Advanced Hierarchical Control and Stability Analysis of DC Microgrids

Abstract

The paradigm shift in electrical power grids and the increased interest towards decentralisation has opened a new window in the design, control and theoretical analysis of small scale power systems, i.e. microgrids, which aim at the integration and utilisation of renewable energy sources, energy storage systems and responsive loads at a local scale. Given their DC nature, DC microgrids have attracted significant interest as they provide a natural interface to the main grid by avoiding additional conversion steps. The aim of this thesis is to design and analyse novel hierarchical control schemes, both at the primary and secondary control level, that guarantee tight voltage regulation, accurate power sharing, current or voltage limitation, and present a straightforward approach towards deriving stability conditions for DC microgrids that incorporate nonlinear loads. As the microgrid configuration is paramount in the theoretical analysis, a rigorous method of computing the admittance matrix is developed that facilitates the stability analysis of DC microgrid systems supplying a constant impedance (Z), constant current (I) or constant power (P) load. This method is particularly useful as it permits the factorisation of the admittance matrix, while separating the singular matrices. In this way, the closed-loop asymptotic stability proof can be more easily approached by isolating the singularities and then, employing straightforward linear algebra tools, such as quadratic eigenvalue problem (QEP) theory, to derive the stability conditions. As stated in the technical specifications of every source, a crucial issue is represented by the ability to protect itself and its interface device (power converter) during faults, transients and unrealistic power demands. That is why current-limiting control is often combined with the primary control, i.e. often droop control, in DC microgrids to ensure the desired unit protection. In this thesis, novel current-limiting droop controllers areformulated for DC microgrids consisting initially of multiple unidirectional DC/DC boost converters and, later on, bidirectional DC/DC boost and three-phase AC/DC converters, that integrate different distributed generation units with the local grid. In contrast to the traditional approaches that use small-signal modelling, here, the accurate nonlinear models of the converter units are taken into account to prove the boundedness and the current-limiting property, by employing Lyapunov methods and the ultimate boundedness theory. Exponential stability at the desired equilibrium point is mathematically guaranteed, and further analysed from a graphical perspective, providing insights of the load’s effect onto the system performance and stability. To address the shortcomings that conventional droop control approaches introduce, i.e. inaccurate power sharing and significant load voltage drop, a DC microgrid architecture that takes into account the power converter dynamics of distributed generation units is deployed under decentralised primary and distributed secondary control scheme, in a hierarchical control framework. At the primary control layer, a novel current-limiting droop control scheme is implemented in a decentralised manner, whereas at the secondary control layer a fully distributed controller that performs a voltage restoration and improves the power sharing is deployed using a nearest-neighbour coupling communication network. By investigating for the first time both the dynamics of the converters with the nonlinear load and the two-layer control, singular perturbation theory is applied to analytically guarantee the stability of the entire DC microgrid. Finally, apart from the desired overcurrent protection, since DC capacitors are customary used at the output of each converter unit to stabilise the output voltage, they also introduce a maximum voltage limit. Hence, as the need for protection against overvoltages has emerged, droop controllers with inherent overvoltage protection are also proposed for parallel and meshed configuration networks. The upper limit of the voltage of each source is rigorously proven using ultimate boundedness theory. Asymptotic stability to the desired equilibrium for the closed-loop system is analytically guaranteed, and detailed conditions are derived to guide the control design. In order to validate the effectiveness of the different control methodologies developed in this thesis, both simulation and experimental testing are performed for each one of the methods, and are also compared with the conventional approaches to highlight their superiority.