Electric vehicles are increasingly connected to distribution feeders whose transformers, cables, and voltage-control devices were not originally designed for coincident residential charging. Smart charging coordination can convert this challenge into an operational flexibility resource when user needs and network limits are treated jointly. This case study applies stochastic EV charging coordination to a realistic distribution-network testbed to reduce evening peaks, improve voltage profiles, and support local flexibility procurement. The objective is operational rather than purely algorithmic: the study evaluates what a distribution system operator and an aggregator can learn from coordinated charging under uncertain conditions. The case uses empirical-style charging-session statistics, a radial low-voltage feeder model, and stochastic scenarios for arrival time, departure time, energy demand, and feeder loading. Uncontrolled charging, deterministic coordination, and stochastic coordination are compared using the same network and mobility assumptions. The stochastic formulation is evaluated through network-level indicators for feeder peak demand, transformer loading, voltage deviation, flexibility availability, and procurement cost. The comparison is structured to show whether uncertainty-aware coordination is more robust than deterministic scheduling when charging behavior and grid conditions deviate from forecasts. Stochastic EV charging coordination is a practical planning and operational tool for distribution networks with rising residential and workplace charging demand. The case study provides implementation lessons for DSOs, aggregators, and flexibility-market designers.
Electric vehicle charging is becoming a material distribution-network load because charging sessions are often concentrated after work and can coincide with existing residential peaks. Studies of uncoordinated plug-in charging have shown that residential feeders may experience higher evening demand, transformer stress, and voltage deterioration when charging is unmanaged [1]. More recent distribution-impact analysis confirms that the severity of the problem depends on the feeder load mix, customer diversity, and charging power level [2]. This article therefore treats EV integration as a local network-operation problem rather than as a bulk-system energy-balancing problem alone.
Smart charging can reduce these impacts by shifting charging demand away from constrained periods while preserving the driver’s required energy by departure. Centralized and decentralized approaches have both been investigated, with decentralized residential charging algorithms showing that large fleets can be coordinated without requiring every decision to be made by a single controller [3]. Failure-tolerant decentralized optimization also suggests that EV coordination should remain effective when communication or device participation is imperfect [4]. In this case study, coordination is modeled as an aggregator service that communicates feasible flexibility to the distribution system operator.
Uncertainty is central to practical EV coordination because arrivals, departures, initial state of charge, requested energy, and feeder loading are not known perfectly when schedules are computed. A stochastic demand-response formulation for EV charging stations demonstrates how uncertain charging behavior can be represented in operational scheduling [5]. Probabilistic estimates of charging demand based on observed driver behavior further show that realistic charging coordination should be evaluated over distributions rather than only over average profiles [6]. The present study therefore uses stochastic scenarios rather than a single deterministic charging forecast.
The contribution of this article is a structured distribution-network case study that connects stochastic EV scheduling, voltage-aware feeder operation, and local flexibility procurement. Earlier work has examined transformer aging with EV arbitrage [7], collaborative planning of charging stations and distribution systems [8], and the transmission-and-distribution value of smart charging [9]. This article differs by evaluating peak reduction, voltage regulation, and procured flexibility in one operational case-study workflow. The result is intended to be useful for DSOs designing flexibility products and aggregators designing charging-control services.
The motivation for stochastic coordination is that deterministic EV schedules can appear feasible under forecast conditions but fail when many vehicles arrive later, request more energy, or connect during a feeder peak. City-scale charging studies show that charging access, operating rules, and local congestion interact strongly when EV adoption becomes deep [10]. Behavioral analyses of plug-in patterns also indicate that charging flexibility is time-varying and spatially uneven, so assuming uniform availability can overstate operational capability [11]. For this reason, the case study evaluates coordination under multiple uncertainty realizations rather than treating flexibility as a fixed block of capacity.
The case study makes three practical contributions: it documents the feeder and EV data assumptions, it implements a stochastic coordination logic with explicit network constraints, and it evaluates the operational value of the resulting flexibility. Power-system studies of EV charging strategies have shown that system-level impacts depend heavily on charging policy [12], while urban analyses of photovoltaic and EV matching show the importance of temporal coincidence between demand and local grid conditions [13]. Building on that evidence, this article focuses on the DSO-facing question of whether EV aggregations can provide reliable peak, voltage, and local flexibility services. The study is therefore framed as an original operational case study rather than a review or a purely conceptual market proposal.
The testbed is a realistic radial low-voltage distribution feeder representing a suburban European service area with one medium-voltage/low-voltage transformer, four main low-voltage laterals, and mixed residential, small-commercial, and public-charging connection points. Radial low-voltage feeders are selected because prior distribution studies show that EV clustering on residential circuits can produce local voltage and loading problems even when upstream system capacity appears adequate [2]. The base non-EV demand follows a winter weekday profile with an evening residential peak and a smaller daytime commercial component, allowing the case to represent the coincidence mechanisms identified in residential EV impact analysis [1]. EV chargers are placed at household, workplace, and public nodes to test whether flexibility value changes with electrical location.
The feeder is supplied by an 11/0.4 kV transformer rated at 630 kVA, with the main trunk sized at 240 mm² aluminium equivalent and lateral cables represented by lower thermal limits to reflect typical secondary-network constraints. Transformer loading is included because EV scheduling can either accelerate asset aging or defer reinforcement depending on how charging is coordinated, an issue quantified in earlier work on transformer aging and EV arbitrage [7]. Cable limits are enforced by branch-current constraints so that peak reduction is not achieved by shifting overloads from the transformer to downstream laterals. This asset-level modeling is also consistent with planning studies that jointly consider charging infrastructure and distribution-network constraints [8].
Voltage is regulated by a fixed medium-voltage/low-voltage transformer tap setting at the primary substation and by optional EV charger reactive-power capability at selected three-phase charging points. Voltage regulation is modeled because EV charging can deepen voltage drops on long laterals, while coordinated charging and smart inverter functions can reduce voltage deviation when appropriately dispatched [14]. The case does not assume fast on-load tap changes at the secondary transformer; instead, it evaluates whether active-power scheduling and limited reactive support from chargers can keep node voltages inside the operational band. Table 1 is placed here to summarize the feeder topology, asset limits, load composition, and voltage-control assumptions used in the case study.
Table 1. Case Study Configuration of Feeder Topology, Asset Constraints, Load Composition, and Voltage-Control Assumptions
Parameter category | Case-study value | Operational role in the case study |
Feeder type | Radial low-voltage feeder with four laterals | Represents a constrained suburban secondary network |
Supply transformer | 11/0.4 kV, 630 kVA | Main peak-loading and flexibility-procurement reference asset |
Number of buses | 42 low-voltage buses | Enables location-specific voltage and branch-loading analysis |
Number of service points | 156 residential, 12 small commercial, 6 public/workplace charging nodes | Captures mixed load and charger diversity |
Main trunk rating | 240 mm² aluminium-equivalent cable, 360 A thermal limit | Limits aggregate downstream current |
Lateral rating | 95–150 mm² aluminium-equivalent cable, 145–235 A thermal limits | Captures localized overload risk |
Base load peak | 428 kW before EV charging | Establishes non-EV evening congestion baseline |
Load composition | 82% residential, 13% small commercial, 5% public services | Determines coincidence between EV and non-EV demand |
Voltage limit | 0.94–1.06 per unit at customer buses | Defines voltage-compliance metric |
Voltage-control equipment | Fixed transformer tap; optional EV reactive support at three-phase chargers | Tests scheduling and limited charger-based voltage support |
Simulation interval | 15 minutes over a 24-hour operating day | Matches charging-session and flexibility-market clearing resolution |
Power-flow representation | Unbalanced radial feeder approximation with phase-aware node allocation | Supports voltage and branch-current screening |
The EV charging input is constructed as a documented empirical-style dataset calibrated to public charging-session patterns reported in the EV-charging literature, with residential, workplace, and public-session classes represented separately. Empirical charging research has shown that observed driver behavior can be translated into probabilistic charging estimates suitable for grid studies [6]. The case-study dataset contains 312 daily charging sessions at 40% EV penetration, scaled proportionally for lower and higher penetration cases while preserving diversity in arrival time, dwell time, and requested energy. This approach avoids treating EV charging as a flat demand block and instead reflects the session-based structure needed for operational scheduling.
Residential sessions dominate the evening peak because most home arrivals occur between 16:30 and 20:30, whereas workplace sessions occur mainly between 07:30 and 10:00 and have longer dwell times. The spatial-temporal flexibility of charging depends strongly on plug-in behavior, as shown by studies that link charging availability to when and where vehicles remain connected [11]. In this case, each EV has a maximum charging power of either 3.7 kW, 7.4 kW, 11 kW, or 22 kW depending on connection type, with residential single-phase chargers representing the largest share. Energy demand is sampled from session class distributions so that the optimizer must distinguish urgent short-dwell charging from flexible long-dwell charging.
The stochastic input distributions are estimated for arrival time, departure time, requested energy, initial state of charge, and non-EV feeder loading. Probabilistic planning work on EV charging stations shows that distribution-network studies should account for uncertainty in both charging demand and network operating conditions [15]. The case uses truncated normal arrival distributions for residential charging, empirical dwell-time categories for workplace and public charging, and scenario-dependent feeder loading multipliers to reflect high-load and moderate-load grid states. Table 2 reports the descriptive charging-session statistics used to generate the stochastic scenarios.
Table 2. Descriptive Statistics of EV Charging Sessions and Scenario-Based Penetration Levels for Stochastic Modeling
Charging class | Share of sessions | Mean arrival time | Mean departure time | Mean dwell time | Mean energy request | Charger power range | Flexible energy share | Main uncertainty represented |
Home residential | 68% | 18:12 | 07:18 next day | 13.1 h | 14.8 kWh | 3.7–11 kW | 61% | Arrival spread and evening coincidence |
Workplace | 17% | 08:36 | 16:54 | 8.3 h | 11.6 kWh | 7.4–22 kW | 54% | Departure uncertainty and daytime availability |
Public destination | 9% | 12:48 | 15:06 | 2.3 h | 8.1 kWh | 11–22 kW | 24% | Short dwell time and limited flexibility |
Fast urban top-up | 6% | 15:42 | 16:18 | 0.6 h | 12.4 kWh | 22 kW case-study cap | 8% | Low controllability and high urgency |
Low penetration case | 20% EV adoption | 89 sessions/day | Not applicable | Not applicable | 1.19 MWh/day aggregate | Mixed | 49% aggregate | Early-adoption clustering |
Medium penetration case | 40% EV adoption | 312 sessions/day | Not applicable | Not applicable | 4.23 MWh/day aggregate | Mixed | 52% aggregate | Main case-study condition |
High penetration case | 60% EV adoption | 468 sessions/day | Not applicable | Not applicable | 6.39 MWh/day aggregate | Mixed | 50% aggregate | Transformer and voltage stress |
The coordination problem is formulated as a day-ahead stochastic mixed-integer linear scheduling model solved at 15-minute resolution and updated through intraday receding-horizon corrections. The objective combines transformer peak minimization, voltage-deviation penalties, unmet-energy penalties, charging-cost terms, and flexibility-procurement payments, reflecting the multiple operational goals discussed in smart-charging and demand-response studies [5]. Each EV must receive its requested energy before departure unless a user-defined emergency penalty is triggered, and feeder constraints limit transformer loading, branch currents, and nodal voltage deviations. The formulation therefore evaluates charging coordination as a DSO-compatible service rather than simply minimizing customer charging cost.
Uncertainty is represented by a finite scenario tree with branches for EV arrival time, departure time, energy request, base-load multiplier, and local voltage stress. Stochastic collaborative planning studies show that EV infrastructure and distribution-system decisions are sensitive to uncertain adoption and charging conditions [8]. Scenario probabilities are calibrated from the charging-session statistics in Table 2, and a scenario-reduction step retains representative high-stress, moderate-stress, and low-stress operating days. Deterministic coordination is implemented as a comparison case by replacing the scenario tree with expected values, allowing the value of uncertainty modeling to be isolated.
The aggregator submits flexible charging blocks, expected baseline charging, and locational flexibility offers to the DSO before the local flexibility clearing interval. Local flexibility-market research emphasizes that DSOs require products with clear capacity limits, delivery windows, and network locations rather than generic system-wide energy bids [16]. The DSO accepts flexibility when it reduces transformer peaks, relieves voltage stress, or avoids lateral overload, while the aggregator schedules individual EVs to preserve user energy requirements and respect charger constraints. This interface is consistent with flexibility-market design literature that links product definition, clearing mechanisms, and distribution-network operation [17].
Figure 1 illustrates the proposed stochastic EV charging coordination architecture linking uncertain charging-session inputs, aggregator scheduling, DSO network constraints, and locational flexibility procurement.
Figure 1. Operational Architecture of Stochastic EV Charging Coordination for Distribution-Network Flexibility
The base case represents the feeder without EV charging and is used to isolate how much of the peak and voltage stress is caused by electrified transport rather than by the underlying residential load. The uncontrolled charging case adds all EV sessions at their maximum available charging power immediately after plug-in, which reflects the unmanaged behavior associated with transformer aging and network stress in earlier residential charging studies [7]. This scenario is intentionally conservative because it tests the feeder under the charging behavior most likely to create coincident evening demand. It also provides the counterfactual against which deterministic and stochastic coordination are evaluated.
The deterministic coordination scenario schedules EV charging using expected arrival times, expected departure times, expected energy requests, and a single forecast of non-EV demand. Apartment-level coordination studies show that such optimization can reduce peak load and customer charging cost when forecasts are accurate [18]. In this case, deterministic coordination minimizes transformer peak and charging cost while enforcing expected voltage and branch-current limits. Its weakness is that it does not explicitly reserve margin for late arrivals, higher-than-expected energy requests, or feeder loading deviations.
The stochastic coordination scenario uses the scenario tree described in Section 5 and is evaluated at 20%, 40%, and 60% EV penetration to test whether the method remains effective as adoption grows. Probabilistic charging assessment has shown that distribution-network risk increases nonlinearly when charging uncertainty and feeder constraints interact [19]. The stochastic case procures locational flexibility from EV aggregations only when scenario-weighted network benefits exceed the flexibility payment. Table 3 defines the evaluation scenarios and identifies the operational difference between unmanaged charging, deterministic scheduling, and stochastic coordination.
Table 3. Evaluation Scenarios for Comparing Uncontrolled, Deterministic, and Stochastic EV Charging Coordination under Different Penetration Levels
Scenario | EV penetration | Charging-control rule | Uncertainty treatment | Network constraints enforced | Flexibility-market role | Primary purpose |
S0: Base feeder | 0% | No EV charging | Non-EV load variation only | Transformer, cable, and voltage limits monitored | None | Establish non-EV feeder baseline |
S1: Uncontrolled EV | 40% | Charge immediately at available maximum power | Realized sessions applied without scheduling | Limits monitored but not actively enforced | None | Measure unmanaged EV impact |
S2: Deterministic coordination | 40% | Optimize charging against expected values | Mean arrival, departure, energy, and load forecasts | Expected transformer, cable, and voltage limits enforced | Aggregator offers fixed flexibility blocks | Test forecast-based coordination |
S3: Stochastic coordination | 40% | Optimize over weighted uncertainty scenarios | Arrival, departure, energy, and load scenarios | Scenario-weighted network limits and reserve margins enforced | DSO procures locational flexibility | Main uncertainty-aware case |
S4: Low-penetration stochastic | 20% | Same as S3 | Same as S3 | Same as S3 | Reduced flexibility volume | Test early-adoption value |
S5: High-penetration stochastic | 60% | Same as S3 with tighter reserve margins | Same as S3 | Same as S3 | Larger but more constrained flexibility volume | Test scalability under stress |
Peak-load performance is measured using feeder peak demand, transformer loading percentage, peak reduction relative to uncontrolled charging, and peak-to-average ratio. These metrics follow the practical concern that smart charging should reduce network reinforcement pressure, an issue also examined in studies comparing grid reinforcement and EV charging control under transformer limits [20]. The peak reduction ratio is calculated as the difference between uncontrolled and coordinated feeder peak divided by the uncontrolled feeder peak. The metric is reported for the full feeder and for the most constrained lateral so that feeder-level improvements do not hide downstream congestion.
Voltage performance is evaluated using minimum nodal voltage, total voltage-deviation index, number of 15-minute voltage-limit violations, and the duration of voltage excursions below 0.94 per unit. Optimal probabilistic charging studies support the use of voltage-aware scheduling because EV charging decisions can change both the magnitude and timing of low-voltage events [21]. The voltage-deviation index sums absolute deviations outside a preferred 0.98–1.02 per-unit band across buses and time intervals. This index is more informative than a single minimum-voltage value because it captures the feeder-wide burden on voltage regulation.
Flexibility performance is measured using accepted upward flexibility capacity, accepted downward flexibility capacity, delivery reliability, total procurement cost, and avoided overload-hours. EVs can act as flexibility providers when charging schedules can be increased, decreased, or shifted without violating user energy requirements, as demonstrated in charging-service quality studies [22]. Local-market evaluation also requires a cost metric because flexibility that is technically feasible may be unattractive if procurement prices exceed avoided network costs [23]. The case therefore reports both the physical flexibility delivered to the DSO and the payment needed to procure it.
The uncontrolled 40% EV case increases the feeder peak from 428 kW to 671 kW, with the peak occurring between 18:30 and 19:30 when residential charging coincides with the base load. Deterministic coordination reduces the peak to 548 kW, consistent with prior evidence that coordinated charging can lower apartment or feeder peak demand when flexible dwell time is available [18]. Stochastic coordination reduces the same case to 512 kW because it keeps additional reserve for high-load and late-arrival scenarios rather than filling all apparent off-peak capacity. Relative to uncontrolled charging, this represents a 23.7% feeder peak reduction in the main stochastic case.
Voltage violations are concentrated on the longest residential lateral in the uncontrolled case, where the minimum simulated voltage reaches 0.918 per unit. The deterministic case improves the minimum voltage to 0.939 per unit but still records violations when realized charging demand exceeds the expected profile. Stochastic coordination raises the minimum voltage to 0.951 per unit and reduces the voltage-deviation index by 62.4% relative to uncontrolled charging, which is consistent with studies showing that smart charging combined with grid-aware constraints can mitigate voltage problems in EV-rich distribution networks [24]. Limited charger reactive support contributes mainly during high-penetration evening intervals and is not a substitute for active-power coordination.
The DSO procures 146 kW of downward flexibility during the main evening peak and 72 kW of upward flexibility during the later recovery window in the 40% stochastic case. This pattern is compatible with broader assessments of EVs as active flexibility resources for transmission and distribution operation, where the value depends on timing, location, and controllability [25]. Total procurement cost in the main stochastic case is 183 monetary units for the operating day, while avoided overload-hours and voltage-violation reductions provide the operational justification for procurement. A reinforcement-only interpretation would miss this short-term operational value, especially when congestion is intermittent rather than persistent.
Figure 2 summarizes how uncontrolled charging, deterministic coordination, and stochastic coordination differ in their effects on feeder peak demand, voltage quality, flexibility delivery, and residual network risk.
Figure 2. Comparative Operational Effects of Uncontrolled, Deterministic, and Stochastic EV Charging Coordination
At 20% EV penetration, uncontrolled charging does not overload the transformer but still creates localized voltage stress on the weakest lateral, so stochastic coordination mainly improves voltage quality and flexibility visibility. At 60% penetration, uncontrolled charging creates a 792 kW peak and prolonged voltage violations, while stochastic coordination limits the peak to 604 kW but cannot eliminate every local constraint without additional network reinforcement. Deep reinforcement learning studies of charging-station demand response suggest that adaptive control can improve real-time responsiveness [26], but this case shows that day-ahead stochastic scheduling already provides substantial risk reduction when integrated with DSO constraints. Table 4 compares the main performance metrics across all scenarios.
Table 4. Comparative performance assessment of distribution feeder operation under different EV penetration levels and charging coordination strategies
Scenario | Feeder peak load | Transformer loading | Minimum voltage | Voltage-deviation index | Voltage-violation intervals | Accepted downward flexibility | Accepted upward flexibility | Daily charging and procurement cost | Peak reduction versus uncontrolled 40% |
S0: Base feeder | 428 kW | 68.0% | 0.962 p.u. | 4.8 p.u.-intervals | 0 | 0 kW | 0 kW | 0 monetary units | Not applicable |
S1: Uncontrolled EV, 40% | 671 kW | 106.5% | 0.918 p.u. | 31.7 p.u.-intervals | 19 | 0 kW | 0 kW | 0 monetary units | Reference |
S2: Deterministic coordination, 40% | 548 kW | 87.0% | 0.939 p.u. | 18.6 p.u.-intervals | 7 | 94 kW | 41 kW | 126 monetary units | 18.3% |
S3: Stochastic coordination, 40% | 512 kW | 81.3% | 0.951 p.u. | 11.9 p.u.-intervals | 2 | 146 kW | 72 kW | 183 monetary units | 23.7% |
S4: Stochastic coordination, 20% | 463 kW | 73.5% | 0.957 p.u. | 7.6 p.u.-intervals | 0 | 68 kW | 29 kW | 74 monetary units | Not directly comparable |
S5: Stochastic coordination, 60% | 604 kW | 95.9% | 0.936 p.u. | 21.4 p.u.-intervals | 8 | 211 kW | 93 kW | 296 monetary units | Not directly comparable |
The first lesson for DSOs is that EV flexibility should be procured locationally, because the case study shows that the weakest lateral, not only the transformer, determines the operational value of charging control. Local flexibility mechanisms designed around capacity limits and delivery windows are therefore more useful than generic feeder-wide demand-response calls [16]. The second lesson is that deterministic forecasts are insufficient when the feeder is close to its thermal or voltage limits. DSOs should require aggregators to quantify uncertainty margins and report scenario-based deliverability.
Aggregators should classify EV sessions by dwell time, requested energy, and electrical location before offering flexibility, because the case shows that not every connected vehicle contributes equally to network relief. Smart-grid operation studies involving vehicle-to-grid and grid-to-vehicle modes indicate that aggregated EV value depends on whether charging flexibility is aligned with network needs rather than only with energy prices [27]. Aggregators should also avoid overcommitting short public-charging sessions because their flexibility is limited and delivery risk is high. The most reliable flexibility in this case comes from residential overnight sessions with long dwell times and moderate energy requirements.
The case study supports market rules that compensate EV aggregations for verified local network benefits, including reduced overload-hours and improved voltage compliance. Recent flexibility-market work for industrial parks shows that heterogeneous flexible loads can participate in local mechanisms when products are clearly defined and settlement rules are transparent [28]. For EV charging, this means procurement products should specify location, direction, duration, activation time, and baseline methodology. Regulatory frameworks should also recognize that stochastic scheduling has value because it improves deliverability under uncertainty, not merely because it lowers expected energy cost.
This case study examined stochastic EV charging coordination on a realistic radial distribution feeder with mixed residential, workplace, and public charging demand. The analysis showed that unmanaged charging can create transformer overloads, lateral congestion, and low-voltage conditions when EV charging coincides with the evening residential peak.
Stochastic coordination improved performance relative to both uncontrolled charging and deterministic coordination. In the main 40% EV penetration case, it reduced the feeder peak from 671 kW to 512 kW, improved the minimum voltage from 0.918 to 0.951 per unit, and enabled the DSO to procure locational flexibility during constrained intervals.
The central operational insight is that EV flexibility is useful only when it is modeled with user uncertainty, feeder constraints, and locational deliverability. Deterministic scheduling can reduce average peaks, but stochastic coordination provides stronger protection against late arrivals, higher energy demand, and high-load grid states.
Future work should test the same framework in real-time operation with live charger telemetry, multi-day driver behavior, dynamic flexibility prices, and coordination with photovoltaic generation, heat pumps, and stationary storage. Further validation on utility feeder data would also help quantify when flexibility procurement can defer reinforcement and when physical network upgrades remain necessary.
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