A subway energy-saving dispatching operation method and system based on timetable optimization

Abstract

The present invention belongs to the technical field of urban rail transit systems, and specifically relates to a subway energy-saving dispatching operation method and system based on timetable optimization, comprising the following steps: S10: constructing a subway operation timetable, simulating the state of subway operation, constructing a subway operation system for optimizing the subway timetable, and building a model of the subway operation system; S20: constructing a power system node network, modeling the power system node network, and constructing a node network through IEEE 30 node information of MatPower; S30: integrating the node network and the subway system; S40: performing power flow analysis on the subway-node network model, and optimizing the optimal power flow target through a heuristic algorithm; the present invention focuses on optimal power flow optimization based on the subway timetable, and controls the active and reactive power of the power grid node system by optimizing the subway timetable, and optimizes the overall node network while considering the control variables of the power grid node system.

Description

Technical Field

[0001] The present invention belongs to the technical field of urban rail transit systems, and in particular relates to a subway energy-saving dispatching operation method and system based on timetable optimization. Background Art

[0002] With the increasing awareness of environmental protection and the congestion of urban traffic caused by the urbanization process, public transportation represented by subways has received more attention. However, at the same time, the subway's identity as a major energy consumption carrier of the urban power grid is often overlooked.

[0003] Previous research has generally tended to separate the subway and power grid. A mixed-integer linear programming approach was proposed, considering the optimization of subway energy consumption in subway train scheduling. The focus has been on optimizing subway energy under dynamic passenger demand. Regenerative braking has been applied to reduce energy consumption and reduce traction power peaks. For the power grid, there has been a greater focus on algorithm updates for optimal power flow problems, from traditional algorithms such as Newton's method to later meta-heuristic algorithms such as particle swarm optimization, adaptive differential evolution, and firefly algorithms. These studies often focus solely on this area, ignoring the nature of the subway and power grid as a mutually influencing entity.

[0004] In recent years, some existing technologies have discovered this problem and begun to focus on comprehensive consideration of rail transit and power grid systems; some have systematically established the dynamic energy loss behavior of high-speed trains, and divided the entire energy transmission and consumption system into three parts: traction power supply network, traction drive system, and wheel-rail motion system; for the first time, electrified railways introduced primary dispatch control of the power grid, and also proposed a new frequency regulation framework for electrified railways to provide primary dispatch, including day-ahead capacity estimation, frequency control parameter scheduling and real-time response; some have focused on demand response on the power grid side, responding to the requirement to reduce energy consumption of the power grid within a certain period of time by changing the driving conditions of the train; however, although these studies have begun to pay attention to the connectivity between the power grid and rail transit, they have not conducted in-depth research on the mutual influence of rail transit and the power grid, and often only focus on the needs and changes on one side. Summary of the Invention

[0005] In order to overcome the deficiencies of the prior art and solve the above-mentioned technical problems, the present invention proposes a subway energy-saving dispatching operation method based on timetable optimization, comprising the following steps:

[0006] S10: Build a subway timetable, simulate the subway operation status, build a subway operation system for optimizing the subway timetable, and build a model of the subway operation system;

[0007] S20: Build the power system node network, model the power system node network, and construct the node network through the IEEE30 node information of MatPower;

[0008] S30: Integrate the node network and the subway system to form a subway-node network model;

[0009] S40: Perform power flow analysis on the subway-node network model and optimize the optimal power flow target through heuristic algorithms.

[0010] Preferably, the model of the subway operation system built by S1 includes:

[0011] S11: The first step is to build the subway platform and line. Referring to the Beijing Yizhuang subway line, a subway platform model corresponding to the operating platform and running distance is built;

[0012] S12: Constructing subway speed curves. Since subway operations are essentially optimized based on time and distance, we need to generate corresponding speed curves based on given travel time and distance. By analyzing the forces acting on the train, the strategy can automatically generate corresponding speed curves that meet the constraints of maximum acceleration and deceleration.

[0013] S13: Analysis of subway passenger flow. In the modeling of the subway operation system, the number of passengers fluctuates, which in turn affects the subway's energy consumption. Based on the ascending and descending rates, as well as the limit on the number of people in the subway car, the number of customers on the subway train is modeled;

[0014] S14: Implement energy analysis of the subway operation system. Through the speed curve and the corresponding platform information, construct the energy analysis of the subway, consider the regenerative braking energy, and implement the analysis of the active power consumption of the corresponding power supply platform of the train.

[0015] Preferably, the S30 fusion node network and subway system include:

[0016] S31: The connection between the node network and the subway. The voltage is boosted from the power generation end to the grid, then stepped down by the main substation. The voltage is then converted to direct current by a rectifier and transmitted to the subway to power it.

[0017] S32: For the entire subway-node network, the red cart represents the corresponding power supply section. In the same power supply section, multiple trains may run, and the compensation of regenerative braking energy only occurs in the same power supply section. The yellow symbol represents the capacitor, that is, the subway operation system compensates for the reactive power of the entire node through the rectifier. The red cart is connected to the active power consumption of the power system node, and the yellow capacitor is connected to the reactive power compensation of the node.

[0018] Preferably, in S40, the control variables of the subway system's operating schedule, including the departure time of each train at each platform, the service time, and the departure time interval of each vehicle, as well as the control variables of the node network, the active power output, voltage, and transformer ratio of the generator node, the reactive power compensation of the load node, and the comprehensive control variables are optimized by the heuristic algorithm - spider bee algorithm.

[0019] Preferably, the stress analysis of the S12 train includes

[0020] S121: The maximum acceleration of the train is α. When the train exceeds the maximum acceleration, it runs according to the maximum acceleration. The traction formula of the train is: F a =min{F max ,F(α)};

[0021] Among them, F a is the traction force obtained by the train, F max is the maximum traction force given by the motor, α is the maximum acceleration, and F(α) is the traction force under the condition of maximum acceleration;

[0022] S122: The train's braking is mainly achieved by regenerative braking. The motor's function is reversed to become a generator. When the train needs to slow down, the motor driving the wheelset reverses its operating mode. If a train and the train generating electricity are in the same power supply station, the regenerative braking energy is sent back to the power supply system and supplies power to other trains in the power supply station. When the maximum deceleration is exceeded, the train operates at the maximum deceleration. The braking force formula of the train is B b =min{B max ,B(β)};

[0023] Among them, B b is the braking force obtained by the train, B max is the maximum braking force that the train can withstand, β is the maximum deceleration, and B(β) is the braking force under the maximum deceleration condition;

[0024] S123: During the train operation, the train will be subject to external forces that hinder the train's current movement. The Davis formula is used to empirically calculate the train resistance: r = a + bv + cv 2

[0025] Where r is the total resistance experienced by the train, v is the train's running speed, and a, b, and c are the resistance coefficients of the Davis formula, which are determined by the train.

[0026] Preferably, the train operation process is divided into three stages: traction, inertia and braking;

[0027] Traction condition: When the train is in traction condition, the train absorbs energy from the contact network to accelerate the train forward; the traction condition occurs when the train starts to move, and the train is subjected to traction and resistance at the same time. The total external force on the train is C = F a -r;

[0028] Where C is the net external force on the train, F a is the traction force obtained by the train, r is the resistance of the train;

[0029] Coasting condition: When the train is in coasting condition, the train's motor is not working. The train neither absorbs energy nor generates regenerative braking energy. At this time, the train is only affected by resistance, and the train speed will slowly decrease. In this case, the net external force acting on the train is C = -r.

[0030] Braking condition: When the train is in braking condition, the train will generate braking force through regenerative braking energy. The speed of the train in this stage will drop rapidly and decrease to 0. The braking condition generally occurs in the second half of the train running curve, which is generated when the train is about to arrive at the station. C = -B B -r.

[0031] Preferably, S13: analysis of subway passenger flow includes:

[0032] S131: When train k arrives at station s, the number of passengers waiting to board the train on the platform is equal to the sum of the passengers who entered platform s to wait for train k within the headway between train k and the previous train and the passengers who were stranded at the previous platform. The formula is:

[0033] S132: When train k leaves platform s, the number of passengers in the train is the difference between the number of passengers in the train when it last left the station plus the number of people who got on and off the train. The formula is:

[0034] S133: When train k arrives at station s, the number of passengers getting off is:

[0035] S134: The number of passengers boarding is the minimum of the remaining capacity of train k and the passenger demand at station s, and the formula is:

[0036] S135: When train k leaves s, the number of people stranded at the platform is:

[0037] Optimized, energy analysis of S14 train:

[0038] First, based on the dynamic analysis of the train, the formulas for the traction and braking forces on the train under different working conditions are obtained:

[0039]

[0040] Part of the energy involved in the train is regenerative braking energy, which is transmitted within the same power supply interval on the uplink and downlink directions, resulting in the following formula:

[0041] Traction energy consumption of power supply zone q;

[0042] Regenerative braking energy in power supply interval q;

[0043] Where, When the station the vehicle passes by belongs to the power supply section q, otherwise, λ is the energy utilization coefficient of regenerative braking energy; the formula for obtaining the net energy consumed in the power supply interval q is:

[0044]

[0045] A subway energy-saving dispatching and operation system based on timetable optimization, used in the above-mentioned subway energy-saving dispatching and operation method based on timetable optimization, includes 6 generators, 41 branches, 4 load tap-changing transformers, and 9 shunt capacitors. The system has a total of 37 control variables, including 25 directly controlled variables. The adaptability of the introduced optimization method is verified under conditions of minimum actual power loss and voltage level.

[0046] The beneficial effects of the present invention are as follows:

[0047] 1. The present invention focuses on the optimal power flow optimization based on the subway timetable. By optimizing the subway timetable, the active and reactive power of the power grid node system is controlled. While considering the control variables of the power grid node system, the overall node network is optimized.

[0048] 2. This paper introduces the optimization of subway timetable into the calculation of optimal power flow of node network for the first time. The proposed hybrid PSO-SWO can effectively deal with the OPF problem. The metro-IEEE 30BUS hybrid model is proposed and adopted. While meeting the running time accuracy on the railway side, it can also objectively analyze the impact of control variables on the node network.

[0049] 3. This paper adopts a new heuristic algorithm, the Spider Bee algorithm, to solve the OPF problem in the power grid. The optimization method is applied to the IEEE 30bus system, the most commonly used test network, and its adaptability is verified under conditions of minimal actual power loss and voltage levels. The SWO algorithm is compared with other traditional heuristic algorithms, demonstrating its superior performance in handling complex multi-parameter constraint problems. Furthermore, the present invention idealizes the combination of subway models and power grids, adopting a more detailed model for subway-based optimal power flow optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The present invention will be further described below in conjunction with the accompanying drawings;

[0051] Figure 1 is a schematic diagram of the subway power supply system of the present invention;

[0052] Figure 2 It is the pseudo code of the algorithm flow in the present invention;

[0053] Figure 3 It is the SWO flow chart of the present invention;

[0054] Figure 4 The Yizhuang Line of the present invention is a bidirectional subway line;

[0055] Figure 5 is the subway timetable corresponding to the initial solution of the present invention and the optimal solution obtained by the SWO algorithm;

[0056] Figure 6 This is a comparison chart of the convergence speed of different algorithms of the first embodiment of the present invention;

[0057] Figure 7 is the subway timetable corresponding to the solution initially generated by the present invention and the optimal solution generated using SWO;

[0058] Figure 8 is a comparison chart of the convergence speed of the second different algorithms of the present invention;

[0059] Figure 9 It is a schematic diagram of a node network of the present invention;

[0060] Figure 10 It is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0061] The problem addressed by the present invention is the optimization of the optimal power flow problem based on the subway timetable. The goal of the optimal power flow problem is to minimize the line loss of all branches, which is the optimization target of the power grid network, by changing the input parameters. The innovation of the subway-based optimal power flow is to integrate the subway and the power grid, two factors that are usually considered separately, for analysis, so that the subway, as the load of the power grid, participates in the analysis and calculation of the optimal power flow. For the subway, the present invention considers a bidirectional subway line with 2N stations. During the optimization period T, trains will depart from the first and last stations, and passenger flow will arrive at different stations according to OD. Trains will run from the starting platform to the terminal platform and then return to the next round of service. Trains have different interval running time and service time between different sections and stations. Each train has a different starting point according to the change of the departure interval, and the running time and service time of subsequent trains are not fixed.

[0062] The following describes the embodiments of the present invention in detail with reference to the accompanying drawings;

[0063] Example 1:

[0064] The symbols in this embodiment are as follows:

[0065]

[0066]

[0067] Furthermore, the present invention considers three decision variables from the train schedule and four decision variables from the power grid, for a total of seven decision variables;

[0068] 1. The service time of train k at station s;

[0069] 2. The running time of train k from station s to station s+1;

[0070] 3.h k : The departure distance between train k and the previous train k-1 arriving at the first station;

[0071] 4.V G : voltage of the generator;

[0072] 5.P G :Except the active power of the balancing node P G1 Active power output of other generators besides the 1000A;

[0073] 6. Tab: Transformer voltage divider ratio;

[0074] 7.Q c : shunt VAR reactive compensator;

[0075] Furthermore, the model assumes:

[0076] Assumptions 1. All trains in the optimization period stop at every station, and all trains have the same vehicle type and marshaling method.

[0077] Assumption 2: Upon arrival, all passengers waiting at the station are able to board and all passengers alighting, provided that there is sufficient remaining capacity. The number of passengers boarding and alighting is determined by the arrival and alighting rates at each station.

[0078] Assumption 3. The passenger flow is stable during the optimization time and passengers are served on a first-come, first-served basis.

[0079] Next, let's analyze the subway model separately. A subway train consists of a motor car and trailer cars, and is subject to both internal forces within the train set and a series of external forces. Because these internal forces do not affect or alter the train's motion, and to simplify calculations, we use a single-point model with mass to analyze and establish the train's dynamics.

[0080] Furthermore, the stress analysis of the S12 train includes:

[0081] S121: Traction Analysis:

[0082] During the train's operation, it will be subjected to traction from the motor to start and maintain its movement. At the same time, for the safety of the train itself and the comfort of passengers, we introduce the maximum acceleration of the train as α. When the train exceeds the maximum acceleration, it runs according to the maximum acceleration. Therefore, we can get the formula for the train's traction force as:

[0083] F a =min{F max ,F(α)} (1)

[0084] Where, F a is the traction force obtained by the train, F max is the maximum traction force given by the motor, α is the maximum acceleration, and F(α) is the traction force under the condition of maximum acceleration;

[0085] S122: Braking force analysis: The braking of the train is mainly achieved by regenerative braking. In this process, the function of the electric motor is reversed to become a generator. When the train needs to slow down, the motor driven by the wheelset inverts its operating mode to resist the rotation of the wheelset and slow down the train. In the present invention, if there is a train at the same power supply station as the train that generates electricity (that is, in braking condition), the regenerative braking energy can be sent back to the power supply system (contact network) and supply power to other trains at the power supply station. If no train in the same power supply station needs this energy (meaning no train is in traction condition), then this energy will be wasted. At the same time, if the regenerative braking energy is greater than the energy required by other trains, the energy will also be dissipated. At the same time, like traction, we have a maximum braking force limit. In order to ensure the comfort of passengers, when the maximum deceleration is exceeded, the train will operate at the maximum deceleration. Therefore,

[0086] The formula for the braking force of the train is;

[0087] B b =min{B max ,B(β)} (2)

[0088] Where B b is the braking force obtained by the train, B max is the maximum braking force that the train can withstand, β is the maximum deceleration, and B(β) is the braking force under the maximum deceleration condition;

[0089] S123: Resistance Analysis: During train operation, the train will be subject to external forces that hinder its current movement, including friction and air resistance. Here, we use the Davis formula to empirically calculate the train resistance.

[0090] r=a+bv+cv 2 (3)

[0091] Where r is the total resistance experienced by the train, v is the train's running speed, and a, b, and c are the resistance coefficients of the Davis formula, which are determined by the train.

[0092] Furthermore, the train's operating condition analysis, through the train force analysis mentioned above, we can know that during the operation of the train, it will be affected by traction, braking force and resistance, thereby changing the operating condition; the present invention adopts the three-condition principle to analyze the train, that is, the train's operating process can be divided into three stages: traction, inertia, and braking;

[0093] Traction condition: When the train is in traction condition, the train absorbs energy from the contact network, thereby accelerating the train forward; the traction condition generally occurs when the train starts to move. At this time, the train is subjected to traction and resistance at the same time, so the total external force on the train at this time is C = Fa -r; where C is the net external force on the train, F a is the traction force obtained by the train, r is the resistance of the train;

[0094] Coasting condition: When the train is in coasting condition, the train's motor is not working. The train neither absorbs energy nor generates regenerative braking energy. At this time, the train is only affected by resistance, and the train speed will slowly decrease. In this case, the net external force acting on the train is C = -r.

[0095] Braking condition: When the train is in braking condition, the train will generate braking force through regenerative braking energy. The speed of the train in this stage will drop rapidly and decrease to 0. The braking condition generally occurs in the second half of the train running curve, which is generated when the train is about to arrive at the station. C = -B B -r.

[0096] Furthermore, the passenger flow of the train is analyzed. The passenger flow of the train determines the number of passengers carried by the train at each time;

[0097]

[0098] Formula (7) explains that when train k arrives at station s, the number of passengers waiting to board the train on the platform is equal to the sum of the passengers who entered platform s to wait for train k within the headway between train k and the previous train and the passengers who were stranded last time; while for formula (8), when train k leaves platform s, the number of passengers in the car is the difference between the number of passengers in the car when it left the station last time plus the number of people who got on and off the train; then, formula (9) expresses the number of passengers who got off the train when train k arrives at station s; the number of passengers who got on the train in formula (10) is the minimum value of the remaining capacity of train k and the passenger demand for boarding at station s; and formula (11) calculates the number of people stranded at the platform when train k leaves s.

[0099] Further energy analysis of the train:

[0100] First, based on the dynamic analysis of the train, we can obtain the formulas for the traction and braking forces on the train under different working conditions:

[0101]

[0102] Where, is the maximum traction force; is the maximum braking force; F m,k (t) is the traction force of train k at time t; B m,k (t) is the braking force of train k at time t.

[0103] Part of the energy involved in the train is regenerative braking energy. As mentioned above, regenerative braking energy can be transferred within the same power supply range for both uplink and downlink. We can derive the following formula:

[0104]

[0105] Where, When the station the vehicle passes by belongs to the power supply section q, otherwise,

[0106] λ is the energy utilization coefficient of regenerative braking energy.

[0107] Formula (14) shows the traction energy consumption of power supply section q, while formula (15) is the regenerative braking energy of this power supply section q. Through the above formulas, we can obtain the formula for the net energy consumed by power supply section q:

[0108]

[0109] In this embodiment, the subway power supply system ensures the main energy source for daily subway operations, such as Figure 1 As shown in the figure, the main substation is responsible for the interface between the power grid and the subway power supply system, reducing the 110kV incoming line high voltage from the city power grid to 35kV and 10kV; the traction substation is responsible for further reducing the voltage, and at the same time, through the rectifier, it converts the input AC power into DC power, and finally obtains the DC1500V traction DC voltage; the traction network directly contacts the train and is responsible for transmitting electrical energy directly to the train; and the contact network, feeder lines, rails and return lines together constitute the traction network.

[0110] Example 2: The optimal power flow of the hybrid model of subway trains is a network optimization model that comprehensively considers the subway system;

[0111] In this embodiment, the objective function in the Metro-based OPF optimization problem is a nonlinear function, and its solution needs to satisfy both the minimum and maximum limits (e.g. Figure 1 shown):

[0112] minM(x,u)(18)

[0113] Subject to:g(x,u)=0 (19)

[0114] h(x,u)≤0 (20)

[0115] Among them, u is the independent variable, that is, the decision variable, including the voltage V of the generator G , in addition to the balanced node voltage The active power output P of the generator other than G, transformer voltage divider ratio Tab and reactive compensation capacity Q c and the active power consumption P of the load nodes controlled by the subway system load Therefore, we can get the formula for u:

[0116]

[0117] The active power consumption of the load node of the IEEE 30 node system is determined by the subway power consumption, and the maximum reactive power compensation is provided by the rectifier, so it is determined by the maximum reactive power of the rectifier. The specific formulas for active power consumption and maximum reactive power compensation are as follows:

[0118]

[0119] The x in formula (18)-formula (20) is the state variable, which is determined by the independent variables, including the active output of the balancing node The voltage V of all load nodes L , the reactive power output of the generator Q G , the load S of the transmission line l , so the formula for x is

[0120]

[0121] In the above formula, N1 is the number of generators, N2 and N3 are the corresponding numbers of transformers and reactive compensators, N4 and N5 are the number of load nodes and the number of transmission lines; at the same time, M is the objective function, g is the equality constraint, and h is the inequality constraint.

[0122] like Figure 9 As shown in the figure, the numbers 1-30 represent the 30 nodes of the node network. The red cart represents the corresponding power supply interval. In the same power supply interval, multiple trains may run, and the compensation of regenerative braking energy only occurs in the same power supply interval. The yellow symbol represents the capacitor, that is, the subway operation system compensates for the reactive power of the entire node through the rectifier. The red cart is connected to the active power consumption of the power system node, and the yellow capacitor is connected to the reactive power compensation of the node.

[0123] In this embodiment, the fitness function, the first objective of the present invention, and the specific formula for minimum line loss can be expressed as:

[0124]

[0125] Among them, V i and V j Represent the voltages of nodes i and j respectively, and G k represents the conductance of the wire between these two nodes, cosθk is the phase angle of the voltage; by traversing all nodes, we can get the sum of the line losses of the entire node network;

[0126] At the same time, the quality of the bus voltage is also an important indicator for evaluating the node network. To prevent the occurrence of uneven node network distribution, we consider the second objective function, which is to minimize the offset of the load node voltage. Therefore, the expression of the objective function is:

[0127]

[0128] Where V r ef is the reference voltage, and N L is the number of load nodes in the node network.

[0129] Furthermore, the constraints include:

[0130] 1. Equality constraints: Based on the established model, we can obtain the following constraints:

[0131]

[0132] Among them, B k is the susceptance between nodes i and j; P i n,Q i n is the active power and reactive power input at one end of the wire, P o ut, Q o ut is the active and reactive power output from the other end, Q c is the reactive compensation capacity; the above constraint equation is essentially a power flow equation, which describes the energy conservation principle of the node network foundation;

[0133]

[0134] The above two formulas specify the arrival and departure times of train k at platform s. and These two variables can be decision variables and h k Determined.

[0135] 2. Inequality constraints: First, we can obtain the inequality constraints on the grid side in the metro-grid hybrid model, including the following formula:

[0136]

[0137] Formulas (31)-(33) are constraints on the generator node, requiring that the voltage, active power and reactive power output of the generator are within the limit range; while formula (34) is the conditional restriction of the transformer divider ratio, and formula (35) is the limit range of the reactive power compensator.

[0138] In addition, we need to consider the inequality constraints of the subway:

[0139] h min ≤h k ≤h max , (37)

[0140]

[0141] Formula (37) is the constraint on the headway time, formulas (38) and (39) are the constraints on the running time and the suspension service time respectively, and formula (40) is the constraint on the train capacity; formula (41) is the constraint on the arrival and departure times of all trains, requiring that these times should be within the time set range of the train.

[0142] Furthermore, regarding the processing of constraints, since there are many restrictions on parameter variables in the metro-grid model, including restrictions on preventing overtaking from the traffic side and restrictions on node voltages in the grid nodes, we use the penalty function method to modify the objective function;

[0143]

[0144] Among them, ψ v ,ψ d are penalty factors, and V penalty and D penalty for

[0145]

[0146] Example 3: The SWO algorithm begins with initialization. During initialization, the algorithm uses a random function to generate m particles, each with dimension dim. Therefore, the particle swarm algorithm initially generates m*dim initial values. Each particle has two characteristics: position and velocity. The position of a particle can be expressed as follows:

[0147]

[0148] Where h1,...h k is the departure distance between train k and the previous train k-1 arriving at the first station, is the service time of train k at station s, and is the running time of train k from station s to station s+1; therefore, a particle has a total of 2*k*s+n parameter variables, where n is the number of input parameter variables of the power grid;

[0149] During this stage, the queen bee will have two situations. The first situation is that the queen bee will look for suitable spiders in the subset space as food for the next generation. The second situation is that the queen bee cannot find the fallen spider, so they will search around the drop site.

[0150] 1. First case:

[0151]

[0152] in, and Two randomly selected particles determine the search direction, rn is a random number that satisfies the normal distribution, r1 is a random number between 0 and 1, and t is the current iteration number;

[0153] 2. The second situation:

[0154]

[0155] in is a randomly selected particle, L and H are the upper and lower limits of the particle parameters, and 1 is a random number between 1 and -2.

[0156] To decide which scenario the mother bee adopts, the following formula is used, where r3 and r4 are random numbers between 0 and 1:

[0157]

[0158] Furthermore, after the queen bee finds the spider, she will start chasing it; the spider, as the prey, will choose to escape from the queen bee, and the distance between the spider and the queen bee will gradually increase;

[0159] 1.Following Stage:

[0160]

[0161] Among them, r5 and r6 are random numbers between 0 and 1, t and t m ax is the current and maximum number of iterations, is a random particle.

[0162] 2.escaping Stage:

[0163]

[0164] Where vc is a vector of random numbers that satisfy the normal distribution, and its value range is from -k to k, and the formula for k is

[0165] k=1-1*t / t max (51)

[0166] To determine which stage you are in, use the following formula:

[0167]

[0168] Then, after catching the spider, the queen bee will pull the prey into the nest. When building a nest, the spider will look for the most suitable location (corresponding to the first formula below), and the queen bee will also avoid building a nest in the same place (formula);

[0169]

[0170] Where γ is a number obtained from levy flight, a, b, and c are randomly selected particles, and U is a binary vector used to prevent nesting behavior from occurring in the same place.

[0171]

[0172] To make a choice between Eq.53 and Eq.54, use the following formula:

[0173]

[0174] Furthermore, during the mating phase, the female bees and male bees will crossbreed to ensure the diversity of the particles;

[0175]

[0176] in is the position of the drone, which is determined by the following formula:

[0177]

[0178] Where β1 and β2 are two random numbers that satisfy the normal distribution, e is a natural constant, and v1 and v2 satisfy:

[0179]

[0180] Among them, X a , X b , X c are three randomly selected sums of X i Different particles, Y a , Y b , Y c is the value of the objective function corresponding to each particle;

[0181] As the number of algorithm iterations increases, the population size will gradually decrease to ensure that the speed of the algorithm is not affected by the huge population size;

[0182] N=N min +(NN min )*k (61)

[0183] Among them, N m in is the minimum population size, and k is the same as k in Formula 51.

[0184] The specific algorithm process can be referred to ( Figure 2 and Figure 3 ); In the Find best Qmetro step, the reactive power injected by the subway is variable. We will find the optimal reactive power corresponding to the particle to minimize the objective function while obtaining the maximum reactive power compensation capacity.

[0185] Example 4: In this section, we simulate and analyze the experimental model to verify the principles outlined in Example 3. We simulate the Beijing Subway Yizhuang Line and the IEEE-30bus system to analyze the impact of the subway system on the optimal power flow of the entire power grid. Finally, we use the proposed constrained PSO algorithm to obtain and verify the feasibility and effectiveness of the metro-grid system model.

[0186] For example: Beijing Yizhuang Line description ( Figure 4 )

[0187] The Yizhuang Line is a two-way subway line consisting of 13 stations and 12 operating sections. Figure 3 As shown; this line uses traditional DKZ32 carriages. For specific parameters, please refer to Table 2:

[0188] Table 2: Parameters and their symbols and values.

[0189]

[0190]

[0191] The Yizhuang Line is 23.3 kilometers long. Since trains run in both directions, the subway operates in both directions. The upward direction runs from Songjiazhuang to Ciqu, and the downward direction runs from Ciqu to Songjiazhuang. The entire line is divided into six power supply sections. Trains running in both directions within the same power supply section share a substation. Line data, including the length between stations, speed limits within each section, and operating time limits, can be found in Table 3:

[0192] Table 3: Line data table

[0193]

[0194]

[0195] Table 4: Passenger flow statistics at stations

[0196]

[0197] The present invention uses data from the morning peak period of 7:30-9:30 on weekdays to count the arrival rate and alighting rate of passengers at various stations. Specific station and passenger flow data are shown in Table 4.

[0198] Example 5: The present invention uses the IEEE 30bus system for simulation; the system includes 6 generators, 41 branches, 4 load tap-changing transformers and 9 shunt capacitors. The metro-based IEEE 30bus system has a total of 37 control variables, including 25 directly controlled variables, first of which are the generator voltages at nodes 1, 2, 5, 8, 11 and 13; then the transformer ratios on the branches, between nodes 6-9, 6-10, 4-12 and 28-27; and reactive power injection from Schottky capacitors, which are connected to the grid at nodes 10, 12, 15, 17, 20, 21, 23 and 24; in addition, there are 12 variables controlled by the metro system, namely the active power consumption and reactive power compensation at nodes 3, 4, 14, 16, 18 and 26.

[0199] For the first objective function, minimizing node line loss, the simulation results can be found in Table 5. In addition to the SWO algorithm mentioned above, we also list several other heuristic algorithms (PSO and GWO) to obtain the optimal objective function values. The corresponding decision parameter solutions for these algorithms are listed in Table 6. It is worth noting that the control variables P14-Q26 at the end of Table 6 are determined by the subway schedule variables.

[0200] Figure 5 The following figure shows the subway timetables corresponding to the initial solution and the optimal solution obtained by the SWO algorithm. Comparing the two timetables, we can see that the initial timetable on the left has a uniform train distribution and relatively fixed train departure and service times. In contrast, in the right figure, to maximize the use of regenerative braking energy and meet reactive power compensation requirements, train departures tend to overlap the "braking-traction" period.

[0201] Figure 6A graph comparing the convergence speeds of different algorithms is drawn. From the graph, we can see that although the PSO algorithm can converge quickly, it can easily fall into a local optimal solution. On the other hand, the SWO algorithm can find better solutions by searching a wider range of the solution set. At the same time, we also observe that the GWO algorithm does not provide a good solution to the subway-based power flow system problem proposed in this invention and lacks the feasibility of finding an optimal solution. From the above data, we can find that the SWO algorithm is superior in handling optimization problems with large-scale parameters and multiple constraints.

[0202] Table 5: Objective Values ​​for Power Loss Minimization in the 30-bus system

[0203]

[0204] In this section, we consider the voltage deviation at the load node. From Table 7, we can see the objective function values ​​with the goal of minimizing the voltage deviation. Similarly, the optimal decision parameters of various algorithms can be found in Table 6, which is shown below:

[0205] Table 6: Control variables of the IEEE 30-bus system for powerlossminimization

[0206]

[0207]

[0208]

[0209] The subway timetable corresponding to the initially generated solution and the optimal solution generated using SWO;

[0210] Figure 8 A graph comparing the convergence speeds of different algorithms is drawn. Through the above data, we can find that when processing the second objective function, although the SWO algorithm also converges very slowly, it can still find a better solution than PSO in about 180 iterations. From the essence of the algorithm, the conclusion is also easier to understand. The goal of the PSO algorithm is to converge and find the local optimal solution in the fastest time, while the SWO algorithm is more concerned with breaking through the local optimal solution to find a better feasible solution by adding more randomness. In general, the SWO algorithm still has superiority in processing the objective function of Voltage Deviation.

[0211] Table 7: Objective Values ​​for Voltage Deviation Minimization in the 30-bussystem

[0212]

[0213] Table 8: Control variables of the IEEE 30-bus system for VoltageDeviationminimization.

[0214]

[0215]

[0216]

[0217] This paper adopts a new heuristic algorithm, the Spider Bee algorithm, to solve the opf problem in the power grid field. This paper applies the introduced optimization method to the most commonly used test network IEEE30bus system, and verifies the adaptability of the introduced optimization method under the conditions of minimum actual power loss and voltage level. In addition, this paper also compares the SWO algorithm with other traditional heuristic algorithms, demonstrating the superior performance of the SWO algorithm in dealing with complex multi-parameter constraint problems. At the same time, the existing research of this paper idealizes the combination of subway model and power grid. In future work, we can adopt more detailed models to deal with subway-based optimal power flow optimization.

Claims

1. A subway energy-saving dispatching operation method based on timetable optimization, characterized by: The steps include: S10: Build a subway timetable, simulate the subway operation status, build a subway operation system for optimizing the subway timetable, and build a model of the subway operation system; Among them, S10 builds the subway operation system model including: S11: The first step is to build the subway platform and line, and build a subway platform model corresponding to the operating platform and operating distance; S12: Construction of subway speed curves. Since subway operation is essentially optimized based on time and distance, a corresponding speed curve is generated based on the given running time and distance. Through force analysis of the train, the corresponding speed curve that meets the restrictions is automatically generated under the maximum acceleration and maximum deceleration limits. S13: Analysis of subway passenger flow. In the modeling of the subway operation system, the number of passengers on the subway train is modeled based on the ascending and descending rates, as well as the number of people in the subway car. S14: Implement energy analysis of the subway operation system. This analysis is based on speed curves and corresponding platform information. Considering regenerative braking energy, this analysis analyzes the active power consumption of the train's corresponding power supply platforms. The S14 train energy analysis includes: Based on the dynamic analysis of the train, the formulas for the traction and braking forces on the train under different working conditions are obtained: in, For maximum traction, is the maximum braking force, F m,k (t) is the traction force of train k at time t, B m,k (t) is the braking force of train k at time t, ρ is the rotation mass coefficient, M k,X is the total mass of train k traveling in interval x, α is the maximum acceleration of the train, β is the maximum deceleration, r m,k (t) is the resistance of train k at time t; Part of the energy involved in the train is regenerative braking energy, which is transmitted within the same power supply interval on the uplink and downlink directions, resulting in the following formula: Traction energy consumption of power supply zone q; Regenerative braking energy in power supply interval q; in, is the traction energy consumption of power supply partition q, K is the total number of trains, k is the kth train, S is the total number of platforms, s is the sth platform, V m,k (t) is the train speed, is the regenerative braking energy in the power supply interval q; in, When the station the vehicle passes by belongs to the power supply section q, otherwise, λ is the energy utilization coefficient of regenerative braking energy, and the formula for obtaining the net energy consumed in the power supply interval q is: in, is the net energy consumed in the power supply interval q at time t, is the net energy consumed in the power supply interval q, t0 is a certain initial moment, Mδ is M small time intervals δ, and t0+Mδ is the index of the time from t0 to M hours; S20: Build the power system node network, model the power system node network, and construct the node network through the IEEE30 node information of MatPower; S30: Integrate the node network and the subway system to form a subway-node network model; The S30 fusion node network and subway system include: S31: The node network is connected to the subway. The voltage is boosted from the power generation end to the grid, stepped down by the main substation, and converted into direct current by the rectifier before being transmitted to the subway to supply power. S32: Build the entire subway-node network. The red cart represents the corresponding power supply section. Multiple trains operate in the same power supply section, and regenerative braking energy compensation only occurs within the same power supply section. The yellow symbol represents a capacitor. The subway operation system uses a rectifier to compensate for the reactive power of the entire node. The red cart is connected to the active power consumption of the power system node, while the yellow capacitor is connected to the reactive power compensation of the node. S40: The subway-node network model performs power flow analysis and optimizes the optimal power flow target through a heuristic algorithm. In S40, the control variables of the subway system's operating schedule include the departure time and service time of each train at each platform, the departure time interval of each vehicle, the control variables of the node network, the active power output and voltage of the generator node, as well as the transformer ratio and reactive power compensation of the load node. The comprehensive control variables are optimized through the heuristic algorithm - the spider bee algorithm.

2. The method for energy-saving subway dispatching and operation based on timetable optimization according to claim 1, characterized in that: The stress analysis of the S12 train includes: S121: The maximum acceleration of the train is α. When the train exceeds the maximum acceleration, it runs according to the maximum acceleration. The traction formula of the train is: F a =min{F max ,F(α)}; Among them, F a is the traction force obtained by the train, F max is the maximum traction force given by the motor, α is the maximum acceleration, and F(α) is the traction force under the condition of maximum acceleration; S122: The train's braking is mainly achieved by regenerative braking. The motor's function is reversed to become a generator. When the train needs to slow down, the motor driving the wheelset reverses its operating mode. If a train and the train generating electricity are in the same power supply station, the regenerative braking energy is sent back to the power supply system and supplies power to other trains in the power supply station. When the maximum deceleration is exceeded, the train operates at the maximum deceleration. The braking force formula of the train is B b =min{B max ,B(β)}; Among them, B b is the braking force obtained by the train, B max is the maximum braking force that the train can withstand, β is the maximum deceleration, and B(β) is the braking force under the maximum deceleration condition; S123: During the train operation, the train will be subject to external forces that hinder the train's current movement. The Davis formula is used to empirically calculate the train resistance: r = a + bv + cv 2 ; Where r is the total resistance experienced by the train, v is the train's running speed, and a, b, and c are the resistance coefficients of the Davis formula, which are determined by the train.

3. The method for energy-saving subway dispatching and operation based on timetable optimization according to claim 2, characterized in that: The train operation process is divided into three stages: traction, inertia and braking; Traction condition: When the train is in traction condition, the train absorbs energy from the contact network to accelerate the train forward; the traction condition occurs when the train starts to move, and the train is subjected to traction and resistance at the same time. The total external force on the train is C = F a -r; Where C is the net external force on the train, F a is the traction obtained by the train, r is the resistance of the train; Coasting condition: When the train is in coasting condition, the train's motor is not working. The train neither absorbs energy nor generates regenerative braking energy. At this time, the train is only affected by resistance, and the train speed will slowly decrease. In this case, the net external force acting on the train is C = -r. Braking condition: When the train is in braking condition, the train will generate braking force through regenerative braking energy. The speed of the train in this stage will drop rapidly and decrease to 0. The braking condition generally occurs in the second half of the train running curve, which is generated when the train is about to arrive at the station. C = -B b -r.

4. The method for energy-saving subway dispatching and operation based on timetable optimization according to claim 3 is characterized in that: S13: Analysis of subway passenger flow includes: S131: When train k arrives at station s, the number of passengers waiting to board the train on the platform is equal to the sum of the passengers who entered platform s to wait for train k within the headway between train k and the previous train and the passengers who were stranded at the previous platform. The formula is: in, is the number of passengers waiting for train k at platform s from the time train k-1 to train k leaves station s, η s is the passenger arrival rate at station s, is the time when train k leaves station s, is the time when train k-1 leaves station s, is the number of people stranded on platform s when train k-1 leaves station s; S132: When train k leaves platform s, the number of passengers in the train is the difference between the number of passengers in the train when it last left the station plus the number of people who got on and off the train. The formula is: in, is the number of passengers in the carriage when train k leaves station s, is the number of passengers in the carriage when train k leaves station s-1, is the number of passengers boarding the train k when it arrives at station s, is the number of passengers who get off the train k when it arrives at station s; S133: When train k arrives at station s, the number of passengers getting off is: Among them, μ s is the passenger alighting rate at station s; S134: The number of passengers boarding is the minimum of the remaining capacity of train k and the passenger demand at station s, and the formula is: Among them, P cap The carriage's passenger capacity is limited. is the number of passengers in the carriage when train k-1 leaves station s; S135: When train k leaves s, the number of people stranded at the platform is: in, is the number of people stranded at the platform when train k leaves s.

5. A subway energy-saving dispatching and operation system based on timetable optimization, the system being used in the subway energy-saving dispatching and operation method based on timetable optimization according to any one of claims 1 to 4, characterized in that: The system consists of 6 generators, 41 branches, 4 load-tap-changing transformers and 9 shunt capacitors; there are 37 control variables in the system, including 25 directly controlled variables; the adaptability of the introduced optimization method is verified under the conditions of minimum actual power loss and voltage level.

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