Separately Excited DC Generators | Electrical Machines - Electrical Engineering (EE) PDF Download

Separately excited DC generators

A separately excited DC generator is a DC machine whose field winding is supplied from an independent DC source so that the field current is under separate control. The machine converts mechanical input (prime mover) into DC electrical output by rotating the armature in the field produced by the separately excited field winding. The following sections explain the structure, steady-state relations, magnetic behaviour, characteristic curves, armature reaction, field compounding and worked examples.

Structure and electrical representation of the armature

The cross-section of a two-pole DC machine shows the pole pieces (with field winding) and the armature with commutator and brushes. The armature winding is formed by many coils placed in slots around the armature core. Although the actual armature winding is a continuous set of coils which change position relative to the brushes as the armature rotates, it is convenient to represent the armature electrically as several identical coils arranged in parallel paths. The number of parallel paths is equal to the number of poles for a lap-wound armature and equal to two for a wave-wound armature.

Basic steady-state electrical model

For steady state (DC conditions) the inductances in the field and armature have no effect on the DC operating point and may be ignored. The electrical circuits reduce to resistances and induced voltages. Typical circuit variables and relations for generator convention (machine producing electrical output) are:

• Field circuit: Vf = Rf If
• Armature circuit (generator): Vt = E - Ia·ra - Ebrush
• Induced voltage (back e.m.f.): E = k φ ωr
• Developed torque: Te = k φ Ia

Here Vf is the applied field voltage, Rf the field resistance, If the field current, Vt the terminal voltage, E the induced emf in the armature, Ia the armature current, ra the armature resistance, Ebrush the (approximate) fixed brush contact drop, ωr the mechanical angular speed and k a machine constant. For motoring operation the sign of armature current reverses and the terminal relation becomes Vt = E + Ebrush + Ia·ra (with appropriate sign conventions).

Brush contact drop and simplifications

Brush contact drop is commonly modelled as a constant voltage drop (Ebrush) independent of Ia and speed. For many practical problems this constant is taken as about 2 V, but the exact value depends on brush design. For steady state problems we usually neglect inductances and use the resistive model together with the induced voltage relation E = k φ ωr.

Magnetic circuit, saturation and residual magnetism

The magnetic circuit of a DC machine consists of air gaps and iron paths (pole cores, armature teeth, stator core). Except for the air gap the flux paths traverse ferromagnetic iron which saturates at higher magnetising ampere-turns. As the field magnetomotive force (m.m.f.) increases, flux per pole φ initially rises nearly linearly; after iron begins to saturate the increase in φ with further m.m.f. becomes small and the curve flattens. Iron also exhibits residual magnetism: a small flux remains in the magnetic circuit even when field excitation is removed. Residual magnetism is important for self-excited generators but is also relevant when establishing open-circuit characteristics.

Open-circuit characteristic (OCC)

The open-circuit characteristic (OCC) is the relation between induced armature voltage E (with armature open-circuited) and field current If at a constant speed. Since E ∝ φ and φ is a non-linear function of If (because of saturation and residual flux), the OCC shows the same general shape as the φ versus If curve: an initial near-linear region followed by saturation.

OCC is obtained experimentally by driving the generator at a fixed speed, keeping armature terminals open, and varying the field current slowly (to avoid hysteresis effects). If OCC at speed N1 is known, OCC at another speed N2 is obtained by scaling E by the ratio N2/N1 because E ∝ speed.

Separately excited generator model and relation to load

For a separately excited generator supplying a load the key relations are:

• Vt = E - Ia·ra - Ebrush (generator convention)
• Vf = Rf·If
• E = k φ(If) · ωr
• Te = k φ(If) · Ia

The load connected to the armature determines Ia. For a purely resistive load RL fed by the generator terminal voltage Vt, we have Vt = RL·Ia. Combining Vt = RL·Ia with the armature equation gives the operating point as the intersection of the generator internal characteristic and the load line.

Output (external) characteristics

The external characteristic (or output characteristic) is a plot of terminal voltage Vt versus load current IL (IL = Ia) at fixed speed and fixed field excitation (If = If,rated). If armature reaction is neglected and field flux is assumed constant at its no-load value, the induced emf E stays constant and Vt falls with load only because of the armature resistance drop:

Vt = Erated - Ia·ra

The load line for a particular load resistance RL is Vt = RL·Ia. The intersection of the load line and the generator line gives the operating Vt and Ia.

Armature reaction and its effect on voltage

Armature reaction is the distortion and partial neutralisation of the main field flux by the magnetic field produced by the armature current. The armature mmf shifts and distorts the flux distribution; under saturation the net effect is typically a reduction of the useful flux per pole as Ia increases. Consequently the induced voltage E falls with increasing Ia even if If is held constant.

When armature reaction is present the induced voltage with armature current is less than the induced voltage without armature reaction for the same If and speed. Therefore the terminal voltage drop with load has two components:

• Reduction of E due to armature reaction.
• Ohmic drop Ia·ra and brush drop Ebrush.

Field compounding curve (field compensation)

The effect of armature reaction can be expressed in terms of equivalent demagnetising field ampere-turns. The field compounding curve (or field compensation curve) is a plot of field current If required to maintain a constant terminal voltage Vt for various load currents IL, at fixed speed. In the absence of armature reaction the required compensation is only for Ia·ra (ohmic drop) and the If versus IL curve would be nearly linear. With armature reaction an extra increase in If is required and the curve deviates accordingly. The armature reaction demagnetising mmf can be experimentally converted to an equivalent field current by dividing demagnetising ampere-turns by the number of field turns Nf.

Determination of equivalent demagnetising field current

To find equivalent field amperes for armature reaction at a desired terminal voltage, the field compounding curve must be measured at that terminal voltage and speed. The quantity A-B (in the standard experimental plot) gives the additional field current required at a given Ia, and this extra current represents the equivalent field current to balance armature reaction.

Worked examples

Worked Example 1 - Change of speed (neglecting armature reaction)

Problem statement: A separately excited DC machine has armature resistance ra = 0.04 Ω and brush contact drop Ebrush = 2 V. It supplies a load current of 200 A at terminal voltage Vt = 125 V when rotated at 1200 rpm. If the speed is reduced to 1000 rpm, find the new armature current. Armature reaction is neglected.

SOLUTION

Compute the induced emf at 1200 rpm.

E(1200) = Vt + Ebrush + Ia·ra

E(1200) = 125 + 2 + 200 × 0.04 = 135 V

Scale the induced emf to 1000 rpm using proportionality with speed.

E(1000) = E(1200) × (1000 / 1200) = 135 × (5 / 6) = 112.5 V

Compute the load resistance RL using the known terminal voltage and current at 1200 rpm.

RL = Vt / Ia = 125 / 200 = 0.625 Ω

Total effective armature circuit resistance seen by induced emf at 1000 rpm is ra + RL.

rtotal = ra + RL = 0.04 + 0.625 = 0.665 Ω

Solve for Ia at 1000 rpm using the circuit: (E(1000) - Ebrush) = Ia × rtotal.

Ia(1000) = (E(1000) - Ebrush) / rtotal = (112.5 - 2) / 0.665 ≈ 166 A

Worked Example 2 - Including armature reaction

Problem statement (data preserved from experiment): A separately excited DC generator has rated terminal voltage 110 V, rated speed 1500 rpm, rated power 3.3 kW and 4 poles. The open-circuit characteristic (OCC) data are: residual (If = 0) 5 V; If = 0.25 A → 40 V; If = 0.5 A → 65 V; If = 0.75 A → 82.5 V; If = 1.0 A → 95 V; If = 1.25 A → (table entry not listed); If = 2.3 A → 120 V. The armature resistance is ra = 0.2 Ω, number of field turns Nf = 200, brush drop Ebrush = 2 V. Demagnetising ampere-turns per pole due to armature current are proportional to Ia and are equal to 1.5 × Ia. Find the terminal voltage at Ia = 20 A when the machine runs at constant speed and field excitation is such that no-load terminal voltage is 110 V.

SOLUTION

First compute the terminal voltage neglecting armature reaction.

Armature circuit drop = Ia·ra + Ebrush = 20 × 0.2 + 2 = 6 V

Vt (no armature reaction) = 110 - 6 = 104 V

Now include armature reaction. Compute demagnetising ampere-turns and convert to equivalent field current.

Demagnetising AT = 1.5 × Ia = 1.5 × 20 = 30 AT

Equivalent demagnetising If = Demagnetising AT / Nf = 30 / 200 = 0.15 A (demagnetising)

Determine the field current required for 110 V no-load from the OCC data.

Required If for 110 V (no load) = 1.5 A (from the OCC table as given)

Compute net effective field current under load after subtracting the demagnetising equivalent.

If,net = If (no-load) - Equivalent demagnetising If = 1.5 - 0.15 = 1.35 A

Read off (or interpolate from) the OCC to find induced voltage E at If = 1.35 A.

E(If = 1.35 A) ≈ 107 V (approximately, from the OCC data)

Subtract the armature circuit drop to obtain terminal voltage under load including armature reaction.

Vt = E(If,net) - (Ia·ra + Ebrush) = 107 - 6 = 101 V

Conclusion: With armature reaction included the terminal voltage falls to about 101 V for Ia = 20 A, while neglecting armature reaction would predict 104 V. This demonstrates the additional voltage reduction due to armature reaction beyond the resistive drop.

Applications and practical remarks

• Separately excited DC generators allow independent control of field flux and thus precise control of terminal voltage and reactive response for a given speed.
• OCC is a fundamental test for machine design and inspection; it allows prediction of induced emf for different field currents and speeds.
• Field compounding and compensating windings are used in practical machines to reduce the adverse effects of armature reaction and to improve voltage regulation under load.
• Brush contact drop, commutation, armature reaction and saturation must all be considered in accurate machine modelling, controller design and performance prediction.

End of chapter.