Is it possible to measure three-phase power in an unbalanced load by the two Wattmeter method?

Unbalanced loads are a common occurrence in electrical systems, and accurately measuring their power consumption is crucial for effective monitoring and analysis. Let’s understand how to accurately measure power in these situations is essential for optimizing system performance and ensuring efficient energy management

What is balanced load and unbalanced load?

A balanced load is a condition when all the three phases carry the same magnitude of current along with the same phase differences.

Ex- Three phase electric motors, electric heaters

An unbalanced load occurs when there is significantly more power drawn on one side of the panel than the other.

Ex- Faulty three-phase motors, faulty three-phase heaters.

Two-wattmeter method

The two-wattmeter method is a technique used to measure three-phase power in an electrical system, especially in an unbalanced load.

The two-wattmeter method is based on the principle of superposition, which states that the total power in a system is the sum of the powers measured individually in each phase.

This method utilizes two wattmeters connected appropriately to measure the power in each phase of a three-phase system.

The key principle behind the two-wattmeter method is based on the fact that “the sum of power in a balanced three-phase system is zero“. However, in an unbalanced load, “the sum of power is non-zero due to the unequal distribution of loads among the phases“.

Mathematical Explanation

In this method, we use two wattmeter.

Let us name wattmeter 1 as W₁ and wattmeter 2 as W₂ . The wattmeter 1 is connected to phase 1 and the wattmeter 2 is connected to the phase 2 as shown in the fig.below.

The wattmeter consists of current coil and the potential / voltage coil. The current coil is always connected in series with the load and the potential coil is connected in parallel to the load.

From the diagram we can see the connection of current coil as well as potential coil. The potential terminal of both the wattmeters is connected to the 3rd phase.

Each wattmeter has four terminals.

Let wattmeter W₁ and W₂ has four terminlas as M,L,C,V

where, M- main , L- Load, C- common point, V- potential .

Current I₁ is flowing through phase 1 and the current I₂ is flowing through phase 2. As there are two wattmeter so there will be two power.

P₁ = Power for wattmeter 1

P₂ = Power For wattmeter 2

We know that Power is the product of voltage and Current . So , it is given by

P= VI

The wattmeter 1 is connected between phases 1 and 3 . So its power will be given by

P₁ = (V₁-V₃)I₁

Similarly, wattmeter 2 is connected between phases 2 and 3 so, its power will begiven by,

P₂ = (V₂-V₃) I₂

The instantaneous power is given by ,

P₁= (V₁-V₃)i₁

P₂= (V₂-V₃)i₂

where i₁ and i₂ is the instantaneous current.

Let us calculate Power for star connection

For Star-connection,

P₁= (V₁-V₃)i₁ , P₂= (V₂-V₃)i₂

P = P₁ + P₂

= (V₁-V₃)i₁ + (V₂-V₃)i₂

P = V₁i₁ + V₂i₂ – V₃(i₁+i₂) ——(i)

As the load is connection in star so, according to KCL

i₁+i₂+i₃ = 0

i₁ + i₂ = -i₃ ——(ii)

Here, incoming current = Outgoing current

Substituting this equation in the wattmeter equation , we get

P = V₁i₁ + V₂i₂ – V₃(i₁+i₂)

P = V₁i₁ + V₂i₂ – V₃(-i₃)

P = V₁i₁ + V₂i₂ + V₃i₃

Therefore, we can see that Sum of two watmeter readings is equal to power consumed by the load.

We can conclude that , with the help of two Wattmeter, we can measure the three-phase power. This is nothing but the unbalanced load. (www.echelon.health)

So, with the help of Two Wattmeter method, we can measure the three-phase power in an unbalanced load.

Advantages of Two Wattmeter method :-

The two-wattmeter method for measuring power in unbalanced load has some advantages:-

1. Accurate Measurements

2. Simplicity and Ease of Implementation

3. Flexibility in Load types

4. Cost -Effective solution.

Overall, the two-wattmeter method offers a reliable and practical approach to measuring three-phase power in unbalanced loads. Its advantages lie in its accuracy, simplicity, flexibility, and usefulness for energy management, billing accuracy, and system analysis.

Hope, so that this article have cleared the concept that it is possible to measure power in an unbalanced load .