Search

Given the complexity of power systems, particularly the high-dimensional variability of net loads, accurately depicting the entire operational range of net loads poses a challenge. To address this, recent methodologies have sought to gauge the maximum range of net load uncertainty across all buses. In this paper, we consider the stochastic nature of the net load and introduce a distributionally robust optimization framework that assesses system flexibility stochastically, accommodating a minimal extent of system violations. We verify the proposed method by solving the flexibility of the real-time economic dispatch problem on four IEEE standard test systems. Compared to traditional deterministic flexibility evaluations, our approach consistently yields less conservative flexibility outcomes.

The interaction between power systems and wildfires can be dangerous and costly. Damaged structures, load shedding, and high operational costs are potential consequences when the grid is unprepared. In fact, the operation of distribution grids can be liable for the outbreak of wildfires when extreme weather conditions arise. Within this context, investment planning should consider the impact of operational actions on the uncertainty related to wildfires that can directly affect line failure likelihood. Neglecting this can compromise the cost-benefit evaluation in planning system investments for wildfire risk. In this paper, we propose a decision-dependent uncertainty (DDU) aware methodology that provides the optimal portfolio of investments for distribution systems while considering that high power-flow levels through line segments in high-threat areas can ignite wildfires and, therefore, increase the probability of line failures. The methodology identifies the best combination of system upgrades (installation of new lines, hardening existing lines, and placement of switching devices) to provide the necessary leeway to operate the distribution system under wildfire-prone conditions. Our case study demonstrates that by modeling the DDU relationship between power flow prescriptions and line failures, investment decisions are more accurate and better prepare the grid infrastructure to deal with wildfire risk.

The transition from traditional bus fleets to zero-emission ones necessitates the development of effective planning models for battery electric bus (BEB) charging infrastructure. On-route fast charging stations, distinct from on-base charging stations, present unique challenges related to safe operation and power supply capacity, making it difficult to control grid operational costs. This paper establishes a novel framework that integrates the bus route network and power network, which leverages the inter-dependency between both networks to optimize the planning outcomes of on-route BEB charging stations in South King County. The problem is formulated as a mixed-integer second-order cone programming model, aiming to minimize the overall planning cost, which includes investments in charging equipment, power facility, and grid operation. Furthermore, fairness measurements are incorporated into the planning process, allowing for the consideration of both horizontal transit equity and vertical transit equity based on different zone merging criteria within the county's existing census tracts. The results of this planning model offer valuable insights into achieving both economic efficiency and social justice in the design of on-route charging facilities for BEBs in South King County., Comment: 18 pages, 16 figures

Trust-region methods based on Kullback-Leibler divergence are pervasively used to stabilize policy optimization in reinforcement learning. In this paper, we exploit more flexible metrics and examine two natural extensions of policy optimization with Wasserstein and Sinkhorn trust regions, namely Wasserstein policy optimization (WPO) and Sinkhorn policy optimization (SPO). Instead of restricting the policy to a parametric distribution class, we directly optimize the policy distribution and derive their closed-form policy updates based on the Lagrangian duality. Theoretically, we show that WPO guarantees a monotonic performance improvement, and SPO provably converges to WPO as the entropic regularizer diminishes. Moreover, we prove that with a decaying Lagrangian multiplier to the trust region constraint, both methods converge to global optimality. Experiments across tabular domains, robotic locomotion, and continuous control tasks further demonstrate the performance improvement of both approaches, more robustness of WPO to sample insufficiency, and faster convergence of SPO, over state-of-art policy gradient methods.

Optimal power flow (OPF) is an important tool for Independent System Operators (ISOs) to deal with the power generation management. With the increasing penetration of renewable energy into power grids, challenges arise in tackling the OPF problem due to the intermittent nature of renewable energy output. To address these challenges, we develop a multi-stage distributionally robust approach for the direct-current optimal power flow (DC-OPF) problem to minimize total generation cost under renewable energy uncertainty. In our model, we assume the renewable energy output follows an ambiguous distribution that can be characterized by a confidence set. By utilizing the revealed data sequentially, the proposed approach can provide a reliable and robust optimal OPF decision without restricting the renewable energy output distribution to any particular distribution class. The computational results also verify the effectiveness of our approach to reduce the conservativeness and meanwhile maintain the reliability.

In this paper, we present a Distributionally Robust Markov Decision Process (DRMDP) approach for addressing the dynamic epidemic control problem. The Susceptible-Exposed-Infectious-Recovered (SEIR) model is widely used to represent the stochastic spread of infectious diseases, such as COVID-19. While Markov Decision Processes (MDP) offers a mathematical framework for identifying optimal actions, such as vaccination and transmission-reducing intervention, to combat disease spreading according to the SEIR model. However, uncertainties in these scenarios demand a more robust approach that is less reliant on error-prone assumptions. The primary objective of our study is to introduce a new DRMDP framework that allows for an ambiguous distribution of transition dynamics. Specifically, we consider the worst-case distribution of these transition probabilities within a decision-dependent ambiguity set. To overcome the computational complexities associated with policy determination, we propose an efficient Real-Time Dynamic Programming (RTDP) algorithm that is capable of computing optimal policies based on the reformulated DRMDP model in an accurate, timely, and scalable manner. Comparative analysis against the classic MDP model demonstrates that the DRMDP achieves a lower proportion of infections and susceptibilities at a reduced cost.

Demand response (DR) has been demonstrated to be an effective method for reducing peak load and mitigating uncertainties on both the supply and demand sides of the electricity market. One critical question for DR research is how to appropriately adjust electricity prices in order to shift electrical load from peak to off-peak hours. In recent years, reinforcement learning (RL) has been used to address the price-based DR problem because it is a model-free technique that does not necessitate the identification of models for end-use customers. However, the majority of RL methods cannot guarantee the stability and optimality of the learned pricing policy, which is undesirable in safety-critical power systems and may result in high customer bills. In this paper, we propose an innovative nonparametric constrained policy optimization approach that improves optimality while ensuring stability of the policy update, by removing the restrictive assumption on policy representation that the majority of the RL literature adopts: the policy must be parameterized or fall into a certain distribution class. We derive a closed-form expression of optimal policy update for each iteration and develop an efficient on-policy actor-critic algorithm to address the proposed constrained policy optimization problem. The experiments on two DR cases show the superior performance of our proposed nonparametric constrained policy optimization method compared with state-of-the-art RL algorithms., Comment: 2023 IEEE PES General Meeting. arXiv admin note: text overlap with arXiv:2006.07815

Wildfires can severely damage electricity grids leading to long periods of power interruption. Climate change will exacerbate this threat by increasing the frequency of dry climate conditions. Under these climate conditions, human-related actions that initiate wildfires should be avoided, including those induced by power systems operation. In this paper, we propose a novel optimization model that is capable of determining appropriate network topology changes (via switching actions) to alleviate the levels of power flows through vulnerable parts of the grid so as to decrease the probability of wildfire ignition. Within this framework, the proposed model captures the relationship between failure probabilities and line-flow decisions by explicitly considering the former as a function of the latter. The resulting formulation is a two-stage model with endogenous decision-dependent probabilities, where the first stage determines the optimal switching actions and the second stage evaluates the worst-case expected operation cost. We propose an exact iterative method to deal with this intricate problem and the methodology is illustrated with a 54-bus and a 138-bus distribution system.

The optimal power flow (OPF) problem, as a critical component of power system operations, becomes increasingly difficult to solve due to the variability, intermittency, and unpredictability of renewable energy brought to the power system. Although traditional optimization techniques, such as stochastic and robust optimization approaches, could be leveraged to address the OPF problem, in the face of renewable energy uncertainty, i.e., the dynamic coefficients in the optimization model, their effectiveness in dealing with large-scale problems remains limited. As a result, deep learning techniques, such as neural networks, have recently been developed to improve computational efficiency in solving OPF problems with the utilization of data. However, the feasibility and optimality of the solution may not be guaranteed, and the system dynamics cannot be properly addressed as well. In this paper, we propose an optimization model-informed generative adversarial network (MI-GAN) framework to solve OPF under uncertainty. The main contributions are summarized into three aspects: (1) to ensure feasibility and improve optimality of generated solutions, three important layers are proposed: feasibility filter layer, comparison layer, and gradient-guided layer; (2) in the GAN-based framework, an efficient model-informed selector incorporating these three new layers is established; and (3) a new recursive iteration algorithm is also proposed to improve solution optimality and handle the system dynamics. The numerical results on IEEE test systems show that the proposed method is very effective and promising.

Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO), as the widely employed policy based reinforcement learning (RL) methods, are prone to converge to a sub-optimal solution as they limit the policy representation to a particular parametric distribution class. To address this issue, we develop an innovative Optimistic Distributionally Robust Policy Optimization (ODRPO) algorithm, which effectively utilizes Optimistic Distributionally Robust Optimization (DRO) approach to solve the trust region constrained optimization problem without parameterizing the policies. Our algorithm improves TRPO and PPO with a higher sample efficiency and a better performance of the final policy while attaining the learning stability. Moreover, it achieves a globally optimal policy update that is not promised in the prevailing policy based RL algorithms. Experiments across tabular domains and robotic locomotion tasks demonstrate the effectiveness of our approach.

As the installation of electronically interconnected renewable energy resources grows rapidly in power systems, system frequency maintenance and control become challenging problems to maintain the system reliability in bulk power systems. As two of the most important frequency control actions in the control centers of independent system operators (ISOs) and utilities, the interaction between Economic Dispatch (ED) and Automatic Generation Control (AGC) attracts more and more attention. In this paper, we propose a robust optimization based framework to measure the system flexibility by considering the interaction between two hierarchical processes (i.e., ED and AGC). We propose a cutting plane algorithm with the reformulation technique to obtain seven different indices of the system. In addition, we study the impacts of several system factors (i.e., the budget of operational cost, ramping capability, and transmission line capacity) and show numerically how these factors can influence the system flexibility., Comment: 8 pages, submitted

Topology design is a critical task for the reliability, economic operation, and resilience of distribution systems. This paper proposes a distributionally robust optimization (DRO) model for designing the topology of a new distribution system facing random contingencies (e.g., imposed by natural disasters). The proposed DRO model optimally configures the network topology and integrates distributed generation to effectively meet the loads. Moreover, we take into account the uncertainty of contingency. Using the moment information of distribution line failures, we construct an ambiguity set of the contingency probability distribution, and minimize the expected amount of load shedding with regard to the worst-case distribution within the ambiguity set. As compared with a classical robust optimization model, the DRO model explicitly considers the contingency uncertainty and so provides a less conservative configuration, yielding a better out-of-sample performance. We recast the proposed model to facilitate the column-and-constraint generation algorithm. We demonstrate the out-of-sample performance of the proposed approach in numerical case studies.