Tamás Keviczky

Minh Dang Doan, Pontus Giselsson, Tamás Keviczky et al.

A distributed model predictive control (DMPC) approach based on distributed optimization is applied to the power reference tracking problem of a hydro power valley (HPV) system. The applied optimization algorithm is based on accelerated gradient methods and achieves a convergence rate of O(1/k^2), where k is the iteration number. Major challenges in the control of the HPV include a nonlinear and large-scale model, nonsmoothness in the power-production functions, and a globally coupled cost function that prevents distributed schemes to be applied directly. We propose a linearization and approximation approach that accommodates the proposed the DMPC framework and provides very similar performance compared to a centralized solution in simulations. The provided numerical studies also suggest that for the sparsely interconnected system at hand, the distributed algorithm we propose is faster than a centralized state-of-the-art solver such as CPLEX.

Minh Dang Doan, Tamás Keviczky, Bart De Schutter

We present a hierarchical model predictive control approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible solution within a finite number of iterations, using primal averaging and a constraint tightening approach. The primal update is performed in a distributed way and does not require exact solutions, while the dual problem uses an approximate subgradient method. Stability of the scheme is established using bounded suboptimality.

Arman Sharifi Kolarijani, Peyman Mohajerin Esfahani, Tamás Keviczky

Treating optimization methods as dynamical systems can be traced back centuries ago in order to comprehend the notions and behaviors of optimization methods. Lately, this mind set has become the driving force to design new optimization methods. Inspired by the recent dynamical system viewpoint of Nesterov's fast method, we propose two classes of fast methods, formulated as hybrid control systems, to obtain pre-specified exponential convergence rate. Alternative to the existing fast methods which are parametric-in-time second order differential equations, we dynamically synthesize feedback controls in a state-dependent manner. Namely, in the first class the damping term is viewed as the control input, while in the second class the amplitude with which the gradient of the objective function impacts the dynamics serves as the controller. The objective function requires to satisfy the so-called Polyak--Łojasiewicz inequality which effectively implies no local optima and a certain gradient-domination property. Moreover, we establish that both hybrid structures possess Zeno-free solution trajectories. We finally provide a mechanism to determine the discretization step size to attain an exponential convergence rate.

Mohammad Amin Sheikhi, Gabriel de Albuquerque Gleizer, Peyman Mohajerin Esfahani et al.

We study the problem of fault isolation in linear systems with actuator and sensor faults within a data-driven framework. We propose a nullspace-based filter that uses solely fault-free input-output data collected under process and measurement noises. By reparameterizing the problem within a behavioral framework, we achieve a direct fault isolation filter design that is independent of any explicit system model. The underlying classification problem is approached from a geometric perspective, enabling a characterization of mutual fault discernibility in terms of fundamental system properties given a noise-free setting. In addition, the provided conditions can be evaluated using only the available data. Finally, a simulation study is conducted to demonstrate the effectiveness of the proposed method.

Oscar Sondermeijer, Roel Dobbe, Daniel Arnold et al.

Electronic power inverters are capable of quickly delivering reactive power to maintain customer voltages within operating tolerances and to reduce system losses in distribution grids. This paper proposes a systematic and data-driven approach to determine reactive power inverter output as a function of local measurements in a manner that obtains near optimal results. First, we use a network model and historic load and generation data and do optimal power flow to compute globally optimal reactive power injections for all controllable inverters in the network. Subsequently, we use regression to find a function for each inverter that maps its local historical data to an approximation of its optimal reactive power injection. The resulting functions then serve as decentralized controllers in the participating inverters to predict the optimal injection based on a new local measurements. The method achieves near-optimal results when performing voltage- and capacity-constrained loss minimization and voltage flattening, and allows for an efficient volt-VAR optimization (VVO) scheme in which legacy control equipment collaborates with existing inverters to facilitate safe operation of distribution networks with higher levels of distributed generation.