interactive demos

Interactive experiments in power systems and mathematics.

Explore power factor, network flows, and a few mathematical ideas by changing the numbers and watching the result. Each demo includes a short explanation of what you’re seeing.

Power Systems

A truck carrying the useful load along a ramp representing the phase angle.

Power Factor Correction

Deliver the same useful power with less line current. Add compensation and watch the power triangle and waveforms change.

Blue and orange particles illustrating useful power and reactive exchange.

Reactive Power in Motion

See the difference between useful power and reactive exchange. Keep the kVA rating fixed and explore leading and lagging power factor.

The same four-bus power grid with its tie line connected and removed.

Braess's Paradox

Can removing a line lower the cost of running a grid? Compare power flows and generator dispatch, then explore the traffic version of the paradox.

A six-bus grid with nodal prices and a monitored line at its limit during an outage.

Grid Operations & Dispatch

Follow a grid from its day-ahead plan to real-time dispatch. Change demand, remove a line, and see how generation and nodal prices respond.

Math

Polya's Urn 🏺

Draw a ball, then add another of the same color. See how a small early advantage can grow through repeated reinforcement.

Sierpinski Triangle

Pick a vertex at random, move halfway toward it, and repeat. Watch a triangle emerge from a simple rule.

Euler's Identity

Follow a rotating point around the complex plane to see why $e^{i\pi} + 1 = 0$ brings five familiar constants together.