Transient Component Steady-State Componentfehmibardak.cbu.edu.tr/wp-content/uploads/2018/02/...Transient Component Steady-State Component Now we focus on steady-state power calculations.

Transient Component Steady-State Component

Now we focus on steady-state power calculations.

We are primarily interested in the average power delivered to or supplied

from a pair of terminals as a result of sinusoidal voltages and currents.

Other measures, such as reactive power, complex power, and apparent

power, will also be presented.

We are operating in the sinusoidal steady state, so we may choose any

convenient reference for zero time. This reference system requires a shift of

both the voltage and current by 𝜃𝑖, Thus:

Figure 10.2 Instantaneous power, voltage, and current versus v(t ) for steady-state sinusoidal operation.

Unit for reactive power is

VAR (volt-amp reactive).

Unit for real power is

W (watt)

The instantaneous real power can

never be negative.

Power cannot be extracted from a

purely resistive network.

Rather, all the electric energy is

dissipated in the form of thermal

energy.

In a purely inductive circuit, the average

power is zero. Therefore no transformation

of energy from electric to nonelectric form

takes place.

The instantaneous power at the terminals

continually exchanged between the circuit

and the source driving the circuit

The average power is zero, so there is no

transformation of energy from electric to

nonelectric form.

The power is continually exchanged

between the source driving the circuit and

the electric field associated with the

capacitive elements

The average power and the reactive power

can be written in terms of effective values:

Complex power is the complex sum of real power and reactive power

The magnitude of complex power is referred to as apparent power.

Apparent power, like complex power, is measured in volt-amps. The

apparent power, or volt-amp, requirement of a device designed to

convert electric energy to a nonelectric form is more important than the

average power requirement. Although the average power represents the

useful output of the energy-converting device, the apparent power

represents the volt-amp capacity required to supply the average power.

𝑺 = 𝑷𝟐 + 𝑸𝟐𝟐

𝑺 = 𝑽𝒆𝒇𝒇. 𝑰𝒆𝒇𝒇∗

𝑺 = 𝑽𝒆𝒇𝒇. 𝑰𝒆𝒇𝒇∗

𝑺 = 𝑽𝒆𝒇𝒇. 𝑰𝒆𝒇𝒇∗

X is positive for an inductor

and negative for a capacitor

For maximum average power transfer, 𝑍𝐿 must be equal to the conjugate of the Thévenin impedance