1. Introduction and Research Background
The escalating contradiction between technological progress, energy ecosystem imbalance, and environmental crises has become increasingly prominent in human society. The current global energy framework remains heavily dependent on conventional fossil fuels, whose extensive utilization not only exacerbates greenhouse gas accumulation and climate anomalies but also elevates energy security risks due to resource non-renewability. Within this context, electric vehicles serve as novel transportation carriers and demonstrate dual benefits: mitigating urban tailpipe pollution through cleaner mobility and fostering energy mix transitions toward renewable sources through the “electricity-replacing-oil” paradigm.
From the perspective of power system operation, large-scale electric vehicle grid integration will trigger structural transformations in load characteristics. Unlike traditional static loads, electric vehicle charging behaviors exhibit pronounced spatiotemporal randomness—charging demand is coupled with factors such as user travel habits and grid tariff policies, rendering load distributions highly uncertain. Research indicates that uncoordinated charging could expand the grid peak-valley difference by 20%-30% and precipitate voltage violation risks in localized regions. At high penetration levels, the synchronized start-stop of clustered electric vehicles may induce instantaneous node voltage sags and even trigger protective relay malfunctions, threatening system security.
The precision of load modeling directly impacts the reliability of power system planning and operation. Conventional empirical load models (e.g., ZIP models and composite motor models) are primarily developed from industrial and residential load characteristics, rendering them insufficient for representing the dynamic response discrepancies induced by nonlinear control strategies in electric vehicle chargers, such as the CC-CV switching mechanism. Moreover, the mobile access attributes of electric vehicles result in dynamic coupling features in load spatiotemporal distributions, where existing equivalence methods fail to precisely characterize the group interaction effects of large-scale charging clusters. These issues engender a chain reaction of model mismatch, decision deviation, and risk accumulation within grid simulation analyses, necessitating multi-level refined modeling research covering equipment characteristics, cluster behaviors, and system interactions.
As a core indicator of secure power system operation, voltage stability warrants investigation because novel load integrations may alter the distribution characteristics of system weak links. With continuously rising electric vehicle penetration, spatiotemporal aggregation effects of charging power introduce two categories of risks: at the static level, expanded peak-valley differentials cause frequent voltage regulation equipment operations, accelerating asset aging; at the transient level, the low-voltage ride-through behavior of chargers during faults may deteriorate the system recovery process. Therefore, establishing multi-timescale voltage stability assessment frameworks becomes imperative to furnish theoretical support for grid security defense under high-penetration electric vehicle integration scenarios.
2. Mechanism-Oriented Load Modeling of Electric Vehicles
2.1 Lithium Battery Charging Characteristics and Modeling
Contemporary electric vehicle power systems predominantly employ three technological routes: lead-acid batteries, nickel-metal hydride batteries, and lithium batteries. Lithium batteries dominate market adoption due to their exceptional energy density and service life characteristics. In charging strategy optimization, the two-stage CC-CV charging method has been widely recognized as an effective approach for prolonging battery lifespan. During the initial phase, constant current mode rapidly replenishes energy; when terminal voltage reaches the threshold (e.g., maximum allowable charging voltage), the system transitions to constant voltage mode, thereby circumventing initial current surges and overcharging risks in the later period.
For a representative lithium battery with nominal voltage \(U_n = 380\ \text{V}\) and capacity \(Q = 500\ \text{A·h}\), the terminal voltage can be modeled as:
$$
U_{bat} = E_0 – K\frac{Q}{Q – \int i\,dt} + A e^{(-B \int i\,dt)} – R i \tag{2-1}
$$
The state-of-charge dynamic evolution follows:
$$
\mathrm{SOC}(t) = \left[ 1 – \frac{\int_0^t i(\tau)\,d\tau}{Q} \right] + \int i\,dt \tag{2-2}
$$
where \(U_{bat}\) is the output voltage, \(i\) the charging current, \(Q\) the rated capacity, \(R\) the equivalent resistance, \(K\) the polarization constant, \(E_0\) the battery constant potential, and \(A\), \(B\) are exponential-zone constants.
For slow charging under the CC-CV protocol, the CV phase duration is significantly abbreviated. Experimental observations indicate that in a typical 10-hour charging cycle, the constant voltage stage occupies approximately 7 minutes, corresponding to less than 1.2% of the total duration. Under such scenarios, dynamic responses during the CV stage can be reasonably neglected, justifying simplified constant-current-focused models as engineering approximations.
For fast charging equipment, however, both CC and CV phases exhibit co-dominant characteristics. During fast charging, the SOC linearly increases throughout the constant current stage, accounting for 45%-55% of the total charging time. During the constant voltage stage, which extends to 40%-50% of the duration due to heat dissipation considerations, current decay rates slow down markedly. Consequently, unlike conventional slow charging, the grid interactive effects during the CV phase under fast charging scenarios cannot be ignored. Developing dual-stage models that accurately characterize fast-charging behavior is therefore essential to overcoming the limitations of simplified modeling.
2.2 Practical Load Models for Electric Vehicle Charging Stations
The commonly adopted topology for electric vehicle chargers includes the “three-phase PWM rectifier + isolated DC/DC converter” configuration, which achieves sinusoidal grid-side current control through PWM modulation and enables power factor improvement to above 0.99. Simultaneously, the DC/DC conversion stage employing soft-switching technology brings overall system efficiency beyond 95%. The topology structure is presented in Fig. 2-1, and the corresponding control architecture is depicted in Fig. 2-2.
For typical operational regimes, the DC-DC power conversion module achieves efficiency levels surpassing 96%, with energy losses typically within acceptable engineering margins—hence, idealized treatment is generally adopted in system-level modeling. For the rectification unit, contemporary power electronic equipment universally employs dynamic-regulation-oriented PWM-based power factor correction schemes, maintaining input-side power factors above 0.97. The resulting reactive power generated during rectification amounts to only around 1% of the active power, thus warranting neglect in analyses. Following these simplifications, when considering only active power, the static equivalent circuit of electric vehicles is shown in Fig. 2-3.
Applying Kirchhoff’s Voltage Law to the two independent loops of the equivalent circuit yields:
$$
\begin{cases}
U_s’ = U_{dc} + R_s I_{dc} \\[4pt]
U_{dc} = E_{eq} + R_{eq} I_{dc}
\end{cases} \tag{2-3}
$$
The power factor is computed as:
$$
\cos\varphi = \frac{P}{S} = \frac{U_{dc} I_{dc}}{U_s I_s} \tag{2-4}
$$
Active and reactive power expressions can be derived as:
$$
\begin{cases}
P = \dfrac{R_{eq} U_s^2 + R_s E_{eq} U_s – R_s E_{eq}^2}{\left(R_{eq} U_s + R_s E_{eq}\right)^2} \\[8pt]
Q = P \sqrt{\dfrac{1}{\cos^2\varphi} – 1}
\end{cases} \tag{2-5}
$$
Through power normalization with initial power \(P_0\) and reference voltage \(U_0\), and with appropriate simplification of minor terms in the reactive denominator, the following model is established:
$$
\begin{cases}
P = P_0 \left[ a_p \left(\dfrac{U}{U_0}\right)^2 + b_p \left(\dfrac{U}{U_0}\right) + c_p + K_{pf} \Delta f \right] \\[8pt]
Q = Q_0 \left[ a_q \left(\dfrac{U}{U_0}\right)^2 + b_q \left(\dfrac{U}{U_0}\right) + c_q + K_{qf} \Delta f \right]
\end{cases} \tag{2-6}
$$
This derivation verifies that the electric vehicle static load model shares architectural similarity with the classical ZIP model, with the parameter constraints dictating coefficient sign characteristics. The simplified form is:
$$
\begin{cases}
P = P_0 \left[ a_p \left(\dfrac{U}{U_0}\right)^2 + b_p \left(\dfrac{U}{U_0}\right) + c_p \right] \\[8pt]
Q = Q_0 \left[ a_q \left(\dfrac{U}{U_0}\right)^2 + b_q \left(\dfrac{U}{U_0}\right) + c_q \right]
\end{cases} \tag{2-7}
$$
2.3 Simulation Model and Parameter Identification for Fast Charging
A simulation environment was developed on the MATLAB/Simulink platform to characterize the load behavior of high-power fast charging equipment. The system employs a 380 V AC source, with DC output set at 500 V after rectification. For battery representation, the built-in Battery module in MATLAB 2023b was utilized, configured with rated voltage 400 V, capacity 500 A·h, internal resistance parameter 0.005 Ω, and support for initial state-of-charge configuration. Semiconductor switches in both the rectifier bridge and BUCK circuit were idealized.
The charging control architecture adopts a dual closed-loop configuration with an outer voltage loop and an inner current loop. The operational parameters specify: voltage threshold of 230 V and current threshold of 400 A as constraints. For SOC within the 0%-80% range, constant current charging is performed; upon reaching the 80% SOC threshold, automatic transition to constant voltage charging occurs until full charge.
The functional model fitting results yielded:
$$
P = P_0 \left( 0.023 \left(\frac{U}{U_0}\right)^2 – 0.057 \left(\frac{U}{U_0}\right) + 1.034 \right) \tag{2-8}
$$
The fitted model parameters indicate that for active power, the constant impedance component \(a_p = 0.02\), constant current component \(b_p = -0.06\), and constant power component \(c_p = 1.04\). This parameter distribution demonstrates that charging loads exhibit predominantly constant power characteristics even under quasi-steady-state conditions, consistent with the power closed-loop control attributes of charging devices. The subtle negative constant-current component reveals an adaptive regulation mechanism: when grid voltage increases, the charging current spontaneously diminishes to sustain approximate constant power output—a negative feedback feature that significantly enhances the voltage support capability of charging equipment.
2.4 Two-Machine Dynamic Equivalent Model for Charging Stations
To address the computational complexity associated with detailed modeling of large-scale charging station clusters, a two-machine dynamic aggregation method based on operational mode classification was developed. This method achieves model order reduction through a hierarchical equivalence strategy, as represented in Fig. 2-6.
The approach first partitions the load cluster into CC and CV groups based on charging mode. Subsequently, system-level equivalence of key components is performed: mean-value model theory is used for dynamic order reduction of converters and DC/DC converters, after which the equivalent circuit of the charging loop is constructed.
For multi-vehicle parallel charging scenarios with differing initial states, dynamic parameter aggregation is employed for load characteristic equivalence. The extraction of dynamic circuit parameters from the third-order battery dynamic models and cluster aggregation yields the simplified model shown in Fig. 2-7.
During constant voltage charging, multiple vehicle battery systems exhibit parallel topology. The equivalent circuit of the cluster can be expressed as an arrangement of \(n\) battery units in parallel. In this operational state, electric vehicle charging stations can be effectively modeled as constant impedance loads. The aggregate admittance is:
$$
Y_{\text{eq}} = \frac{1}{R_{eq,1}} + \frac{1}{R_{eq,2}} + \cdots + \frac{1}{R_{eq,n}} \tag{2-9}
$$
For constant current charging mode, vehicle traction batteries convert to series architecture. Each electric vehicle can be represented by its Thevenin equivalent, where the equivalent parameters are:
$$
\begin{cases}
R_{eq} = R_0 + R_1 + R_2 \\[4pt]
E_{eq} = E
\end{cases} \tag{2-10}
$$
For \(n\) vehicles in series, the aggregate cluster model yields the equivalent total resistance and back-EMF:
$$
\begin{cases}
R_{\text{total}} = R_{eq,1} + R_{eq,2} + \cdots + R_{eq,n} \\[4pt]
E_{\text{total}} = E_{eq,1} + E_{eq,2} + \cdots + E_{eq,n}
\end{cases} \tag{2-11}
$$
The simulation fitting results validate that the aggregated equivalent model achieves high accuracy under steady-state conditions, confirming the correctness of the proposed method. During transient load disturbance, simplification of the DC-DC converter structure yields faster dynamic response characteristics; the simulated current and active power trajectories exhibit certain modeling errors, whereas reactive power dynamics and voltage responses achieve good tracking performance.
The simulations further reveal that electric vehicle charging loads consistently demonstrate pronounced resistive characteristics under various integration scales. Particularly in the constant voltage charging mode, the equivalent impedance is positively correlated with the number of connected devices. For dynamic simulations of large-scale electric vehicle charging, the aggregated impedance model is recommended for system-level dynamics research. Fig. 2-11 shows the active power at the grid-connection point from the simulation.
| Parameter | Symbol | Value | Physical Interpretation |
|---|---|---|---|
| Constant Impedance Coefficient | \(a_p\) | 0.023 | Voltage-proportional-power component |
| Constant Current Coefficient | \(b_p\) | -0.057 | Adaptive current regulation effect |
| Constant Power Coefficient | \(c_p\) | 1.034 | Dominant power-holding behavior |
| Voltage Reference | \(U_0\) | 380 V | Nominal system voltage |
| Rated Power | \(P_0\) | 150 kW | Fast charger rated capacity |
3. Segmented Probabilistic Load Modeling of Electric Vehicles
3.1 Probability Models for Charging Load Impact Factors
Electric vehicle charging load formation is governed by multi-dimensional complexity—essentially a dynamic system jointly determined by vehicle technical parameters, infrastructure conditions, and user behavior characteristics. Three primary influence dimensions are identified: vehicle power performance, charging equipment configuration, and user driving patterns.
(1) Charging Start Time
Based on travel survey statistical data, residential electric vehicle charging initiation times follow a multi-peak piecewise normal distribution, reflecting that users typically charge immediately upon completing their final trip. The charging start time probability density curve exhibits a significant peak at 18:00-19:00, aligning with the “charge after work” behavior pattern in urban commuting:
$$
f_s(t_s) = \frac{1}{\sigma_s \sqrt{2\pi}} \exp\left[ -\frac{(t_s – \mu_s)^2}{2\sigma_s^2} \right] \tag{3-1}
$$
where \(t_s\) represents the start charging time, \(\mu_s\) the expected value of the final trip end time, and \(\sigma_s\) the standard deviation.
(2) Daily Driving Mileage
Daily mileage directly determines total charging demand and follows a log-normal distribution. Most users concentrate within short-distance zones (< 50 km), yet the long-tail distribution suggests that occasional long-distance trips create exceptional charging demands requiring specific modeling attention:
$$
f_D(d) = \frac{1}{d \sigma_D \sqrt{2\pi}} \exp\left[ -\frac{(\ln d – \mu_D)^2}{2\sigma_D^2} \right] \tag{3-2}
$$
where \(d\) denotes the daily driving mileage in km, \(\mu_D\) is the expectation of \(\ln d\), and \(\sigma_D\) is the standard deviation.
(3) Charging Power
For the 150 kW fast charging mode, a two-stage power model is established. Using a representative battery capacity of 75 kWh, the fast charging process includes: constant current phase (20 minutes, SOC 20%-80%), with power maintained at 150 kW; constant voltage phase (20 minutes, SOC 80%-100%), with average power reduced to 45 kW. Conventional charging employs a constant power simplification.
(4) Charging Duration
The charging duration is determined by the initial state of charge and the charging power curve. Establishing the SOC-mileage mapping relation converts user travel behavior into charging time parameters. The SOC before and after travel is given by:
$$
\mathrm{SOC}(t_2) = \mathrm{SOC}(t_1) – \frac{d}{d_m} \tag{3-3}
$$
where \(\mathrm{SOC}(t_1)\) is the initial SOC (set to 1.0 assuming full-charge strategy), \(\mathrm{SOC}(t_2)\) is the SOC at final trip termination, \(d\) is the trip mileage, and \(d_m\) denotes the full-charge range.
The charging duration can be computed as:
$$
T_c = \frac{(1 – \mathrm{SOC}_{init}) \cdot E_{bat}}{\eta \cdot P_{rate}} \tag{3-4}
$$
where \(T_c\) represents the charging time, \(\mathrm{SOC}_{init}\) is the initial SOC at the start of charging, \(E_{bat}\) denotes battery rated capacity, \(\eta\) is the integrated charging system efficiency, and \(P_{rate}\) is the rated charging power.
3.2 Monte Carlo Simulation Methodology and Assumptions
Core modeling assumptions were established based on rationality and engineering constraints: charging power, daily driving mileage, and charging start time satisfy statistical independence; users initiate charging immediately after trip completion—a deterministic mapping between travel end time and charge start time; each charging event terminates at 100% SOC; and conventional charging power fluctuations follow normal distributions calibrated from historical charger operational data.
The Monte Carlo approach generates random samples from the input probability distributions and constructs aggregate load profiles through temporal superposition:
$$
P_{\text{sum}} = \sum_{j=1}^{1440} \sum_{i=1}^{N} P_i(t_j) \tag{3-5}
$$
where \(P_{\text{sum}}\) is the total regional charging load (kW), \(N\) is the electric vehicle fleet size, and \(P_i(t_j)\) represents the instantaneous charging power of the \(i\)-th vehicle at time \(t_j\).
The computational framework includes: vehicle type composition ratios, charging initiation time and mileage distribution parameters, battery technical parameters (capacity and charging efficiency), and charger specifications comprising the key inputs for scenario generation.
3.3 Multi-Type Vehicle Load Modeling Framework
(1) Electric Buses
Electric buses require two daily charging events. During daytime operation (09:00-16:30), fast charging at 150 kW is adopted. The charging start times follow a normal distribution centered at 14:00, and initial SOC is normally distributed with mean 0.5 and standard deviation 0.12. Overnight charging (23:00-05:00) employs conventional slow charging where the start times follow a uniform distribution between 23:00 and 24:00.
| Event | Time Window | Charging Start Time Distribution | Initial SOC Distribution | Charging Mode |
|---|---|---|---|---|
| 1 | 09:00-16:30 | \(N(14, 0.5^2)\) | \(N(0.5, 0.12^2)\) | Fast Charging 150 kW |
| 2 | 23:00-05:00 | \(U(23, 24)\) | \(N(0.5, 0.12^2)\) | Slow Charging 21 kW |
(2) Electric Taxis
Electric taxis operate throughout the day and require two sessions of rapid charging during meal or rest periods. Charging start times conform to uniform distributions during shift-change windows: 02:00-04:00 and 11:00-14:00. Initial SOC follows normal distributions with mean 0.3.
| Event | Time Window | Charging Start Time Distribution | Initial SOC Distribution | Charging Mode |
|---|---|---|---|---|
| 1 | 02:00-04:00 | \(U(2, 4)\) | \(N(0.3, 0.12^2)\) | Fast Charging 150 kW |
| 2 | 11:00-14:00 | \(U(11, 14)\) | \(N(0.3, 0.12^2)\) | Fast Charging 150 kW |
(3) Electric Official Vehicles
Official vehicles adopt task-driven charging mechanisms. Their shorter daily mileages permit a single charging event. Charging starts after task completion between 18:00 and 24:00 according to uniform distributions. Initial SOC is distributed with a mean of 0.4. Conventional charging at 7 kW is employed.
(4) Electric Private Cars
Private electric vehicles demonstrate significant behavioral uncertainty. The charging start times follow normal distributions with peaks during evening commute hours. For this study, 80% of private vehicles are assumed to charge with slow chargers (7 kW), while 20% utilize fast chargers (150 kW/45 kW two-stage). The SOC initial values are determined by the daily mileage-to-range ratio.
| Parameter | Electric Bus | Electric Taxi | Official Vehicle | Private Vehicle |
|---|---|---|---|---|
| Fleet Size (units) | 1000 | 2000 | 2000 | 10000 |
| Battery Capacity (kWh) | 180 | 75 | 75 | 75 |
| Slow Charging Power (kW) | 21 | — | 7 | 7 |
| Fast Charging Power (kW) | 150/45 | 150/45 | — | 150/45 |
| Charging Efficiency (%) | 90 | 90 | 90 | 90 |
3.4 Simulation Results and Load Profile Analysis
(1) Electric Bus Charging Load Distribution
The electric bus charging load exhibits distinctive dual-peak impact characteristics. The daytime fast-charging window (09:00-16:30) generates a peak at approximately 14:30, reaching up to 55,275 kW, causing voltage sags at critical distribution nodes and amplifying voltage instability risks in the vicinity. The nighttime conventional charging, while exhibiting a 52% reduction in peak values, still produces notable local line voltage fluctuations due to concentrated charging.
(2) Electric Taxi Charging Load Distribution
The taxi fast-charging load reveals pronounced dual-peak impact behavior. Morning shift-change charging around 02:50 and midday meal-period charging near 12:30 respectively generate load peaks of up to 39,000 kW and 28,350 kW. These concentrated high-power demands induce voltage sags at distribution network nodes, negatively impacting voltage stability.
(3) Official Vehicle Charging Load Distribution
Official vehicle charging requirements concentrate predominantly during nighttime hours between 21:00 and 04:00 the following morning, with peak loading reaching approximately 12,558 kW around midnight. Due to the utilization of conventional 7 kW charging rather than fast charging, peak load magnitudes are substantially reduced, with the extended charging durations providing effective load leveling capabilities.
(4) Private Vehicle Charging Load Distribution
The private vehicle charging patterns yield load peaks concentrated in the evening window of 18:00-20:00, coinciding with residential peak demand. The superposition of electric vehicle charging with base loads amplifies transformer outlet voltage fluctuations. The introduction of fast charging elevates peak loads, potentially forcing node voltages downward. Table 3-4 presents representative hourly charging loads for private electric vehicles.
| Hour | Load (kW) | Hour | Load (kW) | Hour | Load (kW) |
|---|---|---|---|---|---|
| 01:00 | 28,707 | 09:00 | 1,342 | 17:00 | 32,200 |
| 02:00 | 22,499 | 10:00 | 1,657 | 18:00 | 38,238 |
| 03:00 | 16,663 | 11:00 | 2,891 | 19:00 | 42,759 |
| 04:00 | 11,657 | 12:00 | 5,036 | 20:00 | 45,397 |
| 05:00 | 7,676 | 13:00 | 8,218 | 21:00 | 45,606 |
| 06:00 | 4,761 | 14:00 | 13,074 | 22:00 | 43,654 |
| 07:00 | 2,817 | 15:00 | 18,897 | 23:00 | 39,904 |
| 08:00 | 1,727 | 16:00 | 25,342 | 24:00 | 34,707 |
(5) Aggregated Charging Load
The composite charging load across all vehicle categories demonstrates distinct spatiotemporal heterogeneity. Fluctuations are strongly coupled with user travel patterns, resulting in a binary peak-valley structure. Peak periods coincide with the residential electricity consumption window, whereas valley periods are situated in low grid demand intervals. Load spikes are short-duration but periodic, where fast-charging instantaneous power surges induce immediate voltage sags at critical nodes, amplifying regional voltage regulation burdens.
The system load curve analysis considers a receiving-end system with a winter peak load and electric vehicle penetration levels. The simulation results demonstrate that at 10% penetration, the peak-valley difference expands from 4,350 MW in the base case to 4,830 MW—an increase of 480 MW. The mechanisms stem from temporal coupling between electric vehicle charging peaks (19:00-20:00) and system peak periods. When penetration levels exceed critical thresholds, regional grid structural loading pressures escalate substantially, potentially evoking node voltage violation risks.
| EV Penetration | Initial Peak-Valley Difference (MW) | Post-EV Peak-Valley Difference (MW) | Difference (MW) |
|---|---|---|---|
| 0% | 4,350 | 4,350 | 0 |
| 10% | 4,350 | 4,830 | 480 |
4. Voltage Stability Impact Assessment
4.1 Static Voltage Stability Analysis Framework
When adopting the load voltage open-loop control assumption, the relation between node-injected power \(P\), bus voltage \(V\), and transmission capacity can be quantified through \(P\)-\(V\) curve theory. Loads can be categorized into three types based on voltage characteristics:
- Constant Impedance Load (Z-type): Power demand is proportional to the square of voltage. When voltage drops, power naturally attenuates, reducing line current and mitigating voltage collapse risk—exhibiting inherent self-stabilizing behavior.
- Constant Current Load (I-type): Power varies linearly with voltage. The power adjustment rate is constrained by voltage fluctuation amplitude, with a neutral effect on system stability.
- Constant Power Load (P-type): Power demand remains strictly constant. During voltage decline, the negative impedance characteristic actively elevates current, causing equivalent impedance to shrink—establishing a reverse regulation mechanism.
For the constructed ZIP composite load model representing electric vehicle charging, when grid voltage descends below critical threshold \(U_1\), the power demand exhibits complex dynamics. Compared to pure constant power loads, this model initially behaves as quasi-constant power during early voltage decline. However, further voltage reduction activates the constant impedance component’s power attenuation, which partially alleviates the power shortage. The negative constant-current component introduces weak negative feedback. While these combined effects may delay voltage collapse progression, their mitigative strength proves insufficient to fully counteract the P-component’s rigid power demand, preserving the risk of deteriorated power imbalance.
Continuation Power Flow Methodology
The CPF method serves as the principal tool for determining critical operating states in static voltage stability assessments. This methodology tracks system equilibrium trajectories under load growth scenarios, effectively solving ill-conditioned power flow equations and identifying nose points corresponding to maximum loading limits. For the WSCC 9-bus system, node 6 was designated as the observation point, and various proportions of electric vehicle loads were integrated to evaluate static voltage stability evolution.
| Load Model Scenario | Critical Voltage (p.u.) | Maximum Loading Parameter (p.u.) |
|---|---|---|
| No EV Load | 0.3922 | 6.8305 |
| 20% EV Load | 0.5834 | 3.1130 |
| 30% EV Load | 0.6156 | 2.8806 |
The nose curve analysis reveals that as electric vehicle load proportions increase, nose-tip power decreases while voltage magnitudes rise. This shift indicates that the system maintains higher voltage levels before reaching stability limits—voltage decline rates slow during gradual load increments, enabling higher voltage retention under heavy loads, yet weakening the system’s load-carrying capacity. Consequently, systems approach their stability limits more readily under elevated load conditions.
Time-domain simulations further clarify the static voltage stability degradation. Under progressive load increments commencing at \(t = 1\ \text{s}\), node 6 voltage trajectories reveal that higher electric vehicle proportions permit fewer additional loads before voltage collapse, exhibiting earlier collapse times and degraded static voltage stability margins. Specifically, at 20% electric vehicle load composition, even a 40% active load increase only produces bounded voltage excursions; however, at 40% electric vehicle composition, a mere 30% active load increase triggers voltage collapse. These results robustly validate that increasing electric vehicle load shares significantly diminish system static voltage stability.
4.2 Static Voltage Stability in IEEE 24-Node System with EV Integration
Simulations on the IEEE 24-node receiving-end grid system were pursued with nodes 8, 10, and 12 selected as weak voltage points. The integrated fast-charging static model and Monte Carlo-generated time-varying load profiles from the previous sections, combined with continuation power flow methods, enabled quantitative assessment of static voltage stability margin degradation under 10%, 20%, and 30% electric vehicle penetration levels.
As penetration rises, the PV curves demonstrate pronounced shape evolution. Nose-point maximum power stability levels undergo substantial reductions, while corresponding voltage magnitudes increase. With penetration above 30%, the system maximum transmission power exhibits larger declining gradients, exposing insufficient load-bearing capacity under high-proportion charging loads—a manifestation of “power contraction-voltage elevation” coupling phenomena.
Incorporating the spatiotemporal migration attributes of electric vehicle charging behavior, where private vehicles concentrate at node 8 for daytime charging and return to node 6 for nighttime charging, alters static voltage stability outcomes. The simulations show that voltage stability margins improve relative to uniform distribution assumptions due to the power flow balancing effects induced by load spatial migration. Daytime fast-charging loads directed toward node 8 mitigate adjacent feeder overload risks, while nighttime migration toward node 6 optimizes local reactive power distribution profiles. This validates that the spatiotemporal schedulability of electric vehicle charging can beneficially enhance receiving-end grid voltage stability characteristics.
| Scenario | EV Penetration | Critical Voltage (p.u.) | Maximum Loading (p.u.) | Stability Margin Trend |
|---|---|---|---|---|
| Uniform Distribution | 10% | 0.921 | 1.021 | Baseline +10% EV |
| 20% | 0.918 | 0.943 | Reduced margin | |
| 30% | 0.915 | 0.867 | Further reduction | |
| With Spatial Migration | 10% | 0.934 | 1.142 | Improved margin |
| 20% | 0.926 | 1.078 | Moderate improvement | |
| 30% | 0.922 | 0.982 | Relative improvement |
4.3 Transient Voltage Stability Analysis
4.3.1 Influence of Load Characteristics on Transient Voltage Stability
In transient voltage stability investigations, three representative load types were contrasted under identical disturbance conditions: constant impedance loads, constant power loads, and induction motor loads. The simulations reveal fundamentally different voltage recovery trajectories. Constant impedance loads maintain higher initial voltages and demonstrate rapid voltage restoration after fault clearance. Constant power loads exhibit oscillatory instability patterns. Induction motor loads show damped oscillations with intermediate voltage minima but prolonged recovery durations.
| Transient Feature / Load Type | Induction Motor Load | Constant Power Load | Constant Impedance Load |
|---|---|---|---|
| Minimum Voltage (p.u.) | 0.454 | 0.321 | 0.420 |
| Oscillation Mode | Damped Oscillation | Amplified Oscillation | Damped Oscillation |
| Recovery Time (s) | 0.685 | 0.125 | 0.125 |
When the fault-induced voltage decline exceeds 10%, the stabilizing efforts of the Z and I components become overwhelmed by the power-maintenance attributes of the P component, propelling the system back into positive-feedback instability regions. This composite dynamic behavior reveals the dual effect of electric vehicle charging loads: the constant power nature fundamentally constitutes a voltage instability risk source, while the subtle adaptive regulation provides limited voltage support potential for novel power systems.
4.3.2 Transient Voltage Stability in the CSEE-VS Receiving-End System
Transient simulation employing the PSD-BPA platform, on the CSEE-VS high-proportion renewable-energy conventional DC receiving-end benchmarking system, investigated electric vehicle charging effects on transient voltage stability. The main grid structure includes thermal power, wind power, photovoltaic generation, and DC transmission interconnections. Node B36 serves as the typical distribution network node for load model modifications.
The system operating configuration is presented in Table 4-4.
| Unit Type | Access Node | Output (MW) |
|---|---|---|
| Thermal Power Unit 2 | B14 | 600 |
| Photovoltaic Plant (P1) | B18 | 453 |
| Photovoltaic Plant (P2) | B16 | 413 |
| Wind Farm (W1) | B13 | 1600 |
| Wind Farm (W2) | B01 | 600 |
| Wind Farm (W3) | B19 | 300 |
| DC Transmission | B13 | 1600 |
For a three-phase sustained ground fault at 1.00 s on one circuit of the double-circuit transmission corridor B03-B05, protective relays initiate breaker trips in sequence at 1.09 s and 1.10 s. In the voltage collapse basic mode (VC), the event produced sustained power oscillations at converter stations and continuous voltage drops across all grid nodes. Voltages at nodes B1, B2, B34, and B36 collapse sequentially, with B36 experiencing the most severe decline.
Employing the fast-charging device dynamic model from Chapter 2 combined with spatiotemporal migration-aware Monte Carlo load profiles, multi-timescale transient voltage stability evaluation was conducted. Electric vehicle load compositions at bus B36 were parametrically varied under identical fault conditions. In the VC mode, the minimum voltage at bus B36 declined progressively and voltage recovery duration extended as electric vehicle proportions increased, confirming the degradation mechanism.
| EV Proportion | Minimum Voltage (p.u.) | Low Voltage Duration (s) |
|---|---|---|
| 10% | 0.352 | 0.62 |
| 20% | 0.312 | 0.85 |
| 30% | 0.268 | 1.20 |
In the continuous low voltage basic operating mode (CLV), synchronous condensers configured at receiving-end bus B05 provide reactive support for sustained low-voltage operations. Under identical N-2 contingency conditions, although DC blocking is avoided, voltage support weakness persists at receiving-end grid B01-B04, producing sustained voltage depression accompanied by cascading renewable unit disconnections. The system was adjudged to have entered voltage instability conditions.
Under the same fault in CLV mode, raising electric vehicle proportions at bus B36 decreases minimum voltage levels, extends low-voltage durations, and introduces oscillations. Although the spatiotemporal distribution of electric vehicles partially mitigates low-voltage states through load migration effects, load gradient growth still dominates the voltage stability margin attenuation trajectory. The consideration of spatial load distribution generally yields improved voltage recovery trajectories compared to uniform load distribution assumptions, consistent with the static stability findings.
| EV Proportion | Minimum Voltage (p.u.) | Low Voltage Oscillation |
|---|---|---|
| 10% | 0.884 | Moderate |
| 20% | 0.842 | Intensified |
| 30% | 0.798 | Pronounced |
Figure 4-1 provides a visual summary of electric vehicle integration into power grids during the transition toward renewable-based energy systems.
5. Conclusions and Future Work
5.1 Key Conclusions
This research addresses high-penetration electric vehicle integration challenges through a multi-level modeling and voltage stability assessment framework. The principal conclusions are summarized as follows:
(1) High-Power Fast Charging Refined Modeling
A system-level charger modeling approach based on CC-CV coordinated control was developed. By integrating detailed dynamic models of PWM rectifiers and DC/DC converters with measured parameter identification, a static load model capturing two-stage temporal coupling characteristics was established. The model distinguishes itself from conventional representations by simultaneously accommodating CC and CV dynamic responses. The constant power component dominates, while weak negative constant-current components provide adaptive regulation factors. Model accuracy improvements over conventional ZIP approximations enable high-precision device-level simulations where, under fast charging, the constant power characteristics constitute primary voltage sensitivity sources.
(2) Two-Machine Dynamic Equivalencing for Large-Scale Charging Clusters
Overcoming single-machine modeling dimensionality constraints, the proposed approach categorizes charging clusters into CC and CV groups with corresponding equivalent circuits. Mean-value models aggregate power electronic converter dynamics to establish a computationally efficient equivalent circuit capturing spatiotemporal load distribution patterns. The dynamic model demonstrates predominantly resistive characteristics at the system level. The transient voltage profile fittings from validation data exceed conventional equivalence methods in precision, offering an effective tool for transient voltage stability analysis in high-penetration environments.
(3) Segmented Probabilistic Load Modeling Theory
A segmented probabilistic framework decomposes charging power into CC/CV dual-phase representations for multi-scenario modeling. Monte Carlo simulations, integrating user behavior distributions and spatially heterogeneous charging patterns, produce time-varying load curves that accurately reproduce peak-valley expansion phenomena under fast-charging saturation. The simulations quantify that for every 10% increase in electric vehicle penetration, system peak-valley differences rise by nearly 10%. These quantitative outputs provide analytic foundations for peak-shaving strategy development in grids experiencing high electric vehicle integration.
(4) Voltage Stability Assessment Methodology
The integrated static-transient verification framework clarifies non-linear PV curve distortion mechanisms under fast-charging load distributions. Static analysis at 20% electric vehicle load composition shows system stability margins degrading by up to 25%, confirming static voltage stability reduction. Transient analysis on the benchmarking system demonstrates that electric vehicle clusters, through converter-based load characteristics, induce voltage sag phenomena, decrease minimum voltage thresholds, prolong low-voltage durations with increasing electric vehicle share, and introduce oscillatory responses. These findings collectively offer supplementary dynamic reactive power configuration criteria for receiving-end grid systems.
5.2 Future Research Directions
Although significant progress has been achieved, future high-penetration scenarios under double-high system characteristics necessitate further research efforts:
(1) V2G Dynamic Coupled Modeling
Current models concentrate on unidirectional power flow and overlook impedance reshaping effects under bidirectional V2G operation. Future research should investigate impedance modeling of four-quadrant power converters, revealing harmonic oscillation mechanisms during charging-discharging mode transitions.
(2) Multi-Energy Coupled System Extensions
Cluster equivalence models do not yet incorporate photovoltaic output fluctuations, energy storage SOC constraints, and charging loads within integrated PV-storage-charging stations. Multi-timescale collaborative modeling should explore renewable penetration modulation effects on aggregate load characteristics.
(3) Data-Model Hybrid-Driven Paradigms
For data-sparse observational environments, transfer learning combined with physics-informed meta-modeling frameworks would enable adaptive parameter configurations. Transferring operational data across charging stations improves model generalization capabilities under extreme scenarios.
(4) Distributed Resource Aggregation Control Validation
Future integration with virtual power plant architectures should develop equivalence-model-based distributed resource coordination strategies, with real-time control validation executed on hardware-in-loop platforms for operational deployment readiness.
These prospective directions ensure continuous evolution of modeling methodologies commensurate with technological innovations and system expansion trajectories.