TEL202 — Applied Electricity II: Lecture Note

About this lecture note

This is the complete lecture note for TEL202 Applied Electricity II. You can read it online below, open it in the full viewer, or download the PDF for offline study. It pairs with the course's video lectures, so you can read and watch together.

Preview: opening of the note

Course code: TEL 202 Course title: Applied Electricity II Course credit load: 3 Units Series 1: AC Power, Power Factor, Resonance, and Three-Phase Circuits • Part 1.1: Power in AC Circuits o Sub Part 1.1.1: Active, reactive, and apparent power in an AC circuit o Sub Part 1.1.2: The power triangle o Sub Part 1.1.3: Power factor and its improvement • Part 1.2: Resonance in RLC Series Circuits o Sub Part 1.2.1: Introduction to resonance in an RLC series circuit o Sub Part 1.2.2: Resonant frequency and Q-factor of a series RLC circuit o Sub Part 1.2.3: Bandwidth and selectivity of a series RLC circuit • Part 1.3: Resonance in RLC Parallel Circuits o Sub Part 1.3.1: Introduction to resonance in an RLC parallel circuit o Sub Part 1.3.2: Resonant frequency and dynamic resistance of a parallel RLC circuit o Sub Part 1.3.3: Comparison of series and parallel resonance • Part 1.4: Three-Phase Voltages and Connections o Sub Part 1.4.1: Voltages of a balanced three-phase system o Sub Part 1.4.2: The star-connected three-phase system o Sub Part 1.4.3: The delta-connected three-phase system • Part 1.5: Line-Phase Relationships and Phasor Diagrams o Sub Part 1.5.1: Relationship between line and phase quantities in a star-connected system

o Sub Part 1.5.2: Relationship between line and phase quantities in a delta-connected system o Sub Part 1.5.3: Phasor diagrams for three-phase systems Introduction This course builds on the foundations of basic electrical principles to examine more advanced topics in applied electricity. This first Series addresses power in AC circuits and power factor, resonance in series and parallel RLC circuits, and the analysis of balanced three-phase circuits, forming the essential groundwork for the machines, transformers, and power systems topics that follow later in this course. The aim of this Series is to equip you with a sound understanding of power in AC circuits and power factor, the condition and characteristics of resonance in series and parallel RLC circuits, and the voltages, connections, and phasor relationships of balanced three-phase systems. We shall commence this Series by examining active, reactive, and apparent power and power factor. Next, we will consider resonance in series RLC circuits, followed by resonance in parallel RLC circuits. Following that, our attention turns to the voltages and connections of balanced three-phase systems. Finally, we will conclude by examining the relationship between line and phase quantities and the use of phasor diagrams. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1: calculate the active, reactive, and apparent power in an AC circuit, • SLO 1.2: explain the significance of power factor and the methods used to improve it, • SLO 1.3: analyse the condition for resonance in a series RLC circuit, • SLO 1.4: calculate the Q-factor and bandwidth of a series RLC circuit, • SLO 1.5: analyse the condition for resonance in a parallel RLC circuit, • SLO 1.6: compare the characteristics of series and parallel resonance, • SLO 1.7: describe the star-connected and delta-connected three-phase systems, • SLO 1.8: calculate the voltages of a balanced three-phase system, • SLO 1.9: calculate the line and phase quantities in star- and delta-connected systems,

• SLO 1.10: construct phasor diagrams for three-phase systems. 1.1 Power in AC Circuits 1.1.1 Active, reactive, and apparent power in an AC circuit Active power (P), also called real or true power, is the power actually converted into useful work or heat in an AC circuit, given by P = VI cosφ, measured in watts (W), and represents the portion of the supplied power that performs genuinely useful work in the load. Unlike in a purely resistive DC circuit, where the simple product of voltage and current already gives the true power, an AC circuit containing inductance or capacitance introduces a phase difference φ between voltage and current that must be accounted for using the cosine term. Apparent power (S) is the simple product of the RMS voltage and current, S = VI, measured in volt-amperes (VA), without any regard to the phase angle between them, while reactive power (Q) is the power that oscillates back and forth between the source and the reactive elements of the circuit without being converted into useful work, given by Q = VI sinφ, measured in reactive volt-amperes (VAR). Together, active, reactive, and apparent power describe the complete power behaviour of an AC circuit, and an electrical engineer must be equally comfortable calculating all three. Worked example: A single-phase load draws 15 A from a 230 V supply at a phase angle of 25°; the apparent power is S = VI = 230 × 15 = 3450 VA, the active power is P = VI cosφ = 3450 × cos25° ≈ 3127 W, and the reactive power is Q = VI sinφ = 3450 × sin25° ≈ 1458 VAR. Application: Electricity supply networks must be sized to carry the full apparent power drawn by every connected load, even though only the active power performs useful work, which is why apparent power, not active power alone, determines the required rating of cables, transformers, and generators throughout a power system. Fill in the blank: Active power in an AC circuit is given by P = VI × ________. Apparent power is measured in the SI unit called the ________. 1.1.2 The power triangle The power triangle is a right-angled triangle representation of the relationship between active power, reactive power, and apparent power, with active power P drawn along the horizontal side, reactive power Q drawn along the vertical side, and apparent power S forming the hypotenuse, related by the Pythagorean relationship S² = P² + Q². The angle φ between the active power side and the apparent power hypotenuse is the same phase angle between voltage and current in the circuit, so that tanφ = Q/P. Constructing the power triangle for a given circuit provides an immediate, intuitive graphical check on any power calculation, since the three quantities must always satisfy S² = P² + Q²

regardless of how each was individually calculated, and errors in a calculation often become obvious once the values are plotted and clearly fail to form a consistent right-angled triangle. Worked example: A circuit has an active power of 3127 W and a reactive power of 1458 VAR; the apparent power from the power triangle is S = √(P²+Q²) = √(3127²+1458²) ≈ 3452 VA, confirming, to within rounding, the value obtained directly from S = VI in the previous example. Application: The power triangle is used routinely to determine how much reactive power a capacitor bank must supply to correct a circuit's power factor to a desired target value, a calculation examined further in the next sub-Part. Fill in the blank: In the power triangle, apparent power S is related to active power P and reactive power Q by S² = P² + ________. The angle φ in the power triangle satisfies tanφ = ________/P. 1.1.3 Power factor and its improvement Power factor (pf) is the ratio of active power to apparent power, pf = P/S = cosφ, a dimensionless number between 0 and 1 that indicates how effectively a load converts the supplied apparent power into useful active power, with a lagging power factor typical of inductive loads such as motors and transformers, and a leading power factor typical of capacitive loads. Improving a low power factor, most commonly achieved by connecting capacitors in parallel with an inductive load, supplies leading reactive power that cancels some or all of the load's lagging reactive power, reducing the net reactive power, and hence the total current, that the source must supply for the same active power delivered. A higher power factor consequently reduces I²R losses in cables and transformers and allows existing electrical infrastructure to supply more useful load without being overloaded. Worked example: A factory drawing 150 A at a power factor of 0.72 could, if the power factor were corrected to 0.96, draw only 150 × (0.72/0.96) = 112.5 A for the same active power delivered, a substantial reduction in current and the associated I²R losses throughout the installation. Application: Because many electricity tariffs charge a financial penalty when a consumer's power factor falls below a specified threshold, typically around 0.9, power factor correction is usually justified on direct financial grounds, in addition to its purely technical benefits. Fill in the blank: Power factor is defined as the ratio of active power to ________ power. Power factor correction typically involves connecting ________ in parallel with an inductive load.

Figure 1.1: The power triangle showing the relationship between active, reactive, and apparent power. Pilot questions 1.1 1. State the formula for active power in an AC circuit. (Linked to SLO 1.1) 2. State the formula for reactive power in an AC circuit. (Linked to SLO 1.1) 3. State the relationship between P, Q, and S in the power triangle. (Linked to SLO 1.1) 4. Define power factor. (Linked to SLO 1.2) 5. Calculate the current drawn by a load corrected from a power factor of 0.72

This is the opening of the note. Read the full note or download the PDF to continue.