Power measurement in three-phase star connected circuit with balanced and unbalanced load using two Wattmeter method

Experiment Number: 11

Title of the Experiment:

Power measurement in three-phase star connected circuit with balanced and unbalanced load using two Wattmeter method.

Objectives:

To be written by student.

Apparatus Required:

Sl. No. NameSpecificationQuantity
1Wattmeter(0-1500)W, 5A/10A, UPF2 Nos.
2Voltmeter(0-250)V, MI1 Nos.
3Ammeter(0-5)A, MI3 Nos.
4Connecting WiresPVC Insulated CopperAs per requirement
5Three-phase Variac(0-500)V, (5A/10A), 1 Nos.
6Rheostat(0-80)Ω, 5A3 Nos.
Table No: 11.1

Circuit Diagram:

Theory:

A watt meter is an instrument for measuring active power directly in a circuit. It has two
coils i.e. current coil & pressure coil. Current coil measures the current through the circuit &pressure coil measures the voltage. Current coil is connected in series & pressure coil in parallel in the circuit. Two wattmeter can be used to measure power in a three phase 3-wire circuit, by making the connections as shown in circuit diagram. The load may be balanced or unbalanced. The current coils are connected in series with two phases and the pressure coils is connected between both phase and the third phase. The total power consumed by the two wattmeter = W1+W2 (algebraic sum).

Here current through the current coil of W1=IR and W2=IB
While potential difference across pressure coil of W1=VRY and W2=VBY

According to the phasor diagram

\[W_1 = V_{RY}I_RCos(30+\theta)\] \[W_2 = V_{BY}I_BCos(30-\theta)\]

Total Power drawn by Three phase load is

\[W_1+W_2\] \[ = V_{RY}I_RCos(30+\theta)+V_{BY}I_BCos(30-\theta)\] \[here Y_{RY} = V_{BY} = V_L\] \[then\] \[ W_1 + W_2 = \sqrt3V_LICos\theta\]

Precautions:

  1. Don’t switch on power supply without concerning respective teachers.
  2. Three phase auto transformer must be kept at minimum potential point before starting.
  3. Resistant value of all rheostats should be kept at maximum position at starting.

Procedures:

(i) Connect all the instruments as per circuit diagram.

(ii) Make sure i. e all instruments are showing zero error.

(iii) After connection, keep the rheostat in maximum position and slowly increase the output voltage of the Variac so that current in each phase is about 1A.

(iv) Then vary the resistance of the rheostats so the load is deliberately unbalanced, i.e. the
current in each phase becomes different.

(v) Calculate the Three-phase power.

Observation Table: for Balance Load

Sl. No.Power in Watts
(W1)		Power in Watts
(W2)		Line Voltage in Volts.
(VL=VRY)		Phase Current in Amp.
(IR)		Phase Current in Amp.
(IY)		 Phase Current in Amp.
(IB)		Total Power in watts.
P=W1+W2
1
2
3
4
5
6
7
Table No: 11.2

Observation Table: for Un-balance Load

Sl. No.Power in Watts
(W1)		Power in Watts
(W2)		Line Voltage in Volts.
(VL=VRY)		Phase Current in Amp.
(IR)		Phase Current in Amp.
(IY)		 Phase Current in Amp.
(IB)		Total Power in watts.
P=W1+W2
1
2
3
4
5
6
7
Table No: 11.3

Conclusion:

To be written by students.

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For your Reference:

In a three-phase AC circuit, electrical power is transmitted or distributed using three alternating currents that are 120 degrees out of phase with each other. This configuration offers several advantages over single-phase systems, including higher power transmission capacity, improved efficiency, and balanced power delivery.

Here’s a breakdown of the theory behind three-phase AC circuits:

Phases and Waveforms:
In a three-phase system, there are three sinusoidal voltage waveforms, typically labeled as phases R, Y, and B. These waveforms are identical in frequency and amplitude but are offset from each other by 120 degrees. As one phase reaches its peak, the others are at different points in their cycle, ensuring a continuous and smooth supply of power.

Generation:
Three-phase power can be generated using a three-phase generator or by using three single-phase generators connected together. In rotating electrical machinery such as alternators or synchronous motors, three-phase power is naturally produced due to the arrangement of the windings.

Balanced Loads:
In an ideal three-phase system, loads are evenly distributed across all three phases. This balanced configuration ensures that the total power demand is evenly spread, minimizing voltage drops and current imbalances. Balanced loads result in efficient power transmission and utilization.

Connection Methods:
Three-phase systems can be connected in either a star (Y) or delta (Δ) configuration. In a star connection, one end of each phase winding is connected together to form a common neutral point, while in a delta connection, the phases are connected end-to-end in a loop. Each configuration has its advantages depending on the application.

Power Calculation:
Power in a three-phase system can be calculated using various formulas. For balanced loads, the total power (P) is the sum of the power in each phase. The formula for calculating power (P) in a balanced three-phase system is:

\[\color{red}{P = \sqrt{3} \times V_{\text{line}} \times I_{\text{line}} \times \cos(\phi) }\] \[\color{green}{Where,}\] \[\color{green}{( V_{\text{line}} ) \;is\; the\; line\; voltage\; (phase voltage),}\] \[\color{green}{( I_{\text{line}} ) \;is \;the\; line\; current,}\] \[\color{green}{( \phi )\; is \;the\; phase\; angle\; between\; voltage\; and\; current.}\]

Applications:
Three-phase AC power is commonly used in industrial and commercial applications for powering machinery, motors, pumps, and other equipment. It is also used in residential settings for large appliances such as air conditioners and electric stoves.

Advantages:
Three-phase power offers several advantages over single-phase systems, including higher power transmission capacity, improved efficiency, smoother power delivery, and reduced conductor size requirements for the same power rating.

Difference Between Three Phase and Single Phase AC Circuit.

Three-phase and single-phase AC circuits differ in several key aspects, including their configuration, power transmission characteristics, applications, and efficiency. Here’s a breakdown of the main differences between the two:

  1. Number of Phases:
  • Single-phase: Single-phase AC circuits consist of one sinusoidal voltage waveform and one current waveform. This configuration is commonly used in residential applications and smaller commercial setups.
  • Three-phase: Three-phase AC circuits consist of three sinusoidal voltage waveforms, each offset by 120 degrees from the others. These circuits are typically used in industrial applications and large commercial setups.

2. Power Transmission:

  • Single-phase: Single-phase circuits are suitable for low to moderate power transmission and are commonly used for lighting, small appliances, and single-phase motors.
  • Three-phase: Three-phase circuits are capable of transmitting higher power levels more efficiently than single-phase circuits. They are used for heavy-duty industrial machinery, motors, pumps, and large-scale commercial applications.

3. Efficiency:

  • Single-phase: Single-phase circuits may suffer from higher losses and voltage drops, especially over long distances or when transmitting high power loads.
  • Three-phase: Three-phase circuits offer improved efficiency due to balanced loads and reduced voltage drops. They are more suitable for high-power transmission over long distances.

4. Applications:

  • Single-phase: Single-phase circuits are commonly found in residential buildings for powering lighting, small appliances, air conditioning units, and single-phase motors.
  • Three-phase: Three-phase circuits are used in industrial settings for powering heavy machinery, motors, compressors, pumps, and other large-scale equipment. They are also used in commercial buildings for large HVAC systems, elevators, and data centers.

5. Voltage and Current Characteristics:

  • Single-phase: In single-phase circuits, voltage and current waveforms peak and reverse polarity at regular intervals. Power delivery fluctuates with each cycle.
  • Three-phase: In three-phase circuits, voltage and current waveforms maintain a steady and balanced flow, resulting in smoother power delivery and reduced fluctuations.

6. Connection Methods:

  • Single-phase: Single-phase circuits typically have two conductors: one for the phase and one for the neutral. Loads can be connected between the phase and neutral.
  • Three-phase: Three-phase circuits can be connected in either a star (Y) or delta (Δ) configuration. Each configuration has its advantages depending on the application’s requirements.

Understanding the differences between three-phase and single-phase AC circuits is essential for designing, installing, and maintaining electrical systems in various settings, from residential buildings to industrial complexes.

Viva-Voce Question: –

  1. What are the advantages of using a three-phase AC circuit over a single-phase AC circuit ?

Answer: There are several advantages of using a three-phase AC circuit over a single-phase AC circuit:

a. Higher Power Transmission Capacity: Three-phase circuits can transmit higher power levels more efficiently compared to single-phase circuits. This is because three-phase systems utilize three alternating currents that are 120 degrees out of phase with each other, providing a continuous and balanced power flow.

b. Efficiency: Due to the balanced nature of three-phase circuits, they experience fewer voltage drops and losses compared to single-phase circuits. This results in improved efficiency, especially over long transmission distances.

c. Balanced Loads: In a three-phase system, loads are evenly distributed across all three phases, leading to balanced current flow. This minimizes voltage fluctuations and ensures stable power delivery to connected loads.

d. Reduced Conductor Size: For the same power rating, three-phase circuits require smaller conductor sizes compared to single-phase circuits. This is because the three-phase system utilizes the space between phases more effectively, reducing the overall size and cost of the conductors.

e. Suitability for Industrial Applications: Three-phase circuits are well-suited for powering heavy machinery, motors, pumps, and other industrial equipment due to their higher power transmission capacity and efficiency. They are commonly used in industrial settings where high-power requirements are prevalent.

f. Flexibility in Connection Methods: Three-phase circuits can be connected in either a star (Y) or delta (Δ) configuration, providing flexibility in system design based on specific application requirements.

2. How is power measured in a three-phase star-connected circuit with balanced and unbalanced loads using the two-wattmeter method ?

Answer: The two-wattmeter method is a commonly used technique for measuring power in a three-phase circuit, particularly in star (Y) connected configurations.

Here’s how power measurement is carried out using this method for both balanced and unbalanced loads:

1. Balanced Load:

Setup:

  • Connect two wattmeters, labeled as W1 and W2, to the three-phase circuit.
  • Connect the phase voltages to the potential coils of the wattmeters.
  • Connect the current coils of each wattmeter in series with one of the phases and the load.
  • Ensure that the load across all phases is balanced, meaning each phase has the same impedance.

Measurement:

Record the readings (W1) and (W2) displayed on each wattmeter.

Total power (Ptotal) in the circuit is given by the sum of the readings of the two watt meters:

Ptotal=W1+W2

This method provides accurate measurement of total power in a balanced three-phase circuit.

2. Unbalanced Load:

Setup:

  • Follow the same setup as for the balanced load.
  • Introduce different impedances or loads across the phases to create an unbalanced condition.

Measurement:

Record the readings (W1) and (W2) displayed on each wattmeter.

Total power (Ptotal) in the circuit is still given by the sum of the readings of the two wattmeters:
Ptotal=W1+W2

Despite the unbalanced load, the two-wattmeter method accurately measures the total power in the circuit by accounting for the individual power contributions from each phase.

Significance:

The two-wattmeter method is advantageous as it can accurately measure power in both balanced and unbalanced three-phase circuits.

It is particularly useful in practical scenarios where loads may not always be perfectly balanced.