Measurement of Dielectric Properties

Abstract

The ageing of the insulation of HV apparatus is not only caused by the high electric field strength but also by thermal and mechanical stresses that evolve during normal operation condition. This may lead to chemical processes associated with a gradual deterioration of the integral insulation properties. Finally, weak spots and, in extreme case, an ultimate breakdown might occur, which causes not only an unexpected outage of HV equipment but also physical, environmental and financial damages. To ensure a reliable operation of HV assets encourages high standards of quality assurance tests after manufacturing as well as advanced tools for preventive diagnostics in service. As treated already in Chap. 4, PD measurements have become an indispensable tool to trace local dielectric imperfections since the 1960s, while the measurement of integral dielectric properties, such as capacitance and loss factor measurements, became of interest for insulation condition assessment of HV equipment already since the beginning of the last century when the first HV transmission systems above 100 kV were erected. In this context, it should be noted that the dielectric properties are often determined at test frequencies different from the service frequency (50/60 Hz). So valuable information on the insulation condition may also be gathered by measuring the dielectric response under DC voltage after this is switched on and even off, as will also be treated in the following.

5.1 Dielectric Response Measurements

Considering a capacitance, where the solid dielectric is arranged between plane parallel electrodes, which are suddenly subjected to a DC voltage ramp, the capacitance will rapidly be charged. Immediately thereafter, however, a comparatively low current is measurable, which is not only caused by the volume resistivity of the dielectric material but also by polarization phenomena. This is due to the Coulomb force (Coulomb 1785), which causes a displacement of the always present positive and negative charges neutralizing each other under zero field condition. That means a dipole moment is established after a certain time period. Vice versa, a depolarization occurs just after the DC voltage is switched off and the electrodes of the test sample are short-circuited. As the return of the charge carriers to its origin position occurs again after a certain time lag, a so-called return voltage (sometimes also referred to as “recovery voltage”) would be measurable across the electrodes of the test sample, i.e. after a certain relaxation time, provided the electrodes of the capacitance under investigation are not short circuited. This phenomenon has originally been discovered by Maxwell in 1888 and explained more in detail by Wagner in 1914 based on the equivalent circuit shown in Fig. 5.1. This network is composed of the basic capacitor C₀ and the parallel resistor R₀ representing the DC resistance of the capacitance. Additionally, various R–C elements representing various relaxation time constants τ₁ = R₁ C₁, τ₂ = R₂ C₂, … τ_n = R_n C_n have been introduced to characterize transition frequencies, which are associated with typical polarization phenomena, such as the trapping of charge carriers as well as interfacial and orientation polarization and even ion and electron polarization.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig1_HTML.gif — Fig. 5.1
Equivalent circuit of solid dielectrics

Nowadays, the return voltage measurement (RVM) is one of the most established diagnostic tools to assess the global insulation condition of HV equipment and their components (Boening 1938; Nemeth 1966, 1972; Reynolds 1985; Csepes et al. 1994; Lemke and Schmiegel 1995; Gubanski et al. 2002). The basic circuit used for the RVM method as well as typical voltage signals are illustrated in Fig. 5.2. Here the test sample is first excited by a constant DC voltage of magnitude V_e. For this purpose the switch S₁ is suddenly closed, while the switch S₂ remains still open. As a result of the continuous DC stress, the basic capacitance C₀ (Fig. 5.1) is rapidly charged. Different to this a certain time lag for charging the other capacitances C₁, C₂, C₃, … C_n can be encountered This is due to the previously mentioned relaxation time constants τ₁, τ₂, … τ_n. After a certain DC stressing time t₁, which lasts often several tens of minutes or even more, the switch S₁ is opened (Fig. 5.2). Immediately thereafter the test sample is short-circuited, closing the switch S₂ at instant t₁ for several minutes or even longer. Under this condition, the basic capacitance C₀ is completely discharged, while the capacitances C₁, C₂, C₃, … C_n are only partially discharged due to the characteristic relaxation time constants τ₁, τ₂, τ₃, … τ_n.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig2_HTML.gif — Fig. 5.2
Principle of return voltage measurement (*RVM*). a Basic circuit. b Characteristic signals

At instant t₂, when the switch S₂ is opened again, the residual charges stored in the capacitances C₂, C₃, … C_n cause a re-charging of the basic capacitance C₀. Thus, a so-called return voltage v_r(t) is measurable across the electrodes of the test object. However, C₀ is also discharged due to the parallel connected resistor R₀ representing the volume resistance of the dielectric material under investigation. Consequently, after an initial voltage rise, which is characterized by the initial slope dv_r(t)/dt and the maximum value V_r appearing at instant t₃, the return voltage decays again and approaches thus finally zero, see Fig. 5.2b.

Additional information on the insulation condition is gained by the establishment of so-called polarization spectra. For this purpose a series of recovery voltage measurements at constant DC test voltage is applied, while the DC stress period t₁ as well as the short-circuit duration (t₂–t₁) are stepwise increased. With respect to reproducible measurements the ratio (t₂–t₁)/t₁ is commonly kept constant and often chosen as 50%. Under this condition the initial slope dv_r(t)/dt at instant t₂ and the peak value V_r of the return voltage versus the charging time t₁ is plotted for each test sequence. A practical measuring example is shown in Fig. 5.3, which was gained for oil-impregnated paper insulation with the moisture content as parameter. Generally, it can be stated that each maximum of the return voltage belongs to a dominant relaxation time constant, which is unambiguous correlated to a typical ageing phenomenon. This offers the opportunity to assess the condition of technical insulation, such as the moisture content and the depolymerization of oil-impregnated paper used for power transformers and power cables.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig3_HTML.gif — Fig. 5.3
Depolarization spectra measured for oil-impregnated paper at moisture content of 1, 2 and 5%

Another approach is the analysis of the polarization and depolarization current using the basic circuit sketched in Fig. 5.4a. In compliance with the above presented return voltage measurement the test sample is first subjected to a DC voltage step V_c where the switch S₁ remains closed up to the instant t₂. Under this condition, the main capacitance C₀ is completely charged, usually within less than one second.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig4_HTML.gif — Fig. 5.4
Principle of polarization and depolarization measurement. a Basic circuit. b Characteristic signals

To avoid an overload on account of the high magnitude of the charging current and thus a possible damage of the sensitive ammeter in the ground connection lead of the test sample, this instrument is initially short-circuited by the switch S₂, which is opened shortly delayed at instant t₁ in order to measure the time-dependent polarization current i_p (t) charging the partial capacitances C₁, C₂, C₃, … C_n at various time constants, see Fig. 5.1. This current decays more or less exponentially down to a steady-state value I_DC, which is being governed by the DC resistance R₀.

The next step starts at instant t₂ when the switch S₂ is again short-circuited and the switch S₁ is opened to disconnected the test sample from the DC source. Just thereafter the switch S₃ is closed so that the main capacitance C₀ will be discharged almost completely. Few seconds thereafter, i.e. at instant t₃, the switch S₂ is opened, whereas S₃ remains closed. Under this condition, the time-dependent depolarization current i_d(t) is measured. Even if the polarity of this current is opposite to that of the polarization current, the time function fits more or less the exponential function of the polarization current. The only difference is that a resistive current component occurring during the first phase is not detectable due to the short-circuited terminals of the test object.

In this context it should be noted that also other tools than the above are utilized to assess the insulation condition, such as the measurement of isothermal relaxation currents (Simmons et al. 1973; Beigert et al. 1991). In principle, the circuits adopted for this purpose provide more or less modifications of those presented above. As an example, the measurement of the so-called recovery charge shall briefly be presented in the following, which is based on an electronic integration of the depolarization current (Lemke and Schmiegel 1995). A schematic of the circuit developed for this procedure as well as typical voltage signals are depicted in Fig. 5.5.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig5_HTML.gif — Fig. 5.5
Basic circuit developed for recovery charge measurements (a) and characteristic voltage signals (b)

As usual for both return voltage and polarization/depolarization measurements, the test object capacitance is first exposed to a DC voltage step V_e, usually in the order of few kV. Based on practical experience, the duration of the pre-stressing time is preferably chosen between 2 and 10 min. During this time span the switch S₁ is closed, while all other switches remain still open. The second step starts at instant t₁ when the switch S₁ is opened and just thereafter the switch S₂ is closed. Provided, the condition C_m >> C₀ is satisfied, the charge amount stored originally in the main capacitance C₀ of the test object will be transferred almost completely to the measuring capacitor C_m. Thus, the test object capacitance C₀ can simply be deduced from the ratio between the voltage V_m occurring across C_m within the time interval t₁–t₂ and the exciting voltage V_e occurring across C₀ during the time interval t₀–t₁:

$C_{0} \approx C_{m} \cdot \frac{{V_{m} }}{{V_{e} }}.$

(5.1)

The next step starts at instant t₂ when the switch S₂ is opened in order to disconnect the measuring capacitor C_m from the test object. Few seconds thereafter the switch S₃ is closed in order to transfer the residual charge, which was previously stored in the test object capacitance, to the integrating capacitor C_r. Fundamental studies revealed that both time intervals t₁–t₀ and t₂–t₁ should preferably be chosen close to 10 s. For a known capacitance C_r, which provides the decisive part of the active integrator, the recovery charge q_r(t) stored in C_r can simply be deduced from the output voltage v_r(t) using the following relation:

$q_{r} \left( t \right) = C_{r} \cdot v_{r} \left( t \right).$

(5.2)

The measurement is commonly finished at instant t₃, when steady-state conditions appear, i.e. the output voltage v_r(t) of the electronic integrator remains nearly constant, which appears usually after approx. 10 min. An appropriate quantity used for assessing the insulation condition is the polarization factor F_p, which provides the ratio between the magnitudes the measured maximum recovery charge Q_r and the total charge Q_m stored during the DC stress period in the main capacitance C₀. Combining the Eqs. (5.1) and (5.2), the polarization factor can be expressed as follows:

$F_{P} = \frac{{Q_{r} }}{{Q_{m} }} = \frac{{C_{r} }}{{C_{m} }} \cdot \frac{{V_{r} }}{{V_{m} }}.$

(5.3)

The ratio $C_{r} /C_{m}$ provides in principle a scale factor of the measuring system so that the polarization factor F_P is proportional to the ratio between the voltage magnitudes V_r and V_m measurable across C_r and C_m, respectively. Based on practical experiences gained for XLPE-insulated power cables, the insulation condition can be assessed as “good” as long as the condition F_p < 10⁻⁴ is satisfied.

Example Figure 5.6 shows typical voltage signals recorded for a service aged 20 kV XLPE cable. To get appropriate readings, the following settings of the polarization factor measuring instruments have been chosen:
Fig. 5.6
Record of a recovery charge measurement performed on an aged MV XLPE power cable

Divider ratio
R₂/R₁ = 1:400
Measuring capacitance
C_m = 100 μF
Integrating capacitance
C_r = 1 μF
Using the Eqs. (5.1) and (5.3), the following values can be drawn from the record shown in Fig. 5.6:
Test voltage
V_e = (5 V)∙400 = 2000 V
Main capacitance
C₀ = (100 μF)∙(2.3 V)/2,000 V = 145 nF
Polarization factor
F_p = [(1 μF)/(100 μF)]∙[(0.64 V)/(2.3 V)] = 28 × 10⁻⁴
As this value exceeds substantially the above mentioned limit F_p < 10⁻⁴, a strong exposition to water trees was supposed, which could be confirmed based on microscopic investigations.

Divider ratio	R₂/R₁ = 1:400
Measuring capacitance	C_m = 100 μF
Integrating capacitance	C_r = 1 μF

Test voltage	V_e = (5 V)∙400 = 2000 V
Main capacitance	C₀ = (100 μF)∙(2.3 V)/2,000 V = 145 nF
Polarization factor	F_p = [(1 μF)/(100 μF)]∙[(0.64 V)/(2.3 V)] = 28 × 10⁻⁴

5.2 Loss Factor and Capacitance Measurement

As the insulation of HVAC apparatus is mainly stressed by power frequency voltages of 50/60 Hz, the knowledge of dielectric properties exposed to such low-frequency alternating voltages is primarily of interest. Under this condition the equivalent circuit according to Fig. 5.1 can substantially be simplified, as shown in Fig. 5.7. Here the capacitance C_s of the test object can either be assumed as connected in series with the hypothetical resistance R_s (Fig. 5.7a), or even the test object capacitance C_p is bridged by a parallel resistance R_p (Fig. 5.7b). Here R_s or R_p reflect in principle the thermal losses dissipating in the dielectric material.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig7_HTML.gif — Fig. 5.7
Equivalent circuits and associated vector diagrams commonly used for the definition of the loss factor tanδ. a Series circuit. b Parallel circuit

As the resistivity of technical insulations decreases at rising temperature, the current density may increase, particularly in regions where the convection of the dissipated power is limited. As a result, so-called hot spots may occur, which accelerate the insulation deterioration and lead finally to an ultimate insulation puncture. Thus, the measurement of dielectric losses became an indispensable tool for quality assurance tests of HV apparatus since the beginning of the last century, when high alternating voltage was increasingly employed for long-distance power transmission links.

Considering the equivalent circuit shown in Fig. 5.7a, the current I_S flowing through both the capacitance C_S and the in series connected resistance R_S causes a phase shifting δ_S between the applied test voltage V_S and the voltage vectors V_C and V_R, respectively. From a practical point of view it seems convenient to evaluate the tangent δ, commonly referred to as loss factor , which follows from the ratio between the both voltage vectors V_R and V_C:

$\tan \,\delta_{S} = /\frac{{V_{R} }}{{V_{C} }}/ = /\frac{{I_{S} \cdot R_{S} }}{{I_{S} /j\omega \cdot C_{S} }}/ = \omega \cdot C_{S} \cdot R_{S} .$

(5.4)

With respect to Fig. 5.7b, where C_P and R_P are connected in parallel, the following relation applies:

$\tan \,\delta_{P} = /\frac{{I_{R} }}{{I_{C} }}/ = /\frac{{V_{P} /j\omega \cdot C_{P} }}{{V_{P} \cdot R_{P} }}/ = \frac{1}{{\omega \cdot C_{P} \cdot R_{P} }} .$

(5.5)

Multiplying Eq. (5.4) on one hand with the current I_S flowing through C_S and R_S and, on the other hand, Eq. (5.5) with the test voltage V_P dropping across C_P and R_P, it can readily be shown that the loss factor becomes equal for both circuits shown in Fig. 5.7 and can simply be expressed by the ratio between active (resistive) and reactive (capacitive) power:

$\tan \,\delta_{P} = /\frac{{V_{R} \cdot I_{S} }}{{V_{c} \cdot I_{S} }}/ = /\frac{{V_{P} \cdot I_{R} }}{{V_{P} \cdot I_{C} }}/ = \frac{{P_{R} }}{{P_{C} }}$

(5.6)

As known from the classical network theory, each series circuit can be converted into a parallel circuit and vice versa. Considering the equivalent circuits shown in Figure 5.7a and b, the following relations apply (Küpfmüller 1990):

$C_{P} = C_{S} \cdot \frac{1}{{1 + \left( {\omega \cdot C_{S} \cdot R_{S} } \right)^{2} }} = C_{s} \cdot \frac{1}{{1 + \left( {\tan \,\delta_{S} } \right)^{2} }}.$

(5.7)

$R_{P} = R_{S} \cdot \left[ {1 + \frac{1}{{\left( {\omega \cdot C_{S} \cdot R_{S} } \right)^{2} }}} \right] = R_{S} \cdot \left[ {1 + \frac{1}{{\left( {\tan \,\delta_{S} } \right)^{2} }}} \right].$

(5.8)

$C_{S} = C_{P} \cdot \left[ {1 + \frac{1}{{\left( {\omega \cdot C_{P} \cdot R_{P} } \right)^{2} }}} \right] = C_{P} \cdot \left[ {1 + \left( {\tan \,\delta_{P} } \right)^{2} } \right].$

(5.9)

$R_{S} = R_{P} \cdot \frac{1}{{1 + \left( {\omega \cdot C_{P} \cdot R_{P} } \right)^{2} }} = \frac{{\left( {\tan \,\delta_{P} } \right)^{2} }}{{1 + \left( {\tan \,\delta_{P} } \right)^{2} }}.$

(5.10)

These relations enable the determination of the loss-factor based on the settings of the Schering bridge under balanced conditions, as will be treated in the following.

5.2.1 Schering Bridge

To measure the relative dielectric constant ε_r of insulating materials as well as the capacitance and loss factor under high voltage, the bridge circuit according to Fig. 5.8, which has been proposed by Schering in 1919, is commonly applied. This is in principle composed of two parallel connected voltage dividers, in the following referred to as measuring and a reference branch. As sketched in Fig 5.8, the HV arm of the measuring branch is formed by the test sample simulated by the series connection of C_S and R_S, see Fig. 5.7a, while the HV-arm of the reference branch is formed by the loss-free standard capacitor C_N.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig8_HTML.gif — Fig. 5.8
Circuit elements of a Schering bridge

As the voltage vectors V_S and V₃ appearing across the HV and LV arm of the measuring branch are proportional to their impedances, it can be written

$\frac{{V_{S} }}{{V_{3} }} = \frac{{\left( {1/j\omega \cdot C_{S} } \right) + R_{S} }}{{R_{3} }} = \frac{{1 + j\omega \cdot C_{S} \cdot R_{S} }}{{j\omega \cdot C_{S} \cdot R_{3} }}.$

(5.11)

Considering the reference branch, the ratio between the voltage vectors V_N and V₄ is given by

$\frac{{V_{N} }}{{V_{4} }} = \frac{1}{{j\omega \cdot C_{N} }} \cdot \frac{{R_{4} + \left( {1/j\omega \cdot C_{4} } \right)}}{{R_{4} /j\omega \cdot C_{4} }} = \frac{{1 + j\omega \cdot C_{4} \cdot R_{4} }}{{j\omega \cdot C_{N} \cdot R_{4} }}.$

(5.12)

To balance the bridge circuit, the tunable elements R₃ and C₄ are adjusted such that the reading of the indicating instrument Z_I shown Fig. 5.8 approaches zero. Obviously, this is accomplished when the voltage appearing across the LV arm of the measuring branch is equal in amplitude and phase to that appearing across the LV arm of the reference branch. Based on this the balance criterion can be expressed as follows:

$\frac{{V_{S} }}{{V_{3} }} = \frac{{V_{N} }}{{V_{4} }}.$

(5.13a)

$\frac{{1 + j\omega \cdot C_{S} \cdot R_{S} }}{{j\omega \cdot C_{S} \cdot R_{3} }} = \frac{{1 + j\omega \cdot C_{4} \cdot R_{4} }}{{j\omega \cdot C_{N} \cdot R_{4} }},$

(5.13b)

$\frac{1}{{j\omega \cdot C_{S} \cdot R_{3} }} + \frac{{R_{S} }}{{R_{3} }} = \frac{1}{{j\omega \cdot C_{N} \cdot R_{4} }} + \frac{{C_{4} }}{{C_{N} }}.$

(5.13c)

Comparing only those terms, which are divided by jω, one gets the following relation, which enables the determination of the equivalent series capacitance C_S from the settings of the Schering bridge under balanced conditions:

$C_{S} = \frac{{C_{N} \cdot R_{4} }}{{R_{3} }},$

(5.14)

Comparing the remaining terms, one gets the following hypothetical series resistance R_S, which can be deduced from the settings of R₃, R₄, and C₄ under balanced conditions:

$R_{S} = \frac{{R_{3} \cdot C_{4} }}{{C_{N} }},$

(5.15)

Combining these Eqs., the loss factor can be calculated for using the following relation:

$\tan \,\delta_{S} = \omega \cdot C_{S} \cdot R_{S} = \omega \cdot \frac{{C_{N} \cdot R_{4} }}{{R_{3} }} \cdot \frac{{R_{3} C_{4} }}{{C_{N} }} = \omega \cdot C_{4} \cdot R_{4} .$

(5.16)

Commercially available Schering bridges are often equipped with a fixed LV resistor R₄ used for grounding the test object. Provided the measurement of C_S and tan δ_S is performed under 50 Hz AC voltage, this resistor is adjusted exactly to R₄ = 318.5 Ohm. Inserting this in Eq. (5.12) one gets

$\tan \,\delta_{S} = \left( {314 s^{ - 1} } \right) \cdot \left( {318.5 V \cdot A^{ - 1} } \right) \cdot C_{4} = C_{4} /\left( {10\,{\upmu {\text{F}}}} \right).$

Obviously, this simplifies the determination of the loss factor considerably. Assuming, for instance, that the balanced condition was accomplished for C₄ = 0.027 μF, one gets

${ \tan }\,\delta_{S} = \left( {0.027\,,{\upmu {\text{F}}}} \right)/\left( {10\,,{\upmu {\text{F}}}} \right) = 0.0027 = 2.7 \cdot 10^{ - 3} .$

In this context it should be noted, that additional information on the insulation condition of HV equipment is obtained when besides the equivalent capacitance C_S according to Eq. (5.14) and the loss factor tan δ_S according to Eq. (5.16) also the time-dependent trend of these quantities under service condition is determined.

In this context it must be emphasized that the above treatment refers to an equivalent circuit where the elements C_S and R_S are connected in series, see Fig. 5.7a. As already mentioned previously, each series circuit can be converted into the parallel circuit. Thus, to determine the values of the parallel connected elements shown in Fig. 5.7b, the Eqs. (5.9) and (5.10) have to be combined with Eqs. (5.14) and (5.15). From this follows for the parallel capacitance:

$C_{P} = \frac{{C_{S} }}{{1 + \left( {\omega \cdot C_{S} \cdot R_{S} } \right)^{2} }} = C_{N} \cdot \frac{{R_{4} }}{{R_{3} }} \cdot \frac{1}{{1 + \left( {\omega \cdot C_{4} \cdot R_{4} } \right)^{2} }}$

(5.17a)

As for technical insulation the loss factor is usually considerably below 1, i.e. the condition tanδ_S = ω ⋅ C₄ ⋅ R₄ ≪ 1 applies, Eq. (5.17a) can be simplified as follows:

$C_{P} \approx C_{N} \cdot \frac{{R_{4} }}{{R_{3} }}$

(5.17b)

Based on Eq. (5.8) the parallel resistance R_P can be expressed as follows:

$R_{P} = R_{S} \frac{{1 + \left( {\omega \cdot C_{S} \cdot R_{S} } \right)^{2} }}{{\left( {\omega \cdot C_{S} \cdot R_{S} } \right)^{2} }} = R_{3} \cdot \frac{{C_{4} }}{{C_{N} }} \cdot \frac{{1 + \left( {\omega \cdot C_{4} \cdot R_{4} } \right)^{2} }}{{\left( {\omega \cdot C_{4} \cdot R_{4} } \right)^{2} }}$

(5.18a)

Provided, the condition tanδ_S = ω ⋅ C₄ ⋅ R₄ ≪ 1 is satisfied, one gets the following simplification:

$R_{P} \approx R_{3} \cdot \frac{{C_{4} }}{{C_{N} }} \cdot \frac{1}{{\left( {\omega \cdot C_{4} \cdot R_{4} } \right)^{2} }} = R_{3} \cdot \frac{{C_{4} }}{{C_{N} }} \cdot \frac{1}{{\left( {\tan \delta_{S} } \right)^{2} }}$

(5.18b)

Inserting the above expressions in Eq. (5.5), the loss factor can be expressed as follows:

$\tan \delta_{P} = \frac{1}{{\omega \cdot C_{P} \cdot R_{P} }} = \frac{{\left( {\omega \cdot C_{S} \cdot R_{S} } \right)^{2} }}{{\omega \cdot C_{S} \cdot R_{S} }} = \omega \cdot C_{S} \cdot R_{S} = \omega \cdot C_{4} \cdot R_{4} = \tan \,\delta_{S} .$

(5.19)

Obviously, this is equal to Eq. (5.16), as has to be expected.

For high-capacitive test objects, such as power cables, power transformers and rotating machines, it has to be taken into account that the capacitive current through the test object could heat up the measuring resistor R₃. To prevent a possible damage, this resistor must be shunted by a well-known parallel resistor, which has to be chosen considerably lower than R₃ in order to carry almost the entire load current flowing through the test object.

As the loss factor of technical insulation, such as polyethylene-insulated cables, is often below 10⁻⁴, the impedances of the low voltage elements of the Schering bridge might be affected by stray capacitances. Therefore, these LV parts should be screened accordingly. Connecting the screening electrodes to the ground potential, however, acts like a bypass and causes thus a non-controlled phase shifting of the AC voltage dropping across the LV arms. To overcome this crucial problem, the LV parts are commonly screened using an auxiliary branch with adjustable potential (Wagner 1912). This can advantageously be done by shifting the potential of the screening electrode automatically using an impedance converter of extremely high input impedance and low output impedance, see Fig. 5.9.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig9_HTML.gif — Fig. 5.9
Schering bridge with an auxiliary branch for automatic potential control of the screening electrodes

Another challenge is to measure the loss factor of grounded HV apparatus, such as power transformers, rotating machines and power cables. This method, commonly referred to as grounded specimen test (GST) , requires a disconnection of the HVAC test voltage supply from the earth potential (Poleck 1939). Under this condition, however, the test results may also strongly be affected by non-controlled stray capacitances between the HV test supply and the bridge circuit. To overcome this crucial problem, the Schering bridge has to be modified, as illustrated in Fig. 5.10. Just prior starting the actual loss factor measurement, a pre-balancing of the circuit is performed where the test specimen is disconnected from the HV terminal by opening the switch S_X and closing the switch S₄ in order to adjust the auxiliary elements R₅ and C₅ accordingly. After that S₄ is opened and S_X is closed to start the actual C-tanδ measurement under high voltage, where only the elements R₃ and C₄ are adjusted in order to balance the bridge circuit.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig10_HTML.gif — Fig. 5.10
Schering bridge modified for C-tanδ measurement of grounded specimen test (*GST*)

For GST measurements of three-phase arrangements, such as power transformers, various modifications of the bridge circuit have been proposed, such as GST-ground-guard, GST-ground-ground and GST-guard-guard. For more information on the basic configurations recommended for C-tanδ measurements of HV apparatus see the relevant standards IEC 60250: 1969 and IEC 60505: 2011.

5.2.2 Automatic C-tanδ Bridges

Classical Schering bridges are capable of measuring tanδ variations down to 10⁻⁵ as well as capacitances below 1 pF. The measuring uncertainty is in the order of 1% for the loss factor and approx. 0.1% for capacitances. However, the main drawback is the time-consuming balancing procedure so that fast changing dielectric properties cannot be measured. To overcome this obstacle, fully automatic computer-based C-tanδ measuring bridges have been introduced in the 1970s when the first micro-computers were available (Seitz and Osvath 1979).

The basic concept employed is schematically illustrated in Fig. 5.11. Here the current I_X flowing through the test specimen is compensated by the current I_N flowing through the standard capacitor C_N. For this purpose a high precision differential current transformer is utilized, which is controlled by a micro-computer. The primary coils with windings W₁ and W₂ provide the low-voltage arms of the bridge and induce inverse magnetic fluxes in the magnetic core.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig11_HTML.gif — Fig. 5.11
Concept of an automatic C-tanδ bridge circuit

The residual flux is detected by the secondary coil with W₃ windings. The output signal controls the further data signal processing by means of a micro-computer. So the flux through the magnetic core of the differential transformer can fully be compensated by adjusting the currents through the auxiliary coils with windings W₄ and W₅, respectively. When the bridge is balanced, the computer calculates the actual values of C_X and tanδ depending on the applied AC test voltage level.

Due to the progress in digital signal processing (DSP), nowadays advanced computer-based C-tanδ measuring systems are available (Kaul et al. 1993; Strehl and Engelmann 2003). A simplified block diagram of such a measuring system is shown in Fig. 5.12. Basically, the circuit comprises two capacitive voltage dividers. The measuring branch contains the test object symbolized by the series connection of C_X + R_X, which is grounded via the measuring capacitor C_M. The reference branch contains the loss-free HV standard capacitor C_N, which is grounded via the reference capacitor C_R.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig12_HTML.gif — Fig. 5.12
Concept of a computerized DSP-based C-tanδ measuring system

Different to the automatic C-tanδ bridge, where the current I_X through the test object is compensated by the reference current I_N, an exact balancing is not required. This is because the loss factor is independent from the actual voltage magnitudes dropping across the LV arms comprising the capacitances C_M and C_R, so that the dielectric properties can also be determined by a direct measurement of the voltage vectors captured from C_R and C_M, see Fig. 5.13. Thus, it seems sufficient to adjust the voltage across C_M only to a peak value which approaches nearly the peak value of the voltage dropping across C_R where a deviation of several tens of percentages is acceptable.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig13_HTML.gif — Fig. 5.13
Digitalization of the reference and measuring signal used by the *DSP*-*based C*-tanδ measuring system

The major components of a computerized DSP-based C-tanδ measuring system are shown in Fig. 5.14. The LV signals dropping across C_M and C_R are captured by the battery powered, potential-free operating sensors. Both sensors are equipped with a low noise differential amplifier of extremely high input impedance (>1 GΩ), a fast A/D converter (resolution 16 bit at 10 kHz sample rate), and an electro-optical interface. The digitized signals are transmitted via fiber optic links (FOL) to the computerized C-tanδ measuring system, which transmits also the control signals from the computer to both sensors. After a fast discrete Fourier transformation, which is performed by the use of a digital signal processor (DSP), the data are acquired, calculated, stored and displayed accordingly.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig14_HTML.gif — Fig. 5.14
Components of a DSP-based computerized C-tanδ measuring system
(Courtesy Doble-Lemke GmbH)

Real-time multitasking software enables a calculation of the dielectric quantities for each cycle of the applied HVAC test voltage. Using the averaging mode, a very high measuring accuracy is achieved. As the measuring principle is based on the determination of the phase angle of a non-balanced bridge in a frequency-independent but frequency-selective mode, the actual test frequency can be varied over a wide range, typically between 0.01 and 500 Hz.

All measured quantities can be displayed numerically in the real-time mode. Moreover, the data, such as the loss factor, the capacitance, the current through the test object, the test frequency and the test voltage level in terms of rms or even the peak value can be exported using an Excel-compatible data-format. Another benefit is that the dielectric quantities can be displayed on the PC screen depending on various parameters, such as the applied AC test voltage, as exemplarily shown in Fig. 5.15, and even versus the recording time, which is useful for trending purposes. Under power frequency (50/60 Hz) test voltages an “internal” measuring uncertainty below 10⁻⁵ for the loss factor is achievable. The “extended” measuring uncertainty, however, is mainly governed by the behaviour of the standard capacitor C_N (Schering and Vieweg 1928; Keller 1959).

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig15_HTML.gif — Fig. 5.15
Screenshot showing the loss factor versus the test voltage gained for an aged machine bar

It has to be taken care that the measuring uncertainty is not only governed by the computerized measuring system but also affected by the design of the test sample. To minimize the impact of stray capacitances as well as parasite surface currents, the use of so-called guard electrodes is highly recommended, as illustrated in Fig. 5.16.

../images/214133_2_En_5_Chapter/214133_2_En_5_Fig16_HTML.gif — Fig. 5.16
Electrode configuration of a test sample for C-tanδ measurement using a guard electrode

5. Measurement of Dielectric Properties

Abstract

5.1 Dielectric Response Measurements

5.2 Loss Factor and Capacitance Measurement

5.2.1 Schering Bridge

5.2.2 Automatic C-tanδ Bridges