Minimally Constrained Stable Switched Systems and Application to Co-simulation

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation, where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.Comment: Technical report complementing the following conference publication: Gomes, Cl\'audio, Beno\^it Legat, Rapha\"el Jungers, and Hans Vangheluwe. "Minimally Constrained Stable Switched Systems and Application to Co-Simulation." In IEEE Conference on Decision and Control. Miami Beach, FL, USA, 201

Large-Scale Invariant Sets for Safe Coordination of Thermostatic Loads

Extended version of ACC 2021 paper.Systems often face constraints at multiple levels. For example, in coordinating a collection of thermostatically controlled loads to provide grid services, the controller must ensure temperature constraints for each load (local constraints) and distribution network constraints (global constraints) are satisfied. In this paper, we leverage invariant sets to ensure safe coordination of systems with both local and global constraints. Specifically, we develop a method for constructing a controlled invariant set for a collection of subsystems, modeled as transition systems, to ensure they indefinitely satisfy the constraints, based on cycles in individual transition systems. Then, we develop a control algorithm that keeps the state inside the maximal controlled invariant set. We apply these algorithms to a demand response problem, specifically, the tracking of a power trajectory (e.g., a frequency regulation signal) by a population of homogeneous air conditioners. The algorithm simultaneously maintains local temperature requirements and aggregate power consumption limits, ensuring the control is nondisruptive to consumers and benign to the distribution network.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166595/1/ACC2021_FInal_LongerVer.pdfSEL

Control Synthesis for Permutation-Symmetric High-Dimensional Systems With Counting Constraints

General-purpose correct-by-construction synthesis methods are limited to systems with low dimensionality or simple specifications. In this paper, we consider highly symmetrical counting problems and exploit the symmetry to synthesize provably correct controllers for systems with tens of thousands of states. The key ingredients of the solution are an aggregate abstraction procedure for mildly heterogeneous systems and a formulation of counting constraints as linear inequalities

Control Synthesis for Permutation-Symmetric High-Dimensional Systems With Counting Constraints

General-purpose correct-by-construction synthesis methods are limited to systems with low dimensionality or simple specifications. In this paper, we consider highly symmetrical counting problems and exploit the symmetry to synthesize provably correct controllers for systems with tens of thousands of states. The key ingredients of the solution are an aggregate abstraction procedure for mildly heterogeneous systems and a formulation of counting constraints as linear inequalities

Control of Electric Load Aggregations for Power System Services

In electrical power systems, when the supply from wind or solar-powered generation fluctuates, other resources adjust their power to maintain the system’s balance between demand and supply. Traditionally, gas, coal, and hydro-powered generators have provided this balancing service. In the future, as the proportion of renewable power generation increases, additional balancing resources will be needed. In this work, we develop methods that enable a new resource—aggregations of flexible loads—to provide energy balancing. Load aggregations are a promising resource for transmission-level energy balancing, but this service should not come at the expense of lower-level services and requirements. Specifically, an aggregator’s control should not compromise the loads’ service to the end-user and should not cause operational issues on the distribution network. Thermostatically controlled loads (TCLs), such as air conditioners and water heaters, have user-set temperature limits and cycling constraints that must be satisfied. Distribution networks have loading and voltage constraints to ensure reliable operation. When providing balancing services, aggregators partially synchronize loads, which can cause constraint violations on the distribution network. Third-party aggregators are unaware of conditions on the network and must coordinate with the distribution operator to ensure network reliability. The objective of this dissertation is to develop control methods by which a third-party aggregator can provide energy balancing without disrupting consumers and without causing unsafe conditions on the distribution network. Multiple methods are proposed for identifying and protecting distribution constraints that are at risk of violation due to load control. We conduct a simulation study of realistic distribution networks and find only a small subset of network constraints is at risk of violation. This result implies that network-safe control strategies may need to account for only a subset of network constraints, enhancing computational efficiency. We propose using a ``mode-count algorithm’’ to control a group of TCLs to minimize their impact on an at-risk network constraint. Results show that the mode-count algorithm can effectively reduce the variability of voltage at a constrained distribution node. Developing an online method to identify the set of at-risk constraints is non-trivial; towards this end, we propose an optimization-based method that identifies the network’s most at-risk individual constraint and provides a conservative, global safety constraint on power deviations caused by the aggregator. Because the method is computationally intensive, we develop techniques based on power-flow analysis to reduce the problem size; we are able to reduce the problem size by more than 60% for a test network. Two network-safe control strategies for energy balancing are proposed. Both strategies are hierarchical: the aggregator controls loads to track an energy-balancing signal, and the operator removes particular TCLs from the aggregator’s control when necessary for network safety. The strategies differ in terms of modeling and communication requirements. In a case study, the more complex strategy achieves a root-mean-square tracking error of 0.10% of the TCLs’ baseline power consumption while removing fewer than 1% of TCLs from the aggregator’s control; the other strategy achieves a 0.70% tracking error while removing approximately 15% of TCLs. The two strategies provide options — one better performing, one less costly — for operators and aggregators with different capabilities and preferences. Overall, these strategies enable third-party aggregators to control larger proportions of distribution-network load, enhancing competition in wholesale markets and providing the greater balancing capacities that will be needed by future, low-carbon power systems.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155144/1/sjcrock_1.pd