Models of Electric Vehicle Charging Demands in Distribution Grid Operation: A Review

I. INTRODUCTION

• EVCD models based on mobility, arrival and departure times, battery state of charge, or required energy have often been developed outside PDS operation.The review focuses on models that explicitly formulate EVCD and integrate it into DOPF.Source: §I · p. 1
• The literature search covered five databases and included publications from 2018 onward.Searches used combinations of EVCD-related terms across titles, abstracts, and keywords.Source: §I · p. 1

II. EVCD MODELING: OVERVIEW AND CLASSIFICATION

• Deterministic models use EV characteristics or historical data to produce EVCD as a known DOPF input, while practical systems lack complete information about EV parameters.Deterministic models are computationally simple but may not reflect real-world variability.Source: §II · pp. 1–2
• EVCD models are classified as deterministic or uncertainty-aware, with uncertainty-aware formulations using stochastic, robust, chance-constrained, or distributionally robust optimization paradigms.Uncertainty may be exogenous or induced by system-level decisions.Source: §II · p. 2

III. MATHEMATICAL MODELS USED IN DOPF

• Inadequately representing spatiotemporally variable EV charging loads may produce suboptimal dispatch and potentially compromise secure PDS operation.The review focuses on studies that explicitly integrate EVCD models into DOPF.Source: §III · p. 2
• The section presents the principal modeling approaches for integrating EVCD into DOPF.Fig. 2 is identified as a taxonomy of EVCD models in DOPF.Source: §III · p. 2, Figure 2 · p. 2
• The review frames EVCD representation as necessary for DSO operational decision-making.Its stated focus is EVCD models explicitly formulated within DOPF.Source: §III · p. 2

1) Attribute-Based EVCD models:

• In centralized optimization, the DSO has the information to determine EVCD and jointly formulates its model with DOPF for unidirectional or bidirectional charging.The reviewed formulations model EV characteristics including charging and discharging behavior and SOC constraints.Source: 1) Attribute-Based EVCD models · p. 2
• In DSO–EVA coordination, the EVA holds EV characteristics, submits fleet energy bids, and coordinates slow and fast charging to reduce peak demand.The DSO obtains aggregated EVCD for each time period through the coordination of interconnected DSO and EVA optimization problems.Source: 1) Attribute-Based EVCD models · p. 3
• In DSO–TSO coordination, traffic-flow dynamics produce a boundary-condition EVCD signal that the DSO can use without direct transportation-system information.The DSO and TSO independently optimize the PDS and transportation system, respectively, and exchange information through a coordination interface.Source: 1) Attribute-Based EVCD models · p. 3

2) ML-Based Predictive Models:

• ML-based predictive models forecast future EVCD from historical load data and use the forecast as a known DOPF parameter.The described procedure has a training phase to estimate model parameters and an inference phase to forecast demand over the dispatch horizon.Source: 2) ML-Based Predictive Models · p. 3
• Forecasting approaches include supervised, unsupervised, deep-learning, ensemble, and transfer-learning methods for demand prediction or characterization.Examples include linear regression, random forests, ARIMA, clustering, LSTM, generative models, neural networks, CNNs, and transformers.Source: 2) ML-Based Predictive Models · p. 3
• Deep-learning architectures have been proposed for spatiotemporal EVCD forecasting because of their capacity to capture nonlinear temporal dependencies.Source: 2) ML-Based Predictive Models · p. 3

• EVCD uncertainty reflects variability in electricity price, SOC, AT, DT, and EV-owner preferences and decisions.Source: B. Uncertainty-aware Models · p. 3
• The review classifies uncertainty-aware EVCD models into four categories according to their underlying solution methodology.Source: B. Uncertainty-aware Models · p. 3
• A range of modeling approaches has been proposed to capture these uncertainties.Source: B. Uncertainty-aware Models · p. 3

1) SO Model:

• SO models treat arrival time, departure time, required charging energy, and initial SOC as random variables with known distributions.Examples include Poisson, uniform, normal, lognormal, and truncated normal distributions.Source: 1) SO Model · p. 3
• Monte Carlo simulation generates scenarios from the known distributions, and the DSO formulates a two-stage stochastic problem.Source: 1) SO Model · p. 3

2) RO Model:

• RO models declare an uncertainty set for uncertain initial EV energy, SOC, or EVCD.Source: 2) RO Model · p. 4
• RO models use historical averages and standard deviations, with Γw indicating the uncertainty budget; total EVCD enters the DOPF power balance,,,,.Source: 2) RO Model · p. 4

3) CCO Model:

• CCO models use probabilistic constraints for uncertain driving distance, charging availability, aggregate power injection, and EV-owner response.Source: 3) CCO Model · p. 4
• These chance constraints enforce operational feasibility up to a specified confidence level.Source: 3) CCO Model · p. 4
• Tractable formulations use deterministic reformulation, CVaR approximation, or binary-variable representations.Source: 3) CCO Model · p. 4

4) DRO Model:

• DRO and DRCCO optimize worst-case expectations or chance constraints over an ambiguity set instead of assuming a fully known distribution.Source: 4) DRO Model · p. 4
• Ambiguity sets may be characterized by moments, 1-norm or inf-norm divergence, Wasserstein distance, or KL divergence.Source: 4) DRO Model · p. 4
• The moment-based set uses empirical EVCD mean and covariance, with γ1 ≥ 0 and γ2 ≥ 1 reflecting confidence in those estimates.Source: 4) DRO Model · p. 4
• The chance constraint uses uncertain variables, lower and upper bounds, and violation level ϵ, and is reformulated into deterministic tractable equations using the ambiguity set.Source: 4) DRO Model · p. 4

IV. RESEARCH GAP AND DISCUSSION

• Most uncertainty-aware models treat EVCD as independent of DSO decisions, although pricing and dispatch signals influence charging behavior; decision-dependent formulations remain scarce.The review cites,,, and for exogenous uncertainty, and,,, and [32] for emerging endogenous formulations.Source: §IV · p. 4
• Most models assume homogeneous EV owners; explicit behavioral heterogeneity in coupled EVCD-DOPF frameworks remains largely absent.Survey data and willingness-to-charge formulations appear in isolated efforts.Source: §IV · p. 4
• Transportation–power interactions appear in deterministic EVCD studies, while uncertainty-aware formulations have largely omitted transportation-system dynamics.The review cites for studies accounting for TS-PDS interactions, and and for uncertainty-aware formulations that largely omit TS dynamics.Source: §IV · p. 5
• No generalized EVCD formulation currently encompasses all relevant parameters and system interactions.The review calls for uncertainty-aware models integrating behavioral heterogeneity and explicit TS-PDS coupling within a unified DOPF framework.Source: §IV · p. 5

V. CONCLUSION

• The review examines EVCD modeling and DOPF integration exclusively from the DSO’s perspective, classifying literature by EVCD representation and solution methodology.Source: §V · p. 5
• EVCD remains difficult to model because charging demand depends on interdependent parameters across systems, and no consensus exists on deterministic, exogenous-uncertainty, or endogenous-uncertainty representations.Source: §V · p. 5
• The review provides a structured reference for researchers and a foundation for developing a unified EVCD modeling framework.Source: §V · p. 5