Technical Report: Optimal Current Trajectories for Power Converters with Minimal Common Mode Voltage

This article addresses the topic of computing optimized pulse patterns with common mode voltage constraints. The main thrust is to obtain tractable reformulations of the CMV constraints in the frequency domain in order to avoid complex mixed time-frequency formulations. The resulting optimization problem is a nonlinear one for which efficient numerical solvers are readily available. Moreover, we provide an algorithmic way of reducing the conservatism in the reformulated problem and validate our method with numerical illustrations that highlight the benefit of the proposed approach

Interior Point Decomposition for Multi-Agent Optimization

In this paper we present the application of the interior-point decomposition (IPD) method, which was originally formulated for stochastic programming, to optimization problems involving multiple agents that are coupled through constraints and objectives. IPD eliminates the need to communicate local constraints and cost functions for all variables that relate to internal dynamics and objectives of the agents. Instead, by using embedded barrier functions, the problem is solved in the space of coupling variables, which are in general much lower in dimension compared to internal variables of individual agents. Therefore, IPD contributes to both problem size reduction as well as data hiding. The method is a distributed version of the primal barrier method, with locally and globally feasible iterations and faster convergence compared to first-order distributed optimization methods. Hence, IPD is suitable for early termination in time-critical applications. We illustrate these attractive properties of the IPD method with a distributed Model Predictive Control (MPC) application in the context of smart-grids, where a collection of commercial buildings provide voltage support to a distribution grid operator

Technical Report: Control of Nonlinear Systems with Explicit-MPC-like Controllers

This paper describes synthesis of controllers involving Quadratic Programming (QP) optimization problems for control of nonlinear systems. The QP structure allows an implementation of the controller as a piecewise affine function, pre-computed offline, which is a technique extensively studied in the field of explicit model predictive control (EMPC). The nonlinear systems being controlled are assumed to be described by polynomial functions and the synthesis also generates a polynomial Lyapunov function for the closed-loop system involving the obtained controller. The synthesis is based on a sum-of-squares (SOS) stability verification for polynomial discrete-time systems, described in continuous-time in this paper. The presented synthesis method allows a design of EMPC controllers with closed-loop stability guarantees without relying on a terminal cost and/or constraint, and even without using the prediction horizon concept to formulate the control optimization problem. In particular, for a specified QP structure the method directly searches for the stabilizing coefficients in the cost and/or the constraint set. The method involves two phases, where the first searches for stabilizing controllers by minimizing a polynomial slack function introduced to the SOS stability condition and the second phase optimizes some user-specified performance criteria. The two phases are formulated as optimization problems which can be tackled by using a black-box optimization technique such as Bayesian optimization, which is used in this paper. The synthesis is demonstrated on a numerical example involving a bilinear model of a permanent magnet synchronous machine (PMSM), where in order to demonstrate the modeling flexibility of the proposed synthesis method a QP-based controller for speed regulation of PMSM is synthesized that is robust to parametric uncertainty coming from the temperature-dependent stator resistance of the PMSM

Technical Report: Voltage Source Converter MPC with Optimized Pulse Patterns and minimization of Integrated Squared Tracking Error

Model predictive control schemes for power electronic applications are characterized by a great variety of problem formulations. In this paper, we consider a three phase voltage source converter with an arbitrary number of voltage levels and derive a model predictive control scheme involving a combination of optimized pulse patterns and the integral of squared predicted tracking error as a cost function. We obtain a nonlinear optimization problem with the switching times as optimization variables, and solve it using gradient projection algorithm. To obtain an easier optimization problem to be solved on-line, a linearization around nominal switching instants is performed bringing the problem to a quadratic programming form. Simulation results demonstrating the performance of the derived scheme are provided for the case of a grid-tied converter with LCL filter

Low-Complexity Optimization-Based Control: Design, Methods and Applications

Optimization-based controllers are advanced control systems whose mechanism of determining control inputs requires the solution of a mathematical optimization problem. In this thesis, several contributions related to the computational effort required for optimization-based controller execution are provided. The content of the thesis is divided into three parts: The first part provides methods capable of performing automatic controller tuning for constrained control of nonlinear systems. Given a specified controller structure, the presented methods are able to perform an offline tuning of the controller parameters such that some user-specified performance metric is optimized while imposing stability guarantees on the obtained closed-loop system. The methods are characterized by a broad flexibility that allows their application to many control schemes that are widely popular in practice, but also to novel user-specified control schemes that are convenient from a computational or some other point of view. The controller tuning is formulated as an optimization problem that can be tackled by black-box optimization techniques such as Bayesian optimization. The methods are demonstrated by application examples involving speed control of a permanent magnet synchronous machine and position control of a mechanical gyroscopic system. The second part provides an accelerated version of the alternating direction method of multipliers (ADMM) optimization algorithm derived by using a recently proposed accelerated Douglas-Rachford (DR) splitting. The obtained method is an accelerated ADMM version that replaces the internal proximal point convergence mechanism of the classical ADMM by the accelerated gradient method applied on a specially constructed scaled DR envelope function. The form of the accelerated ADMM is derived and conditions are provided under which the underlying accelerated DR splitting is validly addressing the Fenchel dual problem. The third part describes a model predictive control scheme for power electronics control which involves a combination of the integral of squared predicted tracking error as the controller's cost function together with offline computed optimal steady-state voltage signals. These offline computed optimal steady-state signals are in the power electronics community referred to as Optimized Pulse Patterns (OPPs). The method is presented by considering an industrial case study involving a grid-tied converter with LC filter. After introducing an optimal control problem based on OPPs, low computational complexity approximate versions are provided. The resulting approximate controller versions are addressed by using memory storage of the dynamic behavior of the system, leading to controller forms whose execution can be performed on embedded hardware

One solution for cross-country transport-sustainability evaluation using a modified ELECTRE method

Transport is an economic activity having complex interactions with the environment, and since the concept of sustainable development was identified as a global priority, there has been a growing interest in assessing the performance of transport systems with respect to sustainability issues. Although the Ecological Economics literature deals extensively with the strategy of sustainable development, far less attention has been paid to its application in the transport sector as of yet. The main purpose of this study was to introduce the noncompensatory analytical tool, which integrates multidimensional conditions present in the sustainability concept. The focus was on the potential of the outranking approach, namely the ELECTRE (ELimination Et Choix Traduisant la REalité; Elimination And Choice Corresponding to Reality) method for the evaluation of transport sustainability at the macro level, using the indicator set as a starting point. The method has been applied to selected European countries within a case study. As a result, according to transport-sustainability issues, pairwise relations between countries have been established. Based on these relations, and according to the chosen criteria, a set of countries with a better level of performance was selected as the core subset of the relation graph. To control and avoid the appearance of indifference relations between countries, as well as to reduce the subjectivity of decision makers, we propose a modification of ELECTRE I. Finally, we apply both the original and the modified methods, together with the sensitivity analysis. The results are presented in a convenient graph form and then compared.Sustainable-transport indicators Cross-country evaluation Outranking approach Modified ELECTRE method