Bumblebee circuit

The Hummel circuit and the related Polek circuit are used in electrical measurement technology to generate a sinusoidal alternating current with a phase shift of 90 ° in the case of sinusoidal alternating voltage . Applications are in the area of electromechanical measuring devices such as the Ferraris meter , a type of electricity meter . The circuit is used to measure the reactive power occurring in single-phase AC voltage networks with these measuring devices, which usually record the active power .

The circuit is named after its inventor Georg Hummel , who received DRP patent no. 98 897 from the German Reich Patent Office in 1895 .

In practical use, these circuits are increasingly being replaced by electronic measuring devices such as intelligent meters , where, in addition to the effective values, the phase shift between voltage and current is determined and from this the active and reactive power is determined using digital signal processing.

application

Power meters and Ferraris meters contain a current and a voltage path; the instantaneous values of the currents in the two paths are multiplied, averaged and added over time in the energy meter to measure the power. If the current through the voltage path of the measuring device matches the load voltage (mains voltage) in the phase angle , the active power is measured. If the current in the voltage path is shifted by 90 ° in the phase angle, reactive power is recorded.

Bumblebee circuit

The Hummel circuit for phase shifting is shown schematically in the adjacent figure. The voltage corresponds to the applied consumer voltage , complex values are underlined. The voltage path of the meter is represented by the equivalent resistance and the inductance . The resistor , the inductance and the balancing resistor are components required in addition to the electricity meter. The value of the balancing resistor is chosen so that ${\ displaystyle {\ underline {U}}}$ ${\ displaystyle R_ {2}}$ ${\ displaystyle L_ {2}}$ ${\ displaystyle R_ {1}}$ ${\ displaystyle L_ {1}}$ ${\ displaystyle R_ {3}}$ ${\ displaystyle R_ {3}}$

{\ displaystyle R_ {3} = {\ frac {\ omega ^ {2} \ cdot L_ {1} \ cdot L_ {2} -R_ {1} \ cdot R_ {2}} {R_ {1} + R_ { 2}}}}

applies. In this case, the current follows the voltage by 90 °. Since the angular frequency appears in the equation, the phase shift is frequency-dependent. The circuit is usually designed for a line frequency of 50 Hz. ${\ displaystyle {\ underline {I}} _ {2}}$ ${\ displaystyle {\ underline {U}}}$ ${\ displaystyle \ omega}$

Pole circuit

The similarly structured Polek circuit uses a capacitor instead of an ohmic resistor, as shown in the adjacent figure , whose value for the same phase shift of 90 ° as in the Hummel circuit ${\ displaystyle C}$

{\ displaystyle C = {\ frac {R_ {1} + R_ {2}} {\ omega ^ {2} (R_ {1} \ cdot L_ {2} + R_ {2} \ cdot L_ {1})} }}

is set.

The voltage path of the meter is again represented by the equivalent resistance and the inductance . The inductance is usually on the order of up to 50 mH. At low frequency, the voltage path is practically a purely ohmic load, since it has between 10 kΩ and 50 kΩ. ${\ displaystyle R_ {2}}$ ${\ displaystyle L_ {2}}$ ${\ displaystyle R_ {2}}$

Since the current should flow 90 degrees out of phase with the operating voltage with the help of the Polek circuit , it is necessary to shift the voltage by 90 degrees with respect to the operating voltage. The capacitor is used for this . ${\ displaystyle {\ underline {I}} _ {2}}$ ${\ displaystyle {\ underline {U}}}$ ${\ displaystyle C}$

Basically, it should be noted that both circuits, due to the frequency dependence of the reactances , only deliver correct phase shifts at a certain frequency and allow a measurement of the reactive power or reactive energy.

literature

Karl Küpfmüller, Wolfgang Mathis, Albrecht Reibiger: Introduction to theoretical electrical engineering . 18th edition. Springer, 2008, ISBN 978-3-540-78589-7 .