Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Define and differentiate between real, reactive, and apparent power.
• Represent P, Q, and S using the power triangle.
• Calculate power factor (PF) and explain its significance.
• Explain the causes and consequences of poor power factor.
• Describe the principles of power factor correction using capacitors.

Lesson summary

Welcome, Grade 12 Electrical Technology students, to a fascinating journey into the world of Advanced AC Theory and Power Factor Correction! This isn't just abstract theory; it's the foundation of how our electrical grid functions and how efficiently we use electricity in South Africa. From powering our homes and businesses to driving our industries and essential services, understanding AC power and power factor correction is crucial. Poor power factor leads to wasted energy, increased electricity bills, and strain on the national grid - issues that directly impact the economy and sustainability of our country.

Lesson notes

2.1 AC Power: Real, Reactive, and Apparent Power In a purely resistive AC circuit, voltage and current are in phase, and power is simply the product of voltage and current (P = V I). This is real power (P), also known as active power, measured in watts (W). It’s the power actually consumed by the load and used to do work (e.g., heating, lighting, mechanical work).

However, most AC circuits in the real world contain inductive (e.g., motors, transformers) or capacitive (e.g., capacitors, long cables) components. These components introduce a phase shift between voltage and current.

Inductive Loads: Inductors cause the current to lag behind the voltage.

Capacitive Loads: Capacitors cause the current to lead the voltage. This phase difference (represented by the angle θ, measured in degrees) introduces two new types of power: Reactive Power (Q): Reactive power is the power that is constantly exchanged between the source and the reactive components (inductors and capacitors) in the circuit. It is measured in volt-amperes reactive (VAR). Reactive power does not do useful work; it merely circulates in the circuit, placing an extra burden on the generation and distribution system. Q = V I * sin(θ)

Apparent Power (S): Apparent power is the vector sum of real power (P) and reactive power (Q). It is the total power supplied by the source, regardless of how much of it is actually used to do work. It is measured in volt-amperes (VA). S = V I 2.2 The Power Triangle The relationship between real power (P), reactive power (Q), and apparent power (S) can be visually represented by the power triangle. The base of the triangle represents real power (P). The height of the triangle represents reactive power (Q). The hypotenuse represents apparent power (S). The angle between the real power (P) and apparent power (S) is the phase angle (θ). Using the Pythagorean theorem and trigonometric functions: S = √(P² + Q²) P = S cos(θ) Q = S sin(θ) tan(θ) = Q/P 2.3 Power Factor (PF) Power factor (PF) is defined as the ratio of real power (P) to apparent power (S): PF = P/S = cos(θ) A power factor of 1 (or 100%) indicates that all the apparent power is being used as real power, meaning voltage and current are perfectly in phase. A power factor less than 1 indicates that some of the apparent power is reactive power, and the circuit is less efficient. Power factors are usually quoted as either "lagging" (for inductive loads) or "leading" (for capacitive loads). Most industrial loads are inductive, resulting in a lagging power factor. 2.4 Causes of Poor Power Factor Inductive Loads: As mentioned, motors, transformers, and other inductive devices are the primary cause of lagging power factor.

Under-loaded Motors: Motors operating significantly below their rated capacity draw more reactive power than necessary.

Harmonic Currents: Non-linear loads (e.g., electronic devices, variable speed drives) can generate harmonic currents, which distort the current waveform and reduce power factor. 2.5 Consequences of Poor Power Factor Increased Current: For the same amount of real power delivered, a lower power factor means higher current is required. This necessitates larger conductors and equipment to handle the increased current, increasing infrastructure costs. Think about informal settlements in South Africa that often experience overloaded power lines due to unauthorized connections drawing excessive current. This is partially worsened by poor power factor.

Increased Losses: Higher current leads to increased I²R (copper) losses in transmission and distribution lines, resulting in wasted energy and higher electricity bills.

Reduced Capacity: The increased current demand reduces the capacity of the electrical system to deliver real power to other loads.

Voltage Drop: Increased current causes larger voltage drops in the system, potentially affecting the performance of sensitive equipment.

Penalties from Utility Companies: Utility companies like Eskom often charge industrial customers penalties for maintaining a power factor below a certain threshold (e.g., 0.85 lagging). 2.6 Power Factor Correction Using Capacitors Power factor correction involves adding capacitors to the electrical system to compensate for the reactive power drawn by inductive loads. Capacitors generate leading reactive power, which partially cancels out the lagging reactive power of the inductive loads, improving the overall power factor. The size of the capacitor needed for power factor correction can be calculated as follows: Qc = P (tan(θ1) - tan(θ2))

Where: Qc is the reactive power provided by the capacitor (in VAR). P is the real power (in watts). θ1 is the original phase angle. θ2 is the desired phase angle after correction.