 136.3 98.64 99.7 62.47 62.0 NULL NULL
Table 4. Measured and standard values of area ratio.

S12 S13 S14 S23 S24 S34

N Table 4. Measured and standard values of area ratio.
M S M S M S M S M S M S
(a) 1.80 1.77 3.62 3.68 NULL NULL 1.98 2.08 NULL NULL NULL NULL
.5 S12 S13 S14 S23 S24 S34
N (b) 2.14 2.12 4.88 4.94 NULL NULL 2.30 2.33 NULL NULL NULL NULL
(c) M 1.56 S 1.56 2.79 M 2.74S 5.78M 5.85S 1.79M 1.75 S 3.66 M 3.74 S 2.08 M 2.14 S
(a) (d)1.801.92 1.77 1.87 4.793.62 4.83 3.68 NULL NULLNULL NULL2.561.982.59 2.08 NULLNULL NULLNULL NULLNULL NULL NULL
(b) 2.14 2.12 4.88 4.94 NULL NULL 2.30 2.33 NULL NULL NULL NULL
(c) 1.56
In Table1.56 2.79 ratios
4, the area 2.74of each5.78 5.85
layer of 1.79insulators
the four 1.75 are3.66 3.74 the deviations
listed, and 2.08 2.14
(d)between
1.92 the 1.87
measured 4.79 4.83 from
area ratios NULL NULL values
the standard 2.56 are 2.59 NULL
within 0.1, whichNULL NULL
indicates NULL
that the
contour fitting used in the proposed method is effective and accurate, and the feature of area ratio
canTable
In greatly assist
4, the theratios
area featureofofeach
radius to accurately
layer of the fourdistinguish
insulatorsthearetype.
listed, and the deviations between
In Table 5, the matching errors are calculated from the previously measured structural
the measured area ratios from the standard values are within 0.1, which indicates that the contour
parameters and the matching types of the insulator are sought. The experimental results including
fitting used in the proposed method is effective and accurate, and the feature of area ratio can greatly
the matching errors, the absolute error of the structural parameters, the matching models and the
assistobtained
the feature of radius
creepage to accurately
distances are clearlydistinguish
presented in the type. Here (a) and (b) are insulators with the
the table.
In Table
same 5, the distance
creepage matching of errors
450 mm, arebut
calculated from the different
they are obviously previously measured
in structure structural
which parameters
can be clearly
and the seenmatching types of models;
from the insulator the insulator
(a) andare
(c) sought. The experimental
are the insulators results
whose creepage including
distances the
differ matching
greatly
errors, the absolute error of the structural parameters, the matching models and the obtained creepage
and their structure are also significantly different. Therefore, these experimental results indicate that
the proposed
distances are clearlymethod in thisinpaper,
presented which
the table. obtains
Here the (b)
(a) and creepage distance with
are insulators of thetheinsulators by
same creepage
distance of 450 mm, but they are obviously different in structure which can be clearly seen from
the insulator models; (a) and (c) are the insulators whose creepage distances differ greatly and
their structure are also significantly different. Therefore, these experimental results indicate that the
 Energies
Energies 2018,
2018, 11, x11,
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5. Corresponding
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Parameters
Parameters distance
and of the insulators by calculating
Models.
calculating
calculating
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structural
value.
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Corresponding
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Parameters and
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and practical application value.
Models.
application
applicationMatching
Matching value.
value. Result Creepage
Result Creepage
N N Absolute
Absolute Error
Error (mm)
(mm) Insulator
Insulator Model
Model
Error
Error (mm)
Matching(mm) Table 5. Corresponding
Table Parameters
5. Corresponding andand
Parameters Models.
Models. Y/N Distance
Y/NResult
Result Distance (mm)
(mm)
Creepage
Matching Creepage
N N Table
Absolute Corresponding
5. Error
Absolute (mm)
Error Parameters
(mm) Parameters and Models.
Insulator Model
Error (mm)
Error (mm) Table
Table 5. Corresponding
5. Corresponding andInsulator
Parameters and
Models. Model
Models. Y/NY/N Distance (mm)
Distance (mm)
Matching
Matching 3.0 3.0 Result
Result Creepage
Creepage
N N Absolute Error
Absolute (mm)
Error (mm) (a) (a) Insulator Model
Insulator Model
Error (mm)
Error (mm)
Matching
Matching Y/NY/N Distance (mm)
Distance
Result Creepage
Result (mm)
Creepage
Creepage
N
N N Matching 3.0
2.5
3.0
2.5
Absolute
Absolute Error
Error (mm)
(mm) Insulator
Insulator Model
Model Result
Error
Error (mm)(mm) Absolute Error (mm) (a) (a) Insulator Model Y/NY/N Distance
Distance
Distance (mm)
(mm)
Error (mm) 3.0
2.5 3.0
Y/N (mm)
2.5 Absolute error(mm)
Absolute error(mm)

2.0 2.0
(a) (a)
3.0 3.0
error(mm)

2.5
2.0 2.5
error(mm)

2.0
1.5 (a) (a)
1.5
1.27651.2765 1.30321.3032
(a) (a) 0.7511
0.7511 2.5 2.5 Y Y 450 450
error(mm)

error(mm)

2.0
1.5 2.01.5
1.0
1.0 1.2765 1.30321.3032
Absolute

1.2765
Absolute

(a) (a) 0.7511

0.7511 Y Y 450 450
error(mm)
error(mm)

2.0 2.0
1.5 1.5
1.0 1.2765
1.0 1.30321.3032
0.5 1.2765
Absolute

Absolute

(a) (a) 0.7511

0.7511 0.5 Y Y 450 450
1.5 1.5 0.1
1.30321.3032
1.27651.2765 0.13370.1337 0.03 0.03 0.06 0.06 0.1
Absolute
Absolute

1.0
(a)
(a) (a) 0.7511
0.7511
0.7511 0.5 1.0
0.0
0.5
0.0 YY Y 450 450
450
R1 R1 R2 R2 R3 R3 S12 S12 S13 S13 S23 S23
1.0 1.0 0.13370.1337 0.03 0.03 0.06 0.06 0.1 0.1
0.5
0.0 0.5 Parameters
Parameters
0.0
R1 R1 R2 R2 R3 R3 S12 S12 S13 S13 S23 S23
0.5 0.5 0.13370.1337 0.03 0.03 0.06 0.06 0.1 0.1
0.0 0.0 Parameters
Parameters
1.5 R11.5 R1 R20.1337 R3
R20.1337 R3 S12 S12 S13
0.06 S13
0.06 S23
0.1 0.1
S23
0.03 0.03
0.0 0.0 Parameters
Parameters (b)
1.5
R1 R1 R2 R2 R3 R3 S12 S12 S13 S13 (b) S23 S23
1.5
Parameters
Parameters
(b) (b)
1.5 1.5
Absolute error(mm)
Absolute error(mm)

1.0 1.0
(b) (b)
1.5 1.5
0.744 0.744
error(mm)

error(mm)

1.0 1.0
(b) (b)
0.58080.5808
(b) (b) 0.4365
0.4365 0.744 0.744
0.49710.4971 Y Y 450 450
error(mm)

error(mm)

1.0 1.0
0.5 0.5
0.5808
Absolute

0.5808
Absolute

(b) (b) 0.4365

0.4365 0.744 0.744 0.49710.4971 Y Y 450 450
error(mm)
error(mm)

1.0 1.0
0.5
0.5 0.5808
0.5808
Absolute

Absolute

0.744 0.744
(b) (b)
(b) 0.4365
0.4365
0.4365 0.49710.4971
0.02 0.02
0.06 0.06 0.03 0.03 YY Y 450
450 450
0.5 0.5808
Absolute

0.5 0.5808
Absolute

(b) (b) 0.4365

0.4365 0.0 0.0
R1 R1 R2 R2 R3 R3 S12
0.49710.4971 0.06S130.06 Y Y 450 450
0.02S120.02
S13 0.03S230.03
S23
0.5 0.5
0.0 Parameters
Parameters
0.0
R1 R1 R2 R2 R3 R3 S12 0.06
S13 0.06 S23
0.02 S12
0.02 S13 0.03 S230.03
0.0 0.0
Parameters
Parameters
0.06 0.06 0.03 0.03
0.02S13
R1 R1 R2 R2 R3 0.02 S12
R3 S12 S13 S23 S23
1.5 1.5
0.0 0.0 Parameters
Parameters
R1 R1 R2 R2 R3 R3 S12 S12 S13 S13 S23 S23
(c) (c)
1.5 1.5 Parameters
Parameters
(c) (c)
1.5 0.9878
1.5 0.9878
Absolute error(mm)
Absolute error(mm)

1.0 1.0
1.5 1.5 (c) (c)
0.98780.9878
error(mm)

error(mm)

1.0 1.0
(c) (c)
(c) (c) 0.5239
0.5239 0.98780.9878 Y Y 560 560
error(mm)

error(mm)

1.0 1.0 0.484 0.484

0.5 0.5 0.4375
0.4375
Absolute

0.9878
Absolute

(c) (c) 0.5239 0.9878

(c) 0.5239
0.5239 YY Y 560 560
560
error(mm)
error(mm)

1.0 1.0
0.484 0.484
0.5 0.5 0.43750.4375
Absolute

Absolute

(c) (c) 0.5239

0.5239 0.08 0.08
Y Y 560 560
0.484 0.484 0.07 0.07
0.05 0.04 0.04 0.06 0.06
0.5 0.5 0.008 0.008 00.05
0.43750.4375
Absolute

0
Absolute

(c) (c) 0.5239

0.5239 0.0
0.484R3
0.0 Y Y 560 560
0.484 0.07 0.07 0.08 0.08
0.06
0.5R1 0.5R1
R2 R2
R30.008 R4 R4
S12
0.4375
0.008 0
S12 S13
S130.05
0.4375 S140.05S14
S23 S23
S24
0.04 0.04S24
S34 S340.06
0
0.0 0.0 Parameters
Parameters
R1 R1 R2 R2 R3 R3 R4 S12R4 S12S13 0.07 S14
S14
0.05 S13
0.05 0.07
S23 0.08 S24
S24
S23 0.08
0.06 S34
S34 0.06
0.008 0.008 0 0.04 0.04
0
0.0 0.0 Parameters
Parameters 0.07 0.08 0.08
0.05 0.07 0.04 0.04 0.06 0.06
0.05
R1 R1 R2 R2 R3 R4
0.008S12
0.008R3 R4 S13
0 S120 S14 S14
S13 S23 S23S24 S24S34 S34
3.0
3.0 0.0
0.0 Parameters
Parameters
R1 R1
R2 R2
R3 R3
R4 R4
S12 S12
S13 S13
S14 S14
S23 S23
S24 S24
(d) S34
S34 (d)
3.0 2.5
3.0
2.5 Parameters
Parameters
(d) (d)
3.0 3.0
2.5 2.0
Absolute error(mm)

2.5
Absolute error(mm)

2.0
(d) (d)
3.0 3.0
2.5 2.5
error(mm)

error(mm)

2.0 1.5
2.0
1.5 (d)
(d)
(d)
(d) (d) 0.5665
0.5665
0.5665 2.5 2.5 1.05871.0587 YY Y 410 410
410
error(mm)

error(mm)

2.0 2.0
1.5 1.01.50.7597
1.0 0.7597
Absolute

(d) (d) 0.5665 Y 410 410

Absolute

0.5665 1.05871.0587 Y
error(mm)
error(mm)

2.0 2.0 0.472 0.472

1.5
1.0 0.51.5
0.5 0.7597
1.0 0.7597
Absolute

Absolute

(d) (d) 0.5665

0.5665 1.5 1.5
1.05871.0587
0.05 0.05 0.04 0.04 0.03 0.03
0.472 0.472 Y Y 410 410
1.0 1.0
0.50.7597
0.5 0.7597
Absolute

(d) (d) 0.5665 0.0

Y Y 410 410
Absolute

0.5665 0.0 1.05871.0587

0.05
1.0R1 1.0R1
0.7597 R2 R2 R3
0.7597 S12 S120.05
0.472R30.472 S130.04 S230.03
S130.04 S230.03
0.5
0.0 0.5 0.0 Parameters
Parameters
0.472 0.4720.05 0.05 0.04 0.04 0.03 0.03
R1 R1 R2 R2 R3 R3 S12 S12 S13 S13 S23 S23
0.5 0.5
0.0 0.0 Parameters
Parameters
0.05 0.05 0.04 0.04 0.03 0.03
R1 R1 R2 R2 R3 R3 S12 S12 S13 S13 S23 S23
0.0 0.0
5.5.Conclusions
5. Conclusions
Conclusions Parameters
Parameters
R1 R1 R2 R2 R3 R3 S12 S12 S13 S13 S23 S23
Parameters
Parameters
5. Conclusions
5.
In Conclusions
Inorder
order to
to measure
In order to measure
measure thethecreepage
creepage
creepage distance
distance
distance ofofinsulators
ofinsulators
insulators online,
online,
online, whichis ais
which
which a very
isvery significant
significant
significant andandand
5. Conclusions
5. Conclusions
challenging
challenging
challenging task
In order task inmeasure
totask the
in in
theinspection
the
inspection of transmission
theinspection
creepage of
of distance
transmission oflines,
transmission an
lines,
insulators online
lines, an an measurement
online
online
online, method
measurement
measurement
which is aisvery that
method
method
significant indirectly
that
andthat
In order to measure the creepage distance of insulators online, which a very significant and
5. Conclusions
5. Conclusions
indirectly
obtains Inthe
indirectly
challenging
order obtains
creepage
In obtains
challenging task tothe
to task
order the
thecreepage
distance
creepage
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measure in inspection
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ofdistance calculating
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by calculating the
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obtains thein
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a measurement
creepage distance
distance of
of system
by transmission
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consisting
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online
electronic
structural
structural measurement
measurement
total of
parameters
parameters of method
station
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and
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indirectly obtains
obtains
to obtain the the
thedepth creepage
creepage distance
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distance andby theby calculating
calculating
image thethe
information structural
structural parameters
parameters
of the insulators. of the insulators
ofSimultaneously,
the insulators is
is this
Energies 2018, 11, 1781 17 of 18

paper also establishes an error correction model to reduce the errors introduced by the geometric layout
of the designed measurement system, which could improve the measurement accuracy of the structural
parameters. Next, by matching the measured insulator with the standard insulators and calculating the
matching errors, the insulator type can be obtained, thereby the acquisition of the creepage distance
is achieved. Finally, multiple sets of outdoor experiments show that the established measurement
system has good measurement stability when the insulators undergo slight postural changes; the
designed error correction model can effectively improve the measurement accuracy; the proposed
online measurement method can accurately achieve the online creepage distance measurement of
glass insulators on multiple transmission lines. Therefore, experimental results verify that the online
measurement method proposed in this paper has a good practical engineering application value.
In the future, our research group will carry out further work in the following areas: the
measurement range will be expanded to include glass, ceramic and composite insulators, so that
this online measurement method for insulator creepage distance can be widely applied in various
transmission lines and improve the working efficiency of electric power engineers, the use of the
random forest and other optimized algorithms to efficiently fit the insulator profile will be examined
and the integration and automation of this measurement system will be improved to make it more
compact and convenient.

Author Contributions: Z.Z., D.Z., J.H. and K.L. developed the system modeling and algorithm design; Z.Z. has
supervised the research work; J.H. and K.L. performed the experiments; J.H. and K.L. analyzed the experimental
data; J.H. wrote the paper. All authors reviewed the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.

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