CN114977182B - Flexible traction power supply system interval optimal power flow optimization method considering photovoltaic access - Google Patents

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

Interval optimal power flow optimization method for flexible traction power supply system considering photovoltaic access

Technical Field

The present invention belongs to the technical field of flexible traction power supply systems, and in particular relates to a method for optimizing interval optimal power flow of a flexible traction power supply system taking photovoltaic access into account.

Background technique

The rapid construction of electrified railways in my country has promoted the development of my country's economy and society, but it has also put forward higher requirements for the railway power supply system. In traditional electrified railways, especially high-speed railways, power quality problems, mainly negative sequence problems, are becoming increasingly serious. The existence of power phase separation seriously restricts the increase in locomotive speed and vehicle load, reduces power supply efficiency and quality, and seriously affects the reliability, safety and economy of railway operations. The traction power supply system of the single-phase industrial frequency AC power supply system is limited by its own topological structure and traction load, and usually has the following two problems during operation:

(1) Power quality issues mainly caused by negative sequence

The traction load has the characteristics of single-phase high power and asymmetry, which will generate negative sequence current in the three-phase power grid and cause negative sequence problems. Moreover, as the traction power and traffic density of locomotives running on high-speed and heavy-load railways continue to increase, the asymmetry problem caused by the traction load is becoming more and more obvious. For example, affected by the negative sequence current generated by the Shuohuang heavy-load railway, the wind turbines of the Shenchi Wind Farm in Inner Mongolia often shut down due to "current asymmetry" faults.

(2) Excessive phase problem

When the locomotive is over-phased, it cannot continuously draw current from the traction network and can only pass through by inertia, resulting in the loss of locomotive traction speed and traction power. For example, due to the existence of electrical phase separation, the one-way operation time of the Beijing-Shanghai High-Speed Railway is extended by about 20 minutes. At the same time, the locomotive over-phase will produce electrical transient processes such as overvoltage and overcurrent, increasing the risk of equipment burning and failure, and easily causing the malfunction of the protection device, which directly affects the efficient and safe operation of the railway.

On the other hand, my country's new energy research has developed rapidly in recent years, and the trend of national energy structure reform is obvious. my country has a vast territory, a wide distribution of electrified railways, and many geographical intersections between the railway network and the renewable energy network, which has a high potential for consumption. Taking the Sichuan-Tibet Railway as an example, a large number of renewable energy sources are distributed along the electrified railway. If these renewable energy sources can be consumed nearby, it can not only reduce the long-distance transmission cost of photovoltaic power generation, but also reduce the operating cost of electrified railways.

Summary of the invention

In view of the above problems, the present invention provides a method for optimizing the optimal power flow in a flexible traction power supply system taking photovoltaic access into account.

A method for optimizing the optimal power flow in a flexible traction power supply system taking photovoltaic access into account in the present invention comprises the following steps:

Step 1: Obtain traction load data and light intensity data during train operation.

Step 2: According to the electricity price parameters and the traction load data and light intensity data during train operation obtained in step 1, establish the objective function of the optimization model.

Step 3: According to the power capacity parameters of the hybrid energy storage device and the photovoltaic system, the converter power balance, and the traction load data and light intensity data during the train operation obtained in step 1, the constraints of the optimization model are established, and the constraints of the optimization model are linearized.

Step 4: Based on the objective function obtained in step 2 and the constraints obtained in step 3, considering the volatility of photovoltaic energy and the random volatility of train traction load, the prediction error is realized by statistically analyzing the light intensity data and traction load data in the specified area, performing interval optimization, and establishing a mixed integer programming model.

Step 5: Solve the model obtained in step 4 to obtain the minimum daily operating cost of the traction substation, the comparison of train power peak shaving and valley filling, and the charge state of the hybrid energy storage device, thus completing the optimization of the optimal power flow in the flexible traction power supply system interval.

Furthermore, the load process data of the traction substation in step 1 is calculated by load process simulation software, such as ELBAS/WEBANET, according to the high-speed railway line, trains and timetable.

Furthermore, the typical light intensity scene in step 1 is obtained by reducing the light intensity scene historical data based on a scene reduction method, such as a synchronous back-substitution elimination method.

Furthermore, the objective function in step 2 is:

minf＝ECC+DC+PC (1)

DC＝max(P _t ^dem )×c _dem (5)

Where: f is the total operating cost, ECC (energy consumption charge) is the electricity cost per kWh, PC (penalty charge) is the feedback electricity cost, DC (demand charge) is the demand electricity cost, P _t ^grid is the electricity purchased from the grid by the same-direction traction power supply station, is the price of electricity purchased from the grid, _Ptfed ^is the power fed back to the grid by the railway grid, /> is the price of the feedback electricity, _Ptdem is ^the amount of electricity demand, _cdem is the demand electricity price, Δt and Nt represent the sampling interval and the number of samples respectively. Since the collection standards for feedback electricity charges for railway grid connection are different in different regions, the price of feedback electricity will also vary due to different standards in different regions.

Furthermore, the constraints in step 3 include photovoltaic power constraints, power balance constraints, energy storage and charging and discharging constraints, energy storage sameness constraints at the beginning and end, and charging and discharging power constraints.

Photovoltaic power constraints:

0≤P _t ^pv ≤S _pv (8)

Where: P _t ^pv is the photovoltaic consumption, η ^pv is the photovoltaic efficiency, A ^pv is the photovoltaic effective area, is the predicted value of photovoltaic intensity,/> is the upper limit of photovoltaic output, S _pv is the photovoltaic converter capacity; it is proposed that η ^pv is 12%, A ^pv is 10000m ² , and S _pv is 1MVA.

Power balance constraints:

Where: P _t ^batdis is the battery discharge power, P _t ^ucdis is the capacitor discharge power, P _t ^back is the train feedback power, P _t ^load is the train traction power, P _t ^batch is the battery charging power, and P _t ^ucch is the capacitor charging power.

Charge and discharge constraints:

Where: Represents the energy stored in the battery and supercapacitor at time t;/> and They represent the charging and discharging efficiencies of the battery and supercapacitor respectively; ε _b and ε _c are the self-discharge rates of the battery and supercapacitor respectively.

Reserve constraints:

Where: are the upper and lower limits of the battery state of charge,/> are the upper and lower limits of the supercapacitor charge state, /> Represents the total rated stored energy of the battery and supercapacitor.

Through the energy storage same constraints:

Where: Indicates the initial state of charge of the battery and supercapacitor, /> Represents the energy stored in the battery and supercapacitor at time t.

Charge and discharge power constraints:

Where: and/> is a binary number; /> When the supercapacitor is discharged, it is charged. The battery discharges, and vice versa, it charges. The charging and discharging power of the energy storage element is also limited by the capacity of its converter;/> are the discharge and charge power ratings of the battery and supercapacitor, respectively.

Furthermore, for the interval optimization in step 4, in view of the volatility of photovoltaic energy and the random volatility of train traction load, it is necessary to statistically analyze the light intensity data and traction load data in the specified area, establish a prediction error model, and predict the ultra-short-term errors of photovoltaic and traction loads in the future. Under different photovoltaic and traction load conditions, the output plan of the hybrid energy storage system is modified to obtain the system control strategy.

Photovoltaic interval optimization:

In view of the uncertainty of photovoltaic, the Gaussian distribution model is adopted, and the photovoltaic average value _St = ave(solar _t ^N ) is taken as the expected value. Then the expected value of the error is 0 and the standard deviation is Photovoltaic prediction error/> Then the probability distribution density function is:

Where solar _t ^N is the light intensity data within N days.

Traction load range optimization:

When performing system load forecasting, the normal distribution is often used to describe the load forecast error, and it is believed that the forecast error has the following relationship with time t.

Load power forecast error:

Regenerative braking power prediction error:

Where ρ _L , ρ _B are prediction error coefficients.

The beneficial technical effects of the present invention are:

The present invention improves the utilization rate of photovoltaic energy and train regenerative braking energy, reduces the electricity cost of electrified railways, realizes peak shaving and valley filling of traction loads, and can effectively solve a series of cost problems.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a novel flexible traction power supply system of the present invention.

FIG. 2 is a diagram showing the peak-shaving and valley-filling effect of the traction load in the embodiment.

FIG3 is an example of optimizing the light intensity interval in the embodiment, using the Matlab solver to predict the photovoltaic output of the simulated area for 24 hours a day.

FIG. 4 is a diagram showing the optimization of the traction load interval in the embodiment, and obtaining the power prediction interval of the traction load.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

The present invention takes the new flexible traction power supply system as the research object, takes the lowest daily operating cost of the traction substation as the goal, takes the single-day hour as the coordinate variable, and takes the energy flow, the operating power of the hybrid energy storage system, and the maximum capacity of the photovoltaic substation as constraints. Considering the uncertainty of photovoltaics and the volatility of traction load, a mixed integer programming model is used for interval optimization, and an interval optimal power flow optimization method for the flexible traction power supply system taking into account photovoltaic access is established. The data of previous years in a certain area of my country are analyzed, and finally the correctness and effectiveness of the above optimization model are verified through example analysis.

The structure of the traction power supply system targeted by the present invention is shown in FIG1 . A method for optimizing the optimal power flow of a flexible traction power supply system taking into account photovoltaic access according to the present invention comprises the following steps:

Step 1: Use traction load process simulation software, such as ELBAS/WEBANET software from German company SIGNON, to input high-speed railway line, train and timetable parameters, and simulate to obtain traction substation load process data.

The light intensity scene data is input, and the light intensity scenes are reduced based on the synchronous back-substitution elimination method to obtain four typical light intensity scenes.

Step 2: According to the electricity price parameters and the traction load data and light intensity data during train operation obtained in step 1, establish the objective function of the optimization model.

The objective function is:

minf＝ECC+DC+PC (1)

DC＝max(P _t ^dem )×c _dem (5)

Where: f is the total operating cost, ECC (energy consumption charge) is the electricity cost per kWh, PC (penalty charge) is the feedback electricity cost, DC (demand charge) is the demand electricity cost, P _t ^grid is the electricity purchased from the grid by the same-direction traction power supply station, is the price of electricity purchased from the grid, _Ptfed ^is the power fed back to the grid by the railway grid, /> is the price of the feedback electricity, _Ptdem is the amount of electricity demand, and _cdem is the demand electricity price. Since different regions ^have different standards for the collection of feedback electricity charges for railway grid connection, the price of feedback electricity will also vary due to different standards in different regions.

Step 3: According to the power capacity parameters of the hybrid energy storage device and the photovoltaic system, the converter power balance, and the traction load data and light intensity data during the train operation obtained in step 1, the constraints of the optimization model are established, and the constraints of the optimization model are linearized.

The constraints include photovoltaic power constraints, power balance constraints, energy storage and charging and discharging constraints, energy storage consistency constraints at the beginning and end, and charging and discharging power constraints.

Photovoltaic power constraints:

0≤P _t ^pv ≤S _pv (8)

Where: P _t ^pv is the photovoltaic consumption, η ^pv is the photovoltaic efficiency, A ^pv is the photovoltaic effective area, is the predicted value of photovoltaic intensity,/> is the upper limit of photovoltaic output, S _pv is the photovoltaic converter capacity; it is proposed that η ^pv is 12%, A ^pv is 10000m ² , and S _pv is 1MVA.

Power balance constraints:

Where: P _t ^batdis is the battery discharge power, P _t ^ucdis is the capacitor discharge power, P _t ^back is the train feedback power, P _t ^load is the train traction power, P _t ^batch is the battery charging power, and P _t ^ucch is the capacitor charging power.

Charge and discharge constraints:

Where: Represents the energy stored in the battery and supercapacitor at time t;/> and They represent the charging and discharging efficiencies of the battery and supercapacitor respectively; ε _b and ε _c are the self-discharge rates of the battery and supercapacitor respectively.

Reserve constraints:

Where: are the upper and lower limits of the battery state of charge,/> are the upper and lower limits of the supercapacitor charge state, /> Represents the total rated stored energy of the battery and supercapacitor.

Through the energy storage same constraints:

Where: Indicates the initial state of charge of the battery and supercapacitor, /> Represents the energy stored in the battery and supercapacitor at time t.

Charge and discharge power constraints:

Where: and/> is a binary number; /> When the supercapacitor is discharged, it is charged. The battery discharges, and vice versa, it charges. The charging and discharging power of the energy storage element is also limited by the capacity of its converter;/> are the discharge and charge power ratings of the battery and supercapacitor, respectively.

Step 4: Based on the objective function obtained in step 2 and the constraints obtained in step 3, considering the volatility of photovoltaic energy and the random volatility of train traction load, the prediction error is realized by statistically analyzing the light intensity data and traction load data in the specified area, performing interval optimization, and establishing a mixed integer programming model (MILP).

The interval optimization is as follows:

Photovoltaic interval optimization:

In view of the uncertainty of photovoltaic, the Gaussian distribution model is adopted, and the photovoltaic average value _St = ave(solar _t ^N ) is taken as the expected value. Then the expected value of the error is 0 and the standard deviation is Photovoltaic prediction error/> Then the probability distribution density function is:

Where solar _t ^N is the light intensity data within N days.

Traction load range optimization:

When performing system load forecasting, the normal distribution is often used to describe the load forecast error, and it is believed that the forecast error has the following relationship with time t.

Load power forecast error:

Regenerative braking power prediction error:

Where ρ _L , ρ _B are prediction error coefficients.

Step 5: Use optimization software, such as MATLAB R2018b, the integrated optimization toolbox YALMIP and the solver Gurobi (version 9.1.2), to solve the mixed integer linear programming in step 4, and obtain the minimum daily operating cost of the traction substation, the peak-shaving and valley-filling comparison of train power, and the charge state of the hybrid energy storage device, thus completing the interval optimal power flow optimization of the flexible traction power supply system.

Example

The topology of the electrified railway traction power supply system integrating the hybrid energy storage device and photovoltaics in the present invention is shown in FIG1 , and its parameters and electricity costs are shown in Tables 1 and 2:

Table 1 Simulation model setting parameters

Table 2 Electricity fee parameters and billing methods

As for other parameters, η ^pv is proposed to be 12%, A ^pv is proposed to be 10000m ² , and S _pv is proposed to be 1MVA.

In order to analyze the traditional traction power supply system and the traction power supply system connected to new energy, considering the two billing methods of fixed electricity price and time-of-use electricity price in different regions, a comparative analysis of three feedback electricity billing methods under the two charging methods is proposed. Table 3 gives the comparison results of electricity charges under time-of-use electricity price and fixed electricity price.

Case I: Flexible traction power supply system without energy storage device and photovoltaic;

Case II: Flexible traction power supply system including energy storage device and photovoltaic;

Table 3 Comparison of time-of-use electricity prices and fixed electricity prices

Analysis of the effect of peak shaving and valley filling:

Since the battery has high energy density, the state of charge changes slowly, and the power change is not obvious in a short time, the battery can be used to store the electric energy fed back by the train to a certain extent. Supercapacitors have the characteristics of fast charging speed, high power density, and fast change of state of charge, which can perform good instantaneous charging and discharging tasks while saving costs. Therefore, when the train obtains electricity from the power grid and the train brakes to generate feedback energy, the battery will play a role in peak shaving, while the supercapacitor plays a role in valley filling. In the simulation, the upper and lower limits of the storage state of the battery and capacitor are set to 0.2 and 0.8, and the initial state is 0.5.

After the specific model is established, by importing the data of traditional power supply mode and access to hybrid energy storage and photovoltaic, and using the software platform to draw a graph of the single-day grid output power, it can be clearly concluded that after access to hybrid energy storage and solar energy, the load peak is significantly reduced, as shown in Figure 2. The energy absorption of regenerative braking is increased, which means that the model can achieve the effect of peak shaving and valley filling, verifying the effectiveness of the model after access to new energy.

Interval Optimization:

In the above calculations, we will combine the energy storage and photovoltaic traction power supply system to obtain the optimal energy management strategy under different circumstances. On this basis, we will optimize the fixed photovoltaic energy, consider the uncertainty during train operation, perform interval optimization on the model, and perform calculations again.

Due to the volatility of photovoltaic energy and the uncertainty of the train traction power supply system, a mixed integer programming model is used to collect statistics on the light intensity data and traction load data in the specified area and bring them into the model to solve the electricity cost reduction caused by the traction power supply system connected to new energy.

Light intensity range optimization:

Due to the large volatility of photovoltaics, it is not very meaningful to average the data for the whole year. Therefore, after considering the lighting characteristics of each region and comparing it with the light intensity data of a certain area, the daily average value of the data from the 160th to the 189th day of the year in this area was selected for analysis and calculation.

The value of N in formulas (22)-(25) can be determined according to your needs.

In the analysis, the mixed Gaussian distribution solution method was used, and the Matlab solver was used to predict the photovoltaic output of the simulated area for 24 hours a day, and the upper and lower bounds of the photovoltaic range were obtained, as shown in Figure 3.

Traction load range optimization:

Considering the particularity of the traction load, a fixed error coefficient α is set here, and the Gaussian distribution method is used to set a 90% interval confidence level to obtain the power prediction interval of the traction load, as shown in Figure 4. The error coefficient is 0.04.

The prediction error coefficients ρ _L , ρ _B in formulas (26)-(27) are set to 0.04.

Optimization of electricity cost range:

In the above process, the upper and lower bounds of the prediction intervals of photovoltaic output and traction load have been obtained. At this time, the two uncertain factors in train operation have been transformed into two deterministic factors. Therefore, the upper and lower extreme cases of train operation are selected for research and analysis, and combined with the electricity cost factors discussed above to obtain the upper and lower bounds of electricity cost. At the same time, due to the difference between the two billing methods of fixed electricity price and time-of-use electricity price, the optimization research on the electricity cost interval of the train is still divided into two parts for research, and the upper and lower bounds of electricity cost of the two different billing methods are obtained respectively.

Two extreme cases are defined here: the lowest electricity price is the electricity price under the best environmental conditions during train operation, that is, the train traction load factor takes the lower bound and the photovoltaic output takes the upper bound; the highest electricity price is the electricity price under the worst environmental conditions during train operation, that is, the train traction load factor takes the upper bound and the photovoltaic output takes the lower bound. Due to the lack of data on other possible factors during train operation, it is impossible to effectively substitute other possible factors for analysis, so the analysis here is only for photovoltaic output and train traction load factors. Table 4 gives a comparison of the optimization effects of electricity price intervals.

Table 4 Comparison of optimization results of electricity price interval

Minimum electricity price: Considering the optimal cost situation, the traction load takes the lower limit and the photovoltaic load takes the upper limit.

Maximum electricity price: Considering the worst cost scenario, traction load takes the upper limit and photovoltaic takes the lower limit.

The present invention considers connecting a photovoltaic power generation system and a hybrid energy storage system to the DC link of the back-to-back converter of the traction power supply system. At the same time, a model is built to perform interval optimization based on the volatility of photovoltaic and traction loads. This fully proves the superiority of this system over traditional systems in reducing electricity costs and improving power quality, and can effectively solve a series of economic problems.

Claims (3)

1. A method for optimizing the optimal power flow of a flexible traction power supply system taking into account photovoltaic access, characterized in that it comprises the following steps: Step 1: Obtain traction load data and light intensity data during train operation; Step 2: According to the electricity price parameters and the traction load data and light intensity data obtained in step 1 during the train operation, the objective function of the optimization model is established; the objective function is: minf＝ECC+DC+PC(1) Where: f is the total operating cost, ECC is the electricity cost, PC is the feedback cost, DC is the demand cost, _Ptgrid is the electricity purchased from ^the grid by the same-direction traction power supply station, is the price of electricity purchased from the grid, _Ptfed ^is the power fed back to the grid by the railway grid, /> is the price of the collected electricity fee, P _t ^dem is the electricity demand, c _dem is the demand electricity price, Δt and Nt represent the sampling interval and the number of samples respectively; Step 3: According to the power capacity parameters of the hybrid energy storage device and the photovoltaic system, the converter power balance, and the traction load data and light intensity data during the train operation obtained in step 1, the constraints of the optimization model are established, and the constraints of the optimization model are linearized; Step 4: Based on the objective function obtained in step 2 and the constraints obtained in step 3, considering the volatility of photovoltaic energy and the random volatility of train traction load, the prediction error is realized by statistically analyzing the light intensity data and traction load data in the specified area, performing interval optimization, and establishing a mixed integer programming model; Step 5: Solve the model obtained in step 4 to obtain the minimum daily operating cost of the traction substation, the comparison of train power peak shaving and valley filling, and the charge state of the hybrid energy storage device, thus completing the optimization of the optimal power flow in the flexible traction power supply system interval. 2. According to the method for optimizing the optimal power flow of a flexible traction power supply system taking into account photovoltaic access in claim 1, it is characterized in that the constraints in step 3 include photovoltaic power constraints, power balance constraints, energy storage and charging and discharging constraints, the same energy storage constraints at the beginning and end, and charging and discharging power constraints; Photovoltaic power constraints: Where: P _t ^pv is the photovoltaic consumption, η ^pv is the photovoltaic efficiency, A ^pv is the photovoltaic effective area, S _t ^pv is the predicted value of photovoltaic intensity, is the upper limit of photovoltaic output, S _pv is the photovoltaic converter capacity; it is proposed that η ^pv is 12%, A ^pv is 10000m ² , and S _pv is 1MVA; Power balance constraints: Where: P _t ^batdis is the battery discharge power, P _t ^ucdis is the capacitor discharge power, P _t ^back is the train feedback power, P _t ^load is the train traction power, P _t ^batch is the battery charging power, and P _t ^ucch is the capacitor charging power; Charge and discharge constraints: Where: Represents the energy stored in the battery and supercapacitor at time t;/> and/> Represent the charging and discharging efficiency of the battery and supercapacitor respectively; ε _b and ε _c are the self-discharge rates of the battery and supercapacitor respectively; Reserve constraints: Where: are the upper and lower limits of the battery state of charge,/> are the upper and lower limits of the supercapacitor charge state, /> Indicates the total rated stored energy of the battery and supercapacitor; Through the energy storage same constraints: Where: Indicates the initial state of charge of the battery and supercapacitor, /> Represents the energy stored in the battery and supercapacitor at time t; Charge and discharge power constraints: Where: and/> is a binary number; /> When the supercapacitor is discharged, it is charged. The battery discharges, and vice versa, it charges. The charging and discharging power of the energy storage element is also limited by the capacity of its converter;/> are the discharge and charge power ratings of the battery and supercapacitor, respectively. 3. According to the method for optimizing the optimal power flow of a flexible traction power supply system with photovoltaic access in accordance with claim 2, it is characterized in that the interval optimization in step 4 requires statistics of the light intensity data and traction load data in the specified area for the volatility of photovoltaic energy and the random volatility of train traction load, establishes a prediction error model, predicts the ultra-short-term errors of photovoltaic and traction loads in the future, and modifies the output plan of the hybrid energy storage system under different photovoltaic and traction load conditions to obtain a system control strategy; Photovoltaic interval optimization: In view of the uncertainty of photovoltaic, the Gaussian distribution model is adopted, and the photovoltaic average value _St = ave(solar _t ^N ) is taken as the expected value. Then the expected value of the error is 0 and the standard deviation is Photovoltaic prediction error/> Then the probability distribution density function is: Where solar _t ^N is the light intensity data within N days; Traction load range optimization: When forecasting system load, the normal distribution is often used to describe the load forecast error, and it is believed that the forecast error has the following relationship with time t: Load power forecast error: Regenerative braking power prediction error: Where ρ _L , ρ _B are prediction error coefficients.