What is the Power?

Before delving into active power, let's first understand the basic concept of power. Power refers to the rate of doing work or the rate at which energy is transferred from one system to another. In electrical circuits, power is defined as the rate at which electrical energy is transferred by a circuit and is measured in watts (W). The instantaneous power in any electrical circuit is given by the product of instantaneous voltage and current as:

Power (P) = Voltage (V) × Current (I) 

In direct current (DC) circuits, power can be computed directly using the above formula since voltage and current remain constant with time. However, in alternating current (AC) circuits, the voltage and current waveforms vary continuously with time. This leads to the classification of power terms in AC like active power, reactive power, and apparent power based on their phase relations.

True power, also known as active power or real power, refers to the power that is actually consumed or utilized in an AC circuit. This is the power that effectively operates the electrical circuits or loads within a system. It is measured in kilowatts (kW) or megawatts (MW) and represents the actual output of the electrical system.

Since resistance offers no opposition to current flow, the current through a resistor leads or lags the applied voltage by zero phase angle. As a result, the active power expression for a resistive AC circuit reduces to:

True power = voltage x current in phase with the voltage

Or

Active Power (P) = Voltage (V) × Current (I) × Power Factor (PF)

\(P = VI\cos \phi\) 

 =V × I (for resistive circuits where θ = 0°)

Where, θ is the phase angle between the voltage and current waveforms. For a purely resistive circuit, θ is zero degrees since voltage and current remain in phase. Thus, the active power formula is simply the product of RMS voltage and current.

Types of Power

There are three main types of power parameters defined in AC systems based on their phase relationships:

• Active Power or Real Power (P): As discussed above, it is the portion of supplied power that is consumed or used to perform work. Measured in Watts (W).
• Reactive Power (Q): It is the portion of supplied power that oscillates between source and load due to their phase difference but is not consumed in the load. Measured in Volt-Amperes Reactive (VAR).
• Apparent Power (S): It is the total power supplied by the source and is equal to the vectorial sum of active and reactive powers. Measured in Volt-Amperes (VA).

The relationships between these three power parameters can be better understood using the power triangle as shown below:

Formula of Active Power

This power triangle diagram illustrates that the Apparent Power S is the hypotenuse of the right triangle formed by the Active Power P and Reactive Power Q vectors. It helps visualize their phase relationships in AC circuits.

Fig- Power Triangle

For a single-phase AC circuit with sinusoidal voltage and current waveforms given by:

Voltage (V) = VmSin(ωt)
Current (I) = ImSin(ωt - θ)

Where,
Vm = Peak Voltage amplitude
Im = Peak Current amplitude
ω = Angular frequency
θ = Phase angle between V and I

Using the definition of active power as the product of instantaneous voltage and current, the average active power formula derived is:

\(P= \left ( 1/T \right )\int v\left ( t \right )i \left ( t \right )dt\)

\(= \left ( 1/2 \right )V_{m}I_{m}\cos \phi\) 

\(= VI\cos \phi\) 

Thus, the final RMS active power formula for a single-phase AC circuit is:

Active Power (P) = VRMS × IRMS × Cosθ 

Where, VRMS and IRMS are the Root Mean Square (RMS) values of the voltage and current waveforms.

Features of Active Power

Some key features of active power include:

• Measured in watts (W) and commonly in kilowatts (kW) or megawatts (MW).
• It is the real power consumed or utilized in a load circuit to produce heat, light, motion etc.
• Accounts for 100% of the supplied power in pure resistive circuits when power factor is unity (Cosθ = 1).
• Always flows in the same direction from source to load and does mechanical work.
• Does not change direction periodically unlike reactive power.
• Can be measured using an ordinary wattmeter which integrates instantaneous power over time.

Measurement of Active Power in AC Circuits

Active power in AC circuits is measured using a wattmeter, which calculates the average power over time. The wattmeter integrates the product of voltage and current waveforms in real-time to give a reading in watts.

In single-phase circuits, a single wattmeter is sufficient. In three-phase systems, depending on the connection (balanced or unbalanced), one of the following methods is used:

• One-Wattmeter Method: For balanced loads with known power factor.
• Two-Wattmeter Method: Standard method for balanced or unbalanced three-phase loads.
• Three-Wattmeter Method: Used when all phase voltages and currents are measured separately.

Table: Wattmeter Methods for Active Power Measurement

Difference between Active Power and Reactive Power

The key differences between active and reactive power are:

• Active power (P) does actual work whereas reactive power (Q) is periodically interchanged between source and load.
• P is measured in watts (W) and contributes to energy usage billing. Q is measured in volt-ampere reactive (VAR) and does not represent real energy usage.
• In resistive circuits, P accounts for 100% of the total power while Q is zero. However, in most loads both P and Q are present.
• Improving power factor (by reducing Q) leads to lower currents and distribution costs without affecting work output.

Power Factor and Its Effect on Active Power

In AC circuits, the power factor plays a vital role in determining how effectively electrical power is converted into useful work. It is defined as the cosine of the angle between the voltage and current waveforms, denoted as Cosθ. A power factor of 1 (or unity) means the circuit is purely resistive, and all the supplied power is converted into active power.

However, when the power factor is low (due to inductive or capacitive loads), more current is required to deliver the same active power. This leads to higher losses and inefficient operation. Therefore, improving power factor enhances power delivery and reduces energy wastage.

Table: Effect of Power Factor on Active Power

Power and Current Relations

From the basic circuit theory, we know:

Current (I) = Power (P) / (Voltage (V) × Power Factor (PF))
= P / (V × Cosθ)

Taking the active power expression, P = VIcosθ, we get:

I = P / (V × Cosθ)
= P / (V × Cosθ × Cosθ)
= P / (V × Cos2θ)

This clearly shows that the circuit current is inversely proportional to the power factor Cosθ. For a given load demand (P), a lower power factor implies higher circuit current (I) for the same voltage (V).

Therefore, improving the power factor helps reduce line/circuit currents and associated power losses. This is a important consideration while designing efficient power systems and motor drives.

Active Power in Three-Phase Systems

Three-phase AC systems are widely used in industrial and power transmission networks. In such systems, active power is delivered across three alternating voltage and current phases. Unlike single-phase circuits, three-phase circuits offer more stable power flow and higher efficiency.

Active power in a balanced three-phase system is calculated using the following formula:

P = √3 × VL × IL × Cosθ

Where:

• P is active power (in watts),
• VL is the line voltage,
• IL is the line current,
• Cosθ is the power factor.

Table: Active Power in 1-Phase vs 3-Phase Systems

Importance of Active Power in Electrical Machines

Active power is directly responsible for the functioning of electrical machines like motors and generators. In motors, it is the portion of power converted into mechanical energy to drive mechanical loads like fans, pumps, or conveyors. For generators, it represents the useful energy output supplied to the load.

Machines are typically rated based on their active power capacity in kilowatts (kW) or horsepower (HP), not on apparent or reactive power. Therefore, ensuring that a machine receives sufficient active power is crucial for optimal performance.

Proper power factor correction in motor circuits ensures maximum active power availability and helps reduce overloading of the supply system.

Conclusion

Active power or real power is theportion of supplied power that is consumed and utilized in a load circuit, while the remaining power cycles between source and load without doing work. Its accurate determination and improvement of power factor are important parameters for efficient power system design and operation.

This article concludes all the information related to Active Power, which helps to propel your preparation for various AE/JE examinations. To boost your preparation, you should test yourself through a series of Mock Tests for Electrical Engineering Exams. You can check the syllabus for the AE/JE exam. You can visit the Testbook app to keep yourself updated with all the exam-oriented information related to the upcoming examinations, including GATE Electrical, SSC JE, ESE, RRB JE, and state AE/JE Electrical exam.