Series resonance is a special phenomenon that occurs in a series circuit composed of R, L, and C components under certain conditions. The complex impedance of the R, L, and C series circuit shown in Figure 1, excited by a sine voltage Us, is:
Figure 1 Figure 2
When changing from zero to infinity, X changes from - ∞ to+∞; When ω<ω o, X＜0, The circuit is capacitive; When ω>ω o, X＞0, The circuit is inductive; When ω=ω o, the circuit impedance Z (ω o)=R is pure resistance; Voltage and current are in phase, and the working state of the circuit at this time is called resonance. Since this resonance occurs in a series circuit of R, L, and C, it is also called series resonance. Equation 1 is the condition for the series circuit to resonate. From this equation, the resonant angular frequency ω o can be obtained as follows:
According to equation (2), the resonant frequency of a series circuit is determined by its own parameters L and C, and is independent of external conditions. It is also known as the natural frequency of the circuit; When the power frequency is constant, the circuit parameters L or C can be adjusted to make the natural frequency of the circuit consistent with the power frequency and resonate, such as the induction method of power frequency resonance boosting; When the circuit parameters are constant, resonance can occur by changing the power frequency to match the natural frequency of the circuit, also known as frequency modulation method.
When a series circuit resonates, its reactance X (ω o)=0, so the complex impedance of the circuit appears as a pure resistance, and the impedance is at its minimum value; During resonance, although the reactance is present, both the inductive and capacitive reactance are non-zero. The inductive or capacitive reactance during resonance is the characteristic impedance of the series resonant circuit, denoted as ρ, i.e
The ratio of characteristic impedance to resistance is commonly used in engineering to characterize the performance of resonant circuits, and this ratio is called the quality factor of the series circuit, represented by Q, which is a quantity determined by the circuit parameters R, L, and C.
When in series resonance, the voltages of each component in the circuit are
From equation (3), it can be seen that although the total reactive voltage is 0 during resonance, the inductor voltage and capacitor voltage are not zero, their effective values are equal, and both are Q times the applied voltage. However, the inductor voltage leads the applied voltage by 900, the capacitor voltage lags behind the applied voltage by 900, and the resistance voltage and applied voltage are equal and in phase. The applied voltage is all applied to the resistor R, and the voltage on the resistor reaches its maximum value. The voltage current phasor relationship of each component is shown in Figure 3.
When the Q value of the circuit is high (the Q value of the series resonant device boost is generally greater than 10, up to 10-30), the values of the inductor voltage and capacitor voltage will be much larger than the value of the applied voltage. A relatively small test voltage can be used to generate a high test voltage on the tested equipment, thereby reducing the capacity of the resonant excitation power supply to only 1/Q of the test capacity.
Figure 3 phasor diagram of series resonant circuit
According to the analysis of equation (2), there are two resonant boosting methods: power frequency resonant boosting method and frequency conversion resonant boosting method. The power frequency resonance boosting method is mainly used for testing generators, transformers, and capacitive voltage transformers. The frequency conversion resonant boost method is mainly used for testing cross-linked cables, which can meet the requirements of cables with varying lengths and capacitance within a large range.
The power frequency resonant boost system is a system that causes resonance between the inductor and the capacitor of the test object under power frequency conditions (50Hz in field testing), generating high power frequency voltage. The power frequency resonant boost system generally uses the method of adjusting the inductance reactance to cause resonance between the reactor and the capacitor of the test object under the action of the excitation source, which is commonly referred to as inductive modulation. It is also possible to change the capacitance of the test system by parallel connecting capacitors at both ends of the test sample, so that it resonates with the reactor under the action of the excitation source, which is commonly referred to as capacitance adjustment. It is also possible to simultaneously change the inductance of the reactor and the capacitance of the tested system to achieve resonance, which is commonly referred to as inductance and capacitance modulation. The induction type usually adopts the method of adjusting the air gap of the iron core reactor, which can continuously and smoothly adjust the inductance value and is relatively easy to operate. However, the capacitance cannot be continuously adjusted, so the induction method or capacitance adjustment method is generally used for on-site operation.