1 erik.sperling@pmw.ch

Dimensions of influence of RC-dividers on the measurement of power quality parameters in high-voltage transmission networks

Erik SPERLING

1

PFIFFNER Instrument Transformers Ltd.

Switzerland

Prof. Peter SCHEGNER

Technical University of Dresden

Germany

SUMMARY Energy production is currently moving away from conventional methods, such as nuclear power plants or coal and gas power plants, towards new resources such as wind, solar or geothermal power. The connection of these new resources to power networks will mostly be implemented by electronic converters. Some of these energy sources are dependent on natural phenomena and lead to increasing switching operations. A second important issue is the locally concentrated production of new energy, for example in off-shore wind parks, with respect to the location of the main industrial centres in Europe. The existing transmission line system is currently operating on the limits of their initial design. Today, ideas such as combined transmission overhead lines (hybrid networks) with AC and DC power are becoming more and more important with respect to the transmission of high quantities of energy to the region where it is needed. All the examples mentioned above, as well as the increased use of intermeshed network systems in Europe, have an influence on the power quality of the energy. Thus, continuous voltage signals beginning from DC as an offset up to several kHz can appear. For transient voltage signals, the resulting frequency may be in the range from 1MHz up to 10MHz. The results of initial measurements made with conventional instrument transformers in HV and EHV networks show that frequency response is dependent on system voltage. Based on these results and the technical report IEC/TR61869-103 published in 2012, the necessity of correct measurement results up to a higher frequency range is required in order to attain the required power quality parameters and protect the installed high voltage equipment. In the non-conventional instrument transformer (NCIT) field, an alternative solution exists which has the ability to measure signals from DC up to several MHz to a very high accuracy. This kind of NCIT is a resistive-capacitive divider (RC-divider). Theoretical discussions verify an almost non-frequency dependent behaviour of the transfer function when considering the existing limits. Starting from DC voltage and up to a voltage with a frequency of 10kHz, a voltage error of lower than 0.2% is attainable with a 420kV RC-divider. The total divider ratio provided by a resistive divider and a capacitive divider. The crossing-point frequency defines the highest possible change in accuracy and occurs, when both individual divider ratios have the same share in the total divider ratio. A very important characteristic is the accuracy linearity with respect to voltage variations. The measurement results

21, rue d’Artois, F-75008 PARIS A3-111 CIGRE 2014 http : //www.cigre.org

1

show an excellent behaviour and guarantee high accuracy at very low voltages as well as at the overvoltage factor limit. Transient impulses are mainly caused by natural phenomena or during switching operations. For analysing or monitoring applications, tests with lightning impulse voltages show a very good characteristic for voltage curve transmission compared to an optimized impulse divider. The self-resonance frequency limits the measurable frequency band. Theoretical discussions illustrate the physical background. Under consideration of equation (21) and specified network requirements, a guideline provides information on how the self-resonance frequency can be modified.

KEYWORDS

Frequency Response Behaviour, Power Quality, RC-Divider, NCIT, Harmonic Voltage Measurement, Self-resonance Frequency

2

1. Introduction The characteristics of electrical energy in distribution networks are defined according to EN 50160. Transmission networks are subjected to similar requirements. The main parameters are voltage amplitude, waveform, frequency and balance of the phase voltages. Because of the increasing use of alternative sources in energy production and the type of feed-in technology, the power quality is substantially affected by various causes. Figure 1 illustrates the frequency components to be found in

an electric power supply system. The blue line represents the rated network frequency component; the orange line specifies sub-harmonics and flicker; the green lines define the harmonics; the red lines are typical transient impulses. The DC component which may occur as an offset is also shown. It is not possible to measure this very wide frequency range, from DC up to several MHz, with conventional instrument transformers with reasonable accuracy [1,3,9]. As an alternative, a non-conventional instrument transformer, e.g.

Figure 1: Frequency content in a network [8] resistive-capacitive voltage divider

(RC- divider), can be used for power quality measurement. In this paper we demonstrate that, with this type of technology, a very high accuracy is achievable.

2. Theoretical aspects of RC-dividers An RC-divider consists of a capacitive divider and a resistive divider, which are electrically connected in parallel. The very simplified equivalent circuit diagram is shown in figure 2. Any expected stray capacitances are not considered.

V1: Primary voltage

V2: Secondary voltage

C1: Primary capacitance

R1: Primary resistance

C2: Secondary capacitance

R2: Secondary resistance

iC: Capacitive current

iR: Resistive current

As shown in figure 2, the system current consists of a resistive part and a capacitive part. Depending on the selection of the resistances R1 and R2 (R-divider), and the capacitances C1 and C2 (C-divider) and under consideration of frequency and amplitude of the voltage, one of both divider ratios is more dominant. The transformation ratio r(ω) is defined in equation 1. It shows the complex ratio between the primary and secondary voltages.

Figure 2: Simplified equivalent circuit diagram of a RC-divider [1]

Formula 2 represents the complex transfer function k(ω) and describes the mathematical representation of the relation between the input and output voltage of a time-invariant system within zero initial conditions and zero-point equilibrium [2]. ��(�)��(�) = ����� = (�) (1)

��(�)��(�) = ����� = �(�) (2)

With respect to equation 2, the complex transfer function k(ω) of the secondary voltage V2 divided by the primary voltage V1 is:

3

���� = �(�) = ���� + �� ∙ (1 + 1 (������)⁄ )(1 + 1 (������)⁄ )

(3)

���� = �(�) = ���� + �� ∙ (1 + ������)(1 + ������)

(4)

Equations 3 and 4 represent the mathematical results for the simplified equivalent circuit diagram of figure 2 and can be mutually transformed. For the following detailed discussions and a better understanding, the more suitable version of the equations will be used. Both equations indicate that the transfer function characteristic is frequency dependent. Depending on the angular frequency ω=2πf, the following conclusions can be made: � → ∞ ���� = �� = ���� + ��

(5)

� → 0 ���� = �� = ���� + ��

(6)

For high frequencies(� → ∞), the capacitive divider is the dominant part of the transfer function and is comparable with a pure capacitive divider. This condition represents the first of both worst-case scenarios. From the theoretical point of view, an RC-divider is able to measure voltage signals up to an unlimited frequency. Later discussions will show that there are physical limits. For very low frequencies down to DC (� → 0), the resistive divider dominates the transfer function. This condition is equivalent to a purely resistive divider and will be defined as the second of both worst-case scenarios. Such RC-dividers can also be used for DC voltage measurements.[1,4,5]

Depending on the selection of the resistance values R1 and R2 (R-divider) and the capacitance values C1 and C2 (C-divider) and also under consideration of the frequency and amplitude of the voltage, one of both divider ratios is more dominant. At the crossing point of the resistance current curve and the capacitive current curve, the influence of both dividers on the ratio is equal. Considering this, the exact crossing point frequency fCP can be calculated by following formula: ��� = 12� ∙ �� ∙ ��

(7)

At f = fCP the inaccuracy is at its highest value compared to both extreme points at f→0 and f→∞ within any particular RC-divider ratio. Example: The divider ratios kR and kC have a variation in accuracy of ±0.5%. The calculated frequency-dependent results shown in figure 3 are based on formulas 3 or 4 and a combination of all possible ratio variations. The crossing-point frequency fCP is at 0.3Hz with a capacitance value of C1=2338.56pF and resistance value of R1 = 230.88MΩ. Figure 3 illustrates that both a constant and a dynamic state exist. The range between DC and 40mHz

can be defined as a constant state. The dependency of the total divider ratio on frequency variation is very low. The other constant range starts from 2Hz up to the highest frequency. The second state represents the dynamic behaviour. The change of the total accuracy within the tolerances of kR and kC is at its highest at the crossing point fCP in the case of frequency variations from 40mHz up to 2Hz. Very small frequency steps have a very high influence on the total divider ratio.

Figure 3: Function of total ratio error depending on the combination of different ratio tolerances of kR and kC.

4

As a result, the crossing point should not be placed close to the system frequency. As a second conclusion, both divider ratios should be adjusted to be as identical as possible.

Another very important condition can be derived from equation 3 or 4. The compensation condition demands that the resistive divider ratio kR has to correspond to the capacitive divider ratio kC. The time constant τ is defined as an RC term. For a frequency-independent divider ratio of V1/V2, up to very high frequency values, the time constant τ1 of the primary part has to be identical to the time constant τ2 of the secondary part. � = � → �� ∙ �� = �� ∙ �� (8)

Three main system states can be distinguished.

1 τ1 > τ2 , undercompensated 2 τ1 = τ2 , compensated 3 τ1 < τ2 , overcompensated

In the case of system state 2, the secondary voltage follows the primary voltage with a constant frequency-independent time delay. The rise-time Ta depends on the following formula.[5] !� = 2.2 ∙ � = 2.2 ∙ � (9)

The main divider ratio V1/V2 itself is constant at all times during this state.

The components of the primary part used, as well as those of the secondary part of an RC-divider are subjected to different physical impacts. The capacitance and resistance are affected mainly by temperature or amplitude of voltage variations. The temperature dependency for a capacitor and a resistor can be calculated by following formulas: �(!) = �#$1 + %�(! − ')( (10) �(!) = �#$1 + %�(! − ')( (11)

The material-dependent temperature coefficients are defined as αC and αR. The unit used is ppm/K. The parameter T represents the current temperature and δ defines the reference temperature. Using formula 10 in formula 5, the ratio kC(T) is shown in equation 12 for the extreme point f→∞. The same discussions concerning formulas 11 and 6 show the result for the ratio kR(T) in equation 13 for the extreme point f→0. ���� = ��(!) = 1

1 + ��#$1 + %��(! − ))(��#$1 + %��(! − ))(

(12)

���� = ��(!) = 11 + ��#$1 + %��(! − ))(��#$1 + %��(! − ))(

(13)

The single components themselves can vary depending on their own temperature coefficients. When the temperature coefficients of the capacitor material αC1 and αC2 as well as the temperature coefficients of the resistor material αR1 and αR2 are identical and under the same ambient conditions, the divider ratio will not be affected by changes in temperature. For voltage variation dependencies, the same theoretical discussions and conclusions can be made. Voltage coefficients are defined in ppm/V.[6]

3. Measuring tasks In the high voltage network, the nominal system voltage is defined as a sinusoidal voltage signal with a rated frequency of fR. In addition to this fundamental voltage, signals with a bandwidth close to DC and up to high frequency could also be contained in the system voltage. As a second important phenomenon, transient voltage signals occur as a result of impacts like natural lightning strikes, switching operations or system fault conditions. Are RC-dividers designed for metering, measuring and protection functions or for diagnostics and monitoring purposes up to higher frequency ranges, the complex transfer function k(ω) has to be discussed for the non-ideal case. This is the case when the time constant τ1 of the primary part is not identical to the time constant τ2 of the secondary part. Typically, it is not possible to adjust the primary components as well as the secondary components in an ideal way. � ≠ � → �� ∙ �� ≠ �� ∙ �� (14)

5

With respect to the information in formula 14, a frequency-dependent divider ratio of V1/V2 can be found. Formulas 3 and 4 have to be used for the final calculation of the voltage error ɛU and the phase displacement ∆φ.

+�,-.�� + = 1 + ���� /1 + 1 (�����)�⁄1 + 1 (�����)�⁄ (15) or +�,-.�� + = 1 + ���� /1 + (�����)�1 + (�����)� (16)

The formula for the calculation of voltage error ɛU is defined in IEC61869-3, sub-clause 3.4.3 as:

01 = 2�,-.�� 2 ∙ �� − ���� ∙ 100$%( (17)

The definition of the phase displacement ∆φ can be found in IEC61869-1, sub-clause 3.4.4. It is defined that, in the case of positive phase displacement, the secondary voltage leads the primary voltage. The phase displacement calculation is defined as: ∆5 = −arctan(1 (�����)⁄ ) + arctan(1 (�����)⁄ ) (18) or ∆5 = arctan(�����) − arctan(�����) (19)

The introduction of equation 15 or 16 in equation 17 and in equations 18 and 19, shows a frequency-dependent behaviour of both the voltage error as well as the phase displacement. On the other hand, with these equations, it is possible to perform pre-calculations for an active modification to the characteristics.

With respect to the discussions above, a measurement of the frequency-response behaviour of a RC-divider for a system voltage level of 420kV was performed. Firstly, the test setup will be described. After this, the measuring results will be presented.

A single-phase power amplifier provides a test signal up to a voltage level of 280V (RMS) in a frequency range from 15Hz up to 10kHz. The sinusoidal signal was generated by an external generator and fed to the power amplifier. Data acquisition was realized using ADC-boards with a sampling rate of 2MS/s. The measurement system used, including all components and necessary sampling rates, were discussed in detail in a former paper [3]. The test starts at a predefined frequency of 15Hz with incremental steps up to the maximum frequency of 10kHz. Initially, the step width was changed in an adaptive manner in order to determine possible resonance frequencies. Later, with respect to the initial results and analyses of data, more suitable frequency steps were used. The test conditions were: [1] 1. A 420kV RC-divider in an upright position 2. The test voltage applied to the primary terminal was realized using a coaxial cable 3. A rated burden was connected to the secondary terminals 4. The test voltage measured directly at the primary terminal 5. Coaxial conductors were used for all measurement cables 6. Earthing was realized as a star-point connection to prevent inductive loops.

For each frequency, the primary voltage V1 divided by the nominal ratio r and the secondary voltage V2 were measured simultaneously.[3] Based on international standards on the display of accuracy for instrument transformers (see formula 17), the frequency-dependent voltage error and phase displacement are shown in figure 4.

6

Figure 4: Frequency response of voltage accuracy ɛU(f)(blue) and phase displacement ∆φ(f)(green)[1]

The voltage error characteristic ɛU (blue curve) shows that the RC-divider has no resonance frequency in the measured frequency range. The accuracy obtained is within ±0.2% over the whole range. The phase displacement over the frequency range is displayed in green. The phase displacement error is low enough for the identification of the direction of the spurious signal sources. Several series of measurements confirmed the findings stated.

Another important aspect is the linearity of the divider ratio depending on voltage variation. As described above, the primary voltage can vary due to different system conditions and failures. For example, a low primary voltage can occur in the case of voltage dips and swells or interruptions. Overvoltage phenomena may occur in cases of failure within the network, switching operations or lightning impulses. Therefore, the relevant standard for instrument transformer defines accuracy classes for measuring und protection functions. For accuracy classes concerning measurement purposes, the IEC61869-3 standard defines compliance with regulation of voltage variation between 80% and 120% of rated voltage VR. The accuracy classes defined are 0.1, 0.2, 0.5, 1.0 and 3.0 and include definitions for voltage error and phase displacement. For protection purposes the accuracy class has to be fulfilled for a voltage variation of 5% and for the rated voltage factor (1.5 or 1.9) of the nominal voltage. The two classes are defined as 3P and 6P with voltage error limits as well as phase displacement limits. The behaviour of an RC-divider with respect to its linearity is illustrated in figures 5 and 6. The measurement was performed according to international measuring rules for instrument transformers. The test objects were two different RC-dividers for a system voltage level of 145kV. The measurement performed also included the transmission cable and the rated burden connected to the secondary terminals. Figure 5 shows the voltage error against voltage variation. The accuracy class limits are indicated as dashed red lines, according to IEC accuracy class 0.2 and IEC protection class 3P. Figure 6 shows the behaviour of the corresponding phase displacement. The limits are also marked as dashed red lines.

Figure 5: Linearity measurement of voltage error, basic type ROF145; design type 1: light blue, design type 2: dark blue; Limits of classes: dashed red lines.

Figure 6: Linearity measurement of phase displacement, basic type ROF145; design type 1: light green, design type 2: dark green; Limits of classes: dashed red lines.

7

Both types of RC-dividers show very good performance with respect to the linearity of the voltage error as well as the linearity of the phase displacement. The difference between both types can be found in the capacitive part. Different capacitor winding designs and impregnation oils were used to investigate optimal performance. The design type 1 has a slightly better linearity response compared to design type 2.

Another important aspect is the transient voltage measurement for monitoring purposes. The measurement of impulse voltage signals in test laboratories has been realized using voltage dividers for many decades. One of the best types of divider is the CR-divider, also well known as Zaengl-divider, where the capacitor elements and the resistors are connected in series. This kind of connection is important to prevent voltage oscillations. Also, the secondary device is optimized for fast or very fast transient voltage signals. On the base of the discussions in chapter 2, the theoretical bandwidth of an RC-divider seems to be close to infinity. In reality, each component, especially the primary capacitive part, has a self-inductance. This parasitic circuit element will limit the frequency response of the RC-divider. For in-depth discussions regarding dependencies and modifications, see chapter 4. In cases of acceptable transmission quality of transient signals in terms of voltage peak and wave shape, RC-dividers could be used as a monitoring device in common high voltage networks. Transient voltage impulses up to 1.5 MHz would cover typical lightning impulses according to IEC with a rise-time of 1.2μs. For the determination of the behaviour of an RC-divider, lightning impulse tests were performed and measured directly at the secondary terminal output. Lightning impulse test were made according to IEC61869-1, IEC60060-1 and -2 procedures. Figure 7 provides an overview of the test setup and the measuring instruments used.

Figure 7: Impulse voltage test setup with test object “RC-Divider”

Test equipment

Test object: type RGK420 2. Charging unit 3. Impulse voltage generator 4. Impulse voltage divider, type CR 5. Peak-Voltmeter 6. Divider 100/1 (probe) 7. Pearson I-U-Transformer 8. Digital oscilloscope

Figure 8 illustrates the difference between an optimized impulse voltage divider, blue curve, and an RC-divider, red curve, which is optimized for a frequency bandwidth of DC up to 20kHz. During the first 5μs (rise time and time to peak), the red curve shows some oscillations. After 5μs, the red curve follows the blue curve of the reference measuring system to a sufficient accuracy.

The measured peak voltage of the RC-divider is 603kVpeak compared to 637kVpeak. The measurement error is -5.4%, which is a very good result.

8

Figure 8: Lightning impulse test, blue curve: impulse reference divider, red curve: RC-divider 420kV

Figure 9: Oscillation in the rising curve, blue curve: impulse reference divider, red curve: RC-divider 420kV

An enlarged view of the oscillation in the rising voltage curve is shown in figure 9. The frequency of this oscillation is about 2.1MHz and seems to be a reflection phenomenon. First reason: this RC-divider measuring system, including the design of the secondary equipment and the connection to the oscilloscope, was not specially optimized for impulse voltage measurement. The second important point is non-series damping. When a series damping resistor is used, the behaviour can be improved.

4. Design influence parameters Based on the discussions in the previous chapters, the performance of the measuring system is limited by its self-resonance frequency. In the range around the self-resonance frequency, the voltage error, as well as the phase displacement, shows a very high inaccuracy. It is not possible to use such measurements for analysis purposes. First of all, it is recommended that the self-resonance frequency of the RC-divider is measured. In a second step, more detailed examination will show which parameters can be modified in order to change the resonance behaviour. A reference on how to measure the self-resonance frequency is given in the IEC60358 standards family. A very important aspect is the parasitic inductance which comes from the test circuit. As it provides a very accurate measuring result, a coaxial design of the test setup is highly recommended. Figure 10 shows a self-resonance frequency measurement for an RC-divider at a system voltage of 145kV. The test setup shows an optimized low inductance design, realized using aluminium foil in a coaxial installation. The electrical connection was as short as possible with very low impedance. The signal source and analysing system used are combined in an HP 4192A LF Impedance Analyzer.

Figure 10: Test setup for self-resonance frequency measurement of an RC-divider type ROF145

Figure 11: Main impedance curve for a 145kV RC-divider

9

Figure 11 shows the behaviour of the main impedance with respect to the applied frequency. At resonance frequency, the capacitive part XC is compensated by the inductive part XL. Only the resistance component is still measurable. According to formula 21 and under consideration of the result obtained for the natural frequency fR=2.07MHz as well as the main capacitance C1=4400pF, the calculated parasitic inductance within the primary part of the RC-divider is LPara=1.34µH.[1] ;��<� = 1(2���)� ∙ �� (21)

The parasitic inductance of the RC-divider in this example corresponds to a statement made in the IEC60358 standard. As a rule of thumb for column-type capacitors, the self-inductance of a capacitor with a particular active part height is defined as L’Para ≈ 1μH/m. If we adapt this value to the above-mentioned test object with a capacitor active part height of llenght-C = 1.29m, the calculated parasitic inductance is LPara = L’Para · llenght-C = 1.29μH. The theoretical result is very close to the measured value. Several measurements with different types of RC-dividers confirm this characteristic.

Figure 12: Various influences on resonance frequency fR

In compliance with the theoretical discussions above, it is possible to modify the self-resonance frequency of the divider by considering the following aspects:

1. Depending on the system voltage, the international standard defines various test voltages for the measuring equipment. With respect to specified dielectric performance, the resulting arcing distance and creepage distance demand a minimum unit height.

2. The arcing distance is defined as the distance between both end-flanges of the insulator. For a linear voltage distribution over the insulator length, the primary active part has approximately the same length as the arcing distance.

3. For column type capacitors, the self-inductance is approx. L’Para ≈1μH/m and depends on point 2.

4. A stray capacitance CE exists between the upright position of the RC-divider to another potential (ground or other phase).

5. The primary capacitance value for C1 has to be at least 3 to 10 times higher than for CE. The capacitance value of C1 is also affected by the requirements of the burden connected.[5]

With figure 12 in mind, the most variable parameter is the primary capacitance C1. Points 2, 3 and 4 depend mainly on the voltage requirements, as discussed under point 1.

5. Comparison with conventional instrument transformers

World-wide, almost 99% of voltage measurements in HV and EHV networks are realized using conventional instrument transformers. For voltage measurement in EHV networks, two different measuring systems are in operation. One variant is the conventional inductive voltage transformer (VT), the other one is the capacitive voltage transformer (CVT). In the case of power quality parameter measurement functions, it is firstly recommended that the behaviour of the conventional instrument transformer is known. A technical report from the IEC TC38 committee was published in 2012. This report IEC/TR 61869-103 gives advice on the usage of all known measuring technologies. It includes very important information concerning the influence of the system voltage level on the frequency response behaviour of conventional measuring transformers. [9]

10

Figure 13: Frequency response of ɛU(f) for 36kV-VT(light green), 72.5kV-VT(dark green), 123kV-VT(blue), 245kV-VT(purple),420kV-CTVT(red) and 420kV-RC-divider (yellow), as measured at PFIFFNER

Figure 14: Frequency response of ∆ϕ(f) for 36kV-VT(light green), 72.5kV-VT(dark green), 123kV-VT(blue), 245kV-VT(purple),420kV-CTVT(red) and 420kV-RC-divider (yellow); as measured at PFIFFNER

All conventional instrument transformers have resonance frequencies with very high accuracy errors in the frequency range up to 5kHz, see figure 13 and 14. In comparison, the 420kV RC-divider shows a linear frequency response (see yellow curve). The accuracy results were measured with the same test system and test method, under the same test conditions as described above. No burden was connected to these conventional instrument transformers. By increasing the system voltage level, the first resonance peak moves to a lower frequency. For several test objects, figure 13 shows the first resonance peak depending on the system voltage Vm. It confirms the behaviour of results published in the IEC/TR 61869-103 report.[9] The accuracy of capacitive voltage transformers (CVT) is affected by frequency variations. A compensation coil, connected between the capacitive divider and the intermediate voltage transformer, is in resonance with the C-divider at system frequency. Frequency variations have a very large influence on the ratio error as well as on the phase displacement. A common CVT cannot be used for power quality measurements.

6. CONCLUSIONS This paper is a contribution on the possibilities of measuring power quality parameters in electrical high-voltage networks using a non-conventional instrument transformer with a very high accuracy starting from DC up to several kHz. The theoretical aspects are described as well as the technical solutions which explain the behaviour of this kind of technology. In the case of hybrid networks, with a combination of AC and DC power transmission in the same corridor, an expected DC offset on the AC part can be measured to a high accuracy. The linearity of accuracy, independent of primary voltage amplitude as well as of the performance of impulse voltage measurement, confirms very high performance. Transient impulses can be measured to a sufficient accuracy for the peak voltage level. The possibility of controlling the resonance frequency within given limits allows optimized behaviour depending on the functions expected. As a summary of the discussions above, the wide frequency range, as shown in figure 1, can be measured to a high degree of accuracy using this technology.

In comparison with conventional inductive instrument transformers with their resonances, this technical solution has a much better performance when measuring harmonics to a high level of accuracy up to high frequencies for all voltage networks.

Up to now, accuracy classes for instrument transformers with their ratio error and phase displacement limits are only related to the rated system frequency (see IEC61869-1). For the definition of new accuracy classes for frequencies other than the rated frequency, applications have a large influence. The demands placed by metering, measurement or protection applications vary. Also, the consequences on the network, as well as for the operator, vary depending on requirements. It is therefore necessary to define useful classes which cover the various functions. Because of the complexity of this subject, several technical committees of IEC need to work together.

11

BIBLIOGRAPHY [1] E.Sperling, P.Schegner, 2013 “A possibility to measure power quality with RC-divider”, CIRED

conference Stockholm (Sweden), Paper 0195 [2] Wikipedia: Definition of “Transfer function” [3] J.Meier, R.Stiegler, M.Klatt, M.Elst, E.Sperling, 2011, "Accuracy of harmonic voltage

transformers in the frequency range up to 5kHz using conventional insulation transformers", 21st. Int. Conference on Electricity Distribution, CIRED, Frankfurt (Germany), Paper 0917

[4] Küchler, Andreas: High-voltage technology, 3.Rev. 2009; Springer-Verlag [5] Schwab, Adolf J.: High-voltage measurement technic, 2. Rev. 1981; Springer-Verlag [6] E.Sperling, 2013 „Resistive capacitive voltage divider – non-conventional instrument

transformer for AC and DC voltages“, OMICRON Diagnosewoche 22. – 26. April 2013, Dornbirn (Österreich)

[7] M.Klatt, J.Meyer, M.Elst, P.Schegner, 2010, “Frequency Responses of MV voltage transformers in the range of 50 Hz to 10 kHz”, International Conference on Harmonics and Quality of Power (ICHQP), IEEE, Bergamo (Italy)

[8] E. Sperling, Dr. R. Vogelsang “New and extended requirements on instrument transformer” (Bulletin number 12/2013, December 2013, pages 40-44)

[9] IEC/TR 61869-103, 2012-05, “Instrument transformer –The use of instrument transformer for power quality measurement”