arXiv subjects

Bernard Knueven

Publications and source records attributed to Bernard Knueven.

5 recordsLinked to original sources

arXiv2026

From Zonal to Nodal Capacity Expansion Planning: Spatial Aggregation Impacts on a Realistic Test-Case

Solving power system capacity expansion planning (CEP) problems at realistic spatial resolutions is computationally challenging. Thus, a common practice is to solve CEP over zonal models with low spatial resolution rather than over full-scale nodal power networks. Due to improvements in solving large-scale stochastic mixed integer programs, these computational limitations are becoming less relevant, and the assumption that zonal models are realistic and useful approximations of nodal CEP is worth revisiting. This work is the first to conduct a systematic computational study on the assumption that spatial aggregation can reasonably be used for ISO-scale CEP. By considering a realistic, large-scale test network based on the state of California with over 8,000 buses, we find that well-designed small spatial aggregations can yield good approximations but that coarser zonal models may result in large distortions of investment decisions, e.g., capacity under-investment of up to 41% for the lowest resolution model considered.

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arXiv2026

A hard-constrained NN learning framework for rapidly restoring AC-OPF from DC-OPF

This paper proposes a hard-constrained unsupervised learning framework for rapidly solving the non-linear and non-convex AC optimal power flow (AC-OPF) problem in real-time operation. Without requiring ground-truth AC-OPF solutions, feasibility and optimality are ensured through a properly designed learning environment and training loss. Inspired by residual learning, the neural network (NN) learns the correction mapping from the DC-OPF solution to the active power setpoints of the generators through re-dispatch. A subsequent optimization model is utilized to restore the optimal AC-OPF solution, and the resulting projection difference is employed as the training loss. A replay buffer is utilized to enhance learning efficiency by fully leveraging past data pairs. The optimization model is cast as a differentiable optimization layer, where the gradient is derived by applying the implicit function theorem to the KKT conditions at the optimal solution. Tested on IEEE-118 and PEGASE-9241 bus systems, numerical results demonstrate that the proposed NN can obtain strictly feasible and near-optimal solutions with reduced computational time compared to conventional optimization solvers. In addition, aided by the updated DC-OPF solution under varying topologies, the trained NN, together with the PF solver, can rapidly find the corresponding AC solution. The proposed method achieves a $40\times$ time speedup, while maintaining an average constraint violation on the order of $10^{-4}$ and an optimization gap below $1\%$.

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arXiv2024

Beyond Price-Taker: Multiscale Optimization of Wind and Battery Integrated Energy Systems

Decarbonizing global energy systems requires extensive integration of renewable energy into the electric grid. However, the intermittency and variable nature of wind and other non-dispatchable renewable resources make integration a great challenge. Hybridizing renewables with energy storage to form integrated energy systems (IESs) helps mitigate these concerns by improving reliability and resiliency. This paper systematically studies the limitations of the prevailing price-taker assumption for techno-economic analysis (TEA) and optimization of hybrid energy systems. As an illustrative case study, we retrofit an existing wind farm in the RTS-GMLC test system (which loosely mimics the Southwest U.S.) with battery energy storage to form an IES. We show that the standard price-taker model overestimates the electricity revenue and the net present value (NPV) of the IES up to 178% and 50%, respectively, compared to our more rigorous multiscale optimization. These differences arise because introducing storage creates a more flexible resource that impacts the larger wholesale electricity market. Moreover, this work highlights the impact of the IES has on the market via various strategic bidding, and underscores the importance of moving beyond price-taker for optimal storage sizing and TEA of IESs. We conclude by discussing opportunities to generalize the proposed framework to other IESs, and highlight emerging research questions regarding the complex interactions between IESs and markets.

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arXiv2024

Curriculum-based Reinforcement Learning for Distribution System Critical Load Restoration

This paper focuses on the critical load restoration problem in distribution systems following major outages. To provide fast online response and optimal sequential decision-making support, a reinforcement learning (RL) based approach is proposed to optimize the restoration. Due to the complexities stemming from the large policy search space, renewable uncertainty, and nonlinearity in a complex grid control problem, directly applying RL algorithms to train a satisfactory policy requires extensive tuning to be successful. To address this challenge, this paper leverages the curriculum learning (CL) technique to design a training curriculum involving a simpler steppingstone problem that guides the RL agent to learn to solve the original hard problem in a progressive and more effective manner. We demonstrate that compared with direct learning, CL facilitates controller training to achieve better performance. To study realistic scenarios where renewable forecasts used for decision-making are in general imperfect, the experiments compare the trained RL controllers against two model predictive controllers (MPCs) using renewable forecasts with different error levels and observe how these controllers can hedge against the uncertainty. Results show that RL controllers are less susceptible to forecast errors than the baseline MPCs and can provide a more reliable restoration process.

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arXiv2020

The Impacts of Convex Piecewise Linear Cost Formulations on AC Optimal Power Flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. These results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, a important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

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