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1. Kullback-Leibler-Quadratic Optimal Control of Flexible Power Demand

   https://doi.org/10.1109/CDC40024.2019.9029512  

   Cammardella, Neil; Busic, Ana; Ji, Yuting; Meyn, Sean (December 2019, IEEE Conference Decision and Control)

   null (Ed.)

   A new stochastic control methodology is introduced for distributed control, motivated by the goal of creating virtual energy storage from flexible electric loads, i.e. Demand Dispatch. In recent work, the authors have introduced Kullback- Leibler-Quadratic (KLQ) optimal control as a stochastic control methodology for Markovian models. This paper develops KLQ theory and demonstrates its applicability to demand dispatch. In one formulation of the design, the grid balancing authority simply broadcasts the desired tracking signal, and the hetero-geneous population of loads ramps power consumption up and down to accurately track the signal. Analysis of the Lagrangian dual of the KLQ optimization problem leads to a menu of solution options, and expressions of the gradient and Hessian suitable for Monte-Carlo-based optimization. Numerical results illustrate these theoretical results. 

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2. Balancing the Power Grid with Cheap Assets

   https://doi.org/10.1109/CDC49753.2023.10383996  

   Meyn, Sean; Lu, Fan; Mathias, Joel (December 2023, IEEE)

   We have all heard that there is growing need to secure resources to obtain supply-demand balance in a power grid facing increasing volatility from renewable sources of energy. There are mandates for utility scale battery systems in regions all over the world, and there is a growing science of “demand dispatch” to obtain virtual energy storage from flexible electric loads such as water heaters, air conditioning, and pumps for irrigation. The question addressed in this tutorial is how to manage a large number of assets for balancing the grid. The focus is on variants of the economic dispatch problem, which may be regarded as the “feed-forward” component in an overall control architecture. 1) The resource allocation problem is identical to a finite horizon optimal control problem with degenerate cost—so called “cheap control”. This implies a form of state space collapse, whose form is identified: the marginal cost for each load class evolves in a two-dimensional subspace, spanned by a scalar co-state process and its derivative. 2) The implication to distributed control is remarkable. Once the co-state process is synthesized, this common signal may be broadcast to each asset for optimal control. However, the optimal solution is extremely fragile, in a sense made clear through results from numerical studies. 3) Several remedies are proposed to address fragility. One is described through “robust training” in a particular Q-learning architecture (one approach to reinforcement learning). In numerical studies it is found that specialized training leads to more robust control solutions. 

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3. 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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4. Virtual Energy Storage from Flexible Loads: Distributed Control with QoS Constraints.

   https://doi.org/10.1007/978-3-319-98310-3_6  

   Barooah, Prabir (September 2018, Smart Grid Control. Power Electronics and Power Systems)

   Stoustrup J., Annaswamy A. (Ed.)

   Loads are expected to help the power grid of the future in balancing the highs and lows caused by intermittent renewables such as solar and wind. With appropriate intelligence, loads will be able manipulate demand around a nominal baseline so that the increase and decrease of demand appears like charging and discharging of a battery, thereby creating a virtual energy storage (VES) device. An important question for the control systems community is: how to control these flexible loads so that the apparently conflicting goal of maintaining consumers’ quality of service (QoS) and providing reliable grid support are achieved? We advocate a frequency domain thinking of handling both of these issues, along the lines of a recent paper. In this article, we discuss some of the challenges and opportunities in designing appropriate control algorithms and coordination architectures in obtaining reliable VES from flexible loads. 

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5. Evaluating Coupling Models for Cloud Datacenters and Power Grids

   https://doi.org/10.1145/3447555.3464868  

   Lin, Liuzixuan; Zavala, Victor M.; Chien, Andrew A. (June 2021, InThe TwelfthACM International Conference on Future Energy Systems (e-Energy ’21),)

   Ardakanian, Omid; Niesse, Astrid (Ed.)

   The rapid growth of datacenter (DC) loads can be leveraged to help meet renewable portfolio standard (RPS, renewable fraction)targets in power grids. The ability to manipulate DC loads over time(shifting) provides a mechanism to deal with temporal mismatch between non-dispatchable renewable generation (e.g. wind and solar) and overall grid loads, and this flexibility ultimately facilitates the absorption of renewables and grid decarbonization. To this end, we study DC-grid coupling models, exploring their impact on grid dispatch, renewable absorption, power prices, and carbon emissions.With a detailed model of grid dispatch, generation, topology, and loads, we consider three coupling approaches: fixed, datacenter-local optimization (online dynamic programming), and grid-wide optimization (optimal power flow). Results show that understanding the effects of dynamic DC load management requires studies that model the dynamics of both load and power grid. Dynamic DC-grid coupling can produce large improvements: (1) reduce grid dispatch cost (-3%), (2) increase grid renewable fraction (+1.58%), and (3) reduce DC power cost (-16.9%).It also has negative effects: (1) increase cost for both DCs and non-DC customers, (2) differentially increase prices for non-DC customers, and (3) create large power-level changes that may harm DC productivity. 

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