Optimized scheduling of energy-transport coupling systems considering uncertain traffic flow

To address energy and nature-related issues, the development of new energy vehicles has been rapid in recent years, gradually replacing traditional vehicles. This paper specifically focuses on the uncertainty of traffic flow for new energy vehicles within the transport system. We analyze the consequence of output from various equipment units in the energy system and their optimized scheduling. We construct an optimization scheduling model for integrating the electric-gas network and the transportation network, known as the energy-transport coupling system (ETCS). By incorporating the uncertainty of traffic flow and utilizing a data-driven approach to generate a set of uncertain traffic flow, we conduct a case study using an improved ETCS consisting of an IEEE-33 node distribution network, a 7-node natural gas network, and a 12-node transportation network to validate the scheduling method. The results demonstrate that the uncertainty of traffic flow does indeed affect the output of equipment units in the ETCS. Furthermore, through optimized scheduling, we can achieve positive interactions between different systems.


Introduction
With the social and economic progress of mankind, there has been an increasing use of fossil energy, leading to the gradual depletion of resources and environmental damage.Conventional fuel vehicles emit a significant amount of carbon dioxide, contributing to air pollution, the greenhouse effect, and other environmental problems.To address these issues, greater attention is being given to gas vehicles (GVs) and electric vehicles (EVs), which rely on natural gas as a clean energy source [1].Integrating the transport system, consisting of GVs and EVs, with the integrated energy system to create an energy transport coupling system (ETCS) represents a significant breakthrough in integrated energy system research.It is expected to be a focal point for future studies.However, there are several uncertainties associated with ETCS, such as fluctuations in energy prices, weather changes, and variations in traffic flow.These uncertainties have a substantial effect on the operation and optimization of the system.In particular, the scheduling and optimization problem of ETCS becomes even more complex and challenging when considering the uncertainty of traffic flow.
Currently, there is well-established research on the integration of energy and transport systems.Yao et al. [2] introduced a coordinated multi-objective planning model for integrated power distribution and EV charging systems.They incorporated a user-equilibrium (UE)-based traffic assignment model to analyze traffic flow distribution in a TN.The impact of large-scale integration of EVs on power and transport networks is investigated in [3], which also considers the system-level impacts of charging EV batteries in the presence of traffic congestion and grid congestion.Hou et al. [4] presented a reliability assessment methodology for coupled transport and power systems for EVs.In contrast, Falahati et al.
2 [5] focused on the reliability of an integrated transport and electricity system (ITES) from a transport system perspective.The adverse effects of large-scale charging on the power system are explored in [6] and [7].Additionally, Veldman and Verzijlbergh [8] demonstrated the significant cost reduction potential of flexible EV charging in the presence of voltage violation penalty costs.
The aforementioned studies primarily consider the impact on the transport network after the integration of energy and transport, with limited consideration for the impact on the integrated energy system.Moreover, the research on EVs has been extensively explored, while the impact of GVs on the transport network has been neglected.Therefore, this paper aims to integrate the electric-gas network, which forms the integrated energy system (IES).Additionally, the traffic network is used to establish the energy transport coupling system (ETCS) and examine the influence of traffic flow on optimal energy scheduling in the traffic network.
The optimal scheduling problems in ETCS, considering uncertainty, can be tackled using heuristic algorithms and robust optimization methods.Ali et al. [9] presented studies on various types of uncertainty problems, where robust optimization methods prioritize system reliability without requiring detailed knowledge of the actual distributional characteristics of the uncertainty.To address the challenge of traffic flow uncertainty, a data-driven approach is employed to construct an uncertainty set for the traffic flows in the model.By leveraging a large amount of historical data, the data-driven algorithm enhances model reliability and robustly optimizes the final outcome, effectively dealing with uncertainty in the model.

Model construction
Within the scope of this research, the ETCS comprises the power distribution network (PDN), gas network (GN), and traffic network (TN).Given that electric vehicles are more prevalent than gas vehicles in real-life scenarios, the focus is on converting gas-electric energy through gas turbines in the coupling process between the gas network and the power network.The integration of the electric grid, gas grid, and transport network is achieved through the charging and refueling behaviors of electric and gas vehicles within the urban transport network.Based on this system, robust optimal scheduling is conducted while considering the uncertainty of traffic flow.Simulations are performed to model traffic flow under uncertain conditions, which are then utilized to make decisions regarding the outputs of coalfired units (CF), wind turbines (WT), gas turbines (GT), and gas wells (GW).
To ensure the economic operation of the integrated energy-transportation system, a robust optimal scheduling model is formulated with the aim of minimizing the total cost.The total cost encompasses the operating cost in the grid, the cost of gas well output in the gas network, and the cost associated with the operating time of traffic flow in the transportation network.Thus, the objective function can be expressed as: ( ) where PDN t C denotes the operating cost of the distribution network in time period, GW t C denotes the cost of the output of the gas wells in the natural gas network in time period, and TN t C denotes the time cost of the volume of vehicular traffic in the transport network in time period.

Power system modelling
Since the power system model in this paper does not need to consider reactive power and voltage, the DC current model is directly employed.The DC current model can be represented as: Taking into account the energy supply equipment in the power system, such as coal-fired units, wind turbines, and gas turbines, the operating cost of the distribution network should consider both the cost of power consumption by this energy supply equipment and the cost of purchasing power from the main grid.The operating cost of the distribution network is: where CF t C denotes the cost of operating a coal-fired unit at capacity, WT t C denotes the cost of the capacity penalty for a wind turbine, GT t C denotes the cost of operating a gas turbine at capacity, and M t C denotes the cost of purchasing electricity from the main grid by the distribution network.
The operating output costs of coal-fired units and gas turbines are primarily influenced by the amount of electricity they generate, which can be expressed as a quadratic relationship: where ) denote the cost coefficients for the coal-fired unit and gas turbine in the system, respectively.
To maintain the safety and stability of the power subsystem, certain constraints need to be met.The operational constraints of coal-fired units and gas turbines in the power system encompass maximum and minimum output limits, unit creep constraints, and unit startup and shutdown constraints.x and ,

GT it
x denote the start-stop action variables of CF and GT, respectively, ,

CF it
 and ,

GT it
 denote the start-stop state variables of CF and GT, respectively.
WT is a type of renewable energy technology that harnesses wind energy and converts it into electricity.Since wind power is a clean energy source, there is no need to consider the cost of generating electricity from wind turbines.However, the availability of wind energy is subject to meteorological conditions, such as wind speed and direction.As a result, the power output of wind turbines is unstable and exhibits a certain degree of randomness and volatility.Hence, the first step is to predict the output of wind power.If the actual power output falls short of the predicted power output, additional conventional energy sources are required to compensate for the shortfall.On the other hand, if the actual power output exceeds the predicted power output, it leads to energy wastage [10].Therefore, when the actual power output of wind power deviates from the predicted power output, penalties are imposed, resulting in a penalty cost of: where W  denotes the penalty tariff, W N denotes the number of WT, , WP it P denotes the predicted output of WT and , W it P denotes the actual output of WT.The cost of purchasing electricity from the main grid by the distribution network is: where M   denotes the purchase price of electricity and M t P denotes the size of the purchased electricity.
2.2 Natural gas system modeling A natural gas system typically consists of gas wells, gas pipelines, gas turbines, and conventional natural gas loads.The schematic structure of a natural gas system is illustrated in Figure 1.Natural gas is primarily transmitted through natural gas pipelines using the pressure difference between the two ends.By regulating the air pressure on both sides of the pipeline, the flow direction of natural gas can be controlled.In this study, the Weymouth trend is applied to analyze the natural gas network.Specifically, the analysis focuses on a tree-type acyclic network natural gas system, where the flow direction of the gas in the pipelines has already been determined.This approach aligns with actual operating conditions [11].
,. denote the maximum and minimum values of the transmission flow in the gas pipelines, respectively; and ij C is a constant whose magnitude is related to the length of the gas pipeline ij , the temperature, the air pressure, and other factors.
The cost of output from a natural gas network gas well can be expressed as: , where  denotes the natural gas cost coefficient and ,

GW it
Q denotes the output value of GW at time t .

Transport system modeling
The traffic system is primarily composed of traffic nodes, traffic routes, traffic flow, and charging and refueling stations, as illustrated in Figure 2. To facilitate analysis and calculations, the following assumptions are made: 1) When a vehicle travels on any route within the traffic network, it is assumed to move at a standard speed consistently, disregarding variations in vehicle speeds on the same route at different times.
2) In the traffic network, there is a maximum capacity limit.When the capacity limit is not reached, assumption 1) allows us to assume that all vehicles take the same amount of time to pass through a given route.This can be referred to as the basic elapsed time.However, when a traffic route reaches its maximum capacity, additional time called congestion time needs to be added to the basic elapsed time.
3) The time spent by vehicles at refueling or charging stations is relatively short compared to the entire driving process.Therefore, it is considered as part of the basic elapsed time, and the time spent at refueling or charging stations is not considered separately.
Since vehicles on the traffic network have distinct starting and ending points, each vehicle completes an origin-destination (o-d) process during its journey.This is represented in the traffic network as the corresponding traffic flow, denoted as od q − .For any combination of starting and ending points on the traffic network composed of multiple traffic lines, it can be considered a traffic network line selection scheme, referred to as od K − .Furthermore, any valid line scheme that satisfies certain criteria can be denoted as  − denotes the coefficient of the relationship between k and l , i.e., the choice of route option k over route l , with a yes of 1 and a no of 0.
Additionally, the user route selection scheme must adhere to the Wardrop equilibrium principle, which involves achieving both user equilibrium (UE) and system optimization (SO) for the entire transportation system [12].
In conclusion, when users travel, they consider both the optimal time cost and the selection of charging and refueling stations.To account for users' willingness to trade off energy consumption for increased time costs, a coefficient  is introduced.This allows us to calculate the time cost of vehicle traffic in the transportation network as follows: (24)

Constructing effective intervals for traffic flow uncertainty
This paper employs a data-driven approach to model and analyze the uncertainty of traffic flow in a coupled energy-transportation system.A fuzzy set is constructed to represent the uncertainty of traffic flow in a traffic network.Our objective is to generate the empirical cumulative distribution ( )

( ) ( ) ( )
 − experimentally using historical data, where ( ) ( ) ( ) , to obtain the 1  − coverage of the true cumulative distribution.By sampling the historical traffic flow data and arranging the sampled data in ascending order, we obtain the sampling set c Q : Then the statistical data boundary value of o d q − can be found to be: .
The empirical cumulative distribution probabilities obtained from the historical data are positioned at the upper and lower boundary values of ( ) , respectively: where , k n B  denotes the quantile with respect to  that satisfies ( ) . Afterwards, the sampling set is expanded by adding ( ) max : Based on the above model, a fuzzy set of intervals of traffic flow, i.e., the most probable range of traffic flow, can be calculated.Meanwhile, using the probability distribution model, the intervals of the traffic flow at different probability levels can be calculated, thus providing the effective intervals of the traffic flow considering the risk.Such a set of uncertainties can be used to guide the decision-making of the charging station and the refueling station.With the opportunity constraints, the most suitable effective intervals of traffic flow for the charging and fueling stations can be selected, taking into account the risks, to ensure the rational allocation of resources and efficient operation.

Solution method
For the optimal scheduling model constructed in this paper, the branch definition method is selected to solve the model, and CPLEX is invoked through MATLAB 2022b platform and YALMIP to solve the model constructed in this paper in a unified way.

Construction of a coupled energy-transport system
In this paper, an energy-transportation coupling system is constructed using a 33-node power distribution network, a 7-node natural gas network, and a 12-node transport network.The structure of each network and the placement of units in the system are depicted in Figure 3.The energytransportation coupling system consists of three gas turbines, two coal-fired units, three wind turbines, a gas refueling master station, and a charging master station.The gas turbines convert natural gas into electricity, which is then transmitted to the power network, facilitating the interconnection between the power grid and the gas network.The charging and refueling stations play a crucial role in coupling the distribution network, the gas network, and the transport network.From the figure, it is evident that the charging and refueling schedules for electric vehicles (EVs) and gas vehicles differ in different time periods due to the uncertainty of traffic flow and the spatial and temporal characteristics of the traffic network.The overlapping loads of EVs and natural gas vehicles in the energy-transportation coupling system result in "double peak" characteristics.Specifically, the time periods from 3:00 to 4:00 and 14:00 to 15:00 exhibit valley load characteristics, while the time periods from 8:00 to 13:00 and 19:00 to 21:00 exhibit peak load characteristics.

Analysis of results
To adjust between adjacent phases in the scheduling cycle, a coal-fired unit with lower operating costs can be selected for regulation.On the other hand, when there are significant fluctuations in peakto-valley differences, a gas turbine with lower starting and stopping costs is primarily used as the primary means of regulation.The optimized scheduling results for gas turbines are displayed in Figure 5, where the gas turbines are mostly switched off except during peak periods.This effectively reduces pressure on the natural gas network and minimizes energy losses.Currently, coal-fired units are typically used as standby units for real-time adjustment of output, while gas turbines serve as peaking units for regulating peak output.
Furthermore, it can be observed that the system relies on each unit to handle the electricity load during peak tariff periods without increasing the amount of power purchased from the main grid.However, during off-peak tariff periods, the amount of power purchased from the main grid exceeds that from other distributed units.This realization of a beneficial interaction between the energytransportation coupling system and the main grid facilitates effective "peak shaving" and "valley filling," resulting in "peak reduction" and "valley filling" for the main grid.

Conclusion
The development and widespread adoption of new energy vehicles indicate the future trend of society.Analyzing the impact of electric vehicles (EVs) and gas vehicles (GVs) on energy networks like power grids and gas grids will undoubtedly be a significant focus of future academic research.In this paper, we comprehensively consider the coupling of an integrated energy system comprising electric-gas networks and the traffic network.We construct an optimal scheduling model for the energy-t ransportation coupling system and obtain the uncertainty set of traffic flow in the traffic network t hrough a data-driven approach.Based on the study of traffic flow uncertainty, we obtain the optimal s cheduling scheme for the energy-transportation coupling system.
It can be concluded that the uncertainty of traffic flow in the traffic network has an impact on the energy demand in the energy-transportation coupling system, resulting in peak and valley load characteristics.To address the imbalance between energy supply and demand caused by the uncertainty of traffic flow, the integrated energy system composed of the electric-gas network can be optimized by adjusting the outputs of each unit.This optimization facilitates a beneficial interaction between the energy-transportation coupling system and the main network, ensuring the economic and stable operation of the system.
The research findings of this paper hold reference value and practical significance for the planning and management of urban energy systems.By considering the interactions and influences between different energy systems comprehensively, we can achieve efficient energy utilization and promote the sustainable and green development of cities.
denotes the power flowing from m to n on line l ; l B is the electro-anaerobic parameter of line l .m  and n  are the phase angles of the voltages at nodes m and n at the ends of the line l , respectively.

Figure 1 .
Figure 1.Schematic diagram of natural gas system structure.

Figure 2 .
Figure 2. Schematic diagram of the structure of the transport system.

.
Based on this concept, the Nesterov traffic distribution model can be constructed as follows: the volume of traffic in a traffic route and , k l o d 25) where o d q − and o d q − represent the boundary values obtained from analyzing the historical traffic flow data.( ) o d q  − A represents the characteristics of the actual cumulative probability distribution that follows a certain probability distribution o d q − .( ) the boundary values of the cumulative probability distribution derived from analyzing the historical traffic flow.( ) o d q  − is unknown, but it is known to lie within the range of ( ) allowing us to determine the distribution characteristics of o d q − .
to the empirical cumulative set.This allows us to determine the bounding value of the probability for the true cumulative distribution:(

Figures 4
and 5 display the scheduling results for the distribution network and gas network, respectively.
denotes the airflow from node i to node j in the pipeline; the set of gas pipelines with node j as the end node and the first node, respectively; W vjdenote