Conference Paper

An automatic technique to obtain the equivalent circuit of aluminum electrolytic capacitors

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Abstract

This paper presents an economic and automatic experimental technique that allows the determination of the equivalent circuit of aluminum electrolytic capacitors at their operating conditions. The equivalent circuit of an electrolytic capacitor comprises an equivalent series inductance (ESL), an equivalent series resistance (ESR) and a capacitance (C). Both C and ESR values change with frequency, temperature and aging. The knowledge of the capacitor ESR value is essential to achieve the best design proposal for switch mode power supplies (SMPS) and in the selection of the best capacitors used in the DC link of adjustable speed drives (ASD). On the other hand, the accurate knowledge of the capacitor capacitance is also very important in the rectifiers design and in the choice of the best capacitor for the DC link of ASD. Moreover, the knowledge of both parameters allows the evaluation of the capacitor state condition. To implement the proposed technique, two distinct circuits should be considered. The first one accounts for the estimation of the ESR and reactance of the capacitor, while the second one allows the estimation of the capacitor capacitance. To implement the first circuit, it is necessary to put the capacitor under test in series with a resistor and connect them to a sinusoidal voltage. The relationship between the gain and phase of the capacitor voltage and current waveforms, obtained from sinusoidal fitting, gives enough information to compute both ESR and reactance of the capacitor. The second circuit is a simple charge/discharge circuit. From the relationship between the capacitor current and voltage, during discharge, it is possible to compute its capacitance using the least mean square algorithm.

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... The relationship between capacitance and temperature differs between dielectrics, with variations of up to 10% rated capacitance between room and maximum temperatures in some cases. A variety of relationships between dissipation factor (the ratio of ESR to capacitive reactance) and temperature is seen in different polymer films, but in general an increase is seen above room temperature, reflecting mainly an increase in lead resistance [9]. Conversely, the dissipation factor of aluminium electrolytic capacitors decreases with increasing temperature [10]. ...
... Increasing temperature has a similar effect on the insulation resistance of both aluminium electrolytic and film capacitors -an approximately exponential decrease [9]. The corresponding rise in leakage current for a given applied DC voltage is a source of self-heating. ...
... The other major advantage of electrolytic capacitors is their low cost per unit capacitance [16,15,9]. However, it is misleading to conclude solely from this that electrolytic capacitors are a more cost-effective solution for DC links. ...
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... 2) Fig. 6(b), Eqs. (18) and (19) are examples of Principle II. For different charging or discharging modes, the profiles and equations are different. ...
... Referring to Fig. 6(b), during the shutdown process of converter, the dc-link capacitors discharge through the equivalent resistor Req. The capacitor parameters can be estimated based on the discharging profile and (18). During the start-up process of converter, the capacitors charge through R'eq. ...
... Content may change prior to final publication. (9)-(11), (18) and (19). Moreover, some optimization algorithms, such as particle swarm optimization (PSO) algorithm, genetic algorithm (GA) can be used to identify capacitor parameters. ...
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... In order to overcome the aforementioned shortcomings, different algorithms were used in [10]- [17]. Laplace transform algorithm in [10], Newton-Raphson (NR) in [11] and [16], discrete Fourier transform (DFT) in [12], [13], and [17], and least mean square (LMS) in [14] and [15]. All the algorithms are used to calculate the relationship between the input voltage and the output voltage of the experimental circuit shown in Fig. 7. ...
... The method estimated the ESR and capacitance with a maximum error of 11% and 2.8%, respectively. In [14], a simple modification to the same setup in Fig. 7 is carried out to estimate the ESR and capacitance. The modified circuit uses a control circuit to charge and discharge the capacitor. ...
... Based on the same method proposed in [14] and the setup shown in Fig. 7, a wider range of frequencies and temperatures are considered in [15] for the estimation of ESR and capacitance. In addition, [15] uses two methods: 1) based on a sinusoidal generator; and 2) based on charge/discharge circuit, and compares each method. ...
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... In general though, an increase is seen above room temperature. This increase reflects the increase in ESR, mainly due to the increase in resistance of leads, etc. against an ESL which is relatively constant with temperature [9]. Conversely, the dissipation factor of aluminium electrolytic capacitors decreases with increasing temperature. ...
... The disadvantage of this is that balancing resistors (which result in extra loss in the system) or over-rating to allow for significant over-voltages, are required [14]. The other major advantage of electrolytic capacitors is their low cost per unit capacitance [15,14,9]. However, it is misleading to conclude solely from this that electrolytic capacitors are a more costeffective solution for DC links. ...
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... Regarding the short lifetime of electrolytic capacitors, many methods have been proposed to estimate the health status of capacitors through monitoring C and ESR. Some of them require removing the capacitors from the power circuit, which makes them inappropriate for many on-site application demands [11][12][13]. Therefore, avoiding removing the capacitors from power circuit is one of the important requirements when we design a condition monitoring method for capacitors in power converters. ...
... The IDpuls is the maximum pulsed drain current of the switch (i.g., MOSFET), ic(t) is the discharging current. Substituting (12) into (11), we can determine the upper limit of capacitor voltage U2 (the start voltage point to turn on the branch X2) in (13). ) ( ...
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... Once the learning mode is complete, the algorithm will enter monitoring mode where it estimates the present health status (PHS) of the capacitor using (12) and (13). ...
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... In [3], according to the amplitude of AC voltage and capacitor voltage, the ESR and C are calculated by using Newton-Raphson method. The ESR is calculated by discrete Fourier transform by detecting the capacitor current and voltage of the buck circuit driven by the sine-wave pulse-width modulation signal [4][5][6]. ...
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... An aluminum EL. CAP. is formed by a cylindrical winding of an aluminum anode foil, an aluminum cathode foil, and paper that separate these foils [3]. EL. ...
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... The electrolytic capacitor is fed by a sinusoidal voltage source in series with a resistor. ESR and C can be obtained from the impedance vector defined by the capacitor voltage and current according to the discrete fourier transformation (DFT) [4][5]. In [6], a power amplifier together with a signal generator is used to create a sinusoidal waveform with desired frequency to feed the RC circuit. ...
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Aluminum electrolytic capacitors are the leading choice for ac variable-frequency drive (VFD) bus filters. Predicting the expected life of these components in this application is complicated by four factors. First, the electrical impedance of aluminum electrolytic capacitors is nonlinear with both frequency and temperature. Second, motor drives produce a spectrally rich ripple current waveform that makes energy loss difficult to compute. Third, the heat transfer characteristic of capacitor banks is dependent on design geometry. Fourth, the expected life of aluminum electrolytic capacitors is extremely sensitive to operating temperature. This paper describes a method for predicting bus capacitor life that addresses these problems by using a multiple component model for capacitor impedance, a motor drive simulation to create ripple current waveforms, a heat transfer model based on bank geometry, and a capacitor life model derived from the device physics of failure. An example is given showing the effect of ac line impedance on the relative expected life.
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Impedance modeling of aluminum electrolytic capacitors presents a challenge to design engineers, due to the complex nature of the capacitor construction. Unlike an electrostatic capacitor, an electrolytic capacitor behaves like a lossy coaxial distributed RC circuit element whose series and distributed resistances are strong functions of temperature and frequency. This behavior gives rise to values of capacitance, effective series resistance, and impedance that vary by several orders of magnitude over the typical frequency and temperature range of power inverter applications. Existing public-domain Spice models do not accurately account for this behavior. In this paper, a physics-based approach is used to develop an improved impedance model that is interpreted both in pure Spice circuit models and in math functions.
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This paper describes the most important factors influencing the aluminum electrolyte capacitor showing, in particular, the effect of temperature on the lifetime of this device. The automation of the measurement system, with the oven interfaced with a PC, was also completed to control all the involved parameters.
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A simple, low-component active- RC circuit is given for the measurement of in-circuit, discrete, and incremental capacitances. The measurement circuit provides the measured value of capacitance directly in terms of the circuit's output voltage. The proposed system provides good accuracy for these measurements. The capacitance measurements are independent of the signal frequency. Experimental results that support the theory are included
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Errors introduced in an operational-amplifier-based sine-wave oscillator applied in capacitance measurement are considered. The errors due to the nonideal characteristics of the operational amplifier are addressed. The oscillator circuit was simulated using the SPICE program, and gives the opportunity to study the behavior of the circuit under nonideal conditions, and to estimate the errors introduced in the measured capacitance and the frequency of oscillation. It is shown that major sources of error are the gain-bandwidth product and the output resistance of the operational amplifier. Compensation techniques to reduce errors related to the gain-bandwidth product are presented. Experimental results confirming the error reduction are included
Application Guide, Aluminum Electrolytic Capacitors
  • Cornell Dubilier