Measurement of power and power factor in a single phase ac series inductive circuit and study of improvement of power factor using capacitor

Experiment Number: 10

Title of The Experiment: –

Measurement of power and power factor in a single phase ac series inductive circuit and study of improvement of power factor using capacitor.

Objectives:

To be written by student.

Apparatus Required: –

Sl. No.NameSpecificationQuantity
1Single-phase auto transformer5KVA, (0-270)V1 Nos.
2Voltmeter(0-250)V, MI1 Nos.
3Watt-meter(0-1500)W, 1 Nos.
4Ammeter(0-5)A, MI1 Nos.
5Rheostat(0-80)Ω, 5A1 Nos.
6Inductor1 Nos.
7Capacitor1 Nos.
8Connecting WiresPVC Insulated CopperAs per required
Table 10.1

Circuit Diagram: –

Fig. No. 10.1 : Circuit diagram for measurement of power and power factor with R-L Load.
Fig. No. 10.2: Circuit diagram for Improvement of power factor.

Theory: –

In R-L series AC circuit a resistor of resistance R ohm, and Inductor of inductance L henry are connected across single phase ac supply of V volts as shown in above fig.

Power consumed by the Inductive load is given by

\[\color\red{P = V I Cos\phi}\] \[ \color\red{Power\; factor\; (Cos\phi) \;= \;\dfrac{P}{VI}}\]

where, P is active power in watt, V is supplied voltage in volts, I is current flowing through the circuit elements in Amp.

thus, by using above formula the power consumed by the load and power factor can be determined.

Procedures: –

  1. Connect all the instruments as per circuit diagram given above.
  2. Before switch on the main power supply make sure that single-phase auto transformer knobe is at zero position.
  3. Now slowly increase the supply voltage to the circuit after giving supply to the single-phase auto-transformer.
  4. Take all the corresponding readings of the connected instruments in the circuit as per observation table.
  5. Now power factor Cosɸ and % error as per formula given in observation table.
  6. Now connect the capacitor in parallel with the R-L load and take readings as per observation table and analyze the power factor. (Fig. No. 10.2)

Precaution: –

  1. Don’t switch on power supply without concerning teacher.
  2. Single phase autotransformer must be kept at minimum potential point before switch on the experiment.

Observation Table: –

Sl. No.V (in volts.)I (in Amp.)P (in watts.)Cosɸ= {P/(V*I)}
1
2
3
4
5
6
7
8
Table 10.2

After Connecting Capacitor in the circuit:

Sl. No.V (in volts.)I (in Amp.)P (in watts.)Cosɸ= {P/(V*I)}
1
2
3
4
5
6
7
8
Table 10.3

Conclusion:

To be written by student.

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For Your Reference: –

In a single-phase AC series inductive circuit,

Power in AC Circuits:
In an AC circuit, power consists of two components: real power (P) and reactive power (Q). Real power represents the actual energy transfer and performs useful work in the circuit. Reactive power represents the energy stored and released by the inductive or capacitive elements in the circuit, without performing useful work.

Formula for Real Power (P):
Real power (P) in an AC circuit can be calculated using the formula:

\[\color{red}{ P = V_{rms} \times I_{rms} \times \cos(\phi)}\] \[\color{green}{Where,}\] \[\color{green}{( V_{rms} ) \;is \;the\; RMS \;(Root Mean Square)}\] \[\color{green}{ voltage \;across\; the \;circuit,}\] \[\color{green}{( I_{rms} ) \;is \;the \;RMS\; current\; flowing\; through \;the\; circuit,}\] \[\color{green}{( \cos(\phi) )\; is \;the\; power\; factor\; (cosine\; of\; the\; phase \;angle\; φ)}\] \[\color{green}{ between\; voltage\; and\; current.}\]

Formula for Power Factor (PF):
Power factor (PF) is the ratio of real power (P) to apparent power (S). It indicates how effectively electrical power is being converted into useful work output. Mathematically:

\[\color{red}{PF = \frac{P}{S}}\] \[\color{green}{Where,}\] \[\color{green}{( P )\; is\; the\; real\; power,}\] \[\color{green}{( S )\; is\; the \;apparent \;power,}\] \[\color{green}{ which \;is \;the \;product\; of\; RMS\; voltage}\] \[\color{green}{ and\; RMS\; current\; without\; considering \;phase \;difference.}\]

Measurement of Power and Power Factor:
To measure power and power factor in a single-phase AC series inductive circuit, you can use various instruments:

  • Wattmeter: It measures real power directly.
  • Voltmeter and Ammeter: These instruments measure RMS voltage and current, respectively, from which you can calculate real power using the formula mentioned above.
  • Power Analyzer: Modern power analyzers can directly measure real power, reactive power, apparent power, and power factor in AC circuits.
  • Power Factor Meter: Specifically measures power factor by comparing the phase difference between voltage and current.

Handling Inductive Circuit:
In an inductive circuit, the current lags behind the voltage by a phase angle (φ). The power factor (cosφ) is less than 1 in an inductive circuit. This lagging power factor can be improved by using capacitors (power factor correction capacitors) in parallel with the load.

Power Factor Improvement using Capacitor:

Improving power factor in an AC circuit, especially inductive circuits, can be achieved by adding capacitors in parallel with the load. This process is known as power factor correction.

Let’s looks into how capacitors help improve power factor:

  1. Understanding Power Factor Correction:
    In an AC circuit, the power factor (PF) is influenced by the phase difference between voltage and current. In inductive circuits, such as those containing motors, transformers, or ballasts, the current lags behind the voltage due to the inductive nature of the load. This lagging current leads to a lower power factor.
  2. Role of Capacitors:
    Capacitors have a reactive power component that is opposite in nature to that of inductors. When capacitors are connected in parallel with the load, they generate a leading current to counteract the lagging current produced by the inductive load. This leads to a more balanced current waveform and an improved power factor.
  3. Effect on Power Factor:
    By adding capacitors, the reactive power drawn from the system decreases, while the real power (which does useful work) remains the same. This results in an increase in power factor towards unity (1). Ideally, power factor correction aims to achieve a power factor as close to 1 as possible.
  4. Calculation and Sizing of Capacitors:
    The amount of capacitance required for power factor correction depends on various factors, including the magnitude of the reactive power, the desired power factor, and the operating conditions of the system. Capacitors are sized to provide the necessary reactive power to offset the reactive power of the load.
  5. Benefits of Power Factor Correction:
  • Reduced energy losses: Improved power factor reduces losses in the distribution system, leading to energy savings.
  • Increased system capacity: Power factor correction can free up capacity in electrical systems, allowing for additional loads to be connected without requiring upgrades.
  • Compliance with regulations: In many regions, utilities impose penalties for low power factor, so correcting it helps avoid these penalties.

Implementation:
Capacitor banks are commonly used for power factor correction. These banks consist of multiple capacitors connected in parallel or series-parallel configurations, depending on the application. Automatic power factor correction systems are also available, which dynamically adjust capacitor switching based on real-time load conditions.

Overall, by adding capacitors in parallel with inductive loads, power factor correction enhances the efficiency and capacity of electrical systems while reducing energy costs and ensuring compliance with regulatory standards.

Viva-voce Questions: –

  1. What is power factor in an AC circuit ?
    Answer: Power factor is the ratio of real power to apparent power in an AC circuit. It indicates how effectively electrical power is being converted into useful work output.

2. How does an inductive load affect power factor ?
Answer: An inductive load, such as a motor or transformer, causes the current to lag behind the voltage in an AC circuit. This lagging current reduces the power factor of the circuit.

3. How is power measured in a single-phase AC series inductive circuit ?
Answer: Power in such a circuit can be measured using instruments like a wattmeter, which directly measures real power, or by using a voltmeter and an ammeter to calculate real power using the formula:

\[\color{red}{( P = V_{rms} \times I_{rms} \times \cos(\phi) )}\] \[\color{green}{where,}\] \[\color{green}{ ( V_{rms} ) \;is \;the\; RMS\; voltage}\] \[\color{green}{( I_{rms} ) \;is \;the\; RMS\; current.}\]

4. What is the significance of power factor in electrical systems ?
Answer: Power factor is crucial for efficient utilization of electrical power. A low power factor can lead to increased energy losses, reduced system capacity, and penalties from utilities. Hence, maintaining a high power factor is essential for minimizing costs and optimizing system performance.

5. How can power factor be improved in a single-phase AC series inductive circuit ?
Answer: Power factor can be improved by adding capacitors in parallel with the inductive load. These capacitors generate a leading current to counteract the lagging current produced by the inductive load, thus improving the overall power factor of the circuit.

6. Define apparent power and reactive power in an AC circuit.
Answer: Apparent power is the product of RMS voltage and RMS current in an AC circuit. It represents the total power consumed by the circuit. Reactive power is the component of apparent power that is due to the reactive elements (inductors or capacitors) in the circuit. It represents the power that oscillates between the source and the load without being consumed.

7. What is power factor correction, and why is it necessary ?
Answer: Power factor correction is the process of improving the power factor of an electrical system, typically by adding capacitors. It’s necessary because a low power factor can result in increased energy losses, reduced system capacity, and penalties from utilities.

8. How do capacitors improve power factor ?
Answer: Capacitors generate a leading current that counteracts the lagging current produced by inductive loads in the circuit. This balances the current waveform, reducing the overall reactive power drawn from the system and improving the power factor.

9. What is the relationship between power factor and capacitors in power factor correction ?
Answer: Capacitors are used in power factor correction to supply reactive power that compensates for the lagging reactive power in the system. By adding capacitors, the system’s reactive power is reduced, leading to an improved power factor.

10. How are capacitors sized for power factor correction ?
Answer: Capacitors are sized based on factors such as the magnitude of the reactive power, the desired power factor, and the operating conditions of the system. They are designed to provide the necessary reactive power to offset the reactive power of the load.

11. What are the benefits of power factor correction using capacitors ?
Answer: Power factor correction using capacitors leads to reduced energy losses, increased system capacity, and compliance with regulatory standards. It also helps in avoiding penalties imposed by utilities for low power factor.

12. Can you explain the difference between leading and lagging power factor ?
Answer: A leading power factor occurs when the current leads the voltage in the circuit, typically due to capacitive loads. A lagging power factor occurs when the current lags behind the voltage, commonly seen in inductive loads. Power factor correction using capacitors aims to shift the power factor closer to unity (1) by introducing a leading component to counteract the lagging component.