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This paper introduces the design and implementation of PyOptInterface, a modeling language for mathematical optimization embedded in Python programming language. PyOptInterface uses lightweight and compact data structure to bridge high-level entities in optimization models like variables and constraints to internal indices of optimizers efficiently. It supports a variety of optimization solvers and a range of common problem classes. We provide benchmarks to exhibit the competitive performance of PyOptInterface compared with other state-of-the-art modeling languages., Comment: 10 pages

The development of energy conversion techniques enhances the coupling between the gas network and power system. However, challenges remain in the joint optimal dispatch of electricity-gas systems. The dynamic model of the gas network, described by partial differential equations, is complex and computationally demanding for power system operators. Furthermore, information privacy concerns and limited accessibility to detailed gas network models by power system operators necessitate quantifying the equivalent energy storage capacity of gas networks. This paper proposes a multi-port energy storage model with time-varying capacity to represent the dynamic gas state transformation and operational constraints in a compact and intuitive form. The model can be easily integrated into the optimal dispatch problem of the power system. Test cases demonstrate that the proposed model ensures feasible control strategies and significantly reduces the computational burden while maintaining high accuracy in the joint optimal dispatch of electricity-gas systems. In contrast, the existing static equivalent model fails to capture the full flexibility of the gas network and may yield infeasible results., Comment: 12 pages, 8 figures

Storage-concerned Optimal Power Flow (OPF) with complementarity constraints is highly non-convex and intractable. In this paper, we propose two generalized sufficient conditions which guarantee no simultaneous charging and discharging (SCD) in the relaxed multi-period OPF excluding the complementarity constraints. Moreover, we prove that the regions on the locational marginal prices (LMPs) formed by the proposed two conditions both contain the other existing representative ones. We also generalize the application premise of sufficient conditions from the positive electricity price requirements to the negative electricity price scenarios. In contrast to participating solely in the energy dispatch, we highlight that offering reserve services can broaden the application range of relaxation conditions for storages. The case studies verify the exactness and advantages of the proposed conditions.

With numerous distributed energy resources (DERs) integrated into the distribution networks (DNs), the coordinated economic dispatch (C-ED) is essential for the integrated transmission and distribution grids. For large scale power grids, the centralized C-ED meets high computational burden and information privacy issues. To tackle these issues, this paper proposes a spatio-temporal decomposition algorithm to solve the C-ED in a distributed and parallel manner. In the temporal dimension, the multi-period economic dispatch (ED) of transmission grid (TG) is decomposed to several subproblems by introducing auxiliary variables and overlapping time intervals to deal with the temporal coupling constraints. Besides, an accelerated alternative direction method of multipliers (A-ADMM) based temporal decomposition algorithm with the warm-start strategy, is developed to solve the ED subproblems of TG in parallel. In the spatial dimension, a multi-parametric programming projection based spatial decomposition algorithm is developed to coordinate the ED problems of TG and DNs in a distributed manner. To further improve the convergence performance of the spatial decomposition algorithm, the aggregate equivalence approach is used for determining the feasible range of boundary variables of TG and DNs. Moreover, we prove that the proposed spatio-temporal decomposition method can obtain the optimal solution for bilevel convex optimization problems with continuously differentiable objectives and constraints. Numerical tests are conducted on three systems with different scales, demonstrating the high computational efficiency and scalability of the proposed spatio-temporal decomposition method.

Multilevel, multiarea, and hierarchically interconnected electrical power grids confront substantial challenges with the increasing integration of many volatile energy resources. The traditional isolated operation of interconnected power grids is uneconomical due to a lack of coordination; it may result in severe accidents that affect operational safety. However, the centralized operation of interconnected power grids is impractical, considering the operational independence and information privacy of each power grid. This paper proposes a nested decomposition method for the coordinated operation of hierarchical electrical power grids, which can achieve global optimization by iterating among upper- and lower-level power grids with exchange of boundary information alone. During each iteration, a projection function, which embodies the optimal objective value of a lower-level power grid projected onto its boundary variable space, is computed with second-order exactness. Thus, the proposed method can be applied widely to nonlinear continuous optimizations and can converge much more rapidly than existing decomposition methods. We conducted numerical tests of coordinated operation examples with a trilevel power grid that demonstrate the validity and performance of the proposed method., Comment: 27 pages