Final Equivalent Circuit

To produce the final per-phase equivalent circuit for an induction machine, it is necessary to refer the rotor part of the model over to the stator side. The rotor circuit model that will be referred to the stator side is shown in Figure 3.19, which has all the speed variation effects concentrated in the impedance term.

In an ordinary trans former, the voltages, currents and the impedances on the secondary side of the device can be referred to the primary side by means of the turns ratio of the transformer:

s

where the prime refers to the referred values of voltage, current and impedance.

Exactly the same sort of transformation can be done for the induction machine’s rotor circuit. If the effective turns ratio of an induction machine is aeff, then the transformed rotor voltage becomes;

0

and the rotor current becomes;

eff R

2 a

I = I (3.37)

and the rotor impedance becomes



Figure 3.20 The per-phase equivalent circuit for induction machines

In wind energy conversion systems, depending on the speed of the wind, the generator may act either as a generator, supplying power to the grid, or as a motor (acting as a sink of power from the grid). In either case, there will be a difference in speed between the shaft speed n_r and the output n_s. This is known as generator slip, and may be expressed as;

s

n_s : Electrical speed of the magnetic field (or stator speed) (rpm) nr : Rotor mechanical speed (rpm)

The slip is defined as negative when the machine is acting as a generator, and positive when acting as a motor. (Chapman, 1999, pp.369-370)

Figure 3.21 Torque -Speed curve for a MW-size induction machine

The torque-speed characteristic curve in Figure 3.21 shows that, if an induction motor is driven at a speed greater than synchronous speed by an external effect (i.e.

wind), the direction of its induced torque will reverse and it will act as a generator.

As the torque applied to its shaft increases, the amount of power produced by that generator increases. There is a maximum possible induced torque in the generator mode of operation. This torque is known as the pushover torque of the ge nerator. If a torque is applied to the shaft of the induction generator which is greater than the pushover torque, the generator will over-speed. (Chapman, 1999, p.436)

As a generator, an induction machine has severe limitations. Because it lacks a separate field circuit, an induction generator cannot produce reactive power. In fact, it consumes reactive power, and an external source of reactive power must be connected to it at all times to maintain its stator magnetic field. This external source of reactive power must also control the terminal voltage of the generator—with no field current, an induction generator cannot control its own output voltage. Normally, the generator's voltage is maintained by the external power system to which it is connected.

The one great advantage of an induction generator is its simplicity. An induction generator does not need a separate field circuit and does not have to be driven continuously at a fixed speed. As long as the machine's speed is some value greater than synchronous speed for the power system to which it is connected, it will function as a generator. The greater the torque applied to its shaft (up to a certain point), the greater its resulting output power. The fact that no fancy regulation is required makes this generator a good choice for windmills, heat recovery systems, and similar supplementary power sources attached to an existing power system. In such applications, power- factor correction can be provided by capacitors, and the generator's terminal voltage can be controlled by the external power system.

(Chapman, 1999, p.437)

Wind machines driving electrical generators operate at either variable or constant speed. In variable-speed operation, rotor speed varies with wind speed. In constant-speed machines, rotor constant-speed remains relatively constant, despite changes in wind speed. (Gipe, 1995, p.211)

Small wind turbines typically operate at variable speed. This simplifies the turbine’s controls while improving aerodynamic performance. When these small wind machines drive an induction generator, both the voltage and frequency vary with wind speed. The electricity they produce is incompatible with the constant-voltage, constant- frequency alternating current (AC) produced by the utility, but can

be used as is for resistive heating or pumping water at variable rates, or it can be rectified to direct current (DC) for charging batteries.

If a grid-connected turbine is fitted with an AC generator, this must produce power that is in phase with the utility's grid supply. Many commercial grid-connected turbines use induction AC ge nerators, whose magnetizing current is drawn from the grid, ensuring that the generator's output frequency is locked to that of the utility and so controlling the rotor speed within limits. Synchronous generators produce electricity in synchronization with the generator's rotating shaft frequency.

Thus, the rotor speed of grid-connected turbines must exactly match the utility supply frequency.

To generate utility-compatible electricity, the output from a variable-speed generator must be conditioned. Although it is possible to use rotary inverters for this task, variable-speed turbines typically use a form of synchronous inverter to produce constant- voltage 50 or 60 Hz AC like that of the utility. Most of these inverters use the utility’s alternating current as a signal to trigger electronic switches that transfer the variable-frequency electricity at just the right moment to deliver 50 or 60 Hz AC at the proper voltage.

Although some manufacturers of medium-sized wind turbines build variable-speed turbines, most operate the rotor at or near constant variable-speed. These machines produce utility-compatible power directly via induction (asynchronous) generators.

Induction generators have two advantages over alternators;

• They are inexpensive.

• They can supply utility-compatible electricity without complicated controls.

For AC generators, a critical design factor, that is synchronous speed, must be considered. AC generators produce alternating current, the frequency of which varies directly with the speed of the rotor and indirectly with the number of poles in the

generator. For a given number of poles, frequency increases with increasing

Manufacturers should decide the number of poles of the generator (for either synchronous or asynchronous) for optimum conditions.

Table 3.2 Common Synchronous Speeds for Generators

Pole Number Europe (50 Hz) North America (60 Hz)

4-pole 1500 rpm 1800 rpm

6-pole 1000 rpm 1200 rpm

An induction generator begins producing electricity when it is driven above its synchronous speed which is generally 1000 or 1500 rpm in Europe (1200 or 1800 rpm in North America). Induction generators are not true constant-speed machines.

As torque increases, generator speed increases 2 to 5 %, or 20 to 50 rpm on a 1000-rpm generator. This increase of 1 to 3 1000-rpm in rotor speed is imperceptible in a wind turbine operating at a nominal speed of 50 rpm. As torque increases, the magnetic field in the induction generator also increases. This continues until the generator reaches its limit, which is about 5 % greater than its synchronous speed. Induction generators are readily available in a range of sizes and are easily interconnected with the utility. Medium- sized wind turbines use induction generators almost exclusively.

3.3.4. RECENT DEVELOPMENTS IN GENERATORS FOR WIND