Uplift Pricing for Inertia and Reserve via ML-Based Frequency-Constrained Unit Commitment

Abstract

High penetration of inverter-based sources makes power systems susceptible to frequency excursions, leaving power systems short of synchronous inertia and uncompensated spinning reserve headroom. Traditional unit commitment (UC) approaches are incapable of catering to the needs of modern power systems. This paper proposes a transparent, regulator-friendly remedy that requires no real-time market redesign. A linear logistic regression surrogate, trained on 117 000 dynamic simulations, is embedded in the MILP to enforce post-fault frequency constraint. Spinning reserve headroom is remunerated through a fixed uplift tariff proportional to each generator’s marginal energy cost. Three deterministic day-ahead scenarios are compared on a real power system—La Palma (Spain): S0—reserve free; S1—tariff applied ex-post; S2—tariff co-optimised with energy. Co-optimisation (S2) increases weekly expenditure only 4.2 % relative to the cost-only baseline and is 0.2 % cheaper than the ex-post variant (S1). Fuel (operation) cost and renewable curtailment remain unchanged, depicting that the tariff does not distort the merit order. Although worst-case system inertia drops by 9 MW•s, the nadir limit binds 75 h/wk−1 versus 59 h/wk−1 in S0/S1, impeding under-frequency risk without raising RoCoF exposure. Reserve payments become less concentrated; the Gini coefficient, a measure of inequality, falls from 0.26 to 0.24, and the share captured by the three highest-earning units drops slightly to 56%. These results demonstrate that a single co-optimised uplift tariff—underpinned by an ML-based nadir constraint—thus delivers frequency security and fair cost recovery at negligible economic and operational impact, offering an immediately deployable solution for low-inertia grids.

High penetration of inverter-based sources makes power systems susceptible to frequency excursions, leaving power systems short of synchronous inertia and uncompensated spinning reserve headroom. Traditional unit commitment (UC) approaches are incapable of catering to the needs of modern power systems. This paper proposes a transparent, regulator-friendly remedy that requires no real-time market redesign. A linear logistic regression surrogate, trained on 117 000 dynamic simulations, is embedded in the MILP to enforce post-fault frequency constraint. Spinning reserve headroom is remunerated through a fixed uplift tariff proportional to each generator’s marginal energy cost. Three deterministic day-ahead scenarios are compared on a real power system—La Palma (Spain): S0—reserve free; S1—tariff applied ex-post; S2—tariff co-optimised with energy. Co-optimisation (S2) increases weekly expenditure only 4.2 % relative to the cost-only baseline and is 0.2 % cheaper than the ex-post variant (S1). Fuel (operation) cost and renewable curtailment remain unchanged, depicting that the tariff does not distort the merit order. Although worst-case system inertia drops by 9 MW•s, the nadir limit binds 75 h/wk−1 versus 59 h/wk−1 in S0/S1, impeding under-frequency risk without raising RoCoF exposure. Reserve payments become less concentrated; the Gini coefficient, a measure of inequality, falls from 0.26 to 0.24, and the share captured by the three highest-earning units drops slightly to 56%. These results demonstrate that a single co-optimised uplift tariff—underpinned by an ML-based nadir constraint—thus delivers frequency security and fair cost recovery at negligible economic and operational impact, offering an immediately deployable solution for low-inertia grids.