Optimal fiscal policy in a Schumpeterian model

Master'sMASTER OF SOCIAL SCIENCE

An Analytical Methodology To Security Constraints Management In Power System Operation

In a deregulated electricity market, Independent System Operators (ISOs) are responsible for dispatching power to the load securely, efficiently, and economically. ISO performs Security Constrained Unit Commitment (SCUC) to guarantee sufficient generation commitment, maximized social welfare and facilitating market-driven economics. A large number of security constraints would render the model impossible to solve under time requirements. Developing a method to identify the minimum set of security constraints without overcommitting is necessary to reduce Mixed Integer Linear Programming (MILP) solution time. To overcome this challenge, we developed a powerful tool called security constraint screening. The proposed approach effectively filters out non-dominating constraints by integrating virtual transactions and capturing changes online in real-time or look-ahead markets. The security-constraint screening takes advantage of both deterministic and statistical methods, which leverages mathematical modeling and historical data. Effectiveness is verified using Midcontinent Independent System Operator (MISO) data. The research also presented a data-driven approach to forecast congestion patterns in real-time utilizing machine learning applications. Studies have been conducted using real-world data. The potential benefit is to provide the day-ahead operators with a tool for supporting decision-making regarding modeling constraints

Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point

The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al. Nature 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors, i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in non-chiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.Comment: 15 pages, 11 figure