Resonance is a physical simple harmonic vibration, in which the acceleration of an object is proportional to the displacement from the equilibrium position and always points towards the equilibrium position under the action of the restoring force. Its dynamic equation is F=- kx. The phenomenon of resonance is that the current increases and the voltage decreases. The closer it is to the resonance center, the faster the rotation of the ammeter, voltmeter, and power meter. However, the difference from a short circuit is that there will be no zero sequence quantity.
A circuit composed of an inductor L and a capacitor C that can resonate at one or several frequencies is collectively referred to as a resonant circuit. In power engineering, certain hazards such as overvoltage or overcurrent may occur due to resonance in the circuit. Therefore, research on resonant circuits is of great significance, both in terms of utilization and limiting their hazards.
A passive (referring to a circuit without an independent power source) linear time invariant circuit containing an inductor coil and a capacitor exhibits a purely resistive property when subjected to an external power source at a specific frequency. This specific frequency is the resonant frequency of the circuit, and circuits that mainly operate in resonance are called resonant circuits. Radio equipment uses resonant circuits to complete functions such as tuning and filtering. The power system needs to prevent resonance to avoid causing overcurrent and overvoltage.
There are linear resonance, nonlinear resonance, and parametric resonance in circuits. The former is a resonance that occurs in a linear time invariant passive circuit, with series resonance (or series resonance device) circuits as a typical example. Nonlinear resonance occurs in circuits containing nonlinear components, and can occur in circuits composed of iron core coils and linear capacitors in series (or parallel) (commonly known as ferromagnetic resonance circuits). Under sinusoidal excitation, fundamental resonance, high-order harmonic resonance, subharmonic resonance, and amplitude and phase jumps of current (or voltage) will occur in the circuit. These phenomena are collectively referred to as ferromagnetic resonance, while parametric resonance occurs in circuits containing time-varying components. Parametric resonance may occur in a circuit with a capacitive load in a salient pole synchronous generator.
The so-called resonance, according to circuit theory, is a sine voltage applied to an ideal (parasitic resistance free) series circuit of inductors or capacitors. When the sine frequency is at a certain value, the capacitance and inductance are equal, the impedance of the circuit is zero, and the circuit current reaches infinity. If a sine voltage is applied to a parallel circuit of inductance and capacitance, when the frequency of the sine voltage is a certain value, the total admittance of the circuit (admittance is the reciprocal of impedance) is zero, and the voltage on the inductance and capacitance components is infinite. The former is called series resonance, and the latter is called parallel resonance.
formulation
Z=R+j (XL-XC), where Z is impedance, R is resistance, XL-XC=X is inductance+capacitance=reactance. It can be clearly seen from the formula that when the inductance XL and capacitance XC are equal, Z only contains the real component R, which is pure resistance, and this is resonance.