Robust optimization based energy dispatch in smart grids considering demand uncertainty

In this study we discuss the application of robust optimization to the problem of economic energy dispatch in smart grids. Robust optimization based MPC strategies for tackling uncertain load demands are developed. Unexpected additive disturbances are modelled by defining an affine dependence between the control inputs and the uncertain load demands. The developed strategies were applied to a hybrid power system connected to an electrical power grid. Furthermore, to demonstrate the superiority of the standard Economic MPC over the MPC tracking, a comparison (e.g average daily cost) between the standard MPC tracking, the standard Economic MPC, and the integration of both in one-layer and two-layer approaches was carried out. The goal of this research is to design a controller based on Economic MPC strategies, that tackles uncertainties, in order to minimise economic costs and guarantee service reliability of the system.Postprint (author's final draft

Guaranteeing Input Tracking For Constrained Systems: Theory and Application to Demand Response

A method for certifying exact input trackability for constrained discrete time linear systems is introduced in this paper. A signal is assumed to be drawn from a reference set and the system must track this signal with a linear combination of its inputs. Using methods inspired from robust model predictive control, the proposed approach certifies the ability of a system to track any reference drawn from a polytopic set on a finite time horizon by solving a linear program. Optimization over a parameterization of the set of reference signals is discussed, and particular instances of parameterization of this set that result in a convex program are identified, allowing one to find the largest set of trackable signals of some class. Infinite horizon feasibility of the methods proposed is obtained through use of invariant sets, and an implicit description of such an invariant set is proposed. These results are tailored for the application of power consumption tracking for loads, where the operator of the load needs to certify in advance his ability to fulfill some requirement set by the network operator. An example of a building heating system illustrates the results.Comment: Technical Not

FACT : A Probabilistic Model Checker for Formal Verification with Confidence Intervals

We introduce FACT, a probabilistic model checker that computes confidence intervals for the evaluated properties of Markov chains with unknown transition probabilities when observations of these transitions are available. FACT is unaffected by the unquantified estimation errors generated by the use of point probability estimates, a common practice that limits the applicability of quantitative verification. As such, FACT can prevent invalid decisions in the construction and analysis of systems, and extends the applicability of quantitative verification to domains in which unknown estimation errors are unacceptable

Optimal Dosing of Breast Cancer Chemotherapy Using Robust MPC Based on Linear Matrix Inequalities

In this paper, we consider an application of robust model predictive control to optimal dosing of breast cancer chemotherapy. The model-patient mismatch is handled by computing an ellipsoidal invariant set containing the measured patient's states at each sampling time. An optimal dose of chemotherapeutic agent is obtained by solving a convex optimization problem subject to linear matrix inequalities. In the case study of simulated patients, the results show that the tumor volume can be reduced to a specified target with up to 30% model-patient mismatch. Moreover, the robust model predictive control algorithm can achieve better treatment results as compared with the nonlinear model predictive control algorithm while the on-line computational time is significantly reduced

Data-Driven Superstabilization of Linear Systems under Quantization

This paper focuses on the stabilization and regulation of linear systems affected by quantization in state-transition data and actuated input. The observed data are composed of tuples of current state, input, and the next state's interval ranges based on sensor quantization. Using an established characterization of input-logarithmically-quantized stabilization based on robustness to sector-bounded uncertainty, we formulate a nonconservative infinite-dimensional linear program that enforces superstabilization of all possible consistent systems under assumed priors. We solve this problem by posing a pair of exponentially-scaling linear programs, and demonstrate the success of our method on example quantized systems.Comment: 12 pages, 2 figures, 3 table