Electric power (P) consumed by a load (R) supplied from a dc power supply is the product of the voltage across the load (V_{R}) and the current flowing through the load (I_{R}):

P = V_{R} x I_{R}

Thus, power measurement in a dc circuit can be carried out using a voltmeter (V) and an ammeter (A) with any one of the arrangements shown in Figure 1.

**Figure 1. Two arrangements for power measurement in dc circuits**

One thing should be kept in mind while using any of the two measuring arrangements shown in Figure 1; that both the voltmeter and the ammeter requires power for their own operations. In the arrangement of Figure 1(a), the voltmeter is connected between the load and the ammeter. The ammeter thus, in this case measures the current flowing into the voltmeter, in addition to the current flowing into the load.

Power consumed by the load= Power indicated by instruments - Power loss in voltmeter

Thus, **Power indicated = Power consumed + Power loss in voltmeter**

In alternating current circuits, the instantaneous power varies continuously as the voltage and current varies. In such case, the power at any instant is given by

p(t) = v(t) × i(t)

where, p(t), v(t), and i(t) are values of instantaneous power, voltage and current respectively.

Thus, if both voltage and current can be assumed to be sinusoidal, with the current lagging the voltage by phase-angle φ, then

V(t) = V_{m} sin(ωt)

i(t) = I_{m }sin(ωt – φ)

where V_{m} and I_{m} are peak values of voltage and current respectively, and ω is the angular frequency.

The instantaneous power p(t) is therefore given by,

p(t) = V_{m} I_{m} sin(ωt)sin(ωt – φ)

Average value of Power over a complete cycle in such a case will be = VI cos φ

where, V and I are rms values of voltage and current respectively and cos j is power factor of the load.

**POWER MEASUREMENT IN POLYPHASE SYSTEMS **

**Blondel's Theorem **

The theorem states that 'in an n-phase network, the total power can be obtained by taking summation of the n wattmeter so connected that current elements of the wattmeter are each in one of the n lines and the corresponding voltage element is connected between that line and a common point'.

**TWO-WATTMETER METHOD **

This is the most common method of measuring three-phase power. It is particularly useful when the load is unbalanced

**Star-Connected System**

The connections for measurement of power in the case of a star-connected three-phase load are shown in figure 2

**Figure 2: Two-wattmeter method for star-connected load**

The current coils of the wattmeter are connected in lines R and B, and their voltage coils are connected between lines R and Y, and B and Y respectively.

Power consumed by the load

P = V_{RN} × I_{R} + V_{YN} × I_{Y} + V_{BN} × I_{B}

Reading of wattmeter W_{1}, P_{1} = V_{RY} x I_{R} = (V_{RN} × V_{YN}) X I_{R}

Reading of wattmeter W_{2}, P_{2} = V_{BY} x I_{B} = (V_{BN} – V_{YN}) X I_{B}

Summation of the two wattmeter readings:

= P_{1} + P_{2} = (V_{RN} – V_{YN}) x I_{R} + (V_{BN} –V_{YN}) XI_{B}

= V_{RN} × I_{R} + V_{BN} × I_{B} – V_{YN} × (I_{R} +I_{B})

From Kirchhoff 's law, summation of currents at node N must be zero, i.e.,

I_{R} + I_{Y }+ I_{B} = 0

I_{R} + I_{B} = –I_{Y}

Thus, we can re-write,

P_{1} + P_{2} = V_{RN} × I_{R }+ V_{YN} × I_{Y} + V_{BN} × I_{B}

It can thus, be concluded that sum of the two wattmeter readings is equal to the total power consumed by the load. This is irrespective of fact whether the load is balanced or not.

Let, V_{RN}, V_{RN}, and V_{YN} are phase voltages and I_{R}, I_{B} is and l_{Y} are phase currents for the balanced three phase star connected system under study.

For a balanced system, phase voltages, V_{RN} = V_{BN} = V_{YN} = V(say)

And, phase currents, I_{R} = I_{R} = l_{y} = I (say)

For a star-connected system,

Line voltages V_{RN} = V_{BN} = V_{BR} = V

Line currents I_{R} = I_{B} = l_{Y} = I

Power factor = cos ϕ,

where ϕ is the angle by which each of the phase currents lag the corresponding phase voltages.

Current through the CC of wattmeter W_{1} is I_{R} and voltage across its potential coil is V_{RY}.

The current I_{R} leads the voltage by V_{RY} an angle (30° – ϕ).

∴ reading of wattmeter W_{1} is,

P_{1} = VIcos(Φ* *-30^{o})

Current through the CC of wattmeter W_{2} is I_{B} and voltage across its potential coil is V_{BY}. The current I_{B} lags the voltage by V_{BY} an angle (30° + ϕ), as shown above.

∴ reading of wattmeter W_{2} is,

P_{2} = VIcos(Φ* *-30^{o})

Sum of these two-wattmeter readings:

P_{1} + P_{2} = VIcos(Φ* *+30^{o}) + VIcos(Φ-30^{o})

= VI[cos(Φ+30^{o}) + cos(Φ-30^{o})]

=VIcosΦ** **

This is the total power consumed by the load, adding together the three individual phases.

Thus, at any power factor, the total power consumed by the load will be, in any case, summation of the two wattmeter readings.

There is way to find out value of the load power factor, if unknown, by a few steps of manipulation.

Consider** P _{1}= W_{1} & P_{2} =W_{2}**

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_{by using above formula we can easily calculate the condition of Power Factor.}

**Measurement of Energy**

Energy, heat, work and power are four concepts that are often confused. If force is exerted on an object and moves it over a distance, work is done, heat is released (under anything other than unrealistically ideal conditions) and energy is transformed. Energy, heat and work are three facets of the same concept. Energy is the capacity to do (and often the result of doing) work.

- The
**SI unit of energy**, heat and work is the*joule*(J)**British thermal unit (Btu)**or one of its multiples; and the**kilowatt hour (kWh).** - Power is the rate at which work is done (or heat released, or energy converted).
- A light bulb draws 100 joules of energy per second of electricity, and uses that electricity to emit light and heat (both forms of energy). The rate of one joule per second is called a
*watt*. The light bulb, operating at 100 J/s, is drawing power of 100 Watts.

**Energy meter or watt hour meter is classified in accordance with several factors such as**

- Type of display like analog or digital electric meter.
- Type of metering point like grid, secondary transmission, primary and local distribution.
- End applications like domestic, commercial and industrial.
- Technical like three phases, single phase, HT, LT and accuracy class meters.

### Electro-Mechanical induction type Energy meter

- It is the popularly known and most common type of age old watt hour meter.
- It consists of rotating aluminum disc mounted on a spindle between two electro magnets.
- Speed of rotation of disc is proportional to the power and this power is integrated by the use of counter mechanism and gear trains.
- It comprises of two silicon steel laminated electromagnets i.e., series and shunt magnets.

### Electronic Energy meters

- These are of accurate, high procession and reliable types of measuring instruments as compared to conventional mechanical meters.
- It consumes less power and starts measuring instantaneously when connected to load.
- These meters might be analog or digital.
- In analog meters, power is converted to proportional frequency or pulse rate and it is integrated by counters placed inside it.
- In digital electric meter power is directly measured by high end processor.
- The power is integrated by logic circuits to get the energy and also for testing and calibration purpose. It is then converted to frequency or pulse rate.

### Smart Energy Meters

It is an advanced metering technology involving placing intelligent meters to read, process and feedback the data to customers. It measures energy consumption, remotely switches the supply to customers and remotely controls the maximum electricity consumption. Smart metering system uses the advanced metering infrastructure system technology for better performance.

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