Abstract With the rapid proliferation of electric vehicles (EVs), their integration into DC microgrids has become a critical area of study. This paper investigates how the charging and discharging behaviors of EVs affect the stability of DC microgrids. We develop a comprehensive model of a DC microgrid comprising photovoltaic (PV) units, energy storage systems, and EV charging/discharging units. By establishing an equivalent constant power model for EVs and analyzing system impedance through Bode and Nyquist plots, we reveal that increasing EV charging numbers degrade microgrid stability, while discharging operations enhance it. Switching between charging and discharging behaviors emerges as an effective strategy to improve stability. The findings provide valuable insights for optimizing EV-grid interactions in DC microgrid environments.
Keywords: DC microgrid; electric vehicle; constant power model; stability; impedance analysis; charging-discharging behavior
1. Introduction
The growing adoption of electric vehicles (EVs) has transformed their role in power systems, evolving from mere consumers to flexible energy resources. EVs can function as both loads (during charging) and energy storage units (during discharging), making their interaction with DC microgrids a complex yet crucial topic. As large-scale EVs connect to DC microgrids, their collective charging and discharging behaviors can significantly impact grid stability .
Traditional power systems face challenges like voltage fluctuations and power quality issues when integrating high penetrations of distributed energy resources (DERs). DC microgrids, with their ability to efficiently manage DERs such as PV panels and energy storage systems (ESS), have gained traction. However, the dynamic nature of EVs—especially their potential to draw or inject power—introduces uncertainties. For instance, during peak demand, EV charging can exacerbate load peaks, while discharging can provide much-needed power support .
This study aims to quantify the stability impacts of EV charging and discharging in DC microgrids. We employ impedance-based stability analysis, a robust method for assessing microgrid dynamics. By modeling EVs as constant power loads (CPLs) during charging and as voltage-controlled sources during discharging, we derive system impedance models and use Nyquist and Bode plots to evaluate stability thresholds .
2. DC Microgrid System Modeling
2.1 Photovoltaic (PV) Unit
The PV unit serves as the primary energy source, converting solar radiation into DC power via a Boost converter. The circuit model includes a PV array, an inductor (L_PV), a capacitor (C_PV), and a filter capacitor (C_S1) .
State Space Equations:\(\begin{cases} C_{PV} \frac{dU_{PV}}{dt} = I_{PV} – I_{LPV} \\ L_{PV} \frac{dI_{LPV}}{dt} = U_{PV} – R_{PV}I_{LPV} – (1-d_1)U_{bus} \\ C_{S1} \frac{dU_{bus}}{dt} = (1-d_1)I_{LPV} – I_{PVDC} \end{cases}\) where \(U_{PV}\) and \(I_{PV}\) are the PV array voltage and current, \(d_1\) is the duty cycle, and \(U_{bus}\) is the DC bus voltage .
Output Impedance (\(Z_{PV}\)):\(Z_{PV} = Z_2 – \frac{G_1 G_{PV} G_3}{1 + G_{PV} H_1}\) with \(G_1\), \(G_3\), \(G_{PV}\), and \(H_1\) as transfer functions derived from small-signal analysis .
2.2 Energy Storage Unit (ESU)
Lithium-ion batteries, modeled using a first-order Thevenin equivalent circuit, serve as the ESU. The model includes an open-circuit voltage (E), internal resistance (r), and a parallel RC network (R_0, C_0) to capture polarization effects .
State Space Equations:\(\begin{cases} C_0 \frac{dU_{C0}}{dt} = I_E – \frac{U_{C0}}{R_0} \\ E = rI_E + U_{C0} + U_E \end{cases}\) where \(I_E\) is the battery current, and \(U_E\) is the terminal voltage .
The ESU connects to the microgrid via a bidirectional DC/DC converter with voltage-current dual-loop droop control. The output impedance (\(Z_{BAT}\)) is derived from the small-signal model:\(Z_{BAT} = \frac{Z_3 – R_d P_1 G_9 G_{10} – G_6 G_9 G_{10}}{1 + P_1 G_9 G_{10}}\) where \(R_d\) is the droop coefficient, and \(P_1\), \(G_9\), \(G_{10}\) are controller and transfer functions .
2.3 EV Charging Unit (Constant Power Load)
During charging, EVs are modeled as parallel-connected constant power loads (CPLs). For n EVs, the total load impedance is the parallel combination of individual CPLs.
Single CPL Model:\(P_{qpli} = U_{cpli} I_{cpli}, \quad I_{cpli} = \frac{P_{qpli}}{U_{cpli}}\) where \(P_{qpli}\) is the charging power, and \(U_{cpli}\) is the input voltage .
Total Charging Impedance (\(Z_q\)):\(Z_q = \frac{1}{\sum_{i=1}^n \frac{1}{Z_{q_i}}}, \quad Z_{q_i} = R_{q_i} + sL_{q_i} + \frac{1}{sC_{q_i} – \frac{P_{q_i}}{U_{cpli}^2}}\)
2.4 EV Discharging Unit (Voltage-Controlled Source)
During discharging, EVs act as voltage-controlled sources via a bidirectional converter. The model includes an inductor (L_F), resistor (R_F), and filter capacitor (C_S3) .
State Space Equations:\(\begin{cases} L_F \frac{dI_{LF}}{dt} = U_F – R_F I_{LF} – (1-d_3)U_{bus} \\ C_{S3} \frac{dU_{bus}}{dt} = (1-d_3)I_{LF} – I_{FDC} \end{cases}\) where \(U_F\) is the EV terminal voltage, and \(d_3\) is the duty cycle .
Output Impedance (\(Z_F\)):\(Z_F = \frac{Z_4 – G_{12} G_{15} G_{16}}{1 + P_3 G_{15} G_{16}}\) with \(Z_4\), \(G_{12}\), \(G_{15}\), and \(G_{16}\) derived from converter dynamics .
3. System Impedance Stability Analysis
3.1 Stability Criteria
We use a modified impedance ratio method to assess stability, considering bidirectional power flow. Key criteria include:
- Real part of system impedance \(Re[Z(s)] \geq 0\).
- Phase angle within \(\pm 90^\circ\) in Bode plots.
- Nyquist plot of \(Z(s)\) does not encircle the origin in the left half-plane .
3.2 Equivalent System Impedance
The total impedance of the DC microgrid is the parallel combination of all components:\(Z = Z_{PV} \parallel Z_{BAT} \parallel Z_F \parallel Z_{bus} \parallel Z_q\) where \(Z_{bus} = 1/(sC_{bus})\) is the bus capacitance impedance .
4. Case Studies and Results
4.1 Case 1: Impact of EV Charging Numbers
Setup:
- PV power: 500 kW
- Single EV charging power: 5 kW
- EVs charged: 10, 20, 30 vehicles
Results: As charging numbers increase, the Nyquist plot of \(Z(s)\) shifts toward the left half-plane, violating stability criteria. Bode plots show phase angles exceeding \(\pm 90^\circ\), indicating instability .
Table 1: Stability Metrics for Varying EV Charging Numbers
| EVs Charging | Nyquist Plot Location | Phase Angle (Bode) | Stability Status |
|---|---|---|---|
| 10 | Right half-plane | Within \(\pm 90^\circ\) | Stable |
| 20 | Near origin | Slightly exceeding | Marginal |
| 30 | Left half-plane | Exceeding \(\pm 90^\circ\) | Unstable |
4.2 Case 2: Impact of EV Discharging on Unstable Microgrids
Setup:
- PV power: 500 kW
- EVs charged: 100 vehicles (500 kW total load)
- EVs discharged: 0 vs. 16 kW discharge power
Results: Without discharging, the microgrid is unstable (Nyquist plot in left half-plane). Adding EV discharging shifts the Nyquist plot to the right half-plane, with phase angles within safe limits .
4.3 Case 3: Stability During EV State Transition
Setup:
- Total EVs: 100 vehicles
- Scenarios:
- 100 charging, 0 discharging
- 75 charging, 25 discharging
- 50 charging, 50 discharging
Results: Increasing discharging EVs shifts the Nyquist plot rightward and narrows phase angles, improving stability. A 50-50 mix achieves optimal stability .
Table 2: Stability Metrics During State Transition
| Charging EVs | Discharging EVs | Re[Z(s)] (Ω) | Phase Angle (°) |
|---|---|---|---|
| 100 | 0 | -0.12 | -110 |
| 75 | 25 | 0.05 | -85 |
| 50 | 50 | 0.18 | -70 |
4.4 Case 4: Impact of High EV Penetration
Setup:
- PV power: 1000 kW
- EVs charged: 140, 150, 160 vehicles (5 kW each)
Results: At 160 EVs (800 kW, 80% of PV power), the microgrid becomes unstable. This highlights a critical threshold for EV charging penetration .
5. Discussion
The results confirm that EV charging behaves as a destabilizing factor due to the negative incremental impedance of CPLs, which can cause resonance and voltage collapse. Conversely, EV discharging acts as a stabilizing source by providing reactive power support and damping oscillations .
Switching between charging and discharging modes offers a dynamic control strategy. For example, during peak PV generation, EVs can charge to store excess energy; during high load, they can discharge to relieve stress on the microgrid. This flexibility enhances resilience and optimizes energy utilization .
However, managing large-scale EV fleets requires sophisticated coordination, such as vehicle-to-grid (V2G) communication and predictive load forecasting. Future work should explore probabilistic modeling of EV behavior and adaptive control strategies to further enhance stability .
6. Conclusion
This study systematically analyzes the impacts of electric vehicle charging and discharging on DC microgrid stability. Key findings include:
- Increasing EV charging numbers degrade stability, while discharging improves it.
- A critical threshold exists at ~80% PV power capacity for EV charging before instability occurs.
- Dynamic switching between charging and discharging is an effective stability control measure.
These insights provide a foundation for designing robust DC microgrids with high EV integration, emphasizing the need for intelligent EV-grid coordination. Further research into real-time control and probabilistic modeling will enhance the practical applicability of these findings.