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 to use stochastic conic programming to address the challenge of large-scale wind power integration to the power system. Multiple wind farms are connected through the voltage source converter (VSC) based multi-terminal DC (VSC-MTDC) system to the power network supported by the Flexible AC Transmission System (FACTS). The optimal operation of the power network incorporating the VSC-MTDC system and FACTS devices is formulated in a stochastic conic programming framework accounting the uncertainties of the wind power generation. A methodology to generate representative scenarios of power generations from the wind farms is proposed using wind speed measurements and wind turbine models. The nonconvex transmission network constraints including the VSC-MTDC system and FACTS devices are convexified through the proposed second-order cone AC optimal power flow model (SOC-ACOPF) that can be solved to the global optimality using interior point method. In order to tackle the computational challenge due to the large number of wind power scenarios, a modified Benders decomposition algorithm (M-BDA) accelerated by parallel computation is proposed. The energy dispatch of conventional power generators is formulated as the master problem of M-BDA. Numerical results for up to 50000 wind power scenarios show that the proposed M-BDA approach to solve stochastic SOC-ACOPF outperforms the traditional single-stage (without decomposition) solution approach in both convergence capability and computational efficiency. The feasibility performance of the proposed stochastic SOC-ACOPF model is also demonstrated.
