Gaussian Elimination — Cubic Cost Fit

Cost Fitting

We fit a proper cubic TC(q) = a + bq + cq² + dq³ using 4 equations: equation 1 is the fixed/no-load cost TC(0) = a (your fixed cost input), and equations 2–4 are the three observed (q, TC) data points. This is textbook-consistent — a is the structural intercept, not a free variable. Marginal cost MC = dTC/dq is then a quadratic.

Generator Ingestion

TC(0) = a — the 4th equation

Augmented Matrix

Rows: [q, q², q³ | TC−a] for each data point

│101001000100│
│204008000290│
│3090027000580│

Awaiting solve…

Price Discovery

Solve the matrix to derive cost curves.

Interactive Dispatch
Demand:15 MW
Solve the matrix to render cost curves.