Allocation of the transient-stability settlement residual

Determine how to allocate the settlement residual produced by shadow-price settlement for transient stability-constrained optimal power flow, including the residual that remains even in lossless and uncongested networks.

Background

The proposed asset-specific shadow prices charge or remunerate generators and loads according to their effects on transient-stability constraints. However, the resulting market settlement can leave a residual: in the lossless and uncongested WECC 9-bus case, load payments exceed generator revenues solely because of the transient-stability price components. The paper notes that this residual is distinct from the residual associated with losses and congestion and does not provide an allocation rule for it.

The unresolved issue is therefore to establish a principled mechanism for distributing or otherwise treating the residual generated by transient-stability pricing, so that the market settlement is economically complete.

References

As future work, the allocation of this residual should be addressed.

— Shadow Pricing in Transient Stability-Constrained Optimal Power Flow  (2610.18563 - Coelho et al., 13 Oct 2026) in Section 5, Conclusions