Project PS-D: Control – Managing Complexity and Diversity
Manager: Glenn Vinnicombe
Investigator: Glenn Vinnicombe
Research Staff: Richard Pates (PhD student/Research Associate), Tom Voice (Research Associate)
Collaborators: Tim Green
Start date: 01/10/2009
Linked Projects: UT-D and
PS-A
Summary. The largest man-made control system in existence is that for flow control on the Internet. This is a highly successful and entirely decentralized system. The TCP algorithm, which runs in each computer, requires only information from surrounding nodes and aggregated congestion information from the communication links. In this case it is possible to scale the local control system parameters in a way that gives satisfactory performance, whilst guaranteeing the stability of the entire network.
Aided by insights from Project UT-D, we shall investigate the potential benefits for modern power systems of control algorithms which have a scalability property. The goal is to achieve, within a highly decentralized control structure, new design and operation strategies for power systems that achieve enhanced power system stabilization, dynamic response and fault security. Powerful techniques for the analysis of information flows on the internet involve identifying interconnection conditions or 'protocols' that guarantee network stability, in the presence of small perturbations and changes of network topology. A key step will be the formulation of appropriate protocols within the context of modern power systems.
Current Status. In the first year of the project, a new modelling methodology for power networks was developed, which incorporates detailed synchronous generator models and yet maintains the graphical structure of the network and allows the application of scalable control techniques. Previous methodologies using graphs have only managed to retain the structure by the use of overly simplified and unrealistic models, whilst standard detailed models quickly lose this structure. This was excellent progress for the first year of a PhD.
In the second year, the scalable techniques used for Internet analysis and design have been extended so as to make them appropriate to power systems. In the Internet, the dynamics at the nodes relate flow rates and loss probabilities, whereas for realistic power system models the nodes are multivariate, relating real and reactive power flows to voltages and angles. This extension has been successfully done, and has in fact led to a considerable improvement of the original conditions even when applied to the single variate case. The new conditions are more intuitive, easier to state and admit nonlinear generalizations, leading to network versions of the classical stability tests such as the Popov and circle criterion. It has been demonstrated that, at least for simple networks of synchronous generators and loads, these techniques are capable of informing local controller designs with guaranteed network stability properties.
A one-day workshop has been held at the Power Group at Imperial College, where these results were presented and numerous points of contact made.
The third year was primarily focused on investigating nonlinear generalisations and conservatism of the scalable network conditions. Although the details of the nonlinear conditions are yet to be fully resolved, this work led to a KYP lemma based method for decentralised controller synthesis and a significant tightening of the conditions in the multivariate case. In addition through a decentralised scaling of local constants it was demonstrated that the scalable conditions were tight in the single variate case for underlying tree topologies. The new theory was applied to the power systems models, and a design procedure based on the length and loading of transmission lines local to each synchronous machine developed.
A paper covering the scalable techniques for networks of linear systems was presented at the Conference on Decision and Control, Dec 2012 [PV12]. A PhD thesis has been submitted. The PhD student, Richard Pates has now been appointed to an Research Associate position on the programme grant, and the results have been further strengthened. The underlying theory is now known to be non-conservative in the case of chordal graph structures. The application to power systems has also been strengthened, for example it has been possible to show that all power grids built out of the components of the Kundar two area model (a standard benchmark) are known to be stable provided decentralised constraints on line loading are observed. A journal article containing both this and the previous material is under preparation and will shortly be submitted.
In addition, Tom Voice was appointed to a Research Associate position from September 2012. Journal articles on disturbance propagation in networks and on a stochastic approach to decentralised and scalable power system demand management of smart grids are in an advanced stage of preparation. In this latter work, probability distributions for load are designed, and then local control laws synthesised to realise them.
Publications
[PV12]
R. Pates and G. Vinnicombe,
Stability Certificates for Networks of Heterogeneous Systems,
51st IEEE Conference on Decision and Control, 10-13 Dec 2012 Hawaii, pp6915-6920,
2012
