Short circuit ratio (synchronous generator)

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In an electromechanical generator, [1] 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. [1] [2] This ratio can also be expressed as an inverse of the saturated [3] direct-axis synchronous reactance (in p.u.): [4]

Contents

Effects of SCR values

Both high and low levels of SCR have their benefits: [5]

Therefore, in practice the design of a generator is seeking an SCR that balances benefits and drawbacks for a particular application. [6]

Effects of construction

The larger the SCR, the smaller is alternator reactance (Xd) and inductance Ld. This is the result of larger air gaps in generator design (As in Hydro generators or Salient Pole Machines). It results into Machine loosely coupled to the grid, and its response will be slow. This increases the machines’ stability while operating on the grid, but simultaneously will increase the short circuit current delivery capability of the machine (higher short circuit current) and subsequently larger machine size and its cost. Typical values of SCR for Hydro alternators may be in the range of 1 to 1.5.

Conversely, the smaller the SCR, the larger is alternator's reactance (Xd), the larger is Ld. It results from small air gaps in machine design (As in Turbo generators or Cylindrical rotor Machines). Machines are tightly coupled to the grid, and their response will be fast. This reduces the machine's stability while operating on the grid and will reduce the short circuit current delivery capability (lower short circuit current), smaller machine size, and lower cost subsequently. Typical values of SCR for turbo alternators may be in the range of 0.45 to 0.9.

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Short circuit ratio has multiple meanings:

<span class="mw-page-title-main">Capability curve</span>

Capability curve of an electrical generator describes the limits of the active (MW) and reactive power (MVAr) that the generator can provide. The curve represents a boundary of all operating points in the MW/MVAr plane; it is typically drawn with the real power on the horizontal axis, and, for the synchronous generator, resembles a letter D in shape, thus another name for the same curve, D-curve. In some sources the axes are switched, and the curve gets a dome-shaped appearance.

In an electrical grid, the short circuit ratio is the ratio of the short circuit apparent power (SCMVA) in the case of a line-line-line-ground (3LG) fault at the location in the grid where some generator is connected to the power rating of the generator itself (GMW). Since the power that can be delivered by the grid varies by location, frequently a location is indicated, for example, at the point of interconnection (POI):

The reactances of synchronous machines comprise a set of characteristic constants used in the theory of synchronous machines. Technically, these constants are specified in units of the electrical reactance (ohms), although they are typically expressed in the per-unit system and thus dimensionless. Since for practically all machines the resistance of the coils is negligibly small in comparison to the reactance, the latter can be used instead of (complex) electrical impedance, simplifying the calculations.

References

  1. 1 2 Lawrence F. Drbal; Patricia G. Boston; Kayla L. Westra; Black & Veatch. Power Plant Engineering (1996 ed.). Springer. p. 241.
  2. A.K.Sawney (2011). A Course in Electrical Machine Design (6th ed.). Dhanpat Rai and co. p. 11.18.
  3. Das 2017, p. 493.
  4. Louis 2014, p. 641.
  5. Ehya & Faiz 2022, pp. 33–34.
  6. Ehya & Faiz 2022, p. 34.

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