Abstract
Electrical smart grids are complex MIMO systems whose operation can be noticeably affected by the presence of uncertainties such as load demand uncertainty. In this paper, based on a restricted representation of the demand uncertainty, we propose a robust economic model predictive control method that guarantees an optimal energy dispatch in a smart micro-grid. Load demands are uncertain, but viewed as bounded. The proposed method first decomposes control inputs into dependent and independent components, and then tackles the effect of demand uncertainty by tightening the system constraints as the uncertainty propagates along the prediction horizon using interval arithmetic and local state feedback control law. The tightened constraints’ upper and lower limits are computed off-line. The proposed method guarantees stability through a periodic terminal state constraint. The method is faster and simpler compared to other approaches based on Closed-loop min–max techniques. The applicability of the proposed approach is demonstrated using a smart micro-grid that comprises a wind generator, some photovoltaic (PV) panels, a diesel generator, a hydroelectric generator and some storage devices linked via two DC-buses, from which load demands can be adequately satisfied.
Highlights
The most trivial approach of tackling uncertainties is to neglect them i.e., to consider only the nominal system, and rely on the receding horizon control principle of Model Predictive Control (MPC), which introduces a Closed-loop mechanism that could minimize the effects of uncertain disturbances
The dependent components have further been divided into two parts, whereby one of the parts is bounded by a zonotope and is employed to compensate for any deviation of the actual demand from the forecasted one
We have developed a novel robust economic MPC method for guaranteeing an optimal control of a smart micro-grid considering an unknown but bounded demand uncertainty
Summary
The most trivial approach of tackling uncertainties is to neglect them i.e., to consider only the nominal system, and rely on the receding horizon control principle of MPC, which introduces a Closed-loop mechanism that could minimize the effects of uncertain disturbances. We extend the method presented in [25] by adding a feedback control law, which results in a Closed-loop system This could palliate shortcomings of the Open-loop approach such as tackling higher demand uncertainty, thereby improving the overall feasibility and stability of the controller. The proposed method first decomposes control inputs into dependent and independent components, and considers the effect of demand uncertainty by tightening the system constraints along the prediction horizon. Development and application of a novel robust MPC Method based on zonotopes extending classical tube-based approaches for tackling an uncertain energy dispatch problem in smart micro-grids including several heterogeneous generators and storage elements.
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