DC Generator Characteristics

Three curves are used to describe a DC generator, and they answer three different questions.

Also called the magnetic characteristic or open-circuit characteristic (O.C.C.).

• It is the relation between \(E_0\) and \(I_f\) at a given fixed speed.

• It is essentially the magnetisation curve for the material of the electromagnets.

• Its shape is practically the same for all generators, whatever their excitation arrangement.

Chapter 28 treated this curve in detail — its residual offset, its straight initial portion, its saturation, and the critical resistance and critical speed that follow from its slope at the origin. The two recapitulations below are given because they bear directly on the characteristics that follow.

Recap — voltage build-up

\[E_g\uparrow \Rightarrow V\uparrow \Rightarrow I_f\uparrow \Rightarrow \Phi\uparrow \Rightarrow E_g\uparrow\]

A positive-feedback loop, limited by saturation and started by residual flux, with \(E_g = K\Phi_{res}N\) giving one or two volts to begin.

Recap — critical values

A decrease in \(R_f\) reduces the slope of the \(R_f\) line, giving a higher voltage, and vice versa. If \(R_f\) is raised to \(R_c\) the line becomes tangent to the initial part of the curve; above \(R_c\) the generator fails to excite. Likewise at the critical speed \(N_c\) the line becomes tangential, and below \(N_c\) the voltage will not build up.

• It is the relation between the EMF \(E\) actually induced in the armature — that is, after the demagnetising effect of armature reaction — and the armature current \(I_a\).

• This characteristic is mainly of interest to the designer.

Chapter 30 explains the mechanism. In outline: the armature current sets up its own mmf on the quadrature axis, which distorts the main field, and because the machine is worked past the knee of its magnetisation curve, the flux gained on one pole tip is less than the flux lost on the other. The net effect is demagnetising, and it grows with load.

• Also called the performance characteristic or voltage-regulating curve.

• It is the relation between the terminal voltage \(V\) and the load current \(I\).

• It is of great importance in judging the suitability of a generator for a practical purpose.

This is the simplest case, because the field current — and hence \(E_0\) — is held constant by an external supply whatever the load does.

The external characteristic says what the generator will supply at each current. The load says what current it will draw at each voltage. Both must hold at once.

This is the same graphical device as Chapter 28's field-resistance line, applied to the output instead of the field. A resistive load is a straight line through the origin of slope \(R_L\), and reducing the load resistance flattens the line, moving the operating point to higher current and lower voltage.

A shunt generator droops more steeply than a separately excited one, and for an additional reason.

Here the field carries the load current, so more load means more flux — and the characteristic rises instead of drooping.

• On no load the current is zero, so the flux is only residual and the machine generates a few volts.

• As load current rises, \(\Phi \propto I_{se}\) below saturation, so the EMF climbs steeply.

• Eventually the field saturates and the EMF levels off, while the resistive drop \(I_a(R_a + R_{se})\) continues to grow linearly.

• The external characteristic therefore reaches a maximum and then falls.

A compound machine has both windings, so the drooping shunt characteristic and the rising series characteristic are superimposed. The designer chooses the balance by the number of series turns.

Depending upon the number of series turns \(N_{se}\), a cumulative compound generator can be over-, flat- or under-compounded. If the series-winding ampere-turns are adjusted so that as \(I_L\) increases:

• \(V_T\) also increases \(\Rightarrow\) over-compounded

• \(V_T\) remains constant \(\Rightarrow\) flat-compounded

• If \(N_{se}\) is less than required to be flat-compounded, the generator is said to be under-compounded

In a differentially compounded machine, \(V_T\) falls steeply as \(I_a\) increases, because the series field opposes the shunt field.

• The no-load or open-circuit characteristic relates \(E_0\) to \(I_f\) at fixed speed. It is the magnetisation curve of the pole material and is practically the same shape for all generators.

• The internal characteristic relates \(E\) to \(I_a\) after armature reaction, and is of interest to the designer.

• The external characteristic relates \(V\) to \(I\) and decides the generator's suitability for a purpose.

• \(V = E_0 - \Delta V_{AR} - I_aR_a - 2v_b\). Without armature reaction the internal characteristic would be a horizontal line.

• The operating point is where the external characteristic meets the load line \(V_L = I_LR_L\).

• A shunt generator droops for three reasons, the third being the fall in field current as \(V\) falls. Past the breakdown point the curve turns back, and the short-circuit current is only \(E_{res}/R_a\) — the machine is largely self-protecting.

• A series generator rises with load until saturation, then peaks where \(\mathrm{d}E/\mathrm{d}I = R_a + R_{se}\), then falls. It cannot excite on no load.

• Compound machines may be over-, flat- or under-compounded according to the series turns, or differentially compounded for a steeply drooping characteristic.

• Flat compounding needs \(N_{se} = \Delta I_f N_{sh}/I_L\) series turns per pole, where \(\Delta I_f\) is the equivalent extra field current.

• Confusing the internal and external characteristics. Internal plots \(E\) against \(I_a\); external plots \(V\) against \(I\), and the two differ by the resistive drop.

• Plotting the external characteristic against \(I_a\). In a shunt machine \(I \ne I_a\) — the field current must be subtracted.

• Forgetting the third cause of droop in a shunt machine. The falling terminal voltage weakens the field, which is what produces the turning-back.

• Expecting a large short-circuit current from a shunt generator. It is only \(E_{res}/R_a\), because the field dies with the voltage.

• Applying that reasoning to a separately excited machine. Its field is unaffected and its fault current is enormous.

• Treating the breakdown point as a normal operating condition. It lies well beyond rated load and the characteristic there is steep and unstable.

• Assuming a series generator's voltage rises indefinitely. It peaks where the magnetisation slope equals the circuit resistance.

• Trying to run a series generator on no load. With no current there is no field and only the residual voltage appears.

• Confusing over-compounding with over-excitation. Over-compounding means the series turns give a rising characteristic; it says nothing about the shunt field setting.

• Thinking a negative regulation is a fault. An over-compounded generator is designed to produce it.

Decide first which characteristic is wanted, and whether the current on the axis is \(I_a\) or \(I_L\).

1. P29.1 A separately excited generator has \(E_0 = 300\) V, an armature-reaction drop of \(0.04I_a\) volts and \(R_a = 0.12~\Omega\). Find the terminal voltage at 150 A and the regulation.

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   \[V = 300 - (0.04 + 0.12)(150) = 300 - (0.16)(150) = 300 - 24 = 276~\mathrm{V}\]

   \[\text{regulation} = \frac{300 - 276}{276} = 8.70\,\%\]

2. P29.2 The generator of P29.1 feeds a 2.0 \(\Omega\) resistive load. Find the operating point.

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   \[I = \frac{300}{2.0 + 0.16} = \frac{300}{2.16} = 138.9~\mathrm{A}, \qquad V = (138.9)(2.0) = 277.8~\mathrm{V}\]

3. P29.3 A shunt generator has \(R_a = 0.10~\Omega\) and a residual EMF of 10 V. Estimate its short-circuit current, and compare with a separately excited machine of the same \(R_a\) generating 240 V.

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   \[I_{sc,\text{shunt}} = \frac{10}{0.10} = 100~\mathrm{A}\]

   \[I_{sc,\text{sep}} = \frac{240}{0.10} = 2400~\mathrm{A}\]

   A factor of 24. The shunt machine's field collapses with the voltage; the separately excited machine's does not.

4. P29.4 A series generator has \(R_a + R_{se} = 0.30~\Omega\). Between 100 A and 120 A its EMF rises from 190 V to 196 V. Is the terminal voltage still rising?

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   \[\frac{\mathrm{d}E}{\mathrm{d}I} = \frac{196 - 190}{120 - 100} = \frac{6}{20} = 0.30~\mathrm{V/A}\]

   This equals \(R_a + R_{se}\), so the terminal voltage is at its maximum over this interval. Checking: \(V(100) = 190 - 30 = 160\) V and \(V(120) = 196 - 36 = 160\) V \(\checkmark\)

5. P29.5 A shunt generator gives 220 V no-load and 205 V at 80 A full load. The magnetisation slope is 50 V/A and the shunt winding has 1000 turns per pole. Find the series turns for flat compounding.

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   \[\Delta V = 15~\mathrm{V}, \qquad \Delta I_f = \frac{15}{50} = 0.30~\mathrm{A}\]

   \[\Delta(NI) = (0.30)(1000) = 300~\mathrm{AT/pole}, \qquad N_{se} = \frac{300}{80} = 3.75\]

   So 4 turns per pole, rounded up — giving slight over-compounding, which a diverter resistor can trim back.

6. P29.6 Why does the internal characteristic of a separately excited generator droop at all, when its field current and speed are both constant?

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   Because of armature reaction. The armature current sets up its own mmf, which distorts the main field. Since the machine works past the knee of its magnetisation curve, the flux gained at one pole tip is less than the flux lost at the other, so the net flux falls.

   The effect grows with armature current, so the induced EMF falls below \(E_0\) by an amount \(\Delta V_{AR}\) that increases with load. Without armature reaction the internal characteristic would be a horizontal straight line.

7. P29.7 Explain the turning-back of a shunt generator's external characteristic.

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   Up to the breakdown point, reducing the load resistance increases the current. But the terminal voltage falls, and since the shunt field sees that voltage, the field current and hence the flux fall too.

   Beyond a certain point the loss of flux outweighs the reduction in load resistance, so the current begins to fall as well as the voltage. This is Chapter 28's build-up loop running in reverse — a collapse rather than a build-up. The curve therefore doubles back and meets the current axis at the small short-circuit value \(E_{res}/R_a\).

8. P29.8 A generator is required to hold constant voltage at a load 500 m away. Which type, and why not a flat-compounded machine?

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   An over-compounded machine. Its terminal voltage rises with load, and the rise is designed to match the \(IR\) drop in the cable so that the voltage at the far end stays constant.

   A flat-compounded machine holds its own terminals constant, which means the load at the far end sees a voltage falling with current. The customer is at the far end, not at the generator.

9. P29.9 Why is the external characteristic the one that matters commercially?

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   It is the only one that can be measured at the terminals and the only one the load experiences. The no-load characteristic requires the armature to be open-circuited, and the internal characteristic involves an EMF that exists inside the winding and cannot be reached by a voltmeter.

   The external characteristic answers the customer's question directly: how much will the voltage sag when I draw current? That is what determines whether the machine suits the duty.

10. P29.10 A series generator is started with its load disconnected and produces almost nothing. Is it faulty?

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    No — it is behaving exactly as it must. The field winding carries the load current, so with no load there is no field current, no flux beyond the residual, and therefore only a few volts.

    A series generator must be started with its load connected. This is the mirror image of the series motor rule from Chapter 20: a series motor must never run unloaded, and a series generator must never be excited unloaded — both because the field and the load current are the same thing.