For inclusion in large-scale power system models, various aggregations and simplifications in the modeling of relevant actors are needed. This paper focuses on reduced models of hydropower, so called area Equivalent models. They use a simplified topology but are not a direct aggregation of the real hydropower system. Instead, the area Equivalent is constructed to mimic the simulated power production of a more detailed hydropower reference model. Here, this goal is fulfilled by formulating a bilevel problem minimizing the difference in simulated power production between the area Equivalent and its reference. Solving this can be computationally heavy. Thus, for a fast solution of this bilevel problem, a single-level reduction is done, which is then solved using two methods. The first method includes McCormick envelopes to form a linear single-level problem. Second is a modified Benders with a relaxed sub-problem to handle the non-convex single-level. These are then also compared to Particle Swarm Optimization. Moreover, six new upper-level objective functions are investigated for a case study of hydropower in northern Sweden. The method using McCormick envelopes is fast (2–5 min), but the area Equivalent shows lower average performance. The modified Benders finds a solution in 5–31 min with good performance.