Dynamic modeling and simulation of 5 kW synchronous generator

Dissertation for Master's degree

Field of study: electricity-power

Preference: electric machines

In a synchronous generator, a dc current is applied to the rotor coil to produce a magnetic field. Then the rotor of the generator is rotated by a prime mover, to create a rotating magnetic field in the machine. This magnetic field induces a three-phase voltage in the stator coils of the generator.

In this machine, two terms are widely used to describe the coils: one is field coils and the other is armature coils. In general, the term field coils refers to the coils that produce the main magnetic field in the machine. The term armature windings refers to the windings in which the main voltage is induced. For synchronous machines, it is the field windings in the rotor. The rotor of a synchronous generator is essentially a large electromagnet. The magnetic poles in the rotor can be prominent or non-prominent. A salient pole is a magnetic pole protruding from the surface of the rotor. On the other hand, a salient pole is a magnetic pole flush with the surface of the rotor. A non-prominent or flat rotor is usually used for 2- or 4-pole applications. While salient rotors are used for 4 or more poles. Because the magnetic field in the rotor is variable, to reduce losses, it is made of thin layers. A constant current must be applied to the field circuit in the rotor. Because the rotor rotates, it needs a special arrangement to deliver DC power to its field coils. There are 2 ways to do this:

1- from an external source to the rotor with sliding rings and brushes. 2- Providing DC power from a DC power source, which is installed directly on the shaft of the synchronous generator.

The sliding rings completely surround the machine shaft but are separate from it. One end of the DC coil is connected to each of the two ends of the slip ring on the shaft of the synchronous motor, and a fixed brush slides on each slip ring. The wipers are a block of graphic-like compounds that conduct electricity easily, but have very little friction and therefore do not cause corrosion on the rims. If the positive end of the DC voltage source is connected to one sweep and the negative end to the other. A constant voltage is then applied to the coil throughout, regardless of its location and angular velocity, the field. Slip rings and brushes create several problems for synchronous machine field windings when DC voltage is applied. They increase maintenance on the machine, as the brush must be checked frequently for wear. In addition, the sweep voltage drop may result in significant power losses along with the field currents. Despite these problems, slip rings are used on all smaller synchronous machines. Because there is no more economical way to apply the field current.

In larger motors and generators, brushless actuators are used to deliver the DC field current to the machine. A brushless actuator is a small AC generator whose field circuit is installed on the stator and its armature circuit is installed on the rotor. It can be directly applied to the main DC field circuit. By controlling a small DC field current from the drive generator (which is mounted on the stator), the field current can be set on the main machine without using slip rings and brushes. Because there is never a mechanical connection between the rotor and the stator, a brush drive requires less maintenance than slip rings and brushes. In order for the generator excitation to be completely independent of external excitation sources, a small pilot actuator is often included in the system. The pilot drive is a small AC generator with permanent magnets mounted on the rotor shaft and a winding on the stator. This actuator provides energy for the actuator field circuit, which in turn controls the main machine field circuit. If a pilot drive is mounted on the generator shaft then no external electrical power is required to operate the generator.

Many synchronous generators that have brushless drives also have slip rings and brushes so an additional source of DC field current is available in case of emergency.The stator of synchronous generators is usually made in two layers: the winding itself is distributed and has small steps to reduce the harmonic components of output voltages and currents.

Because the rotor rotates at a speed equal to the speed of the magnetic field, electric power is produced with a frequency of 50 or 60 Hz, and the generator must rotate at a constant speed depending on the number of poles, for example, to generate power 60 Hz in a two-pole machine, the rotor must rotate at a speed of 3600 rpm. To produce 50Hz power in a 4-pole machine, the rotor must rotate at a speed of 1500 rpm. The required speed of an assumed frequency can always be calculated from the following equation [1]:

1- Frequency

2- Mechanical speed

3- Number of poles

The induced voltage in the stator depends on the flux in the machine, the frequency or speed of rotation, and the construction of the machine. The internal generated voltage is directly proportional to the flux and speed, but the flux itself depends on the current in the rotor field circuit.

The internal voltage is not equal to the output voltage. There are several factors that cause the difference between the two: 1- The distortion in the magnetic field of the air gap due to the current in the stator, which is called armature reaction. 2- The self-inductance of the armature coils 3- The resistance of the armature coils 4- The effect of the shape of the salient poles of the rotor when a generator works and feeds the loads of the system then: 1- The direct and reactive power produced by the generator is equal to the amount of power demanded by the load connected to it. 2- Generator governor setting points control the working frequency of the power system. 3- The field current (or field regulator setting points) controls the terminal voltage of the power system. This is the situation that exists in separate and widely spaced generators.

1.1     Voltage equations in machine variables:

A star-connected, three-phase, two-pole salient-pole synchronous machine is shown in Figure 2-1. The stator windings are similar windings with a sinusoidal distribution with a difference of 120 degrees with an effective number of turns Ns and resistance rs[

The machine rotor is equipped with one excitation winding and three damping windings. The excitation coil (coil Nfd) has an effective number of turns Nfd and resistance rfd. A damping coil is located on the same magnetic axis as the excitation coil. This winding i.e. kd has effective number of turns Nkd with resistance rkd. The magnetic axis of the second and third damping coils, coils Kq1 and Kq2, is 90 degrees ahead of the magnetic axis of the coils fd and kd. The coils Kq1 and Kq2 have the effective number of turns Nkq1 and Nkq2 with resistances rkq1 and rkq2, respectively. It is assumed that all rotor windings are sinusoidally distributed.  In Figure 2-1, the magnetic axes of the stator coils are marked with as, bs, and cs axes. The transverse axis q and the longitudinal axis d are shown in the figure. The q axis is the magnetic axis of coils kq1 and kq2. But d axis is the magnetic axis of fd and kd coils. d and q axis were used before park work. Park used fd,fq,fo notation in his conversion. In this seminar, we have used fds, fqs, fos and fdr, fqr, for to display the transferred variables of the induction machine without implicit reference to the d and q axis. These variables have constant physical implications that are independent of park conversion.

Although the supply voltage is applied to the damping coils. But in reality, these windings are short-circuited and present paths for rotor transfer currents. Currents may flow in cage windings similar to the squirrel cage windings of induction machines or in the actual iron of the rotor. In salient pole machines, at least the rotor is laminated. As a result, the damping winding currents are, for the most part, confined to the cage windings embedded in the rotor surface. In high speed two or four pole machines, the rotor is cylindrical. And it is made of solid iron with a cage coil that is placed on the surface of the rotor. In these machines, current may flow in the rack winding or solid iron. [3]

Efficiency of almost all types of synchronous machines can be adequately predicted with simple corrections and equations describing machine efficiency as shown in Figure 2-1.