If you have an electrical circuit consisting of a capacitor (capacitance C) and an inductive coil (inductance L) and you load the capacitor, you will observe a sin-wave oscillation in this circuit as soon as you remove the supply. Caused by the losses, the amplitude of the oscillation will decrease with every cycle. The frequency of the oscillation is the natural frequency of this circuit and is given by 2*π*f=1/sqrt(L*C).
If you connect a frequency variable supply (exciter) in series to the coil and the capacitor, you will observe an enormous increasing of the voltage as soon as you excite the circuit with its natural frequency. This effect is called resonance and the corresponding frequency is called resonance frequency. Because of the increase in voltage, we are talking about a voltage resonance.
If you connect the exciter in parallel to the coil and the capacitor, you will have the same effect with the current flowing in the circuit. In this case we are talking about a current resonance.
Both cases are important for testing of capacitive transmission line equipment as cables, generators or GIS/GIL systems because modern high voltage test sets use either the parallel resonance mode or the series resonance mode to generate the required testing power.
In a series LC ckt, when connected to variable frequency source, frequency on varying reaches to a point when inductive reactance becomes equal to capacitive reactance the current flow in circuit would become very high ( theoretically infinite in purely non-resistive circuit) , its extent guided by total inherited resistance of inductive coil and capacitor. Frequency at this point is called resonant frequency. Natural frequency as normally understood is normal supply source frequency which is normally 50 Hz or 60 Hz. Resonant frequency is equal to 1/2pi multiplied by 1/LC.
The natural frequency is either 50Hz or 60Hz depending on where you live. Resonance may occur at any multiple of the fundamental (natural). Resonance should be understood by reading any number of basic courses in electrical engineering. In power systems, resonance occurs with a series network or parallel network consisting of an inductor and capacitor. A typical application involves power factor correction capacitors. These capacitors are essentially in series with the system inductance. When resonance occurs, the combination of the LC network impedances drop to near zero, resulting in extremely high current at the resonant frequency. In power systems this is typically at 5th or 7th harmonic, but is not limited to these frequencies.
In the event of a parallel resonance, the current circulating in the LC loop is very high, but the voltage at the two terminals becomes very high. This has damaged motors and, in some cases, transformers. More frequently, it results in cable damage.
When we use power factor correction capacitors we are actually creating a parallel resonance at 50Hz/60Hz, so the fundamental power frequency is natural + parallel resonance frequency. apart from fundamental resonance there is partial series resonance (which amplifies the reactive current of higher order frequency) due to non-linear loads (having higher order frequencies as predominant in their current cycle) so when these types of loads are operated by 50Hz / 60Hz power source there are chances of higher order frequency resonance (due to X(ind) and X(cap) components of source and load respectively) which increases the harmonics current loading on transformer(s) and capacitor(s) in the network.