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Electric Generators and their Control for Large Wind Turbines 237

When Q > 0, the machine may “deliver” reactive power (i < 0), while Q < 0 means “absorbing”
e
d
e
reactive power. Now operating at about unity power factor (in the case of the diode rectifier machine
interface, the fundamental power factor is unity) is rather simple, but the reluctance torque is nega-
tive as L − L > 0 and i < 0 (Q = 0), while i > 0 for the generating mode. The bottleneck in the
d
e
q
q
d
design is to provide sufficient voltage under load at minimum speed to deliver the reference power
at that speed. So the highest excitation current is required at lowest speed, and thus, the design meth-
odology has to carefully follow this aspect. If a PWM voltage source converter (rectifier) is used on
the machine stator side, this constraint is not so severe by using some voltage boosting, corroborated
with excitation current rise at low speeds, so the final solution may lead to a higher efficiency system
(excitation losses in the generator are reduced).
If the speed range is small (±10%), the generator excitation losses to cover the power control for
a diode rectified output may be acceptable and result in a lower-cost solution. However, the motor-
ing is not possible.
9.5.1 Optimal Design of DCE-SG
The general design methodology of the DCE-SG model is rather similar to that of standard SGs [4],
and it contains

• The specifications (short-circuit ratio, transient inductance, reactive–active power capa-
bility and power factor, excitation system and its voltage ceiling, voltage and frequency
[speed] control range, negative sequence voltages and currents, harmonics of generator at
no-load voltages, temperature ratings, start–stop cycles, forces, armature voltage, runaway
speed)
• Design issues (output coefficient and base stator geometry; number of stator slots; design
of stator winding; design of stator core; salient pole rotor design; open-circuit saturation
curve; field current at full load and lowest assigned power factor; stator resistance; leakage
inductance; and synchronous inductance L , L ; calculated losses and efficiency; time con-
d
q
stants and subtransient (transient) inductance; cooling system and thermal design; design
of brushes and slip rings [if any], design of bearings, frame, etc.; brakes and jacks design;
exciter design)

The SG design heritage is incorporated into an optimal design of a 7.6 MW, 3.6 kV, n = 11 rpm
wind generator [4], based on modified Hooke–Jeeves method [20]. A parameter variable is left to
choose the number of pole pairs p, which defines the stator frequency:

f s = pf n (9.33)

A higher number of poles lead to a better efficiency, and lower weight up to a point, but, at the
cost of a large outer diameter of the stator, can be expected, as shown in Figure 9.24.
From Figure 9.24, more illustrative data are selected, and they are shown in Table 9.5.
The result for the fifth optimal design case (180 poles, 12 m outer stator diameter) in Table 9.5
is followed in detail.
A few cost function components are considered:

• Active material cost
• Overtemperature penalty
• Energy loss
• Initial generator cost
• Total cost function