CN110188401B - Tramcar operation energy consumption optimization method based on improved PSO - Google Patents
Tramcar operation energy consumption optimization method based on improved PSO Download PDFInfo
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Abstract
The invention discloses a tramcar operation energy consumption optimization method based on improved PSO. The method comprises the following steps: establishing a tramcar operation energy consumption model: in an operation interval, the operation process of the tramcar is divided into: under the full-force traction working condition, starting the tramcar from the speed of 0, starting the tramcar with the maximum traction force, and reaching the maximum speed of the interval; under the constant-speed cruising working condition, the tramcar moves at a constant speed at the maximum interval speed, and the traction force is equal to the comprehensive resistance; under the condition of the coasting, the tramcar performs coasting, and the traction force is 0; under the full-force braking working condition, the tramcar brakes with the maximum braking force and feeds back and stores the braking energy; analyzing multiple constraint conditions of the tramcar, and simplifying the optimization problem of the tramcar operation energy consumption model; and adding a selective learning mechanism on the classical PSO algorithm, solving the operating condition turning points in the model, and calculating the energy consumption of each running interval of the tramcar. The invention has the advantages of accurate calculation, high convergence rate, high processing efficiency and strong practicability.
Description
Technical Field
The invention belongs to the technical field of tramcar energy optimization, and particularly relates to a tramcar operation energy consumption optimization method based on improved PSO.
Background
The tramcar is the first choice for developing urban rail transportation in medium and small cities due to the advantages of large transportation capacity, small investment, environmental protection, long service life and the like. In the face of the current situation of global energy shortage, how to effectively reduce the running energy consumption of the tramcar becomes the central importance of energy optimization of the tramcar.
The tramcar has four operating conditions including traction, cruising, inertia and braking, and in the braking link, a large amount of braking energy is generated, and the recovery of the braking energy is beneficial to reducing the operating energy consumption. The tramcar operation strategy is divided into a maximum capacity operation strategy and a timing operation strategy, wherein the maximum capacity operation strategy has no inertia link, the operation time is short, and the energy consumption is large; the latter has smaller energy consumption and is a comparatively energy-saving operation strategy. At present, the tramcar running energy consumption model established by adopting an energy-saving running strategy only considers indexes such as safety, accurate parking, punctuality and comfort level, and does not consider the influence of the total quality of the tramcar under different passenger load conditions on the running energy consumption, so that the running energy consumption model is inaccurate. In addition, aiming at the energy consumption optimization problem of energy-saving operation of the tramcar, namely the energy consumption optimization problem under the multi-constraint condition, the classic PSO algorithm is mostly adopted for solving, the algorithm is strong in searching capability and high in convergence speed, but the problem of easy falling into local optimum exists, and the operation energy consumption calculation is inaccurate. In conclusion, the energy consumption model of the conventional tramcar energy optimization technology is inaccurate, the running energy consumption cannot be accurately calculated, and the optimization problem of the running energy consumption of the tramcar is solved.
Disclosure of Invention
The invention aims to provide the tramcar running energy consumption optimization method based on the improved PSO, which is accurate in calculation, high in convergence speed and capable of effectively avoiding local optimization.
The technical solution for realizing the purpose of the invention is as follows: a tramcar operation energy consumption optimization method based on improved PSO comprises the following steps:
and 4, calculating the energy consumption of each running interval of the tramcar by using the working condition turning points calculated in the step 3.
Further, the step 1 of establishing a tramcar operation energy consumption model based on the tramcar operation condition specifically includes:
in an operation interval, the tramcar operation process is divided into four working conditions:
working condition I: under the condition of full-force traction, the tramcar starts from the speed of 0 and starts with the maximum traction force to reach the maximum speed V of the interval max ；
Working condition II: at constant cruising speed, the tramcar is at the maximum speed V max The uniform motion is carried out, and the traction force is equal to the comprehensive resistance;
working condition III: under the condition of coasting, the tramcar performs coasting, and the traction force is 0;
working condition IV: under the full-force braking working condition, the tramcar brakes with the maximum braking force, and the braking energy is fed back and stored;
according to tram operating characteristic, punctual, safe, comfortable, accurate parking index, add passenger load index, establish tram operation energy consumption model, promptly:
in the formula: f (x) is an energy consumption objective function; f t (v)、F tmax (v)、F m (v)、F mmax (v) Respectively the traction force of the tramcar at the running speed v, the maximum value of the traction force of the tramcar, the brake force of the tramcar and the maximum value of the brake force of the tramcar; x is the current operating kilometer post; v, V max Respectively representing the instantaneous running speed of the tramcar and the maximum running speed of the whole interval; rho is a braking energy feedback coefficient; m is the total mass of the tramcar under different passenger loads; g 1 (x)、g 2 (x)、g 3 (x)、g 4 (x)、g 5 (x) Respectively representing on-time, accurate parking, safety, comfort and passenger load index constraint conditions; s 0 、S p 、D 1 、D 2 、D 3 Respectively as interval starting point kilometer post, end point kilometer post, turning point kilometer posts from working condition I to working condition II, turning point kilometer posts from working condition II to working condition III, and working condition III to working condition IIIMile of the turning point of condition IV; Δ t and Δ s are a time error and a distance error, respectively.
Further, analyzing the multiple constraint conditions of the tramcar in the step 2, and simplifying the optimization problem of the tramcar operation energy consumption model, specifically as follows:
the tramcar runs on
Within the interval, operating time Δ T, there are:
wherein F is the resultant force of the tramcar, F t 、F m 、F z Respectively traction force, braking force and resistance, wherein the resistance consists of mechanical friction resistance, ramp additional resistance, curve additional resistance and air resistance, a is running acceleration, M is the total mass of the tramcar under different passenger loads, and x 1 、x 2 Respectively a starting highway mark, an end highway mark, v of the operation subinterval 1 、v 2 Respectively the speed at the starting highway sign and the speed at the destination kilometer sign of the operation subinterval, S 0 、 S p The starting kilometer post and the end kilometer post of the whole operation interval are provided;
in a working condition I interval, the tramcar starts and accelerates to a maximum speed limit value by using the maximum traction force, and the traction force characteristic curve is as follows:
in the formula, F t (v) Traction of trams at instantaneous speed v, F max Constant torque zone tramcar traction, v t1 、 V max Respectively the train running speed at the starting end of the constant power area and the maximum running speed in the whole running interval;
the optimization problem of the running energy consumption of the tramcar is converted into four-stage optimization problem, namely three-stage turning pointsThe optimization problem of (2): turning point D of working condition I to working condition II 1 Turning point D of working condition II to working condition III 2 Turning point D of working conditions III to IV 3 ；
Determination of F from the traction force characteristic diagram max 、v t1 And V max Determining F from the braking force characteristic curve m Further determining resultant force F, acceleration a, running distance and running time, and further determining turning point D of working conditions I-II 1 (ii) a Similarly, for the turning point D of the working condition II to the working condition III 2 Can determine V max Calculating the acceleration of the tramcar in the working condition III interval and the working condition IV interval to obtain the turning point D of the working condition 3 Velocity V of 3 And the interval maximum running speed V max By determining the turning point D of the working conditions III to IV 3 Thereby reversely pushing the turning point D of the working condition II to the working condition III 2 Converting the optimization problem of the running energy consumption of the tramcar in a fixed interval into a working condition turning point D 3 Velocity V 3 To the optimization problem of (2).
Further, the improved PSO algorithm, that is, a selective learning mechanism is added on the basis of the classical PSO algorithm to solve the operating condition turning point in the energy consumption model of the tramcar operation, which is specifically as follows:
step 3.1, simulation data input: line data, train data and algorithm related parameters;
step 3.2, population initialization: setting the size N of the population, and randomly giving the value of a single particle, wherein the given value of the single particle does not exceed the speed limit value in the simulation interval;
initializing a population of m particles, each particle having an n-dimensional position attribute x i ＝(x i,1 (t),x i,2 (t),...x i,n (t)) and n-dimensional velocity attribute v i ＝(v i,1 (t),v i,2 (t),...v i,n (t))；
Step 3.3, solving an energy consumption index adaptive value function, and updating the particle speed and position: calculating the energy consumption objective function of tramcar operation according to the value corresponding to each particle in the population to obtain the energy consumption index adaptive value corresponding to each particle; adopting a selective learning mechanism, comparing the particles in the population in pairs in a selected area, directly entering the next generation of population by the winning particles, and entering the next generation of population after self-updating by the speed and the position of the failed particles by learning the winning particles;
for setting the selection area, in order to prevent the particles from being prematurely aggregated in a single range, the particles are firstly put into the selection area from large to small according to the fitness, the sum of the position differences between the particles to be added and the added particles is calculated, a threshold value is set, and when the sum of the position differences exceeds the threshold value, the particles are not put into the selection area; when the sum of the position differences is less than the threshold value, placing the particle in the selected area;
setting the threshold value to R, x i To be added to the particles, x j Adding particles, wherein j belongs to 1, and b are the number of the added particles;
if the position difference sum of the two satisfies:
then x is i Placing the particles into a selected area, otherwise, discarding the particles;
the threshold value R is selected, and as the iteration number is increased, the following conditions are met:
in the formula, R min 、R max Minimum and maximum thresholds, G, G respectively max Respectively representing the current iteration times and the maximum iteration times;
the position and speed of the failed particle after selective learning are updated as follows:
in the formula (I), the compound is shown in the specification,
selecting the position and the speed of the failed particles after learning for the G iteration and the k;
selecting the position and the speed of the failed particles after learning for the G +1 th iteration and the kth iteration;
selecting the positions and speeds of the winning particles after learning for the G iteration and the k; g is the current iteration number;
is a random number in the interval (0,1),
selecting a learning time position average value for all particles in the group at the G iteration and the k selection; omega is an inertia factor;
step 3.4, judging the finishing conditions: if the current iteration times reach the maximum iteration times, the ending condition is met, and the iteration loop is exited; otherwise, step 3.3 is carried out, the adaptive value of the energy consumption index is solved, and the selective learning and updating are continuously carried out on the particle speed and the particle position until the end condition is met;
the end conditions are as follows:
G≥G max
in the formula, G, G max The current iteration times and the maximum iteration times are respectively.
Further, the step 4 of calculating the energy consumption of each running interval of the tramcar by using the operating condition turning point calculated in the step 3 specifically includes:
and 3, solving the optimal solution and the relevant operation curve through the step 3, extracting the optimal solution, substituting the optimal solution into the energy-saving optimization model of the tramcar for calculation, and finishing the calculation of the interval operation energy consumption.
Compared with the prior art, the invention has the following remarkable advantages: (1) passenger load indexes are added into the tramcar operation energy consumption model, so that the accuracy of the energy consumption model is improved; (2) based on the improved PSO algorithm, the convergence speed of the algorithm is ensured, and the problem of falling into local optimum is effectively avoided; (3) the multi-target problem of the operation energy consumption is converted into the single-target problem, and the complexity of the problem is reduced.
Drawings
Fig. 1 is a schematic flow chart of the tramcar operation energy consumption optimization method based on the improved PSO.
Fig. 2 is a schematic view of the operation condition of the tramcar in the invention.
Fig. 3 is a schematic diagram of a tramcar operation line in the embodiment of the invention.
Fig. 4 is a schematic drawing of the traction characteristics of the tramcar in the embodiment of the invention.
Fig. 5 is a schematic diagram of the braking force characteristic of the tramcar in the embodiment of the invention.
Fig. 6 is a schematic diagram of an optimal adaptive value and a change in traction energy consumption in a certain interval in an embodiment of the present invention, where (a) is a schematic diagram of a change in the optimal adaptive value, and (b) is a schematic diagram of a change in traction energy consumption.
Fig. 7 is a schematic diagram of an energy consumption-distance curve and a speed-distance curve in a certain interval in an embodiment of the present invention, where (a) is a schematic diagram of an energy consumption-distance curve, and (b) is a schematic diagram of a speed-distance curve.
Fig. 8 is a schematic diagram of simulated energy consumption and actual operation energy consumption in the embodiment of the present invention.
Detailed Description
A tramcar operation energy consumption optimization method based on improved PSO comprises the following steps:
and 4, calculating the energy consumption of each running interval of the tramcar by using the working condition turning points calculated in the step 3.
Further, the step 1 of establishing a tramcar operation energy consumption model based on the tramcar operation condition specifically includes:
in an operation interval, the tramcar operation process is divided into four working conditions:
working condition I: under the condition of full-force traction, the tramcar starts from the speed of 0 and starts with the maximum traction force to reach the maximum speed V of the interval max ；
Working condition II: at constant cruising speed, the tramcar is at the maximum speed V max The constant-speed movement is carried out, and the traction force is equal to the comprehensive resistance;
working condition III: under the condition of the coasting, the tramcar performs coasting, and the traction force is 0;
working condition IV: under the full-force braking working condition, the tramcar brakes with the maximum braking force and feeds back and stores the braking energy;
according to tram operating characteristic, punctual, safe, comfortable, accurate parking index, add passenger load index, establish tram operation energy consumption model, promptly:
in the formula: (x) is an energy consumption objective function; f t (v)、F tmax (v)、F m (v)、F mmax (v) Respectively the traction force of the tramcar at the running speed v, the maximum value of the traction force of the tramcar, the brake force of the tramcar and the maximum value of the brake force of the tramcar; x is whenRunning kilometer posts in front; v, V max Respectively the instantaneous running speed of the tramcar and the maximum running speed of the whole interval; rho is a braking energy feedback coefficient; m is the total mass of the tramcar under different passenger loads; g 1 (x)、g 2 (x)、g 3 (x)、g 4 (x)、g 5 (x) Respectively representing punctual, accurate parking, safety, comfort and passenger load index constraint conditions; s 0 、S p 、D 1 、D 2 、D 3 Respectively as interval starting point kilometer post, end point kilometer post, turning point kilometer post of working condition I-working condition II, turning point kilometer post of working condition II-working condition III, and turning point kilometer post of working condition III-working condition IV; Δ t and Δ s are a time error and a distance error, respectively.
Further, analyzing the multiple constraint conditions of the tramcar in the step 2, and simplifying the optimization problem of the tramcar operation energy consumption model, specifically as follows:
the tramcar runs on
Within the interval, the operating time Δ T, there are:
wherein F is the resultant force of the tramcar, F t 、F m 、F z Respectively traction force, braking force and resistance, wherein the resistance consists of mechanical friction resistance, ramp additional resistance, curve additional resistance and air resistance, a is running acceleration, M is the total mass of the tramcar under different passenger loads, and x 1 、x 2 Respectively a starting highway mark, an end highway mark, v of the operation subinterval 1 、v 2 Respectively the speed at the starting highway sign and the speed at the end kilometer post of the operation subinterval, S 0 、 S p The starting kilometer post and the end kilometer post of the whole operation interval are provided;
in a working condition I interval, the tramcar starts and accelerates to a maximum speed limit value by using the maximum traction force, and the traction force characteristic curve is as follows:
in the formula, F t (v) Traction of trams at instantaneous speed v, F max Constant torque zone tramcar traction, v t1 、 V max Respectively the train running speed at the starting end of the constant power area and the maximum running speed in the whole running interval;
the optimization problem of the running energy consumption of the tramcar is converted into four-stage optimization problem, namely the optimization problem of turning points of three stages: turning point D between working conditions I and II 1 Turning point D of working condition II to working condition III 2 Turning point D of working conditions III to IV 3 ；
Determining F from the traction force characteristic diagram max 、v t1 And V max Determining F from the braking force characteristic curve m Further determining resultant force F, acceleration a, running distance and running time, and further determining turning point D of working conditions I-II 1 (ii) a Similarly, for the turning point D of the working condition II to the working condition III 2 Can determine V max Calculating the acceleration of the tramcar in the working condition III interval and the working condition IV interval to obtain the turning point D of the working condition 3 Velocity V of 3 And the interval maximum running speed V max By determining the turning point D of the working conditions III to IV 3 Thereby reversely pushing the turning point D of the working condition II to the working condition III 2 Converting the optimization problem of the running energy consumption of the tramcar in a fixed interval into a working condition turning point D 3 Velocity V 3 To the optimization problem of (2).
Further, the improved PSO algorithm, that is, a selective learning mechanism is added on the basis of the classical PSO algorithm to solve the operating condition turning point in the energy consumption model of the tramcar operation, which is specifically as follows:
step 3.1, simulation data input: line data, train data and algorithm related parameters;
step 3.2, population initialization: setting the size N of the population, and randomly giving the value of a single particle, wherein the given value of the single particle does not exceed the speed limit value in the simulation interval;
initializing a population of m particles, each particle having an n-dimensional position attribute x i ＝(x i,1 (t),x i,2 (t),...x i,n (t)) and n-dimensional velocity attribute v i ＝(v i,1 (t),v i,2 (t),...v i,n (t))；
Step 3.3, solving an energy consumption index adaptive value function, and updating the particle speed and position: calculating the energy consumption objective function of tramcar operation according to the value corresponding to each particle in the population to obtain the energy consumption index adaptive value corresponding to each particle; adopting a selective learning mechanism, comparing the particles in the population in pairs in a selected area, directly entering the next generation of population by the winning particles, and entering the next generation of population after self-updating by the speed and the position of the failed particles by learning the winning particles;
for setting the selection area, in order to prevent the particles from being prematurely aggregated in a single range, the particles are firstly put into the selection area from large to small according to the fitness, the sum of the position differences between the particles to be added and the added particles is calculated, a threshold value is set, and when the sum of the position differences exceeds the threshold value, the particles are not put into the selection area; when the sum of the position differences is less than the threshold value, placing the particle in the selected area;
setting the threshold value to R, x i To be added to the particles, x j Adding particles, wherein j belongs to 1, and b are the number of the added particles;
if the position difference sum of the two satisfies:
then x is i Placing the particles into a selected area, otherwise, discarding the particles;
the threshold value R is selected, and as the iteration number is increased, the following conditions are satisfied:
in the formula, R min 、R max Minimum and maximum thresholds, G, G respectively max Respectively the current iteration times and the maximum iteration times;
the position and speed of the failed particle after selective learning are updated as follows:
in the formula (I), the compound is shown in the specification,
selecting the position and the speed of the failed particles after learning for the G iteration and the k iteration;
selecting the position and the speed of the failed particles after learning for the G +1 iteration and the kth time;
selecting the position and the speed of the winning particle after learning for the G iteration and the k; g is the current iteration number;
is a random number in the interval (0,1),
selecting a learning time position average value for all particles in the group at the G iteration and the k selection; omega is an inertia factor;
step 3.4, judging the finishing conditions: if the current iteration times reach the maximum iteration times, the end condition is met, and the iteration loop is exited; otherwise, step 3.3 is carried out, the adaptive value of the energy consumption index is solved, and the selective learning and updating are continuously carried out on the particle speed and the particle position until the end condition is met;
the end conditions are as follows:
G≥G max
in the formula, G, G max Respectively the current iteration times and the maximum iteration times.
Further, the step 4 of calculating the energy consumption of each running interval of the tramcar by using the operating condition turning point calculated in the step 3 specifically includes:
and 3, solving the optimal solution and the relevant operation curve through the step 3, extracting the optimal solution, substituting the optimal solution into the energy-saving optimization model of the tramcar for calculation, and finishing the calculation of the interval operation energy consumption.
The invention is described in further detail below with reference to the figures and the embodiments.
Example 1
With reference to fig. 1, the method for optimizing the running energy consumption of the tramcar based on the PSO of the invention comprises the following steps:
at S 0 ～S p In the operation interval, the energy-saving operation process of the tramcar is divided into four working conditions: the schematic operation conditions of the full-force traction (I), the constant-speed cruise (II), the coasting (III) and the full-force brake (IV) are shown in figure 2, wherein:
1) in the working condition I interval, the tramcar starts from the speed 0 and starts with the maximum traction force to reach the interval maximum speed V max ；
2) In the working condition II interval, the tramcar has the interval maximum speed V max The uniform motion is carried out, and the traction force is equal to the comprehensive resistance;
3) in the working condition III interval, the tramcar performs coasting, and the traction force is 0;
4) and in the working condition IV interval, the tramcar brakes with the maximum braking force, and feeds back and stores the braking energy.
The target function of the energy consumption of the tramcar is as follows:
in the formula: f t 、F m Respectively is tramcar traction force and tramcar braking force; s 0 、S p Respectively a starting point kilometer post and a terminal point kilometer post of the operation interval; rho is a braking energy feedback coefficient.
The conventional indexes related to the operation energy consumption comprise tramcar operation characteristics, accurate parking, punctuality, safety and comfort, and in addition, passenger load indexes are set, so that the change of the overall quality of the tramcar under the condition of uninterrupted passenger load is reflected, and then the operation energy consumption is influenced, and therefore the operation energy consumption model has more authenticity and practicability.
The punctual index related constraint conditions are as follows:
g 1 (x)＝T-T 0 ≤Δt
in the formula, T and T 0 Respectively setting time for the actual running time of the tramcar and a schedule, wherein delta t is a time error;
the related constraint conditions of the accurate parking index are as follows:
g2(x)＝|S-S p |≤Δs
in the formula, S and S p Respectively setting the distance error deltas to be 0.25m for the actual parking position and the specified parking position of the tramcar;
the related constraint conditions of the safety indexes are as follows:
in the formula, V and V max Respectively the actual running speed and the maximum allowable speed of the tramcar, when g 3 (x) When 0 is taken, the safety index is met;
the comfort index related constraint conditions are as follows:
g 4 (x)＝0
chinese medicine for treating rheumatismThe moderate index only considers whether auxiliary equipment such as an air conditioner, lighting and the like works normally, and the normal work is 0. In general, to satisfy passenger comfort, the acceleration should not exceed 1.8m/s during acceleration 2 The deceleration in the deceleration process should not exceed 1.5m/s 2 The maximum acceleration of the tramcar is 1.28m/s through the analysis of the motion equation of the tramcar 2 Maximum deceleration of m/s 2 And the limit value is not exceeded, so that the comfort index does not need to consider the acceleration factor.
The constraint conditions related to the passenger load index are as follows:
wherein AW 0 、AW 1 、AW 2 、AW 3 Respectively indicate no load (dead weight), standard (dead weight + full seat), full load (dead weight + full seat + n) 1 Human/m 2 ) Overload (dead weight + full seat + n) 2 Human/m 2 ) And M is the mass of the whole vehicle. Under the condition of different passenger loads, the whole train has different whole train masses, and the whole train masses influence the traction force, the braking force and the resistance of the train, so that the running energy consumption is influenced. The passenger load index is added, so that the change of the operation energy consumption pair under different load conditions can be effectively reflected.
Other constraints are:
in the formula, at S 0 ～S p Starting the instantaneous speed v (S) in the running interval 0 ) And a stop instant velocity v (S) p ) Are all 0, the running speed V is not more than the maximum running speed V max Operating mode turning point D 1 、D 2 、D 3 Are all at S 0 ～S p And (4) within the operation interval.
To sum up, the tramcar operation energy consumption model is:
the tramcar runs on
Interval, operating time Δ T, has:
wherein F is the resultant force of the tramcar, F t 、F m 、F z Respectively traction force, braking force and resistance, wherein the resistance consists of mechanical friction resistance, ramp additional resistance, curve additional resistance and air resistance, a is running acceleration, M is the total mass of the tramcar under different passenger loads, and x 1 、x 2 Respectively a starting highway mark, an end highway mark, v of the operation subinterval 1 、v 2 Respectively the speed at the starting highway sign and the speed at the end kilometer post of the operation subinterval, S 0 、 S p The starting kilometer post and the end kilometer post of the whole operation interval are adopted.
In a working condition I interval, the tramcar starts and accelerates to a maximum speed limit value by using the maximum traction force, and the traction force characteristic curve is as follows:
in the formula, F t (v) Traction of trams at instantaneous speed v, F max Constant torque zone tramcar traction, v t1 、 V max Are respectively constantThe train running speed at the starting end of the power area and the maximum running speed of the whole running interval.
The optimization problem of the running energy consumption of the tramcar is converted into four-stage optimization problem, namely the optimization problem of turning points of three stages: turning point D of working condition I to working condition II 1 Turning point D of working condition II to working condition III 2 Turning point D of working conditions III to IV 3 . From the traction characteristic diagram F can be determined max 、v t1 And V max From the braking force characteristic curve, the corresponding F can be determined m Further determining resultant force F, acceleration a, running distance and running time, thereby determining turning point D of working conditions I-II 1 . Similarly, for the turning point D of the working condition II to the working condition III 2 V can be determined max Calculating the acceleration of the tramcar in the working condition III working condition interval and the working condition IV working condition interval to obtain a working condition turning point D 3 Velocity V of 3 And the maximum running speed V of the interval max By determining the turning point D of the working conditions III to IV 3 Thereby reversely pushing the turning point D of the working conditions II to III 2 . Therefore, the optimization problem of the running energy consumption in the fixed interval of the tramcar can be converted into a working condition turning point D 3 Velocity V 3 To the optimization problem of (2).
the improved PSO algorithm is characterized in that a selection learning mechanism is added on the basis of a classical Particle Swarm Optimization (PSO), and the basic idea is as follows: initializing a population of m particles, each particle having an n-dimensional position attribute x i ＝(x i,1 (t),x i,2 (t),...x i,n (t)) and n-dimensional velocity attribute v i ＝(v i,1 (t),v i,2 (t),...v i,n (t)). Canceling local optimal solution and global optimal solution updating particles in the classical Particle Swarm Optimization (PSO), taking out particles in the population in pairs in a selected area, comparing adaptive values of the particles, directly entering the next generation of population as winning particles with better fitness, learning the speed of the winning particles as failing particles with worse fitness, and updating the particles with the global optimal solution,Self-updating the position, and then entering the next generation of population; for setting the selection area, in order to prevent the particles from being prematurely gathered in a single range, the particles are firstly put into the selection area in sequence according to the fitness, the sum of the position differences between the particles to be added and the added particles is calculated, a certain threshold value is set, and when the sum of the position differences exceeds the threshold value, the particles are not put into the selection area; when the sum of the position differences is less than the threshold value, the particle is placed in the selected region.
Setting the threshold value to R, x i To be added to the particles, x j Adding particles, wherein j belongs to 1, and k is the number of the added particles;
if the position difference sum of the two satisfies:
then x is i Placing the particles into a selected area, otherwise, discarding the particles;
for the selection of the threshold value R, the first iteration is set as R max With the increase of the iteration number, R satisfies:
in the formula, R min 、R max Minimum and maximum thresholds, G, G respectively max The current iteration times and the maximum iteration times are respectively.
The position and speed of the failed particle after selective learning are updated as follows:
in the formula (I), the compound is shown in the specification,
selecting the position and the speed of the failed particles after learning for the G iteration and the k;
selecting the position and the speed of the failed particles after learning for the G +1 th iteration and the kth iteration;
selecting the positions and speeds of the winning particles after learning for the G iteration and the k; g is the current iteration number;
is a random number in the interval of (0,1),
selecting a position average value of all particles in the group at the G iteration and the k selection learning; omega is an inertia factor;
the improved PSO algorithm comprises the following steps:
step 3.1, simulation data input: line data, train data and algorithm-related parameters;
step 3.2, population initialization: setting the size N of a population, and randomly giving a value of a single particle, wherein the given value of the single particle cannot exceed a speed limit value in a simulation interval;
step 3.3, solving an energy consumption index adaptive value function, and updating the particle speed and position: and calculating the energy consumption objective function of the tramcar operation according to the value corresponding to each particle in the population to obtain the energy consumption index adaptive value corresponding to each particle. Adopting a selective learning mechanism, comparing particles in the population in pairs in a selected area, directly entering the next generation of population by the winning particles, and entering the next generation of population after self-updating by the speed and the position of the failed particles for learning the winning particles;
step 3.4, judging the finishing conditions: if the current iteration times reach the maximum iteration times, the ending condition is met, and the iteration loop is exited; otherwise, step 3.3 is carried out, the adaptive value of the energy consumption index is solved, the particle speed and the particle position are continuously selected, learned and updated until the end condition is met, namely:
G≥G max
in the formula, G, G max Respectively representing the current iteration times and the maximum iteration times;
and 4, calculating the energy consumption of each running interval of the tramcar by using the working condition turning points calculated in the step 3, wherein the method specifically comprises the following steps:
and 3, solving the optimal solution and the relevant operation curve through the step 3, extracting the optimal solution, substituting the optimal solution into the energy-saving optimization model of the tramcar for calculation, and finishing the calculation of the interval operation energy consumption.
By adopting the method for optimizing the running energy consumption of the tramcar based on the improved PSO, and establishing an energy consumption optimization model by using MATLAB for simulation: the Guangzhou Zhuhai tramcar THZ1 line is used as a research object, and the running circuit diagram is shown in FIG. 3; the traction characteristics of the tramcar THZ1 line locomotive are shown in FIG. 4, the tramcar is a constant power point at a speed of 26.5km/h, and the maximum traction is 96 kN; the brake force characteristic of the tramcar THZ1 line locomotive is shown in FIG. 5, the tramcar is a constant power point at a speed of 56km/h, and the maximum brake force is 102 kN.
Analyzing the tramcar running energy consumption model to obtain the final energy consumption optimization variable, namely the working condition turning point D 3 Taking the speed into consideration of the maximum running speed V of the running section max I.e. the speed of the turning point of the operating condition is 0,50]In the interval range, in order to more intuitively observe the convergence result in the iterative process of the algorithm, the initial particle group velocity is set to (0,10,20,30,40, 50); meanwhile, in order to accelerate convergence, the maximum particle movement speed is set to 2; and finally, taking the difference value between the simulation running time and the specified running time as a particle adaptive value solving function to judge the particle quality. Substituting data of each interval, performing competition mechanism particle swarm algorithm iteration, taking Zhou bridge-Hui Zuo interval as an example, performing iterative energy consumption iteration and optimal solution of adaptive value of the intervalAs shown in (a) and (b) in fig. 6, in the initial stage of the algorithm, as the inertia factor w is large when the iteration times are small, the particle moving speed and the search range are large, the up-down jitter amplitude of the optimal solution adaptive value is large; with the increase of the iteration times, the inertia factor w is reduced, the moving speed is reduced, the convergence speed is accelerated, and the optimal particle solution gradually approaches to the global optimal value.
Energy consumption modeling is carried out on the tramcar by inputting the THZ1 line tramcar data and the line data of the Guangzhou Zhuhai tramcar, particle swarm algorithm calculation is carried out on each station-station operation interval to seek the optimal working condition conversion point of the interval, and then energy consumption calculation simulation is carried out on each station-station interval. Taking continental bridge-exhibitor interval as an example, the energy consumption-distance curve and the speed-distance curve in this interval are shown in fig. 7 (a) and (b), respectively.
The operation energy consumption calculated by the energy consumption operation model is compared with the actual operation energy consumption of each interval, as shown in fig. 8. The energy consumption operation model makes full use of the idle running working condition, ensures safe, accurate parking, punctuality and comfort level indexes of the tramcar operation, reduces the traction energy consumption, calculates the working condition point of the energy-saving optimization model by improving the PSO optimization algorithm, has high convergence speed, avoids falling into local optimization, and has obvious calculation effect.
Claims (4)
1. A tramcar operation energy consumption optimization method based on improved PSO is characterized by comprising the following steps:
step 1, establishing a tramcar operation energy consumption model based on the tramcar operation condition;
step 2, analyzing the multi-constraint conditions of the tramcar, and simplifying the optimization problem of the tramcar operation energy consumption model, which is specifically as follows:
the tramcar runs on
Within the interval, operating time Δ T, there are:
wherein F is the resultant force of the tramcar, F t 、F m 、F z Respectively traction force, braking force and resistance, wherein the resistance consists of mechanical friction resistance, ramp additional resistance, curve additional resistance and air resistance, a is running acceleration, M is the total mass of the tramcar under different passenger loads, and x 1 、x 2 Respectively a starting highway mark, an end highway mark, v of the operation subinterval 1 、v 2 Respectively the speed at the starting highway sign and the speed at the end kilometer post of the operation subinterval, S 0 、S p The starting kilometer post and the end kilometer post of the whole operation interval are provided;
in a working condition I interval, the tramcar starts and accelerates to a maximum speed limit value by using the maximum traction force, and the traction force characteristic curve is as follows:
in the formula, F t (v) Traction of trams at instantaneous speed v, F max Constant torque zone tramcar traction, v t1 、V max Respectively the train running speed at the starting end of the constant power area and the maximum running speed in the whole running interval;
the optimization problem of the running energy consumption of the tramcar is converted into four-stage optimization problem, namely the optimization problem of turning points of three stages: turning point D between working conditions I and II 1 Turning point D of working conditions II to III 2 Turning point D of working conditions III to IV 3 ；
Determination of F from the traction force characteristic diagram max 、v t1 And V max Determining F from the braking force characteristic curve m Further determining resultant force F, acceleration a, running distance and running time, and further determining turning point D of working conditions I-II 1 (ii) a Similarly, for the turning point D of the working condition II to the working condition III 2 Can determine V max Obtaining the working condition III interval by calculationAnd the acceleration of the tramcar in the working condition IV interval to obtain a working condition turning point D 3 Velocity V of 3 And the maximum running speed V of the interval max By determining the turning point D of the working conditions III to IV 3 Thereby reversely pushing the turning point D of the working condition II to the working condition III 2 Converting the optimization problem of the running energy consumption of the tramcar in a fixed interval into a working condition turning point D 3 Velocity V 3 The optimization problem of (2);
step 3, solving a working condition turning point in the tramcar operation energy consumption model by utilizing an improved PSO algorithm, namely adding a selective learning mechanism on the basis of a classical PSO algorithm;
and 4, calculating the energy consumption of each running interval of the tramcar by using the working condition turning points calculated in the step 3.
2. The method for optimizing the running energy consumption of the tramcar based on the improved PSO as claimed in claim 1, wherein the step 1 is to establish a model of the running energy consumption of the tramcar based on the running condition of the tramcar, and the model specifically comprises the following steps:
in an operation interval, the tramcar operation process is divided into four working conditions:
working condition I: under the condition of full-force traction, the tramcar starts from the speed of 0 and starts with the maximum traction force to reach the maximum speed V of the interval max ；
Working condition II: at constant cruising speed, the tramcar is at the maximum speed V max The uniform motion is carried out, and the traction force is equal to the comprehensive resistance;
working condition III: under the condition of the coasting, the tramcar performs coasting, and the traction force is 0;
working condition IV: under the full-force braking working condition, the tramcar brakes with the maximum braking force, and the braking energy is fed back and stored;
according to tram operating characteristic, punctual, safe, comfortable, accurate parking index, add passenger load index, establish tram operation energy consumption model, promptly:
in the formula: (x) is an energy consumption objective function; f t (v)、F tmax (v)、F m (v)、F mmax (v) Respectively the traction force of the tramcar at the running speed v, the maximum value of the traction force of the tramcar, the brake force of the tramcar and the maximum value of the brake force of the tramcar; x is the current operating kilometer post; v, V max Respectively representing the instantaneous running speed of the tramcar and the maximum running speed of the whole interval; rho is a braking energy feedback coefficient; m is the total mass of the tramcar under different passenger loads; g 1 (x)、g 2 (x)、g 3 (x)、g 4 (x)、g 5 (x) Respectively representing punctual, accurate parking, safety, comfort and passenger load index constraint conditions; s. the 0 、S p 、D 1 、D 2 、D 3 Respectively as interval starting point kilometer post, end point kilometer post, turning point kilometer post of working condition I-working condition II, turning point kilometer post of working condition II-working condition III, and turning point kilometer post of working condition III-working condition IV; Δ t and Δ s are a time error and a distance error, respectively.
3. The method for optimizing the running energy consumption of the tramcar based on the improved PSO according to claim 2, wherein the step 3 of solving the operating condition turning point in the running energy consumption model of the tramcar by using the improved PSO algorithm, namely adding a selective learning mechanism on the basis of the classical PSO algorithm, is as follows:
step 3.1, simulation data input: line data, train data and algorithm related parameters;
step 3.2, population initialization: setting the size N of the population, and randomly giving the value of a single particle, wherein the given value of the single particle does not exceed the speed limit value in the simulation interval;
initializing a population of m particles, each particle having an n-dimensional position attribute x i ＝(x i,1 (t),x i,2 (t),...x i,n (t)) and n-dimensional velocity attribute v i ＝(v i,1 (t),v i,2 (t),...v i,n (t))；
Step 3.3, solving an energy consumption index adaptive value function, and updating the particle speed and position: calculating the energy consumption objective function of tramcar operation according to the value corresponding to each particle in the population to obtain the energy consumption index adaptive value corresponding to each particle; adopting a selective learning mechanism, comparing the particles in the population in pairs in a selected area, directly entering the next generation of population by the winning particles, and entering the next generation of population after self-updating by the speed and the position of the failed particles by learning the winning particles;
for setting the selection area, in order to prevent the particles from being prematurely aggregated in a single range, the particles are firstly put into the selection area from large to small according to the fitness, the sum of the position differences between the particles to be added and the added particles is calculated, a threshold value is set, and when the sum of the position differences exceeds the threshold value, the particles are not put into the selection area; when the sum of the position differences is less than the threshold value, placing the particle in the selected area;
setting the threshold value to R, x i To be added to the particles, x j Adding particles, wherein j belongs to 1, and b are the number of the added particles;
if the sum of the position differences satisfies:
then x is added i Placing the particles into a selection area, otherwise, discarding the particles;
the threshold value R is selected, and as the iteration number is increased, the following conditions are satisfied:
in the formula, R min 、R max Minimum and maximum thresholds, G, G respectively max Are respectively the currentIteration times and maximum iteration times;
the position and speed of the failed particle after selective learning are updated as follows:
in the formula (I), the compound is shown in the specification,
selecting the position and the speed of the failed particles after learning for the G iteration and the k;
selecting the position and the speed of the failed particles after learning for the G +1 th iteration and the kth iteration;
selecting the positions and speeds of the winning particles after learning for the G iteration and the k; g is the current iteration number;
is a random number in the interval of (0,1),
selecting a learning time position average value for all particles in the group at the G iteration and the k selection; omega is an inertia factor;
step 3.4, judging the finishing condition: if the current iteration times reach the maximum iteration times, the ending condition is met, and the iteration loop is exited; otherwise, step 3.3 is carried out, the adaptive value of the energy consumption index is solved, and the selective learning and updating are carried out on the particle speed and the particle position continuously until the end condition is met;
the end conditions are as follows:
G≥G max
in the formula, G, G max Respectively the current iteration times and the maximum iteration times.
4. The method for optimizing the running energy consumption of the tramcar based on the improved PSO as claimed in claim 3, wherein the step 4 is to calculate the energy consumption of each running section of the tramcar by using the operating condition turning point calculated in the step 3, and specifically comprises the following steps:
and (4) solving the optimal solution and the related operation curve through the step (3), extracting the optimal solution, substituting the optimal solution into the energy-saving optimization model of the tramcar for calculation, and finishing the calculation of the interval operation energy consumption.
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