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# Synchronous Impedance Method (EMF Method) for Finding Voltage Regulation of Alternator

The *synchronous impedance method* or *EMF method* is used to determine the voltage regulation of the larger alternators. The synchronous impedance method is based on the concept of replacing the effect of armature reaction by an imaginary reactance.

For an alternator,

$$\mathrm{𝑽 = 𝑬_{𝒂} − 𝑰_{𝒂}𝒁_{𝒔} = 𝑬_{𝒂} − 𝑰_{𝒂}(𝑅_{𝒂} + 𝑗𝑋_{𝑠}) … (𝟏)}$$

At first, the synchronous impedance (𝑍_{𝑠}) is measured and then, the value of actual generated EMF (𝐸_{a}) is calculated. Thus, from the values of (𝐸_{a}) and V, the voltage regulation of the alternator can be calculated.

## Measurement of Synchronous Impedance

In order to determine the value of synchronous impedance, following tests are performed on an alternator −

- DC Resistance Test
- Open-Circuit Test
- Short-Circuit Test

## DC Resistance Test

The circuit diagram for the DC resistance test is shown in Figure-1.

Consider the alternator is star-connected with the field winding open-circuited. Now, measure the DC resistance between each pair of terminals either by using Wheatstone’s bridge or ammeter-voltmeter method. The average of three sets of resistance values R_{t} is taken. This value of R_{t} is divided by 2 to obtain the DC resistance per phase.

While performing the test, the alternator should be at rest, because the AC effective resistance is greater than DC resistance due to skin effect. The AC effective resistance per phase may be obtained by multiplying the DC resistance by a factor 1.20 to 1.75 depending upon the size of the alternator.

## Open-Circuit Test

To perform the open-circuit test, the load terminals are kept open and the alternator is run at rated synchronous speed. The circuit diagram of the open-circuit test is shown in Figure-2.

Initially, the field current is set to zero. Then, the field current is gradually increased in steps and the open-circuit terminal voltage E_{t} is measured in each step. The field current may be increased to obtain 25 % more than rated voltage of the alternator.

A graph is plotted between the open-circuit phase voltage $((𝐸_{𝑝ℎ} = 𝐸_{𝑡}/ \sqrt{3}))$ and the field current (𝐼_{𝑓}). The obtained characteristic curve is known as **open-circuit characteristic (O.C.C)** of the alternator (see Figure-3).

The shape of O.C.C. is same as a normal magnetisation curve. When the linear portion of the O.C.C. is extended, it given the *air-gap line* of the characteristic.

## Short-Circuit Test

For performing the short-circuit test, the armature terminals are short-circuited through three ammeters as shown in Figure-4.

Before starting the alternator, the field current should be decreased to zero. Each ammeter should have a range more than the rated full-load value. Now, the alternator is run at synchronous speed. Then, the field current is gradually increased in steps and the armature current is measured at each step. The field current may be increased to obtain the armature currents up to 150 % of the rated value.

The field current (𝐼_{𝑓}) and the average of the three ammeter readings is taken at each step. A graph is plotted between the armature current (𝐼_{a}) and the field current (𝐼_{𝑓}). The obtained characteristic is known as **short-circuit characteristic (S.C.C.)** of the alternator and this characteristic is a *straight line* as shown in Figure-5.

## Calculation of Synchronous Impedance (𝒁_{𝒔})

In order to calculate the synchronous impedance of the alternator, the O.C.C. and the S.C.C. are drawn on the same curve sheet, as shown in Figure-6.

Then, determine the value of short-circuit current **(𝐼 _{𝑆𝐶})** at the field current that gives the rated voltage per phase of the alternator. The synchronous impedance (𝑍

_{𝑠}) will then be equal to the ratio of the open-circuit voltage to the short-circuit current at the field current which gives the rated voltage per phase, i.e.,

$$\mathrm{𝑍_{𝑠} =\frac{open\:circuit\:voltage\:per \:phase}{short\:circuit\:armature\:current}… (2)}$$

From the figure-6, the synchronous impedance can be written as

$$\mathrm{\Rightarrow\: 𝑍_{𝑠} =\frac{𝐴𝐵\:(volts)}{𝐴𝐶\: (amperes)}… (3)}$$

Also, the synchronous reactance of the alternator is

$$\mathrm{𝑋_{𝑠} =\sqrt{𝑍^{2}_{𝑠}-𝑅^{2}_{𝑎}}… (4)}$$

Therefore, the percentage voltage regulation of the alternator will be,

$$\mathrm{Percentage\:voltage\:regulation =\frac{𝐸_{𝑎} − 𝑉}{𝑉}× 100 … (5)}$$

## Numerical Example

A 400 V, 35 kVA single-phase alternator has an effective armature resistance of 0.3Ω. An excitation current 15 A produces 250 A armature current on short-circuit and an EMF of 380 V on open-circuit. Calculate the synchronous impedance and synchronous reactance of the alternator.

**Solution**

Synchronous impedance of the given alternator is,

$$\mathrm{𝑍_{𝑠} =\frac{Open\:circuit\:voltage}{Short \:circuit\:armature\:current}=\frac{380}{250}= 1.52\:Ω}$$

The synchronous reactance of the alternator is,

$$\mathrm{𝑋_{𝑠} =\sqrt{𝑍^{2}_{𝑠}-𝑅^{2}_{𝑎}}=\sqrt{1.52^{2} − 0.3^{2}}= 1.49 Ω}$$

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