Q8Computer Aided Design of Electrical Machines

(a) Short Circuit Ratio and Its Effects

The Short Circuit Ratio (SCR) of a synchronous machine (alternator) is defined as the ratio of the field current required to produce rated (normal) open-circuit terminal voltage, to the field current required to circulate rated full-load armature (short-circuit) current when the machine's armature terminals are short-circuited:

SCR is determined experimentally from the machine's open-circuit characteristic (OCC, plotting terminal voltage against field current at no load) and short-circuit characteristic (SCC, plotting armature short-circuit current against field current), by reading off the two respective field current values at the machine's rated voltage and rated current points on these two curves.

Effects of SCR on Synchronous Machine Performance

• Voltage regulation: a machine with a higher SCR (physically corresponding to a machine with a larger air gap and lower synchronous reactance) exhibits better (smaller) inherent voltage regulation, meaning its terminal voltage changes less between no-load and full-load conditions for a given field current setting, since a lower synchronous reactance produces a smaller internal voltage drop for a given armature current.
• Steady-state stability limit: a higher SCR machine (lower synchronous reactance) has a higher theoretical maximum steady-state power transfer capability and hence a greater steady-state stability margin, since maximum power transfer for a synchronous machine is inversely proportional to its synchronous reactance.
• Parallel operation and synchronizing power: a higher SCR machine has a stronger synchronizing power coefficient, meaning it more effectively resists falling out of step with other machines operating in parallel on the same system, an important consideration for generators required to operate reliably in a large interconnected grid.
• Short-circuit fault current: paradoxically, a higher SCR (lower reactance) machine also produces a higher fault current magnitude during an actual short-circuit fault condition, requiring correspondingly higher-rated switchgear and protection systems to safely handle this increased fault current.
• Physical size and cost: achieving a high SCR (large air gap, low reactance) generally requires a physically larger machine (more field MMF capacity to overcome the larger air-gap reluctance), increasing both material cost and, for a given rating, the machine's overall physical size and weight — representing the central design trade-off in selecting an appropriate SCR value for a given application (typically higher SCR values, around 1.0-1.5, chosen for machines requiring good stability/voltage regulation performance such as those on weak or isolated systems, versus lower SCR values, around 0.5-0.7, more common in modern, more compact, economically-optimized turbo-alternator designs connected to strong interconnected grids where the machine's own individual stability contribution is less critical).

SCR is Inversely Proportional to Synchronous Reactance

Proof: consider the machine's per-unit synchronous reactance, Xs(pu), defined as the ratio of the armature reaction/leakage-reactance voltage drop at rated current to the rated terminal voltage. From the open-circuit characteristic, the field current If(OC) required to produce rated voltage V(rated) can be read directly. From the short-circuit characteristic (which, since the machine's magnetic circuit remains largely unsaturated during a short-circuit test, is very nearly a straight line through the origin), the field current If(SC) required to circulate rated armature current I(rated) can similarly be read directly, and this same field current If(SC), if instead applied with the machine open-circuited (operating on the unsaturated, linear portion of the OCC, extrapolated as needed), would produce some corresponding voltage, V'.

Since the short-circuit condition itself represents the internal generated EMF (corresponding to field current If(SC)) being entirely consumed across the machine's own synchronous impedance (predominantly reactance Xs) to drive the rated short-circuit current I(rated), we have, using the unsaturated (linear) OCC extrapolation: V'=I(rated)*Xs(actual ohms). Meanwhile, by definition of SCR:

Substituting V'=I(rated)*Xs(actual):

since the per-unit synchronous reactance is, by its own standard definition, Xs(pu)=Xs(actual)/(Vrated/Irated) (actual reactance divided by the base/rated impedance Vrated/Irated). This directly demonstrates that:

confirming that the Short Circuit Ratio is exactly the reciprocal of (i.e., inversely proportional to) the machine's per-unit synchronous reactance, under the standard unsaturated-characteristic approximation used in this analysis — this simple, elegant inverse relationship is precisely why SCR and per-unit synchronous reactance are often used interchangeably (in reciprocal form) as equivalent indicators of a synchronous machine's fundamental electrical design character, air-gap size, and expected regulation/stability performance.

(b) Design of Stator Core and Winding; Rotor Design

Stator core design: the stator core of a synchronous machine is built up from thin, insulated silicon-steel laminations (typically 0.35-0.5mm thick) stacked axially and clamped together, with the lamination thickness and insulating coating chosen to minimize eddy-current losses in the core. The core's internal (bore) surface is punched with slots to house the armature (stator) winding conductors, with slot shape, number, and dimensions chosen based on the required number of slots per pole per phase (a key winding design parameter affecting winding factor, harmonic content, and mechanical/electrical balance), and with ventilating (radial cooling) ducts typically provided at intervals along the core's axial length for machines above a certain size, to allow adequate heat dissipation from the core interior.

Stator winding design: the stator (armature) winding is typically a distributed, double-layer, short-pitched three-phase winding, with the number of slots, coils per phase, coil pitch (chordal factor), and distribution across multiple slots per pole per phase (distribution factor) all chosen to optimize the winding factor Kw (maximizing useful fundamental EMF while suppressing unwanted harmonic EMF components), balance the mechanical/thermal loading around the periphery, and achieve the required voltage rating and current-carrying capacity within the available slot space, consistent with the specific electric loading value assumed during the main-dimension design calculation.

Rotor design: synchronous machine rotors are constructed in one of two principal forms depending on the machine's operating speed — salient-pole rotors (used for lower-speed machines, such as hydro-generators, with distinctly projecting pole pieces carrying concentrated field windings, offering a naturally larger, non-uniform air gap that reduces certain harmonic effects and simplifies damper winding integration) or cylindrical (non-salient/round) rotors (used for high-speed machines, such as steam/gas-turbine-driven turbo-alternators, with the field winding embedded in slots machined into a solid, mechanically robust cylindrical forging, providing the mechanical strength required to withstand the very high centrifugal stresses at typical turbo-alternator speeds of 3000 or 3600 rpm). Rotor design must account for mechanical strength and dynamic balancing (particularly critical at high rotational speeds), adequate field-winding current-carrying capacity and cooling (especially for large machines using hydrogen or direct water/hydrogen inner-conductor cooling, as discussed in an earlier answer), and, for salient-pole machines, the inclusion of damper (amortisseur) windings embedded in the pole faces, providing damping torque against rotor oscillations and assisting asynchronous starting/synchronizing performance.