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Register a new userFrom Instantaneous Schedulability to Worst Case Schedulability: A Significant Moment Approach
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The method of significant moment analysis has been employed to derive instantaneous schedulability tests for real-time systems. However, the instantaneous schedulability can only be checked within a finite time window. On the other hand, worst-case schedulability guarantees schedulability of systems for infinite time. This paper derives the classical worst-case schedulability conditions for preemptive periodic systems starting from instantaneous schedulability, hence unifying the two notions of schedulability. The results provide a rigorous justification on the critical time instants being the worst case for scheduling of preemptive periodic systems. The paper also show that the critical time instant is not the only worst case moments.
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In this paper, we shed new light on a classical scheduling problem: given a slot-timed, constant-capacity server, what short-run scheduling decisions must be made to provide long-run service guarantees to competing flows of unit-sized tasks? We model the flows long-run guarantees as worst-case services that map each arrival vector recording a flows cumulative task arrivals to a worst-case acceptable departure vector lower-bounding its cumulative task departures. We show that these services are states that can be updated as tasks arrive and depart, introduce state-based scheduling, and find the schedulability condition that must be preserved to maintain all flows long-run guarantees. We then use this condition to identify, in each slot, all short-run scheduling decisions that preserve schedulability. To illustrate how scheduling complexity can be reduced, we additionally show that special schedules can be efficiently identified by maximizing the servers capacity slack, and that special services can be efficiently specified and updated using properties of the min-plus algebra.
A system of a systems approach that analyzes energy and water systems simultaneously is called energy-water nexus. Neglecting the interrelationship between energy and water drives vulnerabilities whereby limits on one resource can cause constraints on the other resource. Power plant energy production directly depends on water availability, and an outage of the power systems will affect the wastewater treatment facility processes. Therefore, it is essential to integrate energy and water planning models. As mathematical energy-water nexus problems are complex, involve many uncertain parameters, and are large-scale, we proposed a novel multi-stage adjustable Fuzzy robust approach that balances the solutions robustness against the budget-constraints. Scenario-based analysis indicates that the proposed approach generates flexible and robust decisions that avoid excessive costs compared to conservative methods. Keywords: Energy-water Nexus, Renewable Energy, Optimization under Uncertainty, Fuzzy logic, Robust Optimization
We consider some crucial problems related to the secure and reliable operation of power systems with high renewable penetrations: how much reserve should we procure, how should reserve resources distribute among different locations, and how should we price reserve and charge uncertainty sources. These issues have so far been largely addressed empirically. In this paper, we first develop a scenario-oriented energy-reserve co-optimization model, which directly connects reserve procurement with possible outages and load/renewable power fluctuations without the need for empirical reserve requirements. Accordingly, reserve can be optimally procured system-wide to handle all possible future uncertainties with the minimum expected system total cost. Based on the proposed model, marginal pricing approaches are developed for energy and reserve, respectively. Locational uniform pricing is established for energy, and the similar property is also established for the combination of reserve and re-dispatch. In addition, properties of cost recovery for generators and revenue adequacy for the system operator are also proven.
With the emergence of cost effective battery storage and the decline in the solar photovoltaic (PV) levelized cost of energy (LCOE), the number of behind-the-meter solar PV systems is expected to increase steadily. The ability to estimate solar generation from these latent systems is crucial for a range of applications, including distribution system planning and operation, demand response, and non-intrusive load monitoring (NILM). This paper investigates the problem of disaggregating solar generation from smart meter data when historical disaggregated data from the target home is unavailable, and deployment characteristics of the PV system are unknown. The proposed approach entails inferring the physical characteristics from smart meter data and disaggregating solar generation using an iterative algorithm. This algorithm takes advantage of solar generation data (aka proxy measurements) from a few sites that are located in the same area as the target home, and solar generation data synthesized using a physical PV model. We evaluate our methods with 4 different proxy settings on around 160 homes in the United States and Australia, and show that the solar disaggregation accuracy is improved by 32.31% and 15.66% over two state-of-the-art methods using only one real proxy along with three synthetic proxies. Furthermore, we demonstrate that using the disaggregated home load rather than the net load data could improve the overall accuracy of three popular NILM methods by at least 22%.
Given a stochastic dynamical system modelled via stochastic differential equations (SDEs), we evaluate the safety of the system through characterisations of its exit time moments. We lift the (possibly nonlinear) dynamics into the space of the occupation and exit measures to obtain a set of linear evolution equations which depend on the infinitesimal generator of the SDE. Coupled with appropriate semidefinite positive matrix constraints, this yields a moment-based approach for the computation of exit time moments of SDEs with polynomial drift and diffusion dynamics. To extend the capability of the moment approach, we propose a state augmentation method which allows us to generate the evolution equations for a broader class of nonlinear stochastic systems and apply the moment method to previously unsupported dynamics. In particular, we show a general augmentation strategy for sinusoidal dynamics which can be found in most physical systems. We employ the methodology on an Ornstein-Uhlenbeck process and stochastic spring-mass-damper model to characterise their safety via their expected exit times and show the additional exit distribution insights that are afforded through higher order moments.
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