Model-based and data-driven formal synthesis of power systems

Abstract

This thesis is motivated by the increased embedding of cyber components inside physical real-world systems where properties such as safety are paramount. Smart energy systems are one such example of cyber-physical systems(CPS). In a world looking for net-zero emissions, uncertain renewable generation sources are being relied on over traditional turbine generators. Additionally, plug-in electric vehicles (EVs) are becoming attractive options of reducing an individual’s carbon footprint at an increasingly affordable price point. The systemwide delicate balance between power generation and consumption is captured by the power network’s frequency. Frequency regulation, the control mechanism to maintain safe operating limits, is a pressing area for research, with serious instability causing potential load shedding, blackouts, or cascading failures. Supervisory Control and Data Acquisition, PID control and model-predictive control are examples of some regulation techniques. At present, these techniques do not provide guarantees for the system’s behaviour, e.g. satisfying grid code standards, and they may require manual intervention in emergency scenarios. A growing area in computer science is formal methods, with the goal of verifying that system controlled by a software, satisfy a given formal specification. The formal specification uses temporal logic to define complex logical properties the system should satisfy. Examples of these properties include safety, reachability, or reach-avoid. Formal controllers can be synthesised with guarantees on the satisfaction of the specification. One of the main formal controller synthesis approaches is based on the construction of simplified abstract models using state-space discretisation. This is an immensely powerful approach but it suffers from the curse of dimensionality. As the number of state variables increases, the size of the abstract model explodes exponentially, making computations intractable at higher dimensions. Due to this, case studies and results in the formal methods community tend to use simpler academic examples with low dimensions. This thesis brings together the concepts from power systems, computer science, and control engineering. The power system community benefits from the tangible guarantees provided by formal control approaches, and the formal methods Summary community benefit from complex real-world case studies. In particular, this thesis provides several novel contributions: This thesis proposes a formal controller synthesis approach for integrating a population of EVs for centralised continuous-time frequency regulation of power systems. This approach was the first application of formal methods to the frequency regulation of smart grids. A novel symbolic controller using abstraction-based schemes for the Great Britain power system is designed and simulated under a large outage event. The symbolic controller satisfies a specification with formal guarantees that the frequency returns to a specified safe interval unlike the baseline controller taken from literature. Furthermore, this thesis studies formal synthesis of centralised controllers for continuous-space systems with unknown dynamics to satisfy requirements expressed as linear temporal logic formulas over finite and infinite horizons. As formal abstraction-based synthesis schemes rely on a precise mathematical model of the system to build a finite abstract model, the abstraction-based schemes are not applicable when the dynamics of the system are unknown. The approach casts the computation of the growth bound of the system as a robust convex optimisation program (RCP). Since the unknown dynamics appear in the optimisation, a scenario convex program (SCP) is formulated corresponding to the RCP using a finite number of sampled trajectories. The growth bound together with the sampled trajectories are then used to construct the abstraction and synthesise a controller. The performance of the approach is demonstrated on a reduced-order power system model. Model reduction involves loss of information from the original system which is not accounted for formally. Simulation functions are Lyapunov-like functions that relate the output trajectories of two systems, with the mismatch between the two systems remaining within some guaranteed error bounds. This thesis approximates concrete systems with large perturbations by reduced order abstract models. It develops robust simulation functions (RSF) further to consider the perturbation in the abstract system by designing an interface function for the disturbance. Accordingly, this enables controllers designed using the reduced-order form of the concrete system and reduces the computational load required for formal synthesis. The efficacy of the approach is demonstrated by synthesising a formal controller for a 9-state area of New England 39-Bus Test System (NETS), using only a 3-state abstract system. Finally, this thesis presents an assume-guarantee approach to decentralised compositional control of the 27-state NETS. Based on RSFs with disturbance refinement alongside the composition of multiple subsystems, the approach tackles the scalability problem associated with the curse of dimensionality, particularly for synthesising controllers for high-dimensional systems. This thesis proposes two control methods to provide guarantees for NETS: one using the principle of interconnected synchronous machines and another considering the power flows in the network between neighbouring subsystems. In summary, this thesis contributes to the scalability of formal approaches through compositionality and robust simulation functions with disturbance refinement. Both model-based and data-driven controllers are synthesised for real-world examples relating to the frequency regulation of smart grids. This outcomes of this thesis point toward some interesting future directions. To adapt to the evolving smart grid, fully distributed formal control techniques would be of interest using multi-agent control schemes. Increased complexities of smart grids would encourage further developments in data-driven control techniques including the need for parallelised tool implementations. Robust simulation functions provide an valuable support to quantify the error from model-order reduction techniques, these can be extended to find optimal interface functions which provide guarantees on the maximal error between trajectories and upper bounds on control inputs.