This paper introduces the full Low-carbon Expansion Generation Optimization (LEGO) model available on Github (https://github.com/wogrin/LEGO). LEGO is a mixed-integer quadratically constrained optimization problem and has been designed to be a multi-purpose tool, like a Swiss army knife, that can be employed to study many different aspects of the energy sector. Ranging from short-term unit commitment to long-term generation and transmission expansion planning. The underlying modeling philosophies are: modularity and flexibility. Its unique temporal structure allows LEGO to function with either chronological hourly data, or all kinds of representative periods. LEGO is also composed of thematic modules that can be added or removed from the model easily via data options depending on the scope of the study. Those modules include: unit commitment constraints; DC- or AC-OPF formulations; battery degradation; rate of change of frequency inertia constraints; demand-side management; or the hydrogen sector. LEGO also provides a plethora of model outputs (both primal and dual), which is the basis for both technical but also economic analyses. To our knowledge, there is no model that combines all of these capabilities, which we hereby make freely available to the scientific community.
This paper proposes a Clustered Unit Commitment (CUC) formulation to accurately model flexibility requirements such as ramping, reserve, and startup/shutdown constraints. The CUC is commonly applied in large and long-term planning models to approximate the units operational flexibility in power systems due to its computational advantages. However, the classic CUC intrinsically and hiddenly overestimates the individual units flexibility, thus being unable to replicate the result of the individual UC. This paper then present a set of constraints to correctly represent the units hidden flexibility within the cluster, mainly defined by the individual units ramping and startup/shutdown capabilities, including up/down reserves. Different case studies show that the proposed CUC replicates the objective function of the individual UC while solving significantly faster, between 5 to 311 times faster. Therefore, the proposed CUC correctly represents the individual units ramping and reserve flexibility within the cluster and could be directly applied to long-term planning models without significantly increasing their computational burden.
