Method of calculating effective power relating to capacitor, method of measuring effective power consumed by capacitor, capacitor selection method, calculation apparatus for calculating effective power relating to capacitor, and recording medium storing the calculation program therefor

• US 7,158,898 B2
• Filed: 11/24/2003
• Issued: 01/02/2007
• Est. Priority Date: 11/22/2002
• Status: Active Grant

• Current Assignee: Murata Manufacturing Co Limited
• Original Assignee: Murata Manufacturing Co Limited
• Inventors: Kubota, Kazuyuki, Yamaoka, Osamu, Yamada, Hirohisa
• Primary Examiner(s): Barlow; John
• Assistant Examiner(s): Lau; Tung S.
• Application Number:
  US10/718,797
• Publication Number:
  US 20040167730A1
• Time in Patent Office: 1,135 Days
• Field of Search: 702/60, 324/427, 324/650, 219/216, 331/96, 333/182, 320/107, 320/106, 320/132, 361/331, 361/321, 374/175, 417/12, 422/88
• US Class Current: 702/60
• CPC Class Codes: G01R 21/1331 Measuring real or reactive component, measuring apparent energy

Abstract

In a method of calculating effective power relating to a capacitor, the waveform of a periodic voltage applied to a capacitor is set. The capacitance of a desired capacitor is input. The waveform of the periodic voltage applied to both ends of the capacitor is subjected to Fourier expansion. More specifically, the periodic voltage is Fourier-expanded in terms of sine and cosine-wave series of high-order frequency components. Further, an effective power consumed by the capacitor is calculated using data regarding temperature characteristics, voltage characteristics and a frequency characteristic of the capacitance and dielectric tangent of the capacitor.

Claims

1. A method of calculating effective power relating to a capacitor, comprising the steps of:

obtaining a equilibrium temperature of the capacitor for each of a plurality of sine waves, and substituting a first capacitance and a first dielectric tangent of the capacitor for each of a plurality of equilibrium temperatures into the following equation;

$\mathrm{Pe}=\frac{\tan <br><br><br><br>\mathrm{\delta <br><br>}}{1+{\left(\tan <br><br><br><br>\mathrm{\delta <br><br>}\right)}^2}·<br><br>{\mathrm{\pi <br><br>}<br><br>\mathrm{fCb}}^2$

Pe;

effective power

tan δ

;

dielectric tangent

C;

capacitance

f;

frequency

b;

sine-wave amplitude

in order to obtain a first effective power for each of the equilibrium temperatures;

obtaining a voltage value and a frequency from the waveform of a periodic voltage applied to both ends of the capacitor, and setting a plurality of provisional temperatures, and obtaining a second capacitance and a second dielectric tangent for each of the provisional temperatures, and substituting the second capacitance and the second dielectric tangent into the following equation;

$\mathrm{Pe}=\frac{\tan <br><br><br><br>\mathrm{\delta <br><br>}}{1+{\left(\tan <br><br><br><br>\mathrm{\delta <br><br>}\right)}^2}·<br><br>\mathrm{\pi <br><br>}<br><br>\mathrm{fC}\left(a^2+b^2\right)$

Pe;

effective power

tan δ

;

dielectric tangent

C;

capacitance

f;

frequency

a;

cosine-wave amplitude

b;

sine-wave amplitude

in order to obtain second effective power corresponding to the periodic voltage for each of the provisional temperatures;

determining a temperature at which the first effective power is approximately equal to the second effective power as a target equilibrium temperature of the capacitor; and

determining the first and second effective powers corresponding to the target equilibrium temperature as a target effective power corresponding to the periodic voltage.

2. A method of calculating effective power relating to a capacitor according to claim 1, wherein the step of calculating the second effective power comprises the steps of:

performing Fourier expansion for the periodic voltage;

calculating effective power for each of a plurality of harmonics; and

determining the sum of the calculated effective powers of the harmonics as the second effective power corresponding to the periodic voltage.

3. A method of measuring effective power consumed by a capacitor, wherein a periodic voltage is applied to the capacitor, and the waveform of the periodic voltage applied to both ends of the capacitor is measured, and the effective power consumed by the capacitor is calculated from the measured waveform of the periodic voltage using the method of calculating the effective power relating to the capacitor according to claim 1.

4. A method of selecting a capacitor, comprising the steps of:

obtaining an equilibrium temperature of the capacitor for each of a plurality of sine waves, and substituting a first capacitance and a first dielectric tangent of the capacitor for each of a plurality of equilibrium temperatures into the following equation;

$\mathrm{Pe}=\frac{\tan <br><br><br><br>\mathrm{\delta <br><br>}}{1+{\left(\tan <br><br><br><br>\mathrm{\delta <br><br>}\right)}^2}·<br><br>\mathrm{\pi <br><br>}<br><br><br><br>{\mathrm{fCb}}^2$

Pe;

effective power

tan δ

;

dielectric tangent

C;

capacitance

f;

frequency

b;

sine-wave amplitude

in order to obtain a first effective power for each of the equilibrium temperatures;

obtaining a voltage value and a frequency from the waveform of a periodic voltage applied to both ends of the capacitor, and setting a plurality of provisional temperatures, and obtaining a second capacitance and a second dielectric tangent for each of the provisional temperatures, and substituting the second capacitance and the second dielectric tangent into the following equation;

$\mathrm{Pe}=\frac{\tan <br><br><br><br>\mathrm{\delta <br><br>}}{1+{\left(\tan <br><br><br><br>\mathrm{\delta <br><br>}\right)}^2}·<br><br>\mathrm{\pi <br><br>}<br><br>\mathrm{fC}\left(a^2+b^2\right)$

Pe;

effective power

tan δ

;

dielectric tangent

C;

capacitance

f;

frequency

a;

cosine-wave amplitude

b;

sine-wave amplitude

in order to obtain a second effective power corresponding to the periodic voltage for each of the provisional temperatures;

determining a temperature at which the first effective power is approximately equal to the second effective power as a target equilibrium temperature of the capacitor, and determining the first and second effective powers corresponding to this target equilibrium temperature as a target effective power corresponding to the periodic voltage; and

comparing the target effective power corresponding to the periodic voltage with an allowable power capacity of the capacitor in order to determine whether or not the capacitor is available.