Effective or RMS Value, Apparent Power and Power Factor & Complex Power

RMS Value (Effective Value) 

Root-mean-square (rms) refers to the most common mathematical method of defining the effective voltage or current of an ac wave. In a direct current dc, voltage and current are simple to define, but in an alternating current ac , the definition is more complicated, and can be done in several ways. That is why, root-mean-square (rms) is very applicable in dealing with ac because it is the most common mathematical method of defining the effective voltage or current of an ac wave.

The root-mean-square (rms) value or effective value of an ac waveform is a measure of how effective the waveform is in producing heat in a resistance. That's why rms (or effective) values are useful: they give us a way to compare ac voltages to dc voltages.

Practical Example:

            If you connect a 5 V_rms source across a resistor, it will produce the same amount of heat as you would get if you connected a 5 V dc source across that same resistor. On the other hand, if you connect a 5 V peak source or a 5 V peak-to-peak source across that resistor, it will not produce the same amount of heat as a 5 V dc source.

APPARENT POWER AND POWER FACTOR

Total power in an AC circuit, both dissipated and absorbed or returned is referred to an apparent power. Apparent power is symbolized by the letter S and is measured in the unit of Volt-Amps (VA). In an AC circuit, the product of the rms voltage and the rms current is called apparent power. When the impedance is a pure resistance, the apparent power is the same as the true power. But when reactance exists, the apparent power is greater than the true power. The vector difference between the apparent and true power is called reactive power. The apparent power is the absolute value of the complex power, so it is defined only for sinusoidal excitation. It is a function of a circuit's total impedance (Z). 

Power Factor has an economic impact on consumers of large power (industrial loads)A load with a low power factor that consumes P watts of power draws higher current from a constant voltage source. Higher currents increase line losses and increase the amount of supplied power. Such loads can be charged at a higher rate by power companies. Ideally a pf of 1.0 is desired. Most loads that consume a large amount of power are inductive. Inductive load can be changed by adding capacitors to increase the pf towards unity value, thus optimizing cost.

COMPLEX POWER

In power system analysis the concept of Complex Power is frequently used to calculate the real and reactive power. This is a very simple and important representation of real and reactive power when voltage and current phasors are known. Complex Power is defined as the product of Voltage phasor and conjugate of current phasor. Complex power is applicable only to circuits with sinusoidal excitation because complex effective or peak values exist and are defined only for sinusoidal signals. The unit for complex power is VA. It is composed of a real number which is the average power (P) and an imaginary number which is the reactive power (Q).

                                         

POWER TRIANGLE

             



These three types of power -- real, reactive, and apparent -- relate to one another in trigonometric form. We call this the power triangle:

RESISTIVE LOAD

            

In a purely resistive circuit, all circuit power is dissipated by the resistor(s). Voltage and current are in phase with each other.

 REACTIVE LOAD

  In a purely reactive circuit, no circuit power is dissipated by the load(s). Rather, power is alternately absorbed from and returned to the AC source. Voltage and current are 90^o out of phase with each other.

RESISTIVE/REACTIVE

 In a circuit consisting of resistance and reactance mixed, there will be more power dissipated by the load(s) than returned, but some power will definitely be dissipated and some will merely be absorbed and returned. Voltage and current in such a circuit will be out of phase by a value somewhere between 0^o and 90^o.

LEARNINGS:

    I’ve learned that reactive loads such as inductors and capacitors dissipate zero power and the fact that they drop voltage and draw current gives the deceptive impression that they actually do dissipate power.

   I’ve also learned that Poor power factor in an AC circuit may be corrected, or re established at a value close to 1, by adding a parallel reactance opposite the effect of the load's reactance. If the load's reactance is inductive in nature (which is almost always will be), parallel capacitance is what is needed to correct poor power factor. Low power factor has higher current, otherwise lower. Leading power factor means that current is leading while lagging power factor means lagging current. Mostly, inductive loads consume high current while resistive loads consume less.