Robust Tracking Commitment

Abstract

Many engineering problems that involve hierarchical control applications, such as demand side ancillary service provision to the power grid, can be posed as a robust tracking commitment problem. In this setting, the lower-level controller commits a set of possible reference trajectories over a finite horizon to an external entity in exchange for a reward corresponding to the size of the reference set and the allowed margin of tracking error. If the commitment is accepted, the lower-level system is required to track any reference trajectory that can be sampled from the committed set. This paper presents the framework of robust tracking commitment and a method to solve the optimal commitment problem for constrained linear systems subject to uncertain disturbance and reference signals. The proposed method allows tractable computations via convex optimization for conic representable uncertainty sets and lends itself to distributed solution methods. We demonstrate the proposed method in a simulation based case study with a commercial building that offers frequency regulation service to the power grid.

Optimal Virtual Power Plant Management for Multiple Grid Support Services

“…Furthermore, a robust approach [15] is adopted to mitigate the uncertainty related to the unbalance fee costs. Alternative robust frameworks are available in the literature, e.g., [16], however they are not suitable for the problem addressed in this study because they require a convex problem formulation. Furthermore, in [16] the optimization is performed over closed-loop control policies, which would be computationally significantly demanding.…”

“…Considering the generic VPP in Fig. 4, which includes all the flexibility assets, the total power flow for Energy Arbitrage EA operations is given by (16).…”

“…Importantly the global symmetrical modeling of the regulation margins in (17) does not imply a symmetric regulation for each single unit. Furthermore, each assets may provide different contributions to the two services (EA and FR): all the technologies play a role in the energy arbitrage (16), but BESS units only can guarantee a reliable provision of the fast frequency regulation (17) within the time set by the grid standards [18]- [19]. The 3 rd and 2 nd layers act on day-ahead and intra-day time scales respectively, and the optimization approaches in each of these layers are described in the following sections.…”

Unlocking the Potential of Flexible Energy Resources to Help Balance the Power Grid

“…However, the particular structure of the problem, that is its decomposable objective and the linear coupling constraints (17c) and (17d), allow us to apply decentralized optimization methods, such as ADMM, cf. [17], [33] for more details.…”

Robust Model Predictive Control with Adjustable Uncertainty Sets

“…Notice that Definition II.2 is a generalization of the standard robust control invariant set, which can be recovered by fixing W t−1 = W t in (9). Furthermore, when W t−1 = W t = {0}, (9) recovers the standard control invariant set [15].…”