Start strategies by case

A flat start sets every bus to 1 pu and 0 degrees, PV and slack buses to their setpoint magnitudes. The file's VM and VA columns are what the case author stored: a solved state on some files, a rough profile on others. Whether plain Newton converges from a flat start depends on the distance between start and solution and on how the step is applied (Newton update), not on the solver or the case alone.

The ladder

From the cheapest to the most expensive, each with its key under power_flow:

1. Flat start, plain Newton: flatstart: true, autodamp: false, start_mode.start_projection: false.
2. More iterations: max_iter: 80 instead of 30; decides nothing below, a flat start that diverges in 16 steps diverges in 80 too.
3. Adaptive damping: autodamp: true; the step is shortened whenever the full step does not reduce the mismatch.
4. DC-seed angles: flatstart: false, start_mode.angle_mode: dc, start_mode.dc_seed_unconditional: true; flat magnitudes with the angles of a DC power flow.
5. Projection with blend scan: flatstart: false, start_mode.start_projection: true, try_dc_start: true, try_blend_scan: true, voltage_mode: profile_blend; the start with the smallest mismatch among the raw state, the DC candidate and the blends.
6. Current-iteration pre-solve: start_current_iteration.enabled: true; a few guarded current-injection iterations before Newton.
7. APSLF start values: apslf_start.enabled: true; the analytic power-series solution as the Newton start.
8. The file's columns: flatstart: false with no start machine.
9. Rescue: rescue: true; after a non-converged solve, alternate start, damping, DC seed and settled Q limits are tried in turn.
10. Auto mode: mode: auto; the configuration is filled from the imported network and the stages above are escalated as needed.

flatstart: true sets only the start profile: every start machine follows its own key and runs from the flat profile. The two start modes (angle_mode, voltage_mode) choose a profile themselves and count as classic under a flat start; the DC angles stay available through the projection's DC candidate. Recipe 1 therefore needs the projection off as well.

With the projection on, a flat start also tries the ratio profile (start_mode.ratio_profile, default true): the flat magnitudes scaled per voltage level by the off-nominal transformer ratios on the path from the reference. A flat start drives a circulating current through every off-nominal transformer, and a stiff winding off nominal (the star equivalent of a three-winding transformer) can dominate the start: on the CGMES MiniGrid it is 164 pu of active power on a 9 MW case and the polar update diverges; the ratio profile starts at 0.09 pu and converges in three steps to the delivery's own state.

Independent of the projection, every flat start sets the auxiliary buses (the star points of three-winding transformers) to the current-free value of their lowest-impedance winding, the visible buses keep 1.0 pu and 0 degrees; that alone lets the MiniGrid converge from the bare flat start (polar update, projection off) in four steps. A network without auxiliary buses starts as before.

Recipes

Plain Newton from the flat start with the polar update, no damping, 30 iterations, and what to set where that is not enough. Iterations are mismatch evaluations (Newton steps plus one). The APSLF column is solver: apslf, order 24 with the Newton polish.

A converged state is not always the operating state: a low-voltage branch satisfies the equations to the tolerance like the operating solution, only the voltages tell them apart. The wrong-branch check (power_flow.wrong_branch_detection, Power-Flow Configuration) judges every voltage level of the result and names the reason.

Where the cases come from

Sparlectra ships none of the cases above. Obtain them from their sources under their own license and citation terms:

• case14, case118, case300, case1354pegase, case2869pegase, case9241pegase, case13659pegase, case1888rte, case2848rte, case6495rte, case3120sp, case4_dist, case18, case33bw: MATPOWER case files, data/<name>.m in https://github.com/MATPOWER/matpower; cite MATPOWER (Citation and case-file usage). The PEGASE and RTE files ask for case-specific citations in their headers (Fliscounakis et al. 2013 and Josz et al. 2016 for PEGASE, Josz et al. 2016 for RTE); case3120sp is the Polish system model distributed with MATPOWER; the distribution feeders name their papers in their headers.
• mvlv1004, mvlv10616, mvlv29840: synthetic radial MV/LV distribution grids, generated with a fixed seed by scripts/generate_distribution.py of https://github.com/m-mirz/benchmark-grids (directory generated/; the generator is the port of power-grid-model's FictionalGridGenerator in gridoxide 0.0.2, Apache-2.0) and exported to MATPOWER format. Their loading is power-grid-model's benchmark loading (0.67 to 0.89 pu), not an operating point.

Conventions

The standard MATPOWER reading (shift in degrees, sign +1, ratio as stored, bus shunt as admittance) satisfies the power balance of the file on every case above; the alternative readings (radians, sign -1, reciprocal ratio) fail wherever a file has a phase shift or an off-nominal tap. The PEGASE VM and VA columns are not a solved state under any reading (best fit 0.5 to 3.9 pu at the worst bus; a solved state scores below 0.1 pu), so a scan of those columns must not change the reading. Overrides and scan are experimental and off by default: MATPOWER conventions (experimental).

Q limits

With reactive limits on, the enforcement method selects the solution: on case300 from the flat start the in-iteration active set converts 48 PV buses and ends at 422.7 MW of losses, the classic simultaneous and one-at-a-time methods convert 28 and end at 395.4 and 457.9 MW, without limits the case solves at 408.3 MW. All satisfy the equations with their limit sets, so a comparison with limits on names the method (power_flow.qlimits.enforcement_mode, Q-limit Switching Strategy).