# What is Two Wattmeter Method and Its Working

All the electrical equipment and machines work on supplying electric power and dissipate large amounts of energy. The supplied power is usually measured in terms of watts using a device namely wattmeter. A wattmeter is also called as deflection meter which is mainly used in electrical labs. It not only measure power in terms of watts but also measures in terms of kilowatts and megawatts. The wattmeter usually consists of two coils “CC” current coil which is usually connected in series with load current and a voltage/ pressure / potential coil “PC”, this coil is usually connected across the load circuit. The electrical power can be represented in three forms they are real power, reactive power, and apparent power. The following article describes the two wattmeter method at balanced load condition.

## What is Two Wattmeter Method?

A three-phase two-watt meter measures the current and voltage from any of the 2 supply lines of 3 phase corresponding to the 3rd supply line of 3 phase. The 3 phase 2 wattmeter is said to be at a balanced load condition if the current in every phase lag at an angle “φ” with phase voltage.

### Construction of Two Wattmeter Method

The 3-phase power of a 3-phase circuit can be measured using 3 ways they are,

- 3 Wattmeter Method
- 2 Wattmeter Method
- 1 Wattmeter Method.

The main concept of 2 Wattmeter with 3 phase voltage is to balance the 3 phase load by satisfying the condition of current lagging at an angle ‘φ’ with the voltage phase. The schematic diagram of 3 phase 2 wattmeter is shown below

It consists of 2 wattmeters like W1 and W2, where each wattmeter has a current coil ‘CC’ and a pressure coil ‘PC’. Here, one end of wattmeter ‘W1’ is connected to ‘R’ terminal whereas one end of wattmeter’ W2′ is connected to’ Y’ terminal. The circuit also consists of 3 inductors ‘Z’ which are constructed in a star topology. The 2 ends of inductors are connected to 2 terminals of a wattmeter whereas the third terminal of the inductor is connected to B.

### Derivation of Two Wattmeter Method

Two Wattmeter is used to determine two main parameters they are,

Consider the load used as an inductive load which is represented by following the phasor diagram as shown below.

The voltages V_{RN, }V_{YN, }and V_{BN }are electrically 120^{0} in phase with one other, we can observe that the current phase lags at the “φ^{0} ” angle with voltage phase.

The current in wattmeter W_{1 }is represented as

**W _{1 }= I_{R} …….. (1)**

where I_{R} is current

The potential difference across the wattmeter W1 coil is given as

**W _{1 }= ~ V_{RB }= [ ~ V_{RN} – ~ V_{BN} ] ……… (2)**

Where **V _{RN} and V_{BN}** are voltages

The phase difference between the voltage ‘V_{YB}‘ and current ‘I_{Y }‘ is given as (30^{0 }+ φ )

Hence the power measured by wattmeter is given as

**W _{2} = V_{YB} I_{Y} cos ( 30^{0 }+ φ ) ………….. (3)**

At balanced load condition,

**I _{R }= I_{Y} = I_{B} = I_{L} and ………….. (4)**

**V _{RY} = V_{YB} = V_{BR} = V_{L} ………… (5)**

Therefore we obtain wattmeter readings as

**W _{1 }= V_{L }I_{L }cos( 30^{0} – φ ) and ……………. (6)**

**W _{2 }= V_{L }I_{L} cos ( 30^{0} + φ ) …………….. (7)**

### Total Power Derivation

The total wattmeter reading is given as

**W _{1 }+ W_{2} = V_{L} I_{L} cos( 30^{0} – φ ) + V_{L }I_{L} cos ( 30^{0} + φ ) ………….. (8)**

** = V _{L} I_{L} [ cos( 30^{0} – φ ) + cos ( 30^{0} + φ ) ]**

** = V _{L} I_{L} [ cos 30^{0} cos φ + sin 30^{0} sin φ + cos 30^{0} cos φ – sin 30^{0} sin φ ]**

** = V _{L} I_{L} [ 2 cos 30^{0} cos φ ]**

** = V _{L} I_{L} [ (2 √3**

**/ 2 ) cos 30**

^{0}cos φ]** = √3**** [ ****V _{L} I_{L} cos φ ] ……… (9)**

** W1 + W2 =P ….. (10)**

Where ‘P’ is the total observed power in a 3-phase balanced load condition.

#### Power Factor Derivation

**Definition**: It is the ratio between actual power observed by the load to apparent power flowing in the circuit.

The power factor of three phase balanced load condition can be determined and derived from wattmeter readings as follows

From equation 9

** W1 + W2 = √3 V _{L} I_{L} cos φ **

**Now W1 – W2 ** **= ****V _{L} I_{L} [ cos( 30^{0} – φ ) – cos ( 30^{0} + φ ) ]**

** = V _{L} I_{L} [ cos 30^{0} cos φ + sin 30^{0} sin φ – cos 30^{0} cos φ + sin 30^{0} sin φ ]**

** = 2 V _{L} I_{L} sin 30^{0} sin φ**

** W1 – W2 = ****V _{L} I_{L} sin φ ………….. (11)**

Dividing equations 11 and 9

**[W1 – W2 **** \ W1 +W2] ****= ****V _{L} I_{L} sin φ **

**/ √3**

**V**

_{L}I_{L}cos φ**Tan φ = √3 ****[W1 – W2\W1 +W2]**

The power factor of the load is given as

**cos φ = cos tan ^{-1} **

**[√3] [W1 – W2 \ W1 +W2]**

**………(12)**

#### Reactive Power Derivation

**Definition**: It is the ratio between complex power corresponding to storage and revival of energy rather than consumption.

To obtain reactive power, we multiply equation 11 with

**√3 [W1 – W2 ]= √3 [****V _{L} I_{L} sin φ] = P_{r}**

**P _{r} = √3 [W1 – W2 ] …………. (13)**

Where P_{r }is the reactive power obtained from 2 wattmeters.

### Two Wattmeter Method Table

The two wattmeter method observations can be noted practically by following the table.

S .NO | Voltage VL (volts) | Current IL (amp) | Power W1 (watts) | Power W2 (watts) | Total Power P = W1 + W2 | Power Factor = cos φ |

1 | | | | | | |

2 | | | | | | |

3 | | | | | | |

### Precaution

The following are the precautions to be followed

- Connections are to be made tightly
- Avoid the parallel axial error.

### Advantages of Two Wattmeter

The following are the advantages

- Both balanced and unbalanced load can be balanced using this method
- In a star connected load, it is optional to connect neutral point and wattmeter
- In a delta, connected load connections need not be opened to connect wattmeter
- 3 phase power can be measured using two wattmeter’s
- Both power and power factor is determined on a balanced load condition.

### Disadvantages of Two Wattmeter

The following are the disadvantages

- Not suitable for 3 phase, 4 wire system
- Primary windings W1 and secondary windings W2 must be identified correctly to prevent incorrect results.

### Applications of Two Wattmeter

The following are the applications

- Wattmeters are used to measure the power consumption of any electrical appliances and verify their power ratings.

### FAQs

**1). What is a WattMeter?**

A wattmeter is an electrical device that is used to measure the electrical power of electrical equipment.

**2). What are the Units of Power?**

Power can be measure using wattmeter in a range of Watts, Kilowatts, Mega Watts.

**3). What is Balanced Condition in 3 Phase Two Wattmeter?**

The 3 phase 2 wattmeter is said to be at a balanced load condition if the current in every phase lag at an angle φ with phase voltage.

**4). What is the power equation of 3 Phase Two Wattmeter?**

The power equation is given as P= √3 VL IL cos φ

**5). What is the Power Factor of 3 Phase Two Wattmeter?**

The power factor is given as cos φ = cos tan-1 √3 [ ( [ W1- W2 ] \ [ W1+ W2 ] )

**6). What is the Reactive Power equation of 3 Phase Two Wattmeter?**

The reactive power is given as Pr = √3( W1- W2 )

All the electrical device dissipates energy when electrical power is supplied, this power can be measured using an electrical device named wattmeter, which usually measures in watts/kilowatts/megawatts. The 3-phase power of a 3-phase circuit can be measured using 3 ways using 3 Wattmeter Method, 2 Wattmeter Method, 1 Wattmeter Method. This article describes 3 phase 2 wattmeter under balanced load conditions. This condition is valid if the current in every phase lag at an angle φ with phase voltage. The main advantage of this method is that it can measure both balanced and unbalanced load conditions.