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PROC. 29th INTERNATIONAL CONFERENCE ON MICROELECTRONICS (MIEL 2014), BELGRADE, SERBIA, 12-14 MAY, 2014

Equipment for the Automatic Testing of Power Capacitors

V. Papež, S. Papežová

Abstract: The paper describes a special method for testing power capacitors by means of their loading by alternating current with the effective value up to 100 A at frequencies in the order of units up to tens of kHz. There is described the realization of the test equipment enabling a precise compensation of the reactive power of the capacitor and the input minimisation at the testing. It discusses the realization of the key components and parts of the measuring equipment.

I. INTRODUCTION

The measurement and testing of capacitors is usually carried out namely by the low level signals also in case of power capacitors. Only the testing of breakdown voltage is carried out by the defined testing voltage with the frequency of 50 Hz or by a DC voltage.

The process of testing is based on the assumption that the tested capacitors are purely linear. The dependences detected during the low-level signal measurements were extrapolated to the field with high-level signals.

But it is impossible to use this technique in checking the maximal acceptable values of a capacitor load by e.g. an applied AC voltage, passing current, under the defined frequencies and temperatures. In this case, the testing is carried out especially designed test circuits which are designed so that the circuit parameters were approximated by the defined test parameters with minimal deviation [1].

The testing circuit has to be designed as power electrical equipment; i.e. with regard both to an electrical stress of all used elements and their cooling. It has to be supplied with a high power signal. The power is real only in an ideal case. In testing high-quality capacitors, the power supplied to the tested circuit is solely a reactive power that is approximately equal to the apparent capacitor power and it can be even by 3 orders higher than the real power.

The power supply of the testing circuits is loaded with an apparent power that is greater than hundreds of VA. Its power factor is low and hardly defined at frequencies different from the mains frequency. This power supply working at the frequencies different from the mains

frequency can be realized by a linear power amplifier. The amplifier is at reactive power demand strongly

overloaded. In the amplifier, which is loaded almost by purely reactive loading, practically all power, which the amplifier takes from a power supply unit, is lost in an amplifier output stage. In comparison with the operation with optimal real loading, the power input of the amplifier has to be reduced. Then, in a definite range of reactance, where maximal currents and voltages of active elements are not exceeded, a maximal reactive power which the amplifier can add is about 1/3 of a real power in an optimal real loading.

The operation of the amplifier with pure reactance loading is inadmissible then this reactance has to be completed with the resistance so that the resulting impedance may show an acceptable reflection factor at the output of the amplifier (e.g. .Γ ≤ 0,5, VSWR ≤ 3). If the amplifier is loaded with a low reactance, then the reactance has to be completed with the resistance greater than 1/3 of a nominal load impedance of the amplifier. All the power output of the amplifier is lost in the resistance, and therefore a reflected power in the loading is low, i.e. several per cent of the output power. The highest reactive power, approximately 20% of the nominal real power, can be achieved, if the loading reactance is equal to 4/3 of the nominal load impedance of the amplifier and if it is completed with an effective resistance of the value of 5/3 of the amplifier nominal load impedance.

II. TESTING EQUIPMENT FOR POWER CAPACITORS

It is possible to reach an ultra precise reactive-power compensation of the tested capacitor in the measuring circuit and the matching of the measuring circuit to the driving generator by completing the tested capacitor with the inductor so that the resonant circuit tuned on the measuring frequency can be created.[2] The driving power from the signal generator is then real. Supplied real power covering losses in the elements of the measuring circuit is then about 1 up to 2 orders less than the reactive power of the tested capacitor.

But a resonant inductor is also a key element of the measuring equipment. It must show minimal losses, or a maximal Q factor, because the power losses of the inductor represent a dominant part of total losses in the testing of capacitors of high quality in the measuring circuit. The inductor must also show a minimal dependence of all parameters on the changes of the surrounding environment

V. Papež is with the Department of Electrotechnology, CTU inPrague, Faculty of Electrical Engineering, Technicka 2, 166 27Prague 6, Czech Republic, E-mail: papez@feld.cvut.cz

S. Papezova is with the Department of Electrical Engineeringand Automation, Czech University of Life Sciences Prague,Faculty of Engineering, Kamycka 129, 16521 Prague 6, CzechRepublic, E-mail: papezovas@tf.czu.cz

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and on the time. For a long-term measuring, the testing equipment must automatically compensate these changes.

Considering a Q factor definition according to (1), the design of an optimal inductor usually seeks for a construc-tion of the inductor with a maximal inductance made up of a sample of a definite wire cross - section and length or a construction of the inductor with a requested inductivity made up of a wire with a minimal length and maximal cross - section.

s

s

RfL

Q2

, (1)

where Ls represents an equivalent series inductance of the coil, Rs represents an equivalent series resistance of the coil and f represents the frequency.

The inductance of the inductor with a given configuration and number of turns is usually expressed by various empirical formulas in the first approximation. Nagaokas formula (2) is the most widely known formulafor the inductor with a configuration of a single layer solenoid with an air core, whose usage is supposed in our case.

l

KNDL4

03948,0 22

, (2)

where L represents the inductance of the coil [μH], D represents a mean diameter of the coil [cm], l represents an overall length of the coil [cm], N represents the number of turns and K factor is an empirical factor dependent only on the ratio of D/l and its value is determined according to a graph, table or approximate relations. (3)

lD

K/4,01

1

. (3)

The dimensions of an optimal inductor can be searched for by establishing the formula (3) into (2) expressed as a maximum inductance relationship (4) [3], which can be realized out of the wire of a given length and diameter.

Dl

wDl

NDL4,0

104,0

10 23

2223

, (4)

where w represents an overall length of the wire [cm]. After the substitution of the length l of the coil needed

to wind a wire of the length w with the distance s between the centres of adjacent turns, the formula (4) changes into the form (5) which shows a maximal inductance on condition that l = 0,4D.

2

23

4,010

DwsDwL

. (5)

Further optimalization supposes respecting a frequency dependent increase of wire resistance at high frequencies in comparison with DC resistance which occurs at high frequencies due to the concentration of a current density on a surface of the wire.

This “skin effect” phenomenon- is usually described by a current penetration depth δ. But this relation was derived

for the boundary of a "conductive half - space" where only here it is valid without any exception.

f1

, (6)

where µ is permeability of the conductor and σ is conduc-tivity of the conductor.

Current density in each wire of the coil is influenced not only by a magnetic field of the current which passes through this wire but also by a magnetic field of the current which passes through all the wires of the coil, and therefore further increase of RF wire resistance caused by the field of the wires occurs in the neighbourhood. This effect is called a proximity effect and due to its influence, the windings of the wires with the biggest diameter practically touching in the layer, does not show a minimal RF resistance. On the contrary, a minimal RF resistance occurs at the winding with the same number of windings of smaller diameter, where there are spaces in the layer.

An optimum ratio of the gap width and diameter of the wire depends also on the dimensions of the inductor [4] and it can be approximated for the inductors of common dimensions (0,1≤l/D≤10) e.g. by the relation (7).

)/05,0(5,16

154,0lDs

d

, (7)

where d represents a diameter of each wire. To operate on frequencies from units to tens of kHz and

higher, the highest values of the Q factor are achieved by the winding made of even cylindrical wires or conductors of a tube-like shape with not very thin tube wall, whose thickness several fold exceeds a supposed current penetration depth, or it is possible to use a litz wire for a defined frequency, whose structure should also be optimized.

Only at low frequencies, where a current density is practically constant all over the wire cross section, the highest values of Q factor are achieved with the winding composed of homogeneous wires or cables of a large cross - section.

To determine an achievable value of Q factor, relation (1) can be used in case that the achieved equivalent series inductance of the coil and equivalent series resistance of this coil are substituted. Namely, the change in wire resistance caused by winding up the wire onto the coil creates problems.

In an RF band, when the current stops passing through the wire core and it is carried only along a thin surface layer, whose thickness is proportional to the current penetration depth the availability value of Q factor is approximated by simple relations.

For the coil winding with an optimal ratio d/s dependent on the length of the coil, the achievable value of Q factor is proportional to the product of a square root of the operating frequency and diameter of the coil that are multiplied by

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another correction factor dependent on the ratio of the diameter and length of the coil (8).

lD

DfQ/2

15,0

. (8)

After the substitution of the coil length l necessary for winding up the wire of the length w with the distance s between the centres of adjacent turns, formula (8) changes into the form (9) which shows a maximal Q factor on condition that l=D/2, which is the result differing a little from the result of the optimization according to the relation (5).

22

15,0Dws

DfwsQ

. (9)

A maximal Q factor of the inductor can be achieved in case of a maximal conductivity of the used wire, in our case for copper and a room temperature σ = 58.106 S/m. A conductivity drop, if the operating temperature of the inductor increases, leads to a Q factor drop by approximately about 16 % if the inductor warms up to 100 0C. Therefore, the inductor of the measuring equipment has to be realized with regard to a maximal suppression of its warming owing to the power dissipation. The winding of the inductor is made up of a bare wire, so that the wire insulation does not lower a heat-transfer coefficient on its surface. A coil frame is made of 1-2 spacers only, which do not limit a natural air flow through the winding. Thus it is possible to achieve the heat resistance of the cooling of 0,1 K/W at the inductor of large dimensions, where the surface area of the wire is approximately 1 m2, and to load the inductor by a power dissipation up to 200 W without a marked decrease of its Q factor (max. 5 %).

Typical frequency dependences of the measured Q factor for the realized inductors with the inductance of approximately 20 H for different constructions are displayed in Fig. 1.

Fig. 1. Frequency dependences of Q factor

Current and voltage frequency dependences in the

measuring circuit with a driving power of 100 W, a tested capacitor having a power loss factor of 10-3 and the above-mentioned inductors, are introduced in Fig. 2.

Fig. 2. Current and voltage frequency dependences with a

driving power of 100 W.

The equipment for a long-term testing of power capacitors is equipped with an automatic frequency control loop (AFC) which controls a measuring frequency. The phase of complex impedance of the measuring resonant circuit is monitored on a phase detector, and the measuring frequency is set up exactly on the value of the resonant frequency, where a complex impedance of the measuring resonant circuit is full-real.

The first sample of the measuring system has been realized with a simple switch as a high- level power amplifier. A block diagram of this equipment is illustrated in figure 3.

Fig. 3. Block diagram of a measuring equipment.

A power test signal from the switch with MOS - FET is led onto the resonant circuit through the LP filter, or at small output power, through a small protective power resistor that protects the switch from the overload by high pulse currents which could cause a capacity load. Power supply of the power switch circuit is provided by a controllable stabilized DC power supply PS, whose output voltage magnitude is also used for the amplitude control of an alternating current magnitude in the measuring circuit. A control signal for the power switch is generated by the counter CNT from the output signal by the voltage controlled oscillator VCO, together with a reference signal for the phase detector FD. The phase shift of both signals is ensured by a form of synchronization and it sets up the decoding of the counter exactly to 90o. The input signal of the phase detector is sampled by an electromagnetic coupling with a coupling coil loop from the circuit of a compensative inductor. The output signal of the phase

LPPSCNT

FD

VCO

AFCAMP

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detector is proportional to the deviation of the phase shift between the incoming signals from the value of 90o, and therefore it represents the phase deviation of the impedance of the measuring resonant circuit from the zero value. The output signal of the phase detector is led to an integrating AFC amplifier which generates a control signal, by which the frequency of a voltage controlled oscillator OSC is automatically tuned to a resonant frequency of the measuring circuit.

In case of higher demands on a spectral purity of the testing signal, a high-level amplifier PA can be realized as a linear amplifier. A block diagram of this equipment is illustrated in Fig.4.

Fig. 4. Block diagram of a measuring equipment with linear

power amplifier.

The testing signal is generated by a voltage controlled oscillator OSC, from which a high power amplifier PA is led to a controllable attenuation element ATT. A PA signal is further led across the matching transformer M TRANS up to the parallel resonant circuit with a capacitor and inductor. A transformation ratio of the transformer element is chosen so that the transformed resonant resistance of this resonant circuit in resonance should correspond to the optimal load resistance of the power amplifier.

The current transformers C TRANS are used for monitoring the resonance circuit. Their output signals are the images both of the current in the tested power capacitor and of a drive current of the parallel resonant circuit. Both signals are led onto the phase detector FD, whose output signal is proportional to the deviation of the phase shift between the incoming signals from the value of 90o. The output signal of the phase detector is led to an integrating AFC amplifier which generates a control signal, by which the frequency of a voltage controlled oscillator OSC is automatically tuned to a resonant frequency of the measuring circuit. The output signal of the current sensor connected in series to the tested capacitor is further led into the control amplifier C AMP. Here the level of the current sensor output signal is compared with a reference level, and a control signal for a controllable attenuator ATT is generated. The input voltage of the power amplifier PA is continuously adjusted by the ATT to the level, at which the current in the power capacitor reaches its required value.

The realized power measuring circuit for the frequency of 3,8 kHz and current 100 A is displayed in Fig. 5.

Fig. 5. Power measuring resonant circuit.

III. CONCLUSIONS

The equipment for the automatic testing of power capacitors has been realized according to the introduced principles. It is used for testing the power capacitors with the capacity of 100 F by the current of 100 A, at the frequencies of 4 - 40 kHz with the driving power of about 100 W. The equipment enables to carry out the testing with less driving generator output power and less electric power consumption than in other cases.

High efficiency of a lower power amplifier, demands on cooling and less power consumption are the advantages ofthe switching PA equipment.

The automatic frequency control causes the change in frequency only by several per cent and it does not influence the test conditions markedly.

The work was supported by the Pre-seed project “Life Expectancies power capacitors for switched pulse sources based on the degradation of the polymer dielectric and electrodes by current pulses” No CZ.105/3100/140301 too.

REFERENCES [1] Mindl,P., Čerovský,Z: Compensation Capacitor Temperature

Diagnostics, Sborník XV. International Symposium on Elec-tric Machinery, ISEM 2007, str. 144-148, ISBN 978-80-01-03807-9

[2] Papez, V.: Apparatus for automatic testing power capacitors, Utility model 25418, Industrial Property Office CR

[3] Vackar, J.F., Vysilace-Teoreticke zaklady 1. dil, SNTL,Praha, 1960

[4] Medhurst,R.G.,H.F. Resistance and Self-capacitance of Single-layer Solenoids, Wireless Engineer, 1947 , vol 2,3, pp. 35-43, 80-92