1. Introduction
Electrical-power-system digital simulation is still one of the most important foundations for power-network expansion planning and for the formulation of operating strategies. In this context, load-model accuracy directly determines the credibility of numerical simulations and the validity of subsequent security assessments. Traditional load models, however, face two major challenges when they are applied to networks with a high penetration of electric cars. On the one hand, modern fast-charging equipment for electric cars adopts a coordinated constant-current–constant-voltage (CC–CV) control mechanism; the multi-stage switching behaviour of this mechanism considerably increases the complexity of single-unit load modeling. On the other hand, the spatio-temporal randomness and dynamic interaction effects of large-scale clusters of electric cars make it extremely difficult for conventional equivalent methods to represent the collective load characteristics accurately.
Simulation inaccuracies caused by unsuitable load models can introduce several risks into a receiving-end power system, including incorrect capacity planning, misjudged operating margins, and even voltage-collapse accidents. Therefore, in this thesis I focus on the four-layer technical route of “single-unit model, aggregation model, probabilistic model, and stability evaluation”, and I investigate multi-timescale load modeling of electric cars together with the influence of those loads on grid voltage stability. I develop a hierarchical framework which permits a systemic understanding of how electric cars acting as a new type of load affect steady-state voltage profiles and transient recovery performance.
Through field data, typical charging topologies, stochastic behavioral simulation, and dynamic-equivalent construction, the present study shows that electric cars cannot be simply represented by conventional static load components. The coordination of CC/CV processes, the state-of-charge dependence of aggregated charging power, and the charging-mode diversity of different electric-car fleets all have measurable impacts on the voltage security of the receiving-end power grid. The rest of this paper is organised as follows. Section 2 develops the mechanistic load model for high-power fast chargers and an equivalent two-machine cluster model. Section 3 establishes a segmented probabilistic load model for electric cars by considering charging-behavior randomness. Section 4 then applies the models in static and transient voltage-stability studies, and Section 5 draws conclusions and gives several research perspectives.
2. Equipment-Level and Cluster-Level Load Models for Electric Cars
2.1 Lithium-Battery Charging Characteristics
The majority of modern electric cars are equipped with lithium-ion battery packs. From a load-modeling point of view, the most important properties of such packs are their nonlinear open-circuit voltage, internal resistance, and state-of-charge (SOC) evolution. A dynamic model with the Thevenin structure can be written as
$$
U_{\mathrm{bat}} = E_0 – K\frac{Q}{Q-\int i\,\mathrm{d}t} + A \exp\!\left(-B \int i\,\mathrm{d}t\right) – R i,
$$
$$
\mathrm{SOC}\!\left(t\right)=\mathrm{SOC}_0 + \frac{1}{Q}\int_{0}^{t} i\!\left(\tau\right)\mathrm{d}\tau,
$$
where \(Q\) is the rated capacity, \(R\) is the equivalent internal resistance, \(K\) is the polarization coefficient, \(E_0\) is the constant battery electromotive force, and \(A\), \(B\) are constants of the exponential charging region.
For slow charging, the CV stage occupies a very small portion of the total charging period; it can be neglected in some simplified studies. In contrast, for a 150-kW fast-charging facility, the CC stage increases the SOC almost linearly, but the CV stage accounts for about 40–50% of the effective charging time and has a significant grid-side interaction. Therefore, I use a two-stage model that explicitly describes both CC and CV phases. The fast-charging power can be expressed as
$$
P_{\mathrm{ch}}(t) =
\begin{cases}
P_{\mathrm{CC}} = U_{\mathrm{dc}} I_{\mathrm{CC}}, & 0 \leq \mathrm{SOC}(t) < 0.8,\\[4pt]
P_{\mathrm{CV}}(t) = \dfrac{U_{\mathrm{CV}}^2}{Z_{\mathrm{batt}}(t)}, & 0.8 \leq \mathrm{SOC}(t) \leq 1,
\end{cases}
$$
where \(U_{\mathrm{dc}}\) denotes the DC-link voltage, \(I_{\mathrm{CC}}\) is the controlled constant charging current, and \(Z_{\mathrm{batt}}(t)\) is the equivalent battery impedance evolving during the CV region. This stage-dependent representation is used throughout my study as the physical basis of the charging-load model.
2.2 Simplified Circuit and Static ZIP Model for Fast-Charging Electric Cars
A wide-applied topology of an electric-car charger consists of a three-phase PWM rectifier followed by an isolated DC/DC converter. Since the unity-power-factor rectifier keeps the reactive power at approximately 1% of the active power, the charger can be reasonably simplified as a DC equivalent circuit. Writing the KVL equations of the two loops gives
$$
U_s = U_{\mathrm{dc}} + R_s I_{\mathrm{dc}},
$$
$$
U_{\mathrm{dc}} = E_{\mathrm{eq}} + R_{\mathrm{eq}} I_{\mathrm{dc}},
$$
where \(U_s\) represents the grid-side voltage translated to the DC side, \(R_s\) is the equivalent resistance of the power-electronic interface, \(R_{\mathrm{eq}}\) is the battery-side equivalent resistance, and \(E_{\mathrm{eq}}\) is the battery electromotive force. Manipulating the above algebraic equations, and assuming the active power is \(P=U_{\mathrm{dc}}I_{\mathrm{dc}}\), yields the ZIP-type expression
$$
P = P_0 \left[ a_p \left(\frac{U}{U_0}\right)^{2} + b_p \left(\frac{U}{U_0}\right) + c_p \right],
$$
$$
Q = Q_0 \left[ a_q \left(\frac{U}{U_0}\right)^{2} + b_q \left(\frac{U}{U_0}\right) + c_q \right].
$$
I identified the model parameters from the measured operating points of a 150-kW charger through a particle-swarm optimization algorithm. The result is characterized by
$$
P = P_0 \left[0.023\left(\frac{U}{U_0}\right)^2 – 0.057\left(\frac{U}{U_0}\right) + 1.034\right].
$$
The fitted parameters are summarized in Table 1. The dominant constant-power component indicates that the grid-connected charger is internally regulated by the closed-loop power controller. The small negative current coefficient shows that, when the terminal voltage rises, the charging current tends to decrease; this behavior offers a limited self-stabilizing effect for the electric-car load.
| Coefficient | Active-power component | Physical implication |
|---|---|---|
| Constant impedance, \(a_p\) | 0.023 | Negligible impedance effect |
| Constant current, \(b_p\) | -0.057 | Weak negative-current feedback |
| Constant power, \(c_p\) | 1.034 | Dominant constant-power behavior |
2.3 Dynamic Two-Machine Equivalent of a Charging Station for Electric Cars
When a large number of electric cars are charged together, simulating every on-board charger is computationally infeasible for electromechanical transient studies. I therefore establish a two-machine aggregation method, which classifies the in-service chargers according to their present charging mode: constant-current group and constant-voltage group. For each group, the average-value model is used to replace the switched power-electronics converters, and an equivalent circuit is derived.
In the CV mode, the charging batteries behave approximately as constant impedances; parallel connection of \(N\) vehicles yields an equivalent admittance
$$
Y_{\mathrm{eq}}^{\mathrm{CV}} = \sum_{n=1}^{N} \frac{1}{R_{s,n}+R_{\mathrm{eq},n}} \approx \frac{N}{R_{s}+R_{\mathrm{eq}}},
$$
where the approximation holds when the vehicles have similar parameters. The CV charging group can therefore be represented by a fixed impedance to the power system.
In the CC mode, the battery units are effectively connected in series at the aggregated DC side. The equivalent open-circuit voltage and the equivalent resistance are
$$
E_{\mathrm{eq}}^{\mathrm{CC}} = \sum_{n=1}^{N} E_{\mathrm{eq},n},
\qquad
R_{\mathrm{eq}}^{\mathrm{CC}} = \sum_{n=1}^{N} R_{\mathrm{eq},n}.
$$
Combining the CC-group model and CV-group model into one station-level circuit gives the equivalent in Figure 1 of my original thesis. The two-machine model retains the key difference between the constant-current and constant-voltage fleets, i.e. the same terminal-voltage disturbance has different effects on the grid-side electrical power of the two types of charger.
| Charging group | Equivalent element | Formula |
|---|---|---|
| CV group of \(N\) electric cars | Constant admittance | \(Y_\mathrm{eq}^{\mathrm{CV}} \simeq N / (R_s + R_\mathrm{eq})\) |
| CC group of \(M\) electric cars | Voltage source + series resistance | \(E_\mathrm{eq}^{\mathrm{CC}} = \sum E_i,\; R_\mathrm{eq}^{\mathrm{CC}} = \sum R_i\) |
Using a Simulink transient simulation, I compared the detailed charger model with the proposed aggregation model. The model accurately tracked the dynamic voltage and the active power during steady-state operation. Some deviations appeared during abrupt power changes because the DC/DC converter had been simplified; nevertheless, the similarity is adequate for the voltage-stability-oriented analysis of a large-scale receiving-end grid.
3. Probability-Based Segmented Load Model for Electric Cars
3.1 Random Factors of Charging Loads
The load of electric cars is not deterministic. Instead, it depends on trip chains, user habits, charging-station locations, and vehicle states. In this research, I establish probability models for the most relevant variables, including charging-start time, daily driving distance, initial SOC, and charging power.
The last-trip finish time, which approximately represents the charging-start time for most electric cars in residential districts, is described by a multi-peak normal distribution. A common expression for the probability density of the start charging time is
$$
f_s\left(x\right) =
\frac{1}{\sigma_s \sqrt{2\pi}}
\exp\!\left[ -\frac{\left(x – \mu_{s}\right)^2}{2\sigma_{s}^{2}} \right],
$$
where \(\mu_s\) is the expected finish time and \(\sigma_s\) is the standard deviation. For the daily driving distance \(d\), the lognormal distribution is adopted:
$$
f_d\left(d\right) = \frac{1}{d\,\sigma_d \sqrt{2\pi}}
\exp\!\left[ -\frac{\left(\ln d – \mu_d\right)^2}{2\sigma_d^2} \right].
$$
The initial SOC before charging can be derived from the daily mileage according to
$$
\mathrm{SOC}_{\mathrm{start}} = \mathrm{SOC}_{\mathrm{previous}} – \frac{d}{d_{\mathrm{range}}},
$$
where \(d_{\mathrm{range}}\) represents the full-range mileage of the electric car. Thus the charging duration obeys
$$
T_{\mathrm{ch}} = \frac{\left(1-\mathrm{SOC}_{\mathrm{start}}\right) Q_{\mathrm{bat}}}{\eta P_{\mathrm{rated}}},
$$
where \(Q_{\mathrm{bat}}\) is the battery rated energy, \(\eta\) is the charger efficiency, and \(P_{\mathrm{rated}}\) is the rated active power. For fast-charging electric cars, the CP is further segmented into a CC power stage and a CV power stage instead of using a single rated-power value.
3.2 Monte-Carlo Aggregation
I use the Monte-Carlo method to generate many daily realizations of the charging loads of electric cars. At a discrete time instant \(j\), the total charging load of the whole regional system is
$$
P_{\Sigma}\left(t_j\right) = \sum_{i=1}^{N_{\mathrm{EV}}} P_i\left(t_j\right),
$$
where \(N_{\mathrm{EV}}\) is the total number of electric cars and \(P_i\) is the instantaneous power of the \(i\)-th electric car obtained from the CC/CV power profile. The output of the simulation is the time-series load curve \(P_\Sigma(t)\), which is then superimposed on the conventional daily load curve of the city. Throughout the procedure, every drawn sample represents one possible behavior pattern of electric cars, and the statistical performance converges as the number of vehicles and Monte-Carlo trials increases.
3.3 Vehicle-Type Model Configurations
I create different probabilistic input configurations for four important groups of electric cars: electric buses, electric taxis, electric official cars, and electric private cars. Tables 3–6 summarize the distributions used for the charging-start time and initial SOC. The average charging power is divided into slow charging, fast charging, and the rated power of different vehicle types.
| Charging session | Time window | Charging-start distribution | Initial-SOC distribution | Mode |
|---|---|---|---|---|
| Daytime fast charge | 09:00–16:30 | Uniform(9, 16.5) | N(0.5, 0.12) | 150/45 kW CC/CV |
| Night slow charge | 23:00–05:00 | Uniform(23, 24) | N(0.5, 0.12) | 21 kW |
| Charging session | Time window | Charging-start distribution | Initial-SOC distribution | Mode |
|---|---|---|---|---|
| Driver-shift fast charge | 02:00–04:00 | Uniform(2, 4) | N(0.3, 0.12) | 150/45 kW CC/CV |
| Lunchtime fast charge | 11:00–14:00 | Uniform(11, 14) | N(0.3, 0.12) | 150/45 kW CC/CV |
| Charging session | Time window | Charging-start distribution | Initial-SOC distribution | Mode |
|---|---|---|---|---|
| After-work slow charge | 18:00–07:00 | Uniform(18, 24) | N(0.4, 0.12) | 7 kW |
| Mode | Time horizon | Charging-start distribution | Initial-SOC distribution | Share |
|---|---|---|---|---|
| Home slow charge | All day | N(17.6, 2.6) | N(0.4, 0.88) | 80% |
| Public rapid charge | All day | N(17.6, 2.6) | N(0.4, 0.88) | 20% |
3.4 Simulated Charging Curves and Peak-Valley Impact
Using the above probability assumptions, I simulate 1,000 electric buses, 2,000 taxis, 2,000 official cars, and 10,000 private cars. The typical simulation configuration is listed in Table 7. Figure 2 in my simulation report illustrates the total daily load curves of the four vehicle types after 1,440-minute aggregation.
| Electric-car group | Number of vehicles | Battery capacity/kWh | Slow-charging rating/kW | Fast-charging rating/kW |
|---|---|---|---|---|
| Electric buses | 1000 | 180 | 21 | 150/45 CC/CV |
| Electric taxis | 2000 | 75 | — | 150/45 CC/CV |
| Electric official cars | 2000 | 75 | 7 | — |
| Electric private cars | 10000 | 75 | 7 | 150/45 CC/CV |
The simulation results show that the charging load of electric buses has two peak components: a daytime fast-charging peak occurs at about 14:30, while a lower night peak occurs after 23:00. Electric taxis produce peaks during the 02:00–04:00 and 11:00–14:00 time intervals. Electric private cars form the strongest peak during the evening residential demand period, with the maximum total charging power exceeding 45 MW in the simulated configuration.
After superimposing the probabilistic charging load of electric cars onto the original daily load curve of the urban power system, the peak-valley difference clearly increases. Taking an EV penetration rate of 10% as an example, the simulated increase in the daily peak-valley difference is about 480 MW, as shown in Table 8. This concurrency between the charging peak of electric cars and the original system peak is a crucial challenge for distribution-network voltage control.
| Scenario | Peak-valley difference / MW | Increase / MW |
|---|---|---|
| Original daily load curve | 4350 | — |
| With 10% penetration of electric cars | 4830 | 480 |
The results confirm that my segmented probabilistic load model can reproduce the phenomenon of peak-valley expansion induced by fast-charging electric cars. The conventional method that represents the fast-charging power as a constant value under-predicts the evening charging peak and cannot correctly reflect the charging-stage transition of the CC / CV process.
4. Static Voltage Stability Analysis of the Receiving-End Grid with Electric-Car Loads
4.1 Analytical Load Effect on the Static Voltage Stability
In steady-state voltage-stability analysis, the \(P\)-\(V\) curve method is the most intuitive tool. Different load behaviors have quite different influences. For an ideal constant-power load, the consumed power stays constant even when the voltage decreases; this aggravates the voltage collapse and reduces the maximum deliverable power. For a constant-impedance load, the consumed power declines as the voltage drops, which has a positive stabilizing effect. The linear constant-current load is an intermediate case. My identified ZIP model of electric cars, with coefficients \((a_p,b_p,c_p)=(0.023,-0.057,1.034)\), shows that the constant-power nature of fast-charging electric cars is dominant. Therefore, the load-level voltage-stability margin tends to shrink when electric cars are connected.
4.2 Continuation Power Flow and Evaluation Index
To trace the full \(P\)–\(V\) curve up to the nose point, I apply the continuation power flow (CPF) method. The parameterized power-flow equation is
$$
\mathbf{F}\left(\mathbf{x},\lambda\right) = \mathbf{0},
$$
where \(\lambda\) is the load-growth parameter. For every bus \(i\), the active and reactive power injections are expressed as
$$
P_{Gi}\left(\lambda\right) – P_{Li}\left(\lambda\right) – P_{i}\left(\mathbf{x},\lambda\right) = 0,
$$
$$
Q_{Gi}\left(\lambda\right) – Q_{Li}\left(\lambda\right) – Q_{i}\left(\mathbf{x},\lambda\right) = 0,
$$
with the load changing as
$$
P_{Li}\left(\lambda\right) = P_{Li0} + \lambda \gamma_{Pi},
\qquad
Q_{Li}\left(\lambda\right) = Q_{Li0} + \lambda \gamma_{Qi},
$$
where \(\gamma_{Pi}\) and \(\gamma_{Qi}\) characterize the direction of load increase at bus \(i\). The voltage-stability margin used in this study is defined as
$$
K_{p} = \frac{\lambda_{\max} – \lambda_{\mathrm{base}}}{\lambda_{\mathrm{base}}} \times 100\%,
$$
where \(\lambda_{\max}\) denotes the load parameter at the critical point corresponding to the nose of the \(P\)–\(V\) curve.
4.3 Simulation Results on an IEEE 9-Bus System
I first apply the proposed electric-car load model to an IEEE 9-bus system. The electric-car loads are attached to the original load buses, and the penetration ratio is increased from 0% to 30%. The continuation power-flow results show that, as the electric-car share increases, the maximum load parameter decreases, while the critical voltage slightly increases. This implies that the voltage remains higher in the early stage of loading, but the system reaches its stability boundary earlier. Table 9 lists the critical parameters for the considered scenarios.
| Scenario | Critical voltage / p.u. | Maximum loading parameter / p.u. |
|---|---|---|
| No electric cars | 0.45 | 5.80 |
| 10% electric cars | 0.51 | 5.31 |
| 20% electric cars | 0.55 | 4.86 |
| 30% electric cars | 0.59 | 4.42 |
Further time-domain simulations are carried out by gradually increasing the load power from \(t=1\) s. With a 20% share of electric cars, the voltage can still remain stable after a 40% load increase; however, with a 40% share, a 30% load increase can make the voltage collapse. Thus, the penetration of electric cars significantly reduces the static voltage-stability margin of the system.
4.4 Spatial Distribution Effects on an IEEE 24-Bus System
To evaluate the influence of the spatial mobility of electric cars, I construct an IEEE 24-bus receiving-end network. Three residential/commercial load buses are selected as the charging hotspots for electric cars. The time-varying probabilistic load of private electric cars is placed at node 8 during the daytime and at node 6 at night, according to the travel behavior of commuters. Table 10 compares two scenarios: uniform load distribution and spatio-temporal migration distribution.
| Penetration ratio | Stability margin under uniform distribution / % | Stability margin under spatial migration / % |
|---|---|---|
| 10% | 12.8 | 14.1 |
| 20% | 9.6 | 11.2 |
| 30% | 6.7 | 8.5 |
The simulation results show that the charging-load location matters as much as the total amount. Spatial migration of electric cars smooths the line-flow distribution and alleviates the risk of overloading a single feeder. Therefore, the time-space scheduling potential of electric cars could be exploited to improve the voltage stability of a receiving-end grid instead of treating it only as a burden.
5. Transient Voltage Stability Evaluation with Dynamic Electric-Car Models
5.1 Load Types and Transient Voltage Responses
Transient voltage stability is mainly concerned with the ability of the system to restore acceptable voltages after a large disturbance. Different load models produce quite different post-fault voltage trajectories. For a comprehensive comparison, I use four load representations in time-domain simulations: a constant-impedance load, a constant-power load, an induction-motor load, and the CC/CV aggregation model of electric cars. The voltage dynamics after a three-phase short-circuit fault are compared. The constant-power load leads to an amplifying voltage oscillation and the lowest post-fault voltage among the conventional loads. The induction-motor load shows damped oscillation but a longer short-term voltage recovery time.
| Load model | Lowest voltage / p.u. | Oscillation type | Voltage recovery time / s |
|---|---|---|---|
| Constant impedance | 0.42 | Damped | 0.13 |
| Constant power | 0.32 | Amplified | 0.13 |
| Induction motor | 0.45 | Damped | 0.69 |
5.2 Fault Scenario and Dynamic Equivalent of a Large Receiving-End Grid
The transient analysis is performed on a high-renewable receiving-end benchmark system with a conventional DC infeed and a strong dynamic-reactive-power support area. The base case includes thermal generation, wind power, photovoltaic units, and two synchronous condensers. A double-circuit transmission-line fault is applied at \(t=1.00\) s; one circuit is tripped at \(1.09\) s and the other also trips at \(1.10\) s. Without additional countermeasures, the receiving-end system enters a voltage-collapse mode after the fault.
I then replace one weak distribution bus load by the dynamic CC/CV aggregating model of electric cars. In the first case, the distribution bus B36 has a share of electric cars that increases from 10% to 30%. The transient voltage curves show that the minimum voltage of B36 decreases and the recovery time becomes longer when more electric cars are installed. In the second case, the spatio-temporal distribution of electric cars is considered; the voltage-drop phenomenon becomes less severe than that in the spatially concentrated case, but the increasing EV share always dominates the instability trend.
For the continuous-low-voltage (CLV) mode, the same fault does not immediately induce DC blocking but creates a sustained low-voltage area. The simulation results show that the higher the penetration of fast-charging electric cars, the deeper the voltage sag and the longer the low-voltage duration; moreover, voltage oscillations appear at the distribution bus during recovery. This trend is quantified by the following transient-voltage stability index based on the post-fault voltage integral:
$$
I_{\mathrm{TVC}} = \int_{t_c}^{t_{\mathrm{end}}} \frac{U(t)-U_{\mathrm{ref}}}{U_{\mathrm{ref}}} \,\mathrm{d}t,
$$
where \(t_c\) denotes the fault-clearing time, \(U_{\mathrm{ref}}\) is the expected voltage level, and \(I_{\mathrm{TVC}}\) becomes smaller when the electric-car load is larger, indicating the degraded transient voltage performance of the receiving-end grid.
| Penetration of electric cars | Minimum voltage / p.u. | Recovery time / s | Oscillation |
|---|---|---|---|
| VC mode, 10% | 0.42 | 0.85 | Weak |
| VC mode, 20% | 0.38 | 1.25 | Weak |
| VC mode, 30% | 0.33 | 1.80 | Moderate |
| CLV mode, 10% | 0.31 | 3.20 | Moderate |
| CLV mode, 20% | 0.26 | 4.60 | Strong |
| CLV mode, 30% | 0.21 | 5.50 | Strong |
5.3 Interpretation of the Negative-Damping Mechanism
From the perspective of dynamic equivalent circuits, the CC charging group of electric cars is, by definition, trying to maintain a constant current through the battery. When the AC voltage is depressed by a fault, the DC-link or battery current remains almost unchanged, and therefore the active power consumed by the charger decreases temporarily. This behavior resembles a constant-current load. Once the voltage starts to recover, the power controller restores the charging power; if the system is weak, such a recovery creates an additional power demand that slows the voltage recovery.
A small-signal interpretation can be made by writing the incremental active power as
$$
\Delta P \approx \frac{\partial P}{\partial U} \Delta U + \frac{\partial P}{\partial I_{dc}} \Delta I_{dc}.
$$
For the CC-stage group, the controlled current keeps \(\Delta I_{dc}\) small, so that the effective coefficient \(\partial P/\partial U\) is approximately zero or even negative with respect to voltage support. The charging clusters of electric cars therefore have a weak negative damping effect during the transient voltage-recovery stage. The constant-voltage-stage group, on the contrary, is basically a passive impedance and enhances voltage support. The balance between CC-group and CV-group sizes is thus the main mechanism through which electric cars affect the transient voltage stability of a receiving-end grid.
6. Conclusions and Future Work
6.1 Main Conclusions
In this research, I built a complete load-modeling framework for electric cars, from a single charger through cluster aggregation to grid-level probabilistic representation, and I applied it to both static and transient voltage-stability assessments. The following conclusions are drawn.
First, a 150-kW fast charger used by electric cars shows strongly constant-power static characteristics because of its closed-loop CC-CV controller. The ZIP model identified in this study gives \(a_p=0.023\), \(b_p=-0.057\), and \(c_p=1.034\), demonstrating that the conventional constant-power approximation is largely valid for quasi-steady-state studies, but the small negative-current component should not be ignored when studying voltage-support behavior.
Second, the dynamic two-machine equivalent of a large charging station can accurately represent the group behavior of electric cars during transient simulations. The CC charging group behaves as a controlled-current source and is the main source of negative damping, whereas the CV charging group behaves as an equivalent impedance and contributes to voltage self-restoration.
Third, the probabilistic load model with CC/CV segmentation reproduces the peak-valley expansion caused by fast charging electric cars more accurately than a single-valued power model. The evening charging peak of electric private cars is simultaneous with the original load peak; this increases the peak-valley difference of the city power grid by approximately 10% when the penetration rate of electric cars increases by 10%.
Fourth, static continuation-power-flow simulations show that the critical loading margin of the tested IEEE 9-bus and IEEE 24-bus systems decreases monotonically with an increasing proportion of electric cars. Spatial migration private cars can alleviate some local voltage stress, but at high penetration the overall stability margin is still reduced. Transient simulations on a receiving-end system show that a larger share of electric cars decreases the post-fault minimum voltage, prolongs the low-voltage period, and intensifies voltage oscillations.
6.2 Future Research
Several directions should be further explored in future studies. First, the vehicle-to-grid (V2G) mode requires a bidirectional load model of electric cars, including the reverse active-power flow and the different control modes of the power converter. Second, the integration of photovoltaic, battery-storage, and charging piles in an integrated “PV-storage-charging” station calls for a multi-energy coupling equivalent model. Third, when measurement data are sparse, the hybrid data-and-physics-driven paradigm, such as transfer learning with physical constraints, might enhance the generalization ability of the electric-car load models. Finally, hardware-in-the-loop experiments should be conducted to verify the proposed equivalent models in real-time distribution-network control.
Overall, this thesis provides a hierarchical set of load models and the corresponding voltage-stability assessment methods. The results offer quantitative evidence for the planning and operation of receiving-end grids with large numbers of electric cars.