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Expand and correct math details in the power flow docs#64

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ck/docs-math
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Expand and correct math details in the power flow docs#64
cameronkhanpour wants to merge 2 commits into
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ck/docs-math

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Improves the mathematical detail in the docs/src/math/ pages, with every added formula checked against the sensitivity code. Docs only; no code changes.

DC Power Flow

  • Spell out the switching flow sensitivity as explicit direct and indirect terms, and expand the angle sensitivity into closed form.

DC OPF

  • Gate the angle difference limits by sw to match the model and KKT system.
  • Add the explicit per-branch KKT switching derivative blocks.

AC Power Flow

  • New Admittance and Topology Sensitivity section: voltage sensitivity to branch conductance and susceptance via implicit differentiation, plus the sw gate in the bus admittance matrix.

AC OPF

  • Note the implicit function framing of the KKT differentiation.

Cites Talkington et al. (arXiv:2510.17071) in the AC docs.

Verify each added formula against the sensitivity implementations.

- DC power flow: write out the switching flow sensitivity (direct and indirect parts) and expand the angle sensitivity term into explicit form
- DC OPF: gate the angle difference limits by sw to match the model, and add the explicit per-branch KKT switching derivative blocks
- AC power flow: add an Admittance and Topology Sensitivity section and show the sw gate in the bus admittance matrix
- AC OPF: note the implicit function framing of the KKT differentiation
- Cite Talkington et al. (arXiv:2510.17071) in the AC docs
@cameronkhanpour cameronkhanpour added the documentation Improvements or additions to documentation label Jun 16, 2026
@cameronkhanpour cameronkhanpour requested a review from samtalki June 16, 2026 08:05
Branch current and flow sensitivities to g and b include a direct term on
the perturbed branch (its own admittance acting on its voltage drop), in
addition to the term through the voltage change. This matches the
implementation (the direct topology current contribution) and the paper's
line current and flow sensitivity equations.
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