Exploring the Use of Autonomous Unmanned Vehicles for Supporting Power Grid Operations

Cong Feng; Mingzhi Zhang; Rui Yang; Yuqi Zhou

REVIEW 3 major objections 3 minor 16 references

Exploring the Use of Autonomous Unmanned Vehicles for Supporting Power Grid Operations

T0 review · 3 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Idle autonomous vehicles can be routed and dispatched as 'mobile batteries' to cut grid operating costs, with the two-layer optimization reducing costs by 26.27% on the IEEE 14-bus system and solving 1354-bus cases in under 10 seconds.

desk verdict The routing MILP never forces the vehicle to reach the destination, so the travel costs that feed the grid dispatch are invalid; the rest is competent but unoriginal mobile-storage work. read the letter →

arxiv 2411.09783 v2 pith:ZV5RQ5KE submitted 2024-11-14 eess.SY cs.SY

Yuqi Zhou , Cong Feng , Mingzhi Zhang , Rui Yang This is my paper · ORCID

classification eess.SYcs.SY

keywords autonomousvehiclespowergridoperationsmobileenergystorageoptimalflowvehicleroutingMcCormickrelaxationmixed-integeroptimizationvehicle-to-grid

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that idle autonomous vehicles carrying batteries can serve as a mobile, dispatchable resource for power grid operations, and that using them this way is computationally practical. The proposed method works in two layers: an offline shortest-path routing problem computes each vehicle's travel cost to every candidate bus, and a mixed-integer DC optimal power flow then decides which vehicle goes where and how much power it supplies. A McCormick relaxation replaces the bilinear product of each vehicle's power output and its binary assignment variable with four linear inequalities, and because one factor is binary the relaxation is exact rather than approximate. On the IEEE 14-bus test, integrating three vehicle fleets reduces total operating cost by 26.27%; on systems up to 1354 buses the optimization solves in under 10 seconds on a laptop. If correct, the work offers grid operators a concrete way to turn the growing autonomous vehicle fleet into flexible storage without new infrastructure.

What carries the argument

The load-bearing object is the exact McCormick relaxation of the bilinear term in the power balance equation. For each vehicle $v$ and bus $i$, the product $y_i^v = p_v z_i^v$ is bounded by four linear inequalities, (13a)–(13d); because the assignment variable $z_i^v$ is binary, the inequalities are exact, meaning they enforce the product identity rather than a convex envelope around it. This exactness converts the nonlinear optimal power flow with vehicle routing into the mixed-integer linear program (14) that can be solved by standard solvers, and it is what makes the two-layer architecture practical: shortest-path routing (6) is solved offline to generate travel costs, and the OPF layer decides vehicle assignment and dispatch in seconds.

What would settle it

Take the reported IEEE 14-bus dispatch ($p_a=17.28$ MW, $p_b=20$ MW, $p_c=40$ MW) and check it against a battery energy constraint $E_v$ and support duration $T$ requiring $p_v T \le E_v$; if any vehicle's required discharge energy exceeds its onboard storage, the schedule is infeasible under any model that accounts for state of charge.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that the nonlinear coupling between vehicle power and vehicle location in the grid's power balance constraint can be handled exactly by a McCormick relaxation. For each vehicle $v$ and bus $i$, the product $y_i^v = p_v z_i^v$ is replaced by the four inequalities (13a)–(13d); because $z_i^v$ is binary, these inequalities force $y_i^v=0$ when the vehicle is not assigned to $i$ and $y_i^v=p_v$ when it is, so the reformulated problem (14) is equivalent to the original nonlinear problem (10), not an approximation. Combined with a shortest-path routing layer that supplies travel costs offline, the resulting mixed-integer program coordinates autonomous vehicles as 'mobile batteries' to maintain power balance and reduce operating cost, demonstrated by a 26.27% cost reduction on the IEEE 14-bus system and sub-10-second solve times on test systems up to 1354 buses.

Load-bearing premise

The entire dispatch plan assumes every selected vehicle can reliably deliver its nominal power $p_v$ once dispatched, ignoring battery state of charge and discharging efficiency; if a dispatched vehicle is undercharged or cannot discharge at the assumed rate, the power balance at its assigned bus fails and the solution is infeasible.

Editorial extensions

If this is right

A grid operator could schedule a fleet of idle autonomous vehicles as a low-cost, driverless generation resource, with assignment and power decisions produced by a single mixed-integer program.
The sub-10-second solve times on systems up to 1354 buses indicate the method is fast enough for intra-day or near-real-time scheduling on current hardware.
The 26.27% cost reduction in the 14-bus test comes from displacing costly generators with cheaper vehicle battery power, so the potential saving grows with the share of vehicle capacity in the system.
Because the routing layer is solved offline and only travel costs enter the OPF, the plan can adapt to changing road conditions by re-solving the routing problem in real time.
The paper's runtimes assume a small number of vehicle fleets; it notes that a significantly larger fleet would require a more coordinated decision process and could increase computation time.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A realistic battery model with state of charge and discharge efficiency would likely shrink the 26.27% saving, since some dispatched vehicles might not be able to deliver their nominal power for the full support window; a rolling-horizon extension with energy limits would quantify that shrink.
The same exact-McCormick trick applies to any optimization where a continuous variable multiplies a binary assignment variable, so the approach generalizes to siting mobile energy storage, temporary generators, or other relocatable resources in power systems.
The reported saving is tied to one synthetic 14-node transportation network with random weights; applying the method to a real city's road network with congestion and time-varying travel costs could change routes and costs, making the result a proof-of-concept rather than a guaranteed figure.
A testable extension is to compare the dispatch from the random-weight network with one from a real road network, holding the power system data fixed, to see how much the route layer affects the achievable cost reduction.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here is the thing you need to know: the routing formulation in (6) does not require the vehicle to reach its destination. Constraint (2) only forbids outgoing edges from e. There is no constraint that forces an incoming edge to e, and incoming edges to s are not forbidden. As a result, a directed cycle through s (s→a→b→s) is feasible, and with positive edge weights it can be cheaper than any actual s–e path. The "optimal route" and the travel cost c_v in (7) may therefore have nothing to do with reaching e, and the dispatch problem (14) uses those costs as coefficients. This is a genuine, load-bearing flaw, not a simplification. The fix is simple: add Σ_{i∈A_e} x_{ie}=1 and typically Σ_{i∈A_s} x_{is}=0, but without it the method does not do what the paper claims.

What works: the power-system formulation is standard but correctly assembled. The binary placement variables, the DC power flow, and the McCormick relaxation are all fine; the exactness argument for (13) is right because one factor is binary. The writing is clear and the runtimes in Table I are plausible.

The remaining soft spots are secondary but real. There is no comparison to existing mobile energy storage dispatch, so the 26.27% cost reduction is not contextualized. The numerical study uses a single synthetic 14-node network with random weights and three vehicle fleets, which is thin. And Assumption 1 ignores battery state-of-charge and discharge efficiency; the authors acknowledge this, but it means the feasibility claims rest on nominal capacities.

Novelty is low. This is mobile energy storage with autonomous vehicles as the motivating case, and the routing MILP is a textbook shortest-path formulation. No new mechanism distinguishes autonomous vehicles from conventional mobile storage in the model.

My recommendation: I would not send this to peer review in its current form. The routing flaw is a basic modeling error in the first component of the two-layer method, and the contribution is not novel enough to justify referee time. A desk reject with detailed comments, or a note to the authors to fix the routing constraints, add a baseline, and either model battery energy or defend the nominal-power approximation, would be appropriate. If those changes are made, the paper could become a modest but useful contribution.

Referee Report

3 major / 3 minor

Summary. The paper proposes a two-layer framework for dispatching idle autonomous unmanned vehicles to power-system buses so that their onboard batteries can supply energy and reduce operating cost. The transportation layer is a shortest-path MILP (problem (6)), and the power layer is a DC optimal power flow with vehicle-dispatch binaries and a McCormick linearization of the bilinear product p_v z_i^v (problem (14)). Numerical experiments on the IEEE 14-bus system report a 26.27% cost reduction, and additional tests up to a 1354-bus system report solve times under 10 seconds.

Significance. If the result holds, the paper addresses a timely and relevant problem: using autonomous vehicles as mobile batteries in grid operations. Its main mathematical contribution, replacing the bilinear term p_v z_i^v with the McCormick inequalities (13a)-(13d), is correct and exact because z_i^v is binary; this is a genuine strength. The two-layer decomposition is clean, and the scalability table (up to 1354 buses in under 10 seconds) is useful evidence of computational tractability. However, the routing-layer correctness gap and the idealized battery assumption mean the validity of the downstream claims is not yet established. With the routing fix and stronger numerical validation, the framework would be a useful addition to the mobile-energy-storage literature.

major comments (3)

[Section II, Eqs. (1)-(6)] The routing formulation is missing an arrival constraint. Eq. (2) only forbids outgoing edges from the destination e; nothing forces an incoming edge to e or forbids incoming edges to s, and flow conservation in Eq. (3) is imposed only for nodes other than s and e. As a result, a directed cycle through s, e.g., s→a→b→s in a four-node graph, satisfies all algebraic constraints while never visiting e, and with positive weights it can be strictly cheaper than the true shortest s–e path. Since the resulting c_v from Eq. (7) feeds the dispatcher objective (14a), every downstream dispatch claim is affected. The fix is to add ∑_{i∈A_e} x_{i e}=1 and ∑_{i∈A_s} x_{i s}=0, and to add subtour-elimination constraints if zero- or negative-weight edges are to be allowed. This is an internal inconsistency in the optimization model, not a modeling simplification.
[Section III, Assumption 1 and Eq. (14c)] The model assumes each dispatched vehicle can reliably inject its nominal power p_v for the entire support horizon. Because state of charge and discharge efficiency are ignored, the power balance equality (14c) may be infeasible in practice even when the MILP reports a feasible solution. The paper acknowledges this simplification and defers it to future work, but the headline results (the 26.27% cost reduction and the feasibility of dispatch) currently rest on this assumption. I ask the authors to either incorporate battery-energy constraints (or a conservative energy limit) in the dispatch model, or to reframe the quantitative claims as an idealized upper bound and add a sensitivity study with respect to available vehicle energy.
[Section IV, IEEE 14-bus results and Table I] The numerical evidence for the economic benefit is based on a single synthetic transportation network with weights randomly drawn between 1 and 12 and cost coefficients 'designed' so that neither term dominates. No comparison is made against a no-vehicle baseline, stationary batteries, or the mobile-storage formulations cited in [5], [6], and no sensitivity analysis is reported. The 26.27% cost reduction should therefore be presented as an illustrative example rather than a validated performance claim. I recommend adding multiple random instances, a small sensitivity study over weights and cost coefficients, and at least one baseline comparison.

minor comments (3)

[Section II, paragraph after Eq. (7)] The notation R_v = {(i,j) | x*_ij = 1} is correct only if the routing problem is repaired so that the selected edges actually form an s–e path; please add a sentence clarifying that this set is the intended route after the missing constraints are included.
[Algorithm 1] The output list includes e_v, but e_v is not defined until Eq. (15); please move or define the notation before the algorithm or add a pointer to Eq. (15).
[Table I and Section IV] Table I reports only the solve time for the dispatch MILP (14); please state explicitly whether the offline routing solves of problem (6) are included in any of the reported times, and if not, what their total computational cost is.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the optimization derivations are self-contained and the McCormick exactness argument is proved in the paper.

full rationale

The paper's central derivation chain is not circular. The routing problem (6) produces travel costs from network weights, and the dispatch MILP (14) uses those costs plus generator cost functions to minimize total operating cost; the reported 26.27% cost reduction is an output of the optimization, not a fitted target. The exactness claim for the McCormick relaxation is argued directly in the text: if z_v^i = 0, inequalities (13a) and (13c) force y_v^i = 0, and if z_v^i = 1, inequalities (13b) and (13d) force y_v^i = p_v, so the linear relaxation exactly represents the bilinear product p_v z_v^i. This is a standard mathematical property and does not assume the conclusion. The cited references, including the authors' own prior work, are used only as background for the McCormick relaxation and are not load-bearing. The routing layer has a possible correctness issue: constraints (1)-(5) do not explicitly require the route to reach the destination e, so a cycle through s could satisfy the constraints. However, that is an internal modeling flaw, not a circularity, because the predicted route cost is not equivalent to an input by construction. Overall, no step reduces the claimed result to its own assumptions.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The model introduces no new physical entities. It uses standard power system and transportation modeling components. The main ledger items are the simplified behavioral assumptions about vehicle batteries and the synthetic network parameters that drive the numerical results.

free parameters (3)

Transportation network weights w_ij = randomly assigned between 1 and 12
The routing costs and therefore the dispatch decisions depend on these arbitrary edge weights; no real road network data is used.
Generator and vehicle cost coefficients = not specified numerically
The 26.27 percent cost reduction is a function of the chosen linear cost coefficients, which are described only as 'different cost coefficients' and not released.
Vehicle generation limits = p_a=20MW, p_b=20MW, p_c=40MW
These capacity values are chosen to make vehicle capacity comparable to generator capacity, but they are test-specific assumptions.

assumptions (4)

domain assumption DC power flow model (Eq. 9)
Line flows are linearized as b_ij(theta_i - theta_j), ignoring reactive power and losses. This is a standard approximation in transmission planning.
domain assumption Assumption 1: ignore battery state of charge and discharging efficiency
The model assigns a fixed nominal power p_v to each vehicle regardless of its actual energy content, which is required for tractability but is a strong simplification.
domain assumption Transportation and power networks share the same node set
Section II states this is 'a widely used assumption' to simplify modeling; in practice the networks have different topologies and geographies.
domain assumption Vehicles can arrive within the operational time frame
Section III assumes travel time is negligible relative to the dispatch interval, so routing is decoupled from temporal grid constraints.

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Cite this review

Pith. "Pith review of Exploring the Use of Autonomous Unmanned Vehicles for Supporting Power Grid Operations." pith.science (2026). https://pith.science/paper/ZV5RQ5KE

@misc{pith2026241109783,
  author       = {Pith},
  title        = {Pith review of: Exploring the Use of Autonomous Unmanned Vehicles for Supporting Power Grid Operations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZV5RQ5KE}},
  note         = {Machine review of arXiv:2411.09783}
}

read the original abstract

This paper explores the use of autonomous unmanned vehicles to support power grid operations. With built-in batteries and the capability to carry additional battery energy storage, the rising number of autonomous vehicles can represent a substantial amount of capacity that is currently underutilized in the power grid. Unlike traditional electric vehicles that require drivers, the operations of autonomous vehicles can be performed without human intervention. To guide idle vehicles to autonomously support power grids, we propose a tractable optimization-based method to effectively integrate these "mobile batteries" into grid operations. During real-time operations, the vehicles are strategically routed to target locations to maintain power balance and reduce operating costs. Numerical studies have confirmed both the validity and the scalability of the proposed algorithm to efficiently integrate autonomous vehicles into routine power system operations.

Figures

Figures reproduced from arXiv: 2411.09783 by the authors.

**Figure 2.** The optimal route of a vehicle in a 10-node network [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** A synthetic 14-node meshed transportation network. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: The minimum total travel costs of vehicles [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: Optimal routes for candidate autonomous vehicles. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 15 canonical work pages

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [5]

Enhancing distribution system resilience with mobile energy storage and microgrids,

J. Kim and Y . Dvorkin, “Enhancing distribution system resilience with mobile energy storage and microgrids,” IEEE Transactions on Smart Grid, vol. 10, no. 5, pp. 4996–5006, 2018

work page 2018

[2] [6]

Optimal management of mobile battery energy storage as a self-driving, self-powered and movable charging station to promote electric vehicle adoption,

H. Saboori, S. Jadid, and M. Savaghebi, “Optimal management of mobile battery energy storage as a self-driving, self-powered and movable charging station to promote electric vehicle adoption,” Energies, 2021

work page 2021

[3] [1]

[Online]

Waymo robotaxi services available to public in Los Angeles. [Online]. Available: https://waymo.com/waymo-one-los-angeles/

work page

[4] [2]

Integration of electric vehicles in the electric power system,

J. A. P. Lopes, F. J. Soares, and P. M. R. Almeida, “Integration of electric vehicles in the electric power system,” Proceedings of the IEEE, vol. 99, no. 1, pp. 168–183, 2010

work page 2010

[5] [3]

Autonomous distributed V2G (vehicle-to-grid) satisfying scheduled charging,

Y . Ota, H. Taniguchi, T. Nakajima, K. M. Liyanage, J. Baba, and A. Yokoyama, “Autonomous distributed V2G (vehicle-to-grid) satisfying scheduled charging,” IEEE Transactions on Smart Grid , vol. 3, no. 1, pp. 559–564, 2011

work page 2011

[6] [4]

Dominated GSO algorithm for optimal scheduling of renewable microgrids with penetration of electric vehicles and energy storages considering DRP,

N. Taghizadegan, S. Cheshmeh Khavar, A. Abdolahi, F. Arasteh, and R. Ghoreyshi, “Dominated GSO algorithm for optimal scheduling of renewable microgrids with penetration of electric vehicles and energy storages considering DRP,” International Journal of Ambient Energy , vol. 43, no. 1, pp. 6380–6391, 2022

work page 2022

[7] [7]

Design and optimization of electric autonomous vehicles with renewable energy source for smart cities,

P. Zhou, C. Wang, and Y . Yang, “Design and optimization of electric autonomous vehicles with renewable energy source for smart cities,” in IEEE Conference on Computer Communications , 2020, pp. 1399–1408

work page 2020

[8] [8]

Electric autonomous mobility- on-demand: Jointly optimal vehicle design and fleet operation,

F. Paparella, T. Hofman, and M. Salazar, “Electric autonomous mobility- on-demand: Jointly optimal vehicle design and fleet operation,” IEEE Transactions on Intelligent Transportation Systems , 2024

2024