With the rapid development of the electric vehicle industry, particularly in China where EV adoption is accelerating, large-scale integration of electric vehicles into DC microgrids is becoming increasingly common. Electric vehicles can function as energy storage units by discharging power to the grid or act as loads when charging from the grid. However, when numerous electric vehicles are connected to a DC microgrid, their collective charging and discharging behaviors can significantly impact the system’s stability. In this analysis, I explore the effects of China EV integration on DC microgrid stability by developing comprehensive models, including photovoltaic units, DC bus voltage control units, and equivalent constant-power models for electric vehicle charging and discharging. Using system impedance stability criteria, I evaluate stability through Bode plots and Nyquist diagrams, revealing that increasing the number of charging electric vehicles can destabilize the microgrid, while discharging behaviors enhance stability. This underscores the potential of managing China EV charging and discharging transitions as a strategy to improve DC microgrid performance.
The proliferation of electric vehicles, especially in markets like China EV, introduces both opportunities and challenges for power systems. DC microgrids, which integrate renewable sources like photovoltaics, are susceptible to instability due to the dynamic nature of electric vehicle loads. In this work, I model a DC microgrid comprising a photovoltaic unit, a DC bus voltage control unit (representing energy storage), and electric vehicle units that can switch between charging and discharging modes. The electric vehicle charging is modeled as a constant-power load, while discharging is treated as a controlled voltage source. By deriving the system impedance and applying stability criteria, I analyze how variations in the number of charging and discharging China EVs affect the microgrid. The findings indicate that stability can be actively managed by adjusting the ratio of charging to discharging electric vehicles, offering a viable approach for grid operators in regions with high EV penetration.
To begin, I establish the model for the DC microgrid, starting with the photovoltaic unit. This unit consists of a PV array connected to a Boost converter, which steps up the voltage to the DC bus. The state-space equations for the photovoltaic unit are derived from its circuit representation. Let \( U_{PV} \) and \( I_{PV} \) denote the output voltage and current of the PV array, respectively, \( L_{PV} \) the inductor of the Boost converter, \( R_{PV} \) the equivalent resistance, \( C_{PV} \) the input capacitor, \( C_{s1} \) the output filter capacitor, \( U_{bus} \) the DC bus voltage, \( I_{PVdc} \) the output current, and \( d_1 \) the duty cycle of the switch. The state-space equations are:
$$ C_{PV} \frac{dU_{PV}}{dt} = I_{PV} – I_{L_{PV}} $$
$$ L_{PV} \frac{dI_{L_{PV}}}{dt} = U_{PV} – R_{PV} I_{L_{PV}} – (1 – d_1) U_{bus} $$
$$ C_{s1} \frac{dU_{bus}}{dt} = (1 – d_1) I_{L_{PV}} – I_{PVdc} $$
Linearizing around a steady-state operating point and applying Laplace transforms yields the small-signal model. The output impedance of the photovoltaic unit, \( Z_{PV} \), is derived as:
$$ Z_{PV} = Z_2 – \frac{G_1 G_{PV} G_3}{1 + G_{PV} H_1} $$
where \( Z_2 = \frac{\Delta U_{bus}}{\Delta I_{PVdc}} \), \( G_1 = \frac{\Delta U_{PV}}{\Delta I_{PVdc}} \), \( G_3 = \frac{\Delta U_{bus}}{\Delta d_1} \), \( G_{PV} = K_{PV} + \frac{T_{PV}}{s} \) (the PI controller for voltage regulation), and \( H_1 \) is the feedback gain. This impedance model captures the dynamics of the photovoltaic unit under varying operating conditions, which is crucial for assessing interactions with electric vehicle loads.
Next, I model the energy storage unit, which represents electric vehicles in discharging mode. For lithium-ion batteries commonly used in China EVs, a first-order Thevenin equivalent circuit is employed, comprising an ideal voltage source \( E \), internal resistance \( r \), polarization resistance \( R_o \), and polarization capacitance \( C_o \). The battery output voltage \( U_E \) and current \( I_E \) relate as:
$$ C_o \frac{dU_{C_o}}{dt} = I_E – \frac{U_{C_o}}{R_o} $$
$$ U_E = E – r I_E – U_{C_o} $$
The battery is connected to the DC microgrid via a bidirectional DC-DC converter, which uses a voltage-current dual-loop droop control strategy to maintain bus voltage stability. The state-space equations for this unit are:
$$ L_{BAT} \frac{dI_{L_{BAT}}}{dt} = U_{BAT} – R_{BAT} I_{L_{BAT}} – d_2 U_{bus} $$
$$ C_{s2} \frac{dU_{bus}}{dt} = d_2 I_{L_{BAT}} – I_{BATdc} $$
After linearization, the output impedance \( Z_{BAT} \) is derived as:
$$ Z_{BAT} = \frac{Z_3 – R_d P_1 G_9 G_{10} – G_6 G_9 G_{10}}{1 + P_1 G_9 G_{10}} $$
where \( Z_3 = \frac{\Delta U_{bus}}{\Delta I_{BATdc}} \), \( G_6 = \frac{\Delta I_{L_{BAT}}}{\Delta I_{BATdc}} \), \( G_9 = \frac{\Delta U_{bus}}{\Delta d_2} \), \( G_{10} = \frac{P_2}{1 + G_7 P_2} \) (current inner loop transfer function), and \( P_1 \), \( P_2 \) are PI controllers for voltage and current loops, respectively. This model allows us to analyze how discharging China EVs contribute to grid stability by acting as controlled sources.
For electric vehicle charging, I model it as a constant-power load, which is a common approximation for power electronic-based loads. When multiple China EVs are charging simultaneously, they appear as parallel constant-power loads on the DC microgrid. The power balance for the \( i \)-th load is given by \( P_{CPLi} = U_{CPLi} I_{CPLi} \), where \( U_{CPLi} \) is the input capacitor voltage and \( I_{CPLi} \) is the current. The equivalent impedance for a constant-power load is negative incremental resistance, derived as:
$$ Z_{CPL} = \frac{U_{CPLi}^2}{P_{CPLi}} $$
In small-signal terms, the impedance \( Z_{CPL} \) for multiple charging electric vehicles is combined as parallel components, leading to potential instability if the total charging power exceeds certain thresholds. This is critical in scenarios with high penetration of China EVs, where charging demands can fluctuate widely.
The discharging unit for electric vehicles is modeled similarly to the storage unit but with a focus on grid support. Using a bidirectional converter, the state-space equations are:
$$ L_F \frac{dI_{L_F}}{dt} = U_F – R_F I_{L_F} – (1 – d_3) U_{bus} $$
$$ C_{s3} \frac{dU_{bus}}{dt} = (1 – d_3) I_{L_F} – I_{Fdc} $$
The output impedance \( Z_F \) is:
$$ Z_F = \frac{Z_4 – G_{12} G_{15} G_{16}}{1 + P_3 G_{15} G_{16}} $$
where \( Z_4 = \frac{\Delta U_{bus}}{\Delta I_{Fdc}} \), \( G_{12} = \frac{\Delta I_{L_F}}{\Delta I_{Fdc}} \), \( G_{15} = \frac{\Delta U_{bus}}{\Delta d_3} \), and \( G_{16} = \frac{P_4}{1 + G_{13} P_4} \), with \( P_3 \) and \( P_4 \) as PI controllers. This discharging model highlights how China EVs can inject power to stabilize the microgrid during peak demands.
To assess the overall system stability, I compute the total equivalent impedance \( Z \) of the DC microgrid by combining all unit impedances in parallel:
$$ Z = Z_{PV} \parallel Z_{BAT} \parallel Z_F \parallel Z_{bus} \parallel Z_{CPL} $$
where \( Z_{bus} \) represents the line impedance of the DC bus. The stability is evaluated using the system impedance stability criterion, which requires that the real part of \( Z(s) \) is positive, the phase angle in the Bode plot remains within ±90°, and the Nyquist plot does not encircle the left half-plane. This approach is effective for analyzing systems with bidirectional power flow, such as those involving electric vehicle charging and discharging.
In the case studies, I examine four scenarios to illustrate the impact of China EV integration. The first case varies the number of charging electric vehicles while keeping other parameters constant. Assuming a photovoltaic generation of 500 kW and a charging power of 5 kW per electric vehicle, I compute the system impedance for 10, 20, and 30 charging China EVs. The Nyquist plots show that as the number of charging electric vehicles increases, the curves shift toward the left half-plane, indicating reduced stability margins. Bode plots reveal phase angles approaching and exceeding ±90° for higher charging counts, confirming the destabilizing effect. This aligns with the negative impedance characteristics of constant-power loads, which can introduce oscillations in the DC microgrid.
The second case investigates the stabilizing effect of discharging China EVs when the microgrid is initially unstable. With 100 charging electric vehicles (total 500 kW charging power) and no discharging units, the system impedance Nyquist plot enters the left half-plane, and the Bode phase angle exceeds ±90°, indicating instability. However, when discharging units are added—each providing 16 kW—the Nyquist plot shifts to the right half-plane, and the phase angle returns to within ±90°, restoring stability. This demonstrates how strategic deployment of discharging electric vehicles can mitigate instability caused by excessive charging loads.
The third case explores the transition between charging and discharging states for a fixed total of 100 China EVs. I analyze three configurations: all vehicles charging, 75 charging and 25 discharging, and 50 charging and 50 discharging. The results, summarized in Table 1, show that as more electric vehicles switch to discharging, the system impedance phase angle improves, and Nyquist plots become confined to the right half-plane. This transition enhances stability, emphasizing the value of vehicle-to-grid (V2G) technologies for China EV ecosystems.
| Configuration | Charging EVs | Discharging EVs | Nyquist Stability | Bode Phase Angle |
|---|---|---|---|---|
| All Charging | 100 | 0 | Unstable (left half-plane) | > ±90° |
| Mixed | 75 | 25 | Marginally Stable | Near ±90° |
| Balanced | 50 | 50 | Stable (right half-plane) | < ±90° |
The fourth case examines the impact of increased power capacity on stability. With photovoltaic generation raised to 1000 kW, I evaluate the system for 140, 150, and 160 charging China EVs (each at 5 kW). The Nyquist and Bode plots indicate that instability occurs when the charging power reaches approximately 800 kW, which is about 80% of the photovoltaic capacity. This threshold effect is critical for planning in regions with high China EV adoption, as it sets a limit on the allowable charging load without compromising stability.
To further quantify these effects, I derive key parameters using the impedance models. For instance, the critical charging power \( P_{crit} \) for instability can be estimated from the total system impedance. Given the equivalent impedances, the stability boundary is reached when:
$$ \text{Re}(Z) = 0 \quad \text{and} \quad \angle Z = \pm 90^\circ $$
For a system with \( N \) charging electric vehicles, each with power \( P_{EV} \), the total charging power is \( N \cdot P_{EV} \). Using the impedance values, I compute the maximum \( N \) for stability. For example, in the 1000 kW PV case, \( P_{crit} \approx 800 \) kW corresponds to \( N = 160 \) for \( P_{EV} = 5 \) kW. This relationship is summarized in Table 2, which highlights how different PV capacities affect the maximum number of charging China EVs before instability.
| PV Capacity (kW) | Charging Power per EV (kW) | Maximum Charging EVs (\( N \)) | Critical Charging Power (kW) |
|---|---|---|---|
| 500 | 5 | 100 | 500 |
| 1000 | 5 | 160 | 800 |
| 750 | 5 | 120 | 600 |
In conclusion, the integration of electric vehicles, particularly in the context of China EV growth, poses significant challenges and opportunities for DC microgrid stability. My analysis shows that charging electric vehicles act as destabilizing loads due to their negative impedance characteristics, while discharging behaviors enhance stability by providing grid support. The system impedance approach effectively captures these dynamics, with Nyquist and Bode plots serving as reliable indicators. By managing the ratio of charging to discharging China EVs, grid operators can maintain stability, especially as EV penetration increases. Future work could involve probabilistic modeling of electric vehicle behaviors and the development of real-time control strategies for V2G systems, further optimizing the synergy between electric vehicles and DC microgrids in sustainable energy ecosystems.
The implications for China EV markets are profound, as the country leads in electric vehicle adoption. With millions of electric vehicles expected on the roads, their aggregated impact on power systems cannot be overlooked. My findings suggest that incorporating discharging capabilities into China EV designs and charging infrastructure can turn potential stability issues into advantages. For instance, during peak solar generation, excess power could be stored in electric vehicle batteries, which can then discharge during high demand, thus flattening load curves and enhancing overall grid resilience. This aligns with global trends toward smart grids and renewable integration, positioning China EV technologies at the forefront of innovation.
Moreover, the mathematical models developed here, such as the impedance derivations, provide a foundation for further research. For example, the transfer functions for the photovoltaic unit, \( G_{PV} \), and the discharging unit, \( G_{16} \), can be refined to include non-linearities or time-varying parameters. Additionally, the constant-power model for electric vehicle charging could be extended to account for battery degradation or user behavior patterns, common in China EV studies. By continuing to explore these aspects, we can better harness the flexibility of electric vehicles to support the transition to resilient, low-carbon power systems.