• The team has developed a scalable multi-timescale T&D co-simulation framework and has studied large test systems successfully . The multi-timescale co-simulation was developed using the Hierarchical Engine for Large-scale Infrastructure Co-Simulation (HELICS). This framework is extended for synthetic sensor data generation that can emulate noise and packet drops that is required for the data analytics block. Since the project focuses on developing an output-based system identification and characterization method, we utilized the synthetic data for the investigation of relevant distribution system representation with DG for voltage stability margin assessment . Developed co-simulation tool has been shared with ISO-NE and is being evaluated to simulate the eastern interconnect system with distribution systems.

• The team has developed the theory and robust methodology for output-based system identification with limited state measurements. A novel robust ‘Extended subspace identification (ESI)’ approach is formulated that extends the notion of subspace identification in Koopman function space for PMU measurement-based system identification . The developed framework is suitable for modal identification, participation factor computation and inertia estimation. The inertia of individual machines in a power system are estimated using the Koopman-based approach. The ability to estimate the inertia from ambient data without the need to introduce severe faults besides the fast estimation are the salient features of the proposed algorithm.

• We presented a convex formulation of the data-driven optimal control of nonlinear systems with a discounted cost function. We considered optimal control problems with both positive and negative discount factors. The convex approach relies on lifting nonlinear system dynamics in the space of densities using the linear Perron-Frobenius operator. This lifting leads to an infinite-dimensional convex optimization formulation of the optimal control problem. The data-driven approximation of the optimization problem relies on the approximation of the Koopman operator and its dual: the Perron-Frobenius operator, using a polynomial basis function. We formulate the approximate finite-dimensional optimization problem as a polynomial optimization which is then solved efficiently using a sum-of-squares-based optimization framework. Simulation results demonstrate the efficacy of the developed data-driven optimal control framework.

• We have quantified the flow of information transfers or causal interactions among nodes in a network system following linear discrete stochastic dynamics. To capture the causal interaction, a notion of information transfer, based on freezing the system variables is used. We also formulated an optimal control problem for steering these information transfers at desired values in both finite and infinite time horizons. We provided the necessary and sufficient conditions for control of information transfer at finite and infinite horizons. We found that the information transfer control problem can be transformed into the state covariance control problem. We provided characterization for the space of covariance matrices that lead to desired value of information transfers at any instant. Optimal control of information transfer involves choosing an optimal covariance matrix among the set of positive definite matrices that will result in the same information transfer. We also solved this problem of finding the optimal covariance matrix by enforcing additional constraints on our optimization problem.

• We presented an approach based on the spectral analysis of the Koopman operator for the approximate solution of the Hamilton Jacobi equation that arises while solving the optimal control problem. It is well-known that one can associate a Hamiltonian dynamical system with the Hamilton Jacobi equation. Furthermore, the Lagrangian submanifold of the Hamiltonian dynamical system plays a fundamental role in solving the Hamilton Jacobi equation. We show that the principal eigenfunctions of the Koopman operator associated with the Hamiltonian dynamical system can be used in constructing the Lagrangian submanifold, thereby approximating the solution of the Hamilton Jacobi equation. We presented simulation results to verify the main findings.

• We developed reduced order models of distribution system (DS) for bulk system planning activities. We found that a composite load model (CLM) model can accurately replicate the voltage response for a severe fault close to the interconnection, but it is unable to accurately replicate the response for a severe fault far from interconnection. To address the limitation of the single CLM, we proposed a DS structure preserving reduced order model (DS-ROM) that clusters nodes in the DS using electrical distances and retains the radial nature of the DS . We used CLM sub-models to represent each cluster and then presented a python based automated approach to determine the parameters of the CLMs. The overall acceleration of the dynamic simulation is ~3x compared to the full transmission and distribution simulation, making it possible for more cases to be considered during planning with the same computation budget.

• PI presented an invited talk  titled “Analyzing impact of active distribution system on voltage stability” during a tutorial “Understanding Voltage Stability: Theory to Industry Practice considering Inverter Based Resources” at IEEE Power & Energy Society – General Meeting in July 2024.

Last Modified: 12/11/2024
Modified by: Venkataramana Ajjarapu