Emrah Biyik

Area aggregation and time-scale modeling for sparse nonlinear networks

Model reduction and aggregation are of key importance for simulation and analysis of large-scale systems, such as molecular dynamics, large swarms of robotic vehicles, and animal aggregations. We study a nonlinear network which exhibits areas of internally dense and externally sparse interconnections. The densely connected nodes in these areas synchronize in the fast time-scale, and behave as aggregate nodes that dominate the slow dynamics of the network. We first derive a singular perturbation model which makes this time-scale separation explicit and, next, prove the validity of the reduced-model approximation on the infinite time interval

A hybrid redesign of Newton observers in the absence of an exact discrete-time model

Abstract We study the Newton observer design, developed by Moraal and Grizzle, when the exact discrete-time model of the sampled-data plant is not known analytically. We eliminate the dependence on this exact model with a “hybrid” reconstruction that makes use of continuous-time filters to produce the numerical value of the exact model. We then implement the Newton method with finite-difference and secant approximations for the Jacobian. Despite the continuous-time filters, the proposed hybrid redesign preserves the sampled-data characteristic of the Newton observer because it only employs discrete-time measurements of the output. It also offers flexibility to be implemented with nonuniform, or event-driven, sampling. We finally study how a line search scheme can be incorporated in this hybrid Newton observer to enlarge the region of convergence.

Area Aggregation and Time Scale Modeling for Sparse Nonlinear Networks

Model reduction and aggregation are of key importance for simulation and analysis of large-scale systems, such as molecular dynamics, large swarms of robotic vehicles, and animal aggregations. We study a nonlinear network which exhibits areas of internally dense and externally sparse interconnections. The densely connected nodes in these areas synchronize in the fast time-scale, and behave as aggregate nodes that dominate the slow dynamics of the network. We first derive a singular perturbation model which makes this time-scale separation explicit and, next, prove the validity of the reduced-model approximation on the infinite time interval.

A model predictive control design for selective modal damping in power systems

This paper presents a novel real-time predictive control technique to damp dominant inter-area oscillation modes in power systems. We first show that conventional Power System Stabilizers (PSS) in synchronous generators are best suited to damp only the intra-area oscillation modes, and participate poorly in inter-area damping. We then design a centralized Model Predictive Controller (MPC) to provide supplementary control to these conventional PSSs based on a Selective Discrete Fourier Transform (SDFT) approach. The SDFT extracts the energies associated with the inter-area frequency components in the output spectrum of the system, and uses this information to construct a weighting matrix Q. The MPC is then formulated as a quadratic minimization of the outputs using Q, resulting in damping only the inter-area modes of interest. In reality, however, the most dominant DFT magnitudes will not be known ahead of time since they are decided by the location of the disturbance. Therefore, we next augment the MPC design by predicting the dominant DFT magnitudes in the desired low frequency range using online measured data, and tuning Q accordingly. We illustrate the effectiveness of the proposed approach using an IEEE 39-bus prototype power system model for the New England system.

An online structurally constrained LQR design for damping oscillations in power system networks

This paper presents an online distributed control design for suppressing inter-area oscillations in large power systems under structural constraints posed on the underlying communication network. The presence of multiple clusters of generators in a power system results in several inter-area oscillation modes. By modal analysis, we first show that the contribution of each inter-area mode on the electromechanical state response of the generators is heavily dependent on the perturbed initial state of the system. We then take advantage of this observation to design structural constraints on the communication graph. A parallelized constrained linear quadratic regulator (LQR) design is then proposed to balance the tradeoff between performance and the level of sparsity induced in the network. Algorithms for practical implementation of the design are provided. Results are compared with the full order LQR, and illustrated on the New England 39-bus power system model.

Optimal control of microgrids - algorithms and field implementation

A microgrid is a collection of distributed generation assets, storage devices and electrical and/or thermal loads connected to each other. In this paper, a generic model-predictive control algorithm for microgrids is presented. The algorithm has been implemented at Bella Coola, a remote community in British Columbia, Canada. The approach comprises two parts: unit commitment to decide the optimal set of distributed generators that must be switched on to meet predicted load requirements, and convex optimal control to minimize operational costs once the commitment is known. The unit commitment problem is recast as a 0-1 Knapsack problem and is solved via dynamic programming, while the optimal dispatch problem is posed as a sparse linear programming problem and solved via off-the-shelf software. Worst-case complexity and scalability considerations, and not optimality, often drive algorithm choice in industrial control settings; therefore, the solution proposed in this paper is efficient and can be rigorously bounded in terms of memory and run-time. Simulation results using real field data, practical considerations, and details of the implementation at Bella Coola are provided.

Hybrid Newton observer design using the inexact Newton method and GMRES

We study the Newton observer design, developed by Moraal and Grizzle (1995), when the exact discrete-time model of the sampled-data system is not available analytically. The hybrid reconstruction of the Newton observer in (Arcak, 2006) eliminates the dependence on this exact discrete-time model by numerical integration and finite difference Jacobian approximations. This paper reduces the computational cost of (Arcak, 2006) using an inexact Newton method and the generalized minimum residuals (GM-RES) algorithm. It then studies how a line search scheme can be incorporated in this modified Newton observer to enlarge the region of convergence

Model predictive building thermostatic controls of small-to-medium commercial buildings for optimal peak load reduction incorporating dynamic human comfort models: Algorithm and implementation

The peak kW of a typical New York State office building is thought to primarily be a function of the HVAC system, often the buildings largest load, but may also be influenced by occupancy and other loads. First, a simple lumped parameter model with a minimum amount of buildings physical input data, and trained with actual thermal and electrical data, is considered to approximate the thermal/electric consumption performance of the building and HVAC system on a zonal basis. Then, the lumped parameter model integrated with a dynamic human comfort model is used to develop optimized zonal thermostat setpoint schedules to minimize the cooling systems contribution to the buildings peak power load while maintaining human comfort at a desired level. A 24-hour weather and occupancy forecasts are also incorporated into the optimization algorithm. The key difference of our approach compared to previous approaches that utilize model-predictive control is that a minimal set of measurement profiles are utilized to reduce the installation cost resulting in a cost effective advanced controls solution for a large number of small and medium size office buildings. The model predictive optimization approach is implemented at multiple demonstration sites. The hardware architecture and software platform installed at one of the demonstration buildings are discussed. Finally, it is demonstrated that the proposed controller can effectively minimize peak cooling load on the HVAC equipment while achieving a satisfactory thermal comfort inside the building.

Cloud-based model predictive building thermostatic controls of commercial buildings: Algorithm and implementation

The contribution of this paper is in two-folds: 1) If more predictive and intelligent control of the thermostat setpoints with no explicit models of Root Top Units (RTUs) yet with simplistic lumped parameter thermal models of buildings can be effective in reducing a small commercial buildings summer-time peak load while adequately maintaining comfort levels, and 2) how this simplistic indirect control approach to RTUs compare to more sophisticated direct control approaches in terms of peak-load reduction and cost. First, the model-predictive control approach is presented. Second, the results of cloud-based implementation of the optimization algorithm at the two demonstration commercial buildings owned by General Electric (GE), optimizer characteristics, different set point trajectories and their implication with regards to peak load and comfort, and observations are described. On average, the savings from the indirect optimal control strategy utilized in our approach through a cloud-based control implementation architecture is shown to be comparable to previously stated savings in literature from more sophisticated direct optimal control of RTUs while the comfort levels are the same as the non-optimal strategy or slightly better in some cases.

Passivity-Based Agreement Protocols: Continuous-Time and Sampled-Data Designs

We pursue a group agreement problem where the objective is to achieve synchronization of group variables. We assume a bidirectional information flow between members, and study a class of feedback laws that are implementable with local information available to each member. We first review a unifying passivity framework for the group agreement problem in continuous-time. Then, we extend the results to a class of sampled-data systems by exploiting the passivity properties of the underlying continuous-time system, and prove semiglobal asymptotic stability as the sampling period and a feedback gain are reduced.