Protection & Control calculator
Power Swing Calculator: Classical Rotor-Angle Model
Explore rotor angle and slip frequency with a classical swing-equation model. Compare mechanical input with electrical transfer capability.
ProtectionBasis: Classical single-machine infinite-bus dynamics
Results
- Enter values to calculate
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How to use this calculator
A power swing is an oscillation in relative machine angle and power transfer after a disturbance. Some swings settle; others lead to loss of synchronism. This educational single-machine infinite-bus model calculates a rotor-angle trajectory from the initial angle and zero initial slip.
Change transfer reactance or mechanical input to see how electrical transfer capability changes. The maximum and final angles describe only the selected simulation window. Out-of-step protection settings need a system study that considers actual generator dynamics and relay measurements. A stable swing may enter a distance-relay characteristic; entry alone is not proof of instability.
Formula
Pmax = EV/X; Pe = Pmax sin δ
dδ/dt = Δω; dΔω/dt = ωs/(2H) [Pm − Pe − D Δω/ωs]
ωs = 2πf; slip frequency = Δω/(2π)
δ is electrical radians internally. Δω is electrical rad/s relative to the infinite bus. H is seconds on the selected power base; D multiplies per-unit speed deviation. Voltage, power and reactance must use a consistent per-unit system. The engine uses fourth-order Runge–Kutta with a maximum 1 ms step.
Worked example
For E = 1.1 p.u., V = 1 p.u. and X = 0.6 p.u., Pmax = 1.8333 p.u. At 40°, Pe = 1.1784 p.u. With Pm = 0.8 p.u., initial acceleration is negative. The stable equilibrium candidate is arcsin(0.8/1.8333) = 25.87° under this fixed-network model.
Assumptions and standards
- Classical constant internal voltage, fixed transfer reactance, constant mechanical input and optional linear damping.
- No fault-on/clearing sequence, exciter, governor or multimachine dynamics; finite-window results are not a stability certification.
- Not a relay blinder, PSB timer or out-of-step tripping settings calculator.
Calculation model checked: November 4, 2026
Frequently asked questions
Does every power swing mean loss of synchronism?
No. A stable swing remains bounded and can return to equilibrium. An unstable swing can lead to pole slipping and require controlled system separation.
Can this calculate out-of-step relay settings?
No. It illustrates the classical machine dynamics. Settings require actual relay algorithms, impedance trajectories, contingencies and validated transient-stability cases.
Can I use these results for final design?
Use them for preliminary design and checking. Final designs must be verified by a qualified engineer against the code edition and standards adopted where the work is installed.
Is my data sent anywhere?
No. Every calculation runs in your browser. Nothing you type is uploaded or stored on our servers.
References and further reading
Power system calculations: formulas and model guide