3. MEASUREMENT OF ELECTRIC POWER (EE3003)

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3. MEASUREMENT OF ELECTRIC POWER

3.1 Dynamometer Type Wattmeter: Construction and Working

• Construction:

  • A dynamometer type wattmeter is used to measure the active power in a circuit. It consists of two coils: a current coil (which carries the current) and a potential coil (which is connected in parallel with the load to sense the voltage).
  • The current coil is usually a fixed coil, while the potential coil is a moving coil, mounted on a spindle and connected to a pointer. The instrument also has a spring that provides restoring force to the moving coil.
  • The instrument is designed so that the deflection of the pointer is proportional to the power being measured.

• Working:

  • The current coil carries the current to be measured, and the potential coil is connected across the load, where the voltage is measured.
  • The interaction between the magnetic fields created by the two coils produces a torque that causes the movement of the pointer. The deflection of the pointer on the calibrated scale represents the active power.
  • Deflection is given by: $$P = V \times I \times \cos(\theta)$$ where $P$ is the active power, $V$ is the voltage, $I$ is the current, and $\theta$ is the phase angle between the current and the voltage.

• Salient Features:

  • Suitable for both AC and DC measurements.
  • Highly accurate for measuring real (active) power in various systems.
  • Can be used for both single-phase and three-phase systems.

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3.2 Range: Multiplying Factor and Extension of Range Using CT and PT

• Range of Wattmeter:

  • The range of a wattmeter refers to the maximum power it can measure. This range is determined by the number of turns in the coils and the size of the meter.

• Multiplying Factor:

  • The multiplying factor (MF) of a wattmeter is used to extend the range of the instrument. It accounts for the scale of the measurement and is defined as the ratio of the full-scale reading to the actual power.
  • It can be used to adjust the meter’s output for use in various voltage and current ranges.
  • MF formula: $$\text{Multiplying Factor} = \frac{V \times I}{\text{Scale reading}}$$

• Extension of Range Using CT and PT:

  • CT (Current Transformer) and PT (Potential Transformer) can be used to extend the range of the wattmeter by reducing the high current or high voltage to a manageable level for the wattmeter.

    • Current Transformer (CT): Used to reduce the current. The primary side of the CT is connected in series with the load, and the secondary is connected to the current coil of the wattmeter.
    • Potential Transformer (PT): Used to reduce the voltage. The primary side of the PT is connected across the load, and the secondary side is connected to the potential coil of the wattmeter.

  • By using CT and PT, the wattmeter can measure very high power values without being overloaded. The power measured will be the product of the current and voltage in the secondary side of the transformers, which is then scaled up using the respective multiplying factors.

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3.3 Errors and Compensations

• Types of Errors in Wattmeters:

  • Instrumental Errors: Errors due to the inherent imperfections in the design and construction of the wattmeter, such as friction in the moving parts and zero error.
  • Connection Errors: Errors caused by incorrect connections of the coils or faulty wiring.
  • Magnetic Errors: Errors resulting from magnetic flux leakage or non-linearity in the magnetic core.
  • Power Factor Errors: Errors caused by the phase difference between voltage and current, especially if the system has a low power factor.
  • Temperature Effects: Variations in temperature can affect the resistance of the coils, leading to errors.

• Compensation Methods:

  • Zero Adjustment: A zero-adjustment screw can be used to eliminate any initial deflection of the needle (zero error).
  • Damping Mechanism: To minimize mechanical oscillations or vibrations in the moving coil, a damping mechanism (often a metallic vane in air) is used.
  • Correcting for Power Factor: Use power factor correction devices or compensating circuits when measuring circuits with low power factors. Alternatively, ensure the measurement is done at standard operating conditions.
  • Temperature Compensation: Using materials with low temperature coefficients for coils or compensating for known temperature effects on the instrument.

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3.4 Active and Reactive Power Measurement: One, Two, and Three Wattmeter Method

• Active Power Measurement:

  • Active power is the real power consumed by the load, and it is measured using a wattmeter. In a single-phase system, the active power can be measured directly. For a three-phase system, active power can be measured using multiple wattmeters, depending on the system configuration.

• Reactive Power:

  • Reactive power is the power that oscillates between the source and load without performing any useful work (measured in VARs – Volt-Ampere Reactive). It is associated with inductive and capacitive loads.

One-Wattmeter Method (for Single-Phase Systems):

• In a single-phase system, active power is directly measured using one wattmeter. This is a straightforward method, where the wattmeter is connected across the load, and the power is read from the scale.

Two-Wattmeter Method (for Three-Phase Systems):

• For a balanced three-phase load, the two-wattmeter method is commonly used.
• Working: Two wattmeters are connected to the two lines (typically between two phases in a three-phase system) to measure the power. The total power is the sum of the readings of the two wattmeters.
  • Formula: $$P_{total} = W_1 + W_2$$ where $W_1$ and $W_2$ are the readings of the two wattmeters.
• This method can be used for both star-connected and delta-connected systems.

Three-Wattmeter Method (for Unbalanced Loads):

• The three-wattmeter method is used when the system is unbalanced (i.e., when the loads are not equally distributed in the three phases).
• Three wattmeters are used to measure the active power in each of the three phases. This method works for both balanced and unbalanced loads.
• The total active power is the sum of the three wattmeter readings: $$P_{total} = W_1 + W_2 + W_3$$
• This method can also be used to measure the power factor and reactive power if the readings are combined appropriately.

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Summary

• Dynamometer type wattmeters measure active power by using two coils: current and potential coils. They are accurate for AC and DC measurements but can have various types of errors, such as power factor and temperature effects, which can be compensated for.
• The range extension of wattmeters can be achieved using CTs (Current Transformers) and PTs (Potential Transformers), which scale down high currents or voltages for the wattmeter to handle.
• Different methods such as the one, two, and three-wattmeter methods are used for measuring active and reactive power in single-phase and three-phase systems.