Probabilistic Hosting Capacity Analysis via Bayesian Optimization

This paper studies the probabilistic hosting capacity analysis (PHCA) problem in distribution networks considering uncertainties from distributed energy resources (DERs) and residential loads. PHCA aims to compute the hosting capacity, which is defined as the maximal level of DERs that can be securely integrated into a distribution network while satisfying operational constraints with high probability. We formulate PHCA as a chance-constrained optimization problem, and model the uncertainties from DERs and loads using historical data. Due to non-convexities and a substantial number of historical scenarios being used, PHCA is often formulated as large-scale nonlinear optimization problem, thus computationally intractable to solve. To address the core computational challenges, we propose a fast and extensible framework to solve PHCA based on Bayesian Optimization (BayesOpt). Comparing with state-of-the-art algorithms such as interior point and active set, numerical results show that the proposed BayesOpt approach is able to find better solutions (25% higher hosting capacity) with 70% savings in computation time on average.

[1]  Shayan Behzadirafi,et al.  Determination of photovoltaic hosting capacity on radial electric distribution feeders , 2016, 2016 IEEE International Conference on Power System Technology (POWERCON).

[2]  Lei Wu,et al.  Distributed Generation Hosting Capacity Evaluation for Distribution Systems Considering the Robust Optimal Operation of OLTC and SVC , 2016, IEEE Transactions on Sustainable Energy.

[3]  Almoataz Y. Abdelaziz,et al.  State-of-the-art of hosting capacity in modern power systems with distributed generation , 2019, Renewable Energy.

[4]  Luis F. Ochoa,et al.  Assessing the Potential of Network Reconfiguration to Improve Distributed Generation Hosting Capacity in Active Distribution Systems , 2015, IEEE Transactions on Power Systems.

[5]  Said F. Al-Sarawi,et al.  Probabilistic Hosting Capacity for Active Distribution Networks , 2017, IEEE Transactions on Industrial Informatics.

[6]  Jian Zhao,et al.  Enhancing photovoltaic hosting capacity—A stochastic approach to optimal planning of static var compensator devices in distribution networks , 2019, Applied Energy.

[7]  Math Bollen,et al.  Integration of Distributed Generation in the Power System , 2008 .

[8]  Steven H. Low,et al.  Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence , 2014, IEEE Transactions on Control of Network Systems.

[9]  Peter I. Frazier,et al.  A Tutorial on Bayesian Optimization , 2018, ArXiv.

[10]  Jin Ma,et al.  Probabilistic Assessment of Hosting Capacity in Radial Distribution Systems , 2018, IEEE Transactions on Sustainable Energy.

[11]  Zhong-kai Feng,et al.  A hybrid short-term load forecasting model based on variational mode decomposition and long short-term memory networks considering relevant factors with Bayesian optimization algorithm , 2019, Applied Energy.

[12]  Renzhi Lu,et al.  Bayesian Learning-Based Multi-Objective Distribution Power Network Reconfiguration , 2021, IEEE Transactions on Smart Grid.

[13]  Miadreza Shafie-Khah,et al.  New Multistage and Stochastic Mathematical Model for Maximizing RES Hosting Capacity—Part I: Problem Formulation , 2017, IEEE Transactions on Sustainable Energy.

[14]  G. Saridis,et al.  Journal of Optimization Theory and Applications Approximate Solutions to the Time-invariant Hamilton-jacobi-bellman Equation 1 , 1998 .

[15]  Le Xie,et al.  Data-driven decision making in power systems with probabilistic guarantees: Theory and applications of chance-constrained optimization , 2019, Annu. Rev. Control..

[16]  Desta Z. Fitiwi,et al.  New Multi-Stage and Stochastic Mathematical Model for Maximizing RES Hosting Capacity—Part II: Numerical Results , 2017, IEEE Transactions on Sustainable Energy.

[17]  Nando de Freitas,et al.  Taking the Human Out of the Loop: A Review of Bayesian Optimization , 2016, Proceedings of the IEEE.

[18]  Ufuk Topcu,et al.  Exact Convex Relaxation of Optimal Power Flow in Radial Networks , 2013, IEEE Transactions on Automatic Control.

[19]  Wenchuan Wu,et al.  Data-Driven DG Capacity Assessment Method for Active Distribution Networks , 2017, IEEE Transactions on Power Systems.

[20]  Guangzhong Dong,et al.  Data-Driven Energy Management in a Home Microgrid Based on Bayesian Optimal Algorithm , 2019, IEEE Transactions on Industrial Informatics.

[21]  Jasper Snoek,et al.  Practical Bayesian Optimization of Machine Learning Algorithms , 2012, NIPS.

[22]  Vassilis Kekatos,et al.  Fast Probabilistic Hosting Capacity Analysis of Feeders with Distributed Energy Resources , 2020 .

[23]  Christodoulos A. Floudas.  Generalized Benders Decomposition , 2009, Encyclopedia of Optimization.

[24]  Xin Chen,et al.  Robust Capacity Assessment of Distributed Generation in Unbalanced Distribution Networks Incorporating ANM Techniques , 2017, IEEE Transactions on Sustainable Energy.