DC Power Flow

DC power flow is a linearized approximation of AC power flow, suitable for economic dispatch and contingency analysis.

DC Approximations

1. Lossless lines - Ignore resistance (R ≈ 0)
2. Flat voltage - All bus voltages = 1.0 pu
3. Small angles - sin(θ) ≈ θ, cos(θ) ≈ 1

Result: Power flow depends only on bus angles (θ) and line reactances (X).

Bus Number Mapping

Power system bus numbers may not be contiguous (e.g., case300 has non-sequential bus IDs). Always create a mapping from bus numbers to 0-indexed array positions:

# Create mapping: bus_number -> 0-indexed position
bus_num_to_idx = {int(buses[i, 0]): i for i in range(n_bus)}