Robust optimization method and system for charging facility deployment and scheduling for electric buses

Abstract

This invention relates to the field of urban public transportation technology and discloses a robust optimization method and system for the deployment and scheduling of charging facilities for electric buses. The method includes: establishing an integrated planning problem involving the number of chargers deployed, battery specifications, and charging schedules; constructing a mixed-integer linear programming model; merging box-shaped, budgetary, and ellipsoidal uncertainty sets into a robust logarithmic problem; and reconstructing the model into a solvable one and calculating it using a commercial solver. The system includes an integrated planning module, a basic modeling module, a robust transformation module, and a model solving module. This invention achieves coordinated optimization of charging facilities, battery configuration, and charging scheduling, comprehensively considering charging capacity, time-of-use pricing, and energy consumption uncertainties. It effectively solves problems such as unreasonable charger layout, high electricity costs, inaccurate battery configuration, and weak robustness of the solution, reducing operating costs, improving system reliability and resource utilization, and is adaptable to various urban electric bus system plans.

Description

Technical Field

[0001] This invention relates to the field of urban public transportation technology, specifically to a robust optimization method and system for the deployment and scheduling of charging facilities for electric buses. Background Technology

[0002] With the global trend of advocating green environmental protection and sustainable development, electric buses are being widely promoted in the field of urban public transportation due to their advantages such as zero emissions and low noise.

[0003] However, the large-scale operation of electric buses still faces several key technical challenges: First, the deployment and planning of chargers are unreasonable, failing to comprehensively consider charging capacity limitations, demand costs, and time-of-use pricing, easily leading to redundancy or insufficient chargers at stations, resulting in resource waste or charging congestion and reduced operational efficiency; Second, the formulation of charging plans lacks coordination, failing to combine time-of-use pricing fluctuations with actual energy consumption patterns, often resulting in charging during peak electricity price periods, significantly increasing electricity costs; Third, battery configuration lacks precise quantitative methods, with excessive capacity increasing vehicle weight and energy consumption, while insufficient capacity cannot meet the operational needs of the routes; Fourth, traditional planning methods do not consider uncertainties such as energy consumption, passenger capacity, and road conditions, making deterministic optimal solutions prone to infeasibility or excessively high costs in actual operation.

[0004] Existing technologies typically break down charger deployment, battery configuration, and charging scheduling into independent problems and solve them sequentially, failing to achieve coordinated optimization among the three and lacking robust mechanisms to handle uncertainties. This results in high overall operating costs, low resource utilization, and insufficient operational stability for electric bus systems. Therefore, developing a robust optimization method and system that coordinates charging facility deployment, battery configuration, and charging scheduling, and can withstand energy consumption uncertainties, is of great significance for improving the economic efficiency and reliability of electric bus operations. Summary of the Invention

[0005] The purpose of this invention is to provide a robust optimization method and system for the deployment and scheduling of charging facilities for electric buses, which can solve the above-mentioned problems.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention proposes a robust optimization method for the deployment and scheduling of charging facilities for electric buses, comprising the following steps:

[0008] S1. Define the scope of the integrated planning for the electric bus system. Based on charging capacity limitations, demand costs, and time-of-use pricing, establish an integrated planning framework to determine the number of chargers to be deployed at each terminal station, the battery specifications of the electric buses, and an effective charging plan at the system level.

[0009] S2. Construct a mixed-integer linear programming model for the integrated planning problem;

[0010] S3. Merge the box, budget, and ellipsoidal uncertainty sets to transform the mixed integer linear programming model into a robust logarithmic problem;

[0011] S4. Reconstruct robust logarithmic problems into solvable mixed-integer linear programming models or mixed-integer second-order cone models, and solve them using commercial solvers.

[0012] Preferably, step S1 comprises the following steps:

[0013] S101. Based on historical data from the urban rail transit automatic fare collection system, establish a planning problem to determine the battery specifications for electric buses.

[0014] S102. With the constraints that the number of charging vehicles does not exceed the number of chargers and parking spaces, and the charging process meets the minimum charging time, establish a planning problem for the number of chargers deployed at each terminal station.

[0015] S103. Planning problem of establishing an effective charging plan at the level of electric bus system by combining the consumption cost, demand cost and time-of-use electricity rate of commercial electricity customers.

[0016] Preferably, in step S2, before constructing the mixed-integer linear programming model, the following assumptions need to be made about the entire integrated programming problem:

[0017] (1) Only costs directly related to the charger and battery are included in the calculation, and the purchase cost of electric buses, driver costs and maintenance costs are not considered;

[0018] (2) A cost amortization mechanism is adopted, with the monthly purchase cost amortization amount of each charger and the monthly battery purchase cost amortization amount per kilowatt-hour as a unified measurement standard;

[0019] (3) To address the difference between demand charges calculated monthly and time-of-use electricity charges calculated daily, the time dimension of the two types of costs is unified, thereby constructing a complete cost calculation system to support optimization decisions.

[0020] Preferably, in step S2, a mixed-integer linear programming model is constructed, and the specific steps are as follows:

[0021] S202. Set the objective function of the integrated planning problem as follows:

[0022] (13)

[0023] In the formula, This refers to the average monthly amortized purchase cost of the charger. It is a collection of all bus terminals. The number of chargers to deploy at terminal station s. This is the average monthly amortization cost per kilowatt of battery. It refers to the collection of all bus routes. It is a collection of electric buses serving the R line. The battery capacity for electric bus B on line R. This is the demand-based electricity price cost. This refers to the cost of time-of-use electricity.

[0024] S203, Set constraints for leaving the bus terminal:

[0025] (14)

[0026] In the formula, This refers to the battery's highest state of charge. It is the battery capacity of the electric bus b serving route r; The state of battery energy of electric bus b serving route r at the departure time of its lth trip; This refers to the departure time of the electric bus's first trip. This refers to the energy consumption of electric bus B during its journey from its designated parking lot to its first stop. Refers to specific bus routes. It is the mission sequence number;

[0027] S204. Set constraints for arrival at the depot:

[0028] (15)

[0029] In the formula, The battery energy state of electric bus b serving route r at the arrival time of its lth trip; Let l be the arrival time of a certain trip for an electric bus. This is the lowest state of charge of the battery. This refers to the energy consumption of electric bus B during its journey from the last stop of its last trip to its designated parking lot. It is the last trip number of electric bus b serving route r;

[0030] S205. Set energy consumption-related constraints:

[0031] (16)

[0032] In the formula, This refers to a road segment where i is the starting station and j is the ending station. This is the set of all road segments for the l-th trip. It is the fixed energy consumption generated when electric bus b performs its lth trip and travels through road segment (i, j); The energy consumption coefficient related to battery capacity refers to the energy consumption of electric bus b when it makes its lth trip and travels through road segment (i, j).

[0033] S206. Set constraints for the charging process:

[0034] (17)

[0035] In the formula, The battery energy state of electric bus b serving route r at the departure time of its (l+1)th trip. To determine the duration of a single time interval within the planning period, This is the departure time of the electric bus's (l+1)th trip. The continuous decision variable refers to the charging power of electric bus b within the time interval t.

[0036] S207, Setting constraints on charging capacity:

[0037] (18)

[0038] (19)

[0039] (20)

[0040] In the formula, Refers to the set of time intervals within the planning period; For a specific time interval; It is an extremely small positive number; Whether the electric bus b on service route r is charged during time interval t; Refers to a sufficiently large positive number; Let be the set of electric buses located at terminal s and serving route r within the time interval t; This refers to the number of parking spaces at terminal s;

[0041] S208, Set a minimum charging time constraint:

[0042] (twenty one),

[0043] (twenty two),

[0044] (twenty three),

[0045] In the formula, This refers to the charging start / stop status indicator. For minimum charging time, It is the total number of time intervals within the planning period. It refers to the set of all time intervals within a single day;

[0046] S209. Set upper and lower limits for SOC constraints:

[0047] (twenty four),

[0048] (25),

[0049] (26)

[0050] S210, Set upper and lower limits for charging power constraints:

[0051] (27)

[0052] In the formula, This refers to the maximum charging power of the electric bus charger;

[0053] S211. Set the optimization model:

[0054] (28)

[0055] (29)

[0056] In the formula, This refers to the maximum average charging power of terminal station s during peak demand periods. Let be the average charging power of terminal s during the o-th demand metering interval. It is a set of peak demand measurement intervals. This refers to the maximum average charging power of terminal s during off-peak demand periods. It is a set of intervals for measuring demand during off-peak hours;

[0057] The comprehensive programming problem can be expressed as a mixed-integer linear programming model in the following form:

[0058] (30)

[0059] The constraints are equations (14)-(21), (23)-(29) and (31), with equation (31) as follows:

[0060] (31),

[0061] In the formula, The unit price of electricity during peak demand. The unit price of electricity during off-peak hours. It is the set of all demand measurement intervals. This refers to the time range from the start to the end of the 0th demand measurement interval. It is the duration of the demand measurement interval; Refers to the service route located at terminal s within the basic time interval t. A collection of electric buses;

[0062] The above model is a mixed-integer linear programming model that can be solved by commercial solvers and can also be converted into a robust model that is easy to handle.

[0063] Preferably, step S3 comprises the following steps:

[0064] S301. The following assumptions are made regarding the transformation of the model into a robust pairwise problem:

[0065] (1) The parameters in the deterministic model will vary within a certain range, which may lead to the infeasibility or suboptimal nature of the optimal solution obtained by the deterministic model;

[0066] (2) Provide a flexible and robust method to hedge against the uncertainty of energy consumption in the operation of electric buses;

[0067] S302. To address the uncertainty of energy consumption, a robust logistic regression problem was developed by considering the actual electricity consumption of public transportation trips. for:

[0068] (32),

[0069] In the formula, The actual energy consumption of electric bus b serving route r when performing the lth trip and traveling on route segment (i, j); The average fixed energy consumption of electric bus b during its l-th trip, on route (i, j); It is the average energy consumption coefficient related to the battery when electric bus b performs its lth trip and travels along route (i, j); The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b when it makes its lth trip and travels on route (i, j). It is the maximum deviation of battery-related energy consumption when electric bus b travels on road segment (i, j); The maximum deviation coefficient of battery-related energy consumption when electric bus b travels on road segment (i, j);

[0070] S303, Establish a system based on merged box-shaped uncertainty sets. Statement:

[0071] (33),

[0072] In the formula, The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b serving route r when it makes its lth trip. The set of merged box-shaped uncertainties to which it belongs; This is the energy consumption deviation coefficient vector. It is a real vector space of dimension l, which is the number of road segments in the l-th trip. This refers to the collection of all routes taken by electric bus b during its lth trip;

[0073] S304. Establish a budget uncertainty set. Statement:

[0074]

[0075] (34),

[0076] In the formula, The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b serving route r when it makes its lth trip. The set of budget uncertainty to which it belongs; This is the maximum permissible sum of the absolute values ​​of the energy consumption deviation coefficients for all road segments during this trip;

[0077] S305, Establishing a set of uncertainties based on ellipsoids Statement:

[0078] (35),

[0079] In the formula, The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b serving route r when it makes its lth trip. The set of uncertainties on the ellipsoid to which it belongs; The maximum permissible second norm of the energy consumption deviation coefficient vector for this trip;

[0080] S306. Problems involving deriving robust pairs through constraint substitution:

[0081] The robustness of the model can be derived by replacing the constraint formula (16) involving energy consumption terms with the following constraints:

[0082] (36)

[0083] In the formula, This refers to the set of all travel tasks that need to be performed when the electric bus (b) serves route (r).

[0084] Preferably, step S4 comprises the following steps:

[0085] S401, Restating the merged box-shaped uncertainty set:

[0086] In settings all =1 yields a tractable restatement in robust equivalence problems, resulting in the following constraint:

[0087] (37);

[0088] S402, Restating the set of budgetary uncertainties:

[0089]

[0090] The constraints are:

[0091]

[0092]

[0093] The dual of the above function is:

[0094]

[0095] The constraints are:

[0096]

[0097]

[0098]

[0099] In the formula, The dual variable refers to the energy cost per unit of budget. Dual variables, understood as exceeding The additional energy cost at the upper limit;

[0100] Constraint (36) is equivalent to equations (30)-(32) and (45), and equation (45) is as follows:

[0101]

[0102] Therefore, the robust problem is transformed into a tractable mixed-integer linear programming model;

[0103] S403, Restating the Uncertainty Set of the Ellipsoid:

[0104]

[0105] The constraints are:

[0106]

[0107]

[0108] In the formula The mathematical representation of an n-dimensional second-order cone;

[0109] According to the theory of conical duality, the dual equation is obtained:

[0110]

[0111] The constraints are:

[0112]

[0113]

[0114] In the formula, The dual variable is understood as the energy cost of the unit norm. The dual variable is understood as the maximum energy consumption deviation cost of road segment (i, j); Auxiliary dual variables are used to ensure that the dual solution covers the original problem. Non-negative scenarios; Auxiliary dual variables refer to the vector elements that constitute the dual second-order cone;

[0115] To address this, the robust problem of ellipsoidal uncertainty sets is transformed into a mixed-integer second-order cone model that can be handled and solved directly by commercial solvers.

[0116] Preferably, a robust optimization system for the deployment and scheduling of charging facilities for electric buses is provided to implement the robust optimization method for the deployment and scheduling of charging facilities for electric buses, comprising:

[0117] The integrated planning module is used to execute step S1 and establish an integrated planning problem for the number of chargers deployed, battery specifications, and charging schedule.

[0118] The basic modeling module is used to execute step S2 and construct a mixed-integer linear programming model.

[0119] The robust conversion module is used to execute step S3 and convert the problem to obtain the robust parallel problem;

[0120] The model solver module is used to execute step S4, reconstruct the model, and solve it using a commercial solver.

[0121] Preferably, the planning problem definition module includes:

[0122] A battery configuration unit is used to perform step S101;

[0123] A charger deployment unit is used to perform step S102;

[0124] The charging plan formulation unit is used to execute step S103.

[0125] Preferably, the robust conversion module is used to perform the steps described in claim S3 to construct an energy consumption uncertainty model and three uncertainty sets.

[0126] Preferably, the model solving module is used to perform the steps described in S4, namely, to reformulate, perform dual transformation, and solve the model for the three uncertainty sets.

[0127] The beneficial effects of this invention are as follows:

[0128] (1) The method of the present invention integrates the deployment of charging facilities, battery specification configuration and charging scheduling into a unified integrated planning framework, which solves the problems of unreasonable distribution of chargers, resource surplus or shortage and charging congestion in the prior art in one go, greatly improves the utilization rate of charging facilities and the efficiency of public transportation operation, and avoids the resource mismatch defects caused by segmented planning from the root.

[0129] (2) The method of the present invention takes into account the charging capacity limit, demand cost and time-of-use electricity price factors in the planning process, which can automatically avoid peak electricity prices and optimize charging time periods, effectively reduce the overall electricity cost and operating expenses of electric buses, and solve the problem of high electricity cost caused by the failure of traditional charging plans to take into account electricity price fluctuations.

[0130] (3) The method of the present invention accurately determines the battery capacity and the number of chargers through systematic modeling, avoiding the problems of excessive battery capacity causing increased vehicle energy consumption and cost waste, or insufficient capacity failing to meet operational needs, and achieving accurate matching between battery configuration and line operation needs.

[0131] (4) The method of the present invention adopts a robust optimization approach. By merging box, budget and ellipsoid uncertainty sets to handle uncertain factors such as energy consumption fluctuations, the planning scheme remains feasible and optimal under actual road conditions, passenger volume and energy consumption changes, solving the problem that traditional deterministic planning is prone to infeasibility and poor adaptability.

[0132] (5) The method of the present invention reconstructs the complex robust optimization model into a standard mathematical model that can be directly solved, which improves the computational efficiency while ensuring the optimization accuracy. It can quickly output an integrated solution for charger deployment, battery configuration and charging plan, solving the problem that the existing technology planning process is complex and difficult to implement in engineering. Attached Figure Description

[0133] Figure 1 The overall flowchart of the method of this invention. Detailed Implementation

[0134] The present invention will be further described below with reference to the embodiments. It should be noted that these are merely examples and descriptions of the inventive concept. Those skilled in the art can make various modifications or additions to the specific embodiments described or use similar methods to replace them, as long as they do not deviate from the inventive concept or exceed the scope defined in the claims, they should all be considered to fall within the protection scope of the present invention.

[0135] Example 1:

[0136] like Figure 1 As shown, the present invention proposes a robust optimization method for the deployment and scheduling of charging facilities for electric buses, comprising the following steps:

[0137] S1. Define the scope of the electric bus system integration plan. Based on charging capacity limitations, demand costs, and time-of-use pricing, establish an integration plan to determine the number of chargers deployed at each terminal station, the battery specifications of the electric buses, and the effective charging schedule at the system level. The specific steps are as follows:

[0138] S101. Specifically, we first use the equations developed by Fontana to deeply mine information such as mileage, passenger volume, and charging frequency contained in the historical data of the automatic fare collection system, and then establish a planning problem for determining the size and specifications of electric bus batteries.

[0139] S102. Given the constraints that the number of charging vehicles does not exceed the number of chargers and parking spaces, and that the charging process meets the minimum charging time, establish a planning problem for the number of chargers deployed at each terminal station.

[0140] Based on the number of parking spaces at each terminal station and the charging demand at different times in the electric bus operation scheduling plan, the number of chargers deployed at each terminal station is determined to ensure that the number of charging vehicles does not exceed the number of chargers or parking spaces. To improve charging efficiency, through research on charger and battery performance and analysis of actual operation, the minimum charging time for each charging process is determined to avoid losses and time waste caused by frequent plugging and unplugging, thus establishing a planning problem for determining the number of chargers deployed at each terminal station.

[0141] S103. Planning problem of establishing an effective charging plan at the level of electric bus system by combining the consumption cost, demand cost and time-of-use electricity rate of commercial electricity customers.

[0142] By collecting data on consumption costs, demand costs, and time-of-use pricing rates from commercial electricity customers, and conducting in-depth analysis of the changing patterns of these costs at different times, and combining this with the operating schedule of electric buses, charging can be scheduled during periods with lower time-of-use pricing rates, while also taking into account the impact of demand costs on total costs. This will help establish a planning framework for an effective charging plan at the electric bus system level.

[0143] Considering the total cost of integrated electric bus planning, before building the model, it is assumed that all electric buses have a uniform model, type, and passenger capacity, except for battery size. Each electric bus has a service path b. A set of itineraries will be completed by This indicates the last trip of the electric bus service, for each trip task. , This represents the set of all road segments between two consecutive bus stops.

[0144] It should be noted that 1 represents the departure station. Represents the energy consumption of electric bus b in the segment arriving at the station. Represented as This is related to the battery and passenger weight between bus stops i and j.

[0145] Battery size and weight-related energy consumption are primarily determined by the Fontana equation:

[0146] (1),

[0147] In the formula, Indicates efficiency. It is air density. The drag coefficient is A, and the surface area of ​​the electric bus is A. Indicates the coefficient of friction on the segment. This refers to the mass of the electric bus on that segment, where g is the gravitational constant. It is the slope of the road segment. It is the additional energy consumption coefficient of electric buses. It is the length of road segment (i, j).

[0148] Based on passenger information from the urban rail transit automatic fare collection system, the energy consumption formula for electric buses is derived:

[0149] (2),

[0150] (3),

[0151] (4),

[0152] (5),

[0153] (6),

[0154] (7),

[0155] In the formula, Refers to the fixed mass of an electric bus. For the battery-related quality of electric buses. This refers to the battery quality factor. Let be the fixed energy consumption of electric bus b on route segment (i, j). This refers to the battery-related energy consumption coefficient of electric bus b on route segment (i, j).

[0156] Commercial electricity customers are typically billed in two different ways: consumption charges and demand charges. Consumption charges are proportional to the amount of energy a customer uses, measured in kilowatt-hours (kWh); demand charges are additional charges levied on non-residential or commercial customers, related to the energy used within a given time period, measured in kilowatts (kWh). The purpose of demand charges is to allocate more of the cost associated with the customers who use the most electricity, thereby shaping their electricity consumption behavior and reducing peak demand. Here, we consider the general case where both peak and off-peak demand charges exist. Let κ be the measurement time interval for demand charges. It is a time division ratio coefficient, and then the entire time period T is divided into... A length of The interval, here, For each interval ,use and Let κ represent the lower limit and the upper limit, respectively. Therefore, κ = - And further divide all sub-interval sets It consists of two subsets, namely and , and For each interval The final stop s is in the section Average charging power It can be calculated using the following formula:

[0157] (8),

[0158] In the formula, It refers to the set of all demand measurement intervals. This refers to the average charging power of bus terminal s within the o-th demand metering interval. Specifically, it includes the following settings: This is used to record the time interval t between electric buses at their terminal stations. Since the timetable for each bus route is known and pre-assigned to the electric buses, the location of each electric bus can be determined, and further defined... and The peak and off-peak periods, representing the maximum charging demand at the terminal station, are given by the following formulas:

[0159] (9),

[0160] (10)

[0161] In the formula, This refers to the maximum average charging power of the bus terminal 's' during peak demand periods. This represents the maximum average charging power of bus terminal 's' during off-peak demand periods. The set of intervals for measuring peak demand. It is the set of demand measurement intervals during the valley period.

[0162] Then, the total demand cost can be calculated using the following formula:

[0163] (11),

[0164] In the formula, and These are the unit prices for demand during peak and off-peak hours, respectively.

[0165] In addition, the time-of-use electricity rate can be given by the following formula:

[0166] (12),

[0167] In the formula, It is the unit cost of time-of-use electricity within the basic time interval t. It is a coefficient related to time-of-use electricity pricing.

[0168] S2. Construct a mixed-integer linear programming model for the integrated planning problem.

[0169] S201. Before constructing the mixed-integer linear programming model, the following assumptions need to be made about the entire integrated programming problem:

[0170] (1) Only costs directly related to the charger and battery are included in the calculation, and the purchase cost of electric buses, driver costs and maintenance costs are not considered;

[0171] (2) A cost amortization mechanism is adopted, with the monthly purchase cost amortization amount of each charger and the monthly battery purchase cost amortization amount per kilowatt-hour as a unified measurement standard;

[0172] (3) To address the difference between demand charges calculated monthly and time-of-use electricity charges calculated daily, the time dimension of the two types of costs is unified, thereby constructing a complete cost calculation system to support optimization decisions.

[0173] The specific steps for constructing a mixed-integer linear programming model are as follows:

[0174] S202. Set the objective function of the integrated planning problem as follows:

[0175] (13)

[0176] In the formula, This refers to the average monthly amortized purchase cost of the charger. It is a collection of all bus terminals. The number of chargers to deploy at terminal station s. This is the average monthly amortization cost per kilowatt of battery. It refers to the collection of all bus routes. It is a collection of electric buses serving the R line. The battery capacity for electric bus B on line R. This is the demand-based electricity price cost. This refers to the time-of-use electricity cost. The first objective function represents the monthly amortized charger purchase cost, the second objective function represents the monthly battery purchase cost, the third objective function represents the monthly total demand cost, and the fourth objective function represents the monthly total time-of-use electricity cost.

[0177] S203, Set constraints for leaving the bus terminal:

[0178] (14)

[0179] In the formula, This refers to the battery's highest state of charge. It is the battery capacity of the electric bus b serving route r; The state of battery energy of electric bus b serving route r at the departure time of its lth trip; This refers to the departure time of the electric bus's first trip. This refers to the energy consumption of electric bus B during its journey from its designated parking lot to its first stop. Refers to specific bus routes. It is the mission sequence number. This refers to the possibility of fully charging the electric bus at night in the warehouse. Assuming the electric bus will begin its first journey from the departure station without any charging activity, then... This indicates the energy consumption of an electric bus as it travels from its parking lot to the starting point of its first journey.

[0180] S204. Set constraints for arrival at the depot:

[0181] (15)

[0182] In the formula, The battery energy state of electric bus b serving route r at the arrival time of its lth trip; Let l be the arrival time of a certain trip for an electric bus. This is the lowest state of charge of the battery. This refers to the energy consumption of electric bus B during its journey from the last stop of its last trip to its designated parking lot. This is the last trip sequence number of the electric bus b serving route r. Specifically, the formula indicates that the remaining distance energy should ensure the electric bus can successfully return to its attached depot.

[0183] S205. Set energy consumption-related constraints:

[0184] (16)

[0185] In the formula, This refers to a road segment where i is the starting station and j is the ending station. This is the set of all road segments for the l-th trip. It is the fixed energy consumption generated when electric bus b performs its lth trip and travels through road segment (i, j); This refers to the energy consumption coefficient related to battery capacity when electric bus b performs its l-th trip, traversing route segment (i, j). Specifically, the term on the right-hand side of the formula represents the total energy consumption l of the route, and the sum of the energy consumption of the bus for each route segment. .

[0186] S206. Set constraints for the charging process:

[0187] (17)

[0188] In the formula, The battery energy state of electric bus b serving route r at the departure time of its (l+1)th trip. To determine the duration of a single time interval within the planning period, This is the departure time of the electric bus's (l+1)th trip. This refers to a continuous decision variable, representing the charging power of electric bus b within the time interval t. Specifically, This indicates the amount of energy consumed during the stay.

[0189] S207, Setting constraints on charging capacity:

[0190] (18)

[0191] (19)

[0192] (20)

[0193] In the formula, Refers to the set of time intervals within the planning period; For a specific time interval; It is an extremely small positive number; Whether the electric bus b on service route r is charged during time interval t; Refers to a sufficiently large positive number; Let be the set of electric buses located at terminal s and serving route r within the time interval t; This refers to the number of parking spaces at terminal s.

[0194] S208, Set a minimum charging time constraint:

[0195] (twenty one),

[0196] (twenty two),

[0197] (twenty three),

[0198] In the formula, This refers to the charging start / stop status indicator. For minimum charging time, It is the total number of time intervals within the planning period. It refers to the set of all time intervals within a single day.

[0199] S209. Set upper and lower limits for SOC constraints:

[0200] (twenty four),

[0201] (25),

[0202] (26).

[0203] S210, Set upper and lower limits for charging power constraints:

[0204] (27)

[0205] In the formula, This refers to the maximum charging power of the electric bus charger.

[0206] S211. Set the optimization model:

[0207] (28)

[0208] (29)

[0209] In the formula, This refers to the maximum average charging power of terminal station s during peak demand periods. Let be the average charging power of terminal s during the o-th demand metering interval. It is a set of peak demand measurement intervals. This refers to the maximum average charging power of terminal s during off-peak demand periods. It is a set of demand measurement intervals during off-peak hours.

[0210] The comprehensive programming problem can be expressed as a mixed-integer linear programming model in the following form:

[0211] (30)

[0212] The constraints are equations (14)-(21), (23)-(29) and (31), with equation (31) as follows:

[0213] (31),

[0214] In the formula, The unit price of electricity during peak demand. The unit price of electricity during off-peak hours. It is the set of all demand measurement intervals. This refers to the time range from the start to the end of the 0th demand measurement interval. It is the duration of the demand measurement interval; Refers to the service route located at terminal s within the basic time interval t. A collection of electric buses.

[0215] The above model is a mixed-integer linear programming model that can be solved by commercial solvers and can also be converted into a robust model that is easy to handle.

[0216] S3. By considering the merging of box-shaped uncertainty sets, budget uncertainty sets, and ellipsoidal uncertainty sets, the mixed-integer linear programming model is transformed into a robust logarithmic problem. The specific steps are as follows:

[0217] S301. The following assumptions are made regarding the transformation of the model into a robust pairwise problem:

[0218] (1) The actual operation of electric bus systems usually encounters many uncertainties. Therefore, the parameters in the deterministic model will vary within a certain range, which may lead to the infeasibility or suboptimal nature of the optimal solution obtained by the deterministic model;

[0219] (2) Develop robust formulas for integrated planning problems, aiming to provide a flexible and robust approach to hedge against the uncertainty of energy consumption in electric bus operations, allowing operators to choose their risk attitudes and preferences according to their needs.

[0220] S302. Many parameters in the energy consumption model may be disturbed under actual operating conditions, and some of these parameters are difficult to measure accurately. To address the uncertainty of energy consumption, a robust logistic problem was developed by considering the realized electricity consumption of public transportation. for:

[0221] (32),

[0222] In the formula, The actual energy consumption of electric bus b serving route r when performing the lth trip and traveling on route segment (i, j); The average fixed energy consumption of electric bus b during its l-th trip, on route (i, j); It is the average energy consumption coefficient related to the battery when electric bus b performs its lth trip and travels along route (i, j); The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b when it makes its lth trip and travels on route (i, j). It is the maximum deviation of battery-related energy consumption when electric bus b travels on road segment (i, j); This refers to the maximum deviation coefficient of battery-related energy consumption when electric bus b travels on route segment (i, j). .

[0223] S303, Establish a system based on merged box-shaped uncertainty sets. Statement:

[0224] (33),

[0225] In the formula, The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b serving route r when it makes its lth trip. The set of merged box-shaped uncertainties to which it belongs; This is the energy consumption deviation coefficient vector. It is a real vector space of dimension l, which is the number of road segments in the l-th trip. This refers to the set of all road segments that electric bus b will travel on during its l-th trip. However, this uncertainty set is overly conservative, and the worst-case scenario is unlikely to occur on every road segment.

[0226] S304. Establish a budget uncertainty set. Statement:

[0227]

[0228] (34),

[0229] In the formula, The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b serving route r when it makes its lth trip. The set of budget uncertainty to which it belongs; This represents the maximum permissible sum of the absolute values ​​of the energy consumption deviation coefficients for all road segments during this trip. This is a predetermined uncertainty budget, meaning that the total energy consumption deviation for each bus trip is limited by parameters. The following considers an ellipsoidal uncertainty set, which is another way to prevent all realized values ​​from simultaneously reaching their worst values.

[0230] S305, Establishing a set of uncertainties based on ellipsoids Statement:

[0231] (35),

[0232] In the formula, The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b serving route r when it makes its lth trip. The set of uncertainties on the ellipsoid to which it belongs; Let be the maximum permissible second norm of the energy consumption deviation coefficient vector for this trip. Here, It is the 2-norm of a vector. and Similar to Amidst budget uncertainty.

[0233] S306. Problems involving deriving robust pairs through constraint substitution:

[0234] The robustness of the model can be derived by replacing the constraint formula (16) involving energy consumption terms with the following constraints:

[0235] (36)

[0236] In the formula, Let $\mathbf$ be the set of all travel tasks that need to be performed when electric bus $b$ serves route $r$. The robust logarithmic problem above is a semi-infinite programming model because it has an infinite number of constraints, making it cumbersome for commercial solvers. Therefore, it is necessary to consider reformulating the robust logarithmic problem into a more tractable form, i.e., by redefining the constraints.

[0237] S4. Reconstruct the robust logarithmic problem into a solvable mixed-integer linear programming model or a mixed-integer second-order cone model, and solve it using a commercial solver. The specific steps are as follows:

[0238] S401, Restating the merged box-shaped uncertainty set:

[0239] Set all =1 In robust equivalence problems, it is easy to obtain a tractable restatement, resulting in the following constraint:

[0240] (37).

[0241] S402, Restating the set of budgetary uncertainties:

[0242] Considering the worst-case energy consumption for each bus trip This is equivalent to finding the maximum value as shown below:

[0243]

[0244] The constraints are:

[0245]

[0246]

[0247] The dual of the above function is:

[0248]

[0249] The constraints are:

[0250]

[0251]

[0252]

[0253] In the formula, The dual variable refers to the energy cost per unit of budget. Dual variables, understood as exceeding The additional energy cost at the upper limit. Here and These are the dual variables corresponding to constraint formulas (27) and (28):

[0254] Constraint (36) is equivalent to equations (30)-(32) and (45), and equation (45) is as follows:

[0255]

[0256] Therefore, the robust problem is transformed into a tractable mixed-integer linear programming model.

[0257] S403, Restating the Uncertainty Set of the Ellipsoid:

[0258] Similar to the set of budget uncertainties, considering the worst-case energy consumption scenario is equivalent to finding the maximum value shown below:

[0259]

[0260] The constraints are:

[0261]

[0262]

[0263] In the formula This refers to the mathematical representation of an n-dimensional second-order cone. Equation (47) represents a second-order circular cone. Since the problem is feasible and bounded, according to the theory of conical duality, the dual equation is obtained:

[0264]

[0265] The constraints are:

[0266]

[0267]

[0268] In the formula, The dual variable is understood as the energy cost of the unit norm. The dual variable is understood as the maximum energy consumption deviation cost of road segment (i, j); Auxiliary dual variables are used to ensure that the dual solution covers the original problem. Non-negative scenarios; Auxiliary dual variables refer to the vector elements that constitute the dual second-order cone.

[0269] To address this, the robust problem of ellipsoidal uncertainty sets is transformed into a mixed-integer second-order cone model that can be handled and solved directly by commercial solvers.

[0270] Example 2:

[0271] This invention proposes a robust optimization system for the deployment and scheduling of charging facilities for electric buses, used to implement the robust optimization method for the deployment and scheduling of charging facilities for electric buses disclosed in Example 1, including:

[0272] The integrated planning module is used to execute step S1 and establish an integrated planning problem for the number of chargers deployed, battery specifications, and charging schedule.

[0273] The basic modeling module is used to execute step S2 and construct a mixed-integer linear programming model.

[0274] The robust conversion module is used to execute step S3 and convert the problem to obtain the robust parallel problem;

[0275] The model solver module is used to execute step S4, reconstruct the model, and solve it using a commercial solver.

[0276] Example 3:

[0277] This invention proposes a robust optimization system for the deployment and scheduling of charging facilities for electric buses, used to implement the robust optimization method for the deployment and scheduling of charging facilities for electric buses disclosed in Example 1, including:

[0278] The integrated planning module is used to execute step S1 and establish an integrated planning problem for the number of chargers deployed, battery specifications, and charging schedule.

[0279] The basic modeling module is used to execute steps S201-S211 described in S2 to construct a mixed-integer linear programming model.

[0280] The robust transformation module is used to execute steps S301-S306 described in S3, transforming to obtain robust equivalence problems, and constructing an energy consumption uncertainty model and three uncertainty sets.

[0281] The model solving module is used to execute steps S401-S403 described in S4, reconstruct the model and solve it using a commercial solver, thereby restating, transforming and solving the three uncertainty sets respectively.

[0282] The planning problem definition module includes: a battery configuration unit for executing step S101; a charger deployment unit for executing step S102; and a charging plan formulation unit for executing step S103.

[0283] The above is an exemplary description of the invention. Obviously, the specific implementation of the invention is not limited to the above-described manner. Any non-substantial improvement made using the inventive concept and technical solution of the invention, or the direct application of the inventive concept and technical solution to other situations without modification, is within the protection scope of the invention.

Claims

1. A robust optimization method for the deployment and scheduling of charging facilities for electric buses, characterized in that, Includes the following steps: S1. Define the scope of the integrated planning for the electric bus system. Based on charging capacity limitations, demand costs, and time-of-use pricing, establish an integrated planning framework to determine the number of chargers to be deployed at each terminal station, the battery specifications of the electric buses, and an effective charging plan at the system level. S2. Construct a mixed-integer linear programming model for the integrated planning problem; S3. Merge the box, budget, and ellipsoidal uncertainty sets to transform the mixed integer linear programming model into a robust logarithmic problem; S4. Reconstruct robust logarithmic problems into solvable mixed-integer linear programming models or mixed-integer second-order cone models, and solve them using commercial solvers.

2. The robust optimization method for the deployment and scheduling of charging facilities for electric buses according to claim 1, characterized in that, The specific steps of step S1 are as follows: S101. Based on historical data from the urban rail transit automatic fare collection system, establish a planning problem to determine the battery specifications for electric buses. S102. With the constraints that the number of charging vehicles does not exceed the number of chargers and parking spaces, and the charging process meets the minimum charging time, establish a planning problem for the number of chargers deployed at each terminal station. S103. Planning problem of establishing an effective charging plan at the level of electric bus system by combining the consumption cost, demand cost and time-of-use electricity rate of commercial electricity customers.

3. The robust optimization method for the deployment and scheduling of charging facilities for electric buses according to claim 1, characterized in that, In step S2, before constructing the mixed-integer linear programming model, the following assumptions need to be made about the entire integrated programming problem: (1) Only costs directly related to the charger and battery are included in the calculation, and the purchase cost of electric buses, driver costs and maintenance costs are not considered; (2) A cost amortization mechanism is adopted, with the monthly purchase cost amortization amount of each charger and the monthly battery purchase cost amortization amount per kilowatt-hour as a unified measurement standard; (3) To address the difference between demand charges calculated monthly and time-of-use electricity charges calculated daily, the time dimension of the two types of costs is unified, thereby constructing a complete cost calculation system to support optimization decisions.

4. A robust optimization method for the deployment and scheduling of charging facilities for electric buses according to claim 1, characterized in that, In step S2, the mixed-integer linear programming model is constructed, and the specific steps are as follows: S202. Set the objective function of the integrated planning problem as follows: （13）， In the formula, This refers to the average monthly amortized purchase cost of the charger. It is a collection of all bus terminals. The number of chargers to deploy at terminal station s, This is the average monthly amortization cost per kilowatt of battery. It refers to the collection of all bus routes. It is a collection of electric buses serving the R line. The battery capacity for electric bus B on line R. It is the demand-based electricity price cost. This refers to the cost of time-of-use electricity. S203, Set constraints for leaving the bus terminal: （14）， In the formula, This refers to the battery's highest state of charge. It is the battery capacity of the electric bus b serving route r; The state of battery energy of electric bus b serving route r at the departure time of its lth trip; This refers to the departure time of the electric bus's first trip. This refers to the energy consumption of electric bus B during its journey from its designated parking lot to its first stop. Refers to specific bus routes. It is the mission sequence number; S204. Set constraints for arrival at the depot: （15）， In the formula, The battery energy state of electric bus b serving route r at the arrival time of its lth trip; Let l be the arrival time of a certain trip for an electric bus. This is the lowest state of charge of the battery. This refers to the energy consumption of electric bus B during its journey from the last stop of its last trip to its designated parking lot. It is the last trip number of electric bus b serving route r; S205. Set energy consumption-related constraints: （16）， In the formula, This refers to a road segment where i is the starting station and j is the ending station. This is the set of all road segments for the l-th trip. It is the fixed energy consumption generated when electric bus b performs its lth trip and travels through road segment (i, j); The energy consumption coefficient related to battery capacity refers to the energy consumption of electric bus b when it makes its lth trip and travels through road segment (i, j). S206. Set constraints for the charging process: （17）， In the formula, The battery energy state of electric bus b serving route r at the departure time of its (l+1)th trip. To determine the duration of a single time interval within the planning period, This is the departure time of the electric bus's (l+1)th trip. The continuous decision variable refers to the charging power of electric bus b within the time interval t. S207, Setting constraints on charging capacity: （18）， （19）， （20）， In the formula, Refers to the set of time intervals within the planning period; For a specific time interval; It is an extremely small positive number; Whether the electric bus b on service route r is charged during time interval t; Refers to a sufficiently large positive number; Let be the set of electric buses located at terminal s and serving route r within the time interval t; This refers to the number of parking spaces at terminal s; S208, Set a minimum charging time constraint: （21）， （22）， （23）， In the formula, This refers to the charging start / stop status indicator. For minimum charging time, It is the total number of time intervals within the planning period. It refers to the set of all time intervals within a single day; S209. Set upper and lower limits for SOC constraints: （24）， （25）， （26）， S210, Set upper and lower limits for charging power constraints: （27）， In the formula, This refers to the maximum charging power of the electric bus charger; S211. Set up the optimization model: （28）， （29）， In the formula, This refers to the maximum average charging power of terminal station s during peak demand periods. Let be the average charging power of terminal s during the o-th demand metering interval. It is a set of peak demand measurement intervals. This refers to the maximum average charging power of terminal s during off-peak demand periods. It is a set of intervals for measuring demand during off-peak hours; The comprehensive programming problem can be expressed as a mixed-integer linear programming model in the following form: （30）， The constraints are: equations (14)-(21), (23)-(29) and (31), with equation (31) as follows: （31）， In the formula, The unit price of electricity during peak demand. The unit price of electricity during off-peak hours. It is the set of all demand measurement intervals. This refers to the time range from the start to the end of the 0th demand measurement interval. It is the duration of the demand measurement interval; Refers to the service route located at terminal s within the basic time interval t. A collection of electric buses; The above model is a mixed-integer linear programming model that can be solved by commercial solvers and can also be converted into a robust model that is easy to handle.

5. The robust optimization method for the deployment and scheduling of charging facilities for electric buses according to claim 4, characterized in that, The specific steps of step S3 are as follows: S301. The following assumptions are made regarding the transformation of the model into a robust pairwise problem: (1) The parameters in the deterministic model will vary within a certain range, which may lead to the infeasibility or suboptimal nature of the optimal solution obtained by the deterministic model; (2) Provide a flexible and robust method to hedge against the uncertainty of energy consumption in the operation of electric buses; S302. To address the uncertainty of energy consumption, a robust logistic regression problem was developed by considering the actual electricity consumption of public transportation trips. for: （32）， In the formula, The actual energy consumption of electric bus b serving route r when performing the lth trip and traveling on route segment (i, j); The average fixed energy consumption of electric bus b during its l-th trip, on route (i, j); It is the average energy consumption coefficient related to the battery when electric bus b performs its lth trip and travels along route (i, j); The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b when it makes its lth trip and travels on route (i, j). It is the maximum deviation of battery-related energy consumption when electric bus b travels on road segment (i, j); The maximum deviation coefficient of battery-related energy consumption when electric bus b travels on road segment (i, j); S303, Establish a system based on merged box-shaped uncertainty sets. Statement: （33）， In the formula, The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b serving route r when it makes its lth trip. The set of merged box-shaped uncertainties to which it belongs; This is the energy consumption deviation coefficient vector. It is a real vector space of dimension l, which is the number of road segments in the l-th trip. This refers to the collection of all routes taken by electric bus b during its lth trip; S304. Establish a budget uncertainty set. Statement: （34）， In the formula, The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b serving route r when it makes its lth trip. The set of budget uncertainty to which it belongs; This is the maximum permissible sum of the absolute values ​​of the energy consumption deviation coefficients for all road segments during this trip; S305, Establishing a set of uncertainties based on ellipsoids Statement: （35）， In the formula, The energy consumption deviation coefficient refers to the energy consumption deviation coefficient of electric bus b serving route r when it makes its lth trip. The set of uncertainties on the ellipsoid to which it belongs; The maximum permissible second norm of the energy consumption deviation coefficient vector for this trip; S306. Problems involving deriving robust pairs through constraint substitution: The robustness of the model can be derived by replacing the constraint formula (16) involving energy consumption terms with the following constraints: （36）， In the formula, This refers to the set of all travel tasks that need to be performed when the electric bus (b) serves route (r).

6. The robust optimization method for the deployment and scheduling of charging facilities for electric buses according to claim 5, characterized in that, The specific steps of step S4 are as follows: S401, Restating the merged box-shaped uncertainty set: In settings all =1 yields a tractable restatement in robust equivalence problems, resulting in the following constraint: （37）； S402, Restating the set of budgetary uncertainties: The constraints are: The dual of the above function is: The constraints are: In the formula, The dual variable refers to the energy cost per unit of budget. Dual variables, understood as exceeding The additional energy cost at the upper limit; Constraint (36) is equivalent to equations (30)-(32) and (45), and equation (45) is as follows: Therefore, the robust problem is transformed into a tractable mixed-integer linear programming model; S403, Restating the Uncertainty Set of the Ellipsoid: The constraints are: In the formula The mathematical representation of an n-dimensional second-order cone; According to the theory of conical duality, the dual equation is obtained: The constraints are: In the formula, The dual variable is understood as the energy cost of the unit norm. The dual variable is understood as the maximum energy consumption deviation cost of road segment (i, j); Auxiliary dual variables are used to ensure that the dual solution covers the original problem. Non-negative scenarios; Auxiliary dual variables refer to the vector elements that constitute the dual second-order cone; To address this, the robust problem of ellipsoidal uncertainty sets is transformed into a mixed-integer second-order cone model that can be handled and solved directly by commercial solvers.

7. A robust optimization system for the deployment and scheduling of charging facilities for electric buses, characterized in that, The system is used to implement the robust optimization method for the deployment and scheduling of charging facilities for electric buses as described in any one of claims 1-6, including: The integrated planning module is used to execute step S1 and establish an integrated planning problem for the number of chargers deployed, battery specifications, and charging schedule. The basic modeling module is used to execute step S2 and construct a mixed-integer linear programming model. The robust conversion module is used to execute step S3 and convert the problem to obtain the robust parallel problem; The model solver module is used to execute step S4, reconstruct the model, and solve it using a commercial solver.

8. The robust optimization system for charging facility deployment and scheduling of electric buses according to claim 7, characterized in that, The planning problem definition module includes: A battery configuration unit for performing step S101 as described in claim 2; A charger deployment unit is configured to perform step S102 as described in claim 2; A charging plan formulation unit is used to perform step S103 as described in claim 2.

9. The robust optimization system for charging facility deployment and scheduling for electric buses according to claim 7, characterized in that, The robust conversion module is used to perform the steps described in claim 5 to construct an energy consumption uncertainty model and three uncertainty sets.

10. The robust optimization system for charging facility deployment and scheduling for electric buses according to claim 7, characterized in that, The model solving module is used to perform the steps described in claim 6, which involve restating, dualizing, and solving the three uncertainty sets respectively.

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