Power Factor is defined as the ratio of the active power to total power. When the load has linear behavior (motor for instance) the current is sinusoidal and power factor equals the cosine of the angle between current and voltage. Voltage (or current depending on the circuit) injection is used in nonlinear circuits in order to increase Power Factor.
In case of nonlinear loads, generally associated with power supplies and rectifiers used to feed computers and battery chargers, the input line current has generally a pulsed waveform. It consists in addition to the fundamental (line frequency) sinusoidal wave (which is generally in such cases in phase with the voltage) also additional odd harmonics with frequencies, which according to Fourier transform are odd multiples of the fundamental. These harmonics cause parasitic losses without any contribution to the net power (Watt power), needed for operation of the computer circuits or for charging the battery.
Power Factor in such case is the ratio between the fundamental frequency amperes to the total current defined as the square root of the sum of squared amperes of all harmonics in the current waveform, (It is also equal to the ratio between consumer's net power measured in Watt units, to total power measured by Volt-Ampere units).
Elimination of harmonics in the current waveform decreases the denominator increasing power factor. Generally the amplitude of the harmonics is proportional to the inverse ratio of harmonic frequency; thus reducing the third and the fifth harmonic (150Hz and 250Hz for a 50Hz line) has the highest impact on the power factor.
It is common therefore to inject third or fifth harmonic current (or voltage) with a phase delayed by 180 degrees to the third or fifth harmonic of the line current waveform, in order to eliminate this harmonic and improve power factor.
Consider a load of 10HP Induction Motor at 0.8pf. This means, the motor draws 7.46KW, 5.6KVAR & 9.325KVA at constant voltage. This implies that the utility needs to supply 5.6KVAR. Suppose, if 5.6KVAR capacitor bank has been installed then utility need not to be supplying the desired reactive power of 5.6KVAR. This means the plant consumption is at unity power factor.
Hence, power factor shall be looked into the Load and Supply manner. Motor demand of reactive power can't be changed because it has been designed like that for a physical size.
In context of FACTS technology, the voltage control is used to control the Reactive Power by maintaining the same Real Power. As in the above example of 10HP motor, the voltage injected at source will be more without the 5.6KVAR capacitor. vis-a-vis voltage injected at source will be less with the 5.6KVAR capacitor. Hence, it will be said that by Voltage injection the power factor is controlled.
Actually, above is misnomer concept. The reality is use of capacitor or variation of the consumption of the reactive power. Hence, lesser the reactive power consumption, less is the voltage and lesser the Losses. That is why, all utilities demands to install power factor improvement capacitors at the load end which will be benefitted to the energy supplier and consumer.