Low complexity model predictive control in power electronics and power systems

Abstract

This thesis focuses on Model Predictive Control (MPC) of discrete-time hybrid systems. Hybrid systems contain continuous and discrete valued components, and are located at the intersection between the fields of control theory and computer science. MPC uses an internal model of the controlled plant to predict the future evolution of the controlled variables over a prediction horizon. A cost function is minimized to obtain the optimal control input sequence, which is applied to the plant by means of a receding horizon policy. The latter implies that only the first control input of the input sequence is implemented, the horizon is shifted by one time-step and the above procedure is repeated at the next sampling instant. Most importantly, theory and tools are available to off-line derive the piecewise affine (PWA) state-feedback control law. Hence, any time-consuming on-line computation of the control input is avoided and plants with high sampling frequencies can be controlled. The thesis is divided into two parts: The first part is devoted to theory and algorithms, whereas the second part tackles applications in the fields of power electronics and power systems. In the first part, using the notion of cell enumeration in hyperplane arrangements from computational geometry, we propose an algorithm that efficiently enumerates all feasible modes of a composition of hybrid systems. This technique allows the designer to evaluate the complexity of the compound model, to efficiently translate the model into a PWA representation, and to reduce the computational burden of optimal control schemes by adding cuts that prune infeasible modes from the model. With respect to implementation, an important issue is the complexity reduction of PWA state-feedback controllers. Hence, we propose two algorithms that solve the problem of deriving a PWA representation that is both equivalent to the given one and minimal in the number of regions. As both algorithms refrain from solving additional Linear Programs, they are not only optimal but also computationally feasible. In many cases, the optimal complexity reduction constitutes an enabling technique when implementing the optimal controllers as look-up tables in hardware. In the second part of the thesis, we consider the field of power electronics that is intrinsically hybrid, since the positions of semiconductor switches are described by binary variables. The fact that the methodologies of MPC and hybrid systems are basically unknown in the power electronics community has motivated us to consider such problems, namely