Objective-consistent bi-level co-design of planning and operation for Pareto-optimal carbon-economic microgrids

Achieving optimal carbon-economic goals in microgrids is challenging due to the deep coupling between capacity planning and operational dispatch. Existing bi-level optimization frameworks often suffer from objective misalignment, as multi-objective planning is typically paired with fixed, non-cooperative operational strategies, leading to suboptimal, dominated solutions. To address this, this paper proposes a novel objective-consistent bi-level co-design framework that aligns microgrid operation with planning, ensuring globally Pareto-optimal carbon-economic trade-offs that are unattainable by conventional mismatched strategies. Specifically, the upper level utilizes bi-objective Bayesian optimization to determine component capacities along with a crucial operational objective balance factor (α). This factor dynamically tunes the lower-level carbon-economic balancing model predictive control, forcing operational strategies to align with planning goals. The framework reveals the complete, convex carbon-economic trade-off frontier, quantifying the sharply increasing marginal cost of decarbonization and validated by a multi-regional analysis. Furthermore, a critical technological turning point is uncovered: while initial decarbonization relies on solar–wind compensation, deep decarbonization necessitates a strategic shift towards wind-heavy configurations to address night-time grid carbon intensity. Regarding methodological performance, quantitative analysis shows that the proposed method achieves a superior Pareto frontier with a larger hypervolume, significantly outperforming objective-misaligned strategies, while exhibiting superior computational efficiency compared to traditional meta-heuristic methods. In practical terms, the optimized α can be directly translated into a practical internal carbon price for microgrid operators, and the proposed operation strategy is robust to prediction errors, outperforming rule-based methods even at 15% MAPE. This work provides an efficient tool for finding practically implementable and globally Pareto-optimal systematic microgrid designs.