Publications
Currently excited about results reported in*
Per-unit Modeling via Similarity Transformation
(Abstract) This paper presents an approach to normalize dynamical-system models into per-unit transcriptions via similarity transformation. The method applies to nonlinear control-affine and linear state-space models. In this framework, parameters of the per-unit model are not determined a priori; rather, they emerge from the similarity transformation. This is a significant upgrade to the conventional approach of identifying base values for parameters with dimensional analysis so they can be normalized. Since the approach is grounded in system theory, several frequency- and time-domain attributes of per-unit models can be formalized. Furthermore, per-unit phasor models can be derived as a special instance. Case studies demonstrate these attributes in practice for linear and nonlinear systems including RLC circuits, transformers, and grid-following and grid-forming inverters. Numerical simulations incorporating these in a modified IEEE 37-bus network demonstrate accuracy and scalability
Time-domain Generalization of Kron Reduction
(Abstract) Kron reduction is a network-reduction method that eliminates nodes with zero current injections from electrical networks operating in sinusoidal steady state. In the time domain, the state-of-the-art application of Kron reduction has been in networks with transmission lines that have constant R/L ratios. In contrast, this paper considers the generalized setting of RL networks without such restriction and puts forth a provably exact time-domain version of Kron reduction. Exemplifying empirical tests on a wye-Delta network are provided to validate the analytical results.
Spontaneous Phase Balancing in Delta-connected Single-phase Droop-controlled Inverters
(Abstract) In this paper, we investigate whether systems built with interconnected single-phase droop-controlled GFM inverters are capable of self organizing into balanced three-phase systems. We model, analyze, and build a system comprised of three delta-connected droop-controlled single-phase inverters connected across loads. After deriving a model of the angle dynamics for this system, we show that its stable equilibria coincide with balanced conditions where each phase is offset by 1/3 of an ac cycle. Furthermore, we observe that the desirable equilibrium with balanced phase offsets is robust against voltage and load imbalances.
Reexamining the Distributed Slack Bus
(Abstract) Power flow formulated with a distributed slack bus involves modeling the active-power output of each generator with three elements: a nominal injection modulated by a fraction of the net-load imbalance allocated via a participation factor. This setup acknowledges generator dynamics and system operations, but it has long been plagued by ambiguous and inconsistent interpretations of its constituent elemental quantities. In this paper, we establish that, with the: i) nominal active-power injections set to be the economic dispatch setpoints, ii) participation factors fixed to be the ones used in automatic generation control, and iii) net-load imbalance considered to be the total load and loss unaccounted in economic dispatch, the power flow solution best matches results from a simulation of the system differential algebraic equation (DAE) model.