Measurement Instruments: Power and Energy Measurement

Two Wattmeter Method for Three-Phase Power Measurement

Measuring power in a three-phase system is crucial for understanding the energy consumption and efficiency of electrical loads. For a balanced or unbalanced three-phase load supplied by a balanced three-phase voltage source, the total power can be accurately determined using only two wattmeters. This method is known as the two-wattmeter method.

The principle behind this method is that the sum of the readings of two wattmeters, properly connected in the circuit, will give the total power for a three-phase, three-wire system. The connection involves placing one wattmeter to measure the power in one phase and the other wattmeter to measure the power in another phase, with their current coils connected in series with the respective phases and their voltage coils connected across the respective phases and the third, un-metered phase.

Connection Diagram and Working Principle

Consider a three-phase load connected to phases R, Y, and B.

• Wattmeter 1 (W1): Its current coil is connected in series with phase R. Its voltage coil is connected between phase R and phase Y.
• Wattmeter 2 (W2): Its current coil is connected in series with phase Y. Its voltage coil is connected between phase Y and phase R.

Let $P_1$ be the reading of W1 and $P_2$ be the reading of W2. The total power $P_{total}$ is given by $P_{total} = P_1 + P_2$.

The instantaneous power in phase R is $v_R i_R$, in phase Y is $v_Y i_Y$, and in phase B is $v_B i_B$. The total instantaneous power is $P(t) = v_R i_R + v_Y i_Y + v_B i_B$. For a balanced system, $v_R + v_Y + v_B = 0$.

The reading of a wattmeter is the average of the instantaneous power. The voltage across the voltage coil of W1 is $v_{RY} = v_R - v_Y$. The current through its current coil is $i_R$. So, $P_1 = \text{Average}(v_{RY} i_R) = \text{Average}((v_R - v_Y) i_R) = \text{Average}(v_R i_R - v_Y i_R)$.

The voltage across the voltage coil of W2 is $v_{YB} = v_Y - v_B$. The current through its current coil is $i_Y$. So, $P_2 = \text{Average}(v_{YB} i_Y) = \text{Average}((v_Y - v_B) i_Y) = \text{Average}(v_Y i_Y - v_B i_Y)$.

Adding $P_1$ and $P_2$: $P_1 + P_2 = \text{Average}(v_R i_R - v_Y i_R + v_Y i_Y - v_B i_Y)$. Using the fact that for a three-wire system, $i_R + i_Y + i_B = 0$, so $i_B = -(i_R + i_Y)$. Also, in a balanced system, $v_R i_R + v_Y i_Y + v_B i_B$ is the total power. It can be shown that $P_1 + P_2 = \text{Average}(v_R i_R + v_Y i_Y + v_B i_B) = P_{total}$.

Advantages and Limitations

• Advantages: Requires only two wattmeters, simpler connection than three wattmeters, can measure power for balanced and unbalanced loads.
• Limitations: The readings can be negative if the power factor is low, requiring a change in voltage coil connection or a subtraction of readings.

Energy Measurement: Energy Meter

An energy meter, also known as a watt-hour meter, is an instrument used to measure the electrical energy consumed by a residence, business, or an electrically powered device. It measures energy in kilowatt-hours (kWh).

The most common type of energy meter is the electromechanical induction type, which operates on the principle of induction. It consists of an aluminum disc mounted on a spindle, which rotates in the magnetic field produced by two electromagnets: a series magnet and a shunt magnet.

Components and Working Principle

• Series Magnet (Current Coil): Wound with a few turns of thick wire, it carries the load current. It creates a magnetic field proportional to the load current.
• Shunt Magnet (Voltage Coil): Wound with many turns of fine wire, it is connected in parallel with the supply. It creates a magnetic field proportional to the supply voltage.
• Aluminum Disc: Placed between the poles of the two magnets, eddy currents are induced in it due to the alternating magnetic fields.
• Braking Magnet: A permanent magnet placed such that the disc rotates in its field. The interaction between the eddy currents and the braking magnet's field produces a braking torque proportional to the speed of the disc.
• Registering Mechanism: A system of gears that counts the number of revolutions of the disc and displays the energy consumed.

The torque produced by the series and shunt magnets causes the disc to rotate. The driving torque is proportional to the product of voltage, current, and the cosine of the phase angle between them (i.e., power). The speed of the disc is proportional to the power consumed. The braking torque is proportional to the speed. Therefore, at a steady speed, the driving torque equals the braking torque. The speed of rotation is directly proportional to the power. The total number of revolutions in a given time is proportional to the total energy consumed.

The energy meter has a constant, often marked as 'Wh/rev' or 'kWh/rev', which indicates how much energy is consumed for one revolution of the disc.

Ammeter and Voltmeter

Ammeters and voltmeters are fundamental measuring instruments used to measure electric current and voltage, respectively.

Ammeter

An ammeter is used to measure the electric current flowing through a circuit. It must be connected in series with the circuit element through which the current is to be measured.

• Ideal Characteristics: An ideal ammeter has zero internal resistance so that it does not affect the circuit's current when connected.
• Practical Ammeter: A practical ammeter has a very low internal resistance. This is achieved by connecting a low resistance called a "shunt resistance" ($R_{sh}$) in parallel with the galvanometer movement.

If $I_m$ is the full-scale deflection current of the galvanometer and $R_m$ is its internal resistance, and we want to measure a maximum current $I$ with a shunt resistance $R_{sh}$, then the current through the galvanometer is $I_m$ and the current through the shunt is $I_{sh} = I - I_m$. Since $R_{sh}$ and $R_m$ are in parallel, the voltage drop across them is the same:

$I_m R_m = I_{sh} R_{sh} = (I - I_m) R_{sh}$

Therefore, the required shunt resistance is: $R_{sh} = \frac{I_m R_m}{I - I_m}$

The range of the ammeter can be extended by changing the value of $R_{sh}$.

Voltmeter

A voltmeter is used to measure the electric potential difference (voltage) between two points in a circuit. It must be connected in parallel across the component whose voltage is to be measured.

• Ideal Characteristics: An ideal voltmeter has infinite internal resistance so that it draws no current from the circuit and does not alter the voltage being measured.
• Practical Voltmeter: A practical voltmeter has a very high internal resistance. This is achieved by connecting a high resistance called a "multiplier resistance" ($R_m$) in series with the galvanometer movement.

If $I_m$ is the full-scale deflection current of the galvanometer, $R_g$ is its internal resistance, and we want to measure a maximum voltage $V$, then the current through the galvanometer is $I_m$. The total resistance of the voltmeter is $R_{total} = R_g + R_m$. According to Ohm's law, $V = I_m R_{total} = I_m (R_g + R_m)$.

Therefore, the required multiplier resistance is: $R_m = \frac{V}{I_m} - R_g$

The range of the voltmeter can be extended by changing the value of $R_m$.

Multimeter

A multimeter is a versatile electronic measuring instrument that combines several measurement functions in a single unit. It typically includes functions for measuring voltage, current, and resistance. Modern digital multimeters (DMMs) also often include features like capacitance, frequency, temperature, and continuity testing.

A multimeter essentially contains a sensitive galvanometer, appropriate range multipliers (for voltage) and shunts (for current), and a resistance measuring circuit (often using a battery to supply current). The user selects the desired function (voltage, current, resistance) and range using a rotary switch.

Functions of a Multimeter

• Voltage Measurement: The multimeter is set to the voltage function (AC or DC) and the appropriate range. It is connected in parallel with the component. Internally, it acts as a voltmeter with a high input impedance.
• Current Measurement: The multimeter is set to the current function (AC or DC) and the appropriate range. It is connected in series with the circuit. Internally, it acts as an ammeter with a low input impedance, using internal shunts. Care must be taken not to blow the internal fuse by connecting it in parallel when set for current measurement.
• Resistance Measurement: The multimeter is set to the resistance function ($\Omega$) and the appropriate range. The circuit or component under test should be de-energized. The multimeter applies a small voltage and measures the resulting current to calculate resistance using Ohm's law ($R = V/I$).
• Continuity Test: Many multimeters have a continuity test function, often indicated by a buzzer symbol. It checks if there is a low-resistance path between two points, usually indicated by an audible beep. This is useful for checking fuses, wires, and switches.

Digital multimeters display readings on an LCD or LED screen, providing a clear numerical output. Analog multimeters use a needle that moves across a calibrated scale.

Megger (Megohmmeter)

A megger, or megohmmeter, is a specialized type of ohmmeter used for measuring extremely high electrical resistance values, typically in the range of megaohms (M$\Omega$) to gigaohms (G$\Omega$). Its primary application is to test the insulation resistance of electrical equipment such as motors, generators, transformers, cables, and switchgear.

High insulation resistance is critical for the safe and reliable operation of electrical systems. Low insulation resistance can indicate damaged insulation, moisture ingress, or contamination, leading to potential electrical shock hazards, equipment failure, and short circuits.

Principle of Operation

Unlike a standard ohmmeter that uses a battery to provide a low voltage, a megger typically uses a hand-cranked generator or a battery-powered electronic circuit to produce a high DC voltage (commonly 250V, 500V, 1000V, or higher, depending on the application). This high voltage is necessary to drive a measurable current through the high resistance of the insulation.

The megger has a sensitive galvanometer movement. The resistance under test is connected between the "Line" and "Earth" terminals of the megger. When the generator is cranked (or the electronic circuit is activated), the high voltage is applied across the insulation. A small current flows through the insulation. The galvanometer measures this current and indicates the resistance on a scale calibrated in megaohms.

A typical analog megger has three terminals: Line (L), Earth (E), and often a Guard (G) terminal.

• Line (L): Connected to one end of the insulation being tested (e.g., a motor winding).
• Earth (E): Connected to the grounded casing or frame of the equipment (e.g., the motor frame).
• Guard (G): Used to bypass leakage currents that do not pass through the insulation under test, thus ensuring a more accurate measurement of the insulation resistance itself. It's connected to the surface leakage path.

The megger scale is often marked with "Good" and "Bad" regions. Readings below a certain threshold (e.g., 1 M$\Omega$/kV of operating voltage) are considered unacceptable.

Earth Fault Detection

An earth fault occurs when an unintended conductive path is established between an electrical conductor and the earth (ground). This can happen due to damaged insulation, moisture, or improper wiring. Earth faults are dangerous as they can lead to electric shock, fire, and equipment damage. Earth fault detection systems are designed to identify and isolate these faults quickly.

The primary device for detecting earth faults in modern electrical systems is the Residual Current Device (RCD), also known as a Residual Current Circuit Breaker (RCCB) or Ground Fault Circuit Interrupter (GFCI).

How RCDs Work

An RCD monitors the current flowing into a circuit and the current returning from it. In a healthy circuit, these currents should be equal. The RCD uses a core balance transformer (also known as a summation transformer) to measure the difference between the outgoing (line) and returning (neutral) currents.

The line and neutral conductors of the circuit are passed through separate openings in the core of the transformer. If the circuit is functioning normally, the magnetic fluxes produced by the currents in the line and neutral conductors are equal and opposite, resulting in zero net flux in the core.

However, if an earth fault occurs, some current will leak to earth through the faulty path. This means the current returning through the neutral conductor will be less than the current flowing out through the line conductor. This imbalance creates a net magnetic flux in the core of the summation transformer. This changing flux induces a voltage in a sensing coil wound around the core, which triggers a mechanism to rapidly trip the RCD, disconnecting the power supply.

RCDs are rated by their sensitivity, which is the maximum residual current at which they will trip. Common sensitivities are 30 mA (for personal protection), 100 mA, and 300 mA (for fire protection and equipment protection).

Other Earth Fault Detection Methods

In industrial and high-voltage systems, more sophisticated earth fault detection methods are employed, often involving current transformers (CTs) and protective relays.

• In a three-phase system, a neutral earth fault relay can monitor the residual current by summing the currents from the three phases (often using a zero-sequence CT). An imbalance indicates an earth fault.
• In unearthed systems (IT systems), specialized earth fault locators are used to detect and pinpoint the location of a first earth fault without causing a system shutdown, allowing for planned maintenance.

Importance of Earthing: Proper earthing is fundamental to earth fault detection and protection. The earth conductor provides the path for the fault current to flow to the ground, allowing protective devices like RCDs and MCBs to operate.

CRO (Cathode Ray Oscilloscope)

A Cathode Ray Oscilloscope (CRO) is a versatile laboratory instrument used to display and analyze the waveform of electronic signals. It allows us to visualize the instantaneous changes in voltage over time, making it invaluable for troubleshooting, testing, and analyzing electronic circuits.

The core component of a CRO is the cathode ray tube (CRT).

Components and Working Principle

The main components of a CRO are:

• Electron Gun: This consists of a heater filament, a control grid, and accelerating anodes. The filament heats a cathode, causing it to emit electrons (thermionic emission). The control grid controls the intensity (brightness) of the electron beam, and the accelerating anodes speed up and focus the electrons into a narrow beam.
• Deflection System: This comprises two pairs of parallel plates:
  • Vertical Deflection Plates: Mounted horizontally, these plates control the vertical movement of the electron beam. A voltage applied to these plates causes the beam to deflect upwards or downwards.
  • Horizontal Deflection Plates: Mounted vertically, these plates control the horizontal movement of the electron beam. A voltage applied to these plates causes the beam to sweep across the screen from left to right.
• Screen: The inside of the front face of the CRT is coated with a fluorescent material (phosphor). When the electron beam strikes this material, it glows, creating a visible spot.
• Time Base Generator: This circuit generates a sawtooth voltage waveform. When applied to the horizontal deflection plates, it causes the electron beam to sweep horizontally across the screen at a constant speed. This sweep provides the time axis for displaying the waveform.

Operation: 1. The electron gun produces a focused beam of electrons. 2. The input signal to be displayed is applied to the vertical deflection plates. 3. A sawtooth voltage from the time base generator is applied to the horizontal deflection plates. 4. The electron beam strikes the fluorescent screen, creating a bright spot. 5. As the sawtooth voltage sweeps the beam horizontally and the input signal deflects it vertically, the spot traces out the waveform of the input signal against time. The persistence of vision allows us to see a continuous trace.

Applications of CRO

• Observing and measuring voltage waveforms (amplitude, shape, frequency).
• Measuring time intervals and periods.
• Analyzing the phase relationship between two signals.
• Troubleshooting electronic circuits by observing signal behavior at different points.
• Measuring rise time, fall time, and other transient characteristics.