Problem 12 - Applied Physics

Question

Find the power factor of a generating station whose apparent power is \(645,000 \mathrm{kVA}\) and whose actual power is \(587,000 \mathrm{~kW}\).

Step-by-Step Solution

Answer

The power factor is 0.91.

Step 1: Understand the Power Factor Formula

The power factor (PF) is the ratio of actual power (real power) to apparent power in an electrical circuit. It can be expressed using the formula: \[ \text{Power Factor} (\text{PF}) = \frac{\text{Real Power} (P)}{\text{Apparent Power} (S)} \] where the real power is measured in kilowatts (kW) and the apparent power is measured in kilovolt-amperes (kVA).

Step 2: Identify the Values

From the problem, we have the real power \( P = 587,000 \, \text{kW} \) and the apparent power \( S = 645,000 \, \text{kVA} \).

Step 3: Calculate the Power Factor

Use the formula to calculate the power factor: \[ \text{PF} = \frac{587,000}{645,000} \] Simplifying this gives: \[ \text{PF} = 0.91 \]

Step 4: Interpret the Result

A power factor of 0.91 means that 91% of the power is being effectively converted into real work. The rest is reactive power, which does not perform any actual work in the system.

Key Concepts

Apparent Power

Apparent power is a key concept in electrical circuits, representing the total power flow in the system. It's not just the power used for productive work, but the combination of different power types.

• Measured in kilovolt-amperes (kVA).
• Combines both real and reactive power.

It reflects the overall power produced, including what might be lost or stored temporarily in the electrical system. When you see a generator rated in kVA, it indicates the apparent power capacity rather than the usable power output.

Real Power

Real power, sometimes called actual power, is the power component in an electrical circuit that performs the actual task.

• Measured in kilowatts (kW).
• Represents the energy used to do actual work.

Real power is the portion of power that is effectively converted into useful work output, such as lighting your home or powering machines. It's important because it tells how efficiently the electrical energy is being utilized.

Reactive Power

Reactive power deals with the stored energy in the system that doesn't directly contribute to performing work but is necessary for maintaining the voltage stability.

• Measured in reactive volt-amperes (kVAR).
• Enables the system to maintain the correct voltage levels for the safe operation of electrical equipment.

Unlike real power, reactive power is not used for actual work but ensures efficient functioning of the circuit. It's like the power that makes sure all equipment runs smoothly without affecting their operational efficiency.

Electrical Circuits

Electrical circuits are the pathways through which electricity flows, consisting of various electrical elements like resistors, capacitors, and inductors.

• Include components that either consume, store, or release electrical energy.
• Follow laws of physics to guide the flow and distribution of electrical power.

Understanding electrical circuits is critical for grasping the concepts of power like apparent, real, and reactive power. These concepts help us design, operate, and troubleshoot electrical systems efficiently to ensure reliable power supply.