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1. Pricing Multi-Interval Dispatch under Uncertainty Part II: Generalization and Performance

   https://doi.org/10.1109/TPWRS.2020.3045162  

   Chen, Cong ; Guo, Ye ; Tong, Lang ( December 2020 , 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 for generators under the locational marginal pricing (LMP) and temporal locational marginal pricing (TLMP) policies. Extending the theoretical results developed in Part I, Part II evaluates a broader set of performance measures under a general network model. For networks with power flow constraints, TLMP is shown to have an energy-congestion-ramping price decomposition. Under the one-shot dispatch and pricing model, this decomposition leads to a nonnegative merchandising surplus equal to the sum of congestion and ramping surpluses. It is also shown that, comparing with LMP, TLMP imposes a penalty on generators with limited ramping capabilities, thus giving incentives for generators to reveal their ramping limits truthfully and improve their ramping capacities. Several benchmark pricing mechanisms are evaluated under the rolling-window dispatch and pricing models. The performance measures considered are the level of out-of-the-market uplifts, the revenue adequacy of the system operator, consumer payment, generator profit, level of discriminative payment, and price volatility. 

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2. 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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3. Continuous-Time Marginal Pricing of Electricity

   https://doi.org/10.1109/TPWRS.2016.2597288  

   Parvania, Masood ; Khatami, Roohallah ( August 2016 , IEEE Transactions on Power Systems)

   The current practice of discrete-time electricity pricing starts to fall short in providing an accurate economic signal reflecting the continuous-time variations of load and generation schedule in power systems. This paper introduces the fundamental mathematical theory of continuous-time marginal electricity pricing. We first formulate the continuous-time unit commitment (UC) problem as a constrained variational problem, and subsequently define the continuous-time economic dispatch (ED) problem where the binary commitment variables are fixed to their optimal values. We then prove that the continuous-time marginal electricity price equals to the Lagrange multiplier of the variational power balance constraint in the continuous-time ED problem. The proposed continuous-time marginal price is not only dependent to the incremental generation cost rate, but also to the incremental ramping cost rate of the units, thus embedding the ramping costs in calculation of the marginal electricity price. The numerical results demonstrate that the continuous-time marginal price manifests the behavior of the constantly varying load and generation schedule in power systems. 

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4. Pricing flexibility of shiftable demand in electricity markets

   https://doi.org/10.1145/3447555.3464847  

   Werner, Lucien ; Wierman, Adam ; Low, Steven H. ( June 2021 , ACM International Conference on Future Energy Systems)

   Enabling participation of demand-side flexibility in electricity markets is key to improving power system resilience and increasing the penetration of renewable generation. In this work we are motivated by the curtailment of near-zero-marginal-cost renewable resources during periods of oversupply, a particularly important cause of inefficient generation dispatch. Focusing on shiftable load in a multi-interval economic dispatch setting, we show that incompatible incentives arise for loads in the standard market formulation. While the system's overall efficiency increases from dispatching flexible demand, the overall welfare of loads can decrease as a result of higher spot prices. We propose a market design to address this incentive issue. Specifically, by imposing a small number of additional constraints on the economic dispatch problem, we obtain a mechanism that guarantees individual rationality for all market participants while simultaneously obtaining a more efficient dispatch. Our formulation leads to a natural definition of a uniform, time-varying flexibility price that is paid to loads to incentivize flexible bidding. We provide theoretical guarantees and empirically validate our model with simulations on real-world generation data from California Independent System Operator (CAISO). 

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5. State Space Collapse in Resource Allocation for Demand Dispatch and its Implications for Distributed Control Design

   https://doi.org/10.1109/TAC.2023.3293037  

   Mathias, Joel ; Meyn, Sean ; Moye, Robert ; Warrington, Joseph ( January 2023 , IEEE Transactions on Automatic Control)

   Alessandro Astolfi (Ed.)

   Demand dispatch is the science of extracting virtual energy storage through the automatic control of deferrable loads to provide balancing or regulation services to the grid, while maintaining consumer-end quality of service.The control of a large collection of heterogeneous loads is in part a resource allocation problem, since different classes of loads are more valuable for different services. The goal of this paper is to unveil the structure of the optimal solution to the resource allocation problem, and investigate short-term market implications. It is found that the marginal cost for each load class evolves in a two-dimensional subspace: spanned by a co-state process and its derivative. The resource allocation problem is recast to construct a dynamic competitive equilibrium model, in which the consumer utility is the negative of the cost of deviation from ideal QoS. It is found that a competitive equilibrium exists with the equilibrium price equal to the negative of an optimal co-state process. Moreover, the equilibrium price is different than what would be obtained based on the standard assumption that the consumer's utility is a function of power consumption. 

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