Electrical Generator

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6.1 Electromechanical Energy Conversion

The conversion of the mechanical power of the wind turbine into the electrical power can be accomplished by any one of the following types of the electrical machines:

• the synchronous machine.

• the induction machine.

These machines work on the principles of the electromagnetic actions and reactions. The resulting electromechanical energy conversion is reversible. The same machine can be used as the motor for converting the electrical power into mechanical power, or as the generator converting the mechanical power into the electrical power.

Figure 6-1 depicts common features of the electrical machines. Typically, there is an outer stationary member (stator) and an inner rotating member (rotor). The rotor is mounted on bearings fixed to the stator. Both the stator and the rotor carry cylindrical iron cores, which are separated by an air gap. The cores are made of magnetic iron of high permeability, and have conductors embedded in slots distributed on the core surface. Alternatively, the conductors are wrapped in the coil form around salient magnetic poles. Figure 6-2 is the cross-sectional view of the rotating electrical machine with the stator with salient poles and the rotor with distributed conductors. The magnetic flux, created by the excitation current in one of the two members, passes from one core to the other in the combined magnetic circuit always forming a closed loop. The electromechanical energy conversion is accomplished by interaction of the magnetic flux produced by one member with the electric current in the other member. The latter may be externally supplied or electromagnetically induced. The induced current is proportional to the rate of change in the flux linkage due to rotation.

Rate Flux Linkage


Common constructional features of the rotating electrical machines.


Common constructional features of the rotating electrical machines.

Generator Pole Salient Embedded


Cross section of the electrical machine stator and rotor.


Cross section of the electrical machine stator and rotor.

The various types of machines differ fundamentally in the distribution of the conductors forming the windings, and in whether the elements have continuous slotted cores or salient poles. The electrical operation of any given machine depends on the nature of the voltages applied to its windings. The narrow annular air gap between the stator and the rotor is the critical region of the machine operation, and the theory of performance is mainly concerned with the conditions in or near the air gap.

6.1.1 DC Machine

All machines are internally alternating current (AC) machines because of the conductor rotation in the magnetic flux of alternate north and south polarity. The DC machine must convert the AC into DC, and does so by using the mechanical commutator. The commutator performs this function by sliding carbon brushes on a series of copper segments. The positive output terminal is, thus, continuously switched to the conductor generating the positive polarity voltage, as is the negative polarity terminal. The sliding contacts inherently result in low reliability and high maintenance cost. Despite this disadvantage, the DC machine had been used extensively until early 1980s because of its extremely easy speed control. It has been used in a limited number of wind power installations of small capacity, particularly where electricity can be locally used in the DC form. However, the conventional DC machine with mechanical commutator has fallen out of favor.

The conventional DC machine is either self-excited by shunt or series coils carrying DC current to produce a magnetic field. The DC machine of the present day is often designed with permanent magnets to eliminate the field current requirement, hence, the commutator. It is designed in the "inside-out" configuration. The rotor carries the permanent magnet poles and the stator carries the wound armature which produces AC current. The AC is then rectified using the solid state rectifiers. Such machines do not need the commutator and the brushes, hence, the reliability is greatly improved. The permanent magnet DC machine is used with small wind turbines, however, due to limitation of the permanent magnet capacity and strength. The brush-less DC machine is expected to be limited to ratings below one hundred kW.

6.1.2 Synchronous Machine

Most of the electrical power consumed in the world is generated by the synchronous generator. For this reason, the synchronous machine is an established machine. The machine works at a constant speed related to the fixed frequency. Therefore, it is not well suited for variable-speed operation in the wind plants. Moreover, the synchronous machine requires DC current to excite the rotor field, which needs sliding carbon brushes on slip rings on the rotor shaft. This poses a limitation on its use. The need of the DC field current and the brushes can be eliminated by using the reluctance rotor, where the synchronous operation is achieved by the reluctance torque. The reliability is greatly improved while reducing the cost. The machine rating, however, is limited to tens of kW. The reluctance synchronous generator is being investigated at present for small wind generators.1

The synchronous machine is ideally suited in constant-speed systems, such as in the solar thermal power plants. The machine is, therefore, covered in some detail in Chapter 9.

Unlike the induction machine covered later in this chapter, the synchronous machine, when used in the grid-connected system, has some advantage. It does not require the reactive power from the grid. This results in a better quality of power at the grid interface. This advantage is more pronounced when the wind farm is connected to a small capacity grid using long low voltage lines. For this reason, early California plants used synchronous generators. Today's wind plants generally connect to larger grids using shorter lines, and almost universally use the induction generator.

6.1.3 Induction Machine

Most of the electrical power in the industry is consumed by the induction machine driving the mechanical load. For this reason, the induction machine represents a well established technology. The primary advantage of the induction machine is the rugged brushless construction and no need for separate DC field power. The disadvantages of both the DC machine and the synchronous machine are eliminated in the induction machine, resulting in low capital cost, low maintenance, and better transient performance. For these reasons, the induction generator is extensively used in small and large wind farms and small hydroelectric power plants. The machine is available in numerous power ratings up to several megawatts capacity, and even larger.

The induction machine needs AC excitation current. The machine is either self-excited or externally excited. Since the excitation current is mainly reactive, a stand-alone system is self-excited by shunt capacitors. The induction generator connected to the grid draws the excitation power from the network. The synchronous generators connected to the network must be capable of supplying this reactive power.

For economy and reliability, many wind power systems use induction machines as the electrical generator. The remaining part of this chapter is, therefore, devoted to the construction and the theory of operation of the induction generator.

6.2 Induction Generator 6.2.1 Construction

In the electromagnetic structure of the induction generator, the stator is made of numerous coils with three groups (phases), and is supplied with three-phase current. The three coils are physically spread around the stator periphery and carry currents which are out of time-phase. This combination produces a rotating magnetic field, which is a key feature of the working of

Solar Generator Design Drawings


Squirrel cage rotor of the induction machine under rotating magnetic field.


Squirrel cage rotor of the induction machine under rotating magnetic field.

the induction machine. The angular speed of the rotating magnetic field is called the synchronous speed. It is denoted by Ns and is given by the following:

p where f = frequency of the stator excitation p = number of magnetic pole pairs.

The stator coils are embedded in slots of high-permeability magnetic core to produce the required magnetic field intensity with low exciting current.

The rotor, however, has a completely different structure. It is made of solid conducting bars embedded in the slots of a magnetic core. The bars are connected together at both ends by the conducting end rings (Figure 6-3). Because of its resemblance, the rotor is called the squirrel cage rotor, or the cage rotor in short.

6.2.2 Working Principle

The stator magnetic field is rotating at the synchronous speed determined by Equation 6-1. This field is conceptually represented by the rotating magnets in Figure 6-3. The relative speed between the rotating field and the rotor induces the voltage in each rotor turn linking the stator flux 0. The magnitude of the induced voltage is given by Faraday's law of electromagnetic induction, namely:

dt where ^ = the magnetic flux linking the rotor turn.

This voltage in turn sets up the circulating current in the rotor. The electromagnetic interaction of the rotor current and the stator flux produces the torque. The amplitude of this torque is given by the following:

where K = constant of proportionality

O = amplitude of the stator flux wave

I2 = amplitude of induced current in the rotor bars

= phase angle by which the rotor current lags the rotor voltage.

The rotor will accelerate under this torque. If the rotor was on frictionless bearings with no mechanical load attached, it is completely free to rotate with zero resistance. Under this condition, the rotor will attain the same speed as the stator field, namely, the synchronous speed. At this speed, the current induced in the rotor speed is zero, no torque is produced and none is required. The rotor finds equilibrium at this speed and will continue to run at the synchronous speed.

If the rotor is now attached to a mechanical load such as a fan, it will slow down. The stator flux, which always rotates at the constant, synchronous speed, will have relative speed with respect to the rotor. As a result, the electromagnetically induced voltage, current, and torque are produced in the rotor. The torque produced must equal that needed to drive the load at that speed. The machine works as the motor in this condition.

If we attach the rotor to a wind turbine and drive it faster than the synchronous speed, the induced current and the torque in the rotor reverse the direction. The machine now works as the generator, converting the mechanical power of the turbine into electrical power delivered to the load connected to the stator terminals. If the machine was connected to a grid, it would feed power into the grid.

Thus, the induction machine can work as the electrical generator only at speeds higher than the synchronous speed. The generator operation, for that reason, is often called the super-synchronous speed operation of the induction machine.

As described above, the induction machine needs no electrical connection between the stator and the rotor. Its operation is entirely based on the electromagnetic induction, hence, the name. The absence of rubbing electrical contacts and simplicity of its construction make the induction generator very

robust, reliable, and a low-cost machine. For this reason, it is widely used in numerous applications in the industry.

The working principle of the induction machine can be seen as the transformer. The high voltage coil on the stator is excited and the low voltage coil on the rotor is shorted on itself. The power from one to the other can flow in either direction. The theory of operation of the transformer, therefore, holds true when modified to account for the relative motion between the stator and the rotor. This motion is expressed in terms of the slip of the rotor relative to the synchronously rotating magnetic field.

6.2.3 Rotor Speed and Slip

The slip of the rotor is defined as the ratio of the speed of the rotating magnetic field sweeping past the rotor and the synchronous speed of the stator magnetic field. That is, s = Ns - Nr (6-4)

where s = slip of the rotor

Ns = synchronous speed = 60f/p Nr = rotor speed.

The slip is generally considered positive in the motoring operation. In the generator mode, the slip would therefore be negative. In both the motoring mode and the generating mode, higher rotor slips induce higher current in the rotor and higher electromechanical power conversion. In both modes, the value of the slip is generally a few to several percent. Higher slips result in greater electrical loss, which must be effectively dissipated from the rotor to keep the operating temperature below the allowable limit.

The heat is removed from the machine by the fan blades attached to one end-ring of the rotor. The fan is enclosed in a shroud at the end. The forced air travels axially along the machine exterior, which has fins to increase the dissipation area. Figure 6-4 is an exterior view of a 150 kW induction machine showing the end shroud and the cooling fins running axially. Figure 6-5 is a cutaway view of the machine interior of a 2 MW induction machine.

The induction generator feeding the 60 or 50 Hz grid must run at speed higher than 3,600 rpm in a two-pole design, 1,800 rpm in a four-pole design, and 1,200 rpm in a six-pole design. The wind turbine speed, on the other hand, varies from a few hundred rpm in the kW range machines to a few tens of rpm in the MW rage machines. The wind turbine therefore must interface the generator via a mechanical gear. Since this somewhat degrades the efficiency and reliability, many small stand-alone plants operate with custom designed generators operating at lower speed without the mechanical gear.

Induction Generator Stand Alone


A 150 kW induction machine. (Source: General Electric Company, Fort Wayne, IN.)


A 150 kW induction machine. (Source: General Electric Company, Fort Wayne, IN.)

Teco Generator


Two MW induction machine. (Source: Teco Westinghouse Motor Company, Round Rock, Texas, With permission.)


Two MW induction machine. (Source: Teco Westinghouse Motor Company, Round Rock, Texas, With permission.)


Equivalent electrical circuit of induction machine for performance calculations.


Equivalent electrical circuit of induction machine for performance calculations.

Under the steady state operation at slip "s", the induction generator has the following operating speeds:

• stator flux wave speed Ns

• stator flux speed with respect to rotor s • Ns rotor flux speed with respect to stator Nr + s • Ns = Ns

6.2.4 Equivalent Circuit for Performance Calculations

The theory of operation of the induction machine is represented by the equivalent circuit shown in Figure 6-6. It is similar to that of the transformer. The left-hand side of the circuit represents the stator and the right hand side, the rotor. The stator and the rotor currents are represented by I1 and I2, respectively. The vertical circuit branch at the junction carries the magnetizing (or excitation) current Io, which sets the magnetic flux required for the electromagnetic operation of the machine. The total stator current is then the sum of the rotor current and the excitation current. The air-gap separation is not shown, nor is the difference in the number of turns in the stator and rotor windings. This essentially means that the rotor is assumed to have the same number of turns as the stator and has an ideal 100 percent magnetic coupling. We calculate the performance parameters taking the stator winding as the reference. The actual rotor voltage and current would be related with the calculated values through the turn ratio between the two windings. Thus, the calculations are customarily performed in terms of the stator, as we shall do in this chapter. This matches the practice, as the performance measurements are always done on the stator side. The rotor is inaccessible for any routine measurements.

Most of the flux links both the stator and the rotor. The flux which does not link both is called the leakage flux. The leakage flux is represented by the leakage reactance. One-half of the total leakage reactance is attributed to each side, namely the stator leakage reactance Xx and the rotor leakage reactance X2 in Figure 6-6(b). The stator and the rotor conductor resistance are represented by R1 and R2, respectively. The magnetizing parameters Xm and Rm represent the permeability and losses (hysteresis and eddy current) in the magnetic circuit of the machine.

The slip dependent rotor resistance R2(1-s)/s represents the electromechanical power conversion. The power conversion per phase of the three-phase machine is given by I22 R2 ■ (1 -s)/s. The three-phase power conversion is then as follows:

The machine capacity rating is the power developed under rated conditions, that is as follows:

Machine Rating = emrate kW or emrate horsepower. (6-7)

15 1000 746

The electromechanical power conversion given by Equation 6-6 is physically appreciated as follows. If the machine is not loaded and has zero friction, it runs at the synchronous speed, the slip is zero and the value of R2(1-s)/s becomes infinite. The rotor current is then zero, and so is Pem, as it should be. When the rotor is standing still, the slip is unity and the value of R2 ■ (1-s)/s is zero. The rotor current is not zero, but the Pem is zero, as the mechanical power delivered by the standstill rotor is zero.

At any slip other than zero or unity, neither the rotor current nor the speed is zero, resulting in a non-zero value of Pem.

The mechanical torque is given by the power divided by the angular speed, that is as follows:

where Tem = electromechanical torque developed in the rotor in newton-meters ra = angular speed of the rotor = 2n.Ns ■ (1-s)/60 in mechanical radians/sec.

Combining the above equations, we obtain the torque at any slip s, as follows: Tem = (180/2nNs)./ R2/s Newton-meters (6-9)

The value of 12 in equation (6-9) is determined by the equivalent circuit parameters, and is slip dependent. The torque developed by the induction machine rotor is, therefore, highly slip-dependent, as is discussed later in this chapter.

We take a note here that the performance of the induction machine is completely determined by the equivalent circuit parameters. The circuit parameters are supplied by the machine manufacturer, but can be determined by two basic tests on the machine. The full-speed test under no load and the zero-speed test with blocked rotor determine the complete equivalent circuit of the machine.2-3

The equivalent circuit parameters are generally expressed in perunit of their respective rated values per phase. The rated impedance per phase is defined as the following:

_ Rated voltage per phase Rated current per phase

For example, the perunit (pu) stator resistance is expressed as the following:

and similar expressions for all other circuit parameters. When expressed as such, X1 and X2 are equal, each a few to several percent. The R1 and R2 are approximately equal, each a few percent of the rated impedance. The magnetizing parameters Xm and Rm are usually large, in several hundred percent of Zrated , hence, drawing negligible current compared to the rated current. For this reason, the magnetizing branch of the circuit is often ignored in making approximations of the machine performance calculations.

All of the above performance equations hold true for both the induction motor and the induction generator by taking the proper sign of the slip. In the generator mode, the value of the slip is negative in the performance equations wherever it appears. We must also remember that the real power output is negative, that is the shaft receives power instead of delivering it. The reactive power drawn from the stator terminals remains lagging with respect to the line voltage, hence, we say that the induction generator delivers leading reactive power. Both of these mean that the magnetizing volt-amperes are supplied by an external source.

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Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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