7.4
Complex Power
Consider a load connected to an AC source. The voltage and currents across this load can be represented in the frequency domain.
The complex power is defined as half the product of the voltage and the complex conjugate of the current.
The magnitude of complex power is known as the apparent power.
When expressing complex power in rectangular form, the real part represents the average power, while the imaginary part represents the reactive power.
Complex power can also be expressed in terms of impedance, which is the ratio of voltage to current.
Separating the resistive and the reactance parts of the impedance and comparing these with the obtained complex power expression gives an expression that involves impedance.
The real part of the power is the only useful power delivered to the load.
Reactive power reflects energy exchange between the source and the load. It is zero for resistive, negative for capacitive, and positive for inductive loads.
The complex, real, and reactive power can be visualized in the form of a triangle, known as the power triangle.
Power engineers have introduced the concept of complex power to determine the cumulative effect of parallel loads. This idea plays a crucial role in power analysis because it encompasses all the details related to the power consumed by a specific load.
Complex power is defined as the multiplication of the voltage and the complex conjugate of the current. The magnitude of this power, known as apparent power, is measured in volt-amperes (VA). Notably, the angle of the complex power equates to the power factor angle.
In terms of rms values, complex power is represented by
It can also be expressed in terms of the load impedance, as
Complex power is the product of the rms voltage phasor and the complex conjugate of the rms current phasor. Being a complex quantity, its real portion is referred to as real power P, and its imaginary part is termed reactive power Q. The introduction of complex power allows the direct retrieval of real and reactive powers from voltage and current phasor, demonstrating how complex power encapsulates all pertinent power information in a specific load.
Reactive power represents the energy transfer between the source and the load. For resistive loads, it's zero, for capacitive loads, it's negative, and for inductive loads, it's positive.
One can visualize the complex, real, and reactive power in the form of a triangle, commonly known as the power triangle. This visualization aids in understanding these power concepts.
Consider a load connected to an AC source. The voltage and currents across this load can be represented in the frequency domain.
The complex power is defined as half the product of the voltage and the complex conjugate of the current.
The magnitude of complex power is known as the apparent power.
When expressing complex power in rectangular form, the real part represents the average power, while the imaginary part represents the reactive power.
Complex power can also be expressed in terms of impedance, which is the ratio of voltage to current.
Separating the resistive and the reactance parts of the impedance and comparing these with the obtained complex power expression gives an expression that involves impedance.
The real part of the power is the only useful power delivered to the load.
Reactive power reflects energy exchange between the source and the load. It is zero for resistive, negative for capacitive, and positive for inductive loads.
The complex, real, and reactive power can be visualized in the form of a triangle, known as the power triangle.
From Chapter 7:
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