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1. Transferable Deep Kernel Emulator for Probabilistic Load Margin Assessment With Topology Changes, Uncertain Renewable Generations and Loads

   https://doi.org/10.1109/TPWRS.2022.3231240  

   Tan, Bendong; Zhao, Junbo; Xie, Le (December 2022, IEEE Transactions on Power Systems)

   The increasing uncertainties caused by the high-penetration of stochastic renewable generation resources and flexible loads pose challenges to the power system voltage stability. To address this issue, this paper proposes a probabilistic transferable deep kernel emulator (DKE) to extract the hidden relationship between uncertain sources, i.e., wind generations and loads, and load margin for probabilistic load margin assessment (PLMA). This emulator extends the Gaussian process kernel to the deep neural network (DNN) structure and thus gains the advantages of DNN in dealing with high-dimension uncertain inputs and the uncertainty quantification capability of the Gaussian process. A transfer learning framework is also developed to reduce the invariant representation space distance between the old topology and new one. It allows the DKE to be quickly fine tuned with only a few samples under the new topology. Numerical results carried out on the modified IEEE 39-bus and 118-bus power systems demonstrate the strong robustness of the proposed transferable DKE to uncertain wind and load power as well as topology changes while maintaining high accuracy. 

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2. A Data-Driven Nonparametric Approach for Probabilistic Load-Margin Assessment considering Wind Power Penetration

   https://doi.org/10.1109/TPWRS.2020.2987900  

   Xu, Yijun; Mili, Lamine; Korkali, Mert; Karra, Kiran; Zheng, Zongsheng; Chen, Xiao (April 2020, IEEE Transactions on Power Systems)

   A modern power system is characterized by an increasing penetration of wind power, which results in large uncertainties in its states. These uncertainties must be quantified properly; otherwise, the system security may be threatened. Facing this challenge, we propose a cost-effective, data-driven approach for the probabilistic load-margin assessment problem. Using actual wind data, a kernel-density-estimator is applied to infer the nonparametric wind speed distributions, which are further merged into the framework of a vine copula. The latter enables us to simulate complex multivariate and highly dependent model inputs with a variety of bivariate copulae that precisely represent the tail dependence in the correlated samples. Furthermore, to reduce the prohibitive computational time of the traditional Monte-Carlo simulations processing a large amount of samples, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model through a Bayesian learning framework. To accelerate the convergence rate of this Bayesian algorithm, a truncated polynomial chaos surrogate is developed, which serves as a highly efficient, parametric Bayesian prior. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. Simulation results reveal the impressive performances of the proposed method. 

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3. Using demand response to improve power system small-signal stability

   https://doi.org/10.1016/j.segan.2023.101214  

   Yao, Mengqi; Roy, Sandip; Mathieu, Johanna L. (December 2023, Sustainable Energy, Grids and Networks)

   With the increase of uncertain and intermittent renewable energy supply on the grid, the power system has become more vulnerable to instability. In this paper, we develop a demand response strategy to improve power system small-signal stability. We pose the problem as an optimization problem wherein the total demand-responsive load is held constant at each time instance but shifted between different buses to improve small-signal stability, which is measured by small-signal stability metrics that are functions of subsets of the system’s eigenvalues, such as the smallest damping ratio. To solve the problem, we use iterative linear programming and generalized eigenvalue sensitivities. We demonstrate the approach via a case study that uses the IEEE 14-bus system. Our results show that shifting the load between buses, can improve a small-signal stability margin. We explore the use of models of different fidelity and find that it is important to include models of the automatic voltage regulators and power system stabilizers. In addition, we show that load shifting can achieve similar improvements to generation shifting and better improvement than simply tuning power system stabilizers. 

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4. Deep Learning-Based Adaptive Remedial Action Scheme with Security Margin for Renewable-Dominated Power Grids

   https://doi.org/10.3390/en14206563  

   Zhao, Yinfeng; You, Shutang; Mandich, Mirka; Zhu, Lin; Zhang, Chengwen; Li, Hongyu; Su, Yu; Zeng, Chujie; Zhao, Yi; Liu, Yilu; et al (October 2021, Energies)

   The Remedial Action Scheme (RAS) is designed to take corrective actions after detecting predetermined conditions to maintain system transient stability in large interconnected power grids. However, since RAS is usually designed based on a few selected typical operating conditions, it is not optimal in operating conditions that are not considered in the offline design, especially under frequently and dramatically varying operating conditions due to the increasing integration of intermittent renewables. The deep learning-based RAS is proposed to enhance the adaptivity of RAS to varying operating conditions. During the training, a customized loss function is developed to penalize the negative loss and suggest corrective actions with a security margin to avoid triggering under-frequency and over-frequency relays. Simulation results of the reduced United States Western Interconnection system model demonstrate that the proposed deep learning–based RAS can provide optimal corrective actions for unseen operating conditions while maintaining a sufficient security margin. 

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5. Load Embeddings for Scalable {AC-OPF} Learning

   Mak, Terrence W.; Fioretto, Ferdinando; Van Hentenryck, Pascal (March 2023, ArXivorg)

   AC Optimal Power Flow (AC-OPF) is a fundamental building block in power system optimization. It is often solved repeatedly, especially in regions with large penetration of renewable generation, to avoid violating operational limits. Recent work has shown that deep learning can be effective in providing highly accurate approximations of AC-OPF. However, deep learning approaches may suffer from scalability issues, especially when applied to large realistic grids. This paper addresses these scalability limitations and proposes a load embedding scheme using a 3-step approach. The first step formulates the load embedding problem as a bilevel optimization model that can be solved using a penalty method. The second step learns the encoding optimization to quickly produce load embeddings for new OPF instances. The third step is a deep learning model that uses load embeddings to produce accurate AC-OPF approximations. The approach is evaluated experimentally on large-scale test cases from the NESTA library. The results demonstrate that the proposed approach produces an order of magnitude improvements in training convergence and prediction accuracy. 

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