sensors Article

Decomposition of Composite Electric Field in a Three-Phase D-Dot Voltage Transducer Measuring System Xueqi Hu 1,† , Jingang Wang 1, *, Gang Wei 2,† and Xudong Deng 2,† 1 2

* †

State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China; [email protected] Maintenance Branch of State Grid Chongqing Electric Power Company, Chongqing 400039, China; [email protected] (G.W.); [email protected] (X.D.) Correspondence: [email protected]; Tel.: +86-135-2756-8565 These authors contributed equally to this work.

Academic Editor: Vittorio M.N. Passaro Received: 22 July 2016; Accepted: 28 September 2016; Published: 12 October 2016

Abstract: In line with the wider application of non-contact voltage transducers in the engineering field, transducers are required to have better performance for different measuring environments. In the present study, the D-dot voltage transducer is further improved based on previous research in order to meet the requirements for long-distance measurement of electric transmission lines. When measuring three-phase electric transmission lines, problems such as synchronous data collection and composite electric field need to be resolved. A decomposition method is proposed with respect to the superimposed electric field generated between neighboring phases. The charge simulation method is utilized to deduce the decomposition equation of the composite electric field and the validity of the proposed method is verified by simulation calculation software. With the deduced equation as the algorithm foundation, this paper improves hardware circuits, establishes a measuring system and constructs an experimental platform for examination. Under experimental conditions, a 10 kV electric transmission line was tested for steady-state errors, and the measuring results of the transducer and the high-voltage detection head were compared. Ansoft Maxwell Stimulation Software was adopted to obtain the electric field intensity in different positions under transmission lines; its values and the measuring values of the transducer were also compared. Experimental results show that the three-phase transducer is characterized by a relatively good synchronization for data measurement, measuring results with high precision, and an error ratio within a prescribed limit. Therefore, the proposed three-phase transducer can be broadly applied and popularized in the engineering field. Keywords: three-phase D-dot voltage transducer; Ansoft Maxwell; decomposition of composite field

1. Introduction The operational status and health level of alternating-current transmission lines could be directly reflected by the amplitude and phase position of three-phase voltage, offering direct data references for the operation and maintenance of an electric system [1]. The conventional measuring method is to install a mutual voltage inductor in transformer substations of line start and end ports to detect line voltage [2]. With the continuous development of smart power grids, the need for real-time status monitoring of the line voltage along overhead transmission lines has become increasingly urgent, as has the development of intelligent early-warning and automatic control mechanism [3]. To address this problem, we designed the D-dot voltage transducer based on the electric-field coupling principle, which recognizes that non-contact measurement indeed overcomes a series of problems caused by

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direct contact between traditional voltage transducers and detected wires or instruments during the measuring process [4]. In addition, the non-contact measuring method decreases ferromagnetic resonance, reduces reactive power consumption, and has good dynamic response as well as small volume. This method has been proven to be a safe and convenient measurement method [1,5]. Currently, a large amount of research work has been carried out to improve the performance of field-type transducers. The authors of [6] proposed an optical voltage transducer based on the Pockels/Kerr effect to achieve the non-contact measurement for voltage. This method has high measurement accuracy, however, optical devices are expensive and have limited precision, which limits their wider, practical application. In a wider scope; authors of [7,8] proposed the non-contact voltage transducer based on the electric-field coupling principle; the transducer provides a simple structure non-contact transducer, still in prototype form. In references [9–11], a self-integral D-dot voltage transducer was introduced to increasingly perfect the transducer in aspects of calculation principle and structural design. These are based on the measurement of single transducer. The author of [12] considered the use of a three-phase transmission line in order to establish a D-dot voltage simulation model, and studied the distribution parameter of the three-phase voltage transducer. However, the transducer was premised on the condition that the sensor installation location would be close to the wire. In current projects, three-phase transmission lines are simultaneously measured with the condition that a safe distance is needed between the transducer and the transmission lines. With this condition, the measurement values of each transducer are the result of the simultaneous action of the three-phase transmission lines. The problem of the simultaneous synthesis of the electric field in the three-phase voltage transducer measuring system has not been studied before. Therefore, research on the three-phase D-dot voltage transducer measuring system is based on decomposition of the composite field using non-contact measurement with convenient and efficient parameters of the voltage in a transmission line. Thus, charge simulation method is used to deduce a composite electric field equation at any point of a three-phase transmission line. This paper establishes a mathematical model for horizontally arranged lines, to decompose the composite electric field, calculate the electric field component and obtain a derived inversion equation of the electric field component. Simulation calculation software has been adopted to determine the voltage of three-phase lines by measuring the data of a three-phase transducer, and an experimental platform has been constructed to verify the performance of the studied measuring system and validate values of theoretical studies and actual systematic projects. 2. Detection Principle 2.1. Analysis of Measuring Principle for D-Dot Transducer The working principle of a D-dot transducer can be summarized as follows: performing non-contact indirect measurements of the voltage by measuring the rate of change for electric displacement vector [13]. Specific measurement principles can be found in references [14,15]. For the measurement of the wire, the relationship between the surrounding electric field and the conductor potential is as shown in Equation (2) and in boundary conditions as Equation (1): (

ϕ R ≤ r 0 = ϕ0 ( t ) ϕ R→∞ = 0

→

E (t) =

→ ϕ0 ( t ) ln(r0 ) · e R r

(1)

(2)

where ϕ0 (t) is represented as the measured cable potential, E(t) as the electric field intensity of the measured point, r as the distance of the measured point to the wire center, and r0 as the radius of the electric cable.

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where 0 (t ) is represented as the measured cable potential, E(t) as the electric field intensity of the Sensors 2016, 16, 1683 measured point,

14 r as the distance of the measured point to the wire center, and r0 as the radius 3ofofthe

electric cable. Furthermore, the the resistance resistance drop drop has has aa positive positive relationship relationship with with the the rate rate of of change change related related to to Furthermore, the electric field in the electrode [14], which can be proven by Gauss theorem. By using Equation the electric field in the electrode [14], which can be proven by Gauss theorem. By using Equation (2), (2),relationship the relationship between the detected potential and transducer output can be obtained: the between the detected potential and transducer output can be obtained:

U00 = U

 A R

eq R dd ε00Aeq 0 (t ) rrln dtϕ0 (t) ln( (rr00)) dt

(3) (3)

Inthe theequation, equation,AAeqeqisisrepresented representedasasthe theequivalent equivalentarea areaofof the voltage transducer, whereas In the voltage transducer, whereas R isR is the load resistance value. the load resistance value. 2.2. 2.2. Three-Phase Three-PhaseElectrical ElectricalField FieldSolved Solvedby bythe theCharge ChargeSimulation SimulationMethod Method Based Based on onthe theuniqueness uniqueness theorem theorem of ofthe theelectric electricfield, field,Charge ChargeSimulation Simulation Method Method isis to toreplace replace electric electric charges charges distributed distributed continuously continuously in in the the surface surface of of energized energized conductor conductor by by aa set set of of discrete discrete charges (such as asset setaagroup groupofofpoint, point,line lineand and ring charges), and charges charges in in the conductor (such ring charges), and all all thethe charges are are simulative ones [16,17]. Simulative charge valuescan canbe beacquired acquiredby by solving solving the linear simulative ones [16,17]. Simulative charge values linear algebraic algebraic group group in inpotential potentialboundary boundary conditions. conditions. Thereafter, Thereafter, the the superposition superposition theorem theorem can can be be adopted adopted to to calculate the electric potential and intensity of any position in the electric field. When the transmission calculate the electric potential and intensity of any position in the electric field. When the conductor is parallel to the ground,toif the the ground, conductor radius is muchradius smaller than the height of the transmission conductor is parallel if the conductor is much smaller than the transmission line to the ground andtothe voltage in the is three-phase symmetrical sinusoidal height of the transmission line the ground andconductor the voltage in the conductor is three-phase then the charges in the transmission conductor will be distributed evenly symmetrical sinusoidal then the charges in the transmission conductor will[18]. be distributed evenly [18]. For For the theconvenience convenience of ofengineering engineering calculations, calculations, the the simplified simplified treatment treatment isis conducted conducted for for the the model model of ofthree-phase three-phase transmission transmission lines: lines: the the ground ground is is an an infinitely infinitely great great conductor conductor plane plane with with an an electric 0; charges have no electric field distortion. In the In computational domain,domain, the electric electricpotential potentialofof 0; charges have no electric field distortion. the computational the three-phase conductorconductor shall only shall be considered surrounding be neglected electric three-phase only be and considered and conductors surroundingcanconductors can[19], be such as the influence of the tower and metal fittings. neglected [19], such as the influence of the tower and metal fittings. Figure charge simulation method andand three simulative charges Qj Figure 11shows showsa adiagram diagramofofthethe charge simulation method three simulative charges (jQ=j (j1,2,3) that areare setset in in thethe interior ofof the transmission = 1,2,3) that interior the transmissionconductor conductorwith withthree threephases, phases,namely, namely,A, A,BB and andC. C.In Inaddition, addition,aarectangular rectangularcoordinate coordinatesystem systemisisestablished establishedin inaatwo-dimensional two-dimensionalcomputational computational domain domainwith withgiven givenpotential potentialboundary boundaryconditions, conditions,and and(x, (x,y) y)isisregarded regardedasasits itscoordinate. coordinate.

Figure1.1.Map Mapof ofthe thecharge chargesimulation simulationmethod. method. Figure

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According to the superposition theorem, electric potential expression Q = P− 1 ϕ can be obtained [19], which is constructed by three simulative charges set above.    P11 Q1 + P12 Q2 + P13 Q3 = ϕ A P21 Q1 + P22 Q2 + P23 Q3 = ϕB   P Q +P Q +P Q =ϕ 32 2 33 3 31 1 C

(4)

In Equation (4), Pii is represented as the electric potential value of jth simulative charge generated in ith point; ϕ A , ϕB , ϕC , are the voltages of the three phases in the conductor. In the P electric potential coefficient matrix, the Pij solution equation based on image theory is:   Pii =  P = ij

2hi 1 2πε0 ln Ri 2L0 ij 1 2πε0 ln Lij , Pij

= P0 ij , (i 6= j)

(5)

In Equation (5), ε0 is the air dielectric coefficient; hi is the height of the conductor to the ground; Rn is the radius of the conductor; L0 ij and Lij are the distance of i conductor and its mirror image to j conductor. Based on superposition theorem, the values of the electric field intensity Ex and Ey respectively in the horizontal and vertical directions for any point (x, y) in the computational domain can be obtained:     Ex =

1 2πε0

   Ey =

1 2πε0

N + n0

x−x ∑ Q i ( L2 i −

i =1 N + n0

∑ Qi (

i =1

i

y − yi L2i

−

x − xi 0 ) Li 2 y − yi 0 ) Li 2

(6)

The transducer is installed under the transmission conductor. Given that the electric field intensity in the x direction is quite small, only the y direction shall be considered, namely, the electrical field intensity in the vertical direction. According to Equation (6), the composite electric field intensity of any position near the conductor can be calculated [20]. In order to further calculate the electric field components of neighboring phases, the conductor voltage could finally be obtained by decomposing the composite electric field when the transmission conductor is arranged horizontally and backward substituting the acquired electric field components into Equation (3). 2.3. Calculation Example Taking the horizontally arranged 10 kV overhead transmission line as the case, its composite electric field detected by a three-phase transducer is decomposed for simulation calculation. Based on LGJ-500-45 regulations, the sectional area of the conductor radius is 35 mm2 , the distance between phases is L = 1.38 m, and the vertical height from the ground is 1.8 m. Three D-dot voltage transducers are respectively installed right under the three phases of the conductor, namely, Sensor A, Sensor B and Sensor C, h = 0.15 m, as shown in Figure 2.

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Figure 2. Decomposition of the electric field for the horizontally arranged line. Figure 2. Decomposition of the electric field for the horizontally arranged line.

In a 10 kV transmission line, a three phase transmission line is arranged horizontally, as shown In Figure a 10 kV2.transmission line, afield threecomponent phase transmission line is arranged as shown in in EAZ is the electric of the transducer arrangedhorizontally, vertically under an A-phase EC1 isfield represented as theofelectric field component of the C-phaseunder conductor to Figure 2. EAZconductor; is the electric component the transducer arranged vertically an A-phase Transducer and EB1 is the field field component of theof B-phase to Transducer A. Meanwhile, conductor; EC1 isA;represented as electric the electric component the C-phase conductor to Transducer A; the electric field components of all phases in Transducers B and C are as shown by the marks of the field and EB1 is the electric field component of the B-phase to Transducer A. Meanwhile, the electric figure and the distances of the three transducers to the conductor are all equal to h. From Figure 2, the components of all phases in Transducers B and C are as shown by the marks of the figure and the mathematical relationship between electrical field measured by the transducer and the electric distances of the three transducers to the conductor are all equal to h. From Figure 2, the mathematical field components of all phases can be obtained by taking advantage of trigonometric function, as relationship between electrical field measured by the transducer and the electric field components of shown below:

all phases can be obtained by taking advantage of trigonometric function, as shown below:   E  E  E B1E h ·h EC1E h ·h 2 2 C12 2 2  E AA = EAZAZ +L2√ B1 +√   h+ h Lh2 +h2 4 L 4L    EC2 E A2 ·h E E h  √ √ EEB = EBZ + A 2 2 2 + C 2 2h·h 2 (7) (7) L +h L +h  B  E BZ   2 2 2 2   L h L h   E · h E · h   E = E + √ B2 + √ A12 2 CZ 2 2 C E B 2L h+h E A14L  h +h   EC  ECZ  2 2 2 2 4 L  h A is composed of three electric field L  From Equation (7), the electric field intensity ofh Transducer components: component and the disturbance variables of of the B and C conductors. FromA-phase Equationconductor (7), the electric field intensity of Transducer A is composed three electric field Similarly, the electric field conductor intensity measured Transducers B and C is respectively components: A-phase componentbyand the disturbance variables of the constituted B and C by the electric fieldSimilarly, component of the respective conductors disturbanceB variables of neighboring conductors. the electric field intensity measuredand by Transducers and C is respectively constituted by the electric field component the respective conductors two-phase conductors. Equation (6) shall beofsubstituted into Equationand (7):disturbance variables of neighboring two-phase  conductors. Equation (6) shall be substituted into Equation (7):

N + n0  y − yi y − yi EC1 ·h EB1 ·h 1 N  n0   ∑ Q  E AZ = 12πε y i ( yiL2 y− yLi0 2 ) −EB√1 L 2h+h2 − E√C4L  1 2h 0  + h2 i  ( ) E Q    i i = 1  AZ  i  2 2 2  20 i 1N +n0 L2i L'2i  L h 4 L  h2 y − yi y − yi E ·h E A2 ·h 1 √ (8) E = − ) − − Q (  N n  BZ 12πε0 0 ∑ y i y L2 y  yL0 2 E Lh2 +h2 E√ LC2 2h + h2  i i C 2 A 2 i i)  i= 1(  E Q     (8)  BZ  i  2  20 i N1 +n0 L2i y−y L'2i y−y  L2  L2 EA1h·2h   E h·h 1  √ −  ECZ = 2πεN0 n0∑ Qi ( L2 i − L0 2 i ) − √ LB2 2 + h2 EB 2 2h+h2 EA4L 1 i =1 y  yi i y  yii 1 h  ECZ  Qi ( 2  '2 )    20 i 1 Li Li 4 L2  h 2 L2  h 2  After the measurement, the above results in Table 1 are incorporated into Equation (8), in order to obtain the electric field strength component of the three-phase transmission line that is EAz , EBz and ECz . The line voltage of the three-phase transmission line can be calculated by Equations (1)–(3). When the voltage phase is 0[deg] and contrasts with the reverse generation results of the actual voltage of transmission line, the relative amplitude errors are as shown in the following table:

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Table 1. Measurement results of electric field intensity under different voltages. Voltage (kV)

EA (v/m)

εA (v/m)

ϕu (◦ )

EB (v/m)

εB (v/m)

ϕu (◦ )

EC (v/m)

εC (v/m)

ϕu (◦ )

1 2 3 4 5 6 7 8 9 10 11 12

119.7 337.5 457.8 560.9 684.2 895.3 933.6 989.5 1005.7 1123.5 1322.3 1436.4

13.9 28.1 35.7 38.9 40.4 42.9 46.5 47.8 49.2 50 54.1 55.2

2.98 2.65 2.07 1.78 1.23 1.05 0.98 0.81 0.58 0.34 0.30 0.23

68.7 191.5 246.1 290.3 390.6 495.5 533.5 559.7 583.5 616.2 672.3 756.4

6.9 11.1 16.7 18.8 22.4 25.9 28.7 29.2 30.3 30.5 31.1 33.6

1.68 1.55 1.47 1.38 1.29 1.25 1.19 0.98 0.94 0.82 0.77 0.53

66.7 181.4 245.2 277.3 329.5 395.8 413.5 459.1 495.2 521.1 587.3 668.7

7.0 13.1 14.2 15.6 19.8 22.5 26.4 27.2 29.3 31.5 33.1 36.3

1.66 1.53 1.41 1.35 1.28 1.23 1.20 0.94 0.84 0.79 0.74 0.63

Based on the data from Table 2, the proposed synthesis algorithm is effective and has high precision. The algorithm for the synthesis of the field decomposition is to be written in the data processing module of the hardware circuit in the measurement system. Table 2. Relative amplitude error. Voltage (kV)

εA %

εB %

εC %

1 2 3 4 5 6 7 8 9 10 11 12

0.42 0.38 0.39 0.31 0.25 0.26 −0.13 −0.19 −0.22 −0.30 −0.35 −0.41

−0.38 −0.37 −0.30 −0.26 −0.21 −0.18 −0.11 0.18 0.29 0.31 0.34 0.36

−0.38 −0.31 −0.27 0.13 0.23 0.21 0.35 0.32 0.38 0.41 0.43 0.44

The data further show that the voltage amplitude has slight errors, which are caused by errors of the device module, and data conversion errors, among others, in a simulation environment. The inductance exists in loops with slightly declinational phases. Results show that theoretical values acquired by a non-contact voltage transducer are highly consistent with measured ones. 3. Simulation In this paper, Ansoft software is used to implement the simulation of the electric field distribution under the transmission line. The results of the simulation are compared with the results of the subsequent measurement system. The model parameters of the three-phase transmission line to be established are listed in the following Table 3 and the simulation results are shown in the Figure 3. Table 3. Parameters of the simulation model. Phase

Radius (mm)

X-Coordinates (m)

V (kV)

Phase (◦ )

Distance

Material

A B C

3.34 3.34 3.34

0.185 0.540 0.903

10 10 10

0 120

1.8 1.8 1.8

aluminum aluminum aluminum

Table 3. Parameters of the simulation model. Table 3. Parameters of the simulation model.

Phase Radius (mm) Phase Radius A 3.34(mm) A 3.34 B 3.34 Sensors 2016, 16, 1683 3.34 B C 3.34 C 3.34

X-Coordinates (m) X-Coordinates (m) 0.185 0.185 0.540 0.540 0.903 0.903

V (kV) V 10 (kV) 10 10 10 10 10

Phase (°) Phase 0 (°) 0 120 120

Distance Distance 1.8 1.8 1.8 1.8 1.8 1.8

Material Material aluminum aluminum aluminum aluminum 7 of 14 aluminum aluminum

Figure line under under the the 10 10 kV kV voltage voltage level. level. Figure 3. 3. Voltage Voltage distribution distribution of of three-phase three-phase transmission transmission line Figure 3. Voltage distribution of three-phase transmission line under the 10 kV voltage level.

Voltage(kV) Voltage(kV)

A line is drawn under each phase of the transmission line. The voltage value is checked at each A line is drawn under each phase of the transmission line. The voltage value is checked at each point of the three lines, as shown in Figure 4. point of the three lines, as shown shown in in Figure Figure 4. 4. 10 10 8 8 6 6 4 4 2 2 0 0 -2 -2 -4 -4 -6 -6

A Phase A Phase Phase B B Phase C C Phase

0 0

2 2

4 4

6 6

8 8

10 10

Distance(m) Distance(m) Figure 4. Voltage value under three phase transmission lines. Figure under three three phase phase transmission transmission lines. lines. Figure 4. 4. Voltage Voltage value value under

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4. Measurement System 4. Measurement System

The voltage measurement system of three-phase D-dot transducer as show in Figure 5 is The voltage measurement of three-phase D-dot transducer as show in circuits Figure 5 is Sensors 16, 1683 8 of 14and the composed of2016, two parts, namely, system parts that respectively measure the hardware composed of two parts, namely, parts that respectively measure the hardware circuits and the PC-port software program. Based on the condition that the distance between conductor and PC-port software System program. Based on the condition that the distance between conductor and 4. Measurement transducer is not smaller than the distance between conductors, the composite electric field is inversely transducer is not smaller than the distance between conductors, the composite electric field is inversely The voltage measurement system ofsolution three-phase D-dot transducer as which show incan Figure 5 is substituted intointo thethe algorithm for after decomposition, be achieved by substituted foraa voltage voltage solution after decomposition, can be achieved composed of twoalgorithm parts, namely, parts that respectively measure the which hardware circuits and by thethe the measurement system. measurement system. PC-port software program. Based on the condition that the distance between conductor and transducer is not smaller than the distance between conductors, the composite electric field is inversely substituted into the algorithm for a voltage solution after decomposition, which can be achieved by the measurement system.

Figure 5. Structure of measurement system.

Figure 5. Structure of measurement system.

The D-dot electric field transducer is madeofinto the formsystem. of a PCB (Printed Circuit Board) in Figure 5. Structure measurement

The D-dot field is made of a PCB (Printed Board) Figure 6. Theelectric top layer andtransducer the bottom layer of theinto PCBthe are form respectively provided withCircuit a plurality of in The D-dot electric field transducer is made into the form of a PCB (Printed Circuit Board) in annular electrodes with different radii, and the annular electrodes are respectively connected in Figure 6. The top layer and the bottom layer of the PCB are respectively provided with a plurality Figure 6. The top layer and the bottom layer of the PCB are respectively provided with a plurality of parallel and have the same potential. of annular electrodes with different radii, and the annular electrodes are respectively connected in annular electrodes with different radii, and the annular electrodes are respectively connected in parallel and have the same potential. parallel and have the same potential.

Figure 6. PCB of D-dot. Figure 6. PCB of D-dot.

6. PCB of D-dot. are processed for pre-amplification Voltage signals measured by the Figure D-dot voltage transducer Voltage signals measured by the D-dot transducer areAfter processed for pre-amplification and electrical-level lifting by an analog signalvoltage processing module. the treatment, a single-chip and electrical-level lifting by an analog signal processing module. After the treatment, a single-chip carries out high-speed collection and AD converter for the treated analog signals. Then the acquired and Voltage signals measured by the D-dot voltage transducer are processed for pre-amplification carries out high-speed collection and ADwireless convertercommunication for the treated analog signals. Then the acquired digital signals are delivered to a WIFI module according to the UART electrical-level lifting by an analog signal processing module. After the treatment, a single-chip carries digital signals are delivered to a WIFI wireless communication module according to the are UART (Universal Asynchronous Receiver/Transmitter) Communication Protocol. The signals then out high-speed collection and AD converter for the treated analog signals. Then the acquired digital (Universal Asynchronous Receiver/Transmitter) Communication Protocol. The signals are then

signals are delivered to a WIFI wireless communication module according to the UART (Universal Asynchronous Receiver/Transmitter) Communication Protocol. The signals are then transformed to

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transformed to the UDP (User Datagram Protocol) protocol format and transferred to a data the UDP (User Protocol) protocol format networks. and transferred to a data acceptance unit in the acceptance unitDatagram in the PC-port software by wireless PC-port software by wireless networks. After the data measured by the transducer is received by the data acceptance unit in a PC-port Afterpart, the data measured by the transducer is received by the data unit in a software iterative computations are executed by a digital signalacceptance processing unit toPC-port restore software part, iterative computations are executed by a digital signal processing unit to restore voltage voltage waveforms of three phases. Moreover, the discrete signal collected by the sensor is waveforms of three phases. Moreover, discretethe signal by theand sensor converted field into converted into a continuous signal the through ADcollected conversion, theis synthetic adecomposition continuous signal through the AD conversion, and the synthetic field decomposition algorithm algorithm proposed in the theoretical analysis is utilized. Then, the voltage proposed in the theoretical analysis is utilized. Then, the voltage waveform analysis unit analyzes this waveform analysis unit analyzes this voltage signal to obtain information such as its voltage voltage signal to obtainand information as its voltage amplitude,record frequency and degreethe of waveform distortion. amplitude, frequency degree ofsuch distortion. The waveform unit performs The waveform record unit performs the waveform storage for follow-up consultation and usage. storage for follow-up consultation and usage. To the D-dot D-dot transducer transducerand andthe theworking working performance of measurement its measurement system, To test test the performance of its system, the the three-phase experimental platform is established measure theresults resultsand andanalyze analyze the the electric three-phase experimental platform is established to to measure the electric field field environment environment of of the the 10 10 kV kV voltage voltage power powerline linetransmission transmissionline. line. The The measurement measurement spot spot of of the the voltage transducer is shown in Figure 7. In Figure 7, number 1 represents the three-phase voltage voltage transducer is shown in Figure 7. In Figure 7, number 1 represents the three-phase voltage transducers; they are transducers; they are installed installed under under each each of of the the three three transmission transmission lines lines respectively. respectively. Number Number 22 refers to the signal sample and the process circuit, hanging over it is a wireless transmission module. refers to the signal sample and the process circuit, hanging over it is a wireless transmission Number is standard transformer. 4 indicates support the measurement module. 3Number 3 voltage is standard voltageNumber transformer. Number 4 ofindicates support system, of the and number 5 represents the host computer. measurement system, and number 5 represents the host computer.

Figure 7. 7. Sketch of measuring measuring three-phase three-phase voltage. voltage. Figure Sketch map map of

After the voltage regulator, the three-phase alternating current is loaded to three-phase After the voltage regulator, the three-phase alternating current is loaded to three-phase transmission line after boosting the standard voltage transformer. The transducer is installed right transmission line after boosting the standard voltage transformer. The transducer is installed right under the transmission line and measuring circuits are connected to the transducer by signal lines. under the transmission line and measuring circuits are connected to the transducer by signal lines. Collected data are then sent to the host computer by wireless module and the upper computer Collected data are then sent to the host computer by wireless module and the upper computer adopts the LabVIEW software for programming. Following the UDP Communication Protocol, data adopts the LabVIEW software for programming. Following the UDP Communication Protocol, data are received and transferred to corresponding iterative calculation module to a finally acquire the are received and transferred to corresponding iterative calculation module to a finally acquire the three-phase voltage waveform. three-phase voltage waveform. As shown in Figure 8, the display interface of LabVIEW is represented with an effective value of As shown in Figure 8, the display interface of LabVIEW is represented with an effective value the measured-phase voltage, 5.8 kV, and a peak value of 8.2 kV. In the left side of the figure, the of the measured-phase voltage, 5.8 kV, and a peak value of 8.2 kV. In the left side of the figure, communication setting as well as the frequency and effective value of the three-phase voltage are the communication setting as well as the frequency and effective value of the three-phase voltage are illustrated. In the host computer section, the curves with colors of yellow, green and red are illustrated. In the host computer section, the curves with colors of yellow, green and red are represented represented as domain waveforms of the three-phase voltage, whereas the lower part shows the as domain waveforms of the three-phase voltage, whereas the lower part shows the analysis chart of analysis chart of the frequency spectrum. the frequency spectrum.

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Figure 8. Interface of display on PC. Figure 8. Interface of display on PC.

5. Experiment 5. Experiment The experimental part of the article will be analyzed from two aspects, according to the The experimental part of the article will be analyzed from two aspects, according to the IEC60044-7 IEC60044-7 Standard. The results of the two aspect experiment determine whether the performance Standard. The results of the two aspect experiment determine whether the performance of the of the transducer can meet the requirements of the actual application. transducer can meet the requirements of the actual application. 5.1. Steady-State Error Experiment Experiment 5.1. Steady-State Error The steady-state steady-state error experiment is implemented in experimental the built experimental platform. The error experiment is implemented in the built platform. According to According to IEC60044-7 Standard, the value of the three-phase voltage is adjusted during the IEC60044-7 Standard, the value of the three-phase voltage is adjusted during the experiment. experiment. The proportion of the rated20%, voltage 10%, 20%, 40%, 100% and 120% The proportion of the rated voltage is 10%, 40%, is 60%, 80%, 100% and60%, 120%80%, respectively, using the respectively, using the high-voltage detection head and the non-contact voltage transformer for high-voltage detection head and the non-contact voltage transformer for measurement. In addition, measurement. addition,head the is high-voltage head conductor is connected a three-phase conductor the high-voltageIndetection connected todetection a three-phase andtothe oscilloscope is adopted and the oscilloscope is adopted to synchronously measure voltage. Finally, data in two to synchronously measure voltage. Finally, data in two different voltage measuring points different are fit to voltage ameasuring points are fit to acquire a comparison of thedetection linearityhead between the experimental high-voltage acquire comparison of the linearity between the high-voltage and the detection head and the and to obtain the error ratio of the voltage. system and to obtain theexperimental error ratio ofsystem the voltage. The detection results of High-voltage probe are represented represented by byUUH. . Output Output voltages voltages of of the the The detection results of High-voltage probe are H transducer are aresent sentto to computing exist on based on Equations acquire transducer thethe computing unit,unit, whichwhich exist based Equations (1)–(8) to(1)–(8) acquireto measured measured voltage U M by inverse substitution. Dynamic range and linearity of the transducer are voltage UM by inverse substitution. Dynamic range and linearity of the transducer are measured and measured results are shown in Table 4. results are and shown in Table 4. Based on the obtained detected data, a comparative experiment, the calibration curve and the error Table 4. Accuracy test of three-phase D-dot voltage transformer. curve of the output voltage of the transducer and high-voltage detection head are shown in Figure 9. Phase Voltage/kV UH/kV UM/kV Ratio Error/% 1 0.64 0.604 0.18 2 1.322 1.221 0.17 4 2.655 2.599 0.22 6 4.051 4.139 0.41 A 8 5.323 5.416 0.43 10 6.676 6.508 0.41 12 8.087 8.127 0.21

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Table 4. Accuracy test of three-phase D-dot voltage transformer. Phase

B

A

B

C

1 Voltage/kV0.673UH /kV 1 2 1.341 0.64 2 4 2.6711.322 4 2.655 6 4.0364.051 6 8 8 5.3435.323 10 10 6.6836.676 12 8.087 12 7.976 1 0.673 1 0.6411.341 2 4 2 1.3222.671 6 4 2.6554.036 8 5.343 6 4.0516.683 10 12 8 5.3237.976 10 6.6760.641 1 2 12 8.0871.322

U0.601 M /kV

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Ratio Error/% 0.27

0.604 1.212 1.221 2.791 2.599 3.802 4.139 5.416 5.595 6.508 6.909 8.127

0.18 0.17 0.22 0.41 0.43 0.41 0.21

0.601 0.596 1.212 2.791 1.232 3.802 2.592 5.595 3.979 6.909 8.009 5.294

0.27 0.19 0.31 0.27 0.24 0.4 0.28

8.009

0.19 0.31 0.27 0.24 0.4 0.28 0.48 0.43 0.4 0.38 0.35 0.3 0.19

6.603 0.596 0.48 1.232 0.43 8.037 4 2.655 2.592 0.4 6 4.051 3.979 0.38 C Based on the obtained detected8 data, a comparative experiment, the 5.323 5.294 0.35 calibration curve and the 10 the transducer 6.676 and 6.603 0.3 error curve of the output voltage of high-voltage detection head are shown in 12 8.087 8.037 0.19 Figure 9.

UM(kV)

UM(kV)

8

ratio error(%) Fitting line

UM(kV)/ratio error(%)

UM(kV)/ratio error(%)

8

6

4

2

ratio error(%) Fitting line

6

4

2

0

0 0

2

4

6

0

8

2

4

(a) A phase

8

(b) B phase UM(kV)

8

UM(kV)/ratio error(%)

6

UH(kV)

UH(kV)

ratio error(%) Fitting line

6

4

2

0 0

2

4

6

8

UH(kV)

(c) C phase Figure 9. 9. Calibration Figure Calibration and and ratio ratio curve curveof ofthe thesensor sensorand andthe theHV-probe. HV-probe.

5.2. Sensor Accuracy Test When the initial phase of three-phase transmission line is 0, we use sensors to measure different positions under the transmission line to obtain their voltage values, and simultaneously extract voltage values from the Ansoft simulation results at the same point. We then contrast the two

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5.2. Sensor Accuracy Test When the initial phase of three-phase transmission line is 0, we use sensors to measure different Sensors 2016, 16, 1683 12 of 14 positions under the transmission line to obtain their voltage values, and simultaneously extract voltage values the Ansoft simulation results at the same We then contrast twohollow voltagetriangle values. voltagefrom values. The solid triangle represents the point. simulation results andthethe The solid triangle represents the simulation results and the hollow triangle represents the result of the represents the result of the measurement as shown in the figure below. measurement as shown in the figure below.

5.3. Result Analysis 5.3. Result Analysis Our comparison and analysis of the results measured by the high-voltage detection head and Our comparison and analysis of the results measured by the high-voltage detection head and the the transducer, are as follows. transducer, are as follows. (1) As shown in the LabVIEW display from Figure 8, the three-phase waveform is close to a (1) standard As shownsinusoidal in the LabVIEW display from Figure 8, the three-phase close to a standarda waveform with a relatively small degree ofwaveform distortion,iswhich represents sinusoidal waveform with a relatively small degree of distortion, which represents a three-phase three-phase measuring system that can realize synchronous acquisition by multipath signals. measuring system that can realize synchronous by multipath (2) When the three-phase voltage changed withinacquisition range of 10%–120% of signals. the rated voltage, the (2) specific When the three-phase voltage changed within range of 10%–120% of the rated voltage, specific value error of the electric-field coupling voltage transducer is ε% < 0.5%. Thethe measured value error of the 9electric-field coupling transducer ε% < 0.5%. The measured voltage voltage in Figure was fitted once withvoltage a goodness of fit ofis0.9988, 0.9989 and 0.9993, proving in Figure 9 was fitted once with a goodness of fit of 0.9988, 0.9989 and 0.9993, proving that the that the transducer has a relatively good linearity in all voltage measuring points. transducer has a relatively good linearity in all voltage measuring points. The measured results of the software simulation and transducer are compared and analyzed. The measured results of the software simulation transducer are compared and analyzed. In the comparative curve in Figure 10, the and values measured by the transducer are in In the comparative curve in Figure 10, the values measured by the transducer are in accordance accordance with the change trend of simulation graphics and these two curves are extremely close with the change trend ofmeans simulation and these two are extremely to each other, to each other, which that graphics the measurement withcurves the transducer is close of relatively high which means that the measurement with the transducer is of relatively high precision. precision.

Figure 10. Comparison of simulation and measurement results. Figure 10. Comparison of simulation and measurement results.

From the two experiments above, we observe that the measured results have some errors and Frombecomes the two experiments above, we observe that in thethe measured results have some errors and the the error more significant with an increase measured distance. This observation is error becomes more significant with an increase in the measured distance. This observation is because because the boundary conditions adopted in the simulation calculation are ideal, but the conductor the boundary conditions adopted in the ideal, butthus the conductor length, length, sag and transducer location allsimulation deviated calculation from ideal are conditions, largely affecting sag and transducer location all deviated from ideal conditions, thus largely affecting precision. precision. 6. Conclusions 6. Conclusions The three-phase D-dot voltage transducer measuring system was constructed and tested. With the The three-phase D-dot voltage transducer measuring system was constructed and tested. With aim of addressing the composite electric field problem during the measurement process of a three-phase the aim of addressing the composite electric field problem during the measurement process of a transmission line, we proposed a decomposition method and verified its feasibility with experiments. three-phase transmission line, we proposed a decomposition method and verified its feasibility with experiments. The measuring system can realize synchronous acquisition by multipath signals and successfully meet the accuracy class of the 0.5-level voltage transformer used for measurement when the rated voltage is within the range of 10%–120%. Furthermore it has relatively good linearity across all voltage measuring points.

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The measuring system can realize synchronous acquisition by multipath signals and successfully meet the accuracy class of the 0.5-level voltage transformer used for measurement when the rated voltage is within the range of 10%–120%. Furthermore it has relatively good linearity across all voltage measuring points. The non-contact voltage measuring system of a three-phase field-type transducer further promotes non-contact voltage measuring work in electric power projects. In cases where the measuring precision requirement is not high, the measuring system can achieve a rapid, convenient and safe measurement, which has relatively high engineering value in measuring electric parameters of distribution automation. In current projects, influences of tower sag and locations places of multiple transducers will result in errors of the voltage measurement in an experimental system. Thus, for future studies, the complexity degree and algorithm precision of the model should be improved to gradually resolve this problem. Acknowledgments: This work was supported by and the National Natural Science Foundations of China (Grant No. 51677009 and 51477015). Author Contributions: Jingang Wang is the head of the research group that conducted this study, and proposed the improved structure of the sensor. Gang Wei and Xudong Deng conducted experimental data collection. Xueqi Hu used Ansoft to carry on the data simulation to the model. All authors contributed to the writing and revision of the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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