Equivalent Circuit Programming

2019-10-11T20:44:14Z (GMT) by Marko Jereminov
Optimal decision-making processes represent the key component of everyday life and can be found everywhere, from the atomic level in nature, to the emerging technologies that are becoming increasingly dependent on various Machine Learning algorithms and Artificial Intelligence. Consequently, finding the mathematical modeling formulations and algorithms for solving these decision-making problems now represents one of the significant, on-going research topics in science. Most importantly, after the publication of the so-called “No Free Lunch” (NFL)
theorems that proves existence of no algorithm that can efficiently and robustly solve all classes of optimization problems, it became clear that the algorithms and mathematical modeling of the optimization problems have to take into the consideration all of the available domain specific knowledge in order to achieve the best efficiency, robustness and scalability. The primary focus of this thesis is to develop a novel generic framework for continuous
network optimization problems. Our approach, Equivalent Circuit Programming (ECP), incorporates all of the available domain knowledge and translates it into the efficient and robust simulation algorithms. Inspired by the NFL theory and circuit simulation algorithms developed around the state-of-art circuit simulator SPICE, we first address the key issues of applying the generic local optimization algorithms to network optimization problems. To that effect, we
generalize the adjoint circuit theory to include the nonlinear network models and show that the complete set of optimality conditions of a network optimization problem can be represented by a combination of the network and its uniquely defined adjoint circuit. With the circuit representation of the considered class of optimization problems established, we next embed the domain-specific
knowledge within the existing optimization heuristics to develop a completely new set of algorithms to ensure a more efficient, robust and scalable solution process.
To prove the concept and demonstrate the significant improvements in simulation efficiency, scalability and robustness, the proposed Equivalent Circuit Programming framework is applied to power system optimization problems. This is achieved by first introducing a generalized methodology for modeling the power grid steady-state response in terms of equivalent circuit equations that further allows us to incorporate them within the ECP framework. The examined power system optimization problems include the newly introduced Power Flow Feasibility analyses, AC Optimal Power Flow (AC-OPF) and Security Constrained AC Optimal Power Flow (SC-OPF) problems. Optimization results are compared with the existing state-of-art local
optimization algorithms for available network examples that include various realistic-size power system test cases of up to the 80k buses (nodes).