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# Voltage Build-Up in a Self-Excited DC Generator

A self-excited DC generator has its own field excitation. Consider a shunt generator in which the field winding is connected in parallel with the armature, thus armature voltage supplies the field current.

Assume that the generator has no-load connected to it and the armature is driven at a certain speed by a prime mover. The voltage build up in a DC generator depends upon the presence of the residual flux in the field poles of the generator. Because of this residual flux, a small voltage E0r of the order of 1 V or 2 V will be generated and is given by,

$$\mathrm{E_{0r}\:=\:k\varphi_{res}\omega}$$

This voltage causes a current I_{f} to flow through the field winding of the self-excited generator and this field current is given by,

$$\mathrm{I_{f}=\frac{V}{R_{f}}}$$

This field current increases the magnetic flux in the generator. The increase in the flux increases the generated voltage E_{0}. The increased generated voltage E_{0} increases the terminal voltage V. With the increase in V, the field current I_{f} increases further. This in turn increases the magnetic flux and therefore, the E_{0} increases further. This process of voltage build up continues. The terminal voltage of the generator limits to the steady state value, when the magnetic saturation of field pole cores being reached.

As we have assumed that the generator is on no-load during the voltage build-up process, hence the steady state operation can be described by the following equations −

$$\mathrm{I_{a}\:=\:I_{f}}$$

$$\mathrm{V\:=\:E_{0}-I_{a}R_{a}\:=\:E_{0}-I_{f}R_{a}}$$

Since the I_{f} is very small, therefore the drop I_{f}R_{a} can be neglected. Hence,

$$\mathrm{V = E_{0}}$$

The curve plotted between the E_{0} and I_{f} is called as the *magnetisation curve*.

And,

$$\mathrm{V\:=\:I_{f}R_{f}}$$

This equation shows a straight line, which is known as *field-resistance line*. The field resistance line is a curve plotted between the voltage (I_{f}R_{f}) across the field winding and the field current I_{f}. The slope of this line is equal to the resistance of the field winding.

The point of intersection (P) of the magnetisation curve and the field-resistance line gives the no-load terminal voltage V_{0} of the self-excited DC generator. If the field current corresponding to the point P is increased further, there is no further increase in the terminal voltage.

Hence, we arrive at a very important conclusion that the voltage build-up of the DC generator is given by the point of intersection of magnetisation curve and field resistance line.

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