CN114977182B - Flexible traction power supply system interval optimal power flow optimization method considering photovoltaic access - Google Patents
Flexible traction power supply system interval optimal power flow optimization method considering photovoltaic access Download PDFInfo
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Abstract
The invention discloses a flexible traction power supply system interval optimal power flow optimization method considering photovoltaic access, which specifically comprises the following steps: acquiring traction load data and illumination intensity data in the running process of a train; establishing an objective function of an optimization model according to the data and the electricity charge parameters; establishing constraint conditions of an optimization model according to power capacity parameters of the hybrid energy storage device and the photovoltaic system and power balance of the converter, and linearizing the constraint conditions of the optimization model; taking the random fluctuation of the photovoltaic energy source and the train traction load into consideration, performing interval optimization, and establishing a mixed integer programming model; and solving the model to obtain the lowest daily running cost of the traction substation, peak clipping and valley filling comparison of the train power, and the charge state of the hybrid energy storage device, thereby completing the optimal power flow optimization of the flexible traction power supply system interval. The invention improves the utilization ratio of photovoltaic energy and train regenerative braking energy, reduces the cost of electric charge of the electrified railway, realizes peak clipping and valley filling of traction load, and can effectively solve a series of cost problems.
Description
Technical Field
The invention belongs to the technical field of flexible traction power supply systems, and particularly relates to a section optimal power flow optimization method of a flexible traction power supply system considering photovoltaic access.
Background
The rapid construction of electrified railways in China promotes the development of economy and society in China, but has higher requirements on a power supply system of the railways. In traditional electrified railways, especially high-speed railways, the electric energy quality problem mainly comprising negative sequence problems is increasingly serious, the existence of electric split phases severely restricts the improvement of locomotive speed and vehicle capacity, reduces the power supply efficiency and quality, and seriously influences the reliability, safety and economy of railway operation. The traction power supply system of the single-phase power frequency alternating current power supply system is limited by the topological structure and traction load of the traction power supply system, and the following two problems generally exist in the operation process:
(1) Negative sequence based power quality problem
The traction load has the characteristics of single-phase high power and asymmetry, negative sequence current can be generated in a three-phase power grid, so that the negative sequence problem is caused, and the asymmetry problem caused by the traction load is more obvious along with the continuous increase of the traction power and the driving density of a locomotive running on a high-speed and heavy-load railway. For example, the wind turbine generator in the inner Mongolian God pool wind farm is often shut down due to an "asymmetric current" fault under the influence of negative sequence current generated by a plastic heavy load railway.
(2) Problem of excessive phase separation
The locomotive cannot continuously take current from the traction network during passing through the phase separation, and only inertia is utilized to cause the loss of the traction speed and the traction power of the locomotive, for example, the one-way running time of the high-speed rail of the Beijing is prolonged by about 20 minutes due to the existence of the electric phase separation. Meanwhile, the excessive phase of the locomotive can generate overvoltage, overcurrent and other electrical transient processes, so that the risk of equipment burning loss and faults is increased, misoperation of a protection device is easy to cause, and the high-efficiency and safe operation of the railway is directly influenced.
On the other hand, new energy research in China has been rapidly developed in recent years, and the trend of the reform of the national energy structure is obvious. The electric railway has wide distribution, and the railway network has a large number of geographic intersections with renewable new energy networks, thus having high digestion potential. Taking a Sichuan railway as an example, a large amount of renewable new energy sources are distributed along the electrified railway, if the renewable new energy sources can be consumed nearby, the remote transmission cost of photovoltaic power generation can be reduced, and the operation cost of the electrified railway can be reduced.
Disclosure of Invention
Aiming at the problems, the invention provides a flexible traction power supply system interval optimal power flow optimization method considering photovoltaic access.
The invention relates to a flexible traction power supply system interval optimal power flow optimization method considering photovoltaic access, which comprises the following steps:
Step 1: and acquiring traction load data and illumination intensity data in the running process of the train.
Step 2: and (3) establishing an objective function of the optimization model according to the electric charge parameters and the traction load data and the illumination intensity data in the train operation process obtained in the step (1).
Step 3: and (3) establishing constraint conditions of an optimization model based on traction load data and illumination intensity data in the running process of the train obtained in the step (1) according to power capacity parameters of the hybrid energy storage device and the photovoltaic system and power balance of the converter, and linearizing the constraint conditions of the optimization model.
Step 4: according to the objective function obtained in the step 2 and the constraint condition obtained in the step 3, taking the fluctuation of the photovoltaic energy source and the random fluctuation of the traction load of the train into consideration, realizing the prediction error by carrying out statistics on the illumination intensity data and the traction load data of the designated area, carrying out interval optimization, and establishing a mixed integer programming model.
Step 5: and (3) solving the model obtained in the step (4) to obtain the lowest daily running cost of the traction substation, peak clipping and valley filling comparison of the train power, and the charge state of the hybrid energy storage device, thereby completing the optimal power flow optimization of the flexible traction power supply system interval.
Further, the load process data of the traction substation in the step 1 is calculated by load process simulation software according to the high-speed railway lines, trains and schedules, for example ELBAS/WEBANET.
Further, the typical illumination intensity scene in step1 is obtained by clipping the illumination intensity scene history data based on a scene clipping method, such as a synchronous back-substitution cancellation method.
Further, the objective function in step 2 is:
minf＝ECC+DC+PC (1)
DC＝max(Pt dem)×cdem (5)
Wherein: f is total operation cost, ECC (energy consumption charge) is electricity rate cost, PC (penalty charge) is feedback electricity rate cost, DC (demand charge) is required electricity rate cost, P t grid is electric energy purchased from a power grid of the same-direction traction power supply station, For the price of electricity charge purchased from the power grid, P t fed is the power fed back to the power grid for the railway grid connection,/>To feed back the charge price of the electric energy, P t dem is the electric energy demand, c dem is the electric charge price of the electric energy demand, and Δt and Nt represent the sampling interval and the sample number, respectively. Because the collection standards of the feedback electric energy and the electric charge of the railway grid connection in different areas are different, the cost price of the feedback electric energy can also be changed according to the different standards of the areas.
Further, constraint conditions in the step 3 include photovoltaic power constraint, power balance constraint, energy storage and charge-discharge constraint, and energy storage same constraint at beginning and end and charge-discharge power constraint.
Photovoltaic power constraint:
0≤Pt pv≤Spv (8)
Wherein: p t pv is the photovoltaic consumption, η pv is the photovoltaic efficiency, A pv is the photovoltaic effective area, Is a photovoltaic intensity predictive value,/>S pv is the capacity of the photovoltaic converter, which is the upper limit value of the photovoltaic output; let η pv be 12%, a pv be 10000m 2,Spv be 1MVA.
Power balance constraint:
wherein: p t batdis is battery discharge power, P t ucdis is capacitor discharge power, P t back is train feedback power, P t load is train traction power, P t batch is battery charge power, and P t ucch is capacitor charge power.
And (3) charge and discharge constraint:
Wherein: the energy stored by the battery and the super capacitor at the moment t is represented; /(I) AndRespectively representing the charging and discharging efficiency of the battery and the super capacitor; epsilon b and epsilon c are the self-discharge rates of the battery and the supercapacitor, respectively.
Reserve constraints:
Wherein: Is the upper limit value and the lower limit value of the charge state of the battery,/> Is the upper and lower limit value of the charge state of super-capacitor,/>Representing the total rated stored energy of the battery and super capacitor.
The energy storage at beginning and end is the same constraint:
Wherein: Representing initial state of charge values of the storage battery and the super capacitor,/> And the energy stored by the battery and the super capacitor at the time t is represented.
And (3) charge and discharge power constraint:
Wherein: And/> Is a one-bit binary number; /(I)When the super capacitor discharges, the super capacitor is charged in the reverse way,/>The battery is discharged, otherwise, the battery is charged, and the charging and discharging power of the energy storage element is limited by the capacity of the converter; /(I)The discharge and charge power ratings for the battery and super capacitor, respectively.
Further, in the interval optimization in the step 4, aiming at the fluctuation of the photovoltaic energy and the random fluctuation of the traction load of the train, the illumination intensity data and the traction load data of a designated area are required to be counted, a prediction error model is established, the ultra-short-term errors of the photovoltaic and the traction load in a future period are predicted, and the output plan of the hybrid energy storage system is modified under different photovoltaic and traction load conditions to obtain a system control strategy.
Photovoltaic interval optimization:
For uncertainty of photovoltaic, a Gaussian distribution model is adopted, a photovoltaic average value S t＝ave(solart N) is taken as an expected value, the expected error value is 0, and the standard deviation is Photovoltaic prediction error/>The probability distribution density function is:
where solar t N is the light intensity data over N days.
Traction load interval optimization:
when predicting the system load, a normal distribution is often used to describe the load prediction error, and the prediction error is considered to have the following relation with time t.
Load power prediction error:
regenerative braking power prediction error:
where ρ L,ρB is the prediction error coefficient.
The beneficial technical effects of the invention are as follows:
The invention improves the utilization ratio of photovoltaic energy and train regenerative braking energy, reduces the cost of electric charge of the electrified railway, realizes peak clipping and valley filling of traction load, and can effectively solve a series of cost problems.
Drawings
Fig. 1 is a schematic diagram of a novel flexible traction power supply system of the present invention.
FIG. 2 is a graph showing peak load shifting effects of traction load in an embodiment.
FIG. 3 is an illustration of illumination intensity interval optimization in an example, using a Matlab solver to predict photovoltaic output conditions 24 hours a day for an analog region.
Fig. 4 is a graph showing traction load interval optimization to obtain a power prediction interval of traction load in the embodiment.
Detailed Description
The invention will be further described with reference to the drawings and specific examples.
The invention takes a novel flexible traction power supply system as a research object, takes the lowest daily operation cost of a traction substation as a target, takes a single daily hour as a coordinate variable, takes the operation power of an energy flow and hybrid energy storage system and the maximum capacity of a photovoltaic transformer substation as a constraint, considers the uncertainty of photovoltaic and the fluctuation of traction load, utilizes a hybrid integer planning model to perform interval optimization, establishes an interval optimal power flow optimization method of the flexible traction power supply system considering photovoltaic access, analyzes the annual data of a certain region in China, and finally verifies the correctness and the effectiveness of the optimization model through calculation case analysis.
The invention discloses a traction power supply system structure shown in figure 1, and relates to a flexible traction power supply system interval optimal power flow optimization method considering photovoltaic access, which comprises the following steps:
Step 1: and inputting parameters of the high-speed railway line, the train and the schedule by using traction load process simulation software, such as ELBAS/WEBANET software of SIGNON Germany, and obtaining traction substation load process data through simulation.
And inputting illumination intensity scene data, and performing scene reduction on the illumination intensity scene based on a synchronous back-substitution elimination method to obtain four typical illumination intensity scenes.
Step 2: and (3) establishing an objective function of the optimization model according to the electric charge parameters and the traction load data and the illumination intensity data in the train operation process obtained in the step (1).
The objective function is:
minf＝ECC+DC+PC (1)
DC＝max(Pt dem)×cdem (5)
Wherein: f is total operation cost, ECC (energy consumption charge) is electricity rate cost, PC (penalty charge) is feedback electricity rate cost, DC (demand charge) is required electricity rate cost, P t grid is electric energy purchased from a power grid of the same-direction traction power supply station, For the price of electricity charge purchased from the power grid, P t fed is the power fed back to the power grid for the railway grid connection,/>To feed back the charge price of the electric energy, P t dem is the electric energy demand, and c dem is the electric charge price of the demand. Because the collection standards of the feedback electric energy and the electric charge of the railway grid connection in different areas are different, the cost price of the feedback electric energy can also be changed according to the different standards of the areas.
Step 3: and (3) establishing constraint conditions of an optimization model based on traction load data and illumination intensity data in the running process of the train obtained in the step (1) according to power capacity parameters of the hybrid energy storage device and the photovoltaic system and power balance of the converter, and linearizing the constraint conditions of the optimization model.
The constraint conditions comprise photovoltaic power constraint, power balance constraint, energy storage and charge-discharge constraint, and energy storage start and end the same constraint and charge-discharge power constraint.
Photovoltaic power constraint:
0≤Pt pv≤Spv (8)
Wherein: p t pv is the photovoltaic consumption, η pv is the photovoltaic efficiency, A pv is the photovoltaic effective area, Is a photovoltaic intensity predictive value,/>S pv is the capacity of the photovoltaic converter, which is the upper limit value of the photovoltaic output; let η pv be 12%, a pv be 10000m 2,Spv be 1MVA.
Power balance constraint:
wherein: p t batdis is battery discharge power, P t ucdis is capacitor discharge power, P t back is train feedback power, P t load is train traction power, P t batch is battery charge power, and P t ucch is capacitor charge power.
And (3) charge and discharge constraint:
Wherein: the energy stored by the battery and the super capacitor at the moment t is represented; /(I) AndRespectively representing the charging and discharging efficiency of the battery and the super capacitor; epsilon b and epsilon c are the self-discharge rates of the battery and the supercapacitor, respectively.
Reserve constraints:
Wherein: Is the upper limit value and the lower limit value of the charge state of the battery,/> Is the upper and lower limit value of the charge state of super-capacitor,/>Representing the total rated stored energy of the battery and super capacitor.
The energy storage at beginning and end is the same constraint:
Wherein: Representing initial state of charge values of the storage battery and the super capacitor,/> And the energy stored by the battery and the super capacitor at the time t is represented.
And (3) charge and discharge power constraint:
Wherein: And/> Is a one-bit binary number; /(I)When the super capacitor discharges, the super capacitor is charged in the reverse way,/>The battery is discharged, otherwise, the battery is charged, and the charging and discharging power of the energy storage element is limited by the capacity of the converter; /(I)The discharge and charge power ratings for the battery and super capacitor, respectively.
Step 4: according to the objective function obtained in the step 2 and the constraint condition obtained in the step 3, taking the fluctuation of the photovoltaic energy source and the random fluctuation of the traction load of the train into consideration, realizing the prediction error by carrying out statistics on the illumination intensity data and the traction load data of the designated area, carrying out interval optimization, and establishing a mixed integer programming Model (MILP).
The interval optimization is as follows:
photovoltaic interval optimization:
For uncertainty of photovoltaic, a Gaussian distribution model is adopted, a photovoltaic average value S t＝ave(solart N) is taken as an expected value, the expected error value is 0, and the standard deviation is Photovoltaic prediction error/>The probability distribution density function is:
where solar t N is the light intensity data over N days.
Traction load interval optimization:
when predicting the system load, a normal distribution is often used to describe the load prediction error, and the prediction error is considered to have the following relation with time t.
Load power prediction error:
regenerative braking power prediction error:
where ρ L,ρB is the prediction error coefficient.
Step 5: and (3) integrating an optimization tool box YALMIP and a solver Gurobi (version 9.1.2) by utilizing optimization software, such as software MATLAB R2018b, and solving the mixed integer linear programming in the step 4 to obtain the minimum daily running cost of the traction substation, peak load shifting comparison of train power and the charge state of the hybrid energy storage device, thereby completing the optimal power flow optimization of the flexible traction power supply system interval.
Examples
The topological structure of the electrified railway traction power supply system integrating the hybrid energy storage device and the photovoltaic is shown in figure 1, and the parameters and the electric energy cost are shown in tables 1 and 2:
TABLE 1 simulation model setup parameters
TABLE 2 electric charge parameters and billing methods
Other parameters were 12% η pv, 10000m 2,Spv a pv and 1MVA.
In order to analyze the traditional traction power supply system and the traction power supply system connected with new energy, the situation that feedback electric energy charging is carried out by using two charging modes of fixed electricity price and time-of-use electricity price in different areas is considered, and three feedback electric energy charging modes under the situation of the two charging modes are compared and analyzed. Table 3 shows the comparison result of the time-of-use electricity price and the electricity fee at a fixed electricity price.
Case I: a flexible traction power supply system that does not include an energy storage device and a photovoltaic;
Case II: a flexible traction power supply system comprising an energy storage device and a photovoltaic;
Table 3 time-of-use electricity price and fixed electricity price electricity fee comparison
Peak clipping and valley filling effect analysis:
Because the energy density of the battery is high, the change speed of the state of charge is slower, and the power change is not obvious when the time is shorter, the battery can be used for storing the electric energy fed back by the train to a certain extent. The super capacitor has the characteristics of high charging speed, high power density and the like, so that the change speed of the charge state is high, and the super capacitor can perform good instantaneous charge and discharge tasks while saving the cost. Therefore, when the train obtains electric energy from the power grid and the train brakes to generate feedback electric energy, the battery plays a role in peak clipping, and the super capacitor plays a role in valley filling. In the simulation, the upper and lower limits of the battery and capacitor in the electricity storage state are 0.2 and 0.8, and the initial states are 0.5.
After a specific model is established, the image drawing of the output power of the single-day power grid is carried out by utilizing a software platform by introducing a traditional power supply mode and accessing the data of the hybrid energy storage and the photovoltaic, so that the method can clearly obtain that after the hybrid energy storage and the light energy are accessed, the load peak is obviously reduced, as shown in figure 2. The energy absorption of regenerative braking is increased, which means that the model can realize the peak clipping and valley filling effects, and the effectiveness of the model after the new energy is accessed is verified.
Interval optimization:
In the calculation, the hybrid energy storage and photovoltaic traction power supply system is used for solving the optimal energy management strategy under different conditions. On the basis, the fixed photovoltaic energy is optimized, the uncertainty problem in the train running process is considered, the section of the model is optimized, and calculation is performed again.
Because of the fluctuation of the photovoltaic energy and the uncertainty of the train traction power supply system, a mixed integer programming model is used for counting the illumination intensity data and the traction load data of a designated area and is brought into the model, so that the electricity cost reduced by the traction power supply system which takes account of new energy access is solved.
Optimizing an illumination intensity interval:
because the fluctuation of the photovoltaic is large, the average analysis of the annual data is not significant, so that the daily average value of the data from 160 days to 189 days of the current year in a certain region is selected for analysis and calculation after the illumination characteristics of each region are considered and compared with the illumination intensity data of the certain region.
N in the formulas (22) - (25) is taken according to the own needs.
In the analysis, a mixed Gaussian distribution solving mode is used, a Matlab solver is utilized to predict the photovoltaic output condition of 24 hours a day of an analog region, and the upper bound and the lower bound of a photovoltaic region are obtained, as shown in fig. 3.
Traction load interval optimization:
In consideration of the specificity of the traction load, a fixed error coefficient alpha is set, and a 90% interval confidence level is set by using a Gaussian distribution method to obtain a power prediction interval of the traction load, as shown in fig. 4. The error coefficient is taken to be 0.04.
The prediction error coefficient ρ L,ρB in the formulas (26) - (27) is taken as 0.04.
Optimizing an electric energy cost interval:
In the above process, the upper and lower boundaries of the predicted interval of the photovoltaic output and the traction load are both found, and at this time, two uncertainty factors in the train operation have been converted into two certainty factors. Therefore, the upper and lower extreme cases in the running of the train are selected for research and analysis, and are combined with the electric energy cost factors discussed above for analysis, so that the upper and lower boundaries of the electric energy cost are obtained. Meanwhile, because of the difference of two charging modes of fixed electricity price and time-sharing electricity price, the electric energy cost interval optimization research of the train is still divided into two parts for research, and the upper and lower bounds of the electric energy cost of the two different charging modes are respectively obtained.
Two extreme cases are defined here: the lowest electricity price condition is the electricity price under the condition that each environmental condition is optimal in the comprehensive consideration of the train operation period, namely, the train traction load factor is taken as a lower bound, and the photovoltaic output condition is taken as an upper bound; the highest electricity price condition is the electricity price under the worst condition of each environmental condition in the running period of the train, namely the traction load factor of the train is taken as an upper bound, and the photovoltaic output condition is taken as a lower bound. Because other possible factors data are missing during the running of the train, effective substitution analysis cannot be performed on other possible factors, and therefore the analysis herein is only directed to the photovoltaic output condition and the train traction load factor. Table 4 shows the comparison of the electricity fee interval optimizing effect.
TABLE 4 comparison of electric charge interval optimization results
Minimum electricity price: and considering the optimal condition of cost, taking the lower limit of traction load and the upper limit of photovoltaic.
Highest electricity price: considering the worst case of cost, the traction load takes the upper limit and the photovoltaic takes the lower limit.
The invention considers that the photovoltaic power generation system and the hybrid energy storage system are connected in the direct current link of the back-to-back converter of the traction power supply system, and simultaneously builds a model aiming at the fluctuation of the photovoltaic and traction load to perform interval optimization, thereby fully proving the superiority of the system in the aspects of reducing the electric charge and improving the electric energy quality compared with the traditional system and effectively solving a series of economic problems.
Claims (3)
1. The optimal power flow optimization method for the flexible traction power supply system interval taking photovoltaic access into account is characterized by comprising the following steps of:
Step 1: acquiring traction load data and illumination intensity data in the running process of a train;
Step 2: establishing an objective function of an optimization model according to the electric charge parameters and traction load data and illumination intensity data in the train operation process obtained in the step 1; the objective function is:
minf＝ECC+DC+PC(1)
wherein: f is total operation cost, ECC is electricity charge cost, PC is feedback electricity charge cost, DC is required electricity charge cost, P t grid is electric energy purchased from a power grid of the same-direction traction power supply station, For the price of electricity charge purchased from the power grid, P t fed is the power fed back to the power grid for the railway grid connection,/>For the collection cost price of the feedback electric energy, P t dem is the electric energy demand, c dem is the electric charge price of the demand, and Deltat and Nt respectively represent the sampling interval and the sample number;
Step 3: establishing constraint conditions of an optimization model based on traction load data and illumination intensity data in the running process of the train obtained in the step 1 according to power capacity parameters of the hybrid energy storage device and the photovoltaic system and power balance of the converter, and linearizing the constraint conditions of the optimization model;
Step 4: according to the objective function obtained in the step 2 and the constraint condition obtained in the step 3, taking the fluctuation of the photovoltaic energy source and the random fluctuation of the traction load of the train into consideration, realizing the prediction error by carrying out statistics on the illumination intensity data and the traction load data of the designated area, carrying out interval optimization, and establishing a mixed integer planning model;
Step 5: and (3) solving the model obtained in the step (4) to obtain the lowest daily running cost of the traction substation, peak clipping and valley filling comparison of the train power, and the charge state of the hybrid energy storage device, thereby completing the optimal power flow optimization of the flexible traction power supply system interval.
2. The method for optimizing the optimal power flow between flexible traction power supply system sections according to claim 1, wherein the constraint conditions in the step 3 comprise photovoltaic power constraint, power balance constraint, energy storage and charge-discharge constraint, energy storage start-end same constraint and charge-discharge power constraint;
photovoltaic power constraint:
Wherein: p t pv is the photovoltaic consumption, eta pv is the photovoltaic efficiency, A pv is the photovoltaic effective area, S t pv is the photovoltaic intensity predicted value, S pv is the capacity of the photovoltaic converter, which is the upper limit value of the photovoltaic output; let η pv be 12%, a pv be 10000m 2,Spv be 1MVA;
Power balance constraint:
Wherein: p t batdis is battery discharge power, P t ucdis is capacitor discharge power, P t back is train feedback power, P t load is train traction power, P t batch is battery charge power, and P t ucch is capacitor charge power;
And (3) charge and discharge constraint:
Wherein: the energy stored by the battery and the super capacitor at the moment t is represented; /(I) And/>Respectively representing the charging and discharging efficiency of the battery and the super capacitor; epsilon b and epsilon c are the self-discharge rates of the battery and the super capacitor respectively;
Reserve constraints:
Wherein: Is the upper limit value and the lower limit value of the charge state of the battery,/> Is the upper and lower limit value of the charge state of super-capacitor,/>Representing the total rated stored energy of the battery and the super capacitor;
The energy storage at beginning and end is the same constraint:
Wherein: Representing initial state of charge values of the storage battery and the super capacitor,/> The energy stored by the battery and the super capacitor at the moment t is represented;
and (3) charge and discharge power constraint:
Wherein: And/> Is a one-bit binary number; /(I)When the super capacitor discharges, the super capacitor is charged in the reverse way,/>The battery is discharged, otherwise, the battery is charged, and the charging and discharging power of the energy storage element is limited by the capacity of the converter; /(I)The discharge and charge power ratings for the battery and super capacitor, respectively.
3. The method for optimizing the optimal power flow of the interval of the flexible traction power supply system taking photovoltaic access into account according to claim 2, wherein the interval optimization in the step4 is characterized in that the illumination intensity data and traction load data of a designated area are required to be counted aiming at the fluctuation of the photovoltaic energy source and the random fluctuation of the traction load of the train, a prediction error model is established, the ultra-short-term errors of the photovoltaic and the traction load in a future period are predicted, and the output plan of the hybrid energy storage system is modified under different photovoltaic and traction load conditions to obtain a system control strategy;
photovoltaic interval optimization:
For uncertainty of photovoltaic, a Gaussian distribution model is adopted, a photovoltaic average value S t＝ave(solart N) is taken as an expected value, the expected error value is 0, and the standard deviation is Photovoltaic prediction error/>The probability distribution density function is:
Wherein solar t N is the light intensity data over N days;
traction load interval optimization:
When predicting the system load, normally distributing is often adopted to describe the load prediction error, and the prediction error is considered to have the following relation with time t:
Load power prediction error:
regenerative braking power prediction error:
where ρ L,ρB is the prediction error coefficient.
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