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Optimal Control Strategies for a Network of Electric Vehicle Charging Energy Hubs with Smart Scheduling via Distributed Optimization
Diego Fernandez-Zapico, Finn Vehlhaber, Maedeh Izadi, Theo Hofman, Mauro Salazar
TL;DR
The paper addresses how to coordinate physically interconnected charging hubs while optimizing both inter-hub exchanges and internal EV charging. It formulates a convex optimal-control problem and decomposes it for distributed ADMM solution; in the reported comparison, V1G reduces electricity costs and emissions relative to the baseline.
Problem
The paper addresses the lack of distributed coordination methods that jointly optimize inter-hub power exchange and internal hub management, including shapeable EV charging loads.
Source: §I · pp. 1–2Method
A convex optimal-control formulation optimizes EV charging and hub/grid power exchanges, with a hub-level ADMM decomposition coordinating inter-hub exchanges through limited information sharing.
Source: §I · pp. 1–2Results
30% reduction in total electricity cost and 25% reduction in total electricity emissions during evaluation for V1G compared with the Baseline.
Source: A. V1G Performance · p. 5Takeaways & Limitations
The convex formulation guarantees global optimality, while its ADMM decomposition supports distributed solution for large networks while preserving privacy.
Source: §VI · pp. 5–6
Abstract
from arXiv · showhide
This paper studies the cost-optimal operation of a network of charging energy hubs for electric vehicles, which provide onsite renewable energy sources and stationary battery storage and are connected with each other via DC-lines as well as with the distribution grid. Specifically, we first formulate a dynamic optimal control problem for the entire network as a convex quadratic program, whereby the charging power profiles of the individual vehicles and the energy flows between hubs and the grid are subject to optimization. Second, we propose a problem decomposition that allows for a distributed solution via ADMM algorithms that preserves global optimality guarantees and privacy of the individual stations. We showcase our framework on a case-study for the Netherlands considering a two-day ahead deterministic formulation with perfect foresight. Our results show that compared to the case where charging powers are fixed a priori, optimizing their profiles (V1G) can significantly reduce the operational costs and emissions by more than 25%. Moreover, we verify our distributed algorithm against a centralized solution, paving the way to the optimal operation of large networks and online implementations.
I. INTRODUCTION
Interconnected Charging Energy Hubs can flexibly coordinate power but raise coordination and privacy challenges. The paper formulates their operation as a convex optimization problem and decomposes it for distributed hub-level coordination.
I. INTRODUCTION
- Interconnected hubs offer additional flexibility to transfer power, while creating coordination challenges alongside privacy concerns about information sharing.The broader motivation is to operate and design charging infrastructure amid transport electrification and renewable-energy development.Source: §I · p. 1
- The framework targets the gap of jointly optimizing inter-hub power exchange and internal management, including shapeable EV charging loads, across physically interconnected hubs.The distributed formulation coordinates inter-hub exchanges with limited information sharing.Source: §I · p. 2
- The proposed convex optimal-control formulation optimizes EV charging profiles and power exchanges among hubs and with the main grid.A hub-level ADMM decomposition seeks consensus on inter-hub exchanges with limited information sharing.Source: §I · p. 2
II. CHARGING ENERGY HUB NETWORK
- A Charging Energy Hub network combines hubs with onsite generation and battery storage, connected to each other and the power grid.The network is modeled as a directed graph whose vertices are hubs and whose edges are DC interconnections.Source: §I · p. 1, §II · p. 2
A. BESS
The battery model represents losses, storage dynamics, and operating bounds, and uses an epigraph relaxation to introduce convexity.
A. BESS
- The battery model uses a constant efficiency to represent BESS losses and describes battery dynamics with a discrete linear expression.The initial battery value is set to its minimum operational level.Source: A. BESS · p. 2
- The external battery-power constraint can be relaxed to its epigraph to introduce convexity.Source: A. BESS · p. 2
- Battery energy is constrained between minimum and maximum operational levels, and battery output power is also constrained.Source: A. BESS · p. 2
B. Optimized EV Charging Power
The formulation shapes charging for individual EV sessions while modeling grid purchases and sales at day-ahead prices.
B. Optimized EV Charging Power
- Each EV session’s requested energy must be fully delivered, with charging power optimized within the session and constrained by its availability.Charging is restricted to the scheduled connection and disconnection window.Source: B. Optimized EV Charging Power · pp. 2–3
C. Power Grid
- Grid exchanges allow buying and selling at hourly day-ahead electricity prices under an assumption of perfect efficiency.The grid-power variable is constrained, and the cost model uses a losslessly relaxed convex version.Source: C. Power Grid · p. 3
D. Solar Plant
The model treats photovoltaic output as an input, then optimizes network operation over time using electricity cost and profile-smoothing terms.
D. Solar Plant
- Photovoltaic power after accounting for losses is treated as an exogenous model input.Source: D. Solar Plant · p. 3
III. CENTRALIZED OPTIMIZATION
- The centralized objective covers all time steps and combines total electricity cost with regularization terms intended to smooth EV-charging and interconnection power profiles.The hub-connection regularization has its own weight.Source: §III · p. 3
- The V1G problem optimizes EV charging profiles, while the baseline fixes charging at each session’s average power and optimizes battery and interconnection power.The baseline does not control EV charging power.Source: §III · p. 3
IV. DISTRIBUTED OPTIMIZATION
The distributed formulation lets each hub retain its local information while coordinating shared inter-hub power flows through consensus. ADMM solves hub-level subproblems and iterates on the shared variables until the stopping criteria are met.
IV. DISTRIBUTED OPTIMIZATION
- Each hub keeps its local parameters and variables private; a central collector seeks consensus among local versions of shared inter-hub power flows.The formulation distinguishes each hub's private flow variable from the public shared version.Source: §IV · p. 3
- The local objectives are separated by hub, and the interconnection regularization term depends only on public variables.The formulation defines private and public versions of each inter-hub flow.Source: §IV · p. 3
- ADMM separates the optimization into hub-level subproblems while preserving equivalence to Problem 1 and requiring hubs to share only local inter-hub flows and associated dual values.A collector updates the public shared variables until convergence.Source: §IV · pp. 3–4
- The iterative procedure enforces feasibility of shared-flow elements and checks primal and dual residual stopping criteria against fixed tolerances.The primal criterion uses stacked shared-flow variables and absolute and relative tolerances; the dual criterion uses the stacked dual variable.Source: §IV · p. 4
V. CASE STUDY RESULTS
The case study evaluates a three-hub charging network using Dutch EV-user data and electricity and weather inputs. It uses a two-day-ahead optimization with 15-minute steps and perfect knowledge of the listed inputs.
V. CASE STUDY RESULTS
- The case study uses three hubs connected by two edges; hub 1 has all components, hub 2 lacks a main-grid connection, and hub 3 lacks a BESS and PV panels.The network has hubs 1, 2, and 3, with connections (1, 2) and (1, 3).Source: §V · p. 4
- The case study uses real-life EV-user data from the Netherlands, historical Dutch weather from Open-Meteo for PV production, and reduces charging sessions per evaluation day for hubs 2 and 3.Source: §V · p. 4
- Evaluation covers 30 days in 2025 at 15-minute resolution, with a two-day-ahead horizon of 192 steps and each day initialized at 11:00.The study assumes perfect knowledge of PV production, day-ahead prices, and EV energy demand.Source: §V · p. 4
- The reported comparison covers total electricity cost and emissions for V1G and the baseline over a 30-day evaluation.Source: Figure 2 · p. 4
A. V1G Performance
Optimizing EV charging profiles reduces total electricity cost and emissions relative to the baseline. The reported results also show greater reductions at the hub with higher capacity to sell power to the grid, while charging profiles respond to within-session prices.
A. V1G Performance
- Hub 1 has greater cost and emissions reductions than the other hubs, and it has higher capacity to sell power to the main grid.Source: A. V1G Performance · p. 5
- The sample-day charging profiles show higher EV charging power when within-session prices are lower.The paper presents optimal V1G charging profiles for hub 1.Source: A. V1G Performance · p. 5, Figure 3 · p. 5
- 30% lower total electricity cost and 25% lower total electricity emissions are reported for V1G versus the baseline during the 30-day evaluation.Source: Table II · p. 5, A. V1G Performance · p. 5
B. ADMM Convergence
The section evaluates ADMM’s agreement with the centralized solution using normalized mean absolute error and reports residual-based stopping criteria. Average error is below 1% across optimization variables, with a 2.4% worst case for BESS power injections at hub 2.
B. ADMM Convergence
- For the distributed optimization in Problem 3, ADMM uses ρ = 2 and εrel = εabs = 10−3; its stopping criteria are reported for an evaluation day in Fig. 4.Source: B. ADMM Convergence · p. 5
- Average daily nMAE is below 1% for all optimization variables on the evaluation day.The error is normalized using the corresponding maximum value, and the section also reports average, maximum, and minimum nMAE.Source: B. ADMM Convergence · p. 5
- 2.4% is the worst-case error, for BESS power injections on hub 2.This is the reported worst case during the evaluation.Source: B. ADMM Convergence · p. 5
- For an evaluation day, Fig. 4 presents ADMM convergence at the method’s stopping criteria, while Fig. 5 shows optimal CEH Network operation, including all component variables.Source: Figure 4 · p. 5, B. ADMM Convergence · p. 5
VI. CONCLUSION
The conclusion reports that optimizing EV charging profiles can substantially reduce energy costs relative to fixed-power profiles. The convex formulation and ADMM decomposition preserve global optimality while supporting distributed operation and privacy; receding-horizon operation with stochastic predictions is left for future work.
VI. CONCLUSION
- Optimizing EV charging profiles substantially reduces energy costs compared with fixed-power profiles.The conclusion states this result without giving a numerical reduction in the supplied passage.Source: §VI · p. 5
- The convex formulation guarantees global optimality, and its ADMM decomposition supports distributed solution of large networks while preserving privacy.The decomposition coordinates hubs through distributed optimization.Source: §VI · p. 6
- Receding-horizon implementation with stochastic predictions is identified as future work.The authors also propose studying coordination among multiple hub owners using the algorithm’s privacy-preserving features.Source: §VI · p. 6
DECLARATION ON GENERATIVE AI
The authors report using LLMs to improve the clarity and structure of some sections.
DECLARATION ON GENERATIVE AI
- LLMs were used to improve the clarity and structure of some sections.The statement is from the declaration on generative AI.Source: DECLARATION ON GENERATIVE AI · p. 6