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1. Pricing Conditional Value at Risk-Sensitive Economic Dispatch

   https://doi.org/10.1109/PESGM46819.2021.9637845  

   Ndrio, Mariola; Madavan, Avinash N.; Bose, Subhonmesh (January 2021, 2021 IEEE Power & Energy Society General Meeting (PESGM))

   There are growing concerns over the ability of current electricity market designs to adequately model and optimize against the stochastic nature of renewable resources such as wind and solar. In this paper, we consider an economic dispatch problem that explicitly accounts for said uncertainty and enforces network and generation limits using conditional value at risk. Our key contribution is the definition and analysis of risk-sensitive locational marginal prices (risk-LMPs) derived from such a market clearing problem. Risk-LMPs extend conventional LMPs to the uncertain setting. Settlements defined via risk-LMPs compensate resources for both energy and reserve schedules. We study these prices via sample average approximation (SAA) on example power networks to demonstrate their viability for electricity pricing with large-scale integration of renewables. 

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2. Stochastic Planning of a Mostly-Renewable Power Grid

   https://doi.org/10.1109/CCTA54093.2023.10253007  

   Chen, Sunny; Mathieu, Johanna L.; Seiler, Peter (August 2023, IEEE Conference on Control Technology and Applications (CCTA))

   Power grid resource adequacy can be difficult to ensure with high penetrations of intermittent renewable energy. We explore enhancing resource adequacy by overbuilding renewables while modeling statistical correlations in renewable power at different sites. Overbuilding allows production during times of low power, and exploiting statistical correlations can reduce power variability and, subsequently, reduce needed renewable capacity. In this work, we present a stochastic optimization problem to size renewables and expand transmission while minimizing the expected dispatch cost. Our method uses statistical profiles of renewable production and embeds network constraints using the DC power flow equations. We assess our method’s effects on feasibility, load shedding, locational marginal prices, and generator curtailment. On the IEEE 9-bus system, we found that anti-correlation between generators reduced generation capacity needs with sufficient transmission. On the IEEE 30-bus system, we found that the optimal solution required significant overbuilding and curtailment of renewables regardless of the marginal cost of schedulable generation. 

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3. Risk-aware electricity dispatch with large-scale distributed renewable integration under climate extremes

   https://doi.org/10.1073/pnas.2426620122  

   Xu, Luo; Zeng, Hongtai; Lin, Ning; Yang, Yue; Guo, Qinglai; Poor, H Vincent (May 2025, Proceedings of the National Academy of Sciences)

   Distribution networks, with large-scale integration of distributed renewable resources, particularly rooftop solar photovoltaic systems, represent the most extensive yet vulnerable components of modern electric power systems during climate extremes such as hurricanes. However, existing day-ahead electricity dispatch approaches primarily focus on the transmission network and lack the capability to manage the spatiotemporal risks associated with the vast distribution networks, which can potentially lead to significant power imbalances due to the mismatches between scheduled generation and actual demand. To address this increasingly critical gap under intensifying climate extremes and growing distributed renewable integration, we introduce Risk-aware Electricity Dispatch under Climate Extremes with Renewable integration (REDUCER), a risk-aware day-ahead electricity dispatch model that incorporates high-resolution spatiotemporal risk analysis for distribution networks with large-scale distributed renewable integration into an Entropic Value-at-Risk-constrained mixed-integer convex optimization framework. Applied to the 2022 Puerto Rico power grid under Hurricane Fiona, the proposed REDUCER model is seen to effectively manage these risks with substantially less reliance on additional flexibility resources to cope with power imbalances, reducing overall operational costs by about 30% under extreme cases compared to standard unit commitment strategies already informed by average demand loss. Also, the proposed REDUCER model consistently demonstrates its effectiveness in managing the increasing temporal net demand variability introduced by growing large-scale distributed solar integration while maintaining minimal operational costs. This model offers a practical solution for cost-effective and resilient electricity dispatch of modern power systems with large-scale renewable integration facing intensifying climate risks. 

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4. Scenario-based Economic Dispatch with Tunable Risk Levels in High-renewable Power Systems

   https://doi.org/10.1109/TPWRS.2018.2874464  

   Modarresi, M. Sadegh; Xie, Le; Campi, Marco; Garatti, Simone; Care, Algo; Thatte, Anupam; Kumar, P. R. (January 2018, IEEE Transactions on Power Systems)

   This paper introduces an empirical approach to dispatch resources in real-time power system operation with growing levels of uncertainties emerging from intermittent and distributed energy resources in the supply and the demand side. It is shown that by taking empirical data of specific sizes, the dispatch results can lead to a quantifiable and rigorous bound on the risk of violating constraints at the implementation stage. In particular, we formulate the look-ahead real-time economic dispatch problem using the scenario approach. This approach takes empirical data as input and guarantees a tunable probability of violating the constraints according to the input data size. By exploiting the structure of the economic dispatch, we show that in the absence of transmission constraints, the number of samples theory requires does not grow with the size of the problem. In the more general case with consideration of transmission constraints, it is shown that the posterior bound on the risk of dispatch can be quantified and can be much smaller than the risk bound before solving the dispatch. Numerical examples based on a standard test system suggest that the scenario approach can provide a practically attractive solution with theoretically rigorous properties for risk-limiting power system operations. 

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5. Pricing Multi-Interval Dispatch under Uncertainty Part I: Dispatch-Following Incentives

   https://doi.org/10.1109/TPWRS.2021.3055730  

   Guo, Ye; Chen, Cong; Tong, Lang (January 2021, IEEE Transactions on Power Systems)

   null (Ed.)

   Pricing multi-interval economic dispatch of electric power under operational uncertainty is considered in this two- part paper. Part I investigates dispatch-following incentives of profit-maximizing generators and shows that, under mild conditions, no uniform-pricing scheme for the rolling-window economic dispatch provides dispatch-following incentives that avoid discriminative out-of-the-market uplifts. A nonuniform pricing mechanism, referred to as the temporal locational marginal pricing (TLMP), is proposed. As an extension of the standard locational marginal pricing (LMP), TLMP takes into account both generation and ramping-induced opportunity costs. It eliminates the need for the out-of-the-market uplifts and guarantees full dispatch-following incentives regardless of the accuracy of the demand forecasts used in the dispatch. It is also shown that, under TLMP, a price-taking market participant has incentives to bid truthfully with its marginal cost of generation. Part II of the paper extends the theoretical results developed in Part I to more general network settings. It investigates a broader set of performance measures, including the incentives of the truthful revelation of ramping limits, revenue adequacy of the operator, consumer payments, generator profits, and price volatility under the rolling-window dispatch model with demand forecast errors. 

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