Constantino M. Lagoa

Fiaz Hossain, Nilanjan Ray Chaudhuri, Constantino M. Lagoa

We propose a generalized dynamic phasor (DP) framework to analyze inverter-based resources (IBRs) connected to multi-machine systems under balanced and unbalanced conditions. It captures subsynchronous oscillations (SSOs) induced by grid-following (GFL) IBRs. The linearizability and time invariance of the framework enables us to perform eigen decomposition, which is a powerful tool for root-cause analysis of the SSO modes and damping controller design. The same framework also enables analysis of excitation of the SSO modes in presence of data center (DC) loads. The GFL IBRs are modeled in their respective $dq$-frame DPs and the detailed model of synchronous generators (SGs) along with dynamic transmission network models are represented in $pnz$-frame DPs. Several case studies are performed on the modified IEEE two-area benchmark system, where $2$ SGs are replaced by GFL IBRs and validated with EMTDC/PSCAD simulations. First, time- and frequency-domain analyses of the SSO mode are presented followed by the design of a robust decentralized $\mathcal{H}_\infty$ damping controller based on local signals of the GFL IBRs. Second, the dynamic behavior of the system following an unbalanced fault is demonstrated that is damped by the proposed damping controller. Finally, excitation of the SSO mode in presence of DC load is exhibited and its locational impact is analytically quantified.

Fiaz Hossain, Nilanjan Ray Chaudhuri, Constantino M. Lagoa et al.

Although the electromagnetic transient (EMT) framework can capture subsynchronous oscillations (SSOs), it faces scalability issues for large-scale systems. Thus motivated, we propose a generalized dynamic phasor (DP) framework to analyze SSOs in multi-machine systems with inverter-based resources (IBRs) and large loads such as artificial intelligence data centers (AI DCs) under balanced and unbalanced conditions. The grid-following (GFL) and grid-forming (GFM) IBRs are modeled in their respective $dq$-frame DPs. In contrast, the detailed model of multi-mass turbine driven synchronous generators (SGs) along with dynamic transmission network models and loads are represented in $pnz$-frame DPs. The linearizability and time-invariance of the framework enable us to perform eigen decomposition, which is a powerful tool for root-cause analysis of SSO modes and the design of damping controllers. In addition, the DP modeling approach facilitates faster simulation of large-scale systems. The generalized framework is validated with EMTDC/PSCAD simulations using the IEEE first benchmark model for subsynchronous resonance and the modified IEEE 4-machine system. Several use cases are presented on the modified IEEE 68-bus system with two GFL IBRs to show the applicability of the framework. First, time- and frequency-domain analyses of the IBR-induced SSO mode are presented. Then, two solutions are proposed to damp the poorly damped SSO mode: (a) a decentralized controller is designed using particle swarm optimization, and (b) the control of one GFL IBR is replaced by GFM control. Finally, the impact of AI DC load on primary frequency response of the system and the multi-mass turbines of the SGs are studied.