Zhongda Chu

Zhongda Chu, Fei Teng

Conventional optimization frameworks for power-system operation and planning primarily focus on steady-state conditions, which become increasingly inadequate as rising penetrations of inverter-based resources (IBRs) strengthen the coupling between stability and steady-state operating conditions. Meanwhile, the software-defined nature of IBRs provides additional flexibility to co-optimize operating points and dynamic behavior. This paper proposes a unified stability-constrained optimization framework that incorporates synchronization, voltage, and frequency stability within a single scheduling model. Established stability criteria are selected and translated into explicit operational limits, after which a general formulation is developed to embed all three criteria in a common structure. The resulting second-order cone (SOC) constraints are convex and can be integrated seamlessly into existing optimization models. The proposed framework enables the simultaneous pursuit of economic efficiency and multi-dimensional stability enhancement, providing a tractable pathway for secure operation in future IBR-dominated power systems.

Zhongda Chu, Fei Teng

Multiple operational constraints of power system stability are derived analytically and reformulated into Second-Order Cone (SOC) form through a unification method in Part I of this paper. The accuracy and conservativeness of the proposed methods are illustrated in the second part. The validity of the developed constraints is tested against dynamic simulations carried out based on the modified IEEE 39-bus system. Furthermore, the developed power system stability constraints are applied to the optimal system scheduling model. The resulting stability-constrained system scheduling problem aims to achieve most economic system operation while ensuring different stability in power systems with high Inverter-Based Resources (IBR) penetration. Moreover, based on the stability-constrained optimization model, a novel marginal unit pricing scheme is proposed to quantify the stability services of different units appropriately according to their economic value in maintaining system stability, thus providing rational incentives to the stability service provider and insightful information for the stability market development.

Wangkun Xu, Qian Chen, Pudong Ge et al.

Encoding frequency stability constraints in the operation problem is challenging due to its complex dynamics. Recently, data-driven approaches have been proposed to learn the stability criteria offline with the trained model embedded as a constraint of online optimization. However, random sampling of stationary operation points is less efficient in generating balanced stable and unstable samples. Meanwhile, the performance of such a model is strongly dependent on the quality of the training dataset. Observing this research gap, we propose a gradient-based data generation method via forward-mode automatic differentiation. In this method, the original dynamic system is augmented with new states that represent the dynamic of sensitivities of the original states, which can be solved by invoking any ODE solver for a single time. To compensate for the contradiction between the gradient of various frequency stability criteria, gradient surgery is proposed by projecting the gradient on the normal plane of the other. In the end, we demonstrate the superior performance of the proposed sampling algorithm, compared with the unrolling differentiation and finite difference. All codes are available at https://github.com/xuwkk/frequency_sample_ad.

Aoun Abbas, Zhongda Chu, Charalambos Konstantinou

The large-scale replacement of synchronous machines with inverter-based generation (IBG) introduces critical challenges to both voltage and frequency stability. This work builds on a mixed-integer second-order cone programming (MISOCP) framework that co-optimizes unit commitment (UC) model which embeds frequency-nadir constraints through synthetic inertia (SI) dispatch and an SOC voltage stability boundary for IBG buses. The formulation extends by modeling a STATCOM as a reactive-power decision variable in the same MISOCP model. A modified IEEE 30-bus system is used to assess three scheduling strategies: (i) baseline UC with SI only, (ii) voltage-stability-constrained (VSC) UC with SI, and (iii) the joint UC with SI and reactive power support from IBGs. The impact of incorporating a 30~MVAr STATCOM at a weak grid location near the IBG buses is investigated. Simulation results show that the proposed framework enhances voltage security, maintains frequency-nadir compliance, and reduces operating cost, while STATCOM integration further improves dispatch feasibility under high IBG.

Wangkun Xu, Zhongda Chu, Fei Teng

With the high penetration of renewables, traditional model-based power system operation is challenged to deliver economic, stable, and robust decisions. Machine learning has emerged as a powerful modeling tool for capturing complex dynamics to address these challenges. However, its separate design often lacks systematic integration with existing methods. To fill the gap, this paper proposes a holistic framework of Learning-Augmented Power System Operations (LAPSO, pronounced as Lap-So). Adopting a native optimization perspective, LAPSO is centered on the operation stage and aims to break the boundary between temporally siloed power system tasks, such as forecast, operation and control, while unifying the objectives of machine learning and model-based optimizations at both training and inference stages. Systematic analysis and simulations demonstrate the effectiveness of applying LAPSO in designing new integrated algorithms, such as stability-constrained optimization (SCO) and objective-based forecasting (OBF), while enabling end-to-end tracing of different sources of uncertainties. In addition, a dedicated Python package-lapso is introduced to automatically augment existing power system optimization models with learnable components. All code and data are available at https://github.com/xuwkk/lapso_exp.