Scalability, Resilience, and Complexity Management in Laminar Control of Ultra-Large Scale Systems Jeffrey Taft, PhD Paul De Martini Connected Energy Networks Resnick Institute Cisco Systems, Inc. California Institute of Technology Abstract Ultra-large scale control systems that are based on layered optimization decomposition and Network Utility Maximization (NUM) have structural properties and operational modes that givesuch control systems useful scalabilityand anti-fragile properties. We denote control architectures based on these principles as Laminar Control and we suggest that the structure so defined has properties such as layer-by-layer segmentation of control signal traffic, abstraction of local state into scalar signal flows, self-similarity of data flow patterns at each layer, and support for islanded operation and re-connection. While the underlying physical networks (such as power systems) and associated communication networks are not necessarily self-similar, the imposition of the Laminar Control paradigm allows the creation such a structure at the application node level. Consequently, instead of having a set of agents with randomly structured logical connections, the optimization nodes become hubs and furthermore,it may be possible to restrict peer-to-peer communication at any level in the hierarchy to delimited specifiable domains. State determination can be similarly partitioned so that domain state need not be shared globally. In combination, these properties can invest distributed control networks with three valuable characteristics: scalability of control system real time network communications, resilience of the logical control network, and complexity bounds. Introduction: Laminar Control Architecture and Data Flows Distributed and hierarchical control methods have been available for decades. In the case of electric power systems, some of these concepts have been used in portions of the grid, but not as an Ultra-Large Scale (ULS) control. By ULS we mean the concept developed at the Software Engineering Institute to describe extremely large, complex systems with the following characteristics:1 • Decentralized data, development, and control • Inherently conflicting diverse requirements • Continuous (or at least long time scale) evolution and deployment • Heterogeneous, inconsistent, and changing elements • Normal failures (failures are expected as a normal part of operation) In the power grid domain, certain approaches to wide area grid control have employed a single physical variable that presumes to characterize a key aspect of system state. At the transmission and generation level, system frequency is used for this purpose. It is widely used in incremental area balancing via Area Control Error and Automatic Generator Control (AGC).2System frequency has also been proposed as the basis for control of large number of responsive loads not owned by the electric utility.3At the distribution level, feeder voltage is used in Volt/VAr control systems, both inthose that act centrally and those that are composed of a collection of independent agents.4Such methods have enjoyed a degree of success but encounter difficulties in two areas: 1) Such systems can become unstable due to feedback through the grid itself 2) When multiple functions want to use the same infrastructure for possibly competing or even conflicting purposes, as is happening with 1Peter Feiler, John Goodenough, et al., Ultra‐Large‐Scale Systems The Software Challenge of the Future, Software Engineering Institute, June 2006 2 NERC Resources Subcommittee, Balancing and Frequency Control, available online: http://www.nerc.com/docs/oc/rs/NERC%20Balancing%20and%20Frequency%20Control%20040520111.pd f 3 PNNL Staff, Grid Friendly Controller Helps balance Energy Supply and Demand, available online: http://readthis.pnl.gov/MarketSource/ReadThis/B3099_not_print_quality.pdf 4Naveen Venkatesan and S K Solanki, Coordination of Demand Response and Volt/VAR Control Algorithm Using Multi‐Agent System, IEEE 2012 Transmission and Distribution Conference and Exposition, 2012 IEEE PES, Orlando, Fla. May 2012. distributedenergy resources,5 then a single variable is not sufficient to enable proper coordination or federation of the multiple control processes involved Recently a method based on Network Utility Maximization6 and Layering for Optimization Decomposition7 has emerged as a distributed control paradigm for ultra-large scale controls, especially for power grid control.8 In this approach, a structured network of optimization nodes communicates hierarchicallyvia scalar signals to cooperate in solving a joint optimal control problem. The nodes are arranged in a manner that corresponds to a layered decomposition of the full optimization problem. This layered decomposition can be mapped onto the structure of a physical system such as a power gridtosolve the control issues of federation, disaggregation, and constraint fusion whileallowing for local “selfish” optimization.This approach is a hybrid of central and decentralized control, made distributed by virtue of the various parts engaging in cooperation to solve a common problem: that of grid control. In the layered decomposition approach Network Utility Maximization is used to provide overall coordination, with most nodes acting as both a coordinator for sub-problems at the next tier below, aswell as a sub-problem solver for the coordinator for the next tier above. The optimization decomposition consists of breaking the problem at each layer into a master problem and set of sub-problems, using iteration to decouple the constraints. The master problem and sub-problems cooperate by exchanging simple signals which, depending on the decomposition type, can be seen as either resource allocation signals (primal decomposition) or prices (dual decomposition). Problems may be decomposed recursively, leading to a multi-layer structure that inherently supports distributed computation. When this type of mapping is done for hierarchical controls, especially for power grids, it leads to a logical data flow structure that has useful characteristics. 5 P. De Martini, DR 2.0:A Future of Customer Response, available on line: http://www.demandresponsesmartgrid.org/Resources/Documents/FINAL_DR%202.0_13.07.08.pdf 6Mung Chiang, Steven Low, et al., Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures, Proceedings of the IEEE, Vol. 95, No. 1, January 2007. 7Daniel P. Palomar and Mung Chiang, A Tutorial on Decomposition Methods for Network Utility Maximization, IEEE Journal on Selected Areas in Communication, August 2006,pp. 1439‐1451. 8 Jeffrey Taft and Paul De Martini, Ultra‐Large Scale Power System Control Architecture A Strategic Framework for Integrating Advanced Grid Functionality., available online: http://www.cisco.com/web/strategy/docs/energy/control_architecture.pdf There are three principal data flows that matter here: 1. “Vertical” signal exchange among optimization nodes for multi-tier coordination 2. Hub and spoke signal exchange among master and sub-problems nodes for tier level coordination 3. Peer to peer flows within a layer for local cooperation Figure 1 shows these primary data flows. Note that the first flow in the list is essentially a subset of the second on the list, but it is helpful to consider an entire vertical optimization signal chain as one of the flows. We view this model as having two axes of distributed intelligence and refer to the vertical single flow and optimization chain as coordination distributed intelligence, and the tier hub-and spoke and peer-to peer interactions as application distributed intelligence. The overall vertical flow across all tiers with optimization node operation is denoted asDeep Area Coordination (DAC). Note that in this method we are explicitly providing a multi-tier and intra-tier coordination mechanism for control. This is a “team” approach, wherein explicit deterministic communication is used to implement coordination, as opposed to swarm or flock behavior, as exhibited in some biological systems and as mimicked in some agent-based software systems.9 However, the potential advantage of flock behavior in avoiding hazardous regions of operation via trajectory steering can be achieved in the Laminar Control framework in a manner that is well-behaved and manageable by human grid operators who are supervising the overall operation of the control system but are not “inside the control loop.” By setting and adjusting optimization criteria and constraints, humans supervising the control system can guide the system to avoid entering regions of reduced stability margin. Doing this via a few top level control nodes (as opposed to adjusting all of the nodes in the entire system) is roughly the equivalent of steering the trajectory of the dynamic system (the grid) in state space; adjusting goals at a few nodes is essentially the same idea as leading the “flock.” 9 Felipe Cucker and Steven Smale, The Mathematics of Emergence, Japanese Journal of Mathematics, October 2006. Available online: http://ttic.uchicago.edu/~smale/papers/math‐of‐emergence.pdf Figure 1 Primary Data Flow Patterns in Laminar Control for Power Grids Note that we decompose the optimization problem by tiers that match physical power grid tiers. In addition, the elements are broken up at each tier into domains, with the definition of a domain depending on the level in the power grid hierarchy. Domain definition is flexible providing the system designer with freedom to bound complexity.