Distributed Control and Optimization of DC Microgrids: A Port-Hamiltonian Approach

This article proposes a distributed secondary control scheme that drives a dc microgrid to an equilibrium point where the generators share optimal currents, and their voltages have a weighted average of nominal value. The scheme does not rely on the electric system topology nor its specifications; it guarantees plug-and-play design and functionality of the generators. First, the incremental model of the microgrid system with constant impedance, current, and power devices is shown to admit a port-Hamiltonian (pH) representation, and its passive output is determined. The economic dispatch problem is then solved by the Lagrange multipliers method; the Karush-Kuhn-Tucker conditions and weighted average formation of voltages are then formulated as the control objectives. We propose a control scheme that is based on the Control by Interconnection design philosophy, where the consensus-based controller is viewed as a virtual pH system to be interconnected with the physical one. We prove the regional asymptotic stability of the closed-loop system using Lyapunov and LaSalle theorems. Equilibrium analysis is also conducted based on the concepts of graph theory and economic dispatch. Finally, the effectiveness of the presented scheme for different case studies is validated with a test microgrid system, simulated in both MATLAB/Simulink and OPAL-RT environments

Generalized Voltage-based State-Space Modelling of Modular Multilevel Converters with Constant Equilibrium in Steady-State

This paper demonstrates that the sum and difference of the upper and lower arm voltages are suitable variables for deriving a generalized state-space model of an MMC which settles at a constant equilibrium in steady-state operation, while including the internal voltage and current dynamics. The presented modelling approach allows for separating the multiple frequency components appearing within the MMC as a first step of the model derivation, to avoid variables containing multiple frequency components in steady-state. On this basis, it is shown that Park transformations at three different frequencies ($+\omega$, $-2\omega$ and $+3\omega$) can be applied for deriving a model formulation where all state-variables will settle at constant values in steady-state, corresponding to an equilibrium point of the model. The resulting model is accurately capturing the internal current and voltage dynamics of a three-phase MMC, independently from how the control system is implemented. The main advantage of this model formulation is that it can be linearised, allowing for eigenvalue-based analysis of the MMC dynamics. Furthermore, the model can be utilized for control system design by multi-variable methods requiring any stable equilibrium to be defined by a fixed operating point. Time-domain simulations in comparison to an established average model of the MMC, as well as results from a detailed simulation model of an MMC with 400 sub-modules per arm, are presented as verification of the validity and accuracy of the developed model

PID passivity-based droop control of power converters:Large-signal stability, robustness and performance

We present a full review of PID passivity-based controllers (PBC) applied to power electronic converters, discussing limitations, unprecedented merits and potential improvements in terms of large-signal stability, robustness and performance. We provide four main contributions. The nominal case is first considered and it is shown—under the assumption of perfect knowledge of the system parameters—that the PID-PBC is able to guarantee global exponential stability of a desired operating point for any positive gains. Second, we analyze robustness of the controller to parameters uncertainty for a specific class of power converters, by establishing precise stability margins. Third, we propose a modification of the controller by introducing a leakage, in order to overcome some of the intrinsic performance and robustness limitations. Interestingly, such controller can be interpreted at steady-state as a droop between the input and the passive output, similar to traditional primary controllers. Fourth, we robustify the design against saturation of the control input via an appropriate monotone transformation of the controller. The obtained results are thoroughly discussed and validated by simulations on two relevant power applications: a DC/DC boost converter and an HVDC grid-connected voltage source converter

On the tuning of fractional order resonant controllers for a voltage source converter in a weak AC grid context

This paper proposes a method for tuning the fractional exponent of different types of fractional order resonant controllers for a voltage source converter in a weak AC grid context. The main objective is to ensure the stability of the controlled system in a weak AC grid environment and to achieve an adequate dynamic response under disturbances. Therefore, six commonly used integer order proportional resonant (PR) control structures are selected from the literature and compared with each other according to their frequency behaviour. Afterwards, a rational approximation for the fractional order term is selected based on continuous fraction expansion technique. The inclusion of a fractional exponent in each integer order PR structure generates the fractional order proportional resonant (FPR) control transfer functions. Once the FPR controllers have been obtained, their closed-loop responses are tested via eigenvalue trajectory analysis. For each FPR control structure, a range of the fractional exponent that ensures stability is obtained. The conclusions of eigenvalue trajectory analysis are tested by implementing the FPR control structures in an specific application consisting in a modular multi-level converter (MMC) connected to a weak AC grid with adjustable short-circuit ratio. By means of time-domain simulations, not only the previous eigenvalue analyses are validated, but also new tuning criteria are given for the fractional exponent in combination with other control parameters, such as the damping frequency and the inductance of the complementary feedback branch. Moreover, a sensitivity analysis of the tuning criteria is carried out for other sizes of the AC filter inductance.This work was supported by the Basque Government through the Project of Research Group GISEL under Grant IT1083-16. Besides, TECNALIA is a ‘‘CERVERA Technology Centre of Excellence’’ recognised by the Ministry of Science and Innovation

Commande adaptée pour le convertisseur modulaire multiniveaux pour les liaisons à courant continues

Following Europe’s 2020 growth program, the Energy Roadmap 2050 launched by the European Commission (EC) has officially set a long term path for a low-carbon economy, assuming a reduction of at least 80% of greenhouse gas emissions by the year 2050. Meeting such ambitious requirements will imply a major change in paradigm, including the electricity grid infrastructure as we know it.The breakthroughs in semi-conductor technology and the advances in power electronics topologies and control have added momentum to the on-going process of turning the SuperGrid into a reality. Perhaps the most recent breakthrough occurred in 2003, when Prof. Marquardt introduced the Modular Multilevel Converter (MMC or M2C) which is now the preferred power electronic topology that is starting to be used in VSC-HVDC stations. It does however, introduce a number of rather complex challenges such as “additional” circulating currents within the converter itself, causing extra losses and potentially unstable operation. In addition, the MMC will be required to properly balance the capacitive energy stored within its different arms, while transferring power between the AC and DC grids that it interfaces.The present Thesis project aimed to design adequate “high-level” MMC control strategies suited for HVDC applications, under balanced and unbalanced AC grid conditions. The resulting control strategy is derived with a “top-to-bottom” design approach, inherent to optimization strategies, where the desired performance of the MMC results in the control scheme that will be applied. More precisely, the Lagrange multipliers optimization methodology is used to calculate the minimal MMC circulating current reference signals in phase coordinates, capable of successfully regulating the capacitive arm energies of the converter, while reducing losses and voltage fluctuations, and effectively decoupling any power oscillations that would take place in the AC grid and preventing them from propagating into the DC grid.Dans le cadre du programme de croissance Européen 2020, la commission européenne a mis en place officiellement un chemin à long terme pour une économie à faible émission de carbone, en aspirant une réduction d’au moins 80% des émissions de gaz à effet de serre, d’ici 2050. Répondre à ces exigences ambitieuses, impliquera un changement majeur de paradigme, et notamment en ce qui concerne les infrastructures du réseau électrique. Les percées dans la technologie des semi-conducteurs et les avancées avec les nouvelles topologies d’électronique de puissance et leurs contrôle-commandes, ont contribué à l’impulsion donnée au processus en cours de réaliser un tel SuperGrid. Une percée technologique majeure a eu lieu en 2003, avec le convertisseur modulaire multi-niveaux (MMC ou M2C), présenté par le professeur Marquardt, et qui est actuellement la topologie d’électronique de puissance la plus adaptée pour les stations HVDC. Cependant, cette structure de conversion introduit également un certain nombre de défis relativement complexes tels que les courants “additionnels” qui circulent au sein du convertisseur, entrainant des pertes supplémentaires et un fonctionnement potentiellement instable. Ce projet de thèse vise à concevoir des stratégies de commande “de haut niveau” pour contrôler le MMC adaptées pour les applications à courant continue-haute tension (HVDC), dans des conditions de réseau AC équilibrés et déséquilibrés. La stratégie de commande optimale identifiée est déterminée via une approche pour la conception du type “de haut en bas”, inhérente aux stratégies d’optimisation, où la performance souhaitée du convertisseur MMC donne la stratégie de commande qui lui sera appliquée. Plus précisément, la méthodologie d’optimisation des multiplicateurs de Lagrange est utilisée pour calculer le signal minimal de référence du courant de circulation du MMC dans son repère naturel

Tuning of control loops for grid-connected Modular Multilevel Converters under a simplified port representation for large system studies

One of the present barriers to the widespread use of Modular Multilevel Converters (MMC) is the complexity of its control with respect to its predecessors. This paper presents a simple procedure to tune the current and energy control loops of the MMC, based on standard PI controllers and resembles control tuning approaches commonly used for 2-Level Voltage Source Converters (2L-VSC). The control design is based on a recently proposed simplified model of the MMC which is able to accurately represent the interface variables dynamics on the ac- and dc-side, which are considered as the main variables of concern from a macroscopic point of view. Furthermore, the tuning methodology guarantees the stable behaviour and correct tracking of the states. The paper presents simulation results of a typical case under the proposed tuning procedure

Port-Hamiltonian modelling of Modular Multilevel Converters with fixed equilibrium point

The paper presents the derivation of a port-Hamiltonian model of an averaged Modular Multilevel Converter (MMC) that reaches a fixed equilibrium point solution. This MMC model can not be expressed in a straightforward way in a port-Hamiltonian framework due to the lack of skew-symmetry of its interconnection matrices. This work proposes a change of variable and a new per unit notation to overcome this limitation, obtaining a port-Hamiltonian model of the MMC with static equilibrium, useful for control design purposes

Avoiding AC/DC grid interaction in MMC based MTDC Systems

In this paper, the interaction between ac and dc grids is studied for two types of MMC control structures; conventional and non-conventional control structures. Linear analysis methods that are based mode shapes and participation factors are used to identify dynamic interaction in a hybrid ac-dc power system. The analysis uses as a test system a three terminal Modular Multilevel Converter (MMC) based Multi-terminal High Voltage DC (MTDC) grid connecting three multi-machine asynchronous ac grids. The results show that there is some dynamic interaction between ac and dc grids under conventional MMC converter control structure, while the non-conventional MMC converter control structure decouples the ac and dc side of the MMC converter, thus avoiding interaction between the ac and dc grids

Particle Swarm Optimization Tuning of Modular Multilevel Converters in a Time-Invariant Framework

This work investigates the Particle Swarm Optimization (PSO) algorithm as a tool to tune the control parameters of a Modular Multilevel Converter (MMC) in a single-terminal HVdc configuration. More precisely, due to its inherent capacity of handling system non-linearities, the PSO algorithm is used to tune a nonlinear control structure based on passivity arguments capable of ensuring global asymptotic stability of the converter. This nonlinear control strategy was successfully applied to the MMC in previous efforts, albeit with sub-optimal tuning, and therefore below par performance. Thus, this work aims to contribute to the state of the art by proving that system performance under the nonlinear control structure of interest can be further improved via PSO-tuning. Finally, to reduce the computational burden, we propose to apply the PSO algorithm directly to a recent state-space representation of an MMC with a constant equilibrium point