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The Design and Characterization of a Prototype Wideband Voltage Sensor Based on a Resistive Divider Fernando Garnacho *, Abderrahim Khamlichi and Jorge Rovira Laboratorio Central Oficial de Electrotecnia (LCOE), Fundación para el Fomento de la Innovación Industrial (FFII), c/Eric Kandel, 1, 28906 Getafe, Madrid, Spain; [email protected] (A.K.); [email protected] (J.R.) * Correspondence: [email protected]; Tel.: +34-914-918-168 Received: 19 August 2017; Accepted: 12 October 2017; Published: 17 November 2017

Abstract: The most important advantage of voltage dividers over traditional voltage transformers is that voltage dividers do not have an iron core with non-linear hysteresis characteristics. The voltage dividers have a linear behavior with respect to over-voltages and a flat frequency response larger frequency range. The weak point of a voltage divider is the influence of external high-voltage (HV) and earth parts in its vicinity. Electrical fields arising from high voltages in neighboring phases and from ground conductors and structures are one of their main sources for systematic measurement errors. This paper describes a shielding voltage divider for a 24 kV medium voltage network insulated in SF6 composed of two resistive-capacitive dividers, one integrated within the other, achieving a flat frequency response up to 10 kHz for ratio error and up to 5 kHz for phase displacement error. The metal shielding improves its immunity against electric and magnetic fields. The characterization performed on the built-in voltage sensor shows an accuracy class of 0.2 for a frequency range from 20 Hz to 5 kHz and a class of 0.5 for 1 Hz up to 20 Hz. A low temperature effect is also achieved for operation conditions of MV power grids. Keywords: resistive divider; voltage sensor; high-voltage calibration; electric field; frequency response; capacitive effect

1. Introduction High-voltage (HV) dividers are a good alternative to traditional voltage transformers for power frequency measurements on medium- and high-voltage power lines [1,2]. An HV divider connected to a digital recorder is an appropriate measuring system for both continuous operation voltages (50 or 60 Hz, harmonics and subharmonics) and temporal or transient over-voltages (such as ferroresonances, switching, and lightning over-voltages) [3]. However, at present, the traceability for the measurement of harmonics and over-voltages is missing in most of the electrical grids because conventional voltage transformers are used. Distributed generation of electric power, a common feature of smart grids, involves increasing levels of power electronics integration, such as power converters, electronic controllers, and loads with a greater number of semiconductor components. Consequently, the voltage wave of smart grids contains an increasing amount of harmonics. The international standards [4,5] evolved in recent years require measurements in frequency ranges up to 5 kHz. However, it is known that conventional measuring transformers [6–9] have a cut-off frequency no higher than 1 kHz. Furthermore, saturation phenomena appear for frequencies below grid frequency (50/60 Hz). For these reasons, new HV measuring systems have to be developed with metrological capabilities from a few hertz to several kilohertz for smart grids that are characterized in accordance with present international standards [10].

Sensors 2017, 17, 2657; doi:10.3390/s17112657

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date, high voltage resistive dividers [11,12] have in electrical networks as ToTo date, high voltage resistive dividers [11,12] have not not beenbeen usedused in electrical networks as voltage voltage transfer devices. At first, this was due to the power supply requirements of voltmeters, transfer devices. At first, this was due to the power supply requirements of voltmeters, energy meters energy meters and relays; at present, this is due to the challenges different technical challenges to the be capacitive solved, and relays; at present, this is due to the different technical to be solved, such as such as the capacitive influence of nearby metal parts connected to earth or high voltage that causes influence of nearby metal parts connected to earth or high voltage that causes significant ratio and significant ratio and angle errors. Influence of overvoltages and high temperature changes are other angle errors. Influence of overvoltages and high temperature changes are other challenges that must challenges that must be solved. However, classical technology of HV dividers has been developed to be solved. However, classical technology of HV dividers has been developed to design a double design a double resistive-capacitive divider, one integrated inside the other, insulated in SF6, and resistive-capacitive divider, one integrated inside the other, insulated in SF6, and with a flat frequency with a flat frequency response (±0.2%) from 20 Hz to 5 kHz, for use in 20 kV power grids. The response ±0.2%)and from Hz to 5 magnitudes kHz, for useofineach 20 kV power grids. design andtothe divider (design the20electrical component have The beendivider carefully chosen electrical magnitudes of each component have been carefully chosen to achieve an industrial solution achieve an industrial solution to be used in power grids. The prototype has passed the insulation tocoordination be used in power grids.kVThe passedand the insulation tests (125 kV for tests (125 forprototype lightning has impulses 50 kV for coordination power frequency voltage) lightning impulses and 50performances kV for power(afrequency maintaining its technical performances maintaining its technical class of 0.2voltage) from 20 Hz up to 5 kHz). This prototype opens (a aclass of 0.2 from 20 Hz up to 5 kHz). This prototype opens a practical industrial approach to the practical industrial approach to the on-line monitoring of power quality and to knowledge of grid on-line monitoring of power quality and to knowledge of grid overvoltages (temporary, switching, overvoltages (temporary, switching, and lightning) to be supported by the grid components (powerand lightning) to besurge supported by the gridetc.). components (power transformers, surge arresters, cables, etc.). transformers, arresters, cables,

2. 2. Voltage Sensor Voltage Sensor 2.1. Physical 2.1. PhysicalDesign Design The voltage divider consists of aof50a MΩ HV resistive branch, composed of two The voltage divider consists 50 MΩ HV resistive branch, composed ofHV twofilm HVresistors, film R1resistors, and R2 , of each one each connected in seriesin(Figure 1). The1). low-voltage (LV) resistive branch R1 25 andMΩ, R2, of 25 MΩ, one connected series (Figure The low-voltage (LV) resistive ofbranch the divider, of 50 kΩ composed of four of 200four kΩ200 resistors arranged in parallel in a coaxial of the r,divider, r, ofis50 kΩ is composed kΩ resistors arranged in parallel in a coaxial configuration. Two of blocks four capacitors, a rated capacitance of 202 each formtwo configuration. Two blocks fourofcapacitors, with with a rated capacitance of 202 pF pF each form two capacitances, p, of pF, 808 connected pF, connected in series TheHV HVresistor resistor is is placed placed on thethe setset of of capacitances, Cp , ofC808 in series The onthe theaxis axisofof capacitors(Figure (Figure1). 1). The is connected in parallel with with the first of the of capacitors The first firstblock blockofofcapacitors capacitors is connected in parallel theresistor first resistor through anan upper electrode and a central electrode. The second block of of capacitors is is theHV HVbranch branch through upper electrode and a central electrode. The second block capacitors connected between the central electrode and the metallic enclose (see Figure 1). The central electrode connected between the central electrode and the metallic enclose (see Figure 1). The central electrode servesasasmechanical mechanicalsupport support for for the the two resistors of of thethe HVHV branch. serves two capacitor capacitorblocks blocksand andthe thetwo two resistors branch. The configuration is designed to achieve a voltage distribution along each HV resistor for higher The configuration is designed to achieve a voltage distribution along each HV resistor for higher frequencies as close as possible to the voltage distribution obtained for 50 Hz. The voltage frequencies as close as possible to the voltage distribution obtained for 50 Hz. The voltage distribution distribution along the HV resistors was determined by FEM simulation for the frequency range from along the HV resistors was determined by FEM simulation for the frequency range from 50 Hz to 5 kHz 50 Hz to 5 kHz (see Figure 2a). The central electrode is connected to joint point of both HV (see Figure 2a). The central electrode is connected to joint point of both HV resistances. The set is in resistances. The set is in a steel–aluminum casing to achieve a good shielding. The LV branch is also a steel–aluminum casing to achieve a good shielding. The LV branch is also arranged in an aluminum arranged in an aluminum compartment, different to the HV branch, although sharing the same gas compartment, different to the HV MPa branch, although sharing theinsulation same gas insulation. The SF6tests gas at insulation. The SF6 gas at 0.2 is used as an internal to pass dielectric 0.2corresponding MPa is used as an internal insulation to pass dielectric tests corresponding to the insulation level to the insulation level of 24 kV. A plug-in connector is used to be connected to the of 24cable kV. Aentry plug-in connector usedbox. to be connected to the cable entry of the enclosed metal box. of the enclosedismetal

(a)

(b)

(c)

Figure1. 1.Voltage Voltagedivider dividerfor forMV MV switchgear switchgear under cut-away view of the Figure under metal metalenclosure: enclosure:(a)(a)The The cut-away view of the voltage divider enclosed in a metallic enveloping; (b) schematic electrical circuit; (c) general view of voltage divider enclosed in a metallic enveloping; (b) schematic electrical circuit; (c) general view of the HV divider sensor to be connected in a MV cabin. the HV divider sensor to be connected in a MV cabin.

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(a)

(b)

Figure 2. 2. Voltage Figure Voltage distribution: distribution: (a) (a) Cut-away Cut-away view view of of equipotential equipotential lines lines in in the the voltage voltage divider; divider; (b) voltage voltage distribution distribution along along the the two two resistors resistors of of the the HV HV branch branch for forfrequency frequencyrange range50 50Hz–5 Hz–5kHz. kHz. (b) (a)

(b)

2.2. Simplified Simplified Electrical Model Figure 2. Voltage distribution: 2.2. Electrical Model

(a) Cut-away view of equipotential lines in the voltage divider; (b) voltage distribution along the two resistors of the HV branch for frequency range 50 Hz–5 kHz.

The simplified voltage divider is shown in Figure 3a. No The simplified electric electric circuit circuit ofofthe thedouble doubleRCRC voltage divider is shown in Figure 3a. inductance effect is considered because the cylindrical configuration of the divider and its size lead 2.2. Simplified Model because the cylindrical configuration of the divider and its size lead No inductance effectElectrical is considered to an an inductance inductance less less than than 11 μH, which does not the operation range of the divider. to µH,circuit which not affect affect the frequency frequency The simplified electric ofdoes the double RC voltage divider isoperation shown in range Figure of 3a.the Nodivider. Each resistor resistor of the the HVisbranch, branch, R1 because and R2, is an R, in parallel with inductance effect considered cylindricalthrough configuration of theresistance, divider andR, its in size lead with Each of HV R is modeled modeled through an ideal ideal resistance, parallel 1 and R2 ,the a capacitance: C s for the first resistor R 1 and C s ′ for the second one R 2 . The parallel capacitance C s and 0 to an inductance lessfirst than resistor 1 μH, which does C not thesecond frequency operation range of thecapacitance divider. a capacitance: Cs for the R1 and for the one R2 . The parallel Cs s affect Each resistor of the HV branch, R 1 and R2, is modeled through an ideal resistance, R, in parallel with C s′ includes not only the stray capacitance of the resistor but also the capacitance between the end 0 and Cs includes not only the stray capacitance of the resistor but also the capacitance between the a capacitance: Cs for the first resistor RR 1 and Cs′ for the second R2. The value parallelof capacitance Cs and electrodes of each HV resistor, R1 and 2. Consequently, a one different capacitances Cs end electrodes of each HV resistor, R1 and R2 . Consequently, a different value these of these capacitances C s′ includes not only the stray capacitance of the resistor but also the capacitance between the end and C s′ associated to each HV resistor is expected. The LV branch is represented by an ideal resistor 0 Cs and electrodes Cs associated each HV Rresistor is expected. The LV branch is represented by an idealr of eachtoHV resistor, 1 and R2. Consequently, a different value of these capacitances Cs and a parallel capacitance Cc′ (see Figure 3a) inFigure which two capacitive effects are included: resistor r and a paralleltocapacitance Cc 0is(see inadditional which two additional capacitive and Cs′ associated each HV resistor expected. The3a) LV branch is represented by an ideal resistor r effects the coaxial cable C c and of the digital recorder Cr (20 pF). In practice, the impedance of the recorder is and a parallel capacitance ′ (see Figure 3a) digital in whichrecorder two additional capacitive are included: are included: the coaxial cableCcC of the Cr (20 pF). In effects practice, the impedance c and considered a resistance of 1 MΩ, r*, that must be added to the value of the LV resistance. the coaxial cable C c and of the digital recorder C r (20 pF). In practice, the impedance of the recorder is theThe of the recorder is considered a resistance of 1 MΩ, r*, that must be added to the value of LV considered a e2p resistance 1 MΩ, r*, that added to effect the value of the LV The capacitances, Ce1capacitances, ,C , and Ceof ′, C represent the must earth capacitive between the resistance. metallic enveloping 0 be resistance. The e1 , Ce2p , and Ce , represent the earth capacitive effect between the Ce1, Ce2pthe , and Ce′, represent the earth capacitive effect between the metallic enveloping and thecapacitances, upper electrode, electrode, andcentral the LV electrode, resistor respectively. Ce2p also includes metallic enveloping and the central upper electrode, the and the LVThe resistor respectively. and the upper electrode, the central electrode, and the LV resistor respectively. The Ce2p also includes any C smallalso difference thedifference first and the second capacitor The includesbetween any small between the first andblocks. the second capacitor blocks. e2pany small difference between the first and the second capacitor blocks.

(a)

(a)

(b) *



'

'

(b)



'

If r  C c  C e  R  C s

 then *

'

'



'

If r  CC CCe  c   CR  C s t

p

s

Ct CCpCCs then C't  C p eq e2 p (c)

C't  Cp  Ceq  Ce2 p(d) Figure 3. Equivalent electric schemes: (a) simplified divider model; (b) equivalent circuit replacing

electric schemes: (a) simplified divider model; circuit replacing (c) Figure 3.theEquivalent (d) (b) equivalent 1st RC divider by two impedances in parallel Zeq1 and Zeq2; (c) equivalent model 2nd RC divider;

the 1st RC divider by two impedances ininparallel Zeq1 and Zeq2 ; (c) equivalent model 2nd RC divider; (d) improved divider model analyzed Section 4. Figure 3. Equivalent electric schemes: (a) simplified divider model; (b) equivalent circuit replacing (d) improved divider model analyzed in Section 4. the 1st RC divider by two impedances in parallel Zeq1 and Zeq2; (c) equivalent model 2nd RC divider; (d) improved divider model analyzed in Section 4.

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The circuit of Figure 3a is a simplified circuit for a specific frequency range to be determined. In this circuit, the LV branch (r*//Cc ' + Ce 0 )) with the second block (R//Cs 0 ) of the HV branch form the first RC divider, whose equivalent circuit is composed of two parallel impedances Zeq1 and Zeq2 shown in Figure 3b. ! ! 1 − ( s · c )2 1 − ( s · c )2 Zeq1 = ·R+ · r∗ (1) 2 2 1 − (s · a) 1 − (s · b) !  !   
1 − ( s · c )2 R 2 0 1 − ( s · c )2 r∗ 2 Zeq2 = · · Cs + · · Cc0 + Ce0 (2) 2 2 Req Req 1 − (s · a) 1 − (s · b) where
a = R · Cs0 , b = r ∗ · Cc0 + Ce0 , c = Req · Ceq

(3)

if the following condition is met:
r ∗ · Cc0 + Ce0 = R · Cs0

(4)

Thus, both impedances Zeq1 and Zeq2 become Req and Ceq : Req1 = R + ·r ∗  Ceq =

R Req

2

· Cs0



+

r∗ Req

2

(5)

· Cc0 + Ce0




(6)

Consequently, the circuit of Figure 3b leads to the circuit of Figure 3c in the second RC divider, in which the first RC divider is therein. It justifies the name “double RC divider” that the authors have given to this voltage sensor. Using this design, the earth capacitances Ce2 and Ce 0 became a part of the total parallel capacitances of the circuit shown in Figure 3c. An appropriate selection of the capacities Ce2p , Ce 0 , Cs , Cs 0 , and Cc is required to compensate the ratio and phase displacement errors of the divider. An improved model is shown in Figure 3d, in which the main difference from the simplified one is that the second resistor R of the HV branch is split into two parts and a stray capacitance is associated with each one. In addition, a parallel leakage resistance is introduced in each capacitor block to represent its insulation resistance. The behavior of this improved model is explained in detail by simulation in Section 4. The transfer function of the divider is given by the following formula: Gd (s) =

1 + s · Req · Ceq U2 1  i . =r· 00 · h 1+ s · R · C 0 U1 1 + s · r ∗ · Cc Req + R · 1+s· Req·C t

(7)

t

For direct voltage (s = 0) the transfer function is transformed in the following: Gd (s = 0) =

r∗ Req + R

(8)

and the normalized Laplace transfer function (G*nd (s = 0) = 1) by the following one: ∗ Gnd (s) =

R + Req 1 + s · Req · Ceq Gd (s) = · ·h G0 (s = 0) Req 1 + s · r ∗ · Cc0 1+

R Req

·

1 

1+s· Req ·Ct0 1+s· R·Ct

i .

(9)

Each RC divider should be designed to meet the following requirements: Requirement of the 1st RC divider: R · Cs0 = r ∗ · (Cc0 + Ce0 ) = r ∗ · Cc

00

(10)

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Requirement of the 2nd RC divider: Req · Ct0 = R · Ct

(11)

Ct = C p + Cs , Ct0 = C p + Ceq + Ce2p

(12)

where If both RC dividers meet these requirements, the normalized transfer function will be 1 p.u. The capacitances, Cs and Cs 0 , must be designed to comply with Equation (13), taking into account Equation (6): Req Req ( Req − R) Cs = · Ceq + · Ce + · Cp (13) R R R and the length of the coaxial cable must be chosen to comply the following condition: Length coaxial cable =

Cc0 − Cr cc

(14)

where cc is the capacitance per length unit of the coaxial cable of 66 pF/m, and Cr is the capacitance of the digital recorder. 3. Frequency Response Analysis 3.1. Frequency Response Analysis Using the Simplified Model In general, Equations (10) and (11) are not fully complied. One of the most common causes is the cable length of the coaxial cable used to connect with the digital recorder that modifies the Cc value. It can be slightly different from the theoretical value that satisfies Equations (10) and (11). The theoretical ratio error and the phase displacement error caused by the length of the coaxial cable can be determined using the transfer function, i.e., Equation (9), derived from the simplified circuit. In this simplified circuit, the theoretical maximum ratio error caused by the cable length of the coaxial cable can be determined through that equation for s → ∞: lims→∞ Gnd (s) =

Req + R Ceq Ct · 0 · ∗ r Cc (Ct + Ct0 )

(15)

To apply Equation (9) to the designed sensor, its electrical parameters must be determined. Most of them are determined by measurements. The electrical data of the digital recorder (Zr and Cr ) are collected from the manufacturer’s data sheet. Other parameters were estimated by modeling in order to achieve the best fitting to the actual measured in the laboratory. All parameter values of the built HV sensor are shown in Table 1. The theoretical frequency response derived from Equation (9) of the built HV sensor is shown in Figure 4 for different coaxial cable lengths. The difference between the real length of the coaxial cable and the reference length value given by Equation (10) provokes a clear ratio and angle errors for frequencies higher than 2 kHz. When the cable length is larger than the reference value, a negative ratio error is expected (see Figure 4). Length variations around ±5% (around ±5 cm of the coaxial cable) are acceptably to keep ratio error within an accuracy class of 0.2, but length variations lower than ±2.5% are recommended if the phase displacement error is to be kept within the admissible limits for a maximum frequency of 5 kHz. This length requirement for the coaxial cable can be easily fulfilled if the global measuring set, composed of the HV divider, a coaxial cable, and a digital recorder, is supplied by the same manufacturer.

809.2 pF Measurements 809.2 pF 809.2 pF 809.2 pF Cp 63.8 pF Measurements Cc (1) 20.0 pF Data sheet Cr 83.8 pF Derived C c′ = C c + C r 12.1 pF Measurements 12.1 pF 12.1 pF 12.1 pF Ce′ Derived 95.9 pF 95.9 pF 95.9 pF Cc′′ = Cc′+ Ce′ Sensors 2017, 17, 2657 6 of 11 29.5 pF Measurements 29.5 pF Ce1 (3) 12.5 pF Measurements 12.5 pF 12.5 pF 12.5 pF Ce2p 2.2 pF Measurements 2.2 pF (2) 2.2 pF (2) 2.2 pF (2) Cs Table 1. Electrical parameters (HV) 0.18 pF Modeling of the built 0.18high-voltage pF 0.18sensor. pF Cs′ Modeling 0.20/0.87 pF Cs′′/Cs′′′ Simplified Model Simplified Model Improved - Value Derived (5) 25 048 kΩ 25 048 kΩ - Model Requ Parameter Primary Determined By Figure 3b Figure Figure Derived (6) 0.15 pF - 3b - 3d Cequ 25-MΩ Measurements 25 MΩ 25 MΩ 25- MΩ Derived (12) 811.4 pF CRt 50- kΩ Measurements -Derived (12) 821.9- pF -Ct’r 1 -MΩ Data Sheet -Modeling -865 MΩ RZs r r* = r·Zr /(r + Zr ) Derived 47.6 kΩ 47.6 kΩ 47.6 kΩ Modeling 658 MΩ Re2 Cp 809.2 pF Measurements 809.2 pF 809.2 pF 809.2 pF k Modeling 0.96 63.8 pF Measurements Cc (1) (1) This (2) corresponds toData a length The measured Cr capacitance20.0 pF sheet of the coaxial- cable 97 cm (66 pF/m). 0 Cvalue + Cdifferent 83.8 pFreference value Derived (3) The capacitance c = Cc is r to the 14.3 pF given by Equations (11) and (12). Ce 0 12.1 pF Measurements 12.1 pF 12.1 pF 12.1 pF 00 = C 0 + C 0 between the 1st one in the of the 2nd capacitor95.9 block Ccdifference - magnitudes Derived pF Cp and the 95.9 pF is included95.9 pF c e (3) 29.5 pF Measurements 29.5 pF Ce1value. Ce2p Ce2p 12.5 pF Measurements 12.5 pF 12.5 pF 12.5 pF (2) HV sensor (2) 2.2 pF Measurements TheCstheoretical frequency response derived from2.2 Equation (9) of the built pF (2) 2.2 pF 2.2 is pF shown 0 Cs 0.18 pF 0.18 pF 0.18 pF in Figure 4 for different coaxial cableModeling lengths. The difference between the real length of the- coaxial Cs 00 /Cs 000 Modeling 0.20/0.87 pF cable and valueDerived given(5) by Equation (10) a clear Requthe reference length 25 048 kΩprovokes 25 048 kΩratio and angle - errors Cequ pF is larger than - the reference -value, a for frequencies higher than 2 kHz.Derived When(6)the cable 0.15 length Ct Derived (12) 811.4 pF negativeCt’ratio error is expected (seeDerived Figure(12)4). Length variations around ±5% 821.9 pF (around ±5 cm - of the Rs MΩ coaxial cable) are acceptably to keep Modeling ratio error within an- accuracy class of- 0.2, but length865 variations Re2 Modeling 658 MΩ lower than ±2.5% are recommended if the phase displacement error is to be kept within the k Modeling 0.96

admissible for a maximum frequency of 5 kHz. This length requirement for the coaxial cable (1) This limits capacitance corresponds to a length of the coaxial cable 97 cm (66 pF/m). (2) The measured value is can be easily fulfilled if the global measuring set, composed of (3) the HV divider,difference a coaxial cable,theand a different to the reference value 14.3 pF given by Equations (11) and (12). The capacitance between magnitudes of the 2nd capacitor block C and the 1st one is included in the C value. p e2p digital recorder, is supplied by the same manufacturer. 3

60

2

40

1

Error(min)

Error(%)

20

5 kHz

0.2% 0 l= l= l= l= l= l= l=

-1 -2 -3 -4 0 10

-5.0 % -2.5 % -1.0 % 0.0 % +1.0 % +2.5 % +5.0 %

1

0 l= l= l= l= l= l= l=

-20 -40 -60

2

10

10

10 Frecuency(Hz)

3

4

-80 0 10

5

10

10

5 kHz

10'

-5.0 % -2.5 % -1.0 % 0.0 % +1.0 % +2.5 % +5.0 %

1

2

10

10

(a)

3

10 Frecuency(Hz)

10

4

10

5

(b)

Figure 4. 4. Errors Errors due due to to difference difference of of length length of of coaxial coaxial cable cable C Ccc regarding regarding to to the the theoretical theoretical value value Figure regarding the simplified model of Figure 3: (a) ratio error; (b) phase displacement error. regarding the simplified model of Figure 3: (a) ratio error; (b) phase displacement error.

The frequency response response derived derivedfrom fromthe thesimplified simplifiedmodel model(Equation (Equation (9)) shown The theoretical frequency (9)) is is shown in in Figure 5 for different Cs values referred a percentage . It justifies the change the ratio Figure 5 for different Cs values referred to ato percentage of Cpof. ItCpjustifies the change of theofratio error error and angle for lower frequencies to changes Cs value regarding the reference and angle error error for lower frequencies due todue changes of theof Csthe value regarding the reference value value by Equation given given by Equation (11). (11). Sensors 2017, 17, 2657

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20

1.5

C = -2.21 %C s p C = -0.44 %C s p C = 0.00 %C s p

5 kHz

0.2%

C = +0.44 %C s p Cs= +1.10 %Cp

0

C = +2.21 %C s p -0.5

C = -1.10 %C s p

5 kHz

10'

10 Error(min)

Error(%)

0.5

C = -2.21 %C s p

15

Cs= -1.10 %Cp

1

C = -0.44 %C s p C = 0.00 %C s p

5

C = +0.44 %C s p C = +1.10 %C s p

0

C = +2.21 %C s p

-5 -10

-1 -1.5 0 10

-15 1

10

2

10

10 Frecuency(Hz)

3

4

10

5

10

-20 0 10

(a)

1

10

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2

10 Frecuency(Hz)

3

4

10

10

5

(b)

5. Errors to differentCCs s values values using thethe simplified modelmodel of Figure (a) ratio3:error; (b) error; Figure Figure 5. Errors due due to different using simplified of 3:Figure (a) ratio phase displacementerror. error. (b) phase displacement

3.2. Measuring the Response Frequency of the Built Sensor Taking into account the data of Table 1, the two restrictions referred in Equations (10) and (11) are checked for the built sensor (see Table 2). It can be observed that Equation (10), corresponding to the restriction of the 1st divider, is better complied (0.5%) with than the restriction given by Equation (11) associated with the 2nd divider (1.5%). The deviation due to the 2nd divider is caused by a real value of Cs = 2.2 pF (measured) when it should be 14.3 pF to satisfy Equation (11). An improved design of

-0.5 -10

-1

-15

-1.5 0 10

1

2

10

10

10 Frecuency(Hz)

3

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-20 0 10

5

10

10

1

10

10

2

(a)

10 Frecuency(Hz)

3

4

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(b)

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Figure 5. Errors due to different Cs values using the simplified model of Figure 3: (a) ratio error; (b) phase displacement error.

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3.2. Measuring the Response Frequency of the Built Sensor 3.2. Measuring the Response Frequency of the Built Sensor Taking into account the data of Table 1, the two restrictions referred in Equations (10) and (11) are Taking into account the data of Table 1, the two restrictions referred in Equations (10) and (11) checked for the built sensor (see Table 2). It can be observed that Equation (10), corresponding to the are checked for the built sensor (see Table 2). It can be observed that Equation (10), corresponding to restriction of the 1st divider, is better complied (0.5%) with than the restriction given by Equation (11) the restriction of the 1st divider, is better complied (0.5%) with than the restriction given by Equation (11) associated withthe the2nd 2nddivider divider(1.5%). (1.5%).The The deviation due to the divider is caused real value associated with deviation due to the 2nd2nd divider is caused by a by reala value of C = 2.2 pF (measured) when it should be 14.3 pF to satisfy Equation (11). An improved design of Css = 2.2 pF (measured) when it should be 14.3 pF to satisfy Equation (11). An improved design of of the electrode and and the the central centralelectrode electrodewould wouldpermit permita areduction reductionininthis this discrepancy order to the upper upper electrode discrepancy in in order obtain a class of 0.2 from 1 Hz to 5 kHz with the same divider ratio value, as is shown in Figure to obtain a class of 0.2 from 1 Hz to 5 kHz with the same divider ratio value, as is shown in Figure 5a.5a. Table2.2.Checking Checkingrestrictions restrictions Equations voltage sensor. Table of of Equations (10)(10) andand (11)(11) for for the the builtbuilt voltage sensor. Restriction Restriction of 1st RC Divisorof

0 of 2nd EquationEquation (1) R·Cs 0 =(1) r*·(Cc 0 + CRestriction Restriction of 2ndR·C RCtDivisor e ) = Req·Ct′

1st RC Divisor R·Cs (kΩ·pF) s′·pF) (kΩ·pF) r*·(Cc ' + Ce 0 )R·C (kΩ r*·(Cc' + Ce′) (kΩ·pF)

R·Cs′ = r*·(Cc′ + Ce′) 4545 4545 4568 4568

0

R·Ct = Req ·Ct 0

RC Divisor R·Ct (kΩ·pF) R·Ct (kΩ·pF) Req ·Ct ' (kΩ·pF)20,284 Req·Ct' (kΩ·pF) 20,587

20,284 20,587

The frequency response of the built voltage sensor was measured (see Figure 6) for different Cc The frequency response of the built voltage sensor was measured (see Figure 6) for different Cc values (different cable lengths) in the LCOE calibration laboratory in order to check Equation (9) of the values (different cable lengths) in the LCOE calibration laboratory in order to check Equation (9) of simplified model. It was also also observed that,that, for lengths of the cablecable largerlarger than than the reference the simplified model. It was observed for lengths ofcoaxial the coaxial the value (97 value cm), the of the ratio error anderror the angle error is negative for higher reference (97tendency cm), the tendency of the ratio and the angle error is negative for frequencies higher (>200 kHz) according the simplified butmodel, a preliminary oscillationoscillation is observed the interest frequencies (>200 kHz)toaccording to the model, simplified but a preliminary is in observed frequency range (2–100 range kHz).(2–100 This effect noteffect detectable by the simplified model. For thisFor reason, in the interest frequency kHz). is This is not detectable by the simplified model. the shown in Figure introduced in Sectionin4.Section 4. thisimproved reason, themodel improved model shown3d in is Figure 3d is introduced 10

150

5kHz

8

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85.0 %C

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Figure 6. 6. Measured Measurederrors errorsininthe thereal real design Figure 1 due to the difference in length the length of coaxial Figure design of of Figure 1 due to the difference in the of coaxial cable C Cccwith withrespect respecttotothe thetheoretical theoretical value: ratio error; phase displacement cable value: (a)(a) ratio error; (b) (b) phase displacement error.error.

In range (1–10 Hz),Hz), the rated ratio of the of divider increases up to 0.7% In the the low lowfrequency frequency range (1–10 the rated ratio the divider increases up (see to 0.7% Figure 7), while the angle error maintains lower than 10 min for the C c values analyzed (see Figure 7), while the angle error maintains lower than 10 min for the Cc values analyzed (85.0–101.1% C Sensors 2017, 8 of 11 (85.0–101.1% Cc).17, ). 2657 c

ratio(%)

0.6

93.4 %C

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101.1 %C

85.0 %C 89.5 %C

c

100.0 %C

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c c

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0 -0.2 0 10

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10 f (Hz)

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(a)

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10 f (Hz)

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FigureFigure 7. Measured errors of the built HV sensor frequencyrange range difference lengths 7. Measured errors of the built HV sensorin inthe the low low frequency forfor difference lengths of of the coaxial cablecable Cc : (a) error; (b)(b) phase error. (a) ratio error; phasedisplacement displacement error. the coaxial Cc: ratio

Both frequency responses, of the simplified model derived from Equation (9) and of the built divider measured in the LCOE laboratory, are shown in Figure 8. It can be observed that the simplified model follows the real frequency behavior for a frequency range up to 3 kHz. -4

10

x 10

100

-0.2 0 10

1

10 f (Hz)

10

-10 0 10

2

1

10 f (Hz)

(a)

10

2

(b)

Figure 7. Measured errors of the built HV sensor in the low frequency range for difference lengths of 8 of 11 the coaxial cable Cc: (a) ratio error; (b) phase displacement error.

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Both frequency responses, Equation (9) (9)and andofofthe thebuilt built Both frequency responses,ofofthe thesimplified simplifiedmodel model derived derived from Equation divider measured LCOElaboratory, laboratory, shown in Figure can be that observed that the divider measuredin in the LCOE are are shown in Figure 8. It can8.beItobserved the simplified simplified model the follows the real frequency behavior for a range frequency model follows real frequency behavior for a frequency up torange 3 kHz.up to 3 kHz. -4

x 10

100

9

8 0 10

phase(min)

ratio(pu)

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Measured Curve Simplified model 1

10

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3

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(a)

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0 Measured Curve Simplified model

-100 -200 -300 0 10

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f (Hz)

(b)

Figure 8. Frequency response curves:the thered redcurve curveisisobtained obtained via via Equation Figure 8. Frequency response curves: Equation (9) (9)and andthe theblue bluecurve curve was measured in the LCOE laboratory: (a) ratio error; (b) phase displacement error. was measured in the LCOE laboratory: (a) ratio error; (b) phase displacement error.

4. Improved Electrical Model 4. Improved Electrical Model improve thesimplified simplified model model shown 3a,3a, thethe 2nd resistor of the is splitisinto To To improve the shownininFigure Figure 2nd resistor of HV the branch HV branch split two parts, as is shown in the circuit of Figure 3d. Each resistance part k·R and (1 − k) · R has a different into two parts, as is shown in the circuit of Figure 3d. Each resistance part k·R and (1 − k) · R has a stray capacitance Cs 00 and Cs 000 in parallel depending on the geometrical location between the resistance different stray capacitance Cs′′ and Cs′′′ in parallel depending on the geometrical location between and the central electrode (see Figure 2a), which it is considered in the PSPICE circuit shown in Figure 9 the resistance00and the central electrode (see Figure 2a), which it is considered in the PSPICE circuit by Csp1 (Cs ) and Csp2 (Cs 000 ), respectively. For the built sensor, an equivalent capacitance of Cs 00 is shown in Figure 9 by Csp1 (Cs′′) and Csp2 (Cs′′′), respectively. For the built sensor,000 an equivalent in parallel with the first part of the resistance part k·R and another capacitance of Cs is in parallel capacitance of Cs′′ is in parallel with the first part of the resistance part k·R and another capacitance with the other resistance part (1 − k) · R. The values of the coefficient k (0.96) and of the capacitances of CCs′′′ the other resistance part (1 − k) · R. The values of the coefficient k (0.96) and 00 is in parallel with 000 (0.87 pF) have been determined by an iterative process by means of circuit s (0.20 pF) and Cs of the capacitances C s′′ (0.20 pF) and Cs′′′ (0.87 pF) have been determined by an iterative process by analysis and synthesis using PSPICE modeling and MATLAB in order to fit the theoretical curve of the means of circuit analysis and usinginPSPICE modeling and MATLAB in order resistors to fit the frequency response to the realsynthesis one measured the laboratory. Furthermore, two additional theoretical of the frequency response to the real oneof measured in the blocks laboratory. Furthermore, (Rsp andcurve Re2p ) that mainly represent leakage resistances both capacitor are also added to twosimulate additional resistors (R sp and R e2p ) that mainly represent leakage resistances of both capacitor in a better way the real behavior of the built divider. The Rsp magnitude also includes any blocks are also addedthe to1st simulate a HV better way the The realimproved behaviormodel of theachieves built divider. The Rsp difference between and thein 2nd resistances. a good fitting magnitude also includes any difference between thevalues 2nd HV resistances. Theofimproved to the measured frequency response (see Figurethe 10) 1st for and the set of the parameters Table 1, model achieves a goodmodel fittingdoes to the frequency (see Figure for the response set values while the simplified notmeasured fit the high frequencyresponse range (Figure 8). The10) frequency measured in the of built divider with athe small change inmodel the emplacement the high 2nd resistance also of the parameters Table 1, while simplified does not fitofthe frequencyis range included in Figure 10. Theresponse emplacement change in moved 2 mmwith from athesmall relative position (Figure 8). The frequency measured the vertically built divider change in of the the 2nd resistance regarding the central influence in the frequency response emplacement of the 2nd resistance is alsoelectrode. includedAinsignificant Figure 10. The emplacement change moved 000 in the improved curve can be observed, justifies the inclusion of stray capacitances Cs 00 and s vertically 2 mm from thewhich relative position of the 2nd resistance regarding theCcentral electrode. A circuit model shown Figure 3d andresponse in its simulate shown in Figure 9. the inclusion significant influence in in the frequency curvePSPICE can be circuit observed, which justifies

of stray capacitances Cs′′ and Cs′′′ in the improved circuit model shown in Figure 3d and in its simulate PSPICE circuit shown in Figure 9.

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CCpp

CCpp k·R k·R

RR

II11

UU22

(1-k)·R (1-k)·R

rr

CCss UU11

RRspsp RRe2p e2p

CCe1e1

CCcc

CCss’’’ ’’’

CCss’’’’

CCee’’

CCe2p e2p

(a) (a)

(b) (b) Figure 9. Improved model model of of the the sensor: (a) equivalent equivalent electric electric circuit; circuit; (b) (b) PSPICE PSPICE model model to to fit fit the the Figure Figure 9. Improved Improved model of the sensor: sensor: (a) (a) equivalent electric circuit; (b) PSPICE model to fit the frequency response frequency response to the measured one. frequency response to the measured one. -4

-4 xx 10 10

200 200

9.4 9.4 9.2 9.2 99 8.8 8.8 0 0 10 10

phase(min) phase(min)

ratio(pu) ratio(pu)

9.6 9.6

Measured Measuredbest best emplacement emplacement Improved Improvedmodel model Measured 2mm Measured 2mm displacement displacement 1

1 10 10

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Measured Measuredbest best emplacement emplacement Improved Improvedmodel model Measured 2mm Measured 2mm displacement displacement 1

1 10 10

2

2 10 10

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ff(Hz) (Hz)

3 10 10

4

4 10 10

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5 10 10

(b) (b)

Figure 10. 10. Frequency Frequency response response curves curves measured measured with with the the best best emplacement emplacement of of the the 2nd 2nd HV HV resistance resistance Figure Figure 10. Frequency response curves measured with the best emplacement of the 2nd HV resistance (blue curve), with a vertical displacement of 2 mm (red curve), and obtained by PSPICE simulating the (blue (blue curve), curve), with with aa vertical vertical displacement displacement of of 22 mm mm (red (red curve), curve), and and obtained obtained by by PSPICE PSPICE simulating simulating frequency response of best emplacement of the 2ndthe HV resistance (green curve) using the coefficient the the frequency frequency response response of of best best emplacement emplacement of of the 2nd 2nd HV HV resistance resistance (green (green curve) curve) using using the the k = 0.96 to the frequency response measured: (a) ratio error; (b) phase displacement error. coefficient coefficient kk == 0.96 0.96 to to the the frequency frequency response response measured: measured: (a) (a) ratio ratio error; error; (b) (b) phase phase displacement displacement error. error.

5. High-Voltage High-Voltage Calibration 5. 5. High-Voltage Calibration and and Insulation Insulation Testing Testing 5.1. Ratio and and Angle Errors Errors 5.1. 5.1. Ratio Ratio and Angle Angle Errors √ The voltage voltage sensor sensor was was calibrated calibrated in in aa HV range from 11 to 14 kV (24/ 3 kV) for for a sinusoidal The HV range from to 14 kV (24/√3 The voltage sensor was calibrated in a HV range from 1 to 14 kV (24/√3 kV) kV) for aa sinusoidal sinusoidal frequency of 50 50 Hzusing using voltagestandard standard transformers.The The calibrationwas was complemented with frequency frequency of of 50 Hz Hz using voltage voltage standard transformers. transformers. The calibration calibration was complemented complemented with with aa √ a power frequency test of 60 Hz at 14 kV (24/ 3 kV). An uncertainty of 0.08% for the HV calibration power calibration power frequency frequency test test of of 60 60 Hz Hz at at 14 14 kV kV (24/√3 (24/√3 kV). kV). An An uncertainty uncertainty of of 0.08% 0.08% for for the the HV HV calibration ◦ C and 40 ◦ C. was achieved. achieved. The The calibration calibration was was performed performed for for two two environment environment temperatures: temperatures:20 20°C was and was achieved. The calibration was performed for two environment temperatures: 20 °C and 40 40 °C. °C. The The ratio ratio errors errors obtained obtained are are inside inside the the admissible admissible tolerances tolerances corresponding corresponding to to an an accuracy accuracy class class of of 0.2 0.2 (see (see Figure Figure 11). 11).

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The ratio errors obtained are inside the admissible tolerances corresponding to an accuracy class of 0.2 (see Figure 11). Sensors 2017, 17, 17, 2657 10 of of 11 11 Sensors 2017, 2657 10 50Hz 50Hz

0.25 0.25 0.2 0.2 23ºC 23ºC

0.15 0.15

40ºC 40ºC

Lineal(23ºC) (23ºC) Lineal

Lineal(40ºC) (40ºC) Lineal

0.1 0.1

(%) (%)

0.05 0.05

00 1.00 1.00 -0.05 -0.05

3.00 3.00

5.00 5.00

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-0.1 -0.1 -0.15 -0.15 -0.2 -0.2

kVAC ACRMS kV RMS

(a) (a) 0.1 0.1

60Hz 60Hz

(%) (%)

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kVAC ACRMS RMS kV

(b) (b) ◦ C and 40 ◦ C, (b) ratio errors Figure 11. 11. (a) (a)Ratio Ratioerrors errors for for HV HV calibration calibration from from 11 to to 14 14 kV, kV, 50 Hz at 20 kV, 50 50 Hz Hz at at 20 20 °C °C and 40 °C, °C, (b) ratio errors Figure ◦ C. for HV HV calibration calibration from from 11 11 to to 14 14 kV, kV, kV,60 60Hz Hzat at20 20 °C. °C. for 60 Hz at 20

Insulation Tests Tests 5.2. Insulation 5.2. Insulation tests testswere wereusefully usefullypassed passed corresponding to the the insulation level for material material to be Insulation corresponding to to the insulation level for material to beto used Insulation tests were usefully passed corresponding insulation level for be used in a power grid of 24 kV. Fifteen positive and negative lightning impulses 1.2/50 of 125 kV in a power grid of 24 kV. Fifteen positive and negative lightning impulses 1.2/50 of 125 kV were used in a power grid of 24 kV. Fifteen positive and negative lightning impulses 1.2/50 of 125 were √ without any any breakdown breakdownand andaaapower powerfrequency frequencyvoltage voltageofof of5050 50kV kV (U peak /√2) for minute was was applied without (U(U //√2) 2)for foraaaminute applied breakdown and power frequency voltage kV peak peak breakdown (see (see Figure Figure 12). 12). applied without without any any breakdown applied 00 -20 -20 -40 -40

UU (kV) (kV)

-60 -60 -80 -80

-100 -100 -120 -120 00

(a) (a)

10 10

20 20

30 30

40 40 s) tt((s)

50 50

60 60

70 70

80 80

(b) (b)

Figure 12. (a) Testing layout of the voltage divider prototype connected to to aaa medium medium voltage voltagecable, cable, Figure 12. 12. (a) (a) Testing Testing layout layout of of the the voltage voltage divider divider prototype prototype connected connected to medium voltage cable, Figure (b) negative lightning impulse (125 kV) applied during the withstand test. (b) negative negative lightning lightning impulse impulse (125 (125 kV) kV) applied applied during during the the withstand withstand test. test. (b)

6. Conclusions Conclusions 6. A voltage voltage sensor sensor on the basis basis of of aa shielding shielding double double RC designed, on the RC voltage voltage divider divider has has been been designed, designed, A developed, built, and tested. The design is based in two RC dividers, one inside the built, and tested. The design is based in two RC dividers, one inside the other. This developed, built, and tested. The design is based in two RC dividers, one inside the other. other. This This design permits to transform earth capacitances of HV resistive branchto parallelcapacitances. capacitances. design permits to transform transform earth capacitances of the thethe HV resistive branch totoparallel parallel capacitances. design permits to earth capacitances of HV resistive branch The frequency frequency response response of frequency response response from from 20 20 Hz Hz to to 555 kHz, kHz, of the the built built sensor sensor shows shows aa flat flat frequency frequency response from 20 Hz to kHz, The with error and a phase displacement error inside the admissible errors of a class of 0.2. The with aa ratio ratio error and a phase displacement error inside the admissible errors of a class of 0.2. The ratio error and a phase displacement error inside the admissible errors of a class of 0.2. class The class increases increases to to 0.5 0.5 ifif the the sensor sensor is is used used from from 11 to to 20 20 Hz. Hz. An An optimized optimized design design to to maintain maintain the the 0.2 0.2 class class from from DC DC to to 55 kHz kHz is is attainable attainable ifif the the parallel parallel capacitance capacitance C Css,, of of the the first first HV HV resistor, resistor, R, R, is is class increased. The insulation tests demonstrate that the built sensor can be used in power grids up to increased. The insulation tests demonstrate that the built sensor can be used in power grids up to 24 kV. kV. 24

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increases to 0.5 if the sensor is used from 1 to 20 Hz. An optimized design to maintain the 0.2 class from DC to 5 kHz is attainable if the parallel capacitance Cs , of the first HV resistor, R, is increased. The insulation tests demonstrate that the built sensor can be used in power grids up to 24 kV. Acknowledgments: The work reported here has received support from the EMRP program jointly funded by the EMRP participating countries within EURAMET and the European Union. The authors wish to acknowledge the comments and suggestions received from Jari Hällström from the VTT Technical Research Centre of Finland Ltd., the Centre for Metrology MIKES, Finland, Renata Styblikova from CMI Cesky Metrologicky Institut of Brno, Czech Republic, and Juraj Sluciak from SMU Slovenský Metrologický Ústav, Slovakia. Author Contributions: F.G. and A.K. conceived and designed the experiments and the tests; A.K. and J.R. performed the experiments and the tests; A.K. and F.G. analyzed the data; J.R. contributed reagents/materials/analysis tools; F.G. and A.K. wrote the paper. Conflicts of Interest: The authors declare no conflicts of interest.

References 1. 2. 3. 4. 5. 6.

7.

8.

9. 10. 11. 12.

International Electrotechnical Commission. IEC 61869-1 Instrument Transformers—Part 1: General Requirements; IEC: Geneva, Switzerland, 2007. International Electrotechnical Commission. IEC 61869-3 Additional Requirements for Inductive Voltage Transformers; IEC: Geneva, Switzerland, 2011. International Electrotechnical Commission. IEC 60060-2 High Voltage Test Techniques—Part 2 Measuring Techniques; IEC: Geneva, Switzerland, 2010. International Electrotechnical Commission. IEC 61000 Electromagnetic Compatibility (EMC); IEC: Geneva, Switzerland, 1992. EN 50160 European Standard. Voltage Characteristics in Public Distribution Systems-Voltage Disturbances; CENELEC: Brussels, Belgium, 1999. Klatt, M.; Meyer, J.; Elst, M.; Schegner, P. Frequency Responses of MV voltage transformers in the range of 50 Hz to 10 kHz. In Proceedings of the 14th International Conference on Harmonics and Quality of Power (ICHQP), Bergamo, Italy, 26–29 September 2010. Seljeseth, H.; Saethre, E.A.; Ohnstad, T.; Lien, I. Voltage transformer frequency response. Measuring harmonics in Norwegian 300 kV and 132 kV power systems. In Proceedings of the 8th International Conference on Harmonics and Quality of Power, Athens, Greece, 14–16 October 1998; Volume 2, pp. 820–824. Kunde, K.; Däumling, H.; Huth, R.; Schlierf, H.W.; Schmid, J. Frequency Response of Instrument Transformers in the kHz Range. Available online: http://www.trench.at/content/download/1604/14169/ file/Frequency%20Response%20of%20Instrument%20Transformers%20in%20the%20kHz%20range.pdf (accessed on 17 November 2017). Crotti, G.; Gallo, D.; Giordano, D.; Landi, C.; Luiso, M.; Modarres, M. Frequency response of MV voltage transformer under actual waveforms. IEEE Trans. Instrum. Meas. 2017, 66, 1146–1154. [CrossRef] International Electrotechnical Commission. IEC 60044-7 Instrument Transformers—Part 7: Electronic Voltage Transformers. Additional Requirements for Electronic Voltage Transformers; IEC: Geneva, Switzerland, 1999. Hlavacek, J.; Draxler, K.; Styblikova, R. 20 kV AC Divider with ratio correction. In Proceedings of the 19th International Symposium on High Voltage Engineering, Pilsen, Czech Republic, 23–28 August 2015. Crotti, G.; Gallo, D.; Giordano, D.; Landi, C.; Luiso, M.; Modarres, M.; Zucca, M. Frequency compliance of MV voltage sensors for smart grid application. IEEE Sens. J. 2017, 17, 7621–7629. [CrossRef] © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).