Nowadays, the rise in energy consumption and the integration of renewable energy resources (RES) have introduced significant challenges to the existing power grid, making it necessary to upgrade the current power system. However, considering the high variability in load and RES and the large number of possible investment options, the power system expansion planning problem results in a large mixed integer linear problem (MILP), or in some cases, a non-linear problem, impractical to solve for real-world scenarios. Time-series aggregation (TSA), capturing representative load and RES patterns, has emerged to reduce the temporal complexity, making the power system expansion planning model much easier to solve while providing similar final results.

Current TSA methods mainly rely on passive clustering, focusing on the statistical proximity between the representative periods and the full-space time-series. However, this approach does not guarantee a satisfactory solution for the final expansion planning problem in general cases, even with predefined extreme periods implemented such as days with maximum load and minimum available RES. The operation of the power system and extreme conditions are highly sensitive to the specific power system configurations, making the standalone TSA method unreliable in practical applications.

To improve the time-series aggregation in terms of the power system operation, firstly, the methods of assessing the performance of the estimated investment decision are explored directly in terms of the objective function. By introducing the full-space operational cost model for the power system with the estimated investment decision, the operational cost error made by representative periods can be obtained, referred to as the operational estimation error. The actual objective difference between the estimated investment decision and the optimal investment decision found by the full-space expansion planning model can also be evaluated, denoted as the optimality gap. It is found that the optimality gap is bounded by the difference in the operational estimation error of representative periods for the power system with the two investment decisions. As the operations of the power system with the estimated and optimal investment decisions are better estimated, the simplified model can provide a closer investment decision.

Subsequently, looking into the operational estimation error, the performance of representative periods in estimating the full-space operational cost is highly unevenly distributed among the full-space time-series. Representative periods fail to accurately estimate a minor portion of the full-space time-series, causing extremely high operational estimation errors that contribute to the majority of the total operational estimation error. This uneven distribution remains as the number of representative periods increases, indicating that standalone TSA methods are not capable of capturing the extreme conditions of the specific power system operation.

Therefore, to improve the time-series aggregation in terms of its ability to better estimate the operation of the power system, bad-performing representative periods and original periods with high operational estimation error can be identified and prioritized, forming a feedback enhancement loop. Case studies show that the feedback enhancement with re-clustering on the bad-performing representative periods improves the optimality gap by more than 50% compared with the standard mean-based clustering method.