With the widespread adoption of electric cars, the integration of large-scale electric vehicles into park integrated energy systems has become a crucial approach to enhance energy utilization and alleviate grid pressure. To achieve low-carbon operation, this paper proposes a two-tier low-carbon optimized operation strategy that combines electric cars with efficient hydrogen utilization. First, based on spatio-temporal feature correlations, the disordered charging of electric cars is simulated, and real-time electricity prices are used to guide orderly charging. Then, by integrating an improved two-stage power-to-gas technology and allowing the park integrated energy system to participate in the carbon trading market with a laddered carbon trading mechanism, the objective is to minimize system energy purchase costs, carbon trading costs, and wind curtailment penalty costs. An improved whale optimization algorithm is employed for solution. Finally, scenario comparisons validate the economic and environmental benefits of the proposed two-tier low-carbon optimized scheduling strategy.
The rapid proliferation of electric cars, particularly in regions like China with strong policy support for China EV adoption, presents both challenges and opportunities for energy systems. The intermittent and volatile nature of renewable energy sources, such as wind and solar, coupled with the uncertainty of user energy behavior, leads to frequent wind and solar curtailment. Moreover, the disordered integration of electric cars into the grid poses new challenges for the optimized scheduling of park integrated energy systems. Therefore, how to reasonably dispatch high-proportion renewable energy and large-scale electric cars, scientifically analyze the impacts of various factors, and effectively improve the utilization rate of wind and solar energy, reduce peak-valley differences, and decrease carbon emissions has become a critical issue that needs urgent resolution.
Current research has extensively explored the use of orderly charging of electric cars as flexible resources in system optimization scheduling. For instance, some studies treat electric cars and renewable energy microgrids as different stakeholders, using improved multi-objective particle swarm optimization for hierarchical optimization to achieve a win-win situation for operational costs and environmental benefits. Others consider electric car charging behavior in regional integrated energy combined heat and power systems to effectively reduce operational costs. Additionally, dynamic time-of-use electricity prices have been proposed to guide orderly charging of electric cars, studying the impact of price-guided charging strategies on energy optimization scheduling and operational costs in integrated energy systems. Results show that such strategies can effectively reduce the peak-valley difference of the system load and improve operational efficiency.
With the emergence of hydrogen energy, low-carbon sustainable development has become a major direction in the energy sector. Some scholars suggest using power-to-gas devices to convert surplus electricity into hydrogen through electrolyzers. However, traditional P2G processes are often oversimplified, and environmental benefits are not fully considered. By refining the P2G process into two stages and replacing traditional P2G with electrolyzers, methane reactors, and hydrogen fuel cells, an economic dispatch model that considers system operational costs and environmental costs can be established, achieving efficient energy utilization. It is noted that the energy conversion efficiency of traditional P2G, specifically electricity to natural gas, is only 55%, while the energy utilization efficiency of electricity to hydrogen can be as high as 80%. Moreover, the use of hydrogen is cleaner compared to natural gas. Therefore, in-depth research on methods to improve hydrogen utilization in P2G technology and explore different pathways for hydrogen use is of great significance.
Existing studies have focused on single scheduling of electric cars without combining them with clean technologies or fully considering the significant carbon reduction potential of carbon trading markets. The future energy market will involve multi-energy collaborative operation, making it essential to深入研究 the synergistic operation of these three elements on park integrated energy systems. Based on the above research, this paper comprehensively considers the charging uncertainty of electric cars and improved P2G technology. To further reduce system carbon emissions, the park integrated energy system is taken as the scheduling entity, with electric cars as direct scheduling resources. A two-stage P2G and laddered carbon trading mechanism are introduced to achieve rapid and low-carbon optimal scheduling of electricity, heat, and gas within the park integrated energy system. The impact of multi-energy collaborative operation strategies on the optimized scheduling of park integrated energy systems is thoroughly studied. Finally, an economic low-carbon scheduling model with the goal of minimizing comprehensive costs is constructed, and the effectiveness and rationality of the proposed method are verified by comparing different scenarios.
Park Integrated Energy System Operation Framework
The constructed park integrated energy system operation framework considering electric car participation in an electric hydrogen production park includes wind turbine systems, photovoltaic systems, energy storage systems, combined heat and power units, gas boilers, an improved two-stage P2G hydrogen production system, and various loads such as electricity, heat, gas, and hydrogen within the park. The energy storage system includes multiple storage devices for electricity, heat, gas, and hydrogen. The improved two-stage P2G hydrogen production system introduces methane reactors, hydrogen fuel cells, and hydrogen storage tanks on the basis of traditional electrolyzers, enabling real-time information interaction within the system to achieve dynamic power balance.
The mathematical model for the combined heat and power unit is as follows. The CHP unit generates electricity by burning natural gas and recovers waste heat to provide energy for heat loads. Its operation model and related constraints are:
$$ P_{\text{CHP,e}}(t) = \eta_{\text{CHP,e}} P_{\text{CHP,g}}(t) $$
$$ P_{\text{CHP,h}}(t) = \eta_{\text{CHP,h}} P_{\text{CHP,g}}(t) $$
$$ P_{\text{CHP,g}}^{\text{min}} \leq P_{\text{CHP,g}}(t) \leq P_{\text{CHP,g}}^{\text{max}} $$
$$ \Delta P_{\text{CHP,g}}^{\text{min}} \leq P_{\text{CHP,g}}(t+1) – P_{\text{CHP,g}}(t) \leq \Delta P_{\text{CHP,g}}^{\text{max}} $$
$$ \kappa_{\text{CHP}}^{\text{min}} \leq \frac{P_{\text{CHP,h}}(t)}{P_{\text{CHP,e}}(t)} \leq \kappa_{\text{CHP}}^{\text{max}} $$
where $P_{\text{CHP,e}}(t)$ and $P_{\text{CHP,h}}(t)$ are the power generation and heat production of the CHP unit at time $t$, respectively; $\eta_{\text{CHP,e}}$ and $\eta_{\text{CHP,h}}$ are the power generation and heat production efficiencies of the CHP unit, respectively; $P_{\text{CHP,g}}(t)$ is the natural gas power consumed by the CHP unit at time $t$; $P_{\text{CHP,g}}^{\text{min}}$ and $P_{\text{CHP,g}}^{\text{max}}$ are the lower and upper limits of the natural gas power consumed by the CHP unit, respectively; $\Delta P_{\text{CHP,g}}^{\text{min}}$ and $\Delta P_{\text{CHP,g}}^{\text{max}}$ are the lower and upper limits of the ramp power of the CHP unit, respectively; $\kappa_{\text{CHP}}^{\text{min}}$ and $\kappa_{\text{CHP}}^{\text{max}}$ are the lower and upper limits of the heat-to-power ratio of the CHP unit, respectively.
The improved two-stage P2G operation model is as follows. Traditional P2G equipment can convert excess electricity into hydrogen or, after treatment by hydrogen methanation equipment, generate methane for use or storage. The improved P2G operation model adds the utilization of renewable energy. The improved two-stage P2G operation process includes an electrolyzer device that can use excess electricity for water electrolysis to obtain hydrogen. Its operation model and related constraints are:
$$ P_{\text{EL,H}_2}(t) = \eta_{\text{EL}} P_{\text{EL,e}}(t) $$
$$ P_{\text{EL,e}}^{\text{min}} \leq P_{\text{EL,e}}(t) \leq P_{\text{EL,e}}^{\text{max}} $$
$$ \Delta P_{\text{EL,e}}^{\text{min}} \leq P_{\text{EL,e}}(t+1) – P_{\text{EL,e}}(t) \leq \Delta P_{\text{EL,e}}^{\text{max}} $$
where $P_{\text{EL,H}_2}(t)$ is the hydrogen output at time $t$; $P_{\text{EL,e}}(t)$ is the electrical power input to the EL at time $t$; $\eta_{\text{EL}}$ is the energy conversion efficiency of the EL; $P_{\text{EL,e}}^{\text{min}}$ and $P_{\text{EL,e}}^{\text{max}}$ are the lower and upper limits of the electrical power input to the EL, respectively; $\Delta P_{\text{EL,e}}^{\text{min}}$ and $\Delta P_{\text{EL,e}}^{\text{max}}$ are the lower and upper limits of the ramp power of the EL, respectively.
The hydrogen methanation device combines hydrogen with CO₂ to generate natural gas, which is then supplied to the gas load. Its operation model and related constraints are:
$$ P_{\text{MR,g}}(t) = \eta_{\text{MR}} P_{\text{MR,H}_2}(t) $$
$$ P_{\text{MR,H}_2}^{\text{min}} \leq P_{\text{MR,H}_2}(t) \leq P_{\text{MR,H}_2}^{\text{max}} $$
$$ \Delta P_{\text{MR,H}_2}^{\text{min}} \leq P_{\text{MR,H}_2}(t+1) – P_{\text{MR,H}_2}(t) \leq \Delta P_{\text{MR,H}_2}^{\text{max}} $$
where $P_{\text{MR,g}}(t)$ is the output natural gas power at time $t$; $\eta_{\text{MR}}$ is the efficiency of MR absorbing carbon dioxide and converting it to methane; $P_{\text{MR,H}_2}(t)$ is the hydrogen power input to MR at time $t$; $P_{\text{MR,H}_2}^{\text{min}}$ and $P_{\text{MR,H}_2}^{\text{max}}$ are the lower and upper limits of the hydrogen power input to MR, respectively; $\Delta P_{\text{MR,H}_2}^{\text{min}}$ and $\Delta P_{\text{MR,H}_2}^{\text{max}}$ are the lower and upper limits of the ramp power of MR, respectively.
Fuel cells can efficiently and pollution-free convert between electrical, thermal, and gas energy. When there is a shortage of electrical and thermal energy supply, they can quickly generate electricity and heat, ensuring the safe and stable operation of the park integrated energy system. Their operation model and related constraints are:
$$ P_{\text{HFC,e}}(t) = \eta_{\text{HFC,e}} P_{\text{HFC,H}_2}(t) $$
$$ P_{\text{HFC,h}}(t) = \eta_{\text{HFC,h}} P_{\text{HFC,H}_2}(t) $$
$$ P_{\text{HFC,H}_2}^{\text{min}} \leq P_{\text{HFC,H}_2}(t) \leq P_{\text{HFC,H}_2}^{\text{max}} $$
$$ \Delta P_{\text{HFC,H}_2}^{\text{min}} \leq P_{\text{HFC,H}_2}(t+1) – P_{\text{HFC,H}_2}(t) \leq \Delta P_{\text{HFC,H}_2}^{\text{max}} $$
$$ \kappa_{\text{HFC}}^{\text{min}} \leq \frac{P_{\text{HFC,h}}(t)}{P_{\text{HFC,e}}(t)} \leq \kappa_{\text{HFC}}^{\text{max}} $$
where $P_{\text{HFC,e}}(t)$ and $P_{\text{HFC,h}}(t)$ are the electrical and thermal power output of the HFC at time $t$, respectively; $P_{\text{HFC,H}_2}(t)$ is the hydrogen power input to the HFC at time $t$; $\eta_{\text{HFC,e}}$ and $\eta_{\text{HFC,h}}$ are the efficiencies of hydrogen conversion to electricity and heat in the HFC, respectively; $P_{\text{HFC,H}_2}^{\text{min}}$ and $P_{\text{HFC,H}_2}^{\text{max}}$ are the lower and upper limits of the hydrogen power input to the HFC, respectively; $\Delta P_{\text{HFC,H}_2}^{\text{min}}$ and $\Delta P_{\text{HFC,H}_2}^{\text{max}}$ are the lower and upper limits of the ramp power of the HFC, respectively; $\kappa_{\text{HFC}}^{\text{min}}$ and $\kappa_{\text{HFC}}^{\text{max}}$ are the lower and upper limits of the heat-to-power ratio of the HFC, respectively.
Electric Car Load Modeling Based on Travel Characteristics
Electric car users have strong traffic randomness and no relatively fixed travel patterns. According to data released by the U.S. Department of Transportation, load prediction models can be divided into four categories: residential areas (A1), work areas (A2), commercial areas (A3), and other areas (A4). Using big data analysis methods, the travel purposes and travel times of electric cars are analyzed and summarized. The data used in this paper comes from the 2017 U.S. Department of Transportation’s National Household Travel Survey results.
To describe the travel purposes of electric cars, the probability of electric car users going to different destinations in different areas varies. This paper divides 24 hours a day into 12 time periods with 2-hour intervals. $P_k$ is the spatial transfer probability within the k-th time period, and the matrix element $P_{ij}$ is the transfer probability from the current location Ai to the next destination Aj. According to historical data, the spatial transfer probability matrix P for 12 time periods of electric car travel can be obtained. $P_7$ is the spatial transfer probability matrix from 12:00 to 14:00 in a day, as shown in the following equation:
$$ P_7 = \begin{bmatrix}
0.166 & 0.172 & 0.53 & 0.132 \\
0.292 & 0.266 & 0.39 & 0.053 \\
0.385 & 0.17 & 0.404 & 0.041 \\
0.432 & 0.108 & 0.334 & 0.127
\end{bmatrix} $$
The first travel time and location of an electric car can be in any area. According to the data fitting results, the first travel time follows a multidimensional normal distribution, i.e.,
$$ f(t_f) = \sum_{i=1}^{n} \alpha_i N(\mu_i, \sigma_i) $$
where $t_f$ is the first travel time; $f(t_f)$ is the probability density function of the first travel time; $n$ is the dimension of the multidimensional normal distribution; $\alpha_i$ is the proportion of each standard normal distribution in the multidimensional normal distribution, $\sum_{i=1}^{n} \alpha_i = 1$; $N(\mu_i, \sigma_i)$ is the standard normal distribution function, $\mu_i$ is its expectation, and $\sigma_i$ is its standard deviation. The parameters of the second-order Gaussian distribution probability density are shown in Table 1.
| Order | Parameter |
|---|---|
| First Order | α₁ = 0.34 |
| μ₁ = 7.46 | |
| σ₁ = 0.77 | |
| Second Order | α₂ = 0.66 |
| μ₂ = 9.20 | |
| σ₂ = 2.75 |
The travel time of an electric car is related to the starting point and follows a log-normal distribution. The probability density function of the electric car’s travel time is:
$$ f(t_d) = \frac{1}{t_d \sigma_d \sqrt{2\pi}} \exp\left[ -\frac{(\ln t_d – \mu_d)^2}{2\sigma_d^2} \right] $$
where $t_d$ is the travel duration; $\mu_d$ and $\sigma_d$ are the expectation and standard deviation corresponding to the origin-destination pair, respectively, as shown in the following equation:
$$ \mu_d \in \{2.80, 2.89, 2.51, 2.61\} $$
$$ \sigma_d \in \{1.13, 0.81, 0.80, 0.93\} $$
The parking duration of electric cars varies in the four types of areas. According to the different parking locations, the data is fitted, and the probability density function of the parking duration is:
$$ f(t_p) = \frac{1}{t_p \sigma_p \sqrt{2\pi}} \exp\left[ -\frac{(\ln t_p – \mu_p)^2}{2\sigma_p^2} \right] $$
where $t_p$ is the parking duration; $\sigma_p$ and $\mu_p$ are the standard deviation and expectation of the parking duration at the corresponding location, respectively. The parameters of the log-normal distribution of parking duration are shown in Table 2.
| Area | A1 | A2 | A3 | A4 |
|---|---|---|---|---|
| σ_p | 1.18 | 1.15 | 1.00 | 1.39 |
| μ_p | 4.34 | 6.20 | 3.12 | 3.70 |
The travel mileage satisfies the conditional probability normal distribution of travel time. The electric car can be considered as traveling at a constant speed. The travel mileage can be obtained from the travel duration and its average travel speed.
$$ S = v(t_d) t_d $$
where $S$ is the travel mileage; $v(t_d)$ is the travel speed, which is considered a constant during the trip.
At this stage, domestic electric cars usually use lithium batteries, and their charging process can be regarded as constant power charging. According to big data, more than 70% of car owners prefer a one-charge-per-day charging mode to extend battery life. Generally, car owners judge whether charging is needed based on the current battery status. If the battery power is insufficient to support the next destination, charging is required at the current location. Additionally, to ensure safety, a remaining power of 30% must be considered. This paper assumes that the charging condition when an electric car travels to destination A_D is:
$$ S_D E – h d_{D+1} < 0.3 E $$
where $S_D$ is the state of charge when arriving at destination A_D; $E$ is the battery capacity (kW·h); $h$ is the power consumption per kilometer of the electric car (kW·h/km); $d_{D+1}$ is the travel distance to the next destination.
For users charging in H and W areas, due to the long parking time, time-of-use electricity price strategy is used to adjust the user’s charging start time. While meeting the user’s charging needs, it can reduce the peak-valley difference and lower the user’s charging cost. For users charging in B and O areas, it is generally unplanned emergency charging, with high demand for short charging time. Therefore, the charge-upon-arrival strategy is used to meet user needs. Under the above two methods, when the car owner ends the D-th trip and charges at destination A_{D+1}, the battery power is judged. If equation (12) is satisfied, slow charging is used; otherwise, fast charging is selected.
$$ S_D E – h d_{D+1} + P_c t_c \geq 0.2 E $$
where $P_c$ is the slow charging power; $t_c$ is the charging duration. After charging, the state of charge for the D+1 trip is:
$$ S_{D+1} = \frac{S_D E – h d_{D+1} + P t_c \eta}{E} $$
where $\eta$ is the charging efficiency; $P$ is the fast or slow charging power.
The simulation parameters set for electric cars in this paper are shown in Table 3.
| Parameter | Value |
|---|---|
| Number of Electric Cars | 200 |
| Battery Capacity (kW·h) | 30 |
| Charging Efficiency | 0.9 |
| Power Consumption per 100 km (kW·h) | 15 |
| Slow Charging Power (kW) | 7 |
| Fast Charging Power (kW) | 20 |
| Travel Speed (km/h) | 60 |
Based on the above theory, the charging duration and charging power of each electric car in each partition can be collected. Then, the electric car loads in each partition are accumulated to obtain the total electric car load information in each area and each time period. The charging demand calculation process involves simulating the travel behavior and charging decisions based on the described models.
Two-tier Optimization Scheduling Model for PIES Considering Electric Car Orderly Charging
Two-tier Scheduling Strategy
In the actual operation of the park integrated energy system with electricity, heat, gas, and hydrogen multi-energy coupling, to meet the real-time production and consumption balance of various powers in PIES, the system needs to comprehensively consider the influence of various factors and formulate the optimal scheduling plan. However, due to the randomness of renewable energy output and the uncertainty of multi-energy load power, the system faces huge challenges in real-time scheduling. To reduce the impact of renewable energy output and electric car load charging randomness, a two-tier optimization scheduling model for renewable energy and electric cars cooperating to access PIES is established, as shown in Figure 4.
The two-tier optimization scheduling model is divided into two layers. The upper layer is the electric car orderly charging layer, which uses real-time electricity prices as a guide to transfer electric car loads in different areas and time periods without affecting the car owners’ travel, achieving orderly charging of electric car groups. Meanwhile, the electric car load data obtained from the upper layer is transmitted to the PIES optimization scheduling layer. By inputting existing data and combining the output of lower-layer units, comprehensively considering load uncertainty, the capacity configuration problem is solved with the goal of minimizing system comprehensive cost.
Upper Layer: Electric Car Orderly Charging
Objective Function
(1) Minimum Grid Load Mean Square Difference
$$ f_1 = \min \sum_{t=1}^{T} \left( \sum_{i=1}^{m} P_{ti} + P_t^B – P_{\text{av}} \right)^2 $$
where $P_{ti}$ is the charging power of the i-th electric car in time period t; $P_t^B$ is the basic electrical load of the park in time period t; $P_{\text{av}}$ is the average value of the electrical load within 24 hours a day; m is the total number of electric cars; T is the number of hours in a day, T=24.
(2) Maximum Grid Load Average-to-Peak Ratio
$$ P_{\text{max}} = \max \left( \sum_{i=1}^{m} P_{ti} + P_t^B \right) $$
$$ P_{\text{ave}} = \text{average} \left( \sum_{i=1}^{m} P_{ti} + P_t^B \right) $$
$$ f_2 = \max \frac{P_{\text{ave}}}{P_{\text{max}}} $$
where $P_{\text{max}}$ is the highest load of the grid in a day; $P_{\text{ave}}$ is the average load of the grid in a day.
(3) Minimum Electric Car Charging Cost (T=96, 1 hour divided into 4 segments)
$$ f_3 = \min \sum_{t=1}^{T} \sum_{i=1}^{m} P_{ti} C_t X_{ti} \Delta t $$
where $C_t$ is the electricity price in time period t; $\Delta t$ is the duration of the time period; $X_{ti}$ is a 0-1 variable, $X_{ti} = 1$ indicates that the i-th car is in charging state in time period t, $X_{ti} = 0$ indicates that the i-th car is not in charging state in time period t.
Considering the impact of electric car charging on PIES, comprehensively considering multiple factors, the total objective function is obtained:
$$ F = \lambda_1 f_1 – \lambda_2 f_2 + \lambda_3 f_3 $$
where $\lambda_1$, $\lambda_2$, $\lambda_3$ are the weighting coefficients of each objective function, and $\lambda_1 + \lambda_2 + \lambda_3 = 1$, take $\lambda_1 = \lambda_2 = \lambda_3 = 1/3$.
Constraints
(1) Charging Load Constraint
$$ \sum_{i=1}^{m} P_{ti} + P_t^B \leq P_t^{\text{max}} $$
where $P_t^{\text{max}}$ is the maximum power that a certain community distribution network can withstand.
(2) Electric Car Battery Capacity Constraint
$$ 10\% \leq S_{\text{end}} \leq 95\% $$
where $S_{\text{end}}$ is the state of charge after charging.
(3) Charging Time Constraint
$$ T_l – T_s \geq \frac{B (S_{\text{end}} – S_{\text{start}}) E}{P \eta} $$
where $T_s$, $T_l$ are the charging start time and end time, respectively; $S_{\text{start}}$ is the state of charge at the start of charging; B is the number of minutes in an hour, B=60.
Lower Layer: PIES Optimization Scheduling
Objective Function
The objectives include minimizing the total system cost and maximizing the renewable energy absorption rate. The economic objective function is:
$$ \min F = C_{\text{buy}} + C_{\text{CO}_2} + C_{\text{waste}} $$
where $C_{\text{buy}}$ is the energy purchase cost; $C_{\text{CO}_2}$ is the ladder carbon transaction cost; $C_{\text{waste}}$ is the wind curtailment penalty cost.
(1) Energy Purchase Cost
$$ C_{\text{buy}} = \sum_{t=1}^{T} \left( \alpha_t^e P_{\text{buy,e}}(t) + \beta_t P_{\text{buy,g}}(t) \right) $$
where $\alpha_t^e$ is the grid electricity price at time t; $\beta_t$ is the natural gas selling price at time t; $P_{\text{buy,e}}(t)$ is the power purchased from the upper-level grid; $P_{\text{buy,g}}(t)$ is the natural gas purchased from the upper-level gas network.
(2) Ladder Carbon Transaction Cost
$$ E_{\text{IES}} = E_{\text{IES,pai}} – E_{\text{IES,pei}} $$
where $E_{\text{IES}}$ is the actual carbon emissions of the integrated energy system; $E_{\text{IES,pai}}$ is the actual carbon emissions during the scheduling process of the system; $E_{\text{IES,pei}}$ is the carbon transaction quota obtained by the system. The specific actual quota and actual carbon emissions of IES are not repeated here, refer to Appendix A. From this, the ladder carbon transaction cost can be obtained:
$$ C_{\text{CO}_2} = \begin{cases}
\lambda E_{\text{IES}} & E_{\text{IES}} \leq l \\
\lambda (1+\alpha) (E_{\text{IES}} – l) + \lambda l & l < E_{\text{IES}} \leq 2l \\
\lambda (1+2\alpha) (E_{\text{IES}} – 2l) + \lambda l (1+\alpha) + \lambda l & 2l < E_{\text{IES}} \leq 3l \\
\lambda (1+3\alpha) (E_{\text{IES}} – 3l) + \lambda l (1+2\alpha) + \lambda l (1+\alpha) + \lambda l & 3l < E_{\text{IES}} \leq 4l \\
\lambda (1+4\alpha) (E_{\text{IES}} – 4l) + \lambda l (1+3\alpha) + \lambda l (1+2\alpha) + \lambda l (1+\alpha) + \lambda l & 4l < E_{\text{IES}} \leq 5l \\
\lambda (1+5\alpha) (E_{\text{IES}} – 5l) + \lambda l (1+4\alpha) + \lambda l (1+3\alpha) + \lambda l (1+2\alpha) + \lambda l (1+\alpha) + \lambda l & E_{\text{IES}} > 5l
\end{cases} $$
where $\lambda$ is the system carbon transaction base price, $\lambda = 250$ yuan/t; $\alpha$ is the carbon transaction price growth rate, $\alpha = 0.25$; $l$ is the carbon emission interval length, $l = 2$ t.
(3) Wind Curtailment Penalty Cost
$$ C_{\text{waste}} = K_{\text{waste}} \sum_{t=1}^{T} P_{\text{waste}}(t) $$
where $K_{\text{waste}}$ is the energy waste penalty coefficient; $P_{\text{waste}}(t)$ is the renewable energy excess power in time period t.
Constraints
(1) Electrical Power Balance Constraint
This paper does not consider selling electricity to the upper-level grid.
$$ P_{\text{buy,e}}(t) = P_{\text{E,e}}(t) + P_{\text{EL,e}}(t) + P_{\text{ES,e}}(t) – P_{\text{DG}}(t) – P_{\text{CHP,e}}(t) – P_{\text{HFC,e}}(t) $$
where $P_{\text{E,e}}(t)$ is the electrical load power; $P_{\text{ES,e}}(t)$ is the electrical energy storage power; $P_{\text{DG}}(t)$ is the actual output of the wind turbine.
(2) Thermal Power Balance Constraint
$$ P_{\text{HFC,h}}(t) + P_{\text{CHP,h}}(t) + P_{\text{GB,h}}(t) = P_{\text{E,h}}(t) + P_{\text{ES,h}}(t) $$
where $P_{\text{GB,h}}(t)$ is the heat power of the gas boiler; $P_{\text{E,h}}(t)$ is the heat load power; $P_{\text{ES,h}}(t)$ is the heat storage power.
(3) Natural Gas Balance Constraint
This paper does not consider selling natural gas to the upper-level gas network.
$$ P_{\text{buy,g}}(t) = P_{\text{load,g}}(t) + P_{\text{ES,g}}(t) + P_{\text{CHP,g}}(t) + P_{\text{GB,g}}(t) – P_{\text{MR,g}}(t) $$
where $P_{\text{load,g}}(t)$ is the gas load power; $P_{\text{ES,g}}(t)$ is the gas storage power; $P_{\text{GB,g}}(t)$ is the gas consumption power of the gas boiler.
(4) Hydrogen Balance Constraint
$$ P_{\text{EL,H}_2}(t) = P_{\text{MR,H}_2}(t) + P_{\text{HFC,H}_2}(t) + P_{\text{ES,H}_2}(t) $$
where $P_{\text{ES,H}_2}(t)$ is the hydrogen storage power.
(5) Wind Power Output Constraint
$$ 0 \leq P_{\text{DG}}(t) \leq P_{\text{DG}}^{\text{max}} $$
where $P_{\text{DG}}^{\text{max}}$ is the maximum output power of the wind turbine.
(6) CHP, EL, MR, HFC Operation Constraints
As shown in equations (1) to (4) above.
(7) Energy Storage Operation Constraints (Electrical, Thermal, Gas, Hydrogen Storage Devices)
Electrical, thermal, gas, and hydrogen energy storage are modeled equivalently and uniformly.
$$ 0 \leq P_{\text{ES},x}^c(t) \leq \zeta_{\text{ES},x}^c P_{\text{ES},x}^{\text{max}} $$
$$ 0 \leq P_{\text{ES},x}^d(t) \leq \zeta_{\text{ES},x}^d P_{\text{ES},x}^{\text{max}} $$
$$ P_{\text{ES},x}(t) = \eta_{\text{ES},x}^d P_{\text{ES},x}^d(t) – \frac{P_{\text{ES},x}^c(t)}{\eta_{\text{ES},x}^c} $$
$$ S_x(t) = S_x(t-1) + \left( \eta_{\text{ES},x}^c P_{\text{ES},x}^c(t) – \frac{P_{\text{ES},x}^d(t)}{\eta_{\text{ES},x}^d} \right) \Delta t $$
$$ S_x(1) = S_x(T) $$
$$ S_x^{\text{min}} \leq S_x(t) \leq S_x^{\text{max}} $$
$$ \zeta_{\text{ES},x}^c + \zeta_{\text{ES},x}^d \leq 1 $$
where $P_{\text{ES},x}^c(t)$, $P_{\text{ES},x}^d(t)$ are the charging and discharging power of the x-th energy storage at time t, respectively; $\zeta_{\text{ES},x}^c$, $\zeta_{\text{ES},x}^d$ are 0-1 variables used to represent the charging and discharging states of the energy storage device, $\zeta_{\text{ES},x}^c = 1$, $\zeta_{\text{ES},x}^d = 0$ indicates the energy storage charging state, $\zeta_{\text{ES},x}^c = 0$, $\zeta_{\text{ES},x}^d = 1$ indicates the energy storage discharging state; $P_{\text{ES},x}^{\text{max}}$ is the maximum charging and discharging power of the x-th energy storage at one time; $P_{\text{ES},x}(t)$ is the output power of different types of energy storage at time t; $\eta_{\text{ES},x}^c$, $\eta_{\text{ES},x}^d$ are the charging and discharging efficiencies of different types of energy storage, respectively; $P_{\text{ES},x}^{\text{cap}}$ is the rated capacity of different types of energy storage devices; $S_x(t)$ is the capacity of different types of energy storage devices; $S_x^{\text{max}}(t)$, $S_x^{\text{min}}(t)$ are the upper and lower limits of the capacity of different types of energy storage devices, respectively.
Solution Algorithm
This paper uses the improved whale optimization algorithm for solution. The traditional whale optimization algorithm often has limited hunting speed during the hunting process, leading to decreased convergence speed and the iterative process easily falling into local optima. Moreover, the traditional whale algorithm uses probability distribution to generate random solutions when initializing the population, and the obtained initial population distribution is not uniform, leading to relatively dense situations, which in turn affects the convergence speed. Therefore, to address these defects, based on the traditional WOA, the population initialization and update iteration parts are improved to increase the optimization speed when facing large amounts of data prediction and improve search accuracy. The specific IWOA process is as follows.
The improved whale optimization algorithm introduces Tent chaotic mapping for population initialization and a hunting speed control factor for iterative updates. The Tent chaotic mapping generates initial solutions that are uniformly distributed in the search space, expanding the search range and improving convergence speed. The chaotic value $X(m)$ is expressed as:
$$ X(m+1) = \begin{cases}
2X(m) & 0 \leq X(m) \leq 0.5 \\
2(1 – X(m)) & 0.5 < X(m) \leq 1
\end{cases} $$
The hunting speed control factor $V$ is introduced to adjust the update strategy based on the iteration progress:
$$ V = \gamma \left(1 – \left(\frac{t_{\text{gen}}}{t_{\text{gen}}^{\text{max}}}\right)^\theta\right) $$
where $t_{\text{gen}}$ is the current iteration number; $t_{\text{gen}}^{\text{max}}$ is the total iteration number; $\gamma$ and $\theta$ are speed determination parameters.
The position update strategies include encircling prey, spiral update, and random search, all incorporating the speed control factor:
(1) Encircling Prey (p < 0.5):
$$ X(t+1) = X^*(t) – A \cdot D \cdot V $$
(2) Spiral Update (p ≥ 0.5):
$$ X(t+1) = D’ \cdot e^{b l} \cdot \cos(2\pi l) \cdot V + X^*(t) $$
(3) Random Search:
$$ X(t+1) = X_{\text{rand}}(t) – A \cdot D \cdot V $$
where $X^*(t)$ is the best solution; $A$ and $D$ are coefficients; $b$ is a constant; $l$ is a random number in [-1,1]; $X_{\text{rand}}(t)$ is a random position.
The IWOA process involves initializing the population with Tent chaotic mapping, calculating fitness, updating positions with the speed control factor, and iterating until convergence.
Case Study Analysis
Basic Case Parameters
To verify the feasibility of the proposed low-carbon operation strategy considering electric car orderly charging participating in the electrolytic hydrogen park, a case study is set up for simulation. The park system operation cycle is 24 hours, with 1 hour as the time step. The wind turbine output, electrical, thermal, and gas load data of the park system are shown in Figure 5. The electricity purchased by the park system from the upper level all comes from thermal power units, and the carbon emission right quota consumed is 0.798 kg/(kW·h). The carbon emission quota consumed by gas units is 0.386 kg/(kW·h). The natural gas price is 0.35 yuan/(kW·h). The unit wind curtailment penalty cost is 0.2 yuan/(kW·h). The parameters of each energy storage device, each device, and time-of-use electricity prices are shown in Table 4, Table 5, and Table 6, respectively.
| Device | Capacity (kW) | Upper Capacity Limit (%) | Lower Capacity Limit (%) | Ramp Rate (%) |
|---|---|---|---|---|
| Electrical Storage | 800 | 90 | 10 | 20 |
| Thermal Storage | 600 | 90 | 10 | 20 |
| Gas Storage | 400 | 90 | 10 | 20 |
| Hydrogen Storage | 300 | 90 | 10 | 20 |
| Device | Capacity (kW) | Energy Conversion Efficiency (%) | Ramp Rate (%) |
|---|---|---|---|
| CHP | 600 | 92 | 20 |
| GB | 700 | 95 | 20 |
| MR | 300 | 60 | 20 |
| HFC | 200 | 95 | 20 |
| EL | 500 | 87 | 20 |
| Time Period | Price [yuan/(kW·h)] |
|---|---|
| Peak: 11:00-14:00, 18:00-23:00 | 1.218 |
| Flat: 07:00-11:00, 14:00-18:00 | 0.779 |
| Valley: 00:00-07:00, 23:00-24:00 | 0.339 |
Orderly Charging Strategy Analysis
1) Cost Analysis of Electric Car Orderly Charging Strategy
To verify the impact of the proposed electric car orderly charging method on system economy, reduce the load peak-valley difference, and increase wind power absorption, two scenarios are set. Scenario 1 is electric car disordered charging, and Scenario 2 is electric car orderly charging. The system operation costs and various indicators under the two scenarios are shown in Table 7.
| Parameter | Scenario 1 | Scenario 2 |
|---|---|---|
| Total System Cost (yuan) | 10,685.21 | 10,176.79 |
| Energy Purchase Cost (yuan) | 7,795.82 | 7,516.08 |
| Carbon Transaction Cost (yuan) | 2,837.33 | 2,637.07 |
| Wind Curtailment Cost (yuan) | 48.06 | 23.64 |
| Electric Car Charging Cost (yuan) | 1,494.03 | 1,167.46 |
| Load Mean Square Difference | 0.03435 | 0.00469 |
| Load Average-to-Peak Ratio | 0.81724 | 0.85095 |
From Table 7, it can be seen that after introducing electric car orderly charging, from an economic perspective, compared with Scenario 1, the electric car charging cost in Scenario 2 decreases significantly, by 326.57 yuan, and the total system operation cost also decreases significantly. From the impact on the system, after introducing electric car orderly charging, the load mean square difference decreases significantly, while the load average-to-peak ratio increases significantly, indicating that the load peak-valley difference in the park decreases. From the perspective of renewable energy absorption, electric car orderly charging can effectively improve the absorption of renewable energy, which is conducive to better building a low-carbon integrated energy system.
The comparison of electrical load before and after introducing electric car orderly charging shows that in the early morning hours, wind power is abundant, while the electrical load is at a low point, and the electricity price is low. At this time, the electric car load significantly increases compared to disordered charging, which can promote the utilization of wind power and simultaneously store excess electricity through electrolysis as much as possible, reducing wind curtailment. During peak load periods, by shifting charging time periods, the electric car load significantly decreases. The orderly charging strategy of electric car groups can reduce the park’s electricity purchase from the grid, lowering user costs and system operation costs. This shows that the orderly charging of electric car groups can effectively suppress the peak-valley fluctuation of the load while improving the utilization rate of renewable energy.
The electrical power balance diagram and the comparison of electrical load before and after optimization show that after considering orderly charging of electric cars, the park load becomes flatter, and the peak-valley difference decreases. During the 01:00-06:00 period, wind power is surplus, and concentrating the electric car charging load in this period as much as possible can achieve the goal of maximizing the absorption of renewable energy. During the 18:00-22:00 period, the park’s electrical load should be reduced as much as possible to alleviate the park’s electricity pressure, reduce electricity purchases during peak hours, and improve scheduling economy.
2) Sensitivity Analysis
The comparison before and after orderly charging participation of different numbers of electric cars is shown in Table 8.
| Number | Charging Cost Before Participation (yuan) | Charging Cost After Participation (yuan) | Load Mean Square Difference | Load Average-to-Peak Ratio |
|---|---|---|---|---|
| 200 | 1,494.03 | 1,167.46 | 0.004692 | 0.85095 |
| 400 | 2,773.76 | 2,283.48 | 0.002751 | 0.85171 |
| 600 | 4,446.83 | 3,729.36 | 0.001224 | 0.85464 |
| 800 | 5,595.40 | 4,630.72 | 0.001134 | 0.85515 |
From the data in Table 8, it can be seen that the charging cost of electric car owners before participating in orderly charging is higher than after participating in orderly charging. As the number of electric cars increases, the load mean square difference of the system decreases, indicating that the overall load curve in the park becomes flatter, and the peak-valley difference becomes smaller. At the same time, the load average-to-peak ratio increases, reflecting that more and more electric cars participating in orderly charging is conducive to ensuring the power supply stability of the park system. The electric car load is closely coordinated with the overall load, and various units can operate coordinatively with high efficiency, thereby achieving multi-energy complementation.
Refined P2G Benefit Analysis
To verify the economy of system operation after adding improved two-stage P2G technology to PIES, the following two scenarios are set up for comparative analysis. Scenario 3 is PIES considering traditional P2G, and Scenario 4 is PIES considering improved two-stage P2G technology. The benefit comparison before and after considering improved two-stage P2G technology is shown in Table 9.
| Parameter | Scenario 3 | Scenario 4 |
|---|---|---|
| Total System Cost (yuan) | 11,048.30 | 10,176.79 |
| Energy Purchase Cost (yuan) | 7,652.39 | 7,516.08 |
| Carbon Transaction Cost (yuan) | 3,352.40 | 2,637.07 |
| Wind Curtailment Cost (yuan) | 43.51 | 23.64 |
From Table 9, it can be seen that in Scenario 3, P2G can convert excess electrical energy into hydrogen during wind-rich periods, and then the hydrogen absorbs CO₂ and is converted into natural gas, providing for thermal and gas loads, thereby greatly achieving local absorption of wind energy and reducing the cost of purchasing energy from the grid and gas network. In Scenario 4, after introducing the improved two-stage P2G operation equipment, the total cost, energy purchase cost, and carbon transaction cost of the system all decrease significantly, and the renewable energy absorption rate of PIES also improves. This is mainly because the combined operation unit of EL, HFC, and MR is introduced. The hydrogen obtained from electrolysis of excess electricity is first supplied to HFC. The high-efficiency power generation and heat production capacity of HFC reduces losses in the energy conversion process and improves energy utilization. The remaining part of the hydrogen is converted into natural gas through MR for combined heat and power supply. Although MR can absorb some CO₂ and convert hydrogen into natural gas for consumption, the combustion of natural gas still produces CO₂. In Scenario 4, HFC directly burns hydrogen, which can undertake part of the output of CHP and GB units and does not produce CO₂, reducing carbon emissions. Therefore, compared with traditional P2G, the refined two-stage P2G technology is more likely to achieve low-carbon optimized operation of PIES.
System Low-carbon Mechanism Analysis
To reflect the scheduling advantages after introducing the ladder carbon transaction mechanism, the following scenarios are set up for comparative analysis. Scenario 5 considers the traditional carbon transaction mechanism but the objective function does not consider the carbon transaction cost. Scenario 6 considers the traditional carbon transaction mechanism and the objective function considers the carbon transaction cost. Scenario 7 considers the ladder carbon transaction mechanism and the objective function considers the carbon transaction cost. The operation costs of PIES in the three scenarios are shown in Table 10.
| Parameter | Scenario 5 | Scenario 6 | Scenario 7 |
|---|---|---|---|
| Total System Cost (yuan) | 11,542.04 | 9,895.20 | 10,176.79 |
| Energy Purchase Cost (yuan) | 7,168.35 | 7,332.64 | 7,516.08 |
| Carbon Transaction Cost (yuan) | 4,308.47 | 2,524.40 | 2,637.07 |
| Wind Curtailment Cost (yuan) | 65.22 | 38.16 | 23.64 |
From Table 10, it can be seen that in Scenario 5, the optimization objective does not consider the carbon transaction cost. The energy purchase cost is lower than other scenarios because the gas price is always lower than the electricity price, so the system purchases a large amount of natural gas for energy supply. However, the extensive use of natural gas results in more CO₂ emissions, keeping the system’s carbon emissions at a high level. In Scenario 6, the system considers the carbon transaction cost, but the natural gas is already at a certain level. At this time, the cost saved by purchasing gas compared to electricity is already lower than the carbon transaction cost of CO₂ generated by natural gas combustion. At this time, electricity purchases increase, and gas purchases decrease. In Scenario 7, the total system operation cost decreases by 1,365.25 yuan compared to Scenario 5 and increases by 281.59 yuan compared to Scenario 6. However, due to the consideration of the ladder carbon transaction mechanism, the increase in carbon transaction price greatly limits the system’s carbon emissions. At this time, electricity purchases increase, and carbon emissions decrease significantly. Simultaneously, the ladder carbon transaction mechanism also promotes the utilization of renewable energy. This shows that after introducing the ladder carbon transaction mechanism, the park system can effectively reduce carbon emissions and has good economy and environmental protection.
Algorithm Comparison Analysis
To verify the effectiveness of the improved whale optimization algorithm, two scenarios are set up for comparison, with the number of electric cars taken as 200. The comparison results of different optimization algorithms are shown in Table 11, and the convergence results of different optimization algorithms are compared in Figure 9.
| Algorithm | Electric Car Charging Cost (yuan) | Iteration Count | Solution Time (s) |
|---|---|---|---|
| IWOA | 1,167.46 | 25 | 19.3 |
| WOA | 1,292.48 | 120 | 30.9 |
| Particle Swarm Optimization | 1,326.78 | 57 | 32.0 |
| Grey Wolf Optimizer | 1,287.12 | 27 | 39.4 |
Combining Figure 9 and Table 11, it can be seen that when the number of electric cars is 200, the overall performance of the grey wolf optimizer is the worst. Although its iteration count is lower than other algorithms except IWOA, its solution time is the largest, which does not meet the requirement of quickly generating scheduling strategies. The particle swarm optimization cannot meet the economic需求 of electric car charging and discharging costs. Meanwhile, the convergence speed of WOA is slow, the iteration count is the highest, and it easily falls into a convergence deadlock. The IWOA proposed in this paper significantly improves the iteration count and solution time compared to WOA.
To further verify the effectiveness of the proposed IWOA, the convergence times of different algorithms under different numbers of electric cars are given in Table 12. From Table 12, it can be seen that under different numbers of electric cars, the convergence time of IWOA is better than that of WOA. It is worth noting that as the number of electric cars increases, the difference in convergence time between the two becomes more prominent, and the solution time and iteration count of WOA increase significantly, further proving the effectiveness of the proposed IWOA.
| Number of Electric Cars | IWOA (s) | WOA (s) | Particle Swarm Optimization (s) | Grey Wolf Optimizer (s) |
|---|---|---|---|---|
| 200 | 19.3 | 30.9 | 32.0 | 39.4 |
| 300 | 22.8 | 38.6 | 39.3 | 123.9 |
| 400 | 25.4 | 43.1 | 45.6 | Does not converge |
Conclusion
This paper takes the multi-energy coupled park integrated energy system of electricity, heat, and gas as the research object, constructs a low-carbon optimized operation model of PIES with combined heat and power units, refined two-stage P2G operation, and ladder carbon transaction. Simultaneously, considering the different charging methods of electric cars in different areas, a two-tier optimized scheduling strategy with the goal of minimum operation cost is proposed. Through comparative analysis, the following conclusions are drawn:
1) Combined with residential travel data analysis, the constructed traffic behavior characteristic model with spatio-temporal feature variable interaction basically conforms to the driving characteristics of electric cars. For users charging in H and W areas, due to the long parking time of users, the time-of-use electricity price strategy is used to adjust the user’s charging start time. While meeting the user’s charging needs, it can reduce the peak-valley difference, and the electric car user charging cost decreases by 21.85%.
2) Replacing traditional electrolyzer hydrogen production to absorb renewable energy with refined two-stage P2G operation, the generated hydrogen is preferentially supplied to HFC for combined heat and power generation. Meanwhile, MR can absorb CO₂, combined with the ladder carbon transaction mechanism, reducing the carbon emission cost by 38.79% and the renewable energy abandonment cost by 63.75%.
3) Aiming at the problem of slow optimization of traditional WOA, IWOA generates the initial population through Tent chaotic mapping and uses the iterative update strategy based on the hunting speed control factor, improving the optimization speed when facing large amounts of data prediction and improving search accuracy.
The widespread adoption of electric cars, especially in markets like China EV, underscores the importance of integrating them into energy systems efficiently. The proposed strategy not only enhances economic benefits but also promotes environmental sustainability, aligning with global trends towards low-carbon energy systems. Future work could explore real-time dynamic pricing and more advanced hydrogen utilization pathways to further optimize system performance.