Nonlinear Robust Control and Optimisation of Microgrids

The modern power grid is entering a new ``smart grid" era, which promises more efficient power transmission/distribution, decentralised power generation and seamless integration of renewable energy resources to the electricity distribution grid. In the heart of this new era lies the Microgrid, which represents a scaled, local version of the grid and allows the integration of various renewable energy resources, energy storage systems and loads via power converters. Along with a plethora of distinct advantages, Microgrids also introduce many new challenges in designing an appropriate controller that ensures tight regulation of the grid voltage/frequency and economic operation of the network. The continuously advancement of technology enabled the rise of complex and sophisticated load architectures, the majority of which are of DC nature. A prime example is the constant power load, which introduces a nonlinear, destabilising behaviour and poses a threat to the operation of the network. Another issue is associated with the long physical distances between the individual units and the requirement to exchange information in a fast communication rate. Despite the existence of a vast literature on Microgrid control, the majority of the studies are case-specific, offer only numerical investigations of system stability and focuses on the implementation of each proposed control scheme with extensive simulation scenarios or experiments. Due to the continuously increasing complexity of loads and network topologies, it is essential to study the problem from a control-theoretic perspective, in order to provide a deep insight into the dynamical behaviour of the system and develop control techniques that provide strong theoretic guarantees regarding a safe and reliable operation. Furthermore, even though it has not been extensively studied so far, the ability to satisfy constraints is crucial to the Microgrid operation in order to protect the electronic components from overcurrent surges or overvoltage cases that can cause expensive damages and disrupt the network operation. This thesis aims to fill this gap by thoroughly investigating the nonlinear behaviour of the Microgrids under the influence of nonlinear loads. More specifically, the first main contribution is the development of a distributed control scheme for meshed DC Microgrids that employs neighbour-to-neighbour communication and guarantees both local and coupled constraint satisfaction. Contrary to the majority of the approaches found in the literature, the proposed method utilises only locally available information at each node in order to enhance the system scalability and enlarge the range of potential applications. This first part includes a rigorous theoretic analysis to formulate explicit conditions such that the system achieves the desired behaviour and admits asymptotically stable equilibrium points. The following parts of this thesis focus specifically on the effect of the nonlinear loads. The problem is studied from a geometric point of view in order to shed light into the dynamic interaction between the loads and the network and design a control scheme that enhances the system robustness to perturbations of the load demand. First, a local low-level current controller is proposed that guarantees overcurrent protection without the use of saturation devices. Then, theoretic tools are used to guarantee that the voltage trajectory of each local node remains close to a desired reference trajectory and prove that the deviations between the two are bounded in a positive invariant set. This is ultimately used to design a unified control scheme, \ie for both the output voltage and inner current states of each interfacing power converter, that achieves a constraint-based operation with reduced conservativeness compared to the original method. The overall system stability is analytically proven by the use of control Lyapunov functions. The final contribution of this thesis is the extension of the provided theoretic analysis from a DC to the case of an isolated AC Microgrid. A robust controller is proposed in order to show that similar results can be obtained even in the case of a more complicated system model. An analytic characterisation of a closed positive invariant subset of the system state space is obtained and it is shown how this property can be used to design a constraint-based approach for AC Microgrids. Each proposed method is tested in a simulation scenario to validate the results and illustrate the associated theoretic properties.