We conduct a two-stage, steady-state assessment for Oujda City. In the first stage, a stochastic EV-charging model generates an 8,760-hour load profile customized to the city's vehicle fleet and seasonal usage patterns. In the second stage, the annual average power derived from this profile serves as the steady-state input for an alternating-current power-flow simulation using GridCal API. Voltage levels and line loading are analyzed under 0%, 10%, and 30% EV adoption scenarios to provide actionable insights for utility planners.

This article offers three main contributions: (i) a city-level assessment that spatially allocates public EV charging to real candidate sites (i.e., gas stations), with load injections mapped to the nearest buses in a geo-referenced medium-voltage network model; (ii) a data-efficient and reproducible workflow that generates planner-relevant indicators ‒ such as the proportion of grid elements within ≤70%, 70 ‒ 90%, 90 ‒ 100%, and >100% loading bands, as well as the number of buses operating below 0.95 per unit voltage under unmanaged charging scenarios; (iii) an evidence-based identification of grid “hotspots” in Oujda at 10% and 30% EV adoption levels, enabling feeder-level hosting capacity planning in data-constrained environments.

The workflow proceeds in six steps (illustrated in Figure 1):

1. Stochastic charging profile generation. A full 8,760-hour, seasonal load profile is generated for each vehicle class (cars, motorcycles, and buses) as detailed in Stochastic charging model and assumptions.

2. Average power calculation. From the hourly profile, an annual average charging power (MW) is computed to represent the steady-state injection.

3. Spatial allocation of charging. Average EV power is partitioned and mapped to the network at proposed public charging sites (gas stations) and at home/work locations.

4. Network coupling. For each adoption scenario (0%, 10%, 30%), the bus-level average EV demand is superposed on the base (non-EV) load.

5. Power-flow solution. A single steady-state alternating-current Newton ‒ Raphson solve provides bus voltages and branch flows.

6. Stress quantification. Thermal-loading bands and voltage-compliance metrics are computed (definitions in Line-loading definition and stress metrics).

Design priorities are portability (explicit inputs and tolerances), operator relevance (loading bands and voltage-band compliance), and transparency (tabular artefacts suitable for audit).

Figure 1.

Overview of the approach

The Oujda distribution network is implemented in GridCal from operator spreadsheets (buses, lines/transformers, loads, and generators) with geospatial attributes and ratings (Table 1).

• Buses: identifier, nominal voltage (kV), latitude/longitude, voltage limits [V_min, V_max], slack flag.

• Branches (overhead/transformer): series R,X, thermal rating S_rate (MVA), connectivity (from, to).

• Loads: connection bus, base active P and reactive Q.

The model represents the 22 kV network with 91 buses and 102 lines. The total non-EV base load is 177.01 MW and 141.61 Mvar. All simulations use a 400 MVA base. Units were harmonized, graph connectivity verified, and per-unit voltage limits set to 0.95 – 1.05. A complete description of input field names and units is provided in the Appendix.

In the absence of a finalized siting plan, fuel-retail locations (gas stations) are used as proposed public charging sites. Public-session energy is mapped to the nearest site (great-circle distance), preserving corridor clustering.

Home/work charging attaches to the nearest load buses via proximity and basic land-use/population weights. When polygonal land-use data are coarse or missing, Euclidean proximity is used as a fallback, yielding bus-level weights for the home/work fractions.

Coordinate harmonization (WGS84), connectivity checks, rating/limit defaults (0.95–1.05 per unit), and base-load reconciliation to substation meters within ±5% (set to your actual value if different) were performed. Cleaned tables (buses, branches, loads, stations) are versioned and used as the single source of truth.

Hourly EV demand is generated using a Monte Carlo model that specifies fleet composition, SoC/energy requirements, hour-of-day and seasonal shaping, charger selection, spatial mapping to buses, and exported artefacts.

Three fleets capture Oujda’s transport modes Table 2.

Daily charging probability p_chg: cars 0.20, motorcycles 0.90, buses 0.50. Location split (w_h, w_w, w_p): home 0.20, work 0.20, public 0.60. Available charger powers: home 3.7 kW; public 22/50/120 kW (brand-dependent mix). EV demand is modelled at unity power factor unless stated otherwise.

This fleet mix was chosen specifically to reflect the unique transportation landscape of Oujda, where motorcycles and public buses represent a significant portion of urban mobility. A 'car-only' model, as seen in many European or US-based studies [26], would fail to capture this local reality, and our multi-vehicle approach provides a more realistic composite load profile.

Daily energy per vehicle Edaily_v :

where D_v represents the daily distance traveled (for instance, in Morocco D_car = 30 [km] ) [27] and η_v denotes the vehicle’s energy efficiency, parameters derived from regional driving surveys and manufacturer specifications. Furthermore, the Python code simulates the state-of-charge SOC dynamics for each vehicle, determining the charging requirement based on battery capacity (C_v) and predefined thresholds. For example, a car with C_car = 44[kWh] that needs to recharge from 30% to 80% SOC would require an energy input calculated as:

To introduce realism, stochasticity is incorporated via probabilistic charging behavior, modeled as [28]:

Addressing temporal variability, the simulation further incorporates two essential mechanisms. First, it applies time-of-use weighting by assigning hourly charging probabilities P(h) based on normalized weights w_h which capture peak and off-peak charging preferences (for instance, higher weights for overnight residential charging):

Evening-dominant kernel (urban after-work arrivals): 18–23 → 8; 06–08 → 2; other hours → 1. (This corrects the earlier inversion and matches the observed evening peak.)

Monthly multipliers α_s adjust EV energy for HVAC and thermal-management overheads (eq. (5)). Values are bounded in [0.95, 1.10] (temperate–hot climates). Table 3 lists the factors used.

At the selected node, a charger type is drawn (home 3.7 kW; public 22/50/120 kW). Session power is bounded by the charger rating, and cumulative session energy is capped to deliver α_sE_charge. Hourly resolution (Δt =1 h) is used; the final hour may be partial:

Session duration equals the smallest integer hours satisfying energy delivery; partial final-hour energy is allowed.

If a session occurs, location 𝓁 ∈ {home, work, public} is drawn with probabilities (w_h, w_w, w_p). Public sessions map to the nearest station and then to its serving bus; home/work map to the nearest load bus (proximity/land-use weights). Summation over sessions mapped to bus b yields hourly EV demand L_EV(t, b).

Each scenario is simulated for 8,760 h. A single run draws {D_i}, daily charging decisions, locations, and start times; optional uncertainty uses multiple seeds to summarize median and 5–95% bands. For each scenario/seed, exported artefacts include: (i) L_EV(t, b); (ii) bus-level net loads; and (iii) station/session summaries (counts, energy, mean session length).

A full-year, seasonal Monte Carlo simulation produces the high-resolution electric-vehicle load L_EV(t, b) for each scenario; this file is the primary artefact of the demand model.

Three adoption levels are assessed: 0% (no EV), 10%, and 30%.To ensure policy relevance, the 10% and 30% penetration scenarios were grounded in national-level adoption forecasts for Morocco. Projections from a 2019 technical report on sustainable mobility by Morocco's Energy Federation [29] outline several adoption pathways. Our scenarios are derived from these national-level forecasts, representing conservative and ambitious bounds.

This study uses a single steady-state snapshot for the grid impact assessment. To create the input for this grid model, we first calculate the annual average EV power L_EV,avg(b) for each bus from the 8760-hour load profile generated by Model 1.

The total load for each bus L_total(b) is then calculated by superposing this annual average EV power onto the base network load L_base(b):

A single steady-state power flow is solved for each scenario using GridCal and the net nodal demands above:

• Algorithm: alternating-current Newton–Raphson

• Tolerance: 1 × 10⁻⁶ per unit; maximum iterations: 25

• Slack bus: primary supply node at the 225/60/22 kV interface

• Load models: base loads as P–Q; EV charging at unity power factor

• Operating limits: bus voltages checked against 0.95–1.05 per unit; branches/transformers flagged above 100% of S_rate

Line/transformer loading uses apparent power (active P_line and reactive Q_line) normalized by the nameplate rating S_rate, [30], [31]:

This subsection defines the indicators computed from each single steady-state snapshot (0%, 10%, 30%) and how they are used to compare performance across adoption levels.

• Voltage quality

• Record bus voltages (per unit) on all energized buses.

• Report the minimum bus voltage in the network.

• Count buses below the 0.95 per unit planning limit (and optionally below 0.90 per unit).

Solver performance for the steady-state snapshots is reported here. Using annual-average charging injections, a single alternating-current Newton ‒ Raphson solve was executed for each scenario (0%, 10%, 30%) with a mismatch tolerance of 1×10^-6. All cases converged cleanly, with final residuals well below tolerance: 0%: 9.11×10^-11 p.u.; 10%: 3.36×10^-6 p.u.; 30%: 9.58×10^-11 p.u. Computation time was negligible.

Figure 3 displays the EV-only average charging power (excluding base load) mapped to the nearest primary substation for 10% and 30% adoption. The distribution is non-uniform: several corridors absorb disproportionate shares. The increase from 10% to 30% is not proportional across substations, as proposed public charging sites (gas stations) act as spatial proxies, concentrating sessions where site density is higher.

Figure 2.

(a) Charging power by location—10% adoption (Home, Work, Public); (b) Total system EV-charging power—10% adoption; (c) Charging power by location—30% adoption (Home, Work, Public); (d) Total system EV-charging power—30% adoption

Figure 3.

Average Load Distribution Across EV Charging Stations at Different Utilization Levels (10%, 30%)

Figure 4a – 4c presents branch loading across the network for 0%, 10%, and 30% scenarios, using the study bands: ≤70% (green), 70 ‒ 90% (yellow), 90 ‒ 100% (orange), and >100% (red). As adoption rises, yellow/orange/red segments expand along corridors with multiple proposed sites, indicating spatial clustering of stress. For illustration, Line_Autohall ‒ Oujda ‒ Omran3 increases from ~73% (baseline) to ~86% (10%) and ~96% (30%).

Thermal headroom remains concentrated in the ≤70% band, but a discernible tail moves into higher bands as EV adoption increases, thermal stress intensifies modestly across the network. At baseline (0% EV), 78.6% of lines operate at ≤70% of their thermal rating, 9.4% fall within the 70 ‒ 90% band, 3.4% within 90 ‒ 100%, and 6% exceed 100%. At 10% EV penetration, these shares shift to 76.9%, 10.3%, 5.4%, and 7%, respectively. At 30% EV, the distribution becomes 75.2%, 10.4%, 6.3%, and 9%. The largest increases occur on feeders serving corridors with multiple proposed public-charging sites, consistent with the spatial clustering illustrated in Figure 4 and quantified in Figure 5.

This subsection summarizes voltage quality at energized buses. Figure 6. eports per-bus voltage drop (1−V) for the 0%, 10%, and 30% snapshots. The distribution is concentrated at small drops: 94 of 103 buses (≈91%) exhibit ≤3% drop in all scenarios, while a narrow, persistent tail of 7/103 lies >10%, co-located with charging hotspots. In per-unit terms, the system bulk is stable (median voltage ≈ 0.974 p.u. across scenarios). Relative to planning thresholds, about 9 buses fall below 0.95 p.u., and none fall below 0.90 p.u.; these counts change little with adoption.

Figure 4.

Comparative Visualization of Urban Grid Loading under Different EV Penetration Scenarios (0%, 10%, and 30%) is depicted as: Figure 4a (a); Figure 4b (b); and Figure 4c (c)

Figure 5.

Loading Percentage Across Different Lines at Various Utilization Levels (0[%], 10[%], 30[%])

Figure 6.

Voltage Drop Profiles Across Substations under Varying EV Penetration