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Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) PDF Download

Two-wattmeter Method of Power Measurement in a Threephase Circuit 

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Fig. 20.1 Connection diagram for two-wattmeter method of power measurement  in a three-phase balanced system with  star-connected load  \

The connection diagram for the measurement of power in a three-phase circuit using two wattmeters, is given in Fig. 20.1. This is irrespective of the circuit connection – star or delta. The circuit may be taken as unbalanced one, balanced type being only a special case. Please note the connection of the two wattmeters. The current coils of the wattmeters, 1 & 2, are in series with the two phases, R & B , with the pressure or voltage coils being connected across R − Y and B − Y respectively. Y is the third phase, in which no current coil is connected.  

If star-connected circuit is taken as an example, the total instantaneous power consumed in the circuit is,

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Each of the terms in the above expression is the instantaneous power consumed for the phases. From the connection diagram, the current in, and the voltage across the respective (current, and pressure or voltage) coils in the wattmeter,W1  are Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)  and  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) So, the instantaneous power measured by the wattmeter,W1is,

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Similarly, the instantaneous power measured by the wattmeter, Wis,  

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

The sum of the two readings as given above is, 

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Since,  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Substituting the above expression for in the earlier one,

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

If this expression is compared with the earlier expression for the total instantaneous power consumed in the circuit, they are found to be the same. So, it can be concluded that the sum of the two wattmeter readings is the total power consumed in the three-phase circuit, assumed here as a star-connected one. This may also be easily proved for deltaconnected circuit. As no other condition is imposed, the circuit can be taken as an unbalanced one, the balanced type being only a special case, as stated earlier. 

Phasor diagram for a three-phase balanced star-connected circuit

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Fig. 20.2 Phasor diagram for two-wattmeter method of power measurement   in a three-phase system with balanced star-connected load  

The phasor diagram using the two-wattmeter method, for a three-phase balanced starconnected circuit is shown in Fig. 20.2. Please refer to the phasor diagrams shown in the figures 18.4 &18.6b. As given in lesson No. 18, the phase currents lags the respective phase voltages by φ = φ p , the angle of the load impedance per phase. The angle, φ  is taken as positive for inductive load. Also the neutral point on the load (N ) is same as the neutral point on the source (N' ), if it is assumed to be connected in star. The voltage at that point is zero (0).

The reading of the first wattmeter is,

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

The reading of the second wattmeter is, 

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

The line voltage, Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) leads the respective phase voltage, Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) by Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) , and the phase voltage, Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)leads the phase current, Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)  by φ . So, the phase difference betweenMeasurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)is  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) Similarly, the phase difference between &  in the second case,  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) &  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) in the second case, can be found and also checked from the phasor diagram.

The sum of the two wattmeter readings is, 

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

So, ( W1 + W2 ) is equal to the total power consumed by the balanced load. This method is also valid for balanced delta-connected load, and can be easily obtained. The phasor diagram for this case is shown in the example No. 20.2. 

Determination of power factor for the balanced load 

The difference of the two wattmeter readings is, 

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

 If the two sides is multiplied by √3 , we get  

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

From the two expressions, we get, 

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

The power factor, cosφ of the balanced load can be obtained as given here, using two wattmeter readings.

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

The two relations, cosφ and sin φ can also be found as, 

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)  and  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Comments on Two Wattmeter Readings 

When the balanced load is only resistive (φ = 0° ), i.e. power factor ( cosφ = 1.0 ), the readings of the two wattmeters  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) are equal and positive.  Before taking the case of purely reactive (inductive/capacitive) load, let us take first lagging power factor as ( cosφ = 0.5 ), i.e. φ = +60° . Under this condition,   

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) \

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

It may be noted that the magnitudes of the phase or line voltage and also phase current are assumed to be constant, which means that the magnitude of the load impedance (inductive) is constant, but the angle, φ varies as stated. 

 As the lagging power factor decreases from 1.0 to 0.5, with φ increasing from  to  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) the reading of the first wattmeter wdecreases from a certain positive value to zero (0). But the reading of the second wattmeter W2,  increases from a certain positive value to positive maximum, as the lagging power factor is decreased from 1.0 to 0.866 (= cos 30°) φ increasing from 0° to + 30° . As the lagging power factor decreases from 0.866 to 0.5, with φ increasing from + 30° to + 60° , the reading of the second wattmeter,  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)decreases from positive maximum to a certain positive value. It may be noted that, in all these cases, Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)  , with both the readings being positive. If the lagging power factor is 0.0 (φ = +90° ), the circuit being purely inductive, the readings of the two wattmeters  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) are equal and opposite, i.e.,  is negative and  is positive. The total power consumed is zero, being the sum of the two wattmeter readings, as the circuit is purely inductive. This means that, as the lagging power decreases from 0.5 to 0.0, with φ increasing from  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) to , the reading of the first wattmeter,W1  decreases from zero (0) to a certain negative value, while the reading of the second wattmeter W2,  decreases from a certain positive value to lower positive one. It may be noted that  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) which means that the total power consumed, i.e., ( W+ W2 ) is positive, with only  being negative. The variation of two wattmeter readings as stated earlier, with change in power factor (or phase angle) is now summarized in Table 20.1. The power factor [pf] (=cosθ) is taken as lagging, the phase current lagging the phase voltage by the angle, φ (taken as positive (+ve)), as shown for balanced star-connected load in Fig. 20.2. The circuit is shown in Fig. 20.1. All these are also valid for balanced delta-connected load. 

Sl. No. Power factor [pf] (Phase angle) Wattmeter readings (W)Remarks 
W1W2
1.pf = unity [1.0] (φ = 0° ) +ve+veW 1 = W2
2.0.5 < pf < 1.0 ( 60° >φ > 0° )+ve+veW 1 > W2
3.pf = 0.5 (φ = 60° ) +vezero (0.0)Total power = W1
4.0.0 < pf < 0.5 ( 90° >φ > 6 0° ) +ve-veMeasurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)
5.pf  = zero [0.0] (φ = 90° ) +ve-veMeasurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Table 20.1 Variation of two wattmeter readings with change in power factor of the load current  

It may be noted that, if the power factor is leading (φ = negative (-ve)), the circuit being capacitive, the readings of the two wattmeters change with the readings interchanging, i.e.,W1 taking the value of Wand vice versa. All the points as stated earlier, remain valid, with the comments as given earlier. The first one (#1) in Table 20.1 is a special case, neither lagging, nor leading, with pf = 1.0. But in second one (#2), both readings remain +ve, with W1 < WSame is the case in fourth one (#4), where Wis –ve and W is +ve, with  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)  total power being positive (+ve). For third case (#3), W1 = 0.0 and Wis +ve, with total power= WFor last (fifth) case (#5), W1   is –ve and  Wis +ve, with  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)  total power being zero (0.0).    

Power measurement using one wattmeter only for a balanced load 

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Fig. 20.4 Connection diagram for power measurement using only one wattmeter in a three-phase system with balanced star-connected load  

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Fig. 20.5 Connection diagram for power measurement using only one wattmeter in a three-phase system with balanced delta-connected load

The circuit diagram for measuring power for a balanced three-phase load is shown in Fig. 20.3. The only assumption made is that, either the neutral point on the load or source side is available. The wattmeter measures the power consumed for one phase only, and the reading is Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) . The total power is three times the above reading, as the circuit is balanced. So, the load must be star-connected and of course balanced one, with the load neutral point being available. The load may also be delta-connected balanced one, if the neutral pinpoint on the source side is available. Otherwise for measuring total power for delta-connected balanced load using one wattmeter only, the connection diagram is given in Fig. 20.4. The wattmeter as stated earlier, measures power for one phase only, with the total power consumed may be obtained by multiplying it by three.  

Example 20.1  

Calculate the readings of the two wattmeters ( W1& W2) connected to measure the total power for a balanced star-connected load shown in Fig. 20.6a, fed from a three phase, 400 V balanced supply with phase sequence as R-Y-B. The load impedance per phase is  Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) Also find the line and phase currents, power factor, total power, total reactive VA and total VA. 

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE)

Fig. 20.6 (a) Circuit diagram for a three-phase system with balanced starconnected load (Example 20.1)  (b) Phasor di agram

The document Measurement of Power in a Three phase Circuit | Basic Electrical Technology - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Basic Electrical Technology.
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FAQs on Measurement of Power in a Three phase Circuit - Basic Electrical Technology - Electrical Engineering (EE)

1. How is power measured in a three-phase circuit?
Ans. Power in a three-phase circuit is measured using a wattmeter. The wattmeter is connected in the circuit and measures the product of the line voltage, line current, and power factor, giving the total power consumed.
2. What is the difference between single-phase power measurement and three-phase power measurement?
Ans. In single-phase power measurement, only one line voltage and one line current are considered. However, in three-phase power measurement, three line voltages and three line currents are considered, and the power is calculated using the relationship between them.
3. How is apparent power calculated in a three-phase circuit?
Ans. Apparent power in a three-phase circuit is calculated by multiplying the line voltage by the line current and dividing the result by the square root of three (sqrt(3)). This accounts for the fact that the line voltages are 120 degrees out of phase with each other.
4. What is power factor in a three-phase circuit?
Ans. Power factor in a three-phase circuit is a measure of how effectively the circuit converts electrical power into useful work. It is the ratio of real power (measured in watts) to apparent power (measured in volt-amperes). A higher power factor indicates better efficiency.
5. Can power factor be improved in a three-phase circuit?
Ans. Yes, the power factor in a three-phase circuit can be improved using power factor correction techniques. These techniques involve adding capacitors to the circuit, which help to offset the reactive power and bring the power factor closer to unity (1.0). This improves the efficiency of the circuit.
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