Before a lunar base adds a habitat module, an oxygen plant, or a rover depot, someone has to say how much load its surface network can carry, and what happens when a cable fails. On Earth, the same question decides where a data center connects and how large a generating project can be. The usual answer re-runs a power-flow study for every outage and every demand case, and hands back a number without its reasons. Tensor Grid hands back the number with its certificate: the megawatts you can rely on across your whole range of demand and every single-line outage, and the exact demand and outage that would take them away — checked independently, before you build.
1,000,000 buses, every single-line outage, one desktop computer. Lower is better.
A new load at 1,000,000 buses. Demand rises by q at every bus, and by r more at alternating buses and the project.
| question | Tensor | comparator | result |
|---|---|---|---|
| DC headroom, 1,000,000 buses, every single-line outage | 0.0202 ms 25.3 MB | warm HiGHS 605.607 ms, 2.8 GB | 115 MW certified 794-byte certificate |
| Ready to answer at 1,000,000 buses | 16.50 s all 1,998,000 outages | warm HiGHS 15.37 s, one outage | every outage in the time of one |
| AC headroom, 1,000,000 buses, every single-line outage | 6.52 µs 26.0 MB | warm Newton, replay 3.094 s, 211.7 MB | 27.529101 MW 439-byte certificate |
| AC headroom on the PGLib 14‑bus network, new load at bus 14 | 4 MW certified 18 proof cells | — | every original limit intact and two outages |
| DC-OPF exact certificates on public PGLib cases | 14 of 14 through 78,484 buses | independent checker | certified optimal built in 108.0 s checked in 68.7 s |
| DC-OPF, 250,000 buses, meshed network | 3.15 s 0.6 GB | Mehrotra interior point 481.89 s, 4.1 GB | 153× faster |
| AC-OPF, 250,000 buses, peak memory | 10.3 GB | MIPS, in Python 22.4 GB | 54.0% less memory |
At a million buses, Tensor proved all 1,998,000 single-line outages in 16.50 s, about the time HiGHS took to prepare a single outage model (15.37 s). From then on every question is a lookup: 100,000 exact questions in about three seconds, each answered safe or proved infeasible, at every network size from 1,024 buses to a million.
A data center needs its full load, every hour; a generating project is certified on what it can actually deliver, never on nameplate it would have to curtail. On PGLib’s public 14-bus network, a conservative DC study certified 61.1 MW of new load at bus 14 across its declared demand range and network states, and, in a companion study, 90.9 MW of new generation. The same study names the limit: with line 9–14 out, the project sits behind the 76 MW line 13–14, with 14.9 MW of local demand already on it.
On the same public network, with every voltage, reactive-power, line-rating, and angle limit of the original case, 4 MW of new load at bus 14 is certified across 0 to 2% demand growth, intact and with either of two lines out. On a million-bus AC network at 2% growth, 27.529101 MW is guaranteed for every one of 1,998,000 single-line outages against a proved upper bound of 28.000000 MW, by a 439-byte certificate; each question is answered in 6.52 µs from 26.0 MB, against 3.094 s and 211.7 MB for a warm Newton solve with replay.
The 14 public PGLib-OPF networks through 78,484 buses were each certified optimal and independently verified, the largest built in 108.0 s and checked in 68.7 s. On a 250,000-bus meshed network, Tensor solved DC optimal power flow in 3.15 s and 0.6 GB, against 481.89 s and 4.1 GB for a sparse Mehrotra interior-point solver on the same equations: 153× faster. On AC optimal power flow at the same size it used 54% less memory than MIPS, MATPOWER’s interior-point solver, in Python. Across 66 public PGLib-OPF cases and six meshed networks, 297 of 297 qualification jobs were accepted, including case8387_pegase, where MIPS failed.