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Uploaded on

14 Sep 2022

Skill-Lync

The definition of electric power can be said as the rate at which energy is being consumed in a circuit. Any electrical or electronic device has a limit to the amount of electrical power that can be safely handled. Power is measured in watts. In DC circuits and pure AC circuits without any nonlinear components, the current and voltage waveforms are ‘in phase’.

So the power at any instant of time in that circuit is obtained by multiplying the voltage and current. In a DC circuit, the power can be calculated by the product of the DC voltage times the DC current. However, for AC circuits with reactive components, we must calculate the consumed power in a different way.

The AC circuits contain a combination of resistive, inductive and capacitive elements. These elements cause the phase shift between the electrical parameters such as voltage and current. Due to the behaviour of voltage and currents, especially when subjected to these components, power quantity comes in different forms. In DC circuits and pure AC circuits without any nonlinear components, the current and voltage waveforms are ‘in phase’. Consider the below circuit in which AC supply is given to a load.

The AC input will be changing its magnitude at every instant. So, it is not easy to find the power like in a DC circuit. Here we consider the instantaneous voltage which is given by v = Vm sin ωt and i = Im sin ωt.

The power at any instant of time in that circuit is obtained by multiplying the voltage and current. If I consider the RMS value of voltage and current,

v = Vm sin ωt

p = vi = 2 VI sin wt sin (ωt ± ϕ)

= VI (cos ϕ – cos (2ωt ± ϕ)

=VI(cos ϕ-cos2ωt -sinϕsin2ωt )

p = VI cos ϕ (1 – cos 2wt) ± VI sin ϕ sin2wt

We know that if a waveform is “shifted” to the right or left of 0o when compared to another sine wave the expression for this waveform becomes Am sin(ωt ± Φ). But if the waveform crosses the horizontal zero axes with a positive-going slope 90o or π/2 radians before the reference waveform, the waveform is called a Cosine Waveform and the expression becomes.VI (cos ϕ – cos (2ωt ± ϕ)

The above power equation consists of two terms, namely

- A term proportional to VI cos ϕ which is pulsating around the average value of VI cos ϕ
- A term proportional to VI sin ϕ pulsating at twice the supply frequency, producing an average of zero over a cycle.

So, there are 3 forms of power in AC circuits. They are

- An active power or True power or Real power
- Reactive power
- Apparent power

The power which is consumed in an AC Circuit is called True power/Active power (P) or Real power. The actual amount of power that performs useful work in the circuit. It is measured in kilowatt (kW) or MW.

We know that reactive loads such as Inductors and capacitors dissipate zero power, yet the fact that they drop voltage and draw current gives the deceptive impression that they dissipate power.

Reactive power (Q), (sometimes called watt less power) is the power consumed in an AC circuit that does not perform any useful work but has a big effect on the phase shift between the voltage and current waveforms. Reactive power is linked to the reactance produced by inductors and capacitors and counteracts the effects of real power.

The product of the RMS voltage, V applied to an AC circuit and the RMS current, flowing into that circuit is called the “volt-ampere product” (VA) given the symbol S and whose magnitude is known generally as apparent power. It is the vector sum of P and Q given in volt-amps (VA). It is a complex power that is represented by the power triangle.

Reactive power has a reflective effect on the safety of power systems because it affects voltages throughout the system. Since the reactive power is moving back and forth in the line (transmission line or any other conductor), it acts as an additional load. So, the reactive power is considered when we consider the overall rating of any electrical systems (cables, switch gears, transformers etc.)

This infers that all installations need to be designed for the apparent power which considers both active and reactive power. If the reactive power exists in a surplus amount, it will significantly reduce the power

factor of the system. Power factor reduction can hence drop operational efficiency. This causes undesirable voltage drops, high conduction losses, excess heating and higher operational costs.

Here is a simple Simulink model to find the active and reactive power of the RL load circuit.

The load is considered to be an RL load to show the difference in the voltage and current waveforms. If the load is considered resistive the voltage and current waveforms will be in phase and all power is dissipated by the resistor.

Input voltage =100V

Resistance=1 ohm

Inductance 1 mH

Voltage measurement and current measurement block are given in the circuit to measure the Load voltage and input current. An RMS block is provided to check the RMS value of the AC signal in the circuit. The multimeter measures the branch current through RL load.

We need the effective value of AC quantities for better calculation. The RMS value is the effective value of a varying voltage or current. It is the equivalent steady DC (constant) value which gives the same effect. Here the input current measured is around 28.5A

The active power is calculated using a Power measurement block by giving the output voltage and current measured from the circuit. It is equal to 4556W here.

The below figure shows the resultant plot from Scope 1 (Marked yellow)

It is clearly visible that the voltage and current are out of phase. The red waveform represents voltage and the green represents current. As it is an RL circuit the current is lagging.

The below figure shows the active power and reactive power measured from the circuit. The red waveform indicated Active power and the blue indicates reactive power.

If I change the load to be pure resistive the reactive power measured is zero

A zoomed view of the results is given below

The value of active power measured also has changed

You can try with different load conditions and input voltage values and see how the active power and reactive is varying.

Author

Navin Baskar

Author

Skill-Lync

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