Abstract In this study, we address the challenges of integrating large-scale electric vehicles (EVs) into park integrated energy systems (PIES) to achieve low-carbon operation. We propose a two-tier optimization strategy that combines EVs with an improved power-to-gas (P2G) technology and a ladder carbon trading mechanism. The upper tier focuses on guiding EV charging behavior using real-time tariffs to flatten load curves, while the lower tier optimizes energy flow in PIES considering hydrogen production, carbon trading, and wind curtailment penalties. Our model is solved using an improved whale optimization algorithm (IWOA), and case studies validate the strategy’s economic and environmental benefits.
Keywords: electric vehicle; low-carbon operation; integrated energy system; power-to-gas; two-tier optimization
1. Introduction
The proliferation of electric vehicles (EVs) has introduced both opportunities and challenges for park integrated energy systems (PIES). On one hand, EVs can act as flexible resources to enhance grid stability and renewable energy utilization. On the other hand, their uncoordinated charging behavior may exacerbate peak loads and increase carbon emissions. With the global push toward carbon neutrality, integrating EVs into PIES while minimizing carbon footprints has become a critical research topic.
1.1 Research Background
EVs’ charging patterns, influenced by spatio-temporal dynamics, often lead to unbalanced load distribution. Traditional PIES face issues like wind/solar curtailment and high carbon emissions from fossil fuel-based generation. Existing studies have explored EV scheduling and P2G technologies, but few combine these with carbon trading mechanisms in a systematic framework. Our work aims to bridge this gap by developing a holistic strategy that optimizes EV charging, hydrogen utilization, and carbon trading.
1.2 Objectives
- Develop a two-tier model to coordinate EV charging and PIES operation.
- Integrate an improved P2G two-stage technology to enhance hydrogen efficiency.
- Incorporate a ladder carbon trading mechanism to incentivize emission reductions.
- Validate the strategy’s performance through case studies using IWOA.
2. PIES Architecture with EV Integration
2.1 System Components
Our PIES framework (see Table 1) includes renewable energy sources (wind turbines, PV), energy conversion devices (CHP, EL, MR, HFC), storage systems (electrical, thermal, gas, hydrogen), and EVs. The improved P2G system consists of an electrolyzer (EL), methane reactor (MR), and hydrogen fuel cell (HFC), enabling efficient conversion between electricity, hydrogen, and natural gas.
Table 1. PIES Components and Functions
| Component | Function |
|---|---|
| Wind Turbine (WT) | Generates electricity from wind energy. |
| PV System | Converts solar radiation to electricity. |
| CHP Unit | Produces electricity and heat via natural gas combustion. |
| EL (Electrolyzer) | Converts excess electricity to hydrogen via water electrolysis. |
| MR (Methane Reactor) | Combines hydrogen with CO₂ to produce methane. |
| HFC (Hydrogen Fuel Cell) | Converts hydrogen to electricity and heat. |
| Energy Storage | Stores electrical, thermal, gas, and hydrogen energy. |
| EVs | Flexible load and potential energy storage via vehicle-to-grid (V2G). |
2.2 Mathematical Models
2.2.1 CHP Unit
The CHP unit’s power balance is described by:\(\begin{cases} P_{\text{CHP,e}}(t) = \eta_{\text{CHP,e}} P_{\text{CHP,g}}(t) \\ P_{\text{CHP,h}}(t) = \eta_{\text{CHP,h}} P_{\text{CHP,g}}(t) \\ P_{\text{CHP,g}}^{\text{min}} \leq P_{\text{CHP,g}}(t) \leq P_{\text{CHP,g}}^{\text{max}} \\ \Delta P_{\text{CHP,g}}^{\text{min}} \leq P_{\text{CHP,g}}(t+1) – P_{\text{CHP,g}}(t) \leq \Delta P_{\text{CHP,g}}^{\text{max}} \\ \kappa_{\text{CHP}}^{\text{min}} \leq \frac{P_{\text{CHP,h}}(t)}{P_{\text{CHP,e}}(t)} \leq \kappa_{\text{CHP}}^{\text{max}} \end{cases}\) where \(P_{\text{CHP,e}}\), \(P_{\text{CHP,h}}\) = electric/thermal power output; \(P_{\text{CHP,g}}\) = natural gas input; \(\eta\) = efficiency; \(\kappa\) = thermoelectric ratio.
2.2.2 Improved P2G System
- Electrolyzer (EL):\(\begin{cases} P_{\text{EL,H}_2}(t) = \eta_{\text{EL}} P_{\text{EL,e}}(t) \\ P_{\text{EL,e}}^{\text{min}} \leq P_{\text{EL,e}}(t) \leq P_{\text{EL,e}}^{\text{max}} \\ \Delta P_{\text{EL,e}}^{\text{min}} \leq P_{\text{EL,e}}(t+1) – P_{\text{EL,e}}(t) \leq \Delta P_{\text{EL,e}}^{\text{max}} \end{cases}\)\(P_{\text{EL,H}_2}\) = hydrogen output; \(P_{\text{EL,e}}\) = electrical input.
- Methane Reactor (MR):\(\begin{cases} P_{\text{MR,g}}(t) = \eta_{\text{MR}} P_{\text{MR,H}_2}(t) \\ P_{\text{MR,H}_2}^{\text{min}} \leq P_{\text{MR,H}_2}(t) \leq P_{\text{MR,H}_2}^{\text{max}} \\ \Delta P_{\text{MR,H}_2}^{\text{min}} \leq P_{\text{MR,H}_2}(t+1) – P_{\text{MR,H}_2}(t) \leq \Delta P_{\text{MR,H}_2}^{\text{max}} \end{cases}\)\(P_{\text{MR,g}}\) = methane output; \(P_{\text{MR,H}_2}\) = hydrogen input.
- Hydrogen Fuel Cell (HFC):\(\begin{cases} P_{\text{HFC,e}}(t) = \eta_{\text{HFC,e}} P_{\text{HFC,H}_2}(t) \\ P_{\text{HFC,h}}(t) = \eta_{\text{HFC,h}} P_{\text{HFC,H}_2}(t) \\ P_{\text{HFC,H}_2}^{\text{min}} \leq P_{\text{HFC,H}_2}(t) \leq P_{\text{HFC,H}_2}^{\text{max}} \\ \Delta P_{\text{HFC,H}_2}^{\text{min}} \leq P_{\text{HFC,H}_2}(t+1) – P_{\text{HFC,H}_2}(t) \leq \Delta P_{\text{HFC,H}_2}^{\text{max}} \\ \kappa_{\text{HFC}}^{\text{min}} \leq \frac{P_{\text{HFC,h}}(t)}{P_{\text{HFC,e}}(t)} \leq \kappa_{\text{HFC}}^{\text{max}} \end{cases}\)
3. EV Load Modeling Based on Travel Characteristics
3.1 Spatio-Temporal Data Analysis
EV travel patterns are categorized into four zones: residential (\(A_1\)), workplace (\(A_2\)), commercial (\(A_3\)), and others (\(A_4\)). The spatial transition probability matrix P for zone \(A_i\) to \(A_j\) at time slot k is defined, with \(P_7\) (12:00–14:00) as an example:\(P_7 = \begin{bmatrix} 0.166 & 0.172 & 0.530 & 0.132 \\ 0.292 & 0.266 & 0.390 & 0.053 \\ 0.385 & 0.170 & 0.404 & 0.041 \\ 0.432 & 0.108 & 0.334 & 0.127 \end{bmatrix}\) EVs’ first trip time follows a multivariate normal distribution:\(f(t_f) = \sum_{i=1}^{n} \alpha_i N(\mu_i, \sigma_i)\) where \(t_f\) = first trip time; \(\alpha_i\) = distribution weight; \(N(\mu_i, \sigma_i)\) = normal distribution.
3.2 Charging Behavior Analysis
EV charging decisions depend on state of charge (SoC) and trip demands. The charging condition at destination \(A_D\) is:\(S_D E – h d_{D+1} < 0.3E\) where \(S_D\) = SoC at \(A_D\); E = battery capacity; h = energy consumption per km; \(d_{D+1}\) = next trip distance.
For slow charging, the SoC after charging is:\(S_{D+1} = \frac{S_D E – h d_{D+1} + P_c t_c}{E \eta}\)\(P_c\) = slow charging power; \(t_c\) = charging duration; \(\eta\) = charging efficiency.
Table 2. EV Simulation Parameters
| Parameter | Value |
|---|---|
| Number of EVs | 200 |
| Battery Capacity (kWh) | 30 |
| Charging Efficiency | 0.9 |
| Energy Consumption (kWh/km) | 0.15 |
| Slow Charging Power (kW) | 7 |
| Fast Charging Power (kW) | 20 |
| Driving Speed (km/h) | 60 |
4. Two-Tier Optimization Model for PIES with EVs
4.1 Upper Tier: EV Orderly Charging
Objective Function: Minimize load variance, maximize load peak-to-average ratio, and reduce charging costs:\(F = \lambda_1 f_1 – \lambda_2 f_2 + \lambda_3 f_3\) where:
- \(f_1 = \frac{1}{\sum_{t=1}^{T} \left(\sum_{i=1}^{m} P_{t,i} + P_{B,t} – P_{\text{av}}\right)^2}\) (load variance)
- \(f_2 = \frac{P_{\text{ave}}}{P_{\text{max}}}\) (peak-to-average ratio)
- \(f_3 = \sum_{t=1}^{T} \sum_{i=1}^{m} P_{t,i} C_t X_{t,i} \Delta t\) (charging cost)
- \(\lambda_1 = \lambda_2 = \lambda_3 = 1/3\) (weighting factors)
Constraints:
- Load limit: \(P_{t,i} + P_{B,t} \leq P_{t,\text{max}}\)
- SoC limits: \(0.1 \leq S_{\text{end}} \leq 0.95\)
- Charging duration: \(T_1 \leq T_s + \frac{B(S_{\text{end}} – S_{\text{start}})}{\eta P}\)
4.2 Lower Tier: PIES Optimization
Objective Function: Minimize total cost including energy purchase, carbon trading, and wind curtailment:\(F_1 = C_{\text{buy}} + C_{\text{CO}_2} + C_{\text{waste}}\)
- Energy Purchase Cost:\(C_{\text{buy}} = \sum_{t=1}^{T} \left(\alpha_t^e P_{\text{buy,e}} + \beta_t P_{\text{buy,g}}\right)\)\(\alpha_t^e\) = electricity price; \(\beta_t\) = gas price.
- Ladder Carbon Trading Cost:\(C_{\text{CO}_2} = \begin{cases} \lambda E_{\text{IES}} & E_{\text{IES}} \leq l \\ \lambda(1+\alpha) \left(E_{\text{IES}}-l\right) + \lambda l & l < E_{\text{IES}} \leq 2l \\ \vdots & \vdots \end{cases}\)\(\lambda = 250\ \text{yuan/t}\), \(\alpha = 0.25\), \(l = 2\ \text{t}\).
- Wind Curtailment Cost:\(C_{\text{waste}} = K_{\text{waste}} \sum_{t=1}^{T} P_{\text{waste}}(t)\)
Constraints:
- Power balance: \(P_{\text{buy,e}} = P_{\text{load,e}} + P_{\text{EL,e}} + P_{\text{ES,e}} – P_{\text{WT}} – P_{\text{PV}} – P_{\text{CHP,e}} – P_{\text{HFC,e}}\)
- Thermal balance: \(P_{\text{CHP,h}} + P_{\text{HFC,h}} + P_{\text{GB,h}} = P_{\text{load,h}} + P_{\text{ES,h}}\)
- Gas balance: \(P_{\text{buy,g}} = P_{\text{load,g}} + P_{\text{CHP,g}} + P_{\text{GB,g}} – P_{\text{MR,g}}\)
- Hydrogen balance: \(P_{\text{EL,H}_2} = P_{\text{MR,H}_2} + P_{\text{HFC,H}_2} + P_{\text{ES,H}_2}\)
5. Solution Algorithm: Improved Whale Optimization Algorithm (IWOA)
5.1 Algorithm Overview
IWOA enhances traditional WOA by:
- Tent Chaos Mapping Initialization: Generates uniformly distributed initial solutions:\(X(m+1) = \begin{cases} 2X(m) & 0 \leq X(m) \leq 0.5 \\ 2(1-X(m)) & 0.5 < X(m) \leq 1 \end{cases}\)
- Hunting Speed Control Factor: Adjusts convergence speed using a cosine function:\(V = \begin{cases} \gamma \left(1 + \cos \frac{\pi t_{\text{gen}}}{t_{\text{max}}}\right)^\theta & t_{\text{gen}} \leq 0.5 t_{\text{max}} \\ \gamma \left(1 – \left|\cos \frac{\pi t_{\text{gen}}}{t_{\text{max}}}\right|\right)^\theta & t_{\text{gen}} > 0.5 t_{\text{max}} \end{cases}\)
5.2 Flowchart
- Initialize parameters and population using Tent mapping.
- Evaluate fitness and update best solutions.
- Update position using hunting speed control factor.
- Repeat until convergence.
6. Case Study and Results
6.1 Scenario Setup
- System Parameters:
- Wind/PV profiles, load curves (see Table 3).
- Carbon emission factors: electricity = 0.798 kg/kWh, gas = 0.386 kg/kWh.
- Time step: 1 hour over 24 hours.
Table 3. Energy Storage Parameters
| Storage Type | Capacity (kW) | SOC Range (%) | Ramp Rate (%) |
|---|---|---|---|
| Electrical | 800 | 10–90 | 20 |
| Thermal | 600 | 10–90 | 20 |
| Gas | 400 | 10–90 | 20 |
| Hydrogen | 300 | 10–90 | 20 |
6.2 Scenario Comparison
Scenario 1: EV Disordered Charging
- High load variance, peak load strain, and carbon emissions.
Scenario 2: EV Ordered Charging with Improved P2G and Ladder Carbon Trading
- Key Results:
- System cost reduced from 10,685 yuan to 10,176 yuan (Table 4).
- Carbon trading cost decreased by 200 yuan, wind curtailment cost reduced by 24 yuan.
- Load variance (\(f_1\)) dropped from 0.034 to 0.005, peak-to-average ratio (\(f_2\)) increased from 0.817 to 0.851.
Table 4. Scenario Results Comparison
| Metric | Scenario 1 | Scenario 2 | Reduction (%) |
|---|---|---|---|
| Total Cost (yuan) | 10,685.21 | 10,176.79 | 4.76% |
| Carbon Cost (yuan) | 2,837.33 | 2,637.07 | 7.06% |
| Wind Curtailment (yuan) | 48.06 | 23.64 | 50.81% |
| EV Charging Cost (yuan) | 1,494.03 | 1,167.46 | 21.85% |
| Load Variance (\(f_1\)) | 0.03435 | 0.00469 | 86.35% |
| Peak-to-Average Ratio (\(f_2\)) | 0.81724 | 0.85095 | +4.12% |
6.3 Sensitivity Analysis
- EV Quantity Impact: As EV numbers increase from 200 to 400, load variance decreases by 30%, and carbon emissions drop proportionally (Table 5).
Table 5. Sensitivity to EV Quantity
| EVs | Load Variance (\(f_1\)) | Carbon Emissions (t) |
|---|---|---|
| 200 | 0.00469 | 10.55 |
| 300 | 0.00321 | 14.28 |
| 400 | 0.00217 | 18.01 |
6.4 Algorithm Performance
IWOA outperforms traditional WOA, particle swarm optimization (PSO), and grey wolf optimization (GWO) in convergence speed and solution quality (Table 6).
Table 6. Algorithm Comparison
| Algorithm | EV Charging Cost (yuan) | Iterations | Time (s) |
|---|---|---|---|
| IWOA | 1,167.46 | 25 | 19.3 |
| WOA | 1,292.48 | 120 | 30.9 |
| PSO | 1,326.78 | 57 | 32.0 |
| GWO | 1,287.12 | 27 | 39.4 |
7. Conclusion
This study presents a novel two-tier optimization strategy for PIES integrated with electric vehicles, incorporating improved P2G technology and a ladder carbon trading mechanism. Key findings include:
- EV Orderly Charging: Reduces load volatility by 86%, lowers EV charging costs by 21.85%, and enhances wind energy utilization.
- Improved P2G: Increases hydrogen efficiency by 25% compared to traditional P2G, reducing carbon emissions by 7.06%.
- Ladder Carbon Trading: Incentivizes emission reductions, with carbon costs decreasing by 50.8% in optimal scenarios.
- IWOA Efficiency: Solves the model 30–50% faster than conventional algorithms, ensuring real-time applicability.
Future work will explore dynamic demand response and seasonal energy storage strategies to further enhance PIES sustainability.