Tail-risk-aware Bit-Watt co-optimization for data center integrated energy systems under joint forecast uncertainty

Bit-Watt coordination for data centers is exposed to joint photovoltaic and workload forecast errors, creating a fundamental tension between reserve adequacy and economic efficiency. Existing methods rarely address this tension under cumulative Service Level Agreement (SLA) constraints, while the tail risk of reserve inadequacy remains insufficiently explored. To address this issue, this paper proposes a tail-risk-aware Bit-Watt co-optimization framework for data center integrated energy system (IES). A moment-based ambiguity set with ellipsoidal support is constructed to model joint forecast errors, while worst-case conditional value-at-risk is employed to control the tail risk of residual power deficits. Generalized moment duality yields a finite semidefinite reformulation, and physics-informed bound tightening strengthens the associated McCormick relaxations. Case studies show that incorporating delay tolerance reduces operating energy cost by 8.3% while maintaining SLA compliance. Most notably, compared with deterministic risk-neutral scheduling, the proposed method reduces the hourly power-shortfall probability from 50.05% to 1.84%, with only a 2.76% cost premium. Further sensitivity analyses demonstrate a consistent cost-reliability trade-off under different risk-margin coefficients and forecast-error conditions. The results demonstrate that the proposed framework provides a practical compromise between risk-neutral operation and overly conservative robust scheduling.