QC

API path: power_flow_relaxations.models.qc

class QC(

scenario,

configuration,

degree=8,

seed=42,

local_sampling=True,

eps_V=0.1,

eps_theta=0.15,

custom_envelope_bounds=None,

**kwargs,

)

Bases: Jabr

Implementation of QC relaxation for ACOPF using CVXPY.

Initialize Jabr relaxation variables on top of the base nodal model.

Parameters:

• scenario – Unit-based scenario (network, bids, periods).

• configuration – Solver configuration object.

• **kwargs – Extra options forwarded to NodalBaseModel.

Notes

Creates per-period dense matrices c_vwt and s_vwt of shape [n_nodes, n_nodes] used in relaxed AC flow equations.

cos_envelope(t, x, xL, xU)

Add convex relaxation bounds for the nonlinear term t = cos(x).

Uses a quadratic-cone-supported upper bound and a chord lower bound over [xL, xU] to approximate the cosine graph.

global_qmc_envelope_bounds()

Compute bounds on theta_v - theta_w, sin(theta_v - theta_w), cos(theta_v - theta_w) by sampling voltage magnitudes and angles, then filtering based on thermal limits.

Returns:

delta_theta_min, delta_theta_max, sin_min, sin_max, cos_min, cos_max

Return type:

arrays [N, N]

local_qmc_envelope_bounds(jabr_allocation, eps_V, eps_theta)

Compute per-edge bounds on theta_v - theta_w, sin(theta_v - theta_w), cos(theta_v - theta_w) by sampling around the Jabr solution with Sobol sequences, filtering based on thermal limits. Adaptive theta perturbation is applied per edge.

mccormick_envelope(t, x, y, xL, xU, yL, yU)

Add McCormick envelope constraints for the bilinear term t = x * y.

Uses variable bounds (xL, xU) and (yL, yU) to add the four linear inequalities that define the convex hull relaxation.

power_constraints()

Add Jabr SOCP power-flow constraints for every period and branch.

Includes: - active/reactive flow consistency with (c_vw, s_vw) terms, - cone constraints coupling diagonal and off-diagonal voltage products, - symmetry/skew-symmetry structure (c = c^T, s = -s^T), - voltage magnitude bounds on diagonal entries of c.

Finally delegates thermal current limits to NodalBaseModel.current_rating_constraints().

sin_envelope(t, x, xL, xU)

Add convex relaxation bounds for the nonlinear term t = sin(x).

Builds tangent/chord-based bounds over [xL, xU] to approximate the sine graph with linear constraints.

solve(**kwargs)

Solve the relaxation and return an allocation-like result object.

Parameters:

• results_file – Optional CSV path for raw variable dumps (or failure status).

• stats_file – Optional path for computed run statistics.

• u_fixed – Optional fixed commitments to enforce during solve.

• min_vol – Objective mode flag for zonal-tracking formulations.

• zonal_allocation – Optional target allocation for redispatch-style tracking objective.

• verbose – Enable MOSEK solver logs and build-step prints.

• force_integrality – If relaxed commitments produce fractional values, rerun once with rounded binary commitments fixed.

• **kwargs – Reserved for compatibility.

Returns:

Allocation-like object on success; lightweight error object otherwise.

Return type:

Allocation | Error

square_envelope(t, x, xL, xU)

Add convex-envelope constraints for the quadratic term t = x^2.

Uses an upper linear secant bound on [xL, xU] and a rotated-cone lower bound to keep t as a convex relaxation of x^2.