External electricity supplementation for islanded microgrids at expressway service areas is often settled under tiered electricity pricing based on cumulative energy consumption, where marginal prices increase discontinuously once tier thresholds are exceeded. This mechanism reshapes battery dispatch behavior and may alter economically optimal storage sizing. This paper proposes a unified planning–-operation optimization framework for wind–PV–battery microgrids that jointly determines the storage capacity and hourly scheduling while enforcing power balance, battery state-of-charge dynamics, and tiered settlement costs. By introducing tier-wise energy allocation variables and tier cap constraints, the nonlinear settlement rule is reformulated into an equivalent piecewise-linear structure, leading to a mixed-integer linear programming (MILP) model that can be solved using standard optimization solvers. A season-weighted annualized case study using four typical seasonal days reveals critical cross-tier dispatch behaviors, where charging–discharging schedules shift near tier boundaries and external electricity purchases are actively suppressed from entering higher-priced tiers. The proposed framework quantifies the premium-avoidance value of storage and provides a practical decision support tool for premium risk-aware sizing and operation of islanded expressway service-area microgrids.
Shi et al. (Mon,) studied this question.