Demand price sensitivity and market power in a congested fuel and electricity network

IN restructured electricity markets, generating companies submit bids to supply electricity at prices based on their marginal costs, which are driven largely by fuel costs. In each regional wholesale power market, an independent system operator (ISO) manages electricity transmission and sets locational marginal prices (LMPs) to match supplies with demands at each location on the constrained grid. To understand the interaction between constraints on fuel supply and constraints on electricity transmission, we recently developed and tested a game theoretic model that combines both sets of constraints [1][2]. It includes (1) costs of extracting and transporting finite supplies of fuels across routes with limited capacity, (2) strategic decisions of generators at different locations across a congested electricity transmission network, (3) price-sensitive demands for electricity, and (4) matching of electricity supply and demand across the network to maximize total social welfare subject to physical transmission constraints. Given the fuel and electricity network topology and capacities, fuel supplies and costs, transmission line reactances, and demand functions, the model produces LMPs and quantities of electricity generated and consumed at each location on the grid. These represent a static view of, say, a particular hour in some scenario of cost, capacity and demand

Capacity expansion with lead times and autocorrelated random demand

The combination of uncertain demand and lead times for installing capacity creates the risk of shortage during the lead time, which may have serious consequences for a service provider. This paper analyzes a model of capacity expansion with autocorrelated random demand and a fixed lead time for adding capacity. To provide a specified level of service, a discrete time expansion timing policy uses a forecast error-adjusted minimum threshold level of excess capacity position to trigger an expansion. Under this timing policy, the expansion cost can be minimized by solving a deterministic dynamic program. We study the effects of demand characteristics and the lead time length on the capacity threshold. Autocorrelation acts similarly to randomness in hastening expansions but has a smaller impact, especially when lead times are short. However, the failure either to recognize autocorrelation or to accurately estimate its extent can cause substantial policy errors

An Exploration of Spatial Radiomic Features in Pulmonary Sarcoidosis

Sarcoidosis is a rare, multi-systemic, inflammatory disease, primarily affecting the lungs. High-resolution computed tomography (CT) scans are used to clinically characterize pulmonary sarcoidosis. In the medical imaging field, there is growing recognition to switch from visual examination of CT images to more rapid, objective assessments of the abnormalities. In this work, we explore the usefulness of various objective measures of spatial heterogeneity---fractal dimension, Moran's I, and Geary's C ---for distinguishing between abnormal sarcoidosis and normal lung parenchyma. CT data for N=58 sarcoidosis subjects enrolled at National Jewish Health were obtained from the GRADS study. CT data for N=101 control patients were obtained from the COPDGene study. Radiomic measures were computed for each two-dimensional slice of a given scan, in the axial, coronal, and sagittal planes. Functional regression was applied to identify lung regions where CT nodules tend to proliferate. Moran's I, Geary's C and fractal dimension significantly differentiate between subjects with and without sarcoidosis throughout the majority of the lung, with disease abnormalities most apparent in the top axial, middle coronal, and outer sagittal regions. A trend appeared across Scadding stages, with CT scans from patients with Scadding stages I and III appearing the healthiest, and Scadding stage IV appearing the least healthy. The radiomic measures and techniques presented herein successfully characterize CT images in sarcoidosis by objectively and efficiently approximating what we know about the pathology of sarcoidosis

Day-ahead hourly electricity load modeling by functional regression

Short-term load forecasting is important for power system generation planning and operation. For unit commitment and dispatch processes to incorporate uncertainty, a short-term load model must not only provide accurate load predictions but also enable the generation of reasonable probabilistic scenarios or uncertainty sets. This paper proposes a temporal and weather conditional epi-splines based load model (TWE) using functional approximation. TWE models the dependence of load on time and weather separately by functional approximation using epi-splines, conditional on season and area, in each segment of similar weather days. Load data are transformed from various day types to a specified reference day type among similar weather days in the same season and area, in order to enrich the data for capturing the non-weather dependent load pattern. In an instance derived from an Independent System Operator in the U.S., TWE not only provides accurate hourly load prediction and narrow bands of prediction errors, but also yields serial correlations among forecast hourly load values within a day that are similar to those of actual hourly load

Risk-Averse Stochastic Integer Programs for Mixed-Model Assembly Line Sequencing Problems

A variety of optimization formulations have been proposed for mixed-model assembly sequencing problems with stochastic demand and task times. In the real world, however, mixed-model assembly lines are faced with more challenging uncertainties including timely part delivery, material quality, upstream sub-assembly completion and availability of other resources. In addition, sub-assembly lines must meet deadlines imposed by downstream stations. The inevitable disruptions require resequencing. We present a risk-averse stochastic mixed-integer model for mixed-model assembly line resequencing problems to increase on-time performance

Reliability of Wind Power Scenarios and Stochastic Unit Commitment Cost

Probabilistic wind power scenarios constitute a crucial input for stochastic day-ahead unit commitment in power systems with deep penetration of wind generation. To minimize the expected cost, the scenario time series of wind power amounts available should accurately represent the stochastic process for available wind power as it is estimated on the day ahead. The high computational demands of stochastic programming motivate a search for ways to evaluate scenarios without extensively simulating the stochastic unit commitment procedure. Reliability of wind power scenario sets can be assessed by statistical verification approaches. In this study, we examine the relationship between the statistical evaluation metrics and the results of stochastic unit commitment. Lack of uniformity in a mass transportation distance rank histogram can eliminate scenario sets that might lead to either excessive no-load costs of committed units or high penalty costs for violating energy balance. Event-based metrics can help to predict the cost performance of the remaining scenario sets

Capacity expansion for a loss system with exponential demand growth

We study a loss system to forecast the demand for capacity based on the forecast demand for service and a specified service level. A little-used property of the Erlang loss formula allows the linear transformation of demand for service into demand for capacity. Next, given the forecast demand for capacity, we approximate a long-run optimal capacity expansion policy by optimizing over successively longer finite time horizons. Analytical formulas together with regression analysis show the significance of the number of potential customers, frequency and duration of their requests for service, and the specified service level on the demand for capacity. Numerical sensitivity analysis exposes the effects of cost parameters, the demand growth rate and the required rate of return on the optimal time intervals between expansions

Solution Sensitivity-Based Scenario Reduction for Stochastic Unit Commitment

A two-stage stochastic program is formulated for day-ahead commitment of thermal generating units to minimize total expected cost considering uncertainties in the day-ahead load and the availability of variable generation resources. Commitments of thermal units in the stochastic reliability unit commitment are viewed as first-stage decisions, and dispatch is relegated to the second stage. It is challenging to solve such a stochastic program if many scenarios are incorporated. A heuristic scenario reduction method termed forward selection in recourse clusters (FSRC), which selects scenarios based on their cost and reliability impacts, is presented to alleviate the computational burden. In instances down-sampled from data for an Independent System Operator in the US, FSRC results in more reliable commitment schedules having similar costs, compared to those from a scenario reduction method based on probability metrics. Moreover, in a rolling horizon study, FSRC preserves solution quality even if the reduction is substantial

Allocating work in process in a multiple-product CONWIP system with lost sales

To operate a multiple-product manufacturing system under a CONWIP control policy, one must decide how to assign kanbans to products. With a fixed total number of kanbans in a competitive environment, the goal is to determine their allocation to product types in order to minimize lost sales equitably. In particular, we consider systems in which the products may make multiple visits to the same station with a different processing time distribution on each repeat visit. With a fixed number of kanbans dedicated to each product, the system is modeled as a multiple-chain multiple-class closed queuing network. A nonlinear program simultaneously provides an approximate performance evaluation and optimizes the allocation of kanbans to product types. In numerical examples, the allocations identified are similar to those obtained by exhaustive enumeration with simulation, but frequently differ significantly from a naïve allocation according to demand rates. A variant of the model that minimizes the total work-in-process to achieve specified throughput targets yields results similar to a previous heuristic method

Optimal Replacement in the Proportional Hazards Model with Semi-Markovian Covariate Process and Continuous Monitoring

Motivated by the increasing use of condition monitoring technology for electrical transformers, this paper deals with the optimal replacement of a system having a hazard function that follows the proportional hazards model with a semi-Markovian covariate process, which we assume is under continuous monitoring. Although the optimality of a threshold replacement policy to minimize the long-run average cost per unit time was established previously in a more general setting, the policy evaluation step in an iterative algorithm to identify optimal threshold values poses computational challenges. To overcome them, we use conditioning to derive an explicit expression of the objective in terms of the set of state-dependent threshold ages for replacement. The iterative algorithm is customized for our model to find the optimal threshold ages. A three-state example illustrates the computational procedure, as well as the effects of different sojourn time distributions of the covariate process on the optimal policy and cost. Numerical examples and sensitivity analysis provide some insights into the suitability of a Markov approximation, and the sources of variability in the cost. The optimization method developed here is much more efficient than the approach that approximates continuous monitoring as periodic, and then optimizes the periodic monitoring parameters