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Synchronous electrical generator (one gigawatt capacity, open, the stator end cooling channels exposed)

The synchronous generator is one of the three main types of electric generators design (when classified by the principle of operation, the other two being asynchronous generator and parametric generator).

The output of each phase of a synchronous generator is an electrical sine wave. This waveform is chosen due to its additive property: adding or subtracting time-shifted sine waves produce yet another sinewave. Modern electrical grid relies on hundreds or even thousands of synchronous generators tied together via the electromagnetic couplings so that their output frequencies and phases are synchronized, until the mass introduction of the solar and wind power, almost all electrical power in the grids was produced by the synchronous generators. The design of synchronous generators makes them into natural providers of ancillary services critical to the security of the grid (like the inertial response and the reactive power management).

Synchronous generator is a synchronous machine, sharing many details of construction and operation with a synchronous motor. This commonality is exploited in the design of "reversible" machines that can operate both as a generator and a motor (used, for example, in the pumped-storage hydroelectricity.

Construction

A diagram of a two-pole (heteropolar) three-phase synchronous generator and output waveforms. The three phases are U, V, W; each phase has two terminals connected to the close end of the wire (U2 and U1 for U), far ends of each pair of wires are tied together. The voltages below are U2-U1, etc. The vertical dotted line corresponds to the current position of the rotor. Dots and crosses on the wires indicate the direction of current. The rotor rotates clockwise. The diagram shown is oversimplified: in practical designs, the two-pole rotors are of non-salient type, stator coils have multiple turns.

A synchronous generator consists of a rotating part (rotor) coupled with a source of power (prime mover) and an enclosing stationary part (stator) that contains the armature, coils that produce the output electrical current. Usually the rotor is a source of magnetic excitation and is designed in a way to produce a nearly-sinusoidal distribution of the magnetic field along the air gap between the rotor and the stator in the (radial) direction orthogonal to the gap. This arrangement - an excitation field source on the rotor and armature on the stator is due to high output power that would be difficult to pass through slip rings had the armature been attached to the rotor. The opposite arrangement (fixed excitation field, rotating armature, like in the DC generators) is uncommon, yet sometimes used for low-power synchronous generators.

The stators of synchronous generators mostly use construction with equally spaced slots that contain three-phase windings (occasionally generators are designed for a single-phase or two-phase circuit). The stators are constructed of thin laminated sheets of electrical steel.

Typical parameters

A magnet has two magnetic poles, thus the number of poles in the rotor is even ($2\cdot p$). A full revolution of the two-pole rotor (like the one on a diagram) provides a full cycle of alternating current, so to achieve the frequency f with p pole pairs, the rotor shall rotate at the speed $n=f/p$. For example, a two-pole design for the standard line frequencies of 60 Hz and 50 Hz shall rotate at 3600 RPM and 3000 RPM respectively. These are comfortable speeds for many steam and gas turbines, thus many turbogenerator rotors are of two-pole design (the centrifugal forces in the largest turbines dictate slower speeds, so for these cases the four-pole rotors are used rotating at 1800 RPM or 1500 RPM). These rotors use a cylindrical (non-salient design constructed of solid iron and have a diameter under 1 meter. The rotor can be few meters long.

High-power hydroelectric turbines have very large diameters and therefore need to run much slower (for example, a 200 MW turbine can reach 14 meters in diameter and rotates at just 75 RPM, therefore the rotor of its generator needs $p=40$ pole pairs for 50 Hz line frequency). This results in a different design of the generator rotor, with salient pole shoes made of laminated cores (the rest of the construction utilizes solid mild steel). The axial length of the stator for these machines is much smaller than its diameter, with ratio usually under 1⁄5.

The stators of synchronous generators are mostly of the same construction with equally spaced slots that contain three-phase windings (occasionally generators are designed for a single-phase or two-phase circuit). Due to the magnetic saturation of iron, the maximum field in the air gap is approximately one tesla, corresponding to about 150 V per square meter of the area swept by the turn of the stator coil (at the typical line frequencies). For the high-power generators, the target voltage is measure in thousands of Volts (11 kV to 25 kV), so stator windings contain multiple turns.

Larger turbines have higher efficiency, so the generators used in electrical grids tend to be very powerful, up to 1.5 gigawatt for steam turbine driver units.

Classification

Boldea proposes the following classification scheme for synchronous generators based on the rotor construction:

• using heteropolar excitation. This is the traditional arrangement where the stator is presented with both N and S poles of the rotor (as in the diagram);
  • electrical rotor excitation using direct current. The current is provided by an exciter device;
    • salient pole rotor, typically used for multipole ($2\cdot p>4$) slow-speed hydroelectric generators;
    • non-salient rotor (also known as cylindrical or round rotor) is typically used for two- or our-pole high-speed generators attached to the gas and steam turbines;
    • superconducting rotor;
  • claw pole rotor with electrical excitation. This design is currently only used for low-power, low-voltage car alternators;
  • permanent magnet rotor. The magnets are used to provide excitation in small generators;
  • variable reluctance rotor;
    • pure electrical;
    • with permanent magnet assistance;
    • permanent magnet and electrical excitation;
• using homopolar excitation where the stator is only presented with poles of one polarity;
  • electrical excitation;
  • permanent magnet excitation.

• 
  Salient pole generator cross-cut. Pole rotation is clockwise
• 
  Non-salient pole generator
• 
  Claw pole rotor

Characteristics

D-curve. Active power is on the horizontal axis, reactive power is on the vertical axis.

The behavior of synchronous generators is described by multiple characteristics.

Main article: Capability curve

The capability curve (also known as D-curve) characterizes the ability of the generator to deliver both active and reactive power. While a generator operates within its D-curve, the marginal cost of providing and absorbing the reactive power is close to zero.

Main article: Short circuit ratio (synchronous generator)

The short circuit ratio is the ratio of field current required to produce rated armature voltage at the open circuit to the field current required to produce the rated armature current at short circuit. This ratio can also be expressed as an inverse of the saturated direct-axis synchronous reactance (in p.u.):

$SCR={\frac {1}{X_{S}}}$

pen-circuit saturation curve , synchronous impedance curve, zero power factor curve

Main articles: Open-circuit saturation curve, Synchronous impedance curve, and Zero power factor curve

History

A 1987 replica of the 1887 Haselwander's generator

The first industrial synchronous generators date back to the 1880s once the transmission range limits of the DC current (due to lack of transformers) were understood. These were primitive devices with the roles of the stator and rotor reversed when compared to the modern design: the stator provided the excitation field, while the rotor was fit with the armature connected to the slip rings, like in a DC generator. Single-phase synchronous motors had problems starting, so already in the late 1880s Galileo Ferraris suggested using the two-phase system (his idea dates back to 1885). The design of the first three-phase generator with armature in the stator and four-pole rotor is credited to Friedrich August Haselwander (1887). First commercial three-phase synchronous generator followed in the 1891 (Charles Eugene Lancelot Brown). The early 1900s saw introduction of high-speed generators to match the steam turbines and a victory of the three-phase systems over two-phase ones.

Roebel's patent

With the basic of the synchronous generator design were established early in the 20th century, the next 100 years witnessed incremental improvements:

• copper loss reduction utilizing the skin effect (discovered in the 1905−1908) in a stranded "Roebel cables" (1912, Ludwig Roebel);
• stray loss reduction via laminated pressplate to decrease the stator core end heating (Georges Jean Marie Darrieus of the wind turbine fame);
• cooling improvements: transition from air cooling to hydrogen cooling (a 1915 French patent by Maximilian Schuler, practical use since 1938 in the US, 1945 in Europe) reduced the windage loss, the use of direct conductor oil cooling and, later, water cooling to a large extent is associated with Eugen Wiedemann;
• development of high voltage insulation in the 1950s-1960s (mica-glass fibre) enabled output voltages up to 27 kV;
• use of new materials (alloyed forging steel for the rotor, nonmagnetic steel for the rotor retaining rings, glass-fibre reinforced plastics;
• development of solid-state rectifiers enabled DC excitation using AC power sources;

Combined together, these changes brought the generator efficiency into the 97-99% range and increased the unit power 4000 times over the course of a century.

Sources

• Al-Akayshee, Q.H.; Eastham, J.F. (1996). A comparison between AC side excited heteropolar and homopolar synchronous machines. Proceedings of International Conference on Power Electronics, Drives and Energy Systems for Industrial Growth. Vol. 1. IEEE. pp. 530–534. doi:10.1109/PEDES.1996.539669. ISBN 978-0-7803-2795-5.
• Boldea, I. (2005). Synchronous Generators. The Electric Generators Handbook. CRC Press. ISBN 978-1-4200-3725-8. Retrieved 2024-09-07.
• Boldea, I. (2015). Synchronous Generators (Second ed.). CRC Press. ISBN 978-1-4987-2355-8. Retrieved 2024-09-09.
• Denholm, Paul; Mai, Trieu; Kenyon, Rick Wallace; Kroposki, Ben; O’Malley, Mark (2020). Inertia and the Power Grid: A Guide Without the Spin (PDF). Golden, Colorado: National Renewable Energy Laboratory.
• Geocaris, Madeline (August 10, 2022). "Assessing Power System Reliability in a Changing Grid, Environment". NREL.gov. National Renewable Energy Laboratory. Retrieved 10 May 2023.
• Ehya, H.; Faiz, J. (2022). "Operation Principles, Structure, and Design of Synchronous Generators". Electromagnetic Analysis and Condition Monitoring of Synchronous Generators. IEEE Press Series on Power and Energy Systems. Wiley. pp. 9–51. ISBN 978-1-119-63607-6. Retrieved 2024-09-10.
• Neidhofer, Gerhard (2007). "Early Three-Phase Power [History]". IEEE Power and Energy Magazine. 5 (5): 88–100. doi:10.1109/MPE.2007.904752. ISSN 1540-7977.
• Neidhöfer, Gerhard (1992). "The evolution of the synchronous machine" (PDF). Engineering Science and Education Journal. 1 (5): 239–248. doi:10.1049/esej:19920050.
• Savage, M.A. (1930). Economic Developments in Turbine Generators in the United States (PDF). Transactions: Second World Power Conference. Vol. XII. Berlin: VDI-Verlag Gmbh. pp. 42–59.
• Staff Report (February 4, 2005). Principles for Efficient and Reliable Reactive Power Supply and Consumption (PDF). Washington, D.C.: Federal Energy Regulatory Commission.

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