Multi-Level Multi-Objective Programming and Optimization for Integrated Air Defense System Disruption

The U.S. military\u27s ability to project military force is being challenged. This research develops and demonstrates the application of three respective sensor location, relocation, and network intrusion models to provide the mathematical basis for the strategic engagement of emerging technologically advanced, highly-mobile, Integrated Air Defense Systems. First, we propose a bilevel mathematical programming model for locating a heterogeneous set of sensors to maximize the minimum exposure of an intruder\u27s penetration path through a defended region. Next, we formulate a multi-objective, bilevel optimization model to relocate surviving sensors to maximize an intruder\u27s minimal expected exposure to traverse a defended border region, minimize the maximum sensor relocation time, and minimize the total number of sensors requiring relocation. Lastly, we present a trilevel, attacker-defender-attacker formulation for the heterogeneous sensor network intrusion problem to optimally incapacitate a subset of the defender\u27s sensors and degrade a subset of the defender\u27s network to ultimately determine the attacker\u27s optimal penetration path through a defended network

A bi-level model for the design of dynamic electricity tariffs with demand-side flexibility

This paper addresses the electricity pricing problem with demand-side flexibility. The interaction between an aggregator and the prosumers within a coalition is modeled by a Stackelberg game and formulated as a mathematical bi-level program where the aggregator and the prosumer, respectively, play the role of upper and lower decision makers with conflicting goals. The aggregator establishes the pricing scheme by optimizing the supply strategy with the aim of maximizing the profit, prosumers react to the price signals by scheduling the flexible loads and managing the home energy system to minimize the electricity bill. The problem is solved by a heuristic approach which exploits the specific model structure. Some numerical experiments have been carried out on a real test case. The results provide the stakeholders with informative managerial insights underlining the prominent roles of aggregator and prosumers

Prescriptive Analytics in Electricity Markets

Electricity markets are a clear example of a sector in which decision making plays a crucial role in its daily activity. Moreover, uncertainty is intrinsic to electricity markets and affects most of the tasks that agents operating in them must carry out. Many of these tasks involve decisions characterized by low risk and being addressed periodically. In this thesis, we refer to these tasks as iterative decisions. This thesis applies the aforementioned innovative frameworks for decision making under uncertainty using contextual information in iterative decision making tasks faced daily by electricity market agents.Decision making is critical for any business to survive in a market environment. Examples of decision making tasks are inventory management, resource allocation or portfolio selection. Optimization, understood as the scientific discipline that studies how to solve mathematical programming problems, can help make more efficient decisions in many of these situations. Particularly relevant, because of their frequency and difficulty, are those decisions affected by uncertainty, i.e., in which some of the parameters that precisely determine the optimization problem are unknown when the decision must be made. Fortunately, the development of information technologies has led to an explosion in the availability of data that can be used to assist decisions affected by uncertainty. However, most of the available historical data do not correspond to the unknown parameter of the problem but originate from other related sources. This subset of data, potentially valuable for obtaining better decisions, is called contextual information. This thesis is framed within a new scientific effort that seeks to exploit the potential of data and, in particular, of contextual information in decision making. To this end, in this thesis, we have developed mathematical frameworks and data-driven optimization models that exploit contextual information to make better decisions in problems characterized by the presence of uncertain parameters

Optimal Carbon Taxes for Emissions Targets in the Electricity Sector

The most dangerous effects of anthropogenic climate change can be mitigated by using emissions taxes or other regulatory interventions to reduce greenhouse gas (GHG) emissions. This paper takes a regulatory viewpoint and describes the Weighted Sum Bisection method to determine the lowest emission tax rate that can reduce the anticipated emissions of the power sector below a prescribed, regulatorily-defined target. This bi-level method accounts for a variety of operating conditions via stochastic programming and remains computationally tractable for realistically large planning test systems, even when binary commitment decisions and multi-period constraints on conventional generators are considered. Case studies on a modified ISO New England test system demonstrate that this method reliably finds the minimum tax rate that meets emissions targets. In addition, it investigates the relationship between system investments and the tax-setting process. Introducing GHG emissions taxes increases the value proposition for investment in new cleaner generation, transmission, and energy efficiency; conversely, investing in these technologies reduces the tax rate required to reach a given emissions target

Electricity prices and tariffs to keep everyone happy: a framework for fixed and nodal prices coexistence in distribution grids with optimal tariffs for investment cost recovery

Some consumers, particularly households, are unwilling to face volatile electricity prices, and they can perceive as unfair price differentiation in the same local area. For these reasons, nodal prices in distribution networks are rarely employed. However, the increasing availability of renewable resources and emerging price-elastic behaviours pave the way for the effective introduction of marginal nodal pricing schemes in distribution networks. The aim of the proposed framework is to show how traditional non-flexible consumers can coexist with flexible users in a local distribution area. Flexible users will pay nodal prices, whereas non-flexible consumers will be charged a fixed price derived from the underlying nodal prices. Moreover, the developed approach shows how a distribution system operator should manage the local grid by optimally determining the lines to be expanded, and the collected network tariff levied on grid users, while accounting for both congestion rent and investment costs. The proposed model is formulated as a non-linear integer bilevel program, which is then recast as an equivalent single optimization problem, by using integer algebra and complementarity relations. The power flows in the distribution area are modelled by resorting to a second-order cone relaxation, whose solution is exact for radial networks under mild assumptions. The final model results in a mixed-integer quadratically constrained program, which can be solved with off-the-shelf solvers. Numerical test cases based on both 5-bus and 33-bus networks are reported to show the effectiveness of the proposed method