I've described everything needed to implement the fitting algorithm to the Veloclinic model. All that remained was to tune the parameters.
I started with a CP-model fit, yielding parameters CP and AWC. I used these to generate initial guesses for the VC model parameters. P2 = CP, then I set τ2 = 24000 seconds (an arbitrary value), then P1 = 1-second power - CP, then τ1 = AWC / P1. It's important with nonlinear fits to have a good initial guess, and this seems to get close enough for the algorithm to find its way.
Then there's the question of the damping factor and the weighting factor. A damping factor of 0.5 works fairly well, but I relaxed it to 0.25, which results in slow convergence but helped in one difficult case. Then there's the weighting factor. 10 thousand yields a nice envelope fit, but I relaxed it to 1000 because this also helped the fit converge.
Here's results generated from 28 datasets I had laying around. In one dataset the algorithm failed to converge. I can improve things by tuning the fitting further, for example applying adaptive or nonlinear damping. But this gives a good idea for how well it works:
One thing which is clear is the model almost universally overpredicts sprint power. I'm not going to try to explain why that is, but simply to observe the two-component form of the model is very simplistic.
Veloclinic continues to work on his modeling, for example as described here.