As environmental protection and sustainable development become priorities for governments and advocates worldwide, the integration of large-scale electric vehicles into modern power grids is accelerating. This trend presents a challenging goal: establishing, designing, and managing clean, efficient, low-carbon, and sustainable energy systems. Currently, clean energy sources like photovoltaics and electric vehicles have been incorporated into the optimization dispatch of distribution networks. In traditional distribution network dispatch, scholars have proposed numerous factors. For instance, some studies have introduced dispatch models for source-grid-load-storage协同 operation, while others have considered electro-thermal-hydrogen loads and dynamic reconfiguration. Hierarchical dispatch and post-prediction dispatch methods have also been explored, alongside strategies addressing power quality and uncertainties in photovoltaic-load and spinning reserve constraints. Additionally, the integration of electric vehicles into dispatch has been considered, and with the implementation of carbon reduction policies, factors like carbon emissions and carbon trading prices have been incorporated. However, these approaches often lack consideration for hydrogen energy integration and fail to unify wind-photovoltaic-storage flexibility resources, vehicle-to-grid (V2G) electric vehicles, and carbon-hydrogen aspects into a cohesive system. Moreover, most existing dispatch schemes for distribution network storage are deterministic, with limited attention to robustness in decision-making.
To enhance system robustness and flexibility, information gap decision theory (IGDT) has been applied to various decision systems, providing adaptive strategies for model uncertainties. For example, IGDT has been used in integrated energy systems to establish risk-aversion and opportunity-seeking models, defining fault-tolerant intervals for decisions. It has also been applied to uncertainties in electricity-heat-gas systems, source-load models, truck-mounted mobile charging stations, virtual power plants, and carbon capture systems with concentrating solar power stations. Despite this, research on distribution network storage dispatch that fully incorporates flexibility resource uncertainties remains scarce. In terms of optimization solution methods, while reinforcement learning has been employed for dispatch, it often lacks strong interpretability and struggles with uncertainty models. Therefore, this study adopts traditional modeling approaches and heuristic algorithms, proposing a multi-objective optimization dispatch method with high interpretability.
The main contributions of this work are threefold. First, a smart terrace energy storage unit is constructed, integrating carbon-hydrogen aspects into the dispatch system. A multi-objective optimization dispatch model is established, incorporating carbon emissions, operational costs, and net load variance, while considering electric vehicle charging demands and distribution network security constraints. Second, source-load uncertainties are addressed through IGDT, forming a robust model that ensures system fault tolerance and impact resistance. Third, an improved UGNSGA-II algorithm is proposed, utilizing uniform aggregation intervals and Gini weights to mitigate local optima issues.
The system framework is based on an energy management structure that incorporates storage, hydrogen, electric vehicles (with V2G technology), photovoltaics, wind power, and thermal power generation. The grid serves as the core, coordinating flexibility resources (e.g., wind, photovoltaics, and thermal power), the smart terrace energy storage unit (including lithium-ion batteries, electric vehicles, and hydrogen energy), and load demands. Flexibility resources primarily consist of wind and photovoltaic power, which are intermittent and unstable, used for peak shaving and valley filling to reduce system carbon emissions. Thermal power acts as a backup source, providing peak regulation when renewable output is insufficient. Through carbon capture and methanation, thermal power and hydrogen systems enable carbon recycling, further lowering emissions. The smart terrace energy storage unit comprises lithium-ion batteries for short-term storage, regulating instantaneous power balance; electric vehicles with V2G technology enabling bidirectional power flow, serving as mobile storage; and hydrogen energy for long-term storage, utilizing excess electricity to produce hydrogen for fuel cells or direct chemical reactions. The V2G charging pile acts as an intermediary between electric vehicles and the grid, storing electricity during charging and feeding power back when needed, enhancing grid flexibility and reliability. It also coordinates with upper-layer dispatch for optimized storage allocation and load curve management.
Carbon-hydrogen integration involves capturing carbon dioxide from electric vehicles and flexibility resources (especially thermal power) via carbon capture devices, which then reacts with hydrogen through methanation to produce methane. This process not only reduces carbon emissions but also supports the sustainability of thermal power by enabling resource closure. The chemical reactions for hydrogen production through water electrolysis are as follows:
$$2H_2O \rightarrow 2H_2 + O_2$$
$$CO_2 + 4H_2 \rightarrow CH_4 + 2H_2O$$
This results in methane and water, with methane serving as a primary component for gas-fired power plants, forming a closed-loop carbon-hydrogen system.
To comprehensively address multiple factors in distribution network operations, achieving environmental sustainability, reduced grid load fluctuations, and minimized operational costs and grid impacts from electric vehicle integration, this study focuses on three main objectives: minimizing operational costs, minimizing net load variance, and minimizing carbon emissions.
The first objective function aims to minimize operational costs in distribution network optimization dispatch:
$$f_1 = C_{iesu} + C_{pv} + C_{wt} + C_{MT} + C_{grid}$$
where \( f_1 \) represents the operational cost, \( C_{iesu} \) is the dispatch cost of the smart terrace energy storage unit, \( C_{pv} \) is the maintenance cost of photovoltaic generation equipment, \( C_{wt} \) is the maintenance cost of wind turbine equipment, \( C_{MT} \) is the combustion cost of micro-gas turbine units, and \( C_{grid} \) is the cost of purchasing electricity from the main grid. The smart terrace energy storage unit dispatch cost \( C_{iesu} \) includes the cost of lithium battery energy storage dispatch \( C_{ess} \), the cost of electric vehicle dispatch in V2G mode \( C_{ev} \), and the cost of hydrogen production through electrolysis \( C_h \):
$$C_{iesu} = C_{ess} + C_{ev} + C_h$$
Here, \( C_{ess} \) is expressed as:
$$C_{ess} = \sum_{t=1}^{T} \sum_{h=1}^{N_{ess}} \lambda_{ess} (P_{h,t,ce} + P_{h,t,de})$$
where \( \lambda_{ess} \) is the unit power storage dispatch cost, \( T \) is the number of optimization time periods, \( N_{ess} \) is the number of storage devices, and \( P_{h,t,ce} \) and \( P_{h,t,de} \) are the charging and discharging power of the \( h \)-th lithium battery storage device at time \( t \), respectively. The electric vehicle dispatch cost \( C_{ev} \) is:
$$C_{ev} = \sum_{t=1}^{T} \sum_{h=1}^{N_{ev}} \lambda_{ev} (P_{h,t,cev} + P_{h,t,dev})$$
where \( \lambda_{ev} \) is the unit power electric vehicle dispatch cost, \( N_{ev} \) is the number of V2G electric vehicles, and \( P_{h,t,cev} \) and \( P_{h,t,dev} \) are the charging and discharging power of the \( h \)-th electric vehicle at time \( t \), respectively. The cost of hydrogen production through electrolysis is calculated as:
$$E_h = \frac{m_h \Delta H}{M_{H_2} \eta_h}$$
$$C_h = \lambda_h E_h$$
where \( E_h \) is the electrical energy used for electrolysis in kWh, \( m_h \) is the mass of hydrogen produced in kg, \( \Delta H \) is the enthalpy change of water decomposition (approximately 285.83 kJ/mol for hydrogen), \( M_{H_2} \) is the molar mass of hydrogen (0.002016 kg/mol), \( \eta_h \) is the electrolysis efficiency (taken as 70% in this study), and \( \lambda_h \) is the unit power cost of water electrolysis. The operation and maintenance cost of photovoltaic stations \( C_{pv} \) is:
$$C_{pv} = \sum_{t=1}^{T} \sum_{d=1}^{N_{pv}} \lambda_{pv} P_{d,t,pv}$$
where \( N_{pv} \) is the number of photovoltaic generation devices, \( P_{d,t,pv} \) is the generation power of the \( d \)-th photovoltaic device at time \( t \), and \( \lambda_{pv} \) is the maintenance cost coefficient of photovoltaic equipment. The maintenance cost of wind turbines \( C_{wt} \) is:
$$C_{wt} = \sum_{t=1}^{T} \sum_{d=1}^{N_{wt}} \lambda_{wt} P_{d,t,wt}$$
where \( N_{wt} \) is the number of wind turbine devices, \( P_{d,t,wt} \) is the generation power of the \( d \)-th wind turbine device at time \( t \), and \( \lambda_{wt} \) is the maintenance cost coefficient of wind turbine equipment. The combustion cost of micro-gas turbine units \( C_{MT} \) is:
$$C_{MT} = \sum_{t=1}^{T} \sum_{l=1}^{N_{MT}} (a_l + b_l P_{l,t,MT} + c_l P_{l,t,MT}^2)$$
where \( N_{MT} \) is the number of micro-gas turbines, \( P_{l,t,MT} \) is the generation power of micro-gas turbine \( l \) at time \( t \), and \( a_l \), \( b_l \), and \( c_l \) are the constant, linear, and quadratic coefficients of the combustion characteristics of micro-gas turbine \( l \), respectively. The cost of purchasing electricity from the main grid \( C_{grid} \) is:
$$C_{grid} = \sum_{t=1}^{T} \omega_t P_{t,grid} \Delta t$$
where \( \omega_t \) is the electricity price at time \( t \), \( P_{t,grid} \) is the average power supply of the distribution network at time \( t \), and \( \Delta t \) is the length of time period \( t \).
The second objective function minimizes the system net load variance. The grid requires traditional power sources to meet the net load, which is the remaining load after deducting new energy output from the total power load. By optimizing the charging power of electric vehicles while maintaining existing traditional loads, the net load difference is minimized. The net load determines the peak load demand of generators, and the load mean square error is an indicator of grid load fluctuations, quantifying load changes for grid stability. A smaller system net load variance implies a more stable load curve:
$$f_2 = \frac{1}{T} \sum_{t=1}^{T} (P_{t,net} – P_{ave})^2$$
$$P_{t,net} = P_{t,load} + P_{t,ev} – P_{t,wt} – P_{t,pv}$$
where \( f_2 \) represents the net load variance of the distribution network, \( P_{t,load} \) is the basic load at time \( t \) excluding electric vehicle charging, \( P_{ave} \) is the average net load, \( P_{t,ev} \) is the power generated by electric vehicles at time \( t \), \( P_{t,wt} \) is the power generated by wind power at time \( t \), and \( P_{t,pv} \) is the power generated by photovoltaics at time \( t \).
The third objective function minimizes carbon emissions, which primarily involve thermal power, electric vehicles, photovoltaics, and wind power, with thermal power being the highest emitter. The total carbon emissions \( f_3 \) are given by:
$$f_3 = Q_{MT} + Q_{pv} + Q_{wt} + Q_{ev} – Q_h$$
For micro-gas turbines, the carbon emissions \( Q_{MT} \) are calculated as:
$$Q_{MT} = \sum_{t=1}^{T} \phi_{MT} P_{t,MT}$$
$$P_{t,MT} = \frac{m_{CH_4} q_{CH_4} \eta_{CH_4}}{3.6 \times 10^6}$$
where \( P_{t,MT} \) is the generation power of the gas turbine at time \( t \) in watts, \( \phi_{MT} \) is the CO₂ emission rate of gas turbine generation, \( q_{CH_4} \) is the calorific value of methane (taken as \( 55.5 \times 10^6 \) J/kg), \( m_{CH_4} \) is the mass of methane consumed in kg, and \( \eta_{CH_4} \) is the power plant efficiency (taken as 0.4). The carbon emissions of photovoltaics \( Q_{pv} \) and wind power \( Q_{wt} \) are:
$$Q_{pv} = \sum_{t=1}^{T} \phi_{pv} P_{t,pv}$$
$$Q_{wt} = \sum_{t=1}^{T} \phi_{wt} P_{t,wt}$$
where \( \phi_{pv} \) and \( \phi_{wt} \) are the CO₂ emission rates of photovoltaics and wind power, respectively. The carbon emissions of electric vehicles \( Q_{ev} \) consider phased emissions, expressed as:
$$Q_{ev} = \sum_{t=1}^{T} \frac{\phi_{ev} P_{t,ev}}{\mu}$$
where \( \mu \) is the charging efficiency of the electric vehicle battery, and \( \phi_{ev} \) is the carbon emission factor of electric vehicles. The carbon consumption \( Q_h \) from hydrogen production is:
$$Q_h = \sum_{t=1}^{T} \frac{m_h M_{CO_2}}{M_{H_2}}$$
where \( M_{CO_2} \) is the molar mass of CO₂ (approximately 0.044 kg/mol).
To handle these multiple objectives, the functions are first normalized and then linearly reconstructed using weights derived from the Analytic Hierarchy Process (AHP). The normalization function \( F \) is:
$$F = \sum_{i=1}^{N} \theta_i \frac{f_i – f_{i}^{min}}{f_{i}^{max} – f_{i}^{min}}$$
where \( N \) is the number of objective functions (here, \( N = 3 \)), \( \theta_i \) is the weight of the \( i \)-th objective function, \( f_i \) is the \( i \)-th objective function, and \( f_{i}^{min} \) and \( f_{i}^{max} \) are the minimum and maximum values of the \( i \)-th objective function, respectively. The AHP judgment matrix is constructed as follows:
| Importance | Economy | Fluctuation | Carbon Emissions |
|---|---|---|---|
| Economy | 1 | 2 | 3 |
| Fluctuation | 0.5 | 1 | 2 |
| Carbon Emissions | 0.33 | 0.5 | 1 |
Consistency checks yield \( VCI = 0.00276 < 0.52 \), passing the consistency test. The weights are \( \theta_1 = 0.540 \) for economy, \( \theta_2 = 0.297 \) for fluctuation, and \( \theta_3 = 0.163 \) for carbon emissions.
The constraints of the optimization model include system power balance, electric vehicle charging power limits, photovoltaic and wind power limits, and energy storage constraints. The system power balance constraint is:
$$P_{t,load} + P_{t,ev} + P_{t,cha} = P_{t,wt} + P_{t,pv} + P_{t,MT} + P_{t,dis}$$
where \( P_{t,dis} \) and \( P_{t,cha} \) are the discharging and charging power of the grid at time \( t \), respectively. The electric vehicle charging power constraints are:
$$0 \leq P_{t,ev} \leq P_{ev,max}$$
$$E_{t,ev} = E_{t-1,ev} + \eta_{ev,cha} P_{t,ev} \Delta t$$
$$E_{ev,min} \leq E_{t,ev} \leq E_{ev,max}$$
where \( P_{ev,max} \) is the maximum charging power of electric vehicles, \( E_{t,ev} \) is the energy storage capacity of electric vehicles in the charging station at time \( t \), \( \eta_{ev,cha} \) is the charging efficiency coefficient of electric vehicles, and \( E_{ev,min} \) and \( E_{ev,max} \) are the minimum and maximum energy storage capacities of electric vehicles in the charging station, respectively. The photovoltaic and wind power constraints are:
$$0 \leq P_{t,fr} \leq P_{t,fr,max}$$
where \( P_{t,fr} \) is the output power of flexibility resources (photovoltaics and wind power) at time \( t \), and \( P_{t,fr,max} \) is the maximum output power of these resources at time \( t \). The energy storage constraint is:
$$E_{h,t,ess} = E_{h,t-1,ess} + \eta_{ess} (P_{h,t,ce} – P_{h,t,de}) \Delta t$$
where \( E_{h,t,ess} \) is the energy storage capacity of the \( h \)-th storage device at time \( t \), and \( \eta_{ess} \) is the efficiency of the storage device.
Due to uncertainties in wind power, photovoltaics, and load, the deterministic scenario must be enhanced. The envelope constraint model is used, with the source-load uncertainty model defined as:
$$P_{uc} \in U(\alpha_{uc}, \bar{P}_{uc}) = \left\{ P_{uc} : \left| \frac{P_{uc} – \bar{P}_{uc}}{\bar{P}_{uc}} \right| \leq \alpha_{uc} \right\}$$
where \( P_{uc} \) is the actual value of source-load uncertainty during the dispatch period, \( \bar{P}_{uc} \) is the predicted value of source-load uncertainty, and \( \alpha_{uc} \) is the source-load uncertainty degree. The robust model (RM) is adopted for conservative risk strategies, formulated as:
$$\alpha_{rm} = \max \left\{ \alpha_{uc1} : \max_{P_{uc} \in U(\alpha_{uc1}, \bar{P}_{uc})} F \leq (1 + \beta_{rm}) F_0 \right\}$$
where \( \alpha_{rm} \) is the uncertainty degree of the RM model, \( \beta_{rm} \) is the deviation factor of the RM model, and \( F_0 \) is the optimal solution under deterministic parameters. This double-layer nested model is complex, so it is simplified to:
$$\alpha_{rm} = \max \alpha$$
$$\text{subject to } F \leq (1 + \beta_{rm}) F_0 \text{ for all } P_{uc} \in U(\alpha_{uc1}, \bar{P}_{uc})$$
This means that for any disturbance \( P_{uc} \in U(\alpha_{uc1}, \bar{P}_{uc}) \), the decision solution ensures that the cost does not exceed \( (1 + \beta_{rm}) F_0 \). In other words, even with arbitrary fluctuations in photovoltaic output, wind power output, and load within a certain interval, the decision solution guarantees cost control.
Wind, photovoltaic, and load uncertainties are normalized, and the entropy weight method is applied to calculate their respective weights: 0.313 for photovoltaics, 0.328 for wind power, and 0.359 for load. The IGDT model based on entropy weight is:
$$\alpha = \min(\alpha_{pv}, \alpha_{wt}, \alpha_L)$$
$$\text{where } \alpha_{pv} = \frac{\alpha}{\omega_{pv}}, \alpha_{wt} = \frac{\alpha}{\omega_{wt}}, \alpha_L = \frac{\alpha}{\omega_L}$$
Here, \( \alpha_{pv} \), \( \alpha_{wt} \), and \( \alpha_L \) are the uncertainty degrees for photovoltaics, wind power, and load, respectively; \( \omega_{pv} \), \( \omega_{wt} \), and \( \omega_L \) are their corresponding weights; and \( \alpha \) is the overall system robustness.
For solving the optimization model, the traditional NSGA-II algorithm is improved to UGNSGA-II, incorporating uniform aggregation intervals and Gini weights. The Gini coefficient \( G_i \) for the population under the \( i \)-th objective function is calculated as:
$$G_i = \frac{\sum_{j=1}^{n-1} s_{i,j}}{2(n-1) \mu_i}$$
$$s_{i,j} = f’_{i,j+1} – f’_{i,j}$$
where \( s_{i,j} \) is the difference between the function values of the \( (j+1) \)-th and \( j \)-th individuals sorted by the \( i \)-th objective function, \( \mu_i \) is the mean of the \( i \)-th objective function values, and \( f’_{i,j} \) is the membership-standardized function value of \( f_{ij} \) (the function value of the \( j \)-th individual sorted by the \( i \)-th objective function). The Gini weight \( \omega_i \) for the \( i \)-th objective function is:
$$\omega_i = \frac{1 – G_i}{\sum_{k=1}^{m} (1 – G_k)}$$
The uniform aggregation distance for individual \( j \) is:
$$d_j = \sum_{i=1}^{m} u’_{i,j}$$
where \( u’_{i,j} \) represents the uniformity of the aggregation interval formed by individuals \( j-1 \), \( j \), and \( j+1 \) under the \( i \)-th objective function, and \( m \) is the number of objective functions. The UGNSGA-II algorithm process involves initializing the population, calculating uniform aggregation distances, non-dominated sorting, selection, crossover, mutation, combining parent and offspring populations, and iterating until the maximum number of generations is reached.
In the case study, electric vehicle start and end times follow normal distributions \( N(7.32, 0.7822) \) and \( N(18.76, 1.302) \), respectively, and daily driving distance follows a log-normal distribution \( \log-N(3.66, 0.512) \). The time-of-use electricity prices for electric vehicles are as follows:
| Time Period | Charging Price [USD/kWh] | Discharging Price [USD/kWh] |
|---|---|---|
| 23:00-07:00 | 0.34 | 0.17 |
| 07:00-10:00 | 0.72 | 0.47 |
| 10:00-15:00 | 1.25 | 1.01 |
| 15:00-18:00 | 0.72 | 0.47 |
| 18:00-21:00 | 1.25 | 1.01 |
| 21:00-23:00 | 0.72 | 0.47 |
The dispatch period is divided into 24 time intervals. In the MATLAB environment, the UGNSGA-II algorithm is employed with a population size of 120, maximum iterations of 100, crossover rate of 0.7, and mutation rate of 0.4. Under deterministic source-load conditions based on wind-photovoltaic-load predictions, the optimization dispatch results for the distribution network are obtained. A comparison with MOPSO and NSGA-II algorithms shows that UGNSGA-II achieves better convergence and computational efficiency. Although its convergence speed is slightly slower than MOPSO, it effectively avoids local optima. The algorithm comparison results are summarized below:
| Algorithm | Operational Cost (kUSD) | Net Load Variance (MW) | Carbon Emissions (t) |
|---|---|---|---|
| MOPSO | 405.47 | 7.35 | 48.24 |
| NSGA-II | 409.11 | 6.96 | 48.22 |
| UGNSGA-II | 402.59 | 6.54 | 48.12 |
UGNSGA-II reduces operational costs by 0.71% and 1.59% compared to MOPSO and NSGA-II, respectively, net load variance by 6.03% and 11.02%, and carbon emissions by 0.25% and 0.21%. For the robust model under source-load uncertainty, the UGNSGA-II algorithm is used to solve the dispatch problem. Different deviation factors are considered, and the corresponding RM coefficients and objective adjustments are established. The results for various deviation factors are as follows:
| Deviation Factor \( \beta_{rm} \) | Robust Coefficient \( \alpha_{rm} \) | Operational Cost (kUSD) | Net Load Variance (MW) | Carbon Emissions (t) |
|---|---|---|---|---|
| 0 | 0 | 402.59 | 6.54 | 48.12 |
| 0.01 | 0.017 | 406.75 | 6.62 | 48.65 |
| 0.02 | 0.035 | 410.32 | 6.75 | 48.96 |
| 0.03 | 0.051 | 415.26 | 6.83 | 49.32 |
At a 95% confidence level (uncertainty degree of 0.051), the robust model dispatch results demonstrate that decision-making can quantify and address qualitative issues arising from source-load uncertainties. This approach ensures system reliability even under unpredictable fluctuations in photovoltaic output, wind power, and load forecasts.
In conclusion, this study establishes an optimization dispatch model for active distribution networks that considers large-scale electric vehicle integration. The proposed smart terrace energy storage system framework includes objectives to minimize operational costs, net load variance, and carbon emissions. By employing information gap decision theory, a robust model for source-load uncertainties is constructed, enhancing system resilience. The UGNSGA-II algorithm is utilized to solve the optimization model, offering wider solution distribution, better convergence, stronger global search capability, higher economic benefits, and faster convergence speed. Optimizing the charging load of large-scale electric vehicles and other controllable resources in the active distribution network effectively improves economic operation, optimizes load curves, significantly reduces peak-valley differences, and increases the consumption rate of photovoltaic energy. The integration of EV charging station dynamics into the dispatch model underscores the importance of flexible resource management in modern power systems, contributing to a sustainable and low-carbon energy future.