The unit commitment (UC) problem is paramount for optimal operation of power systems, but it faces computational limitations in large-scale settings, especially in investment or stochastic models, because of the binary variables that it contains. A lot of research has attempted to improve the computational performance of UC models, either by reducing model size, resulting in lower fidelity and accuracy, or by improving the tightness of the formulation. Tightness and model size are the best a priori indicators of the computational performance of UC models, but there is no clear overview of what the best formulation is for different generators. In this research, we define models with different levels of detail, and present a formulation for each level that is based on the convex hull. We show new proofs on the tightness of well-known formulations for ramping, for start-up and shut-down costs and capabilities, and for UC with investment. These models, with a different level of detail, can be incorporated into large-scale problems to reduce the computational burden, as demonstrated in Part II.
The unit commitment problem determines the optimal strategy to meet the electricity demand at minimum cost by committing power generation units at each point of time. Solving the unit commitment problem gives rise to a challenging optimization problem due to its combinatorial com…
Optimal power flow (OPF) solved by an interior-point method (IPM) requires repeatedly solving Newton linear systems. When variational quantum linear solvers (VQLS) are used, each IPM iteration involves an additional nested inner variational optimization loop, which can significan…
This study proposes a precipitation control framework integrating a realistic Numerical Weather Prediction (NWP) model with model predictive control (MPC). At each control instant in MPC, a finite-difference sensitivity matrix is constructed from the NWP model and used as a local…
Due to the nonconvex binary constraints of unit commitment (UC), no uniform linear pricing scheme supports the optimal dispatch. Convex hull pricing (CHP) and copositive duality pricing (CDP) both address this problem. CHP derives the price from the subgradient of the value funct…
This paper addresses the problem of designing recommendation systems for social networks and e-commerce platforms from a control-theoretic perspective. We formulate recommendation design as an infinite-horizon state-feedback optimal control problem whose performance index rewards…
This article presents a novel, numerically viable algorithm for solving sparse robust optimal control problems in continuous time. We consider a constrained linear noisy system governed by an ordinary differential equation (ODE), with an $L^1$-type objective function in line with…