Lab Report - Ac Power Factor

LAB REPORT APPLIED PHYSICS COURSE UNIVERSITY OF CINCINNATI Name / ID : Michael Kurniawan / 2018123456 Department : Bachelor of Electrical Practicum Date : November 10, 2023 Engineering AC POWER FACTOR A. Objective To determine the alternating current (AC) power factor both theoretically and experimentally. B. Theoretical Basis In an alternating current circuit, the power absorbed by the circuit is defined as follows: 𝑃 = 𝑉eff ⋅ 𝐼eff ⋅ cos 𝜙 … … … … … (1) with the following explanations: • 𝑃 = actual power measured on a wattmeter (Watts) • 𝑉eff = effective voltage measured on a voltmeter = 𝑉rms [Volt] • 𝐼eff = effective current measured on an ammeter = 𝐼rms [Ampere] • cos 𝜙 = alternating current power factor, = slope of the curve between P and 𝑉eff ⋅ 𝐼eff . The phase angle difference (ϕ) between current and voltage in an alternating current (AC) circuit, also known as the power factor, can also be determined using the following equation: tan 𝜙 = with the following explanations: • 𝑅= circuit resistance [Ω] • 𝑋𝐿 = inductive reactance, formulated as: 𝑋𝐿 = 2𝜋𝑓𝐿[Ω] • 𝑋𝐶 = capacitive reactance, formulated as: 𝑋𝐶 = • 𝑓= alternating current frequency [Hz] • 𝐿= coil inductance or inductor [𝐻𝑒𝑛𝑟𝑦] • 𝐶= capacitor capacitance [𝐹𝑎𝑟𝑎𝑑] 1 [Ω] 2𝜋𝑓𝐶 𝑋𝐿 − 𝑋𝐶 … … … … … … … (2) 𝑅 C. Preliminary Assignment 1. Explain the meaning of power factor in an alternating current (AC) circuit! The power factor is the ratio of average power to apparent power in an alternating current circuit. The power factor indicates the phase angle between active power and apparent power. • Active power is the power that is actually used to operate an electrical load (e.g., a lamp, motor, or electronic device). • Apparent power is the total power generated by the presence of resistive, inductive, and capacitive elements in an electrical circuit. Ideally, the power factor has a maximum value when : cos⁡ 𝜙 = 1 A good power factor value is generally above 0.95. The ratio between actual power (𝑃eff )⁡and apparent power (𝑃sm )⁡is formulated as:: cos⁡ 𝜙 = 𝑃eff 𝑃sm or can be derived as: cos⁡ 𝜙 = 𝐼2 𝑅 𝑅 = 𝐼2𝑍 𝑍 Meanwhile, the relationship between power, voltage, current, and power factor is expressed as: 𝑃 = 𝑉 𝐼 cos⁡ 𝜙 with the following explanations: • 𝑃= apparent power (Watts) • 𝑉= effective voltage (Volts) • 𝐼= effective current (Amperes) • cos 𝜙= power factor 2. What is the maximum power factor value? What is the condition when this phenomenon occurs? The maximum or ideal power factor value occurs when: cos⁡ 𝜙 = 1 This condition is called unity power factor. In this state, the electric current is in phase with the voltage, meaning there is no phase shift between the two. Unity power factor occurs in purely resistive loads, where all the power supplied from the source is converted into active power without energy loss in the form of inductive or capacitive reactance. Mathematically, this condition is achieved when: 𝑍 = 𝑅 ⇒ maximum⁡power⁡factor⁡or 1 3. Prove formula (1) from the definition of instantaneous voltage and current! 𝑃(𝑡) = 𝑉(𝑡) ⋅ 𝐼(𝑡) Where: 𝑉(𝑡) = 𝑉rms ⋅ √2 ⋅ cos⁡(𝜔𝑡) 𝐼(𝑡) = 𝐼rms ⋅ √2 ⋅ cos⁡(𝜔𝑡 − 𝜑) Then: 𝑃(𝑡) = 𝑉rms ⋅ √2 ⋅ cos⁡(𝜔𝑡) ⋅ 𝐼rms ⋅ √2 ⋅ cos⁡(𝜔𝑡 − 𝜑) = 2 ⋅ 𝑉rms ⋅ 𝐼rms ⋅ cos⁡(𝜔𝑡) ⋅ cos⁡(𝜔𝑡 − 𝜑) Use the trigonometric identity: cos⁡ 𝐴 ⋅ cos⁡ 𝐵 = cos⁡ 𝜑 ⋅ cos⁡2 (𝜔𝑡) + sin⁡ 𝜑 ⋅ sin⁡(𝜔𝑡) ⋅ cos⁡(𝜔𝑡) So: 𝑃(𝑡) = 2 ⋅ 𝑉rms ⋅ 𝐼rms ⋅ (cos⁡ 𝜑 ⋅ cos⁡2 (𝜔𝑡) + sin⁡ 𝜑 ⋅ sin⁡(𝜔𝑡) ⋅ cos⁡(𝜔𝑡)) Use the identities: cos⁡2 (𝜔𝑡) = 1 + cos⁡(2𝜔𝑡) sin⁡(2𝜔𝑡) , sin⁡(𝜔𝑡) ⋅ cos⁡(𝜔𝑡) = 2 2 Then: 1 + cos⁡(2𝜔𝑡) sin⁡(2𝜔𝑡) 𝑃(𝑡) = 𝑉rms ⋅ 𝐼rms ⋅ (cos⁡ 𝜑 ⋅ + sin⁡ 𝜑 ⋅ ) 2 2 cos 𝜑 1 1 𝑃(𝑡) = 𝑉rms ⋅ 𝐼rms ⋅ ( + ⋅ cos⁡(2𝜔𝑡) ⋅ cos⁡ 𝜑 + ⋅ sin⁡(2𝜔𝑡) ⋅ sin⁡ 𝜑) 2 2 2 𝑃(𝑡) = 𝑉rms ⋅ 𝐼rms ⋅ ( cos 𝜑 1 + ⋅ cos⁡(2𝜔𝑡 − 𝜑)) 2 2 Explanation: • • • 𝑃 = 𝑉eff ⋅ 𝐼eff ⋅ cos⁡ 𝜑 𝜑= phase angle between voltage and current cos 𝜑= power factor 4. In alternating current equipment such as electric motors, fluorescent lights, etc., there is inductive and capacitive reactance that causes the power factor to be less than 100%. Does this condition have economic significance? Explain! Inductive and capacitive reactance cause the current to shift phase relative to the voltage. This shift causes the power factor to be less than 1. This means that the actual power used is less than the apparent power. As a result: • • • The current flowing is greater than that needed to produce the same power Energy is wasted It is not economical Solution: To improve efficiency and reduce waste, power factor correction must be performed by adding appropriate capacitors or inductors so that the power factor approaches 1. Benefits of power factor correction: • • • Reduces electricity costs Improves system efficiency Very important in industrial electrical installations D. Tools 1. 2. 3. 4. 5. Wattmeter Ammeter, Voltmeter Low-voltage AC power supply 1000-turn coil, 36 mH, 9.8 Ω Several resistors (10, 20, 40, 80 Ω) and capacitors (1000 μF) 6. Cables E. Experiment 1. Room Data 2. Assemble the equipment as shown in the figure. Change the AC voltage, then record the readings of the voltmeter (Vₐₜ), ammeter (Iₐₜ), and wattmeter (Pₐₜ). 3. Perform experiment 2, but connect the coil in series with a specific resistor and capacitor. Circuit constants: R=9.5" Ω L=36“ mH” C=1000“ μ”F" R=10" Ω Experiment results (minimum 10 data points): 4. Conduct experiments to determine the specific values of R, L, and C (in series) that 𝑃 produce the maximum value of 𝑃 eff . teor