Mixed-integer programming in power systems : the interdiction and unit commitment problems

Mixed integer programming (MIP) maximizes (or minimizes) a linear objective subject to a set of constraints. In particular, one of the constraints for a MIP is that at least one of the variables can only take integer values. This technique has been widely studied in operations research and a MIP can be solved efficiently by commercial solvers. In this dissertation, two power system problems namely, an interdiction problem and a unit commitment problem, are formulated and solved with MIP techniques. The studies presented in this dissertation focus on extracting the special features embedded in the problems and formulating the problems such that they can be solved using the available MIP techniques. The objective of an interdiction problem in a power system is to find a set of the most critical or vulnerable components to secure and reliable operation. Before formulating the problem, we need to study the outages and their impacts in power systems in depth. Once a critical component of a power system fails, the outages including generator and load trips can sequentially spread and frequently lead to large blackouts. The efforts to develop a model to analyze cascading outages is first summarized. Reports about cyber attacks on the Ukraine power grid revealed that one or more malwares were deliberately developed to attack industrial facilities, with power systems as one of the major targets. Another potential cyber threat to secure operation of power transmission grids involves Internet of Things (IoT) demand attacks. Increasingly, Internet connections are available to devices with high energy consumption such as air conditioners and water heaters. However, these new connections expose the control of new electric loads to potential manipulation by attackers. To help assess the effects of cyber attacks, we develop numerical experiments and define different types of cyber attacks to simulate Ukraine-style cyber attacks and IoT demand attacks to study the system responses in a North American regional interconnection system. Based on the studies in cascading outage analysis and cyber attack simulations, an interaction problem between a defender (e.g. system operator) and an attacker (e.g. terrorist) in a power system is formulated as a MIP and a "short-term" impact of an attack is considered using a cascading outage anylsis (COA) tool. A demonstrative case study with an existing method is presented and numeric studies with "short-term" impacts with COA model are ongoing. The unit commitment (UC) problem in a power system is another MIP problem. UC determines the start-up and shut down schedules of generating units to meet forecast demand in a short term future (few hours to few days). It is critical to precisely represent the generating units in a UC problem to maximize the social welfare, which is the objective of the problem. The formulation of two types of unit namely, combined-cycle gas units and pumped-storage hydro units in a UC problem are presented in this dissertation. In recent years, combined-cycle units (CCUs) have been operated as providers of flexibility needed due to the increasing shares of renewables. Consequently, optimization models have been proposed to determine the configuration of CCUs. However, most of the existing models assume that any transition between configurations finishes in a single interval. This assumption is often violated in reality, as a transition might last up to a few hours during which the CCU has limited dispatchability. In this work, a mixed-integer programming formulation that represents the transition ramping of CCUs is summarized and the formulations of ramping constraints are discussed. Numerical studies are performed on an illustrative test system and a Mid-continent Independent System Operator (MISO) system. As one of the mature technologies for energy storage, pumped-storage hydro is able to provide services in a time range from minutes to days. Particularly, pumped storage hydro units are useful for enhancing the integration of renewable generations that are naturally intermittent. Optimization models have been proposed to determine strategies to dispatch a energy storage unit in the system. However, most of existing work assumes the output from a energy storage unit is continuous. This assumption is not true for a pumped storage hydro unit. Inspired by the work of modeling a combined cycle unit in the unit commitment problem, this work proposes a configuration based pumped storage hydro model that removes the invalid continuous outputs assumption in order to enhance the use of pumped storage hydro resources in the system. By introducing three "configurations," namely, pumping, generating and "alloff" or off-line, for a pumped storage hydro unit, the proposed model can more accurately reflect the practical operations of pumped storage hydro units in the day-ahead market. A comprehensive review of the existing pumped storage hydro models and industry practices is presented. The definition of configurations of a pumped storage hydro unit and the transitions between the configurations during operation are revealed and discussed in detail to describe the proposed model. A case study is presented to illustrate the proposed model.