Formulations

tellegen solves the DC power flow and DC OPF, the AC power flow, and the Jabr SOCWR relaxation through one interface, each driven from the engine’s public API. Every formulation returns the same result shape (locational marginal prices, voltages, branch flows, and generator dispatch) and exposes analytical sensitivities through the contract described in the sensitivity contract.

DC power flow and DC OPF (B–θ)

The linearized power flow couples bus angles $\theta$ to injections through the susceptance-weighted graph Laplacian

$$ B = A\operatorname{diag}(b)A^\top, \qquad B\theta = p, $$

where $A$ is the branch–bus incidence and $b$ the branch susceptances. The OPF minimizes generation cost subject to the network balance and the thermal and generation limits; it is a convex quadratic program solved with Clarabel. Entry point: solve_network (or solve_prebuilt over a prebuilt DcNetwork).

Generator costs are quadratic. MATPOWER model 2 polynomial rows are read directly; model 1 piecewise linear rows are projected onto a least squares quadratic (a least squares line when the quadratic fit is rejected), so objectives and prices for such cases are for the fitted curve, not the piecewise original.

AC power flow (polar)

The nodal power balance in polar coordinates,

$$ S_i = V_i \sum_j \overline{Y_{ij}} \overline{V_j}, $$

is solved by Newton–Raphson on the reduced system $\partial(P, Q)/\partial(\theta, V_m)$. Buses are typed slack / PV / PQ (PV and slack buses hold the generator voltage setpoint; PQ buses solve for both angle and magnitude), and the solve takes damped steps with a backtracking line search from the setpoint start plus a few perturbations, keeping the lowest-residual result. Entry point: ac_pf.

Conic SOCWR (Jabr)

The Jabr second-order cone relaxation lifts the voltage product to W-space variables $w_i = |V_i|^2$, $w^r_{ij} = \Re(V_i \overline{V_j})$, $w^i_{ij} = \Im(V_i \overline{V_j})$, with the rotated cone coupling

$$ (w^r_{ij})^2 + (w^i_{ij})^2 \le w_i w_j. $$

The relaxation is a convex lower bound on AC OPF, solved with Clarabel’s second-order cone support. Entry point: socwr_opf.

Every formulation is pure Rust and compiles to WebAssembly, so the same code runs on a server and in the browser. The full nonlinear AC OPF (an interior-point program) is on the roadmap; it runs natively, where it can use threads.