What Is the Synchronous Machine d-q Salient Rotor Torque Calculator?
In salient-pole synchronous machines, magnetic saliency (Xd > Xq) generates reluctance torque in addition to rotor field excitation torque.
How Does the Synchronous Machine d-q Salient Rotor Torque Calculator Work?
Rotor poles align with minimum magnetic reluctance paths, producing a double-frequency sin(2*delta) torque component.
Synchronous Machine d-q Salient Rotor Torque Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
P = 3 left[ rac{V_t E_f}{X_d} sin(delta) + rac{V_t^2}{2} left( rac{1}{X_q} - rac{1}{X_d}
ight) sin(2delta)
ight], quad T = rac{P}{omega_s}
Park d-q power-angle equation for salient-pole synchronous electrical machines.
How to Use the Synchronous Machine d-q Salient Rotor Torque Calculator
- Input phase terminal voltage, internal back-EMF Ef, reactances Xd and Xq, and power angle delta.
Step-by-Step Example Calculation
Hydroelectric Salient-Pole Generator
Input Values:
terminalVoltageV:230
fieldInducedVoltageEf:260
directReactanceXd:1.4
quadratureReactanceXq:0.85
powerAngleDeltaDeg:32
Worked Steps: Field torque = 368.5 N·m, Reluctance torque = 94.2 N·m (20.4% contribution), Total torque = 462.7 N·m.
Understanding Your Result
Displays total shaft torque in N·m, breakdown between field and reluctance components, and percentage reluctance contribution.
Factors That Affect the Result
- Reluctance torque allows the machine to maintain stability and deliver mechanical power even under complete loss of DC field excitation.
When Should You Use This Calculator?
- Hydro generator design, synchronous reluctance motors (SynRM), and permanent magnet assisted reluctance motors (PM-aSynRM).
Assumptions & Limitations
- Neglects stator armature resistance and magnetic core saturation.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard classical 2-axis Park formulation.