Competition and Optimization in Electricity Systems

Electricity prices are characterized by high volatility and severe price spikes. At the root of these phenomena is the strategic behavior of market participants. A good understanding of the market competition is key to making better regulation, contract, and investment decisions. The goal of this thesis is to study the following market competition problems: (1) the competition between flexible generators with fast ramping rates and inflexible generators with constant production rates, (2) the effect of the renewable generation penetration and production based subsidies on the competition and operating efficiency, (3) generation competition in transmission constrained networks, and (4) competition in the capacity expansion of electricity networks. We first consider a centralized electricity model and find that reducing the production based subsidies to renewable plants dampens their intermittency effect through controlled curtailment, cuts operational cost, and improves the system's balance. We then consider an oligopoly in which generators submit supply function bids and analyze a supply function equilibrium (SFE) model with generators that have different ramping rates. We find that the controlled curtailment of renewables has an additional benefit in oligopolistic markets as it can reduce generator market power, which has favorable operational efficiency and electricity price ramifications. We also find that the classical SFE model is inadequate for modeling renewables and inflexible generators, and can grossly overestimate the competition intensity. We modify the SFE model to account for these issues. Afterwards, a Bertrand model is used to study the duopoly competition in a transmission constrained network. We find that adding transmission constraints in this model does not change the bidding policy, instead it changes the critical demand levels at which firms revise their position from competitive to aggressive bidding. We also solve the symmetric mixed strategy Nash equilibrium problem for multiple generators in a Bertrand electricity auction. Finally, we study several transmission expansion schemes and devise two investment mechanisms that achieve near social optimality.PhDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107307/1/mmgwaiz_1.pd

Totally real surfaces in C

It has been shown that a totally real surface in CP2 with parallel mean curvature vector and constant Gaussian curvature is either flat or totally geodesic

Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schr\"odinger and Dirac particles. A central issue that should be carefully analyzed when functional series are applied is their convergence. In the present paper, we study the properties of the eigenfunction expansions appearing in nonrelativistic and relativistic $R$-matrix theories. In particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13, 491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761 (1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular formulation of the R-matrix theory for Dirac particles, the functional series fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical Physics, 21 pages, 1 figur

On the Implementation of Constraints through Projection Operators

Quantum constraints of the type Q \psi = 0 can be straightforwardly implemented in cases where Q is a self-adjoint operator for which zero is an eigenvalue. In that case, the physical Hilbert space is obtained by projecting onto the kernel of Q, i.e. H_phys = ker(Q) = ker(Q*). It is, however, nontrivial to identify and project onto H_phys when zero is not in the point spectrum but instead is in the continuous spectrum of Q, because in this case the kernel of Q is empty. Here, we observe that the topology of the underlying Hilbert space can be harmlessly modified in the direction perpendicular to the constraint surface in such a way that Q becomes non-self-adjoint. This procedure then allows us to conveniently obtain H_phys as the proper Hilbert subspace H_phys = ker(Q*), on which one can project as usual. In the simplest case, the necessary change of topology amounts to passing from an L^2 Hilbert space to a Sobolev space.Comment: 22 pages, LaTe

Time-Changed Fast Mean-Reverting Stochastic Volatility Models

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility surfaces induced by these time-changes are examined as a function of the model parameters. Three key features of our framework are that we are able to incorporate jumps into the price process of the underlying asset, allow for the leverage effect, and accommodate multiple factors of volatility, which operate on different time-scales

Clinical outcomes of ED patients with bandemia

BackgroundAlthough an elevated white blood cell count is a widely utilized measure for evidence of infection and an important criterion for evaluation of systemic inflammatory response syndrome, its component band count occupies a more contested position within clinical emergency medicine. Recent studies indicate that bandemia is highly predictive of a serious infection, suggesting that clinicians who do not appreciate the value of band counts may delay diagnosis or overlook severe infections.ObjectivesWhereas previous studies focused on determining the quantitative value of the band count (ie, determining sensitivity, threshold for bandemia, etc.), this study directs attention to patient-centered outcomes, hypothesizing that the degree of bandemia predisposes patients to subsequent negative clinical outcomes associated with underappreciated severe infections.MethodsThis retrospective study of electronic medical records includes patients who initially presented to the emergency department (ED) with bandemia and were subsequently discharged from the ED. These patients were screened for repeat ED visits within 7 days and death within 30 days.ResultsIn patients with severe bandemia who were discharged from the ED, there was a 20.9% revisit rate at 7 days and a 4.9% mortality rate at 30 days, placing severely bandemic patients at 5 times significantly greater mortality compared to nonbandemic patients (P = .032).ConclusionOur review of patient outcomes suggests that the degree of bandemia, especially in the setting of concurrent tachycardia or fever, is associated with greater likelihood of negative clinical outcomes

Marginal Cost of Steam and Power from Cogeneration Systems Using a Rational Value-Allocation Procedure

The problem of pricing steam and power from cogeneration systems has confounded engineers, economists, and accountants for a very long time. Normal industry practice is to fix the cost of one (usually power) at its local market price, and calculate the “