arXiv subjects

Karan Mukhi

Publications and source records attributed to Karan Mukhi.

6 recordsLinked to original sources

arXiv2025

Exact Recourse Functions for Aggregations of EVs Operating in Imbalance Markets

We study optimal charging of large electric vehicle populations that are exposed to a single real-time imbalance price. The problem is naturally cast as a multistage stochastic linear programme (MSLP), which can be solved by algorithms such as Stochastic Dual Dynamic Programming. However, these methods scale poorly with the number of devices and stages. This paper presents a novel approach to overcome this curse of dimensionality. Building prior work that characterises the aggregate flexibility sets of populations of EVs as a permutahdron, we reformulate the original problem in terms of aggregated quantities. The geometric structure of permutahedra lets us (i) construct an optimal disaggregation policy, (ii) derive an exact, lower-dimensional MSLP, and (iii) characterise the expected recourse function as piecewise affine with a finite, explicit partition. In particular, we provide closed-form expressions for the slopes and intercepts of each affine region via truncated expectations of future prices, yielding an exact form for the recourse function and first-stage policy. Comprehensive numerical studies validate our claims and demonstrate the practical utility of this work.

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arXiv2025

Polymatroidal Representations of Aggregate EV Flexibility Considering Network Constraints

The increasing penetration of electric vehicles (EVs) introduces significant flexibility potential to power systems. However, uncoordinated or synchronous charging can lead to overloading of distribution networks. Extending recent approaches that utilize generalized polymatroids, a family of polytopes, to represent the aggregate flexibility of EV populations, we show how to integrate network constraints into this representation to obtain network-constrained aggregate flexibility sets. Furthermore, we demonstrate how to optimize over these network-constrained aggregate flexibility sets, and propose a disaggregation procedure that maps an aggregate load profile to individual EV dispatch instructions, while respecting both device-level and network constraints.

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arXiv2025

Aggregate Flexibility of Thermostatically Controlled Loads using Generalized Polymatroids

Leveraging populations of thermostatically controlled loads could provide vast storage capacity to the grid. To realize this potential, their flexibility must be accurately aggregated and represented to the system operator as a single, controllable virtual device. Mathematically this is computed by calculating the Minkowski sum of the individual flexibility of each of the devices. Previous work showed how to exactly characterize the flexibility of lossless storage devices as generalized polymatroids-a family of polytope that enable an efficient computation of the Minkowski sum. In this paper we build on these results to encompass devices with dissipative storage dynamics. In doing so we are able to provide tractable methods of accurately characterizing the flexibility in populations consisting of a variety of heterogeneous devices. Numerical results demonstrate that the proposed characterizations are tight.

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arXiv2025

Exact Characterization of Aggregate Flexibility via Generalized Polymatroids

It is well established that the aggregate flexibility inherent in populations of distributed energy resources (DERs) can be leveraged to mitigate the intermittency and uncertainty associated with renewable generation, while also providing ancillary grid services. To enable this, aggregators must effectively represent the flexibility in the populations they control to the market or system operator. A key challenge is accurately computing the aggregate flexibility of a population, which can be formally expressed as the Minkowski sum of a collection of polytopes, a problem that is generally computationally intractable. However, the flexibility polytopes of many DERs exhibit structural symmetries that can be exploited for computational efficiency. To this end, we introduce generalized polymatroids, a family of polytopes, into the flexibility aggregation literature. We demonstrate that individual flexibility sets belong to this family, enabling efficient computation of their exact Minkowski sum. For homogeneous populations of DERs we further derive simplifications that yield more succinct representations of aggregate flexibility. Additionally, we develop an efficient optimization framework over these sets and propose a vertex-based disaggregation method, to allocate aggregate flexibility among individual DERs. Finally, we validate the optimality and computational efficiency of our approach through comparisons with existing methods.

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arXiv2024

Robust Aggregation of Electric Vehicle Flexiblity

We address the problem of characterizing the aggregate flexibility in populations of electric vehicles (EVs) with uncertain charging requirements. Extending upon prior results that provide exact characterizations of aggregate flexibility in populations of electric vehicle (EVs), we adapt the framework to encompass more general charging requirements. In doing so we give a characterization of the exact aggregate flexibility as a generalized polymatroid. Furthermore, this paper advances these aggregation methodologies to address the case in which charging requirements are uncertain. In this extended framework, requirements are instead sampled from a specified distribution. In particular, we construct robust aggregate flexibility sets, sets of aggregate charging profiles over which we can provide probabilistic guarantees that actual realized populations will be able to track. By leveraging measure concentration results that establish powerful finite sample guarantees, we are able to give tight bounds on these robust flexibility sets, even in low sample regimes that are well suited for aggregating small populations of EVs. We detail explicit methods of calculating these sets. Finally, we provide numerical results that validate our results and case studies that demonstrate the applicability of the theory developed herein.

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arXiv2023

An Exact Characterisation of Flexibility in Populations of Electric Vehicles

Increasing penetrations of electric vehicles (EVs) presents a large source of flexibility, which can be used to assist balancing the power grid. The flexibility of an individual EV can be quantified as a convex polytope and the flexibility of a population of EVs is the Minkowski sum of these polytopes. In general computing the exact Minkowski sum is intractable. However, exploiting symmetry in a restricted but significant case, enables an efficient computation of the aggregate flexibility. This results in a polytope with exponentially many vertices and facets with respect to the time horizon. We show how to use a lifting procedure to provide a representation of this polytope with a reduced number of facets, which makes optimising over more tractable. Finally, a disaggregation procedure that takes an aggregate signal and computes dispatch instructions for each EV in the population is presented. The complexity of the algorithms presented is independent of the size of the population and polynomial in the length of the time horizon. We evaluate this work against existing methods in the literature, and show how this method guarantees optimality with lower computational burden than existing methods.

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